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


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WORST_CASE(Omega(n^1),?)
* Step 1: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            activate(X) -> X
            activate(n__filter(X1,X2,X3)) -> filter(X1,X2,X3)
            activate(n__nats(X)) -> nats(X)
            activate(n__sieve(X)) -> sieve(X)
            filter(X1,X2,X3) -> n__filter(X1,X2,X3)
            filter(cons(X,Y),0(),M) -> cons(0(),n__filter(activate(Y),M,M))
            filter(cons(X,Y),s(N),M) -> cons(X,n__filter(activate(Y),N,M))
            nats(N) -> cons(N,n__nats(s(N)))
            nats(X) -> n__nats(X)
            sieve(X) -> n__sieve(X)
            sieve(cons(0(),Y)) -> cons(0(),n__sieve(activate(Y)))
            sieve(cons(s(N),Y)) -> cons(s(N),n__sieve(filter(activate(Y),N,N)))
            zprimes() -> sieve(nats(s(s(0()))))
        - Signature:
            {activate/1,filter/3,nats/1,sieve/1,zprimes/0} / {0/0,cons/2,n__filter/3,n__nats/1,n__sieve/1,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {activate,filter,nats,sieve,zprimes} and constructors {0,cons
            ,n__filter,n__nats,n__sieve,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            activate(X) -> X
            activate(n__filter(X1,X2,X3)) -> filter(X1,X2,X3)
            activate(n__nats(X)) -> nats(X)
            activate(n__sieve(X)) -> sieve(X)
            filter(X1,X2,X3) -> n__filter(X1,X2,X3)
            filter(cons(X,Y),0(),M) -> cons(0(),n__filter(activate(Y),M,M))
            filter(cons(X,Y),s(N),M) -> cons(X,n__filter(activate(Y),N,M))
            nats(N) -> cons(N,n__nats(s(N)))
            nats(X) -> n__nats(X)
            sieve(X) -> n__sieve(X)
            sieve(cons(0(),Y)) -> cons(0(),n__sieve(activate(Y)))
            sieve(cons(s(N),Y)) -> cons(s(N),n__sieve(filter(activate(Y),N,N)))
            zprimes() -> sieve(nats(s(s(0()))))
        - Signature:
            {activate/1,filter/3,nats/1,sieve/1,zprimes/0} / {0/0,cons/2,n__filter/3,n__nats/1,n__sieve/1,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {activate,filter,nats,sieve,zprimes} and constructors {0,cons
            ,n__filter,n__nats,n__sieve,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            activate(X) -> X
            activate(n__filter(X1,X2,X3)) -> filter(X1,X2,X3)
            activate(n__nats(X)) -> nats(X)
            activate(n__sieve(X)) -> sieve(X)
            filter(X1,X2,X3) -> n__filter(X1,X2,X3)
            filter(cons(X,Y),0(),M) -> cons(0(),n__filter(activate(Y),M,M))
            filter(cons(X,Y),s(N),M) -> cons(X,n__filter(activate(Y),N,M))
            nats(N) -> cons(N,n__nats(s(N)))
            nats(X) -> n__nats(X)
            sieve(X) -> n__sieve(X)
            sieve(cons(0(),Y)) -> cons(0(),n__sieve(activate(Y)))
            sieve(cons(s(N),Y)) -> cons(s(N),n__sieve(filter(activate(Y),N,N)))
            zprimes() -> sieve(nats(s(s(0()))))
        - Signature:
            {activate/1,filter/3,nats/1,sieve/1,zprimes/0} / {0/0,cons/2,n__filter/3,n__nats/1,n__sieve/1,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {activate,filter,nats,sieve,zprimes} and constructors {0,cons
            ,n__filter,n__nats,n__sieve,s}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          activate(z){z -> n__filter(cons(x,z),0(),v)} =
            activate(n__filter(cons(x,z),0(),v)) ->^+ cons(0(),n__filter(activate(z),v,v))
              = C[activate(z) = activate(z){}]

WORST_CASE(Omega(n^1),?)