Certificate for #22833 ⟨a, b | aaa=1, baabb=abb⟩

Completion settings:

• Auxiliary generators:
  1. c = ab
  2. d = cb
• Reduction order:
  • Left-to-right recursive path with deg(d) = 0; deg(b) = deg(a) = deg(c) = 1, b < a < c

Axiom: aaa=1.

Defines rule #7.

Referenced by [7].

Axiom: baabb=abb.

Referenced by [5].

Axiom: ab=c.

Defines rule #3.

Referenced by [5], [6], [7], [8].

Axiom: cb=d.

Defines rule #5.

Referenced by [5], [6], [9], [10].

Simplify [2] baabb=abb.

Reduce RHS:

Referenced by [6].

Overlap of [5] baabb=d with [3] ab=c:

Critical pair: bacb=d.

Reduce LHS:

Defines rule #2.

Referenced by [8], [9].

Overlap of [1] aaa=1 with [3] ab=c:

Critical pair: aac=b.

Defines rule #8.

Referenced by [10].

Overlap of [3] ab=c with [6] bad=d:

Critical pair: ad=cad.

Flip LHS and RHS.

Defines rule #6.

Overlap of [4] cb=d with [6] bad=d:

Critical pair: cd=dad.

Defines rule #1.

Overlap of [7] aac=b with [4] cb=d:

Critical pair: aad=bb.

Defines rule #4.