Problem:
 pairNs() -> cons(0(),n__incr(oddNs()))
 oddNs() -> incr(pairNs())
 incr(cons(X,XS)) -> cons(s(X),n__incr(activate(XS)))
 take(0(),XS) -> nil()
 take(s(N),cons(X,XS)) -> cons(X,n__take(N,activate(XS)))
 zip(nil(),XS) -> nil()
 zip(X,nil()) -> nil()
 zip(cons(X,XS),cons(Y,YS)) -> cons(pair(X,Y),n__zip(activate(XS),activate(YS)))
 tail(cons(X,XS)) -> activate(XS)
 repItems(nil()) -> nil()
 repItems(cons(X,XS)) -> cons(X,n__cons(X,n__repItems(activate(XS))))
 incr(X) -> n__incr(X)
 take(X1,X2) -> n__take(X1,X2)
 zip(X1,X2) -> n__zip(X1,X2)
 cons(X1,X2) -> n__cons(X1,X2)
 repItems(X) -> n__repItems(X)
 activate(n__incr(X)) -> incr(X)
 activate(n__take(X1,X2)) -> take(X1,X2)
 activate(n__zip(X1,X2)) -> zip(X1,X2)
 activate(n__cons(X1,X2)) -> cons(X1,X2)
 activate(n__repItems(X)) -> repItems(X)
 activate(X) -> X

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [n__cons](x0, x1) = x0 + x1,
   
   [n__repItems](x0) = x0,
   
   [repItems](x0) = 2x0,
   
   [tail](x0) = x0 + 4,
   
   [n__zip](x0, x1) = x0 + x1,
   
   [pair](x0, x1) = 2x0 + x1,
   
   [zip](x0, x1) = 2x0 + 2x1,
   
   [n__take](x0, x1) = x0 + x1 + 2,
   
   [nil] = 0,
   
   [take](x0, x1) = x0 + 2x1 + 4,
   
   [activate](x0) = 2x0,
   
   [s](x0) = 2x0,
   
   [incr](x0) = 4x0,
   
   [cons](x0, x1) = 2x0 + 2x1,
   
   [n__incr](x0) = 2x0,
   
   [oddNs] = 0,
   
   [0] = 0,
   
   [pairNs] = 0
  orientation:
   pairNs() = 0 >= 0 = cons(0(),n__incr(oddNs()))
   
   oddNs() = 0 >= 0 = incr(pairNs())
   
   incr(cons(X,XS)) = 8X + 8XS >= 4X + 8XS = cons(s(X),n__incr(activate(XS)))
   
   take(0(),XS) = 2XS + 4 >= 0 = nil()
   
   take(s(N),cons(X,XS)) = 2N + 4X + 4XS + 4 >= 2N + 2X + 4XS + 4 = cons(X,n__take(N,activate(XS)))
   
   zip(nil(),XS) = 2XS >= 0 = nil()
   
   zip(X,nil()) = 2X >= 0 = nil()
   
   zip(cons(X,XS),cons(Y,YS)) = 4X + 4XS + 4Y + 4YS >= 4X + 4XS + 2Y + 4YS = cons(pair(X,Y),n__zip(activate(XS),activate(YS)))
   
   tail(cons(X,XS)) = 2X + 2XS + 4 >= 2XS = activate(XS)
   
   repItems(nil()) = 0 >= 0 = nil()
   
   repItems(cons(X,XS)) = 4X + 4XS >= 4X + 4XS = cons(X,n__cons(X,n__repItems(activate(XS))))
   
   incr(X) = 4X >= 2X = n__incr(X)
   
   take(X1,X2) = X1 + 2X2 + 4 >= X1 + X2 + 2 = n__take(X1,X2)
   
   zip(X1,X2) = 2X1 + 2X2 >= X1 + X2 = n__zip(X1,X2)
   
   cons(X1,X2) = 2X1 + 2X2 >= X1 + X2 = n__cons(X1,X2)
   
   repItems(X) = 2X >= X = n__repItems(X)
   
   activate(n__incr(X)) = 4X >= 4X = incr(X)
   
   activate(n__take(X1,X2)) = 2X1 + 2X2 + 4 >= X1 + 2X2 + 4 = take(X1,X2)
   
   activate(n__zip(X1,X2)) = 2X1 + 2X2 >= 2X1 + 2X2 = zip(X1,X2)
   
   activate(n__cons(X1,X2)) = 2X1 + 2X2 >= 2X1 + 2X2 = cons(X1,X2)
   
   activate(n__repItems(X)) = 2X >= 2X = repItems(X)
   
