/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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NO

Problem:
 nats() -> cons(0(),n__incr(n__nats()))
 pairs() -> cons(0(),n__incr(n__odds()))
 odds() -> incr(pairs())
 incr(cons(X,XS)) -> cons(s(X),n__incr(activate(XS)))
 head(cons(X,XS)) -> X
 tail(cons(X,XS)) -> activate(XS)
 incr(X) -> n__incr(X)
 nats() -> n__nats()
 odds() -> n__odds()
 activate(n__incr(X)) -> incr(activate(X))
 activate(n__nats()) -> nats()
 activate(n__odds()) -> odds()
 activate(X) -> X

Proof:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
                [1 1 0]  
   [tail](x0) = [0 1 0]x0
                [0 0 1]  ,
   
                [1 0 0]     [1]
   [head](x0) = [0 0 1]x0 + [0]
                [0 0 1]     [0],
   
                      
   [activate](x0) = x0
                      ,
   
             [1 0 0]  
   [s](x0) = [0 0 0]x0
             [0 0 0]  ,
   
                [1 1 0]  
   [incr](x0) = [0 0 0]x0
                [0 0 0]  ,
   
            [1]
   [odds] = [0]
            [1],
   
               [1]
   [n__odds] = [0]
               [1],
   
             [1]
   [pairs] = [0]
             [1],
   
                    [1 0 0]       
   [cons](x0, x1) = [0 0 0]x0 + x1
                    [0 1 1]       ,
   
                   [1 1 0]  
   [n__incr](x0) = [0 0 0]x0
                   [0 0 0]  ,
   
               [1]
   [n__nats] = [0]
               [0],
   
         [0]
   [0] = [0]
         [0],
   
            [1]
   [nats] = [0]
            [0]
  orientation:
            [1]    [1]                               
   nats() = [0] >= [0] = cons(0(),n__incr(n__nats()))
            [0]    [0]                               
   
             [1]    [1]                               
   pairs() = [0] >= [0] = cons(0(),n__incr(n__odds()))
             [1]    [0]                               
   
            [1]    [1]                
   odds() = [0] >= [0] = incr(pairs())
            [1]    [0]                
   
                      [1 0 0]    [1 1 0]      [1 0 0]    [1 1 0]                                     
   incr(cons(X,XS)) = [0 0 0]X + [0 0 0]XS >= [0 0 0]X + [0 0 0]XS = cons(s(X),n__incr(activate(XS)))
                      [0 0 0]    [0 0 0]      [0 0 0]    [0 0 0]                                     
   
                      [1 0 0]    [1 0 0]     [1]         
   head(cons(X,XS)) = [0 1 1]X + [0 0 1]XS + [0] >= X = X
                      [0 1 1]    [0 0 1]     [0]         
   
                      [1 0 0]    [1 1 0]                       
   tail(cons(X,XS)) = [0 0 0]X + [0 1 0]XS >= XS = activate(XS)
                      [0 1 1]    [0 0 1]                       
   
             [1 1 0]     [1 1 0]              
   incr(X) = [0 0 0]X >= [0 0 0]X = n__incr(X)
             [0 0 0]     [0 0 0]              
   
            [1]    [1]            
   nats() = [0] >= [0] = n__nats()
            [0]    [0]            
   
            [1]    [1]            
   odds() = [0] >= [0] = n__odds()
            [1]    [1]            
   
                          [1 1 0]     [1 1 0]                     
   activate(n__incr(X)) = [0 0 0]X >= [0 0 0]X = incr(activate(X))
                          [0 0 0]     [0 0 0]                     
   
                         [1]    [1]         
   activate(n__nats()) = [0] >= [0] = nats()
                         [0]    [0]         
   
                         [1]    [1]         
   activate(n__odds()) = [0] >= [0] = odds()
                         [1]    [1]         
   
                           
   activate(X) = X >= X = X
                           
  problem:
   nats() -> cons(0(),n__incr(n__nats()))
   pairs() -> cons(0(),n__incr(n__odds()))
   odds() -> incr(pairs())
   incr(cons(X,XS)) -> cons(s(X),n__incr(activate(XS)))
   tail(cons(X,XS)) -> activate(XS)
   incr(X) -> n__incr(X)
   nats() -> n__nats()
   odds() -> n__odds()
   activate(n__incr(X)) -> incr(activate(X))
   activate(n__nats()) -> nats()
   activate(n__odds()) -> odds()
   activate(X) -> X
  Matrix Interpretation Processor: dim=3
   
   interpretation:
                 [1 0 0]     [1]
    [tail](x0) = [1 0 0]x0 + [1]
                 [1 0 0]     [0],
    
