fst2(0, Z) -> nil
fst2(s1(X), cons2(Y, Z)) -> cons2(Y, n__fst2(activate1(X), activate1(Z)))
from1(X) -> cons2(X, n__from1(n__s1(X)))
add2(0, X) -> X
add2(s1(X), Y) -> s1(n__add2(activate1(X), Y))
len1(nil) -> 0
len1(cons2(X, Z)) -> s1(n__len1(activate1(Z)))
fst2(X1, X2) -> n__fst2(X1, X2)
from1(X) -> n__from1(X)
s1(X) -> n__s1(X)
add2(X1, X2) -> n__add2(X1, X2)
len1(X) -> n__len1(X)
activate1(n__fst2(X1, X2)) -> fst2(activate1(X1), activate1(X2))
activate1(n__from1(X)) -> from1(activate1(X))
activate1(n__s1(X)) -> s1(X)
activate1(n__add2(X1, X2)) -> add2(activate1(X1), activate1(X2))
activate1(n__len1(X)) -> len1(activate1(X))
activate1(X) -> X
↳ QTRS
↳ DependencyPairsProof
fst2(0, Z) -> nil
fst2(s1(X), cons2(Y, Z)) -> cons2(Y, n__fst2(activate1(X), activate1(Z)))
from1(X) -> cons2(X, n__from1(n__s1(X)))
add2(0, X) -> X
add2(s1(X), Y) -> s1(n__add2(activate1(X), Y))
len1(nil) -> 0
len1(cons2(X, Z)) -> s1(n__len1(activate1(Z)))
fst2(X1, X2) -> n__fst2(X1, X2)
from1(X) -> n__from1(X)
s1(X) -> n__s1(X)
add2(X1, X2) -> n__add2(X1, X2)
len1(X) -> n__len1(X)
activate1(n__fst2(X1, X2)) -> fst2(activate1(X1), activate1(X2))
activate1(n__from1(X)) -> from1(activate1(X))
activate1(n__s1(X)) -> s1(X)
activate1(n__add2(X1, X2)) -> add2(activate1(X1), activate1(X2))
activate1(n__len1(X)) -> len1(activate1(X))
activate1(X) -> X
FST2(s1(X), cons2(Y, Z)) -> ACTIVATE1(X)
ACTIVATE1(n__add2(X1, X2)) -> ACTIVATE1(X2)
ACTIVATE1(n__s1(X)) -> S1(X)
ACTIVATE1(n__fst2(X1, X2)) -> ACTIVATE1(X1)
FST2(s1(X), cons2(Y, Z)) -> ACTIVATE1(Z)
ACTIVATE1(n__len1(X)) -> LEN1(activate1(X))
ACTIVATE1(n__add2(X1, X2)) -> ADD2(activate1(X1), activate1(X2))
LEN1(cons2(X, Z)) -> S1(n__len1(activate1(Z)))
ACTIVATE1(n__from1(X)) -> FROM1(activate1(X))
ACTIVATE1(n__fst2(X1, X2)) -> ACTIVATE1(X2)
ADD2(s1(X), Y) -> ACTIVATE1(X)
ACTIVATE1(n__fst2(X1, X2)) -> FST2(activate1(X1), activate1(X2))
ACTIVATE1(n__len1(X)) -> ACTIVATE1(X)
ACTIVATE1(n__from1(X)) -> ACTIVATE1(X)
ADD2(s1(X), Y) -> S1(n__add2(activate1(X), Y))
LEN1(cons2(X, Z)) -> ACTIVATE1(Z)
ACTIVATE1(n__add2(X1, X2)) -> ACTIVATE1(X1)
fst2(0, Z) -> nil
fst2(s1(X), cons2(Y, Z)) -> cons2(Y, n__fst2(activate1(X), activate1(Z)))
from1(X) -> cons2(X, n__from1(n__s1(X)))
add2(0, X) -> X
add2(s1(X), Y) -> s1(n__add2(activate1(X), Y))
len1(nil) -> 0
len1(cons2(X, Z)) -> s1(n__len1(activate1(Z)))
fst2(X1, X2) -> n__fst2(X1, X2)
from1(X) -> n__from1(X)
s1(X) -> n__s1(X)
add2(X1, X2) -> n__add2(X1, X2)
len1(X) -> n__len1(X)
activate1(n__fst2(X1, X2)) -> fst2(activate1(X1), activate1(X2))
activate1(n__from1(X)) -> from1(activate1(X))
activate1(n__s1(X)) -> s1(X)
activate1(n__add2(X1, X2)) -> add2(activate1(X1), activate1(X2))
