Certificate for #2500 ⟨a, b | aababa=abab⟩

Completion settings:

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

Axiom: aababa=abab.

Referenced by [3].

Axiom: abab=c.

Defines rule #5.

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

Simplify [1] aababa=abab.

Reduce RHS:

Referenced by [4].

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

Critical pair: aca=c.

Defines rule #1.

Referenced by [5], [7].

Overlap of [4] aca=c with [4] aca=c:

Critical pair: acc=cca.

Flip LHS and RHS.

Defines rule #2.

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

Critical pair: abc=cab.

Flip LHS and RHS.

Defines rule #4.

Referenced by [7].

Overlap of [4] aca=c with [6] cab=abc:

Critical pair: aabc=cb.

Flip LHS and RHS.

Defines rule #3.