MAYBE

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

Proof:
 DP Processor:
  DPs:
   a#(x1) -> b#(x1)
   a#(b(x1)) -> c#(x1)
   a#(b(x1)) -> a#(c(x1))
   a#(b(x1)) -> b#(a(c(x1)))
   c#(c(x1)) -> a#(x1)
  TRS:
   a(x1) -> x1
   a(x1) -> b(x1)
   a(b(x1)) -> b(a(c(x1)))
   b(x1) -> x1
   c(c(x1)) -> a(x1)
  TDG Processor:
   DPs:
    a#(x1) -> b#(x1)
    a#(b(x1)) -> c#(x1)
    a#(b(x1)) -> a#(c(x1))
    a#(b(x1)) -> b#(a(c(x1)))
    c#(c(x1)) -> a#(x1)
   TRS:
    a(x1) -> x1
    a(x1) -> b(x1)
    a(b(x1)) -> b(a(c(x1)))
    b(x1) -> x1
    c(c(x1)) -> a(x1)
   graph:
    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)
    c#(c(x1)) -> a#(x1) -> a#(x1) -> b#(x1)
    a#(b(x1)) -> c#(x1) -> c#(c(x1)) -> a#(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)
    a#(b(x1)) -> a#(c(x1)) -> a#(x1) -> b#(x1)
   SCC Processor:
    #sccs: 1
    #rules: 3
    #arcs: 9/25
    DPs:
     c#(c(x1)) -> a#(x1)
     a#(b(x1)) -> c#(x1)
     a#(b(x1)) -> a#(c(x1))
    TRS:
     a(x1) -> x1
     a(x1) -> b(x1)
     a(b(x1)) -> b(a(c(x1)))
     b(x1) -> x1
     c(c(x1)) -> a(x1)
    Arctic Interpretation Processor:
     dimension: 2
     interpretation:
      [c#](x0) = [0  -&]x0 + [0],
      
      [a#](x0) = [0 0]x0 + [0],
      
                [0 0]     [-&]
      [c](x0) = [2 0]x0 + [1 ],
      
                [0  -&]     [-&]
      [b](x0) = [2  0 ]x0 + [1 ],
      
                [0 0]     [-&]
      [a](x0) = [2 2]x0 + [1 ]
     orientation:
      c#(c(x1)) = [0 0]x1 + [0] >= [0 0]x1 + [0] = a#(x1)
      
      a#(b(x1)) = [2 0]x1 + [1] >= [0  -&]x1 + [0] = c#(x1)
      
      a#(b(x1)) = [2 0]x1 + [1] >= [2 0]x1 + [1] = a#(c(x1))
      
              [0 0]     [-&]           
      a(x1) = [2 2]x1 + [1 ] >= x1 = x1
      
              [0 0]     [-&]    [0  -&]     [-&]        
      a(x1) = [2 2]x1 + [1 ] >= [2  0 ]x1 + [1 ] = b(x1)
      
                 [2 0]     [1]    [2 0]     [1]              
      a(b(x1)) = [4 2]x1 + [3] >= [4 2]x1 + [3] = b(a(c(x1)))
      
              [0  -&]     [-&]           
      b(x1) = [2  0 ]x1 + [1 ] >= x1 = x1
      
                 [2 0]     [1]    [0 0]     [-&]        
      c(c(x1)) = [2 2]x1 + [1] >= [2 2]x1 + [1 ] = a(x1)
     problem:
      DPs:
       c#(c(x1)) -> a#(x1)
       a#(b(x1)) -> a#(c(x1))
      TRS:
       a(x1) -> x1
       a(x1) -> b(x1)
       a(b(x1)) -> b(a(c(x1)))
       b(x1) -> x1
       c(c(x1)) -> a(x1)
     Open