Certificate for #2711 ⟨a, b | abbab=abbaa⟩

Back:⟨a, b | abbab=abbaa⟩

Completion settings:

[1] abbab=abbaa

Axiom: abbab=abbaa.

Referenced by [3].

[2] abbaa=c

Axiom: abbaa=c.

Defines rule #3.

Referenced by [3], [4], [6], [7].

[3] abbab=c

Simplify [1] abbab=abbaa.

Reduce RHS:

[2](abbaa)
⇒ c

Defines rule #4.

Referenced by [5], [6], [7].

[4] cbbaa=abbac

Overlap of [2] abbaa=c with [2] abbaa=c:

abba a abbaa

Critical pair: abbac=cbbaa.

Flip LHS and RHS.

Defines rule #5.

[5] cbab=abbc

Overlap of [3] abbab=c with [3] abbab=c:

abb ab abbab

Critical pair: abbc=cbab.

Flip LHS and RHS.

Defines rule #2.

[6] cbaa=abbc

Overlap of [3] abbab=c with [2] abbaa=c:

abb ab abbaa

Critical pair: abbc=cbaa.

Flip LHS and RHS.

Defines rule #1.

[7] cbbab=abbac

Overlap of [2] abbaa=c with [3] abbab=c:

abba a abbab

Critical pair: abbac=cbbab.

Flip LHS and RHS.

Defines rule #6.