YES(?,O(n^3))

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

Proof:
 RT Transformation Processor:
  strict:
   b(x,y) -> c(a(c(y),a(0(),x)))
   a(y,x) -> y
   a(y,c(b(a(0(),x),0()))) -> b(a(c(b(0(),y)),x),0())
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   interpretation:
    [a](x0, x1) = x0 + x1 + 1,
    
    [0] = 16,
    
    [c](x0) = x0 + 3,
    
    [b](x0, x1) = x0 + x1
   orientation:
    b(x,y) = x + y >= x + y + 24 = c(a(c(y),a(0(),x)))
    
    a(y,x) = x + y + 1 >= y = y
    
    a(y,c(b(a(0(),x),0()))) = x + y + 37 >= x + y + 36 = b(a(c(b(0(),y)),x),0())
   problem:
    strict:
     b(x,y) -> c(a(c(y),a(0(),x)))
    weak:
     a(y,x) -> y
     a(y,c(b(a(0(),x),0()))) -> b(a(c(b(0(),y)),x),0())
   Matrix Interpretation Processor:
    dimension: 3
    interpretation:
                   [1 0 0]     [1 0 0]     [0]
     [a](x0, x1) = [0 1 2]x0 + [0 0 0]x1 + [0]
                   [0 0 1]     [0 0 0]     [4],
     
           [0]
     [0] = [0]
           [4],
     
               [1 0 0]  
     [c](x0) = [0 0 0]x0
               [0 0 0]  ,
     
                   [1 1 0]     [1 0 0]     [1]
     [b](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0]
                   [0 0 1]     [0 0 0]     [0]
    orientation:
              [1 1 0]    [1 0 0]    [1]    [1 0 0]    [1 0 0]                       
     b(x,y) = [0 0 0]x + [0 0 0]y + [0] >= [0 0 0]x + [0 0 0]y = c(a(c(y),a(0(),x)))
              [0 0 1]    [0 0 0]    [0]    [0 0 0]    [0 0 0]                       
     
              [1 0 0]    [1 0 0]    [0]         
     a(y,x) = [0 0 0]x + [0 1 2]y + [0] >= y = y
              [0 0 0]    [0 0 1]    [4]         
     
                               [1 0 0]    [1 0 0]    [9]    [1 0 0]    [1 0 0]    [2]                          
     a(y,c(b(a(0(),x),0()))) = [0 0 0]x + [0 1 2]y + [0] >= [0 0 0]x + [0 0 0]y + [0] = b(a(c(b(0(),y)),x),0())
                               [0 0 0]    [0 0 1]    [4]    [0 0 0]    [0 0 0]    [4]                          
    problem:
     strict:
      
     weak:
      b(x,y) -> c(a(c(y),a(0(),x)))
      a(y,x) -> y
      a(y,c(b(a(0(),x),0()))) -> b(a(c(b(0(),y)),x),0())
    Qed