/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:
 strict:
  n(s(x1)) -> s(x1)
  o(s(x1)) -> s(x1)
  n(o(p(x1))) -> o(n(x1))
 weak:
  t(x1) -> t(c(n(x1)))
  p(s(x1)) -> s(x1)
  o(n(x1)) -> n(o(x1))
  p(n(x1)) -> m(p(x1))
  p(m(x1)) -> m(p(x1))
  o(m(x1)) -> n(o(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,
   
   [c](x0) = x0,
   
   [t](x0) = 4x0,
   
   [p](x0) = 10x0,
   
   [o](x0) = x0,
   
   [n](x0) = x0,
   
   [s](x0) = 5x0
  orientation:
   n(s(x1)) = 5x1 >= 5x1 = s(x1)
   
   o(s(x1)) = 5x1 >= 5x1 = s(x1)
   
   n(o(p(x1))) = 10x1 >= x1 = o(n(x1))
   
   t(x1) = 4x1 >= 4x1 = t(c(n(x1)))
   
   p(s(x1)) = 15x1 >= 5x1 = s(x1)
   
   o(n(x1)) = x1 >= x1 = n(o(x1))
   
   p(n(x1)) = 10x1 >= 10x1 = m(p(x1))
   
   p(m(x1)) = 10x1 >= 10x1 = m(p(x1))
   
   o(m(x1)) = x1 >= x1 = n(o(x1))
   
   n(p(x1)) = 10x1 >= 10x1 = p(n(x1))
   
   c(p(x1)) = 10x1 >= 10x1 = p(c(x1))
   
   c(m(x1)) = x1 >= x1 = m(c(x1))
   
   c(n(x1)) = x1 >= x1 = n(c(x1))
   
   c(o(x1)) = x1 >= x1 = o(c(x1))
   
   c(o(x1)) = x1 >= x1 = o(x1)
  problem:
   strict:
    n(s(x1)) -> s(x1)
    o(s(x1)) -> s(x1)
   weak:
    t(x1) -> t(c(n(x1)))
    o(n(x1)) -> n(o(x1))
    p(n(x1)) -> m(p(x1))
    p(m(x1)) -> m(p(x1))
    o(m(x1)) -> n(o(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)
  Arctic Interpretation Processor:
   dimension: 1
   interpretation:
    [m](x0) = x0,
    
    [c](x0) = x0,
    
    [t](x0) = x0,
    
    [p](x0) = 6x0,
    
    [o](x0) = 1x0,
    
    [n](x0) = x0,
    
    [s](x0) = x0
   orientation:
    n(s(x1)) = x1 >= x1 = s(x1)
    
    o(s(x1)) = 1x1 >= x1 = s(x1)
    
    t(x1) = x1 >= x1 = t(c(n(x1)))
    
    o(n(x1)) = 1x1 >= 1x1 = n(o(x1))
    
    p(n(x1)) = 6x1 >= 6x1 = m(p(x1))
    
    p(m(x1)) = 6x1 >= 6x1 = m(p(x1))
    
    o(m(x1)) = 1x1 >= 1x1 = n(o(x1))
    
    n(p(x1)) = 6x1 >= 6x1 = p(n(x1))
    
    c(p(x1)) = 6x1 >= 6x1 = p(c(x1))
    
    c(m(x1)) = x1 >= x1 = m(c(x1))
    
    c(n(x1)) = x1 >= x1 = n(c(x1))
    
    c(o(x1)) = 1x1 >= 1x1 = o(c(x1))
    
    c(o(x1)) = 1x1 >= 1x1 = o(x1)
   problem:
    strict:
     n(s(x1)) -> s(x1)
    weak:
     t(x1) -> t(c(n(x1)))
     o(n(x1)) -> n(o(x1))
     p(n(x1)) -> m(p(x1))
     p(m(x1)) -> m(p(x1))
     o(m(x1)) -> n(o(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]     [0]
     [m](x0) = [0 2]x0 + [1],
     
