R
↳Dependency Pair Analysis
AEQ(s(X), s(Y)) -> AEQ(X, Y)
MARK(eq(X1, X2)) -> AEQ(X1, X2)
MARK(inf(X)) -> AINF(mark(X))
MARK(inf(X)) -> MARK(X)
MARK(take(X1, X2)) -> ATAKE(mark(X1), mark(X2))
MARK(take(X1, X2)) -> MARK(X1)
MARK(take(X1, X2)) -> MARK(X2)
MARK(length(X)) -> ALENGTH(mark(X))
MARK(length(X)) -> MARK(X)
R
↳DPs
→DP Problem 1
↳Argument Filtering and Ordering
→DP Problem 2
↳AFS
AEQ(s(X), s(Y)) -> AEQ(X, Y)
aeq(0, 0) -> true
aeq(s(X), s(Y)) -> aeq(X, Y)
aeq(X, Y) -> false
aeq(X1, X2) -> eq(X1, X2)
ainf(X) -> cons(X, inf(s(X)))
ainf(X) -> inf(X)
atake(0, X) -> nil
atake(s(X), cons(Y, L)) -> cons(Y, take(X, L))
atake(X1, X2) -> take(X1, X2)
alength(nil) -> 0
alength(cons(X, L)) -> s(length(L))
alength(X) -> length(X)
mark(eq(X1, X2)) -> aeq(X1, X2)
mark(inf(X)) -> ainf(mark(X))
mark(take(X1, X2)) -> atake(mark(X1), mark(X2))
mark(length(X)) -> alength(mark(X))
mark(0) -> 0
mark(true) -> true
mark(s(X)) -> s(X)
mark(false) -> false
mark(cons(X1, X2)) -> cons(X1, X2)
mark(nil) -> nil
innermost
AEQ(s(X), s(Y)) -> AEQ(X, Y)
POL(s(x1)) = 1 + x1 POL(A__EQ(x1, x2)) = x1 + x2
AEQ(x1, x2) -> AEQ(x1, x2)
s(x1) -> s(x1)
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 3
↳Dependency Graph
→DP Problem 2
↳AFS
aeq(0, 0) -> true
aeq(s(X), s(Y)) -> aeq(X, Y)
aeq(X, Y) -> false
aeq(X1, X2) -> eq(X1, X2)
ainf(X) -> cons(X, inf(s(X)))
ainf(X) -> inf(X)
atake(0, X) -> nil
atake(s(X), cons(Y, L)) -> cons(Y, take(X, L))
atake(X1, X2) -> take(X1, X2)
alength(nil) -> 0
alength(cons(X, L)) -> s(length(L))
alength(X) -> length(X)
mark(eq(X1, X2)) -> aeq(X1, X2)
mark(inf(X)) -> ainf(mark(X))
mark(take(X1, X2)) -> atake(mark(X1), mark(X2))
mark(length(X)) -> alength(mark(X))
mark(0) -> 0
mark(true) -> true
mark(s(X)) -> s(X)
mark(false) -> false
mark(cons(X1, X2)) -> cons(X1, X2)
mark(nil) -> nil
innermost
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳Argument Filtering and Ordering
MARK(length(X)) -> MARK(X)
MARK(take(X1, X2)) -> MARK(X2)
MARK(take(X1, X2)) -> MARK(X1)
MARK(inf(X)) -> MARK(X)
aeq(0, 0) -> true
aeq(s(X), s(Y)) -> aeq(X, Y)
aeq(X, Y) -> false
aeq(X1, X2) -> eq(X1, X2)
ainf(X) -> cons(X, inf(s(X)))
ainf(X) -> inf(X)
atake(0, X) -> nil
atake(s(X), cons(Y, L)) -> cons(Y, take(X, L))
atake(X1, X2) -> take(X1, X2)
alength(nil) -> 0
alength(cons(X, L)) -> s(length(L))
alength(X) -> length(X)
mark(eq(X1, X2)) -> aeq(X1, X2)
mark(inf(X)) -> ainf(mark(X))
mark(take(X1, X2)) -> atake(mark(X1), mark(X2))
mark(length(X)) -> alength(mark(X))
mark(0) -> 0
mark(true) -> true
mark(s(X)) -> s(X)
mark(false) -> false
mark(cons(X1, X2)) -> cons(X1, X2)
mark(nil) -> nil
innermost
MARK(inf(X)) -> MARK(X)
POL(MARK(x1)) = x1 POL(take(x1, x2)) = x1 + x2 POL(inf(x1)) = 1 + x1 POL(length(x1)) = x1
