Certificate for #4414 ⟨a, b, c | aba=1, acbc=c⟩

Completion settings:

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

Axiom: aba=1.

Referenced by [5], [6], [7], [9].

Axiom: acbc=c.

Referenced by [4].

Axiom: bc=d.

Defines rule #5.

Referenced by [4], [6], [7], [8].

Overlap of [2] acbc=c with [3] bc=d:

Critical pair: acd=c.

Defines rule #4.

Referenced by [6].

Overlap of [1] aba=1 with [1] aba=1:

Critical pair: ab=ba.

Flip LHS and RHS.

Defines rule #6.

Referenced by [9].

Overlap of [1] aba=1 with [4] acd=c:

Critical pair: abc=cd.

Reduce LHS:

Defines rule #2.

Referenced by [7].

Overlap of [1] aba=1 with [6] ad=cd:

Critical pair: abcd=d.

Reduce LHS:

Defines rule #1.

Referenced by [8].

Overlap of [3] bc=d with [7] cdd=d:

Critical pair: bd=ddd.

Defines rule #3.

Overlap of [1] aba=1 with [5] ba=ab:

Critical pair: aab=1.

Defines rule #7.