R
↳Dependency Pair Analysis
AFST(s(X), cons(Y, Z)) -> MARK(Y)
AFROM(X) -> MARK(X)
AADD(0, X) -> MARK(X)
MARK(fst(X1, X2)) -> AFST(mark(X1), mark(X2))
MARK(fst(X1, X2)) -> MARK(X1)
MARK(fst(X1, X2)) -> MARK(X2)
MARK(from(X)) -> AFROM(mark(X))
MARK(from(X)) -> MARK(X)
MARK(add(X1, X2)) -> AADD(mark(X1), mark(X2))
MARK(add(X1, X2)) -> MARK(X1)
MARK(add(X1, X2)) -> MARK(X2)
MARK(len(X)) -> ALEN(mark(X))
MARK(len(X)) -> MARK(X)
MARK(cons(X1, X2)) -> MARK(X1)
R
↳DPs
→DP Problem 1
↳Argument Filtering and Ordering
MARK(cons(X1, X2)) -> MARK(X1)
MARK(len(X)) -> MARK(X)
MARK(add(X1, X2)) -> MARK(X2)
MARK(add(X1, X2)) -> MARK(X1)
AADD(0, X) -> MARK(X)
MARK(add(X1, X2)) -> AADD(mark(X1), mark(X2))
MARK(from(X)) -> MARK(X)
AFROM(X) -> MARK(X)
MARK(from(X)) -> AFROM(mark(X))
MARK(fst(X1, X2)) -> MARK(X2)
MARK(fst(X1, X2)) -> MARK(X1)
MARK(fst(X1, X2)) -> AFST(mark(X1), mark(X2))
AFST(s(X), cons(Y, Z)) -> MARK(Y)
afst(0, Z) -> nil
afst(s(X), cons(Y, Z)) -> cons(mark(Y), fst(X, Z))
afst(X1, X2) -> fst(X1, X2)
afrom(X) -> cons(mark(X), from(s(X)))
afrom(X) -> from(X)
aadd(0, X) -> mark(X)
aadd(s(X), Y) -> s(add(X, Y))
aadd(X1, X2) -> add(X1, X2)
alen(nil) -> 0
alen(cons(X, Z)) -> s(len(Z))
alen(X) -> len(X)
mark(fst(X1, X2)) -> afst(mark(X1), mark(X2))
mark(from(X)) -> afrom(mark(X))
mark(add(X1, X2)) -> aadd(mark(X1), mark(X2))
mark(len(X)) -> alen(mark(X))
mark(0) -> 0
mark(s(X)) -> s(X)
mark(nil) -> nil
mark(cons(X1, X2)) -> cons(mark(X1), X2)
innermost
MARK(from(X)) -> MARK(X)
AFROM(X) -> MARK(X)
afst(0, Z) -> nil
afst(s(X), cons(Y, Z)) -> cons(mark(Y), fst(X, Z))
afst(X1, X2) -> fst(X1, X2)
mark(fst(X1, X2)) -> afst(mark(X1), mark(X2))
mark(from(X)) -> afrom(mark(X))
mark(add(X1, X2)) -> aadd(mark(X1), mark(X2))
mark(len(X)) -> alen(mark(X))
mark(0) -> 0
mark(s(X)) -> s(X)
mark(nil) -> nil
mark(cons(X1, X2)) -> cons(mark(X1), X2)
afrom(X) -> cons(mark(X), from(s(X)))
afrom(X) -> from(X)
aadd(0, X) -> mark(X)
aadd(s(X), Y) -> s(add(X, Y))
aadd(X1, X2) -> add(X1, X2)
alen(nil) -> 0
alen(cons(X, Z)) -> s(len(Z))
alen(X) -> len(X)
POL(from(x1)) = 1 + x1 POL(MARK(x1)) = x1 POL(a__len(x1)) = x1 POL(len(x1)) = x1 POL(A__FROM(x1)) = 1 + x1 POL(mark(x1)) = x1 POL(A__FST(x1, x2)) = x1 + x2 POL(a__add(x1, x2)) = x1 + x2 POL(a__from(x1)) = 1 + x1 POL(add(x1, x2)) = x1 + x2 POL(A__ADD(x1, x2)) = x1 + x2 POL(0) = 0 POL(a__fst(x1, x2)) = x1 + x2 POL(nil) = 0 POL(fst(x1, x2)) = x1 + x2 POL(s) = 0
AFROM(x1) -> AFROM(x1)
MARK(x1) -> MARK(x1)
len(x1) -> len(x1)
AADD(x1, x2) -> AADD(x1, x2)
add(x1, x2) -> add(x1, x2)
mark(x1) -> mark(x1)
AFST(x1, x2) -> AFST(x1, x2)
s(x1) -> s
cons(x1, x2) -> x1
fst(x1, x2) -> fst(x1, x2)
from(x1) -> from(x1)
afst(x1, x2) -> afst(x1, x2)
afrom(x1) -> afrom(x1)
aadd(x1, x2) -> aadd(x1, x2)
alen(x1) -> alen(x1)
