R
↳Dependency Pair Analysis
SEL(s(X), cons(Y, Z)) -> SEL(X, activate(Z))
SEL(s(X), cons(Y, Z)) -> ACTIVATE(Z)
FIRST(0, Z) -> NIL
FIRST(s(X), cons(Y, Z)) -> CONS(Y, nfirst(X, activate(Z)))
FIRST(s(X), cons(Y, Z)) -> ACTIVATE(Z)
FROM(X) -> CONS(X, nfrom(s(X)))
FROM(X) -> S(X)
SEL1(s(X), cons(Y, Z)) -> SEL1(X, activate(Z))
SEL1(s(X), cons(Y, Z)) -> ACTIVATE(Z)
SEL1(0, cons(X, Z)) -> QUOTE(X)
FIRST1(s(X), cons(Y, Z)) -> QUOTE(Y)
FIRST1(s(X), cons(Y, Z)) -> FIRST1(X, activate(Z))
FIRST1(s(X), cons(Y, Z)) -> ACTIVATE(Z)
QUOTE(ns(X)) -> QUOTE(activate(X))
QUOTE(ns(X)) -> ACTIVATE(X)
QUOTE(nsel(X, Z)) -> SEL1(activate(X), activate(Z))
QUOTE(nsel(X, Z)) -> ACTIVATE(X)
QUOTE(nsel(X, Z)) -> ACTIVATE(Z)
QUOTE1(ncons(X, Z)) -> QUOTE(activate(X))
QUOTE1(ncons(X, Z)) -> ACTIVATE(X)
QUOTE1(ncons(X, Z)) -> QUOTE1(activate(Z))
QUOTE1(ncons(X, Z)) -> ACTIVATE(Z)
QUOTE1(nfirst(X, Z)) -> FIRST1(activate(X), activate(Z))
QUOTE1(nfirst(X, Z)) -> ACTIVATE(X)
QUOTE1(nfirst(X, Z)) -> ACTIVATE(Z)
UNQUOTE(01) -> 0'
UNQUOTE(s1(X)) -> S(unquote(X))
UNQUOTE(s1(X)) -> UNQUOTE(X)
UNQUOTE1(nil1) -> NIL
UNQUOTE1(cons1(X, Z)) -> FCONS(unquote(X), unquote1(Z))
UNQUOTE1(cons1(X, Z)) -> UNQUOTE(X)
UNQUOTE1(cons1(X, Z)) -> UNQUOTE1(Z)
FCONS(X, Z) -> CONS(X, Z)
ACTIVATE(nfirst(X1, X2)) -> FIRST(X1, X2)
ACTIVATE(nfrom(X)) -> FROM(X)
ACTIVATE(n0) -> 0'
ACTIVATE(ncons(X1, X2)) -> CONS(X1, X2)
ACTIVATE(nnil) -> NIL
ACTIVATE(ns(X)) -> S(X)
ACTIVATE(nsel(X1, X2)) -> SEL(X1, X2)
R
↳DPs
→DP Problem 1
↳Narrowing Transformation
→DP Problem 2
↳Remaining
→DP Problem 3
↳Remaining
→DP Problem 4
↳Remaining
→DP Problem 5
↳Remaining
→DP Problem 6
↳Remaining
ACTIVATE(nsel(X1, X2)) -> SEL(X1, X2)
FIRST(s(X), cons(Y, Z)) -> ACTIVATE(Z)
ACTIVATE(nfirst(X1, X2)) -> FIRST(X1, X2)
SEL(s(X), cons(Y, Z)) -> ACTIVATE(Z)
SEL(s(X), cons(Y, Z)) -> SEL(X, activate(Z))
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
sel1(0, cons(X, Z)) -> quote(X)
first1(0, Z) -> nil1
first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
quote(n0) -> 01
quote(ns(X)) -> s1(quote(activate(X)))
quote(nsel(X, Z)) -> sel1(activate(X), activate(Z))
quote1(ncons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
quote1(nnil) -> nil1
quote1(nfirst(X, Z)) -> first1(activate(X), activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
fcons(X, Z) -> cons(X, Z)
0 -> n0
cons(X1, X2) -> ncons(X1, X2)
nil -> nnil
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
eight new Dependency Pairs are created:
SEL(s(X), cons(Y, Z)) -> SEL(X, activate(Z))
SEL(s(X), cons(Y, nfirst(X1', X2'))) -> SEL(X, first(X1', X2'))
SEL(s(X), cons(Y, nfrom(X''))) -> SEL(X, from(X''))
SEL(s(X), cons(Y, n0)) -> SEL(X, 0)
SEL(s(X), cons(Y, ncons(X1', X2'))) -> SEL(X, cons(X1', X2'))
SEL(s(X), cons(Y, nnil)) -> SEL(X, nil)
SEL(s(X), cons(Y, ns(X''))) -> SEL(X, s(X''))
SEL(s(X), cons(Y, nsel(X1', X2'))) -> SEL(X, sel(X1', X2'))
SEL(s(X), cons(Y, Z')) -> SEL(X, Z')
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 7
↳Narrowing Transformation
→DP Problem 2
↳Remaining
→DP Problem 3
↳Remaining
→DP Problem 4
↳Remaining
→DP Problem 5
↳Remaining
→DP Problem 6
↳Remaining
SEL(s(X), cons(Y, Z')) -> SEL(X, Z')
SEL(s(X), cons(Y, nsel(X1', X2'))) -> SEL(X, sel(X1', X2'))
SEL(s(X), cons(Y, ns(X''))) -> SEL(X, s(X''))
SEL(s(X), cons(Y, nnil)) -> SEL(X, nil)
SEL(s(X), cons(Y, ncons(X1', X2'))) -> SEL(X, cons(X1', X2'))
SEL(s(X), cons(Y, n0)) -> SEL(X, 0)
SEL(s(X), cons(Y, nfrom(X''))) -> SEL(X, from(X''))
SEL(s(X), cons(Y, nfirst(X1', X2'))) -> SEL(X, first(X1', X2'))
FIRST(s(X), cons(Y, Z)) -> ACTIVATE(Z)
ACTIVATE(nfirst(X1, X2)) -> FIRST(X1, X2)
SEL(s(X), cons(Y, Z)) -> ACTIVATE(Z)
ACTIVATE(nsel(X1, X2)) -> SEL(X1, X2)
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
sel1(0, cons(X, Z)) -> quote(X)
first1(0, Z) -> nil1
first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
quote(n0) -> 01
quote(ns(X)) -> s1(quote(activate(X)))
quote(nsel(X, Z)) -> sel1(activate(X), activate(Z))
quote1(ncons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
quote1(nnil) -> nil1
quote1(nfirst(X, Z)) -> first1(activate(X), activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
fcons(X, Z) -> cons(X, Z)
0 -> n0
cons(X1, X2) -> ncons(X1, X2)
nil -> nnil
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
three new Dependency Pairs are created:
SEL(s(X), cons(Y, nfirst(X1', X2'))) -> SEL(X, first(X1', X2'))
SEL(s(X), cons(Y, nfirst(0, X2''))) -> SEL(X, nil)
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', Z')))) -> SEL(X, cons(Y'', nfirst(X'', activate(Z'))))
SEL(s(X), cons(Y, nfirst(X1'', X2''))) -> SEL(X, nfirst(X1'', X2''))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 7
↳Nar
...
→DP Problem 8
↳Narrowing Transformation
→DP Problem 2
↳Remaining
→DP Problem 3
↳Remaining
→DP Problem 4
↳Remaining
→DP Problem 5
↳Remaining
→DP Problem 6
↳Remaining
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', Z')))) -> SEL(X, cons(Y'', nfirst(X'', activate(Z'))))
SEL(s(X), cons(Y, nfirst(0, X2''))) -> SEL(X, nil)
SEL(s(X), cons(Y, nsel(X1', X2'))) -> SEL(X, sel(X1', X2'))
SEL(s(X), cons(Y, ns(X''))) -> SEL(X, s(X''))
SEL(s(X), cons(Y, nnil)) -> SEL(X, nil)
SEL(s(X), cons(Y, ncons(X1', X2'))) -> SEL(X, cons(X1', X2'))
SEL(s(X), cons(Y, n0)) -> SEL(X, 0)
SEL(s(X), cons(Y, nfrom(X''))) -> SEL(X, from(X''))
ACTIVATE(nsel(X1, X2)) -> SEL(X1, X2)
FIRST(s(X), cons(Y, Z)) -> ACTIVATE(Z)
ACTIVATE(nfirst(X1, X2)) -> FIRST(X1, X2)
SEL(s(X), cons(Y, Z)) -> ACTIVATE(Z)
SEL(s(X), cons(Y, Z')) -> SEL(X, Z')
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
sel1(0, cons(X, Z)) -> quote(X)
first1(0, Z) -> nil1
first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
quote(n0) -> 01
quote(ns(X)) -> s1(quote(activate(X)))
quote(nsel(X, Z)) -> sel1(activate(X), activate(Z))
quote1(ncons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
quote1(nnil) -> nil1
quote1(nfirst(X, Z)) -> first1(activate(X), activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
fcons(X, Z) -> cons(X, Z)
0 -> n0
cons(X1, X2) -> ncons(X1, X2)
nil -> nnil
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
two new Dependency Pairs are created:
SEL(s(X), cons(Y, nfrom(X''))) -> SEL(X, from(X''))
SEL(s(X), cons(Y, nfrom(X'''))) -> SEL(X, cons(X''', nfrom(s(X'''))))
SEL(s(X), cons(Y, nfrom(X'''))) -> SEL(X, nfrom(X'''))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 7
↳Nar
...
→DP Problem 9
↳Narrowing Transformation
→DP Problem 2
↳Remaining
→DP Problem 3
↳Remaining
→DP Problem 4
↳Remaining
→DP Problem 5
↳Remaining
→DP Problem 6
↳Remaining
SEL(s(X), cons(Y, nfrom(X'''))) -> SEL(X, cons(X''', nfrom(s(X'''))))
SEL(s(X), cons(Y, nfirst(0, X2''))) -> SEL(X, nil)
SEL(s(X), cons(Y, Z')) -> SEL(X, Z')
SEL(s(X), cons(Y, nsel(X1', X2'))) -> SEL(X, sel(X1', X2'))
SEL(s(X), cons(Y, ns(X''))) -> SEL(X, s(X''))
SEL(s(X), cons(Y, nnil)) -> SEL(X, nil)
SEL(s(X), cons(Y, ncons(X1', X2'))) -> SEL(X, cons(X1', X2'))
SEL(s(X), cons(Y, n0)) -> SEL(X, 0)
ACTIVATE(nsel(X1, X2)) -> SEL(X1, X2)
FIRST(s(X), cons(Y, Z)) -> ACTIVATE(Z)
ACTIVATE(nfirst(X1, X2)) -> FIRST(X1, X2)
SEL(s(X), cons(Y, Z)) -> ACTIVATE(Z)
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', Z')))) -> SEL(X, cons(Y'', nfirst(X'', activate(Z'))))
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
sel1(0, cons(X, Z)) -> quote(X)
first1(0, Z) -> nil1
first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
quote(n0) -> 01
quote(ns(X)) -> s1(quote(activate(X)))
quote(nsel(X, Z)) -> sel1(activate(X), activate(Z))
quote1(ncons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
quote1(nnil) -> nil1
quote1(nfirst(X, Z)) -> first1(activate(X), activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
fcons(X, Z) -> cons(X, Z)
0 -> n0
cons(X1, X2) -> ncons(X1, X2)
nil -> nnil
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
one new Dependency Pair is created:
SEL(s(X), cons(Y, n0)) -> SEL(X, 0)
SEL(s(X), cons(Y, n0)) -> SEL(X, n0)
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 7
↳Nar
...
→DP Problem 10
↳Narrowing Transformation
→DP Problem 2
↳Remaining
→DP Problem 3
↳Remaining
→DP Problem 4
↳Remaining
→DP Problem 5
↳Remaining
→DP Problem 6
↳Remaining
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', Z')))) -> SEL(X, cons(Y'', nfirst(X'', activate(Z'))))
SEL(s(X), cons(Y, nfirst(0, X2''))) -> SEL(X, nil)
SEL(s(X), cons(Y, Z')) -> SEL(X, Z')
SEL(s(X), cons(Y, nsel(X1', X2'))) -> SEL(X, sel(X1', X2'))
SEL(s(X), cons(Y, ns(X''))) -> SEL(X, s(X''))
SEL(s(X), cons(Y, nnil)) -> SEL(X, nil)
SEL(s(X), cons(Y, ncons(X1', X2'))) -> SEL(X, cons(X1', X2'))
ACTIVATE(nsel(X1, X2)) -> SEL(X1, X2)
FIRST(s(X), cons(Y, Z)) -> ACTIVATE(Z)
ACTIVATE(nfirst(X1, X2)) -> FIRST(X1, X2)
SEL(s(X), cons(Y, Z)) -> ACTIVATE(Z)
SEL(s(X), cons(Y, nfrom(X'''))) -> SEL(X, cons(X''', nfrom(s(X'''))))
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
sel1(0, cons(X, Z)) -> quote(X)
first1(0, Z) -> nil1
first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
quote(n0) -> 01
quote(ns(X)) -> s1(quote(activate(X)))
quote(nsel(X, Z)) -> sel1(activate(X), activate(Z))
quote1(ncons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
quote1(nnil) -> nil1
quote1(nfirst(X, Z)) -> first1(activate(X), activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
fcons(X, Z) -> cons(X, Z)
0 -> n0
cons(X1, X2) -> ncons(X1, X2)
nil -> nnil
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
one new Dependency Pair is created:
SEL(s(X), cons(Y, nnil)) -> SEL(X, nil)
SEL(s(X), cons(Y, nnil)) -> SEL(X, nnil)
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 7
↳Nar
...
