R
↳Dependency Pair Analysis
AFTER(s(N), cons(X, XS)) -> AFTER(N, activate(XS))
AFTER(s(N), cons(X, XS)) -> ACTIVATE(XS)
ACTIVATE(nfrom(X)) -> FROM(activate(X))
ACTIVATE(nfrom(X)) -> ACTIVATE(X)
ACTIVATE(ns(X)) -> S(activate(X))
ACTIVATE(ns(X)) -> ACTIVATE(X)
R
↳DPs
→DP Problem 1
↳Argument Filtering and Ordering
→DP Problem 2
↳Nar
ACTIVATE(ns(X)) -> ACTIVATE(X)
ACTIVATE(nfrom(X)) -> ACTIVATE(X)
from(X) -> cons(X, nfrom(ns(X)))
from(X) -> nfrom(X)
after(0, XS) -> XS
after(s(N), cons(X, XS)) -> after(N, activate(XS))
s(X) -> ns(X)
activate(nfrom(X)) -> from(activate(X))
activate(ns(X)) -> s(activate(X))
activate(X) -> X
ACTIVATE(ns(X)) -> ACTIVATE(X)
ACTIVATE(nfrom(X)) -> ACTIVATE(X)
trivial
ACTIVATE(x1) -> ACTIVATE(x1)
ns(x1) -> ns(x1)
nfrom(x1) -> nfrom(x1)
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 3
↳Dependency Graph
→DP Problem 2
↳Nar
from(X) -> cons(X, nfrom(ns(X)))
from(X) -> nfrom(X)
after(0, XS) -> XS
after(s(N), cons(X, XS)) -> after(N, activate(XS))
s(X) -> ns(X)
activate(nfrom(X)) -> from(activate(X))
activate(ns(X)) -> s(activate(X))
activate(X) -> X
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳Narrowing Transformation
AFTER(s(N), cons(X, XS)) -> AFTER(N, activate(XS))
from(X) -> cons(X, nfrom(ns(X)))
from(X) -> nfrom(X)
after(0, XS) -> XS
after(s(N), cons(X, XS)) -> after(N, activate(XS))
s(X) -> ns(X)
activate(nfrom(X)) -> from(activate(X))
activate(ns(X)) -> s(activate(X))
activate(X) -> X
three new Dependency Pairs are created:
AFTER(s(N), cons(X, XS)) -> AFTER(N, activate(XS))
AFTER(s(N), cons(X, nfrom(X''))) -> AFTER(N, from(activate(X'')))
AFTER(s(N), cons(X, ns(X''))) -> AFTER(N, s(activate(X'')))
AFTER(s(N), cons(X, XS')) -> AFTER(N, XS')
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳Nar
→DP Problem 4
↳Narrowing Transformation
AFTER(s(N), cons(X, XS')) -> AFTER(N, XS')
AFTER(s(N), cons(X, ns(X''))) -> AFTER(N, s(activate(X'')))
AFTER(s(N), cons(X, nfrom(X''))) -> AFTER(N, from(activate(X'')))
from(X) -> cons(X, nfrom(ns(X)))
from(X) -> nfrom(X)
after(0, XS) -> XS
after(s(N), cons(X, XS)) -> after(N, activate(XS))
s(X) -> ns(X)
activate(nfrom(X)) -> from(activate(X))
activate(ns(X)) -> s(activate(X))
activate(X) -> X
five new Dependency Pairs are created:
AFTER(s(N), cons(X, nfrom(X''))) -> AFTER(N, from(activate(X'')))
AFTER(s(N), cons(X, nfrom(X'''))) -> AFTER(N, cons(activate(X'''), nfrom(ns(activate(X''')))))
AFTER(s(N), cons(X, nfrom(X'''))) -> AFTER(N, nfrom(activate(X''')))
AFTER(s(N), cons(X, nfrom(nfrom(X''')))) -> AFTER(N, from(from(activate(X'''))))
AFTER(s(N), cons(X, nfrom(ns(X''')))) -> AFTER(N, from(s(activate(X'''))))
AFTER(s(N), cons(X, nfrom(X'''))) -> AFTER(N, from(X'''))
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳Nar
→DP Problem 4
↳Nar
...
