Certificate for #2017 ⟨a, b, c | abc=ca, cbc=1⟩

Completion settings:

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

Axiom: abc=ca.

Flip LHS and RHS.

Defines rule #4.

Referenced by [5].

Axiom: cbc=1.

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

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

Critical pair: cb=bc.

Defines rule #1.

Referenced by [4], [5].

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

Critical pair: bcc=1.

Defines rule #2.

Referenced by [5], [6].

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

Critical pair: cbabc=a.

Reduce LHS:

Referenced by [6].

Overlap of [5] bab=a with [4] bcc=1:

Critical pair: ba=acc.

Defines rule #3.