/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:
            a(x,s(y),h()) -> a(x,y,s(h()))
            a(x,s(y),s(z)) -> a(x,y,a(x,s(y),z))
            a(h(),h(),x) -> s(x)
            a(s(x),h(),z) -> a(x,z,z)
            app(l,nil()) -> l
            app(cons(x,l),k) -> cons(x,app(l,k))
            app(nil(),k) -> k
            sum(cons(x,cons(y,l))) -> sum(cons(a(x,y,h()),l))
            sum(cons(x,nil())) -> cons(x,nil())
        - Signature:
            {a/3,app/2,sum/1} / {cons/2,h/0,nil/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {a,app,sum} and constructors {cons,h,nil,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            a(x,s(y),h()) -> a(x,y,s(h()))
            a(x,s(y),s(z)) -> a(x,y,a(x,s(y),z))
            a(h(),h(),x) -> s(x)
            a(s(x),h(),z) -> a(x,z,z)
            app(l,nil()) -> l
            app(cons(x,l),k) -> cons(x,app(l,k))
            app(nil(),k) -> k
            sum(cons(x,cons(y,l))) -> sum(cons(a(x,y,h()),l))
            sum(cons(x,nil())) -> cons(x,nil())
        - Signature:
            {a/3,app/2,sum/1} / {cons/2,h/0,nil/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {a,app,sum} and constructors {cons,h,nil,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            a(x,s(y),h()) -> a(x,y,s(h()))
            a(x,s(y),s(z)) -> a(x,y,a(x,s(y),z))
            a(h(),h(),x) -> s(x)
            a(s(x),h(),z) -> a(x,z,z)
            app(l,nil()) -> l
            app(cons(x,l),k) -> cons(x,app(l,k))
            app(nil(),k) -> k
            sum(cons(x,cons(y,l))) -> sum(cons(a(x,y,h()),l))
            sum(cons(x,nil())) -> cons(x,nil())
        - Signature:
            {a/3,app/2,sum/1} / {cons/2,h/0,nil/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {a,app,sum} and constructors {cons,h,nil,s}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          a(x,s(y),z){z -> s(z)} =
            a(x,s(y),s(z)) ->^+ a(x,y,a(x,s(y),z))
              = C[a(x,s(y),z) = a(x,s(y),z){}]

WORST_CASE(Omega(n^1),?)