/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__cons(X1,X2)) -> cons(activate(X1),X2)
            activate(n__filter(X1,X2)) -> filter(activate(X1),activate(X2))
            activate(n__from(X)) -> from(activate(X))
            activate(n__s(X)) -> s(activate(X))
            activate(n__sieve(X)) -> sieve(activate(X))
            cons(X1,X2) -> n__cons(X1,X2)
            filter(X1,X2) -> n__filter(X1,X2)
            filter(s(s(X)),cons(Y,Z)) -> if(divides(s(s(X)),Y)
                                           ,n__filter(n__s(n__s(X)),activate(Z))
                                           ,n__cons(Y,n__filter(X,n__sieve(Y))))
            from(X) -> cons(X,n__from(n__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()))))
            s(X) -> n__s(X)
            sieve(X) -> n__sieve(X)
            sieve(cons(X,Y)) -> cons(X,n__filter(X,n__sieve(activate(Y))))
            tail(cons(X,Y)) -> activate(Y)
        - Signature:
            {activate/1,cons/2,filter/2,from/1,head/1,if/3,primes/0,s/1,sieve/1,tail/1} / {0/0,divides/2,false/0
            ,n__cons/2,n__filter/2,n__from/1,n__s/1,n__sieve/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {activate,cons,filter,from,head,if,primes,s,sieve
            ,tail} and constructors {0,divides,false,n__cons,n__filter,n__from,n__s,n__sieve,true}
    + 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__cons(X1,X2)) -> cons(activate(X1),X2)
            activate(n__filter(X1,X2)) -> filter(activate(X1),activate(X2))
            activate(n__from(X)) -> from(activate(X))
            activate(n__s(X)) -> s(activate(X))
            activate(n__sieve(X)) -> sieve(activate(X))
            cons(X1,X2) -> n__cons(X1,X2)
            filter(X1,X2) -> n__filter(X1,X2)
            filter(s(s(X)),cons(Y,Z)) -> if(divides(s(s(X)),Y)
                                           ,n__filter(n__s(n__s(X)),activate(Z))
                                           ,n__cons(Y,n__filter(X,n__sieve(Y))))
            from(X) -> cons(X,n__from(n__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()))))
            s(X) -> n__s(X)
            sieve(X) -> n__sieve(X)
            sieve(cons(X,Y)) -> cons(X,n__filter(X,n__sieve(activate(Y))))
            tail(cons(X,Y)) -> activate(Y)
        - Signature:
            {activate/1,cons/2,filter/2,from/1,head/1,if/3,primes/0,s/1,sieve/1,tail/1} / {0/0,divides/2,false/0
            ,n__cons/2,n__filter/2,n__from/1,n__s/1,n__sieve/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {activate,cons,filter,from,head,if,primes,s,sieve
            ,tail} and constructors {0,divides,false,n__cons,n__filter,n__from,n__s,n__sieve,true}
    + 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__cons(X1,X2)) -> cons(activate(X1),X2)
            activate(n__filter(X1,X2)) -> filter(activate(X1),activate(X2))
            activate(n__from(X)) -> from(activate(X))
            activate(n__s(X)) -> s(activate(X))
            activate(n__sieve(X)) -> sieve(activate(X))
            cons(X1,X2) -> n__cons(X1,X2)
            filter(X1,X2) -> n__filter(X1,X2)
            filter(s(s(X)),cons(Y,Z)) -> if(divides(s(s(X)),Y)
                                           ,n__filter(n__s(n__s(X)),activate(Z))
                                           ,n__cons(Y,n__filter(X,n__sieve(Y))))
            from(X) -> cons(X,n__from(n__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()))))
            s(X) -> n__s(X)
            sieve(X) -> n__sieve(X)
            sieve(cons(X,Y)) -> cons(X,n__filter(X,n__sieve(activate(Y))))
            tail(cons(X,Y)) -> activate(Y)
        - Signature:
            {activate/1,cons/2,filter/2,from/1,head/1,if/3,primes/0,s/1,sieve/1,tail/1} / {0/0,divides/2,false/0
            ,n__cons/2,n__filter/2,n__from/1,n__s/1,n__sieve/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {activate,cons,filter,from,head,if,primes,s,sieve
            ,tail} and constructors {0,divides,false,n__cons,n__filter,n__from,n__s,n__sieve,true}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          activate(x){x -> n__cons(x,y)} =
            activate(n__cons(x,y)) ->^+ cons(activate(x),y)
              = C[activate(x) = activate(x){}]

WORST_CASE(Omega(n^1),?)