/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:
            first(0(),Z) -> nil()
            first(s(X),cons(Y,Z)) -> cons(Y,first(X,Z))
            from(X) -> cons(X,from(s(X)))
            sel(0(),cons(X,Z)) -> X
            sel(s(X),cons(Y,Z)) -> sel(X,Z)
        - Signature:
            {first/2,from/1,sel/2} / {0/0,cons/2,nil/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {first,from,sel} 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:
            first(0(),Z) -> nil()
            first(s(X),cons(Y,Z)) -> cons(Y,first(X,Z))
            from(X) -> cons(X,from(s(X)))
            sel(0(),cons(X,Z)) -> X
            sel(s(X),cons(Y,Z)) -> sel(X,Z)
        - Signature:
            {first/2,from/1,sel/2} / {0/0,cons/2,nil/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {first,from,sel} 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:
            first(0(),Z) -> nil()
            first(s(X),cons(Y,Z)) -> cons(Y,first(X,Z))
            from(X) -> cons(X,from(s(X)))
            sel(0(),cons(X,Z)) -> X
            sel(s(X),cons(Y,Z)) -> sel(X,Z)
        - Signature:
            {first/2,from/1,sel/2} / {0/0,cons/2,nil/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {first,from,sel} and constructors {0,cons,nil,s}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          first(x,z){x -> s(x),z -> cons(y,z)} =
            first(s(x),cons(y,z)) ->^+ cons(y,first(x,z))
              = C[first(x,z) = first(x,z){}]

WORST_CASE(Omega(n^1),?)