R
↳Dependency Pair Analysis
F(g(X)) -> F(f(X))
F(g(X)) -> F(X)
R
↳DPs
→DP Problem 1
↳Narrowing Transformation
F(g(X)) -> F(X)
F(g(X)) -> F(f(X))
f(g(X)) -> g(f(f(X)))
f(h(X)) -> h(g(X))
two new Dependency Pairs are created:
F(g(X)) -> F(f(X))
F(g(g(X''))) -> F(g(f(f(X''))))
F(g(h(X''))) -> F(h(g(X'')))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳Argument Filtering and Ordering
F(g(g(X''))) -> F(g(f(f(X''))))
F(g(X)) -> F(X)
f(g(X)) -> g(f(f(X)))
f(h(X)) -> h(g(X))
F(g(g(X''))) -> F(g(f(f(X''))))
F(g(X)) -> F(X)
f(g(X)) -> g(f(f(X)))
f(h(X)) -> h(g(X))
POL(g(x1)) = 1 + x1 POL(h) = 0 POL(F(x1)) = 1 + x1 POL(f(x1)) = x1
F(x1) -> F(x1)
g(x1) -> g(x1)
f(x1) -> f(x1)
h(x1) -> h
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳AFS
...
→DP Problem 3
↳Dependency Graph
f(g(X)) -> g(f(f(X)))
f(h(X)) -> h(g(X))