R
↳Dependency Pair Analysis
DBL(s(X)) -> S(ns(ndbl(activate(X))))
DBL(s(X)) -> ACTIVATE(X)
DBLS(cons(X, Y)) -> ACTIVATE(X)
DBLS(cons(X, Y)) -> ACTIVATE(Y)
SEL(0, cons(X, Y)) -> ACTIVATE(X)
SEL(s(X), cons(Y, Z)) -> SEL(activate(X), activate(Z))
SEL(s(X), cons(Y, Z)) -> ACTIVATE(X)
SEL(s(X), cons(Y, Z)) -> ACTIVATE(Z)
INDX(cons(X, Y), Z) -> ACTIVATE(X)
INDX(cons(X, Y), Z) -> ACTIVATE(Z)
INDX(cons(X, Y), Z) -> ACTIVATE(Y)
FROM(X) -> ACTIVATE(X)
ACTIVATE(ns(X)) -> S(X)
ACTIVATE(ndbl(X)) -> DBL(X)
ACTIVATE(ndbls(X)) -> DBLS(X)
ACTIVATE(nsel(X1, X2)) -> SEL(X1, X2)
ACTIVATE(nindx(X1, X2)) -> INDX(X1, X2)
ACTIVATE(nfrom(X)) -> FROM(X)
R
↳DPs
→DP Problem 1
↳Argument Filtering and Ordering
INDX(cons(X, Y), Z) -> ACTIVATE(Y)
INDX(cons(X, Y), Z) -> ACTIVATE(Z)
FROM(X) -> ACTIVATE(X)
ACTIVATE(nfrom(X)) -> FROM(X)
INDX(cons(X, Y), Z) -> ACTIVATE(X)
ACTIVATE(nindx(X1, X2)) -> INDX(X1, X2)
SEL(0, cons(X, Y)) -> ACTIVATE(X)
ACTIVATE(nsel(X1, X2)) -> SEL(X1, X2)
DBLS(cons(X, Y)) -> ACTIVATE(Y)
ACTIVATE(ndbls(X)) -> DBLS(X)
DBLS(cons(X, Y)) -> ACTIVATE(X)
dbl(0) -> 0
dbl(s(X)) -> s(ns(ndbl(activate(X))))
dbl(X) -> ndbl(X)
dbls(nil) -> nil
dbls(cons(X, Y)) -> cons(ndbl(activate(X)), ndbls(activate(Y)))
dbls(X) -> ndbls(X)
sel(0, cons(X, Y)) -> activate(X)
sel(s(X), cons(Y, Z)) -> sel(activate(X), activate(Z))
sel(X1, X2) -> nsel(X1, X2)
indx(nil, X) -> nil
indx(cons(X, Y), Z) -> cons(nsel(activate(X), activate(Z)), nindx(activate(Y), activate(Z)))
indx(X1, X2) -> nindx(X1, X2)
from(X) -> cons(activate(X), nfrom(ns(activate(X))))
from(X) -> nfrom(X)
s(X) -> ns(X)
activate(ns(X)) -> s(X)
activate(ndbl(X)) -> dbl(X)
activate(ndbls(X)) -> dbls(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(nindx(X1, X2)) -> indx(X1, X2)
activate(nfrom(X)) -> from(X)
activate(X) -> X
innermost
INDX(cons(X, Y), Z) -> ACTIVATE(Y)
INDX(cons(X, Y), Z) -> ACTIVATE(Z)
INDX(cons(X, Y), Z) -> ACTIVATE(X)
POL(n__from(x1)) = x1 POL(FROM(x1)) = x1 POL(n__indx(x1, x2)) = 1 + x1 + x2 POL(n__sel(x1, x2)) = x1 + x2 POL(0) = 0 POL(cons(x1, x2)) = x1 + x2 POL(SEL(x1, x2)) = x1 + x2 POL(n__dbls(x1)) = x1 POL(INDX(x1, x2)) = 1 + x1 + x2 POL(ACTIVATE(x1)) = x1 POL(DBLS(x1)) = x1
INDX(x1, x2) -> INDX(x1, x2)
ACTIVATE(x1) -> ACTIVATE(x1)
cons(x1, x2) -> cons(x1, x2)
nindx(x1, x2) -> nindx(x1, x2)
DBLS(x1) -> DBLS(x1)
SEL(x1, x2) -> SEL(x1, x2)
nfrom(x1) -> nfrom(x1)
FROM(x1) -> FROM(x1)
ndbls(x1) -> ndbls(x1)
nsel(x1, x2) -> nsel(x1, x2)
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳Dependency Graph
FROM(X) -> ACTIVATE(X)
ACTIVATE(nfrom(X)) -> FROM(X)
