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

WORST_CASE(Omega(n^1),?)