- : unit = ()
h : heuristic = <heuristic>
- : unit = ()
APPLY CRITERIA (Marked dependency pairs)

TRS termination of:
[1] a__terms(N) -> cons(recip(a__sqr(mark(N))),terms(s(N)))
[2] a__sqr(0) -> 0
[3] a__sqr(s(X)) -> s(add(sqr(X),dbl(X)))
[4] a__dbl(0) -> 0
[5] a__dbl(s(X)) -> s(s(dbl(X)))
[6] a__add(0,X) -> mark(X)
[7] a__add(s(X),Y) -> s(add(X,Y))
[8] a__first(0,X) -> nil
[9] a__first(s(X),cons(Y,Z)) -> cons(mark(Y),first(X,Z))
[10] mark(terms(X)) -> a__terms(mark(X))
[11] mark(sqr(X)) -> a__sqr(mark(X))
[12] mark(add(X1,X2)) -> a__add(mark(X1),mark(X2))
[13] mark(dbl(X)) -> a__dbl(mark(X))
[14] mark(first(X1,X2)) -> a__first(mark(X1),mark(X2))
[15] mark(cons(X1,X2)) -> cons(mark(X1),X2)
[16] mark(recip(X)) -> recip(mark(X))
[17] mark(s(X)) -> s(X)
[18] mark(0) -> 0
[19] mark(nil) -> nil
[20] a__terms(X) -> terms(X)
[21] a__sqr(X) -> sqr(X)
[22] a__add(X1,X2) -> add(X1,X2)
[23] a__dbl(X) -> dbl(X)
[24] a__first(X1,X2) -> first(X1,X2)


Sub problem: 
guided: 

DP termination of:
<Marked_a__terms(N) , Marked_a__sqr(mark(N))>
<Marked_a__terms(N) , Marked_mark(N)>
<Marked_a__add(0,X) , Marked_mark(X)>
<Marked_a__first(s(X),cons(Y,Z)) , Marked_mark(Y)>
<Marked_mark(terms(X)) , Marked_a__terms(mark(X))>
<Marked_mark(terms(X)) , Marked_mark(X)>
<Marked_mark(sqr(X)) , Marked_a__sqr(mark(X))>
<Marked_mark(sqr(X)) , Marked_mark(X)>
<Marked_mark(add(X1,X2)) , Marked_a__add(mark(X1),mark(X2))>
<Marked_mark(add(X1,X2)) , Marked_mark(X1)>
<Marked_mark(add(X1,X2)) , Marked_mark(X2)>
<Marked_mark(dbl(X)) , Marked_a__dbl(mark(X))>
<Marked_mark(dbl(X)) , Marked_mark(X)>
<Marked_mark(first(X1,X2)) , Marked_a__first(mark(X1),mark(X2))>
<Marked_mark(first(X1,X2)) , Marked_mark(X1)>
<Marked_mark(first(X1,X2)) , Marked_mark(X2)>
<Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
<Marked_mark(recip(X)) , Marked_mark(X)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_mark(recip(X)) , Marked_mark(X)> 
      --> <Marked_mark(recip(X)) , Marked_mark(X)>
  <Marked_mark(recip(X)) , Marked_mark(X)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(recip(X)) , Marked_mark(X)> 
     --> <Marked_mark(first(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(recip(X)) , Marked_mark(X)> 
     --> <Marked_mark(first(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(recip(X)) , Marked_mark(X)> 
     --> <Marked_mark(first(X1,X2)) , Marked_a__first(mark(X1),mark(X2))>
  <Marked_mark(recip(X)) , Marked_mark(X)> 
     --> <Marked_mark(dbl(X)) , Marked_mark(X)>
  <Marked_mark(recip(X)) , Marked_mark(X)> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(recip(X)) , Marked_mark(X)> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(recip(X)) , Marked_mark(X)> 
     --> <Marked_mark(add(X1,X2)) , Marked_a__add(mark(X1),mark(X2))>
  <Marked_mark(recip(X)) , Marked_mark(X)> 
     --> <Marked_mark(sqr(X)) , Marked_mark(X)>
  <Marked_mark(recip(X)) , Marked_mark(X)> 
     --> <Marked_mark(terms(X)) , Marked_mark(X)>
  <Marked_mark(recip(X)) , Marked_mark(X)> 
     --> <Marked_mark(terms(X)) , Marked_a__terms(mark(X))>
  <Marked_mark(cons(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(recip(X)) , Marked_mark(X)>
  <Marked_mark(cons(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(cons(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(first(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(cons(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(first(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(cons(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(first(X1,X2)) , Marked_a__first(mark(X1),mark(X2))>
