YES

TRS:

  c(c(c(a(x,y)))) -> b(c(c(c(c(y)))),x)
  c(c(b(c(y),0()))) -> a(0(),c(c(a(y,0()))))
  c(c(a(a(y,0()),x))) -> c(y)

max/plus interpretations on N:

  c_A(x1) = max{53, 13 + x1}
  c#_A(x1) = max{53, 13 + x1}
  a_A(x1,x2) = max{62, x1, 19 + x2}
  a#_A(x1,x2) = max{62, x1, 19 + x2}
  b_A(x1,x2) = max{80, 6 + x1, 38 + x2}
  b#_A(x1,x2) = max{80, 6 + x1, 38 + x2}
  0_A = 44
  0#_A = 44

precedence:

  c > a > b > 0