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


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YES

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

Proof:
 String Reversal Processor:
  b(a(x1)) -> x1
  c(b(x1)) -> a(a(x1))
  a(c(x1)) -> c(c(b(b(x1))))
  DP Processor:
   DPs:
    c#(b(x1)) -> a#(x1)
    c#(b(x1)) -> a#(a(x1))
    a#(c(x1)) -> b#(x1)
    a#(c(x1)) -> b#(b(x1))
    a#(c(x1)) -> c#(b(b(x1)))
    a#(c(x1)) -> c#(c(b(b(x1))))
   TRS:
    b(a(x1)) -> x1
    c(b(x1)) -> a(a(x1))
    a(c(x1)) -> c(c(b(b(x1))))
   TDG Processor:
    DPs:
     c#(b(x1)) -> a#(x1)
     c#(b(x1)) -> a#(a(x1))
     a#(c(x1)) -> b#(x1)
     a#(c(x1)) -> b#(b(x1))
     a#(c(x1)) -> c#(b(b(x1)))
     a#(c(x1)) -> c#(c(b(b(x1))))
    TRS:
     b(a(x1)) -> x1
     c(b(x1)) -> a(a(x1))
     a(c(x1)) -> c(c(b(b(x1))))
    graph:
     a#(c(x1)) -> c#(c(b(b(x1)))) -> c#(b(x1)) -> a#(a(x1))
     a#(c(x1)) -> c#(c(b(b(x1)))) -> c#(b(x1)) -> a#(x1)
     a#(c(x1)) -> c#(b(b(x1))) -> c#(b(x1)) -> a#(a(x1))
     a#(c(x1)) -> c#(b(b(x1))) -> c#(b(x1)) -> a#(x1)
     c#(b(x1)) -> a#(a(x1)) -> a#(c(x1)) -> c#(c(b(b(x1))))
     c#(b(x1)) -> a#(a(x1)) -> a#(c(x1)) -> c#(b(b(x1)))
     c#(b(x1)) -> a#(a(x1)) -> a#(c(x1)) -> b#(b(x1))
     c#(b(x1)) -> a#(a(x1)) -> a#(c(x1)) -> b#(x1)
     c#(b(x1)) -> a#(x1) -> a#(c(x1)) -> c#(c(b(b(x1))))
     c#(b(x1)) -> a#(x1) -> a#(c(x1)) -> c#(b(b(x1)))
     c#(b(x1)) -> a#(x1) -> a#(c(x1)) -> b#(b(x1))
     c#(b(x1)) -> a#(x1) -> a#(c(x1)) -> b#(x1)
    EDG Processor:
     DPs:
      c#(b(x1)) -> a#(x1)
      c#(b(x1)) -> a#(a(x1))
      a#(c(x1)) -> b#(x1)
      a#(c(x1)) -> b#(b(x1))
      a#(c(x1)) -> c#(b(b(x1)))
      a#(c(x1)) -> c#(c(b(b(x1))))
     TRS:
      b(a(x1)) -> x1
      c(b(x1)) -> a(a(x1))
      a(c(x1)) -> c(c(b(b(x1))))
     graph:
      a#(c(x1)) -> c#(b(b(x1))) -> c#(b(x1)) -> a#(x1)
      a#(c(x1)) -> c#(b(b(x1))) -> c#(b(x1)) -> a#(a(x1))
      c#(b(x1)) -> a#(a(x1)) -> a#(c(x1)) -> b#(x1)
      c#(b(x1)) -> a#(a(x1)) -> a#(c(x1)) -> b#(b(x1))
      c#(b(x1)) -> a#(a(x1)) -> a#(c(x1)) -> c#(b(b(x1)))
      c#(b(x1)) -> a#(a(x1)) -> a#(c(x1)) -> c#(c(b(b(x1))))
      c#(b(x1)) -> a#(x1) -> a#(c(x1)) -> b#(x1)
      c#(b(x1)) -> a#(x1) -> a#(c(x1)) -> b#(b(x1))
      c#(b(x1)) -> a#(x1) -> a#(c(x1)) -> c#(b(b(x1)))
      c#(b(x1)) -> a#(x1) -> a#(c(x1)) -> c#(c(b(b(x1))))
     SCC Processor:
      #sccs: 1
      #rules: 3
      #arcs: 10/36
      DPs:
       a#(c(x1)) -> c#(b(b(x1)))
       c#(b(x1)) -> a#(a(x1))
       c#(b(x1)) -> a#(x1)
      TRS:
       b(a(x1)) -> x1
       c(b(x1)) -> a(a(x1))
       a(c(x1)) -> c(c(b(b(x1))))
      Arctic Interpretation Processor:
       dimension: 2
       usable rules:
        b(a(x1)) -> x1
        c(b(x1)) -> a(a(x1))
        a(c(x1)) -> c(c(b(b(x1))))
       interpretation:
        [a#](x0) = [0 1]x0 + [0],
        
