Certificate for #1863 ⟨a, b, c | aba=bc, aca=1⟩

Completion settings:

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

Axiom: aba=bc.

Flip LHS and RHS.

Defines rule #3.

Referenced by [5].

Axiom: aca=1.

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

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

Critical pair: ac=ca.

Defines rule #1.

Referenced by [4], [6].

Overlap of [2] aca=1 with [3] ac=ca:

Critical pair: caa=1.

Defines rule #2.

Referenced by [5].

Overlap of [1] bc=aba with [4] caa=1:

Critical pair: b=abaaa.

Flip LHS and RHS.

Referenced by [6].

Overlap of [2] aca=1 with [5] abaaa=b:

Critical pair: acb=baaa.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.