Certificate for #289 ⟨a, b, c | aab=a, bcb=1⟩

Completion settings:

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

Axiom: aab=a.

Defines rule #1.

Referenced by [4], [5].

Axiom: bcb=1.

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

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

Critical pair: bc=cb.

Defines rule #4.

Referenced by [5], [6].

Overlap of [1] aab=a with [2] bcb=1:

Critical pair: aa=acb.

Flip LHS and RHS.

Referenced by [5].

Overlap of [1] aab=a with [3] bc=cb:

Critical pair: aacb=ac.

Reduce LHS:

Flip LHS and RHS.

Defines rule #3.

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

Critical pair: cbb=1.

Defines rule #2.