Certificate for #17659 ⟨a, b | aaaa=1, abbab=ba

Completion settings:

[1] aaaa=1

Axiom: aaaa=1.

Defines rule #30.

Referenced by [3], [5], [10], [17], [19], [45], [48].

[2] abbab=ba

Axiom: abbab=ba.

Referenced by [3], [4], [6], [7], [11], [13], [14], [17], [18], [20], [29], [32], [36], [38], [39], [40], [41], [44], [46], [47], [50], [57], [60], [61], [66], [70].

[3] aaaba=bbab

Overlap of [1] aaaa=1 with [2] abbab=ba:

aaa a abbab

Critical pair: aaaba=bbab.

Referenced by [5], [6], [21], [27], [30], [31], [45].

[4] babab=abbba

Overlap of [2] abbab=ba with [2] abbab=ba:

abb ab abbab

Critical pair: abbba=babab.

Flip LHS and RHS.

Referenced by [7], [8], [9], [15], [16], [20], [30], [31], [32], [36], [37], [41], [42], [62].

[5] bbabaaa=aaab

Overlap of [3] aaaba=bbab with [1] aaaa=1:

aaab a aaaa

Critical pair: aaab=bbabaaa.

Flip LHS and RHS.

Referenced by [28], [36], [43].

[6] aaabba=bbabbbab

Overlap of [3] aaaba=bbab with [2] abbab=ba:

aaab a abbab

Critical pair: aaabba=bbabbbab.

Referenced by [27], [28], [29], [30], [32].

[7] ababbba=baab

Overlap of [2] abbab=ba with [4] babab=abbba:

ab bab babab

Critical pair: ababbba=baab.

Defines rule #15.

Referenced by [9], [10], [12], [16], [34], [52], [66], [73], [95].

[8] baabbba=abbbaab

Overlap of [4] babab=abbba with [4] babab=abbba:

ba bab babab

Critical pair: baabbba=abbbaab.

Referenced by [25], [26], [75].

[9] abbbabba=bbaab

Overlap of [4] babab=abbba with [7] ababbba=baab:

b abab ababbba

Critical pair: bbaab=abbbabba.

Flip LHS and RHS.

Referenced by [11], [12], [13], [25], [36], [74].

[10] baabaaa=ababbb

Overlap of [7] ababbba=baab with [1] aaaa=1:

ababbb a aaaa

Critical pair: ababbb=baabaaa.

Flip LHS and RHS.

Referenced by [22].

[11] abbbbaab=bbaba

Overlap of [2] abbab=ba with [9] abbbabba=bbaab:

abb ab abbbabba

Critical pair: abbbbaab=babbabba.

Reduce RHS:

[2]b(abbab)ba
bbaba

Referenced by [17], [18], [33], [39].

[12] baabbbbabba=ababbbbbaab

Overlap of [7] ababbba=baab with [9] abbbabba=bbaab:

ababbb a abbbabba

Critical pair: ababbbbbaab=baabbbbabba.

Flip LHS and RHS.

Referenced by [23].

[13] bbaabb=abbbba

Overlap of [9] abbbabba=bbaab with [2] abbab=ba:

abbb abba abbab

Critical pair: abbbba=bbaabb.

Flip LHS and RHS.

Referenced by [14], [15], [16], [18], [20], [24], [25], [26], [37], [68], [71], [73].

[14] aabbbbabba=babaabb

Overlap of [2] abbab=ba with [13] bbaabb=abbbba:

abba b bbaabb

Critical pair: abbaabbbba=babaabb.

Reduce LHS:

[13]a(bbaabb)bba
aabbbbabba

Referenced by [23].

[15] babaabbbba=abbbabaabb

Overlap of [4] babab=abbba with [13] bbaabb=abbbba:

baba b bbaabb

Critical pair: babaabbbba=abbbabaabb.

Referenced by [36], [37].

[16] aabbbabbba=baababb

Overlap of [7] ababbba=baab with [13] bbaabb=abbbba:

abab bba bbaabb

Critical pair: abababbbba=baababb.

Reduce LHS:

[4]a(babab)bbba
aabbbabbba

Referenced by [27], [31], [49].

[17] aabaa=bbbbaab

Overlap of [1] aaaa=1 with [11] abbbbaab=bbaba:

aaa a abbbbaab

Critical pair: aaabbaba=bbbbaab.

Reduce LHS:

[2]aa(abbab)a
aabaa

Referenced by [19], [20], [21], [22].

[18] abbbbabbaab=bbbaa

Overlap of [13] bbaabb=abbbba with [11] abbbbaab=bbaba:

bba abb abbbbaab

Critical pair: bbabbaba=abbbbabbaab.

Reduce LHS:

[2]bb(abbab)a
bbbaa

Flip LHS and RHS.

Referenced by [50].

[19] bbbbbbbbaab=aab

Overlap of [17] aabaa=bbbbaab with [1] aaaa=1:

aab aa aaaa

Critical pair: aab=bbbbaabaa.

Reduce RHS:

[17]bbbb(aabaa)
bbbbbbbbaab

Flip LHS and RHS.

Referenced by [24].

[20] aababa=bbabbbabbba

Overlap of [17] aabaa=bbbbaab with [2] abbab=ba:

aaba a abbab

Critical pair: aababa=bbbbaabbbab.

Reduce RHS:

[13]bb(bbaabb)bab
[4]bbabbb(babab)
bbabbbabbba

Referenced by [21].

[21] bbbbbbabbbabbba=aabbbab

Overlap of [17] aabaa=bbbbaab with [3] aaaba=bbab:

aab aa aaaba

Critical pair: aabbbab=bbbbaababa.

Reduce RHS:

[20]bbbb(aababa)
bbbbbbabbbabbba

Flip LHS and RHS.

Defines rule #29.

Referenced by [86].

[22] bbbbbaaba=ababbb

Overlap of [10] baabaaa=ababbb with [17] aabaa=bbbbaab:

b aabaaa aabaa

Critical pair: bbbbbaaba=ababbb.

Referenced by [35].

[23] ababbbbbaab=bbabaabb

Overlap of [12] baabbbbabba=ababbbbbaab with [14] aabbbbabba=babaabb:

b aabbbbabba aabbbbabba

Critical pair: bbabaabb=ababbbbbaab.

