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

WORST_CASE(Omega(n^1),?)