YES

We show the termination of the TRS R:

  f(c(c(a(),y,a()),b(x,z),a())) -> b(y,f(c(f(a()),z,z)))
  f(b(b(x,f(y)),z)) -> c(z,x,f(b(b(f(a()),y),y)))
  c(b(a(),a()),b(y,z),x) -> b(a(),b(z,z))

-- SCC decomposition.

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

p1: f#(c(c(a(),y,a()),b(x,z),a())) -> f#(c(f(a()),z,z))
p2: f#(c(c(a(),y,a()),b(x,z),a())) -> c#(f(a()),z,z)
p3: f#(c(c(a(),y,a()),b(x,z),a())) -> f#(a())
p4: f#(b(b(x,f(y)),z)) -> c#(z,x,f(b(b(f(a()),y),y)))
p5: f#(b(b(x,f(y)),z)) -> f#(b(b(f(a()),y),y))
p6: f#(b(b(x,f(y)),z)) -> f#(a())

and R consists of:

r1: f(c(c(a(),y,a()),b(x,z),a())) -> b(y,f(c(f(a()),z,z)))
r2: f(b(b(x,f(y)),z)) -> c(z,x,f(b(b(f(a()),y),y)))
r3: c(b(a(),a()),b(y,z),x) -> b(a(),b(z,z))

The estimated dependency graph contains the following SCCs:

  {p5}


-- Reduction pair.

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

p1: f#(b(b(x,f(y)),z)) -> f#(b(b(f(a()),y),y))

and R consists of:

r1: f(c(c(a(),y,a()),b(x,z),a())) -> b(y,f(c(f(a()),z,z)))
r2: f(b(b(x,f(y)),z)) -> c(z,x,f(b(b(f(a()),y),y)))
r3: c(b(a(),a()),b(y,z),x) -> b(a(),b(z,z))

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  weighted path order
  
    base order:
  
      max/plus interpretations on natural numbers:
      
        f#_A(x1) = x1 + 36
        b_A(x1,x2) = max{x1 - 4, x2 + 6}
        f_A(x1) = max{19, x1 + 14}
        a_A = 13
  
    precedence:
    
      f# = b = f = a
    
    partial status:
  
      pi(f#) = []
      pi(b) = []
      pi(f) = [1]
      pi(a) = []

The next rules are strictly ordered:

  p1

We remove them from the problem.  Then no dependency pair remains.