  <Marked_mark(cons(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(dbl(X)) , Marked_mark(X)>
  <Marked_mark(cons(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(cons(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(cons(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(add(X1,X2)) , Marked_a__add(mark(X1),mark(X2))>
  <Marked_mark(cons(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(sqr(X)) , Marked_mark(X)>
  <Marked_mark(cons(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(terms(X)) , Marked_mark(X)>
  <Marked_mark(cons(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(terms(X)) , Marked_a__terms(mark(X))>
  <Marked_mark(first(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(recip(X)) , Marked_mark(X)>
  <Marked_mark(first(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(first(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(first(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(first(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(first(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(first(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(first(X1,X2)) , Marked_a__first(mark(X1),mark(X2))>
  <Marked_mark(first(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(dbl(X)) , Marked_mark(X)>
  <Marked_mark(first(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(first(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(first(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(add(X1,X2)) , Marked_a__add(mark(X1),mark(X2))>
  <Marked_mark(first(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(sqr(X)) , Marked_mark(X)>
  <Marked_mark(first(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(terms(X)) , Marked_mark(X)>
  <Marked_mark(first(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(terms(X)) , Marked_a__terms(mark(X))>
  <Marked_mark(first(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(recip(X)) , Marked_mark(X)>
  <Marked_mark(first(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(first(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(first(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(first(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(first(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(first(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(first(X1,X2)) , Marked_a__first(mark(X1),mark(X2))>
  <Marked_mark(first(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(dbl(X)) , Marked_mark(X)>
  <Marked_mark(first(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(first(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(first(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(add(X1,X2)) , Marked_a__add(mark(X1),mark(X2))>
  <Marked_mark(first(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(sqr(X)) , Marked_mark(X)>
  <Marked_mark(first(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(terms(X)) , Marked_mark(X)>
  <Marked_mark(first(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(terms(X)) , Marked_a__terms(mark(X))>
  <Marked_mark(first(X1,X2)) , Marked_a__first(mark(X1),mark(X2))> 
     --> <Marked_a__first(s(X),cons(Y,Z)) , Marked_mark(Y)>
  <Marked_mark(dbl(X)) , Marked_mark(X)> 
     --> <Marked_mark(recip(X)) , Marked_mark(X)>
  <Marked_mark(dbl(X)) , Marked_mark(X)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(dbl(X)) , Marked_mark(X)> 
     --> <Marked_mark(first(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(dbl(X)) , Marked_mark(X)> 
