/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:
            a__2nd(X) -> 2nd(X)
            a__2nd(cons(X,XS)) -> a__head(mark(XS))
            a__from(X) -> cons(mark(X),from(s(X)))
            a__from(X) -> from(X)
            a__head(X) -> head(X)
            a__head(cons(X,XS)) -> mark(X)
            a__sel(X1,X2) -> sel(X1,X2)
            a__sel(0(),cons(X,XS)) -> mark(X)
            a__sel(s(N),cons(X,XS)) -> a__sel(mark(N),mark(XS))
            a__take(X1,X2) -> take(X1,X2)
            a__take(0(),XS) -> nil()
            a__take(s(N),cons(X,XS)) -> cons(mark(X),take(N,XS))
            mark(0()) -> 0()
            mark(2nd(X)) -> a__2nd(mark(X))
            mark(cons(X1,X2)) -> cons(mark(X1),X2)
            mark(from(X)) -> a__from(mark(X))
            mark(head(X)) -> a__head(mark(X))
            mark(nil()) -> nil()
            mark(s(X)) -> s(mark(X))
            mark(sel(X1,X2)) -> a__sel(mark(X1),mark(X2))
            mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
        - Signature:
            {a__2nd/1,a__from/1,a__head/1,a__sel/2,a__take/2,mark/1} / {0/0,2nd/1,cons/2,from/1,head/1,nil/0,s/1,sel/2
            ,take/2}
        - Obligation:
             runtime complexity wrt. defined symbols {a__2nd,a__from,a__head,a__sel,a__take,mark} and constructors {0
            ,2nd,cons,from,head,nil,s,sel,take}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            a__2nd(X) -> 2nd(X)
            a__2nd(cons(X,XS)) -> a__head(mark(XS))
            a__from(X) -> cons(mark(X),from(s(X)))
            a__from(X) -> from(X)
            a__head(X) -> head(X)
            a__head(cons(X,XS)) -> mark(X)
            a__sel(X1,X2) -> sel(X1,X2)
            a__sel(0(),cons(X,XS)) -> mark(X)
            a__sel(s(N),cons(X,XS)) -> a__sel(mark(N),mark(XS))
            a__take(X1,X2) -> take(X1,X2)
            a__take(0(),XS) -> nil()
            a__take(s(N),cons(X,XS)) -> cons(mark(X),take(N,XS))
            mark(0()) -> 0()
            mark(2nd(X)) -> a__2nd(mark(X))
            mark(cons(X1,X2)) -> cons(mark(X1),X2)
            mark(from(X)) -> a__from(mark(X))
            mark(head(X)) -> a__head(mark(X))
            mark(nil()) -> nil()
            mark(s(X)) -> s(mark(X))
            mark(sel(X1,X2)) -> a__sel(mark(X1),mark(X2))
            mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
        - Signature:
            {a__2nd/1,a__from/1,a__head/1,a__sel/2,a__take/2,mark/1} / {0/0,2nd/1,cons/2,from/1,head/1,nil/0,s/1,sel/2
            ,take/2}
        - Obligation:
             runtime complexity wrt. defined symbols {a__2nd,a__from,a__head,a__sel,a__take,mark} and constructors {0
            ,2nd,cons,from,head,nil,s,sel,take}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            a__2nd(X) -> 2nd(X)
            a__2nd(cons(X,XS)) -> a__head(mark(XS))
            a__from(X) -> cons(mark(X),from(s(X)))
            a__from(X) -> from(X)
            a__head(X) -> head(X)
            a__head(cons(X,XS)) -> mark(X)
            a__sel(X1,X2) -> sel(X1,X2)
            a__sel(0(),cons(X,XS)) -> mark(X)
            a__sel(s(N),cons(X,XS)) -> a__sel(mark(N),mark(XS))
            a__take(X1,X2) -> take(X1,X2)
            a__take(0(),XS) -> nil()
            a__take(s(N),cons(X,XS)) -> cons(mark(X),take(N,XS))
            mark(0()) -> 0()
            mark(2nd(X)) -> a__2nd(mark(X))
            mark(cons(X1,X2)) -> cons(mark(X1),X2)
            mark(from(X)) -> a__from(mark(X))
            mark(head(X)) -> a__head(mark(X))
            mark(nil()) -> nil()
            mark(s(X)) -> s(mark(X))
            mark(sel(X1,X2)) -> a__sel(mark(X1),mark(X2))
            mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
        - Signature:
            {a__2nd/1,a__from/1,a__head/1,a__sel/2,a__take/2,mark/1} / {0/0,2nd/1,cons/2,from/1,head/1,nil/0,s/1,sel/2
            ,take/2}
        - Obligation:
             runtime complexity wrt. defined symbols {a__2nd,a__from,a__head,a__sel,a__take,mark} and constructors {0
            ,2nd,cons,from,head,nil,s,sel,take}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          mark(x){x -> 2nd(x)} =
            mark(2nd(x)) ->^+ a__2nd(mark(x))
              = C[mark(x) = mark(x){}]

WORST_CASE(Omega(n^1),?)