R
↳Dependency Pair Analysis
EQ(ns(X), ns(Y)) -> EQ(activate(X), activate(Y))
EQ(ns(X), ns(Y)) -> ACTIVATE(X)
EQ(ns(X), ns(Y)) -> ACTIVATE(Y)
TAKE(s(X), cons(Y, L)) -> ACTIVATE(Y)
TAKE(s(X), cons(Y, L)) -> ACTIVATE(X)
TAKE(s(X), cons(Y, L)) -> ACTIVATE(L)
LENGTH(nil) -> 0'
LENGTH(cons(X, L)) -> S(nlength(activate(L)))
LENGTH(cons(X, L)) -> ACTIVATE(L)
ACTIVATE(n0) -> 0'
ACTIVATE(ns(X)) -> S(X)
ACTIVATE(ninf(X)) -> INF(activate(X))
ACTIVATE(ninf(X)) -> ACTIVATE(X)
ACTIVATE(ntake(X1, X2)) -> TAKE(activate(X1), activate(X2))
ACTIVATE(ntake(X1, X2)) -> ACTIVATE(X1)
ACTIVATE(ntake(X1, X2)) -> ACTIVATE(X2)
ACTIVATE(nlength(X)) -> LENGTH(activate(X))
ACTIVATE(nlength(X)) -> ACTIVATE(X)
R
↳DPs
→DP Problem 1
↳Polynomial Ordering
→DP Problem 2
↳Remaining
ACTIVATE(nlength(X)) -> ACTIVATE(X)
LENGTH(cons(X, L)) -> ACTIVATE(L)
ACTIVATE(nlength(X)) -> LENGTH(activate(X))
ACTIVATE(ntake(X1, X2)) -> ACTIVATE(X2)
ACTIVATE(ntake(X1, X2)) -> ACTIVATE(X1)
ACTIVATE(ninf(X)) -> ACTIVATE(X)
eq(n0, n0) -> true
eq(ns(X), ns(Y)) -> eq(activate(X), activate(Y))
eq(X, Y) -> false
inf(X) -> cons(X, ninf(ns(X)))
inf(X) -> ninf(X)
take(0, X) -> nil
take(s(X), cons(Y, L)) -> cons(activate(Y), ntake(activate(X), activate(L)))
take(X1, X2) -> ntake(X1, X2)
length(nil) -> 0
length(cons(X, L)) -> s(nlength(activate(L)))
length(X) -> nlength(X)
0 -> n0
s(X) -> ns(X)
activate(n0) -> 0
activate(ns(X)) -> s(X)
activate(ninf(X)) -> inf(activate(X))
activate(ntake(X1, X2)) -> take(activate(X1), activate(X2))
activate(nlength(X)) -> length(activate(X))
activate(X) -> X
innermost
ACTIVATE(nlength(X)) -> ACTIVATE(X)
ACTIVATE(nlength(X)) -> LENGTH(activate(X))
activate(n0) -> 0
activate(ns(X)) -> s(X)
activate(ninf(X)) -> inf(activate(X))
activate(ntake(X1, X2)) -> take(activate(X1), activate(X2))
activate(nlength(X)) -> length(activate(X))
activate(X) -> X
length(nil) -> 0
length(cons(X, L)) -> s(nlength(activate(L)))
length(X) -> nlength(X)
take(0, X) -> nil
take(s(X), cons(Y, L)) -> cons(activate(Y), ntake(activate(X), activate(L)))
take(X1, X2) -> ntake(X1, X2)
0 -> n0
s(X) -> ns(X)
inf(X) -> cons(X, ninf(ns(X)))
inf(X) -> ninf(X)
POL(activate(x1)) = x1 POL(n__length(x1)) = 1 + x1 POL(n__take(x1, x2)) = x1 + x2 POL(take(x1, x2)) = x1 + x2 POL(n__s(x1)) = x1 POL(ACTIVATE(x1)) = x1 POL(n__inf(x1)) = x1 POL(0) = 0 POL(cons(x1, x2)) = x2 POL(inf(x1)) = x1 POL(nil) = 0 POL(n__0) = 0 POL(s(x1)) = x1 POL(LENGTH(x1)) = x1 POL(length(x1)) = 1 + x1
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 3
↳Dependency Graph
→DP Problem 2
↳Remaining
LENGTH(cons(X, L)) -> ACTIVATE(L)
ACTIVATE(ntake(X1, X2)) -> ACTIVATE(X2)
ACTIVATE(ntake(X1, X2)) -> ACTIVATE(X1)
ACTIVATE(ninf(X)) -> ACTIVATE(X)
eq(n0, n0) -> true
eq(ns(X), ns(Y)) -> eq(activate(X), activate(Y))
eq(X, Y) -> false
inf(X) -> cons(X, ninf(ns(X)))
inf(X) -> ninf(X)
take(0, X) -> nil
take(s(X), cons(Y, L)) -> cons(activate(Y), ntake(activate(X), activate(L)))
take(X1, X2) -> ntake(X1, X2)
length(nil) -> 0
length(cons(X, L)) -> s(nlength(activate(L)))
length(X) -> nlength(X)
0 -> n0
s(X) -> ns(X)
activate(n0) -> 0
activate(ns(X)) -> s(X)
activate(ninf(X)) -> inf(activate(X))
activate(ntake(X1, X2)) -> take(activate(X1), activate(X2))
activate(nlength(X)) -> length(activate(X))
activate(X) -> X
innermost
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 3
↳DGraph
...
