/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:
 +(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:
   [h](x0, x1) = 4x0 + x1 + 4,
   
   [g](x0) = x0,
   
   [f](x0) = x0 + 4,
   
   [s](x0) = x0,
   
   [+](x0, x1) = x0 + x1 + 1,
   
   [0] = 0
  orientation:
   +(x,0()) = x + 1 >= x = x
   
   +(x,s(y)) = x + y + 1 >= x + y + 1 = s(+(x,y))
   
   +(0(),y) = y + 1 >= y = y
   
   +(s(x),y) = x + y + 1 >= x + y + 1 = s(+(x,y))
   
   +(x,+(y,z)) = x + y + z + 2 >= x + y + z + 2 = +(+(x,y),z)
   
   f(g(f(x))) = x + 8 >= x + 8 = f(h(s(0()),x))
   
   f(g(h(x,y))) = 4x + y + 8 >= 4x + y + 8 = f(h(s(x),y))
   
   f(h(x,h(y,z))) = 4x + 4y + z + 12 >= 4x + 4y + z + 12 = f(h(+(x,y),z))
  problem:
   +(x,s(y)) -> s(+(x,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))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [h](x0, x1) = 2x0 + 4x1 + 1,
    
    [g](x0) = 6x0 + 1,
    
    [f](x0) = x0 + 3,
    
    [s](x0) = x0,
    
    [+](x0, x1) = x0 + x1,
    
    [0] = 0
   orientation:
    +(x,s(y)) = x + y >= x + y = s(+(x,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))) = 6x + 22 >= 4x + 4 = f(h(s(0()),x))
    
    f(g(h(x,y))) = 12x + 24y + 10 >= 2x + 4y + 4 = f(h(s(x),y))
    
    f(h(x,h(y,z))) = 2x + 8y + 16z + 8 >= 2x + 2y + 4z + 4 = 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=3
    
    interpretation:
                    [0]
     [s](x0) = x0 + [1]
                    [1],
     
                        [1 1 0]  
     [+](x0, x1) = x0 + [0 0 1]x1
                        [0 0 1]  
    orientation:
                     [1 1 0]    [1]        [1 1 0]    [0]            
     +(x,s(y)) = x + [0 0 1]y + [1] >= x + [0 0 1]y + [1] = s(+(x,y))
                     [0 0 1]    [1]        [0 0 1]    [1]            
     
                     [1 1 0]    [0]        [1 1 0]    [0]            
     +(s(x),y) = x + [0 0 1]y + [1] >= x + [0 0 1]y + [1] = s(+(x,y))
                     [0 0 1]    [1]        [0 0 1]    [1]            
     
                       [1 1 0]    [1 1 1]         [1 1 0]    [1 1 0]               
     +(x,+(y,z)) = x + [0 0 1]y + [0 0 1]z >= x + [0 0 1]y + [0 0 1]z = +(+(x,y),z)
                       [0 0 1]    [0 0 1]         [0 0 1]    [0 0 1]               
    problem:
     +(s(x),y) -> s(+(x,y))
     +(x,+(y,z)) -> +(+(x,y),z)
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [s](x0) = x0 + 6,
      
      [+](x0, x1) = x0 + 2x1 + 1
     orientation:
      +(s(x),y) = x + 2y + 7 >= x + 2y + 7 = s(+(x,y))
      
      +(x,+(y,z)) = x + 2y + 4z + 3 >= x + 2y + 2z + 2 = +(+(x,y),z)
     problem:
      +(s(x),y) -> s(+(x,y))
     Matrix Interpretation Processor: dim=1
      
      interpretation:
       [s](x0) = x0 + 1,
       
       [+](x0, x1) = 2x0 + 4x1 + 5
      orientation:
       +(s(x),y) = 2x + 4y + 7 >= 2x + 4y + 6 = s(+(x,y))
      problem:
       
      Qed