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳Dependency Graph
MARK(cons(X1, X2)) -> MARK(X1)
MARK(len(X)) -> MARK(X)
MARK(add(X1, X2)) -> MARK(X2)
MARK(add(X1, X2)) -> MARK(X1)
AADD(0, X) -> MARK(X)
MARK(add(X1, X2)) -> AADD(mark(X1), mark(X2))
MARK(from(X)) -> AFROM(mark(X))
MARK(fst(X1, X2)) -> MARK(X2)
MARK(fst(X1, X2)) -> MARK(X1)
MARK(fst(X1, X2)) -> AFST(mark(X1), mark(X2))
AFST(s(X), cons(Y, Z)) -> MARK(Y)
afst(0, Z) -> nil
afst(s(X), cons(Y, Z)) -> cons(mark(Y), fst(X, Z))
afst(X1, X2) -> fst(X1, X2)
afrom(X) -> cons(mark(X), from(s(X)))
afrom(X) -> from(X)
aadd(0, X) -> mark(X)
aadd(s(X), Y) -> s(add(X, Y))
aadd(X1, X2) -> add(X1, X2)
alen(nil) -> 0
alen(cons(X, Z)) -> s(len(Z))
alen(X) -> len(X)
mark(fst(X1, X2)) -> afst(mark(X1), mark(X2))
mark(from(X)) -> afrom(mark(X))
mark(add(X1, X2)) -> aadd(mark(X1), mark(X2))
mark(len(X)) -> alen(mark(X))
mark(0) -> 0
mark(s(X)) -> s(X)
mark(nil) -> nil
mark(cons(X1, X2)) -> cons(mark(X1), X2)
innermost
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳DGraph
...
→DP Problem 3
↳Argument Filtering and Ordering
MARK(len(X)) -> MARK(X)
MARK(add(X1, X2)) -> MARK(X2)
MARK(add(X1, X2)) -> MARK(X1)
AADD(0, X) -> MARK(X)
MARK(add(X1, X2)) -> AADD(mark(X1), mark(X2))
MARK(fst(X1, X2)) -> MARK(X2)
MARK(fst(X1, X2)) -> MARK(X1)
AFST(s(X), cons(Y, Z)) -> MARK(Y)
MARK(fst(X1, X2)) -> AFST(mark(X1), mark(X2))
MARK(cons(X1, X2)) -> MARK(X1)
afst(0, Z) -> nil
afst(s(X), cons(Y, Z)) -> cons(mark(Y), fst(X, Z))
afst(X1, X2) -> fst(X1, X2)
afrom(X) -> cons(mark(X), from(s(X)))
afrom(X) -> from(X)
aadd(0, X) -> mark(X)
aadd(s(X), Y) -> s(add(X, Y))
aadd(X1, X2) -> add(X1, X2)
alen(nil) -> 0
alen(cons(X, Z)) -> s(len(Z))
alen(X) -> len(X)
mark(fst(X1, X2)) -> afst(mark(X1), mark(X2))
mark(from(X)) -> afrom(mark(X))
mark(add(X1, X2)) -> aadd(mark(X1), mark(X2))
mark(len(X)) -> alen(mark(X))
mark(0) -> 0
mark(s(X)) -> s(X)
mark(nil) -> nil
mark(cons(X1, X2)) -> cons(mark(X1), X2)
innermost
MARK(add(X1, X2)) -> MARK(X2)
MARK(add(X1, X2)) -> MARK(X1)
MARK(add(X1, X2)) -> AADD(mark(X1), mark(X2))
afst(0, Z) -> nil
afst(s(X), cons(Y, Z)) -> cons(mark(Y), fst(X, Z))
afst(X1, X2) -> fst(X1, X2)
mark(fst(X1, X2)) -> afst(mark(X1), mark(X2))
mark(from(X)) -> afrom(mark(X))
mark(add(X1, X2)) -> aadd(mark(X1), mark(X2))
mark(len(X)) -> alen(mark(X))
mark(0) -> 0
mark(s(X)) -> s(X)
mark(nil) -> nil
mark(cons(X1, X2)) -> cons(mark(X1), X2)
afrom(X) -> cons(mark(X), from(s(X)))
afrom(X) -> from(X)
aadd(0, X) -> mark(X)
aadd(s(X), Y) -> s(add(X, Y))
aadd(X1, X2) -> add(X1, X2)
alen(nil) -> 0
alen(cons(X, Z)) -> s(len(Z))
alen(X) -> len(X)
