/export/starexec/sandbox2/solver/bin/starexec_run_ttt2 /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


--------------------------------------------------------------------------------


YES

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

Proof:
 WPO Processor:
  algebra: Max
  weight function:
   w0 = 0
   w(half) = 5
   w(nil) = w(recip) = 4
   w(n__first) = w(n__terms) = 1
   w(activate) = w(first) = w(add) = w(dbl) = w(s) = w(0) = w(cons) = w(
   n__s) = w(sqr) = w(terms) = 0
  status function:
   st(n__first) = st(first) = st(add) = [1, 0]
   st(half) = st(activate) = [0]
   st(nil) = []
   st(dbl) = st(s) = [0]
   st(0) = []
   st(cons) = [0, 1]
   st(n__terms) = st(n__s) = st(recip) = st(sqr) = st(terms) = [0]
  subterm penalty function:
   sp(n__first, 1) = sp(first, 1) = sp(n__terms, 0) = sp(terms, 0) = 4
   sp(half, 0) = sp(n__first, 0) = sp(activate, 0) = sp(first, 0) = sp(
   add, 1) = sp(add, 0) = sp(dbl, 0) = sp(s, 0) = sp(cons, 1) = sp(cons, 0) = sp(
   n__s, 0) = sp(recip, 0) = sp(sqr, 0) = 0
  precedence:
   activate > terms > sqr > half ~ add ~ dbl > s > first > n__first ~ 
   nil ~ 0 ~ cons ~ n__terms ~ n__s ~ recip
  problem:
   
  Qed