Certificate for #2458 ⟨a, b | aaabba=abab⟩

Completion settings:

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

Axiom: aaabba=abab.

Referenced by [3].

Axiom: abab=c.

Defines rule #1.

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

Simplify [1] aaabba=abab.

Reduce RHS:

Defines rule #2.

Referenced by [5], [6].

Overlap of [2] abab=c with [2] abab=c:

Critical pair: abc=cab.

Flip LHS and RHS.

Defines rule #3.

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

Critical pair: aaabbc=caabba.

Flip LHS and RHS.

Defines rule #5.

Overlap of [3] aaabba=c with [2] abab=c:

Critical pair: aaabbc=cbab.

Flip LHS and RHS.

Defines rule #4.