R
↳Dependency Pair Analysis
IMPLIES(false, y) -> NOT(false)
IMPLIES(x, false) -> NOT(x)
IMPLIES(not(x), not(y)) -> IMPLIES(y, and(x, y))
IMPLIES(not(x), not(y)) -> AND(x, y)
R
↳DPs
→DP Problem 1
↳Argument Filtering and Ordering
IMPLIES(not(x), not(y)) -> IMPLIES(y, and(x, y))
and(x, false) -> false
and(x, not(false)) -> x
not(not(x)) -> x
implies(false, y) -> not(false)
implies(x, false) -> not(x)
implies(not(x), not(y)) -> implies(y, and(x, y))
IMPLIES(not(x), not(y)) -> IMPLIES(y, and(x, y))
and(x, false) -> false
and(x, not(false)) -> x
not(not(x)) -> x
implies(false, y) -> not(false)
implies(x, false) -> not(x)
implies(not(x), not(y)) -> implies(y, and(x, y))
POL(false) = 0 POL(implies(x1, x2)) = 1 + x1 + x2 POL(not(x1)) = 1 + x1 POL(IMPLIES(x1, x2)) = x1 + x2
IMPLIES(x1, x2) -> IMPLIES(x1, x2)
not(x1) -> not(x1)
and(x1, x2) -> x1
implies(x1, x2) -> implies(x1, x2)
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳Dependency Graph
and(x, false) -> false
and(x, not(false)) -> x
not(not(x)) -> x
implies(false, y) -> not(false)
implies(x, false) -> not(x)
implies(not(x), not(y)) -> implies(y, and(x, y))