     --> <Marked_mark(first(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(dbl(X)) , Marked_mark(X)> 
     --> <Marked_mark(first(X1,X2)) , Marked_a__first(mark(X1),mark(X2))>
  <Marked_mark(dbl(X)) , Marked_mark(X)> 
     --> <Marked_mark(dbl(X)) , Marked_mark(X)>
  <Marked_mark(dbl(X)) , Marked_mark(X)> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(dbl(X)) , Marked_mark(X)> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(dbl(X)) , Marked_mark(X)> 
     --> <Marked_mark(add(X1,X2)) , Marked_a__add(mark(X1),mark(X2))>
  <Marked_mark(dbl(X)) , Marked_mark(X)> 
     --> <Marked_mark(sqr(X)) , Marked_mark(X)>
  <Marked_mark(dbl(X)) , Marked_mark(X)> 
     --> <Marked_mark(terms(X)) , Marked_mark(X)>
  <Marked_mark(dbl(X)) , Marked_mark(X)> 
     --> <Marked_mark(terms(X)) , Marked_a__terms(mark(X))>
  <Marked_mark(add(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(recip(X)) , Marked_mark(X)>
  <Marked_mark(add(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(add(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(first(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(add(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(first(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(add(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(first(X1,X2)) , Marked_a__first(mark(X1),mark(X2))>
  <Marked_mark(add(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(dbl(X)) , Marked_mark(X)>
  <Marked_mark(add(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(add(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(add(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(add(X1,X2)) , Marked_a__add(mark(X1),mark(X2))>
  <Marked_mark(add(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(sqr(X)) , Marked_mark(X)>
  <Marked_mark(add(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(terms(X)) , Marked_mark(X)>
  <Marked_mark(add(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(terms(X)) , Marked_a__terms(mark(X))>
  <Marked_mark(add(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(recip(X)) , Marked_mark(X)>
  <Marked_mark(add(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(add(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(first(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(add(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(first(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(add(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(first(X1,X2)) , Marked_a__first(mark(X1),mark(X2))>
  <Marked_mark(add(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(dbl(X)) , Marked_mark(X)>
  <Marked_mark(add(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(add(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(add(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(add(X1,X2)) , Marked_a__add(mark(X1),mark(X2))>
  <Marked_mark(add(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(sqr(X)) , Marked_mark(X)>
  <Marked_mark(add(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(terms(X)) , Marked_mark(X)>
  <Marked_mark(add(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(terms(X)) , Marked_a__terms(mark(X))>
  <Marked_mark(add(X1,X2)) , Marked_a__add(mark(X1),mark(X2))> 
     --> <Marked_a__add(0,X) , Marked_mark(X)>
  <Marked_mark(sqr(X)) , Marked_mark(X)> 
     --> <Marked_mark(recip(X)) , Marked_mark(X)>
  <Marked_mark(sqr(X)) , Marked_mark(X)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(sqr(X)) , Marked_mark(X)> 
     --> <Marked_mark(first(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(sqr(X)) , Marked_mark(X)> 
