Certificate for #7424 ⟨a, b, c | ab=1, acba=cc⟩

Completion settings:

• Reduction order:
  • Left-to-right shortlex with c < a < b

Axiom: ab=1.

Defines rule #1.

Referenced by [3].

Axiom: acba=cc.

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

Overlap of [2] acba=cc with [1] ab=1:

Critical pair: acb=ccb.

Defines rule #2.

Referenced by [4], [5].

Overlap of [2] acba=cc with [2] acba=cc:

Critical pair: acbcc=cccba.

Reduce LHS:

Referenced by [6].

Overlap of [2] acba=cc with [3] acb=ccb:

Critical pair: ccba=cc.

Defines rule #3.

Referenced by [6].

Simplify [4] ccbcc=cccba.

Reduce RHS:

Defines rule #4.