Problem Transformed CSR 04 Ex9 BLR02 C

Tool CaT

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 Ex9 BLR02 C

stdout:

MAYBE

Problem:
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))

Proof:
Open

Tool IRC1

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 Ex9 BLR02 C

stdout:

MAYBE

Tool IRC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Transformed CSR 04 Ex9 BLR02 C

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    innermost runtime-complexity with respect to
  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))}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds

Tool RC1

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 Ex9 BLR02 C

stdout:

MAYBE

Tool RC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Transformed CSR 04 Ex9 BLR02 C

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    runtime-complexity with respect to
  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))}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds