Problem CSR 04 Ex15 Luc06

Tool Bounds

Execution Time	2.3768902e-2ms
Answer	YES(?,O(n^1))
Input	CSR 04 Ex15 Luc06

stdout:

YES(?,O(n^1))

We consider the following Problem:

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

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

Proof:
  The problem is match-bounded by 1.
  The enriched problem is compatible with the following automaton:
  {  f_0(1) -> 1
   , f_1(2) -> 1
   , f_1(4) -> 3
   , a_0() -> 1
   , a_1() -> 4
   , g_0(1) -> 1
   , g_1(3) -> 2}

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

Tool CDI

Execution Time	3.1786811ms
Answer	YES(?,O(n^2))
Input	CSR 04 Ex15 Luc06

stdout:

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

This TRS is terminating using the deltarestricted interpretation
a(delta) =  + 2 + 0*delta
g(delta, X0) =  + 0*X0 + 0 + 2*X0*delta + 0*delta
f(delta, X0) =  + 1*X0 + 0 + 3*X0*delta + 0*delta
g_tau_1(delta) = delta/(0 + 2 * delta)
f_tau_1(delta) = delta/(1 + 3 * delta)

Time: 3.141452 seconds
Statistics:
Number of monomials: 259
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	0.34006405ms
Answer	YES(?,O(n^2))
Input	CSR 04 Ex15 Luc06

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs: {f(f(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:
   f(x1) = [1 2] x1 + [0]
           [0 1]      [2]
   a() = [0]
         [0]
   g(x1) = [1 0] x1 + [0]
           [0 0]      [0]

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

Tool IDA

Execution Time	0.471591ms
Answer	YES(?,O(n^2))
Input	CSR 04 Ex15 Luc06

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs: {f(f(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:
   f(x1) = [1 2] x1 + [0]
           [0 1]      [2]
   a() = [0]
         [0]
   g(x1) = [1 0] x1 + [0]
           [0 0]      [0]

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

Tool TRI

Execution Time	0.12996006ms
Answer	YES(?,O(n^1))
Input	CSR 04 Ex15 Luc06

stdout:

YES(?,O(n^1))

We consider the following Problem:

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

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

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

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

Tool TRI2

Execution Time	0.10990095ms
Answer	YES(?,O(n^1))
Input	CSR 04 Ex15 Luc06

stdout:

YES(?,O(n^1))

We consider the following Problem:

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

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

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

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