     --> <Marked_mark(first(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(sqr(X)) , Marked_mark(X)> 
     --> <Marked_mark(first(X1,X2)) , Marked_a__first(mark(X1),mark(X2))>
  <Marked_mark(sqr(X)) , Marked_mark(X)> 
     --> <Marked_mark(dbl(X)) , Marked_mark(X)>
  <Marked_mark(sqr(X)) , Marked_mark(X)> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(sqr(X)) , Marked_mark(X)> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(sqr(X)) , Marked_mark(X)> 
     --> <Marked_mark(add(X1,X2)) , Marked_a__add(mark(X1),mark(X2))>
  <Marked_mark(sqr(X)) , Marked_mark(X)> 
     --> <Marked_mark(sqr(X)) , Marked_mark(X)>
  <Marked_mark(sqr(X)) , Marked_mark(X)> 
     --> <Marked_mark(terms(X)) , Marked_mark(X)>
  <Marked_mark(sqr(X)) , Marked_mark(X)> 
     --> <Marked_mark(terms(X)) , Marked_a__terms(mark(X))>
  <Marked_mark(terms(X)) , Marked_mark(X)> 
     --> <Marked_mark(recip(X)) , Marked_mark(X)>
  <Marked_mark(terms(X)) , Marked_mark(X)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(terms(X)) , Marked_mark(X)> 
     --> <Marked_mark(first(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(terms(X)) , Marked_mark(X)> 
     --> <Marked_mark(first(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(terms(X)) , Marked_mark(X)> 
     --> <Marked_mark(first(X1,X2)) , Marked_a__first(mark(X1),mark(X2))>
  <Marked_mark(terms(X)) , Marked_mark(X)> 
     --> <Marked_mark(dbl(X)) , Marked_mark(X)>
  <Marked_mark(terms(X)) , Marked_mark(X)> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(terms(X)) , Marked_mark(X)> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(terms(X)) , Marked_mark(X)> 
     --> <Marked_mark(add(X1,X2)) , Marked_a__add(mark(X1),mark(X2))>
  <Marked_mark(terms(X)) , Marked_mark(X)> 
     --> <Marked_mark(sqr(X)) , Marked_mark(X)>
  <Marked_mark(terms(X)) , Marked_mark(X)> 
     --> <Marked_mark(terms(X)) , Marked_mark(X)>
  <Marked_mark(terms(X)) , Marked_mark(X)> 
     --> <Marked_mark(terms(X)) , Marked_a__terms(mark(X))>
  <Marked_mark(terms(X)) , Marked_a__terms(mark(X))> 
     --> <Marked_a__terms(N) , Marked_mark(N)>
  <Marked_a__first(s(X),cons(Y,Z)) , Marked_mark(Y)> 
     --> <Marked_mark(recip(X)) , Marked_mark(X)>
  <Marked_a__first(s(X),cons(Y,Z)) , Marked_mark(Y)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_a__first(s(X),cons(Y,Z)) , Marked_mark(Y)> 
     --> <Marked_mark(first(X1,X2)) , Marked_mark(X2)>
  <Marked_a__first(s(X),cons(Y,Z)) , Marked_mark(Y)> 
     --> <Marked_mark(first(X1,X2)) , Marked_mark(X1)>
  <Marked_a__first(s(X),cons(Y,Z)) , Marked_mark(Y)> 
     --> <Marked_mark(first(X1,X2)) , Marked_a__first(mark(X1),mark(X2))>
  <Marked_a__first(s(X),cons(Y,Z)) , Marked_mark(Y)> 
     --> <Marked_mark(dbl(X)) , Marked_mark(X)>
  <Marked_a__first(s(X),cons(Y,Z)) , Marked_mark(Y)> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X2)>
  <Marked_a__first(s(X),cons(Y,Z)) , Marked_mark(Y)> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X1)>
  <Marked_a__first(s(X),cons(Y,Z)) , Marked_mark(Y)> 
     --> <Marked_mark(add(X1,X2)) , Marked_a__add(mark(X1),mark(X2))>
  <Marked_a__first(s(X),cons(Y,Z)) , Marked_mark(Y)> 
     --> <Marked_mark(sqr(X)) , Marked_mark(X)>
  <Marked_a__first(s(X),cons(Y,Z)) , Marked_mark(Y)> 
     --> <Marked_mark(terms(X)) , Marked_mark(X)>
  <Marked_a__first(s(X),cons(Y,Z)) , Marked_mark(Y)> 
     --> <Marked_mark(terms(X)) , Marked_a__terms(mark(X))>
  <Marked_a__add(0,X) , Marked_mark(X)> 
     --> <Marked_mark(recip(X)) , Marked_mark(X)>
