YES

We show the termination of the TRS R:

  f(a(),b()) -> f(a(),c())
  f(c(),d()) -> f(b(),d())

-- SCC decomposition.

Consider the dependency pair problem (P, R), where P consists of

p1: f#(a(),b()) -> f#(a(),c())
p2: f#(c(),d()) -> f#(b(),d())

and R consists of:

r1: f(a(),b()) -> f(a(),c())
r2: f(c(),d()) -> f(b(),d())

The estimated dependency graph contains the following SCCs:

  (no SCCs)