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


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NO

Problem 1: 

(VAR X X1 X2 Y Z)
(RULES
activate(n__cons(X1,X2)) -> cons(X1,X2)
activate(n__filter(X1,X2)) -> filter(X1,X2)
activate(n__from(X)) -> from(X)
activate(X) -> X
cons(X1,X2) -> n__cons(X1,X2)
filter(s(s(X)),cons(Y,Z)) -> if(divides(s(s(X)),Y),n__filter(s(s(X)),activate(Z)),n__cons(Y,n__filter(X,sieve(Y))))
filter(X1,X2) -> n__filter(X1,X2)
from(X) -> cons(X,n__from(s(X)))
from(X) -> n__from(X)
head(cons(X,Y)) -> X
if(false,X,Y) -> activate(Y)
if(true,X,Y) -> activate(X)
primes -> sieve(from(s(s(0))))
sieve(cons(X,Y)) -> cons(X,n__filter(X,sieve(activate(Y))))
tail(cons(X,Y)) -> activate(Y)
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 ACTIVATE(n__cons(X1,X2)) -> CONS(X1,X2)
 ACTIVATE(n__filter(X1,X2)) -> FILTER(X1,X2)
 ACTIVATE(n__from(X)) -> FROM(X)
 FILTER(s(s(X)),cons(Y,Z)) -> ACTIVATE(Z)
 FILTER(s(s(X)),cons(Y,Z)) -> IF(divides(s(s(X)),Y),n__filter(s(s(X)),activate(Z)),n__cons(Y,n__filter(X,sieve(Y))))
 FILTER(s(s(X)),cons(Y,Z)) -> SIEVE(Y)
 FROM(X) -> CONS(X,n__from(s(X)))
 IF(false,X,Y) -> ACTIVATE(Y)
 IF(true,X,Y) -> ACTIVATE(X)
 PRIMES -> FROM(s(s(0)))
 PRIMES -> SIEVE(from(s(s(0))))
 SIEVE(cons(X,Y)) -> ACTIVATE(Y)
 SIEVE(cons(X,Y)) -> CONS(X,n__filter(X,sieve(activate(Y))))
 SIEVE(cons(X,Y)) -> SIEVE(activate(Y))
 TAIL(cons(X,Y)) -> ACTIVATE(Y)
-> Rules:
 activate(n__cons(X1,X2)) -> cons(X1,X2)
 activate(n__filter(X1,X2)) -> filter(X1,X2)
 activate(n__from(X)) -> from(X)
 activate(X) -> X
 cons(X1,X2) -> n__cons(X1,X2)
 filter(s(s(X)),cons(Y,Z)) -> if(divides(s(s(X)),Y),n__filter(s(s(X)),activate(Z)),n__cons(Y,n__filter(X,sieve(Y))))
 filter(X1,X2) -> n__filter(X1,X2)
 from(X) -> cons(X,n__from(s(X)))
 from(X) -> n__from(X)
 head(cons(X,Y)) -> X
 if(false,X,Y) -> activate(Y)
 if(true,X,Y) -> activate(X)
 primes -> sieve(from(s(s(0))))
 sieve(cons(X,Y)) -> cons(X,n__filter(X,sieve(activate(Y))))
 tail(cons(X,Y)) -> activate(Y)

Problem 1: 