  <Marked_a__add(0,X) , Marked_mark(X)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_a__add(0,X) , Marked_mark(X)> 
     --> <Marked_mark(first(X1,X2)) , Marked_mark(X2)>
  <Marked_a__add(0,X) , Marked_mark(X)> 
     --> <Marked_mark(first(X1,X2)) , Marked_mark(X1)>
  <Marked_a__add(0,X) , Marked_mark(X)> 
     --> <Marked_mark(first(X1,X2)) , Marked_a__first(mark(X1),mark(X2))>
  <Marked_a__add(0,X) , Marked_mark(X)> 
     --> <Marked_mark(dbl(X)) , Marked_mark(X)>
  <Marked_a__add(0,X) , Marked_mark(X)> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X2)>
  <Marked_a__add(0,X) , Marked_mark(X)> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X1)>
  <Marked_a__add(0,X) , Marked_mark(X)> 
     --> <Marked_mark(add(X1,X2)) , Marked_a__add(mark(X1),mark(X2))>
  <Marked_a__add(0,X) , Marked_mark(X)> 
     --> <Marked_mark(sqr(X)) , Marked_mark(X)>
  <Marked_a__add(0,X) , Marked_mark(X)> 
     --> <Marked_mark(terms(X)) , Marked_mark(X)>
  <Marked_a__add(0,X) , Marked_mark(X)> 
     --> <Marked_mark(terms(X)) , Marked_a__terms(mark(X))>
  <Marked_a__terms(N) , Marked_mark(N)> 
     --> <Marked_mark(recip(X)) , Marked_mark(X)>
  <Marked_a__terms(N) , Marked_mark(N)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_a__terms(N) , Marked_mark(N)> 
     --> <Marked_mark(first(X1,X2)) , Marked_mark(X2)>
  <Marked_a__terms(N) , Marked_mark(N)> 
     --> <Marked_mark(first(X1,X2)) , Marked_mark(X1)>
  <Marked_a__terms(N) , Marked_mark(N)> 
     --> <Marked_mark(first(X1,X2)) , Marked_a__first(mark(X1),mark(X2))>
  <Marked_a__terms(N) , Marked_mark(N)> 
     --> <Marked_mark(dbl(X)) , Marked_mark(X)>
  <Marked_a__terms(N) , Marked_mark(N)> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X2)>
  <Marked_a__terms(N) , Marked_mark(N)> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X1)>
  <Marked_a__terms(N) , Marked_mark(N)> 
     --> <Marked_mark(add(X1,X2)) , Marked_a__add(mark(X1),mark(X2))>
  <Marked_a__terms(N) , Marked_mark(N)> 
     --> <Marked_mark(sqr(X)) , Marked_mark(X)>
  <Marked_a__terms(N) , Marked_mark(N)> 
     --> <Marked_mark(terms(X)) , Marked_mark(X)>
  <Marked_a__terms(N) , Marked_mark(N)> 
     --> <Marked_mark(terms(X)) , Marked_a__terms(mark(X))>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  a__sqr(s(X)) >= s(add(sqr(X),dbl(X))) ;
  a__sqr(0) >= 0 ;
  a__sqr(X) >= sqr(X) ;
  mark(cons(X1,X2)) >= cons(mark(X1),X2) ;
  mark(recip(X)) >= recip(mark(X)) ;
  mark(terms(X)) >= a__terms(mark(X)) ;
  mark(s(X)) >= s(X) ;
  mark(0) >= 0 ;
  mark(add(X1,X2)) >= a__add(mark(X1),mark(X2)) ;
  mark(sqr(X)) >= a__sqr(mark(X)) ;
  mark(dbl(X)) >= a__dbl(mark(X)) ;
  mark(nil) >= nil ;
  mark(first(X1,X2)) >= a__first(mark(X1),mark(X2)) ;
  a__terms(N) >= cons(recip(a__sqr(mark(N))),terms(s(N))) ;
  a__terms(X) >= terms(X) ;
  a__dbl(s(X)) >= s(s(dbl(X))) ;
  a__dbl(0) >= 0 ;
  a__dbl(X) >= dbl(X) ;
  a__add(s(X),Y) >= s(add(X,Y)) ;
  a__add(0,X) >= mark(X) ;
  a__add(X1,X2) >= add(X1,X2) ;
  a__first(s(X),cons(Y,Z)) >= cons(mark(Y),first(X,Z)) ;
  a__first(0,X) >= nil ;
  a__first(X1,X2) >= first(X1,X2) ;
  Marked_a__first(s(X),cons(Y,Z)) >= Marked_mark(Y) ;
  Marked_a__add(0,X) >= Marked_mark(X) ;
  Marked_a__terms(N) >= Marked_mark(N) ;
  Marked_mark(cons(X1,X2)) >= Marked_mark(X1) ;
  Marked_mark(recip(X)) >= Marked_mark(X) ;
  Marked_mark(terms(X)) >= Marked_a__terms(mark(X)) ;
  Marked_mark(terms(X)) >= Marked_mark(X) ;
  Marked_mark(add(X1,X2)) >= Marked_a__add(mark(X1),mark(X2)) ;
  Marked_mark(add(X1,X2)) >= Marked_mark(X1) ;
