/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(XS)
            from(X) -> cons(X,from(s(X)))
            head(cons(X,XS)) -> X
            sel(0(),cons(X,XS)) -> X
            sel(s(N),cons(X,XS)) -> sel(N,XS)
            take(0(),XS) -> nil()
            take(s(N),cons(X,XS)) -> cons(X,take(N,XS))
        - Signature:
            {2nd/1,from/1,head/1,sel/2,take/2} / {0/0,cons/2,nil/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {2nd,from,head,sel,take} and constructors {0,cons,nil,s}
    + 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(XS)
            from(X) -> cons(X,from(s(X)))
            head(cons(X,XS)) -> X
            sel(0(),cons(X,XS)) -> X
            sel(s(N),cons(X,XS)) -> sel(N,XS)
            take(0(),XS) -> nil()
            take(s(N),cons(X,XS)) -> cons(X,take(N,XS))
        - Signature:
            {2nd/1,from/1,head/1,sel/2,take/2} / {0/0,cons/2,nil/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {2nd,from,head,sel,take} and constructors {0,cons,nil,s}
    + 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(XS)
            from(X) -> cons(X,from(s(X)))
            head(cons(X,XS)) -> X
            sel(0(),cons(X,XS)) -> X
            sel(s(N),cons(X,XS)) -> sel(N,XS)
            take(0(),XS) -> nil()
            take(s(N),cons(X,XS)) -> cons(X,take(N,XS))
        - Signature:
            {2nd/1,from/1,head/1,sel/2,take/2} / {0/0,cons/2,nil/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {2nd,from,head,sel,take} and constructors {0,cons,nil,s}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          sel(x,z){x -> s(x),z -> cons(y,z)} =
            sel(s(x),cons(y,z)) ->^+ sel(x,z)
              = C[sel(x,z) = sel(x,z){}]

WORST_CASE(Omega(n^1),?)