Certificate for #7595 ⟨a, b, c | ab=1, cacc=ca⟩

Completion settings:

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

Axiom: ab=1.

Defines rule #3.

Referenced by [6].

Axiom: cacc=ca.

Referenced by [4].

Axiom: ca=d.

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

Simplify [2] cacc=ca.

Reduce RHS:

Referenced by [5].

Overlap of [4] cacc=d with [3] ca=d:

Critical pair: dcc=d.

Referenced by [8].

Overlap of [3] ca=d with [1] ab=1:

Critical pair: c=db.

Defines rule #2.

Referenced by [7], [8].

Overlap of [3] ca=d with [6] c=db:

Critical pair: dba=d.

Defines rule #5.

Referenced by [9].

Simplify [5] dcc=d.

Reduce LHS:

Defines rule #1.

Referenced by [9].

Overlap of [8] ddbdb=d with [7] dba=d:

Critical pair: ddbd=da.

Flip LHS and RHS.

Defines rule #4.