Certificate for #5042 ⟨a, b | aaababa=abab⟩

Completion settings:

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

Axiom: aaababa=abab.

Referenced by [3].

Axiom: abab=c.

Defines rule #6.

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

Simplify [1] aaababa=abab.

Reduce RHS:

Referenced by [4].

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

Critical pair: aaca=c.

Defines rule #1.

Referenced by [5], [7], [8].

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

Critical pair: aacc=caca.

Flip LHS and RHS.

Defines rule #3.

Referenced by [8].

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

Critical pair: abc=cab.

Flip LHS and RHS.

Defines rule #5.

Referenced by [7].

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

Critical pair: aaabc=cb.

Flip LHS and RHS.

Defines rule #4.

Overlap of [4] aaca=c with [5] caca=aacc:

Critical pair: aaaacc=cca.

Flip LHS and RHS.

Defines rule #2.