/export/starexec/sandbox2/solver/bin/starexec_run_tct_rc /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


--------------------------------------------------------------------------------


WORST_CASE(Omega(n^1),?)
* Step 1: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            a__dbl(X) -> dbl(X)
            a__dbl(0()) -> 0()
            a__dbl(s(X)) -> s(s(dbl(X)))
            a__dbls(X) -> dbls(X)
            a__dbls(cons(X,Y)) -> cons(dbl(X),dbls(Y))
            a__dbls(nil()) -> nil()
            a__from(X) -> cons(X,from(s(X)))
            a__from(X) -> from(X)
            a__indx(X1,X2) -> indx(X1,X2)
            a__indx(cons(X,Y),Z) -> cons(sel(X,Z),indx(Y,Z))
            a__indx(nil(),X) -> nil()
            a__sel(X1,X2) -> sel(X1,X2)
            a__sel(0(),cons(X,Y)) -> mark(X)
            a__sel(s(X),cons(Y,Z)) -> a__sel(mark(X),mark(Z))
            mark(0()) -> 0()
            mark(cons(X1,X2)) -> cons(X1,X2)
            mark(dbl(X)) -> a__dbl(mark(X))
            mark(dbls(X)) -> a__dbls(mark(X))
            mark(from(X)) -> a__from(X)
            mark(indx(X1,X2)) -> a__indx(mark(X1),X2)
            mark(nil()) -> nil()
            mark(s(X)) -> s(X)
            mark(sel(X1,X2)) -> a__sel(mark(X1),mark(X2))
        - Signature:
            {a__dbl/1,a__dbls/1,a__from/1,a__indx/2,a__sel/2,mark/1} / {0/0,cons/2,dbl/1,dbls/1,from/1,indx/2,nil/0,s/1
            ,sel/2}
        - Obligation:
             runtime complexity wrt. defined symbols {a__dbl,a__dbls,a__from,a__indx,a__sel,mark} and constructors {0
            ,cons,dbl,dbls,from,indx,nil,s,sel}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            a__dbl(X) -> dbl(X)
            a__dbl(0()) -> 0()
            a__dbl(s(X)) -> s(s(dbl(X)))
            a__dbls(X) -> dbls(X)
            a__dbls(cons(X,Y)) -> cons(dbl(X),dbls(Y))
            a__dbls(nil()) -> nil()
            a__from(X) -> cons(X,from(s(X)))
            a__from(X) -> from(X)
            a__indx(X1,X2) -> indx(X1,X2)
            a__indx(cons(X,Y),Z) -> cons(sel(X,Z),indx(Y,Z))
            a__indx(nil(),X) -> nil()
            a__sel(X1,X2) -> sel(X1,X2)
            a__sel(0(),cons(X,Y)) -> mark(X)
            a__sel(s(X),cons(Y,Z)) -> a__sel(mark(X),mark(Z))
            mark(0()) -> 0()
            mark(cons(X1,X2)) -> cons(X1,X2)
            mark(dbl(X)) -> a__dbl(mark(X))
            mark(dbls(X)) -> a__dbls(mark(X))
            mark(from(X)) -> a__from(X)
            mark(indx(X1,X2)) -> a__indx(mark(X1),X2)
            mark(nil()) -> nil()
            mark(s(X)) -> s(X)
            mark(sel(X1,X2)) -> a__sel(mark(X1),mark(X2))
        - Signature:
            {a__dbl/1,a__dbls/1,a__from/1,a__indx/2,a__sel/2,mark/1} / {0/0,cons/2,dbl/1,dbls/1,from/1,indx/2,nil/0,s/1
            ,sel/2}
        - Obligation:
             runtime complexity wrt. defined symbols {a__dbl,a__dbls,a__from,a__indx,a__sel,mark} and constructors {0
            ,cons,dbl,dbls,from,indx,nil,s,sel}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            a__dbl(X) -> dbl(X)
            a__dbl(0()) -> 0()
            a__dbl(s(X)) -> s(s(dbl(X)))
            a__dbls(X) -> dbls(X)
            a__dbls(cons(X,Y)) -> cons(dbl(X),dbls(Y))
            a__dbls(nil()) -> nil()
            a__from(X) -> cons(X,from(s(X)))
            a__from(X) -> from(X)
            a__indx(X1,X2) -> indx(X1,X2)
            a__indx(cons(X,Y),Z) -> cons(sel(X,Z),indx(Y,Z))
            a__indx(nil(),X) -> nil()
            a__sel(X1,X2) -> sel(X1,X2)
            a__sel(0(),cons(X,Y)) -> mark(X)
            a__sel(s(X),cons(Y,Z)) -> a__sel(mark(X),mark(Z))
            mark(0()) -> 0()
            mark(cons(X1,X2)) -> cons(X1,X2)
            mark(dbl(X)) -> a__dbl(mark(X))
            mark(dbls(X)) -> a__dbls(mark(X))
            mark(from(X)) -> a__from(X)
            mark(indx(X1,X2)) -> a__indx(mark(X1),X2)
            mark(nil()) -> nil()
            mark(s(X)) -> s(X)
            mark(sel(X1,X2)) -> a__sel(mark(X1),mark(X2))
        - Signature:
            {a__dbl/1,a__dbls/1,a__from/1,a__indx/2,a__sel/2,mark/1} / {0/0,cons/2,dbl/1,dbls/1,from/1,indx/2,nil/0,s/1
            ,sel/2}
        - Obligation:
             runtime complexity wrt. defined symbols {a__dbl,a__dbls,a__from,a__indx,a__sel,mark} and constructors {0
            ,cons,dbl,dbls,from,indx,nil,s,sel}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          mark(x){x -> dbl(x)} =
            mark(dbl(x)) ->^+ a__dbl(mark(x))
              = C[mark(x) = mark(x){}]

WORST_CASE(Omega(n^1),?)