POL(from(x1)) = x1 POL(MARK(x1)) = x1 POL(a__len(x1)) = x1 POL(len(x1)) = x1 POL(mark(x1)) = x1 POL(A__FST(x1, x2)) = x1 + x2 POL(a__add(x1, x2)) = 1 + x1 + x2 POL(a__from(x1)) = x1 POL(add(x1, x2)) = 1 + x1 + x2 POL(A__ADD(x1, x2)) = x1 + x2 POL(0) = 0 POL(a__fst(x1, x2)) = x1 + x2 POL(nil) = 0 POL(s) = 0 POL(fst(x1, x2)) = x1 + x2
MARK(x1) -> MARK(x1)
AADD(x1, x2) -> AADD(x1, x2)
add(x1, x2) -> add(x1, x2)
mark(x1) -> mark(x1)
len(x1) -> len(x1)
fst(x1, x2) -> fst(x1, x2)
AFST(x1, x2) -> AFST(x1, x2)
cons(x1, x2) -> x1
s(x1) -> s
afst(x1, x2) -> afst(x1, x2)
from(x1) -> from(x1)
afrom(x1) -> afrom(x1)
aadd(x1, x2) -> aadd(x1, x2)
alen(x1) -> alen(x1)
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳DGraph
...
→DP Problem 4
↳Dependency Graph
MARK(len(X)) -> MARK(X)
AADD(0, X) -> MARK(X)
MARK(fst(X1, X2)) -> MARK(X2)
MARK(fst(X1, X2)) -> MARK(X1)
AFST(s(X), cons(Y, Z)) -> MARK(Y)
MARK(fst(X1, X2)) -> AFST(mark(X1), mark(X2))
MARK(cons(X1, X2)) -> MARK(X1)
afst(0, Z) -> nil
afst(s(X), cons(Y, Z)) -> cons(mark(Y), fst(X, Z))
afst(X1, X2) -> fst(X1, X2)
afrom(X) -> cons(mark(X), from(s(X)))
afrom(X) -> from(X)
aadd(0, X) -> mark(X)
aadd(s(X), Y) -> s(add(X, Y))
aadd(X1, X2) -> add(X1, X2)
alen(nil) -> 0
alen(cons(X, Z)) -> s(len(Z))
alen(X) -> len(X)
mark(fst(X1, X2)) -> afst(mark(X1), mark(X2))
mark(from(X)) -> afrom(mark(X))
mark(add(X1, X2)) -> aadd(mark(X1), mark(X2))
mark(len(X)) -> alen(mark(X))
mark(0) -> 0
mark(s(X)) -> s(X)
mark(nil) -> nil
mark(cons(X1, X2)) -> cons(mark(X1), X2)
innermost
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳DGraph
...
→DP Problem 5
↳Argument Filtering and Ordering
MARK(cons(X1, X2)) -> MARK(X1)
MARK(fst(X1, X2)) -> MARK(X2)
MARK(fst(X1, X2)) -> MARK(X1)
AFST(s(X), cons(Y, Z)) -> MARK(Y)
MARK(fst(X1, X2)) -> AFST(mark(X1), mark(X2))
MARK(len(X)) -> MARK(X)
afst(0, Z) -> nil
afst(s(X), cons(Y, Z)) -> cons(mark(Y), fst(X, Z))
afst(X1, X2) -> fst(X1, X2)
afrom(X) -> cons(mark(X), from(s(X)))
afrom(X) -> from(X)
aadd(0, X) -> mark(X)
aadd(s(X), Y) -> s(add(X, Y))
aadd(X1, X2) -> add(X1, X2)
alen(nil) -> 0
alen(cons(X, Z)) -> s(len(Z))
alen(X) -> len(X)
mark(fst(X1, X2)) -> afst(mark(X1), mark(X2))
mark(from(X)) -> afrom(mark(X))
mark(add(X1, X2)) -> aadd(mark(X1), mark(X2))
mark(len(X)) -> alen(mark(X))
mark(0) -> 0
mark(s(X)) -> s(X)
mark(nil) -> nil
mark(cons(X1, X2)) -> cons(mark(X1), X2)
innermost
MARK(len(X)) -> MARK(X)
afst(0, Z) -> nil
afst(s(X), cons(Y, Z)) -> cons(mark(Y), fst(X, Z))
afst(X1, X2) -> fst(X1, X2)
mark(fst(X1, X2)) -> afst(mark(X1), mark(X2))
mark(from(X)) -> afrom(mark(X))
mark(add(X1, X2)) -> aadd(mark(X1), mark(X2))
mark(len(X)) -> alen(mark(X))
mark(0) -> 0
mark(s(X)) -> s(X)
mark(nil) -> nil
mark(cons(X1, X2)) -> cons(mark(X1), X2)
afrom(X) -> cons(mark(X), from(s(X)))
afrom(X) -> from(X)
aadd(0, X) -> mark(X)
aadd(s(X), Y) -> s(add(X, Y))
aadd(X1, X2) -> add(X1, X2)
alen(nil) -> 0
alen(cons(X, Z)) -> s(len(Z))
