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


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NO

Problem:
 incr(nil()) -> nil()
 incr(cons(X,L)) -> cons(s(X),n__incr(activate(L)))
 adx(nil()) -> nil()
 adx(cons(X,L)) -> incr(cons(X,n__adx(activate(L))))
 nats() -> adx(zeros())
 zeros() -> cons(0(),n__zeros())
 head(cons(X,L)) -> X
 tail(cons(X,L)) -> activate(L)
 incr(X) -> n__incr(X)
 adx(X) -> n__adx(X)
 zeros() -> n__zeros()
 activate(n__incr(X)) -> incr(activate(X))
 activate(n__adx(X)) -> adx(activate(X))
 activate(n__zeros()) -> zeros()
 activate(X) -> X

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [activate](x0) = x0,
   
   [nats] = 0,
   
   [incr](x0) = x0,
   
   [s](x0) = x0,
   
   [n__incr](x0) = x0,
   
   [0] = 0,
   
   [nil] = 1,
   
   [n__adx](x0) = x0,
   
   [head](x0) = 2x0 + 4,
   
   [n__zeros] = 0,
   
   [zeros] = 0,
   
   [tail](x0) = x0,
   
   [adx](x0) = x0,
   
   [cons](x0, x1) = 2x0 + 4x1
  orientation:
   incr(nil()) = 1 >= 1 = nil()
   
   incr(cons(X,L)) = 4L + 2X >= 4L + 2X = cons(s(X),n__incr(activate(L)))
   
   adx(nil()) = 1 >= 1 = nil()
   
   adx(cons(X,L)) = 4L + 2X >= 4L + 2X = incr(cons(X,n__adx(activate(L))))
   
   nats() = 0 >= 0 = adx(zeros())
   
   zeros() = 0 >= 0 = cons(0(),n__zeros())
   
   head(cons(X,L)) = 8L + 4X + 4 >= X = X
   
   tail(cons(X,L)) = 4L + 2X >= L = activate(L)
   
   incr(X) = X >= X = n__incr(X)
   
   adx(X) = X >= X = n__adx(X)
   
   zeros() = 0 >= 0 = n__zeros()
   
   activate(n__incr(X)) = X >= X = incr(activate(X))
   
   activate(n__adx(X)) = X >= X = adx(activate(X))
   
   activate(n__zeros()) = 0 >= 0 = zeros()
   
   activate(X) = X >= X = X
  problem:
   incr(nil()) -> nil()
   incr(cons(X,L)) -> cons(s(X),n__incr(activate(L)))
   adx(nil()) -> nil()
   adx(cons(X,L)) -> incr(cons(X,n__adx(activate(L))))
   nats() -> adx(zeros())
   zeros() -> cons(0(),n__zeros())
   tail(cons(X,L)) -> activate(L)
   incr(X) -> n__incr(X)
   adx(X) -> n__adx(X)
   zeros() -> n__zeros()
   activate(n__incr(X)) -> incr(activate(X))
   activate(n__adx(X)) -> adx(activate(X))
   activate(n__zeros()) -> zeros()
   activate(X) -> X
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [activate](x0) = x0,
    
    [nats] = 3,
    
    [incr](x0) = x0,
    
    [s](x0) = x0,
    
    [n__incr](x0) = x0,
    
    [0] = 0,
    
    [nil] = 0,
    
    [n__adx](x0) = x0 + 1,
    
    [n__zeros] = 2,
    
    [zeros] = 2,
    
    [tail](x0) = x0 + 2,
    
    [adx](x0) = x0 + 1,
    
    [cons](x0, x1) = 4x0 + x1
   orientation:
    incr(nil()) = 0 >= 0 = nil()
    
    incr(cons(X,L)) = L + 4X >= L + 4X = cons(s(X),n__incr(activate(L)))
    
    adx(nil()) = 1 >= 0 = nil()
    
    adx(cons(X,L)) = L + 4X + 1 >= L + 4X + 1 = incr(cons(X,n__adx(activate(L))))
    