→DP Problem 11
↳Narrowing Transformation
→DP Problem 2
↳Remaining
→DP Problem 3
↳Remaining
→DP Problem 4
↳Remaining
→DP Problem 5
↳Remaining
→DP Problem 6
↳Remaining
SEL(s(X), cons(Y, nfrom(X'''))) -> SEL(X, cons(X''', nfrom(s(X'''))))
SEL(s(X), cons(Y, nfirst(0, X2''))) -> SEL(X, nil)
SEL(s(X), cons(Y, Z')) -> SEL(X, Z')
SEL(s(X), cons(Y, nsel(X1', X2'))) -> SEL(X, sel(X1', X2'))
SEL(s(X), cons(Y, ns(X''))) -> SEL(X, s(X''))
SEL(s(X), cons(Y, ncons(X1', X2'))) -> SEL(X, cons(X1', X2'))
ACTIVATE(nsel(X1, X2)) -> SEL(X1, X2)
FIRST(s(X), cons(Y, Z)) -> ACTIVATE(Z)
ACTIVATE(nfirst(X1, X2)) -> FIRST(X1, X2)
SEL(s(X), cons(Y, Z)) -> ACTIVATE(Z)
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', Z')))) -> SEL(X, cons(Y'', nfirst(X'', activate(Z'))))
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
sel1(0, cons(X, Z)) -> quote(X)
first1(0, Z) -> nil1
first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
quote(n0) -> 01
quote(ns(X)) -> s1(quote(activate(X)))
quote(nsel(X, Z)) -> sel1(activate(X), activate(Z))
quote1(ncons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
quote1(nnil) -> nil1
quote1(nfirst(X, Z)) -> first1(activate(X), activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
fcons(X, Z) -> cons(X, Z)
0 -> n0
cons(X1, X2) -> ncons(X1, X2)
nil -> nnil
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
one new Dependency Pair is created:
SEL(s(X), cons(Y, ns(X''))) -> SEL(X, s(X''))
SEL(s(X), cons(Y, ns(X'''))) -> SEL(X, ns(X'''))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 7
↳Nar
...
→DP Problem 12
↳Narrowing Transformation
→DP Problem 2
↳Remaining
→DP Problem 3
↳Remaining
→DP Problem 4
↳Remaining
→DP Problem 5
↳Remaining
→DP Problem 6
↳Remaining
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', Z')))) -> SEL(X, cons(Y'', nfirst(X'', activate(Z'))))
SEL(s(X), cons(Y, nfirst(0, X2''))) -> SEL(X, nil)
SEL(s(X), cons(Y, Z')) -> SEL(X, Z')
SEL(s(X), cons(Y, nsel(X1', X2'))) -> SEL(X, sel(X1', X2'))
SEL(s(X), cons(Y, ncons(X1', X2'))) -> SEL(X, cons(X1', X2'))
ACTIVATE(nsel(X1, X2)) -> SEL(X1, X2)
FIRST(s(X), cons(Y, Z)) -> ACTIVATE(Z)
ACTIVATE(nfirst(X1, X2)) -> FIRST(X1, X2)
SEL(s(X), cons(Y, Z)) -> ACTIVATE(Z)
SEL(s(X), cons(Y, nfrom(X'''))) -> SEL(X, cons(X''', nfrom(s(X'''))))
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
sel1(0, cons(X, Z)) -> quote(X)
first1(0, Z) -> nil1
first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
quote(n0) -> 01
quote(ns(X)) -> s1(quote(activate(X)))
quote(nsel(X, Z)) -> sel1(activate(X), activate(Z))
quote1(ncons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
quote1(nnil) -> nil1
quote1(nfirst(X, Z)) -> first1(activate(X), activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
fcons(X, Z) -> cons(X, Z)
0 -> n0
cons(X1, X2) -> ncons(X1, X2)
nil -> nnil
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
three new Dependency Pairs are created:
SEL(s(X), cons(Y, nsel(X1', X2'))) -> SEL(X, sel(X1', X2'))
SEL(s(X), cons(Y, nsel(s(X''), cons(Y'', Z')))) -> SEL(X, sel(X'', activate(Z')))
SEL(s(X), cons(Y, nsel(0, cons(X'', Z')))) -> SEL(X, X'')
SEL(s(X), cons(Y, nsel(X1'', X2''))) -> SEL(X, nsel(X1'', X2''))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 7
↳Nar
...
→DP Problem 13
↳Polynomial Ordering
→DP Problem 2
↳Remaining
→DP Problem 3
↳Remaining
→DP Problem 4
↳Remaining
→DP Problem 5
↳Remaining
→DP Problem 6
↳Remaining
SEL(s(X), cons(Y, nsel(0, cons(X'', Z')))) -> SEL(X, X'')
SEL(s(X), cons(Y, nsel(s(X''), cons(Y'', Z')))) -> SEL(X, sel(X'', activate(Z')))
SEL(s(X), cons(Y, nfrom(X'''))) -> SEL(X, cons(X''', nfrom(s(X'''))))
SEL(s(X), cons(Y, nfirst(0, X2''))) -> SEL(X, nil)
SEL(s(X), cons(Y, Z')) -> SEL(X, Z')
SEL(s(X), cons(Y, ncons(X1', X2'))) -> SEL(X, cons(X1', X2'))
ACTIVATE(nsel(X1, X2)) -> SEL(X1, X2)
FIRST(s(X), cons(Y, Z)) -> ACTIVATE(Z)
ACTIVATE(nfirst(X1, X2)) -> FIRST(X1, X2)
SEL(s(X), cons(Y, Z)) -> ACTIVATE(Z)
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', Z')))) -> SEL(X, cons(Y'', nfirst(X'', activate(Z'))))
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
sel1(0, cons(X, Z)) -> quote(X)
first1(0, Z) -> nil1
first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
quote(n0) -> 01
quote(ns(X)) -> s1(quote(activate(X)))
quote(nsel(X, Z)) -> sel1(activate(X), activate(Z))
quote1(ncons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
quote1(nnil) -> nil1
quote1(nfirst(X, Z)) -> first1(activate(X), activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
fcons(X, Z) -> cons(X, Z)
0 -> n0
cons(X1, X2) -> ncons(X1, X2)
nil -> nnil
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
SEL(s(X), cons(Y, nsel(0, cons(X'', Z')))) -> SEL(X, X'')
ACTIVATE(nsel(X1, X2)) -> SEL(X1, X2)
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
first(0, Z) -> nil
first(s(X), cons(Y, Z)) -> cons(Y, nfirst(X, activate(Z)))
first(X1, X2) -> nfirst(X1, X2)
cons(X1, X2) -> ncons(X1, X2)
s(X) -> ns(X)
nil -> nnil
from(X) -> cons(X, nfrom(s(X)))
from(X) -> nfrom(X)
0 -> n0
POL(from(x1)) = x1 POL(activate(x1)) = x1 POL(SEL(x1, x2)) = x2 POL(n__s(x1)) = 0 POL(sel(x1, x2)) = 1 + x2 POL(n__nil) = 0 POL(ACTIVATE(x1)) = x1 POL(n__from(x1)) = x1 POL(n__cons(x1, x2)) = x1 + x2 POL(n__sel(x1, x2)) = 1 + x2 POL(0) = 0 POL(first(x1, x2)) = x2 POL(cons(x1, x2)) = x1 + x2 POL(FIRST(x1, x2)) = x2 POL(nil) = 0 POL(n__0) = 0 POL(s(x1)) = 0 POL(n__first(x1, x2)) = x2
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 7
↳Nar
...
→DP Problem 14
↳Dependency Graph
→DP Problem 2
↳Remaining
→DP Problem 3
↳Remaining
→DP Problem 4
↳Remaining
→DP Problem 5
↳Remaining
→DP Problem 6
↳Remaining
SEL(s(X), cons(Y, nsel(s(X''), cons(Y'', Z')))) -> SEL(X, sel(X'', activate(Z')))
SEL(s(X), cons(Y, nfrom(X'''))) -> SEL(X, cons(X''', nfrom(s(X'''))))
SEL(s(X), cons(Y, nfirst(0, X2''))) -> SEL(X, nil)
SEL(s(X), cons(Y, Z')) -> SEL(X, Z')
SEL(s(X), cons(Y, ncons(X1', X2'))) -> SEL(X, cons(X1', X2'))
FIRST(s(X), cons(Y, Z)) -> ACTIVATE(Z)
ACTIVATE(nfirst(X1, X2)) -> FIRST(X1, X2)
SEL(s(X), cons(Y, Z)) -> ACTIVATE(Z)
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', Z')))) -> SEL(X, cons(Y'', nfirst(X'', activate(Z'))))
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
sel1(0, cons(X, Z)) -> quote(X)
first1(0, Z) -> nil1
first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
quote(n0) -> 01
quote(ns(X)) -> s1(quote(activate(X)))
quote(nsel(X, Z)) -> sel1(activate(X), activate(Z))
quote1(ncons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
quote1(nnil) -> nil1
quote1(nfirst(X, Z)) -> first1(activate(X), activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
fcons(X, Z) -> cons(X, Z)
0 -> n0
cons(X1, X2) -> ncons(X1, X2)
nil -> nnil
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 7
↳Nar
...
→DP Problem 15
↳Polynomial Ordering
→DP Problem 2
↳Remaining
→DP Problem 3
↳Remaining
→DP Problem 4
↳Remaining
→DP Problem 5
↳Remaining
→DP Problem 6
↳Remaining
FIRST(s(X), cons(Y, Z)) -> ACTIVATE(Z)
ACTIVATE(nfirst(X1, X2)) -> FIRST(X1, X2)
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
sel1(0, cons(X, Z)) -> quote(X)
first1(0, Z) -> nil1
first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
quote(n0) -> 01
quote(ns(X)) -> s1(quote(activate(X)))
quote(nsel(X, Z)) -> sel1(activate(X), activate(Z))
quote1(ncons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
quote1(nnil) -> nil1
quote1(nfirst(X, Z)) -> first1(activate(X), activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
fcons(X, Z) -> cons(X, Z)
0 -> n0
cons(X1, X2) -> ncons(X1, X2)
nil -> nnil
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
FIRST(s(X), cons(Y, Z)) -> ACTIVATE(Z)
POL(cons(x1, x2)) = 1 + x2 POL(FIRST(x1, x2)) = x2 POL(s(x1)) = 0 POL(ACTIVATE(x1)) = x1 POL(n__first(x1, x2)) = x2
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 7
↳Nar
...
→DP Problem 17
↳Dependency Graph
→DP Problem 2
↳Remaining
→DP Problem 3
↳Remaining
→DP Problem 4
↳Remaining
→DP Problem 5
↳Remaining
→DP Problem 6
↳Remaining
ACTIVATE(nfirst(X1, X2)) -> FIRST(X1, X2)
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
sel1(0, cons(X, Z)) -> quote(X)
first1(0, Z) -> nil1
first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
quote(n0) -> 01
quote(ns(X)) -> s1(quote(activate(X)))
quote(nsel(X, Z)) -> sel1(activate(X), activate(Z))
quote1(ncons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
quote1(nnil) -> nil1
quote1(nfirst(X, Z)) -> first1(activate(X), activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
fcons(X, Z) -> cons(X, Z)
0 -> n0
cons(X1, X2) -> ncons(X1, X2)
nil -> nnil
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 7
↳Nar
...
→DP Problem 16
↳Polynomial Ordering
→DP Problem 2
↳Remaining
→DP Problem 3
↳Remaining
→DP Problem 4
↳Remaining
→DP Problem 5
↳Remaining
→DP Problem 6
↳Remaining
SEL(s(X), cons(Y, nfrom(X'''))) -> SEL(X, cons(X''', nfrom(s(X'''))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', Z')))) -> SEL(X, cons(Y'', nfirst(X'', activate(Z'))))
SEL(s(X), cons(Y, nfirst(0, X2''))) -> SEL(X, nil)
SEL(s(X), cons(Y, Z')) -> SEL(X, Z')
SEL(s(X), cons(Y, ncons(X1', X2'))) -> SEL(X, cons(X1', X2'))
SEL(s(X), cons(Y, nsel(s(X''), cons(Y'', Z')))) -> SEL(X, sel(X'', activate(Z')))
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
sel1(0, cons(X, Z)) -> quote(X)
first1(0, Z) -> nil1
first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
quote(n0) -> 01
quote(ns(X)) -> s1(quote(activate(X)))
quote(nsel(X, Z)) -> sel1(activate(X), activate(Z))
quote1(ncons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
quote1(nnil) -> nil1
quote1(nfirst(X, Z)) -> first1(activate(X), activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
fcons(X, Z) -> cons(X, Z)
0 -> n0
cons(X1, X2) -> ncons(X1, X2)
nil -> nnil
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
SEL(s(X), cons(Y, nfirst(0, X2''))) -> SEL(X, nil)
cons(X1, X2) -> ncons(X1, X2)
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> nil
first(s(X), cons(Y, Z)) -> cons(Y, nfirst(X, activate(Z)))
first(X1, X2) -> nfirst(X1, X2)
nil -> nnil
from(X) -> cons(X, nfrom(s(X)))
from(X) -> nfrom(X)
0 -> n0
POL(from(x1)) = x1 POL(activate(x1)) = x1 POL(SEL(x1, x2)) = 1 + x2 POL(n__s(x1)) = 0 POL(sel(x1, x2)) = x2 POL(n__nil) = 0 POL(n__cons(x1, x2)) = x1 + x2 POL(n__from(x1)) = x1 POL(n__sel(x1, x2)) = x2 POL(first(x1, x2)) = 1 + x2 POL(0) = 0 POL(cons(x1, x2)) = x1 + x2 POL(nil) = 0 POL(n__0) = 0 POL(s(x1)) = 0 POL(n__first(x1, x2)) = 1 + x2
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 7
↳Nar
...
