/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:
            U11(tt(),N,X,XS) -> U12(splitAt(activate(N),activate(XS)),activate(X))
            U12(pair(YS,ZS),X) -> pair(cons(activate(X),YS),ZS)
            activate(X) -> X
            activate(n__natsFrom(X)) -> natsFrom(X)
            afterNth(N,XS) -> snd(splitAt(N,XS))
            and(tt(),X) -> activate(X)
            fst(pair(X,Y)) -> X
            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(X,Y)) -> Y
            splitAt(0(),XS) -> pair(nil(),XS)
            splitAt(s(N),cons(X,XS)) -> U11(tt(),N,X,activate(XS))
            tail(cons(N,XS)) -> activate(XS)
            take(N,XS) -> fst(splitAt(N,XS))
        - Signature:
            {U11/4,U12/2,activate/1,afterNth/2,and/2,fst/1,head/1,natsFrom/1,sel/2,snd/1,splitAt/2,tail/1,take/2} / {0/0
            ,cons/2,n__natsFrom/1,nil/0,pair/2,s/1,tt/0}
        - Obligation:
             runtime complexity wrt. defined symbols {U11,U12,activate,afterNth,and,fst,head,natsFrom,sel,snd,splitAt
            ,tail,take} and constructors {0,cons,n__natsFrom,nil,pair,s,tt}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            U11(tt(),N,X,XS) -> U12(splitAt(activate(N),activate(XS)),activate(X))
            U12(pair(YS,ZS),X) -> pair(cons(activate(X),YS),ZS)
            activate(X) -> X
            activate(n__natsFrom(X)) -> natsFrom(X)
            afterNth(N,XS) -> snd(splitAt(N,XS))
            and(tt(),X) -> activate(X)
            fst(pair(X,Y)) -> X
            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(X,Y)) -> Y
            splitAt(0(),XS) -> pair(nil(),XS)
            splitAt(s(N),cons(X,XS)) -> U11(tt(),N,X,activate(XS))
            tail(cons(N,XS)) -> activate(XS)
            take(N,XS) -> fst(splitAt(N,XS))
        - Signature:
            {U11/4,U12/2,activate/1,afterNth/2,and/2,fst/1,head/1,natsFrom/1,sel/2,snd/1,splitAt/2,tail/1,take/2} / {0/0
            ,cons/2,n__natsFrom/1,nil/0,pair/2,s/1,tt/0}
        - Obligation:
             runtime complexity wrt. defined symbols {U11,U12,activate,afterNth,and,fst,head,natsFrom,sel,snd,splitAt
            ,tail,take} and constructors {0,cons,n__natsFrom,nil,pair,s,tt}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            U11(tt(),N,X,XS) -> U12(splitAt(activate(N),activate(XS)),activate(X))
            U12(pair(YS,ZS),X) -> pair(cons(activate(X),YS),ZS)
            activate(X) -> X
            activate(n__natsFrom(X)) -> natsFrom(X)
            afterNth(N,XS) -> snd(splitAt(N,XS))
            and(tt(),X) -> activate(X)
            fst(pair(X,Y)) -> X
            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(X,Y)) -> Y
            splitAt(0(),XS) -> pair(nil(),XS)
            splitAt(s(N),cons(X,XS)) -> U11(tt(),N,X,activate(XS))
            tail(cons(N,XS)) -> activate(XS)
            take(N,XS) -> fst(splitAt(N,XS))
        - Signature:
            {U11/4,U12/2,activate/1,afterNth/2,and/2,fst/1,head/1,natsFrom/1,sel/2,snd/1,splitAt/2,tail/1,take/2} / {0/0
            ,cons/2,n__natsFrom/1,nil/0,pair/2,s/1,tt/0}
        - Obligation:
             runtime complexity wrt. defined symbols {U11,U12,activate,afterNth,and,fst,head,natsFrom,sel,snd,splitAt
            ,tail,take} and constructors {0,cons,n__natsFrom,nil,pair,s,tt}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          U11(tt(),y,x_31,x){y -> s(y),x -> cons(w,x)} =
            U11(tt(),s(y),x_31,cons(w,x)) ->^+ U12(U11(tt(),y,w,x),activate(x_31))
              = C[U11(tt(),y,w,x) = U11(tt(),y,x_31,x){x_31 -> w}]

WORST_CASE(Omega(n^1),?)