/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:
            a__a() -> a()
            a__a() -> b()
            a__f(X,X) -> a__h(a__a())
            a__f(X1,X2) -> f(X1,X2)
            a__g(X1,X2) -> g(X1,X2)
            a__g(a(),X) -> a__f(b(),X)
            a__h(X) -> a__g(mark(X),X)
            a__h(X) -> h(X)
            mark(a()) -> a__a()
            mark(b()) -> b()
            mark(f(X1,X2)) -> a__f(mark(X1),X2)
            mark(g(X1,X2)) -> a__g(mark(X1),X2)
            mark(h(X)) -> a__h(mark(X))
        - Signature:
            {a__a/0,a__f/2,a__g/2,a__h/1,mark/1} / {a/0,b/0,f/2,g/2,h/1}
        - Obligation:
             runtime complexity wrt. defined symbols {a__a,a__f,a__g,a__h,mark} and constructors {a,b,f,g,h}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            a__a() -> a()
            a__a() -> b()
            a__f(X,X) -> a__h(a__a())
            a__f(X1,X2) -> f(X1,X2)
            a__g(X1,X2) -> g(X1,X2)
            a__g(a(),X) -> a__f(b(),X)
            a__h(X) -> a__g(mark(X),X)
            a__h(X) -> h(X)
            mark(a()) -> a__a()
            mark(b()) -> b()
            mark(f(X1,X2)) -> a__f(mark(X1),X2)
            mark(g(X1,X2)) -> a__g(mark(X1),X2)
            mark(h(X)) -> a__h(mark(X))
        - Signature:
            {a__a/0,a__f/2,a__g/2,a__h/1,mark/1} / {a/0,b/0,f/2,g/2,h/1}
        - Obligation:
             runtime complexity wrt. defined symbols {a__a,a__f,a__g,a__h,mark} and constructors {a,b,f,g,h}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            a__a() -> a()
            a__a() -> b()
            a__f(X,X) -> a__h(a__a())
            a__f(X1,X2) -> f(X1,X2)
            a__g(X1,X2) -> g(X1,X2)
            a__g(a(),X) -> a__f(b(),X)
            a__h(X) -> a__g(mark(X),X)
            a__h(X) -> h(X)
            mark(a()) -> a__a()
            mark(b()) -> b()
            mark(f(X1,X2)) -> a__f(mark(X1),X2)
            mark(g(X1,X2)) -> a__g(mark(X1),X2)
            mark(h(X)) -> a__h(mark(X))
        - Signature:
            {a__a/0,a__f/2,a__g/2,a__h/1,mark/1} / {a/0,b/0,f/2,g/2,h/1}
        - Obligation:
             runtime complexity wrt. defined symbols {a__a,a__f,a__g,a__h,mark} and constructors {a,b,f,g,h}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          mark(x){x -> f(x,y)} =
            mark(f(x,y)) ->^+ a__f(mark(x),y)
              = C[mark(x) = mark(x){}]

WORST_CASE(Omega(n^1),?)