Certificate for #12723 ⟨a, b | aba=aab, bbbbb=1⟩

Back:⟨a, b | aba=aab, bbbbb=1⟩

Completion settings:

[1] aba=aab

Axiom: aba=aab.

Defines rule #1.

Referenced by [3], [4].

[2] bbbbb=1

Axiom: bbbbb=1.

Defines rule #3.

[3] aabba=aaabb

Overlap of [1] aba=aab with [1] aba=aab:

ab a aba

Critical pair: abaab=aabba.

Reduce LHS:

[1](aba)ab
[1]⇒ a(aba)b
⇒ aaabb

Flip LHS and RHS.

Defines rule #2.

Referenced by [4], [5].

[4] aaabbba=aaaabbb

Overlap of [1] aba=aab with [3] aabba=aaabb:

ab a aabba

Critical pair: abaaabb=aababba.

Reduce LHS:

[1](aba)aabb
[1]⇒ a(aba)abb
[1]⇒ aa(aba)bb
⇒ aaaabbb

Reduce RHS:

[1]a(aba)bba
⇒ aaabbba

Flip LHS and RHS.

Defines rule #4.

[5] aaaabbbba=aaaaabbbb

Overlap of [3] aabba=aaabb with [3] aabba=aaabb:

aabb a aabba

Critical pair: aabbaaabb=aaabbabba.

Reduce LHS:

[3](aabba)aabb
[3]⇒ a(aabba)abb
[3]⇒ aa(aabba)bb
⇒ aaaaabbbb

Reduce RHS:

[3]a(aabba)bba
⇒ aaaabbbba

Flip LHS and RHS.

Defines rule #5.