Certificate for #2745 ⟨a, b, c | abc=a, cbcc=1⟩

Completion settings:

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

Axiom: abc=a.

Referenced by [3], [6].

Axiom: cbcc=1.

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

Overlap of [1] abc=a with [2] cbcc=1:

Critical pair: ab=abcc.

Reduce RHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [6].

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

Critical pair: cbc=bcc.

Flip LHS and RHS.

Referenced by [5].

Overlap of [4] bcc=cbc with [2] cbcc=1:

Critical pair: bc=cbcbcc.

Reduce RHS:

Defines rule #3.

Referenced by [6], [7].

Overlap of [1] abc=a with [5] bc=cb:

Critical pair: acb=a.

Reduce LHS:

Defines rule #1.

Overlap of [2] cbcc=1 with [5] bc=cb:

Critical pair: ccbc=1.

Reduce LHS:

Defines rule #4.