Certificate for #55 ⟨a, b, c | aaa=1, abc=1⟩

Completion settings:

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

Axiom: aaa=1.

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

Axiom: abc=1.

Referenced by [3].

Overlap of [1] aaa=1 with [2] abc=1:

Critical pair: aa=bc.

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

Overlap of [1] aaa=1 with [3] aa=bc:

Critical pair: bca=1.

Referenced by [6].

Overlap of [1] aaa=1 with [3] aa=bc:

Critical pair: aabc=a.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [6].

Overlap of [3] aa=bc with [3] aa=bc:

Critical pair: abc=bca.

Reduce LHS:

Reduce RHS:

Defines rule #1.