Certificate for #2481 ⟨a, b | aabaab=aaba⟩

Completion settings:

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

Axiom: aabaab=aaba.

Referenced by [3].

Axiom: aaba=c.

Defines rule #6.

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

Simplify [1] aabaab=aaba.

Reduce RHS:

Referenced by [4].

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

Critical pair: cab=c.

Defines rule #4.

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

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

Critical pair: aabc=caba.

Reduce RHS:

Defines rule #5.

Referenced by [6], [7], [8].

Overlap of [2] aaba=c with [5] aabc=ca:

Critical pair: aabca=cabc.

Reduce LHS:

Reduce RHS:

Defines rule #3.

Referenced by [7], [8].

Overlap of [5] aabc=ca with [4] cab=c:

Critical pair: aabc=caab.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #1.

Overlap of [5] aabc=ca with [6] caa=cc:

Critical pair: aabcc=caaa.

Reduce LHS:

Reduce RHS:

Defines rule #2.