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


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YES

Problem:
 a__terms(N) -> cons(recip(a__sqr(mark(N))),terms(s(N)))
 a__sqr(0()) -> 0()
 a__sqr(s(X)) -> s(add(sqr(X),dbl(X)))
 a__dbl(0()) -> 0()
 a__dbl(s(X)) -> s(s(dbl(X)))
 a__add(0(),X) -> mark(X)
 a__add(s(X),Y) -> s(add(X,Y))
 a__first(0(),X) -> nil()
 a__first(s(X),cons(Y,Z)) -> cons(mark(Y),first(X,Z))
 mark(terms(X)) -> a__terms(mark(X))
 mark(sqr(X)) -> a__sqr(mark(X))
 mark(add(X1,X2)) -> a__add(mark(X1),mark(X2))
 mark(dbl(X)) -> a__dbl(mark(X))
 mark(first(X1,X2)) -> a__first(mark(X1),mark(X2))
 mark(cons(X1,X2)) -> cons(mark(X1),X2)
 mark(recip(X)) -> recip(mark(X))
 mark(s(X)) -> s(X)
 mark(0()) -> 0()
 mark(nil()) -> nil()
 a__terms(X) -> terms(X)
 a__sqr(X) -> sqr(X)
 a__add(X1,X2) -> add(X1,X2)
 a__dbl(X) -> dbl(X)
 a__first(X1,X2) -> first(X1,X2)

Proof:
 WPO Processor:
  algebra: Max
  weight function:
   w0 = 0
   w(0) = w(cons) = 3
   w(add) = w(recip) = w(a__terms) = 1
   w(first) = w(nil) = w(a__first) = w(a__add) = w(a__dbl) = w(dbl) = w(
   sqr) = w(terms) = w(s) = w(a__sqr) = w(mark) = 0
  status function:
   st(first) = st(a__add) = st(add) = [1, 0]
   st(nil) = []
   st(a__first) = [0, 1]
   st(a__dbl) = st(dbl) = st(sqr) = [0]
   st(0) = []
   st(cons) = [0, 1]
   st(terms) = st(s) = st(recip) = st(a__sqr) = st(mark) = st(a__terms) = [0]
  subterm penalty function:
   sp(terms, 0) = sp(a__terms, 0) = 4
   sp(cons, 0) = 2
   sp(a__add, 1) = sp(add, 1) = sp(sqr, 0) = sp(recip, 0) = sp(a__sqr, 0) = 1
   sp(first, 1) = sp(first, 0) = sp(a__first, 1) = sp(a__first, 0) = sp(
   a__add, 0) = sp(a__dbl, 0) = sp(add, 0) = sp(dbl, 0) = sp(cons, 1) = sp(
   s, 0) = sp(mark, 0) = 0
  precedence:
   mark > a__first > a__add ~ a__dbl ~ a__sqr ~ a__terms > first ~ nil ~ 
   add ~ dbl ~ sqr ~ 0 ~ cons ~ terms ~ s ~ recip
  problem:
   
  Qed