R
↳Dependency Pair Analysis
FIRST(s(X), cons(Y, Z)) -> ACTIVATE(Z)
ACTIVATE(nfirst(X1, X2)) -> FIRST(X1, X2)
ACTIVATE(nfrom(X)) -> FROM(X)
R
↳DPs
→DP Problem 1
↳Argument Filtering and Ordering
ACTIVATE(nfirst(X1, X2)) -> FIRST(X1, X2)
FIRST(s(X), cons(Y, Z)) -> ACTIVATE(Z)
first(0, X) -> nil
first(s(X), cons(Y, Z)) -> cons(Y, nfirst(X, activate(Z)))
first(X1, X2) -> nfirst(X1, X2)
from(X) -> cons(X, nfrom(s(X)))
from(X) -> nfrom(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(X) -> X
ACTIVATE(nfirst(X1, X2)) -> FIRST(X1, X2)
first(0, X) -> nil
first(s(X), cons(Y, Z)) -> cons(Y, nfirst(X, activate(Z)))
first(X1, X2) -> nfirst(X1, X2)
from(X) -> cons(X, nfrom(s(X)))
from(X) -> nfrom(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(X) -> X
POL(from(x1)) = 1 + x1 POL(n__from(x1)) = x1 POL(activate(x1)) = 1 + x1 POL(first(x1, x2)) = x1 + x2 POL(0) = 0 POL(FIRST(x1, x2)) = x1 + x2 POL(nil) = 0 POL(s(x1)) = 1 + x1 POL(ACTIVATE(x1)) = 1 + x1 POL(n__first(x1, x2)) = x1 + x2
ACTIVATE(x1) -> ACTIVATE(x1)
FIRST(x1, x2) -> FIRST(x1, x2)
nfirst(x1, x2) -> nfirst(x1, x2)
s(x1) -> s(x1)
cons(x1, x2) -> x2
first(x1, x2) -> first(x1, x2)
activate(x1) -> activate(x1)
from(x1) -> from(x1)
nfrom(x1) -> nfrom(x1)
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳Dependency Graph
FIRST(s(X), cons(Y, Z)) -> ACTIVATE(Z)
first(0, X) -> nil
first(s(X), cons(Y, Z)) -> cons(Y, nfirst(X, activate(Z)))
first(X1, X2) -> nfirst(X1, X2)
from(X) -> cons(X, nfrom(s(X)))
from(X) -> nfrom(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(X) -> X