Certificate for #4222 ⟨a, b | aabbbbbba=ab⟩

Completion settings:

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

Axiom: aabbbbbba=ab.

Referenced by [3].

Axiom: abbbbbb=c.

Referenced by [3], [4].

Overlap of [1] aabbbbbba=ab with [2] abbbbbb=c:

Critical pair: aca=ab.

Flip LHS and RHS.

Defines rule #3.

Referenced by [4], [5].

Overlap of [2] abbbbbb=c with [3] ab=aca:

Critical pair: acabbbbb=c.

Reduce LHS:

Defines rule #2.

Referenced by [5], [6].

Overlap of [4] acacacacacaca=c with [3] ab=aca:

Critical pair: acacacacacacaca=cb.

Reduce LHS:

Flip LHS and RHS.

Referenced by [7].

Overlap of [4] acacacacacaca=c with [4] acacacacacaca=c:

Critical pair: acc=cca.

Flip LHS and RHS.

Defines rule #1.

Referenced by [7].

Simplify [5] cb=cca.

Reduce RHS:

Defines rule #4.