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

Completion settings:

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

Axiom: aaa=a.

Defines rule #2.

Referenced by [5], [12].

Axiom: bbabb=a.

Referenced by [4].

Axiom: abb=c.

Defines rule #11.

Referenced by [4], [5], [6], [7], [10], [13], [14].

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

Critical pair: bbc=a.

Defines rule #10.

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

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

Critical pair: aac=abb.

Reduce RHS:

Defines rule #3.

Referenced by [9].

Overlap of [3] abb=c with [4] bbc=a:

Critical pair: aa=cc.

Flip LHS and RHS.

Defines rule #1.

Referenced by [8], [9], [11].

Overlap of [3] abb=c with [4] bbc=a:

Critical pair: aba=cbc.

Flip LHS and RHS.

Defines rule #6.

Referenced by [11].

Overlap of [4] bbc=a with [6] cc=aa:

Critical pair: bbaa=ac.

Referenced by [12].

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

Critical pair: caa=aac.

Reduce RHS:

Defines rule #4.

Referenced by [10].

Overlap of [9] caa=c with [3] abb=c:

Critical pair: cac=cbb.

Flip LHS and RHS.

Defines rule #12.

Referenced by [14].

Overlap of [6] cc=aa with [7] cbc=aba:

Critical pair: caba=aabc.

Defines rule #7.

Referenced by [14].

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

Critical pair: bba=aca.

Defines rule #9.

Referenced by [13].

Overlap of [3] abb=c with [12] bba=aca:

Critical pair: abaca=cba.

Flip LHS and RHS.

Defines rule #5.

Overlap of [11] caba=aabc with [3] abb=c:

Critical pair: cabc=aabcbb.

Reduce RHS:

Defines rule #8.