YES(?,O(n^1))

Problem:
 a(a(a(x1))) -> a(c(a(a(x1))))
 c(c(c(x1))) -> a(x1)
 a(x1) -> x1

Proof:
 RT Transformation Processor:
  strict:
   a(a(a(x1))) -> a(c(a(a(x1))))
   c(c(c(x1))) -> a(x1)
   a(x1) -> x1
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   interpretation:
    [c](x0) = x0 + 6,
    
    [a](x0) = x0 + 2
   orientation:
    a(a(a(x1))) = x1 + 6 >= x1 + 12 = a(c(a(a(x1))))
    
    c(c(c(x1))) = x1 + 18 >= x1 + 2 = a(x1)
    
    a(x1) = x1 + 2 >= x1 = x1
   problem:
    strict:
     a(a(a(x1))) -> a(c(a(a(x1))))
    weak:
     c(c(c(x1))) -> a(x1)
     a(x1) -> x1
   Arctic Interpretation Processor:
    dimension: 2
    interpretation:
               [2  1 ]  
     [c](x0) = [0  -&]x0,
     
               [0 2]  
     [a](x0) = [0 3]x0
    orientation:
                   [5 8]      [4 7]                   
     a(a(a(x1))) = [6 9]x1 >= [5 8]x1 = a(c(a(a(x1))))
     
                   [6 5]      [0 2]          
     c(c(c(x1))) = [4 3]x1 >= [0 3]x1 = a(x1)
     
             [0 2]             
     a(x1) = [0 3]x1 >= x1 = x1
    problem:
     strict:
      
     weak:
      a(a(a(x1))) -> a(c(a(a(x1))))
      c(c(c(x1))) -> a(x1)
      a(x1) -> x1
    Qed