Problem Transformed CSR 04 Ex9 BLR02 L

Tool Bounds

Execution Time	5.6306124e-2ms
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex9 BLR02 L

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  zprimes() -> sieve(nats(s(s(0()))))
     , nats(N) -> cons(N)
     , sieve(cons(s(N))) -> cons(s(N))
     , sieve(cons(0())) -> cons(0())
     , filter(cons(X), s(N), M) -> cons(X)
     , filter(cons(X), 0(), M) -> cons(0())}
  StartTerms: all
  Strategy: none

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

Proof:
  The problem is match-bounded by 2.
  The enriched problem is compatible with the following automaton:
  {  cons_0(1) -> 1
   , cons_1(1) -> 1
   , cons_1(3) -> 1
   , cons_1(5) -> 1
   , cons_1(6) -> 1
   , cons_2(3) -> 2
   , cons_2(6) -> 1
   , 0_0() -> 1
   , 0_1() -> 5
   , filter_0(1, 1, 1) -> 1
   , s_0(1) -> 1
   , s_1(1) -> 1
   , s_1(4) -> 3
   , s_1(5) -> 4
   , s_2(4) -> 6
   , sieve_0(1) -> 1
   , sieve_1(2) -> 1
   , nats_0(1) -> 1
   , nats_1(3) -> 2
   , zprimes_0() -> 1}

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

Tool CDI

Execution Time	15.270306ms
Answer	YES(?,O(n^2))
Input	Transformed CSR 04 Ex9 BLR02 L

stdout:

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

This TRS is terminating using the deltarestricted interpretation
zprimes(delta) =  + 0 + 3*delta
nats(delta, X0) =  + 0*X0 + 0 + 2*X0*delta + 1*delta
sieve(delta, X0) =  + 1*X0 + 0 + 0*X0*delta + 1*delta
s(delta, X0) =  + 1*X0 + 0 + 0*X0*delta + 0*delta
filter(delta, X2, X1, X0) =  + 1*X0 + 0*X1 + 0*X2 + 0 + 0*X0*delta + 1*X1*delta + 1*X2*delta + 1*delta
0(delta) =  + 0 + 0*delta
cons(delta, X0) =  + 0*X0 + 0 + 2*X0*delta + 0*delta
nats_tau_1(delta) = delta/(0 + 2 * delta)
sieve_tau_1(delta) = delta/(1 + 0 * delta)
s_tau_1(delta) = delta/(1 + 0 * delta)
filter_tau_1(delta) = delta/(0 + 1 * delta)
filter_tau_2(delta) = delta/(0 + 1 * delta)
filter_tau_3(delta) = delta/(1 + 0 * delta)
cons_tau_1(delta) = delta/(0 + 2 * delta)

Time: 15.230785 seconds
Statistics:
Number of monomials: 955
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	0.17622995ms
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex9 BLR02 L

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  zprimes() -> sieve(nats(s(s(0()))))
     , nats(N) -> cons(N)
     , sieve(cons(s(N))) -> cons(s(N))
     , sieve(cons(0())) -> cons(0())
     , filter(cons(X), s(N), M) -> cons(X)
     , filter(cons(X), 0(), M) -> cons(0())}
  StartTerms: all
  Strategy: none

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

Proof:
  We have the following EDA-non-satisfying matrix interpretation:
  Interpretation Functions:
   cons(x1) = [1] x1 + [0]
   0() = [0]
   filter(x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [3]
   s(x1) = [1] x1 + [0]
   sieve(x1) = [1] x1 + [1]
   nats(x1) = [1] x1 + [1]
   zprimes() = [3]

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

Tool IDA

Execution Time	0.328609ms
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex9 BLR02 L

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  zprimes() -> sieve(nats(s(s(0()))))
     , nats(N) -> cons(N)
     , sieve(cons(s(N))) -> cons(s(N))
     , sieve(cons(0())) -> cons(0())
     , filter(cons(X), s(N), M) -> cons(X)
     , filter(cons(X), 0(), M) -> cons(0())}
  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:
   cons(x1) = [1] x1 + [0]
   0() = [0]
   filter(x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [3]
   s(x1) = [1] x1 + [0]
   sieve(x1) = [1] x1 + [1]
   nats(x1) = [1] x1 + [1]
   zprimes() = [3]

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

Tool TRI

Execution Time	9.1645956e-2ms
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex9 BLR02 L

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  zprimes() -> sieve(nats(s(s(0()))))
     , nats(N) -> cons(N)
     , sieve(cons(s(N))) -> cons(s(N))
     , sieve(cons(0())) -> cons(0())
     , filter(cons(X), s(N), M) -> cons(X)
     , filter(cons(X), 0(), M) -> cons(0())}
  StartTerms: all
  Strategy: none

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

Proof:
  We have the following triangular matrix interpretation:
  Interpretation Functions:
   cons(x1) = [1] x1 + [0]
   0() = [0]
   filter(x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [3]
   s(x1) = [1] x1 + [0]
   sieve(x1) = [1] x1 + [1]
   nats(x1) = [1] x1 + [1]
   zprimes() = [3]

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

Tool TRI2

Execution Time	0.24130201ms
Answer	YES(?,O(n^2))
Input	Transformed CSR 04 Ex9 BLR02 L

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  zprimes() -> sieve(nats(s(s(0()))))
     , nats(N) -> cons(N)
     , sieve(cons(s(N))) -> cons(s(N))
     , sieve(cons(0())) -> cons(0())
     , filter(cons(X), s(N), M) -> cons(X)
     , filter(cons(X), 0(), M) -> cons(0())}
  StartTerms: all
  Strategy: none

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

Proof:
  We have the following triangular matrix interpretation:
  Interpretation Functions:
   cons(x1) = [1 0] x1 + [0]
              [0 0]      [0]
   0() = [0]
         [0]
   filter(x1, x2, x3) = [1 3] x1 + [1 0] x2 + [1 0] x3 + [1]
                        [0 1]      [0 0]      [0 0]      [0]
   s(x1) = [1 0] x1 + [0]
           [0 0]      [0]
   sieve(x1) = [1 0] x1 + [1]
               [0 0]      [0]
   nats(x1) = [1 0] x1 + [1]
              [0 0]      [0]
   zprimes() = [3]
               [3]

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