Flip LHS and RHS.

Referenced by [51].

[24] bbbbbbabbbba=aabb

Overlap of [19] bbbbbbbbaab=aab with [13] bbaabb=abbbba:

bbbbbb bbaab bbaabb

Critical pair: bbbbbbabbbba=aabb.

Defines rule #11.

Referenced by [37], [38], [39], [64], [69], [74], [80], [82], [89].

[25] ababbbbaba=babbaab

Overlap of [8] baabbba=abbbaab with [9] abbbabba=bbaab:

ba abbba abbbabba

Critical pair: babbaab=abbbaabbba.

Reduce RHS:

[13]ab(bbaabb)ba
ababbbbaba

Flip LHS and RHS.

Referenced by [36].

[26] baababbbba=abbbaababb

Overlap of [8] baabbba=abbbaab with [13] bbaabb=abbbba:

baab bba bbaabb

Critical pair: baababbbba=abbbaababb.

Referenced by [53].

[27] bbabaabba=abaababbb

Overlap of [3] aaaba=bbab with [6] aaabba=bbabbbab:

aaab a aaabba

Critical pair: aaabbbabbbab=bbabaabba.

Reduce LHS:

[16]a(aabbbabbba)b
abaababbb

Flip LHS and RHS.

Referenced by [30].

[28] aaabbba=bbabbbabbbab

Overlap of [5] bbabaaa=aaab with [6] aaabba=bbabbbab:

bbab aaa aaabba

Critical pair: bbabbbabbbab=aaabbba.

Flip LHS and RHS.

Defines rule #31.

[29] aaba=bbabbbabb

Overlap of [6] aaabba=bbabbbab with [2] abbab=ba:

aa abba abbab

Critical pair: aaba=bbabbbabb.

Defines rule #13.

Referenced by [31], [32], [33], [34], [35], [36], [40], [44], [49], [53], [54], [65], [71], [73], [79], [99], [103].

[30] aaabbbbabbbab=babbbbbabbbb

Overlap of [6] aaabba=bbabbbab with [6] aaabba=bbabbbab:

aaabb a aaabba

Critical pair: aaabbbbabbbab=bbabbbabaabba.

Reduce RHS:

[27]bbab(bbabaabba)
[4]b(babab)aababbb
[3]babbb(aaaba)bbb
babbbbbabbbb

Referenced by [32].

[31] babbbaa=abbbabbbabbbbbb

Overlap of [3] aaaba=bbab with [29] aaba=bbabbbabb:

aaab a aaba

Critical pair: aaabbbabbbabb=bbababa.

Reduce LHS:

[16]a(aabbbabbba)bb
[29]ab(aaba)bbbb
abbbabbbabbbbbb

Reduce RHS:

[4]b(babab)a
babbbaa

Flip LHS and RHS.

Referenced by [44].

[32] bbbabbaa=babbbbbabbbbb

Overlap of [6] aaabba=bbabbbab with [29] aaba=bbabbbabb:

aaabb a aaba

Critical pair: aaabbbbabbbabb=bbabbbababa.

Reduce LHS:

[30](aaabbbbabbbab)b
babbbbbabbbbb

Reduce RHS:

[4]bbabb(babab)a
[2]bb(abbab)bbaa
bbbabbaa

Flip LHS and RHS.

Referenced by [41], [50].

[33] bbabaa=abbbbbbabbbabb

Overlap of [11] abbbbaab=bbaba with [29] aaba=bbabbbabb:

abbbb aab aaba

Critical pair: abbbbbbabbbabb=bbabaa.

Flip LHS and RHS.

Referenced by [36], [37], [51].

[34] bbabbbabbbbba=abaab

Overlap of [29] aaba=bbabbbabb with [7] ababbba=baab:

a aba ababbba

Critical pair: abaab=bbabbbabbbbba.

Flip LHS and RHS.

Defines rule #22.

Referenced by [36], [37], [73], [74], [99], [103].

[35] bbbbbbbabbbabb=ababbb

Simplify [22] bbbbbaaba=ababbb.

Reduce LHS:

[29]bbbbb(aaba)
bbbbbbbabbbabb

Referenced by [36], [37], [41].

[36] bbbbbaaabbb=babbbbbbaab

Overlap of [35] bbbbbbbabbbabb=ababbb with [5] bbabaaa=aaab:

bbbbbbbabbbab b bbabaaa

Critical pair: bbbbbbbabbbabaaab=ababbbbabaaa.

Reduce LHS:

[33]bbbbbbbab(bbabaa)ab
[4]bbbbbb(babab)bbbbbabbbabbab
[34]bbbb(bbabbbabbbbba)bbbabbab
[15]bbb(babaabbbba)bbab
[15]bbbabb(babaabbbba)b
[2]bbb(abbab)bbabaabbb
[2]bbbb(abbab)aabbb
bbbbbaaabbb

Reduce RHS:

[25](ababbbbaba)aa
[29]babb(aaba)a
[9]babbbb(abbbabba)
babbbbbbaab

Referenced by [55].

[37] abaabbbbabbbbbbbb=abaabbbba

Overlap of [35] bbbbbbbabbbabb=ababbb with [24] bbbbbbabbbba=aabb:

bbbbbbbabbbab b bbbbbbabbbba

Critical pair: bbbbbbbabbbabaabb=ababbbbbbbbabbbba.

Reduce LHS:

[33]bbbbbbbab(bbabaa)bb
[4]bbbbbb(babab)bbbbbabbbabbbb
[34]bbbb(bbabbbabbbbba)bbbabbbb
[15]bbb(babaabbbba)bbbb
[33]bbbab(bbabaa)bbbbbb
[4]bb(babab)bbbbbabbbabbbbbbbb
[34](bbabbbabbbbba)bbbabbbbbbbb
abaabbbbabbbbbbbb

Reduce RHS:

[24]ababb(bbbbbbabbbba)
[13]aba(bbaabb)
abaabbbba

Referenced by [57].

[38] aabbbbab=bbbbbbabbbbba

Overlap of [24] bbbbbbabbbba=aabb with [2] abbab=ba:

bbbbbbabbbb a abbab

Critical pair: bbbbbbabbbbba=aabbbbab.

