Certificate for #5301 ⟨a, b | abaaaba=abab⟩

Completion settings:

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

Axiom: abaaaba=abab.

Referenced by [3].

Axiom: abab=c.

Defines rule #5.

Referenced by [3], [4], [6], [7].

Simplify [1] abaaaba=abab.

Reduce RHS:

Defines rule #6.

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

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

Critical pair: abc=cab.

Flip LHS and RHS.

Defines rule #2.

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

Critical pair: abaac=caaba.

Flip LHS and RHS.

Defines rule #3.

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

Critical pair: abaac=cb.

Flip LHS and RHS.

Defines rule #1.

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

Critical pair: abc=caaaba.

Flip LHS and RHS.

Defines rule #4.