Certificate for #3741 ⟨a, b | abaabbaaab=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: abaabbaaab=a.

Referenced by [3].

Axiom: abb=c.

Defines rule #7.

Referenced by [3], [4].

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

Critical pair: abacaaab=a.

Defines rule #9.

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

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

Critical pair: abacaac=ab.

Defines rule #4.

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

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

Critical pair: abacaaa=aacaaab.

Flip LHS and RHS.

Defines rule #6.

Referenced by [9], [10].

Overlap of [3] abacaaab=a with [4] abacaac=ab:

Critical pair: abacaaab=aacaac.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

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

Overlap of [4] abacaac=ab with [6] aacaac=a:

Critical pair: abaca=abaac.

Flip LHS and RHS.

Defines rule #3.

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

Critical pair: aaca=aaac.

Flip LHS and RHS.

Defines rule #1.

Overlap of [4] abacaac=ab with [5] aacaaab=abacaaa:

Critical pair: abacabacaaa=abaaab.

Flip LHS and RHS.

Defines rule #8.

Overlap of [6] aacaac=a with [5] aacaaab=abacaaa:

Critical pair: aacabacaaa=aaaab.

Flip LHS and RHS.

Defines rule #5.