Certificate for #3516 ⟨a, b | aa=1, abbab=bb⟩

Back:⟨a, b | aa=1, abbab=bb⟩

Completion settings:

[1] aa=1

Axiom: aa=1.

Defines rule #4.

Referenced by [3], [5].

[2] abbab=bb

Axiom: abbab=bb.

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

[3] bbab=abb

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

a a abbab

Critical pair: abb=bbab.

Flip LHS and RHS.

Defines rule #3.

Referenced by [4].

[4] babb=abbbb

Overlap of [2] abbab=bb with [2] abbab=bb:

abb ab abbab

Critical pair: abbbb=bbbab.

Reduce RHS:

[3]b(bbab)
⇒ babb

Flip LHS and RHS.

Defines rule #2.

Referenced by [5].

[5] bbbbbb=bbb

Overlap of [2] abbab=bb with [4] babb=abbbb:

ab bab babb

Critical pair: ababbbb=bbb.

Reduce LHS:

[4]a(babb)bb
[1]⇒ (aa)bbbbbb
⇒ bbbbbb

Defines rule #1.