Flip LHS and RHS.

Referenced by [57].

[39] bbbbbbbbaba=aba

Overlap of [24] bbbbbbabbbba=aabb with [11] abbbbaab=bbaba:

bbbbbb abbbba abbbbaab

Critical pair: bbbbbbbbaba=aabbab.

Reduce RHS:

[2]a(abbab)
aba

Referenced by [40], [41], [42], [43].

[40] babbbbbbbaba=abbbbabbbabb

Overlap of [2] abbab=ba with [39] bbbbbbbbaba=aba:

abba b bbbbbbbbaba

Critical pair: abbaaba=babbbbbbbaba.

Reduce LHS:

[29]abb(aaba)
abbbbabbbabb

Flip LHS and RHS.

Referenced by [70].

[41] abbaa=bbbbbbabbbbbabbbbb

Overlap of [35] bbbbbbbabbbabb=ababbb with [39] bbbbbbbbaba=aba:

bbbbbbbabbbab b bbbbbbbbaba

Critical pair: bbbbbbbabbbababa=ababbbbbbbbbbaba.

Reduce LHS:

[4]bbbbbbbabb(babab)a
[2]bbbbbbb(abbab)bbaa
[32]bbbbb(bbbabbaa)
bbbbbbabbbbbabbbbb

Reduce RHS:

[39]ababb(bbbbbbbbaba)
[2]ab(abbab)a
abbaa

Flip LHS and RHS.

Referenced by [46].

[42] bbbbbbbabbba=abab

Overlap of [39] bbbbbbbbaba=aba with [4] babab=abbba:

bbbbbbb baba babab

Critical pair: bbbbbbbabbba=abab.

Defines rule #12.

Referenced by [70], [71], [83], [84], [108].

[43] abaaa=bbbbbbaaab

Overlap of [39] bbbbbbbbaba=aba with [5] bbabaaa=aaab:

bbbbbb bbaba bbabaaa

Critical pair: bbbbbbaaab=abaaa.

Flip LHS and RHS.

Referenced by [44], [45], [58].

[44] aabbbbbbbaaab=bbbbbabbbbba

Overlap of [29] aaba=bbabbbabb with [43] abaaa=bbbbbbaaab:

aab a abaaa

Critical pair: aabbbbbbbaaab=bbabbbabbbaaa.

Reduce RHS:

[31]bbabb(babbbaa)a
[2]bb(abbab)bbabbbabbbbbba
[2]bbb(abbab)bbabbbbbba
[2]bbbb(abbab)bbbbba
bbbbbabbbbba

Referenced by [59].

[45] bbbbbbbbab=ab

Overlap of [43] abaaa=bbbbbbaaab with [1] aaaa=1:

ab aaa aaaa

Critical pair: ab=bbbbbbaaaba.

Reduce RHS:

[3]bbbbbb(aaaba)
bbbbbbbbab

Flip LHS and RHS.

Referenced by [46], [47], [63].

[46] bbbbbbabbbbbabbbbbb=babbbbbbbab

Overlap of [2] abbab=ba with [45] bbbbbbbbab=ab:

abba b bbbbbbbbab

Critical pair: abbaab=babbbbbbbab.

Reduce LHS:

[41](abbaa)b
bbbbbbabbbbbabbbbbb

Referenced by [57], [64].

[47] bbbbbbbbba=ba

Overlap of [45] bbbbbbbbab=ab with [2] abbab=ba:

bbbbbbbb ab abbab

Critical pair: bbbbbbbbba=abbab.

Reduce RHS:

[2](abbab)
ba

Referenced by [48].

[48] bbbbbbbbb=b

Overlap of [47] bbbbbbbbba=ba with [1] aaaa=1:

bbbbbbbbb a aaaa

Critical pair: bbbbbbbbb=baaaa.

Reduce RHS:

[1]b(aaaa)
b

Defines rule #1.

Referenced by [60], [85], [91], [102].

[49] aabbbabbba=bbbabbbabbbb

Simplify [16] aabbbabbba=baababb.

Reduce RHS:

[29]b(aaba)bb
bbbabbbabbbb

Defines rule #34.

[50] bbbaa=babbbbabbbbbb

Overlap of [18] abbbbabbaab=bbbaa with [32] bbbabbaa=babbbbbabbbbb:

ab bbbabbaab bbbabbaa

Critical pair: abbabbbbbabbbbbb=bbbaa.

Reduce LHS:

[2](abbab)bbbbabbbbbb
babbbbabbbbbb

Flip LHS and RHS.

Referenced by [52], [55], [56], [58], [59], [67].

[51] ababbbbbaab=abbbbbbabbbabbbb

Simplify [23] ababbbbbaab=bbabaabb.

Reduce RHS:

[33](bbabaa)bb
abbbbbbabbbabbbb

Referenced by [52].

[52] baabbbbbabbbbbbb=abbbbbbabbbabbbb

Overlap of [51] ababbbbbaab=abbbbbbabbbabbbb with [50] bbbaa=babbbbabbbbbb:

ababb bbbaab bbbaa

Critical pair: ababbbabbbbabbbbbbb=abbbbbbabbbabbbb.

Reduce LHS:

[7](ababbba)bbbbabbbbbbb
baabbbbbabbbbbbb

Referenced by [74].

[53] baababbbba=abbbbbabbbabbbb

Simplify [26] baababbbba=abbbaababb.

Reduce RHS:

[29]abbb(aaba)bb
abbbbbabbbabbbb

Referenced by [54].

[54] bbbabbbabbbbbba=abbbbbabbbabbbb

Overlap of [53] baababbbba=abbbbbabbbabbbb with [29] aaba=bbabbbabb:

b aababbbba aaba

Critical pair: bbbabbbabbbbbba=abbbbbabbbabbbb.

Defines rule #24.

Referenced by [108], [109].

[55] bbbbbaaabbb=babbbbabbbbabbbbbbb

Simplify [36] bbbbbaaabbb=babbbbbbaab.

Reduce RHS:

[50]babbb(bbbaa)b
babbbbabbbbabbbbbbb

Referenced by [56].

