Problem Transformed CSR 04 Ex18 Luc06 GM

Tool Bounds

Execution Time	60.03157ms
Answer	TIMEOUT
Input	Transformed CSR 04 Ex18 Luc06 GM

stdout:

TIMEOUT

We consider the following Problem:

  Strict Trs:
    {  a__f(X) -> f(X)
     , mark(g(X)) -> g(X)
     , mark(a()) -> a()
     , mark(f(X)) -> a__f(mark(X))
     , a__f(f(a())) -> a__f(g(f(a())))}
  StartTerms: all
  Strategy: none

Certificate: TIMEOUT

Proof:
  Computation stopped due to timeout after 60.0 seconds.

Arrrr..

Tool CDI

Execution Time	5.133511ms
Answer	YES(?,O(n^2))
Input	Transformed CSR 04 Ex18 Luc06 GM

stdout:

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

This TRS is terminating using the deltarestricted interpretation
mark(delta, X0) =  + 1*X0 + 0 + 1*X0*delta + 2*delta
a(delta) =  + 0 + 0*delta
f(delta, X0) =  + 1*X0 + 2 + 2*X0*delta + 0*delta
g(delta, X0) =  + 0*X0 + 0 + 1*X0*delta + 0*delta
a__f(delta, X0) =  + 1*X0 + 2 + 2*X0*delta + 1*delta
mark_tau_1(delta) = delta/(1 + 1 * delta)
f_tau_1(delta) = delta/(1 + 2 * delta)
g_tau_1(delta) = delta/(0 + 1 * delta)
a__f_tau_1(delta) = delta/(1 + 2 * delta)

Time: 4.889243 seconds
Statistics:
Number of monomials: 366
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	0.40292907ms
Answer	YES(?,O(n^2))
Input	Transformed CSR 04 Ex18 Luc06 GM

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  a__f(X) -> f(X)
     , mark(g(X)) -> g(X)
     , mark(a()) -> a()
     , mark(f(X)) -> a__f(mark(X))
     , a__f(f(a())) -> a__f(g(f(a())))}
  StartTerms: all
  Strategy: none

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

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

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

Tool IDA

Execution Time	0.77699685ms
Answer	YES(?,O(n^2))
Input	Transformed CSR 04 Ex18 Luc06 GM

stdout:

YES(?,O(n^2))

We consider the following Problem:

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

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

Tool TRI

Execution Time	0.17782116ms
Answer	YES(?,O(n^2))
Input	Transformed CSR 04 Ex18 Luc06 GM

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  a__f(X) -> f(X)
     , mark(g(X)) -> g(X)
     , mark(a()) -> a()
     , mark(f(X)) -> a__f(mark(X))
     , a__f(f(a())) -> a__f(g(f(a())))}
  StartTerms: all
  Strategy: none

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

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

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

Tool TRI2

Execution Time	0.1542499ms
Answer	YES(?,O(n^2))
Input	Transformed CSR 04 Ex18 Luc06 GM

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  a__f(X) -> f(X)
     , mark(g(X)) -> g(X)
     , mark(a()) -> a()
     , mark(f(X)) -> a__f(mark(X))
     , a__f(f(a())) -> a__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]
         [3]
   f(x1) = [1 2] x1 + [0]
           [0 1]      [2]
   a__f(x1) = [1 2] x1 + [1]
              [0 1]      [2]
   g(x1) = [1 0] x1 + [0]
           [0 0]      [1]
   mark(x1) = [1 2] x1 + [0]
              [0 1]      [0]

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