Certificate for #973 ⟨a, b, c | ab=a, bca=b⟩

Back:⟨a, b, c | ab=a, bca=b⟩

Completion settings:

[1] ab=a

Axiom: ab=a.

Defines rule #1.

Referenced by [3], [4].

[2] bca=b

Axiom: bca=b.

Defines rule #4.

Referenced by [3], [4].

[3] aca=a

Overlap of [1] ab=a with [2] bca=b:

a b bca

Critical pair: ab=aca.

Reduce LHS:

[1](ab)
⇒ a

Flip LHS and RHS.

Defines rule #3.

[4] bb=b

Overlap of [2] bca=b with [1] ab=a:

bc a ab

Critical pair: bca=bb.

Reduce LHS:

[2](bca)
⇒ b

Flip LHS and RHS.

Defines rule #2.