SCC Processor:
-> Pairs:
 ACTIVATE(n__cons(X1,X2)) -> CONS(X1,X2)
 ACTIVATE(n__filter(X1,X2)) -> FILTER(X1,X2)
 ACTIVATE(n__from(X)) -> FROM(X)
 FILTER(s(s(X)),cons(Y,Z)) -> ACTIVATE(Z)
 FILTER(s(s(X)),cons(Y,Z)) -> IF(divides(s(s(X)),Y),n__filter(s(s(X)),activate(Z)),n__cons(Y,n__filter(X,sieve(Y))))
 FILTER(s(s(X)),cons(Y,Z)) -> SIEVE(Y)
 FROM(X) -> CONS(X,n__from(s(X)))
 IF(false,X,Y) -> ACTIVATE(Y)
 IF(true,X,Y) -> ACTIVATE(X)
 PRIMES -> FROM(s(s(0)))
 PRIMES -> SIEVE(from(s(s(0))))
 SIEVE(cons(X,Y)) -> ACTIVATE(Y)
 SIEVE(cons(X,Y)) -> CONS(X,n__filter(X,sieve(activate(Y))))
 SIEVE(cons(X,Y)) -> SIEVE(activate(Y))
 TAIL(cons(X,Y)) -> ACTIVATE(Y)
-> Rules:
 activate(n__cons(X1,X2)) -> cons(X1,X2)
 activate(n__filter(X1,X2)) -> filter(X1,X2)
 activate(n__from(X)) -> from(X)
 activate(X) -> X
 cons(X1,X2) -> n__cons(X1,X2)
 filter(s(s(X)),cons(Y,Z)) -> if(divides(s(s(X)),Y),n__filter(s(s(X)),activate(Z)),n__cons(Y,n__filter(X,sieve(Y))))
 filter(X1,X2) -> n__filter(X1,X2)
 from(X) -> cons(X,n__from(s(X)))
 from(X) -> n__from(X)
 head(cons(X,Y)) -> X
 if(false,X,Y) -> activate(Y)
 if(true,X,Y) -> activate(X)
 primes -> sieve(from(s(s(0))))
 sieve(cons(X,Y)) -> cons(X,n__filter(X,sieve(activate(Y))))
 tail(cons(X,Y)) -> activate(Y)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ACTIVATE(n__filter(X1,X2)) -> FILTER(X1,X2)
 FILTER(s(s(X)),cons(Y,Z)) -> ACTIVATE(Z)
 FILTER(s(s(X)),cons(Y,Z)) -> SIEVE(Y)
 SIEVE(cons(X,Y)) -> ACTIVATE(Y)
 SIEVE(cons(X,Y)) -> SIEVE(activate(Y))
->->-> Rules:
 activate(n__cons(X1,X2)) -> cons(X1,X2)
 activate(n__filter(X1,X2)) -> filter(X1,X2)
 activate(n__from(X)) -> from(X)
 activate(X) -> X
 cons(X1,X2) -> n__cons(X1,X2)
 filter(s(s(X)),cons(Y,Z)) -> if(divides(s(s(X)),Y),n__filter(s(s(X)),activate(Z)),n__cons(Y,n__filter(X,sieve(Y))))
 filter(X1,X2) -> n__filter(X1,X2)
 from(X) -> cons(X,n__from(s(X)))
 from(X) -> n__from(X)
 head(cons(X,Y)) -> X
 if(false,X,Y) -> activate(Y)
 if(true,X,Y) -> activate(X)
 primes -> sieve(from(s(s(0))))
 sieve(cons(X,Y)) -> cons(X,n__filter(X,sieve(activate(Y))))
 tail(cons(X,Y)) -> activate(Y)

Problem 1: 

Narrowing Processor:
-> Pairs:
 ACTIVATE(n__filter(X1,X2)) -> FILTER(X1,X2)
 FILTER(s(s(X)),cons(Y,Z)) -> ACTIVATE(Z)
 FILTER(s(s(X)),cons(Y,Z)) -> SIEVE(Y)
 SIEVE(cons(X,Y)) -> ACTIVATE(Y)
 SIEVE(cons(X,Y)) -> SIEVE(activate(Y))
-> Rules:
 activate(n__cons(X1,X2)) -> cons(X1,X2)
 activate(n__filter(X1,X2)) -> filter(X1,X2)
 activate(n__from(X)) -> from(X)
 activate(X) -> X
 cons(X1,X2) -> n__cons(X1,X2)
 filter(s(s(X)),cons(Y,Z)) -> if(divides(s(s(X)),Y),n__filter(s(s(X)),activate(Z)),n__cons(Y,n__filter(X,sieve(Y))))
 filter(X1,X2) -> n__filter(X1,X2)
 from(X) -> cons(X,n__from(s(X)))
 from(X) -> n__from(X)
 head(cons(X,Y)) -> X
 if(false,X,Y) -> activate(Y)
 if(true,X,Y) -> activate(X)
 primes -> sieve(from(s(s(0))))
 sieve(cons(X,Y)) -> cons(X,n__filter(X,sieve(activate(Y))))
 tail(cons(X,Y)) -> activate(Y)
->Narrowed Pairs:
->->Original Pair:
 SIEVE(cons(X,Y)) -> SIEVE(activate(Y))
->-> Narrowed pairs:
 SIEVE(cons(x15,n__cons(X1,X2))) -> SIEVE(cons(X1,X2))
 SIEVE(cons(x15,n__filter(X1,X2))) -> SIEVE(filter(X1,X2))
 SIEVE(cons(x15,n__from(X))) -> SIEVE(from(X))
 SIEVE(cons(x15,X)) -> SIEVE(X)

