/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__U11(X1,X2) -> U11(X1,X2)
            a__U11(tt(),L) -> a__U12(tt(),L)
            a__U12(X1,X2) -> U12(X1,X2)
            a__U12(tt(),L) -> s(a__length(mark(L)))
            a__length(X) -> length(X)
            a__length(cons(N,L)) -> a__U11(tt(),L)
            a__length(nil()) -> 0()
            a__zeros() -> cons(0(),zeros())
            a__zeros() -> zeros()
            mark(0()) -> 0()
            mark(U11(X1,X2)) -> a__U11(mark(X1),X2)
            mark(U12(X1,X2)) -> a__U12(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(tt()) -> tt()
            mark(zeros()) -> a__zeros()
        - Signature:
            {a__U11/2,a__U12/2,a__length/1,a__zeros/0,mark/1} / {0/0,U11/2,U12/2,cons/2,length/1,nil/0,s/1,tt/0,zeros/0}
        - Obligation:
             runtime complexity wrt. defined symbols {a__U11,a__U12,a__length,a__zeros,mark} and constructors {0,U11,U12
            ,cons,length,nil,s,tt,zeros}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            a__U11(X1,X2) -> U11(X1,X2)
            a__U11(tt(),L) -> a__U12(tt(),L)
            a__U12(X1,X2) -> U12(X1,X2)
            a__U12(tt(),L) -> s(a__length(mark(L)))
            a__length(X) -> length(X)
            a__length(cons(N,L)) -> a__U11(tt(),L)
            a__length(nil()) -> 0()
            a__zeros() -> cons(0(),zeros())
            a__zeros() -> zeros()
            mark(0()) -> 0()
            mark(U11(X1,X2)) -> a__U11(mark(X1),X2)
            mark(U12(X1,X2)) -> a__U12(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(tt()) -> tt()
            mark(zeros()) -> a__zeros()
        - Signature:
            {a__U11/2,a__U12/2,a__length/1,a__zeros/0,mark/1} / {0/0,U11/2,U12/2,cons/2,length/1,nil/0,s/1,tt/0,zeros/0}
        - Obligation:
             runtime complexity wrt. defined symbols {a__U11,a__U12,a__length,a__zeros,mark} and constructors {0,U11,U12
            ,cons,length,nil,s,tt,zeros}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            a__U11(X1,X2) -> U11(X1,X2)
            a__U11(tt(),L) -> a__U12(tt(),L)
            a__U12(X1,X2) -> U12(X1,X2)
            a__U12(tt(),L) -> s(a__length(mark(L)))
            a__length(X) -> length(X)
            a__length(cons(N,L)) -> a__U11(tt(),L)
            a__length(nil()) -> 0()
            a__zeros() -> cons(0(),zeros())
            a__zeros() -> zeros()
            mark(0()) -> 0()
            mark(U11(X1,X2)) -> a__U11(mark(X1),X2)
            mark(U12(X1,X2)) -> a__U12(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(tt()) -> tt()
            mark(zeros()) -> a__zeros()
        - Signature:
            {a__U11/2,a__U12/2,a__length/1,a__zeros/0,mark/1} / {0/0,U11/2,U12/2,cons/2,length/1,nil/0,s/1,tt/0,zeros/0}
        - Obligation:
             runtime complexity wrt. defined symbols {a__U11,a__U12,a__length,a__zeros,mark} and constructors {0,U11,U12
            ,cons,length,nil,s,tt,zeros}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          mark(x){x -> U11(x,y)} =
            mark(U11(x,y)) ->^+ a__U11(mark(x),y)
              = C[mark(x) = mark(x){}]

WORST_CASE(Omega(n^1),?)