Certificate for #4330 ⟨a, b | abbaaabba=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: abbaaabba=ab.

Referenced by [3].

Axiom: abb=c.

Referenced by [3], [4].

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

Critical pair: caaabba=ab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.

Referenced by [4], [5].

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

Critical pair: caacab=c.

Reduce LHS:

Defines rule #3.

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

Overlap of [4] caaccaaca=c with [3] ab=caaca:

Critical pair: caaccaaccaaca=cb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #5.

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

Critical pair: caaccaac=caccaaca.

Flip LHS and RHS.

Defines rule #2.

Referenced by [7].

Overlap of [4] caaccaaca=c with [6] caccaaca=caaccaac:

Critical pair: caaccaacaaccaac=cccaaca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.