Certificate for #5535 ⟨a, b | aaabaa=aaaba⟩

Completion settings:

• Auxiliary generators:
  1. c = aaaba
• Reduction order:
  • Left-to-right shortlex with a < c < b

Axiom: aaabaa=aaaba.

Referenced by [3].

Axiom: aaaba=c.

Defines rule #4.

Referenced by [3], [4], [5], [6], [7].

Simplify [1] aaabaa=aaaba.

Reduce RHS:

Referenced by [4].

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

Critical pair: ca=c.

Defines rule #1.

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

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

Critical pair: aaabc=caaba.

Reduce RHS:

Referenced by [8].

Overlap of [4] ca=c with [2] aaaba=c:

Critical pair: cc=caaba.

Reduce RHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [7], [8].

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

Critical pair: cbc=ccaaba.

Reduce RHS:

Defines rule #3.

Simplify [5] aaabc=cba.

Reduce RHS:

Defines rule #5.