/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:
 +(x,0()) -> x
 +(x,s(y)) -> s(+(x,y))
 +(0(),y) -> y
 +(s(x),y) -> s(+(x,y))
 +(x,+(y,z)) -> +(+(x,y),z)
 f(g(f(x))) -> f(h(s(0()),x))
 f(g(h(x,y))) -> f(h(s(x),y))
 f(h(x,h(y,z))) -> f(h(+(x,y),z))

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [g](x0) = 2x0 + 1,
   
   [+](x0, x1) = x0 + x1,
   
   [f](x0) = 2x0 + 1,
   
   [h](x0, x1) = 4x0 + x1,
   
   [0] = 0,
   
   [s](x0) = x0
  orientation:
   +(x,0()) = x >= x = x
   
   +(x,s(y)) = x + y >= x + y = s(+(x,y))
   
   +(0(),y) = y >= y = y
   
   +(s(x),y) = x + y >= x + y = s(+(x,y))
   
   +(x,+(y,z)) = x + y + z >= x + y + z = +(+(x,y),z)
   
   f(g(f(x))) = 8x + 7 >= 2x + 1 = f(h(s(0()),x))
   
   f(g(h(x,y))) = 16x + 4y + 3 >= 8x + 2y + 1 = f(h(s(x),y))
   
   f(h(x,h(y,z))) = 8x + 8y + 2z + 1 >= 8x + 8y + 2z + 1 = f(h(+(x,y),z))
  problem:
   +(x,0()) -> x
   +(x,s(y)) -> s(+(x,y))
   +(0(),y) -> y
   +(s(x),y) -> s(+(x,y))
   +(x,+(y,z)) -> +(+(x,y),z)
   f(h(x,h(y,z))) -> f(h(+(x,y),z))
  Matrix Interpretation Processor: dim=3
   
   interpretation:
                         
    [+](x0, x1) = x0 + x1
                         ,
    
              [1 0 0]     [1]
    [f](x0) = [0 0 0]x0 + [0]
              [0 0 0]     [0],
    
                  [1 0 0]     [1 0 0]  
    [h](x0, x1) = [0 0 1]x0 + [0 0 0]x1
                  [0 0 0]     [0 1 0]  ,
    
          [1]
    [0] = [0]
          [0],
    
              [1 0 0]  
    [s](x0) = [0 0 0]x0
              [0 0 0]  
   orientation:
                   [1]         
    +(x,0()) = x + [0] >= x = x
                   [0]         
    
                    [1 0 0]     [1 0 0]    [1 0 0]             
    +(x,s(y)) = x + [0 0 0]y >= [0 0 0]x + [0 0 0]y = s(+(x,y))
                    [0 0 0]     [0 0 0]    [0 0 0]             
    
                   [1]         
    +(0(),y) = y + [0] >= y = y
                   [0]         
    
                [1 0 0]         [1 0 0]    [1 0 0]             
    +(s(x),y) = [0 0 0]x + y >= [0 0 0]x + [0 0 0]y = s(+(x,y))
                [0 0 0]         [0 0 0]    [0 0 0]             
    
                                                      
    +(x,+(y,z)) = x + y + z >= x + y + z = +(+(x,y),z)
                                                      
    
                     [1 0 0]    [1 0 0]    [1 0 0]    [1]    [1 0 0]    [1 0 0]    [1 0 0]    [1]                 
    f(h(x,h(y,z))) = [0 0 0]x + [0 0 0]y + [0 0 0]z + [0] >= [0 0 0]x + [0 0 0]y + [0 0 0]z + [0] = f(h(+(x,y),z))
                     [0 0 0]    [0 0 0]    [0 0 0]    [0]    [0 0 0]    [0 0 0]    [0 0 0]    [0]                 
   problem:
    +(x,s(y)) -> s(+(x,y))
    +(s(x),y) -> s(+(x,y))
    +(x,+(y,z)) -> +(+(x,y),z)
    f(h(x,h(y,z))) -> f(h(+(x,y),z))
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [+](x0, x1) = x0 + x1,
     
     [f](x0) = 2x0,
     
     [h](x0, x1) = 4x0 + 2x1 + 1,
     
     [s](x0) = x0 + 4
    orientation:
     +(x,s(y)) = x + y + 4 >= x + y + 4 = s(+(x,y))
     
     +(s(x),y) = x + y + 4 >= x + y + 4 = s(+(x,y))
     
     +(x,+(y,z)) = x + y + z >= x + y + z = +(+(x,y),z)
     
     f(h(x,h(y,z))) = 8x + 16y + 8z + 6 >= 8x + 8y + 4z + 2 = f(h(+(x,y),z))
    problem:
     +(x,s(y)) -> s(+(x,y))
     +(s(x),y) -> s(+(x,y))
     +(x,+(y,z)) -> +(+(x,y),z)
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [+](x0, x1) = x0 + 2x1 + 5,
      
      [s](x0) = x0
     orientation:
      +(x,s(y)) = x + 2y + 5 >= x + 2y + 5 = s(+(x,y))
      
      +(s(x),y) = x + 2y + 5 >= x + 2y + 5 = s(+(x,y))
      
      +(x,+(y,z)) = x + 2y + 4z + 15 >= x + 2y + 2z + 10 = +(+(x,y),z)
     problem:
      +(x,s(y)) -> s(+(x,y))
      +(s(x),y) -> s(+(x,y))
     Matrix Interpretation Processor: dim=3
      
      interpretation:
                     [1 1 0]     [1 1 0]  
       [+](x0, x1) = [0 0 1]x0 + [0 1 0]x1
                     [0 0 1]     [0 0 1]  ,
       
                      [0]
       [s](x0) = x0 + [1]
                      [1]
      orientation:
                   [1 1 0]    [1 1 0]    [1]    [1 1 0]    [1 1 0]    [0]            
       +(x,s(y)) = [0 0 1]x + [0 1 0]y + [1] >= [0 0 1]x + [0 1 0]y + [1] = s(+(x,y))
                   [0 0 1]    [0 0 1]    [1]    [0 0 1]    [0 0 1]    [1]            
       
                   [1 1 0]    [1 1 0]    [1]    [1 1 0]    [1 1 0]    [0]            
       +(s(x),y) = [0 0 1]x + [0 1 0]y + [1] >= [0 0 1]x + [0 1 0]y + [1] = s(+(x,y))
                   [0 0 1]    [0 0 1]    [1]    [0 0 1]    [0 0 1]    [1]            
      problem:
       
      Qed