Certificate for #5933 ⟨a, b | abbbba=abaab⟩

Completion settings:

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

Axiom: abbbba=abaab.

Referenced by [3].

Axiom: abaab=c.

Defines rule #2.

Referenced by [3], [4], [6], [7], [8].

Simplify [1] abbbba=abaab.

Reduce RHS:

Defines rule #5.

Referenced by [5], [6], [7], [9], [11].

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

Critical pair: abac=caab.

Flip LHS and RHS.

Defines rule #1.

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

Critical pair: abbbbc=cbbbba.

Flip LHS and RHS.

Referenced by [10].

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

Critical pair: abbbbc=cbaab.

Defines rule #6.

Referenced by [9], [10], [12].

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

Critical pair: abac=cbbba.

Flip LHS and RHS.

Defines rule #3.

Referenced by [8].

Overlap of [7] cbbba=abac with [2] abaab=c:

Critical pair: cbbbc=abacbaab.

Defines rule #4.

Overlap of [3] abbbba=c with [6] abbbbc=cbaab:

Critical pair: abbbbcbaab=cbbbbc.

Reduce LHS:

Defines rule #8.

Simplify [5] cbbbba=abbbbc.

Reduce RHS:

Defines rule #7.

Referenced by [11], [12].

Overlap of [10] cbbbba=cbaab with [3] abbbba=c:

Critical pair: cbbbbc=cbaabbbbba.

Flip LHS and RHS.

Defines rule #9.

Overlap of [10] cbbbba=cbaab with [6] abbbbc=cbaab:

Critical pair: cbbbbcbaab=cbaabbbbbc.

Flip LHS and RHS.

Defines rule #10.