→DP Problem 18
↳Polynomial Ordering
→DP Problem 2
↳Remaining
→DP Problem 3
↳Remaining
→DP Problem 4
↳Remaining
→DP Problem 5
↳Remaining
→DP Problem 6
↳Remaining
SEL(s(X), cons(Y, nfrom(X'''))) -> SEL(X, cons(X''', nfrom(s(X'''))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', Z')))) -> SEL(X, cons(Y'', nfirst(X'', activate(Z'))))
SEL(s(X), cons(Y, Z')) -> SEL(X, Z')
SEL(s(X), cons(Y, ncons(X1', X2'))) -> SEL(X, cons(X1', X2'))
SEL(s(X), cons(Y, nsel(s(X''), cons(Y'', Z')))) -> SEL(X, sel(X'', activate(Z')))
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
sel1(0, cons(X, Z)) -> quote(X)
first1(0, Z) -> nil1
first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
quote(n0) -> 01
quote(ns(X)) -> s1(quote(activate(X)))
quote(nsel(X, Z)) -> sel1(activate(X), activate(Z))
quote1(ncons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
quote1(nnil) -> nil1
quote1(nfirst(X, Z)) -> first1(activate(X), activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
fcons(X, Z) -> cons(X, Z)
0 -> n0
cons(X1, X2) -> ncons(X1, X2)
nil -> nnil
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
SEL(s(X), cons(Y, Z')) -> SEL(X, Z')
SEL(s(X), cons(Y, nsel(s(X''), cons(Y'', Z')))) -> SEL(X, sel(X'', activate(Z')))
cons(X1, X2) -> ncons(X1, X2)
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
0 -> n0
nil -> nnil
POL(from(x1)) = 1 + x1 POL(activate(x1)) = 1 + x1 POL(SEL(x1, x2)) = 1 + x2 POL(n__s(x1)) = 0 POL(sel(x1, x2)) = x2 POL(n__nil) = 0 POL(n__cons(x1, x2)) = x1 + x2 POL(n__from(x1)) = x1 POL(n__sel(x1, x2)) = x2 POL(first(x1, x2)) = 1 + x2 POL(0) = 0 POL(cons(x1, x2)) = 1 + x1 + x2 POL(nil) = 0 POL(n__0) = 0 POL(s(x1)) = 0 POL(n__first(x1, x2)) = x2
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 7
↳Nar
...
→DP Problem 19
↳Polynomial Ordering
→DP Problem 2
↳Remaining
→DP Problem 3
↳Remaining
→DP Problem 4
↳Remaining
→DP Problem 5
↳Remaining
→DP Problem 6
↳Remaining
SEL(s(X), cons(Y, nfrom(X'''))) -> SEL(X, cons(X''', nfrom(s(X'''))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', Z')))) -> SEL(X, cons(Y'', nfirst(X'', activate(Z'))))
SEL(s(X), cons(Y, ncons(X1', X2'))) -> SEL(X, cons(X1', X2'))
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
sel1(0, cons(X, Z)) -> quote(X)
first1(0, Z) -> nil1
first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
quote(n0) -> 01
quote(ns(X)) -> s1(quote(activate(X)))
quote(nsel(X, Z)) -> sel1(activate(X), activate(Z))
quote1(ncons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
quote1(nnil) -> nil1
quote1(nfirst(X, Z)) -> first1(activate(X), activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
fcons(X, Z) -> cons(X, Z)
0 -> n0
cons(X1, X2) -> ncons(X1, X2)
nil -> nnil
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
SEL(s(X), cons(Y, ncons(X1', X2'))) -> SEL(X, cons(X1', X2'))
cons(X1, X2) -> ncons(X1, X2)
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
0 -> n0
nil -> nnil
POL(from(x1)) = 1 + x1 POL(activate(x1)) = 1 + x1 POL(SEL(x1, x2)) = 1 + x2 POL(n__s(x1)) = 0 POL(sel(x1, x2)) = x2 POL(n__nil) = 0 POL(n__cons(x1, x2)) = 1 + x1 + x2 POL(n__from(x1)) = x1 POL(n__sel(x1, x2)) = x2 POL(first(x1, x2)) = 1 + x2 POL(0) = 0 POL(cons(x1, x2)) = 1 + x1 + x2 POL(nil) = 0 POL(n__0) = 0 POL(s(x1)) = 0 POL(n__first(x1, x2)) = x2
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 7
↳Nar
...
→DP Problem 20
↳Narrowing Transformation
→DP Problem 2
↳Remaining
→DP Problem 3
↳Remaining
→DP Problem 4
↳Remaining
→DP Problem 5
↳Remaining
→DP Problem 6
↳Remaining
SEL(s(X), cons(Y, nfrom(X'''))) -> SEL(X, cons(X''', nfrom(s(X'''))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', Z')))) -> SEL(X, cons(Y'', nfirst(X'', activate(Z'))))
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
sel1(0, cons(X, Z)) -> quote(X)
first1(0, Z) -> nil1
first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
quote(n0) -> 01
quote(ns(X)) -> s1(quote(activate(X)))
quote(nsel(X, Z)) -> sel1(activate(X), activate(Z))
quote1(ncons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
quote1(nnil) -> nil1
quote1(nfirst(X, Z)) -> first1(activate(X), activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
fcons(X, Z) -> cons(X, Z)
0 -> n0
cons(X1, X2) -> ncons(X1, X2)
nil -> nnil
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
nine new Dependency Pairs are created:
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', Z')))) -> SEL(X, cons(Y'', nfirst(X'', activate(Z'))))
SEL(s(X), cons(Y, nfirst(s(X'''), cons(Y''', Z'')))) -> SEL(X, ncons(Y''', nfirst(X''', activate(Z''))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(X1', X2'))))) -> SEL(X, cons(Y'', nfirst(X'', first(X1', X2'))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfrom(X'''))))) -> SEL(X, cons(Y'', nfirst(X'', from(X'''))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', n0)))) -> SEL(X, cons(Y'', nfirst(X'', 0)))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', ncons(X1', X2'))))) -> SEL(X, cons(Y'', nfirst(X'', cons(X1', X2'))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nnil)))) -> SEL(X, cons(Y'', nfirst(X'', nil)))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', ns(X'''))))) -> SEL(X, cons(Y'', nfirst(X'', s(X'''))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(X1', X2'))))) -> SEL(X, cons(Y'', nfirst(X'', sel(X1', X2'))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', Z'')))) -> SEL(X, cons(Y'', nfirst(X'', Z'')))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 7
↳Nar
...
→DP Problem 21
↳Narrowing Transformation
→DP Problem 2
↳Remaining
→DP Problem 3
↳Remaining
→DP Problem 4
↳Remaining
→DP Problem 5
↳Remaining
→DP Problem 6
↳Remaining
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', Z'')))) -> SEL(X, cons(Y'', nfirst(X'', Z'')))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(X1', X2'))))) -> SEL(X, cons(Y'', nfirst(X'', sel(X1', X2'))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', ns(X'''))))) -> SEL(X, cons(Y'', nfirst(X'', s(X'''))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nnil)))) -> SEL(X, cons(Y'', nfirst(X'', nil)))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', ncons(X1', X2'))))) -> SEL(X, cons(Y'', nfirst(X'', cons(X1', X2'))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', n0)))) -> SEL(X, cons(Y'', nfirst(X'', 0)))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfrom(X'''))))) -> SEL(X, cons(Y'', nfirst(X'', from(X'''))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(X1', X2'))))) -> SEL(X, cons(Y'', nfirst(X'', first(X1', X2'))))
SEL(s(X), cons(Y, nfrom(X'''))) -> SEL(X, cons(X''', nfrom(s(X'''))))
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
sel1(0, cons(X, Z)) -> quote(X)
first1(0, Z) -> nil1
first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
quote(n0) -> 01
quote(ns(X)) -> s1(quote(activate(X)))
quote(nsel(X, Z)) -> sel1(activate(X), activate(Z))
quote1(ncons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
quote1(nnil) -> nil1
quote1(nfirst(X, Z)) -> first1(activate(X), activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
fcons(X, Z) -> cons(X, Z)
0 -> n0
cons(X1, X2) -> ncons(X1, X2)
nil -> nnil
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
four new Dependency Pairs are created:
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(X1', X2'))))) -> SEL(X, cons(Y'', nfirst(X'', first(X1', X2'))))
SEL(s(X), cons(Y, nfirst(s(X'''), cons(Y''', nfirst(X1'', X2''))))) -> SEL(X, ncons(Y''', nfirst(X''', first(X1'', X2''))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(0, X2''))))) -> SEL(X, cons(Y'', nfirst(X'', nil)))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', Z')))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', activate(Z'))))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(X1'', X2''))))) -> SEL(X, cons(Y'', nfirst(X'', nfirst(X1'', X2''))))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 7
↳Nar
...
→DP Problem 22
↳Narrowing Transformation
→DP Problem 2
↳Remaining
→DP Problem 3
↳Remaining
→DP Problem 4
↳Remaining
→DP Problem 5
↳Remaining
→DP Problem 6
↳Remaining
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(X1'', X2''))))) -> SEL(X, cons(Y'', nfirst(X'', nfirst(X1'', X2''))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', Z')))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', activate(Z'))))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(0, X2''))))) -> SEL(X, cons(Y'', nfirst(X'', nil)))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(X1', X2'))))) -> SEL(X, cons(Y'', nfirst(X'', sel(X1', X2'))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', ns(X'''))))) -> SEL(X, cons(Y'', nfirst(X'', s(X'''))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nnil)))) -> SEL(X, cons(Y'', nfirst(X'', nil)))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', ncons(X1', X2'))))) -> SEL(X, cons(Y'', nfirst(X'', cons(X1', X2'))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', n0)))) -> SEL(X, cons(Y'', nfirst(X'', 0)))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfrom(X'''))))) -> SEL(X, cons(Y'', nfirst(X'', from(X'''))))
SEL(s(X), cons(Y, nfrom(X'''))) -> SEL(X, cons(X''', nfrom(s(X'''))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', Z'')))) -> SEL(X, cons(Y'', nfirst(X'', Z'')))
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
sel1(0, cons(X, Z)) -> quote(X)
first1(0, Z) -> nil1
first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
quote(n0) -> 01
quote(ns(X)) -> s1(quote(activate(X)))
quote(nsel(X, Z)) -> sel1(activate(X), activate(Z))
quote1(ncons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
quote1(nnil) -> nil1
quote1(nfirst(X, Z)) -> first1(activate(X), activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
fcons(X, Z) -> cons(X, Z)
0 -> n0
cons(X1, X2) -> ncons(X1, X2)
nil -> nnil
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
three new Dependency Pairs are created:
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfrom(X'''))))) -> SEL(X, cons(Y'', nfirst(X'', from(X'''))))
SEL(s(X), cons(Y, nfirst(s(X''''), cons(Y''', nfrom(X'''''))))) -> SEL(X, ncons(Y''', nfirst(X'''', from(X'''''))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfrom(X''''))))) -> SEL(X, cons(Y'', nfirst(X'', cons(X'''', nfrom(s(X''''))))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfrom(X''''))))) -> SEL(X, cons(Y'', nfirst(X'', nfrom(X''''))))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 7
↳Nar
...
→DP Problem 23
↳Narrowing Transformation
→DP Problem 2
↳Remaining
→DP Problem 3
↳Remaining
→DP Problem 4
↳Remaining
→DP Problem 5
↳Remaining
→DP Problem 6
↳Remaining
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfrom(X''''))))) -> SEL(X, cons(Y'', nfirst(X'', nfrom(X''''))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfrom(X''''))))) -> SEL(X, cons(Y'', nfirst(X'', cons(X'''', nfrom(s(X''''))))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', Z')))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', activate(Z'))))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(0, X2''))))) -> SEL(X, cons(Y'', nfirst(X'', nil)))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', Z'')))) -> SEL(X, cons(Y'', nfirst(X'', Z'')))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(X1', X2'))))) -> SEL(X, cons(Y'', nfirst(X'', sel(X1', X2'))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', ns(X'''))))) -> SEL(X, cons(Y'', nfirst(X'', s(X'''))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nnil)))) -> SEL(X, cons(Y'', nfirst(X'', nil)))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', ncons(X1', X2'))))) -> SEL(X, cons(Y'', nfirst(X'', cons(X1', X2'))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', n0)))) -> SEL(X, cons(Y'', nfirst(X'', 0)))
SEL(s(X), cons(Y, nfrom(X'''))) -> SEL(X, cons(X''', nfrom(s(X'''))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(X1'', X2''))))) -> SEL(X, cons(Y'', nfirst(X'', nfirst(X1'', X2''))))
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
sel1(0, cons(X, Z)) -> quote(X)
first1(0, Z) -> nil1
first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
quote(n0) -> 01
quote(ns(X)) -> s1(quote(activate(X)))
quote(nsel(X, Z)) -> sel1(activate(X), activate(Z))
quote1(ncons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
quote1(nnil) -> nil1
quote1(nfirst(X, Z)) -> first1(activate(X), activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
fcons(X, Z) -> cons(X, Z)
0 -> n0
cons(X1, X2) -> ncons(X1, X2)
nil -> nnil
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
two new Dependency Pairs are created:
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', n0)))) -> SEL(X, cons(Y'', nfirst(X'', 0)))
SEL(s(X), cons(Y, nfirst(s(X'''), cons(Y''', n0)))) -> SEL(X, ncons(Y''', nfirst(X''', 0)))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', n0)))) -> SEL(X, cons(Y'', nfirst(X'', n0)))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 7
↳Nar
...