alen(X) -> len(X)
POL(from(x1)) = x1 POL(MARK(x1)) = x1 POL(a__len(x1)) = 1 + x1 POL(len(x1)) = 1 + x1 POL(A__FST(x1, x2)) = x1 + x2 POL(mark(x1)) = x1 POL(a__from(x1)) = x1 POL(a__add(x1, x2)) = x1 + x2 POL(add(x1, x2)) = x1 + x2 POL(0) = 0 POL(a__fst(x1, x2)) = x1 + x2 POL(nil) = 0 POL(s) = 0 POL(fst(x1, x2)) = x1 + x2
MARK(x1) -> MARK(x1)
len(x1) -> len(x1)
fst(x1, x2) -> fst(x1, x2)
AFST(x1, x2) -> AFST(x1, x2)
mark(x1) -> mark(x1)
s(x1) -> s
cons(x1, x2) -> x1
afst(x1, x2) -> afst(x1, x2)
from(x1) -> from(x1)
afrom(x1) -> afrom(x1)
add(x1, x2) -> add(x1, x2)
aadd(x1, x2) -> aadd(x1, x2)
alen(x1) -> alen(x1)
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳DGraph
...
→DP Problem 6
↳Argument Filtering and Ordering
MARK(cons(X1, X2)) -> MARK(X1)
MARK(fst(X1, X2)) -> MARK(X2)
MARK(fst(X1, X2)) -> MARK(X1)
AFST(s(X), cons(Y, Z)) -> MARK(Y)
MARK(fst(X1, X2)) -> AFST(mark(X1), mark(X2))
afst(0, Z) -> nil
afst(s(X), cons(Y, Z)) -> cons(mark(Y), fst(X, Z))
afst(X1, X2) -> fst(X1, X2)
afrom(X) -> cons(mark(X), from(s(X)))
afrom(X) -> from(X)
aadd(0, X) -> mark(X)
aadd(s(X), Y) -> s(add(X, Y))
aadd(X1, X2) -> add(X1, X2)
alen(nil) -> 0
alen(cons(X, Z)) -> s(len(Z))
alen(X) -> len(X)
mark(fst(X1, X2)) -> afst(mark(X1), mark(X2))
mark(from(X)) -> afrom(mark(X))
mark(add(X1, X2)) -> aadd(mark(X1), mark(X2))
mark(len(X)) -> alen(mark(X))
mark(0) -> 0
mark(s(X)) -> s(X)
mark(nil) -> nil
mark(cons(X1, X2)) -> cons(mark(X1), X2)
innermost
MARK(fst(X1, X2)) -> MARK(X2)
MARK(fst(X1, X2)) -> MARK(X1)
MARK(fst(X1, X2)) -> AFST(mark(X1), mark(X2))
afst(0, Z) -> nil
afst(s(X), cons(Y, Z)) -> cons(mark(Y), fst(X, Z))
afst(X1, X2) -> fst(X1, X2)
mark(fst(X1, X2)) -> afst(mark(X1), mark(X2))
mark(from(X)) -> afrom(mark(X))
mark(add(X1, X2)) -> aadd(mark(X1), mark(X2))
mark(len(X)) -> alen(mark(X))
mark(0) -> 0
mark(s(X)) -> s(X)
mark(nil) -> nil
mark(cons(X1, X2)) -> cons(mark(X1), X2)
afrom(X) -> cons(mark(X), from(s(X)))
afrom(X) -> from(X)
aadd(0, X) -> mark(X)
aadd(s(X), Y) -> s(add(X, Y))
aadd(X1, X2) -> add(X1, X2)
alen(nil) -> 0
alen(cons(X, Z)) -> s(len(Z))
alen(X) -> len(X)
POL(from(x1)) = x1 POL(MARK(x1)) = x1 POL(a__len) = 0 POL(len) = 0 POL(A__FST(x1, x2)) = x1 + x2 POL(mark(x1)) = x1 POL(a__from(x1)) = x1 POL(a__add(x1, x2)) = x1 + x2 POL(add(x1, x2)) = x1 + x2 POL(0) = 0 POL(a__fst(x1, x2)) = 1 + x1 + x2 POL(nil) = 0 POL(s(x1)) = x1 POL(fst(x1, x2)) = 1 + x1 + x2
MARK(x1) -> MARK(x1)
fst(x1, x2) -> fst(x1, x2)
AFST(x1, x2) -> AFST(x1, x2)
mark(x1) -> mark(x1)
s(x1) -> s(x1)
cons(x1, x2) -> x1
afst(x1, x2) -> afst(x1, x2)
from(x1) -> from(x1)
afrom(x1) -> afrom(x1)
add(x1, x2) -> add(x1, x2)
aadd(x1, x2) -> aadd(x1, x2)
len(x1) -> len
alen(x1) -> alen
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳DGraph
...
