Certificate for #20273 ⟨a, b | aba=b, aabb=abb⟩

Back:⟨a, b | aba=b, aabb=abb⟩

Completion settings:

[1] aba=b

Axiom: aba=b.

Defines rule #1.

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

[2] aabb=abb

Axiom: aabb=abb.

Defines rule #3.

Referenced by [4], [5].

[3] bba=abb

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

ab a aba

Critical pair: abb=bba.

Flip LHS and RHS.

Defines rule #2.

Referenced by [5].

[4] babb=bbb

Overlap of [1] aba=b with [2] aabb=abb:

ab a aabb

Critical pair: ababb=babb.

Reduce LHS:

[1](aba)bb
⇒ bbb

Flip LHS and RHS.

Defines rule #5.

[5] abbb=bbb

Overlap of [2] aabb=abb with [3] bba=abb:

aab b bba

Critical pair: aababb=abbba.

Reduce LHS:

[1]a(aba)bb
⇒ abbb

Reduce RHS:

[3]ab(bba)
[1]⇒ (aba)bb
⇒ bbb

Defines rule #4.