    nats() = 3 >= 3 = adx(zeros())
    
    zeros() = 2 >= 2 = cons(0(),n__zeros())
    
    tail(cons(X,L)) = L + 4X + 2 >= L = activate(L)
    
    incr(X) = X >= X = n__incr(X)
    
    adx(X) = X + 1 >= X + 1 = n__adx(X)
    
    zeros() = 2 >= 2 = n__zeros()
    
    activate(n__incr(X)) = X >= X = incr(activate(X))
    
    activate(n__adx(X)) = X + 1 >= X + 1 = adx(activate(X))
    
    activate(n__zeros()) = 2 >= 2 = zeros()
    
    activate(X) = X >= X = X
   problem:
    incr(nil()) -> nil()
    incr(cons(X,L)) -> cons(s(X),n__incr(activate(L)))
    adx(cons(X,L)) -> incr(cons(X,n__adx(activate(L))))
    nats() -> adx(zeros())
    zeros() -> cons(0(),n__zeros())
    incr(X) -> n__incr(X)
    adx(X) -> n__adx(X)
    zeros() -> n__zeros()
    activate(n__incr(X)) -> incr(activate(X))
    activate(n__adx(X)) -> adx(activate(X))
    activate(n__zeros()) -> zeros()
    activate(X) -> X
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [activate](x0) = x0,
     
     [nats] = 1,
     
     [incr](x0) = x0,
     
     [s](x0) = x0,
     
     [n__incr](x0) = x0,
     
     [0] = 0,
     
     [nil] = 0,
     
     [n__adx](x0) = x0,
     
     [n__zeros] = 0,
     
     [zeros] = 0,
     
     [adx](x0) = x0,
     
     [cons](x0, x1) = x0 + 4x1
    orientation:
     incr(nil()) = 0 >= 0 = nil()
     
     incr(cons(X,L)) = 4L + X >= 4L + X = cons(s(X),n__incr(activate(L)))
     
     adx(cons(X,L)) = 4L + X >= 4L + X = incr(cons(X,n__adx(activate(L))))
     
     nats() = 1 >= 0 = adx(zeros())
     
     zeros() = 0 >= 0 = cons(0(),n__zeros())
     
     incr(X) = X >= X = n__incr(X)
     
     adx(X) = X >= X = n__adx(X)
     
     zeros() = 0 >= 0 = n__zeros()
     
     activate(n__incr(X)) = X >= X = incr(activate(X))
     
     activate(n__adx(X)) = X >= X = adx(activate(X))
     
     activate(n__zeros()) = 0 >= 0 = zeros()
     
     activate(X) = X >= X = X
    problem:
     incr(nil()) -> nil()
     incr(cons(X,L)) -> cons(s(X),n__incr(activate(L)))
     adx(cons(X,L)) -> incr(cons(X,n__adx(activate(L))))
     zeros() -> cons(0(),n__zeros())
     incr(X) -> n__incr(X)
     adx(X) -> n__adx(X)
     zeros() -> n__zeros()
     activate(n__incr(X)) -> incr(activate(X))
     activate(n__adx(X)) -> adx(activate(X))
     activate(n__zeros()) -> zeros()
     activate(X) -> X
    Matrix Interpretation Processor: dim=3
     
     interpretation:
                       [1 0 0]  
      [activate](x0) = [1 1 0]x0
                       [0 0 1]  ,
      
                   [1 0 1]  
      [incr](x0) = [1 0 1]x0
                   [0 0 1]  ,
      
                [1 0 0]  
      [s](x0) = [0 0 0]x0
                [0 1 0]  ,
      
                      [1 0 1]  
      [n__incr](x0) = [0 0 0]x0
                      [0 0 1]  ,
      
            [0]
      [0] = [0]
            [0],
      
              [0]
      [nil] = [1]
              [1],
      
                     [1 0 0]     [1]
      [n__adx](x0) = [0 0 0]x0 + [0]
                     [0 0 0]     [0],
      
