R
↳Dependency Pair Analysis
AFIRST(s(X), cons(Y, Z)) -> MARK(Y)
AFROM(X) -> MARK(X)
MARK(first(X1, X2)) -> AFIRST(mark(X1), mark(X2))
MARK(first(X1, X2)) -> MARK(X1)
MARK(first(X1, X2)) -> MARK(X2)
MARK(from(X)) -> AFROM(mark(X))
MARK(from(X)) -> MARK(X)
MARK(s(X)) -> MARK(X)
MARK(cons(X1, X2)) -> MARK(X1)
R
↳DPs
→DP Problem 1
↳Polynomial Ordering
MARK(cons(X1, X2)) -> MARK(X1)
MARK(s(X)) -> MARK(X)
MARK(from(X)) -> MARK(X)
AFROM(X) -> MARK(X)
MARK(from(X)) -> AFROM(mark(X))
MARK(first(X1, X2)) -> MARK(X2)
MARK(first(X1, X2)) -> MARK(X1)
MARK(first(X1, X2)) -> AFIRST(mark(X1), mark(X2))
AFIRST(s(X), cons(Y, Z)) -> MARK(Y)
afirst(0, X) -> nil
afirst(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z))
afirst(X1, X2) -> first(X1, X2)
afrom(X) -> cons(mark(X), from(s(X)))
afrom(X) -> from(X)
mark(first(X1, X2)) -> afirst(mark(X1), mark(X2))
mark(from(X)) -> afrom(mark(X))
mark(0) -> 0
mark(nil) -> nil
mark(s(X)) -> s(mark(X))
mark(cons(X1, X2)) -> cons(mark(X1), X2)
MARK(from(X)) -> MARK(X)
MARK(from(X)) -> AFROM(mark(X))
mark(first(X1, X2)) -> afirst(mark(X1), mark(X2))
mark(from(X)) -> afrom(mark(X))
mark(0) -> 0
mark(nil) -> nil
mark(s(X)) -> s(mark(X))
mark(cons(X1, X2)) -> cons(mark(X1), X2)
afrom(X) -> cons(mark(X), from(s(X)))
afrom(X) -> from(X)
afirst(0, X) -> nil
afirst(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z))
afirst(X1, X2) -> first(X1, X2)
POL(from(x1)) = 1 + x1 POL(first(x1, x2)) = x1 + x2 POL(0) = 0 POL(MARK(x1)) = x1 POL(A__FIRST(x1, x2)) = x2 POL(cons(x1, x2)) = x1 POL(nil) = 0 POL(A__FROM(x1)) = x1 POL(s(x1)) = x1 POL(mark(x1)) = x1 POL(a__from(x1)) = 1 + x1 POL(a__first(x1, x2)) = x1 + x2
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Dependency Graph
MARK(cons(X1, X2)) -> MARK(X1)
MARK(s(X)) -> MARK(X)
AFROM(X) -> MARK(X)
MARK(first(X1, X2)) -> MARK(X2)
MARK(first(X1, X2)) -> MARK(X1)
MARK(first(X1, X2)) -> AFIRST(mark(X1), mark(X2))
AFIRST(s(X), cons(Y, Z)) -> MARK(Y)
afirst(0, X) -> nil
afirst(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z))
afirst(X1, X2) -> first(X1, X2)
afrom(X) -> cons(mark(X), from(s(X)))
afrom(X) -> from(X)
mark(first(X1, X2)) -> afirst(mark(X1), mark(X2))
mark(from(X)) -> afrom(mark(X))
mark(0) -> 0
mark(nil) -> nil
mark(s(X)) -> s(mark(X))
mark(cons(X1, X2)) -> cons(mark(X1), X2)
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳DGraph
...
→DP Problem 3
↳Polynomial Ordering
MARK(s(X)) -> MARK(X)
MARK(first(X1, X2)) -> MARK(X2)
MARK(first(X1, X2)) -> MARK(X1)
AFIRST(s(X), cons(Y, Z)) -> MARK(Y)
MARK(first(X1, X2)) -> AFIRST(mark(X1), mark(X2))
MARK(cons(X1, X2)) -> MARK(X1)
afirst(0, X) -> nil
afirst(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z))
afirst(X1, X2) -> first(X1, X2)
afrom(X) -> cons(mark(X), from(s(X)))
afrom(X) -> from(X)
mark(first(X1, X2)) -> afirst(mark(X1), mark(X2))
mark(from(X)) -> afrom(mark(X))
mark(0) -> 0
mark(nil) -> nil
mark(s(X)) -> s(mark(X))
mark(cons(X1, X2)) -> cons(mark(X1), X2)
MARK(s(X)) -> MARK(X)
mark(first(X1, X2)) -> afirst(mark(X1), mark(X2))
mark(from(X)) -> afrom(mark(X))
mark(0) -> 0
mark(nil) -> nil
mark(s(X)) -> s(mark(X))
mark(cons(X1, X2)) -> cons(mark(X1), X2)
afrom(X) -> cons(mark(X), from(s(X)))
afrom(X) -> from(X)
afirst(0, X) -> nil
afirst(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z))
afirst(X1, X2) -> first(X1, X2)
POL(from(x1)) = x1 POL(first(x1, x2)) = x1 + x2 POL(0) = 0 POL(MARK(x1)) = x1 POL(A__FIRST(x1, x2)) = x2 POL(cons(x1, x2)) = x1 POL(nil) = 0 POL(s(x1)) = 1 + x1 POL(mark(x1)) = x1 POL(a__from(x1)) = x1 POL(a__first(x1, x2)) = x1 + x2
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳DGraph
...
