Certificate for #4280 ⟨a, b | abaabbbba=ab⟩

Completion settings:

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

Axiom: abaabbbba=ab.

Referenced by [3].

Axiom: abbbb=c.

Defines rule #10.

Referenced by [3], [4], [7].

Overlap of [1] abaabbbba=ab with [2] abbbb=c:

Critical pair: abaca=ab.

Defines rule #4.

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

Overlap of [3] abaca=ab with [2] abbbb=c:

Critical pair: abacc=abbbbb.

Reduce RHS:

Flip LHS and RHS.

Defines rule #5.

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

Critical pair: abacab=abbaca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #7.

Referenced by [6], [7], [9], [11].

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

Critical pair: abacabb=abbbaca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #9.

Overlap of [5] abbaca=abb with [5] abbaca=abb:

Critical pair: abbacabb=abbbbaca.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #2.

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

Overlap of [3] abaca=ab with [7] caca=c:

Critical pair: abac=abca.

Flip LHS and RHS.

Defines rule #3.

Referenced by [11].

Overlap of [5] abbaca=abb with [7] caca=c:

Critical pair: abbac=abbca.

Flip LHS and RHS.

Defines rule #6.

Overlap of [7] caca=c with [7] caca=c:

Critical pair: cac=cca.

Flip LHS and RHS.

Defines rule #1.

Overlap of [5] abbaca=abb with [8] abca=abac:

Critical pair: abbacabac=abbbca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #8.