| Back: | ⟨a, b | aaaa=1, abbab=ba⟩ |
|---|
Completion settings:
Axiom: aaaa=1.
Defines rule #30.
Referenced by [3], [5], [10], [17], [19], [45], [48].
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].
Overlap of [1] aaaa=1 with [2] abbab=ba:
Critical pair: aaaba=bbab.
Referenced by [5], [6], [21], [27], [30], [31], [45].
Overlap of [2] abbab=ba with [2] abbab=ba:
Critical pair: abbba=babab.
Flip LHS and RHS.
Referenced by [7], [8], [9], [15], [16], [20], [30], [31], [32], [36], [37], [41], [42], [62].
Overlap of [3] aaaba=bbab with [1] aaaa=1:
Critical pair: aaab=bbabaaa.
Flip LHS and RHS.
Referenced by [28], [36], [43].
Overlap of [3] aaaba=bbab with [2] abbab=ba:
Critical pair: aaabba=bbabbbab.
Referenced by [27], [28], [29], [30], [32].
Overlap of [2] abbab=ba with [4] babab=abbba:
Critical pair: ababbba=baab.
Defines rule #15.
Referenced by [9], [10], [12], [16], [34], [52], [66], [73], [95].
Overlap of [4] babab=abbba with [4] babab=abbba:
Critical pair: baabbba=abbbaab.
Referenced by [25], [26], [75].
Overlap of [4] babab=abbba with [7] ababbba=baab:
Critical pair: bbaab=abbbabba.
Flip LHS and RHS.
Referenced by [11], [12], [13], [25], [36], [74].
Overlap of [7] ababbba=baab with [1] aaaa=1:
Critical pair: ababbb=baabaaa.
Flip LHS and RHS.
Referenced by [22].
Overlap of [2] abbab=ba with [9] abbbabba=bbaab:
Critical pair: abbbbaab=babbabba.
Reduce RHS:
| [2] | b(abbab)ba |
| ⇒ bbaba |
Referenced by [17], [18], [33], [39].
Overlap of [7] ababbba=baab with [9] abbbabba=bbaab:
Critical pair: ababbbbbaab=baabbbbabba.
Flip LHS and RHS.
Referenced by [23].
Overlap of [9] abbbabba=bbaab with [2] abbab=ba:
Critical pair: abbbba=bbaabb.
Flip LHS and RHS.
Referenced by [14], [15], [16], [18], [20], [24], [25], [26], [37], [68], [71], [73].
Overlap of [2] abbab=ba with [13] bbaabb=abbbba:
Critical pair: abbaabbbba=babaabb.
Reduce LHS:
| [13] | a(bbaabb)bba |
| ⇒ aabbbbabba |
Referenced by [23].
Overlap of [4] babab=abbba with [13] bbaabb=abbbba:
Critical pair: babaabbbba=abbbabaabb.
Overlap of [7] ababbba=baab with [13] bbaabb=abbbba:
Critical pair: abababbbba=baababb.
Reduce LHS:
| [4] | a(babab)bbba |
| ⇒ aabbbabbba |
Referenced by [27], [31], [49].
Overlap of [1] aaaa=1 with [11] abbbbaab=bbaba:
Critical pair: aaabbaba=bbbbaab.
Reduce LHS:
| [2] | aa(abbab)a |
| ⇒ aabaa |
Referenced by [19], [20], [21], [22].
Overlap of [13] bbaabb=abbbba with [11] abbbbaab=bbaba:
Critical pair: bbabbaba=abbbbabbaab.
Reduce LHS:
| [2] | bb(abbab)a |
| ⇒ bbbaa |
Flip LHS and RHS.
Referenced by [50].
Overlap of [17] aabaa=bbbbaab with [1] aaaa=1:
Critical pair: aab=bbbbaabaa.
Reduce RHS:
| [17] | bbbb(aabaa) |
| ⇒ bbbbbbbbaab |
Flip LHS and RHS.
Referenced by [24].
Overlap of [17] aabaa=bbbbaab with [2] abbab=ba:
Critical pair: aababa=bbbbaabbbab.
