MAYBE

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

Proof:
 RT Transformation Processor:
  strict:
   a(a(x1)) -> b(b(b(x1)))
   a(x1) -> d(c(d(x1)))
   b(b(x1)) -> c(c(c(x1)))
   c(c(x1)) -> d(d(d(x1)))
   c(d(d(x1))) -> a(x1)
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   interpretation:
    [c](x0) = x0 + 4,
    
    [d](x0) = x0 + 12,
    
    [b](x0) = x0 + 4,
    
    [a](x0) = x0 + 16
   orientation:
    a(a(x1)) = x1 + 32 >= x1 + 12 = b(b(b(x1)))
    
    a(x1) = x1 + 16 >= x1 + 28 = d(c(d(x1)))
    
    b(b(x1)) = x1 + 8 >= x1 + 12 = c(c(c(x1)))
    
    c(c(x1)) = x1 + 8 >= x1 + 36 = d(d(d(x1)))
    
    c(d(d(x1))) = x1 + 28 >= x1 + 16 = a(x1)
   problem:
    strict:
     a(x1) -> d(c(d(x1)))
     b(b(x1)) -> c(c(c(x1)))
     c(c(x1)) -> d(d(d(x1)))
    weak:
     a(a(x1)) -> b(b(b(x1)))
     c(d(d(x1))) -> a(x1)
   Matrix Interpretation Processor:
    dimension: 1
    interpretation:
     [c](x0) = x0 + 15,
     
     [d](x0) = x0 + 6,
     
     [b](x0) = x0 + 4,
     
     [a](x0) = x0 + 12
    orientation:
     a(x1) = x1 + 12 >= x1 + 27 = d(c(d(x1)))
     
     b(b(x1)) = x1 + 8 >= x1 + 45 = c(c(c(x1)))
     
     c(c(x1)) = x1 + 30 >= x1 + 18 = d(d(d(x1)))
     
     a(a(x1)) = x1 + 24 >= x1 + 12 = b(b(b(x1)))
     
     c(d(d(x1))) = x1 + 27 >= x1 + 12 = a(x1)
    problem:
     strict:
      a(x1) -> d(c(d(x1)))
      b(b(x1)) -> c(c(c(x1)))
     weak:
      c(c(x1)) -> d(d(d(x1)))
      a(a(x1)) -> b(b(b(x1)))
      c(d(d(x1))) -> a(x1)
    Matrix Interpretation Processor:
     dimension: 1
     interpretation:
      [c](x0) = x0 + 9,
      
      [d](x0) = x0 + 6,
      
      [b](x0) = x0 + 14,
      
      [a](x0) = x0 + 21
     orientation:
      a(x1) = x1 + 21 >= x1 + 21 = d(c(d(x1)))
      
      b(b(x1)) = x1 + 28 >= x1 + 27 = c(c(c(x1)))
      
      c(c(x1)) = x1 + 18 >= x1 + 18 = d(d(d(x1)))
      
      a(a(x1)) = x1 + 42 >= x1 + 42 = b(b(b(x1)))
      
      c(d(d(x1))) = x1 + 21 >= x1 + 21 = a(x1)
     problem:
      strict:
       a(x1) -> d(c(d(x1)))
      weak:
       b(b(x1)) -> c(c(c(x1)))
       c(c(x1)) -> d(d(d(x1)))
       a(a(x1)) -> b(b(b(x1)))
       c(d(d(x1))) -> a(x1)
     Open