Certificate for #3027 ⟨a, b, c | aba=b, abc=a⟩

Back:⟨a, b, c | aba=b, abc=a⟩

Completion settings:

[1] aba=b

Axiom: aba=b.

Defines rule #1.

Referenced by [3], [4].

[2] abc=a

Axiom: abc=a.

Defines rule #2.

Referenced by [4].

[3] bba=abb

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

ab a aba

Critical pair: abb=bba.

Flip LHS and RHS.

Defines rule #3.

[4] bbc=b

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

ab a abc

Critical pair: aba=bbc.

Reduce LHS:

[1](aba)
⇒ b

Flip LHS and RHS.

Defines rule #4.