MAYBE

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

Proof:
 DP Processor:
  DPs:
   a#(b(x1)) -> c#(x1)
   a#(b(x1)) -> a#(c(x1))
   a#(b(x1)) -> b#(a(c(x1)))
   a#(b(x1)) -> b#(b(a(c(x1))))
   c#(c(x1)) -> a#(x1)
   c#(c(x1)) -> b#(a(x1))
  TRS:
   a(x1) -> x1
   a(b(x1)) -> b(b(a(c(x1))))
   b(x1) -> x1
   c(c(x1)) -> b(a(x1))
  TDG Processor:
   DPs:
    a#(b(x1)) -> c#(x1)
    a#(b(x1)) -> a#(c(x1))
    a#(b(x1)) -> b#(a(c(x1)))
    a#(b(x1)) -> b#(b(a(c(x1))))
    c#(c(x1)) -> a#(x1)
    c#(c(x1)) -> b#(a(x1))
   TRS:
    a(x1) -> x1
    a(b(x1)) -> b(b(a(c(x1))))
    b(x1) -> x1
    c(c(x1)) -> b(a(x1))
   graph:
    c#(c(x1)) -> a#(x1) -> a#(b(x1)) -> b#(b(a(c(x1))))
    c#(c(x1)) -> a#(x1) -> a#(b(x1)) -> b#(a(c(x1)))
    c#(c(x1)) -> a#(x1) -> a#(b(x1)) -> a#(c(x1))
    c#(c(x1)) -> a#(x1) -> a#(b(x1)) -> c#(x1)
    a#(b(x1)) -> c#(x1) -> c#(c(x1)) -> b#(a(x1))
    a#(b(x1)) -> c#(x1) -> c#(c(x1)) -> a#(x1)
    a#(b(x1)) -> a#(c(x1)) -> a#(b(x1)) -> b#(b(a(c(x1))))
    a#(b(x1)) -> a#(c(x1)) -> a#(b(x1)) -> b#(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)
   SCC Processor:
    #sccs: 1
    #rules: 3
    #arcs: 10/36
    DPs:
     c#(c(x1)) -> a#(x1)
     a#(b(x1)) -> c#(x1)
     a#(b(x1)) -> a#(c(x1))
    TRS:
     a(x1) -> x1
     a(b(x1)) -> b(b(a(c(x1))))
     b(x1) -> x1
     c(c(x1)) -> b(a(x1))
    Arctic Interpretation Processor:
     dimension: 2
     interpretation:
      [c#](x0) = [0 0]x0,
      
      [a#](x0) = [1 0]x0 + [1],
      
                [-& 0 ]     [0]
      [c](x0) = [1  1 ]x0 + [1],
      
                [0  0 ]     [-&]
      [b](x0) = [-& 0 ]x0 + [0 ],
      
                [1  -&]     [1]
      [a](x0) = [1  0 ]x0 + [1]
     orientation:
      c#(c(x1)) = [1 1]x1 + [1] >= [1 0]x1 + [1] = a#(x1)
      
      a#(b(x1)) = [1 1]x1 + [1] >= [0 0]x1 = c#(x1)
      
      a#(b(x1)) = [1 1]x1 + [1] >= [1 1]x1 + [1] = a#(c(x1))
      
              [1  -&]     [1]           
      a(x1) = [1  0 ]x1 + [1] >= x1 = x1
      
                 [1 1]     [1]    [1 1]     [1]                 
      a(b(x1)) = [1 1]x1 + [1] >= [1 1]x1 + [1] = b(b(a(c(x1))))
      
              [0  0 ]     [-&]           
      b(x1) = [-& 0 ]x1 + [0 ] >= x1 = x1
      
                 [1 1]     [1]    [1 0]     [1]           
      c(c(x1)) = [2 2]x1 + [2] >= [1 0]x1 + [1] = b(a(x1))
     problem:
      DPs:
       c#(c(x1)) -> a#(x1)
       a#(b(x1)) -> a#(c(x1))
      TRS:
       a(x1) -> x1
       a(b(x1)) -> b(b(a(c(x1))))
       b(x1) -> x1
       c(c(x1)) -> b(a(x1))
     Open