R
↳Dependency Pair Analysis
SEL(s(X), cons(Y, Z)) -> SEL(X, activate(Z))
SEL(s(X), cons(Y, Z)) -> ACTIVATE(Z)
ACTIVATE(nfrom(X)) -> FROM(X)
R
↳DPs
→DP Problem 1
↳Narrowing Transformation
SEL(s(X), cons(Y, Z)) -> SEL(X, activate(Z))
from(X) -> cons(X, nfrom(s(X)))
from(X) -> nfrom(X)
sel(0, cons(X, Y)) -> X
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
activate(nfrom(X)) -> from(X)
activate(X) -> X
two new Dependency Pairs are created:
SEL(s(X), cons(Y, Z)) -> SEL(X, activate(Z))
SEL(s(X), cons(Y, nfrom(X''))) -> SEL(X, from(X''))
SEL(s(X), cons(Y, Z')) -> SEL(X, Z')
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳Argument Filtering and Ordering
SEL(s(X), cons(Y, Z')) -> SEL(X, Z')
SEL(s(X), cons(Y, nfrom(X''))) -> SEL(X, from(X''))
from(X) -> cons(X, nfrom(s(X)))
from(X) -> nfrom(X)
sel(0, cons(X, Y)) -> X
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
activate(nfrom(X)) -> from(X)
activate(X) -> X
SEL(s(X), cons(Y, Z')) -> SEL(X, Z')
from(X) -> cons(X, nfrom(s(X)))
from(X) -> nfrom(X)
sel(0, cons(X, Y)) -> X
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
activate(nfrom(X)) -> from(X)
activate(X) -> X
POL(n__from(x1)) = x1 POL(from(x1)) = 1 + x1 POL(activate(x1)) = 1 + x1 POL(cons(x1, x2)) = 1 + x1 + x2 POL(s) = 0
SEL(x1, x2) -> x2
cons(x1, x2) -> cons(x1, x2)
nfrom(x1) -> nfrom(x1)
from(x1) -> from(x1)
s(x1) -> s
sel(x1, x2) -> x2
activate(x1) -> activate(x1)
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳AFS
...
→DP Problem 3
↳Remaining Obligation(s)
SEL(s(X), cons(Y, nfrom(X''))) -> SEL(X, from(X''))
from(X) -> cons(X, nfrom(s(X)))
from(X) -> nfrom(X)
sel(0, cons(X, Y)) -> X
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
activate(nfrom(X)) -> from(X)
activate(X) -> X