Reduce RHS:
| [13] | bb(bbaabb)bab |
| [4] | ⇒ bbabbb(babab) |
| ⇒ bbabbbabbba |
Referenced by [21].
Overlap of [17] aabaa=bbbbaab with [3] aaaba=bbab:
Critical pair: aabbbab=bbbbaababa.
Reduce RHS:
| [20] | bbbb(aababa) |
| ⇒ bbbbbbabbbabbba |
Flip LHS and RHS.
Defines rule #29.
Referenced by [86].
Overlap of [10] baabaaa=ababbb with [17] aabaa=bbbbaab:
Critical pair: bbbbbaaba=ababbb.
Referenced by [35].
Overlap of [12] baabbbbabba=ababbbbbaab with [14] aabbbbabba=babaabb:
Critical pair: bbabaabb=ababbbbbaab.
Flip LHS and RHS.
Referenced by [51].
Overlap of [19] bbbbbbbbaab=aab with [13] bbaabb=abbbba:
Critical pair: bbbbbbabbbba=aabb.
Defines rule #11.
Referenced by [37], [38], [39], [64], [69], [74], [80], [82], [89].
Overlap of [8] baabbba=abbbaab with [9] abbbabba=bbaab:
Critical pair: babbaab=abbbaabbba.
Reduce RHS:
| [13] | ab(bbaabb)ba |
| ⇒ ababbbbaba |
Flip LHS and RHS.
Referenced by [36].
Overlap of [8] baabbba=abbbaab with [13] bbaabb=abbbba:
Critical pair: baababbbba=abbbaababb.
Referenced by [53].
Overlap of [3] aaaba=bbab with [6] aaabba=bbabbbab:
Critical pair: aaabbbabbbab=bbabaabba.
Reduce LHS:
| [16] | a(aabbbabbba)b |
| ⇒ abaababbb |
Flip LHS and RHS.
Referenced by [30].
Overlap of [5] bbabaaa=aaab with [6] aaabba=bbabbbab:
Critical pair: bbabbbabbbab=aaabbba.
Flip LHS and RHS.
Defines rule #31.
Overlap of [6] aaabba=bbabbbab with [2] abbab=ba:
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].
Overlap of [6] aaabba=bbabbbab with [6] aaabba=bbabbbab:
Critical pair: aaabbbbabbbab=bbabbbabaabba.
Reduce RHS:
| [27] | bbab(bbabaabba) |
| [4] | ⇒ b(babab)aababbb |
| [3] | ⇒ babbb(aaaba)bbb |
| ⇒ babbbbbabbbb |
Referenced by [32].
Overlap of [3] aaaba=bbab with [29] aaba=bbabbbabb:
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].
Overlap of [6] aaabba=bbabbbab with [29] aaba=bbabbbabb:
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.
Overlap of [11] abbbbaab=bbaba with [29] aaba=bbabbbabb:
Critical pair: abbbbbbabbbabb=bbabaa.
Flip LHS and RHS.
Referenced by [36], [37], [51].
Overlap of [29] aaba=bbabbbabb with [7] ababbba=baab:
Critical pair: abaab=bbabbbabbbbba.
Flip LHS and RHS.
Defines rule #22.
Referenced by [36], [37], [73], [74], [99], [103].
Simplify [22] bbbbbaaba=ababbb.
Reduce LHS:
| [29] | bbbbb(aaba) |
| ⇒ bbbbbbbabbbabb |
Referenced by [36], [37], [41].
Overlap of [35] bbbbbbbabbbabb=ababbb with [5] bbabaaa=aaab:
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].
Overlap of [35] bbbbbbbabbbabb=ababbb with [24] bbbbbbabbbba=aabb:
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].
Overlap of [24] bbbbbbabbbba=aabb with [2] abbab=ba:
Critical pair: bbbbbbabbbbba=aabbbbab.
Flip LHS and RHS.
Referenced by [57].
Overlap of [24] bbbbbbabbbba=aabb with [11] abbbbaab=bbaba:
Critical pair: bbbbbbbbaba=aabbab.
