MAYBE

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

Proof:
 DP Processor:
  DPs:
   a#(b(x1)) -> c#(x1)
   a#(b(x1)) -> a#(c(x1))
   a#(b(x1)) -> a#(a(c(x1)))
   a#(b(x1)) -> b#(a(a(c(x1))))
   a#(b(x1)) -> b#(b(a(a(c(x1)))))
   a#(b(x1)) -> b#(b(b(a(a(c(x1))))))
  TRS:
   a(x1) -> x1
   a(b(x1)) -> b(b(b(a(a(c(x1))))))
   b(x1) -> x1
   c(c(x1)) -> x1
  TDG Processor:
   DPs:
    a#(b(x1)) -> c#(x1)
    a#(b(x1)) -> a#(c(x1))
    a#(b(x1)) -> a#(a(c(x1)))
    a#(b(x1)) -> b#(a(a(c(x1))))
    a#(b(x1)) -> b#(b(a(a(c(x1)))))
    a#(b(x1)) -> b#(b(b(a(a(c(x1))))))
   TRS:
    a(x1) -> x1
    a(b(x1)) -> b(b(b(a(a(c(x1))))))
    b(x1) -> x1
    c(c(x1)) -> x1
   graph:
    a#(b(x1)) -> a#(c(x1)) -> a#(b(x1)) -> b#(b(b(a(a(c(x1))))))
    a#(b(x1)) -> a#(c(x1)) -> a#(b(x1)) -> b#(b(a(a(c(x1)))))
    a#(b(x1)) -> a#(c(x1)) -> a#(b(x1)) -> b#(a(a(c(x1))))
    a#(b(x1)) -> a#(c(x1)) -> a#(b(x1)) -> a#(a(c(x1)))
    a#(b(x1)) -> a#(c(x1)) -> a#(b(x1)) -> a#(c(x1))
    a#(b(x1)) -> a#(c(x1)) -> a#(b(x1)) -> c#(x1)
    a#(b(x1)) -> a#(a(c(x1))) -> a#(b(x1)) -> b#(b(b(a(a(c(x1))))))
    a#(b(x1)) -> a#(a(c(x1))) -> a#(b(x1)) -> b#(b(a(a(c(x1)))))
    a#(b(x1)) -> a#(a(c(x1))) -> a#(b(x1)) -> b#(a(a(c(x1))))
    a#(b(x1)) -> a#(a(c(x1))) -> a#(b(x1)) -> a#(a(c(x1)))
    a#(b(x1)) -> a#(a(c(x1))) -> a#(b(x1)) -> a#(c(x1))
    a#(b(x1)) -> a#(a(c(x1))) -> a#(b(x1)) -> c#(x1)
   SCC Processor:
    #sccs: 1
    #rules: 2
    #arcs: 12/36
    DPs:
     a#(b(x1)) -> a#(c(x1))
     a#(b(x1)) -> a#(a(c(x1)))
    TRS:
     a(x1) -> x1
     a(b(x1)) -> b(b(b(a(a(c(x1))))))
     b(x1) -> x1
     c(c(x1)) -> x1
    Arctic Interpretation Processor:
     dimension: 2
     interpretation:
      [a#](x0) = [0 3]x0 + [0],
      
                [-& 0 ]     [0]
      [c](x0) = [0  -&]x0 + [0],
      
                [0  -&]     [0]
      [b](x0) = [1  0 ]x0 + [3],
      
                [0  0 ]     [2]
      [a](x0) = [-& 1 ]x0 + [3]
     orientation:
      a#(b(x1)) = [4 3]x1 + [6] >= [3 0]x1 + [3] = a#(c(x1))
      
      a#(b(x1)) = [4 3]x1 + [6] >= [4 0]x1 + [6] = a#(a(c(x1)))
      
              [0  0 ]     [2]           
      a(x1) = [-& 1 ]x1 + [3] >= x1 = x1
      
                 [1 0]     [3]    [1 0]     [3]                       
      a(b(x1)) = [2 1]x1 + [4] >= [2 1]x1 + [4] = b(b(b(a(a(c(x1))))))
      
              [0  -&]     [0]           
      b(x1) = [1  0 ]x1 + [3] >= x1 = x1
      
                      [0]           
      c(c(x1)) = x1 + [0] >= x1 = x1
     problem:
      DPs:
       a#(b(x1)) -> a#(a(c(x1)))
      TRS:
       a(x1) -> x1
       a(b(x1)) -> b(b(b(a(a(c(x1))))))
       b(x1) -> x1
       c(c(x1)) -> x1
     Open