→DP Problem 5
↳Narrowing Transformation
AFTER(s(N), cons(X, nfrom(X'''))) -> AFTER(N, from(X'''))
AFTER(s(N), cons(X, nfrom(nfrom(X''')))) -> AFTER(N, from(from(activate(X'''))))
AFTER(s(N), cons(X, nfrom(ns(X''')))) -> AFTER(N, from(s(activate(X'''))))
AFTER(s(N), cons(X, nfrom(X'''))) -> AFTER(N, cons(activate(X'''), nfrom(ns(activate(X''')))))
AFTER(s(N), cons(X, ns(X''))) -> AFTER(N, s(activate(X'')))
AFTER(s(N), cons(X, XS')) -> AFTER(N, XS')
from(X) -> cons(X, nfrom(ns(X)))
from(X) -> nfrom(X)
after(0, XS) -> XS
after(s(N), cons(X, XS)) -> after(N, activate(XS))
s(X) -> ns(X)
activate(nfrom(X)) -> from(activate(X))
activate(ns(X)) -> s(activate(X))
activate(X) -> X
four new Dependency Pairs are created:
AFTER(s(N), cons(X, ns(X''))) -> AFTER(N, s(activate(X'')))
AFTER(s(N), cons(X, ns(X'''))) -> AFTER(N, ns(activate(X''')))
AFTER(s(N), cons(X, ns(nfrom(X''')))) -> AFTER(N, s(from(activate(X'''))))
AFTER(s(N), cons(X, ns(ns(X''')))) -> AFTER(N, s(s(activate(X'''))))
AFTER(s(N), cons(X, ns(X'''))) -> AFTER(N, s(X'''))
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳Nar
→DP Problem 4
↳Nar
...
→DP Problem 6
↳Argument Filtering and Ordering
AFTER(s(N), cons(X, ns(X'''))) -> AFTER(N, s(X'''))
AFTER(s(N), cons(X, ns(ns(X''')))) -> AFTER(N, s(s(activate(X'''))))
AFTER(s(N), cons(X, ns(nfrom(X''')))) -> AFTER(N, s(from(activate(X'''))))
AFTER(s(N), cons(X, nfrom(nfrom(X''')))) -> AFTER(N, from(from(activate(X'''))))
AFTER(s(N), cons(X, nfrom(ns(X''')))) -> AFTER(N, from(s(activate(X'''))))
AFTER(s(N), cons(X, nfrom(X'''))) -> AFTER(N, cons(activate(X'''), nfrom(ns(activate(X''')))))
AFTER(s(N), cons(X, XS')) -> AFTER(N, XS')
AFTER(s(N), cons(X, nfrom(X'''))) -> AFTER(N, from(X'''))
from(X) -> cons(X, nfrom(ns(X)))
from(X) -> nfrom(X)
after(0, XS) -> XS
after(s(N), cons(X, XS)) -> after(N, activate(XS))
s(X) -> ns(X)
activate(nfrom(X)) -> from(activate(X))
activate(ns(X)) -> s(activate(X))
activate(X) -> X
AFTER(s(N), cons(X, ns(X'''))) -> AFTER(N, s(X'''))
AFTER(s(N), cons(X, ns(ns(X''')))) -> AFTER(N, s(s(activate(X'''))))
AFTER(s(N), cons(X, ns(nfrom(X''')))) -> AFTER(N, s(from(activate(X'''))))
AFTER(s(N), cons(X, nfrom(nfrom(X''')))) -> AFTER(N, from(from(activate(X'''))))
AFTER(s(N), cons(X, nfrom(ns(X''')))) -> AFTER(N, from(s(activate(X'''))))
AFTER(s(N), cons(X, nfrom(X'''))) -> AFTER(N, cons(activate(X'''), nfrom(ns(activate(X''')))))
AFTER(s(N), cons(X, XS')) -> AFTER(N, XS')
AFTER(s(N), cons(X, nfrom(X'''))) -> AFTER(N, from(X'''))
from(X) -> cons(X, nfrom(ns(X)))
from(X) -> nfrom(X)
activate(nfrom(X)) -> from(activate(X))
activate(ns(X)) -> s(activate(X))
activate(X) -> X
s(X) -> ns(X)
AFTER > activate > from > ns
AFTER > activate > from > nfrom
AFTER > activate > from > cons
AFTER > activate > s > ns
AFTER(x1, x2) -> AFTER(x1, x2)
s(x1) -> s(x1)
cons(x1, x2) -> cons(x1, x2)
ns(x1) -> ns(x1)
from(x1) -> from(x1)
nfrom(x1) -> nfrom(x1)
activate(x1) -> activate(x1)
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳Nar
→DP Problem 4
↳Nar
...
→DP Problem 7
↳Dependency Graph
from(X) -> cons(X, nfrom(ns(X)))
from(X) -> nfrom(X)
after(0, XS) -> XS
after(s(N), cons(X, XS)) -> after(N, activate(XS))
s(X) -> ns(X)
activate(nfrom(X)) -> from(activate(X))
activate(ns(X)) -> s(activate(X))
activate(X) -> X