Certificate for #5838 ⟨a, b | abaaab=bbbab⟩

Completion settings:

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

Axiom: abaaab=bbbab.

Flip LHS and RHS.

Referenced by [2], [3].

Axiom: bbbab=c.

Reduce LHS:

Defines rule #2.

Referenced by [3], [5], [6], [7], [11].

Simplify [1] bbbab=abaaab.

Reduce RHS:

Defines rule #9.

Referenced by [4], [5], [6], [8], [10].

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

Critical pair: bbbac=cbbab.

Referenced by [8], [9].

Overlap of [3] bbbab=c with [2] abaaab=c:

Critical pair: bbbc=caaab.

Defines rule #6.

Referenced by [8].

Overlap of [2] abaaab=c with [3] bbbab=c:

Critical pair: abaaac=cbbab.

Flip LHS and RHS.

Defines rule #5.

Referenced by [8], [9], [12].

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

Critical pair: abaac=caaab.

Defines rule #1.

Overlap of [3] bbbab=c with [5] bbbc=caaab:

Critical pair: bbbacaaab=cbbc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #3.

Simplify [4] bbbac=cbbab.

Reduce RHS:

Defines rule #7.

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

Overlap of [3] bbbab=c with [9] bbbac=abaaac:

Critical pair: bbbaabaaac=cbbac.

Defines rule #10.

Overlap of [2] abaaab=c with [9] bbbac=abaaac:

Critical pair: abaaaabaaac=cbbac.

Defines rule #4.

Overlap of [6] cbbab=abaaac with [9] bbbac=abaaac:

Critical pair: cbbaabaaac=abaaacbbac.

Defines rule #8.