Certificate for #1119 ⟨a, b | aa=1, abbab=b⟩

Back:⟨a, b | aa=1, abbab=b⟩

Completion settings:

[1] aa=1

Axiom: aa=1.

Defines rule #1.

Referenced by [3], [5].

[2] abbab=b

Axiom: abbab=b.

Referenced by [3], [4].

[3] bbab=ab

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

a a abbab

Critical pair: ab=bbab.

Flip LHS and RHS.

Defines rule #3.

Referenced by [4].

[4] abbb=ab

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

abb ab abbab

Critical pair: abbb=bbab.

Reduce RHS:

[3](bbab)
⇒ ab

Referenced by [5].

[5] bbb=b

Overlap of [1] aa=1 with [4] abbb=ab:

a a abbb

Critical pair: aab=bbb.

Reduce LHS:

[1](aa)b
⇒ b

Flip LHS and RHS.

Defines rule #2.