→DP Problem 4
↳Polynomial Ordering
→DP Problem 2
↳Remaining
ACTIVATE(ntake(X1, X2)) -> ACTIVATE(X2)
ACTIVATE(ntake(X1, X2)) -> ACTIVATE(X1)
ACTIVATE(ninf(X)) -> ACTIVATE(X)
eq(n0, n0) -> true
eq(ns(X), ns(Y)) -> eq(activate(X), activate(Y))
eq(X, Y) -> false
inf(X) -> cons(X, ninf(ns(X)))
inf(X) -> ninf(X)
take(0, X) -> nil
take(s(X), cons(Y, L)) -> cons(activate(Y), ntake(activate(X), activate(L)))
take(X1, X2) -> ntake(X1, X2)
length(nil) -> 0
length(cons(X, L)) -> s(nlength(activate(L)))
length(X) -> nlength(X)
0 -> n0
s(X) -> ns(X)
activate(n0) -> 0
activate(ns(X)) -> s(X)
activate(ninf(X)) -> inf(activate(X))
activate(ntake(X1, X2)) -> take(activate(X1), activate(X2))
activate(nlength(X)) -> length(activate(X))
activate(X) -> X
innermost
ACTIVATE(ntake(X1, X2)) -> ACTIVATE(X2)
ACTIVATE(ntake(X1, X2)) -> ACTIVATE(X1)
POL(n__inf(x1)) = x1 POL(n__take(x1, x2)) = 1 + x1 + x2 POL(ACTIVATE(x1)) = x1
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 3
↳DGraph
...
→DP Problem 5
↳Polynomial Ordering
→DP Problem 2
↳Remaining
ACTIVATE(ninf(X)) -> ACTIVATE(X)
eq(n0, n0) -> true
eq(ns(X), ns(Y)) -> eq(activate(X), activate(Y))
eq(X, Y) -> false
inf(X) -> cons(X, ninf(ns(X)))
inf(X) -> ninf(X)
take(0, X) -> nil
take(s(X), cons(Y, L)) -> cons(activate(Y), ntake(activate(X), activate(L)))
take(X1, X2) -> ntake(X1, X2)
length(nil) -> 0
length(cons(X, L)) -> s(nlength(activate(L)))
length(X) -> nlength(X)
0 -> n0
s(X) -> ns(X)
activate(n0) -> 0
activate(ns(X)) -> s(X)
activate(ninf(X)) -> inf(activate(X))
activate(ntake(X1, X2)) -> take(activate(X1), activate(X2))
activate(nlength(X)) -> length(activate(X))
activate(X) -> X
innermost
ACTIVATE(ninf(X)) -> ACTIVATE(X)
POL(n__inf(x1)) = 1 + x1 POL(ACTIVATE(x1)) = x1
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 3
↳DGraph
...
→DP Problem 6
↳Dependency Graph
→DP Problem 2
↳Remaining
eq(n0, n0) -> true
eq(ns(X), ns(Y)) -> eq(activate(X), activate(Y))
eq(X, Y) -> false
inf(X) -> cons(X, ninf(ns(X)))
inf(X) -> ninf(X)
take(0, X) -> nil
take(s(X), cons(Y, L)) -> cons(activate(Y), ntake(activate(X), activate(L)))
take(X1, X2) -> ntake(X1, X2)
length(nil) -> 0
length(cons(X, L)) -> s(nlength(activate(L)))
length(X) -> nlength(X)
0 -> n0
s(X) -> ns(X)
activate(n0) -> 0
activate(ns(X)) -> s(X)
activate(ninf(X)) -> inf(activate(X))
activate(ntake(X1, X2)) -> take(activate(X1), activate(X2))
activate(nlength(X)) -> length(activate(X))
activate(X) -> X
innermost
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Remaining Obligation(s)
EQ(ns(X), ns(Y)) -> EQ(activate(X), activate(Y))
eq(n0, n0) -> true
eq(ns(X), ns(Y)) -> eq(activate(X), activate(Y))
eq(X, Y) -> false
inf(X) -> cons(X, ninf(ns(X)))
inf(X) -> ninf(X)
take(0, X) -> nil
take(s(X), cons(Y, L)) -> cons(activate(Y), ntake(activate(X), activate(L)))
take(X1, X2) -> ntake(X1, X2)
length(nil) -> 0
length(cons(X, L)) -> s(nlength(activate(L)))
length(X) -> nlength(X)
0 -> n0
s(X) -> ns(X)
activate(n0) -> 0
activate(ns(X)) -> s(X)
activate(ninf(X)) -> inf(activate(X))
activate(ntake(X1, X2)) -> take(activate(X1), activate(X2))
activate(nlength(X)) -> length(activate(X))
activate(X) -> X
innermost