Certificate for #5387 ⟨a, b, c | ab=a, bcba=b⟩

Back:⟨a, b, c | ab=a, bcba=b⟩

Completion settings:

[1] ab=a

Axiom: ab=a.

Defines rule #1.

Referenced by [3], [4].

[2] bcba=b

Axiom: bcba=b.

Defines rule #4.

Referenced by [3], [4].

[3] acba=a

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

a b bcba

Critical pair: ab=acba.

Reduce LHS:

[1](ab)
⇒ a

Flip LHS and RHS.

Defines rule #3.

[4] bb=b

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

bcb a ab

Critical pair: bcba=bb.

Reduce LHS:

[2](bcba)
⇒ b

Flip LHS and RHS.

Defines rule #2.