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

WORST_CASE(Omega(n^1),?)