R
↳Dependency Pair Analysis
MINUS(s(X), s(Y)) -> P(minus(X, Y))
MINUS(s(X), s(Y)) -> MINUS(X, Y)
DIV(s(X), s(Y)) -> DIV(minus(X, Y), s(Y))
DIV(s(X), s(Y)) -> MINUS(X, Y)
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↳DPs
→DP Problem 1
↳Polynomial Ordering
→DP Problem 2
↳Polo
MINUS(s(X), s(Y)) -> MINUS(X, Y)
minus(X, 0) -> X
minus(s(X), s(Y)) -> p(minus(X, Y))
p(s(X)) -> X
div(0, s(Y)) -> 0
div(s(X), s(Y)) -> s(div(minus(X, Y), s(Y)))
MINUS(s(X), s(Y)) -> MINUS(X, Y)
minus(X, 0) -> X
minus(s(X), s(Y)) -> p(minus(X, Y))
p(s(X)) -> X
div(0, s(Y)) -> 0
div(s(X), s(Y)) -> s(div(minus(X, Y), s(Y)))
POL(0) = 0 POL(minus(x1, x2)) = x1 POL(MINUS(x1, x2)) = 1 + x1 POL(s(x1)) = 1 + x1 POL(div(x1, x2)) = x1 POL(p(x1)) = x1
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 3
↳Dependency Graph
→DP Problem 2
↳Polo
minus(X, 0) -> X
minus(s(X), s(Y)) -> p(minus(X, Y))
p(s(X)) -> X
div(0, s(Y)) -> 0
div(s(X), s(Y)) -> s(div(minus(X, Y), s(Y)))
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polynomial Ordering
DIV(s(X), s(Y)) -> DIV(minus(X, Y), s(Y))
minus(X, 0) -> X
minus(s(X), s(Y)) -> p(minus(X, Y))
p(s(X)) -> X
div(0, s(Y)) -> 0
div(s(X), s(Y)) -> s(div(minus(X, Y), s(Y)))
DIV(s(X), s(Y)) -> DIV(minus(X, Y), s(Y))
minus(X, 0) -> X
minus(s(X), s(Y)) -> p(minus(X, Y))
p(s(X)) -> X
div(0, s(Y)) -> 0
div(s(X), s(Y)) -> s(div(minus(X, Y), s(Y)))
POL(0) = 0 POL(DIV(x1, x2)) = 1 + x1 POL(minus(x1, x2)) = x1 POL(s(x1)) = 1 + x1 POL(div(x1, x2)) = x1 POL(p(x1)) = x1
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 4
↳Dependency Graph
minus(X, 0) -> X
minus(s(X), s(Y)) -> p(minus(X, Y))
p(s(X)) -> X
div(0, s(Y)) -> 0
div(s(X), s(Y)) -> s(div(minus(X, Y), s(Y)))