  Marked_mark(add(X1,X2)) >= Marked_mark(X2) ;
  Marked_mark(sqr(X)) >= Marked_mark(X) ;
  Marked_mark(dbl(X)) >= Marked_mark(X) ;
  Marked_mark(first(X1,X2)) >= Marked_a__first(mark(X1),mark(X2)) ;
  Marked_mark(first(X1,X2)) >= Marked_mark(X1) ;
  Marked_mark(first(X1,X2)) >= Marked_mark(X2) ;
 }
 + Disjunctions:{ 
{
  Marked_a__first(s(X),cons(Y,Z)) > Marked_mark(Y) ;
 }
{
  Marked_a__add(0,X) > Marked_mark(X) ;
 }
{
  Marked_a__terms(N) > Marked_mark(N) ;
 }
{
  Marked_mark(cons(X1,X2)) > Marked_mark(X1) ;
 }
{
  Marked_mark(recip(X)) > Marked_mark(X) ;
 }
{
  Marked_mark(terms(X)) > Marked_a__terms(mark(X)) ;
 }
{
  Marked_mark(terms(X)) > Marked_mark(X) ;
 }
{
  Marked_mark(add(X1,X2)) > Marked_a__add(mark(X1),mark(X2)) ;
 }
{
  Marked_mark(add(X1,X2)) > Marked_mark(X1) ;
 }
{
  Marked_mark(add(X1,X2)) > Marked_mark(X2) ;
 }
{
  Marked_mark(sqr(X)) > Marked_mark(X) ;
 }
{
  Marked_mark(dbl(X)) > Marked_mark(X) ;
 }
{
  Marked_mark(first(X1,X2)) > Marked_a__first(mark(X1),mark(X2)) ;
 }
{
  Marked_mark(first(X1,X2)) > Marked_mark(X1) ;
 }
{
  Marked_mark(first(X1,X2)) > Marked_mark(X2) ;
 }
 } 
=== TIMER virtual : 10.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 10.000000 ===
=== STOPING TIMER real ===
Sat solver returned
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: a__sqr(s(X)) >= s(add(sqr(X),dbl(X)))
constraint: a__sqr(0) >= 0
constraint: a__sqr(X) >= sqr(X)
constraint: mark(cons(X1,X2)) >= cons(mark(X1),X2)
constraint: mark(recip(X)) >= recip(mark(X))
constraint: mark(terms(X)) >= a__terms(mark(X))
constraint: mark(s(X)) >= s(X)
constraint: mark(0) >= 0
constraint: mark(add(X1,X2)) >= a__add(mark(X1),mark(X2))
constraint: mark(sqr(X)) >= a__sqr(mark(X))
constraint: mark(dbl(X)) >= a__dbl(mark(X))
constraint: mark(nil) >= nil
constraint: mark(first(X1,X2)) >= a__first(mark(X1),mark(X2))
constraint: a__terms(N) >= cons(recip(a__sqr(mark(N))),terms(s(N)))
constraint: a__terms(X) >= terms(X)
constraint: a__dbl(s(X)) >= s(s(dbl(X)))
constraint: a__dbl(0) >= 0
constraint: a__dbl(X) >= dbl(X)
constraint: a__add(s(X),Y) >= s(add(X,Y))
constraint: a__add(0,X) >= mark(X)
constraint: a__add(X1,X2) >= add(X1,X2)
constraint: a__first(s(X),cons(Y,Z)) >= cons(mark(Y),first(X,Z))
constraint: a__first(0,X) >= nil
constraint: a__first(X1,X2) >= first(X1,X2)
constraint: Marked_a__first(s(X),cons(Y,Z)) >= Marked_mark(Y)
constraint: Marked_a__add(0,X) >= Marked_mark(X)
constraint: Marked_a__terms(N) >= Marked_mark(N)
constraint: Marked_mark(cons(X1,X2)) >= Marked_mark(X1)
constraint: Marked_mark(recip(X)) >= Marked_mark(X)
constraint: Marked_mark(terms(X)) >= Marked_a__terms(mark(X))
constraint: Marked_mark(terms(X)) >= Marked_mark(X)
constraint: Marked_mark(add(X1,X2)) >= Marked_a__add(mark(X1),mark(X2))
constraint: Marked_mark(add(X1,X2)) >= Marked_mark(X1)
constraint: Marked_mark(add(X1,X2)) >= Marked_mark(X2)
constraint: Marked_mark(sqr(X)) >= Marked_mark(X)
constraint: Marked_mark(dbl(X)) >= Marked_mark(X)
constraint: Marked_mark(first(X1,X2)) >= Marked_a__first(mark(X1),mark(X2))
constraint: Marked_mark(first(X1,X2)) >= Marked_mark(X1)
constraint: Marked_mark(first(X1,X2)) >= Marked_mark(X2)
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_mark(recip(X)) , Marked_mark(X)> 
      --> <Marked_mark(recip(X)) , Marked_mark(X)>
  <Marked_mark(recip(X)) , Marked_mark(X)> 
     --> <Marked_mark(dbl(X)) , Marked_mark(X)>
  <Marked_mark(recip(X)) , Marked_mark(X)> 
     --> <Marked_mark(sqr(X)) , Marked_mark(X)>
  <Marked_mark(dbl(X)) , Marked_mark(X)> 
     --> <Marked_mark(recip(X)) , Marked_mark(X)>
