/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:
            activate(X) -> X
            activate(n__f(X1,X2)) -> f(activate(X1),X2)
            activate(n__g(X)) -> g(activate(X))
            f(X1,X2) -> n__f(X1,X2)
            f(g(X),Y) -> f(X,n__f(n__g(X),activate(Y)))
            g(X) -> n__g(X)
        - Signature:
            {activate/1,f/2,g/1} / {n__f/2,n__g/1}
        - Obligation:
             runtime complexity wrt. defined symbols {activate,f,g} and constructors {n__f,n__g}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            activate(X) -> X
            activate(n__f(X1,X2)) -> f(activate(X1),X2)
            activate(n__g(X)) -> g(activate(X))
            f(X1,X2) -> n__f(X1,X2)
            f(g(X),Y) -> f(X,n__f(n__g(X),activate(Y)))
            g(X) -> n__g(X)
        - Signature:
            {activate/1,f/2,g/1} / {n__f/2,n__g/1}
        - Obligation:
             runtime complexity wrt. defined symbols {activate,f,g} and constructors {n__f,n__g}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            activate(X) -> X
            activate(n__f(X1,X2)) -> f(activate(X1),X2)
            activate(n__g(X)) -> g(activate(X))
            f(X1,X2) -> n__f(X1,X2)
            f(g(X),Y) -> f(X,n__f(n__g(X),activate(Y)))
            g(X) -> n__g(X)
        - Signature:
            {activate/1,f/2,g/1} / {n__f/2,n__g/1}
        - Obligation:
             runtime complexity wrt. defined symbols {activate,f,g} and constructors {n__f,n__g}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          activate(x){x -> n__f(x,y)} =
            activate(n__f(x,y)) ->^+ f(activate(x),y)
              = C[activate(x) = activate(x){}]

WORST_CASE(Omega(n^1),?)