Certificate for #6970 ⟨a, b, c | ab=1, baaca=c⟩

Completion settings:

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

Axiom: ab=1.

Defines rule #1.

Referenced by [3], [4].

Axiom: baaca=c.

Referenced by [3], [4], [5], [6], [7].

Overlap of [1] ab=1 with [2] baaca=c:

Critical pair: ac=aaca.

Flip LHS and RHS.

Defines rule #3.

Referenced by [5], [7].

Overlap of [2] baaca=c with [1] ab=1:

Critical pair: baac=cb.

Flip LHS and RHS.

Defines rule #4.

Overlap of [2] baaca=c with [3] aaca=ac:

Critical pair: baacac=caca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #6.

Referenced by [6].

Overlap of [2] baaca=c with [5] caca=cc:

Critical pair: baacc=cca.

Flip LHS and RHS.

Defines rule #5.

Overlap of [2] baaca=c with [3] aaca=ac:

Critical pair: bac=c.

Defines rule #2.