Certificate for #5487 ⟨a, b | aaaaba=baaba⟩

Completion settings:

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

Axiom: aaaaba=baaba.

Flip LHS and RHS.

Referenced by [2], [3].

Axiom: baaba=c.

Reduce LHS:

Defines rule #5.

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

Simplify [1] baaba=aaaaba.

Reduce RHS:

Defines rule #10.

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

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

Critical pair: baac=caba.

Referenced by [8].

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

Critical pair: baabc=caaaba.

Defines rule #11.

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

Critical pair: aaaac=caba.

Flip LHS and RHS.

Defines rule #4.

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

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

Critical pair: aaaabc=caaaba.

Defines rule #7.

Simplify [4] baac=caba.

Reduce RHS:

Defines rule #8.

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

Overlap of [3] baaba=c with [8] baac=aaaac:

Critical pair: baaaaaac=cac.

Defines rule #9.

Referenced by [13].

Overlap of [2] aaaaba=c with [8] baac=aaaac:

Critical pair: aaaaaaaac=cac.

Defines rule #2.

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

Critical pair: cabc=aaaacaaaba.

Defines rule #6.

Overlap of [6] caba=aaaac with [8] baac=aaaac:

Critical pair: caaaaac=aaaacac.

Flip LHS and RHS.

Defines rule #1.

Overlap of [6] caba=aaaac with [9] baaaaaac=cac:

Critical pair: cacac=aaaacaaaaac.

Flip LHS and RHS.

Defines rule #3.