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

WORST_CASE(Omega(n^1),?)