/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:
 strict:
  p(s(x1)) -> s(x1)
  n(s(x1)) -> s(x1)
  o(s(x1)) -> s(x1)
  o(n(x1)) -> n(o(x1))
  o(m(x1)) -> n(o(x1))
  n(o(p(x1))) -> o(n(x1))
 weak:
  t(x1) -> t(c(n(x1)))
  p(n(x1)) -> m(p(x1))
  p(m(x1)) -> m(p(x1))
  n(p(x1)) -> p(n(x1))
  c(p(x1)) -> p(c(x1))
  c(m(x1)) -> m(c(x1))
  c(n(x1)) -> n(c(x1))
  c(o(x1)) -> o(c(x1))
  c(o(x1)) -> o(x1)

Proof:
 Arctic Interpretation Processor:
  dimension: 1
  interpretation:
   [m](x0) = x0,
   
   [p](x0) = x0,
   
   [o](x0) = 2x0,
   
   [t](x0) = x0,
   
   [s](x0) = x0,
   
   [c](x0) = x0,
   
   [n](x0) = x0
  orientation:
   p(s(x1)) = x1 >= x1 = s(x1)
   
   n(s(x1)) = x1 >= x1 = s(x1)
   
   o(s(x1)) = 2x1 >= x1 = s(x1)
   
   o(n(x1)) = 2x1 >= 2x1 = n(o(x1))
   
   o(m(x1)) = 2x1 >= 2x1 = n(o(x1))
   
   n(o(p(x1))) = 2x1 >= 2x1 = o(n(x1))
   
   t(x1) = x1 >= x1 = t(c(n(x1)))
   
   p(n(x1)) = x1 >= x1 = m(p(x1))
   
   p(m(x1)) = x1 >= x1 = m(p(x1))
   
   n(p(x1)) = x1 >= x1 = p(n(x1))
   
   c(p(x1)) = x1 >= x1 = p(c(x1))
   
   c(m(x1)) = x1 >= x1 = m(c(x1))
   
   c(n(x1)) = x1 >= x1 = n(c(x1))
   
   c(o(x1)) = 2x1 >= 2x1 = o(c(x1))
   
   c(o(x1)) = 2x1 >= 2x1 = o(x1)
  problem:
   strict:
    p(s(x1)) -> s(x1)
    n(s(x1)) -> s(x1)
    o(n(x1)) -> n(o(x1))
    o(m(x1)) -> n(o(x1))
    n(o(p(x1))) -> o(n(x1))
   weak:
    t(x1) -> t(c(n(x1)))
    p(n(x1)) -> m(p(x1))
    p(m(x1)) -> m(p(x1))
    n(p(x1)) -> p(n(x1))
    c(p(x1)) -> p(c(x1))
    c(m(x1)) -> m(c(x1))
    c(n(x1)) -> n(c(x1))
    c(o(x1)) -> o(c(x1))
    c(o(x1)) -> o(x1)
  String Reversal Processor:
   strict:
    s(p(x1)) -> s(x1)
    s(n(x1)) -> s(x1)
    n(o(x1)) -> o(n(x1))
    m(o(x1)) -> o(n(x1))
    p(o(n(x1))) -> n(o(x1))
   weak:
    t(x1) -> n(c(t(x1)))
    n(p(x1)) -> p(m(x1))
    m(p(x1)) -> p(m(x1))
    p(n(x1)) -> n(p(x1))
    p(c(x1)) -> c(p(x1))
    m(c(x1)) -> c(m(x1))
    n(c(x1)) -> c(n(x1))
    o(c(x1)) -> c(o(x1))
    o(c(x1)) -> o(x1)
   Arctic Interpretation Processor:
    dimension: 1
    interpretation:
     [m](x0) = x0,
     
