Certificate for #4332 ⟨a, b | abbaabaab=aa⟩

Completion settings:

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

Axiom: abbaabaab=aa.

Referenced by [3].

Axiom: abb=c.

Defines rule #4.

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

Overlap of [1] abbaabaab=aa with [2] abb=c:

Critical pair: caabaab=aa.

Defines rule #5.

Referenced by [4], [5], [8], [9].

Overlap of [3] caabaab=aa with [2] abb=c:

Critical pair: caabac=aab.

Defines rule #1.

Referenced by [5], [6].

Overlap of [4] caabac=aab with [3] caabaab=aa:

Critical pair: caabaaa=aabaabaab.

Flip LHS and RHS.

Defines rule #8.

Referenced by [9].

Overlap of [4] caabac=aab with [4] caabac=aab:

Critical pair: caabaaab=aabaabac.

Defines rule #6.

Referenced by [7].

Overlap of [6] caabaaab=aabaabac with [2] abb=c:

Critical pair: caabaac=aabaabacb.

Flip LHS and RHS.

Defines rule #7.

Referenced by [8].

Overlap of [3] caabaab=aa with [7] aabaabacb=caabaac:

Critical pair: ccaabaac=aaacb.

Flip LHS and RHS.

Defines rule #2.

Overlap of [3] caabaab=aa with [5] aabaabaab=caabaaa:

Critical pair: ccaabaaa=aaaab.

Flip LHS and RHS.

Defines rule #3.