Certificate for #2262 ⟨a, b | aabbaba=aab⟩

Back:⟨a, b | aabbaba=aab⟩

Completion settings:

[1] aabbaba=aab

Axiom: aabbaba=aab.

Referenced by [3].

[2] bbaba=c

Axiom: bbaba=c.

Defines rule #3.

Referenced by [3], [4], [5], [6].

[3] aab=aac

Overlap of [1] aabbaba=aab with [2] bbaba=c:

aa bbaba bbaba

Critical pair: aac=aab.

Flip LHS and RHS.

Defines rule #1.

Referenced by [4], [5].

[4] cab=cac

Overlap of [2] bbaba=c with [3] aab=aac:

bbab a aab

Critical pair: bbabaac=cab.

Reduce LHS:

[2](bbaba)ac
⇒ cac

Flip LHS and RHS.

Defines rule #2.

Referenced by [6].

[5] aacbaba=aac

Overlap of [3] aab=aac with [2] bbaba=c:

aa b bbaba

Critical pair: aac=aacbaba.

Flip LHS and RHS.

Defines rule #4.

[6] cacbaba=cac

Overlap of [4] cab=cac with [2] bbaba=c:

ca b bbaba

Critical pair: cac=cacbaba.

Flip LHS and RHS.

Defines rule #5.