/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:
            0() -> n__0()
            activate(X) -> X
            activate(n__0()) -> 0()
            activate(n__inf(X)) -> inf(activate(X))
            activate(n__length(X)) -> length(activate(X))
            activate(n__s(X)) -> s(X)
            activate(n__take(X1,X2)) -> take(activate(X1),activate(X2))
            eq(X,Y) -> false()
            eq(n__0(),n__0()) -> true()
            eq(n__s(X),n__s(Y)) -> eq(activate(X),activate(Y))
            inf(X) -> cons(X,n__inf(n__s(X)))
            inf(X) -> n__inf(X)
            length(X) -> n__length(X)
            length(cons(X,L)) -> s(n__length(activate(L)))
            length(nil()) -> 0()
            s(X) -> n__s(X)
            take(X1,X2) -> n__take(X1,X2)
            take(0(),X) -> nil()
            take(s(X),cons(Y,L)) -> cons(activate(Y),n__take(activate(X),activate(L)))
        - Signature:
            {0/0,activate/1,eq/2,inf/1,length/1,s/1,take/2} / {cons/2,false/0,n__0/0,n__inf/1,n__length/1,n__s/1
            ,n__take/2,nil/0,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {0,activate,eq,inf,length,s,take} and constructors {cons,false,n__0
            ,n__inf,n__length,n__s,n__take,nil,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            0() -> n__0()
            activate(X) -> X
            activate(n__0()) -> 0()
            activate(n__inf(X)) -> inf(activate(X))
            activate(n__length(X)) -> length(activate(X))
            activate(n__s(X)) -> s(X)
            activate(n__take(X1,X2)) -> take(activate(X1),activate(X2))
            eq(X,Y) -> false()
            eq(n__0(),n__0()) -> true()
            eq(n__s(X),n__s(Y)) -> eq(activate(X),activate(Y))
            inf(X) -> cons(X,n__inf(n__s(X)))
            inf(X) -> n__inf(X)
            length(X) -> n__length(X)
            length(cons(X,L)) -> s(n__length(activate(L)))
            length(nil()) -> 0()
            s(X) -> n__s(X)
            take(X1,X2) -> n__take(X1,X2)
            take(0(),X) -> nil()
            take(s(X),cons(Y,L)) -> cons(activate(Y),n__take(activate(X),activate(L)))
        - Signature:
            {0/0,activate/1,eq/2,inf/1,length/1,s/1,take/2} / {cons/2,false/0,n__0/0,n__inf/1,n__length/1,n__s/1
            ,n__take/2,nil/0,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {0,activate,eq,inf,length,s,take} and constructors {cons,false,n__0
            ,n__inf,n__length,n__s,n__take,nil,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            0() -> n__0()
            activate(X) -> X
            activate(n__0()) -> 0()
            activate(n__inf(X)) -> inf(activate(X))
            activate(n__length(X)) -> length(activate(X))
            activate(n__s(X)) -> s(X)
            activate(n__take(X1,X2)) -> take(activate(X1),activate(X2))
            eq(X,Y) -> false()
            eq(n__0(),n__0()) -> true()
            eq(n__s(X),n__s(Y)) -> eq(activate(X),activate(Y))
            inf(X) -> cons(X,n__inf(n__s(X)))
            inf(X) -> n__inf(X)
            length(X) -> n__length(X)
            length(cons(X,L)) -> s(n__length(activate(L)))
            length(nil()) -> 0()
            s(X) -> n__s(X)
            take(X1,X2) -> n__take(X1,X2)
            take(0(),X) -> nil()
            take(s(X),cons(Y,L)) -> cons(activate(Y),n__take(activate(X),activate(L)))
        - Signature:
            {0/0,activate/1,eq/2,inf/1,length/1,s/1,take/2} / {cons/2,false/0,n__0/0,n__inf/1,n__length/1,n__s/1
            ,n__take/2,nil/0,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {0,activate,eq,inf,length,s,take} and constructors {cons,false,n__0
            ,n__inf,n__length,n__s,n__take,nil,true}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          activate(x){x -> n__inf(x)} =
            activate(n__inf(x)) ->^+ inf(activate(x))
              = C[activate(x) = activate(x){}]

WORST_CASE(Omega(n^1),?)