Certificate for #3778 ⟨a, b | ababbaaaab=a⟩

Completion settings:

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

Axiom: ababbaaaab=a.

Referenced by [3].

Axiom: abb=c.

Defines rule #7.

Referenced by [3], [4].

Overlap of [1] ababbaaaab=a with [2] abb=c:

Critical pair: abcaaaab=a.

Defines rule #9.

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

Overlap of [3] abcaaaab=a with [2] abb=c:

Critical pair: abcaaac=ab.

Defines rule #4.

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

Overlap of [3] abcaaaab=a with [3] abcaaaab=a:

Critical pair: abcaaaa=acaaaab.

Flip LHS and RHS.

Defines rule #6.

Referenced by [9], [10].

Overlap of [3] abcaaaab=a with [4] abcaaac=ab:

Critical pair: abcaaaab=acaaac.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

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

Overlap of [4] abcaaac=ab with [6] acaaac=a:

Critical pair: abcaaa=abaaac.

Flip LHS and RHS.

Defines rule #3.

Overlap of [6] acaaac=a with [6] acaaac=a:

Critical pair: acaaa=aaaac.

Flip LHS and RHS.

Defines rule #1.

Overlap of [4] abcaaac=ab with [5] acaaaab=abcaaaa:

Critical pair: abcaaabcaaaa=abaaaab.

Flip LHS and RHS.

Defines rule #8.

Overlap of [6] acaaac=a with [5] acaaaab=abcaaaa:

Critical pair: acaaabcaaaa=aaaaab.

Flip LHS and RHS.

Defines rule #5.