MAYBE

Problem:
 a(0(),b(0(),x)) -> b(0(),a(0(),x))
 a(0(),x) -> b(0(),b(0(),x))
 a(0(),a(1(),a(x,y))) -> a(1(),a(0(),a(x,y)))
 b(0(),a(1(),a(x,y))) -> b(1(),a(0(),a(x,y)))
 a(0(),a(x,y)) -> a(1(),a(1(),a(x,y)))

Proof:
 RT Transformation Processor:
  strict:
   a(0(),b(0(),x)) -> b(0(),a(0(),x))
   a(0(),x) -> b(0(),b(0(),x))
   a(0(),a(1(),a(x,y))) -> a(1(),a(0(),a(x,y)))
   b(0(),a(1(),a(x,y))) -> b(1(),a(0(),a(x,y)))
   a(0(),a(x,y)) -> a(1(),a(1(),a(x,y)))
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   interpretation:
    [1] = 4,
    
    [a](x0, x1) = x0 + x1 + 12,
    
    [b](x0, x1) = x0 + x1,
    
    [0] = 21
   orientation:
    a(0(),b(0(),x)) = x + 54 >= x + 54 = b(0(),a(0(),x))
    
    a(0(),x) = x + 33 >= x + 42 = b(0(),b(0(),x))
    
    a(0(),a(1(),a(x,y))) = x + y + 61 >= x + y + 61 = a(1(),a(0(),a(x,y)))
    
    b(0(),a(1(),a(x,y))) = x + y + 49 >= x + y + 49 = b(1(),a(0(),a(x,y)))
    
    a(0(),a(x,y)) = x + y + 45 >= x + y + 44 = a(1(),a(1(),a(x,y)))
   problem:
    strict:
     a(0(),b(0(),x)) -> b(0(),a(0(),x))
     a(0(),x) -> b(0(),b(0(),x))
     a(0(),a(1(),a(x,y))) -> a(1(),a(0(),a(x,y)))
     b(0(),a(1(),a(x,y))) -> b(1(),a(0(),a(x,y)))
    weak:
     a(0(),a(x,y)) -> a(1(),a(1(),a(x,y)))
   Open