Certificate for #1539 ⟨a, b, c | ab=1, ccc=aa⟩

Completion settings:

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

Axiom: ab=1.

Referenced by [3], [5].

Axiom: ccc=aa.

Flip LHS and RHS.

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

Overlap of [2] aa=ccc with [1] ab=1:

Critical pair: a=cccb.

Defines rule #4.

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

Overlap of [2] aa=ccc with [2] aa=ccc:

Critical pair: accc=ccca.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #2.

Overlap of [1] ab=1 with [3] a=cccb:

Critical pair: cccbb=1.

Defines rule #1.

Overlap of [2] aa=ccc with [3] a=cccb:

Critical pair: cccba=ccc.

Reduce LHS:

Defines rule #3.