/export/starexec/sandbox/solver/bin/starexec_run_tct_rci /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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WORST_CASE(Omega(n^1),?)
* Step 1: Sum WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            cond1(true(),x) -> cond2(even(x),x)
            cond2(false(),x) -> cond1(neq(x,0()),p(x))
            cond2(true(),x) -> cond1(neq(x,0()),div2(x))
            div2(0()) -> 0()
            div2(s(0())) -> 0()
            div2(s(s(x))) -> s(div2(x))
            even(0()) -> true()
            even(s(0())) -> false()
            even(s(s(x))) -> even(x)
            neq(0(),0()) -> false()
            neq(0(),s(x)) -> true()
            neq(s(x),0()) -> true()
            neq(s(x),s(y())) -> neq(x,y())
            p(0()) -> 0()
            p(s(x)) -> x
        - Signature:
            {cond1/2,cond2/2,div2/1,even/1,neq/2,p/1} / {0/0,false/0,s/1,true/0,y/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {cond1,cond2,div2,even,neq,p} and constructors {0,false,s
            ,true,y}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            cond1(true(),x) -> cond2(even(x),x)
            cond2(false(),x) -> cond1(neq(x,0()),p(x))
            cond2(true(),x) -> cond1(neq(x,0()),div2(x))
            div2(0()) -> 0()
            div2(s(0())) -> 0()
            div2(s(s(x))) -> s(div2(x))
            even(0()) -> true()
            even(s(0())) -> false()
            even(s(s(x))) -> even(x)
            neq(0(),0()) -> false()
            neq(0(),s(x)) -> true()
            neq(s(x),0()) -> true()
            neq(s(x),s(y())) -> neq(x,y())
            p(0()) -> 0()
            p(s(x)) -> x
        - Signature:
            {cond1/2,cond2/2,div2/1,even/1,neq/2,p/1} / {0/0,false/0,s/1,true/0,y/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {cond1,cond2,div2,even,neq,p} and constructors {0,false,s
            ,true,y}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          div2(x){x -> s(s(x))} =
            div2(s(s(x))) ->^+ s(div2(x))
              = C[div2(x) = div2(x){}]

WORST_CASE(Omega(n^1),?)