→DP Problem 7
↳Dependency Graph
MARK(cons(X1, X2)) -> MARK(X1)
AFST(s(X), cons(Y, Z)) -> MARK(Y)
afst(0, Z) -> nil
afst(s(X), cons(Y, Z)) -> cons(mark(Y), fst(X, Z))
afst(X1, X2) -> fst(X1, X2)
afrom(X) -> cons(mark(X), from(s(X)))
afrom(X) -> from(X)
aadd(0, X) -> mark(X)
aadd(s(X), Y) -> s(add(X, Y))
aadd(X1, X2) -> add(X1, X2)
alen(nil) -> 0
alen(cons(X, Z)) -> s(len(Z))
alen(X) -> len(X)
mark(fst(X1, X2)) -> afst(mark(X1), mark(X2))
mark(from(X)) -> afrom(mark(X))
mark(add(X1, X2)) -> aadd(mark(X1), mark(X2))
mark(len(X)) -> alen(mark(X))
mark(0) -> 0
mark(s(X)) -> s(X)
mark(nil) -> nil
mark(cons(X1, X2)) -> cons(mark(X1), X2)
innermost
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳DGraph
...
→DP Problem 8
↳Argument Filtering and Ordering
MARK(cons(X1, X2)) -> MARK(X1)
afst(0, Z) -> nil
afst(s(X), cons(Y, Z)) -> cons(mark(Y), fst(X, Z))
afst(X1, X2) -> fst(X1, X2)
afrom(X) -> cons(mark(X), from(s(X)))
afrom(X) -> from(X)
aadd(0, X) -> mark(X)
aadd(s(X), Y) -> s(add(X, Y))
aadd(X1, X2) -> add(X1, X2)
alen(nil) -> 0
alen(cons(X, Z)) -> s(len(Z))
alen(X) -> len(X)
mark(fst(X1, X2)) -> afst(mark(X1), mark(X2))
mark(from(X)) -> afrom(mark(X))
mark(add(X1, X2)) -> aadd(mark(X1), mark(X2))
mark(len(X)) -> alen(mark(X))
mark(0) -> 0
mark(s(X)) -> s(X)
mark(nil) -> nil
mark(cons(X1, X2)) -> cons(mark(X1), X2)
innermost
MARK(cons(X1, X2)) -> MARK(X1)
POL(MARK(x1)) = x1 POL(cons(x1, x2)) = 1 + x1 + x2
MARK(x1) -> MARK(x1)
cons(x1, x2) -> cons(x1, x2)
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳DGraph
...
→DP Problem 9
↳Dependency Graph
afst(0, Z) -> nil
afst(s(X), cons(Y, Z)) -> cons(mark(Y), fst(X, Z))
afst(X1, X2) -> fst(X1, X2)
afrom(X) -> cons(mark(X), from(s(X)))
afrom(X) -> from(X)
aadd(0, X) -> mark(X)
aadd(s(X), Y) -> s(add(X, Y))
aadd(X1, X2) -> add(X1, X2)
alen(nil) -> 0
alen(cons(X, Z)) -> s(len(Z))
alen(X) -> len(X)
mark(fst(X1, X2)) -> afst(mark(X1), mark(X2))
mark(from(X)) -> afrom(mark(X))
mark(add(X1, X2)) -> aadd(mark(X1), mark(X2))
mark(len(X)) -> alen(mark(X))
mark(0) -> 0
mark(s(X)) -> s(X)
mark(nil) -> nil
mark(cons(X1, X2)) -> cons(mark(X1), X2)
innermost