Problem Applicative 05 Ex2 6 1Composition

Tool Bounds

Execution Time	2.6630878e-2ms
Answer	YES(?,O(n^1))
Input	Applicative 05 Ex2 6 1Composition

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {app(app(app(compose(), f), g), x) -> app(f, app(g, 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:
  {  compose_0() -> 1
   , app_0(1, 1) -> 1
   , app_1(1, 1) -> 2
   , app_1(1, 2) -> 1
   , app_1(1, 2) -> 2
   , app_1(2, 1) -> 2
   , app_1(2, 2) -> 1
   , app_1(2, 2) -> 2}

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

Tool CDI

Execution Time	3.406543ms
Answer	YES(?,O(n^2))
Input	Applicative 05 Ex2 6 1Composition

stdout:

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

This TRS is terminating using the deltarestricted interpretation
compose(delta) = + 0 + 0*delta
app(delta, X1, X0) = + 0*X0 + 0*X1 + 0 + 2*X0*delta + 2*X1*delta + 2*delta
app_tau_1(delta) = delta/(0 + 2 * delta)
app_tau_2(delta) = delta/(0 + 2 * delta)

Time: 3.370466 seconds
Statistics:
Number of monomials: 427
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	9.2890024e-2ms
Answer	YES(?,O(n^1))
Input	Applicative 05 Ex2 6 1Composition

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {app(app(app(compose(), f), g), x) -> app(f, app(g, x))}
  StartTerms: all
  Strategy: none

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

Proof:
  We have the following EDA-non-satisfying matrix interpretation:
  Interpretation Functions:
   compose() = [1]
   app(x1, x2) = [1] x1 + [1] x2 + [0]

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

Tool IDA

Execution Time	0.1582849ms
Answer	YES(?,O(n^1))
Input	Applicative 05 Ex2 6 1Composition

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {app(app(app(compose(), f), g), x) -> app(f, app(g, 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:
   compose() = [1]
   app(x1, x2) = [1] x1 + [1] x2 + [0]

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

Tool TRI

Execution Time	5.08101e-2ms
Answer	YES(?,O(n^1))
Input	Applicative 05 Ex2 6 1Composition

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {app(app(app(compose(), f), g), x) -> app(f, app(g, x))}
  StartTerms: all
  Strategy: none

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

Proof:
  We have the following triangular matrix interpretation:
  Interpretation Functions:
   compose() = [1]
   app(x1, x2) = [1] x1 + [1] x2 + [0]

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

Tool TRI2

Execution Time	9.8423004e-2ms
Answer	YES(?,O(n^1))
Input	Applicative 05 Ex2 6 1Composition

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {app(app(app(compose(), f), g), x) -> app(f, app(g, x))}
  StartTerms: all
  Strategy: none

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

Proof:
  We have the following triangular matrix interpretation:
  Interpretation Functions:
   compose() = [1]
               [0]
   app(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                 [0 0]      [0 0]      [0]

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