Certificate for #28258 ⟨a, b | aa=1, babab=babb⟩

Completion settings:

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

Axiom: aa=1.

Defines rule #1.

Axiom: babab=babb.

Referenced by [4].

Axiom: bab=c.

Defines rule #5.

Referenced by [4], [5], [6], [7].

Simplify [2] babab=babb.

Reduce RHS:

Referenced by [5].

Overlap of [4] babab=cb with [3] bab=c:

Critical pair: cab=cb.

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

Overlap of [3] bab=c with [3] bab=c:

Critical pair: bac=cab.

Reduce RHS:

Flip LHS and RHS.

Defines rule #3.

Referenced by [7], [8].

Overlap of [6] cb=bac with [3] bab=c:

Critical pair: cc=bacab.

Reduce RHS:

Flip LHS and RHS.

Defines rule #2.

Simplify [5] cab=cb.

Reduce RHS:

Defines rule #4.