Certificate for #3243 ⟨a, b, c | bb=aa, aaac=1⟩

Completion settings:

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

Axiom: bb=aa.

Flip LHS and RHS.

Referenced by [2], [3], [5].

Axiom: aaac=1.

Reduce LHS:

Referenced by [4].

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

Critical pair: abb=bba.

Flip LHS and RHS.

Referenced by [4], [6].

Overlap of [2] bbac=1 with [3] bba=abb:

Critical pair: abbc=1.

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

Overlap of [1] aa=bb with [4] abbc=1:

Critical pair: a=bbbbc.

Defines rule #4.

Referenced by [6], [7].

Overlap of [3] bba=abb with [4] abbc=1:

Critical pair: bb=abbbbc.

Reduce RHS:

Flip LHS and RHS.

Defines rule #3.

Referenced by [8].

Overlap of [4] abbc=1 with [5] a=bbbbc:

Critical pair: bbbbcbbc=1.

Defines rule #2.

Overlap of [6] bbbbcbbbbc=bb with [6] bbbbcbbbbc=bb:

Critical pair: bbbbcbb=bbbbbbc.

Flip LHS and RHS.

Defines rule #1.