Certificate for #2422 ⟨a, b | aaabaa=aaab⟩

Completion settings:

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

Axiom: aaabaa=aaab.

Referenced by [3].

Axiom: aaab=c.

Defines rule #4.

Referenced by [3], [4], [5], [6].

Simplify [1] aaabaa=aaab.

Reduce RHS:

Referenced by [4].

Overlap of [3] aaabaa=c with [2] aaab=c:

Critical pair: caa=c.

Defines rule #1.

Referenced by [5], [6].

Overlap of [4] caa=c with [2] aaab=c:

Critical pair: cc=cab.

Flip LHS and RHS.

Defines rule #3.

Overlap of [4] caa=c with [2] aaab=c:

Critical pair: cac=caab.

Reduce RHS:

Flip LHS and RHS.

Defines rule #2.