Certificate for #4949 ⟨a, b | aaaabaa=aaba⟩

Completion settings:

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

Axiom: aaaabaa=aaba.

Referenced by [3].

Axiom: aaba=c.

Defines rule #8.

Referenced by [3], [4], [6], [7], [9], [10].

Simplify [1] aaaabaa=aaba.

Reduce RHS:

Referenced by [4].

Overlap of [3] aaaabaa=c with [2] aaba=c:

Critical pair: aaca=c.

Defines rule #6.

Referenced by [5], [7], [8].

Overlap of [4] aaca=c with [4] aaca=c:

Critical pair: aacc=caca.

Defines rule #5.

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

Critical pair: aabc=caba.

Referenced by [7], [11].

Overlap of [2] aaba=c with [4] aaca=c:

Critical pair: aabc=caca.

Reduce LHS:

Defines rule #4.

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

Overlap of [4] aaca=c with [7] caba=caca:

Critical pair: aacaca=cba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [10].

Overlap of [7] caba=caca with [2] aaba=c:

Critical pair: cabc=cacaaba.

Reduce RHS:

Defines rule #3.

Overlap of [8] cba=cca with [2] aaba=c:

Critical pair: cbc=ccaaba.

Reduce RHS:

Defines rule #1.

Simplify [6] aabc=caba.

Reduce RHS:

Defines rule #7.