Certificate for #4717 ⟨a, b | aabbbaab=aba⟩

Completion settings:

• Reduction order:
  • Left-to-right recursive path with deg(d) = 0; deg(a) = deg(c) = 1, a < c; deg(b) = 2
• Auxiliary generators:
  1. ab=c
  2. acbb=d

Axiom: aabbbaab=aba.

Referenced by [4].

Axiom: ab=c.

Defines rule #2.

Referenced by [4], [5], [6].

Axiom: acbb=d.

Defines rule #6.

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

Simplify [1] aabbbaab=aba.

Reduce RHS:

Referenced by [5].

Overlap of [4] aabbbaab=ca with [2] ab=c:

Critical pair: acbbaab=ca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.

Referenced by [6], [7].

Overlap of [5] ca=dac with [2] ab=c:

Critical pair: cc=dacb.

Flip LHS and RHS.

Defines rule #4.

Referenced by [8].

Overlap of [5] ca=dac with [3] acbb=d:

Critical pair: cd=daccbb.

Flip LHS and RHS.

Referenced by [9].

Overlap of [6] dacb=cc with [3] acbb=d:

Critical pair: dd=ccb.

Flip LHS and RHS.

Defines rule #5.

Referenced by [9].

Simplify [7] daccbb=cd.

Reduce LHS:

Defines rule #3.