Certificate for #502 ⟨a, b, c | bb=ac, cba=1⟩

Completion settings:

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

Axiom: bb=ac.

Defines rule #4.

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

Axiom: cba=1.

Referenced by [4], [5], [7].

Overlap of [1] bb=ac with [1] bb=ac:

Critical pair: bac=acb.

Flip LHS and RHS.

Referenced by [4], [5].

Overlap of [2] cba=1 with [3] acb=bac:

Critical pair: cbbac=cb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #3.

Referenced by [7].

Overlap of [3] acb=bac with [2] cba=1:

Critical pair: a=baca.

Flip LHS and RHS.

Referenced by [6].

Overlap of [1] bb=ac with [5] baca=a:

Critical pair: ba=acaca.

Defines rule #2.

Overlap of [2] cba=1 with [4] cb=cacac:

Critical pair: cacaca=1.

Defines rule #1.