Certificate for #2612 ⟨a, b, c | aba=b, babc=1⟩

Completion settings:

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

Axiom: aba=b.

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

Axiom: babc=1.

Referenced by [4], [7].

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

Critical pair: abb=bba.

Flip LHS and RHS.

Referenced by [6].

Overlap of [1] aba=b with [2] babc=1:

Critical pair: a=bbc.

Defines rule #4.

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

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

Critical pair: bbcba=b.

Reduce LHS:

Defines rule #3.

Simplify [3] bba=abb.

Reduce LHS:

Reduce RHS:

Defines rule #1.

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

Critical pair: bbbcbc=1.

Defines rule #2.