Certificate for #3032 ⟨a, b, c | aba=b, acb=a⟩

Back:⟨a, b, c | aba=b, acb=a⟩

Completion settings:

[1] aba=b

Axiom: aba=b.

Defines rule #3.

Referenced by [3], [4].

[2] acb=a

Axiom: acb=a.

Defines rule #4.

Referenced by [4].

[3] abb=bba

Overlap of [1] aba=b with [1] aba=b:

ab a aba

Critical pair: abb=bba.

Defines rule #2.

[4] bcb=b

Overlap of [1] aba=b with [2] acb=a:

ab a acb

Critical pair: aba=bcb.

Reduce LHS:

[1](aba)
⇒ b

Flip LHS and RHS.

Defines rule #1.