MAYBE

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

Proof:
 RT Transformation Processor:
  strict:
   a(a(x1)) -> b(b(x1))
   c(c(b(x1))) -> d(c(a(x1)))
   a(x1) -> d(c(c(x1)))
   c(d(x1)) -> b(c(x1))
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   interpretation:
    [d](x0) = x0 + 6,
    
    [c](x0) = x0,
    
    [b](x0) = x0 + 21,
    
    [a](x0) = x0 + 4
   orientation:
    a(a(x1)) = x1 + 8 >= x1 + 42 = b(b(x1))
    
    c(c(b(x1))) = x1 + 21 >= x1 + 10 = d(c(a(x1)))
    
    a(x1) = x1 + 4 >= x1 + 6 = d(c(c(x1)))
    
    c(d(x1)) = x1 + 6 >= x1 + 21 = b(c(x1))
   problem:
    strict:
     a(a(x1)) -> b(b(x1))
     a(x1) -> d(c(c(x1)))
     c(d(x1)) -> b(c(x1))
    weak:
     c(c(b(x1))) -> d(c(a(x1)))
   Matrix Interpretation Processor:
    dimension: 1
    interpretation:
     [d](x0) = x0 + 9,
     
     [c](x0) = x0 + 12,
     
     [b](x0) = x0 + 17,
     
     [a](x0) = x0 + 20
    orientation:
     a(a(x1)) = x1 + 40 >= x1 + 34 = b(b(x1))
     
     a(x1) = x1 + 20 >= x1 + 33 = d(c(c(x1)))
     
     c(d(x1)) = x1 + 21 >= x1 + 29 = b(c(x1))
     
     c(c(b(x1))) = x1 + 41 >= x1 + 41 = d(c(a(x1)))
    problem:
     strict:
      a(x1) -> d(c(c(x1)))
      c(d(x1)) -> b(c(x1))
     weak:
      a(a(x1)) -> b(b(x1))
      c(c(b(x1))) -> d(c(a(x1)))
    Matrix Interpretation Processor:
     dimension: 1
     interpretation:
      [d](x0) = x0 + 15,
      
      [c](x0) = x0 + 16,
      
      [b](x0) = x0 + 6,
      
      [a](x0) = x0 + 7
     orientation:
      a(x1) = x1 + 7 >= x1 + 47 = d(c(c(x1)))
      
      c(d(x1)) = x1 + 31 >= x1 + 22 = b(c(x1))
      
      a(a(x1)) = x1 + 14 >= x1 + 12 = b(b(x1))
      
      c(c(b(x1))) = x1 + 38 >= x1 + 38 = d(c(a(x1)))
     problem:
      strict:
       a(x1) -> d(c(c(x1)))
      weak:
       c(d(x1)) -> b(c(x1))
       a(a(x1)) -> b(b(x1))
       c(c(b(x1))) -> d(c(a(x1)))
     Open