Certificate for #4786 ⟨a, b | abaabaab=abb⟩

Completion settings:

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

Axiom: abaabaab=abb.

Referenced by [3].

Axiom: abb=c.

Defines rule #2.

Referenced by [3], [5], [8].

Simplify [1] abaabaab=abb.

Reduce RHS:

Defines rule #7.

Referenced by [4], [5], [6], [7].

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

Critical pair: abac=caab.

Defines rule #1.

Referenced by [5], [6], [8].

Overlap of [3] abaabaab=c with [2] abb=c:

Critical pair: abaabac=cb.

Reduce LHS:

Defines rule #6.

Referenced by [6], [7], [8].

Overlap of [3] abaabaab=c with [4] abac=caab:

Critical pair: abaabacaab=cac.

Reduce LHS:

Defines rule #5.

Referenced by [7].

Overlap of [6] cbaab=cac with [3] abaabaab=c:

Critical pair: cbac=cacaabaab.

Reduce RHS:

Defines rule #3.

Overlap of [5] caabaab=cb with [2] abb=c:

Critical pair: caabac=cbb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.