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
↳Argument Filtering and Ordering
→DP Problem 2
↳Nar
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)
innermost
CHECK(cons(x, y)) -> CHECK(y)
CHECK(cons(x, y)) -> CHECK(x)
CHECK(rest(x)) -> CHECK(x)
CHECK(sent(x)) -> CHECK(x)
trivial
CHECK(x1) -> CHECK(x1)
rest(x1) -> rest(x1)
cons(x1, x2) -> cons(x1, x2)
sent(x1) -> sent(x1)
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 3
↳Dependency Graph
→DP Problem 2
↳Nar
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)
innermost
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳Narrowing Transformation
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)
innermost
three new Dependency Pairs are created:
TOP(sent(x)) -> TOP(check(rest(x)))
TOP(sent(x'')) -> TOP(rest(check(x'')))
TOP(sent(nil)) -> TOP(check(sent(nil)))
TOP(sent(cons(x'', y'))) -> TOP(check(sent(y')))
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳Nar
→DP Problem 4
↳Argument Filtering and Ordering
TOP(sent(cons(x'', y'))) -> TOP(check(sent(y')))
TOP(sent(nil)) -> TOP(check(sent(nil)))
TOP(sent(x'')) -> TOP(rest(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)
innermost
TOP(sent(cons(x'', y'))) -> TOP(check(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)
rest(nil) -> sent(nil)
rest(cons(x, y)) -> sent(y)
{rest, sent}
TOP(x1) -> TOP(x1)
sent(x1) -> sent(x1)
check(x1) -> x1
cons(x1, x2) -> cons(x1, x2)
rest(x1) -> rest(x1)
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳Nar
→DP Problem 4
↳AFS
...
→DP Problem 5
↳Remaining Obligation(s)
TOP(sent(nil)) -> TOP(check(sent(nil)))
TOP(sent(x'')) -> TOP(rest(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)
innermost