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

WORST_CASE(Omega(n^1),?)