Certificate for #1789 ⟨a, b | ababbaaab=a⟩

Completion settings:

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

Axiom: ababbaaab=a.

Referenced by [3].

Axiom: abb=c.

Defines rule #7.

Referenced by [3], [4].

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

Critical pair: abcaaab=a.

Defines rule #9.

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

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

Critical pair: abcaac=ab.

Defines rule #4.

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

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

Critical pair: abcaaa=acaaab.

Flip LHS and RHS.

Defines rule #6.

Referenced by [9], [10].

Overlap of [3] abcaaab=a with [4] abcaac=ab:

Critical pair: abcaaab=acaac.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

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

Overlap of [4] abcaac=ab with [6] acaac=a:

Critical pair: abcaa=abaac.

Flip LHS and RHS.

Defines rule #3.

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

Critical pair: acaa=aaac.

Flip LHS and RHS.

Defines rule #1.

Overlap of [4] abcaac=ab with [5] acaaab=abcaaa:

Critical pair: abcaabcaaa=abaaab.

Flip LHS and RHS.

Defines rule #8.

Overlap of [6] acaac=a with [5] acaaab=abcaaa:

Critical pair: acaabcaaa=aaaab.

Flip LHS and RHS.

Defines rule #5.