/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:
            del(x,cons(y,xs)) -> if(eq(x,y),x,y,xs)
            del(x,nil()) -> nil()
            double(0()) -> 0()
            double(s(x)) -> s(s(double(x)))
            doublelist(cons(x,xs)) -> cons(double(x),doublelist(del(first(cons(x,xs)),cons(x,xs))))
            doublelist(nil()) -> nil()
            eq(0(),0()) -> true()
            eq(0(),s(y)) -> false()
            eq(s(x),0()) -> false()
            eq(s(x),s(y)) -> eq(x,y)
            first(cons(x,xs)) -> x
            first(nil()) -> 0()
            if(false(),x,y,xs) -> cons(y,del(x,xs))
            if(true(),x,y,xs) -> xs
        - Signature:
            {del/2,double/1,doublelist/1,eq/2,first/1,if/4} / {0/0,cons/2,false/0,nil/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {del,double,doublelist,eq,first,if} and constructors {0,cons,false
            ,nil,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            del(x,cons(y,xs)) -> if(eq(x,y),x,y,xs)
            del(x,nil()) -> nil()
            double(0()) -> 0()
            double(s(x)) -> s(s(double(x)))
            doublelist(cons(x,xs)) -> cons(double(x),doublelist(del(first(cons(x,xs)),cons(x,xs))))
            doublelist(nil()) -> nil()
            eq(0(),0()) -> true()
            eq(0(),s(y)) -> false()
            eq(s(x),0()) -> false()
            eq(s(x),s(y)) -> eq(x,y)
            first(cons(x,xs)) -> x
            first(nil()) -> 0()
            if(false(),x,y,xs) -> cons(y,del(x,xs))
            if(true(),x,y,xs) -> xs
        - Signature:
            {del/2,double/1,doublelist/1,eq/2,first/1,if/4} / {0/0,cons/2,false/0,nil/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {del,double,doublelist,eq,first,if} and constructors {0,cons,false
            ,nil,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            del(x,cons(y,xs)) -> if(eq(x,y),x,y,xs)
            del(x,nil()) -> nil()
            double(0()) -> 0()
            double(s(x)) -> s(s(double(x)))
            doublelist(cons(x,xs)) -> cons(double(x),doublelist(del(first(cons(x,xs)),cons(x,xs))))
            doublelist(nil()) -> nil()
            eq(0(),0()) -> true()
            eq(0(),s(y)) -> false()
            eq(s(x),0()) -> false()
            eq(s(x),s(y)) -> eq(x,y)
            first(cons(x,xs)) -> x
            first(nil()) -> 0()
            if(false(),x,y,xs) -> cons(y,del(x,xs))
            if(true(),x,y,xs) -> xs
        - Signature:
            {del/2,double/1,doublelist/1,eq/2,first/1,if/4} / {0/0,cons/2,false/0,nil/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {del,double,doublelist,eq,first,if} and constructors {0,cons,false
            ,nil,s,true}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          double(x){x -> s(x)} =
            double(s(x)) ->^+ s(s(double(x)))
              = C[double(x) = double(x){}]

WORST_CASE(Omega(n^1),?)