[56] bbbabbbbabbbbbbabbb=babbbbabbbbabbbbbbb

Overlap of [55] bbbbbaaabbb=babbbbabbbbabbbbbbb with [50] bbbaa=babbbbabbbbbb:

bb bbbaaabbb bbbaa

Critical pair: bbbabbbbabbbbbbabbb=babbbbabbbbabbbbbbb.

Referenced by [72].

[57] abaabbbba=babbbbbbabb

Overlap of [37] abaabbbbabbbbbbbb=abaabbbba with [38] aabbbbab=bbbbbbabbbbba:

ab aabbbbabbbbbbbb aabbbbab

Critical pair: abbbbbbbabbbbbabbbbbbb=abaabbbba.

Reduce LHS:

[46]ab(bbbbbbabbbbbabbbbbb)b
[2](abbab)bbbbbbabb
babbbbbbabb

Flip LHS and RHS.

Referenced by [74].

[58] abaaa=bbbbabbbbabbbbbbab

Simplify [43] abaaa=bbbbbbaaab.

Reduce RHS:

[50]bbb(bbbaa)ab
bbbbabbbbabbbbbbab

Referenced by [67], [72], [76].

[59] aabbbbbabbbbabbbbbbab=bbbbbabbbbba

Overlap of [44] aabbbbbbbaaab=bbbbbabbbbba with [50] bbbaa=babbbbabbbbbb:

aabbbb bbbaaab bbbaa

Critical pair: aabbbbbabbbbabbbbbbab=bbbbbabbbbba.

Referenced by [77].

[60] babbbbbbbb=ba

Overlap of [2] abbab=ba with [48] bbbbbbbbb=b:

abba b bbbbbbbbb

Critical pair: abbab=babbbbbbbb.

Reduce LHS:

[2](abbab)
ba

Flip LHS and RHS.

Defines rule #2.

Referenced by [61], [62], [63], [65], [69], [71], [72], [73], [77], [79], [81], [82], [83], [84], [85], [86], [87], [88], [89], [90], [91], [92], [93], [96], [97], [98], [99], [100], [101], [102], [103], [104], [105], [106], [107], [109], [110], [111].

[61] abba=babbbbbbb

Overlap of [2] abbab=ba with [60] babbbbbbbb=ba:

ab bab babbbbbbbb

Critical pair: abba=babbbbbbb.

Defines rule #4.

Referenced by [64], [65], [70], [71], [73], [79], [80], [81], [82], [87], [89], [90], [91], [93], [98], [99], [100], [101], [103], [107].

[62] baba=abbbabbbbbbb

Overlap of [4] babab=abbba with [60] babbbbbbbb=ba:

ba bab babbbbbbbb

Critical pair: baba=abbbabbbbbbb.

Defines rule #6.

Referenced by [66], [67], [73], [80], [83], [84], [85], [86], [90], [91], [92], [97], [99], [101], [103], [109].

[63] bbbbbbbba=abbbbbbbb

Overlap of [45] bbbbbbbbab=ab with [60] babbbbbbbb=ba:

bbbbbbb bab babbbbbbbb

Critical pair: bbbbbbbba=abbbbbbbb.

Defines rule #3.

Referenced by [85], [91].

[64] aabbbba=babbbbbbbabb

Overlap of [24] bbbbbbabbbba=aabb with [61] abba=babbbbbbb:

bbbbbbabbbb a abba

Critical pair: bbbbbbabbbbbabbbbbbb=aabbbba.

Reduce LHS:

[46](bbbbbbabbbbbabbbbbb)b
babbbbbbbabb

Flip LHS and RHS.

Defines rule #14.

Referenced by [79], [80], [81], [101].

[65] bbabbbabbbba=ababbbbbb

Overlap of [29] aaba=bbabbbabb with [61] abba=babbbbbbb:

aab a abba

Critical pair: aabbabbbbbbb=bbabbbabbbba.

Reduce LHS:

[61]a(abba)bbbbbbb
[60]a(babbbbbbbb)bbbbbb
ababbbbbb

Flip LHS and RHS.

Referenced by [82], [83], [84], [85], [86].

[66] baabbbbbbbb=baa

Overlap of [2] abbab=ba with [62] baba=abbbabbbbbbb:

ab bab baba

Critical pair: ababbbabbbbbbb=baa.

Reduce LHS:

[7](ababbba)bbbbbbb
baabbbbbbbb

Defines rule #5.

Referenced by [68].

[67] abbbabbbbbabbbbabbbbbb=bbbbbabbbbabbbbbbab

Overlap of [62] baba=abbbabbbbbbb with [58] abaaa=bbbbabbbbabbbbbbab:

b aba abaaa

Critical pair: bbbbbabbbbabbbbbbab=abbbabbbbbbbaa.

Reduce RHS:

[50]abbbabbbb(bbbaa)
abbbabbbbbabbbbabbbbbb

Flip LHS and RHS.

Referenced by [78].

[68] bbaa=abbbbabbbbbb

Overlap of [13] bbaabb=abbbba with [66] baabbbbbbbb=baa:

b baabb baabbbbbbbb

Critical pair: bbaa=abbbbabbbbbb.

Defines rule #7.

Referenced by [69], [73], [74], [75], [81], [82], [84], [86], [87], [89], [90], [92], [93], [97], [100], [103], [109].

[69] baaabbbbbbbb=baaa

Overlap of [60] babbbbbbbb=ba with [68] bbaa=abbbbabbbbbb:

babbbbbb bb bbaa

Critical pair: babbbbbbabbbbabbbbbb=baaa.

Reduce LHS:

[24]ba(bbbbbbabbbba)bbbbbb
baaabbbbbbbb

Defines rule #18.

Referenced by [72], [92], [93].

[70] babbbbbbabbba=abbbbabbbabbb

Overlap of [2] abbab=ba with [42] bbbbbbbabbba=abab:

abba b bbbbbbbabbba

Critical pair: abbaabab=babbbbbbabbba.

Reduce LHS:

[61](abba)abab
[40](babbbbbbbaba)b
abbbbabbbabbb

Flip LHS and RHS.

Defines rule #21.

Referenced by [89], [101].

