Problem Transformed CSR 04 Ex25 Luc06 L

Tool Bounds

Execution Time	6.807804e-2ms
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex25 Luc06 L

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  h(X) -> c()
     , c() -> d()
     , f(f(X)) -> c()}
  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:
  {  f_0(1) -> 1
   , c_0() -> 1
   , c_1() -> 1
   , d_0() -> 1
   , d_1() -> 1
   , d_2() -> 1
   , h_0(1) -> 1}

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

Tool CDI

Execution Time	4.8251867e-2ms
Answer	YES(?,O(n^2))
Input	Transformed CSR 04 Ex25 Luc06 L

stdout:

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

This TRS is terminating using the deltarestricted interpretation
h(delta, X0) =  + 0*X0 + 0 + 2*X0*delta + 2*delta
d(delta) =  + 0 + 0*delta
f(delta, X0) =  + 0*X0 + 0 + 2*X0*delta + 2*delta
c(delta) =  + 0 + 1*delta
h_tau_1(delta) = delta/(0 + 2 * delta)
f_tau_1(delta) = delta/(0 + 2 * delta)

Time: 0.009357 seconds
Statistics:
Number of monomials: 36
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	9.2494965e-2ms
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex25 Luc06 L

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  h(X) -> c()
     , c() -> d()
     , f(f(X)) -> c()}
  StartTerms: all
  Strategy: none

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

Proof:
  We have the following EDA-non-satisfying matrix interpretation:
  Interpretation Functions:
   f(x1) = [1] x1 + [3]
   c() = [1]
   d() = [0]
   h(x1) = [1] x1 + [3]

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

Tool IDA

Execution Time	0.14474797ms
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex25 Luc06 L

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  h(X) -> c()
     , c() -> d()
     , f(f(X)) -> c()}
  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:
   f(x1) = [1] x1 + [3]
   c() = [1]
   d() = [0]
   h(x1) = [1] x1 + [3]

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

Tool TRI

Execution Time	5.9648037e-2ms
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex25 Luc06 L

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  h(X) -> c()
     , c() -> d()
     , f(f(X)) -> c()}
  StartTerms: all
  Strategy: none

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

Proof:
  We have the following triangular matrix interpretation:
  Interpretation Functions:
   f(x1) = [1] x1 + [3]
   c() = [1]
   d() = [0]
   h(x1) = [1] x1 + [3]

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

Tool TRI2

Execution Time	4.1455984e-2ms
Answer	YES(?,O(n^2))
Input	Transformed CSR 04 Ex25 Luc06 L

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  h(X) -> c()
     , c() -> d()
     , f(f(X)) -> c()}
  StartTerms: all
  Strategy: none

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

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

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