/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:
 top(sent(x)) -> top(check(rest(x)))
 rest(nil()) -> sent(nil())
 rest(cons(x,y)) -> sent(y)
 check(sent(x)) -> sent(check(x))
 check(rest(x)) -> rest(check(x))
 check(cons(x,y)) -> cons(check(x),y)
 check(cons(x,y)) -> cons(x,check(y))
 check(cons(x,y)) -> cons(x,y)

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [cons](x0, x1) = x0 + 4x1 + 5,
   
   [nil] = 0,
   
   [check](x0) = 2x0,
   
   [rest](x0) = x0,
   
   [top](x0) = x0,
   
   [sent](x0) = 4x0
  orientation:
   top(sent(x)) = 4x >= 2x = top(check(rest(x)))
   
   rest(nil()) = 0 >= 0 = sent(nil())
   
   rest(cons(x,y)) = x + 4y + 5 >= 4y = sent(y)
   
   check(sent(x)) = 8x >= 8x = sent(check(x))
   
   check(rest(x)) = 2x >= 2x = rest(check(x))
   
   check(cons(x,y)) = 2x + 8y + 10 >= 2x + 4y + 5 = cons(check(x),y)
   
   check(cons(x,y)) = 2x + 8y + 10 >= x + 8y + 5 = cons(x,check(y))
   
   check(cons(x,y)) = 2x + 8y + 10 >= x + 4y + 5 = cons(x,y)
  problem:
   top(sent(x)) -> top(check(rest(x)))
   rest(nil()) -> sent(nil())
   check(sent(x)) -> sent(check(x))
   check(rest(x)) -> rest(check(x))
  Matrix Interpretation Processor: dim=3
   
   interpretation:
            [0]
    [nil] = [1]
            [1],
    
                  [1 0 0]  
    [check](x0) = [0 0 0]x0
                  [0 0 0]  ,
    
                 [1 1 0]  
    [rest](x0) = [0 1 0]x0
                 [0 1 0]  ,
    
                [1 0 1]     [0]
    [top](x0) = [0 1 0]x0 + [1]
                [0 0 1]     [0],
    
                 [1 0 0]  
    [sent](x0) = [0 0 1]x0
                 [0 1 0]  
   orientation:
                   [1 1 0]    [0]    [1 1 0]    [0]                      
    top(sent(x)) = [0 0 1]x + [1] >= [0 0 0]x + [1] = top(check(rest(x)))
                   [0 1 0]    [0]    [0 0 0]    [0]                      
    
                  [1]    [0]              
    rest(nil()) = [1] >= [1] = sent(nil())
                  [1]    [1]              
    
                     [1 0 0]     [1 0 0]                  
    check(sent(x)) = [0 0 0]x >= [0 0 0]x = sent(check(x))
                     [0 0 0]     [0 0 0]                  
    
                     [1 1 0]     [1 0 0]                  
    check(rest(x)) = [0 0 0]x >= [0 0 0]x = rest(check(x))
                     [0 0 0]     [0 0 0]                  
   problem:
    top(sent(x)) -> top(check(rest(x)))
    check(sent(x)) -> sent(check(x))
    check(rest(x)) -> rest(check(x))
   Matrix Interpretation Processor: dim=3
    
    interpretation:
                   [1 0 1]  
     [check](x0) = [0 1 0]x0
                   [0 1 0]  ,
     
                    
     [rest](x0) = x0
                    ,
     
                 [1 1 0]  
     [top](x0) = [0 0 0]x0
                 [0 0 0]  ,
     
                  [1 0 1]     [0]
     [sent](x0) = [0 1 0]x0 + [1]
                  [0 1 0]     [1]
    orientation:
                    [1 1 1]    [1]    [1 1 1]                       
     top(sent(x)) = [0 0 0]x + [0] >= [0 0 0]x = top(check(rest(x)))
                    [0 0 0]    [0]    [0 0 0]                       
     
                      [1 1 1]    [1]    [1 1 1]    [0]                 
     check(sent(x)) = [0 1 0]x + [1] >= [0 1 0]x + [1] = sent(check(x))
                      [0 1 0]    [1]    [0 1 0]    [1]                 
     
                      [1 0 1]     [1 0 1]                  
     check(rest(x)) = [0 1 0]x >= [0 1 0]x = rest(check(x))
                      [0 1 0]     [0 1 0]                  
    problem:
     check(rest(x)) -> rest(check(x))
    Matrix Interpretation Processor: dim=3
     
     interpretation:
                    [1 0 1]  
      [check](x0) = [0 0 0]x0
                    [0 0 1]  ,
      
                   [1 0 0]     [0]
      [rest](x0) = [0 0 0]x0 + [0]
                   [0 0 1]     [1]
     orientation:
                       [1 0 1]    [1]    [1 0 1]    [0]                 
      check(rest(x)) = [0 0 0]x + [0] >= [0 0 0]x + [0] = rest(check(x))
                       [0 0 1]    [1]    [0 0 1]    [1]                 
     problem:
      
     Qed