Certificate for #1125 ⟨a, b | ababba=baa⟩

Completion settings:

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

Axiom: ababba=baa.

Referenced by [3].

Axiom: baa=c.

Defines rule #3.

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

Simplify [1] ababba=baa.

Reduce RHS:

Defines rule #11.

Referenced by [4], [5], [6], [7], [8].

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

Critical pair: ababbc=cbabba.

Flip LHS and RHS.

Referenced by [6], [13].

Overlap of [3] ababba=c with [2] baa=c:

Critical pair: ababc=ca.

Defines rule #1.

Referenced by [7], [10].

Overlap of [2] baa=c with [3] ababba=c:

Critical pair: bac=cbabba.

Reduce RHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [7], [8], [9], [11], [13], [14].

Overlap of [3] ababba=c with [5] ababc=ca:

Critical pair: ababbca=cbabc.

Reduce LHS:

Defines rule #5.

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

Overlap of [3] ababba=c with [6] ababbc=bac:

Critical pair: ababbbac=cbabbc.

Defines rule #12.

Overlap of [2] baa=c with [6] ababbc=bac:

Critical pair: babac=cbabbc.

Defines rule #4.

Referenced by [12].

Overlap of [7] baca=cbabc with [5] ababc=ca:

Critical pair: bacca=cbabcbabc.

Flip LHS and RHS.

Defines rule #9.

Overlap of [7] baca=cbabc with [6] ababbc=bac:

Critical pair: bacbac=cbabcbabbc.

Flip LHS and RHS.

Defines rule #10.

Overlap of [9] babac=cbabbc with [7] baca=cbabc:

Critical pair: bacbabc=cbabbca.

Flip LHS and RHS.

Defines rule #8.

Simplify [4] cbabba=ababbc.

Reduce RHS:

Defines rule #6.

Referenced by [14].

Overlap of [13] cbabba=bac with [6] ababbc=bac:

Critical pair: cbabbbac=bacbabbc.

Defines rule #7.