     [p](x0) = 8x0,
     
     [o](x0) = x0,
     
     [t](x0) = x0,
     
     [s](x0) = 4x0,
     
     [c](x0) = x0,
     
     [n](x0) = x0
    orientation:
     s(p(x1)) = 12x1 >= 4x1 = s(x1)
     
     s(n(x1)) = 4x1 >= 4x1 = s(x1)
     
     n(o(x1)) = x1 >= x1 = o(n(x1))
     
     m(o(x1)) = x1 >= x1 = o(n(x1))
     
     p(o(n(x1))) = 8x1 >= x1 = n(o(x1))
     
     t(x1) = x1 >= x1 = n(c(t(x1)))
     
     n(p(x1)) = 8x1 >= 8x1 = p(m(x1))
     
     m(p(x1)) = 8x1 >= 8x1 = p(m(x1))
     
     p(n(x1)) = 8x1 >= 8x1 = n(p(x1))
     
     p(c(x1)) = 8x1 >= 8x1 = c(p(x1))
     
     m(c(x1)) = x1 >= x1 = c(m(x1))
     
     n(c(x1)) = x1 >= x1 = c(n(x1))
     
     o(c(x1)) = x1 >= x1 = c(o(x1))
     
     o(c(x1)) = x1 >= x1 = o(x1)
    problem:
     strict:
      s(n(x1)) -> s(x1)
      n(o(x1)) -> o(n(x1))
      m(o(x1)) -> o(n(x1))
     weak:
      t(x1) -> n(c(t(x1)))
      n(p(x1)) -> p(m(x1))
      m(p(x1)) -> p(m(x1))
      p(n(x1)) -> n(p(x1))
      p(c(x1)) -> c(p(x1))
      m(c(x1)) -> c(m(x1))
      n(c(x1)) -> c(n(x1))
      o(c(x1)) -> c(o(x1))
      o(c(x1)) -> o(x1)
    String Reversal Processor:
     strict:
      n(s(x1)) -> s(x1)
      o(n(x1)) -> n(o(x1))
      o(m(x1)) -> n(o(x1))
     weak:
      t(x1) -> t(c(n(x1)))
      p(n(x1)) -> m(p(x1))
      p(m(x1)) -> m(p(x1))
      n(p(x1)) -> p(n(x1))
      c(p(x1)) -> p(c(x1))
      c(m(x1)) -> m(c(x1))
      c(n(x1)) -> n(c(x1))
      c(o(x1)) -> o(c(x1))
      c(o(x1)) -> o(x1)
     Matrix Interpretation Processor: dim=2
      
      interpretation:
                 [1 0]  
       [m](x0) = [0 0]x0,
       
                      [2]
       [p](x0) = x0 + [0],
       
                 [1 0]  
       [o](x0) = [0 0]x0,
       
                 [1 2]  
       [t](x0) = [0 2]x0,
       
                 [1 0]     [0]
       [s](x0) = [0 0]x0 + [1],
       
                 [1 0]  
       [c](x0) = [0 0]x0,
       
                 [1 2]  
       [n](x0) = [0 2]x0
      orientation:
                  [1 0]     [2]    [1 0]     [0]        
       n(s(x1)) = [0 0]x1 + [2] >= [0 0]x1 + [1] = s(x1)
       
                  [1 2]      [1 0]             
       o(n(x1)) = [0 0]x1 >= [0 0]x1 = n(o(x1))
       
                  [1 0]      [1 0]             
       o(m(x1)) = [0 0]x1 >= [0 0]x1 = n(o(x1))
       
               [1 2]      [1 2]                
       t(x1) = [0 2]x1 >= [0 0]x1 = t(c(n(x1)))
       
                  [1 2]     [2]    [1 0]     [2]           
       p(n(x1)) = [0 2]x1 + [0] >= [0 0]x1 + [0] = m(p(x1))
       
                  [1 0]     [2]    [1 0]     [2]           
       p(m(x1)) = [0 0]x1 + [0] >= [0 0]x1 + [0] = m(p(x1))
       
                  [1 2]     [2]    [1 2]     [2]           
       n(p(x1)) = [0 2]x1 + [0] >= [0 2]x1 + [0] = p(n(x1))
       
                  [1 0]     [2]    [1 0]     [2]           
       c(p(x1)) = [0 0]x1 + [0] >= [0 0]x1 + [0] = p(c(x1))
       
                  [1 0]      [1 0]             
       c(m(x1)) = [0 0]x1 >= [0 0]x1 = m(c(x1))
       
