Certificate for #12635 ⟨a, b | babb=ab, bbbb=b⟩

Completion settings:

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

Axiom: babb=ab.

Referenced by [4].

Axiom: bbbb=b.

Defines rule #1.

Referenced by [8].

Axiom: ab=c.

Defines rule #4.

Referenced by [4], [5], [6].

Simplify [1] babb=ab.

Reduce RHS:

Referenced by [5].

Overlap of [4] babb=c with [3] ab=c:

Critical pair: bcb=c.

Referenced by [6], [7], [8], [9].

Overlap of [3] ab=c with [5] bcb=c:

Critical pair: ac=ccb.

Referenced by [10].

Overlap of [5] bcb=c with [5] bcb=c:

Critical pair: bcc=ccb.

Flip LHS and RHS.

Referenced by [10].

Overlap of [2] bbbb=b with [5] bcb=c:

Critical pair: bbbc=bcb.

Reduce RHS:

Defines rule #2.

Referenced by [9].

Overlap of [8] bbbc=c with [5] bcb=c:

Critical pair: bbc=cb.

Flip LHS and RHS.

Defines rule #3.

Simplify [6] ac=ccb.

Reduce RHS:

Defines rule #5.