TRS Standard pair #487069702

details

property	value
status	complete
benchmark	Ex4_7_37_Bor03_FR.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n180.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	1.32223 seconds
cpu usage	3.90942
user time	3.1427
system time	0.766728
max virtual memory	4796872.0
max residence set size	77352.0

stage attributes

key	value
starexec-result	YES

output

YES

Problem:
 from(X) -> cons(X,n__from(n__s(X)))
 sel(0(),cons(X,XS)) -> X
 sel(s(N),cons(X,XS)) -> sel(N,activate(XS))
 minus(X,0()) -> 0()
 minus(s(X),s(Y)) -> minus(X,Y)
 quot(0(),s(Y)) -> 0()
 quot(s(X),s(Y)) -> s(quot(minus(X,Y),s(Y)))
 zWquot(XS,nil()) -> nil()
 zWquot(nil(),XS) -> nil()
 zWquot(cons(X,XS),cons(Y,YS)) -> cons(quot(X,Y),n__zWquot(activate(XS),activate(YS)))
 from(X) -> n__from(X)
 s(X) -> n__s(X)
 zWquot(X1,X2) -> n__zWquot(X1,X2)
 activate(n__from(X)) -> from(activate(X))
 activate(n__s(X)) -> s(activate(X))
 activate(n__zWquot(X1,X2)) -> zWquot(activate(X1),activate(X2))
 activate(X) -> X

Proof:
 DP Processor:
  DPs:
   sel#(s(N),cons(X,XS)) -> activate#(XS)
   sel#(s(N),cons(X,XS)) -> sel#(N,activate(XS))
   minus#(s(X),s(Y)) -> minus#(X,Y)
   quot#(s(X),s(Y)) -> minus#(X,Y)
   quot#(s(X),s(Y)) -> quot#(minus(X,Y),s(Y))
   quot#(s(X),s(Y)) -> s#(quot(minus(X,Y),s(Y)))
   zWquot#(cons(X,XS),cons(Y,YS)) -> activate#(YS)
   zWquot#(cons(X,XS),cons(Y,YS)) -> activate#(XS)
   zWquot#(cons(X,XS),cons(Y,YS)) -> quot#(X,Y)
   activate#(n__from(X)) -> activate#(X)
   activate#(n__from(X)) -> from#(activate(X))
   activate#(n__s(X)) -> activate#(X)
   activate#(n__s(X)) -> s#(activate(X))
   activate#(n__zWquot(X1,X2)) -> activate#(X2)
   activate#(n__zWquot(X1,X2)) -> activate#(X1)
   activate#(n__zWquot(X1,X2)) -> zWquot#(activate(X1),activate(X2))
  TRS:
   from(X) -> cons(X,n__from(n__s(X)))
   sel(0(),cons(X,XS)) -> X
   sel(s(N),cons(X,XS)) -> sel(N,activate(XS))
   minus(X,0()) -> 0()
   minus(s(X),s(Y)) -> minus(X,Y)
   quot(0(),s(Y)) -> 0()
   quot(s(X),s(Y)) -> s(quot(minus(X,Y),s(Y)))
   zWquot(XS,nil()) -> nil()
   zWquot(nil(),XS) -> nil()
   zWquot(cons(X,XS),cons(Y,YS)) -> cons(quot(X,Y),n__zWquot(activate(XS),activate(YS)))
   from(X) -> n__from(X)
   s(X) -> n__s(X)
   zWquot(X1,X2) -> n__zWquot(X1,X2)
   activate(n__from(X)) -> from(activate(X))
   activate(n__s(X)) -> s(activate(X))
   activate(n__zWquot(X1,X2)) -> zWquot(activate(X1),activate(X2))
   activate(X) -> X
  TDG Processor:
   DPs:
    sel#(s(N),cons(X,XS)) -> activate#(XS)
    sel#(s(N),cons(X,XS)) -> sel#(N,activate(XS))
    minus#(s(X),s(Y)) -> minus#(X,Y)
    quot#(s(X),s(Y)) -> minus#(X,Y)
    quot#(s(X),s(Y)) -> quot#(minus(X,Y),s(Y))
    quot#(s(X),s(Y)) -> s#(quot(minus(X,Y),s(Y)))
    zWquot#(cons(X,XS),cons(Y,YS)) -> activate#(YS)
    zWquot#(cons(X,XS),cons(Y,YS)) -> activate#(XS)
    zWquot#(cons(X,XS),cons(Y,YS)) -> quot#(X,Y)
    activate#(n__from(X)) -> activate#(X)
    activate#(n__from(X)) -> from#(activate(X))
    activate#(n__s(X)) -> activate#(X)
    activate#(n__s(X)) -> s#(activate(X))
    activate#(n__zWquot(X1,X2)) -> activate#(X2)
    activate#(n__zWquot(X1,X2)) -> activate#(X1)
    activate#(n__zWquot(X1,X2)) -> zWquot#(activate(X1),activate(X2))
   TRS:
    from(X) -> cons(X,n__from(n__s(X)))
    sel(0(),cons(X,XS)) -> X
    sel(s(N),cons(X,XS)) -> sel(N,activate(XS))
    minus(X,0()) -> 0()
    minus(s(X),s(Y)) -> minus(X,Y)
    quot(0(),s(Y)) -> 0()
    quot(s(X),s(Y)) -> s(quot(minus(X,Y),s(Y)))
    zWquot(XS,nil()) -> nil()
    zWquot(nil(),XS) -> nil()
    zWquot(cons(X,XS),cons(Y,YS)) -> cons(quot(X,Y),n__zWquot(activate(XS),activate(YS)))
    from(X) -> n__from(X)
    s(X) -> n__s(X)
    zWquot(X1,X2) -> n__zWquot(X1,X2)
    activate(n__from(X)) -> from(activate(X))
    activate(n__s(X)) -> s(activate(X))
    activate(n__zWquot(X1,X2)) -> zWquot(activate(X1),activate(X2))
    activate(X) -> X
   graph:
    zWquot#(cons(X,XS),cons(Y,YS)) -> quot#(X,Y) ->
    quot#(s(X),s(Y)) -> s#(quot(minus(X,Y),s(Y)))
    zWquot#(cons(X,XS),cons(Y,YS)) -> quot#(X,Y) ->
    quot#(s(X),s(Y)) -> quot#(minus(X,Y),s(Y))
    zWquot#(cons(X,XS),cons(Y,YS)) -> quot#(X,Y) ->

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