MAYBE

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

Proof:
 RT Transformation Processor:
  strict:
   b(a(x1)) -> a(a(d(x1)))
   a(c(x1)) -> b(b(x1))
   d(a(b(x1))) -> b(d(d(c(x1))))
   d(x1) -> a(x1)
   b(a(c(a(x1)))) -> x1
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   interpretation:
    [c](x0) = x0 + 16,
    
    [d](x0) = x0 + 7,
    
    [b](x0) = x0 + 9,
    
    [a](x0) = x0
   orientation:
    b(a(x1)) = x1 + 9 >= x1 + 7 = a(a(d(x1)))
    
    a(c(x1)) = x1 + 16 >= x1 + 18 = b(b(x1))
    
    d(a(b(x1))) = x1 + 16 >= x1 + 39 = b(d(d(c(x1))))
    
    d(x1) = x1 + 7 >= x1 = a(x1)
    
    b(a(c(a(x1)))) = x1 + 25 >= x1 = x1
   problem:
    strict:
     a(c(x1)) -> b(b(x1))
     d(a(b(x1))) -> b(d(d(c(x1))))
    weak:
     b(a(x1)) -> a(a(d(x1)))
     d(x1) -> a(x1)
     b(a(c(a(x1)))) -> x1
   Matrix Interpretation Processor:
    dimension: 1
    interpretation:
     [c](x0) = x0 + 4,
     
     [d](x0) = x0,
     
     [b](x0) = x0,
     
     [a](x0) = x0
    orientation:
     a(c(x1)) = x1 + 4 >= x1 = b(b(x1))
     
     d(a(b(x1))) = x1 >= x1 + 4 = b(d(d(c(x1))))
     
     b(a(x1)) = x1 >= x1 = a(a(d(x1)))
     
     d(x1) = x1 >= x1 = a(x1)
     
     b(a(c(a(x1)))) = x1 + 4 >= x1 = x1
    problem:
     strict:
      d(a(b(x1))) -> b(d(d(c(x1))))
     weak:
      a(c(x1)) -> b(b(x1))
      b(a(x1)) -> a(a(d(x1)))
      d(x1) -> a(x1)
      b(a(c(a(x1)))) -> x1
    Open