                     [1 0 0]     [0]
    [activate](x0) = [0 1 0]x0 + [1]
                     [1 0 1]     [0],
    
              [1 0 0]  
    [s](x0) = [0 0 0]x0
              [0 0 0]  ,
    
                 [1 0 0]  
    [incr](x0) = [0 0 0]x0
                 [1 0 0]  ,
    
             [0]
    [odds] = [1]
             [1],
    
                [0]
    [n__odds] = [0]
                [1],
    
              [0]
    [pairs] = [1]
              [0],
    
                     [1 1 0]     [1 1 1]  
    [cons](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                     [1 0 0]     [0 0 0]  ,
    
                    [1 0 0]  
    [n__incr](x0) = [0 0 0]x0
                    [0 0 0]  ,
    
                [0]
    [n__nats] = [0]
                [0],
    
          [0]
    [0] = [0]
          [0],
    
             [0]
    [nats] = [1]
             [0]
   orientation:
             [0]    [0]                               
    nats() = [1] >= [0] = cons(0(),n__incr(n__nats()))
             [0]    [0]                               
    
              [0]    [0]                               
    pairs() = [1] >= [0] = cons(0(),n__incr(n__odds()))
              [0]    [0]                               
    
             [0]    [0]                
    odds() = [1] >= [0] = incr(pairs())
             [1]    [0]                
    
                       [1 1 0]    [1 1 1]      [1 0 0]    [1 0 0]                                     
    incr(cons(X,XS)) = [0 0 0]X + [0 0 0]XS >= [0 0 0]X + [0 0 0]XS = cons(s(X),n__incr(activate(XS)))
                       [1 1 0]    [1 1 1]      [1 0 0]    [0 0 0]                                     
    
                       [1 1 0]    [1 1 1]     [1]    [1 0 0]     [0]               
    tail(cons(X,XS)) = [1 1 0]X + [1 1 1]XS + [1] >= [0 1 0]XS + [1] = activate(XS)
                       [1 1 0]    [1 1 1]     [0]    [1 0 1]     [0]               
    
              [1 0 0]     [1 0 0]              
    incr(X) = [0 0 0]X >= [0 0 0]X = n__incr(X)
              [1 0 0]     [0 0 0]              
    
             [0]    [0]            
    nats() = [1] >= [0] = n__nats()
             [0]    [0]            
    
             [0]    [0]            
    odds() = [1] >= [0] = n__odds()
             [1]    [1]            
    
                           [1 0 0]    [0]    [1 0 0]                     
    activate(n__incr(X)) = [0 0 0]X + [1] >= [0 0 0]X = incr(activate(X))
                           [1 0 0]    [0]    [1 0 0]                     
    
                          [0]    [0]         
    activate(n__nats()) = [1] >= [1] = nats()
                          [0]    [0]         
    
                          [0]    [0]         
    activate(n__odds()) = [1] >= [1] = odds()
                          [1]    [1]         
    
                  [1 0 0]    [0]         
    activate(X) = [0 1 0]X + [1] >= X = X
                  [1 0 1]    [0]         
   problem:
    nats() -> cons(0(),n__incr(n__nats()))
    pairs() -> cons(0(),n__incr(n__odds()))
    odds() -> incr(pairs())
    incr(cons(X,XS)) -> cons(s(X),n__incr(activate(XS)))
    incr(X) -> n__incr(X)
    nats() -> n__nats()
    odds() -> n__odds()
    activate(n__incr(X)) -> incr(activate(X))
    activate(n__nats()) -> nats()
    activate(n__odds()) -> odds()
    activate(X) -> X
   Unfolding Processor:
    loop length: 4
    terms:
     incr(cons(X,n__incr(n__nats())))
     cons(s(X),n__incr(activate(n__incr(n__nats()))))
     cons(s(X),n__incr(incr(activate(n__nats()))))
     cons(s(X),n__incr(incr(nats())))
    context: cons(s(X),n__incr([]))
    substitution:
     X -> 0()
    Qed