MAYBE

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

Proof:
 DP Processor:
  DPs:
   a#(a(x1)) -> b#(x1)
   b#(c(x1)) -> a#(x1)
   b#(c(x1)) -> b#(a(x1))
   b#(c(x1)) -> c#(b(a(x1)))
   b#(c(x1)) -> c#(c(b(a(x1))))
  TRS:
   a(x1) -> x1
   a(a(x1)) -> b(x1)
   b(x1) -> x1
   b(c(x1)) -> c(c(b(a(x1))))
   c(x1) -> x1
  TDG Processor:
   DPs:
    a#(a(x1)) -> b#(x1)
    b#(c(x1)) -> a#(x1)
    b#(c(x1)) -> b#(a(x1))
    b#(c(x1)) -> c#(b(a(x1)))
    b#(c(x1)) -> c#(c(b(a(x1))))
   TRS:
    a(x1) -> x1
    a(a(x1)) -> b(x1)
    b(x1) -> x1
    b(c(x1)) -> c(c(b(a(x1))))
    c(x1) -> x1
   graph:
    b#(c(x1)) -> b#(a(x1)) -> b#(c(x1)) -> c#(c(b(a(x1))))
    b#(c(x1)) -> b#(a(x1)) -> b#(c(x1)) -> c#(b(a(x1)))
    b#(c(x1)) -> b#(a(x1)) -> b#(c(x1)) -> b#(a(x1))
    b#(c(x1)) -> b#(a(x1)) -> b#(c(x1)) -> a#(x1)
    b#(c(x1)) -> a#(x1) -> a#(a(x1)) -> b#(x1)
    a#(a(x1)) -> b#(x1) -> b#(c(x1)) -> c#(c(b(a(x1))))
    a#(a(x1)) -> b#(x1) -> b#(c(x1)) -> c#(b(a(x1)))
    a#(a(x1)) -> b#(x1) -> b#(c(x1)) -> b#(a(x1))
    a#(a(x1)) -> b#(x1) -> b#(c(x1)) -> a#(x1)
   SCC Processor:
    #sccs: 1
    #rules: 3
    #arcs: 9/25
    DPs:
     b#(c(x1)) -> b#(a(x1))
     b#(c(x1)) -> a#(x1)
     a#(a(x1)) -> b#(x1)
    TRS:
     a(x1) -> x1
     a(a(x1)) -> b(x1)
     b(x1) -> x1
     b(c(x1)) -> c(c(b(a(x1))))
     c(x1) -> x1
    Arctic Interpretation Processor:
     dimension: 2
     interpretation:
      [b#](x0) = [1 0]x0 + [1],
      
      [a#](x0) = [0 0]x0 + [0],
      
                [0  0 ]     [-&]
      [c](x0) = [-& 0 ]x0 + [0 ],
      
                [1 0]     [1]
      [b](x0) = [1 0]x0 + [1],
      
                [0 0]     [-&]
      [a](x0) = [1 0]x0 + [1 ]
     orientation:
      b#(c(x1)) = [1 1]x1 + [1] >= [1 1]x1 + [1] = b#(a(x1))
      
      b#(c(x1)) = [1 1]x1 + [1] >= [0 0]x1 + [0] = a#(x1)
      
      a#(a(x1)) = [1 0]x1 + [1] >= [1 0]x1 + [1] = b#(x1)
      
              [0 0]     [-&]           
      a(x1) = [1 0]x1 + [1 ] >= x1 = x1
      
                 [1 0]     [1]    [1 0]     [1]        
      a(a(x1)) = [1 1]x1 + [1] >= [1 0]x1 + [1] = b(x1)
      
              [1 0]     [1]           
      b(x1) = [1 0]x1 + [1] >= x1 = x1
      
                 [1 1]     [1]    [1 1]     [1]                 
      b(c(x1)) = [1 1]x1 + [1] >= [1 1]x1 + [1] = c(c(b(a(x1))))
      
              [0  0 ]     [-&]           
      c(x1) = [-& 0 ]x1 + [0 ] >= x1 = x1
     problem:
      DPs:
       b#(c(x1)) -> b#(a(x1))
       a#(a(x1)) -> b#(x1)
      TRS:
       a(x1) -> x1
       a(a(x1)) -> b(x1)
       b(x1) -> x1
       b(c(x1)) -> c(c(b(a(x1))))
       c(x1) -> x1
     Open