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

WORST_CASE(Omega(n^1),?)