/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

Problem:
 app(nil(),k) -> k
 app(l,nil()) -> l
 app(cons(x,l),k) -> cons(x,app(l,k))
 sum(cons(x,nil())) -> cons(x,nil())
 sum(cons(x,cons(y,l))) -> sum(cons(plus(x,y),l))
 sum(app(l,cons(x,cons(y,k)))) -> sum(app(l,sum(cons(x,cons(y,k)))))
 plus(0(),y) -> y
 plus(s(x),y) -> s(plus(x,y))

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [s](x0) = x0,
   
   [0] = 1,
   
   [plus](x0, x1) = x0 + x1,
   
   [sum](x0) = x0,
   
   [cons](x0, x1) = x0 + x1 + 3,
   
   [app](x0, x1) = 6x0 + x1,
   
   [nil] = 0
  orientation:
   app(nil(),k) = k >= k = k
   
   app(l,nil()) = 6l >= l = l
   
   app(cons(x,l),k) = k + 6l + 6x + 18 >= k + 6l + x + 3 = cons(x,app(l,k))
   
   sum(cons(x,nil())) = x + 3 >= x + 3 = cons(x,nil())
   
   sum(cons(x,cons(y,l))) = l + x + y + 6 >= l + x + y + 3 = sum(cons(plus(x,y),l))
   
   sum(app(l,cons(x,cons(y,k)))) = k + 6l + x + y + 6 >= k + 6l + x + y + 6 = sum(app(l,sum(cons(x,cons(y,k)))))
   
   plus(0(),y) = y + 1 >= y = y
   
   plus(s(x),y) = x + y >= x + y = s(plus(x,y))
  problem:
   app(nil(),k) -> k
   app(l,nil()) -> l
   sum(cons(x,nil())) -> cons(x,nil())
   sum(app(l,cons(x,cons(y,k)))) -> sum(app(l,sum(cons(x,cons(y,k)))))
   plus(s(x),y) -> s(plus(x,y))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [s](x0) = x0 + 3,
    
    [plus](x0, x1) = 2x0 + x1 + 1,
    
    [sum](x0) = x0,
    
    [cons](x0, x1) = 2x0 + 2x1,
    
    [app](x0, x1) = 2x0 + 4x1,
    
    [nil] = 1
   orientation:
    app(nil(),k) = 4k + 2 >= k = k
    
    app(l,nil()) = 2l + 4 >= l = l
    
    sum(cons(x,nil())) = 2x + 2 >= 2x + 2 = cons(x,nil())
    
    sum(app(l,cons(x,cons(y,k)))) = 16k + 2l + 8x + 16y >= 16k + 2l + 8x + 16y = sum(app(l,sum(cons(x,cons(y,k)))))
    
    plus(s(x),y) = 2x + y + 7 >= 2x + y + 4 = s(plus(x,y))
   problem:
    sum(cons(x,nil())) -> cons(x,nil())
    sum(app(l,cons(x,cons(y,k)))) -> sum(app(l,sum(cons(x,cons(y,k)))))
   Matrix Interpretation Processor: dim=3
    
    interpretation:
                 [1 1 0]     [0]
     [sum](x0) = [0 0 0]x0 + [1]
                 [1 0 0]     [1],
     
                      [1 1 0]     [1 1 0]  
     [cons](x0, x1) = [0 0 0]x0 + [0 0 1]x1
                      [0 0 0]     [0 0 0]  ,
     
                     [1 0 0]     [1 0 0]     [0]
     [app](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [1]
                     [0 0 0]     [0 1 0]     [0],
     
             [0]
     [nil] = [0]
             [1]
    orientation:
                          [1 1 0]    [1]    [1 1 0]    [0]                
     sum(cons(x,nil())) = [0 0 0]x + [1] >= [0 0 0]x + [1] = cons(x,nil())
                          [1 1 0]    [1]    [0 0 0]    [0]                
     
                                     [1 1 1]    [1 0 0]    [1 1 0]    [1 1 0]    [1]    [1 1 1]    [1 0 0]    [1 1 0]    [1 1 0]    [1]                                     
     sum(app(l,cons(x,cons(y,k)))) = [0 0 0]k + [0 0 0]l + [0 0 0]x + [0 0 0]y + [1] >= [0 0 0]k + [0 0 0]l + [0 0 0]x + [0 0 0]y + [1] = sum(app(l,sum(cons(x,cons(y,k)))))
                                     [1 1 1]    [1 0 0]    [1 1 0]    [1 1 0]    [1]    [1 1 1]    [1 0 0]    [1 1 0]    [1 1 0]    [1]                                     
    problem:
     sum(app(l,cons(x,cons(y,k)))) -> sum(app(l,sum(cons(x,cons(y,k)))))
    Matrix Interpretation Processor: dim=3
     
     interpretation:
                  [1 0 0]  
      [sum](x0) = [0 0 0]x0
                  [0 0 0]  ,
      
                       [1 0 0]     [1 0 0]     [0]
      [cons](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [1]
                       [0 0 0]     [0 0 0]     [0],
      
                      [1 0 0]     [1 1 0]     [0]
      [app](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0]
                      [0 0 0]     [0 0 0]     [1]
     orientation:
                                      [1 0 0]    [1 0 0]    [1 0 0]    [1 0 0]    [1]    [1 0 0]    [1 0 0]    [1 0 0]    [1 0 0]                                      
      sum(app(l,cons(x,cons(y,k)))) = [0 0 0]k + [0 0 0]l + [0 0 0]x + [0 0 0]y + [0] >= [0 0 0]k + [0 0 0]l + [0 0 0]x + [0 0 0]y = sum(app(l,sum(cons(x,cons(y,k)))))
                                      [0 0 0]    [0 0 0]    [0 0 0]    [0 0 0]    [0]    [0 0 0]    [0 0 0]    [0 0 0]    [0 0 0]                                      
     problem:
      
     Qed