[71] abbbbabbbbbabbba=bbbbabb

Overlap of [13] bbaabb=abbbba with [42] bbbbbbbabbba=abab:

bbaa bb bbbbbbbabbba

Critical pair: bbaaabab=abbbbabbbbbabbba.

Reduce LHS:

[29]bba(aaba)b
[61]bb(abba)bbbabbb
[60]bb(babbbbbbbb)bbabbb
[61]bbb(abba)bbb
[60]bbb(babbbbbbbb)bb
bbbbabb

Flip LHS and RHS.

Referenced by [98].

[72] bbbbabbbbabbbbbbab=bbabbbbabbbbabbbbb

Overlap of [58] abaaa=bbbbabbbbabbbbbbab with [69] baaabbbbbbbb=baaa:

a baaa baaabbbbbbbb

Critical pair: abaaa=bbbbabbbbabbbbbbabbbbbbbbb.

Reduce LHS:

[58](abaaa)
bbbbabbbbabbbbbbab

Reduce RHS:

[56]b(bbbabbbbabbbbbbabbb)bbbbbb
[60]bbabbbbabbb(babbbbbbbb)bbbbb
bbabbbbabbbbabbbbb

Referenced by [76], [77], [78].

[73] abbbabbbbabbbba=bbbbbbbabbbbbb

Overlap of [13] bbaabb=abbbba with [34] bbabbbabbbbba=abaab:

bbaab b bbabbbabbbbba

Critical pair: bbaababaab=abbbbababbbabbbbba.

Reduce LHS:

[29]bb(aaba)baab
[68]bbbbabbbab(bbaa)b
[62]bbbbabb(baba)bbbbabbbbbbb
[60]bbbbabbabb(babbbbbbbb)bbbabbbbbbb
[61]bbbb(abba)bbbabbbabbbbbbb
[60]bbbb(babbbbbbbb)bbabbbabbbbbbb
[61]bbbbb(abba)bbbabbbbbbb
[60]bbbbb(babbbbbbbb)bbabbbbbbb
[61]bbbbbb(abba)bbbbbbb
[60]bbbbbb(babbbbbbbb)bbbbbb
bbbbbbbabbbbbb

Reduce RHS:

[7]abbbb(ababbba)bbbbba
[68]abbb(bbaa)bbbbbba
[60]abbbabbb(babbbbbbbb)bbbba
abbbabbbbabbbba

Flip LHS and RHS.

Referenced by [77].

[74] aabbbbbbabbbabbbb=baaabb

Overlap of [34] bbabbbabbbbba=abaab with [9] abbbabba=bbaab:

bbabbbabbbbb a abbbabba

Critical pair: bbabbbabbbbbbbaab=abaabbbbabba.

Reduce LHS:

[68]bbabbbabbbbb(bbaa)b
[34](bbabbbabbbbba)bbbbabbbbbbb
[52]a(baabbbbbabbbbbbb)
aabbbbbbabbbabbbb

Reduce RHS:

[57](abaabbbba)bba
[24]ba(bbbbbbabbbba)
baaabb

Referenced by [87], [88].

[75] baabbba=ababbbbabbbbbbb

Simplify [8] baabbba=abbbaab.

Reduce RHS:

[68]ab(bbaa)b
ababbbbabbbbbbb

Defines rule #19.

Referenced by [96].

[76] abaaa=bbabbbbabbbbabbbbb

Simplify [58] abaaa=bbbbabbbbabbbbbbab.

Reduce RHS:

[72](bbbbabbbbabbbbbbab)
bbabbbbabbbbabbbbb

Defines rule #38.

[77] bbbbbabbbbba=abbbbbbbabbb

Overlap of [59] aabbbbbabbbbabbbbbbab=bbbbbabbbbba with [72] bbbbabbbbabbbbbbab=bbabbbbabbbbabbbbb:

aab bbbbabbbbabbbbbbab bbbbabbbbabbbbbbab

Critical pair: aabbbabbbbabbbbabbbbb=bbbbbabbbbba.

Reduce LHS:

[73]a(abbbabbbbabbbba)bbbbb
[60]abbbbbb(babbbbbbbb)bbb
abbbbbbbabbb

Flip LHS and RHS.

Defines rule #10.

Referenced by [101].

[78] abbbabbbbbabbbbabbbbbb=bbbabbbbabbbbabbbbb

Simplify [67] abbbabbbbbabbbbabbbbbb=bbbbbabbbbabbbbbbab.

Reduce RHS:

[72]b(bbbbabbbbabbbbbbab)
bbbabbbbabbbbabbbbb

Referenced by [92].

[79] bbabbbbabbba=ababbbbbbabb

Overlap of [29] aaba=bbabbbabb with [64] aabbbba=babbbbbbbabb:

aab a aabbbba

Critical pair: aabbabbbbbbbabb=bbabbbabbabbbba.

Reduce LHS:

[61]a(abba)bbbbbbbabb
[60]a(babbbbbbbb)bbbbbbabb
ababbbbbbabb

Reduce RHS:

[61]bbabbb(abba)bbbba
[60]bbabbb(babbbbbbbb)bbba
bbabbbbabbba

Flip LHS and RHS.

Defines rule #23.

Referenced by [87], [103].

[80] abbbabbbbbbbabb=aabbbbbabbbbbbb

Overlap of [64] aabbbba=babbbbbbbabb with [61] abba=babbbbbbb:

aabbbb a abba

Critical pair: aabbbbbabbbbbbb=babbbbbbbabbbba.

Reduce RHS:

[24]bab(bbbbbbabbbba)
[62](baba)abb
abbbabbbbbbbabb

Flip LHS and RHS.

Referenced by [90].

[81] bbbabbbbbbbabb=abbbbbabbbbbbb

Overlap of [68] bbaa=abbbbabbbbbb with [64] aabbbba=babbbbbbbabb:

bb aa aabbbba

Critical pair: bbbabbbbbbbabb=abbbbabbbbbbbbbba.

Reduce RHS:

[60]abbb(babbbbbbbb)bba
[61]abbbb(abba)
abbbbbabbbbbbb

Referenced by [103], [105].

