R
↳Dependency Pair Analysis
TOP(sent(x)) -> TOP(check(rest(x)))
TOP(sent(x)) -> CHECK(rest(x))
TOP(sent(x)) -> REST(x)
CHECK(sent(x)) -> CHECK(x)
CHECK(rest(x)) -> REST(check(x))
CHECK(rest(x)) -> CHECK(x)
CHECK(cons(x, y)) -> CHECK(x)
CHECK(cons(x, y)) -> CHECK(y)
R
↳DPs
→DP Problem 1
↳Polynomial Ordering
→DP Problem 2
↳Remaining
CHECK(cons(x, y)) -> CHECK(y)
CHECK(cons(x, y)) -> CHECK(x)
CHECK(rest(x)) -> CHECK(x)
CHECK(sent(x)) -> CHECK(x)
top(sent(x)) -> top(check(rest(x)))
rest(nil) -> sent(nil)
rest(cons(x, y)) -> sent(y)
check(sent(x)) -> sent(check(x))
check(rest(x)) -> rest(check(x))
check(cons(x, y)) -> cons(check(x), y)
check(cons(x, y)) -> cons(x, check(y))
check(cons(x, y)) -> cons(x, y)
CHECK(cons(x, y)) -> CHECK(y)
CHECK(cons(x, y)) -> CHECK(x)
top(sent(x)) -> top(check(rest(x)))
check(sent(x)) -> sent(check(x))
check(rest(x)) -> rest(check(x))
check(cons(x, y)) -> cons(check(x), y)
check(cons(x, y)) -> cons(x, check(y))
check(cons(x, y)) -> cons(x, y)
rest(nil) -> sent(nil)
rest(cons(x, y)) -> sent(y)
POL(top(x1)) = 1 POL(rest(x1)) = x1 POL(cons(x1, x2)) = 1 + x1 + x2 POL(check(x1)) = x1 POL(nil) = 0 POL(CHECK(x1)) = x1 POL(sent(x1)) = x1
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 3
↳Polynomial Ordering
→DP Problem 2
↳Remaining
CHECK(rest(x)) -> CHECK(x)
CHECK(sent(x)) -> CHECK(x)
top(sent(x)) -> top(check(rest(x)))
rest(nil) -> sent(nil)
rest(cons(x, y)) -> sent(y)
check(sent(x)) -> sent(check(x))
check(rest(x)) -> rest(check(x))
check(cons(x, y)) -> cons(check(x), y)
check(cons(x, y)) -> cons(x, check(y))
check(cons(x, y)) -> cons(x, y)
CHECK(rest(x)) -> CHECK(x)
top(sent(x)) -> top(check(rest(x)))
check(sent(x)) -> sent(check(x))
check(rest(x)) -> rest(check(x))
check(cons(x, y)) -> cons(check(x), y)
check(cons(x, y)) -> cons(x, check(y))
check(cons(x, y)) -> cons(x, y)
rest(nil) -> sent(nil)
rest(cons(x, y)) -> sent(y)
POL(top(x1)) = 0 POL(rest(x1)) = 1 + x1 POL(cons(x1, x2)) = x2 POL(check(x1)) = x1 POL(nil) = 0 POL(CHECK(x1)) = x1 POL(sent(x1)) = x1
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 3
↳Polo
...
→DP Problem 4
↳Polynomial Ordering
→DP Problem 2
↳Remaining
CHECK(sent(x)) -> CHECK(x)
top(sent(x)) -> top(check(rest(x)))
rest(nil) -> sent(nil)
rest(cons(x, y)) -> sent(y)
check(sent(x)) -> sent(check(x))
check(rest(x)) -> rest(check(x))
check(cons(x, y)) -> cons(check(x), y)
check(cons(x, y)) -> cons(x, check(y))
check(cons(x, y)) -> cons(x, y)
CHECK(sent(x)) -> CHECK(x)
top(sent(x)) -> top(check(rest(x)))
check(sent(x)) -> sent(check(x))
check(rest(x)) -> rest(check(x))
check(cons(x, y)) -> cons(check(x), y)
check(cons(x, y)) -> cons(x, check(y))
check(cons(x, y)) -> cons(x, y)
rest(nil) -> sent(nil)
rest(cons(x, y)) -> sent(y)
POL(top(x1)) = 0 POL(rest(x1)) = 1 + x1 POL(cons(x1, x2)) = x2 POL(check(x1)) = x1 POL(nil) = 0 POL(CHECK(x1)) = x1 POL(sent(x1)) = 1 + x1
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 3
↳Polo
...
→DP Problem 5
↳Dependency Graph
→DP Problem 2
↳Remaining
top(sent(x)) -> top(check(rest(x)))
rest(nil) -> sent(nil)
rest(cons(x, y)) -> sent(y)
check(sent(x)) -> sent(check(x))
check(rest(x)) -> rest(check(x))
check(cons(x, y)) -> cons(check(x), y)
check(cons(x, y)) -> cons(x, check(y))
check(cons(x, y)) -> cons(x, y)
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Remaining Obligation(s)
TOP(sent(x)) -> TOP(check(rest(x)))
top(sent(x)) -> top(check(rest(x)))
rest(nil) -> sent(nil)
rest(cons(x, y)) -> sent(y)
check(sent(x)) -> sent(check(x))
check(rest(x)) -> rest(check(x))
check(cons(x, y)) -> cons(check(x), y)
check(cons(x, y)) -> cons(x, check(y))
check(cons(x, y)) -> cons(x, y)