Certificate for #4237 ⟨a, b | abaaaabba=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: abaaaabba=ab.

Referenced by [3].

Axiom: abb=c.

Defines rule #10.

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

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

Critical pair: abaaaca=ab.

Defines rule #8.

Referenced by [4], [5], [6], [8], [11].

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

Critical pair: abaaacc=abbb.

Reduce RHS:

Flip LHS and RHS.

Defines rule #9.

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

Critical pair: abaaacab=abbaaaca.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #4.

Referenced by [6], [7], [9], [10].

Overlap of [3] abaaaca=ab with [5] caaaca=c:

Critical pair: abaaac=abaaca.

Flip LHS and RHS.

Defines rule #7.

Overlap of [5] caaaca=c with [5] caaaca=c:

Critical pair: caaac=caaca.

Flip LHS and RHS.

Defines rule #3.

Referenced by [8], [9], [10].

Overlap of [3] abaaaca=ab with [7] caaca=caaac:

Critical pair: abaaacaaac=abaca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #6.

Overlap of [5] caaaca=c with [7] caaca=caaac:

Critical pair: caaacaaac=caca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [11].

Overlap of [7] caaca=caaac with [7] caaca=caaac:

Critical pair: caacaaac=caaacaca.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #1.

Overlap of [3] abaaaca=ab with [9] caca=caac:

Critical pair: abaaacaac=abca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #5.