Certificate for #1175 ⟨a, b | aaaba=baba⟩

Completion settings:

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

Axiom: aaaba=baba.

Flip LHS and RHS.

Referenced by [2], [3].

Axiom: baba=c.

Reduce LHS:

Defines rule #5.

Referenced by [3], [5], [6], [7], [10], [11].

Simplify [1] baba=aaaba.

Reduce RHS:

Defines rule #10.

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

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

Critical pair: bac=cba.

Referenced by [8].

Overlap of [3] baba=c with [2] aaaba=c:

Critical pair: babc=caaba.

Defines rule #11.

Overlap of [2] aaaba=c with [3] baba=c:

Critical pair: aaac=cba.

Flip LHS and RHS.

Defines rule #4.

Referenced by [8], [11], [12], [13].

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

Critical pair: aaabc=caaba.

Defines rule #7.

Simplify [4] bac=cba.

Reduce RHS:

Defines rule #8.

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

Overlap of [3] baba=c with [8] bac=aaac:

Critical pair: baaaac=cc.

Defines rule #9.

Referenced by [13].

Overlap of [2] aaaba=c with [8] bac=aaac:

Critical pair: aaaaaac=cc.

Defines rule #2.

Overlap of [6] cba=aaac with [2] aaaba=c:

Critical pair: cbc=aaacaaba.

Defines rule #6.

Overlap of [6] cba=aaac with [8] bac=aaac:

Critical pair: caaac=aaacc.

Flip LHS and RHS.

Defines rule #1.

Overlap of [6] cba=aaac with [9] baaaac=cc:

Critical pair: ccc=aaacaaac.

Flip LHS and RHS.

Defines rule #3.