MAYBE

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

Proof:
 RT Transformation Processor:
  strict:
   a(x1) -> x1
   a(a(a(x1))) -> b(x1)
   b(c(x1)) -> c(a(c(b(x1))))
   c(x1) -> x1
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   interpretation:
    [c](x0) = x0 + 10,
    
    [b](x0) = x0 + 24,
    
    [a](x0) = x0
   orientation:
    a(x1) = x1 >= x1 = x1
    
    a(a(a(x1))) = x1 >= x1 + 24 = b(x1)
    
    b(c(x1)) = x1 + 34 >= x1 + 44 = c(a(c(b(x1))))
    
    c(x1) = x1 + 10 >= x1 = x1
   problem:
    strict:
     a(x1) -> x1
     a(a(a(x1))) -> b(x1)
     b(c(x1)) -> c(a(c(b(x1))))
    weak:
     c(x1) -> x1
   Matrix Interpretation Processor:
    dimension: 1
    interpretation:
     [c](x0) = x0,
     
     [b](x0) = x0 + 2,
     
     [a](x0) = x0 + 1
    orientation:
     a(x1) = x1 + 1 >= x1 = x1
     
     a(a(a(x1))) = x1 + 3 >= x1 + 2 = b(x1)
     
     b(c(x1)) = x1 + 2 >= x1 + 3 = c(a(c(b(x1))))
     
     c(x1) = x1 >= x1 = x1
    problem:
     strict:
      b(c(x1)) -> c(a(c(b(x1))))
     weak:
      a(x1) -> x1
      a(a(a(x1))) -> b(x1)
      c(x1) -> x1
    Open