Certificate for #5127 ⟨a, b | aabaaab=baba⟩

Completion settings:

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

Axiom: aabaaab=baba.

Flip LHS and RHS.

Referenced by [3].

Axiom: aabaaa=c.

Defines rule #1.

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

Simplify [1] baba=aabaaab.

Reduce RHS:

Defines rule #4.

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

Overlap of [3] baba=cb with [3] baba=cb:

Critical pair: bacb=cbba.

Flip LHS and RHS.

Defines rule #7.

Overlap of [3] baba=cb with [2] aabaaa=c:

Critical pair: babc=cbabaaa.

Reduce RHS:

Flip LHS and RHS.

Defines rule #6.

Referenced by [8].

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

Critical pair: aabac=cbaaa.

Flip LHS and RHS.

Defines rule #2.

Referenced by [8].

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

Critical pair: aabaac=cabaaa.

Flip LHS and RHS.

Defines rule #3.

Overlap of [5] ccbaa=babc with [6] cbaaa=aabac:

Critical pair: caabac=babca.

Flip LHS and RHS.

Defines rule #5.

Referenced by [9].

Overlap of [3] baba=cb with [8] babca=caabac:

Critical pair: bacaabac=cbbca.

Flip LHS and RHS.

Defines rule #8.