Certificate for #357 ⟨a, b, c | aba=b, aca=1⟩

Completion settings:

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

Axiom: aba=b.

Referenced by [4], [5], [6].

Axiom: aca=1.

Referenced by [3], [4], [5], [7].

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

Critical pair: ac=ca.

Flip LHS and RHS.

Defines rule #1.

Referenced by [4], [6], [7].

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

Critical pair: ab=bca.

Reduce RHS:

Defines rule #3.

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

Critical pair: acb=ba.

Referenced by [6].

Overlap of [3] ca=ac with [1] aba=b:

Critical pair: cb=acba.

Reduce RHS:

Defines rule #4.

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

Critical pair: aac=1.

Defines rule #2.