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


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WORST_CASE(Omega(n^1),?)
* Step 1: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            a__filter(X1,X2) -> filter(X1,X2)
            a__filter(s(s(X)),cons(Y,Z)) -> a__if(divides(s(s(mark(X))),mark(Y))
                                                 ,filter(s(s(X)),Z)
                                                 ,cons(Y,filter(X,sieve(Y))))
            a__from(X) -> cons(mark(X),from(s(X)))
            a__from(X) -> from(X)
            a__head(X) -> head(X)
            a__head(cons(X,Y)) -> mark(X)
            a__if(X1,X2,X3) -> if(X1,X2,X3)
            a__if(false(),X,Y) -> mark(Y)
            a__if(true(),X,Y) -> mark(X)
            a__primes() -> a__sieve(a__from(s(s(0()))))
            a__primes() -> primes()
            a__sieve(X) -> sieve(X)
            a__sieve(cons(X,Y)) -> cons(mark(X),filter(X,sieve(Y)))
            a__tail(X) -> tail(X)
            a__tail(cons(X,Y)) -> mark(Y)
            mark(0()) -> 0()
            mark(cons(X1,X2)) -> cons(mark(X1),X2)
            mark(divides(X1,X2)) -> divides(mark(X1),mark(X2))
            mark(false()) -> false()
            mark(filter(X1,X2)) -> a__filter(mark(X1),mark(X2))
            mark(from(X)) -> a__from(mark(X))
            mark(head(X)) -> a__head(mark(X))
            mark(if(X1,X2,X3)) -> a__if(mark(X1),X2,X3)
            mark(primes()) -> a__primes()
            mark(s(X)) -> s(mark(X))
            mark(sieve(X)) -> a__sieve(mark(X))
            mark(tail(X)) -> a__tail(mark(X))
            mark(true()) -> true()
        - Signature:
            {a__filter/2,a__from/1,a__head/1,a__if/3,a__primes/0,a__sieve/1,a__tail/1,mark/1} / {0/0,cons/2,divides/2
            ,false/0,filter/2,from/1,head/1,if/3,primes/0,s/1,sieve/1,tail/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {a__filter,a__from,a__head,a__if,a__primes,a__sieve,a__tail
            ,mark} and constructors {0,cons,divides,false,filter,from,head,if,primes,s,sieve,tail,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            a__filter(X1,X2) -> filter(X1,X2)
            a__filter(s(s(X)),cons(Y,Z)) -> a__if(divides(s(s(mark(X))),mark(Y))
                                                 ,filter(s(s(X)),Z)
                                                 ,cons(Y,filter(X,sieve(Y))))
            a__from(X) -> cons(mark(X),from(s(X)))
            a__from(X) -> from(X)
            a__head(X) -> head(X)
            a__head(cons(X,Y)) -> mark(X)
            a__if(X1,X2,X3) -> if(X1,X2,X3)
            a__if(false(),X,Y) -> mark(Y)
            a__if(true(),X,Y) -> mark(X)
            a__primes() -> a__sieve(a__from(s(s(0()))))
            a__primes() -> primes()
            a__sieve(X) -> sieve(X)
            a__sieve(cons(X,Y)) -> cons(mark(X),filter(X,sieve(Y)))
            a__tail(X) -> tail(X)
            a__tail(cons(X,Y)) -> mark(Y)
            mark(0()) -> 0()
            mark(cons(X1,X2)) -> cons(mark(X1),X2)
            mark(divides(X1,X2)) -> divides(mark(X1),mark(X2))
            mark(false()) -> false()
            mark(filter(X1,X2)) -> a__filter(mark(X1),mark(X2))
            mark(from(X)) -> a__from(mark(X))
            mark(head(X)) -> a__head(mark(X))
            mark(if(X1,X2,X3)) -> a__if(mark(X1),X2,X3)
            mark(primes()) -> a__primes()
            mark(s(X)) -> s(mark(X))
            mark(sieve(X)) -> a__sieve(mark(X))
            mark(tail(X)) -> a__tail(mark(X))
            mark(true()) -> true()
        - Signature:
            {a__filter/2,a__from/1,a__head/1,a__if/3,a__primes/0,a__sieve/1,a__tail/1,mark/1} / {0/0,cons/2,divides/2
            ,false/0,filter/2,from/1,head/1,if/3,primes/0,s/1,sieve/1,tail/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {a__filter,a__from,a__head,a__if,a__primes,a__sieve,a__tail
            ,mark} and constructors {0,cons,divides,false,filter,from,head,if,primes,s,sieve,tail,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            a__filter(X1,X2) -> filter(X1,X2)
            a__filter(s(s(X)),cons(Y,Z)) -> a__if(divides(s(s(mark(X))),mark(Y))
                                                 ,filter(s(s(X)),Z)
                                                 ,cons(Y,filter(X,sieve(Y))))
            a__from(X) -> cons(mark(X),from(s(X)))
            a__from(X) -> from(X)
            a__head(X) -> head(X)
            a__head(cons(X,Y)) -> mark(X)
            a__if(X1,X2,X3) -> if(X1,X2,X3)
            a__if(false(),X,Y) -> mark(Y)
            a__if(true(),X,Y) -> mark(X)
            a__primes() -> a__sieve(a__from(s(s(0()))))
            a__primes() -> primes()
            a__sieve(X) -> sieve(X)
            a__sieve(cons(X,Y)) -> cons(mark(X),filter(X,sieve(Y)))
            a__tail(X) -> tail(X)
            a__tail(cons(X,Y)) -> mark(Y)
            mark(0()) -> 0()
            mark(cons(X1,X2)) -> cons(mark(X1),X2)
            mark(divides(X1,X2)) -> divides(mark(X1),mark(X2))
            mark(false()) -> false()
            mark(filter(X1,X2)) -> a__filter(mark(X1),mark(X2))
            mark(from(X)) -> a__from(mark(X))
            mark(head(X)) -> a__head(mark(X))
            mark(if(X1,X2,X3)) -> a__if(mark(X1),X2,X3)
            mark(primes()) -> a__primes()
            mark(s(X)) -> s(mark(X))
            mark(sieve(X)) -> a__sieve(mark(X))
            mark(tail(X)) -> a__tail(mark(X))
            mark(true()) -> true()
        - Signature:
            {a__filter/2,a__from/1,a__head/1,a__if/3,a__primes/0,a__sieve/1,a__tail/1,mark/1} / {0/0,cons/2,divides/2
            ,false/0,filter/2,from/1,head/1,if/3,primes/0,s/1,sieve/1,tail/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {a__filter,a__from,a__head,a__if,a__primes,a__sieve,a__tail
            ,mark} and constructors {0,cons,divides,false,filter,from,head,if,primes,s,sieve,tail,true}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          mark(x){x -> cons(x,y)} =
            mark(cons(x,y)) ->^+ cons(mark(x),y)
              = C[mark(x) = mark(x){}]

WORST_CASE(Omega(n^1),?)