Certificate for #1850 ⟨a, b, c | aba=bb, aca=1⟩

Completion settings:

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

Axiom: aba=bb.

Referenced by [4], [5].

Axiom: aca=1.

Referenced by [3], [4], [5], [7], [9].

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

Critical pair: ac=ca.

Flip LHS and RHS.

Defines rule #4.

Referenced by [4], [9].

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

Critical pair: ab=bbca.

Reduce RHS:

Flip LHS and RHS.

Referenced by [6].

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

Critical pair: acbb=ba.

Flip LHS and RHS.

Defines rule #3.

Referenced by [6].

Simplify [4] bbac=ab.

Reduce LHS:

Referenced by [7].

Overlap of [2] aca=1 with [6] acbbcbbc=ab:

Critical pair: acab=cbbcbbc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [8], [10].

Overlap of [7] cbbcbbc=b with [7] cbbcbbc=b:

Critical pair: cbbb=bbbc.

Defines rule #1.

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

Critical pair: aac=1.

Defines rule #6.

Referenced by [10].

Overlap of [9] aac=1 with [7] cbbcbbc=b:

Critical pair: aab=bbcbbc.

Defines rule #5.