→DP Problem 24
↳Narrowing Transformation
→DP Problem 2
↳Remaining
→DP Problem 3
↳Remaining
→DP Problem 4
↳Remaining
→DP Problem 5
↳Remaining
→DP Problem 6
↳Remaining
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', n0)))) -> SEL(X, cons(Y'', nfirst(X'', n0)))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfrom(X''''))))) -> SEL(X, cons(Y'', nfirst(X'', cons(X'''', nfrom(s(X''''))))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(X1'', X2''))))) -> SEL(X, cons(Y'', nfirst(X'', nfirst(X1'', X2''))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', Z')))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', activate(Z'))))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(0, X2''))))) -> SEL(X, cons(Y'', nfirst(X'', nil)))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', Z'')))) -> SEL(X, cons(Y'', nfirst(X'', Z'')))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(X1', X2'))))) -> SEL(X, cons(Y'', nfirst(X'', sel(X1', X2'))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', ns(X'''))))) -> SEL(X, cons(Y'', nfirst(X'', s(X'''))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nnil)))) -> SEL(X, cons(Y'', nfirst(X'', nil)))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', ncons(X1', X2'))))) -> SEL(X, cons(Y'', nfirst(X'', cons(X1', X2'))))
SEL(s(X), cons(Y, nfrom(X'''))) -> SEL(X, cons(X''', nfrom(s(X'''))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfrom(X''''))))) -> SEL(X, cons(Y'', nfirst(X'', nfrom(X''''))))
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
sel1(0, cons(X, Z)) -> quote(X)
first1(0, Z) -> nil1
first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
quote(n0) -> 01
quote(ns(X)) -> s1(quote(activate(X)))
quote(nsel(X, Z)) -> sel1(activate(X), activate(Z))
quote1(ncons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
quote1(nnil) -> nil1
quote1(nfirst(X, Z)) -> first1(activate(X), activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
fcons(X, Z) -> cons(X, Z)
0 -> n0
cons(X1, X2) -> ncons(X1, X2)
nil -> nnil
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
two new Dependency Pairs are created:
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nnil)))) -> SEL(X, cons(Y'', nfirst(X'', nil)))
SEL(s(X), cons(Y, nfirst(s(X'''), cons(Y''', nnil)))) -> SEL(X, ncons(Y''', nfirst(X''', nil)))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nnil)))) -> SEL(X, cons(Y'', nfirst(X'', nnil)))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 7
↳Nar
...
→DP Problem 25
↳Narrowing Transformation
→DP Problem 2
↳Remaining
→DP Problem 3
↳Remaining
→DP Problem 4
↳Remaining
→DP Problem 5
↳Remaining
→DP Problem 6
↳Remaining
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nnil)))) -> SEL(X, cons(Y'', nfirst(X'', nnil)))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfrom(X''''))))) -> SEL(X, cons(Y'', nfirst(X'', nfrom(X''''))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfrom(X''''))))) -> SEL(X, cons(Y'', nfirst(X'', cons(X'''', nfrom(s(X''''))))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(X1'', X2''))))) -> SEL(X, cons(Y'', nfirst(X'', nfirst(X1'', X2''))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', Z')))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', activate(Z'))))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(0, X2''))))) -> SEL(X, cons(Y'', nfirst(X'', nil)))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', Z'')))) -> SEL(X, cons(Y'', nfirst(X'', Z'')))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(X1', X2'))))) -> SEL(X, cons(Y'', nfirst(X'', sel(X1', X2'))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', ns(X'''))))) -> SEL(X, cons(Y'', nfirst(X'', s(X'''))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', ncons(X1', X2'))))) -> SEL(X, cons(Y'', nfirst(X'', cons(X1', X2'))))
SEL(s(X), cons(Y, nfrom(X'''))) -> SEL(X, cons(X''', nfrom(s(X'''))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', n0)))) -> SEL(X, cons(Y'', nfirst(X'', n0)))
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
sel1(0, cons(X, Z)) -> quote(X)
first1(0, Z) -> nil1
first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
quote(n0) -> 01
quote(ns(X)) -> s1(quote(activate(X)))
quote(nsel(X, Z)) -> sel1(activate(X), activate(Z))
quote1(ncons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
quote1(nnil) -> nil1
quote1(nfirst(X, Z)) -> first1(activate(X), activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
fcons(X, Z) -> cons(X, Z)
0 -> n0
cons(X1, X2) -> ncons(X1, X2)
nil -> nnil
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
two new Dependency Pairs are created:
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', ns(X'''))))) -> SEL(X, cons(Y'', nfirst(X'', s(X'''))))
SEL(s(X), cons(Y, nfirst(s(X''''), cons(Y''', ns(X'''''))))) -> SEL(X, ncons(Y''', nfirst(X'''', s(X'''''))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', ns(X''''))))) -> SEL(X, cons(Y'', nfirst(X'', ns(X''''))))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 7
↳Nar
...
→DP Problem 26
↳Narrowing Transformation
→DP Problem 2
↳Remaining
→DP Problem 3
↳Remaining
→DP Problem 4
↳Remaining
→DP Problem 5
↳Remaining
→DP Problem 6
↳Remaining
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', ns(X''''))))) -> SEL(X, cons(Y'', nfirst(X'', ns(X''''))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', n0)))) -> SEL(X, cons(Y'', nfirst(X'', n0)))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfrom(X''''))))) -> SEL(X, cons(Y'', nfirst(X'', nfrom(X''''))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfrom(X''''))))) -> SEL(X, cons(Y'', nfirst(X'', cons(X'''', nfrom(s(X''''))))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(X1'', X2''))))) -> SEL(X, cons(Y'', nfirst(X'', nfirst(X1'', X2''))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', Z')))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', activate(Z'))))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(0, X2''))))) -> SEL(X, cons(Y'', nfirst(X'', nil)))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', Z'')))) -> SEL(X, cons(Y'', nfirst(X'', Z'')))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(X1', X2'))))) -> SEL(X, cons(Y'', nfirst(X'', sel(X1', X2'))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', ncons(X1', X2'))))) -> SEL(X, cons(Y'', nfirst(X'', cons(X1', X2'))))
SEL(s(X), cons(Y, nfrom(X'''))) -> SEL(X, cons(X''', nfrom(s(X'''))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nnil)))) -> SEL(X, cons(Y'', nfirst(X'', nnil)))
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
sel1(0, cons(X, Z)) -> quote(X)
first1(0, Z) -> nil1
first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
quote(n0) -> 01
quote(ns(X)) -> s1(quote(activate(X)))
quote(nsel(X, Z)) -> sel1(activate(X), activate(Z))
quote1(ncons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
quote1(nnil) -> nil1
quote1(nfirst(X, Z)) -> first1(activate(X), activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
fcons(X, Z) -> cons(X, Z)
0 -> n0
cons(X1, X2) -> ncons(X1, X2)
nil -> nnil
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
four new Dependency Pairs are created:
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(X1', X2'))))) -> SEL(X, cons(Y'', nfirst(X'', sel(X1', X2'))))
SEL(s(X), cons(Y, nfirst(s(X'''), cons(Y''', nsel(X1'', X2''))))) -> SEL(X, ncons(Y''', nfirst(X''', sel(X1'', X2''))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(s(X'''), cons(Y''', Z')))))) -> SEL(X, cons(Y'', nfirst(X'', sel(X''', activate(Z')))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(0, cons(X''', Z')))))) -> SEL(X, cons(Y'', nfirst(X'', X''')))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(X1'', X2''))))) -> SEL(X, cons(Y'', nfirst(X'', nsel(X1'', X2''))))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 7
↳Nar
...
→DP Problem 27
↳Narrowing Transformation
→DP Problem 2
↳Remaining
→DP Problem 3
↳Remaining
→DP Problem 4
↳Remaining
→DP Problem 5
↳Remaining
→DP Problem 6
↳Remaining
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(X1'', X2''))))) -> SEL(X, cons(Y'', nfirst(X'', nsel(X1'', X2''))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(0, cons(X''', Z')))))) -> SEL(X, cons(Y'', nfirst(X'', X''')))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(s(X'''), cons(Y''', Z')))))) -> SEL(X, cons(Y'', nfirst(X'', sel(X''', activate(Z')))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nnil)))) -> SEL(X, cons(Y'', nfirst(X'', nnil)))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', n0)))) -> SEL(X, cons(Y'', nfirst(X'', n0)))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfrom(X''''))))) -> SEL(X, cons(Y'', nfirst(X'', nfrom(X''''))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfrom(X''''))))) -> SEL(X, cons(Y'', nfirst(X'', cons(X'''', nfrom(s(X''''))))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(X1'', X2''))))) -> SEL(X, cons(Y'', nfirst(X'', nfirst(X1'', X2''))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', Z')))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', activate(Z'))))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(0, X2''))))) -> SEL(X, cons(Y'', nfirst(X'', nil)))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', Z'')))) -> SEL(X, cons(Y'', nfirst(X'', Z'')))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', ncons(X1', X2'))))) -> SEL(X, cons(Y'', nfirst(X'', cons(X1', X2'))))
SEL(s(X), cons(Y, nfrom(X'''))) -> SEL(X, cons(X''', nfrom(s(X'''))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', ns(X''''))))) -> SEL(X, cons(Y'', nfirst(X'', ns(X''''))))
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
sel1(0, cons(X, Z)) -> quote(X)
first1(0, Z) -> nil1
first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
quote(n0) -> 01
quote(ns(X)) -> s1(quote(activate(X)))
quote(nsel(X, Z)) -> sel1(activate(X), activate(Z))
quote1(ncons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
quote1(nnil) -> nil1
quote1(nfirst(X, Z)) -> first1(activate(X), activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
fcons(X, Z) -> cons(X, Z)
0 -> n0
cons(X1, X2) -> ncons(X1, X2)
nil -> nnil
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
two new Dependency Pairs are created:
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(0, X2''))))) -> SEL(X, cons(Y'', nfirst(X'', nil)))
SEL(s(X), cons(Y, nfirst(s(X'''), cons(Y''', nfirst(0, X2''))))) -> SEL(X, ncons(Y''', nfirst(X''', nil)))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(0, X2''))))) -> SEL(X, cons(Y'', nfirst(X'', nnil)))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 7
↳Nar
...
→DP Problem 28
↳Narrowing Transformation
→DP Problem 2
↳Remaining
→DP Problem 3
↳Remaining
→DP Problem 4
↳Remaining
→DP Problem 5
↳Remaining
→DP Problem 6
↳Remaining
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(0, X2''))))) -> SEL(X, cons(Y'', nfirst(X'', nnil)))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(0, cons(X''', Z')))))) -> SEL(X, cons(Y'', nfirst(X'', X''')))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(s(X'''), cons(Y''', Z')))))) -> SEL(X, cons(Y'', nfirst(X'', sel(X''', activate(Z')))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', ns(X''''))))) -> SEL(X, cons(Y'', nfirst(X'', ns(X''''))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nnil)))) -> SEL(X, cons(Y'', nfirst(X'', nnil)))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', n0)))) -> SEL(X, cons(Y'', nfirst(X'', n0)))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfrom(X''''))))) -> SEL(X, cons(Y'', nfirst(X'', nfrom(X''''))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfrom(X''''))))) -> SEL(X, cons(Y'', nfirst(X'', cons(X'''', nfrom(s(X''''))))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(X1'', X2''))))) -> SEL(X, cons(Y'', nfirst(X'', nfirst(X1'', X2''))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', Z')))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', activate(Z'))))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', Z'')))) -> SEL(X, cons(Y'', nfirst(X'', Z'')))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', ncons(X1', X2'))))) -> SEL(X, cons(Y'', nfirst(X'', cons(X1', X2'))))
SEL(s(X), cons(Y, nfrom(X'''))) -> SEL(X, cons(X''', nfrom(s(X'''))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(X1'', X2''))))) -> SEL(X, cons(Y'', nfirst(X'', nsel(X1'', X2''))))
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
sel1(0, cons(X, Z)) -> quote(X)
first1(0, Z) -> nil1
first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
quote(n0) -> 01
quote(ns(X)) -> s1(quote(activate(X)))
quote(nsel(X, Z)) -> sel1(activate(X), activate(Z))
quote1(ncons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
quote1(nnil) -> nil1
quote1(nfirst(X, Z)) -> first1(activate(X), activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
fcons(X, Z) -> cons(X, Z)
0 -> n0
cons(X1, X2) -> ncons(X1, X2)
nil -> nnil
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
one new Dependency Pair is created:
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(X1'', X2''))))) -> SEL(X, cons(Y'', nfirst(X'', nfirst(X1'', X2''))))
SEL(s(X), cons(Y, nfirst(s(X'''), cons(Y''', nfirst(X1''', X2'''))))) -> SEL(X, ncons(Y''', nfirst(X''', nfirst(X1''', X2'''))))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 7
↳Nar
...
→DP Problem 29
↳Narrowing Transformation
→DP Problem 2
↳Remaining
→DP Problem 3
↳Remaining
→DP Problem 4
↳Remaining
→DP Problem 5
↳Remaining
→DP Problem 6
↳Remaining
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(X1'', X2''))))) -> SEL(X, cons(Y'', nfirst(X'', nsel(X1'', X2''))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(0, cons(X''', Z')))))) -> SEL(X, cons(Y'', nfirst(X'', X''')))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(s(X'''), cons(Y''', Z')))))) -> SEL(X, cons(Y'', nfirst(X'', sel(X''', activate(Z')))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', ns(X''''))))) -> SEL(X, cons(Y'', nfirst(X'', ns(X''''))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nnil)))) -> SEL(X, cons(Y'', nfirst(X'', nnil)))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', n0)))) -> SEL(X, cons(Y'', nfirst(X'', n0)))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfrom(X''''))))) -> SEL(X, cons(Y'', nfirst(X'', nfrom(X''''))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfrom(X''''))))) -> SEL(X, cons(Y'', nfirst(X'', cons(X'''', nfrom(s(X''''))))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', Z')))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', activate(Z'))))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', Z'')))) -> SEL(X, cons(Y'', nfirst(X'', Z'')))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', ncons(X1', X2'))))) -> SEL(X, cons(Y'', nfirst(X'', cons(X1', X2'))))
SEL(s(X), cons(Y, nfrom(X'''))) -> SEL(X, cons(X''', nfrom(s(X'''))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(0, X2''))))) -> SEL(X, cons(Y'', nfirst(X'', nnil)))
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
sel1(0, cons(X, Z)) -> quote(X)
first1(0, Z) -> nil1
first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
quote(n0) -> 01
quote(ns(X)) -> s1(quote(activate(X)))
quote(nsel(X, Z)) -> sel1(activate(X), activate(Z))
quote1(ncons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
quote1(nnil) -> nil1
quote1(nfirst(X, Z)) -> first1(activate(X), activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
fcons(X, Z) -> cons(X, Z)
0 -> n0
cons(X1, X2) -> ncons(X1, X2)
nil -> nnil
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
one new Dependency Pair is created:
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfrom(X''''))))) -> SEL(X, cons(Y'', nfirst(X'', nfrom(X''''))))
SEL(s(X), cons(Y, nfirst(s(X'''), cons(Y''', nfrom(X'''''))))) -> SEL(X, ncons(Y''', nfirst(X''', nfrom(X'''''))))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 7
↳Nar
...
