/export/starexec/sandbox2/solver/bin/starexec_run_ttt2 /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

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

Proof:
 DP Processor:
  DPs:
   a#(a(x1)) -> c#(x1)
   a#(a(x1)) -> a#(b(c(x1)))
   c#(b(x1)) -> c#(x1)
   c#(b(x1)) -> a#(c(x1))
   c#(b(x1)) -> a#(a(c(x1)))
  TRS:
   a(a(x1)) -> a(b(c(x1)))
   c(a(x1)) -> x1
   c(b(x1)) -> a(a(c(x1)))
  TDG Processor:
   DPs:
    a#(a(x1)) -> c#(x1)
    a#(a(x1)) -> a#(b(c(x1)))
    c#(b(x1)) -> c#(x1)
    c#(b(x1)) -> a#(c(x1))
    c#(b(x1)) -> a#(a(c(x1)))
   TRS:
    a(a(x1)) -> a(b(c(x1)))
    c(a(x1)) -> x1
    c(b(x1)) -> a(a(c(x1)))
   graph:
    c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> a#(a(c(x1)))
    c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> a#(c(x1))
    c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1)
    c#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> a#(b(c(x1)))
    c#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> c#(x1)
    c#(b(x1)) -> a#(a(c(x1))) -> a#(a(x1)) -> a#(b(c(x1)))
    c#(b(x1)) -> a#(a(c(x1))) -> a#(a(x1)) -> c#(x1)
    a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> a#(a(c(x1)))
    a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> a#(c(x1))
    a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1)
    a#(a(x1)) -> a#(b(c(x1))) -> a#(a(x1)) -> a#(b(c(x1)))
    a#(a(x1)) -> a#(b(c(x1))) -> a#(a(x1)) -> c#(x1)
   EDG Processor:
    DPs:
     a#(a(x1)) -> c#(x1)
     a#(a(x1)) -> a#(b(c(x1)))
     c#(b(x1)) -> c#(x1)
     c#(b(x1)) -> a#(c(x1))
     c#(b(x1)) -> a#(a(c(x1)))
    TRS:
     a(a(x1)) -> a(b(c(x1)))
     c(a(x1)) -> x1
     c(b(x1)) -> a(a(c(x1)))
    graph:
     c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1)
     c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> a#(c(x1))
     c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> a#(a(c(x1)))
     c#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> c#(x1)
     c#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> a#(b(c(x1)))
     c#(b(x1)) -> a#(a(c(x1))) -> a#(a(x1)) -> c#(x1)
     c#(b(x1)) -> a#(a(c(x1))) -> a#(a(x1)) -> a#(b(c(x1)))
     a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1)
     a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> a#(c(x1))
     a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> a#(a(c(x1)))
    SCC Processor:
     #sccs: 1
     #rules: 4
     #arcs: 10/25
     DPs:
      c#(b(x1)) -> c#(x1)
      c#(b(x1)) -> a#(a(c(x1)))
      a#(a(x1)) -> c#(x1)
      c#(b(x1)) -> a#(c(x1))
     TRS:
      a(a(x1)) -> a(b(c(x1)))
      c(a(x1)) -> x1
      c(b(x1)) -> a(a(c(x1)))
     Arctic Interpretation Processor:
      dimension: 2
      usable rules:
       a(a(x1)) -> a(b(c(x1)))
       c(a(x1)) -> x1
       c(b(x1)) -> a(a(c(x1)))
      interpretation:
       [c#](x0) = [-& 1 ]x0 + [0],
       
                 [-& 0 ]     [1]
       [c](x0) = [0  -&]x0 + [1],
       
       [a#](x0) = [1  -&]x0 + [0],
       
                 [-& 0 ]     [0]
       [a](x0) = [0  1 ]x0 + [2],
       
                 [2 1]     [3]
       [b](x0) = [1 0]x0 + [2]
      orientation:
       c#(b(x1)) = [2 1]x1 + [3] >= [-& 1 ]x1 + [0] = c#(x1)
       
       c#(b(x1)) = [2 1]x1 + [3] >= [1  -&]x1 + [2] = a#(a(c(x1)))
       
       a#(a(x1)) = [-& 1 ]x1 + [1] >= [-& 1 ]x1 + [0] = c#(x1)
       
       c#(b(x1)) = [2 1]x1 + [3] >= [-& 1 ]x1 + [2] = a#(c(x1))
       
                  [0 1]     [2]    [0 1]     [2]              
       a(a(x1)) = [1 2]x1 + [3] >= [1 2]x1 + [3] = a(b(c(x1)))
       