ACTIVATE(nindx(X1, X2)) -> INDX(X1, X2)
SEL(0, cons(X, Y)) -> ACTIVATE(X)
ACTIVATE(nsel(X1, X2)) -> SEL(X1, X2)
DBLS(cons(X, Y)) -> ACTIVATE(Y)
ACTIVATE(ndbls(X)) -> DBLS(X)
DBLS(cons(X, Y)) -> ACTIVATE(X)
dbl(0) -> 0
dbl(s(X)) -> s(ns(ndbl(activate(X))))
dbl(X) -> ndbl(X)
dbls(nil) -> nil
dbls(cons(X, Y)) -> cons(ndbl(activate(X)), ndbls(activate(Y)))
dbls(X) -> ndbls(X)
sel(0, cons(X, Y)) -> activate(X)
sel(s(X), cons(Y, Z)) -> sel(activate(X), activate(Z))
sel(X1, X2) -> nsel(X1, X2)
indx(nil, X) -> nil
indx(cons(X, Y), Z) -> cons(nsel(activate(X), activate(Z)), nindx(activate(Y), activate(Z)))
indx(X1, X2) -> nindx(X1, X2)
from(X) -> cons(activate(X), nfrom(ns(activate(X))))
from(X) -> nfrom(X)
s(X) -> ns(X)
activate(ns(X)) -> s(X)
activate(ndbl(X)) -> dbl(X)
activate(ndbls(X)) -> dbls(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(nindx(X1, X2)) -> indx(X1, X2)
activate(nfrom(X)) -> from(X)
activate(X) -> X
innermost
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳DGraph
...
→DP Problem 3
↳Argument Filtering and Ordering
DBLS(cons(X, Y)) -> ACTIVATE(Y)
ACTIVATE(nfrom(X)) -> FROM(X)
SEL(0, cons(X, Y)) -> ACTIVATE(X)
ACTIVATE(nsel(X1, X2)) -> SEL(X1, X2)
DBLS(cons(X, Y)) -> ACTIVATE(X)
ACTIVATE(ndbls(X)) -> DBLS(X)
FROM(X) -> ACTIVATE(X)
dbl(0) -> 0
dbl(s(X)) -> s(ns(ndbl(activate(X))))
dbl(X) -> ndbl(X)
dbls(nil) -> nil
dbls(cons(X, Y)) -> cons(ndbl(activate(X)), ndbls(activate(Y)))
dbls(X) -> ndbls(X)
sel(0, cons(X, Y)) -> activate(X)
sel(s(X), cons(Y, Z)) -> sel(activate(X), activate(Z))
sel(X1, X2) -> nsel(X1, X2)
indx(nil, X) -> nil
indx(cons(X, Y), Z) -> cons(nsel(activate(X), activate(Z)), nindx(activate(Y), activate(Z)))
indx(X1, X2) -> nindx(X1, X2)
from(X) -> cons(activate(X), nfrom(ns(activate(X))))
from(X) -> nfrom(X)
s(X) -> ns(X)
activate(ns(X)) -> s(X)
activate(ndbl(X)) -> dbl(X)
activate(ndbls(X)) -> dbls(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(nindx(X1, X2)) -> indx(X1, X2)
activate(nfrom(X)) -> from(X)
activate(X) -> X
innermost
DBLS(cons(X, Y)) -> ACTIVATE(Y)
DBLS(cons(X, Y)) -> ACTIVATE(X)
POL(n__from(x1)) = x1 POL(FROM(x1)) = x1 POL(n__sel(x1, x2)) = x1 + x2 POL(0) = 0 POL(cons(x1, x2)) = x1 + x2 POL(SEL(x1, x2)) = x1 + x2 POL(n__dbls(x1)) = 1 + x1 POL(ACTIVATE(x1)) = x1 POL(DBLS(x1)) = 1 + x1
DBLS(x1) -> DBLS(x1)
ACTIVATE(x1) -> ACTIVATE(x1)
cons(x1, x2) -> cons(x1, x2)
SEL(x1, x2) -> SEL(x1, x2)
nfrom(x1) -> nfrom(x1)
FROM(x1) -> FROM(x1)
ndbls(x1) -> ndbls(x1)
nsel(x1, x2) -> nsel(x1, x2)
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳DGraph
...
