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

WORST_CASE(Omega(n^1),?)