R
↳Dependency Pair Analysis
FST(s(X), cons(Y, Z)) -> ACTIVATE(X)
FST(s(X), cons(Y, Z)) -> ACTIVATE(Z)
ADD(s(X), Y) -> ACTIVATE(X)
LEN(cons(X, Z)) -> ACTIVATE(Z)
ACTIVATE(nfst(X1, X2)) -> FST(X1, X2)
ACTIVATE(nfrom(X)) -> FROM(X)
ACTIVATE(nadd(X1, X2)) -> ADD(X1, X2)
ACTIVATE(nlen(X)) -> LEN(X)
R
↳DPs
→DP Problem 1
↳Argument Filtering and Ordering
LEN(cons(X, Z)) -> ACTIVATE(Z)
ACTIVATE(nlen(X)) -> LEN(X)
ADD(s(X), Y) -> ACTIVATE(X)
ACTIVATE(nadd(X1, X2)) -> ADD(X1, X2)
FST(s(X), cons(Y, Z)) -> ACTIVATE(Z)
ACTIVATE(nfst(X1, X2)) -> FST(X1, X2)
FST(s(X), cons(Y, Z)) -> ACTIVATE(X)
fst(0, Z) -> nil
fst(s(X), cons(Y, Z)) -> cons(Y, nfst(activate(X), activate(Z)))
fst(X1, X2) -> nfst(X1, X2)
from(X) -> cons(X, nfrom(s(X)))
from(X) -> nfrom(X)
add(0, X) -> X
add(s(X), Y) -> s(nadd(activate(X), Y))
add(X1, X2) -> nadd(X1, X2)
len(nil) -> 0
len(cons(X, Z)) -> s(nlen(activate(Z)))
len(X) -> nlen(X)
activate(nfst(X1, X2)) -> fst(X1, X2)
activate(nfrom(X)) -> from(X)
activate(nadd(X1, X2)) -> add(X1, X2)
activate(nlen(X)) -> len(X)
activate(X) -> X
ACTIVATE(nlen(X)) -> LEN(X)
POL(FST(x1, x2)) = x1 + x2 POL(cons(x1, x2)) = x1 + x2 POL(n__fst(x1, x2)) = x1 + x2 POL(LEN(x1)) = x1 POL(s(x1)) = x1 POL(n__len(x1)) = 1 + x1 POL(ACTIVATE(x1)) = x1 POL(ADD(x1, x2)) = x1 + x2 POL(n__add(x1, x2)) = x1 + x2
ACTIVATE(x1) -> ACTIVATE(x1)
LEN(x1) -> LEN(x1)
nlen(x1) -> nlen(x1)
nfst(x1, x2) -> nfst(x1, x2)
FST(x1, x2) -> FST(x1, x2)
s(x1) -> s(x1)
cons(x1, x2) -> cons(x1, x2)
ADD(x1, x2) -> ADD(x1, x2)
nadd(x1, x2) -> nadd(x1, x2)
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳Dependency Graph
LEN(cons(X, Z)) -> ACTIVATE(Z)
ADD(s(X), Y) -> ACTIVATE(X)
ACTIVATE(nadd(X1, X2)) -> ADD(X1, X2)
FST(s(X), cons(Y, Z)) -> ACTIVATE(Z)
ACTIVATE(nfst(X1, X2)) -> FST(X1, X2)
FST(s(X), cons(Y, Z)) -> ACTIVATE(X)
fst(0, Z) -> nil
fst(s(X), cons(Y, Z)) -> cons(Y, nfst(activate(X), activate(Z)))
fst(X1, X2) -> nfst(X1, X2)
from(X) -> cons(X, nfrom(s(X)))
from(X) -> nfrom(X)
add(0, X) -> X
add(s(X), Y) -> s(nadd(activate(X), Y))
add(X1, X2) -> nadd(X1, X2)
len(nil) -> 0
len(cons(X, Z)) -> s(nlen(activate(Z)))
len(X) -> nlen(X)
activate(nfst(X1, X2)) -> fst(X1, X2)
activate(nfrom(X)) -> from(X)
activate(nadd(X1, X2)) -> add(X1, X2)
activate(nlen(X)) -> len(X)
activate(X) -> X
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳DGraph
...
