Certificate for #1741 ⟨a, b, c | aab=ca, cbc=1⟩

Completion settings:

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

Axiom: aab=ca.

Defines rule #3.

Referenced by [4].

Axiom: cbc=1.

Referenced by [3], [5], [6], [7].

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

Critical pair: cb=bc.

Flip LHS and RHS.

Defines rule #1.

Referenced by [4], [7].

Overlap of [1] aab=ca with [3] bc=cb:

Critical pair: aacb=cac.

Defines rule #5.

Referenced by [5].

Overlap of [4] aacb=cac with [2] cbc=1:

Critical pair: aa=cacc.

Flip LHS and RHS.

Referenced by [6].

Overlap of [2] cbc=1 with [5] cacc=aa:

Critical pair: cbaa=acc.

Flip LHS and RHS.

Defines rule #4.

Overlap of [2] cbc=1 with [3] bc=cb:

Critical pair: ccb=1.

Defines rule #2.