Problem 1: 

SCC Processor:
-> Pairs:
 ACTIVATE(n__filter(X1,X2)) -> FILTER(X1,X2)
 FILTER(s(s(X)),cons(Y,Z)) -> ACTIVATE(Z)
 FILTER(s(s(X)),cons(Y,Z)) -> SIEVE(Y)
 SIEVE(cons(X,Y)) -> ACTIVATE(Y)
 SIEVE(cons(x15,n__cons(X1,X2))) -> SIEVE(cons(X1,X2))
 SIEVE(cons(x15,n__filter(X1,X2))) -> SIEVE(filter(X1,X2))
 SIEVE(cons(x15,n__from(X))) -> SIEVE(from(X))
 SIEVE(cons(x15,X)) -> SIEVE(X)
-> Rules:
 activate(n__cons(X1,X2)) -> cons(X1,X2)
 activate(n__filter(X1,X2)) -> filter(X1,X2)
 activate(n__from(X)) -> from(X)
 activate(X) -> X
 cons(X1,X2) -> n__cons(X1,X2)
 filter(s(s(X)),cons(Y,Z)) -> if(divides(s(s(X)),Y),n__filter(s(s(X)),activate(Z)),n__cons(Y,n__filter(X,sieve(Y))))
 filter(X1,X2) -> n__filter(X1,X2)
 from(X) -> cons(X,n__from(s(X)))
 from(X) -> n__from(X)
 head(cons(X,Y)) -> X
 if(false,X,Y) -> activate(Y)
 if(true,X,Y) -> activate(X)
 primes -> sieve(from(s(s(0))))
 sieve(cons(X,Y)) -> cons(X,n__filter(X,sieve(activate(Y))))
 tail(cons(X,Y)) -> activate(Y)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ACTIVATE(n__filter(X1,X2)) -> FILTER(X1,X2)
 FILTER(s(s(X)),cons(Y,Z)) -> ACTIVATE(Z)
 FILTER(s(s(X)),cons(Y,Z)) -> SIEVE(Y)
 SIEVE(cons(X,Y)) -> ACTIVATE(Y)
 SIEVE(cons(x15,n__cons(X1,X2))) -> SIEVE(cons(X1,X2))
 SIEVE(cons(x15,n__filter(X1,X2))) -> SIEVE(filter(X1,X2))
 SIEVE(cons(x15,n__from(X))) -> SIEVE(from(X))
 SIEVE(cons(x15,X)) -> SIEVE(X)
->->-> Rules:
 activate(n__cons(X1,X2)) -> cons(X1,X2)
 activate(n__filter(X1,X2)) -> filter(X1,X2)
 activate(n__from(X)) -> from(X)
 activate(X) -> X
 cons(X1,X2) -> n__cons(X1,X2)
 filter(s(s(X)),cons(Y,Z)) -> if(divides(s(s(X)),Y),n__filter(s(s(X)),activate(Z)),n__cons(Y,n__filter(X,sieve(Y))))
 filter(X1,X2) -> n__filter(X1,X2)
 from(X) -> cons(X,n__from(s(X)))
 from(X) -> n__from(X)
 head(cons(X,Y)) -> X
 if(false,X,Y) -> activate(Y)
 if(true,X,Y) -> activate(X)
 primes -> sieve(from(s(s(0))))
 sieve(cons(X,Y)) -> cons(X,n__filter(X,sieve(activate(Y))))
 tail(cons(X,Y)) -> activate(Y)

Problem 1: 