[82] aabbbbbabbbba=bbbbbabbbbabbbb

Overlap of [24] bbbbbbabbbba=aabb with [65] bbabbbabbbba=ababbbbbb:

bbbbbbabb bba bbabbbabbbba

Critical pair: bbbbbbabbababbbbbb=aabbbbbabbbba.

Reduce LHS:

[61]bbbbbb(abba)babbbbbb
[60]bbbbbb(babbbbbbbb)abbbbbb
[68]bbbbb(bbaa)bbbbbb
[60]bbbbbabbb(babbbbbbbb)bbbb
bbbbbabbbbabbbb

Flip LHS and RHS.

Defines rule #36.

Referenced by [107].

[83] ababbbbba=bbbbabbbabbbbb

Overlap of [42] bbbbbbbabbba=abab with [65] bbabbbabbbba=ababbbbbb:

bbbbb bbabbba bbabbbabbbba

Critical pair: bbbbbababbbbbb=ababbbbba.

Reduce LHS:

[62]bbbb(baba)bbbbbb
[60]bbbbabb(babbbbbbbb)bbbbb
bbbbabbbabbbbb

Flip LHS and RHS.

Defines rule #16.

Referenced by [109].

[84] ababbbbabbbba=bbbbbabbbabbbabbbb

Overlap of [42] bbbbbbbabbba=abab with [65] bbabbbabbbba=ababbbbbb:

bbbbbbbab bba bbabbbabbbba

Critical pair: bbbbbbbabababbbbbb=ababbbbabbbba.

Reduce LHS:

[62]bbbbbb(baba)babbbbbb
[60]bbbbbbabb(babbbbbbbb)abbbbbb
[68]bbbbbbab(bbaa)bbbbbb
[60]bbbbbbababbb(babbbbbbbb)bbbb
[62]bbbbb(baba)bbbbabbbb
[60]bbbbbabb(babbbbbbbb)bbbabbbb
bbbbbabbbabbbabbbb

Flip LHS and RHS.

Defines rule #41.

[85] abbbabbbba=bbbbbabbbabbbbb

Overlap of [63] bbbbbbbba=abbbbbbbb with [65] bbabbbabbbba=ababbbbbb:

bbbbbb bba bbabbbabbbba

Critical pair: bbbbbbababbbbbb=abbbbbbbbbbbabbbba.

Reduce LHS:

[62]bbbbb(baba)bbbbbb
[60]bbbbbabb(babbbbbbbb)bbbbb
bbbbbabbbabbbbb

Reduce RHS:

[48]a(bbbbbbbbb)bbabbbba
abbbabbbba

Flip LHS and RHS.

Defines rule #17.

Referenced by [95], [96], [97], [98].

[86] aabbbabbbbba=bbbbabbbabbbabbbb

Overlap of [21] bbbbbbabbbabbba=aabbbab with [65] bbabbbabbbba=ababbbbbb:

bbbbbbab bbabbba bbabbbabbbba

Critical pair: bbbbbbabababbbbbb=aabbbabbbbba.

Reduce LHS:

[62]bbbbb(baba)babbbbbb
[60]bbbbbabb(babbbbbbbb)abbbbbb
[68]bbbbbab(bbaa)bbbbbb
[60]bbbbbababbb(babbbbbbbb)bbbb
[62]bbbb(baba)bbbbabbbb
[60]bbbbabb(babbbbbbbb)bbbabbbb
bbbbabbbabbbabbbb

Flip LHS and RHS.

Defines rule #35.

[87] babbbbabbbbbbabb=baabbbbbbabbbbbb

Overlap of [68] bbaa=abbbbabbbbbb with [74] aabbbbbbabbbabbbb=baaabb:

bb aa aabbbbbbabbbabbbb

Critical pair: bbbaaabb=abbbbabbbbbbbbbbbbabbbabbbb.

Reduce LHS:

[68]b(bbaa)abb
babbbbabbbbbbabb

Reduce RHS:

[60]abbb(babbbbbbbb)bbbbabbbabbbb
[79]abb(bbabbbbabbba)bbbb
[61](abba)babbbbbbabbbbbb
[60](babbbbbbbb)abbbbbbabbbbbb
baabbbbbbabbbbbb

Referenced by [89].

[88] aabbbbbbabbba=baaabbbbbb

Overlap of [74] aabbbbbbabbbabbbb=baaabb with [60] babbbbbbbb=ba:

aabbbbbbabb babbbb babbbbbbbb

Critical pair: aabbbbbbabbba=baaabbbbbb.

Defines rule #37.

Referenced by [89], [90], [91], [92], [93].

[89] baaabbbbbabbb=abaabbbbbbabb

Overlap of [61] abba=babbbbbbb with [88] aabbbbbbabbba=baaabbbbbb:

abb a aabbbbbbabbba

Critical pair: abbbaaabbbbbb=babbbbbbbabbbbbbabbba.

Reduce LHS:

[68]ab(bbaa)abbbbbb
[87]a(babbbbabbbbbbabb)bbbb
[60]abaabbbbb(babbbbbbbb)bb
abaabbbbbbabb

Reduce RHS:

[70]babbbbbb(babbbbbbabbba)
[24]ba(bbbbbbabbbba)bbbabbb
baaabbbbbabbb

Flip LHS and RHS.

Referenced by [93], [103], [104].

[90] aabbbbbabbbabbba=bbabbbbbabbbbabbbb

Overlap of [62] baba=abbbabbbbbbb with [88] aabbbbbbabbba=baaabbbbbb:

bab a aabbbbbbabbba

Critical pair: babbaaabbbbbb=abbbabbbbbbbabbbbbbabbba.

Reduce LHS:

[61]b(abba)aabbbbbb
[68]bbabbbbb(bbaa)bbbbbb
[60]bbabbbbbabbb(babbbbbbbb)bbbb
bbabbbbbabbbbabbbb

Reduce RHS:

[80](abbbabbbbbbbabb)bbbbabbba
[60]aabbbb(babbbbbbbb)bbbabbba
aabbbbbabbbabbba

Flip LHS and RHS.

Defines rule #47.

[91] baaabbbbbbba=aaabbbbbb

Overlap of [88] aabbbbbbabbba=baaabbbbbb with [62] baba=abbbabbbbbbb:

aabbbbbbabb ba baba

Critical pair: aabbbbbbabbabbbabbbbbbb=baaabbbbbbba.

