Certificate for #5659 ⟨a, b | aabaab=abbba⟩

Completion settings:

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

Axiom: aabaab=abbba.

Referenced by [3].

Axiom: aab=c.

Defines rule #2.

Referenced by [3], [4], [5], [7].

Overlap of [1] aabaab=abbba with [2] aab=c:

Critical pair: caab=abbba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #11.

Referenced by [4], [5], [6], [9].

Overlap of [2] aab=c with [3] abbba=cc:

Critical pair: acc=cbba.

Flip LHS and RHS.

Defines rule #1.

Referenced by [7], [8], [10].

Overlap of [3] abbba=cc with [2] aab=c:

Critical pair: abbbc=ccab.

Defines rule #6.

Referenced by [6], [9], [10], [11], [12].

Overlap of [3] abbba=cc with [3] abbba=cc:

Critical pair: abbbcc=ccbbba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #5.

Referenced by [11], [12], [13].

Overlap of [4] cbba=acc with [2] aab=c:

Critical pair: cbbc=accab.

Flip LHS and RHS.

Defines rule #3.

Referenced by [8], [13].

Overlap of [4] cbba=acc with [7] accab=cbbc:

Critical pair: cbbcbbc=accccab.

Defines rule #4.

Overlap of [3] abbba=cc with [5] abbbc=ccab:

Critical pair: abbbccab=ccbbbc.

Reduce LHS:

Defines rule #8.

Referenced by [11].

Overlap of [4] cbba=acc with [5] abbbc=ccab:

Critical pair: cbbccab=accbbbc.

Flip LHS and RHS.

Defines rule #7.

Overlap of [5] abbbc=ccab with [6] ccbbba=ccabc:

Critical pair: abbbccabc=ccabcbbba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #12.

Overlap of [6] ccbbba=ccabc with [5] abbbc=ccab:

Critical pair: ccbbbccab=ccabcbbbc.

Flip LHS and RHS.

Defines rule #10.

Overlap of [6] ccbbba=ccabc with [7] accab=cbbc:

Critical pair: ccbbbcbbc=ccabcccab.

Defines rule #9.