activate1(n__len1(X)) -> len1(activate1(X))
activate1(X) -> X
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
FST2(s1(X), cons2(Y, Z)) -> ACTIVATE1(X)
ACTIVATE1(n__add2(X1, X2)) -> ACTIVATE1(X2)
ACTIVATE1(n__s1(X)) -> S1(X)
ACTIVATE1(n__fst2(X1, X2)) -> ACTIVATE1(X1)
FST2(s1(X), cons2(Y, Z)) -> ACTIVATE1(Z)
ACTIVATE1(n__len1(X)) -> LEN1(activate1(X))
ACTIVATE1(n__add2(X1, X2)) -> ADD2(activate1(X1), activate1(X2))
LEN1(cons2(X, Z)) -> S1(n__len1(activate1(Z)))
ACTIVATE1(n__from1(X)) -> FROM1(activate1(X))
ACTIVATE1(n__fst2(X1, X2)) -> ACTIVATE1(X2)
ADD2(s1(X), Y) -> ACTIVATE1(X)
ACTIVATE1(n__fst2(X1, X2)) -> FST2(activate1(X1), activate1(X2))
ACTIVATE1(n__len1(X)) -> ACTIVATE1(X)
ACTIVATE1(n__from1(X)) -> ACTIVATE1(X)
ADD2(s1(X), Y) -> S1(n__add2(activate1(X), Y))
LEN1(cons2(X, Z)) -> ACTIVATE1(Z)
ACTIVATE1(n__add2(X1, X2)) -> ACTIVATE1(X1)
fst2(0, Z) -> nil
fst2(s1(X), cons2(Y, Z)) -> cons2(Y, n__fst2(activate1(X), activate1(Z)))
from1(X) -> cons2(X, n__from1(n__s1(X)))
add2(0, X) -> X
add2(s1(X), Y) -> s1(n__add2(activate1(X), Y))
len1(nil) -> 0
len1(cons2(X, Z)) -> s1(n__len1(activate1(Z)))
fst2(X1, X2) -> n__fst2(X1, X2)
from1(X) -> n__from1(X)
s1(X) -> n__s1(X)
add2(X1, X2) -> n__add2(X1, X2)
len1(X) -> n__len1(X)
activate1(n__fst2(X1, X2)) -> fst2(activate1(X1), activate1(X2))
activate1(n__from1(X)) -> from1(activate1(X))
activate1(n__s1(X)) -> s1(X)
activate1(n__add2(X1, X2)) -> add2(activate1(X1), activate1(X2))
activate1(n__len1(X)) -> len1(activate1(X))
activate1(X) -> X
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
FST2(s1(X), cons2(Y, Z)) -> ACTIVATE1(X)
ACTIVATE1(n__add2(X1, X2)) -> ACTIVATE1(X2)
ACTIVATE1(n__fst2(X1, X2)) -> ACTIVATE1(X1)
FST2(s1(X), cons2(Y, Z)) -> ACTIVATE1(Z)
ACTIVATE1(n__add2(X1, X2)) -> ADD2(activate1(X1), activate1(X2))
ACTIVATE1(n__len1(X)) -> LEN1(activate1(X))
ACTIVATE1(n__fst2(X1, X2)) -> ACTIVATE1(X2)
ACTIVATE1(n__fst2(X1, X2)) -> FST2(activate1(X1), activate1(X2))
ADD2(s1(X), Y) -> ACTIVATE1(X)
ACTIVATE1(n__len1(X)) -> ACTIVATE1(X)
ACTIVATE1(n__from1(X)) -> ACTIVATE1(X)
LEN1(cons2(X, Z)) -> ACTIVATE1(Z)
ACTIVATE1(n__add2(X1, X2)) -> ACTIVATE1(X1)
fst2(0, Z) -> nil
fst2(s1(X), cons2(Y, Z)) -> cons2(Y, n__fst2(activate1(X), activate1(Z)))
from1(X) -> cons2(X, n__from1(n__s1(X)))
add2(0, X) -> X
add2(s1(X), Y) -> s1(n__add2(activate1(X), Y))
len1(nil) -> 0
len1(cons2(X, Z)) -> s1(n__len1(activate1(Z)))
fst2(X1, X2) -> n__fst2(X1, X2)
from1(X) -> n__from1(X)
s1(X) -> n__s1(X)
add2(X1, X2) -> n__add2(X1, X2)
len1(X) -> n__len1(X)
activate1(n__fst2(X1, X2)) -> fst2(activate1(X1), activate1(X2))
activate1(n__from1(X)) -> from1(activate1(X))
activate1(n__s1(X)) -> s1(X)
activate1(n__add2(X1, X2)) -> add2(activate1(X1), activate1(X2))