                   [1]
      [n__zeros] = [0]
                   [0],
      
                [1]
      [zeros] = [1]
                [0],
      
                  [1 0 0]     [1]
      [adx](x0) = [1 0 0]x0 + [1]
                  [0 0 0]     [0],
      
                       [1 1 0]     [1 0 0]  
      [cons](x0, x1) = [0 0 1]x0 + [1 0 0]x1
                       [0 0 0]     [0 1 1]  
     orientation:
                    [1]    [0]        
      incr(nil()) = [1] >= [1] = nil()
                    [1]    [1]        
      
                        [1 1 1]    [1 1 0]     [1 0 1]    [1 0 0]                                   
      incr(cons(X,L)) = [1 1 1]L + [1 1 0]X >= [1 0 1]L + [0 1 0]X = cons(s(X),n__incr(activate(L)))
                        [0 1 1]    [0 0 0]     [0 0 1]    [0 0 0]                                   
      
                       [1 0 0]    [1 1 0]    [1]    [1 0 0]    [1 1 0]    [1]                                    
      adx(cons(X,L)) = [1 0 0]L + [1 1 0]X + [1] >= [1 0 0]L + [1 1 0]X + [1] = incr(cons(X,n__adx(activate(L))))
                       [0 0 0]    [0 0 0]    [0]    [0 0 0]    [0 0 0]    [0]                                    
      
                [1]    [1]                       
      zeros() = [1] >= [1] = cons(0(),n__zeros())
                [0]    [0]                       
      
                [1 0 1]     [1 0 1]              
      incr(X) = [1 0 1]X >= [0 0 0]X = n__incr(X)
                [0 0 1]     [0 0 1]              
      
               [1 0 0]    [1]    [1 0 0]    [1]            
      adx(X) = [1 0 0]X + [1] >= [0 0 0]X + [0] = n__adx(X)
               [0 0 0]    [0]    [0 0 0]    [0]            
      
                [1]    [1]             
      zeros() = [1] >= [0] = n__zeros()
                [0]    [0]             
      
                             [1 0 1]     [1 0 1]                     
      activate(n__incr(X)) = [1 0 1]X >= [1 0 1]X = incr(activate(X))
                             [0 0 1]     [0 0 1]                     
      
                            [1 0 0]    [1]    [1 0 0]    [1]                   
      activate(n__adx(X)) = [1 0 0]X + [1] >= [1 0 0]X + [1] = adx(activate(X))
                            [0 0 0]    [0]    [0 0 0]    [0]                   
      
                             [1]    [1]          
      activate(n__zeros()) = [1] >= [1] = zeros()
                             [0]    [0]          
      
                    [1 0 0]          
      activate(X) = [1 1 0]X >= X = X
                    [0 0 1]          
     problem:
      incr(cons(X,L)) -> cons(s(X),n__incr(activate(L)))
      adx(cons(X,L)) -> incr(cons(X,n__adx(activate(L))))
      zeros() -> cons(0(),n__zeros())
      incr(X) -> n__incr(X)
      adx(X) -> n__adx(X)
      zeros() -> n__zeros()
      activate(n__incr(X)) -> incr(activate(X))
      activate(n__adx(X)) -> adx(activate(X))
      activate(n__zeros()) -> zeros()
      activate(X) -> X
     Unfolding Processor:
      loop length: 6
      terms:
       incr(cons(X,n__adx(n__zeros())))
       cons(s(X),n__incr(activate(n__adx(n__zeros()))))
       cons(s(X),n__incr(adx(activate(n__zeros()))))
       cons(s(X),n__incr(adx(zeros())))
       cons(s(X),n__incr(adx(cons(0(),n__zeros()))))
       cons(s(X),n__incr(incr(cons(0(),n__adx(activate(n__zeros()))))))
      context: cons(s(X),n__incr([]))
      substitution:
       X -> 0()
      Qed