/home/nowonder/forschung/aprove/TPDB05/TRS/TRCSR/ExAppendixB_AEL03_Z.trs

The program

(VAR N X Y Z)
(RULES 
from(X) -> cons(X,n__from(s(X)))
2ndspos(0,Z) -> rnil
2ndspos(s(N),cons(X,Z)) -> 2ndspos(s(N),cons2(X,activate(Z)))
2ndspos(s(N),cons2(X,cons(Y,Z))) -> rcons(posrecip(Y),2ndsneg(N,activate(Z)))
2ndsneg(0,Z) -> rnil
2ndsneg(s(N),cons(X,Z)) -> 2ndsneg(s(N),cons2(X,activate(Z)))
2ndsneg(s(N),cons2(X,cons(Y,Z))) -> rcons(negrecip(Y),2ndspos(N,activate(Z)))
pi(X) -> 2ndspos(X,from(0))
plus(0,Y) -> Y
plus(s(X),Y) -> s(plus(X,Y))
times(0,Y) -> 0
times(s(X),Y) -> plus(Y,times(X,Y))
square(X) -> times(X,X)
from(X) -> n__from(X)
activate(n__from(X)) -> from(X)
activate(X) -> X
)

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