/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:
            2nd(cons(X,XS)) -> head(activate(XS))
            activate(X) -> X
            activate(n__from(X)) -> from(activate(X))
            activate(n__s(X)) -> s(activate(X))
            activate(n__take(X1,X2)) -> take(activate(X1),activate(X2))
            from(X) -> cons(X,n__from(n__s(X)))
            from(X) -> n__from(X)
            head(cons(X,XS)) -> X
            s(X) -> n__s(X)
            sel(0(),cons(X,XS)) -> X
            sel(s(N),cons(X,XS)) -> sel(N,activate(XS))
            take(X1,X2) -> n__take(X1,X2)
            take(0(),XS) -> nil()
            take(s(N),cons(X,XS)) -> cons(X,n__take(N,activate(XS)))
        - Signature:
            {2nd/1,activate/1,from/1,head/1,s/1,sel/2,take/2} / {0/0,cons/2,n__from/1,n__s/1,n__take/2,nil/0}
        - Obligation:
             runtime complexity wrt. defined symbols {2nd,activate,from,head,s,sel,take} and constructors {0,cons
            ,n__from,n__s,n__take,nil}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            2nd(cons(X,XS)) -> head(activate(XS))
            activate(X) -> X
            activate(n__from(X)) -> from(activate(X))
            activate(n__s(X)) -> s(activate(X))
            activate(n__take(X1,X2)) -> take(activate(X1),activate(X2))
            from(X) -> cons(X,n__from(n__s(X)))
            from(X) -> n__from(X)
            head(cons(X,XS)) -> X
            s(X) -> n__s(X)
            sel(0(),cons(X,XS)) -> X
            sel(s(N),cons(X,XS)) -> sel(N,activate(XS))
            take(X1,X2) -> n__take(X1,X2)
            take(0(),XS) -> nil()
            take(s(N),cons(X,XS)) -> cons(X,n__take(N,activate(XS)))
        - Signature:
            {2nd/1,activate/1,from/1,head/1,s/1,sel/2,take/2} / {0/0,cons/2,n__from/1,n__s/1,n__take/2,nil/0}
        - Obligation:
             runtime complexity wrt. defined symbols {2nd,activate,from,head,s,sel,take} and constructors {0,cons
            ,n__from,n__s,n__take,nil}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            2nd(cons(X,XS)) -> head(activate(XS))
            activate(X) -> X
            activate(n__from(X)) -> from(activate(X))
            activate(n__s(X)) -> s(activate(X))
            activate(n__take(X1,X2)) -> take(activate(X1),activate(X2))
            from(X) -> cons(X,n__from(n__s(X)))
            from(X) -> n__from(X)
            head(cons(X,XS)) -> X
            s(X) -> n__s(X)
            sel(0(),cons(X,XS)) -> X
            sel(s(N),cons(X,XS)) -> sel(N,activate(XS))
            take(X1,X2) -> n__take(X1,X2)
            take(0(),XS) -> nil()
            take(s(N),cons(X,XS)) -> cons(X,n__take(N,activate(XS)))
        - Signature:
            {2nd/1,activate/1,from/1,head/1,s/1,sel/2,take/2} / {0/0,cons/2,n__from/1,n__s/1,n__take/2,nil/0}
        - Obligation:
             runtime complexity wrt. defined symbols {2nd,activate,from,head,s,sel,take} and constructors {0,cons
            ,n__from,n__s,n__take,nil}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          activate(x){x -> n__from(x)} =
            activate(n__from(x)) ->^+ from(activate(x))
              = C[activate(x) = activate(x){}]

WORST_CASE(Omega(n^1),?)