TRS Standard pair #487072562

details

property	value
status	complete
benchmark	5.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n192.star.cs.uiowa.edu
space	Beerendonk_07

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	1.25806 seconds
cpu usage	3.76409
user time	2.99469
system time	0.769403
max virtual memory	4464044.0
max residence set size	69316.0

stage attributes

key	value
starexec-result	YES

output

YES

Problem:
 cond(true(),x) -> cond(and(even(x),gr(x,0())),p(x))
 and(x,false()) -> false()
 and(false(),x) -> false()
 and(true(),true()) -> true()
 even(0()) -> true()
 even(s(0())) -> false()
 even(s(s(x))) -> even(x)
 gr(0(),x) -> false()
 gr(s(x),0()) -> true()
 gr(s(x),s(y())) -> gr(x,y())
 p(0()) -> 0()
 p(s(x)) -> x

Proof:
 DP Processor:
  DPs:
   cond#(true(),x) -> p#(x)
   cond#(true(),x) -> gr#(x,0())
   cond#(true(),x) -> even#(x)
   cond#(true(),x) -> and#(even(x),gr(x,0()))
   cond#(true(),x) -> cond#(and(even(x),gr(x,0())),p(x))
   even#(s(s(x))) -> even#(x)
   gr#(s(x),s(y())) -> gr#(x,y())
  TRS:
   cond(true(),x) -> cond(and(even(x),gr(x,0())),p(x))
   and(x,false()) -> false()
   and(false(),x) -> false()
   and(true(),true()) -> true()
   even(0()) -> true()
   even(s(0())) -> false()
   even(s(s(x))) -> even(x)
   gr(0(),x) -> false()
   gr(s(x),0()) -> true()
   gr(s(x),s(y())) -> gr(x,y())
   p(0()) -> 0()
   p(s(x)) -> x
  TDG Processor:
   DPs:
    cond#(true(),x) -> p#(x)
    cond#(true(),x) -> gr#(x,0())
    cond#(true(),x) -> even#(x)
    cond#(true(),x) -> and#(even(x),gr(x,0()))
    cond#(true(),x) -> cond#(and(even(x),gr(x,0())),p(x))
    even#(s(s(x))) -> even#(x)
    gr#(s(x),s(y())) -> gr#(x,y())
   TRS:
    cond(true(),x) -> cond(and(even(x),gr(x,0())),p(x))
    and(x,false()) -> false()
    and(false(),x) -> false()
    and(true(),true()) -> true()
    even(0()) -> true()
    even(s(0())) -> false()
    even(s(s(x))) -> even(x)
    gr(0(),x) -> false()
    gr(s(x),0()) -> true()
    gr(s(x),s(y())) -> gr(x,y())
    p(0()) -> 0()
    p(s(x)) -> x
   graph:
    even#(s(s(x))) -> even#(x) -> even#(s(s(x))) -> even#(x)
    gr#(s(x),s(y())) -> gr#(x,y()) -> gr#(s(x),s(y())) -> gr#(x,y())
    cond#(true(),x) -> even#(x) -> even#(s(s(x))) -> even#(x)
    cond#(true(),x) -> gr#(x,0()) ->
    gr#(s(x),s(y())) -> gr#(x,y())
    cond#(true(),x) -> cond#(and(even(x),gr(x,0())),p(x)) ->
    cond#(true(),x) -> cond#(and(even(x),gr(x,0())),p(x))
    cond#(true(),x) -> cond#(and(even(x),gr(x,0())),p(x)) ->
    cond#(true(),x) -> and#(even(x),gr(x,0()))
    cond#(true(),x) -> cond#(and(even(x),gr(x,0())),p(x)) ->
    cond#(true(),x) -> even#(x)
    cond#(true(),x) -> cond#(and(even(x),gr(x,0())),p(x)) ->
    cond#(true(),x) -> gr#(x,0())
    cond#(true(),x) -> cond#(and(even(x),gr(x,0())),p(x)) -> cond#(true(),x) -> p#(x)
   SCC Processor:
    #sccs: 3
    #rules: 3
    #arcs: 9/49
    DPs:
     cond#(true(),x) -> cond#(and(even(x),gr(x,0())),p(x))
    TRS:
     cond(true(),x) -> cond(and(even(x),gr(x,0())),p(x))
     and(x,false()) -> false()
     and(false(),x) -> false()
     and(true(),true()) -> true()
     even(0()) -> true()
     even(s(0())) -> false()
     even(s(s(x))) -> even(x)
     gr(0(),x) -> false()
     gr(s(x),0()) -> true()
     gr(s(x),s(y())) -> gr(x,y())
     p(0()) -> 0()
     p(s(x)) -> x
    Usable Rule Processor:
     DPs:
      cond#(true(),x) -> cond#(and(even(x),gr(x,0())),p(x))
     TRS:
      p(0()) -> 0()

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