YES

We show the termination of the TRS R:

  f(x,y) -> h(x,y)
  f(x,y) -> h(y,x)
  h(x,x) -> x

-- SCC decomposition.

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

p1: f#(x,y) -> h#(x,y)
p2: f#(x,y) -> h#(y,x)

and R consists of:

r1: f(x,y) -> h(x,y)
r2: f(x,y) -> h(y,x)
r3: h(x,x) -> x

The estimated dependency graph contains the following SCCs:

  (no SCCs)