Certificate for #3512 ⟨a, b | aa=1, ababb=bb⟩

Back:⟨a, b | aa=1, ababb=bb⟩

Completion settings:

[1] aa=1

Axiom: aa=1.

Defines rule #1.

Referenced by [3].

[2] ababb=bb

Axiom: ababb=bb.

Referenced by [3], [4].

[3] babb=abb

Overlap of [1] aa=1 with [2] ababb=bb:

a a ababb

Critical pair: abb=babb.

Flip LHS and RHS.

Defines rule #3.

Referenced by [4].

[4] bbb=bb

Overlap of [3] babb=abb with [3] babb=abb:

bab b babb

Critical pair: bababb=abbabb.

Reduce LHS:

[2]b(ababb)
⇒ bbb

Reduce RHS:

[3]ab(babb)
[2]⇒ (ababb)
⇒ bb

Defines rule #2.