Problem Transformed CSR 04 Ex4 4 Luc96b L

Tool Bounds

Execution Time	2.5195122e-2ms
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex4 4 Luc96b L

stdout:

YES(?,O(n^1))

We consider the following Problem:

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

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

Tool CDI

Execution Time	4.4057846e-2ms
Answer	YES(?,O(n^2))
Input	Transformed CSR 04 Ex4 4 Luc96b L

stdout:

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

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

Time: 0.006026 seconds
Statistics:
Number of monomials: 26
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	6.529784e-2ms
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex4 4 Luc96b L

stdout:

YES(?,O(n^1))

We consider the following Problem:

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

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

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

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

Tool IDA

Execution Time	9.652591e-2ms
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex4 4 Luc96b L

stdout:

YES(?,O(n^1))

We consider the following Problem:

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

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

Tool TRI

Execution Time	4.3165922e-2ms
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex4 4 Luc96b L

stdout:

YES(?,O(n^1))

We consider the following Problem:

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

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

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

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

Tool TRI2

Execution Time	5.943489e-2ms
Answer	YES(?,O(n^2))
Input	Transformed CSR 04 Ex4 4 Luc96b L

stdout:

YES(?,O(n^2))

We consider the following Problem:

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

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

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

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