Certificate for #20204 ⟨a, b | aba=a, aabb=bba⟩

Back:⟨a, b | aba=a, aabb=bba⟩

Completion settings:

[1] aba=a

Axiom: aba=a.

Defines rule #1.

Referenced by [3].

[2] bba=aabb

Axiom: aabb=bba.

Flip LHS and RHS.

Defines rule #3.

Referenced by [3].

[3] aaabb=aabb

Overlap of [2] bba=aabb with [1] aba=a:

bb a aba

Critical pair: bba=aabbba.

Reduce LHS:

[2](bba)
⇒ aabb

Reduce RHS:

[2]aab(bba)
[1]⇒ a(aba)abb
⇒ aaabb

Flip LHS and RHS.

Defines rule #2.