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

WORST_CASE(Omega(n^1),?)