Problem Transformed CSR 04 Ex15 Luc06 Z

Tool Bounds

Execution Time	6.682205e-2ms
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex15 Luc06 Z

stdout:

YES(?,O(n^1))

We consider the following Problem:

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

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

Proof:
  The problem is match-bounded by 4.
  The enriched problem is compatible with the following automaton:
  {  n__a_0() -> 1
   , n__a_1() -> 1
   , n__a_2() -> 1
   , n__a_3() -> 6
   , n__f_0(1) -> 1
   , n__f_1(1) -> 1
   , n__f_2(1) -> 1
   , n__f_2(1) -> 3
   , n__f_2(2) -> 1
   , n__f_3(1) -> 3
   , n__f_3(2) -> 1
   , n__f_3(2) -> 3
   , n__f_4(4) -> 3
   , n__f_4(6) -> 5
   , f_0(1) -> 1
   , f_1(1) -> 1
   , f_1(1) -> 3
   , f_1(2) -> 1
   , f_2(1) -> 3
   , f_2(2) -> 1
   , f_2(2) -> 3
   , f_3(4) -> 3
   , f_3(6) -> 5
   , n__g_0(1) -> 1
   , n__g_1(1) -> 1
   , n__g_2(1) -> 1
   , n__g_2(3) -> 2
   , n__g_3(5) -> 4
   , a_0() -> 1
   , a_1() -> 1
   , g_0(1) -> 1
   , g_1(1) -> 1
   , activate_0(1) -> 1}

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

Tool CDI

Execution Time	8.598324ms
Answer	YES(?,O(n^2))
Input	Transformed CSR 04 Ex15 Luc06 Z

stdout:

YES(?,O(n^2))
QUADRATIC upper bound on the derivational complexity

This TRS is terminating using the deltarestricted interpretation
activate(delta, X0) =  + 1*X0 + 0 + 0*X0*delta + 2*delta
g(delta, X0) =  + 0*X0 + 0 + 1*X0*delta + 1*delta
a(delta) =  + 0 + 1*delta
n__f(delta, X0) =  + 0*X0 + 2 + 2*X0*delta + 2*delta
n__a(delta) =  + 0 + 0*delta
n__g(delta, X0) =  + 0*X0 + 0 + 1*X0*delta + 0*delta
f(delta, X0) =  + 0*X0 + 2 + 2*X0*delta + 3*delta
activate_tau_1(delta) = delta/(1 + 0 * delta)
g_tau_1(delta) = delta/(0 + 1 * delta)
n__f_tau_1(delta) = delta/(0 + 2 * delta)
n__g_tau_1(delta) = delta/(0 + 1 * delta)
f_tau_1(delta) = delta/(0 + 2 * delta)

Time: 8.559581 seconds
Statistics:
Number of monomials: 521
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	0.4146371ms
Answer	YES(?,O(n^2))
Input	Transformed CSR 04 Ex15 Luc06 Z

stdout:

YES(?,O(n^2))

We consider the following Problem:

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

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

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

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

Tool IDA

Execution Time	0.6903839ms
Answer	YES(?,O(n^2))
Input	Transformed CSR 04 Ex15 Luc06 Z

stdout:

YES(?,O(n^2))

We consider the following Problem:

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

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

Tool TRI

Execution Time	0.20424509ms
Answer	YES(?,O(n^2))
Input	Transformed CSR 04 Ex15 Luc06 Z

stdout:

YES(?,O(n^2))

We consider the following Problem:

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

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

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

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

Tool TRI2

Execution Time	0.14191699ms
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex15 Luc06 Z

stdout:

YES(?,O(n^1))

We consider the following Problem:

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

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

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

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