/home/nowonder/forschung/aprove/TPDB05/TRS/TRCSR/Ex9_BLR02_C.trs

The program

(VAR X Y M N X1 X2 X3)
(RULES 
active(filter(cons(X,Y),0,M)) -> mark(cons(0,filter(Y,M,M)))
active(filter(cons(X,Y),s(N),M)) -> mark(cons(X,filter(Y,N,M)))
active(sieve(cons(0,Y))) -> mark(cons(0,sieve(Y)))
active(sieve(cons(s(N),Y))) -> mark(cons(s(N),sieve(filter(Y,N,N))))
active(nats(N)) -> mark(cons(N,nats(s(N))))
active(zprimes) -> mark(sieve(nats(s(s(0)))))
active(filter(X1,X2,X3)) -> filter(active(X1),X2,X3)
active(filter(X1,X2,X3)) -> filter(X1,active(X2),X3)
active(filter(X1,X2,X3)) -> filter(X1,X2,active(X3))
active(cons(X1,X2)) -> cons(active(X1),X2)
active(s(X)) -> s(active(X))
active(sieve(X)) -> sieve(active(X))
active(nats(X)) -> nats(active(X))
filter(mark(X1),X2,X3) -> mark(filter(X1,X2,X3))
filter(X1,mark(X2),X3) -> mark(filter(X1,X2,X3))
filter(X1,X2,mark(X3)) -> mark(filter(X1,X2,X3))
cons(mark(X1),X2) -> mark(cons(X1,X2))
s(mark(X)) -> mark(s(X))
sieve(mark(X)) -> mark(sieve(X))
nats(mark(X)) -> mark(nats(X))
proper(filter(X1,X2,X3)) -> filter(proper(X1),proper(X2),proper(X3))
proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
proper(0) -> ok(0)
proper(s(X)) -> s(proper(X))
proper(sieve(X)) -> sieve(proper(X))
proper(nats(X)) -> nats(proper(X))
proper(zprimes) -> ok(zprimes)
filter(ok(X1),ok(X2),ok(X3)) -> ok(filter(X1,X2,X3))
cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
s(ok(X)) -> ok(s(X))
sieve(ok(X)) -> ok(sieve(X))
nats(ok(X)) -> ok(nats(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
)

Submit to AProVE Web Frontend

Edit in AProVE Web Frontend