/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:
            fcons(X,Z) -> cons(X,Z)
            first(0(),Z) -> nil()
            first(s(X),cons(Y,Z)) -> cons(Y,first(X,Z))
            first1(0(),Z) -> nil1()
            first1(s(X),cons(Y,Z)) -> cons1(quote(Y),first1(X,Z))
            from(X) -> cons(X,from(s(X)))
            quote(0()) -> 01()
            quote(s(X)) -> s1(quote(X))
            quote(sel(X,Z)) -> sel1(X,Z)
            quote1(cons(X,Z)) -> cons1(quote(X),quote1(Z))
            quote1(first(X,Z)) -> first1(X,Z)
            quote1(nil()) -> nil1()
            sel(0(),cons(X,Z)) -> X
            sel(s(X),cons(Y,Z)) -> sel(X,Z)
            sel1(0(),cons(X,Z)) -> quote(X)
            sel1(s(X),cons(Y,Z)) -> sel1(X,Z)
            unquote(01()) -> 0()
            unquote(s1(X)) -> s(unquote(X))
            unquote1(cons1(X,Z)) -> fcons(unquote(X),unquote1(Z))
            unquote1(nil1()) -> nil()
        - Signature:
            {fcons/2,first/2,first1/2,from/1,quote/1,quote1/1,sel/2,sel1/2,unquote/1,unquote1/1} / {0/0,01/0,cons/2
            ,cons1/2,nil/0,nil1/0,s/1,s1/1}
        - Obligation:
             runtime complexity wrt. defined symbols {fcons,first,first1,from,quote,quote1,sel,sel1,unquote
            ,unquote1} and constructors {0,01,cons,cons1,nil,nil1,s,s1}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            fcons(X,Z) -> cons(X,Z)
            first(0(),Z) -> nil()
            first(s(X),cons(Y,Z)) -> cons(Y,first(X,Z))
            first1(0(),Z) -> nil1()
            first1(s(X),cons(Y,Z)) -> cons1(quote(Y),first1(X,Z))
            from(X) -> cons(X,from(s(X)))
            quote(0()) -> 01()
            quote(s(X)) -> s1(quote(X))
            quote(sel(X,Z)) -> sel1(X,Z)
            quote1(cons(X,Z)) -> cons1(quote(X),quote1(Z))
            quote1(first(X,Z)) -> first1(X,Z)
            quote1(nil()) -> nil1()
            sel(0(),cons(X,Z)) -> X
            sel(s(X),cons(Y,Z)) -> sel(X,Z)
            sel1(0(),cons(X,Z)) -> quote(X)
            sel1(s(X),cons(Y,Z)) -> sel1(X,Z)
            unquote(01()) -> 0()
            unquote(s1(X)) -> s(unquote(X))
            unquote1(cons1(X,Z)) -> fcons(unquote(X),unquote1(Z))
            unquote1(nil1()) -> nil()
        - Signature:
            {fcons/2,first/2,first1/2,from/1,quote/1,quote1/1,sel/2,sel1/2,unquote/1,unquote1/1} / {0/0,01/0,cons/2
            ,cons1/2,nil/0,nil1/0,s/1,s1/1}
        - Obligation:
             runtime complexity wrt. defined symbols {fcons,first,first1,from,quote,quote1,sel,sel1,unquote
            ,unquote1} and constructors {0,01,cons,cons1,nil,nil1,s,s1}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            fcons(X,Z) -> cons(X,Z)
            first(0(),Z) -> nil()
            first(s(X),cons(Y,Z)) -> cons(Y,first(X,Z))
            first1(0(),Z) -> nil1()
            first1(s(X),cons(Y,Z)) -> cons1(quote(Y),first1(X,Z))
            from(X) -> cons(X,from(s(X)))
            quote(0()) -> 01()
            quote(s(X)) -> s1(quote(X))
            quote(sel(X,Z)) -> sel1(X,Z)
            quote1(cons(X,Z)) -> cons1(quote(X),quote1(Z))
            quote1(first(X,Z)) -> first1(X,Z)
            quote1(nil()) -> nil1()
            sel(0(),cons(X,Z)) -> X
            sel(s(X),cons(Y,Z)) -> sel(X,Z)
            sel1(0(),cons(X,Z)) -> quote(X)
            sel1(s(X),cons(Y,Z)) -> sel1(X,Z)
            unquote(01()) -> 0()
            unquote(s1(X)) -> s(unquote(X))
            unquote1(cons1(X,Z)) -> fcons(unquote(X),unquote1(Z))
            unquote1(nil1()) -> nil()
        - Signature:
            {fcons/2,first/2,first1/2,from/1,quote/1,quote1/1,sel/2,sel1/2,unquote/1,unquote1/1} / {0/0,01/0,cons/2
            ,cons1/2,nil/0,nil1/0,s/1,s1/1}
        - Obligation:
             runtime complexity wrt. defined symbols {fcons,first,first1,from,quote,quote1,sel,sel1,unquote
            ,unquote1} and constructors {0,01,cons,cons1,nil,nil1,s,s1}
    + 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),?)