Certificate for #6435 ⟨a, b | aab=b, bbaba=b⟩

Back:⟨a, b | aab=b, bbaba=b⟩

Completion settings:

[1] aab=b

Axiom: aab=b.

Defines rule #1.

Referenced by [3].

[2] bbaba=b

Axiom: bbaba=b.

Referenced by [3], [4], [5], [6], [8].

[3] bbabb=bab

Overlap of [2] bbaba=b with [1] aab=b:

bbab a aab

Critical pair: bbabb=bab.

Referenced by [4], [5].

[4] bababa=bbab

Overlap of [3] bbabb=bab with [2] bbaba=b:

bba bb bbaba

Critical pair: bbab=bababa.

Flip LHS and RHS.

Referenced by [7].

[5] bababb=bb

Overlap of [3] bbabb=bab with [3] bbabb=bab:

bba bb bbabb

Critical pair: bbabab=bababb.

Reduce LHS:

[2](bbaba)b
⇒ bb

Flip LHS and RHS.

Referenced by [6].

[6] babab=b

Overlap of [5] bababb=bb with [2] bbaba=b:

baba bb bbaba

Critical pair: babab=bbaba.

Reduce RHS:

[2](bbaba)
⇒ b

Defines rule #4.

Referenced by [7].

[7] bbab=ba

Simplify [4] bababa=bbab.

Reduce LHS:

[6](babab)a
⇒ ba

Flip LHS and RHS.

Defines rule #3.

Referenced by [8].

[8] baa=b

Overlap of [2] bbaba=b with [7] bbab=ba:

bbaba bbab

Critical pair: baa=b.

Defines rule #2.