Reduce RHS:
| [2] | a(abbab) |
| ⇒ aba |
Referenced by [40], [41], [42], [43].
Overlap of [2] abbab=ba with [39] bbbbbbbbaba=aba:
Critical pair: abbaaba=babbbbbbbaba.
Reduce LHS:
| [29] | abb(aaba) |
| ⇒ abbbbabbbabb |
Flip LHS and RHS.
Referenced by [70].
Overlap of [35] bbbbbbbabbbabb=ababbb with [39] bbbbbbbbaba=aba:
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].
Overlap of [39] bbbbbbbbaba=aba with [4] babab=abbba:
Critical pair: bbbbbbbabbba=abab.
Defines rule #12.
Referenced by [70], [71], [83], [84], [108].
Overlap of [39] bbbbbbbbaba=aba with [5] bbabaaa=aaab:
Critical pair: bbbbbbaaab=abaaa.
Flip LHS and RHS.
Referenced by [44], [45], [58].
Overlap of [29] aaba=bbabbbabb with [43] abaaa=bbbbbbaaab:
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].
Overlap of [43] abaaa=bbbbbbaaab with [1] aaaa=1:
Critical pair: ab=bbbbbbaaaba.
Reduce RHS:
| [3] | bbbbbb(aaaba) |
| ⇒ bbbbbbbbab |
Flip LHS and RHS.
Referenced by [46], [47], [63].
Overlap of [2] abbab=ba with [45] bbbbbbbbab=ab:
Critical pair: abbaab=babbbbbbbab.
Reduce LHS:
| [41] | (abbaa)b |
| ⇒ bbbbbbabbbbbabbbbbb |
Overlap of [45] bbbbbbbbab=ab with [2] abbab=ba:
Critical pair: bbbbbbbbba=abbab.
Reduce RHS:
| [2] | (abbab) |
| ⇒ ba |
Referenced by [48].
Overlap of [47] bbbbbbbbba=ba with [1] aaaa=1:
Critical pair: bbbbbbbbb=baaaa.
Reduce RHS:
| [1] | b(aaaa) |
| ⇒ b |
Defines rule #1.
Referenced by [60], [85], [91], [102].
Simplify [16] aabbbabbba=baababb.
Reduce RHS:
| [29] | b(aaba)bb |
| ⇒ bbbabbbabbbb |
Defines rule #34.
Overlap of [18] abbbbabbaab=bbbaa with [32] bbbabbaa=babbbbbabbbbb:
Critical pair: abbabbbbbabbbbbb=bbbaa.
Reduce LHS:
| [2] | (abbab)bbbbabbbbbb |
| ⇒ babbbbabbbbbb |
Flip LHS and RHS.
Referenced by [52], [55], [56], [58], [59], [67].
Simplify [23] ababbbbbaab=bbabaabb.
Reduce RHS:
| [33] | (bbabaa)bb |
| ⇒ abbbbbbabbbabbbb |
Referenced by [52].
Overlap of [51] ababbbbbaab=abbbbbbabbbabbbb with [50] bbbaa=babbbbabbbbbb:
Critical pair: ababbbabbbbabbbbbbb=abbbbbbabbbabbbb.
Reduce LHS:
| [7] | (ababbba)bbbbabbbbbbb |
| ⇒ baabbbbbabbbbbbb |
Referenced by [74].
Simplify [26] baababbbba=abbbaababb.
Reduce RHS:
| [29] | abbb(aaba)bb |
| ⇒ abbbbbabbbabbbb |
Referenced by [54].
Overlap of [53] baababbbba=abbbbbabbbabbbb with [29] aaba=bbabbbabb:
Critical pair: bbbabbbabbbbbba=abbbbbabbbabbbb.
Defines rule #24.
Simplify [36] bbbbbaaabbb=babbbbbbaab.
Reduce RHS:
| [50] | babbb(bbbaa)b |
| ⇒ babbbbabbbbabbbbbbb |
Referenced by [56].
Overlap of [55] bbbbbaaabbb=babbbbabbbbabbbbbbb with [50] bbbaa=babbbbabbbbbb:
Critical pair: bbbabbbbabbbbbbabbb=babbbbabbbbabbbbbbb.
