/home/nowonder/forschung/aprove/TPDB05/TRS/TRCSR/Ex3_3_25_Bor03_C.trs

The program

(VAR YS X XS Y L X1 X2)
(RULES 
active(app(nil,YS)) -> mark(YS)
active(app(cons(X,XS),YS)) -> mark(cons(X,app(XS,YS)))
active(from(X)) -> mark(cons(X,from(s(X))))
active(zWadr(nil,YS)) -> mark(nil)
active(zWadr(XS,nil)) -> mark(nil)
active(zWadr(cons(X,XS),cons(Y,YS))) -> mark(cons(app(Y,cons(X,nil)),zWadr(XS,YS)))
active(prefix(L)) -> mark(cons(nil,zWadr(L,prefix(L))))
active(app(X1,X2)) -> app(active(X1),X2)
active(app(X1,X2)) -> app(X1,active(X2))
active(cons(X1,X2)) -> cons(active(X1),X2)
active(from(X)) -> from(active(X))
active(s(X)) -> s(active(X))
active(zWadr(X1,X2)) -> zWadr(active(X1),X2)
active(zWadr(X1,X2)) -> zWadr(X1,active(X2))
active(prefix(X)) -> prefix(active(X))
app(mark(X1),X2) -> mark(app(X1,X2))
app(X1,mark(X2)) -> mark(app(X1,X2))
cons(mark(X1),X2) -> mark(cons(X1,X2))
from(mark(X)) -> mark(from(X))
s(mark(X)) -> mark(s(X))
zWadr(mark(X1),X2) -> mark(zWadr(X1,X2))
zWadr(X1,mark(X2)) -> mark(zWadr(X1,X2))
prefix(mark(X)) -> mark(prefix(X))
proper(app(X1,X2)) -> app(proper(X1),proper(X2))
proper(nil) -> ok(nil)
proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
proper(from(X)) -> from(proper(X))
proper(s(X)) -> s(proper(X))
proper(zWadr(X1,X2)) -> zWadr(proper(X1),proper(X2))
proper(prefix(X)) -> prefix(proper(X))
app(ok(X1),ok(X2)) -> ok(app(X1,X2))
cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
from(ok(X)) -> ok(from(X))
s(ok(X)) -> ok(s(X))
zWadr(ok(X1),ok(X2)) -> ok(zWadr(X1,X2))
prefix(ok(X)) -> ok(prefix(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
)

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