/home/nowonder/forschung/aprove/TPDB05/TRS/TRCSR/ExAppendixB_AEL03_GM.trs

The program

(VAR N X Y Z X1 X2)
(RULES 
a__from(X) -> cons(mark(X),from(s(X)))
a__2ndspos(0,Z) -> rnil
a__2ndspos(s(N),cons(X,Z)) -> a__2ndspos(s(mark(N)),cons2(X,mark(Z)))
a__2ndspos(s(N),cons2(X,cons(Y,Z))) -> rcons(posrecip(mark(Y)),a__2ndsneg(mark(N),mark(Z)))
a__2ndsneg(0,Z) -> rnil
a__2ndsneg(s(N),cons(X,Z)) -> a__2ndsneg(s(mark(N)),cons2(X,mark(Z)))
a__2ndsneg(s(N),cons2(X,cons(Y,Z))) -> rcons(negrecip(mark(Y)),a__2ndspos(mark(N),mark(Z)))
a__pi(X) -> a__2ndspos(mark(X),a__from(0))
a__plus(0,Y) -> mark(Y)
a__plus(s(X),Y) -> s(a__plus(mark(X),mark(Y)))
a__times(0,Y) -> 0
a__times(s(X),Y) -> a__plus(mark(Y),a__times(mark(X),mark(Y)))
a__square(X) -> a__times(mark(X),mark(X))
mark(from(X)) -> a__from(mark(X))
mark(2ndspos(X1,X2)) -> a__2ndspos(mark(X1),mark(X2))
mark(2ndsneg(X1,X2)) -> a__2ndsneg(mark(X1),mark(X2))
mark(pi(X)) -> a__pi(mark(X))
mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2))
mark(times(X1,X2)) -> a__times(mark(X1),mark(X2))
mark(square(X)) -> a__square(mark(X))
mark(0) -> 0
mark(s(X)) -> s(mark(X))
mark(posrecip(X)) -> posrecip(mark(X))
mark(negrecip(X)) -> negrecip(mark(X))
mark(nil) -> nil
mark(cons(X1,X2)) -> cons(mark(X1),X2)
mark(cons2(X1,X2)) -> cons2(X1,mark(X2))
mark(rnil) -> rnil
mark(rcons(X1,X2)) -> rcons(mark(X1),mark(X2))
a__from(X) -> from(X)
a__2ndspos(X1,X2) -> 2ndspos(X1,X2)
a__2ndsneg(X1,X2) -> 2ndsneg(X1,X2)
a__pi(X) -> pi(X)
a__plus(X1,X2) -> plus(X1,X2)
a__times(X1,X2) -> times(X1,X2)
a__square(X) -> square(X)
)

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