Referenced by [72].
Overlap of [37] abaabbbbabbbbbbbb=abaabbbba with [38] aabbbbab=bbbbbbabbbbba:
Critical pair: abbbbbbbabbbbbabbbbbbb=abaabbbba.
Reduce LHS:
| [46] | ab(bbbbbbabbbbbabbbbbb)b |
| [2] | ⇒ (abbab)bbbbbbabb |
| ⇒ babbbbbbabb |
Flip LHS and RHS.
Referenced by [74].
Simplify [43] abaaa=bbbbbbaaab.
Reduce RHS:
| [50] | bbb(bbbaa)ab |
| ⇒ bbbbabbbbabbbbbbab |
Referenced by [67], [72], [76].
Overlap of [44] aabbbbbbbaaab=bbbbbabbbbba with [50] bbbaa=babbbbabbbbbb:
Critical pair: aabbbbbabbbbabbbbbbab=bbbbbabbbbba.
Referenced by [77].
Overlap of [2] abbab=ba with [48] bbbbbbbbb=b:
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].
Overlap of [2] abbab=ba with [60] babbbbbbbb=ba:
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].
Overlap of [4] babab=abbba with [60] babbbbbbbb=ba:
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].
Overlap of [45] bbbbbbbbab=ab with [60] babbbbbbbb=ba:
Critical pair: bbbbbbbba=abbbbbbbb.
Defines rule #3.
Overlap of [24] bbbbbbabbbba=aabb with [61] abba=babbbbbbb:
Critical pair: bbbbbbabbbbbabbbbbbb=aabbbba.
Reduce LHS:
| [46] | (bbbbbbabbbbbabbbbbb)b |
| ⇒ babbbbbbbabb |
Flip LHS and RHS.
Defines rule #14.
Referenced by [79], [80], [81], [101].
Overlap of [29] aaba=bbabbbabb with [61] abba=babbbbbbb:
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].
Overlap of [2] abbab=ba with [62] baba=abbbabbbbbbb:
Critical pair: ababbbabbbbbbb=baa.
Reduce LHS:
| [7] | (ababbba)bbbbbbb |
| ⇒ baabbbbbbbb |
Defines rule #5.
Referenced by [68].
Overlap of [62] baba=abbbabbbbbbb with [58] abaaa=bbbbabbbbabbbbbbab:
Critical pair: bbbbbabbbbabbbbbbab=abbbabbbbbbbaa.
Reduce RHS:
| [50] | abbbabbbb(bbbaa) |
| ⇒ abbbabbbbbabbbbabbbbbb |
Flip LHS and RHS.
Referenced by [78].
Overlap of [13] bbaabb=abbbba with [66] baabbbbbbbb=baa:
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].
Overlap of [60] babbbbbbbb=ba with [68] bbaa=abbbbabbbbbb:
Critical pair: babbbbbbabbbbabbbbbb=baaa.
Reduce LHS:
| [24] | ba(bbbbbbabbbba)bbbbbb |
| ⇒ baaabbbbbbbb |
Defines rule #18.
Referenced by [72], [92], [93].
Overlap of [2] abbab=ba with [42] bbbbbbbabbba=abab:
Critical pair: abbaabab=babbbbbbabbba.
Reduce LHS:
| [61] | (abba)abab |
| [40] | ⇒ (babbbbbbbaba)b |
| ⇒ abbbbabbbabbb |
Flip LHS and RHS.
Defines rule #21.
Overlap of [13] bbaabb=abbbba with [42] bbbbbbbabbba=abab:
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].
Overlap of [58] abaaa=bbbbabbbbabbbbbbab with [69] baaabbbbbbbb=baaa:
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].
Overlap of [13] bbaabb=abbbba with [34] bbabbbabbbbba=abaab:
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].
Overlap of [34] bbabbbabbbbba=abaab with [9] abbbabba=bbaab:
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 |
Simplify [8] baabbba=abbbaab.
Reduce RHS:
| [68] | ab(bbaa)b |
| ⇒ ababbbbabbbbbbb |
Defines rule #19.
