Certificate for #26619 ⟨a, b | aa=1, abbabbba=b

Completion settings:

[1] aa=1

Axiom: aa=1.

Defines rule #4.

Referenced by [3], [4], [5], [9], [18], [21].

[2] abbabbba=b

Axiom: abbabbba=b.

Referenced by [3], [4].

[3] bbabbba=ab

Overlap of [1] aa=1 with [2] abbabbba=b:

a a abbabbba

Critical pair: ab=bbabbba.

Flip LHS and RHS.

Referenced by [8], [9], [14], [15].

[4] abbabbb=ba

Overlap of [2] abbabbba=b with [1] aa=1:

abbabbb a aa

Critical pair: abbabbb=ba.

Referenced by [5], [6], [9], [11], [12], [13], [17], [21].

[5] aba=bbabbb

Overlap of [1] aa=1 with [4] abbabbb=ba:

a a abbabbb

Critical pair: aba=bbabbb.

Defines rule #5.

Referenced by [6], [7], [8], [9], [19].

[6] bbabbbbbabbb=abba

Overlap of [5] aba=bbabbb with [4] abbabbb=ba:

ab a abbabbb

Critical pair: abba=bbabbbbbabbb.

Flip LHS and RHS.

Referenced by [13], [16].

[7] bbabbbba=abbbabbb

Overlap of [5] aba=bbabbb with [5] aba=bbabbb:

ab a aba

Critical pair: abbbabbb=bbabbbba.

Flip LHS and RHS.

Referenced by [10].

[8] abbbba=bbbbabbbb

Overlap of [3] bbabbba=ab with [3] bbabbba=ab:

bbab bba bbabbba

Critical pair: bbabab=abbbba.

Reduce LHS:

[5]bb(aba)b
bbbbabbbb

Flip LHS and RHS.

Defines rule #8.

Referenced by [9], [10], [14], [19], [20].

[9] bbbbabbbbbbbb=bbbba

Overlap of [4] abbabbb=ba with [3] bbabbba=ab:

abbab bb bbabbba

Critical pair: abbabab=baabbba.

Reduce LHS:

[5]abb(aba)b
[8](abbbba)bbbb
bbbbabbbbbbbb

Reduce RHS:

[1]b(aa)bbba
bbbba

Referenced by [11], [12], [13], [14].

[10] abbbabbb=bbbbbbabbbb

Simplify [7] bbabbbba=abbbabbb.

Reduce LHS:

[8]bb(abbbba)
bbbbbbabbbb

Flip LHS and RHS.

Referenced by [12].

[11] babba=bbabbbbb

Overlap of [4] abbabbb=ba with [9] bbbbabbbbbbbb=bbbba:

abbab bb bbbbabbbbbbbb

Critical pair: abbabbbbba=babbabbbbbbbb.

Reduce LHS:

[4](abbabbb)bba
babba

Reduce RHS:

[4]b(abbabbb)bbbbb
bbabbbbb

Referenced by [14].

[12] babbba=bbbbbbbab

Overlap of [4] abbabbb=ba with [9] bbbbabbbbbbbb=bbbba:

abbabb b bbbbabbbbbbbb

Critical pair: abbabbbbbba=babbbabbbbbbbb.

Reduce LHS:

[4](abbabbb)bbba
babbba

Reduce RHS:

[10]b(abbbabbb)bbbbb
[9]bbb(bbbbabbbbbbbb)b
bbbbbbbab

Referenced by [15].

[13] bbabbbbba=babb

Overlap of [6] bbabbbbbabbb=abba with [9] bbbbabbbbbbbb=bbbba:

bbab bbbbabbb bbbbabbbbbbbb

Critical pair: bbabbbbba=abbabbbbb.

Reduce RHS:

[4](abbabbb)bb
babb

Referenced by [16].

[14] abbba=bbbbbbab

Overlap of [3] bbabbba=ab with [11] babba=bbabbbbb:

bbabb ba babba

Critical pair: bbabbbbabbbbb=abbba.

Reduce LHS:

[8]bb(abbbba)bbbbb
[9]bb(bbbbabbbbbbbb)b
bbbbbbab

Flip LHS and RHS.

Defines rule #7.

[15] bbbbbbbbab=ab

Overlap of [3] bbabbba=ab with [12] babbba=bbbbbbbab:

b babbba babbba

Critical pair: bbbbbbbbab=ab.

Referenced by [22], [23].

[16] abba=babbbbb

Overlap of [6] bbabbbbbabbb=abba with [13] bbabbbbba=babb:

bbabbbbbabbb bbabbbbba

Critical pair: babbbbb=abba.

Flip LHS and RHS.

Defines rule #6.

Referenced by [17], [18], [21].

[17] babbbbbbbb=ba

Overlap of [4] abbabbb=ba with [16] abba=babbbbb:

abbabbb abba

Critical pair: babbbbbbbb=ba.

Defines rule #2.

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

[18] babbbbba=abb

Overlap of [16] abba=babbbbb with [1] aa=1:

abb a aa

Critical pair: abb=babbbbba.

Flip LHS and RHS.

Referenced by [19], [20], [23].

[19] abbbbbba=bbbabbbbbbb

Overlap of [18] babbbbba=abb with [8] abbbba=bbbbabbbb:

babbbbb a abbbba

Critical pair: babbbbbbbbbabbbb=abbbbbba.

Reduce LHS:

[17](babbbbbbbb)babbbb
[5]b(aba)bbbb
bbbabbbbbbb

Flip LHS and RHS.

Defines rule #10.

[20] abbbbbbba=bbbbbabbbbbb

Overlap of [18] babbbbba=abb with [18] babbbbba=abb:

babbbb ba babbbbba

Critical pair: babbbbabb=abbbbbbba.

Reduce LHS:

[8]b(abbbba)bb
bbbbbabbbbbb

Flip LHS and RHS.

Defines rule #11.

[21] bbbbbbbbb=b

Overlap of [4] abbabbb=ba with [17] babbbbbbbb=ba:

abbabb b babbbbbbbb

Critical pair: abbabbba=baabbbbbbbb.

Reduce LHS:

[16](abba)bbba
[17](babbbbbbbb)a
[1]b(aa)
b

Reduce RHS:

[1]b(aa)bbbbbbbb
bbbbbbbbb

Flip LHS and RHS.

Defines rule #1.

[22] bbbbbbbba=abbbbbbbb

Overlap of [15] bbbbbbbbab=ab with [17] babbbbbbbb=ba:

bbbbbbb bab babbbbbbbb

Critical pair: bbbbbbbba=abbbbbbbb.

Defines rule #3.

[23] abbbbba=bbbbbbbabb

Overlap of [15] bbbbbbbbab=ab with [18] babbbbba=abb:

bbbbbbb bab babbbbba

Critical pair: bbbbbbbabb=abbbbba.

Flip LHS and RHS.

Defines rule #9.