Certificate for #6274 ⟨a, b | aaa=a, bbabb=a⟩

Completion settings:

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

Axiom: aaa=a.

Defines rule #1.

Referenced by [5], [11].

Axiom: bbabb=a.

Referenced by [4].

Axiom: ab=c.

Defines rule #3.

Referenced by [4], [5], [6], [7], [10].

Overlap of [2] bbabb=a with [3] ab=c:

Critical pair: bbcb=a.

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

Overlap of [1] aaa=a with [3] ab=c:

Critical pair: aac=ab.

Reduce RHS:

Defines rule #2.

Referenced by [9], [12].

Overlap of [3] ab=c with [4] bbcb=a:

Critical pair: aa=cbcb.

Flip LHS and RHS.

Defines rule #10.

Referenced by [8], [9].

Overlap of [4] bbcb=a with [4] bbcb=a:

Critical pair: bbca=abcb.

Reduce RHS:

Referenced by [13].

Overlap of [4] bbcb=a with [6] cbcb=aa:

Critical pair: bbaa=acb.

Referenced by [11], [12].

Overlap of [6] cbcb=aa with [6] cbcb=aa:

Critical pair: cbaa=aacb.

Reduce RHS:

Defines rule #4.

Referenced by [10], [15].

Overlap of [9] cbaa=cb with [3] ab=c:

Critical pair: cbac=cbb.

Flip LHS and RHS.

Defines rule #9.

Referenced by [14].

Overlap of [8] bbaa=acb with [1] aaa=a:

Critical pair: bba=acba.

Defines rule #7.

Referenced by [14].

Overlap of [8] bbaa=acb with [5] aac=c:

Critical pair: bbc=acbc.

Defines rule #8.

Referenced by [13].

Simplify [7] bbca=ccb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #5.

Overlap of [10] cbb=cbac with [11] bba=acba:

Critical pair: cacba=cbaca.

Referenced by [15].

Overlap of [14] cacba=cbaca with [9] cbaa=cb:

Critical pair: cacb=cbacaa.

Defines rule #6.