   activate(X) = 2X >= X = X
  problem:
   pairNs() -> cons(0(),n__incr(oddNs()))
   oddNs() -> incr(pairNs())
   incr(cons(X,XS)) -> cons(s(X),n__incr(activate(XS)))
   take(s(N),cons(X,XS)) -> cons(X,n__take(N,activate(XS)))
   zip(nil(),XS) -> nil()
   zip(X,nil()) -> nil()
   zip(cons(X,XS),cons(Y,YS)) -> cons(pair(X,Y),n__zip(activate(XS),activate(YS)))
   repItems(nil()) -> nil()
   repItems(cons(X,XS)) -> cons(X,n__cons(X,n__repItems(activate(XS))))
   incr(X) -> n__incr(X)
   zip(X1,X2) -> n__zip(X1,X2)
   cons(X1,X2) -> n__cons(X1,X2)
   repItems(X) -> n__repItems(X)
   activate(n__incr(X)) -> incr(X)
   activate(n__take(X1,X2)) -> take(X1,X2)
   activate(n__zip(X1,X2)) -> zip(X1,X2)
   activate(n__cons(X1,X2)) -> cons(X1,X2)
   activate(n__repItems(X)) -> repItems(X)
   activate(X) -> X
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [n__cons](x0, x1) = x0 + x1,
    
    [n__repItems](x0) = 4x0 + 4,
    
    [repItems](x0) = 4x0 + 4,
    
    [n__zip](x0, x1) = 2x0 + 4x1,
    
    [pair](x0, x1) = x0 + 4x1,
    
    [zip](x0, x1) = 2x0 + 4x1,
    
    [n__take](x0, x1) = 4x0 + x1 + 4,
    
    [nil] = 1,
    
    [take](x0, x1) = 4x0 + x1 + 4,
    
    [activate](x0) = x0,
    
    [s](x0) = x0,
    
    [incr](x0) = x0,
    
    [cons](x0, x1) = x0 + x1,
    
    [n__incr](x0) = x0,
    
    [oddNs] = 4,
    
    [0] = 0,
    
    [pairNs] = 4
   orientation:
    pairNs() = 4 >= 4 = cons(0(),n__incr(oddNs()))
    
    oddNs() = 4 >= 4 = incr(pairNs())
    
    incr(cons(X,XS)) = X + XS >= X + XS = cons(s(X),n__incr(activate(XS)))
    
    take(s(N),cons(X,XS)) = 4N + X + XS + 4 >= 4N + X + XS + 4 = cons(X,n__take(N,activate(XS)))
    
    zip(nil(),XS) = 4XS + 2 >= 1 = nil()
    
    zip(X,nil()) = 2X + 4 >= 1 = nil()
    
    zip(cons(X,XS),cons(Y,YS)) = 2X + 2XS + 4Y + 4YS >= X + 2XS + 4Y + 4YS = cons(pair(X,Y),n__zip(activate(XS),activate(YS)))
    
    repItems(nil()) = 8 >= 1 = nil()
    
    repItems(cons(X,XS)) = 4X + 4XS + 4 >= 2X + 4XS + 4 = cons(X,n__cons(X,n__repItems(activate(XS))))
    
    incr(X) = X >= X = n__incr(X)
    
    zip(X1,X2) = 2X1 + 4X2 >= 2X1 + 4X2 = n__zip(X1,X2)
    
    cons(X1,X2) = X1 + X2 >= X1 + X2 = n__cons(X1,X2)
    
    repItems(X) = 4X + 4 >= 4X + 4 = n__repItems(X)
    
    activate(n__incr(X)) = X >= X = incr(X)
    
    activate(n__take(X1,X2)) = 4X1 + X2 + 4 >= 4X1 + X2 + 4 = take(X1,X2)
    
    activate(n__zip(X1,X2)) = 2X1 + 4X2 >= 2X1 + 4X2 = zip(X1,X2)
    
    activate(n__cons(X1,X2)) = X1 + X2 >= X1 + X2 = cons(X1,X2)
    
    activate(n__repItems(X)) = 4X + 4 >= 4X + 4 = repItems(X)
    
