/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:
            +(x,h()) -> x
            +(+(x,y),z) -> +(x,+(y,z))
            +(h(),x) -> x
            +(s(x),s(y)) -> s(s(+(x,y)))
            a(l,x,s(y),h()) -> a(l,x,y,s(h()))
            a(l,x,s(y),s(z)) -> a(l,x,y,a(l,x,s(y),z))
            a(l,s(x),h(),z) -> a(l,x,z,z)
            a(h(),h(),h(),x) -> s(x)
            a(s(l),h(),h(),z) -> a(l,z,h(),z)
            app(l,nil()) -> l
            app(cons(x,l),k) -> cons(x,app(l,k))
            app(nil(),k) -> k
            s(h()) -> 1()
            sum(cons(x,cons(y,l))) -> sum(cons(a(x,y,h(),h()),l))
            sum(cons(x,nil())) -> cons(x,nil())
        - Signature:
            {+/2,a/4,app/2,s/1,sum/1} / {1/0,cons/2,h/0,nil/0}
        - Obligation:
             runtime complexity wrt. defined symbols {+,a,app,s,sum} and constructors {1,cons,h,nil}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            +(x,h()) -> x
            +(+(x,y),z) -> +(x,+(y,z))
            +(h(),x) -> x
            +(s(x),s(y)) -> s(s(+(x,y)))
            a(l,x,s(y),h()) -> a(l,x,y,s(h()))
            a(l,x,s(y),s(z)) -> a(l,x,y,a(l,x,s(y),z))
            a(l,s(x),h(),z) -> a(l,x,z,z)
            a(h(),h(),h(),x) -> s(x)
            a(s(l),h(),h(),z) -> a(l,z,h(),z)
            app(l,nil()) -> l
            app(cons(x,l),k) -> cons(x,app(l,k))
            app(nil(),k) -> k
            s(h()) -> 1()
            sum(cons(x,cons(y,l))) -> sum(cons(a(x,y,h(),h()),l))
            sum(cons(x,nil())) -> cons(x,nil())
        - Signature:
            {+/2,a/4,app/2,s/1,sum/1} / {1/0,cons/2,h/0,nil/0}
        - Obligation:
             runtime complexity wrt. defined symbols {+,a,app,s,sum} and constructors {1,cons,h,nil}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            +(x,h()) -> x
            +(+(x,y),z) -> +(x,+(y,z))
            +(h(),x) -> x
            +(s(x),s(y)) -> s(s(+(x,y)))
            a(l,x,s(y),h()) -> a(l,x,y,s(h()))
            a(l,x,s(y),s(z)) -> a(l,x,y,a(l,x,s(y),z))
            a(l,s(x),h(),z) -> a(l,x,z,z)
            a(h(),h(),h(),x) -> s(x)
            a(s(l),h(),h(),z) -> a(l,z,h(),z)
            app(l,nil()) -> l
            app(cons(x,l),k) -> cons(x,app(l,k))
            app(nil(),k) -> k
            s(h()) -> 1()
            sum(cons(x,cons(y,l))) -> sum(cons(a(x,y,h(),h()),l))
            sum(cons(x,nil())) -> cons(x,nil())
        - Signature:
            {+/2,a/4,app/2,s/1,sum/1} / {1/0,cons/2,h/0,nil/0}
        - Obligation:
             runtime complexity wrt. defined symbols {+,a,app,s,sum} and constructors {1,cons,h,nil}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          app(y,z){y -> cons(x,y)} =
            app(cons(x,y),z) ->^+ cons(x,app(y,z))
              = C[app(y,z) = app(y,z){}]

WORST_CASE(Omega(n^1),?)