Term Rewriting System R:
[YS, X, XS, X1, X2, Y, L]
app(nil, YS) -> YS
app(cons(X, XS), YS) -> cons(X, napp(activate(XS), YS))
app(X1, X2) -> napp(X1, X2)
from(X) -> cons(X, nfrom(ns(X)))
from(X) -> nfrom(X)
zWadr(nil, YS) -> nil
zWadr(XS, nil) -> nil
zWadr(cons(X, XS), cons(Y, YS)) -> cons(app(Y, cons(X, nnil)), nzWadr(activate(XS), activate(YS)))
zWadr(X1, X2) -> nzWadr(X1, X2)
prefix(L) -> cons(nil, nzWadr(L, nprefix(L)))
prefix(X) -> nprefix(X)
s(X) -> ns(X)
nil -> nnil
activate(napp(X1, X2)) -> app(activate(X1), activate(X2))
activate(nfrom(X)) -> from(activate(X))
activate(ns(X)) -> s(activate(X))
activate(nnil) -> nil
activate(nzWadr(X1, X2)) -> zWadr(activate(X1), activate(X2))
activate(nprefix(X)) -> prefix(activate(X))
activate(X) -> X

Termination of R to be shown. 



   R
     ↳Dependency Pair Analysis



R contains the following Dependency Pairs:

APP(cons(X, XS), YS) -> ACTIVATE(XS)
ZWADR(cons(X, XS), cons(Y, YS)) -> APP(Y, cons(X, nnil))
ZWADR(cons(X, XS), cons(Y, YS)) -> ACTIVATE(XS)
ZWADR(cons(X, XS), cons(Y, YS)) -> ACTIVATE(YS)
PREFIX(L) -> NIL
ACTIVATE(napp(X1, X2)) -> APP(activate(X1), activate(X2))
ACTIVATE(napp(X1, X2)) -> ACTIVATE(X1)
ACTIVATE(napp(X1, X2)) -> ACTIVATE(X2)
ACTIVATE(nfrom(X)) -> FROM(activate(X))
ACTIVATE(nfrom(X)) -> ACTIVATE(X)
ACTIVATE(ns(X)) -> S(activate(X))
ACTIVATE(ns(X)) -> ACTIVATE(X)
ACTIVATE(nnil) -> NIL
ACTIVATE(nzWadr(X1, X2)) -> ZWADR(activate(X1), activate(X2))
ACTIVATE(nzWadr(X1, X2)) -> ACTIVATE(X1)
ACTIVATE(nzWadr(X1, X2)) -> ACTIVATE(X2)
ACTIVATE(nprefix(X)) -> PREFIX(activate(X))
ACTIVATE(nprefix(X)) -> ACTIVATE(X)

Furthermore, R contains one SCC. 


   R
     ↳DPs
       →DP Problem 1
         ↳Remaining Obligation(s)




The following remains to be proven:
Dependency Pairs:

ZWADR(cons(X, XS), cons(Y, YS)) -> ACTIVATE(YS)
ACTIVATE(nprefix(X)) -> ACTIVATE(X)
ACTIVATE(nzWadr(X1, X2)) -> ACTIVATE(X2)
ACTIVATE(nzWadr(X1, X2)) -> ACTIVATE(X1)
ZWADR(cons(X, XS), cons(Y, YS)) -> ACTIVATE(XS)
ZWADR(cons(X, XS), cons(Y, YS)) -> APP(Y, cons(X, nnil))
ACTIVATE(nzWadr(X1, X2)) -> ZWADR(activate(X1), activate(X2))
ACTIVATE(ns(X)) -> ACTIVATE(X)
ACTIVATE(nfrom(X)) -> ACTIVATE(X)
ACTIVATE(napp(X1, X2)) -> ACTIVATE(X2)
ACTIVATE(napp(X1, X2)) -> ACTIVATE(X1)
ACTIVATE(napp(X1, X2)) -> APP(activate(X1), activate(X2))
APP(cons(X, XS), YS) -> ACTIVATE(XS)


Rules:


app(nil, YS) -> YS
app(cons(X, XS), YS) -> cons(X, napp(activate(XS), YS))
app(X1, X2) -> napp(X1, X2)
from(X) -> cons(X, nfrom(ns(X)))
from(X) -> nfrom(X)
zWadr(nil, YS) -> nil
zWadr(XS, nil) -> nil
zWadr(cons(X, XS), cons(Y, YS)) -> cons(app(Y, cons(X, nnil)), nzWadr(activate(XS), activate(YS)))
zWadr(X1, X2) -> nzWadr(X1, X2)
prefix(L) -> cons(nil, nzWadr(L, nprefix(L)))
prefix(X) -> nprefix(X)
s(X) -> ns(X)
nil -> nnil
activate(napp(X1, X2)) -> app(activate(X1), activate(X2))
activate(nfrom(X)) -> from(activate(X))
activate(ns(X)) -> s(activate(X))
activate(nnil) -> nil
activate(nzWadr(X1, X2)) -> zWadr(activate(X1), activate(X2))
activate(nprefix(X)) -> prefix(activate(X))
activate(X) -> X




Termination of R could not be shown.
Duration:
0:01 minutes