Problem Transformed CSR 04 Ex23 Luc06 Z

Tool Bounds

Execution Time	5.83961e-2ms
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex23 Luc06 Z

stdout:

YES(?,O(n^1))

We consider the following Problem:

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

Certificate: YES(?,O(n^1))

Proof:
  The problem is match-bounded by 2.
  The enriched problem is compatible with the following automaton:
  {  a_0() -> 1
   , a_0() -> 6
   , a_1() -> 10
   , f_0(1) -> 2
   , f_0(1) -> 6
   , f_0(2) -> 2
   , f_0(2) -> 6
   , f_0(3) -> 2
   , f_0(3) -> 6
   , f_0(4) -> 2
   , f_0(4) -> 6
   , f_0(5) -> 2
   , f_0(5) -> 6
   , f_0(6) -> 2
   , f_0(6) -> 6
   , f_1(1) -> 6
   , f_1(2) -> 6
   , f_1(3) -> 6
   , f_1(4) -> 6
   , f_1(5) -> 6
   , f_1(6) -> 6
   , f_1(10) -> 9
   , g_0(1) -> 3
   , g_0(1) -> 6
   , g_0(2) -> 3
   , g_0(2) -> 6
   , g_0(3) -> 3
   , g_0(3) -> 6
   , g_0(4) -> 3
   , g_0(4) -> 6
   , g_0(5) -> 3
   , g_0(5) -> 6
   , g_0(6) -> 3
   , g_0(6) -> 6
   , g_1(9) -> 8
   , n__f_0(1) -> 4
   , n__f_0(1) -> 6
   , n__f_0(2) -> 4
   , n__f_0(2) -> 6
   , n__f_0(3) -> 4
   , n__f_0(3) -> 6
   , n__f_0(4) -> 4
   , n__f_0(4) -> 6
   , n__f_0(5) -> 4
   , n__f_0(5) -> 6
   , n__f_0(6) -> 4
   , n__f_0(6) -> 6
   , n__f_1(1) -> 2
   , n__f_1(1) -> 6
   , n__f_1(2) -> 2
   , n__f_1(2) -> 6
   , n__f_1(3) -> 2
   , n__f_1(3) -> 6
   , n__f_1(4) -> 2
   , n__f_1(4) -> 6
   , n__f_1(5) -> 2
   , n__f_1(5) -> 6
   , n__f_1(6) -> 2
   , n__f_1(6) -> 6
   , n__f_1(8) -> 7
   , n__f_2(1) -> 6
   , n__f_2(2) -> 6
   , n__f_2(3) -> 6
   , n__f_2(4) -> 6
   , n__f_2(5) -> 6
   , n__f_2(6) -> 6
   , n__f_2(10) -> 9
   , c_0(1) -> 5
   , c_0(1) -> 6
   , c_0(2) -> 5
   , c_0(2) -> 6
   , c_0(3) -> 5
   , c_0(3) -> 6
   , c_0(4) -> 5
   , c_0(4) -> 6
   , c_0(5) -> 5
   , c_0(5) -> 6
   , c_0(6) -> 5
   , c_0(6) -> 6
   , c_1(7) -> 2
   , c_1(7) -> 6
   , activate_0(1) -> 6
   , activate_0(2) -> 6
   , activate_0(3) -> 6
   , activate_0(4) -> 6
   , activate_0(5) -> 6
   , activate_0(6) -> 6}

Hurray, we answered YES(?,O(n^1))

Tool CDI

Execution Time	60.039417ms
Answer	TIMEOUT
Input	Transformed CSR 04 Ex23 Luc06 Z

stdout:

TIMEOUT

Statistics:
Number of monomials: 3074
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	0.13253617ms
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex23 Luc06 Z

stdout:

YES(?,O(n^1))

We consider the following Problem:

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

Certificate: YES(?,O(n^1))

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

Hurray, we answered YES(?,O(n^1))

Tool IDA

Execution Time	0.25716615ms
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex23 Luc06 Z

stdout:

YES(?,O(n^1))

We consider the following Problem:

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

Certificate: YES(?,O(n^1))

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

Hurray, we answered YES(?,O(n^1))

Tool TRI

Execution Time	8.4374905e-2ms
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex23 Luc06 Z

stdout:

YES(?,O(n^1))

We consider the following Problem:

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

Certificate: YES(?,O(n^1))

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

Hurray, we answered YES(?,O(n^1))

Tool TRI2

Execution Time	0.17525601ms
Answer	YES(?,O(n^2))
Input	Transformed CSR 04 Ex23 Luc06 Z

stdout:

YES(?,O(n^2))

We consider the following Problem:

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

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

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

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