YES(?,O(n^1))

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

Proof:
 RT Transformation Processor:
  strict:
   c(c(c(a(x1)))) -> d(d(x1))
   d(b(x1)) -> c(c(x1))
   c(x1) -> a(a(a(a(x1))))
   d(x1) -> b(b(b(b(x1))))
   b(d(x1)) -> c(c(x1))
   a(c(c(c(x1)))) -> d(d(x1))
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   interpretation:
    [b](x0) = x0 + 3,
    
    [d](x0) = x0 + 1,
    
    [c](x0) = x0 + 1,
    
    [a](x0) = x0
   orientation:
    c(c(c(a(x1)))) = x1 + 3 >= x1 + 2 = d(d(x1))
    
    d(b(x1)) = x1 + 4 >= x1 + 2 = c(c(x1))
    
    c(x1) = x1 + 1 >= x1 = a(a(a(a(x1))))
    
    d(x1) = x1 + 1 >= x1 + 12 = b(b(b(b(x1))))
    
    b(d(x1)) = x1 + 4 >= x1 + 2 = c(c(x1))
    
    a(c(c(c(x1)))) = x1 + 3 >= x1 + 2 = d(d(x1))
   problem:
    strict:
     d(x1) -> b(b(b(b(x1))))
    weak:
     c(c(c(a(x1)))) -> d(d(x1))
     d(b(x1)) -> c(c(x1))
     c(x1) -> a(a(a(a(x1))))
     b(d(x1)) -> c(c(x1))
     a(c(c(c(x1)))) -> d(d(x1))
   Matrix Interpretation Processor:
    dimension: 1
    interpretation:
     [b](x0) = x0 + 6,
     
     [d](x0) = x0 + 26,
     
     [c](x0) = x0 + 16,
     
     [a](x0) = x0 + 4
    orientation:
     d(x1) = x1 + 26 >= x1 + 24 = b(b(b(b(x1))))
     
     c(c(c(a(x1)))) = x1 + 52 >= x1 + 52 = d(d(x1))
     
     d(b(x1)) = x1 + 32 >= x1 + 32 = c(c(x1))
     
     c(x1) = x1 + 16 >= x1 + 16 = a(a(a(a(x1))))
     
     b(d(x1)) = x1 + 32 >= x1 + 32 = c(c(x1))
     
     a(c(c(c(x1)))) = x1 + 52 >= x1 + 52 = d(d(x1))
    problem:
     strict:
      
     weak:
      d(x1) -> b(b(b(b(x1))))
      c(c(c(a(x1)))) -> d(d(x1))
      d(b(x1)) -> c(c(x1))
      c(x1) -> a(a(a(a(x1))))
      b(d(x1)) -> c(c(x1))
      a(c(c(c(x1)))) -> d(d(x1))
    Qed