Certificate for #4771 ⟨a, b | abaaabab=baa⟩

Completion settings:

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

Axiom: abaaabab=baa.

Referenced by [3].

Axiom: baa=c.

Defines rule #1.

Referenced by [3], [4], [5], [6], [7].

Simplify [1] abaaabab=baa.

Reduce RHS:

Referenced by [4].

Overlap of [3] abaaabab=c with [2] baa=c:

Critical pair: acabab=c.

Defines rule #3.

Referenced by [5], [6], [8].

Overlap of [2] baa=c with [4] acabab=c:

Critical pair: bac=ccabab.

Flip LHS and RHS.

Defines rule #2.

Referenced by [7], [10].

Overlap of [4] acabab=c with [2] baa=c:

Critical pair: acabac=caa.

Defines rule #4.

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

Overlap of [5] ccabab=bac with [2] baa=c:

Critical pair: ccabac=bacaa.

Flip LHS and RHS.

Defines rule #5.

Referenced by [10], [11].

Overlap of [6] acabac=caa with [4] acabab=c:

Critical pair: acabc=caaabab.

Flip LHS and RHS.

Defines rule #7.

Overlap of [6] acabac=caa with [6] acabac=caa:

Critical pair: acabcaa=caaabac.

Flip LHS and RHS.

Defines rule #8.

Overlap of [5] ccabab=bac with [7] bacaa=ccabac:

Critical pair: ccabaccabac=bacacaa.

Defines rule #9.

Overlap of [6] acabac=caa with [7] bacaa=ccabac:

Critical pair: acaccabac=caaaa.

Flip LHS and RHS.

Defines rule #6.