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

WORST_CASE(Omega(n^1),?)