→DP Problem 4
↳Dependency Graph
ACTIVATE(nfrom(X)) -> FROM(X)
SEL(0, cons(X, Y)) -> ACTIVATE(X)
ACTIVATE(nsel(X1, X2)) -> SEL(X1, X2)
ACTIVATE(ndbls(X)) -> DBLS(X)
FROM(X) -> ACTIVATE(X)
dbl(0) -> 0
dbl(s(X)) -> s(ns(ndbl(activate(X))))
dbl(X) -> ndbl(X)
dbls(nil) -> nil
dbls(cons(X, Y)) -> cons(ndbl(activate(X)), ndbls(activate(Y)))
dbls(X) -> ndbls(X)
sel(0, cons(X, Y)) -> activate(X)
sel(s(X), cons(Y, Z)) -> sel(activate(X), activate(Z))
sel(X1, X2) -> nsel(X1, X2)
indx(nil, X) -> nil
indx(cons(X, Y), Z) -> cons(nsel(activate(X), activate(Z)), nindx(activate(Y), activate(Z)))
indx(X1, X2) -> nindx(X1, X2)
from(X) -> cons(activate(X), nfrom(ns(activate(X))))
from(X) -> nfrom(X)
s(X) -> ns(X)
activate(ns(X)) -> s(X)
activate(ndbl(X)) -> dbl(X)
activate(ndbls(X)) -> dbls(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(nindx(X1, X2)) -> indx(X1, X2)
activate(nfrom(X)) -> from(X)
activate(X) -> X
innermost
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳DGraph
...
→DP Problem 5
↳Argument Filtering and Ordering
SEL(0, cons(X, Y)) -> ACTIVATE(X)
ACTIVATE(nsel(X1, X2)) -> SEL(X1, X2)
FROM(X) -> ACTIVATE(X)
ACTIVATE(nfrom(X)) -> FROM(X)
dbl(0) -> 0
dbl(s(X)) -> s(ns(ndbl(activate(X))))
dbl(X) -> ndbl(X)
dbls(nil) -> nil
dbls(cons(X, Y)) -> cons(ndbl(activate(X)), ndbls(activate(Y)))
dbls(X) -> ndbls(X)
sel(0, cons(X, Y)) -> activate(X)
sel(s(X), cons(Y, Z)) -> sel(activate(X), activate(Z))
sel(X1, X2) -> nsel(X1, X2)
indx(nil, X) -> nil
indx(cons(X, Y), Z) -> cons(nsel(activate(X), activate(Z)), nindx(activate(Y), activate(Z)))
indx(X1, X2) -> nindx(X1, X2)
from(X) -> cons(activate(X), nfrom(ns(activate(X))))
from(X) -> nfrom(X)
s(X) -> ns(X)
activate(ns(X)) -> s(X)
activate(ndbl(X)) -> dbl(X)
activate(ndbls(X)) -> dbls(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(nindx(X1, X2)) -> indx(X1, X2)
activate(nfrom(X)) -> from(X)
activate(X) -> X
innermost
ACTIVATE(nfrom(X)) -> FROM(X)
POL(n__from(x1)) = 1 + x1 POL(FROM(x1)) = x1 POL(n__sel(x1, x2)) = x1 + x2 POL(0) = 0 POL(SEL(x1, x2)) = x1 + x2 POL(cons(x1, x2)) = x1 + x2 POL(ACTIVATE(x1)) = x1
ACTIVATE(x1) -> ACTIVATE(x1)
FROM(x1) -> FROM(x1)
nfrom(x1) -> nfrom(x1)
SEL(x1, x2) -> SEL(x1, x2)
cons(x1, x2) -> cons(x1, x2)
nsel(x1, x2) -> nsel(x1, x2)
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳DGraph
...
