/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:
            activate(X) -> X
            activate(n__natsFrom(X)) -> natsFrom(X)
            afterNth(N,XS) -> snd(splitAt(N,XS))
            fst(pair(XS,YS)) -> XS
            head(cons(N,XS)) -> N
            natsFrom(N) -> cons(N,n__natsFrom(s(N)))
            natsFrom(X) -> n__natsFrom(X)
            sel(N,XS) -> head(afterNth(N,XS))
            snd(pair(XS,YS)) -> YS
            splitAt(0(),XS) -> pair(nil(),XS)
            splitAt(s(N),cons(X,XS)) -> u(splitAt(N,activate(XS)),N,X,activate(XS))
            tail(cons(N,XS)) -> activate(XS)
            take(N,XS) -> fst(splitAt(N,XS))
            u(pair(YS,ZS),N,X,XS) -> pair(cons(activate(X),YS),ZS)
        - Signature:
            {activate/1,afterNth/2,fst/1,head/1,natsFrom/1,sel/2,snd/1,splitAt/2,tail/1,take/2,u/4} / {0/0,cons/2
            ,n__natsFrom/1,nil/0,pair/2,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {activate,afterNth,fst,head,natsFrom,sel,snd,splitAt,tail,take
            ,u} and constructors {0,cons,n__natsFrom,nil,pair,s}
    + 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__natsFrom(X)) -> natsFrom(X)
            afterNth(N,XS) -> snd(splitAt(N,XS))
            fst(pair(XS,YS)) -> XS
            head(cons(N,XS)) -> N
            natsFrom(N) -> cons(N,n__natsFrom(s(N)))
            natsFrom(X) -> n__natsFrom(X)
            sel(N,XS) -> head(afterNth(N,XS))
            snd(pair(XS,YS)) -> YS
            splitAt(0(),XS) -> pair(nil(),XS)
            splitAt(s(N),cons(X,XS)) -> u(splitAt(N,activate(XS)),N,X,activate(XS))
            tail(cons(N,XS)) -> activate(XS)
            take(N,XS) -> fst(splitAt(N,XS))
            u(pair(YS,ZS),N,X,XS) -> pair(cons(activate(X),YS),ZS)
        - Signature:
            {activate/1,afterNth/2,fst/1,head/1,natsFrom/1,sel/2,snd/1,splitAt/2,tail/1,take/2,u/4} / {0/0,cons/2
            ,n__natsFrom/1,nil/0,pair/2,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {activate,afterNth,fst,head,natsFrom,sel,snd,splitAt,tail,take
            ,u} and constructors {0,cons,n__natsFrom,nil,pair,s}
    + 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__natsFrom(X)) -> natsFrom(X)
            afterNth(N,XS) -> snd(splitAt(N,XS))
            fst(pair(XS,YS)) -> XS
            head(cons(N,XS)) -> N
            natsFrom(N) -> cons(N,n__natsFrom(s(N)))
            natsFrom(X) -> n__natsFrom(X)
            sel(N,XS) -> head(afterNth(N,XS))
            snd(pair(XS,YS)) -> YS
            splitAt(0(),XS) -> pair(nil(),XS)
            splitAt(s(N),cons(X,XS)) -> u(splitAt(N,activate(XS)),N,X,activate(XS))
            tail(cons(N,XS)) -> activate(XS)
            take(N,XS) -> fst(splitAt(N,XS))
            u(pair(YS,ZS),N,X,XS) -> pair(cons(activate(X),YS),ZS)
        - Signature:
            {activate/1,afterNth/2,fst/1,head/1,natsFrom/1,sel/2,snd/1,splitAt/2,tail/1,take/2,u/4} / {0/0,cons/2
            ,n__natsFrom/1,nil/0,pair/2,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {activate,afterNth,fst,head,natsFrom,sel,snd,splitAt,tail,take
            ,u} and constructors {0,cons,n__natsFrom,nil,pair,s}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          splitAt(y,x){y -> s(y),x -> cons(u,x)} =
            splitAt(s(y),cons(u,x)) ->^+ u(splitAt(y,x),y,u,activate(x))
              = C[splitAt(y,x) = splitAt(y,x){}]

WORST_CASE(Omega(n^1),?)