Certificate for #279 ⟨a, b, c | aaa=b, cbc=1⟩

Completion settings:

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

Axiom: aaa=b.

Defines rule #3.

Referenced by [4].

Axiom: cbc=1.

Referenced by [3], [5].

Overlap of [2] cbc=1 with [2] cbc=1:

Critical pair: cb=bc.

Flip LHS and RHS.

Defines rule #2.

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

Overlap of [1] aaa=b with [1] aaa=b:

Critical pair: ab=ba.

Flip LHS and RHS.

Defines rule #1.

Referenced by [6].

Overlap of [2] cbc=1 with [3] bc=cb:

Critical pair: ccb=1.

Defines rule #5.

Referenced by [6], [8].

Overlap of [5] ccb=1 with [4] ba=ab:

Critical pair: ccab=a.

Referenced by [7].

Overlap of [6] ccab=a with [3] bc=cb:

Critical pair: ccacb=ac.

Referenced by [8].

Overlap of [7] ccacb=ac with [3] bc=cb:

Critical pair: ccaccb=acc.

Reduce LHS:

Defines rule #4.