TRS Standard pair #487071427

details

property	value
status	complete
benchmark	Ex5_DLMMU04_Z.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n183.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	2.72823 seconds
cpu usage	9.51027
user time	7.83553
system time	1.67474
max virtual memory	1992416.0
max residence set size	129380.0

stage attributes

key	value
starexec-result	NO

output

NO

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:
   [cons](x0, x1) = x0 + x1,
   
   [repItems](x0) = 3x0,
   
   [take](x0, x1) = x0 + x1 + 2,
   
   [0] = 0,
   
   [n__incr](x0) = x0,
   
   [n__repItems](x0) = 3x0,
   
   [n__cons](x0, x1) = x0 + x1,
   
   [incr](x0) = x0,
   
   [n__take](x0, x1) = x0 + x1 + 2,
   
   [pairNs] = 0,
   
   [activate](x0) = x0,
   
   [tail](x0) = x0 + 2,
   
   [pair](x0, x1) = 4x0 + x1,
   
   [zip](x0, x1) = 4x0 + x1,
   
   [nil] = 0,
   
   [n__zip](x0, x1) = 4x0 + x1,
   
   [s](x0) = x0,
   
   [oddNs] = 0
  orientation:
   pairNs() = 0 >= 0 = cons(0(),n__incr(oddNs()))
   
   oddNs() = 0 >= 0 = incr(pairNs())
   
   incr(cons(X,XS)) = X + XS >= X + XS = cons(s(X),n__incr(activate(XS)))
   
   take(0(),XS) = XS + 2 >= 0 = nil()
   
   take(s(N),cons(X,XS)) = N + X + XS + 2 >= N + X + XS + 2 = cons(X,n__take(N,activate(XS)))
   
   zip(nil(),XS) = XS >= 0 = nil()
   
   zip(X,nil()) = 4X >= 0 = nil()
   
   zip(cons(X,XS),cons(Y,YS)) = 4X + 4XS + Y + YS >= 4X + 4XS + Y + YS = cons(pair(X,Y),n__zip(activate(XS),activate(YS)))
   
   tail(cons(X,XS)) = X + XS + 2 >= XS = activate(XS)
   
   repItems(nil()) = 0 >= 0 = nil()
   
   repItems(cons(X,XS)) = 3X + 3XS >= 2X + 3XS = cons(X,n__cons(X,n__repItems(activate(XS))))
   
   incr(X) = X >= X = n__incr(X)
   
   take(X1,X2) = X1 + X2 + 2 >= X1 + X2 + 2 = n__take(X1,X2)
   
   zip(X1,X2) = 4X1 + X2 >= 4X1 + X2 = n__zip(X1,X2)
   
   cons(X1,X2) = X1 + X2 >= X1 + X2 = n__cons(X1,X2)
   
   repItems(X) = 3X >= 3X = n__repItems(X)
   
   activate(n__incr(X)) = X >= X = incr(X)

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