/export/starexec/sandbox/solver/bin/starexec_run_ttt2 /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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YES

Problem:
 app(nil(),YS) -> YS
 app(cons(X),YS) -> cons(X)
 from(X) -> cons(X)
 zWadr(nil(),YS) -> nil()
 zWadr(XS,nil()) -> nil()
 zWadr(cons(X),cons(Y)) -> cons(app(Y,cons(X)))
 prefix(L) -> cons(nil())

Proof:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
                     [1 0 0]     [1 1 0]     [1]
   [zWadr](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0]
                     [0 0 0]     [0 0 0]     [0],
   
                   [1 0 1]          [1]
   [app](x0, x1) = [0 1 0]x0 + x1 + [0]
                   [0 0 0]          [0],
   
                [1 0 0]  
   [from](x0) = [0 0 1]x0
                [0 0 0]  ,
   
                  [1 0 0]  
   [prefix](x0) = [0 0 0]x0
                  [0 0 0]  ,
   
           [0]
   [nil] = [0]
           [0],
   
                [1 0 0]  
   [cons](x0) = [0 0 1]x0
                [0 0 0]  
  orientation:
                        [1]           
   app(nil(),YS) = YS + [0] >= YS = YS
                        [0]           
   
                     [1 0 0]         [1]    [1 0 0]           
   app(cons(X),YS) = [0 0 1]X + YS + [0] >= [0 0 1]X = cons(X)
                     [0 0 0]         [0]    [0 0 0]           
   
             [1 0 0]     [1 0 0]           
   from(X) = [0 0 1]X >= [0 0 1]X = cons(X)
             [0 0 0]     [0 0 0]           
   
                     [1 1 0]     [1]    [0]        
   zWadr(nil(),YS) = [0 0 0]YS + [0] >= [0] = nil()
                     [0 0 0]     [0]    [0]        
   
                     [1 0 0]     [1]    [0]        
   zWadr(XS,nil()) = [0 0 0]XS + [0] >= [0] = nil()
                     [0 0 0]     [0]    [0]        
   
                            [1 0 0]    [1 0 1]    [1]    [1 0 0]    [1 0 1]    [1]                       
   zWadr(cons(X),cons(Y)) = [0 0 0]X + [0 0 0]Y + [0] >= [0 0 0]X + [0 0 0]Y + [0] = cons(app(Y,cons(X)))
                            [0 0 0]    [0 0 0]    [0]    [0 0 0]    [0 0 0]    [0]                       
   
               [1 0 0]     [0]              
   prefix(L) = [0 0 0]L >= [0] = cons(nil())
               [0 0 0]     [0]              
  problem:
   from(X) -> cons(X)
   zWadr(cons(X),cons(Y)) -> cons(app(Y,cons(X)))
   prefix(L) -> cons(nil())
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [zWadr](x0, x1) = x0 + x1,
    
    [app](x0, x1) = x0 + x1,
    
    [from](x0) = x0 + 4,
    
    [prefix](x0) = 4x0,
    
    [nil] = 0,
    
    [cons](x0) = x0
   orientation:
    from(X) = X + 4 >= X = cons(X)
    
    zWadr(cons(X),cons(Y)) = X + Y >= X + Y = cons(app(Y,cons(X)))
    
    prefix(L) = 4L >= 0 = cons(nil())
   problem:
    zWadr(cons(X),cons(Y)) -> cons(app(Y,cons(X)))
    prefix(L) -> cons(nil())
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [zWadr](x0, x1) = 2x0 + 2x1 + 2,
     
     [app](x0, x1) = 2x0 + x1 + 4,
     
     [prefix](x0) = 2x0 + 4,
     
     [nil] = 1,
     
     [cons](x0) = x0 + 1
    orientation:
     zWadr(cons(X),cons(Y)) = 2X + 2Y + 6 >= X + 2Y + 6 = cons(app(Y,cons(X)))
     
     prefix(L) = 2L + 4 >= 2 = cons(nil())
    problem:
     zWadr(cons(X),cons(Y)) -> cons(app(Y,cons(X)))
    Matrix Interpretation Processor: dim=3
     
     interpretation:
                        [1 0 0]     [1 0 0]     [1]
      [zWadr](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0]
                        [0 0 0]     [0 0 0]     [0],
      
                      [1 0 0]     [1 0 0]  
      [app](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                      [0 0 0]     [0 0 0]  ,
      
                   [1 0 0]  
      [cons](x0) = [0 0 0]x0
                   [0 0 0]  
     orientation:
                               [1 0 0]    [1 0 0]    [1]    [1 0 0]    [1 0 0]                        
      zWadr(cons(X),cons(Y)) = [0 0 0]X + [0 0 0]Y + [0] >= [0 0 0]X + [0 0 0]Y = cons(app(Y,cons(X)))
                               [0 0 0]    [0 0 0]    [0]    [0 0 0]    [0 0 0]                        
     problem:
      
     Qed