Certificate for #5843 ⟨a, b | abaaba=aaaba⟩

Completion settings:

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

Axiom: abaaba=aaaba.

Referenced by [3].

Axiom: aaaba=c.

Defines rule #8.

Referenced by [3], [4], [7], [8].

Simplify [1] abaaba=aaaba.

Reduce RHS:

Defines rule #9.

Referenced by [5], [6], [7], [8], [9], [10].

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

Critical pair: aaabc=caaba.

Defines rule #6.

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

Critical pair: abac=caba.

Defines rule #3.

Referenced by [9].

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

Critical pair: abaabc=cbaaba.

Referenced by [7], [9], [11].

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

Critical pair: abaabc=caaba.

Reduce LHS:

Defines rule #5.

Referenced by [9], [10], [11].

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

Critical pair: aac=caba.

Defines rule #2.

Overlap of [3] abaaba=c with [5] abac=caba:

Critical pair: abaabcaba=cbac.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.

Overlap of [7] cbaaba=caaba with [3] abaaba=c:

Critical pair: cbaabc=caababaaba.

Reduce RHS:

Defines rule #4.

Simplify [6] abaabc=cbaaba.

Reduce RHS:

Defines rule #7.