Certificate for #542 ⟨a, b | abaab=bab⟩

Completion settings:

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

Axiom: abaab=bab.

Referenced by [3].

Axiom: bab=c.

Defines rule #7.

Referenced by [3], [4], [6], [7], [9].

Simplify [1] abaab=bab.

Reduce RHS:

Defines rule #8.

Referenced by [5], [6], [7], [8].

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

Critical pair: bac=cab.

Defines rule #5.

Referenced by [5].

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

Critical pair: abac=caab.

Reduce LHS:

Defines rule #3.

Referenced by [8], [9].

Overlap of [3] abaab=c with [2] bab=c:

Critical pair: abaac=cab.

Defines rule #6.

Overlap of [2] bab=c with [3] abaab=c:

Critical pair: bc=caab.

Defines rule #4.

Overlap of [5] acab=caab with [3] abaab=c:

Critical pair: acc=caabaab.

Reduce RHS:

Defines rule #1.

Overlap of [5] acab=caab with [2] bab=c:

Critical pair: acac=caabab.

Reduce RHS:

Defines rule #2.