/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:
 a__first(0(),X) -> nil()
 a__first(s(X),cons(Y,Z)) -> cons(mark(Y),first(X,Z))
 a__from(X) -> cons(mark(X),from(s(X)))
 mark(first(X1,X2)) -> a__first(mark(X1),mark(X2))
 mark(from(X)) -> a__from(mark(X))
 mark(0()) -> 0()
 mark(nil()) -> nil()
 mark(s(X)) -> s(mark(X))
 mark(cons(X1,X2)) -> cons(mark(X1),X2)
 a__first(X1,X2) -> first(X1,X2)
 a__from(X) -> from(X)

Proof:
 WPO Processor:
  algebra: Max
  weight function:
   w0 = 0
   w(from) = 1
   w(a__from) = w(first) = w(mark) = w(cons) = w(s) = w(nil) = w(a__first) = w(
   0) = 0
  status function:
   st(cons) = st(a__first) = [1, 0]
   st(from) = st(a__from) = [0]
   st(first) = [0, 1]
   st(mark) = st(s) = [0]
   st(nil) = st(0) = []
  subterm penalty function:
   sp(from, 0) = sp(a__from, 0) = sp(cons, 0) = 1
   sp(first, 1) = sp(first, 0) = sp(mark, 0) = sp(cons, 1) = sp(s, 0) = sp(
   a__first, 1) = sp(a__first, 0) = 0
  precedence:
   mark > a__first > a__from > from ~ first ~ cons ~ s ~ nil ~ 0
  problem:
   
  Qed