Certificate for #5015 ⟨a, b | aaabaaa=abab⟩

Completion settings:

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

Axiom: aaabaaa=abab.

Referenced by [3].

Axiom: aabaaa=c.

Defines rule #7.

Referenced by [3], [5], [6], [7], [9], [12].

Overlap of [1] aaabaaa=abab with [2] aabaaa=c:

Critical pair: ac=abab.

Flip LHS and RHS.

Defines rule #2.

Referenced by [4], [7], [8], [9], [13].

Overlap of [3] abab=ac with [3] abab=ac:

Critical pair: abac=acab.

Flip LHS and RHS.

Defines rule #4.

Referenced by [9], [10].

Overlap of [2] aabaaa=c with [2] aabaaa=c:

Critical pair: aabac=cbaaa.

Flip LHS and RHS.

Defines rule #5.

Referenced by [9].

Overlap of [2] aabaaa=c with [2] aabaaa=c:

Critical pair: aabaac=cabaaa.

Flip LHS and RHS.

Defines rule #6.

Referenced by [10], [11].

Overlap of [2] aabaaa=c with [3] abab=ac:

Critical pair: aabaaac=cbab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.

Referenced by [8].

Overlap of [7] cbab=cc with [3] abab=ac:

Critical pair: cbac=ccab.

Flip LHS and RHS.

Defines rule #3.

Referenced by [11].

Overlap of [5] cbaaa=aabac with [2] aabaaa=c:

Critical pair: cbaac=aabacabaaa.

Reduce RHS:

Flip LHS and RHS.

Referenced by [12].

Overlap of [4] acab=abac with [6] cabaaa=aabaac:

Critical pair: aaabaac=abacaaa.

Flip LHS and RHS.

Defines rule #9.

Referenced by [13].

Overlap of [8] ccab=cbac with [6] cabaaa=aabaac:

Critical pair: caabaac=cbacaaa.

Flip LHS and RHS.

Defines rule #8.

Overlap of [2] aabaaa=c with [9] aacacaaa=cbaac:

Critical pair: aabacbaac=ccacaaa.

Flip LHS and RHS.

Defines rule #10.

Overlap of [3] abab=ac with [10] abacaaa=aaabaac:

Critical pair: abaaabaac=acacaaa.

Flip LHS and RHS.

Defines rule #11.