        [c#](x0) = [1 2]x0 + [3],
        
                  [1 2]     [3]
        [c](x0) = [0 1]x0 + [2],
        
                  [1  0 ]     [2 ]
        [a](x0) = [0  -&]x0 + [-&],
        
                  [-& 0 ]     [0]
        [b](x0) = [0  -&]x0 + [0]
       orientation:
        a#(c(x1)) = [1 2]x1 + [3] >= [1 2]x1 + [3] = c#(b(b(x1)))
        
        c#(b(x1)) = [2 1]x1 + [3] >= [1 0]x1 + [2] = a#(a(x1))
        
        c#(b(x1)) = [2 1]x1 + [3] >= [0 1]x1 + [0] = a#(x1)
        
                   [0  -&]     [0]           
        b(a(x1)) = [1  0 ]x1 + [2] >= x1 = x1
        
                   [2 1]     [3]    [2 1]     [3]           
        c(b(x1)) = [1 0]x1 + [2] >= [1 0]x1 + [2] = a(a(x1))
        
                   [2 3]     [4]    [2 3]     [4]                 
        a(c(x1)) = [1 2]x1 + [3] >= [1 2]x1 + [3] = c(c(b(b(x1))))
       problem:
        DPs:
         a#(c(x1)) -> c#(b(b(x1)))
         c#(b(x1)) -> a#(x1)
        TRS:
         b(a(x1)) -> x1
         c(b(x1)) -> a(a(x1))
         a(c(x1)) -> c(c(b(b(x1))))
       Restore Modifier:
        DPs:
         a#(c(x1)) -> c#(b(b(x1)))
         c#(b(x1)) -> a#(x1)
        TRS:
         b(a(x1)) -> x1
         c(b(x1)) -> a(a(x1))
         a(c(x1)) -> c(c(b(b(x1))))
        EDG Processor:
         DPs:
          a#(c(x1)) -> c#(b(b(x1)))
          c#(b(x1)) -> a#(x1)
         TRS:
          b(a(x1)) -> x1
          c(b(x1)) -> a(a(x1))
          a(c(x1)) -> c(c(b(b(x1))))
         graph:
          a#(c(x1)) -> c#(b(b(x1))) -> c#(b(x1)) -> a#(x1)
          c#(b(x1)) -> a#(x1) -> a#(c(x1)) -> c#(b(b(x1)))
         Usable Rule Processor:
          DPs:
           a#(c(x1)) -> c#(b(b(x1)))
           c#(b(x1)) -> a#(x1)
          TRS:
           b(a(x1)) -> x1
          Arctic Interpretation Processor:
           dimension: 1
           usable rules:
            b(a(x1)) -> x1
           interpretation:
            [a#](x0) = 10x0,
            
            [c#](x0) = x0 + 7,
            
            [c](x0) = 11x0 + 7,
            
            [a](x0) = 10x0 + 12,
            
            [b](x0) = 10x0 + 6
           orientation:
            a#(c(x1)) = 21x1 + 17 >= 20x1 + 16 = c#(b(b(x1)))
            
            c#(b(x1)) = 10x1 + 7 >= 10x1 = a#(x1)
            
            b(a(x1)) = 20x1 + 22 >= x1 = x1
           problem:
            DPs:
             c#(b(x1)) -> a#(x1)
            TRS:
             b(a(x1)) -> x1
           Restore Modifier:
            DPs:
             c#(b(x1)) -> a#(x1)
            TRS:
             b(a(x1)) -> x1
             c(b(x1)) -> a(a(x1))
             a(c(x1)) -> c(c(b(b(x1))))
            EDG Processor:
             DPs:
              c#(b(x1)) -> a#(x1)
             TRS:
              b(a(x1)) -> x1
              c(b(x1)) -> a(a(x1))
              a(c(x1)) -> c(c(b(b(x1))))
             graph:
              
             SCC Processor:
              #sccs: 0
              #rules: 0
              #arcs: 0/1