MAYBE

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

Proof:
 RT Transformation Processor:
  strict:
   a(x1) -> x1
   a(x1) -> b(c(x1))
   b(b(x1)) -> a(a(x1))
   c(c(c(x1))) -> b(x1)
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   interpretation:
    [b](x0) = x0 + 3,
    
    [c](x0) = x0,
    
    [a](x0) = x0 + 8
   orientation:
    a(x1) = x1 + 8 >= x1 = x1
    
    a(x1) = x1 + 8 >= x1 + 3 = b(c(x1))
    
    b(b(x1)) = x1 + 6 >= x1 + 16 = a(a(x1))
    
    c(c(c(x1))) = x1 >= x1 + 3 = b(x1)
   problem:
    strict:
     b(b(x1)) -> a(a(x1))
     c(c(c(x1))) -> b(x1)
    weak:
     a(x1) -> x1
     a(x1) -> b(c(x1))
   Matrix Interpretation Processor:
    dimension: 1
    interpretation:
     [b](x0) = x0 + 5,
     
     [c](x0) = x0 + 3,
     
     [a](x0) = x0 + 12
    orientation:
     b(b(x1)) = x1 + 10 >= x1 + 24 = a(a(x1))
     
     c(c(c(x1))) = x1 + 9 >= x1 + 5 = b(x1)
     
     a(x1) = x1 + 12 >= x1 = x1
     
     a(x1) = x1 + 12 >= x1 + 8 = b(c(x1))
    problem:
     strict:
      b(b(x1)) -> a(a(x1))
     weak:
      c(c(c(x1))) -> b(x1)
      a(x1) -> x1
      a(x1) -> b(c(x1))
    Open