Certificate for #7184 ⟨a, b, c | aa=1, abcb=bc⟩

Completion settings:

• Auxiliary generators:
  1. d = bc
• 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.

Referenced by [6].

Axiom: abcb=bc.

Referenced by [4].

Axiom: bc=d.

Defines rule #3.

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

Simplify [2] abcb=bc.

Reduce RHS:

Referenced by [5].

Overlap of [4] abcb=d with [3] bc=d:

Critical pair: adb=d.

Referenced by [6], [7].

Overlap of [1] aa=1 with [5] adb=d:

Critical pair: ad=db.

Flip LHS and RHS.

Defines rule #2.

Overlap of [5] adb=d with [3] bc=d:

Critical pair: add=dc.

Flip LHS and RHS.

Defines rule #4.