/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:
 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,
   
   [app](x0, x1) = x0 + x1,
   
   [reverse](x0) = x0,
   
   [nil] = 0,
   
   [add](x0, x1) = x0 + x1 + 4
  orientation:
   app(nil(),y) = y >= y = y
   
   app(add(n,x),y) = n + x + y + 4 >= n + x + y + 4 = add(n,app(x,y))
   
   reverse(nil()) = 0 >= 0 = nil()
   
   reverse(add(n,x)) = n + x + 4 >= n + x + 4 = app(reverse(x),add(n,nil()))
   
   shuffle(nil()) = 1 >= 0 = nil()
   
   shuffle(add(n,x)) = n + x + 5 >= n + x + 5 = 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=1
   
   interpretation:
    [shuffle](x0) = 4x0 + 7,
    
    [app](x0, x1) = x0 + x1,
    
    [reverse](x0) = x0,
    
    [nil] = 0,
    
    [add](x0, x1) = 2x0 + x1 + 1
   orientation:
    app(nil(),y) = y >= y = y
    
    app(add(n,x),y) = 2n + x + y + 1 >= 2n + x + y + 1 = add(n,app(x,y))
    
    reverse(nil()) = 0 >= 0 = nil()
    
    reverse(add(n,x)) = 2n + x + 1 >= 2n + x + 1 = app(reverse(x),add(n,nil()))
    
    shuffle(add(n,x)) = 8n + 4x + 11 >= 2n + 4x + 8 = 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()))
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [app](x0, x1) = x0 + x1,
     
     [reverse](x0) = 2x0 + 2,
     
     [nil] = 1,
     
     [add](x0, x1) = x0 + x1 + 2
    orientation:
     app(nil(),y) = y + 1 >= y = y
     
     app(add(n,x),y) = n + x + y + 2 >= n + x + y + 2 = add(n,app(x,y))
     
     reverse(nil()) = 4 >= 1 = nil()
     
     reverse(add(n,x)) = 2n + 2x + 6 >= n + 2x + 5 = app(reverse(x),add(n,nil()))
    problem:
     app(add(n,x),y) -> add(n,app(x,y))
    Matrix Interpretation Processor: dim=3
     
     interpretation:
                      [1 1 1]     [1 0 0]     [0]
      [app](x0, x1) = [0 0 1]x0 + [1 0 0]x1 + [1]
                      [0 1 0]     [1 0 0]     [0],
      
                      [1 0 0]     [1 0 0]     [0]
      [add](x0, x1) = [0 0 0]x0 + [0 0 1]x1 + [1]
                      [0 0 0]     [0 1 0]     [0]
     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 + [1 0 0]y + [1] >= [0 0 0]n + [0 1 0]x + [1 0 0]y + [1] = add(n,app(x,y))
                        [0 0 0]    [0 0 1]    [1 0 0]    [1]    [0 0 0]    [0 0 1]    [1 0 0]    [1]                  
     problem:
      
     Qed