Problem AotoYamada 05 025

Tool Bounds

Execution Time	2.4677992e-2ms
Answer	YES(?,O(n^1))
Input	AotoYamada 05 025

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs: {app(app(apply(), f), x) -> app(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:
  {  apply_0() -> 1
   , app_0(1, 1) -> 1
   , app_1(1, 1) -> 1}

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

Tool CDI

Execution Time	0.13269997ms
Answer	YES(?,O(n^2))
Input	AotoYamada 05 025

stdout:

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

This TRS is terminating using the deltarestricted interpretation
apply(delta) = + 0 + 2*delta
app(delta, X1, X0) = + 0*X0 + 0*X1 + 0 + 3*X0*delta + 3*X1*delta + 0*delta
app_tau_1(delta) = delta/(0 + 3 * delta)
app_tau_2(delta) = delta/(0 + 3 * delta)

Time: 0.095472 seconds
Statistics:
Number of monomials: 61
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	9.5133066e-2ms
Answer	YES(?,O(n^1))
Input	AotoYamada 05 025

stdout:

YES(?,O(n^1))

We consider the following Problem:

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

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

Proof:
  We have the following EDA-non-satisfying matrix interpretation:
  Interpretation Functions:
   apply() = [0]
   app(x1, x2) = [1] x1 + [1] x2 + [3]

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

Tool IDA

Execution Time	0.1508658ms
Answer	YES(?,O(n^1))
Input	AotoYamada 05 025

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs: {app(app(apply(), f), x) -> app(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:
   apply() = [0]
   app(x1, x2) = [1] x1 + [1] x2 + [3]

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

Tool TRI

Execution Time	6.601405e-2ms
Answer	YES(?,O(n^1))
Input	AotoYamada 05 025

stdout:

YES(?,O(n^1))

We consider the following Problem:

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

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

Proof:
  We have the following triangular matrix interpretation:
  Interpretation Functions:
   apply() = [0]
   app(x1, x2) = [1] x1 + [1] x2 + [3]

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

Tool TRI2

Execution Time	5.455208e-2ms
Answer	YES(?,O(n^2))
Input	AotoYamada 05 025

stdout:

YES(?,O(n^2))

We consider the following Problem:

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

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

Proof:
  We have the following triangular matrix interpretation:
  Interpretation Functions:
   apply() = [3]
             [0]
   app(x1, x2) = [1 3] x1 + [1 3] x2 + [2]
                 [0 0]      [0 1]      [3]

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