TRS Standard pair #487071247

details

property	value
status	complete
benchmark	Ex9_BLR02_iGM.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n191.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	9.29849 seconds
cpu usage	33.0961
user time	29.2435
system time	3.85261
max virtual memory	6242072.0
max residence set size	164848.0

stage attributes

key	value
starexec-result	YES

output

YES

Problem:
 active(filter(cons(X,Y),0(),M)) -> mark(cons(0(),filter(Y,M,M)))
 active(filter(cons(X,Y),s(N),M)) -> mark(cons(X,filter(Y,N,M)))
 active(sieve(cons(0(),Y))) -> mark(cons(0(),sieve(Y)))
 active(sieve(cons(s(N),Y))) -> mark(cons(s(N),sieve(filter(Y,N,N))))
 active(nats(N)) -> mark(cons(N,nats(s(N))))
 active(zprimes()) -> mark(sieve(nats(s(s(0())))))
 mark(filter(X1,X2,X3)) -> active(filter(mark(X1),mark(X2),mark(X3)))
 mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
 mark(0()) -> active(0())
 mark(s(X)) -> active(s(mark(X)))
 mark(sieve(X)) -> active(sieve(mark(X)))
 mark(nats(X)) -> active(nats(mark(X)))
 mark(zprimes()) -> active(zprimes())
 filter(mark(X1),X2,X3) -> filter(X1,X2,X3)
 filter(X1,mark(X2),X3) -> filter(X1,X2,X3)
 filter(X1,X2,mark(X3)) -> filter(X1,X2,X3)
 filter(active(X1),X2,X3) -> filter(X1,X2,X3)
 filter(X1,active(X2),X3) -> filter(X1,X2,X3)
 filter(X1,X2,active(X3)) -> filter(X1,X2,X3)
 cons(mark(X1),X2) -> cons(X1,X2)
 cons(X1,mark(X2)) -> cons(X1,X2)
 cons(active(X1),X2) -> cons(X1,X2)
 cons(X1,active(X2)) -> cons(X1,X2)
 s(mark(X)) -> s(X)
 s(active(X)) -> s(X)
 sieve(mark(X)) -> sieve(X)
 sieve(active(X)) -> sieve(X)
 nats(mark(X)) -> nats(X)
 nats(active(X)) -> nats(X)

Proof:
 DP Processor:
  DPs:
   active#(filter(cons(X,Y),0(),M)) -> filter#(Y,M,M)
   active#(filter(cons(X,Y),0(),M)) -> cons#(0(),filter(Y,M,M))
   active#(filter(cons(X,Y),0(),M)) -> mark#(cons(0(),filter(Y,M,M)))
   active#(filter(cons(X,Y),s(N),M)) -> filter#(Y,N,M)
   active#(filter(cons(X,Y),s(N),M)) -> cons#(X,filter(Y,N,M))
   active#(filter(cons(X,Y),s(N),M)) -> mark#(cons(X,filter(Y,N,M)))
   active#(sieve(cons(0(),Y))) -> sieve#(Y)
   active#(sieve(cons(0(),Y))) -> cons#(0(),sieve(Y))
   active#(sieve(cons(0(),Y))) -> mark#(cons(0(),sieve(Y)))
   active#(sieve(cons(s(N),Y))) -> filter#(Y,N,N)
   active#(sieve(cons(s(N),Y))) -> sieve#(filter(Y,N,N))
   active#(sieve(cons(s(N),Y))) -> cons#(s(N),sieve(filter(Y,N,N)))
   active#(sieve(cons(s(N),Y))) -> mark#(cons(s(N),sieve(filter(Y,N,N))))
   active#(nats(N)) -> s#(N)
   active#(nats(N)) -> nats#(s(N))
   active#(nats(N)) -> cons#(N,nats(s(N)))
   active#(nats(N)) -> mark#(cons(N,nats(s(N))))
   active#(zprimes()) -> s#(0())
   active#(zprimes()) -> s#(s(0()))
   active#(zprimes()) -> nats#(s(s(0())))
   active#(zprimes()) -> sieve#(nats(s(s(0()))))
   active#(zprimes()) -> mark#(sieve(nats(s(s(0())))))
   mark#(filter(X1,X2,X3)) -> mark#(X3)
   mark#(filter(X1,X2,X3)) -> mark#(X2)
   mark#(filter(X1,X2,X3)) -> mark#(X1)
   mark#(filter(X1,X2,X3)) -> filter#(mark(X1),mark(X2),mark(X3))
   mark#(filter(X1,X2,X3)) -> active#(filter(mark(X1),mark(X2),mark(X3)))
   mark#(cons(X1,X2)) -> mark#(X1)
   mark#(cons(X1,X2)) -> cons#(mark(X1),X2)
   mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2))
   mark#(0()) -> active#(0())
   mark#(s(X)) -> mark#(X)
   mark#(s(X)) -> s#(mark(X))
   mark#(s(X)) -> active#(s(mark(X)))
   mark#(sieve(X)) -> mark#(X)
   mark#(sieve(X)) -> sieve#(mark(X))
   mark#(sieve(X)) -> active#(sieve(mark(X)))
   mark#(nats(X)) -> mark#(X)
   mark#(nats(X)) -> nats#(mark(X))
   mark#(nats(X)) -> active#(nats(mark(X)))
   mark#(zprimes()) -> active#(zprimes())
   filter#(mark(X1),X2,X3) -> filter#(X1,X2,X3)
   filter#(X1,mark(X2),X3) -> filter#(X1,X2,X3)
   filter#(X1,X2,mark(X3)) -> filter#(X1,X2,X3)
   filter#(active(X1),X2,X3) -> filter#(X1,X2,X3)
   filter#(X1,active(X2),X3) -> filter#(X1,X2,X3)
   filter#(X1,X2,active(X3)) -> filter#(X1,X2,X3)
   cons#(mark(X1),X2) -> cons#(X1,X2)
   cons#(X1,mark(X2)) -> cons#(X1,X2)
   cons#(active(X1),X2) -> cons#(X1,X2)
   cons#(X1,active(X2)) -> cons#(X1,X2)
   s#(mark(X)) -> s#(X)
   s#(active(X)) -> s#(X)
   sieve#(mark(X)) -> sieve#(X)
   sieve#(active(X)) -> sieve#(X)
   nats#(mark(X)) -> nats#(X)
   nats#(active(X)) -> nats#(X)
  TRS:
   active(filter(cons(X,Y),0(),M)) -> mark(cons(0(),filter(Y,M,M)))
   active(filter(cons(X,Y),s(N),M)) -> mark(cons(X,filter(Y,N,M)))
   active(sieve(cons(0(),Y))) -> mark(cons(0(),sieve(Y)))
   active(sieve(cons(s(N),Y))) -> mark(cons(s(N),sieve(filter(Y,N,N))))
   active(nats(N)) -> mark(cons(N,nats(s(N))))
   active(zprimes()) -> mark(sieve(nats(s(s(0())))))

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