/home/nowonder/forschung/aprove/TPDB05/TRS/TRCSR/Ex1_2_AEL03_C.trs

The program

(VAR N X Y Z X1 X2)
(RULES 
active(from(X)) -> mark(cons(X,from(s(X))))
active(2ndspos(0,Z)) -> mark(rnil)
active(2ndspos(s(N),cons(X,cons(Y,Z)))) -> mark(rcons(posrecip(Y),2ndsneg(N,Z)))
active(2ndsneg(0,Z)) -> mark(rnil)
active(2ndsneg(s(N),cons(X,cons(Y,Z)))) -> mark(rcons(negrecip(Y),2ndspos(N,Z)))
active(pi(X)) -> mark(2ndspos(X,from(0)))
active(plus(0,Y)) -> mark(Y)
active(plus(s(X),Y)) -> mark(s(plus(X,Y)))
active(times(0,Y)) -> mark(0)
active(times(s(X),Y)) -> mark(plus(Y,times(X,Y)))
active(square(X)) -> mark(times(X,X))
active(s(X)) -> s(active(X))
active(posrecip(X)) -> posrecip(active(X))
active(negrecip(X)) -> negrecip(active(X))
active(cons(X1,X2)) -> cons(active(X1),X2)
active(rcons(X1,X2)) -> rcons(active(X1),X2)
active(rcons(X1,X2)) -> rcons(X1,active(X2))
active(from(X)) -> from(active(X))
active(2ndspos(X1,X2)) -> 2ndspos(active(X1),X2)
active(2ndspos(X1,X2)) -> 2ndspos(X1,active(X2))
active(2ndsneg(X1,X2)) -> 2ndsneg(active(X1),X2)
active(2ndsneg(X1,X2)) -> 2ndsneg(X1,active(X2))
active(pi(X)) -> pi(active(X))
active(plus(X1,X2)) -> plus(active(X1),X2)
active(plus(X1,X2)) -> plus(X1,active(X2))
active(times(X1,X2)) -> times(active(X1),X2)
active(times(X1,X2)) -> times(X1,active(X2))
active(square(X)) -> square(active(X))
s(mark(X)) -> mark(s(X))
posrecip(mark(X)) -> mark(posrecip(X))
negrecip(mark(X)) -> mark(negrecip(X))
cons(mark(X1),X2) -> mark(cons(X1,X2))
rcons(mark(X1),X2) -> mark(rcons(X1,X2))
rcons(X1,mark(X2)) -> mark(rcons(X1,X2))
from(mark(X)) -> mark(from(X))
2ndspos(mark(X1),X2) -> mark(2ndspos(X1,X2))
2ndspos(X1,mark(X2)) -> mark(2ndspos(X1,X2))
2ndsneg(mark(X1),X2) -> mark(2ndsneg(X1,X2))
2ndsneg(X1,mark(X2)) -> mark(2ndsneg(X1,X2))
pi(mark(X)) -> mark(pi(X))
plus(mark(X1),X2) -> mark(plus(X1,X2))
plus(X1,mark(X2)) -> mark(plus(X1,X2))
times(mark(X1),X2) -> mark(times(X1,X2))
times(X1,mark(X2)) -> mark(times(X1,X2))
square(mark(X)) -> mark(square(X))
proper(0) -> ok(0)
proper(s(X)) -> s(proper(X))
proper(posrecip(X)) -> posrecip(proper(X))
proper(negrecip(X)) -> negrecip(proper(X))
proper(nil) -> ok(nil)
proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
proper(rnil) -> ok(rnil)
proper(rcons(X1,X2)) -> rcons(proper(X1),proper(X2))
proper(from(X)) -> from(proper(X))
proper(2ndspos(X1,X2)) -> 2ndspos(proper(X1),proper(X2))
proper(2ndsneg(X1,X2)) -> 2ndsneg(proper(X1),proper(X2))
proper(pi(X)) -> pi(proper(X))
proper(plus(X1,X2)) -> plus(proper(X1),proper(X2))
proper(times(X1,X2)) -> times(proper(X1),proper(X2))
proper(square(X)) -> square(proper(X))
s(ok(X)) -> ok(s(X))
posrecip(ok(X)) -> ok(posrecip(X))
negrecip(ok(X)) -> ok(negrecip(X))
cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
rcons(ok(X1),ok(X2)) -> ok(rcons(X1,X2))
from(ok(X)) -> ok(from(X))
2ndspos(ok(X1),ok(X2)) -> ok(2ndspos(X1,X2))
2ndsneg(ok(X1),ok(X2)) -> ok(2ndsneg(X1,X2))
pi(ok(X)) -> ok(pi(X))
plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
times(ok(X1),ok(X2)) -> ok(times(X1,X2))
square(ok(X)) -> ok(square(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
)

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