Certificate for #2352 ⟨a, b | abbabba=aab⟩

Completion settings:

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

Axiom: abbabba=aab.

Referenced by [3].

Axiom: aab=c.

Defines rule #1.

Referenced by [3], [5], [6], [8], [9].

Simplify [1] abbabba=aab.

Reduce RHS:

Defines rule #3.

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

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

Critical pair: abbc=cbba.

Flip LHS and RHS.

Defines rule #2.

Referenced by [7], [8], [10], [13].

Overlap of [3] abbabba=c with [2] aab=c:

Critical pair: abbabbc=cab.

Defines rule #4.

Referenced by [7], [10], [11], [12], [13].

Overlap of [2] aab=c with [3] abbabba=c:

Critical pair: ac=cbabba.

Flip LHS and RHS.

Defines rule #8.

Referenced by [9], [11].

Overlap of [4] cbba=abbc with [3] abbabba=c:

Critical pair: cbbc=abbcbbabba.

Reduce RHS:

Flip LHS and RHS.

Defines rule #7.

Referenced by [13].

Overlap of [4] cbba=abbc with [2] aab=c:

Critical pair: cbbc=abbcab.

Flip LHS and RHS.

Defines rule #5.

Referenced by [12].

Overlap of [6] cbabba=ac with [2] aab=c:

Critical pair: cbabbc=acab.

Defines rule #9.

Overlap of [4] cbba=abbc with [5] abbabbc=cab:

Critical pair: cbbcab=abbcbbabbc.

Reduce RHS:

Defines rule #11.

Overlap of [6] cbabba=ac with [5] abbabbc=cab:

Critical pair: cbcab=acbbc.

Defines rule #10.

Overlap of [5] abbabbc=cab with [8] abbcab=cbbc:

Critical pair: abbcbbc=cabab.

Flip LHS and RHS.

Defines rule #6.

Overlap of [7] cabbba=cbbc with [5] abbabbc=cab:

Critical pair: cabbbcab=cbbcbbabbc.

Reduce RHS:

Defines rule #12.