MAYBE

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

Proof:
 RT Transformation Processor:
  strict:
   a(x1) -> x1
   a(x1) -> b(x1)
   a(b(x1)) -> b(a(c(x1)))
   b(x1) -> x1
   c(c(x1)) -> a(x1)
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   interpretation:
    [c](x0) = x0 + 18,
    
    [b](x0) = x0,
    
    [a](x0) = x0 + 30
   orientation:
    a(x1) = x1 + 30 >= x1 = x1
    
    a(x1) = x1 + 30 >= x1 = b(x1)
    
    a(b(x1)) = x1 + 30 >= x1 + 48 = b(a(c(x1)))
    
    b(x1) = x1 >= x1 = x1
    
    c(c(x1)) = x1 + 36 >= x1 + 30 = a(x1)
   problem:
    strict:
     a(b(x1)) -> b(a(c(x1)))
     b(x1) -> x1
    weak:
     a(x1) -> x1
     a(x1) -> b(x1)
     c(c(x1)) -> a(x1)
   Matrix Interpretation Processor:
    dimension: 1
    interpretation:
     [c](x0) = x0 + 6,
     
     [b](x0) = x0 + 3,
     
     [a](x0) = x0 + 9
    orientation:
     a(b(x1)) = x1 + 12 >= x1 + 18 = b(a(c(x1)))
     
     b(x1) = x1 + 3 >= x1 = x1
     
     a(x1) = x1 + 9 >= x1 = x1
     
     a(x1) = x1 + 9 >= x1 + 3 = b(x1)
     
     c(c(x1)) = x1 + 12 >= x1 + 9 = a(x1)
    problem:
     strict:
      a(b(x1)) -> b(a(c(x1)))
     weak:
      b(x1) -> x1
      a(x1) -> x1
      a(x1) -> b(x1)
      c(c(x1)) -> a(x1)
    Open