Problem Transformed CSR 04 Ex18 Luc06 L

Tool Bounds

Execution Time	2.5403023e-2ms
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex18 Luc06 L

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs: {f(f(a())) -> f(g())}
  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:
  {  a_0() -> 1
   , f_0(1) -> 1
   , f_1(2) -> 1
   , g_0() -> 1
   , g_1() -> 2}

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

Tool CDI

Execution Time	0.13495302ms
Answer	YES(?,O(n^2))
Input	Transformed CSR 04 Ex18 Luc06 L

stdout:

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

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

Time: 0.097424 seconds
Statistics:
Number of monomials: 46
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	0.105407ms
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex18 Luc06 L

stdout:

YES(?,O(n^1))

We consider the following Problem:

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

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

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

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

Tool IDA

Execution Time	0.14949489ms
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex18 Luc06 L

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs: {f(f(a())) -> f(g())}
  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:
   a() = [0]
   f(x1) = [1] x1 + [3]
   g() = [1]

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

Tool TRI

Execution Time	6.966591e-2ms
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex18 Luc06 L

stdout:

YES(?,O(n^1))

We consider the following Problem:

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

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

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

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

Tool TRI2

Execution Time	6.408715e-2ms
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex18 Luc06 L

stdout:

YES(?,O(n^1))

We consider the following Problem:

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

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

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

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