Certificate for #2596 ⟨a, b, c | aba=b, aaca=1⟩

Completion settings:

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

Axiom: aba=b.

Referenced by [4], [5], [7], [8].

Axiom: aaca=1.

Referenced by [3], [4], [5], [6], [9].

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

Critical pair: aac=aca.

Flip LHS and RHS.

Referenced by [4], [6], [7], [9].

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

Critical pair: ab=baca.

Reduce RHS:

Defines rule #3.

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

Critical pair: aacb=ba.

Referenced by [7].

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

Critical pair: aacaac=ca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.

Referenced by [8].

Overlap of [3] aca=aac with [1] aba=b:

Critical pair: acb=aacba.

Reduce RHS:

Referenced by [8].

Overlap of [6] ca=ac with [1] aba=b:

Critical pair: cb=acba.

Reduce RHS:

Defines rule #4.

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

Critical pair: aaac=1.

Defines rule #2.