Certificate for #2708 ⟨a, b | abbab=abaaa⟩

Back:⟨a, b | abbab=abaaa⟩

Completion settings:

[1] abbab=abaaa

Axiom: abbab=abaaa.

Referenced by [3].

[2] abaaa=c

Axiom: abaaa=c.

Defines rule #3.

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

[3] abbab=c

Simplify [1] abbab=abaaa.

Reduce RHS:

[2](abaaa)
⇒ c

Defines rule #4.

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

[4] cbaaa=abaac

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

abaa a abaaa

Critical pair: abaac=cbaaa.

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] caaa=abbc

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

abb ab abaaa

Critical pair: abbc=caaa.

Flip LHS and RHS.

Defines rule #1.

[7] cbbab=abaac

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

abaa a abbab

Critical pair: abaac=cbbab.

Flip LHS and RHS.

Defines rule #6.