/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:
            r(xs,ys,zs,nil()) -> xs
            r(xs,cons(y,ys),cons(z,zs),cons(w,ws)) -> r(ys,cons(y,ys),zs,cons(succ(zero()),cons(w,ws)))
            r(xs,cons(y,ys),nil(),cons(w,ws)) -> r(xs,xs,cons(succ(zero()),nil()),ws)
            r(xs,nil(),zs,cons(w,ws)) -> r(xs,xs,cons(succ(zero()),zs),ws)
        - Signature:
            {r/4} / {cons/2,nil/0,succ/1,zero/0}
        - Obligation:
             runtime complexity wrt. defined symbols {r} and constructors {cons,nil,succ,zero}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            r(xs,ys,zs,nil()) -> xs
            r(xs,cons(y,ys),cons(z,zs),cons(w,ws)) -> r(ys,cons(y,ys),zs,cons(succ(zero()),cons(w,ws)))
            r(xs,cons(y,ys),nil(),cons(w,ws)) -> r(xs,xs,cons(succ(zero()),nil()),ws)
            r(xs,nil(),zs,cons(w,ws)) -> r(xs,xs,cons(succ(zero()),zs),ws)
        - Signature:
            {r/4} / {cons/2,nil/0,succ/1,zero/0}
        - Obligation:
             runtime complexity wrt. defined symbols {r} and constructors {cons,nil,succ,zero}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            r(xs,ys,zs,nil()) -> xs
            r(xs,cons(y,ys),cons(z,zs),cons(w,ws)) -> r(ys,cons(y,ys),zs,cons(succ(zero()),cons(w,ws)))
            r(xs,cons(y,ys),nil(),cons(w,ws)) -> r(xs,xs,cons(succ(zero()),nil()),ws)
            r(xs,nil(),zs,cons(w,ws)) -> r(xs,xs,cons(succ(zero()),zs),ws)
        - Signature:
            {r/4} / {cons/2,nil/0,succ/1,zero/0}
        - Obligation:
             runtime complexity wrt. defined symbols {r} and constructors {cons,nil,succ,zero}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          r(x,cons(y,z),v,cons(w,x_6)){v -> cons(u,v)} =
            r(x,cons(y,z),cons(u,v),cons(w,x_6)) ->^+ r(z,cons(y,z),v,cons(succ(zero()),cons(w,x_6)))
              = C[r(z,cons(y,z),v,cons(succ(zero()),cons(w,x_6))) = r(x,cons(y,z),v,cons(w,x_6)){x -> z
                                                                                                ,w -> succ(zero())
                                                                                                ,x_6 -> cons(w,x_6)}]

WORST_CASE(Omega(n^1),?)