R
↳Dependency Pair Analysis
F(a, h(x)) -> F(g(x), h(x))
F(a, h(x)) -> G(x)
H(g(x)) -> H(a)
G(h(x)) -> G(x)
R
↳DPs
→DP Problem 1
↳Argument Filtering and Ordering
→DP Problem 2
↳Remaining
G(h(x)) -> G(x)
f(a, h(x)) -> f(g(x), h(x))
h(g(x)) -> h(a)
h(h(x)) -> x
g(h(x)) -> g(x)
G(h(x)) -> G(x)
f(a, h(x)) -> f(g(x), h(x))
h(g(x)) -> h(a)
h(h(x)) -> x
g(h(x)) -> g(x)
POL(g) = 0 POL(G(x1)) = x1 POL(h(x1)) = 1 + x1 POL(a) = 0 POL(f(x1, x2)) = x1 + x2
G(x1) -> G(x1)
h(x1) -> h(x1)
f(x1, x2) -> f(x1, x2)
g(x1) -> g
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 3
↳Dependency Graph
→DP Problem 2
↳Remaining
f(a, h(x)) -> f(g(x), h(x))
h(g(x)) -> h(a)
h(h(x)) -> x
g(h(x)) -> g(x)
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳Remaining Obligation(s)
F(a, h(x)) -> F(g(x), h(x))
f(a, h(x)) -> f(g(x), h(x))
h(g(x)) -> h(a)
h(h(x)) -> x
g(h(x)) -> g(x)