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

WORST_CASE(Omega(n^1),?)