MAYBE

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

Proof:
 DP Processor:
  DPs:
   a#(a(x)) -> c#(x)
   a#(a(x)) -> b#(c(x))
   b#(b(x)) -> c#(x)
   b#(b(x)) -> a#(c(x))
   c#(c(x)) -> b#(x)
   c#(c(x)) -> a#(b(x))
  TRS:
   a(a(x)) -> b(c(x))
   b(b(x)) -> a(c(x))
   c(c(x)) -> a(b(x))
  ADG Processor:
   DPs:
    a#(a(x)) -> c#(x)
    a#(a(x)) -> b#(c(x))
    b#(b(x)) -> c#(x)
    b#(b(x)) -> a#(c(x))
    c#(c(x)) -> b#(x)
    c#(c(x)) -> a#(b(x))
   TRS:
    a(a(x)) -> b(c(x))
    b(b(x)) -> a(c(x))
    c(c(x)) -> a(b(x))
   graph:
    b#(b(x)) -> c#(x) -> c#(c(x)) -> b#(x)
    b#(b(x)) -> c#(x) -> c#(c(x)) -> a#(b(x))
    b#(b(x)) -> a#(c(x)) -> a#(a(x)) -> c#(x)
    b#(b(x)) -> a#(c(x)) -> a#(a(x)) -> b#(c(x))
    c#(c(x)) -> b#(x) -> b#(b(x)) -> c#(x)
    c#(c(x)) -> b#(x) -> b#(b(x)) -> a#(c(x))
    c#(c(x)) -> a#(b(x)) -> a#(a(x)) -> c#(x)
    c#(c(x)) -> a#(b(x)) -> a#(a(x)) -> b#(c(x))
    a#(a(x)) -> b#(c(x)) -> b#(b(x)) -> c#(x)
    a#(a(x)) -> b#(c(x)) -> b#(b(x)) -> a#(c(x))
    a#(a(x)) -> c#(x) -> c#(c(x)) -> b#(x)
    a#(a(x)) -> c#(x) -> c#(c(x)) -> a#(b(x))
   Restore Modifier:
    DPs:
     a#(a(x)) -> c#(x)
     a#(a(x)) -> b#(c(x))
     b#(b(x)) -> c#(x)
     b#(b(x)) -> a#(c(x))
     c#(c(x)) -> b#(x)
     c#(c(x)) -> a#(b(x))
    TRS:
     a(a(x)) -> b(c(x))
     b(b(x)) -> a(c(x))
     c(c(x)) -> a(b(x))
    SCC Processor:
     #sccs: 1
     #rules: 6
     #arcs: 12/36
     DPs:
      b#(b(x)) -> c#(x)
      c#(c(x)) -> a#(b(x))
      a#(a(x)) -> b#(c(x))
      b#(b(x)) -> a#(c(x))
      a#(a(x)) -> c#(x)
      c#(c(x)) -> b#(x)
     TRS:
      a(a(x)) -> b(c(x))
      b(b(x)) -> a(c(x))
      c(c(x)) -> a(b(x))
     Matrix Interpretation Processor:
      dimension: 1
      interpretation:
       [b#](x0) = x0,
       
       [c#](x0) = x0,
       
       [a#](x0) = x0,
       
       [b](x0) = x0 + 1,
       
       [c](x0) = x0 + 1,
       
       [a](x0) = x0 + 1
      orientation:
       b#(b(x)) = x + 1 >= x = c#(x)
       
       c#(c(x)) = x + 1 >= x + 1 = a#(b(x))
       
       a#(a(x)) = x + 1 >= x + 1 = b#(c(x))
       
       b#(b(x)) = x + 1 >= x + 1 = a#(c(x))
       
       a#(a(x)) = x + 1 >= x = c#(x)
       
       c#(c(x)) = x + 1 >= x = b#(x)
       
       a(a(x)) = x + 2 >= x + 2 = b(c(x))
       
       b(b(x)) = x + 2 >= x + 2 = a(c(x))
       
       c(c(x)) = x + 2 >= x + 2 = a(b(x))
      problem:
       DPs:
        c#(c(x)) -> a#(b(x))
        a#(a(x)) -> b#(c(x))
        b#(b(x)) -> a#(c(x))
       TRS:
        a(a(x)) -> b(c(x))
        b(b(x)) -> a(c(x))
        c(c(x)) -> a(b(x))
      Matrix Interpretation Processor:
       dimension: 1
       interpretation:
        [b#](x0) = 0,
        
        [c#](x0) = 1,
        
        [a#](x0) = 0,
        
        [b](x0) = 0,
        
        [c](x0) = 0,
        
        [a](x0) = 0
       orientation:
        c#(c(x)) = 1 >= 0 = a#(b(x))
        
        a#(a(x)) = 0 >= 0 = b#(c(x))
        
        b#(b(x)) = 0 >= 0 = a#(c(x))
        
        a(a(x)) = 0 >= 0 = b(c(x))
        
        b(b(x)) = 0 >= 0 = a(c(x))
        
        c(c(x)) = 0 >= 0 = a(b(x))
       problem:
        DPs:
         a#(a(x)) -> b#(c(x))
         b#(b(x)) -> a#(c(x))
        TRS:
         a(a(x)) -> b(c(x))
         b(b(x)) -> a(c(x))
         c(c(x)) -> a(b(x))
       Open