Certificate for #3728 ⟨a, b | abaabaaaab=a⟩

Completion settings:

• Reduction order:
  • Right-to-left recursive path with deg(c) = 0; deg(d) = deg(a) = deg(b) = 1, d < a < b
• Auxiliary generators:
  1. aab=c
  2. aaaa=d

Axiom: abaabaaaab=a.

Referenced by [4].

Axiom: aab=c.

Defines rule #7.

Referenced by [4], [5], [8], [10], [11].

Axiom: aaaa=d.

Defines rule #8.

Referenced by [4], [5], [6], [9], [11].

Overlap of [1] abaabaaaab=a with [2] aab=c:

Critical pair: abcaaaab=a.

Reduce LHS:

Referenced by [7].

Overlap of [3] aaaa=d with [2] aab=c:

Critical pair: aac=db.

Flip LHS and RHS.

Defines rule #4.

Referenced by [7].

Overlap of [3] aaaa=d with [3] aaaa=d:

Critical pair: ad=da.

Flip LHS and RHS.

Defines rule #2.

Simplify [4] abcdb=a.

Reduce LHS:

Defines rule #9.

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

Overlap of [2] aab=c with [7] abcaac=a:

Critical pair: aa=ccaac.

Flip LHS and RHS.

Defines rule #3.

Referenced by [9], [11].

Overlap of [7] abcaac=a with [8] ccaac=aa:

Critical pair: abcaaaa=acaac.

Reduce LHS:

Flip LHS and RHS.

Defines rule #6.

Referenced by [10], [11].

Overlap of [7] abcaac=a with [9] acaac=abcd:

Critical pair: abcaabcd=aaac.

Reduce LHS:

Flip LHS and RHS.

Defines rule #5.

Overlap of [8] ccaac=aa with [9] acaac=abcd:

Critical pair: ccaabcd=aaaac.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #1.