YES

TRS:

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

max/plus interpretations on N:

  a_A(x1,x2) = max{21, 1 + x1, 9 + x2}
  a#_A(x1,x2) = max{21, 1 + x1, 9 + x2}
  0_A = 4
  0#_A = 4
  c_A(x1) = max{32, 3 + x1}
  c#_A(x1) = max{32, 3 + x1}

precedence:

  c > a > 0