MAYBE

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

Proof:
 RT Transformation Processor:
  strict:
   a(a(x1)) -> b(b(b(x1)))
   b(x1) -> c(c(d(x1)))
   c(x1) -> d(d(d(x1)))
   b(c(x1)) -> c(b(x1))
   b(c(d(x1))) -> a(x1)
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   interpretation:
    [c](x0) = x0 + 9,
    
    [d](x0) = x0 + 5,
    
    [b](x0) = x0 + 1,
    
    [a](x0) = x0 + 16
   orientation:
    a(a(x1)) = x1 + 32 >= x1 + 3 = b(b(b(x1)))
    
    b(x1) = x1 + 1 >= x1 + 23 = c(c(d(x1)))
    
    c(x1) = x1 + 9 >= x1 + 15 = d(d(d(x1)))
    
    b(c(x1)) = x1 + 10 >= x1 + 10 = c(b(x1))
    
    b(c(d(x1))) = x1 + 15 >= x1 + 16 = a(x1)
   problem:
    strict:
     b(x1) -> c(c(d(x1)))
     c(x1) -> d(d(d(x1)))
     b(c(x1)) -> c(b(x1))
     b(c(d(x1))) -> a(x1)
    weak:
     a(a(x1)) -> b(b(b(x1)))
   Matrix Interpretation Processor:
    dimension: 1
    interpretation:
     [c](x0) = x0 + 17,
     
     [d](x0) = x0 + 16,
     
     [b](x0) = x0,
     
     [a](x0) = x0
    orientation:
     b(x1) = x1 >= x1 + 50 = c(c(d(x1)))
     
     c(x1) = x1 + 17 >= x1 + 48 = d(d(d(x1)))
     
     b(c(x1)) = x1 + 17 >= x1 + 17 = c(b(x1))
     
     b(c(d(x1))) = x1 + 33 >= x1 = a(x1)
     
     a(a(x1)) = x1 >= x1 = b(b(b(x1)))
    problem:
     strict:
      b(x1) -> c(c(d(x1)))
      c(x1) -> d(d(d(x1)))
      b(c(x1)) -> c(b(x1))
     weak:
      b(c(d(x1))) -> a(x1)
      a(a(x1)) -> b(b(b(x1)))
    Matrix Interpretation Processor:
     dimension: 1
     interpretation:
      [c](x0) = x0 + 16,
      
      [d](x0) = x0 + 2,
      
      [b](x0) = x0 + 16,
      
      [a](x0) = x0 + 24
     orientation:
      b(x1) = x1 + 16 >= x1 + 34 = c(c(d(x1)))
      
      c(x1) = x1 + 16 >= x1 + 6 = d(d(d(x1)))
      
      b(c(x1)) = x1 + 32 >= x1 + 32 = c(b(x1))
      
      b(c(d(x1))) = x1 + 34 >= x1 + 24 = a(x1)
      
      a(a(x1)) = x1 + 48 >= x1 + 48 = b(b(b(x1)))
     problem:
      strict:
       b(x1) -> c(c(d(x1)))
       b(c(x1)) -> c(b(x1))
      weak:
       c(x1) -> d(d(d(x1)))
       b(c(d(x1))) -> a(x1)
       a(a(x1)) -> b(b(b(x1)))
     Matrix Interpretation Processor:
      dimension: 1
      interpretation:
       [c](x0) = x0 + 4,
       
       [d](x0) = x0 + 1,
       
       [b](x0) = x0 + 10,
       
       [a](x0) = x0 + 15
      orientation:
       b(x1) = x1 + 10 >= x1 + 9 = c(c(d(x1)))
       
       b(c(x1)) = x1 + 14 >= x1 + 14 = c(b(x1))
       
       c(x1) = x1 + 4 >= x1 + 3 = d(d(d(x1)))
       
       b(c(d(x1))) = x1 + 15 >= x1 + 15 = a(x1)
       
       a(a(x1)) = x1 + 30 >= x1 + 30 = b(b(b(x1)))
      problem:
       strict:
        b(c(x1)) -> c(b(x1))
       weak:
        b(x1) -> c(c(d(x1)))
        c(x1) -> d(d(d(x1)))
        b(c(d(x1))) -> a(x1)
        a(a(x1)) -> b(b(b(x1)))
      Open