Problem Transformed CSR 04 Ex4 7 15 Bor03 FR

Tool Bounds

Execution Time	60.035812ms
Answer	TIMEOUT
Input	Transformed CSR 04 Ex4 7 15 Bor03 FR

stdout:

TIMEOUT

We consider the following Problem:

  Strict Trs:
    {  activate(X) -> X
     , activate(n__0()) -> 0()
     , activate(n__s(X)) -> s(activate(X))
     , activate(n__f(X)) -> f(activate(X))
     , 0() -> n__0()
     , s(X) -> n__s(X)
     , f(X) -> n__f(X)
     , p(s(0())) -> 0()
     , f(s(0())) -> f(p(s(0())))
     , f(0()) -> cons(0(), n__f(n__s(n__0())))}
  StartTerms: all
  Strategy: none

Certificate: TIMEOUT

Proof:
  Computation stopped due to timeout after 60.0 seconds.

Arrrr..

Tool CDI

Execution Time	19.763979ms
Answer	MAYBE
Input	Transformed CSR 04 Ex4 7 15 Bor03 FR

stdout:

MAYBE

Statistics:
Number of monomials: 1385
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	0.6936691ms
Answer	YES(?,O(n^2))
Input	Transformed CSR 04 Ex4 7 15 Bor03 FR

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  activate(X) -> X
     , activate(n__0()) -> 0()
     , activate(n__s(X)) -> s(activate(X))
     , activate(n__f(X)) -> f(activate(X))
     , 0() -> n__0()
     , s(X) -> n__s(X)
     , f(X) -> n__f(X)
     , p(s(0())) -> 0()
     , f(s(0())) -> f(p(s(0())))
     , f(0()) -> cons(0(), n__f(n__s(n__0())))}
  StartTerms: all
  Strategy: none

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

Proof:
  We have the following EDA-non-satisfying matrix interpretation:
  Interpretation Functions:
   0() = [1]
         [2]
   f(x1) = [1 2] x1 + [1]
           [0 1]      [3]
   n__0() = [0]
            [0]
   n__s(x1) = [1 1] x1 + [0]
              [0 1]      [2]
   n__f(x1) = [1 2] x1 + [0]
              [0 1]      [3]
   cons(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                  [0 0]      [0 0]      [3]
   s(x1) = [1 1] x1 + [1]
           [0 1]      [2]
   p(x1) = [1 0] x1 + [0]
           [0 0]      [3]
   activate(x1) = [1 2] x1 + [2]
                  [0 1]      [2]

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

Tool IDA

Execution Time	1.1328721ms
Answer	YES(?,O(n^2))
Input	Transformed CSR 04 Ex4 7 15 Bor03 FR

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  activate(X) -> X
     , activate(n__0()) -> 0()
     , activate(n__s(X)) -> s(activate(X))
     , activate(n__f(X)) -> f(activate(X))
     , 0() -> n__0()
     , s(X) -> n__s(X)
     , f(X) -> n__f(X)
     , p(s(0())) -> 0()
     , f(s(0())) -> f(p(s(0())))
     , f(0()) -> cons(0(), n__f(n__s(n__0())))}
  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:
   0() = [1]
         [1]
   f(x1) = [1 1] x1 + [2]
           [0 1]      [3]
   n__0() = [0]
            [0]
   n__s(x1) = [1 1] x1 + [0]
              [0 1]      [2]
   n__f(x1) = [1 1] x1 + [0]
              [0 1]      [3]
   cons(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                  [0 0]      [0 0]      [3]
   s(x1) = [1 1] x1 + [1]
           [0 1]      [2]
   p(x1) = [1 0] x1 + [0]
           [0 0]      [1]
   activate(x1) = [1 2] x1 + [2]
                  [0 1]      [1]

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

Tool TRI

Execution Time	0.33354783ms
Answer	YES(?,O(n^2))
Input	Transformed CSR 04 Ex4 7 15 Bor03 FR

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  activate(X) -> X
     , activate(n__0()) -> 0()
     , activate(n__s(X)) -> s(activate(X))
     , activate(n__f(X)) -> f(activate(X))
     , 0() -> n__0()
     , s(X) -> n__s(X)
     , f(X) -> n__f(X)
     , p(s(0())) -> 0()
     , f(s(0())) -> f(p(s(0())))
     , f(0()) -> cons(0(), n__f(n__s(n__0())))}
  StartTerms: all
  Strategy: none

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

Proof:
  We have the following triangular matrix interpretation:
  Interpretation Functions:
   0() = [1]
         [2]
   f(x1) = [1 2] x1 + [1]
           [0 1]      [3]
   n__0() = [0]
            [0]
   n__s(x1) = [1 0] x1 + [0]
              [0 1]      [2]
   n__f(x1) = [1 2] x1 + [0]
              [0 1]      [3]
   cons(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                  [0 0]      [0 0]      [3]
   s(x1) = [1 0] x1 + [1]
           [0 1]      [2]
   p(x1) = [1 0] x1 + [2]
           [0 0]      [2]
   activate(x1) = [1 2] x1 + [2]
                  [0 1]      [2]

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

Tool TRI2

Execution Time	0.2651291ms
Answer	YES(?,O(n^2))
Input	Transformed CSR 04 Ex4 7 15 Bor03 FR

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  activate(X) -> X
     , activate(n__0()) -> 0()
     , activate(n__s(X)) -> s(activate(X))
     , activate(n__f(X)) -> f(activate(X))
     , 0() -> n__0()
     , s(X) -> n__s(X)
     , f(X) -> n__f(X)
     , p(s(0())) -> 0()
     , f(s(0())) -> f(p(s(0())))
     , f(0()) -> cons(0(), n__f(n__s(n__0())))}
  StartTerms: all
  Strategy: none

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

Proof:
  We have the following triangular matrix interpretation:
  Interpretation Functions:
   0() = [1]
         [2]
   f(x1) = [1 2] x1 + [1]
           [0 1]      [3]
   n__0() = [0]
            [0]
   n__s(x1) = [1 0] x1 + [0]
              [0 1]      [2]
   n__f(x1) = [1 2] x1 + [0]
              [0 1]      [3]
   cons(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                  [0 0]      [0 0]      [3]
   s(x1) = [1 0] x1 + [1]
           [0 1]      [2]
   p(x1) = [1 0] x1 + [0]
           [0 0]      [2]
   activate(x1) = [1 3] x1 + [3]
                  [0 1]      [3]

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