Certificate for #406 ⟨a, b, c | abc=b, aca=1⟩

Completion settings:

• Reduction order:
  • Left-to-right recursive path with deg(a) = deg(b) = 0, a < b; deg(c) = 1

Axiom: abc=b.

Referenced by [5], [6].

Axiom: aca=1.

Referenced by [3], [4], [6].

Overlap of [2] aca=1 with [2] aca=1:

Critical pair: ac=ca.

Defines rule #3.

Referenced by [4], [6].

Overlap of [2] aca=1 with [3] ac=ca:

Critical pair: caa=1.

Defines rule #2.

Referenced by [5].

Overlap of [1] abc=b with [4] caa=1:

Critical pair: ab=baa.

Flip LHS and RHS.

Defines rule #1.

Overlap of [2] aca=1 with [1] abc=b:

Critical pair: acb=bc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.