→DP Problem 30
↳Narrowing Transformation
→DP Problem 2
↳Remaining
→DP Problem 3
↳Remaining
→DP Problem 4
↳Remaining
→DP Problem 5
↳Remaining
→DP Problem 6
↳Remaining
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(0, X2''))))) -> SEL(X, cons(Y'', nfirst(X'', nnil)))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(0, cons(X''', Z')))))) -> SEL(X, cons(Y'', nfirst(X'', X''')))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(s(X'''), cons(Y''', Z')))))) -> SEL(X, cons(Y'', nfirst(X'', sel(X''', activate(Z')))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', ns(X''''))))) -> SEL(X, cons(Y'', nfirst(X'', ns(X''''))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nnil)))) -> SEL(X, cons(Y'', nfirst(X'', nnil)))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', n0)))) -> SEL(X, cons(Y'', nfirst(X'', n0)))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfrom(X''''))))) -> SEL(X, cons(Y'', nfirst(X'', cons(X'''', nfrom(s(X''''))))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', Z')))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', activate(Z'))))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', Z'')))) -> SEL(X, cons(Y'', nfirst(X'', Z'')))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', ncons(X1', X2'))))) -> SEL(X, cons(Y'', nfirst(X'', cons(X1', X2'))))
SEL(s(X), cons(Y, nfrom(X'''))) -> SEL(X, cons(X''', nfrom(s(X'''))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(X1'', X2''))))) -> SEL(X, cons(Y'', nfirst(X'', nsel(X1'', X2''))))
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
sel1(0, cons(X, Z)) -> quote(X)
first1(0, Z) -> nil1
first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
quote(n0) -> 01
quote(ns(X)) -> s1(quote(activate(X)))
quote(nsel(X, Z)) -> sel1(activate(X), activate(Z))
quote1(ncons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
quote1(nnil) -> nil1
quote1(nfirst(X, Z)) -> first1(activate(X), activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
fcons(X, Z) -> cons(X, Z)
0 -> n0
cons(X1, X2) -> ncons(X1, X2)
nil -> nnil
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
one new Dependency Pair is created:
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', n0)))) -> SEL(X, cons(Y'', nfirst(X'', n0)))
SEL(s(X), cons(Y, nfirst(s(X'''), cons(Y''', n0)))) -> SEL(X, ncons(Y''', nfirst(X''', n0)))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 7
↳Nar
...
→DP Problem 31
↳Narrowing Transformation
→DP Problem 2
↳Remaining
→DP Problem 3
↳Remaining
→DP Problem 4
↳Remaining
→DP Problem 5
↳Remaining
→DP Problem 6
↳Remaining
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(X1'', X2''))))) -> SEL(X, cons(Y'', nfirst(X'', nsel(X1'', X2''))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(0, cons(X''', Z')))))) -> SEL(X, cons(Y'', nfirst(X'', X''')))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(s(X'''), cons(Y''', Z')))))) -> SEL(X, cons(Y'', nfirst(X'', sel(X''', activate(Z')))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', ns(X''''))))) -> SEL(X, cons(Y'', nfirst(X'', ns(X''''))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nnil)))) -> SEL(X, cons(Y'', nfirst(X'', nnil)))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfrom(X''''))))) -> SEL(X, cons(Y'', nfirst(X'', cons(X'''', nfrom(s(X''''))))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', Z')))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', activate(Z'))))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', Z'')))) -> SEL(X, cons(Y'', nfirst(X'', Z'')))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', ncons(X1', X2'))))) -> SEL(X, cons(Y'', nfirst(X'', cons(X1', X2'))))
SEL(s(X), cons(Y, nfrom(X'''))) -> SEL(X, cons(X''', nfrom(s(X'''))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(0, X2''))))) -> SEL(X, cons(Y'', nfirst(X'', nnil)))
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
sel1(0, cons(X, Z)) -> quote(X)
first1(0, Z) -> nil1
first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
quote(n0) -> 01
quote(ns(X)) -> s1(quote(activate(X)))
quote(nsel(X, Z)) -> sel1(activate(X), activate(Z))
quote1(ncons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
quote1(nnil) -> nil1
quote1(nfirst(X, Z)) -> first1(activate(X), activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
fcons(X, Z) -> cons(X, Z)
0 -> n0
cons(X1, X2) -> ncons(X1, X2)
nil -> nnil
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
one new Dependency Pair is created:
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nnil)))) -> SEL(X, cons(Y'', nfirst(X'', nnil)))
SEL(s(X), cons(Y, nfirst(s(X'''), cons(Y''', nnil)))) -> SEL(X, ncons(Y''', nfirst(X''', nnil)))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 7
↳Nar
...
→DP Problem 32
↳Narrowing Transformation
→DP Problem 2
↳Remaining
→DP Problem 3
↳Remaining
→DP Problem 4
↳Remaining
→DP Problem 5
↳Remaining
→DP Problem 6
↳Remaining
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(0, X2''))))) -> SEL(X, cons(Y'', nfirst(X'', nnil)))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(0, cons(X''', Z')))))) -> SEL(X, cons(Y'', nfirst(X'', X''')))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(s(X'''), cons(Y''', Z')))))) -> SEL(X, cons(Y'', nfirst(X'', sel(X''', activate(Z')))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', ns(X''''))))) -> SEL(X, cons(Y'', nfirst(X'', ns(X''''))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfrom(X''''))))) -> SEL(X, cons(Y'', nfirst(X'', cons(X'''', nfrom(s(X''''))))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', Z')))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', activate(Z'))))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', Z'')))) -> SEL(X, cons(Y'', nfirst(X'', Z'')))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', ncons(X1', X2'))))) -> SEL(X, cons(Y'', nfirst(X'', cons(X1', X2'))))
SEL(s(X), cons(Y, nfrom(X'''))) -> SEL(X, cons(X''', nfrom(s(X'''))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(X1'', X2''))))) -> SEL(X, cons(Y'', nfirst(X'', nsel(X1'', X2''))))
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
sel1(0, cons(X, Z)) -> quote(X)
first1(0, Z) -> nil1
first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
quote(n0) -> 01
quote(ns(X)) -> s1(quote(activate(X)))
quote(nsel(X, Z)) -> sel1(activate(X), activate(Z))
quote1(ncons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
quote1(nnil) -> nil1
quote1(nfirst(X, Z)) -> first1(activate(X), activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
fcons(X, Z) -> cons(X, Z)
0 -> n0
cons(X1, X2) -> ncons(X1, X2)
nil -> nnil
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
one new Dependency Pair is created:
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', ns(X''''))))) -> SEL(X, cons(Y'', nfirst(X'', ns(X''''))))
SEL(s(X), cons(Y, nfirst(s(X'''), cons(Y''', ns(X'''''))))) -> SEL(X, ncons(Y''', nfirst(X''', ns(X'''''))))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 7
↳Nar
...
→DP Problem 33
↳Narrowing Transformation
→DP Problem 2
↳Remaining
→DP Problem 3
↳Remaining
→DP Problem 4
↳Remaining
→DP Problem 5
↳Remaining
→DP Problem 6
↳Remaining
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(X1'', X2''))))) -> SEL(X, cons(Y'', nfirst(X'', nsel(X1'', X2''))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(0, cons(X''', Z')))))) -> SEL(X, cons(Y'', nfirst(X'', X''')))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(s(X'''), cons(Y''', Z')))))) -> SEL(X, cons(Y'', nfirst(X'', sel(X''', activate(Z')))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfrom(X''''))))) -> SEL(X, cons(Y'', nfirst(X'', cons(X'''', nfrom(s(X''''))))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', Z')))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', activate(Z'))))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', Z'')))) -> SEL(X, cons(Y'', nfirst(X'', Z'')))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', ncons(X1', X2'))))) -> SEL(X, cons(Y'', nfirst(X'', cons(X1', X2'))))
SEL(s(X), cons(Y, nfrom(X'''))) -> SEL(X, cons(X''', nfrom(s(X'''))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(0, X2''))))) -> SEL(X, cons(Y'', nfirst(X'', nnil)))
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
sel1(0, cons(X, Z)) -> quote(X)
first1(0, Z) -> nil1
first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
quote(n0) -> 01
quote(ns(X)) -> s1(quote(activate(X)))
quote(nsel(X, Z)) -> sel1(activate(X), activate(Z))
quote1(ncons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
quote1(nnil) -> nil1
quote1(nfirst(X, Z)) -> first1(activate(X), activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
fcons(X, Z) -> cons(X, Z)
0 -> n0
cons(X1, X2) -> ncons(X1, X2)
nil -> nnil
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
10 new Dependency Pairs are created:
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(s(X'''), cons(Y''', Z')))))) -> SEL(X, cons(Y'', nfirst(X'', sel(X''', activate(Z')))))
SEL(s(X), cons(Y, nfirst(s(X''''), cons(Y'''', nsel(s(X'''''), cons(Y''', Z'')))))) -> SEL(X, ncons(Y'''', nfirst(X'''', sel(X''''', activate(Z'')))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(s(X''''), cons(Y''', Z'')))))) -> SEL(X, cons(Y'', nfirst(X'', nsel(X'''', activate(Z'')))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(s(X'''), cons(Y''', nfirst(X1', X2'))))))) -> SEL(X, cons(Y'', nfirst(X'', sel(X''', first(X1', X2')))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(s(X'''), cons(Y''', nfrom(X'0))))))) -> SEL(X, cons(Y'', nfirst(X'', sel(X''', from(X'0)))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(s(X'''), cons(Y''', n0)))))) -> SEL(X, cons(Y'', nfirst(X'', sel(X''', 0))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(s(X'''), cons(Y''', ncons(X1', X2'))))))) -> SEL(X, cons(Y'', nfirst(X'', sel(X''', cons(X1', X2')))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(s(X'''), cons(Y''', nnil)))))) -> SEL(X, cons(Y'', nfirst(X'', sel(X''', nil))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(s(X'''), cons(Y''', ns(X'0))))))) -> SEL(X, cons(Y'', nfirst(X'', sel(X''', s(X'0)))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(s(X'''), cons(Y''', nsel(X1', X2'))))))) -> SEL(X, cons(Y'', nfirst(X'', sel(X''', sel(X1', X2')))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(s(X'''), cons(Y''', Z'')))))) -> SEL(X, cons(Y'', nfirst(X'', sel(X''', Z''))))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 7
↳Nar
...
→DP Problem 34
↳Narrowing Transformation
→DP Problem 2
↳Remaining
→DP Problem 3
↳Remaining
→DP Problem 4
↳Remaining
→DP Problem 5
↳Remaining
→DP Problem 6
↳Remaining
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(s(X'''), cons(Y''', Z'')))))) -> SEL(X, cons(Y'', nfirst(X'', sel(X''', Z''))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(s(X'''), cons(Y''', nsel(X1', X2'))))))) -> SEL(X, cons(Y'', nfirst(X'', sel(X''', sel(X1', X2')))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(s(X'''), cons(Y''', ns(X'0))))))) -> SEL(X, cons(Y'', nfirst(X'', sel(X''', s(X'0)))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(s(X'''), cons(Y''', nnil)))))) -> SEL(X, cons(Y'', nfirst(X'', sel(X''', nil))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(s(X'''), cons(Y''', ncons(X1', X2'))))))) -> SEL(X, cons(Y'', nfirst(X'', sel(X''', cons(X1', X2')))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(s(X'''), cons(Y''', n0)))))) -> SEL(X, cons(Y'', nfirst(X'', sel(X''', 0))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(s(X'''), cons(Y''', nfrom(X'0))))))) -> SEL(X, cons(Y'', nfirst(X'', sel(X''', from(X'0)))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(s(X'''), cons(Y''', nfirst(X1', X2'))))))) -> SEL(X, cons(Y'', nfirst(X'', sel(X''', first(X1', X2')))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(s(X''''), cons(Y''', Z'')))))) -> SEL(X, cons(Y'', nfirst(X'', nsel(X'''', activate(Z'')))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(0, X2''))))) -> SEL(X, cons(Y'', nfirst(X'', nnil)))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(0, cons(X''', Z')))))) -> SEL(X, cons(Y'', nfirst(X'', X''')))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfrom(X''''))))) -> SEL(X, cons(Y'', nfirst(X'', cons(X'''', nfrom(s(X''''))))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', Z')))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', activate(Z'))))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', Z'')))) -> SEL(X, cons(Y'', nfirst(X'', Z'')))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', ncons(X1', X2'))))) -> SEL(X, cons(Y'', nfirst(X'', cons(X1', X2'))))
SEL(s(X), cons(Y, nfrom(X'''))) -> SEL(X, cons(X''', nfrom(s(X'''))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(X1'', X2''))))) -> SEL(X, cons(Y'', nfirst(X'', nsel(X1'', X2''))))
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
sel1(0, cons(X, Z)) -> quote(X)
first1(0, Z) -> nil1
first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
quote(n0) -> 01
quote(ns(X)) -> s1(quote(activate(X)))
quote(nsel(X, Z)) -> sel1(activate(X), activate(Z))
quote1(ncons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
quote1(nnil) -> nil1
quote1(nfirst(X, Z)) -> first1(activate(X), activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
fcons(X, Z) -> cons(X, Z)
0 -> n0
cons(X1, X2) -> ncons(X1, X2)
nil -> nnil
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
one new Dependency Pair is created:
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(X1'', X2''))))) -> SEL(X, cons(Y'', nfirst(X'', nsel(X1'', X2''))))
SEL(s(X), cons(Y, nfirst(s(X'''), cons(Y''', nsel(X1''', X2'''))))) -> SEL(X, ncons(Y''', nfirst(X''', nsel(X1''', X2'''))))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 7
↳Nar
...
