MAYBE

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

Proof:
 RT Transformation Processor:
  strict:
   a(b(x1)) -> b(r(x1))
   r(a(x1)) -> d(r(x1))
   r(x1) -> d(x1)
   d(a(x1)) -> a(a(d(x1)))
   d(x1) -> a(x1)
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   interpretation:
    [d](x0) = x0 + 1,
    
    [r](x0) = x0 + 28,
    
    [a](x0) = x0,
    
    [b](x0) = x0
   orientation:
    a(b(x1)) = x1 >= x1 + 28 = b(r(x1))
    
    r(a(x1)) = x1 + 28 >= x1 + 29 = d(r(x1))
    
    r(x1) = x1 + 28 >= x1 + 1 = d(x1)
    
    d(a(x1)) = x1 + 1 >= x1 + 1 = a(a(d(x1)))
    
    d(x1) = x1 + 1 >= x1 = a(x1)
   problem:
    strict:
     a(b(x1)) -> b(r(x1))
     r(a(x1)) -> d(r(x1))
     d(a(x1)) -> a(a(d(x1)))
    weak:
     r(x1) -> d(x1)
     d(x1) -> a(x1)
   Open