                  [1 2]      [1 0]             
       c(n(x1)) = [0 0]x1 >= [0 0]x1 = n(c(x1))
       
                  [1 0]      [1 0]             
       c(o(x1)) = [0 0]x1 >= [0 0]x1 = o(c(x1))
       
                  [1 0]      [1 0]          
       c(o(x1)) = [0 0]x1 >= [0 0]x1 = o(x1)
      problem:
       strict:
        o(n(x1)) -> n(o(x1))
        o(m(x1)) -> n(o(x1))
       weak:
        t(x1) -> t(c(n(x1)))
        p(n(x1)) -> m(p(x1))
        p(m(x1)) -> m(p(x1))
        n(p(x1)) -> p(n(x1))
        c(p(x1)) -> p(c(x1))
        c(m(x1)) -> m(c(x1))
        c(n(x1)) -> n(c(x1))
        c(o(x1)) -> o(c(x1))
        c(o(x1)) -> o(x1)
      String Reversal Processor:
       strict:
        n(o(x1)) -> o(n(x1))
        m(o(x1)) -> o(n(x1))
       weak:
        t(x1) -> n(c(t(x1)))
        n(p(x1)) -> p(m(x1))
        m(p(x1)) -> p(m(x1))
        p(n(x1)) -> n(p(x1))
        p(c(x1)) -> c(p(x1))
        m(c(x1)) -> c(m(x1))
        n(c(x1)) -> c(n(x1))
        o(c(x1)) -> c(o(x1))
        o(c(x1)) -> o(x1)
       Matrix Interpretation Processor: dim=2
        
        interpretation:
                   [1 1]  
         [m](x0) = [0 1]x0,
         
                   [2 0]  
         [p](x0) = [0 2]x0,
         
                        [0]
         [o](x0) = x0 + [1],
         
                   [1 2]     [3]
         [t](x0) = [0 0]x0 + [0],
         
                     
         [c](x0) = x0,
         
                   [1 1]  
         [n](x0) = [0 1]x0
        orientation:
                    [1 1]     [1]    [1 1]     [0]           
         n(o(x1)) = [0 1]x1 + [1] >= [0 1]x1 + [1] = o(n(x1))
         
                    [1 1]     [1]    [1 1]     [0]           
         m(o(x1)) = [0 1]x1 + [1] >= [0 1]x1 + [1] = o(n(x1))
         
                 [1 2]     [3]    [1 2]     [3]              
         t(x1) = [0 0]x1 + [0] >= [0 0]x1 + [0] = n(c(t(x1)))
         
                    [2 2]      [2 2]             
         n(p(x1)) = [0 2]x1 >= [0 2]x1 = p(m(x1))
         
                    [2 2]      [2 2]             
         m(p(x1)) = [0 2]x1 >= [0 2]x1 = p(m(x1))
         
                    [2 2]      [2 2]             
         p(n(x1)) = [0 2]x1 >= [0 2]x1 = n(p(x1))
         
                    [2 0]      [2 0]             
         p(c(x1)) = [0 2]x1 >= [0 2]x1 = c(p(x1))
         
                    [1 1]      [1 1]             
         m(c(x1)) = [0 1]x1 >= [0 1]x1 = c(m(x1))
         
                    [1 1]      [1 1]             
         n(c(x1)) = [0 1]x1 >= [0 1]x1 = c(n(x1))
         
                         [0]         [0]           
         o(c(x1)) = x1 + [1] >= x1 + [1] = c(o(x1))
         
                         [0]         [0]        
         o(c(x1)) = x1 + [1] >= x1 + [1] = o(x1)
        problem:
         strict:
          
         weak:
          t(x1) -> n(c(t(x1)))
          n(p(x1)) -> p(m(x1))
          m(p(x1)) -> p(m(x1))
          p(n(x1)) -> n(p(x1))
          p(c(x1)) -> c(p(x1))
          m(c(x1)) -> c(m(x1))
          n(c(x1)) -> c(n(x1))
          o(c(x1)) -> c(o(x1))
          o(c(x1)) -> o(x1)
        Qed