Problem Transformed CSR 04 Ex18 Luc06 FR

Tool Bounds

Execution Time	60.033184ms
Answer	TIMEOUT
Input	Transformed CSR 04 Ex18 Luc06 FR

stdout:

TIMEOUT

We consider the following Problem:

  Strict Trs:
    {  activate(X) -> X
     , activate(n__a()) -> a()
     , activate(n__f(X)) -> f(activate(X))
     , a() -> n__a()
     , f(X) -> n__f(X)
     , f(f(a())) -> f(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	7.006236ms
Answer	MAYBE
Input	Transformed CSR 04 Ex18 Luc06 FR

stdout:

MAYBE

Statistics:
Number of monomials: 571
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	0.433501ms
Answer	YES(?,O(n^2))
Input	Transformed CSR 04 Ex18 Luc06 FR

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  activate(X) -> X
     , activate(n__a()) -> a()
     , activate(n__f(X)) -> f(activate(X))
     , a() -> n__a()
     , f(X) -> n__f(X)
     , f(f(a())) -> f(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() = [3]
         [0]
   f(x1) = [1 3] x1 + [1]
           [0 1]      [1]
   n__a() = [2]
            [0]
   n__f(x1) = [1 3] x1 + [0]
              [0 1]      [1]
   g(x1) = [1 0] x1 + [0]
           [0 0]      [0]
   activate(x1) = [1 2] x1 + [3]
                  [0 1]      [0]

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

Tool IDA

Execution Time	0.6777179ms
Answer	YES(?,O(n^2))
Input	Transformed CSR 04 Ex18 Luc06 FR

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  activate(X) -> X
     , activate(n__a()) -> a()
     , activate(n__f(X)) -> f(activate(X))
     , a() -> n__a()
     , f(X) -> n__f(X)
     , f(f(a())) -> f(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]
         [1]
   f(x1) = [1 0] x1 + [1]
           [0 1]      [2]
   n__a() = [2]
            [1]
   n__f(x1) = [1 0] x1 + [0]
              [0 1]      [2]
   g(x1) = [1 0] x1 + [0]
           [0 0]      [0]
   activate(x1) = [1 1] x1 + [1]
                  [0 1]      [0]

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

Tool TRI

Execution Time	0.19426513ms
Answer	YES(?,O(n^2))
Input	Transformed CSR 04 Ex18 Luc06 FR

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  activate(X) -> X
     , activate(n__a()) -> a()
     , activate(n__f(X)) -> f(activate(X))
     , a() -> n__a()
     , f(X) -> n__f(X)
     , f(f(a())) -> f(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]
         [1]
   f(x1) = [1 0] x1 + [2]
           [0 1]      [3]
   n__a() = [2]
            [1]
   n__f(x1) = [1 0] x1 + [1]
              [0 1]      [3]
   g(x1) = [1 0] x1 + [1]
           [0 0]      [0]
   activate(x1) = [1 1] x1 + [1]
                  [0 1]      [0]

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

Tool TRI2

Execution Time	0.12929893ms
Answer	YES(?,O(n^2))
Input	Transformed CSR 04 Ex18 Luc06 FR

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  activate(X) -> X
     , activate(n__a()) -> a()
     , activate(n__f(X)) -> f(activate(X))
     , a() -> n__a()
     , f(X) -> n__f(X)
     , f(f(a())) -> f(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]
         [1]
   f(x1) = [1 0] x1 + [2]
           [0 1]      [3]
   n__a() = [2]
            [1]
   n__f(x1) = [1 0] x1 + [1]
              [0 1]      [3]
   g(x1) = [1 0] x1 + [0]
           [0 0]      [0]
   activate(x1) = [1 1] x1 + [1]
                  [0 1]      [0]

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