/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:
            activate(X) -> X
            activate(n__from(X)) -> from(activate(X))
            activate(n__s(X)) -> s(activate(X))
            activate(n__zWquot(X1,X2)) -> zWquot(activate(X1),activate(X2))
            from(X) -> cons(X,n__from(n__s(X)))
            from(X) -> n__from(X)
            minus(X,0()) -> 0()
            minus(s(X),s(Y)) -> minus(X,Y)
            quot(0(),s(Y)) -> 0()
            quot(s(X),s(Y)) -> s(quot(minus(X,Y),s(Y)))
            s(X) -> n__s(X)
            sel(0(),cons(X,XS)) -> X
            sel(s(N),cons(X,XS)) -> sel(N,activate(XS))
            zWquot(X1,X2) -> n__zWquot(X1,X2)
            zWquot(XS,nil()) -> nil()
            zWquot(cons(X,XS),cons(Y,YS)) -> cons(quot(X,Y),n__zWquot(activate(XS),activate(YS)))
            zWquot(nil(),XS) -> nil()
        - Signature:
            {activate/1,from/1,minus/2,quot/2,s/1,sel/2,zWquot/2} / {0/0,cons/2,n__from/1,n__s/1,n__zWquot/2,nil/0}
        - Obligation:
             runtime complexity wrt. defined symbols {activate,from,minus,quot,s,sel,zWquot} and constructors {0,cons
            ,n__from,n__s,n__zWquot,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__from(X)) -> from(activate(X))
            activate(n__s(X)) -> s(activate(X))
            activate(n__zWquot(X1,X2)) -> zWquot(activate(X1),activate(X2))
            from(X) -> cons(X,n__from(n__s(X)))
            from(X) -> n__from(X)
            minus(X,0()) -> 0()
            minus(s(X),s(Y)) -> minus(X,Y)
            quot(0(),s(Y)) -> 0()
            quot(s(X),s(Y)) -> s(quot(minus(X,Y),s(Y)))
            s(X) -> n__s(X)
            sel(0(),cons(X,XS)) -> X
            sel(s(N),cons(X,XS)) -> sel(N,activate(XS))
            zWquot(X1,X2) -> n__zWquot(X1,X2)
            zWquot(XS,nil()) -> nil()
            zWquot(cons(X,XS),cons(Y,YS)) -> cons(quot(X,Y),n__zWquot(activate(XS),activate(YS)))
            zWquot(nil(),XS) -> nil()
        - Signature:
            {activate/1,from/1,minus/2,quot/2,s/1,sel/2,zWquot/2} / {0/0,cons/2,n__from/1,n__s/1,n__zWquot/2,nil/0}
        - Obligation:
             runtime complexity wrt. defined symbols {activate,from,minus,quot,s,sel,zWquot} and constructors {0,cons
            ,n__from,n__s,n__zWquot,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__from(X)) -> from(activate(X))
            activate(n__s(X)) -> s(activate(X))
            activate(n__zWquot(X1,X2)) -> zWquot(activate(X1),activate(X2))
            from(X) -> cons(X,n__from(n__s(X)))
            from(X) -> n__from(X)
            minus(X,0()) -> 0()
            minus(s(X),s(Y)) -> minus(X,Y)
            quot(0(),s(Y)) -> 0()
            quot(s(X),s(Y)) -> s(quot(minus(X,Y),s(Y)))
            s(X) -> n__s(X)
            sel(0(),cons(X,XS)) -> X
            sel(s(N),cons(X,XS)) -> sel(N,activate(XS))
            zWquot(X1,X2) -> n__zWquot(X1,X2)
            zWquot(XS,nil()) -> nil()
            zWquot(cons(X,XS),cons(Y,YS)) -> cons(quot(X,Y),n__zWquot(activate(XS),activate(YS)))
            zWquot(nil(),XS) -> nil()
        - Signature:
            {activate/1,from/1,minus/2,quot/2,s/1,sel/2,zWquot/2} / {0/0,cons/2,n__from/1,n__s/1,n__zWquot/2,nil/0}
        - Obligation:
             runtime complexity wrt. defined symbols {activate,from,minus,quot,s,sel,zWquot} and constructors {0,cons
            ,n__from,n__s,n__zWquot,nil}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          activate(x){x -> n__from(x)} =
            activate(n__from(x)) ->^+ from(activate(x))
              = C[activate(x) = activate(x){}]

WORST_CASE(Omega(n^1),?)