→DP Problem 4
↳Polynomial Ordering
MARK(first(X1, X2)) -> MARK(X2)
MARK(first(X1, X2)) -> MARK(X1)
AFIRST(s(X), cons(Y, Z)) -> MARK(Y)
MARK(first(X1, X2)) -> AFIRST(mark(X1), mark(X2))
MARK(cons(X1, X2)) -> MARK(X1)
afirst(0, X) -> nil
afirst(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z))
afirst(X1, X2) -> first(X1, X2)
afrom(X) -> cons(mark(X), from(s(X)))
afrom(X) -> from(X)
mark(first(X1, X2)) -> afirst(mark(X1), mark(X2))
mark(from(X)) -> afrom(mark(X))
mark(0) -> 0
mark(nil) -> nil
mark(s(X)) -> s(mark(X))
mark(cons(X1, X2)) -> cons(mark(X1), X2)
AFIRST(s(X), cons(Y, Z)) -> MARK(Y)
MARK(cons(X1, X2)) -> MARK(X1)
mark(first(X1, X2)) -> afirst(mark(X1), mark(X2))
mark(from(X)) -> afrom(mark(X))
mark(0) -> 0
mark(nil) -> nil
mark(s(X)) -> s(mark(X))
mark(cons(X1, X2)) -> cons(mark(X1), X2)
afrom(X) -> cons(mark(X), from(s(X)))
afrom(X) -> from(X)
afirst(0, X) -> nil
afirst(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z))
afirst(X1, X2) -> first(X1, X2)
POL(from(x1)) = 1 + x1 POL(first(x1, x2)) = x1 + x2 POL(0) = 0 POL(MARK(x1)) = x1 POL(A__FIRST(x1, x2)) = x2 POL(cons(x1, x2)) = 1 + x1 POL(nil) = 0 POL(s(x1)) = 0 POL(mark(x1)) = x1 POL(a__from(x1)) = 1 + x1 POL(a__first(x1, x2)) = x1 + x2
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳DGraph
...
→DP Problem 5
↳Dependency Graph
MARK(first(X1, X2)) -> MARK(X2)
MARK(first(X1, X2)) -> MARK(X1)
MARK(first(X1, X2)) -> AFIRST(mark(X1), mark(X2))
afirst(0, X) -> nil
afirst(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z))
afirst(X1, X2) -> first(X1, X2)
afrom(X) -> cons(mark(X), from(s(X)))
afrom(X) -> from(X)
mark(first(X1, X2)) -> afirst(mark(X1), mark(X2))
mark(from(X)) -> afrom(mark(X))
mark(0) -> 0
mark(nil) -> nil
mark(s(X)) -> s(mark(X))
mark(cons(X1, X2)) -> cons(mark(X1), X2)
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳DGraph
...
→DP Problem 6
↳Polynomial Ordering
MARK(first(X1, X2)) -> MARK(X1)
MARK(first(X1, X2)) -> MARK(X2)
afirst(0, X) -> nil
afirst(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z))
afirst(X1, X2) -> first(X1, X2)
afrom(X) -> cons(mark(X), from(s(X)))
afrom(X) -> from(X)
mark(first(X1, X2)) -> afirst(mark(X1), mark(X2))
mark(from(X)) -> afrom(mark(X))
mark(0) -> 0
mark(nil) -> nil
mark(s(X)) -> s(mark(X))
mark(cons(X1, X2)) -> cons(mark(X1), X2)
MARK(first(X1, X2)) -> MARK(X1)
MARK(first(X1, X2)) -> MARK(X2)
POL(MARK(x1)) = x1 POL(first(x1, x2)) = 1 + x1 + x2
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳DGraph
...
→DP Problem 7
↳Dependency Graph
afirst(0, X) -> nil
afirst(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z))
afirst(X1, X2) -> first(X1, X2)
afrom(X) -> cons(mark(X), from(s(X)))
afrom(X) -> from(X)
mark(first(X1, X2)) -> afirst(mark(X1), mark(X2))
mark(from(X)) -> afrom(mark(X))
mark(0) -> 0
mark(nil) -> nil
mark(s(X)) -> s(mark(X))
mark(cons(X1, X2)) -> cons(mark(X1), X2)