Reduce LHS:

[61]aabbbbbb(abba)bbbabbbbbbb
[60]aabbbbbb(babbbbbbbb)bbabbbbbbb
[61]aabbbbbbb(abba)bbbbbbb
[63]aa(bbbbbbbba)bbbbbbbbbbbbbb
[48]aaa(bbbbbbbbb)bbbbbbbbbbbbb
[48]aaa(bbbbbbbbb)bbbbb
aaabbbbbb

Flip LHS and RHS.

Referenced by [92], [93], [94].

[92] aaabbbbbbba=bbbabbbbabbbbabb

Overlap of [91] baaabbbbbbba=aaabbbbbb with [62] baba=abbbabbbbbbb:

baaabbbbbb ba baba

Critical pair: baaabbbbbbabbbabbbbbbb=aaabbbbbbba.

Reduce LHS:

[88]ba(aabbbbbbabbba)bbbbbbb
[69]ba(baaabbbbbbbb)bbbbb
[62](baba)aabbbbb
[68]abbbabbbbb(bbaa)bbbbb
[78](abbbabbbbbabbbbabbbbbb)bbbbb
[60]bbbabbbbabbb(babbbbbbbb)bb
bbbabbbbabbbbabb

Flip LHS and RHS.

Defines rule #33.

Referenced by [94].

[93] aaabbbbbba=babbbbbabbbbabb

Overlap of [91] baaabbbbbbba=aaabbbbbb with [68] bbaa=abbbbabbbbbb:

baaabbbbb bba bbaa

Critical pair: baaabbbbbabbbbabbbbbb=aaabbbbbba.

Reduce LHS:

[89](baaabbbbbabbb)babbbbbb
[88]ab(aabbbbbbabbba)bbbbbb
[69]ab(baaabbbbbbbb)bbbb
[61](abba)aabbbb
[68]babbbbb(bbaa)bbbb
[60]babbbbbabbb(babbbbbbbb)bb
babbbbbabbbbabb

Flip LHS and RHS.

Defines rule #32.

Referenced by [100].

[94] bbbbabbbbabbbbabb=aaabbbbbb

Overlap of [91] baaabbbbbbba=aaabbbbbb with [92] aaabbbbbbba=bbbabbbbabbbbabb:

b aaabbbbbbba aaabbbbbbba

Critical pair: bbbbabbbbabbbbabb=aaabbbbbb.

Referenced by [102].

[95] baabbbbba=abbbbbbabbbabbbbb

Overlap of [7] ababbba=baab with [85] abbbabbbba=bbbbbabbbabbbbb:

ab abbba abbbabbbba

Critical pair: abbbbbbabbbabbbbb=baabbbbba.

Flip LHS and RHS.

Defines rule #20.

[96] ababbbbabbba=babbbbbabbbabbbbb

Overlap of [75] baabbba=ababbbbabbbbbbb with [85] abbbabbbba=bbbbbabbbabbbbb:

ba abbba abbbabbbba

Critical pair: babbbbbabbbabbbbb=ababbbbabbbbbbbbbbba.

Reduce RHS:

[60]ababbb(babbbbbbbb)bbba
ababbbbabbba

Flip LHS and RHS.

Defines rule #40.

Referenced by [109].

[97] abbbabbbabbba=bbabbbbbabbbabbbbb

Overlap of [68] bbaa=abbbbabbbbbb with [85] abbbabbbba=bbbbbabbbabbbbb:

bba a abbbabbbba

Critical pair: bbabbbbbabbbabbbbb=abbbbabbbbbbbbbabbbba.

Reduce RHS:

[60]abbb(babbbbbbbb)babbbba
[62]abbb(baba)bbbba
[60]abbbabb(babbbbbbbb)bbba
abbbabbbabbba

Flip LHS and RHS.

Defines rule #42.

[98] bbbbabbbbbba=abbbbbbabbbb

Overlap of [71] abbbbabbbbbabbba=bbbbabb with [85] abbbabbbba=bbbbbabbbabbbbb:

abbbbabbbbb abbba abbbabbbba

Critical pair: abbbbabbbbbbbbbbabbbabbbbb=bbbbabbbbbba.

Reduce LHS:

[60]abbb(babbbbbbbb)bbabbbabbbbb
[61]abbbb(abba)bbbabbbbb
[60]abbbb(babbbbbbbb)bbabbbbb
[61]abbbbb(abba)bbbbb
[60]abbbbb(babbbbbbbb)bbbb
abbbbbbabbbb

Flip LHS and RHS.

Defines rule #9.

Referenced by [99], [100].

[99] abaabbbbbbba=bbbbabbbbabbbb

Overlap of [34] bbabbbabbbbba=abaab with [98] bbbbabbbbbba=abbbbbbabbbb:

bbabbbab bbbba bbbbabbbbbba

Critical pair: bbabbbababbbbbbabbbb=abaabbbbbbba.

Reduce LHS:

[62]bbabb(baba)bbbbbbabbbb
[60]bbabbabb(babbbbbbbb)bbbbbabbbb
[34]bba(bbabbbabbbbba)bbbb
[29]bb(aaba)abbbbb
[61]bbbbabbb(abba)bbbbb
[60]bbbbabbb(babbbbbbbb)bbbb
bbbbabbbbabbbb

Flip LHS and RHS.

Defines rule #39.

[100] bbbabbbbbabbbbabb=aabbbbbbbabbbbbbb

Overlap of [68] bbaa=abbbbabbbbbb with [93] aaabbbbbba=babbbbbabbbbabb:

bb aa aaabbbbbba

Critical pair: bbbabbbbbabbbbabb=abbbbabbbbbbabbbbbba.

Reduce RHS:

[98]a(bbbbabbbbbba)bbbbbba
[60]aabbbbb(babbbbbbbb)bba
[61]aabbbbbb(abba)
aabbbbbbbabbbbbbb

Referenced by [111].

