/home/nowonder/forschung/aprove/TPDB05/TRS/TRCSR/Ex15_Luc98_Z.trs

The program

(VAR X Y Z X1 X2)
(RULES 
and(true,X) -> activate(X)
and(false,Y) -> false
if(true,X,Y) -> activate(X)
if(false,X,Y) -> activate(Y)
add(0,X) -> activate(X)
add(s(X),Y) -> s(n__add(activate(X),activate(Y)))
first(0,X) -> nil
first(s(X),cons(Y,Z)) -> cons(activate(Y),n__first(activate(X),activate(Z)))
from(X) -> cons(activate(X),n__from(n__s(activate(X))))
add(X1,X2) -> n__add(X1,X2)
first(X1,X2) -> n__first(X1,X2)
from(X) -> n__from(X)
s(X) -> n__s(X)
activate(n__add(X1,X2)) -> add(X1,X2)
activate(n__first(X1,X2)) -> first(X1,X2)
activate(n__from(X)) -> from(X)
activate(n__s(X)) -> s(X)
activate(X) -> X
)

Submit to AProVE Web Frontend

Edit in AProVE Web Frontend