Certificate for #1820 ⟨a, b, c | aba=ab, cbb=1⟩

Completion settings:

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

Axiom: aba=ab.

Referenced by [4].

Axiom: cbb=1.

Defines rule #2.

Referenced by [5].

Axiom: ba=d.

Referenced by [4], [5], [7], [8].

Overlap of [1] aba=ab with [3] ba=d:

Critical pair: ad=ab.

Flip LHS and RHS.

Referenced by [6].

Overlap of [2] cbb=1 with [3] ba=d:

Critical pair: cbd=a.

Flip LHS and RHS.

Defines rule #5.

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

Simplify [4] ab=ad.

Reduce LHS:

Reduce RHS:

Referenced by [7], [9].

Overlap of [6] cbdb=cbdd with [3] ba=d:

Critical pair: cbdd=cbdda.

Reduce RHS:

Flip LHS and RHS.

Referenced by [10].

Overlap of [3] ba=d with [5] a=cbd:

Critical pair: bcbd=d.

Defines rule #3.

Referenced by [9], [10].

Overlap of [8] bcbd=d with [6] cbdb=cbdd:

Critical pair: bcbdd=db.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.

Overlap of [8] bcbd=d with [7] cbddcbd=cbdd:

Critical pair: bcbdd=ddcbd.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.