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


--------------------------------------------------------------------------------


YES

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

Proof:
 DP Processor:
  DPs:
   b#(c(x1)) -> b#(x1)
   b#(c(x1)) -> b#(b(x1))
   b#(c(x1)) -> a#(b(b(x1)))
  TRS:
   a(a(x1)) -> x1
   b(b(x1)) -> c(c(c(x1)))
   b(c(x1)) -> a(b(b(x1)))
  TDG Processor:
   DPs:
    b#(c(x1)) -> b#(x1)
    b#(c(x1)) -> b#(b(x1))
    b#(c(x1)) -> a#(b(b(x1)))
   TRS:
    a(a(x1)) -> x1
    b(b(x1)) -> c(c(c(x1)))
    b(c(x1)) -> a(b(b(x1)))
   graph:
    b#(c(x1)) -> b#(b(x1)) -> b#(c(x1)) -> a#(b(b(x1)))
    b#(c(x1)) -> b#(b(x1)) -> b#(c(x1)) -> b#(b(x1))
    b#(c(x1)) -> b#(b(x1)) -> b#(c(x1)) -> b#(x1)
    b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> a#(b(b(x1)))
    b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> b#(b(x1))
    b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> b#(x1)
   SCC Processor:
    #sccs: 1
    #rules: 2
    #arcs: 6/9
    DPs:
     b#(c(x1)) -> b#(b(x1))
     b#(c(x1)) -> b#(x1)
    TRS:
     a(a(x1)) -> x1
     b(b(x1)) -> c(c(c(x1)))
     b(c(x1)) -> a(b(b(x1)))
    Arctic Interpretation Processor:
     dimension: 3
     usable rules:
      a(a(x1)) -> x1
      b(b(x1)) -> c(c(c(x1)))
      b(c(x1)) -> a(b(b(x1)))
     interpretation:
      [b#](x0) = [-2 -& 0 ]x0 + [0],
      
                [-& -2 0 ]     [0 ]
      [c](x0) = [-& 0  -&]x0 + [-1]
                [-2 1  0 ]     [1 ],
      
                [-& 0  1 ]     [0]
      [b](x0) = [-2 1  0 ]x0 + [1]
                [-& 0  -1]     [0],
      
                [0  0  1 ]     [-&]
      [a](x0) = [0  -& 0 ]x0 + [-&]
                [-1 -& -1]     [-1]
     orientation:
      b#(c(x1)) = [-2 1  0 ]x1 + [1] >= [-& 0  -1]x1 + [0] = b#(b(x1))
      
      b#(c(x1)) = [-2 1  0 ]x1 + [1] >= [-2 -& 0 ]x1 + [0] = b#(x1)
      
                 [0  0  1 ]     [0 ]           
      a(a(x1)) = [0  0  1 ]x1 + [-1] >= x1 = x1
                 [-1 -1 0 ]     [-1]           
      
                 [-2 1  0 ]     [1]    [-2 1  0 ]     [1 ]              
      b(b(x1)) = [-1 2  1 ]x1 + [2] >= [-& 0  -&]x1 + [-1] = c(c(c(x1)))
                 [-2 1  0 ]     [1]    [-2 1  0 ]     [1 ]              
      
                 [-1 2  1 ]     [2]    [-1 2  1 ]     [2]              
      b(c(x1)) = [-2 1  0 ]x1 + [1] >= [-2 1  0 ]x1 + [1] = a(b(b(x1)))
                 [-3 0  -1]     [0]    [-3 0  -1]     [0]              
     problem:
      DPs:
       b#(c(x1)) -> b#(x1)
      TRS:
       a(a(x1)) -> x1
       b(b(x1)) -> c(c(c(x1)))
       b(c(x1)) -> a(b(b(x1)))
     Restore Modifier:
      DPs:
       b#(c(x1)) -> b#(x1)
      TRS:
       a(a(x1)) -> x1
       b(b(x1)) -> c(c(c(x1)))
       b(c(x1)) -> a(b(b(x1)))
      EDG Processor:
       DPs:
        b#(c(x1)) -> b#(x1)
       TRS:
        a(a(x1)) -> x1
        b(b(x1)) -> c(c(c(x1)))
        b(c(x1)) -> a(b(b(x1)))
       graph:
        b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> b#(x1)
       Usable Rule Processor:
        DPs:
         b#(c(x1)) -> b#(x1)
        TRS:
         
        Arctic Interpretation Processor:
         dimension: 4
         usable rules:
          
         interpretation:
          [b#](x0) = [0  -& -& -&]x0,
          
                    [1 0 0 0]     [0]
                    [0 0 0 0]     [0]
          [c](x0) = [1 0 0 0]x0 + [0]
                    [0 0 0 0]     [0]
         orientation:
          b#(c(x1)) = [1 0 0 0]x1 + [0] >= [0  -& -& -&]x1 = b#(x1)
         problem:
          DPs:
           
          TRS:
           
         Qed