Certificate for #1853 ⟨a, b, c | aba=bb, bac=1⟩

Completion settings:

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

Axiom: aba=bb.

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

Axiom: bac=1.

Referenced by [4], [7].

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

Critical pair: abbb=bbba.

Flip LHS and RHS.

Referenced by [6].

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

Critical pair: a=bbc.

Defines rule #4.

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

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

Critical pair: bbcba=bb.

Reduce LHS:

Defines rule #3.

Simplify [3] bbba=abbb.

Reduce LHS:

Reduce RHS:

Defines rule #2.

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

Critical pair: bbbcc=1.

Defines rule #1.