Certificate for #2399 ⟨a, b | aaaaba=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: aaaaba=baba.

Flip LHS and RHS.

Referenced by [2], [3].

Axiom: baba=c.

Reduce LHS:

Defines rule #5.

Referenced by [3], [5], [6], [7], [8], [10].

Simplify [1] baba=aaaaba.

Reduce RHS:

Defines rule #10.

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

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

Critical pair: bac=cba.

Referenced by [8], [9], [11], [13].

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

Critical pair: babc=caaaba.

Defines rule #11.

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

Critical pair: aaaac=cba.

Flip LHS and RHS.

Defines rule #4.

Referenced by [8], [9], [10], [11], [12], [13].

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

Critical pair: aaaabc=caaaba.

Defines rule #7.

Overlap of [2] aaaaba=c with [4] bac=cba:

Critical pair: aaaacba=cc.

Reduce LHS:

Defines rule #2.

Referenced by [9].

Overlap of [4] bac=cba with [6] cba=aaaac:

Critical pair: baaaaac=cbaba.

Reduce RHS:

Defines rule #9.

Referenced by [12].

Overlap of [6] cba=aaaac with [2] aaaaba=c:

Critical pair: cbc=aaaacaaaba.

Defines rule #6.

Overlap of [6] cba=aaaac with [4] bac=cba:

Critical pair: ccba=aaaacc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.

Overlap of [6] cba=aaaac with [9] baaaaac=cc:

Critical pair: ccc=aaaacaaaac.

Flip LHS and RHS.

Defines rule #3.

Simplify [4] bac=cba.

Reduce RHS:

Defines rule #8.