→DP Problem 35
↳Polynomial Ordering
→DP Problem 2
↳Remaining
→DP Problem 3
↳Remaining
→DP Problem 4
↳Remaining
→DP Problem 5
↳Remaining
→DP Problem 6
↳Remaining
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(s(X'''), cons(Y''', nsel(X1', X2'))))))) -> SEL(X, cons(Y'', nfirst(X'', sel(X''', sel(X1', X2')))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(s(X'''), cons(Y''', ns(X'0))))))) -> SEL(X, cons(Y'', nfirst(X'', sel(X''', s(X'0)))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(s(X'''), cons(Y''', nnil)))))) -> SEL(X, cons(Y'', nfirst(X'', sel(X''', nil))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(s(X'''), cons(Y''', ncons(X1', X2'))))))) -> SEL(X, cons(Y'', nfirst(X'', sel(X''', cons(X1', X2')))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(s(X'''), cons(Y''', n0)))))) -> SEL(X, cons(Y'', nfirst(X'', sel(X''', 0))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(s(X'''), cons(Y''', nfrom(X'0))))))) -> SEL(X, cons(Y'', nfirst(X'', sel(X''', from(X'0)))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(s(X'''), cons(Y''', nfirst(X1', X2'))))))) -> SEL(X, cons(Y'', nfirst(X'', sel(X''', first(X1', X2')))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(s(X''''), cons(Y''', Z'')))))) -> SEL(X, cons(Y'', nfirst(X'', nsel(X'''', activate(Z'')))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(0, X2''))))) -> SEL(X, cons(Y'', nfirst(X'', nnil)))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(0, cons(X''', Z')))))) -> SEL(X, cons(Y'', nfirst(X'', X''')))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfrom(X''''))))) -> SEL(X, cons(Y'', nfirst(X'', cons(X'''', nfrom(s(X''''))))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', Z')))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', activate(Z'))))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', Z'')))) -> SEL(X, cons(Y'', nfirst(X'', Z'')))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', ncons(X1', X2'))))) -> SEL(X, cons(Y'', nfirst(X'', cons(X1', X2'))))
SEL(s(X), cons(Y, nfrom(X'''))) -> SEL(X, cons(X''', nfrom(s(X'''))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(s(X'''), cons(Y''', Z'')))))) -> SEL(X, cons(Y'', nfirst(X'', sel(X''', Z''))))
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
sel1(0, cons(X, Z)) -> quote(X)
first1(0, Z) -> nil1
first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
quote(n0) -> 01
quote(ns(X)) -> s1(quote(activate(X)))
quote(nsel(X, Z)) -> sel1(activate(X), activate(Z))
quote1(ncons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
quote1(nnil) -> nil1
quote1(nfirst(X, Z)) -> first1(activate(X), activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
fcons(X, Z) -> cons(X, Z)
0 -> n0
cons(X1, X2) -> ncons(X1, X2)
nil -> nnil
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(s(X'''), cons(Y''', nsel(X1', X2'))))))) -> SEL(X, cons(Y'', nfirst(X'', sel(X''', sel(X1', X2')))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(s(X'''), cons(Y''', ns(X'0))))))) -> SEL(X, cons(Y'', nfirst(X'', sel(X''', s(X'0)))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(s(X'''), cons(Y''', nnil)))))) -> SEL(X, cons(Y'', nfirst(X'', sel(X''', nil))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(s(X'''), cons(Y''', ncons(X1', X2'))))))) -> SEL(X, cons(Y'', nfirst(X'', sel(X''', cons(X1', X2')))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(s(X'''), cons(Y''', n0)))))) -> SEL(X, cons(Y'', nfirst(X'', sel(X''', 0))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(s(X'''), cons(Y''', nfrom(X'0))))))) -> SEL(X, cons(Y'', nfirst(X'', sel(X''', from(X'0)))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(s(X'''), cons(Y''', nfirst(X1', X2'))))))) -> SEL(X, cons(Y'', nfirst(X'', sel(X''', first(X1', X2')))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(s(X''''), cons(Y''', Z'')))))) -> SEL(X, cons(Y'', nfirst(X'', nsel(X'''', activate(Z'')))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(0, X2''))))) -> SEL(X, cons(Y'', nfirst(X'', nnil)))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(0, cons(X''', Z')))))) -> SEL(X, cons(Y'', nfirst(X'', X''')))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', Z'')))) -> SEL(X, cons(Y'', nfirst(X'', Z'')))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nsel(s(X'''), cons(Y''', Z'')))))) -> SEL(X, cons(Y'', nfirst(X'', sel(X''', Z''))))
cons(X1, X2) -> ncons(X1, X2)
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> nil
first(s(X), cons(Y, Z)) -> cons(Y, nfirst(X, activate(Z)))
first(X1, X2) -> nfirst(X1, X2)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
s(X) -> ns(X)
nil -> nnil
0 -> n0
from(X) -> cons(X, nfrom(s(X)))
from(X) -> nfrom(X)
POL(from(x1)) = 1 + x1 POL(activate(x1)) = 1 + x1 POL(SEL(x1, x2)) = 1 + x2 POL(n__s(x1)) = 0 POL(sel(x1, x2)) = x2 POL(n__nil) = 0 POL(n__cons(x1, x2)) = x1 + x2 POL(n__from(x1)) = x1 POL(n__sel(x1, x2)) = x2 POL(0) = 0 POL(first(x1, x2)) = 1 + x2 POL(cons(x1, x2)) = 1 + x1 + x2 POL(nil) = 0 POL(n__0) = 0 POL(s(x1)) = 0 POL(n__first(x1, x2)) = x2
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 7
↳Nar
...
→DP Problem 36
↳Polynomial Ordering
→DP Problem 2
↳Remaining
→DP Problem 3
↳Remaining
→DP Problem 4
↳Remaining
→DP Problem 5
↳Remaining
→DP Problem 6
↳Remaining
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfrom(X''''))))) -> SEL(X, cons(Y'', nfirst(X'', cons(X'''', nfrom(s(X''''))))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', Z')))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', activate(Z'))))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', ncons(X1', X2'))))) -> SEL(X, cons(Y'', nfirst(X'', cons(X1', X2'))))
SEL(s(X), cons(Y, nfrom(X'''))) -> SEL(X, cons(X''', nfrom(s(X'''))))
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
sel1(0, cons(X, Z)) -> quote(X)
first1(0, Z) -> nil1
first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
quote(n0) -> 01
quote(ns(X)) -> s1(quote(activate(X)))
quote(nsel(X, Z)) -> sel1(activate(X), activate(Z))
quote1(ncons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
quote1(nnil) -> nil1
quote1(nfirst(X, Z)) -> first1(activate(X), activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
fcons(X, Z) -> cons(X, Z)
0 -> n0
cons(X1, X2) -> ncons(X1, X2)
nil -> nnil
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', ncons(X1', X2'))))) -> SEL(X, cons(Y'', nfirst(X'', cons(X1', X2'))))
cons(X1, X2) -> ncons(X1, X2)
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
0 -> n0
nil -> nnil
POL(from(x1)) = 1 + x1 POL(activate(x1)) = 1 + x1 POL(SEL(x1, x2)) = 1 + x2 POL(n__s(x1)) = 0 POL(sel(x1, x2)) = x2 POL(n__nil) = 0 POL(n__cons(x1, x2)) = 1 + x1 + x2 POL(n__from(x1)) = x1 POL(n__sel(x1, x2)) = x2 POL(first(x1, x2)) = 1 + x2 POL(0) = 0 POL(cons(x1, x2)) = 1 + x1 + x2 POL(nil) = 0 POL(n__0) = 0 POL(s(x1)) = 0 POL(n__first(x1, x2)) = x2
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 7
↳Nar
...
→DP Problem 37
↳Narrowing Transformation
→DP Problem 2
↳Remaining
→DP Problem 3
↳Remaining
→DP Problem 4
↳Remaining
→DP Problem 5
↳Remaining
→DP Problem 6
↳Remaining
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfrom(X''''))))) -> SEL(X, cons(Y'', nfirst(X'', cons(X'''', nfrom(s(X''''))))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', Z')))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', activate(Z'))))))
SEL(s(X), cons(Y, nfrom(X'''))) -> SEL(X, cons(X''', nfrom(s(X'''))))
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
sel1(0, cons(X, Z)) -> quote(X)
first1(0, Z) -> nil1
first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
quote(n0) -> 01
quote(ns(X)) -> s1(quote(activate(X)))
quote(nsel(X, Z)) -> sel1(activate(X), activate(Z))
quote1(ncons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
quote1(nnil) -> nil1
quote1(nfirst(X, Z)) -> first1(activate(X), activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
fcons(X, Z) -> cons(X, Z)
0 -> n0
cons(X1, X2) -> ncons(X1, X2)
nil -> nnil
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
10 new Dependency Pairs are created:
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', Z')))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', activate(Z'))))))
SEL(s(X), cons(Y, nfirst(s(X''''), cons(Y''0, nfirst(s(X'''''), cons(Y'''', Z'')))))) -> SEL(X, ncons(Y''0, nfirst(X'''', cons(Y'''', nfirst(X''''', activate(Z''))))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X''''), cons(Y'''', Z'')))))) -> SEL(X, cons(Y'', nfirst(X'', ncons(Y'''', nfirst(X'''', activate(Z''))))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', nfirst(X1', X2'))))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', first(X1', X2'))))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', nfrom(X'0))))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', from(X'0))))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', n0)))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', 0)))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', ncons(X1', X2'))))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', cons(X1', X2'))))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', nnil)))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', nil)))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', ns(X'0))))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', s(X'0))))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', nsel(X1', X2'))))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', sel(X1', X2'))))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', Z'')))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', Z'')))))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 7
↳Nar
...
→DP Problem 38
↳Polynomial Ordering
→DP Problem 2
↳Remaining
→DP Problem 3
↳Remaining
→DP Problem 4
↳Remaining
→DP Problem 5
↳Remaining
→DP Problem 6
↳Remaining
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', Z'')))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', Z'')))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', nsel(X1', X2'))))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', sel(X1', X2'))))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', ns(X'0))))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', s(X'0))))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', nnil)))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', nil)))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', ncons(X1', X2'))))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', cons(X1', X2'))))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', n0)))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', 0)))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', nfrom(X'0))))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', from(X'0))))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', nfirst(X1', X2'))))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', first(X1', X2'))))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X''''), cons(Y'''', Z'')))))) -> SEL(X, cons(Y'', nfirst(X'', ncons(Y'''', nfirst(X'''', activate(Z''))))))
SEL(s(X), cons(Y, nfrom(X'''))) -> SEL(X, cons(X''', nfrom(s(X'''))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfrom(X''''))))) -> SEL(X, cons(Y'', nfirst(X'', cons(X'''', nfrom(s(X''''))))))
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
sel1(0, cons(X, Z)) -> quote(X)
first1(0, Z) -> nil1
first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
quote(n0) -> 01
quote(ns(X)) -> s1(quote(activate(X)))
quote(nsel(X, Z)) -> sel1(activate(X), activate(Z))
quote1(ncons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
quote1(nnil) -> nil1
quote1(nfirst(X, Z)) -> first1(activate(X), activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
fcons(X, Z) -> cons(X, Z)
0 -> n0
cons(X1, X2) -> ncons(X1, X2)
nil -> nnil
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', Z'')))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', Z'')))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', nsel(X1', X2'))))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', sel(X1', X2'))))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', ns(X'0))))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', s(X'0))))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', nnil)))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', nil)))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', n0)))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', 0)))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X''''), cons(Y'''', Z'')))))) -> SEL(X, cons(Y'', nfirst(X'', ncons(Y'''', nfirst(X'''', activate(Z''))))))
cons(X1, X2) -> ncons(X1, X2)
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> nil
first(s(X), cons(Y, Z)) -> cons(Y, nfirst(X, activate(Z)))
first(X1, X2) -> nfirst(X1, X2)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
s(X) -> ns(X)
nil -> nnil
0 -> n0
from(X) -> cons(X, nfrom(s(X)))
from(X) -> nfrom(X)
POL(from(x1)) = 1 + x1 POL(activate(x1)) = 1 + x1 POL(SEL(x1, x2)) = 1 + x2 POL(n__s(x1)) = 0 POL(sel(x1, x2)) = x2 POL(n__nil) = 0 POL(n__cons(x1, x2)) = x1 + x2 POL(n__from(x1)) = x1 POL(n__sel(x1, x2)) = x2 POL(0) = 0 POL(first(x1, x2)) = 1 + x2 POL(cons(x1, x2)) = 1 + x1 + x2 POL(nil) = 0 POL(n__0) = 0 POL(s(x1)) = 0 POL(n__first(x1, x2)) = x2
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 7
↳Nar
...