    activate(X) = X >= X = X
   problem:
    pairNs() -> cons(0(),n__incr(oddNs()))
    oddNs() -> incr(pairNs())
    incr(cons(X,XS)) -> cons(s(X),n__incr(activate(XS)))
    take(s(N),cons(X,XS)) -> cons(X,n__take(N,activate(XS)))
    zip(cons(X,XS),cons(Y,YS)) -> cons(pair(X,Y),n__zip(activate(XS),activate(YS)))
    repItems(cons(X,XS)) -> cons(X,n__cons(X,n__repItems(activate(XS))))
    incr(X) -> n__incr(X)
    zip(X1,X2) -> n__zip(X1,X2)
    cons(X1,X2) -> n__cons(X1,X2)
    repItems(X) -> n__repItems(X)
    activate(n__incr(X)) -> incr(X)
    activate(n__take(X1,X2)) -> take(X1,X2)
    activate(n__zip(X1,X2)) -> zip(X1,X2)
    activate(n__cons(X1,X2)) -> cons(X1,X2)
    activate(n__repItems(X)) -> repItems(X)
    activate(X) -> X
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [n__cons](x0, x1) = 2x0 + x1,
     
     [n__repItems](x0) = x0,
     
     [repItems](x0) = 2x0,
     
     [n__zip](x0, x1) = x0 + x1,
     
     [pair](x0, x1) = 2x0 + x1,
     
     [zip](x0, x1) = 2x0 + 2x1,
     
     [n__take](x0, x1) = 4x0 + 2x1 + 2,
     
     [take](x0, x1) = 4x0 + 4x1 + 4,
     
     [activate](x0) = 2x0,
     
     [s](x0) = 2x0,
     
     [incr](x0) = 4x0,
     
     [cons](x0, x1) = 4x0 + x1,
     
     [n__incr](x0) = 2x0,
     
     [oddNs] = 0,
     
     [0] = 0,
     
     [pairNs] = 0
    orientation:
     pairNs() = 0 >= 0 = cons(0(),n__incr(oddNs()))
     
     oddNs() = 0 >= 0 = incr(pairNs())
     
     incr(cons(X,XS)) = 16X + 4XS >= 8X + 4XS = cons(s(X),n__incr(activate(XS)))
     
     take(s(N),cons(X,XS)) = 8N + 16X + 4XS + 4 >= 4N + 4X + 4XS + 2 = cons(X,n__take(N,activate(XS)))
     
     zip(cons(X,XS),cons(Y,YS)) = 8X + 2XS + 8Y + 2YS >= 8X + 2XS + 4Y + 2YS = cons(pair(X,Y),n__zip(activate(XS),activate(YS)))
     
     repItems(cons(X,XS)) = 8X + 2XS >= 6X + 2XS = cons(X,n__cons(X,n__repItems(activate(XS))))
     
     incr(X) = 4X >= 2X = n__incr(X)
     
     zip(X1,X2) = 2X1 + 2X2 >= X1 + X2 = n__zip(X1,X2)
     
     cons(X1,X2) = 4X1 + X2 >= 2X1 + X2 = n__cons(X1,X2)
     
     repItems(X) = 2X >= X = n__repItems(X)
     
     activate(n__incr(X)) = 4X >= 4X = incr(X)
     
     activate(n__take(X1,X2)) = 8X1 + 4X2 + 4 >= 4X1 + 4X2 + 4 = take(X1,X2)
     
     activate(n__zip(X1,X2)) = 2X1 + 2X2 >= 2X1 + 2X2 = zip(X1,X2)
     
     activate(n__cons(X1,X2)) = 4X1 + 2X2 >= 4X1 + X2 = cons(X1,X2)
     
     activate(n__repItems(X)) = 2X >= 2X = repItems(X)
     
     activate(X) = 2X >= X = X
    problem:
     pairNs() -> cons(0(),n__incr(oddNs()))
     oddNs() -> incr(pairNs())
     incr(cons(X,XS)) -> cons(s(X),n__incr(activate(XS)))
     zip(cons(X,XS),cons(Y,YS)) -> cons(pair(X,Y),n__zip(activate(XS),activate(YS)))
     repItems(cons(X,XS)) -> cons(X,n__cons(X,n__repItems(activate(XS))))
     incr(X) -> n__incr(X)
     zip(X1,X2) -> n__zip(X1,X2)
     cons(X1,X2) -> n__cons(X1,X2)
     repItems(X) -> n__repItems(X)
     activate(n__incr(X)) -> incr(X)
     activate(n__take(X1,X2)) -> take(X1,X2)
     activate(n__zip(X1,X2)) -> zip(X1,X2)
     activate(n__cons(X1,X2)) -> cons(X1,X2)
     activate(n__repItems(X)) -> repItems(X)
     activate(X) -> X
    Unfolding Processor:
     loop length: 3
     terms:
      oddNs()
      incr(pairNs())
      incr(cons(0(),n__incr(oddNs())))
     context: cons(s(0()),n__incr(activate(n__incr([]))))
     substitution:
      
     Qed