/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

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

Proof:
 String Reversal Processor:
  c(b(a(x1))) -> b(x1)
  b(b(c(x1))) -> a(x1)
  c(x1) -> b(x1)
  a(a(x1)) -> c(a(b(c(x1))))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [a](x0) = x0 + 6,
    
    [b](x0) = x0 + 2,
    
    [c](x0) = x0 + 2
   orientation:
    c(b(a(x1))) = x1 + 10 >= x1 + 2 = b(x1)
    
    b(b(c(x1))) = x1 + 6 >= x1 + 6 = a(x1)
    
    c(x1) = x1 + 2 >= x1 + 2 = b(x1)
    
    a(a(x1)) = x1 + 12 >= x1 + 12 = c(a(b(c(x1))))
   problem:
    b(b(c(x1))) -> a(x1)
    c(x1) -> b(x1)
    a(a(x1)) -> c(a(b(c(x1))))
   String Reversal Processor:
    c(b(b(x1))) -> a(x1)
    c(x1) -> b(x1)
    a(a(x1)) -> c(b(a(c(x1))))
    DP Processor:
     DPs:
      c#(b(b(x1))) -> a#(x1)
      a#(a(x1)) -> c#(x1)
      a#(a(x1)) -> a#(c(x1))
      a#(a(x1)) -> c#(b(a(c(x1))))
     TRS:
      c(b(b(x1))) -> a(x1)
      c(x1) -> b(x1)
      a(a(x1)) -> c(b(a(c(x1))))
     TDG Processor:
      DPs:
       c#(b(b(x1))) -> a#(x1)
       a#(a(x1)) -> c#(x1)
       a#(a(x1)) -> a#(c(x1))
       a#(a(x1)) -> c#(b(a(c(x1))))
      TRS:
       c(b(b(x1))) -> a(x1)
       c(x1) -> b(x1)
       a(a(x1)) -> c(b(a(c(x1))))
      graph:
       a#(a(x1)) -> a#(c(x1)) -> a#(a(x1)) -> c#(b(a(c(x1))))
       a#(a(x1)) -> a#(c(x1)) -> a#(a(x1)) -> a#(c(x1))
       a#(a(x1)) -> a#(c(x1)) -> a#(a(x1)) -> c#(x1)
       a#(a(x1)) -> c#(b(a(c(x1)))) -> c#(b(b(x1))) -> a#(x1)
       a#(a(x1)) -> c#(x1) -> c#(b(b(x1))) -> a#(x1)
       c#(b(b(x1))) -> a#(x1) -> a#(a(x1)) -> c#(b(a(c(x1))))
       c#(b(b(x1))) -> a#(x1) -> a#(a(x1)) -> a#(c(x1))
       c#(b(b(x1))) -> a#(x1) -> a#(a(x1)) -> c#(x1)
      Arctic Interpretation Processor:
       dimension: 1
       usable rules:
        c(b(b(x1))) -> a(x1)
        c(x1) -> b(x1)
        a(a(x1)) -> c(b(a(c(x1))))
       interpretation:
        [a#](x0) = 2x0,
        
        [c#](x0) = x0,
        
        [a](x0) = 3x0,
        
        [b](x0) = 1x0,
        
        [c](x0) = 1x0
       orientation:
        c#(b(b(x1))) = 2x1 >= 2x1 = a#(x1)
        
        a#(a(x1)) = 5x1 >= x1 = c#(x1)
        
        a#(a(x1)) = 5x1 >= 3x1 = a#(c(x1))
        
        a#(a(x1)) = 5x1 >= 5x1 = c#(b(a(c(x1))))
        
        c(b(b(x1))) = 3x1 >= 3x1 = a(x1)
        
        c(x1) = 1x1 >= 1x1 = b(x1)
        
        a(a(x1)) = 6x1 >= 6x1 = c(b(a(c(x1))))
       problem:
        DPs:
         c#(b(b(x1))) -> a#(x1)
         a#(a(x1)) -> c#(b(a(c(x1))))
        TRS:
         c(b(b(x1))) -> a(x1)
         c(x1) -> b(x1)
         a(a(x1)) -> c(b(a(c(x1))))
       Restore Modifier:
        DPs:
         c#(b(b(x1))) -> a#(x1)
         a#(a(x1)) -> c#(b(a(c(x1))))
        TRS:
         c(b(b(x1))) -> a(x1)
         c(x1) -> b(x1)
         a(a(x1)) -> c(b(a(c(x1))))
        EDG Processor:
         DPs:
          c#(b(b(x1))) -> a#(x1)
          a#(a(x1)) -> c#(b(a(c(x1))))
         TRS:
          c(b(b(x1))) -> a(x1)
          c(x1) -> b(x1)
          a(a(x1)) -> c(b(a(c(x1))))
         graph:
          a#(a(x1)) -> c#(b(a(c(x1)))) -> c#(b(b(x1))) -> a#(x1)
          c#(b(b(x1))) -> a#(x1) -> a#(a(x1)) -> c#(b(a(c(x1))))
         Bounds Processor:
          bound: 0
          enrichment: match-dp
          automaton:
           final states: {3}
           transitions:
            a0(15) -> 16*
            a0(5) -> 6*
            a0(22) -> 23*
            a0(43) -> 44*
            c0(47) -> 48*
            c0(24) -> 25*
            c0(4) -> 5*
            c0(21) -> 22*
            f50() -> 4*
            a{#,0}(39) -> 40*
            c{#,0}(7) -> 3*
            b0(35) -> 36*
            b0(51) -> 52*
            b0(26) -> 27*
            b0(6) -> 7*
            b0(23) -> 24*
            b0(13) -> 14*
            4 -> 15,13
            14 -> 5*
            15 -> 21*
            16 -> 22,5
            21 -> 35*
            24 -> 26*
            25 -> 16,5,23,6
            26 -> 43,39
            27 -> 25,6
            36 -> 22*
            40 -> 3*
            43 -> 47*
            44 -> 48,22,25,6,23
            47 -> 51*
            48 -> 22*
            52 -> 48,22
          problem:
           DPs:
            c#(b(b(x1))) -> a#(x1)
           TRS:
            c(b(b(x1))) -> a(x1)
            c(x1) -> b(x1)
            a(a(x1)) -> c(b(a(c(x1))))
          Restore Modifier:
           DPs:
            c#(b(b(x1))) -> a#(x1)
           TRS:
            c(b(b(x1))) -> a(x1)
            c(x1) -> b(x1)
            a(a(x1)) -> c(b(a(c(x1))))
           EDG Processor:
            DPs:
             c#(b(b(x1))) -> a#(x1)
            TRS:
             c(b(b(x1))) -> a(x1)
             c(x1) -> b(x1)
             a(a(x1)) -> c(b(a(c(x1))))
            graph:
             
            SCC Processor:
             #sccs: 0
             #rules: 0
             #arcs: 0/1