Certificate for #2761 ⟨a, b, c | abc=b, aaca=1⟩

Completion settings:

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

Axiom: abc=b.

Referenced by [4], [8].

Axiom: aaca=1.

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

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

Critical pair: aac=aca.

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

Overlap of [2] aaca=1 with [1] abc=b:

Critical pair: aacb=bc.

Reduce LHS:

Flip LHS and RHS.

Referenced by [9].

Overlap of [2] aaca=1 with [3] aac=aca:

Critical pair: acaa=1.

Referenced by [6], [7].

Overlap of [2] aaca=1 with [3] aac=aca:

Critical pair: aacaca=ac.

Reduce LHS:

Flip LHS and RHS.

Defines rule #3.

Referenced by [7], [9].

Simplify [5] acaa=1.

Reduce LHS:

Defines rule #2.

Referenced by [8].

Overlap of [1] abc=b with [7] caaa=1:

Critical pair: ab=baaa.

Flip LHS and RHS.

Defines rule #1.

Simplify [4] bc=acab.

Reduce RHS:

Defines rule #4.