Certificate for #7225 ⟨a, b, c | aa=1, bacb=bc⟩

Completion settings:

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

Axiom: aa=1.

Defines rule #1.

Axiom: bacb=bc.

Referenced by [4].

Axiom: cb=d.

Defines rule #4.

Referenced by [4], [5], [6], [7].

Overlap of [2] bacb=bc with [3] cb=d:

Critical pair: bad=bc.

Flip LHS and RHS.

Defines rule #5.

Referenced by [5], [6].

Overlap of [3] cb=d with [4] bc=bad:

Critical pair: cbad=dc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #6.

Referenced by [7].

Overlap of [4] bc=bad with [3] cb=d:

Critical pair: bd=badb.

Flip LHS and RHS.

Defines rule #2.

Overlap of [5] dc=dad with [3] cb=d:

Critical pair: dd=dadb.

Flip LHS and RHS.

Defines rule #3.