Problem AG01 3.7

Tool Bounds

Execution Time	60.03079ms
Answer	TIMEOUT
Input	AG01 3.7

stdout:

TIMEOUT

We consider the following Problem:

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

Certificate: TIMEOUT

Proof:
  Computation stopped due to timeout after 60.0 seconds.

Arrrr..

Tool CDI

Execution Time	22.511307ms
Answer	YES(?,O(n^2))
Input	AG01 3.7

stdout:

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

This TRS is terminating using the deltarestricted interpretation
log(delta, X0) =  + 1*X0 + 0 + 1*X0*delta + 0*delta
s(delta, X0) =  + 1*X0 + 3 + 0*X0*delta + 1*delta
half(delta, X0) =  + 1*X0 + 0 + 0*X0*delta + 2*delta
0(delta) =  + 0 + 0*delta
log_tau_1(delta) = delta/(1 + 1 * delta)
s_tau_1(delta) = delta/(1 + 0 * delta)
half_tau_1(delta) = delta/(1 + 0 * delta)

Time: 22.475070 seconds
Statistics:
Number of monomials: 999
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	0.70837903ms
Answer	YES(?,O(n^2))
Input	AG01 3.7

stdout:

YES(?,O(n^2))

We consider the following Problem:

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

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

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

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

Tool IDA

Execution Time	0.89274096ms
Answer	YES(?,O(n^2))
Input	AG01 3.7

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  log(s(s(x))) -> s(log(s(half(x))))
     , log(s(0())) -> 0()
     , half(s(s(x))) -> s(half(x))
     , half(0()) -> 0()}
  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:
   0() = [0]
         [0]
   half(x1) = [1 0] x1 + [1]
              [0 1]      [0]
   s(x1) = [1 1] x1 + [0]
           [0 1]      [1]
   log(x1) = [1 2] x1 + [3]
             [0 1]      [0]

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

Tool TRI

Execution Time	0.2518239ms
Answer	YES(?,O(n^2))
Input	AG01 3.7

stdout:

YES(?,O(n^2))

We consider the following Problem:

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

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

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

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

Tool TRI2

Execution Time	0.28032804ms
Answer	YES(?,O(n^2))
Input	AG01 3.7

stdout:

YES(?,O(n^2))

We consider the following Problem:

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

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

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

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