Certificate for #1568 ⟨a, b, c | aaa=bb, aac=1⟩

Completion settings:

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

Axiom: aaa=bb.

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

Axiom: aac=1.

Referenced by [4], [7].

Overlap of [1] aaa=bb with [1] aaa=bb:

Critical pair: abb=bba.

Flip LHS and RHS.

Referenced by [5].

Overlap of [1] aaa=bb with [2] aac=1:

Critical pair: a=bbc.

Defines rule #4.

Referenced by [5], [6], [7].

Simplify [3] bba=abb.

Reduce LHS:

Reduce RHS:

Defines rule #1.

Overlap of [1] aaa=bb with [4] a=bbc:

Critical pair: bbcaa=bb.

Reduce LHS:

Defines rule #3.

Overlap of [2] aac=1 with [4] a=bbc:

Critical pair: bbcac=1.

Reduce LHS:

Defines rule #2.