Certificate for #1355 ⟨a, b, c | ab=1, bbca=c⟩

Completion settings:

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

Axiom: ab=1.

Defines rule #4.

Referenced by [5], [6], [7], [8], [10].

Axiom: bbca=c.

Referenced by [5], [6], [13].

Axiom: ac=d.

Defines rule #7.

Referenced by [5], [9], [11].

Axiom: ad=e.

Defines rule #9.

Referenced by [7], [12].

Overlap of [1] ab=1 with [2] bbca=c:

Critical pair: ac=bca.

Reduce LHS:

Flip LHS and RHS.

Referenced by [7], [8], [13], [14].

Overlap of [2] bbca=c with [1] ab=1:

Critical pair: bbc=cb.

Flip LHS and RHS.

Defines rule #1.

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

Critical pair: ad=ca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #10.

Referenced by [9], [10], [11], [12], [14].

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

Critical pair: bc=db.

Flip LHS and RHS.

Defines rule #3.

Overlap of [3] ac=d with [7] ca=e:

Critical pair: ae=da.

Defines rule #12.

Overlap of [7] ca=e with [1] ab=1:

Critical pair: c=eb.

Flip LHS and RHS.

Defines rule #6.

Overlap of [7] ca=e with [3] ac=d:

Critical pair: cd=ec.

Defines rule #8.

Overlap of [7] ca=e with [4] ad=e:

Critical pair: ce=ed.

Defines rule #11.

Overlap of [2] bbca=c with [5] bca=d:

Critical pair: bd=c.

Defines rule #2.

Overlap of [5] bca=d with [7] ca=e:

Critical pair: be=d.

Defines rule #5.