MARK(x1) -> MARK(x1)
inf(x1) -> inf(x1)
take(x1, x2) -> take(x1, x2)
length(x1) -> length(x1)
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳AFS
→DP Problem 4
↳Argument Filtering and Ordering
MARK(length(X)) -> MARK(X)
MARK(take(X1, X2)) -> MARK(X2)
MARK(take(X1, X2)) -> MARK(X1)
aeq(0, 0) -> true
aeq(s(X), s(Y)) -> aeq(X, Y)
aeq(X, Y) -> false
aeq(X1, X2) -> eq(X1, X2)
ainf(X) -> cons(X, inf(s(X)))
ainf(X) -> inf(X)
atake(0, X) -> nil
atake(s(X), cons(Y, L)) -> cons(Y, take(X, L))
atake(X1, X2) -> take(X1, X2)
alength(nil) -> 0
alength(cons(X, L)) -> s(length(L))
alength(X) -> length(X)
mark(eq(X1, X2)) -> aeq(X1, X2)
mark(inf(X)) -> ainf(mark(X))
mark(take(X1, X2)) -> atake(mark(X1), mark(X2))
mark(length(X)) -> alength(mark(X))
mark(0) -> 0
mark(true) -> true
mark(s(X)) -> s(X)
mark(false) -> false
mark(cons(X1, X2)) -> cons(X1, X2)
mark(nil) -> nil
innermost
MARK(take(X1, X2)) -> MARK(X2)
MARK(take(X1, X2)) -> MARK(X1)
POL(MARK(x1)) = x1 POL(take(x1, x2)) = 1 + x1 + x2 POL(length(x1)) = x1
MARK(x1) -> MARK(x1)
take(x1, x2) -> take(x1, x2)
length(x1) -> length(x1)
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳AFS
→DP Problem 4
↳AFS
...
→DP Problem 5
↳Argument Filtering and Ordering
MARK(length(X)) -> MARK(X)
aeq(0, 0) -> true
aeq(s(X), s(Y)) -> aeq(X, Y)
aeq(X, Y) -> false
aeq(X1, X2) -> eq(X1, X2)
ainf(X) -> cons(X, inf(s(X)))
ainf(X) -> inf(X)
atake(0, X) -> nil
atake(s(X), cons(Y, L)) -> cons(Y, take(X, L))
atake(X1, X2) -> take(X1, X2)
alength(nil) -> 0
alength(cons(X, L)) -> s(length(L))
alength(X) -> length(X)
mark(eq(X1, X2)) -> aeq(X1, X2)
mark(inf(X)) -> ainf(mark(X))
mark(take(X1, X2)) -> atake(mark(X1), mark(X2))
mark(length(X)) -> alength(mark(X))
mark(0) -> 0
mark(true) -> true
mark(s(X)) -> s(X)
mark(false) -> false
mark(cons(X1, X2)) -> cons(X1, X2)
mark(nil) -> nil
innermost
MARK(length(X)) -> MARK(X)
POL(MARK(x1)) = x1 POL(length(x1)) = 1 + x1
MARK(x1) -> MARK(x1)
length(x1) -> length(x1)
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳AFS
→DP Problem 4
↳AFS
...
→DP Problem 6
↳Dependency Graph
aeq(0, 0) -> true
aeq(s(X), s(Y)) -> aeq(X, Y)
aeq(X, Y) -> false
aeq(X1, X2) -> eq(X1, X2)
ainf(X) -> cons(X, inf(s(X)))
ainf(X) -> inf(X)
atake(0, X) -> nil
atake(s(X), cons(Y, L)) -> cons(Y, take(X, L))
atake(X1, X2) -> take(X1, X2)
alength(nil) -> 0
alength(cons(X, L)) -> s(length(L))
alength(X) -> length(X)
mark(eq(X1, X2)) -> aeq(X1, X2)
mark(inf(X)) -> ainf(mark(X))
mark(take(X1, X2)) -> atake(mark(X1), mark(X2))
mark(length(X)) -> alength(mark(X))
mark(0) -> 0
mark(true) -> true
mark(s(X)) -> s(X)
mark(false) -> false
mark(cons(X1, X2)) -> cons(X1, X2)
mark(nil) -> nil
innermost