Certificate for #4311 ⟨a, b | ababbabba=ab⟩

Completion settings:

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

Axiom: ababbabba=ab.

Referenced by [3].

Axiom: abb=c.

Defines rule #4.

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

Overlap of [1] ababbabba=ab with [2] abb=c:

Critical pair: abcabba=ab.

Reduce LHS:

Defines rule #2.

Referenced by [4], [5].

Overlap of [3] abcca=ab with [2] abb=c:

Critical pair: abccc=abbb.

Reduce RHS:

Flip LHS and RHS.

Defines rule #3.

Overlap of [3] abcca=ab with [3] abcca=ab:

Critical pair: abccab=abbcca.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #1.