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


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


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

WORST_CASE(Omega(n^1),?)