Certificate for #4168 ⟨a, b | aabbaabba=ab⟩

Completion settings:

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

Axiom: aabbaabba=ab.

Referenced by [3].

Axiom: abb=c.

Referenced by [3], [4].

Overlap of [1] aabbaabba=ab with [2] abb=c:

Critical pair: acaabba=ab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #3.

Referenced by [4], [5].

Overlap of [2] abb=c with [3] ab=acaca:

Critical pair: acacab=c.

Reduce LHS:

Defines rule #2.

Referenced by [5], [6].

Overlap of [4] acacacaca=c with [3] ab=acaca:

Critical pair: acacacacacaca=cb.

Reduce LHS:

Flip LHS and RHS.

Referenced by [7].

Overlap of [4] acacacaca=c with [4] acacacaca=c:

Critical pair: acc=cca.

Flip LHS and RHS.

Defines rule #1.

Referenced by [7].

Simplify [5] cb=ccaca.

Reduce RHS:

Defines rule #4.