→DP Problem 39
↳Polynomial Ordering
→DP Problem 2
↳Remaining
→DP Problem 3
↳Remaining
→DP Problem 4
↳Remaining
→DP Problem 5
↳Remaining
→DP Problem 6
↳Remaining
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', ncons(X1', X2'))))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', cons(X1', X2'))))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', nfrom(X'0))))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', from(X'0))))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', nfirst(X1', X2'))))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', first(X1', X2'))))))
SEL(s(X), cons(Y, nfrom(X'''))) -> SEL(X, cons(X''', nfrom(s(X'''))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfrom(X''''))))) -> SEL(X, cons(Y'', nfirst(X'', cons(X'''', nfrom(s(X''''))))))
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
sel1(0, cons(X, Z)) -> quote(X)
first1(0, Z) -> nil1
first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
quote(n0) -> 01
quote(ns(X)) -> s1(quote(activate(X)))
quote(nsel(X, Z)) -> sel1(activate(X), activate(Z))
quote1(ncons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
quote1(nnil) -> nil1
quote1(nfirst(X, Z)) -> first1(activate(X), activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
fcons(X, Z) -> cons(X, Z)
0 -> n0
cons(X1, X2) -> ncons(X1, X2)
nil -> nnil
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', ncons(X1', X2'))))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', cons(X1', X2'))))))
cons(X1, X2) -> ncons(X1, X2)
from(X) -> cons(X, nfrom(s(X)))
from(X) -> nfrom(X)
first(0, Z) -> nil
first(s(X), cons(Y, Z)) -> cons(Y, nfirst(X, activate(Z)))
first(X1, X2) -> nfirst(X1, X2)
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
s(X) -> ns(X)
nil -> nnil
0 -> n0
POL(from(x1)) = 1 + x1 POL(activate(x1)) = 1 + x1 POL(SEL(x1, x2)) = 1 + x2 POL(n__s(x1)) = 0 POL(sel(x1, x2)) = x2 POL(n__nil) = 0 POL(n__cons(x1, x2)) = 1 + x1 + x2 POL(n__from(x1)) = x1 POL(n__sel(x1, x2)) = x2 POL(first(x1, x2)) = 1 + x2 POL(0) = 0 POL(cons(x1, x2)) = 1 + x1 + x2 POL(nil) = 0 POL(n__0) = 0 POL(s(x1)) = 0 POL(n__first(x1, x2)) = x2
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳Remaining Obligation(s)
→DP Problem 3
↳Remaining Obligation(s)
→DP Problem 4
↳Remaining Obligation(s)
→DP Problem 5
↳Remaining Obligation(s)
→DP Problem 6
↳Remaining Obligation(s)
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', nfrom(X'0))))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', from(X'0))))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', nfirst(X1', X2'))))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', first(X1', X2'))))))
SEL(s(X), cons(Y, nfrom(X'''))) -> SEL(X, cons(X''', nfrom(s(X'''))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfrom(X''''))))) -> SEL(X, cons(Y'', nfirst(X'', cons(X'''', nfrom(s(X''''))))))
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
sel1(0, cons(X, Z)) -> quote(X)
first1(0, Z) -> nil1
first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
quote(n0) -> 01
quote(ns(X)) -> s1(quote(activate(X)))
quote(nsel(X, Z)) -> sel1(activate(X), activate(Z))
quote1(ncons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
quote1(nnil) -> nil1
quote1(nfirst(X, Z)) -> first1(activate(X), activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
fcons(X, Z) -> cons(X, Z)
0 -> n0
cons(X1, X2) -> ncons(X1, X2)
nil -> nnil
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
UNQUOTE(s1(X)) -> UNQUOTE(X)
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
sel1(0, cons(X, Z)) -> quote(X)
first1(0, Z) -> nil1
first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
quote(n0) -> 01
quote(ns(X)) -> s1(quote(activate(X)))
quote(nsel(X, Z)) -> sel1(activate(X), activate(Z))
quote1(ncons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
quote1(nnil) -> nil1
quote1(nfirst(X, Z)) -> first1(activate(X), activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
fcons(X, Z) -> cons(X, Z)
0 -> n0
cons(X1, X2) -> ncons(X1, X2)
nil -> nnil
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
QUOTE(nsel(X, Z)) -> SEL1(activate(X), activate(Z))
QUOTE(ns(X)) -> QUOTE(activate(X))
SEL1(0, cons(X, Z)) -> QUOTE(X)
SEL1(s(X), cons(Y, Z)) -> SEL1(X, activate(Z))
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
sel1(0, cons(X, Z)) -> quote(X)
first1(0, Z) -> nil1
first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
quote(n0) -> 01
quote(ns(X)) -> s1(quote(activate(X)))
quote(nsel(X, Z)) -> sel1(activate(X), activate(Z))
quote1(ncons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
quote1(nnil) -> nil1
quote1(nfirst(X, Z)) -> first1(activate(X), activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
fcons(X, Z) -> cons(X, Z)
0 -> n0
cons(X1, X2) -> ncons(X1, X2)
nil -> nnil
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
UNQUOTE1(cons1(X, Z)) -> UNQUOTE1(Z)
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
sel1(0, cons(X, Z)) -> quote(X)
first1(0, Z) -> nil1
first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
quote(n0) -> 01
quote(ns(X)) -> s1(quote(activate(X)))
quote(nsel(X, Z)) -> sel1(activate(X), activate(Z))
quote1(ncons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
quote1(nnil) -> nil1
quote1(nfirst(X, Z)) -> first1(activate(X), activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
fcons(X, Z) -> cons(X, Z)
0 -> n0
cons(X1, X2) -> ncons(X1, X2)
nil -> nnil
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
FIRST1(s(X), cons(Y, Z)) -> FIRST1(X, activate(Z))
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
sel1(0, cons(X, Z)) -> quote(X)
first1(0, Z) -> nil1
first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
quote(n0) -> 01
quote(ns(X)) -> s1(quote(activate(X)))
quote(nsel(X, Z)) -> sel1(activate(X), activate(Z))
quote1(ncons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
quote1(nnil) -> nil1
quote1(nfirst(X, Z)) -> first1(activate(X), activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
fcons(X, Z) -> cons(X, Z)
0 -> n0
cons(X1, X2) -> ncons(X1, X2)
nil -> nnil
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
QUOTE1(ncons(X, Z)) -> QUOTE1(activate(Z))
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
sel1(0, cons(X, Z)) -> quote(X)
first1(0, Z) -> nil1
first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
quote(n0) -> 01
quote(ns(X)) -> s1(quote(activate(X)))
quote(nsel(X, Z)) -> sel1(activate(X), activate(Z))
quote1(ncons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
quote1(nnil) -> nil1
quote1(nfirst(X, Z)) -> first1(activate(X), activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
fcons(X, Z) -> cons(X, Z)
0 -> n0
cons(X1, X2) -> ncons(X1, X2)
nil -> nnil
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳Remaining Obligation(s)
→DP Problem 3
↳Remaining Obligation(s)
→DP Problem 4
↳Remaining Obligation(s)
→DP Problem 5
↳Remaining Obligation(s)
→DP Problem 6
↳Remaining Obligation(s)
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', nfrom(X'0))))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', from(X'0))))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', nfirst(X1', X2'))))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', first(X1', X2'))))))
SEL(s(X), cons(Y, nfrom(X'''))) -> SEL(X, cons(X''', nfrom(s(X'''))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfrom(X''''))))) -> SEL(X, cons(Y'', nfirst(X'', cons(X'''', nfrom(s(X''''))))))
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
sel1(0, cons(X, Z)) -> quote(X)
first1(0, Z) -> nil1
first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
quote(n0) -> 01
quote(ns(X)) -> s1(quote(activate(X)))
quote(nsel(X, Z)) -> sel1(activate(X), activate(Z))
quote1(ncons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
quote1(nnil) -> nil1
quote1(nfirst(X, Z)) -> first1(activate(X), activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
fcons(X, Z) -> cons(X, Z)
0 -> n0
cons(X1, X2) -> ncons(X1, X2)
nil -> nnil
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
UNQUOTE(s1(X)) -> UNQUOTE(X)
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
sel1(0, cons(X, Z)) -> quote(X)
first1(0, Z) -> nil1
first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
quote(n0) -> 01
quote(ns(X)) -> s1(quote(activate(X)))
quote(nsel(X, Z)) -> sel1(activate(X), activate(Z))
quote1(ncons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
quote1(nnil) -> nil1
quote1(nfirst(X, Z)) -> first1(activate(X), activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
fcons(X, Z) -> cons(X, Z)
0 -> n0
cons(X1, X2) -> ncons(X1, X2)
nil -> nnil
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
QUOTE(nsel(X, Z)) -> SEL1(activate(X), activate(Z))
QUOTE(ns(X)) -> QUOTE(activate(X))
SEL1(0, cons(X, Z)) -> QUOTE(X)
SEL1(s(X), cons(Y, Z)) -> SEL1(X, activate(Z))
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
sel1(0, cons(X, Z)) -> quote(X)
first1(0, Z) -> nil1
first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
quote(n0) -> 01
quote(ns(X)) -> s1(quote(activate(X)))
quote(nsel(X, Z)) -> sel1(activate(X), activate(Z))
quote1(ncons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
quote1(nnil) -> nil1
quote1(nfirst(X, Z)) -> first1(activate(X), activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
fcons(X, Z) -> cons(X, Z)
0 -> n0
cons(X1, X2) -> ncons(X1, X2)
nil -> nnil
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
UNQUOTE1(cons1(X, Z)) -> UNQUOTE1(Z)
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
sel1(0, cons(X, Z)) -> quote(X)
first1(0, Z) -> nil1
first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
quote(n0) -> 01
quote(ns(X)) -> s1(quote(activate(X)))
quote(nsel(X, Z)) -> sel1(activate(X), activate(Z))
quote1(ncons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
quote1(nnil) -> nil1
quote1(nfirst(X, Z)) -> first1(activate(X), activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
fcons(X, Z) -> cons(X, Z)
0 -> n0
cons(X1, X2) -> ncons(X1, X2)
nil -> nnil
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
FIRST1(s(X), cons(Y, Z)) -> FIRST1(X, activate(Z))
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
sel1(0, cons(X, Z)) -> quote(X)
first1(0, Z) -> nil1
first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
quote(n0) -> 01
quote(ns(X)) -> s1(quote(activate(X)))
quote(nsel(X, Z)) -> sel1(activate(X), activate(Z))
quote1(ncons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
quote1(nnil) -> nil1
quote1(nfirst(X, Z)) -> first1(activate(X), activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
fcons(X, Z) -> cons(X, Z)
0 -> n0
cons(X1, X2) -> ncons(X1, X2)
nil -> nnil
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
QUOTE1(ncons(X, Z)) -> QUOTE1(activate(Z))
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
sel1(0, cons(X, Z)) -> quote(X)
first1(0, Z) -> nil1
first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
quote(n0) -> 01
quote(ns(X)) -> s1(quote(activate(X)))
quote(nsel(X, Z)) -> sel1(activate(X), activate(Z))
quote1(ncons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
quote1(nnil) -> nil1
quote1(nfirst(X, Z)) -> first1(activate(X), activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
fcons(X, Z) -> cons(X, Z)
0 -> n0
cons(X1, X2) -> ncons(X1, X2)
nil -> nnil
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳Remaining Obligation(s)
→DP Problem 3
↳Remaining Obligation(s)
→DP Problem 4
↳Remaining Obligation(s)
→DP Problem 5
↳Remaining Obligation(s)
→DP Problem 6
↳Remaining Obligation(s)
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', nfrom(X'0))))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', from(X'0))))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', nfirst(X1', X2'))))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', first(X1', X2'))))))
SEL(s(X), cons(Y, nfrom(X'''))) -> SEL(X, cons(X''', nfrom(s(X'''))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfrom(X''''))))) -> SEL(X, cons(Y'', nfirst(X'', cons(X'''', nfrom(s(X''''))))))
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
sel1(0, cons(X, Z)) -> quote(X)
first1(0, Z) -> nil1
first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
quote(n0) -> 01
quote(ns(X)) -> s1(quote(activate(X)))
quote(nsel(X, Z)) -> sel1(activate(X), activate(Z))
quote1(ncons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
quote1(nnil) -> nil1
quote1(nfirst(X, Z)) -> first1(activate(X), activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
fcons(X, Z) -> cons(X, Z)
0 -> n0
cons(X1, X2) -> ncons(X1, X2)
nil -> nnil
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
UNQUOTE(s1(X)) -> UNQUOTE(X)
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
sel1(0, cons(X, Z)) -> quote(X)
first1(0, Z) -> nil1
first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
quote(n0) -> 01
quote(ns(X)) -> s1(quote(activate(X)))
quote(nsel(X, Z)) -> sel1(activate(X), activate(Z))
quote1(ncons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
quote1(nnil) -> nil1
quote1(nfirst(X, Z)) -> first1(activate(X), activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
fcons(X, Z) -> cons(X, Z)
0 -> n0
cons(X1, X2) -> ncons(X1, X2)
nil -> nnil
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
QUOTE(nsel(X, Z)) -> SEL1(activate(X), activate(Z))
QUOTE(ns(X)) -> QUOTE(activate(X))
SEL1(0, cons(X, Z)) -> QUOTE(X)
SEL1(s(X), cons(Y, Z)) -> SEL1(X, activate(Z))
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
sel1(0, cons(X, Z)) -> quote(X)
first1(0, Z) -> nil1
first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
quote(n0) -> 01
quote(ns(X)) -> s1(quote(activate(X)))
quote(nsel(X, Z)) -> sel1(activate(X), activate(Z))
quote1(ncons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
quote1(nnil) -> nil1
quote1(nfirst(X, Z)) -> first1(activate(X), activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
fcons(X, Z) -> cons(X, Z)
0 -> n0
cons(X1, X2) -> ncons(X1, X2)
nil -> nnil
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
UNQUOTE1(cons1(X, Z)) -> UNQUOTE1(Z)
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
sel1(0, cons(X, Z)) -> quote(X)
first1(0, Z) -> nil1
first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
quote(n0) -> 01
quote(ns(X)) -> s1(quote(activate(X)))
quote(nsel(X, Z)) -> sel1(activate(X), activate(Z))
quote1(ncons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
quote1(nnil) -> nil1
quote1(nfirst(X, Z)) -> first1(activate(X), activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
fcons(X, Z) -> cons(X, Z)
0 -> n0
cons(X1, X2) -> ncons(X1, X2)
nil -> nnil
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
FIRST1(s(X), cons(Y, Z)) -> FIRST1(X, activate(Z))
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
sel1(0, cons(X, Z)) -> quote(X)
first1(0, Z) -> nil1
first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
quote(n0) -> 01
quote(ns(X)) -> s1(quote(activate(X)))
quote(nsel(X, Z)) -> sel1(activate(X), activate(Z))
quote1(ncons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
quote1(nnil) -> nil1
