/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:
            f(t,x) -> f'(t,g(x))
            f'(triple(a,b,c),A()) -> f''(foldf(triple(cons(A(),a),nil(),c),b))
            f'(triple(a,b,c),B()) -> f(triple(a,b,c),A())
            f'(triple(a,b,c),C()) -> triple(a,b,cons(C(),c))
            f''(triple(a,b,c)) -> foldf(triple(a,b,nil()),c)
            foldf(x,cons(y,z)) -> f(foldf(x,z),y)
            foldf(x,nil()) -> x
            g(A()) -> A()
            g(B()) -> A()
            g(B()) -> B()
            g(C()) -> A()
            g(C()) -> B()
            g(C()) -> C()
        - Signature:
            {f/2,f'/2,f''/1,foldf/2,g/1} / {A/0,B/0,C/0,cons/2,nil/0,triple/3}
        - Obligation:
             runtime complexity wrt. defined symbols {f,f',f'',foldf,g} and constructors {A,B,C,cons,nil,triple}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            f(t,x) -> f'(t,g(x))
            f'(triple(a,b,c),A()) -> f''(foldf(triple(cons(A(),a),nil(),c),b))
            f'(triple(a,b,c),B()) -> f(triple(a,b,c),A())
            f'(triple(a,b,c),C()) -> triple(a,b,cons(C(),c))
            f''(triple(a,b,c)) -> foldf(triple(a,b,nil()),c)
            foldf(x,cons(y,z)) -> f(foldf(x,z),y)
            foldf(x,nil()) -> x
            g(A()) -> A()
            g(B()) -> A()
            g(B()) -> B()
            g(C()) -> A()
            g(C()) -> B()
            g(C()) -> C()
        - Signature:
            {f/2,f'/2,f''/1,foldf/2,g/1} / {A/0,B/0,C/0,cons/2,nil/0,triple/3}
        - Obligation:
             runtime complexity wrt. defined symbols {f,f',f'',foldf,g} and constructors {A,B,C,cons,nil,triple}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            f(t,x) -> f'(t,g(x))
            f'(triple(a,b,c),A()) -> f''(foldf(triple(cons(A(),a),nil(),c),b))
            f'(triple(a,b,c),B()) -> f(triple(a,b,c),A())
            f'(triple(a,b,c),C()) -> triple(a,b,cons(C(),c))
            f''(triple(a,b,c)) -> foldf(triple(a,b,nil()),c)
            foldf(x,cons(y,z)) -> f(foldf(x,z),y)
            foldf(x,nil()) -> x
            g(A()) -> A()
            g(B()) -> A()
            g(B()) -> B()
            g(C()) -> A()
            g(C()) -> B()
            g(C()) -> C()
        - Signature:
            {f/2,f'/2,f''/1,foldf/2,g/1} / {A/0,B/0,C/0,cons/2,nil/0,triple/3}
        - Obligation:
             runtime complexity wrt. defined symbols {f,f',f'',foldf,g} and constructors {A,B,C,cons,nil,triple}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          foldf(x,z){z -> cons(y,z)} =
            foldf(x,cons(y,z)) ->^+ f(foldf(x,z),y)
              = C[foldf(x,z) = foldf(x,z){}]

WORST_CASE(Omega(n^1),?)