                  [0  1 ]     [2]           
       c(a(x1)) = [-& 0 ]x1 + [1] >= x1 = x1
       
                  [1 0]     [2]    [1 0]     [2]              
       c(b(x1)) = [2 1]x1 + [3] >= [2 1]x1 + [3] = a(a(c(x1)))
      problem:
       DPs:
        c#(b(x1)) -> c#(x1)
        a#(a(x1)) -> c#(x1)
        c#(b(x1)) -> a#(c(x1))
       TRS:
        a(a(x1)) -> a(b(c(x1)))
        c(a(x1)) -> x1
        c(b(x1)) -> a(a(c(x1)))
      Restore Modifier:
       DPs:
        c#(b(x1)) -> c#(x1)
        a#(a(x1)) -> c#(x1)
        c#(b(x1)) -> a#(c(x1))
       TRS:
        a(a(x1)) -> a(b(c(x1)))
        c(a(x1)) -> x1
        c(b(x1)) -> a(a(c(x1)))
       EDG Processor:
        DPs:
         c#(b(x1)) -> c#(x1)
         a#(a(x1)) -> c#(x1)
         c#(b(x1)) -> a#(c(x1))
        TRS:
         a(a(x1)) -> a(b(c(x1)))
         c(a(x1)) -> x1
         c(b(x1)) -> a(a(c(x1)))
        graph:
         c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> a#(c(x1))
         c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1)
         c#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> c#(x1)
         a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> a#(c(x1))
         a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1)
        Arctic Interpretation Processor:
         dimension: 2
         usable rules:
          a(a(x1)) -> a(b(c(x1)))
          c(a(x1)) -> x1
          c(b(x1)) -> a(a(c(x1)))
         interpretation:
          [c#](x0) = [0 1]x0,
          
                    [-& 0 ]     [0]
          [c](x0) = [0  -&]x0 + [1],
          
          [a#](x0) = [-& 0 ]x0 + [0],
          
                    [-& 0 ]     [0]
          [a](x0) = [0  1 ]x0 + [2],
          
                    [2 1]     [3]
          [b](x0) = [1 0]x0 + [2]
         orientation:
          c#(b(x1)) = [2 1]x1 + [3] >= [0 1]x1 = c#(x1)
          
          a#(a(x1)) = [0 1]x1 + [2] >= [0 1]x1 = c#(x1)
          
          c#(b(x1)) = [2 1]x1 + [3] >= [0  -&]x1 + [1] = a#(c(x1))
          
                     [0 1]     [2]    [0 1]     [2]              
          a(a(x1)) = [1 2]x1 + [3] >= [1 2]x1 + [3] = a(b(c(x1)))
          
                     [0  1 ]     [2]           
          c(a(x1)) = [-& 0 ]x1 + [1] >= x1 = x1
          
                     [1 0]     [2]    [1 0]     [2]              
          c(b(x1)) = [2 1]x1 + [3] >= [2 1]x1 + [3] = a(a(c(x1)))
         problem:
          DPs:
           c#(b(x1)) -> c#(x1)
           a#(a(x1)) -> c#(x1)
          TRS:
           a(a(x1)) -> a(b(c(x1)))
           c(a(x1)) -> x1
           c(b(x1)) -> a(a(c(x1)))
         Restore Modifier:
          DPs:
           c#(b(x1)) -> c#(x1)
           a#(a(x1)) -> c#(x1)
          TRS:
           a(a(x1)) -> a(b(c(x1)))
           c(a(x1)) -> x1
           c(b(x1)) -> a(a(c(x1)))
          EDG Processor:
           DPs:
            c#(b(x1)) -> c#(x1)
            a#(a(x1)) -> c#(x1)
           TRS:
            a(a(x1)) -> a(b(c(x1)))
            c(a(x1)) -> x1
            c(b(x1)) -> a(a(c(x1)))
           graph:
            c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1)
            a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1)
           SCC Processor:
            #sccs: 1
            #rules: 1
            #arcs: 2/4
            DPs:
             c#(b(x1)) -> c#(x1)
            TRS:
             a(a(x1)) -> a(b(c(x1)))
             c(a(x1)) -> x1
             c(b(x1)) -> a(a(c(x1)))
            Usable Rule Processor:
             DPs:
              c#(b(x1)) -> c#(x1)
             TRS:
              
             Arctic Interpretation Processor:
              dimension: 4
              usable rules:
               
              interpretation:
               [c#](x0) = [0  -& -& -&]x0,
               
                         [1 0 0 0]     [0]
                         [0 0 0 0]     [0]
               [b](x0) = [1 0 0 0]x0 + [0]
                         [0 0 0 0]     [0]
              orientation:
               c#(b(x1)) = [1 0 0 0]x1 + [0] >= [0  -& -& -&]x1 = c#(x1)
              problem:
               DPs:
                
               TRS:
                
              Qed