Referenced by [96].
Simplify [58] abaaa=bbbbabbbbabbbbbbab.
Reduce RHS:
| [72] | (bbbbabbbbabbbbbbab) |
| ⇒ bbabbbbabbbbabbbbb |
Defines rule #38.
Overlap of [59] aabbbbbabbbbabbbbbbab=bbbbbabbbbba with [72] bbbbabbbbabbbbbbab=bbabbbbabbbbabbbbb:
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].
Simplify [67] abbbabbbbbabbbbabbbbbb=bbbbbabbbbabbbbbbab.
Reduce RHS:
| [72] | b(bbbbabbbbabbbbbbab) |
| ⇒ bbbabbbbabbbbabbbbb |
Referenced by [92].
Overlap of [29] aaba=bbabbbabb with [64] aabbbba=babbbbbbbabb:
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.
Overlap of [64] aabbbba=babbbbbbbabb with [61] abba=babbbbbbb:
Critical pair: aabbbbbabbbbbbb=babbbbbbbabbbba.
Reduce RHS:
| [24] | bab(bbbbbbabbbba) |
| [62] | ⇒ (baba)abb |
| ⇒ abbbabbbbbbbabb |
Flip LHS and RHS.
Referenced by [90].
Overlap of [68] bbaa=abbbbabbbbbb with [64] aabbbba=babbbbbbbabb:
Critical pair: bbbabbbbbbbabb=abbbbabbbbbbbbbba.
Reduce RHS:
| [60] | abbb(babbbbbbbb)bba |
| [61] | ⇒ abbbb(abba) |
| ⇒ abbbbbabbbbbbb |
Overlap of [24] bbbbbbabbbba=aabb with [65] bbabbbabbbba=ababbbbbb:
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].
Overlap of [42] bbbbbbbabbba=abab with [65] bbabbbabbbba=ababbbbbb:
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].
Overlap of [42] bbbbbbbabbba=abab with [65] bbabbbabbbba=ababbbbbb:
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.
Overlap of [63] bbbbbbbba=abbbbbbbb with [65] bbabbbabbbba=ababbbbbb:
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].
Overlap of [21] bbbbbbabbbabbba=aabbbab with [65] bbabbbabbbba=ababbbbbb:
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.
Overlap of [68] bbaa=abbbbabbbbbb with [74] aabbbbbbabbbabbbb=baaabb:
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].
Overlap of [74] aabbbbbbabbbabbbb=baaabb with [60] babbbbbbbb=ba:
Critical pair: aabbbbbbabbba=baaabbbbbb.
Defines rule #37.
Referenced by [89], [90], [91], [92], [93].
Overlap of [61] abba=babbbbbbb with [88] aabbbbbbabbba=baaabbbbbb:
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].
Overlap of [62] baba=abbbabbbbbbb with [88] aabbbbbbabbba=baaabbbbbb:
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.
Overlap of [88] aabbbbbbabbba=baaabbbbbb with [62] baba=abbbabbbbbbb:
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].
Overlap of [91] baaabbbbbbba=aaabbbbbb with [62] baba=abbbabbbbbbb:
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].
Overlap of [91] baaabbbbbbba=aaabbbbbb with [68] bbaa=abbbbabbbbbb:
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].
Overlap of [91] baaabbbbbbba=aaabbbbbb with [92] aaabbbbbbba=bbbabbbbabbbbabb:
Critical pair: bbbbabbbbabbbbabb=aaabbbbbb.
Referenced by [102].
Overlap of [7] ababbba=baab with [85] abbbabbbba=bbbbbabbbabbbbb:
Critical pair: abbbbbbabbbabbbbb=baabbbbba.
Flip LHS and RHS.
Defines rule #20.
Overlap of [75] baabbba=ababbbbabbbbbbb with [85] abbbabbbba=bbbbbabbbabbbbb:
Critical pair: babbbbbabbbabbbbb=ababbbbabbbbbbbbbbba.
Reduce RHS:
| [60] | ababbb(babbbbbbbb)bbba |
| ⇒ ababbbbabbba |
Flip LHS and RHS.
