TRS Standard pair #615299388

details

property	value
status	complete
benchmark	ExSec11_1_Luc02a_iGM.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n154.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	8.69260287285 seconds
cpu usage	20.680229325
max memory	1.489846272E9

stage attributes

key	value
output-size	103950
starexec-result	"YES"

output

/export/starexec/sandbox/solver/bin/starexec_run_ttt2 /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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YES

Problem:
 active(terms(N)) -> mark(cons(recip(sqr(N)),terms(s(N))))
 active(sqr(0())) -> mark(0())
 active(sqr(s(X))) -> mark(s(add(sqr(X),dbl(X))))
 active(dbl(0())) -> mark(0())
 active(dbl(s(X))) -> mark(s(s(dbl(X))))
 active(add(0(),X)) -> mark(X)
 active(add(s(X),Y)) -> mark(s(add(X,Y)))
 active(first(0(),X)) -> mark(nil())
 active(first(s(X),cons(Y,Z))) -> mark(cons(Y,first(X,Z)))
 active(half(0())) -> mark(0())
 active(half(s(0()))) -> mark(0())
 active(half(s(s(X)))) -> mark(s(half(X)))
 active(half(dbl(X))) -> mark(X)
 mark(terms(X)) -> active(terms(mark(X)))
 mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
 mark(recip(X)) -> active(recip(mark(X)))
 mark(sqr(X)) -> active(sqr(mark(X)))
 mark(s(X)) -> active(s(mark(X)))
 mark(0()) -> active(0())
 mark(add(X1,X2)) -> active(add(mark(X1),mark(X2)))
 mark(dbl(X)) -> active(dbl(mark(X)))
 mark(first(X1,X2)) -> active(first(mark(X1),mark(X2)))
 mark(nil()) -> active(nil())
 mark(half(X)) -> active(half(mark(X)))
 terms(mark(X)) -> terms(X)
 terms(active(X)) -> terms(X)
 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)
 recip(mark(X)) -> recip(X)
 recip(active(X)) -> recip(X)
 sqr(mark(X)) -> sqr(X)
 sqr(active(X)) -> sqr(X)
 s(mark(X)) -> s(X)
 s(active(X)) -> s(X)
 add(mark(X1),X2) -> add(X1,X2)
 add(X1,mark(X2)) -> add(X1,X2)
 add(active(X1),X2) -> add(X1,X2)
 add(X1,active(X2)) -> add(X1,X2)
 dbl(mark(X)) -> dbl(X)
 dbl(active(X)) -> dbl(X)
 first(mark(X1),X2) -> first(X1,X2)
 first(X1,mark(X2)) -> first(X1,X2)
 first(active(X1),X2) -> first(X1,X2)
 first(X1,active(X2)) -> first(X1,X2)
 half(mark(X)) -> half(X)
 half(active(X)) -> half(X)

Proof:
 DP Processor:
  DPs:
   active#(terms(N)) -> s#(N)
   active#(terms(N)) -> terms#(s(N))
   active#(terms(N)) -> sqr#(N)
   active#(terms(N)) -> recip#(sqr(N))
   active#(terms(N)) -> cons#(recip(sqr(N)),terms(s(N)))
   active#(terms(N)) -> mark#(cons(recip(sqr(N)),terms(s(N))))
   active#(sqr(0())) -> mark#(0())
   active#(sqr(s(X))) -> dbl#(X)
   active#(sqr(s(X))) -> sqr#(X)
   active#(sqr(s(X))) -> add#(sqr(X),dbl(X))
   active#(sqr(s(X))) -> s#(add(sqr(X),dbl(X)))
   active#(sqr(s(X))) -> mark#(s(add(sqr(X),dbl(X))))
   active#(dbl(0())) -> mark#(0())
   active#(dbl(s(X))) -> dbl#(X)
   active#(dbl(s(X))) -> s#(dbl(X))
   active#(dbl(s(X))) -> s#(s(dbl(X)))
   active#(dbl(s(X))) -> mark#(s(s(dbl(X))))
   active#(add(0(),X)) -> mark#(X)
   active#(add(s(X),Y)) -> add#(X,Y)
   active#(add(s(X),Y)) -> s#(add(X,Y))
   active#(add(s(X),Y)) -> mark#(s(add(X,Y)))
   active#(first(0(),X)) -> mark#(nil())
   active#(first(s(X),cons(Y,Z))) -> first#(X,Z)
   active#(first(s(X),cons(Y,Z))) -> cons#(Y,first(X,Z))
   active#(first(s(X),cons(Y,Z))) -> mark#(cons(Y,first(X,Z)))
   active#(half(0())) -> mark#(0())
   active#(half(s(0()))) -> mark#(0())
   active#(half(s(s(X)))) -> half#(X)
   active#(half(s(s(X)))) -> s#(half(X))
   active#(half(s(s(X)))) -> mark#(s(half(X)))
   active#(half(dbl(X))) -> mark#(X)
   mark#(terms(X)) -> mark#(X)
   mark#(terms(X)) -> terms#(mark(X))
   mark#(terms(X)) -> active#(terms(mark(X)))
   mark#(cons(X1,X2)) -> mark#(X1)
   mark#(cons(X1,X2)) -> cons#(mark(X1),X2)
   mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2))
   mark#(recip(X)) -> mark#(X)
   mark#(recip(X)) -> recip#(mark(X))

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