Narrowing Processor:
-> Pairs:
 ACTIVATE(n__filter(X1,X2)) -> FILTER(X1,X2)
 FILTER(s(s(X)),cons(Y,Z)) -> ACTIVATE(Z)
 FILTER(s(s(X)),cons(Y,Z)) -> SIEVE(Y)
 SIEVE(cons(X,Y)) -> ACTIVATE(Y)
 SIEVE(cons(x15,n__cons(X1,X2))) -> SIEVE(cons(X1,X2))
 SIEVE(cons(x15,n__filter(X1,X2))) -> SIEVE(filter(X1,X2))
 SIEVE(cons(x15,n__from(X))) -> SIEVE(from(X))
 SIEVE(cons(x15,X)) -> SIEVE(X)
-> Rules:
 activate(n__cons(X1,X2)) -> cons(X1,X2)
 activate(n__filter(X1,X2)) -> filter(X1,X2)
 activate(n__from(X)) -> from(X)
 activate(X) -> X
 cons(X1,X2) -> n__cons(X1,X2)
 filter(s(s(X)),cons(Y,Z)) -> if(divides(s(s(X)),Y),n__filter(s(s(X)),activate(Z)),n__cons(Y,n__filter(X,sieve(Y))))
 filter(X1,X2) -> n__filter(X1,X2)
 from(X) -> cons(X,n__from(s(X)))
 from(X) -> n__from(X)
 head(cons(X,Y)) -> X
 if(false,X,Y) -> activate(Y)
 if(true,X,Y) -> activate(X)
 primes -> sieve(from(s(s(0))))
 sieve(cons(X,Y)) -> cons(X,n__filter(X,sieve(activate(Y))))
 tail(cons(X,Y)) -> activate(Y)
->Narrowed Pairs:
->->Original Pair:
 SIEVE(cons(x15,n__filter(X1,X2))) -> SIEVE(filter(X1,X2))
->-> Narrowed pairs:
 SIEVE(cons(x31,n__filter(s(s(X)),cons(Y,Z)))) -> SIEVE(if(divides(s(s(X)),Y),n__filter(s(s(X)),activate(Z)),n__cons(Y,n__filter(X,sieve(Y)))))
 SIEVE(cons(x31,n__filter(X1,X2))) -> SIEVE(n__filter(X1,X2))
->->Original Pair:
 SIEVE(cons(x15,n__from(X))) -> SIEVE(from(X))
->-> Narrowed pairs:
 SIEVE(cons(x33,n__from(X))) -> SIEVE(cons(X,n__from(s(X))))
 SIEVE(cons(x33,n__from(X))) -> SIEVE(n__from(X))

Problem 1: 

Infinite Processor:
-> Pairs:
 ACTIVATE(n__filter(X1,X2)) -> FILTER(X1,X2)
 FILTER(s(s(X)),cons(Y,Z)) -> ACTIVATE(Z)
 FILTER(s(s(X)),cons(Y,Z)) -> SIEVE(Y)
 SIEVE(cons(X,Y)) -> ACTIVATE(Y)
 SIEVE(cons(x15,n__cons(X1,X2))) -> SIEVE(cons(X1,X2))
 SIEVE(cons(x15,X)) -> SIEVE(X)
 SIEVE(cons(x31,n__filter(s(s(X)),cons(Y,Z)))) -> SIEVE(if(divides(s(s(X)),Y),n__filter(s(s(X)),activate(Z)),n__cons(Y,n__filter(X,sieve(Y)))))
 SIEVE(cons(x31,n__filter(X1,X2))) -> SIEVE(n__filter(X1,X2))
 SIEVE(cons(x33,n__from(X))) -> SIEVE(cons(X,n__from(s(X))))
 SIEVE(cons(x33,n__from(X))) -> SIEVE(n__from(X))
-> Rules:
 activate(n__cons(X1,X2)) -> cons(X1,X2)
 activate(n__filter(X1,X2)) -> filter(X1,X2)
 activate(n__from(X)) -> from(X)
 activate(X) -> X
 cons(X1,X2) -> n__cons(X1,X2)
 filter(s(s(X)),cons(Y,Z)) -> if(divides(s(s(X)),Y),n__filter(s(s(X)),activate(Z)),n__cons(Y,n__filter(X,sieve(Y))))
 filter(X1,X2) -> n__filter(X1,X2)
 from(X) -> cons(X,n__from(s(X)))
 from(X) -> n__from(X)
 head(cons(X,Y)) -> X
 if(false,X,Y) -> activate(Y)
 if(true,X,Y) -> activate(X)
 primes -> sieve(from(s(s(0))))
 sieve(cons(X,Y)) -> cons(X,n__filter(X,sieve(activate(Y))))
 tail(cons(X,Y)) -> activate(Y)
-> Pairs in cycle:
 SIEVE(cons(x33,n__from(X))) -> SIEVE(cons(X,n__from(s(X))))

The problem is infinite.