                 
     [c](x0) = x0,
     
               [1 0]     [2]
     [t](x0) = [1 0]x0 + [0],
     
               [2 0]  
     [p](x0) = [0 1]x0,
     
               [2 1]  
     [o](x0) = [0 1]x0,
     
               [1 0]     [0]
     [n](x0) = [0 2]x0 + [1],
     
                 
     [s](x0) = x0
    orientation:
                [1 0]     [0]              
     n(s(x1)) = [0 2]x1 + [1] >= x1 = s(x1)
     
             [1 0]     [2]    [1 0]     [2]              
     t(x1) = [1 0]x1 + [0] >= [1 0]x1 + [0] = t(c(n(x1)))
     
                [2 2]     [1]    [2 1]     [0]           
     o(n(x1)) = [0 2]x1 + [1] >= [0 2]x1 + [1] = n(o(x1))
     
                [2 0]     [0]    [2 0]     [0]           
     p(n(x1)) = [0 2]x1 + [1] >= [0 2]x1 + [1] = m(p(x1))
     
                [2 0]     [0]    [2 0]     [0]           
     p(m(x1)) = [0 2]x1 + [1] >= [0 2]x1 + [1] = m(p(x1))
     
                [2 2]     [1]    [2 1]     [0]           
     o(m(x1)) = [0 2]x1 + [1] >= [0 2]x1 + [1] = n(o(x1))
     
                [2 0]     [0]    [2 0]     [0]           
     n(p(x1)) = [0 2]x1 + [1] >= [0 2]x1 + [1] = p(n(x1))
     
                [2 0]      [2 0]             
     c(p(x1)) = [0 1]x1 >= [0 1]x1 = p(c(x1))
     
                [1 0]     [0]    [1 0]     [0]           
     c(m(x1)) = [0 2]x1 + [1] >= [0 2]x1 + [1] = m(c(x1))
     
                [1 0]     [0]    [1 0]     [0]           
     c(n(x1)) = [0 2]x1 + [1] >= [0 2]x1 + [1] = n(c(x1))
     
                [2 1]      [2 1]             
     c(o(x1)) = [0 1]x1 >= [0 1]x1 = o(c(x1))
     
                [2 1]      [2 1]          
     c(o(x1)) = [0 1]x1 >= [0 1]x1 = o(x1)
    problem:
     strict:
      n(s(x1)) -> s(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,
      
                [1 0]  
      [c](x0) = [0 0]x0,
      
                [1 2]     [2]
      [t](x0) = [0 2]x0 + [2],
      
                  
      [p](x0) = x0,
      
                [2 1]  
      [o](x0) = [0 0]x0,
      
                [1 2]  
      [n](x0) = [0 2]x0,
      
                [1 2]     [0]
      [s](x0) = [0 0]x0 + [1]
     orientation:
                 [1 2]     [2]    [1 2]     [0]        
      n(s(x1)) = [0 0]x1 + [2] >= [0 0]x1 + [1] = s(x1)
      
              [1 2]     [2]    [1 2]     [2]              
      t(x1) = [0 2]x1 + [2] >= [0 0]x1 + [2] = t(c(n(x1)))
      
                 [1 2]      [1 0]             
      p(n(x1)) = [0 2]x1 >= [0 0]x1 = m(p(x1))
      
                 [1 0]      [1 0]             
      p(m(x1)) = [0 0]x1 >= [0 0]x1 = m(p(x1))
      
                 [1 2]      [1 2]             
      n(p(x1)) = [0 2]x1 >= [0 2]x1 = p(n(x1))
      
                 [1 0]      [1 0]             
      c(p(x1)) = [0 0]x1 >= [0 0]x1 = 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))
      
                 [2 1]      [2 0]             
      c(o(x1)) = [0 0]x1 >= [0 0]x1 = o(c(x1))
      
                 [2 1]      [2 1]          
      c(o(x1)) = [0 0]x1 >= [0 0]x1 = o(x1)
     problem:
      strict:
       
      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)
     Qed