Certificate for #4925 ⟨a, b | aaaaaba=baba⟩

Completion settings:

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

Axiom: aaaaaba=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=aaaaaba.

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] aaaaaba=c:

Critical pair: babc=caaaaba.

Defines rule #11.

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

Critical pair: aaaaac=cba.

Flip LHS and RHS.

Defines rule #4.

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

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

Critical pair: aaaaabc=caaaaba.

Defines rule #7.

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

Critical pair: aaaaacba=cc.

Reduce LHS:

Defines rule #2.

Referenced by [9].

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

Critical pair: baaaaaac=cbaba.

Reduce RHS:

Defines rule #9.

Referenced by [12].

Overlap of [6] cba=aaaaac with [2] aaaaaba=c:

Critical pair: cbc=aaaaacaaaaba.

Defines rule #6.

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

Critical pair: ccba=aaaaacc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.

Overlap of [6] cba=aaaaac with [9] baaaaaac=cc:

Critical pair: ccc=aaaaacaaaaac.

Flip LHS and RHS.

Defines rule #3.

Simplify [4] bac=cba.

Reduce RHS:

Defines rule #8.