  <Marked_mark(dbl(X)) , Marked_mark(X)> 
     --> <Marked_mark(dbl(X)) , Marked_mark(X)>
  <Marked_mark(dbl(X)) , Marked_mark(X)> 
     --> <Marked_mark(sqr(X)) , Marked_mark(X)>
  <Marked_mark(sqr(X)) , Marked_mark(X)> 
     --> <Marked_mark(recip(X)) , Marked_mark(X)>
  <Marked_mark(sqr(X)) , Marked_mark(X)> 
     --> <Marked_mark(dbl(X)) , Marked_mark(X)>
  <Marked_mark(sqr(X)) , Marked_mark(X)> 
     --> <Marked_mark(sqr(X)) , Marked_mark(X)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  a__sqr(s(X)) >= s(add(sqr(X),dbl(X))) ;
  a__sqr(0) >= 0 ;
  a__sqr(X) >= sqr(X) ;
  mark(cons(X1,X2)) >= cons(mark(X1),X2) ;
  mark(recip(X)) >= recip(mark(X)) ;
  mark(terms(X)) >= a__terms(mark(X)) ;
  mark(s(X)) >= s(X) ;
  mark(0) >= 0 ;
  mark(add(X1,X2)) >= a__add(mark(X1),mark(X2)) ;
  mark(sqr(X)) >= a__sqr(mark(X)) ;
  mark(dbl(X)) >= a__dbl(mark(X)) ;
  mark(nil) >= nil ;
  mark(first(X1,X2)) >= a__first(mark(X1),mark(X2)) ;
  a__terms(N) >= cons(recip(a__sqr(mark(N))),terms(s(N))) ;
  a__terms(X) >= terms(X) ;
  a__dbl(s(X)) >= s(s(dbl(X))) ;
  a__dbl(0) >= 0 ;
  a__dbl(X) >= dbl(X) ;
  a__add(s(X),Y) >= s(add(X,Y)) ;
  a__add(0,X) >= mark(X) ;
  a__add(X1,X2) >= add(X1,X2) ;
  a__first(s(X),cons(Y,Z)) >= cons(mark(Y),first(X,Z)) ;
  a__first(0,X) >= nil ;
  a__first(X1,X2) >= first(X1,X2) ;
  Marked_mark(recip(X)) >= Marked_mark(X) ;
  Marked_mark(sqr(X)) >= Marked_mark(X) ;
  Marked_mark(dbl(X)) >= Marked_mark(X) ;
 }
 + Disjunctions:{ 
{
  Marked_mark(recip(X)) > Marked_mark(X) ;
 }
{
  Marked_mark(sqr(X)) > Marked_mark(X) ;
 }
{
  Marked_mark(dbl(X)) > Marked_mark(X) ;
 }
 } 
=== TIMER virtual : 10.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 10.000000 ===
=== STOPING TIMER real ===
Sat solver returned
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: a__sqr(s(X)) >= s(add(sqr(X),dbl(X)))
constraint: a__sqr(0) >= 0
constraint: a__sqr(X) >= sqr(X)
constraint: mark(cons(X1,X2)) >= cons(mark(X1),X2)
constraint: mark(recip(X)) >= recip(mark(X))
constraint: mark(terms(X)) >= a__terms(mark(X))
constraint: mark(s(X)) >= s(X)
constraint: mark(0) >= 0
constraint: mark(add(X1,X2)) >= a__add(mark(X1),mark(X2))
constraint: mark(sqr(X)) >= a__sqr(mark(X))
constraint: mark(dbl(X)) >= a__dbl(mark(X))
constraint: mark(nil) >= nil
constraint: mark(first(X1,X2)) >= a__first(mark(X1),mark(X2))
constraint: a__terms(N) >= cons(recip(a__sqr(mark(N))),terms(s(N)))
constraint: a__terms(X) >= terms(X)
constraint: a__dbl(s(X)) >= s(s(dbl(X)))
constraint: a__dbl(0) >= 0
constraint: a__dbl(X) >= dbl(X)
constraint: a__add(s(X),Y) >= s(add(X,Y))
constraint: a__add(0,X) >= mark(X)
constraint: a__add(X1,X2) >= add(X1,X2)
constraint: a__first(s(X),cons(Y,Z)) >= cons(mark(Y),first(X,Z))
constraint: a__first(0,X) >= nil
constraint: a__first(X1,X2) >= first(X1,X2)
constraint: Marked_mark(recip(X)) >= Marked_mark(X)
constraint: Marked_mark(sqr(X)) >= Marked_mark(X)
constraint: Marked_mark(dbl(X)) >= Marked_mark(X)
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_mark(recip(X)) , Marked_mark(X)> 
      --> <Marked_mark(recip(X)) , Marked_mark(X)>
  <Marked_mark(recip(X)) , Marked_mark(X)> 
     --> <Marked_mark(dbl(X)) , Marked_mark(X)>
  <Marked_mark(dbl(X)) , Marked_mark(X)> 
     --> <Marked_mark(recip(X)) , Marked_mark(X)>
  <Marked_mark(dbl(X)) , Marked_mark(X)> 
     --> <Marked_mark(dbl(X)) , Marked_mark(X)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  a__sqr(s(X)) >= s(add(sqr(X),dbl(X))) ;
  a__sqr(0) >= 0 ;
  a__sqr(X) >= sqr(X) ;
