Problem Transformed CSR 04 Ex23 Luc06 FR

Tool Bounds

Execution Time	60.038937ms
Answer	TIMEOUT
Input	Transformed CSR 04 Ex23 Luc06 FR

stdout:

TIMEOUT

We consider the following Problem:

  Strict Trs:
    {  activate(X) -> X
     , activate(n__a()) -> a()
     , activate(n__g(X)) -> g(activate(X))
     , activate(n__f(X)) -> f(activate(X))
     , a() -> n__a()
     , g(X) -> n__g(X)
     , f(X) -> n__f(X)
     , f(f(a())) -> c(n__f(n__g(n__f(n__a()))))}
  StartTerms: all
  Strategy: none

Certificate: TIMEOUT

Proof:
  Computation stopped due to timeout after 60.0 seconds.

Arrrr..

Tool CDI

Execution Time	60.04399ms
Answer	TIMEOUT
Input	Transformed CSR 04 Ex23 Luc06 FR

stdout:

TIMEOUT

Statistics:
Number of monomials: 3997
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	0.8069289ms
Answer	YES(?,O(n^2))
Input	Transformed CSR 04 Ex23 Luc06 FR

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  activate(X) -> X
     , activate(n__a()) -> a()
     , activate(n__g(X)) -> g(activate(X))
     , activate(n__f(X)) -> f(activate(X))
     , a() -> n__a()
     , g(X) -> n__g(X)
     , f(X) -> n__f(X)
     , f(f(a())) -> c(n__f(n__g(n__f(n__a()))))}
  StartTerms: all
  Strategy: none

Certificate: YES(?,O(n^2))

Proof:
  We have the following EDA-non-satisfying matrix interpretation:
  Interpretation Functions:
   a() = [1]
         [1]
   f(x1) = [1 1] x1 + [1]
           [0 1]      [2]
   n__a() = [0]
            [0]
   n__f(x1) = [1 1] x1 + [0]
              [0 1]      [2]
   n__g(x1) = [1 0] x1 + [0]
              [0 1]      [1]
   c(x1) = [1 0] x1 + [0]
           [0 0]      [3]
   g(x1) = [1 0] x1 + [1]
           [0 1]      [1]
   activate(x1) = [1 2] x1 + [2]
                  [0 1]      [2]

Hurray, we answered YES(?,O(n^2))

Tool IDA

Execution Time	1.04165ms
Answer	YES(?,O(n^2))
Input	Transformed CSR 04 Ex23 Luc06 FR

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  activate(X) -> X
     , activate(n__a()) -> a()
     , activate(n__g(X)) -> g(activate(X))
     , activate(n__f(X)) -> f(activate(X))
     , a() -> n__a()
     , g(X) -> n__g(X)
     , f(X) -> n__f(X)
     , f(f(a())) -> c(n__f(n__g(n__f(n__a()))))}
  StartTerms: all
  Strategy: none

Certificate: YES(?,O(n^2))

Proof:
  We have the following EDA-non-satisfying and IDA(2)-non-satisfying matrix interpretation:
  Interpretation Functions:
   a() = [3]
         [2]
   f(x1) = [1 0] x1 + [3]
           [0 1]      [2]
   n__a() = [2]
            [2]
   n__f(x1) = [1 0] x1 + [2]
              [0 1]      [2]
   n__g(x1) = [1 0] x1 + [1]
              [0 1]      [3]
   c(x1) = [1 0] x1 + [0]
           [0 0]      [3]
   g(x1) = [1 0] x1 + [3]
           [0 1]      [3]
   activate(x1) = [1 1] x1 + [1]
                  [0 1]      [2]

Hurray, we answered YES(?,O(n^2))

Tool TRI

Execution Time	0.2544272ms
Answer	YES(?,O(n^2))
Input	Transformed CSR 04 Ex23 Luc06 FR

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  activate(X) -> X
     , activate(n__a()) -> a()
     , activate(n__g(X)) -> g(activate(X))
     , activate(n__f(X)) -> f(activate(X))
     , a() -> n__a()
     , g(X) -> n__g(X)
     , f(X) -> n__f(X)
     , f(f(a())) -> c(n__f(n__g(n__f(n__a()))))}
  StartTerms: all
  Strategy: none

Certificate: YES(?,O(n^2))

Proof:
  We have the following triangular matrix interpretation:
  Interpretation Functions:
   a() = [3]
         [0]
   f(x1) = [1 0] x1 + [1]
           [0 1]      [2]
   n__a() = [2]
            [0]
   n__f(x1) = [1 0] x1 + [0]
              [0 1]      [2]
   n__g(x1) = [1 0] x1 + [0]
              [0 1]      [3]
   c(x1) = [1 0] x1 + [1]
           [0 0]      [3]
   g(x1) = [1 0] x1 + [2]
           [0 1]      [3]
   activate(x1) = [1 1] x1 + [2]
                  [0 1]      [1]

Hurray, we answered YES(?,O(n^2))

Tool TRI2

Execution Time	0.22715497ms
Answer	YES(?,O(n^2))
Input	Transformed CSR 04 Ex23 Luc06 FR

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  activate(X) -> X
     , activate(n__a()) -> a()
     , activate(n__g(X)) -> g(activate(X))
     , activate(n__f(X)) -> f(activate(X))
     , a() -> n__a()
     , g(X) -> n__g(X)
     , f(X) -> n__f(X)
     , f(f(a())) -> c(n__f(n__g(n__f(n__a()))))}
  StartTerms: all
  Strategy: none

Certificate: YES(?,O(n^2))

Proof:
  We have the following triangular matrix interpretation:
  Interpretation Functions:
   a() = [3]
         [0]
   f(x1) = [1 0] x1 + [1]
           [0 1]      [3]
   n__a() = [2]
            [0]
   n__f(x1) = [1 0] x1 + [0]
              [0 1]      [3]
   n__g(x1) = [1 0] x1 + [2]
              [0 1]      [2]
   c(x1) = [1 0] x1 + [0]
           [0 0]      [3]
   g(x1) = [1 0] x1 + [3]
           [0 1]      [2]
   activate(x1) = [1 3] x1 + [2]
                  [0 1]      [0]

Hurray, we answered YES(?,O(n^2))