Certificate for #3533 ⟨a, b, c | bb=ac, bca=a⟩

Back:⟨a, b, c | bb=ac, bca=a⟩

Completion settings:

[1] ac=bb

Axiom: bb=ac.

Flip LHS and RHS.

Defines rule #1.

Referenced by [3].

[2] bca=a

Axiom: bca=a.

Defines rule #2.

Referenced by [3], [4].

[3] bcbb=bb

Overlap of [2] bca=a with [1] ac=bb:

bc a ac

Critical pair: bcbb=ac.

Reduce RHS:

[1](ac)
⇒ bb

Defines rule #3.

Referenced by [4].

[4] bcba=ba

Overlap of [3] bcbb=bb with [2] bca=a:

bcb b bca

Critical pair: bcba=bbca.

Reduce RHS:

[2]b(bca)
⇒ ba

Defines rule #4.