/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:
 and(true(),X) -> activate(X)
 and(false(),Y) -> false()
 if(true(),X,Y) -> activate(X)
 if(false(),X,Y) -> activate(Y)
 add(0(),X) -> activate(X)
 add(s(X),Y) -> s(n__add(activate(X),activate(Y)))
 first(0(),X) -> nil()
 first(s(X),cons(Y,Z)) -> cons(activate(Y),n__first(activate(X),activate(Z)))
 from(X) -> cons(activate(X),n__from(n__s(activate(X))))
 add(X1,X2) -> n__add(X1,X2)
 first(X1,X2) -> n__first(X1,X2)
 from(X) -> n__from(X)
 s(X) -> n__s(X)
 activate(n__add(X1,X2)) -> add(activate(X1),X2)
 activate(n__first(X1,X2)) -> first(activate(X1),activate(X2))
 activate(n__from(X)) -> from(X)
 activate(n__s(X)) -> s(X)
 activate(X) -> X

Proof:
 WPO Processor:
  algebra: Max
  weight function:
   w0 = 0
   w(n__from) = w(from) = w(if) = 4
   w(false) = 3
   w(n__first) = w(n__add) = 2
   w(add) = w(0) = 1
   w(n__s) = w(cons) = w(nil) = w(first) = w(s) = w(activate) = w(and) = w(
   true) = 0
  status function:
   st(if) = [0, 2, 1]
   st(n__first) = st(cons) = st(first) = st(n__add) = st(add) = [1, 0]
   st(n__from) = st(n__s) = st(from) = [0]
   st(nil) = []
   st(s) = [0]
   st(0) = st(false) = []
   st(activate) = [0]
   st(and) = [0, 1]
   st(true) = []
  subterm penalty function:
   sp(if, 2) = 6
   sp(n__from, 0) = sp(from, 0) = sp(n__add, 1) = sp(add, 1) = 4
   sp(n__first, 1) = sp(first, 1) = 2
   sp(n__first, 0) = sp(first, 0) = sp(n__add, 0) = sp(add, 0) = sp(and, 0) = 1
   sp(n__s, 0) = sp(cons, 1) = sp(cons, 0) = sp(s, 0) = sp(if, 1) = sp(
   if, 0) = sp(activate, 0) = sp(and, 1) = 0
  precedence:
   if ~ and > activate > add > s > from ~ first > n__from ~ n__s ~ n__first ~ 
   cons ~ nil ~ n__add ~ 0 ~ false ~ true
  problem:
   
  Qed