Certificate for #7400 ⟨a, b, c | ab=1, acaa=ac⟩

Completion settings:

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

Axiom: ab=1.

Defines rule #1.

Referenced by [6], [9].

Axiom: acaa=ac.

Referenced by [4].

Axiom: ac=d.

Defines rule #5.

Referenced by [4], [5], [7], [10].

Simplify [2] acaa=ac.

Reduce RHS:

Referenced by [5].

Overlap of [4] acaa=d with [3] ac=d:

Critical pair: daa=d.

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

Overlap of [5] daa=d with [1] ab=1:

Critical pair: da=db.

Defines rule #2.

Referenced by [7], [8], [9], [10].

Overlap of [5] daa=d with [3] ac=d:

Critical pair: dad=dc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #6.

Overlap of [5] daa=d with [6] da=db:

Critical pair: dba=d.

Defines rule #4.

Overlap of [6] da=db with [1] ab=1:

Critical pair: d=dbb.

Flip LHS and RHS.

Defines rule #3.

Overlap of [6] da=db with [3] ac=d:

Critical pair: dd=dbc.

Flip LHS and RHS.

Defines rule #7.