/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES
Input TRS:
    1: a__primes() -> a__sieve(a__from(s(s(0()))))
    2: a__from(X) -> cons(mark(X),from(s(X)))
    3: a__head(cons(X,Y)) -> mark(X)
    4: a__tail(cons(X,Y)) -> mark(Y)
    5: a__if(true(),X,Y) -> mark(X)
    6: a__if(false(),X,Y) -> mark(Y)
    7: a__filter(s(s(X)),cons(Y,Z)) -> a__if(divides(s(s(mark(X))),mark(Y)),filter(s(s(X)),Z),cons(Y,filter(X,sieve(Y))))
    8: a__sieve(cons(X,Y)) -> cons(mark(X),filter(X,sieve(Y)))
    9: mark(primes()) -> a__primes()
    10: mark(sieve(X)) -> a__sieve(mark(X))
    11: mark(from(X)) -> a__from(mark(X))
    12: mark(head(X)) -> a__head(mark(X))
    13: mark(tail(X)) -> a__tail(mark(X))
    14: mark(if(X1,X2,X3)) -> a__if(mark(X1),X2,X3)
    15: mark(filter(X1,X2)) -> a__filter(mark(X1),mark(X2))
    16: mark(s(X)) -> s(mark(X))
    17: mark(0()) -> 0()
    18: mark(cons(X1,X2)) -> cons(mark(X1),X2)
    19: mark(true()) -> true()
    20: mark(false()) -> false()
    21: mark(divides(X1,X2)) -> divides(mark(X1),mark(X2))
    22: a__primes() -> primes()
    23: a__sieve(X) -> sieve(X)
    24: a__from(X) -> from(X)
    25: a__head(X) -> head(X)
    26: a__tail(X) -> tail(X)
    27: a__if(X1,X2,X3) -> if(X1,X2,X3)
    28: a__filter(X1,X2) -> filter(X1,X2)
Number of strict rules: 28
Direct poly ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #a__from(X) -> #mark(X)
   #2: #a__if(false(),X,Y) -> #mark(Y)
   #3: #mark(tail(X)) -> #a__tail(mark(X))
   #4: #mark(tail(X)) -> #mark(X)
   #5: #mark(primes()) -> #a__primes()
   #6: #mark(from(X)) -> #a__from(mark(X))
   #7: #mark(from(X)) -> #mark(X)
   #8: #mark(head(X)) -> #a__head(mark(X))
   #9: #mark(head(X)) -> #mark(X)
   #10: #mark(if(X1,X2,X3)) -> #a__if(mark(X1),X2,X3)
   #11: #mark(if(X1,X2,X3)) -> #mark(X1)
   #12: #a__filter(s(s(X)),cons(Y,Z)) -> #a__if(divides(s(s(mark(X))),mark(Y)),filter(s(s(X)),Z),cons(Y,filter(X,sieve(Y))))
   #13: #a__filter(s(s(X)),cons(Y,Z)) -> #mark(X)
   #14: #a__filter(s(s(X)),cons(Y,Z)) -> #mark(Y)
   #15: #mark(sieve(X)) -> #a__sieve(mark(X))
   #16: #mark(sieve(X)) -> #mark(X)
   #17: #a__if(true(),X,Y) -> #mark(X)
   #18: #mark(divides(X1,X2)) -> #mark(X1)
   #19: #mark(divides(X1,X2)) -> #mark(X2)
   #20: #mark(s(X)) -> #mark(X)
   #21: #a__head(cons(X,Y)) -> #mark(X)
   #22: #a__primes() -> #a__sieve(a__from(s(s(0()))))
   #23: #a__primes() -> #a__from(s(s(0())))
   #24: #a__sieve(cons(X,Y)) -> #mark(X)
   #25: #mark(filter(X1,X2)) -> #a__filter(mark(X1),mark(X2))
   #26: #mark(filter(X1,X2)) -> #mark(X1)
   #27: #mark(filter(X1,X2)) -> #mark(X2)
   #28: #a__tail(cons(X,Y)) -> #mark(Y)
   #29: #mark(cons(X1,X2)) -> #mark(X1)
Number of SCCs: 1, DPs: 28
	SCC { #1..11 #13..29 }
Sum... Max... succeeded.
  s(x1)		w: (x1)
  #a__head(x1)		w: (66471 + x1)
  #a__from(x1)		w: (66471 + x1)
  a__from(x1)		w: (2 + x1)
  false()		w: (12457)
  #a__filter(x1,x2)		w: (max{66470 + x2, 66472 + x1})
  a__sieve(x1)		w: (2 + x1)
  true()		w: (36070)
  tail(x1)		w: (12619 + x1)
  #mark(x1)		w: (66470 + x1)
  0()		w: (1)
  if(x1,x2,x3)		w: (max{x3, x2, 1 + x1})
  #a__primes()		w: (66475)
  from(x1)		w: (2 + x1)
  mark(x1)		w: (x1)
  sieve(x1)		w: (2 + x1)
  #a__if(x1,x2,x3)		w: (max{66470 + x3, 66470 + x2, 30401 + x1})
  head(x1)		w: (2 + x1)
  cons(x1,x2)		w: (max{x2, 2 + x1})
  a__primes()		w: (6)
  filter(x1,x2)		w: (max{x2, 2 + x1})
  primes()		w: (6)
  #a__sieve(x1)		w: (66471 + x1)
  divides(x1,x2)		w: (max{1 + x2, 1 + x1})
  a__tail(x1)		w: (12619 + x1)
  a__filter(x1,x2)		w: (max{x2, 2 + x1})
  #a__tail(x1)		w: (66471 + x1)
  a__if(x1,x2,x3)		w: (max{x3, x2, 1 + x1})
  a__head(x1)		w: (2 + x1)
    USABLE RULES: { 1..28 }
    Removed DPs: #1 #3..9 #11 #13..16 #18 #19 #21..24 #26 #28 #29
Number of SCCs: 1, DPs: 5
	SCC { #2 #10 #17 #20 #27 }
Sum... succeeded.
  s(x1)		w: (1 + x1)
  #a__head(x1)		w: (0)
  #a__from(x1)		w: (0)
  a__from(x1)		w: (1 + x1)
  false()		w: (2)
  #a__filter(x1,x2)		w: (1)
  a__sieve(x1)		w: (3)
  true()		w: (2)
  tail(x1)		w: (1 + x1)
  #mark(x1)		w: (840 + x1)
  0()		w: (18589)
  if(x1,x2,x3)		w: (2 + x3 + x2 + x1)
  #a__primes()		w: (0)
  from(x1)		w: (2 + x1)
  mark(x1)		w: (1)
  sieve(x1)		w: (4)
  #a__if(x1,x2,x3)		w: (841 + x3 + x2)
  head(x1)		w: (1)
  cons(x1,x2)		w: (3 + x1)
  a__primes()		w: (2)
  filter(x1,x2)		w: (593 + x2 + x1)
  primes()		w: (3)
  #a__sieve(x1)		w: (0)
  divides(x1,x2)		w: (2)
  a__tail(x1)		w: (0)
  a__filter(x1,x2)		w: (592)
  #a__tail(x1)		w: (0)
  a__if(x1,x2,x3)		w: (x2)
  a__head(x1)		w: (0)
    USABLE RULES: { }
    Removed DPs: #2 #10 #17 #20 #27
Number of SCCs: 0, DPs: 0