YES

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

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [c](x0) = 2x0 + 1,
   
   [a](x0, x1) = x0 + 4x1,
   
   [0] = 0
  orientation:
   a(a(y,0()),0()) = y >= y = y
   
   c(c(y)) = 4y + 3 >= y = y
   
   c(a(c(c(y)),x)) = 8x + 8y + 7 >= 8x + 4y + 7 = a(c(c(c(a(x,0())))),y)
  problem:
   a(a(y,0()),0()) -> y
   c(a(c(c(y)),x)) -> a(c(c(c(a(x,0())))),y)
  Bounds Processor:
   bound: 3
   enrichment: match
   automaton:
    final states: {2,1}
    transitions:
     03() -> 148*
     a1(93,17) -> 26,18
     a1(101,59) -> 26*
     a1(69,99) -> 27*
     a1(93,25) -> 27,19
     a1(81,67) -> 17,25
     a1(67,48) -> 90*
     a1(81,79) -> 17,25
     a1(17,48) -> 90*
     a1(85,9) -> 34*
     a1(119,48) -> 144*
     a1(61,4) -> 33*
     a1(79,48) -> 90*
     a1(61,6) -> 25*
     a1(61,8) -> 33*
     a1(59,48) -> 66*
     a1(69,50) -> 43,19,7,27
     a1(61,10) -> 25*
     a1(93,79) -> 26,18
     a1(9,48) -> 66*
     a1(4,48) -> 82*
     a1(93,91) -> 19,27
     a1(52,5) -> 26,18,42,6
     a1(52,9) -> 26,18,42,6
     a1(113,4) -> 99*
     a1(85,59) -> 34*
     a1(113,6) -> 91*
     a1(113,8) -> 99*
     a1(113,10) -> 91*
     a1(81,50) -> 43,19,7,27
     a1(6,48) -> 98*
     a1(1,48) -> 49*
     a1(69,5) -> 43,27,7,16,19,24
     a1(48,48) -> 110*
     a1(69,33) -> 27*
     a1(8,48) -> 82*
     a1(69,41) -> 35*
     a1(3,48) -> 58*
     a1(101,9) -> 26*
     a1(81,5) -> 43,7,16,19,24
     a1(147,4) -> 121*
     a1(147,8) -> 121*
     a1(81,17) -> 25,17
     a1(50,48) -> 78*
     a1(10,48) -> 98*
     a1(5,48) -> 78*
     a1(69,83) -> 35*
     c1(60) -> 61*
     c1(50) -> 51*
     c1(112) -> 113*
     c1(92) -> 93*
     c1(82) -> 83*
     c1(67) -> 68*
     c1(144) -> 145*
     c1(99) -> 100*
     c1(84) -> 85*
     c1(79) -> 80*
     c1(59) -> 60*
     c1(49) -> 50*
     c1(146) -> 147*
     c1(111) -> 112*
     c1(91) -> 92*
     c1(66) -> 67*
     c1(51) -> 52*
     c1(98) -> 99*
     c1(83) -> 84*
     c1(78) -> 79*
     c1(68) -> 69*
     c1(58) -> 59*
     c1(145) -> 146*
     c1(110) -> 111*
     c1(100) -> 101*
     c1(90) -> 91*
     c1(80) -> 81*
     01() -> 48*
     a2(10,119) -> 120*
     a2(131,111) -> 100*
     a2(139,121) -> 93*
     a2(139,129) -> 101*
     a2(4,119) -> 128*
     a2(123,111) -> 92*
     a2(111,119) -> 136*
     a2(6,119) -> 120*
     a2(131,145) -> 122*
     a2(8,119) -> 128*
     c2(137) -> 138*
     c2(122) -> 123*
     c2(129) -> 130*
     c2(136) -> 137*
     c2(121) -> 122*
     c2(138) -> 139*
     c2(128) -> 129*
     c2(130) -> 131*
     c2(120) -> 121*
     f30() -> 1*
     02() -> 119*
     a0(43,9) -> 34*
     a0(8,3) -> 40*
     a0(3,3) -> 8*
     a0(10,3) -> 32*
     a0(35,9) -> 26*
     a0(5,3) -> 16*
     a0(11,4) -> 33*
     a0(11,6) -> 25*
     a0(11,8) -> 33*
     a0(11,10) -> 25*
     a0(17,3) -> 24*
     a0(7,1) -> 2*
     a0(7,5) -> 42,18,6
     a0(7,9) -> 42,26,18,6
     a0(27,17) -> 26,18
     a0(27,25) -> 27,19
     a0(19,5) -> 43,27,19,7
     a0(9,3) -> 16*
     a0(4,3) -> 40*
     a0(19,17) -> 25,17
     a0(19,33) -> 27*
     a0(19,41) -> 35*
     a0(11,1) -> 5*
     a0(6,3) -> 32*
     a0(1,3) -> 4*
     a3(152,129) -> 123*
     a3(145,148) -> 149*
     c0(40) -> 41*
     c0(25) -> 26*
     c0(10) -> 11*
     c0(5) -> 6*
     c0(42) -> 43*
     c0(32) -> 33*
     c0(17) -> 18*
     c0(34) -> 35*
     c0(24) -> 25*
     c0(9) -> 10*
     c0(4) -> 5*
     c0(41) -> 42*
     c0(26) -> 27*
     c0(16) -> 17*
     c0(6) -> 7*
     c0(33) -> 34*
     c0(18) -> 19*
     c0(8) -> 9*
     c3(149) -> 150*
     c3(151) -> 152*
     c3(150) -> 151*
     00() -> 3*
     1 -> 128,82,40,4
     2 -> 5*
     3 -> 128,82,40
     5 -> 41,25,17
     7 -> 24,16
     11 -> 24,16
   problem:
    
   Qed