/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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YES
Input TRS:
    1: a__filter(cons(X,Y),0(),M) -> cons(0(),filter(Y,M,M))
    2: a__filter(cons(X,Y),s(N),M) -> cons(mark(X),filter(Y,N,M))
    3: a__sieve(cons(0(),Y)) -> cons(0(),sieve(Y))
    4: a__sieve(cons(s(N),Y)) -> cons(s(mark(N)),sieve(filter(Y,N,N)))
    5: a__nats(N) -> cons(mark(N),nats(s(N)))
    6: a__zprimes() -> a__sieve(a__nats(s(s(0()))))
    7: mark(filter(X1,X2,X3)) -> a__filter(mark(X1),mark(X2),mark(X3))
    8: mark(sieve(X)) -> a__sieve(mark(X))
    9: mark(nats(X)) -> a__nats(mark(X))
    10: mark(zprimes()) -> a__zprimes()
    11: mark(cons(X1,X2)) -> cons(mark(X1),X2)
    12: mark(0()) -> 0()
    13: mark(s(X)) -> s(mark(X))
    14: a__filter(X1,X2,X3) -> filter(X1,X2,X3)
    15: a__sieve(X) -> sieve(X)
    16: a__nats(X) -> nats(X)
    17: a__zprimes() -> zprimes()
Number of strict rules: 17
Direct poly ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #a__filter(cons(X,Y),s(N),M) -> #mark(X)
   #2: #a__zprimes() -> #a__sieve(a__nats(s(s(0()))))
   #3: #a__zprimes() -> #a__nats(s(s(0())))
   #4: #mark(s(X)) -> #mark(X)
   #5: #mark(nats(X)) -> #a__nats(mark(X))
   #6: #mark(nats(X)) -> #mark(X)
   #7: #mark(cons(X1,X2)) -> #mark(X1)
   #8: #mark(filter(X1,X2,X3)) -> #a__filter(mark(X1),mark(X2),mark(X3))
   #9: #mark(filter(X1,X2,X3)) -> #mark(X1)
   #10: #mark(filter(X1,X2,X3)) -> #mark(X2)
   #11: #mark(filter(X1,X2,X3)) -> #mark(X3)
   #12: #mark(zprimes()) -> #a__zprimes()
   #13: #a__nats(N) -> #mark(N)
   #14: #mark(sieve(X)) -> #a__sieve(mark(X))
   #15: #mark(sieve(X)) -> #mark(X)
   #16: #a__sieve(cons(s(N),Y)) -> #mark(N)
Number of SCCs: 1, DPs: 16
	SCC { #1..16 }
Sum... succeeded.
  zprimes()		w: (77005)
  s(x1)		w: (18588 + x1)
  a__zprimes()		w: (77005)
  a__nats(x1)		w: (18589 + x1)
  #a__filter(x1,x2,x3)		w: (18588 + x1)
  a__sieve(x1)		w: (1 + x1)
  #a__zprimes()		w: (114180)
  #mark(x1)		w: (37176 + x1)
  0()		w: (21238)
  #a__nats(x1)		w: (55765 + x1)
  mark(x1)		w: (x1)
  sieve(x1)		w: (1 + x1)
  nats(x1)		w: (18589 + x1)
  cons(x1,x2)		w: (18589 + x1)
  filter(x1,x2,x3)		w: (16908 + x3 + x2 + x1)
  #a__sieve(x1)		w: (x1)
  a__filter(x1,x2,x3)		w: (16908 + x3 + x2 + x1)
    USABLE RULES: { 1..17 }
    Removed DPs: #1..4 #6..16
Number of SCCs: 0, DPs: 0