/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:
            activate(X) -> X
            activate(n__first(X1,X2)) -> first(activate(X1),activate(X2))
            activate(n__from(X)) -> from(activate(X))
            activate(n__s(X)) -> s(activate(X))
            first(X1,X2) -> n__first(X1,X2)
            first(0(),Z) -> nil()
            first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z)))
            from(X) -> cons(X,n__from(n__s(X)))
            from(X) -> n__from(X)
            s(X) -> n__s(X)
            sel(0(),cons(X,Z)) -> X
            sel(s(X),cons(Y,Z)) -> sel(X,activate(Z))
        - Signature:
            {activate/1,first/2,from/1,s/1,sel/2} / {0/0,cons/2,n__first/2,n__from/1,n__s/1,nil/0}
        - Obligation:
             runtime complexity wrt. defined symbols {activate,first,from,s,sel} and constructors {0,cons,n__first
            ,n__from,n__s,nil}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            activate(X) -> X
            activate(n__first(X1,X2)) -> first(activate(X1),activate(X2))
            activate(n__from(X)) -> from(activate(X))
            activate(n__s(X)) -> s(activate(X))
            first(X1,X2) -> n__first(X1,X2)
            first(0(),Z) -> nil()
            first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z)))
            from(X) -> cons(X,n__from(n__s(X)))
            from(X) -> n__from(X)
            s(X) -> n__s(X)
            sel(0(),cons(X,Z)) -> X
            sel(s(X),cons(Y,Z)) -> sel(X,activate(Z))
        - Signature:
            {activate/1,first/2,from/1,s/1,sel/2} / {0/0,cons/2,n__first/2,n__from/1,n__s/1,nil/0}
        - Obligation:
             runtime complexity wrt. defined symbols {activate,first,from,s,sel} and constructors {0,cons,n__first
            ,n__from,n__s,nil}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            activate(X) -> X
            activate(n__first(X1,X2)) -> first(activate(X1),activate(X2))
            activate(n__from(X)) -> from(activate(X))
            activate(n__s(X)) -> s(activate(X))
            first(X1,X2) -> n__first(X1,X2)
            first(0(),Z) -> nil()
            first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z)))
            from(X) -> cons(X,n__from(n__s(X)))
            from(X) -> n__from(X)
            s(X) -> n__s(X)
            sel(0(),cons(X,Z)) -> X
            sel(s(X),cons(Y,Z)) -> sel(X,activate(Z))
        - Signature:
            {activate/1,first/2,from/1,s/1,sel/2} / {0/0,cons/2,n__first/2,n__from/1,n__s/1,nil/0}
        - Obligation:
             runtime complexity wrt. defined symbols {activate,first,from,s,sel} and constructors {0,cons,n__first
            ,n__from,n__s,nil}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          activate(x){x -> n__first(x,y)} =
            activate(n__first(x,y)) ->^+ first(activate(x),activate(y))
              = C[activate(x) = activate(x){}]

WORST_CASE(Omega(n^1),?)