→DP Problem 3
↳Argument Filtering and Ordering
FST(s(X), cons(Y, Z)) -> ACTIVATE(Z)
ADD(s(X), Y) -> ACTIVATE(X)
ACTIVATE(nadd(X1, X2)) -> ADD(X1, X2)
FST(s(X), cons(Y, Z)) -> ACTIVATE(X)
ACTIVATE(nfst(X1, X2)) -> FST(X1, X2)
fst(0, Z) -> nil
fst(s(X), cons(Y, Z)) -> cons(Y, nfst(activate(X), activate(Z)))
fst(X1, X2) -> nfst(X1, X2)
from(X) -> cons(X, nfrom(s(X)))
from(X) -> nfrom(X)
add(0, X) -> X
add(s(X), Y) -> s(nadd(activate(X), Y))
add(X1, X2) -> nadd(X1, X2)
len(nil) -> 0
len(cons(X, Z)) -> s(nlen(activate(Z)))
len(X) -> nlen(X)
activate(nfst(X1, X2)) -> fst(X1, X2)
activate(nfrom(X)) -> from(X)
activate(nadd(X1, X2)) -> add(X1, X2)
activate(nlen(X)) -> len(X)
activate(X) -> X
ACTIVATE(nfst(X1, X2)) -> FST(X1, X2)
POL(FST(x1, x2)) = x1 + x2 POL(cons(x1, x2)) = x1 + x2 POL(n__fst(x1, x2)) = 1 + x1 + x2 POL(s(x1)) = x1 POL(ACTIVATE(x1)) = x1 POL(ADD(x1, x2)) = x1 + x2 POL(n__add(x1, x2)) = x1 + x2
ACTIVATE(x1) -> ACTIVATE(x1)
FST(x1, x2) -> FST(x1, x2)
nfst(x1, x2) -> nfst(x1, x2)
s(x1) -> s(x1)
cons(x1, x2) -> cons(x1, x2)
ADD(x1, x2) -> ADD(x1, x2)
nadd(x1, x2) -> nadd(x1, x2)
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳DGraph
...
→DP Problem 4
↳Dependency Graph
FST(s(X), cons(Y, Z)) -> ACTIVATE(Z)
ADD(s(X), Y) -> ACTIVATE(X)
ACTIVATE(nadd(X1, X2)) -> ADD(X1, X2)
FST(s(X), cons(Y, Z)) -> ACTIVATE(X)
fst(0, Z) -> nil
fst(s(X), cons(Y, Z)) -> cons(Y, nfst(activate(X), activate(Z)))
fst(X1, X2) -> nfst(X1, X2)
from(X) -> cons(X, nfrom(s(X)))
from(X) -> nfrom(X)
add(0, X) -> X
add(s(X), Y) -> s(nadd(activate(X), Y))
add(X1, X2) -> nadd(X1, X2)
len(nil) -> 0
len(cons(X, Z)) -> s(nlen(activate(Z)))
len(X) -> nlen(X)
activate(nfst(X1, X2)) -> fst(X1, X2)
activate(nfrom(X)) -> from(X)
activate(nadd(X1, X2)) -> add(X1, X2)
activate(nlen(X)) -> len(X)
activate(X) -> X
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳DGraph
...
→DP Problem 5
↳Argument Filtering and Ordering
ADD(s(X), Y) -> ACTIVATE(X)
ACTIVATE(nadd(X1, X2)) -> ADD(X1, X2)
fst(0, Z) -> nil
fst(s(X), cons(Y, Z)) -> cons(Y, nfst(activate(X), activate(Z)))
fst(X1, X2) -> nfst(X1, X2)
from(X) -> cons(X, nfrom(s(X)))
from(X) -> nfrom(X)
add(0, X) -> X
add(s(X), Y) -> s(nadd(activate(X), Y))
add(X1, X2) -> nadd(X1, X2)
len(nil) -> 0
len(cons(X, Z)) -> s(nlen(activate(Z)))
len(X) -> nlen(X)
activate(nfst(X1, X2)) -> fst(X1, X2)
activate(nfrom(X)) -> from(X)
activate(nadd(X1, X2)) -> add(X1, X2)
activate(nlen(X)) -> len(X)
activate(X) -> X
ADD(s(X), Y) -> ACTIVATE(X)
POL(s(x1)) = 1 + x1 POL(ACTIVATE(x1)) = x1 POL(ADD(x1, x2)) = x1 + x2 POL(n__add(x1, x2)) = x1 + x2
ADD(x1, x2) -> ADD(x1, x2)
ACTIVATE(x1) -> ACTIVATE(x1)
s(x1) -> s(x1)
nadd(x1, x2) -> nadd(x1, x2)
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳DGraph
...
→DP Problem 6
↳Dependency Graph
ACTIVATE(nadd(X1, X2)) -> ADD(X1, X2)
fst(0, Z) -> nil
fst(s(X), cons(Y, Z)) -> cons(Y, nfst(activate(X), activate(Z)))
fst(X1, X2) -> nfst(X1, X2)
from(X) -> cons(X, nfrom(s(X)))
from(X) -> nfrom(X)
add(0, X) -> X
add(s(X), Y) -> s(nadd(activate(X), Y))
add(X1, X2) -> nadd(X1, X2)
len(nil) -> 0
len(cons(X, Z)) -> s(nlen(activate(Z)))
len(X) -> nlen(X)
activate(nfst(X1, X2)) -> fst(X1, X2)
activate(nfrom(X)) -> from(X)
activate(nadd(X1, X2)) -> add(X1, X2)
activate(nlen(X)) -> len(X)
activate(X) -> X