→DP Problem 6
↳Dependency Graph
SEL(0, cons(X, Y)) -> ACTIVATE(X)
ACTIVATE(nsel(X1, X2)) -> SEL(X1, X2)
FROM(X) -> ACTIVATE(X)
dbl(0) -> 0
dbl(s(X)) -> s(ns(ndbl(activate(X))))
dbl(X) -> ndbl(X)
dbls(nil) -> nil
dbls(cons(X, Y)) -> cons(ndbl(activate(X)), ndbls(activate(Y)))
dbls(X) -> ndbls(X)
sel(0, cons(X, Y)) -> activate(X)
sel(s(X), cons(Y, Z)) -> sel(activate(X), activate(Z))
sel(X1, X2) -> nsel(X1, X2)
indx(nil, X) -> nil
indx(cons(X, Y), Z) -> cons(nsel(activate(X), activate(Z)), nindx(activate(Y), activate(Z)))
indx(X1, X2) -> nindx(X1, X2)
from(X) -> cons(activate(X), nfrom(ns(activate(X))))
from(X) -> nfrom(X)
s(X) -> ns(X)
activate(ns(X)) -> s(X)
activate(ndbl(X)) -> dbl(X)
activate(ndbls(X)) -> dbls(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(nindx(X1, X2)) -> indx(X1, X2)
activate(nfrom(X)) -> from(X)
activate(X) -> X
innermost
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳DGraph
...
→DP Problem 7
↳Argument Filtering and Ordering
ACTIVATE(nsel(X1, X2)) -> SEL(X1, X2)
SEL(0, cons(X, Y)) -> ACTIVATE(X)
dbl(0) -> 0
dbl(s(X)) -> s(ns(ndbl(activate(X))))
dbl(X) -> ndbl(X)
dbls(nil) -> nil
dbls(cons(X, Y)) -> cons(ndbl(activate(X)), ndbls(activate(Y)))
dbls(X) -> ndbls(X)
sel(0, cons(X, Y)) -> activate(X)
sel(s(X), cons(Y, Z)) -> sel(activate(X), activate(Z))
sel(X1, X2) -> nsel(X1, X2)
indx(nil, X) -> nil
indx(cons(X, Y), Z) -> cons(nsel(activate(X), activate(Z)), nindx(activate(Y), activate(Z)))
indx(X1, X2) -> nindx(X1, X2)
from(X) -> cons(activate(X), nfrom(ns(activate(X))))
from(X) -> nfrom(X)
s(X) -> ns(X)
activate(ns(X)) -> s(X)
activate(ndbl(X)) -> dbl(X)
activate(ndbls(X)) -> dbls(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(nindx(X1, X2)) -> indx(X1, X2)
activate(nfrom(X)) -> from(X)
activate(X) -> X
innermost
SEL(0, cons(X, Y)) -> ACTIVATE(X)
POL(n__sel(x1, x2)) = x1 + x2 POL(0) = 1 POL(SEL(x1, x2)) = x1 + x2 POL(cons(x1, x2)) = x1 + x2 POL(ACTIVATE(x1)) = x1
SEL(x1, x2) -> SEL(x1, x2)
ACTIVATE(x1) -> ACTIVATE(x1)
cons(x1, x2) -> cons(x1, x2)
nsel(x1, x2) -> nsel(x1, x2)
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳DGraph
...
→DP Problem 8
↳Dependency Graph
ACTIVATE(nsel(X1, X2)) -> SEL(X1, X2)
dbl(0) -> 0
dbl(s(X)) -> s(ns(ndbl(activate(X))))
dbl(X) -> ndbl(X)
dbls(nil) -> nil
dbls(cons(X, Y)) -> cons(ndbl(activate(X)), ndbls(activate(Y)))
dbls(X) -> ndbls(X)
sel(0, cons(X, Y)) -> activate(X)
sel(s(X), cons(Y, Z)) -> sel(activate(X), activate(Z))
sel(X1, X2) -> nsel(X1, X2)
indx(nil, X) -> nil
indx(cons(X, Y), Z) -> cons(nsel(activate(X), activate(Z)), nindx(activate(Y), activate(Z)))
indx(X1, X2) -> nindx(X1, X2)
from(X) -> cons(activate(X), nfrom(ns(activate(X))))
from(X) -> nfrom(X)
s(X) -> ns(X)
activate(ns(X)) -> s(X)
activate(ndbl(X)) -> dbl(X)
activate(ndbls(X)) -> dbls(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(nindx(X1, X2)) -> indx(X1, X2)
activate(nfrom(X)) -> from(X)
activate(X) -> X
innermost