Certificate for #4332 ⟨a, b, c | aab=1, cbca=c⟩

Completion settings:

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

Axiom: aab=1.

Defines rule #3.

Referenced by [5].

Axiom: cbca=c.

Referenced by [4].

Axiom: cb=d.

Referenced by [4], [6], [7], [10].

Overlap of [2] cbca=c with [3] cb=d:

Critical pair: dca=c.

Referenced by [5], [6], [8], [9].

Overlap of [4] dca=c with [1] aab=1:

Critical pair: dc=cab.

Flip LHS and RHS.

Referenced by [6].

Overlap of [4] dca=c with [5] cab=dc:

Critical pair: ddc=cb.

Reduce RHS:

Referenced by [7], [8], [11].

Overlap of [6] ddc=d with [3] cb=d:

Critical pair: ddd=db.

Flip LHS and RHS.

Defines rule #2.

Overlap of [6] ddc=d with [4] dca=c:

Critical pair: dc=da.

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

Overlap of [4] dca=c with [8] dc=da:

Critical pair: daa=c.

Flip LHS and RHS.

Defines rule #5.

Overlap of [8] dc=da with [3] cb=d:

Critical pair: dd=dab.

Flip LHS and RHS.

Defines rule #4.

Overlap of [6] ddc=d with [8] dc=da:

Critical pair: dda=d.

Defines rule #1.