R
↳Dependency Pair Analysis
F(f(x, a), a) -> F(f(f(x, a), f(a, a)), a)
F(f(x, a), a) -> F(f(x, a), f(a, a))
F(f(x, a), a) -> F(a, a)
R
↳DPs
→DP Problem 1
↳Argument Filtering and Ordering
F(f(x, a), a) -> F(f(x, a), f(a, a))
F(f(x, a), a) -> F(f(f(x, a), f(a, a)), a)
f(f(x, a), a) -> f(f(f(x, a), f(a, a)), a)
innermost
F(f(x, a), a) -> F(f(x, a), f(a, a))
f(f(x, a), a) -> f(f(f(x, a), f(a, a)), a)
a > f
F(x1, x2) -> F(x1, x2)
f(x1, x2) -> f
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳Narrowing Transformation
F(f(x, a), a) -> F(f(f(x, a), f(a, a)), a)
f(f(x, a), a) -> f(f(f(x, a), f(a, a)), a)
innermost
one new Dependency Pair is created:
F(f(x, a), a) -> F(f(f(x, a), f(a, a)), a)
F(f(f(x'', a), a), a) -> F(f(f(f(f(x'', a), f(a, a)), a), f(a, a)), a)