MAYBE

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

Proof:
 RT Transformation Processor:
  strict:
   a(x1) -> x1
   a(a(x1)) -> a(b(x1))
   b(x1) -> x1
   c(b(x1)) -> a(b(c(c(x1))))
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   interpretation:
    [c](x0) = x0 + 3,
    
    [b](x0) = x0,
    
    [a](x0) = x0 + 24
   orientation:
    a(x1) = x1 + 24 >= x1 = x1
    
    a(a(x1)) = x1 + 48 >= x1 + 24 = a(b(x1))
    
    b(x1) = x1 >= x1 = x1
    
    c(b(x1)) = x1 + 3 >= x1 + 30 = a(b(c(c(x1))))
   problem:
    strict:
     b(x1) -> x1
     c(b(x1)) -> a(b(c(c(x1))))
    weak:
     a(x1) -> x1
     a(a(x1)) -> a(b(x1))
   Matrix Interpretation Processor:
    dimension: 1
    interpretation:
     [c](x0) = x0,
     
     [b](x0) = x0 + 1,
     
     [a](x0) = x0 + 1
    orientation:
     b(x1) = x1 + 1 >= x1 = x1
     
     c(b(x1)) = x1 + 1 >= x1 + 2 = a(b(c(c(x1))))
     
     a(x1) = x1 + 1 >= x1 = x1
     
     a(a(x1)) = x1 + 2 >= x1 + 2 = a(b(x1))
    problem:
     strict:
      c(b(x1)) -> a(b(c(c(x1))))
     weak:
      b(x1) -> x1
      a(x1) -> x1
      a(a(x1)) -> a(b(x1))
    Open