Certificate for #7411 ⟨a, b, c | ab=1, acac=bb⟩

Completion settings:

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

Axiom: ab=1.

Referenced by [3], [6].

Axiom: acac=bb.

Flip LHS and RHS.

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

Overlap of [1] ab=1 with [2] bb=acac:

Critical pair: aacac=b.

Flip LHS and RHS.

Defines rule #4.

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

Overlap of [2] bb=acac with [2] bb=acac:

Critical pair: bacac=acacb.

Reduce LHS:

Reduce RHS:

Defines rule #2.

Overlap of [2] bb=acac with [3] b=aacac:

Critical pair: aacacb=acac.

Reduce LHS:

Defines rule #3.

Overlap of [1] ab=1 with [3] b=aacac:

Critical pair: aaacac=1.

Defines rule #1.