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


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WORST_CASE(Omega(n^1),?)
* Step 1: Sum WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            app(l,nil()) -> l
            app(cons(x,l),k) -> cons(x,app(l,k))
            app(nil(),k) -> k
            plus(0(),y) -> y
            plus(s(x),y) -> s(plus(x,y))
            pred(cons(s(x),nil())) -> cons(x,nil())
            sum(app(l,cons(x,cons(y,k)))) -> sum(app(l,sum(cons(x,cons(y,k)))))
            sum(cons(x,cons(y,l))) -> sum(cons(plus(x,y),l))
            sum(cons(x,nil())) -> cons(x,nil())
            sum(plus(cons(0(),x),cons(y,l))) -> pred(sum(cons(s(x),cons(y,l))))
        - Signature:
            {app/2,plus/2,pred/1,sum/1} / {0/0,cons/2,nil/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {app,plus,pred,sum} and constructors {0,cons,nil,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            app(l,nil()) -> l
            app(cons(x,l),k) -> cons(x,app(l,k))
            app(nil(),k) -> k
            plus(0(),y) -> y
            plus(s(x),y) -> s(plus(x,y))
            pred(cons(s(x),nil())) -> cons(x,nil())
            sum(app(l,cons(x,cons(y,k)))) -> sum(app(l,sum(cons(x,cons(y,k)))))
            sum(cons(x,cons(y,l))) -> sum(cons(plus(x,y),l))
            sum(cons(x,nil())) -> cons(x,nil())
            sum(plus(cons(0(),x),cons(y,l))) -> pred(sum(cons(s(x),cons(y,l))))
        - Signature:
            {app/2,plus/2,pred/1,sum/1} / {0/0,cons/2,nil/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {app,plus,pred,sum} and constructors {0,cons,nil,s}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          app(y,z){y -> cons(x,y)} =
            app(cons(x,y),z) ->^+ cons(x,app(y,z))
              = C[app(y,z) = app(y,z){}]

WORST_CASE(Omega(n^1),?)