/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:
            head(cons(x,l)) -> x
            head(nil()) -> undefined()
            if(false(),x,l,accu,orig) -> accu
            if(true(),x,l,accu,orig) -> rev(s(x),tail(l),cons(head(l),accu),orig)
            length(cons(x,l)) -> s(length(l))
            length(nil()) -> 0()
            lt(x,0()) -> false()
            lt(0(),s(y)) -> true()
            lt(s(x),s(y)) -> lt(x,y)
            rev(x,l,accu,orig) -> if(lt(x,length(orig)),x,l,accu,orig)
            reverse(l) -> rev(0(),l,nil(),l)
            tail(cons(x,l)) -> l
            tail(nil()) -> nil()
        - Signature:
            {head/1,if/5,length/1,lt/2,rev/4,reverse/1,tail/1} / {0/0,cons/2,false/0,nil/0,s/1,true/0,undefined/0}
        - Obligation:
             runtime complexity wrt. defined symbols {head,if,length,lt,rev,reverse,tail} and constructors {0,cons,false
            ,nil,s,true,undefined}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            head(cons(x,l)) -> x
            head(nil()) -> undefined()
            if(false(),x,l,accu,orig) -> accu
            if(true(),x,l,accu,orig) -> rev(s(x),tail(l),cons(head(l),accu),orig)
            length(cons(x,l)) -> s(length(l))
            length(nil()) -> 0()
            lt(x,0()) -> false()
            lt(0(),s(y)) -> true()
            lt(s(x),s(y)) -> lt(x,y)
            rev(x,l,accu,orig) -> if(lt(x,length(orig)),x,l,accu,orig)
            reverse(l) -> rev(0(),l,nil(),l)
            tail(cons(x,l)) -> l
            tail(nil()) -> nil()
        - Signature:
            {head/1,if/5,length/1,lt/2,rev/4,reverse/1,tail/1} / {0/0,cons/2,false/0,nil/0,s/1,true/0,undefined/0}
        - Obligation:
             runtime complexity wrt. defined symbols {head,if,length,lt,rev,reverse,tail} and constructors {0,cons,false
            ,nil,s,true,undefined}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            head(cons(x,l)) -> x
            head(nil()) -> undefined()
            if(false(),x,l,accu,orig) -> accu
            if(true(),x,l,accu,orig) -> rev(s(x),tail(l),cons(head(l),accu),orig)
            length(cons(x,l)) -> s(length(l))
            length(nil()) -> 0()
            lt(x,0()) -> false()
            lt(0(),s(y)) -> true()
            lt(s(x),s(y)) -> lt(x,y)
            rev(x,l,accu,orig) -> if(lt(x,length(orig)),x,l,accu,orig)
            reverse(l) -> rev(0(),l,nil(),l)
            tail(cons(x,l)) -> l
            tail(nil()) -> nil()
        - Signature:
            {head/1,if/5,length/1,lt/2,rev/4,reverse/1,tail/1} / {0/0,cons/2,false/0,nil/0,s/1,true/0,undefined/0}
        - Obligation:
             runtime complexity wrt. defined symbols {head,if,length,lt,rev,reverse,tail} and constructors {0,cons,false
            ,nil,s,true,undefined}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          length(y){y -> cons(x,y)} =
            length(cons(x,y)) ->^+ s(length(y))
              = C[length(y) = length(y){}]

WORST_CASE(Omega(n^1),?)