quote1(nfirst(X, Z)) -> first1(activate(X), activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
fcons(X, Z) -> cons(X, Z)
0 -> n0
cons(X1, X2) -> ncons(X1, X2)
nil -> nnil
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
QUOTE1(ncons(X, Z)) -> QUOTE1(activate(Z))
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
sel1(0, cons(X, Z)) -> quote(X)
first1(0, Z) -> nil1
first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
quote(n0) -> 01
quote(ns(X)) -> s1(quote(activate(X)))
quote(nsel(X, Z)) -> sel1(activate(X), activate(Z))
quote1(ncons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
quote1(nnil) -> nil1
quote1(nfirst(X, Z)) -> first1(activate(X), activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
fcons(X, Z) -> cons(X, Z)
0 -> n0
cons(X1, X2) -> ncons(X1, X2)
nil -> nnil
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳Remaining Obligation(s)
→DP Problem 3
↳Remaining Obligation(s)
→DP Problem 4
↳Remaining Obligation(s)
→DP Problem 5
↳Remaining Obligation(s)
→DP Problem 6
↳Remaining Obligation(s)
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', nfrom(X'0))))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', from(X'0))))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', nfirst(X1', X2'))))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', first(X1', X2'))))))
SEL(s(X), cons(Y, nfrom(X'''))) -> SEL(X, cons(X''', nfrom(s(X'''))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfrom(X''''))))) -> SEL(X, cons(Y'', nfirst(X'', cons(X'''', nfrom(s(X''''))))))
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
sel1(0, cons(X, Z)) -> quote(X)
first1(0, Z) -> nil1
first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
quote(n0) -> 01
quote(ns(X)) -> s1(quote(activate(X)))
quote(nsel(X, Z)) -> sel1(activate(X), activate(Z))
quote1(ncons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
quote1(nnil) -> nil1
quote1(nfirst(X, Z)) -> first1(activate(X), activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
fcons(X, Z) -> cons(X, Z)
0 -> n0
cons(X1, X2) -> ncons(X1, X2)
nil -> nnil
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
UNQUOTE(s1(X)) -> UNQUOTE(X)
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
sel1(0, cons(X, Z)) -> quote(X)
first1(0, Z) -> nil1
first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
quote(n0) -> 01
quote(ns(X)) -> s1(quote(activate(X)))
quote(nsel(X, Z)) -> sel1(activate(X), activate(Z))
quote1(ncons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
quote1(nnil) -> nil1
quote1(nfirst(X, Z)) -> first1(activate(X), activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
fcons(X, Z) -> cons(X, Z)
0 -> n0
cons(X1, X2) -> ncons(X1, X2)
nil -> nnil
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
QUOTE(nsel(X, Z)) -> SEL1(activate(X), activate(Z))
QUOTE(ns(X)) -> QUOTE(activate(X))
SEL1(0, cons(X, Z)) -> QUOTE(X)
SEL1(s(X), cons(Y, Z)) -> SEL1(X, activate(Z))
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
sel1(0, cons(X, Z)) -> quote(X)
first1(0, Z) -> nil1
first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
quote(n0) -> 01
quote(ns(X)) -> s1(quote(activate(X)))
quote(nsel(X, Z)) -> sel1(activate(X), activate(Z))
quote1(ncons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
quote1(nnil) -> nil1
quote1(nfirst(X, Z)) -> first1(activate(X), activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
fcons(X, Z) -> cons(X, Z)
0 -> n0
cons(X1, X2) -> ncons(X1, X2)
nil -> nnil
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
UNQUOTE1(cons1(X, Z)) -> UNQUOTE1(Z)
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
sel1(0, cons(X, Z)) -> quote(X)
first1(0, Z) -> nil1
first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
quote(n0) -> 01
quote(ns(X)) -> s1(quote(activate(X)))
quote(nsel(X, Z)) -> sel1(activate(X), activate(Z))
quote1(ncons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
quote1(nnil) -> nil1
quote1(nfirst(X, Z)) -> first1(activate(X), activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
fcons(X, Z) -> cons(X, Z)
0 -> n0
cons(X1, X2) -> ncons(X1, X2)
nil -> nnil
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
FIRST1(s(X), cons(Y, Z)) -> FIRST1(X, activate(Z))
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
sel1(0, cons(X, Z)) -> quote(X)
first1(0, Z) -> nil1
first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
quote(n0) -> 01
quote(ns(X)) -> s1(quote(activate(X)))
quote(nsel(X, Z)) -> sel1(activate(X), activate(Z))
quote1(ncons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
quote1(nnil) -> nil1
quote1(nfirst(X, Z)) -> first1(activate(X), activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
fcons(X, Z) -> cons(X, Z)
0 -> n0
cons(X1, X2) -> ncons(X1, X2)
nil -> nnil
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
QUOTE1(ncons(X, Z)) -> QUOTE1(activate(Z))
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
sel1(0, cons(X, Z)) -> quote(X)
first1(0, Z) -> nil1
first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
quote(n0) -> 01
quote(ns(X)) -> s1(quote(activate(X)))
quote(nsel(X, Z)) -> sel1(activate(X), activate(Z))
quote1(ncons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
quote1(nnil) -> nil1
quote1(nfirst(X, Z)) -> first1(activate(X), activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
fcons(X, Z) -> cons(X, Z)
0 -> n0
cons(X1, X2) -> ncons(X1, X2)
nil -> nnil
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳Remaining Obligation(s)
→DP Problem 3
↳Remaining Obligation(s)
→DP Problem 4
↳Remaining Obligation(s)
→DP Problem 5
↳Remaining Obligation(s)
→DP Problem 6
↳Remaining Obligation(s)
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', nfrom(X'0))))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', from(X'0))))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', nfirst(X1', X2'))))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', first(X1', X2'))))))
SEL(s(X), cons(Y, nfrom(X'''))) -> SEL(X, cons(X''', nfrom(s(X'''))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfrom(X''''))))) -> SEL(X, cons(Y'', nfirst(X'', cons(X'''', nfrom(s(X''''))))))
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
sel1(0, cons(X, Z)) -> quote(X)
first1(0, Z) -> nil1
first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
quote(n0) -> 01
quote(ns(X)) -> s1(quote(activate(X)))
quote(nsel(X, Z)) -> sel1(activate(X), activate(Z))
quote1(ncons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
quote1(nnil) -> nil1
quote1(nfirst(X, Z)) -> first1(activate(X), activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
fcons(X, Z) -> cons(X, Z)
0 -> n0
cons(X1, X2) -> ncons(X1, X2)
nil -> nnil
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
UNQUOTE(s1(X)) -> UNQUOTE(X)
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
sel1(0, cons(X, Z)) -> quote(X)
first1(0, Z) -> nil1
first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
quote(n0) -> 01
quote(ns(X)) -> s1(quote(activate(X)))
quote(nsel(X, Z)) -> sel1(activate(X), activate(Z))
quote1(ncons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
quote1(nnil) -> nil1
quote1(nfirst(X, Z)) -> first1(activate(X), activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
fcons(X, Z) -> cons(X, Z)
0 -> n0
cons(X1, X2) -> ncons(X1, X2)
nil -> nnil
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
QUOTE(nsel(X, Z)) -> SEL1(activate(X), activate(Z))
QUOTE(ns(X)) -> QUOTE(activate(X))
SEL1(0, cons(X, Z)) -> QUOTE(X)
SEL1(s(X), cons(Y, Z)) -> SEL1(X, activate(Z))
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
sel1(0, cons(X, Z)) -> quote(X)
first1(0, Z) -> nil1
first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
quote(n0) -> 01
quote(ns(X)) -> s1(quote(activate(X)))
quote(nsel(X, Z)) -> sel1(activate(X), activate(Z))
quote1(ncons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
quote1(nnil) -> nil1
quote1(nfirst(X, Z)) -> first1(activate(X), activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
fcons(X, Z) -> cons(X, Z)
0 -> n0
cons(X1, X2) -> ncons(X1, X2)
nil -> nnil
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
UNQUOTE1(cons1(X, Z)) -> UNQUOTE1(Z)
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
sel1(0, cons(X, Z)) -> quote(X)
first1(0, Z) -> nil1
first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
quote(n0) -> 01
quote(ns(X)) -> s1(quote(activate(X)))
quote(nsel(X, Z)) -> sel1(activate(X), activate(Z))
quote1(ncons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
quote1(nnil) -> nil1
quote1(nfirst(X, Z)) -> first1(activate(X), activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
fcons(X, Z) -> cons(X, Z)
0 -> n0
cons(X1, X2) -> ncons(X1, X2)
nil -> nnil
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
FIRST1(s(X), cons(Y, Z)) -> FIRST1(X, activate(Z))
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
sel1(0, cons(X, Z)) -> quote(X)
first1(0, Z) -> nil1
first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
quote(n0) -> 01
quote(ns(X)) -> s1(quote(activate(X)))
quote(nsel(X, Z)) -> sel1(activate(X), activate(Z))
quote1(ncons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
quote1(nnil) -> nil1
quote1(nfirst(X, Z)) -> first1(activate(X), activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
fcons(X, Z) -> cons(X, Z)
0 -> n0
cons(X1, X2) -> ncons(X1, X2)
nil -> nnil
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
QUOTE1(ncons(X, Z)) -> QUOTE1(activate(Z))
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
sel1(0, cons(X, Z)) -> quote(X)
first1(0, Z) -> nil1
first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
quote(n0) -> 01
quote(ns(X)) -> s1(quote(activate(X)))
quote(nsel(X, Z)) -> sel1(activate(X), activate(Z))
quote1(ncons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
quote1(nnil) -> nil1
quote1(nfirst(X, Z)) -> first1(activate(X), activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
fcons(X, Z) -> cons(X, Z)
0 -> n0
cons(X1, X2) -> ncons(X1, X2)
nil -> nnil
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳Remaining Obligation(s)
→DP Problem 3
↳Remaining Obligation(s)
→DP Problem 4
↳Remaining Obligation(s)
→DP Problem 5
↳Remaining Obligation(s)
→DP Problem 6
↳Remaining Obligation(s)
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', nfrom(X'0))))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', from(X'0))))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', nfirst(X1', X2'))))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', first(X1', X2'))))))
SEL(s(X), cons(Y, nfrom(X'''))) -> SEL(X, cons(X''', nfrom(s(X'''))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfrom(X''''))))) -> SEL(X, cons(Y'', nfirst(X'', cons(X'''', nfrom(s(X''''))))))
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
sel1(0, cons(X, Z)) -> quote(X)
first1(0, Z) -> nil1
first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
quote(n0) -> 01
quote(ns(X)) -> s1(quote(activate(X)))
quote(nsel(X, Z)) -> sel1(activate(X), activate(Z))
quote1(ncons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
quote1(nnil) -> nil1
quote1(nfirst(X, Z)) -> first1(activate(X), activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
fcons(X, Z) -> cons(X, Z)
0 -> n0
cons(X1, X2) -> ncons(X1, X2)
nil -> nnil
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
UNQUOTE(s1(X)) -> UNQUOTE(X)
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
sel1(0, cons(X, Z)) -> quote(X)
first1(0, Z) -> nil1
first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
quote(n0) -> 01
quote(ns(X)) -> s1(quote(activate(X)))
quote(nsel(X, Z)) -> sel1(activate(X), activate(Z))
quote1(ncons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
quote1(nnil) -> nil1
quote1(nfirst(X, Z)) -> first1(activate(X), activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
fcons(X, Z) -> cons(X, Z)
0 -> n0
cons(X1, X2) -> ncons(X1, X2)
nil -> nnil
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
QUOTE(nsel(X, Z)) -> SEL1(activate(X), activate(Z))
QUOTE(ns(X)) -> QUOTE(activate(X))
SEL1(0, cons(X, Z)) -> QUOTE(X)
SEL1(s(X), cons(Y, Z)) -> SEL1(X, activate(Z))
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
sel1(0, cons(X, Z)) -> quote(X)
first1(0, Z) -> nil1
first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
quote(n0) -> 01
quote(ns(X)) -> s1(quote(activate(X)))
quote(nsel(X, Z)) -> sel1(activate(X), activate(Z))
quote1(ncons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
quote1(nnil) -> nil1
quote1(nfirst(X, Z)) -> first1(activate(X), activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
fcons(X, Z) -> cons(X, Z)
0 -> n0
cons(X1, X2) -> ncons(X1, X2)
nil -> nnil
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
UNQUOTE1(cons1(X, Z)) -> UNQUOTE1(Z)
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
sel1(0, cons(X, Z)) -> quote(X)
first1(0, Z) -> nil1
first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
quote(n0) -> 01
quote(ns(X)) -> s1(quote(activate(X)))
quote(nsel(X, Z)) -> sel1(activate(X), activate(Z))
quote1(ncons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
quote1(nnil) -> nil1
quote1(nfirst(X, Z)) -> first1(activate(X), activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
fcons(X, Z) -> cons(X, Z)
0 -> n0
cons(X1, X2) -> ncons(X1, X2)
nil -> nnil
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
FIRST1(s(X), cons(Y, Z)) -> FIRST1(X, activate(Z))
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
sel1(0, cons(X, Z)) -> quote(X)
first1(0, Z) -> nil1
first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
quote(n0) -> 01
quote(ns(X)) -> s1(quote(activate(X)))
quote(nsel(X, Z)) -> sel1(activate(X), activate(Z))
quote1(ncons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
quote1(nnil) -> nil1
quote1(nfirst(X, Z)) -> first1(activate(X), activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
fcons(X, Z) -> cons(X, Z)
0 -> n0
cons(X1, X2) -> ncons(X1, X2)
nil -> nnil
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X
QUOTE1(ncons(X, Z)) -> QUOTE1(activate(Z))
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
sel(0, cons(X, Z)) -> X
sel(X1, X2) -> nsel(X1, X2)
first(0, Z) -> 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)
sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
sel1(0, cons(X, Z)) -> quote(X)
first1(0, Z) -> nil1
first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
quote(n0) -> 01
quote(ns(X)) -> s1(quote(activate(X)))
quote(nsel(X, Z)) -> sel1(activate(X), activate(Z))
quote1(ncons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
quote1(nnil) -> nil1
quote1(nfirst(X, Z)) -> first1(activate(X), activate(Z))
unquote(01) -> 0
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1) -> nil
unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
fcons(X, Z) -> cons(X, Z)
0 -> n0
cons(X1, X2) -> ncons(X1, X2)
nil -> nnil
s(X) -> ns(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(nfrom(X)) -> from(X)
activate(n0) -> 0
activate(ncons(X1, X2)) -> cons(X1, X2)
activate(nnil) -> nil
activate(ns(X)) -> s(X)
activate(nsel(X1, X2)) -> sel(X1, X2)
activate(X) -> X