[101] abbbabbbbbabbba=bbbabbbbbbabbbbbb

Overlap of [62] baba=abbbabbbbbbb with [70] babbbbbbabbba=abbbbabbbabbb:

ba ba babbbbbbabbba

Critical pair: baabbbbabbbabbb=abbbabbbbbbbbbbbbbabbba.

Reduce LHS:

[64]b(aabbbba)bbbabbb
[77]bbabb(bbbbbabbbbba)bbb
[61]bb(abba)bbbbbbbabbbbbb
[60]bb(babbbbbbbb)bbbbbbabbbbbb
bbbabbbbbbabbbbbb

Reduce RHS:

[60]abb(babbbbbbbb)bbbbbabbba
abbbabbbbbabbba

Flip LHS and RHS.

Defines rule #43.

[102] bbbbabbbbabbbba=aaabbbb

Overlap of [94] bbbbabbbbabbbbabb=aaabbbbbb with [60] babbbbbbbb=ba:

bbbbabbbbabbb babb babbbbbbbb

Critical pair: bbbbabbbbabbbba=aaabbbbbbbbbbbb.

Reduce RHS:

[48]aaa(bbbbbbbbb)bbb
aaabbbb

Defines rule #27.

[103] aaabbbbbabbbabb=bbbabbbbabbbbb

Overlap of [61] abba=babbbbbbb with [89] baaabbbbbabbb=abaabbbbbbabb:

ab ba baaabbbbbabbb

Critical pair: ababaabbbbbbabb=babbbbbbbaabbbbbabbb.

Reduce LHS:

[62]a(baba)abbbbbbabb
[81]aa(bbbabbbbbbbabb)bbbbabb
[60]aaabbbb(babbbbbbbb)bbbabb
aaabbbbbabbbabb

Reduce RHS:

[68]babbbbb(bbaa)bbbbbabbb
[60]babbbbbabbb(babbbbbbbb)bbbabbb
[79]babbb(bbabbbbabbba)bbb
[62]babb(baba)bbbbbbabbbbb
[60]babbabb(babbbbbbbb)bbbbbabbbbb
[34]ba(bbabbbabbbbba)bbbbb
[29]b(aaba)abbbbbb
[61]bbbabbb(abba)bbbbbb
[60]bbbabbb(babbbbbbbb)bbbbb
bbbabbbbabbbbb

Referenced by [106], [107].

[104] baaabbbbba=abaabbbbbbabbbbbbb

Overlap of [89] baaabbbbbabbb=abaabbbbbbabb with [60] babbbbbbbb=ba:

baaabbbb babbb babbbbbbbb

Critical pair: baaabbbbba=abaabbbbbbabbbbbbb.

Defines rule #44.

[105] bbbabbbbbbba=abbbbbabbbbb

Overlap of [81] bbbabbbbbbbabb=abbbbbabbbbbbb with [60] babbbbbbbb=ba:

bbbabbbbbb babb babbbbbbbb

Critical pair: bbbabbbbbbba=abbbbbabbbbbbbbbbbbb.

Reduce RHS:

[60]abbbb(babbbbbbbb)bbbbb
abbbbbabbbbb

Defines rule #8.

[106] aaabbbbbabbba=bbbabbbbabbb

Overlap of [103] aaabbbbbabbbabb=bbbabbbbabbbbb with [60] babbbbbbbb=ba:

aaabbbbbabb babb babbbbbbbb

Critical pair: aaabbbbbabbba=bbbabbbbabbbbbbbbbbb.

Reduce RHS:

[60]bbbabbb(babbbbbbbb)bbb
bbbabbbbabbb

Defines rule #46.

[107] bbbabbbbabbbbba=abbbbbabbbbabbb

Overlap of [103] aaabbbbbabbbabb=bbbabbbbabbbbb with [61] abba=babbbbbbb:

aaabbbbbabbb abb abba

Critical pair: aaabbbbbabbbbabbbbbbb=bbbabbbbabbbbba.

Reduce LHS:

[82]a(aabbbbbabbbba)bbbbbbb
[60]abbbbbabbb(babbbbbbbb)bbb
abbbbbabbbbabbb

Flip LHS and RHS.

Defines rule #25.

[108] bbbbabbbbbabbbabbbb=ababbbbbbba

Overlap of [42] bbbbbbbabbba=abab with [54] bbbabbbabbbbbba=abbbbbabbbabbbb:

bbbb bbbabbba bbbabbbabbbbbba

Critical pair: bbbbabbbbbabbbabbbb=ababbbbbbba.

Referenced by [110].

[109] babbbbbabbbabbba=abbbbabbbabbbabb

Overlap of [96] ababbbbabbba=babbbbbabbbabbbbb with [54] bbbabbbabbbbbba=abbbbbabbbabbbb:

abab bbbabbba bbbabbbabbbbbba

Critical pair: abababbbbbabbbabbbb=babbbbbabbbabbbbbbbbbbba.

Reduce LHS:

[83]ab(ababbbbba)bbbabbbb
[60]abbbbbabb(babbbbbbbb)abbbb
[68]abbbbbab(bbaa)bbbb
[60]abbbbbababbb(babbbbbbbb)bb
[62]abbbb(baba)bbbbabb
[60]abbbbabb(babbbbbbbb)bbbabb
abbbbabbbabbbabb

Reduce RHS:

[60]babbbbbabb(babbbbbbbb)bbba
babbbbbabbbabbba

Flip LHS and RHS.

Defines rule #45.

[110] bbbbabbbbbabbba=ababbbbbbbabbbb

Overlap of [108] bbbbabbbbbabbbabbbb=ababbbbbbba with [60] babbbbbbbb=ba:

bbbbabbbbbabb babbbb babbbbbbbb

Critical pair: bbbbabbbbbabbba=ababbbbbbbabbbb.

Defines rule #28.

[111] bbbabbbbbabbbba=aabbbbbbbabbbbb

Overlap of [100] bbbabbbbbabbbbabb=aabbbbbbbabbbbbbb with [60] babbbbbbbb=ba:

bbbabbbbbabbb babb babbbbbbbb

Critical pair: bbbabbbbbabbbba=aabbbbbbbabbbbbbbbbbbbb.

Reduce RHS:

[60]aabbbbbb(babbbbbbbb)bbbbb
aabbbbbbbabbbbb

Defines rule #26.