Certificate for #4337 ⟨a, b | abbaabbba=ab⟩

Completion settings:

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

Axiom: abbaabbba=ab.

Referenced by [3].

Axiom: abbb=c.

Referenced by [3], [4], [5], [6], [12].

Overlap of [1] abbaabbba=ab with [2] abbb=c:

Critical pair: abbaca=ab.

Referenced by [4], [5], [7], [8], [10].

Overlap of [3] abbaca=ab with [2] abbb=c:

Critical pair: abbacc=abbbb.

Reduce RHS:

Referenced by [11].

Overlap of [3] abbaca=ab with [3] abbaca=ab:

Critical pair: abbacab=abbbaca.

Reduce LHS:

Reduce RHS:

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

Overlap of [2] abbb=c with [5] abb=caca:

Critical pair: cacab=c.

Referenced by [9].

Overlap of [3] abbaca=ab with [5] abb=caca:

Critical pair: cacaaca=ab.

Flip LHS and RHS.

Defines rule #5.

Referenced by [8], [9], [10], [11], [12], [13].

Overlap of [3] abbaca=ab with [5] abb=caca:

Critical pair: abbaccaca=abbb.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [12].

Simplify [6] cacab=c.

Reduce LHS:

Referenced by [10], [13], [14], [15].

Overlap of [3] abbaca=ab with [9] caccacaaca=c:

Critical pair: abbac=abccacaaca.

Reduce LHS:

Reduce RHS:

Referenced by [11], [12].

Simplify [4] abbacc=cb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #6.

Referenced by [13].

Overlap of [2] abbb=c with [7] ab=cacaaca:

Critical pair: cacaacabb=c.

Reduce LHS:

Defines rule #4.

Referenced by [13], [14], [15].

Overlap of [9] caccacaaca=c with [7] ab=cacaaca:

Critical pair: caccacaaccacaaca=cb.

Reduce LHS:

Reduce RHS:

Defines rule #2.

Referenced by [14], [15].

Overlap of [9] caccacaaca=c with [12] cacaaccaca=c:

Critical pair: caccacaac=ccaaccaca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #3.

Overlap of [9] caccacaaca=c with [13] caccaca=cacaacc:

Critical pair: caccacaacacaacc=cccaca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.