Problem Transformed CSR 04 Ex4 7 15 Bor03 Z

Tool Bounds

Execution Time	4.1896105e-2ms
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex4 7 15 Bor03 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)
     , p(s(0())) -> 0()
     , f(s(0())) -> f(p(s(0())))
     , f(0()) -> cons(0(), n__f(s(0())))}
  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:
  {  0_0() -> 1
   , 0_1() -> 1
   , 0_2() -> 1
   , 0_2() -> 4
   , 0_2() -> 7
   , f_0(1) -> 1
   , f_1(1) -> 1
   , s_0(1) -> 1
   , s_1(1) -> 2
   , s_2(7) -> 6
   , n__f_0(1) -> 1
   , n__f_1(1) -> 1
   , n__f_1(2) -> 3
   , n__f_2(1) -> 1
   , n__f_2(6) -> 5
   , cons_0(1, 1) -> 1
   , cons_1(1, 3) -> 1
   , cons_2(4, 5) -> 1
   , p_0(1) -> 1
   , p_1(2) -> 1
   , activate_0(1) -> 1}

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

Tool CDI

Execution Time	60.038845ms
Answer	TIMEOUT
Input	Transformed CSR 04 Ex4 7 15 Bor03 Z

stdout:

TIMEOUT

Statistics:
Number of monomials: 1262
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	0.60651517ms
Answer	YES(?,O(n^2))
Input	Transformed CSR 04 Ex4 7 15 Bor03 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)
     , p(s(0())) -> 0()
     , f(s(0())) -> f(p(s(0())))
     , f(0()) -> cons(0(), n__f(s(0())))}
  StartTerms: all
  Strategy: none

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

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

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

Tool IDA

Execution Time	1.1204891ms
Answer	YES(?,O(n^2))
Input	Transformed CSR 04 Ex4 7 15 Bor03 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)
     , p(s(0())) -> 0()
     , f(s(0())) -> f(p(s(0())))
     , f(0()) -> cons(0(), n__f(s(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() = [0]
         [0]
   f(x1) = [1 2] x1 + [1]
           [0 1]      [0]
   s(x1) = [1 0] x1 + [0]
           [0 0]      [2]
   n__f(x1) = [1 0] x1 + [0]
              [0 1]      [0]
   cons(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                  [0 0]      [0 0]      [0]
   p(x1) = [1 0] x1 + [3]
           [0 0]      [0]
   activate(x1) = [1 2] x1 + [3]
                  [0 1]      [3]

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

Tool TRI

Execution Time	0.26666403ms
Answer	YES(?,O(n^2))
Input	Transformed CSR 04 Ex4 7 15 Bor03 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)
     , p(s(0())) -> 0()
     , f(s(0())) -> f(p(s(0())))
     , f(0()) -> cons(0(), n__f(s(0())))}
  StartTerms: all
  Strategy: none

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

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

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

Tool TRI2

Execution Time	0.2276299ms
Answer	YES(?,O(n^2))
Input	Transformed CSR 04 Ex4 7 15 Bor03 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)
     , p(s(0())) -> 0()
     , f(s(0())) -> f(p(s(0())))
     , f(0()) -> cons(0(), n__f(s(0())))}
  StartTerms: all
  Strategy: none

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

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

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