/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__dbl(X)) -> dbl(activate(X))
            activate(n__dbls(X)) -> dbls(activate(X))
            activate(n__from(X)) -> from(X)
            activate(n__indx(X1,X2)) -> indx(activate(X1),X2)
            activate(n__s(X)) -> s(X)
            activate(n__sel(X1,X2)) -> sel(activate(X1),activate(X2))
            dbl(X) -> n__dbl(X)
            dbl(0()) -> 0()
            dbl(s(X)) -> s(n__s(n__dbl(activate(X))))
            dbls(X) -> n__dbls(X)
            dbls(cons(X,Y)) -> cons(n__dbl(activate(X)),n__dbls(activate(Y)))
            dbls(nil()) -> nil()
            from(X) -> cons(activate(X),n__from(n__s(activate(X))))
            from(X) -> n__from(X)
            indx(X1,X2) -> n__indx(X1,X2)
            indx(cons(X,Y),Z) -> cons(n__sel(activate(X),activate(Z)),n__indx(activate(Y),activate(Z)))
            indx(nil(),X) -> nil()
            s(X) -> n__s(X)
            sel(X1,X2) -> n__sel(X1,X2)
            sel(0(),cons(X,Y)) -> activate(X)
            sel(s(X),cons(Y,Z)) -> sel(activate(X),activate(Z))
        - Signature:
            {activate/1,dbl/1,dbls/1,from/1,indx/2,s/1,sel/2} / {0/0,cons/2,n__dbl/1,n__dbls/1,n__from/1,n__indx/2
            ,n__s/1,n__sel/2,nil/0}
        - Obligation:
             runtime complexity wrt. defined symbols {activate,dbl,dbls,from,indx,s,sel} and constructors {0,cons,n__dbl
            ,n__dbls,n__from,n__indx,n__s,n__sel,nil}
    + 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__dbl(X)) -> dbl(activate(X))
            activate(n__dbls(X)) -> dbls(activate(X))
            activate(n__from(X)) -> from(X)
            activate(n__indx(X1,X2)) -> indx(activate(X1),X2)
            activate(n__s(X)) -> s(X)
            activate(n__sel(X1,X2)) -> sel(activate(X1),activate(X2))
            dbl(X) -> n__dbl(X)
            dbl(0()) -> 0()
            dbl(s(X)) -> s(n__s(n__dbl(activate(X))))
            dbls(X) -> n__dbls(X)
            dbls(cons(X,Y)) -> cons(n__dbl(activate(X)),n__dbls(activate(Y)))
            dbls(nil()) -> nil()
            from(X) -> cons(activate(X),n__from(n__s(activate(X))))
            from(X) -> n__from(X)
            indx(X1,X2) -> n__indx(X1,X2)
            indx(cons(X,Y),Z) -> cons(n__sel(activate(X),activate(Z)),n__indx(activate(Y),activate(Z)))
            indx(nil(),X) -> nil()
            s(X) -> n__s(X)
            sel(X1,X2) -> n__sel(X1,X2)
            sel(0(),cons(X,Y)) -> activate(X)
            sel(s(X),cons(Y,Z)) -> sel(activate(X),activate(Z))
        - Signature:
            {activate/1,dbl/1,dbls/1,from/1,indx/2,s/1,sel/2} / {0/0,cons/2,n__dbl/1,n__dbls/1,n__from/1,n__indx/2
            ,n__s/1,n__sel/2,nil/0}
        - Obligation:
             runtime complexity wrt. defined symbols {activate,dbl,dbls,from,indx,s,sel} and constructors {0,cons,n__dbl
            ,n__dbls,n__from,n__indx,n__s,n__sel,nil}
    + 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__dbl(X)) -> dbl(activate(X))
            activate(n__dbls(X)) -> dbls(activate(X))
            activate(n__from(X)) -> from(X)
            activate(n__indx(X1,X2)) -> indx(activate(X1),X2)
            activate(n__s(X)) -> s(X)
            activate(n__sel(X1,X2)) -> sel(activate(X1),activate(X2))
            dbl(X) -> n__dbl(X)
            dbl(0()) -> 0()
            dbl(s(X)) -> s(n__s(n__dbl(activate(X))))
            dbls(X) -> n__dbls(X)
            dbls(cons(X,Y)) -> cons(n__dbl(activate(X)),n__dbls(activate(Y)))
            dbls(nil()) -> nil()
            from(X) -> cons(activate(X),n__from(n__s(activate(X))))
            from(X) -> n__from(X)
            indx(X1,X2) -> n__indx(X1,X2)
            indx(cons(X,Y),Z) -> cons(n__sel(activate(X),activate(Z)),n__indx(activate(Y),activate(Z)))
            indx(nil(),X) -> nil()
            s(X) -> n__s(X)
            sel(X1,X2) -> n__sel(X1,X2)
            sel(0(),cons(X,Y)) -> activate(X)
            sel(s(X),cons(Y,Z)) -> sel(activate(X),activate(Z))
        - Signature:
            {activate/1,dbl/1,dbls/1,from/1,indx/2,s/1,sel/2} / {0/0,cons/2,n__dbl/1,n__dbls/1,n__from/1,n__indx/2
            ,n__s/1,n__sel/2,nil/0}
        - Obligation:
             runtime complexity wrt. defined symbols {activate,dbl,dbls,from,indx,s,sel} and constructors {0,cons,n__dbl
            ,n__dbls,n__from,n__indx,n__s,n__sel,nil}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          activate(x){x -> n__dbl(x)} =
            activate(n__dbl(x)) ->^+ dbl(activate(x))
              = C[activate(x) = activate(x){}]

WORST_CASE(Omega(n^1),?)