Certificate for #2717 ⟨a, b, c | abc=a, bbcb=1⟩

Completion settings:

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

Axiom: abc=a.

Referenced by [7], [8], [9].

Axiom: bbcb=1.

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

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

Critical pair: bbc=bcb.

Referenced by [4], [5], [8], [9].

Overlap of [2] bbcb=1 with [3] bbc=bcb:

Critical pair: bcbb=1.

Referenced by [5], [6].

Overlap of [2] bbcb=1 with [3] bbc=bcb:

Critical pair: bbcbcb=bc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.

Referenced by [6].

Simplify [4] bcbb=1.

Reduce LHS:

Defines rule #2.

Referenced by [7].

Overlap of [1] abc=a with [6] cbbb=1:

Critical pair: ab=abbb.

Flip LHS and RHS.

Referenced by [8], [9].

Overlap of [7] abbb=ab with [3] bbc=bcb:

Critical pair: abbcb=abc.

Reduce LHS:

Reduce RHS:

Defines rule #1.

Referenced by [9].

Overlap of [7] abbb=ab with [3] bbc=bcb:

Critical pair: abbbcb=abbc.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #3.