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


--------------------------------------------------------------------------------


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

WORST_CASE(Omega(n^1),?)