Defines rule #40.
Referenced by [109].
Overlap of [68] bbaa=abbbbabbbbbb with [85] abbbabbbba=bbbbbabbbabbbbb:
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.
Overlap of [71] abbbbabbbbbabbba=bbbbabb with [85] abbbabbbba=bbbbbabbbabbbbb:
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.
Overlap of [34] bbabbbabbbbba=abaab with [98] bbbbabbbbbba=abbbbbbabbbb:
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.
Overlap of [68] bbaa=abbbbabbbbbb with [93] aaabbbbbba=babbbbbabbbbabb:
Critical pair: bbbabbbbbabbbbabb=abbbbabbbbbbabbbbbba.
Reduce RHS:
| [98] | a(bbbbabbbbbba)bbbbbba |
| [60] | ⇒ aabbbbb(babbbbbbbb)bba |
| [61] | ⇒ aabbbbbb(abba) |
| ⇒ aabbbbbbbabbbbbbb |
Referenced by [111].
Overlap of [62] baba=abbbabbbbbbb with [70] babbbbbbabbba=abbbbabbbabbb:
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.
Overlap of [94] bbbbabbbbabbbbabb=aaabbbbbb with [60] babbbbbbbb=ba:
Critical pair: bbbbabbbbabbbba=aaabbbbbbbbbbbb.
Reduce RHS:
| [48] | aaa(bbbbbbbbb)bbb |
| ⇒ aaabbbb |
Defines rule #27.
Overlap of [61] abba=babbbbbbb with [89] baaabbbbbabbb=abaabbbbbbabb:
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 |
Overlap of [89] baaabbbbbabbb=abaabbbbbbabb with [60] babbbbbbbb=ba:
Critical pair: baaabbbbba=abaabbbbbbabbbbbbb.
Defines rule #44.
Overlap of [81] bbbabbbbbbbabb=abbbbbabbbbbbb with [60] babbbbbbbb=ba:
Critical pair: bbbabbbbbbba=abbbbbabbbbbbbbbbbbb.
Reduce RHS:
| [60] | abbbb(babbbbbbbb)bbbbb |
| ⇒ abbbbbabbbbb |
Defines rule #8.
Overlap of [103] aaabbbbbabbbabb=bbbabbbbabbbbb with [60] babbbbbbbb=ba:
Critical pair: aaabbbbbabbba=bbbabbbbabbbbbbbbbbb.
Reduce RHS:
| [60] | bbbabbb(babbbbbbbb)bbb |
| ⇒ bbbabbbbabbb |
Defines rule #46.
Overlap of [103] aaabbbbbabbbabb=bbbabbbbabbbbb with [61] abba=babbbbbbb:
Critical pair: aaabbbbbabbbbabbbbbbb=bbbabbbbabbbbba.
Reduce LHS:
| [82] | a(aabbbbbabbbba)bbbbbbb |
| [60] | ⇒ abbbbbabbb(babbbbbbbb)bbb |
| ⇒ abbbbbabbbbabbb |
Flip LHS and RHS.
Defines rule #25.
Overlap of [42] bbbbbbbabbba=abab with [54] bbbabbbabbbbbba=abbbbbabbbabbbb:
Critical pair: bbbbabbbbbabbbabbbb=ababbbbbbba.
Referenced by [110].
Overlap of [96] ababbbbabbba=babbbbbabbbabbbbb with [54] bbbabbbabbbbbba=abbbbbabbbabbbb:
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.
Overlap of [108] bbbbabbbbbabbbabbbb=ababbbbbbba with [60] babbbbbbbb=ba:
Critical pair: bbbbabbbbbabbba=ababbbbbbbabbbb.
Defines rule #28.
Overlap of [100] bbbabbbbbabbbbabb=aabbbbbbbabbbbbbb with [60] babbbbbbbb=ba:
Critical pair: bbbabbbbbabbbba=aabbbbbbbabbbbbbbbbbbbb.
Reduce RHS:
| [60] | aabbbbbb(babbbbbbbb)bbbbb |
| ⇒ aabbbbbbbabbbbb |
Defines rule #26.