Certificate for #22841 ⟨a, b | aaa=1, babab=abb

Completion settings:

[1] aaa=1

Axiom: aaa=1.

Defines rule #9.

Referenced by [5], [6], [7], [14].

[2] babab=abb

Axiom: babab=abb.

Defines rule #7.

Referenced by [3], [4], [5], [6], [8], [9], [10], [11], [12].

[3] baabb=abbab

Overlap of [2] babab=abb with [2] babab=abb:

ba bab babab

Critical pair: baabb=abbab.

Defines rule #6.

Referenced by [4], [5], [9], [12].

[4] baababb=ababbab

Overlap of [3] baabb=abbab with [2] babab=abb:

baab b babab

Critical pair: baababb=abbababab.

Reduce RHS:

[2]ab(babab)ab
ababbab

Defines rule #12.

Referenced by [5], [6], [16].

[5] aabbabb=bbbbab

Overlap of [3] baabb=abbab with [4] baababb=ababbab:

baab b baababb

Critical pair: baabababbab=abbabaababb.

Reduce LHS:

[2]baa(babab)bab
[1]b(aaa)bbbab
bbbbab

Reduce RHS:

[4]abba(baababb)
[4]ab(baababb)ab
[2]a(babab)babab
[2]aabb(babab)
aabbabb

Flip LHS and RHS.

Referenced by [9], [15].

[6] aabbbab=bbbb

Overlap of [4] baababb=ababbab with [2] babab=abb:

baabab b babab

Critical pair: baabababb=ababbababab.

Reduce LHS:

[2]baa(babab)b
[1]b(aaa)bbb
bbbb

Reduce RHS:

[2]abab(babab)ab
[2]a(babab)bab
aabbbab

Flip LHS and RHS.

Referenced by [7].

[7] bbbab=abbbb

Overlap of [1] aaa=1 with [6] aabbbab=bbbb:

a aa aabbbab

Critical pair: abbbb=bbbab.

Flip LHS and RHS.

Defines rule #4.

Referenced by [8], [9], [10], [15].

[8] ababbbb=bbabb

Overlap of [7] bbbab=abbbb with [2] babab=abb:

bb bab babab

Critical pair: bbabb=abbbbab.

Reduce RHS:

[7]ab(bbbab)
ababbbb

Flip LHS and RHS.

Referenced by [10], [12], [13].

[9] babbbbbb=babbb

Overlap of [7] bbbab=abbbb with [3] baabb=abbab:

bbba b baabb

Critical pair: bbbaabbab=abbbbaabb.

Reduce LHS:

[3]bb(baabb)ab
[2]bbab(babab)
[2]b(babab)b
babbb

Reduce RHS:

[3]abbb(baabb)
[7]a(bbbab)bab
[7]aabb(bbbab)
[5](aabbabb)bb
[7]b(bbbab)bb
babbbbbb

Flip LHS and RHS.

Defines rule #2.

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

[10] bbabbab=aabbbbb

Overlap of [8] ababbbb=bbabb with [7] bbbab=abbbb:

abab bbb bbbab

Critical pair: abababbbb=bbabbab.

Reduce LHS:

[2]a(babab)bbb
aabbbbb

Flip LHS and RHS.

Defines rule #8.

[11] abbbbbbb=abbbb

Overlap of [2] babab=abb with [9] babbbbbb=babbb:

ba bab babbbbbb

Critical pair: bababbb=abbbbbbb.

Reduce LHS:

[2](babab)bb
abbbb

Flip LHS and RHS.

Referenced by [14].

[12] bbabbbbb=bbabb

Overlap of [3] baabb=abbab with [9] babbbbbb=babbb:

baab b babbbbbb

Critical pair: baabbabbb=abbababbbbbb.

Reduce LHS:

[3](baabb)abbb
[2]ab(babab)bb
[8](ababbbb)
bbabb

Reduce RHS:

[2]ab(babab)bbbbb
[8](ababbbb)bbb
bbabbbbb

Flip LHS and RHS.

Defines rule #3.

[13] ababbb=bbabbbb

Overlap of [8] ababbbb=bbabb with [9] babbbbbb=babbb:

a babbbb babbbbbb

Critical pair: ababbb=bbabbbb.

Defines rule #5.

Referenced by [16].

[14] bbbbbbb=bbbb

Overlap of [1] aaa=1 with [11] abbbbbbb=abbbb:

aa a abbbbbbb

Critical pair: aaabbbb=bbbbbbb.

Reduce LHS:

[1](aaa)bbbb
bbbb

Flip LHS and RHS.

Defines rule #1.

[15] aabbabb=babbbb

Simplify [5] aabbabb=bbbbab.

Reduce RHS:

[7]b(bbbab)
babbbb

Defines rule #10.

[16] ababbabb=babbabbbb

Overlap of [4] baababb=ababbab with [13] ababbb=bbabbbb:

ba ababb ababbb

Critical pair: babbabbbb=ababbabb.

Flip LHS and RHS.

Defines rule #11.