Certificate for #19154 ⟨a, b | aba=a, bbaabb=a⟩

Back:⟨a, b | aba=a, bbaabb=a⟩

Completion settings:

[1] aba=a

Axiom: aba=a.

Defines rule #1.

Referenced by [3].

[2] bbaabb=a

Axiom: bbaabb=a.

Referenced by [3], [4], [5].

[3] bbaa=aabb

Overlap of [2] bbaabb=a with [2] bbaabb=a:

bbaab b bbaabb

Critical pair: bbaaba=abaabb.

Reduce LHS:

[1]bba(aba)
⇒ bbaa

Reduce RHS:

[1](aba)abb
⇒ aabb

Referenced by [4].

[4] aabbbb=a

Overlap of [2] bbaabb=a with [3] bbaa=aabb:

bbaabb bbaa

Critical pair: aabbbb=a.

Defines rule #3.

Referenced by [5].

[5] bba=abb

Overlap of [2] bbaabb=a with [4] aabbbb=a:

bb aabb aabbbb

Critical pair: bba=abb.

Defines rule #2.