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

WORST_CASE(Omega(n^1),?)