/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:
 not(true()) -> false()
 not(false()) -> true()
 odd(0()) -> false()
 odd(s(x)) -> not(odd(x))
 +(x,0()) -> x
 +(x,s(y)) -> s(+(x,y))
 +(s(x),y) -> s(+(x,y))

Proof:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
                 [1 0 0]     [1 0 0]     [0]
   [+](x0, x1) = [0 1 1]x0 + [0 0 0]x1 + [0]
                 [0 0 1]     [0 0 0]     [1],
   
             [1 0 0]  
   [s](x0) = [0 0 0]x0
             [0 0 0]  ,
   
               [1 0 0]     [0]
   [odd](x0) = [1 0 0]x0 + [0]
               [0 0 0]     [1],
   
         [1]
   [0] = [0]
         [0],
   
             [0]
   [false] = [0]
             [0],
   
               [1 0 0]  
   [not](x0) = [0 0 0]x0
               [0 0 0]  ,
   
            [0]
   [true] = [0]
            [0]
  orientation:
                 [0]    [0]          
   not(true()) = [0] >= [0] = false()
                 [0]    [0]          
   
                  [0]    [0]         
   not(false()) = [0] >= [0] = true()
                  [0]    [0]         
   
              [1]    [0]          
   odd(0()) = [1] >= [0] = false()
              [1]    [0]          
   
               [1 0 0]    [0]    [1 0 0]               
   odd(s(x)) = [1 0 0]x + [0] >= [0 0 0]x = not(odd(x))
               [0 0 0]    [1]    [0 0 0]               
   
              [1 0 0]    [1]         
   +(x,0()) = [0 1 1]x + [0] >= x = x
              [0 0 1]    [1]         
   
               [1 0 0]    [1 0 0]    [0]    [1 0 0]    [1 0 0]             
   +(x,s(y)) = [0 1 1]x + [0 0 0]y + [0] >= [0 0 0]x + [0 0 0]y = s(+(x,y))
               [0 0 1]    [0 0 0]    [1]    [0 0 0]    [0 0 0]             
   
               [1 0 0]    [1 0 0]    [0]    [1 0 0]    [1 0 0]             
   +(s(x),y) = [0 0 0]x + [0 0 0]y + [0] >= [0 0 0]x + [0 0 0]y = s(+(x,y))
               [0 0 0]    [0 0 0]    [1]    [0 0 0]    [0 0 0]             
  problem:
   not(true()) -> false()
   not(false()) -> true()
   odd(s(x)) -> not(odd(x))
   +(x,s(y)) -> s(+(x,y))
   +(s(x),y) -> s(+(x,y))
  Matrix Interpretation Processor: dim=3
   
   interpretation:
                  [1 0 0]     [1 0 0]     [1]
    [+](x0, x1) = [0 1 0]x0 + [0 1 0]x1 + [0]
                  [0 0 0]     [0 0 0]     [1],
    
                   [0]
    [s](x0) = x0 + [1]
                   [0],
    
                [1 1 0]  
    [odd](x0) = [0 0 0]x0
                [0 0 0]  ,
    
              [0]
    [false] = [1]
              [1],
    
                [1 0 1]  
    [not](x0) = [0 1 0]x0
                [0 1 0]  ,
    
             [0]
    [true] = [1]
             [1]
   orientation:
                  [1]    [0]          
    not(true()) = [1] >= [1] = false()
                  [1]    [1]          
    
                   [1]    [0]         
    not(false()) = [1] >= [1] = true()
                   [1]    [1]         
    
                [1 1 0]    [1]    [1 1 0]               
    odd(s(x)) = [0 0 0]x + [0] >= [0 0 0]x = not(odd(x))
                [0 0 0]    [0]    [0 0 0]               
    
                [1 0 0]    [1 0 0]    [1]    [1 0 0]    [1 0 0]    [1]            
    +(x,s(y)) = [0 1 0]x + [0 1 0]y + [1] >= [0 1 0]x + [0 1 0]y + [1] = s(+(x,y))
                [0 0 0]    [0 0 0]    [1]    [0 0 0]    [0 0 0]    [1]            
    
                [1 0 0]    [1 0 0]    [1]    [1 0 0]    [1 0 0]    [1]            
    +(s(x),y) = [0 1 0]x + [0 1 0]y + [1] >= [0 1 0]x + [0 1 0]y + [1] = s(+(x,y))
                [0 0 0]    [0 0 0]    [1]    [0 0 0]    [0 0 0]    [1]            
   problem:
    +(x,s(y)) -> s(+(x,y))
    +(s(x),y) -> s(+(x,y))
   Matrix Interpretation Processor: dim=3
    
    interpretation:
                   [1 0 1]     [1 0 1]  
     [+](x0, x1) = [0 0 1]x0 + [0 0 1]x1
                   [0 0 1]     [0 0 1]  ,
     
               [1 0 0]     [0]
     [s](x0) = [0 0 0]x0 + [0]
               [0 0 1]     [1]
    orientation:
                 [1 0 1]    [1 0 1]    [1]    [1 0 1]    [1 0 1]    [0]            
     +(x,s(y)) = [0 0 1]x + [0 0 1]y + [1] >= [0 0 0]x + [0 0 0]y + [0] = s(+(x,y))
                 [0 0 1]    [0 0 1]    [1]    [0 0 1]    [0 0 1]    [1]            
     
                 [1 0 1]    [1 0 1]    [1]    [1 0 1]    [1 0 1]    [0]            
     +(s(x),y) = [0 0 1]x + [0 0 1]y + [1] >= [0 0 0]x + [0 0 0]y + [0] = s(+(x,y))
                 [0 0 1]    [0 0 1]    [1]    [0 0 1]    [0 0 1]    [1]            
    problem:
     
    Qed