TRS Standard pair #487070732

details

property	value
status	complete
benchmark	Ex15_Luc98_Z.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n074.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	0.865278 seconds
cpu usage	2.25833
user time	1.78261
system time	0.475723
max virtual memory	1165100.0
max residence set size	70792.0

stage attributes

key	value
starexec-result	YES

output

YES

Problem:
 and(true(),X) -> activate(X)
 and(false(),Y) -> false()
 if(true(),X,Y) -> activate(X)
 if(false(),X,Y) -> activate(Y)
 add(0(),X) -> activate(X)
 add(s(X),Y) -> s(n__add(activate(X),activate(Y)))
 first(0(),X) -> nil()
 first(s(X),cons(Y,Z)) -> cons(activate(Y),n__first(activate(X),activate(Z)))
 from(X) -> cons(activate(X),n__from(n__s(activate(X))))
 add(X1,X2) -> n__add(X1,X2)
 first(X1,X2) -> n__first(X1,X2)
 from(X) -> n__from(X)
 s(X) -> n__s(X)
 activate(n__add(X1,X2)) -> add(X1,X2)
 activate(n__first(X1,X2)) -> first(X1,X2)
 activate(n__from(X)) -> from(X)
 activate(n__s(X)) -> s(X)
 activate(X) -> X

Proof:
 DP Processor:
  DPs:
   and#(true(),X) -> activate#(X)
   if#(true(),X,Y) -> activate#(X)
   if#(false(),X,Y) -> activate#(Y)
   add#(0(),X) -> activate#(X)
   add#(s(X),Y) -> activate#(Y)
   add#(s(X),Y) -> activate#(X)
   add#(s(X),Y) -> s#(n__add(activate(X),activate(Y)))
   first#(s(X),cons(Y,Z)) -> activate#(Z)
   first#(s(X),cons(Y,Z)) -> activate#(X)
   first#(s(X),cons(Y,Z)) -> activate#(Y)
   from#(X) -> activate#(X)
   activate#(n__add(X1,X2)) -> add#(X1,X2)
   activate#(n__first(X1,X2)) -> first#(X1,X2)
   activate#(n__from(X)) -> from#(X)
   activate#(n__s(X)) -> s#(X)
  TRS:
   and(true(),X) -> activate(X)
   and(false(),Y) -> false()
   if(true(),X,Y) -> activate(X)
   if(false(),X,Y) -> activate(Y)
   add(0(),X) -> activate(X)
   add(s(X),Y) -> s(n__add(activate(X),activate(Y)))
   first(0(),X) -> nil()
   first(s(X),cons(Y,Z)) -> cons(activate(Y),n__first(activate(X),activate(Z)))
   from(X) -> cons(activate(X),n__from(n__s(activate(X))))
   add(X1,X2) -> n__add(X1,X2)
   first(X1,X2) -> n__first(X1,X2)
   from(X) -> n__from(X)
   s(X) -> n__s(X)
   activate(n__add(X1,X2)) -> add(X1,X2)
   activate(n__first(X1,X2)) -> first(X1,X2)
   activate(n__from(X)) -> from(X)
   activate(n__s(X)) -> s(X)
   activate(X) -> X
  TDG Processor:
   DPs:
    and#(true(),X) -> activate#(X)
    if#(true(),X,Y) -> activate#(X)
    if#(false(),X,Y) -> activate#(Y)
    add#(0(),X) -> activate#(X)
    add#(s(X),Y) -> activate#(Y)
    add#(s(X),Y) -> activate#(X)
    add#(s(X),Y) -> s#(n__add(activate(X),activate(Y)))
    first#(s(X),cons(Y,Z)) -> activate#(Z)
    first#(s(X),cons(Y,Z)) -> activate#(X)
    first#(s(X),cons(Y,Z)) -> activate#(Y)
    from#(X) -> activate#(X)
    activate#(n__add(X1,X2)) -> add#(X1,X2)
    activate#(n__first(X1,X2)) -> first#(X1,X2)
    activate#(n__from(X)) -> from#(X)
    activate#(n__s(X)) -> s#(X)
   TRS:
    and(true(),X) -> activate(X)
    and(false(),Y) -> false()
    if(true(),X,Y) -> activate(X)
    if(false(),X,Y) -> activate(Y)
    add(0(),X) -> activate(X)
    add(s(X),Y) -> s(n__add(activate(X),activate(Y)))
    first(0(),X) -> nil()
    first(s(X),cons(Y,Z)) -> cons(activate(Y),n__first(activate(X),activate(Z)))
    from(X) -> cons(activate(X),n__from(n__s(activate(X))))
    add(X1,X2) -> n__add(X1,X2)
    first(X1,X2) -> n__first(X1,X2)
    from(X) -> n__from(X)
    s(X) -> n__s(X)
    activate(n__add(X1,X2)) -> add(X1,X2)
    activate(n__first(X1,X2)) -> first(X1,X2)
    activate(n__from(X)) -> from(X)
    activate(n__s(X)) -> s(X)
    activate(X) -> X
   graph:
    from#(X) -> activate#(X) -> activate#(n__s(X)) -> s#(X)
    from#(X) -> activate#(X) -> activate#(n__from(X)) -> from#(X)
    from#(X) -> activate#(X) -> activate#(n__first(X1,X2)) -> first#(X1,X2)
    from#(X) -> activate#(X) ->

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job log

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