Certificate for #6773 ⟨a, b | aba=b, aabb=aa⟩

Back:⟨a, b | aba=b, aabb=aa⟩

Completion settings:

[1] aba=b

Axiom: aba=b.

Defines rule #1.

Referenced by [3], [4], [5], [6].

[2] aabb=aa

Axiom: aabb=aa.

Defines rule #4.

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], [6].

[4] babb=ba

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

ab a aabb

Critical pair: abaa=babb.

Reduce LHS:

[1](aba)a
⇒ ba

Flip LHS and RHS.

Defines rule #5.

[5] abbb=ab

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

aab b bba

Critical pair: aababb=aaba.

Reduce LHS:

[1]a(aba)bb
⇒ abbb

Reduce RHS:

[1]a(aba)
⇒ ab

Referenced by [6].

[6] bbb=b

Overlap of [5] abbb=ab with [3] bba=abb:

ab bb bba

Critical pair: ababb=aba.

Reduce LHS:

[1](aba)bb
⇒ bbb

Reduce RHS:

[1](aba)
⇒ b

Defines rule #3.