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

WORST_CASE(Omega(n^1),?)