/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:
 app(nil(),y) -> y
 app(add(n,x),y) -> add(n,app(x,y))
 reverse(nil()) -> nil()
 reverse(add(n,x)) -> app(reverse(x),add(n,nil()))
 shuffle(nil()) -> nil()
 shuffle(add(n,x)) -> add(n,shuffle(reverse(x)))

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [shuffle](x0) = x0 + 1,
   
   [reverse](x0) = x0,
   
   [add](x0, x1) = 2x0 + x1,
   
   [app](x0, x1) = x0 + x1,
   
   [nil] = 0
  orientation:
   app(nil(),y) = y >= y = y
   
   app(add(n,x),y) = 2n + x + y >= 2n + x + y = add(n,app(x,y))
   
   reverse(nil()) = 0 >= 0 = nil()
   
   reverse(add(n,x)) = 2n + x >= 2n + x = app(reverse(x),add(n,nil()))
   
   shuffle(nil()) = 1 >= 0 = nil()
   
   shuffle(add(n,x)) = 2n + x + 1 >= 2n + x + 1 = add(n,shuffle(reverse(x)))
  problem:
   app(nil(),y) -> y
   app(add(n,x),y) -> add(n,app(x,y))
   reverse(nil()) -> nil()
   reverse(add(n,x)) -> app(reverse(x),add(n,nil()))
   shuffle(add(n,x)) -> add(n,shuffle(reverse(x)))
  Matrix Interpretation Processor: dim=3
   
   interpretation:
                    [1 1 0]  
    [shuffle](x0) = [0 1 0]x0
                    [1 0 0]  ,
    
                    [1 0 0]  
    [reverse](x0) = [0 1 0]x0
                    [0 0 0]  ,
    
                    [1 0 1]     [1 0 0]     [0]
    [add](x0, x1) = [0 0 0]x0 + [0 1 0]x1 + [1]
                    [0 0 0]     [0 0 0]     [0],
    
                    [1 0 0]       
    [app](x0, x1) = [0 1 0]x0 + x1
                    [0 0 0]       ,
    
            [0]
    [nil] = [0]
            [0]
   orientation:
                             
    app(nil(),y) = y >= y = y
                             
    
                      [1 0 1]    [1 0 0]        [0]    [1 0 1]    [1 0 0]    [1 0 0]    [0]                  
    app(add(n,x),y) = [0 0 0]n + [0 1 0]x + y + [1] >= [0 0 0]n + [0 1 0]x + [0 1 0]y + [1] = add(n,app(x,y))
                      [0 0 0]    [0 0 0]        [0]    [0 0 0]    [0 0 0]    [0 0 0]    [0]                  
    
                     [0]    [0]        
    reverse(nil()) = [0] >= [0] = nil()
                     [0]    [0]        
    
                        [1 0 1]    [1 0 0]    [0]    [1 0 1]    [1 0 0]    [0]                               
    reverse(add(n,x)) = [0 0 0]n + [0 1 0]x + [1] >= [0 0 0]n + [0 1 0]x + [1] = app(reverse(x),add(n,nil()))
                        [0 0 0]    [0 0 0]    [0]    [0 0 0]    [0 0 0]    [0]                               
    
                        [1 0 1]    [1 1 0]    [1]    [1 0 1]    [1 1 0]    [0]                             
    shuffle(add(n,x)) = [0 0 0]n + [0 1 0]x + [1] >= [0 0 0]n + [0 1 0]x + [1] = add(n,shuffle(reverse(x)))
                        [1 0 1]    [1 0 0]    [0]    [0 0 0]    [0 0 0]    [0]                             
   problem:
    app(nil(),y) -> y
    app(add(n,x),y) -> add(n,app(x,y))
    reverse(nil()) -> nil()
    reverse(add(n,x)) -> app(reverse(x),add(n,nil()))
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [reverse](x0) = 2x0 + 1,
     
     [add](x0, x1) = 4x0 + x1 + 6,
     
     [app](x0, x1) = x0 + x1,
     
     [nil] = 5
    orientation:
     app(nil(),y) = y + 5 >= y = y
     
     app(add(n,x),y) = 4n + x + y + 6 >= 4n + x + y + 6 = add(n,app(x,y))
     
     reverse(nil()) = 11 >= 5 = nil()
     
     reverse(add(n,x)) = 8n + 2x + 13 >= 4n + 2x + 12 = app(reverse(x),add(n,nil()))
    problem:
     app(add(n,x),y) -> add(n,app(x,y))
    Matrix Interpretation Processor: dim=3
     
     interpretation:
                      [1 0 0]     [1 0 0]     [0]
      [add](x0, x1) = [0 0 0]x0 + [0 0 1]x1 + [0]
                      [0 0 0]     [0 1 0]     [1],
      
                      [1 1 1]     [1 0 0]     [0]
      [app](x0, x1) = [0 0 1]x0 + [0 0 0]x1 + [0]
                      [0 1 0]     [0 0 0]     [1]
     orientation:
                        [1 0 0]    [1 1 1]    [1 0 0]    [1]    [1 0 0]    [1 1 1]    [1 0 0]    [0]                  
      app(add(n,x),y) = [0 0 0]n + [0 1 0]x + [0 0 0]y + [1] >= [0 0 0]n + [0 1 0]x + [0 0 0]y + [1] = add(n,app(x,y))
                        [0 0 0]    [0 0 1]    [0 0 0]    [1]    [0 0 0]    [0 0 1]    [0 0 0]    [1]                  
     problem:
      
     Qed