Problem AG01 3.15

Tool Bounds

Execution Time	60.04513ms
Answer	TIMEOUT
Input	AG01 3.15

stdout:

TIMEOUT

We consider the following Problem:

  Strict Trs:
    {  average(0(), s(s(0()))) -> s(0())
     , average(0(), s(0())) -> 0()
     , average(0(), 0()) -> 0()
     , average(x, s(s(s(y)))) -> s(average(s(x), y))
     , average(s(x), y) -> average(x, s(y))}
  StartTerms: all
  Strategy: none

Certificate: TIMEOUT

Proof:
  Computation stopped due to timeout after 60.0 seconds.

Arrrr..

Tool CDI

Execution Time	59.715897ms
Answer	YES(?,O(n^2))
Input	AG01 3.15

stdout:

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

This TRS is terminating using the deltarestricted interpretation
0(delta) =  + 2 + 0*delta
s(delta, X0) =  + 1*X0 + 1 + 0*X0*delta + 3*delta
average(delta, X1, X0) =  + 1*X0 + 1*X1 + 2 + 0*X0*delta + 2*X1*delta + 0*delta
s_tau_1(delta) = delta/(1 + 0 * delta)
average_tau_1(delta) = delta/(1 + 2 * delta)
average_tau_2(delta) = delta/(1 + 0 * delta)

Time: 59.632922 seconds
Statistics:
Number of monomials: 2106
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	0.814687ms
Answer	YES(?,O(n^2))
Input	AG01 3.15

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  average(0(), s(s(0()))) -> s(0())
     , average(0(), s(0())) -> 0()
     , average(0(), 0()) -> 0()
     , average(x, s(s(s(y)))) -> s(average(s(x), y))
     , average(s(x), y) -> average(x, s(y))}
  StartTerms: all
  Strategy: none

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

Proof:
  We have the following EDA-non-satisfying matrix interpretation:
  Interpretation Functions:
   s(x1) = [1 0] x1 + [0]
           [0 1]      [1]
   average(x1, x2) = [1 3] x1 + [1 2] x2 + [1]
                     [0 1]      [0 1]      [0]
   0() = [0]
         [0]

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

Tool IDA

Execution Time	1.116714ms
Answer	YES(?,O(n^2))
Input	AG01 3.15

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  average(0(), s(s(0()))) -> s(0())
     , average(0(), s(0())) -> 0()
     , average(0(), 0()) -> 0()
     , average(x, s(s(s(y)))) -> s(average(s(x), y))
     , average(s(x), y) -> average(x, s(y))}
  StartTerms: all
  Strategy: none

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

Proof:
  We have the following EDA-non-satisfying and IDA(2)-non-satisfying matrix interpretation:
  Interpretation Functions:
   s(x1) = [1 0] x1 + [0]
           [0 1]      [1]
   average(x1, x2) = [1 3] x1 + [1 2] x2 + [1]
                     [0 1]      [0 1]      [0]
   0() = [0]
         [0]

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

Tool TRI

Execution Time	0.30597997ms
Answer	YES(?,O(n^2))
Input	AG01 3.15

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  average(0(), s(s(0()))) -> s(0())
     , average(0(), s(0())) -> 0()
     , average(0(), 0()) -> 0()
     , average(x, s(s(s(y)))) -> s(average(s(x), y))
     , average(s(x), y) -> average(x, s(y))}
  StartTerms: all
  Strategy: none

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

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

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

Tool TRI2

Execution Time	0.3201871ms
Answer	YES(?,O(n^2))
Input	AG01 3.15

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  average(0(), s(s(0()))) -> s(0())
     , average(0(), s(0())) -> 0()
     , average(0(), 0()) -> 0()
     , average(x, s(s(s(y)))) -> s(average(s(x), y))
     , average(s(x), y) -> average(x, s(y))}
  StartTerms: all
  Strategy: none

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

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

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