activate1(n__len1(X)) -> len1(activate1(X))
activate1(X) -> X
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
FST2(s1(X), cons2(Y, Z)) -> ACTIVATE1(X)
ACTIVATE1(n__add2(X1, X2)) -> ACTIVATE1(X2)
ACTIVATE1(n__fst2(X1, X2)) -> ACTIVATE1(X1)
FST2(s1(X), cons2(Y, Z)) -> ACTIVATE1(Z)
ACTIVATE1(n__add2(X1, X2)) -> ADD2(activate1(X1), activate1(X2))
ACTIVATE1(n__len1(X)) -> LEN1(activate1(X))
ACTIVATE1(n__fst2(X1, X2)) -> ACTIVATE1(X2)
ADD2(s1(X), Y) -> ACTIVATE1(X)
ACTIVATE1(n__len1(X)) -> ACTIVATE1(X)
ACTIVATE1(n__from1(X)) -> ACTIVATE1(X)
ACTIVATE1(n__add2(X1, X2)) -> ACTIVATE1(X1)
Used ordering: Polynomial interpretation [21]:
ACTIVATE1(n__fst2(X1, X2)) -> FST2(activate1(X1), activate1(X2))
LEN1(cons2(X, Z)) -> ACTIVATE1(Z)
POL(0) = 0
POL(ACTIVATE1(x1)) = x1
POL(ADD2(x1, x2)) = 1 + 2·x1 + x2
POL(FST2(x1, x2)) = 1 + x1 + x2
POL(LEN1(x1)) = 2·x1
POL(activate1(x1)) = x1
POL(add2(x1, x2)) = 2 + 2·x1 + x2
POL(cons2(x1, x2)) = x2
POL(from1(x1)) = 2 + x1
POL(fst2(x1, x2)) = 1 + x1 + x2
POL(len1(x1)) = 1 + 2·x1
POL(n__add2(x1, x2)) = 2 + 2·x1 + x2
POL(n__from1(x1)) = 2 + x1
POL(n__fst2(x1, x2)) = 1 + x1 + x2
POL(n__len1(x1)) = 1 + 2·x1
POL(n__s1(x1)) = x1
POL(nil) = 1
POL(s1(x1)) = x1
len1(nil) -> 0
from1(X) -> n__from1(X)
activate1(n__add2(X1, X2)) -> add2(activate1(X1), activate1(X2))
len1(X) -> n__len1(X)
fst2(X1, X2) -> n__fst2(X1, X2)
add2(s1(X), Y) -> s1(n__add2(activate1(X), Y))
activate1(n__fst2(X1, X2)) -> fst2(activate1(X1), activate1(X2))
activate1(n__len1(X)) -> len1(activate1(X))
add2(0, X) -> X
activate1(X) -> X
activate1(n__from1(X)) -> from1(activate1(X))
fst2(0, Z) -> nil
from1(X) -> cons2(X, n__from1(n__s1(X)))
activate1(n__s1(X)) -> s1(X)
s1(X) -> n__s1(X)
add2(X1, X2) -> n__add2(X1, X2)
len1(cons2(X, Z)) -> s1(n__len1(activate1(Z)))
fst2(s1(X), cons2(Y, Z)) -> cons2(Y, n__fst2(activate1(X), activate1(Z)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
ACTIVATE1(n__fst2(X1, X2)) -> FST2(activate1(X1), activate1(X2))
LEN1(cons2(X, Z)) -> ACTIVATE1(Z)
fst2(0, Z) -> nil
fst2(s1(X), cons2(Y, Z)) -> cons2(Y, n__fst2(activate1(X), activate1(Z)))
from1(X) -> cons2(X, n__from1(n__s1(X)))
add2(0, X) -> X
add2(s1(X), Y) -> s1(n__add2(activate1(X), Y))
len1(nil) -> 0
len1(cons2(X, Z)) -> s1(n__len1(activate1(Z)))
fst2(X1, X2) -> n__fst2(X1, X2)
from1(X) -> n__from1(X)
s1(X) -> n__s1(X)
add2(X1, X2) -> n__add2(X1, X2)
len1(X) -> n__len1(X)
activate1(n__fst2(X1, X2)) -> fst2(activate1(X1), activate1(X2))
activate1(n__from1(X)) -> from1(activate1(X))
activate1(n__s1(X)) -> s1(X)
activate1(n__add2(X1, X2)) -> add2(activate1(X1), activate1(X2))
activate1(n__len1(X)) -> len1(activate1(X))
activate1(X) -> X