Certificate for #15841 ⟨a, b | aba=ab, aaaaa=a⟩

Completion settings:

• Auxiliary generators:
  1. c = ab
• Reduction order:
  • Left-to-right shortlex with a < c < b

Axiom: aba=ab.

Referenced by [4].

Axiom: aaaaa=a.

Defines rule #4.

Referenced by [7].

Axiom: ab=c.

Defines rule #1.

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

Simplify [1] aba=ab.

Reduce RHS:

Referenced by [5].

Overlap of [4] aba=c with [3] ab=c:

Critical pair: ca=c.

Defines rule #2.

Referenced by [6].

Overlap of [5] ca=c with [3] ab=c:

Critical pair: cc=cb.

Flip LHS and RHS.

Defines rule #3.

Overlap of [2] aaaaa=a with [3] ab=c:

Critical pair: aaaac=ab.

Reduce RHS:

Defines rule #5.