  mark(cons(X1,X2)) >= cons(mark(X1),X2) ;
  mark(recip(X)) >= recip(mark(X)) ;
  mark(terms(X)) >= a__terms(mark(X)) ;
  mark(s(X)) >= s(X) ;
  mark(0) >= 0 ;
  mark(add(X1,X2)) >= a__add(mark(X1),mark(X2)) ;
  mark(sqr(X)) >= a__sqr(mark(X)) ;
  mark(dbl(X)) >= a__dbl(mark(X)) ;
  mark(nil) >= nil ;
  mark(first(X1,X2)) >= a__first(mark(X1),mark(X2)) ;
  a__terms(N) >= cons(recip(a__sqr(mark(N))),terms(s(N))) ;
  a__terms(X) >= terms(X) ;
  a__dbl(s(X)) >= s(s(dbl(X))) ;
  a__dbl(0) >= 0 ;
  a__dbl(X) >= dbl(X) ;
  a__add(s(X),Y) >= s(add(X,Y)) ;
  a__add(0,X) >= mark(X) ;
  a__add(X1,X2) >= add(X1,X2) ;
  a__first(s(X),cons(Y,Z)) >= cons(mark(Y),first(X,Z)) ;
  a__first(0,X) >= nil ;
  a__first(X1,X2) >= first(X1,X2) ;
  Marked_mark(recip(X)) >= Marked_mark(X) ;
  Marked_mark(dbl(X)) >= Marked_mark(X) ;
 }
 + Disjunctions:{ 
{
  Marked_mark(recip(X)) > Marked_mark(X) ;
 }
{
  Marked_mark(dbl(X)) > Marked_mark(X) ;
 }
 } 
=== TIMER virtual : 10.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 10.000000 ===
=== STOPING TIMER real ===
Sat solver returned
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: a__sqr(s(X)) >= s(add(sqr(X),dbl(X)))
constraint: a__sqr(0) >= 0
constraint: a__sqr(X) >= sqr(X)
constraint: mark(cons(X1,X2)) >= cons(mark(X1),X2)
constraint: mark(recip(X)) >= recip(mark(X))
constraint: mark(terms(X)) >= a__terms(mark(X))
constraint: mark(s(X)) >= s(X)
constraint: mark(0) >= 0
constraint: mark(add(X1,X2)) >= a__add(mark(X1),mark(X2))
constraint: mark(sqr(X)) >= a__sqr(mark(X))
constraint: mark(dbl(X)) >= a__dbl(mark(X))
constraint: mark(nil) >= nil
constraint: mark(first(X1,X2)) >= a__first(mark(X1),mark(X2))
constraint: a__terms(N) >= cons(recip(a__sqr(mark(N))),terms(s(N)))
constraint: a__terms(X) >= terms(X)
constraint: a__dbl(s(X)) >= s(s(dbl(X)))
constraint: a__dbl(0) >= 0
constraint: a__dbl(X) >= dbl(X)
constraint: a__add(s(X),Y) >= s(add(X,Y))
constraint: a__add(0,X) >= mark(X)
constraint: a__add(X1,X2) >= add(X1,X2)
constraint: a__first(s(X),cons(Y,Z)) >= cons(mark(Y),first(X,Z))
constraint: a__first(0,X) >= nil
constraint: a__first(X1,X2) >= first(X1,X2)
constraint: Marked_mark(recip(X)) >= Marked_mark(X)
constraint: Marked_mark(dbl(X)) >= Marked_mark(X)
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_mark(recip(X)) , Marked_mark(X)> 
      --> <Marked_mark(recip(X)) , Marked_mark(X)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  a__sqr(s(X)) >= s(add(sqr(X),dbl(X))) ;
  a__sqr(0) >= 0 ;
  a__sqr(X) >= sqr(X) ;
  mark(cons(X1,X2)) >= cons(mark(X1),X2) ;
  mark(recip(X)) >= recip(mark(X)) ;
  mark(terms(X)) >= a__terms(mark(X)) ;
  mark(s(X)) >= s(X) ;
  mark(0) >= 0 ;
  mark(add(X1,X2)) >= a__add(mark(X1),mark(X2)) ;
  mark(sqr(X)) >= a__sqr(mark(X)) ;
  mark(dbl(X)) >= a__dbl(mark(X)) ;
  mark(nil) >= nil ;
  mark(first(X1,X2)) >= a__first(mark(X1),mark(X2)) ;
  a__terms(N) >= cons(recip(a__sqr(mark(N))),terms(s(N))) ;
  a__terms(X) >= terms(X) ;
  a__dbl(s(X)) >= s(s(dbl(X))) ;
  a__dbl(0) >= 0 ;
  a__dbl(X) >= dbl(X) ;
  a__add(s(X),Y) >= s(add(X,Y)) ;
  a__add(0,X) >= mark(X) ;
  a__add(X1,X2) >= add(X1,X2) ;
  a__first(s(X),cons(Y,Z)) >= cons(mark(Y),first(X,Z)) ;
  a__first(0,X) >= nil ;
  a__first(X1,X2) >= first(X1,X2) ;
  Marked_mark(recip(X)) >= Marked_mark(X) ;
 }
 + Disjunctions:{ 
{
  Marked_mark(recip(X)) > Marked_mark(X) ;
 }
 } 
=== TIMER virtual : 10.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 10.000000 ===
=== STOPING TIMER real ===
Sat solver returned
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: a__sqr(s(X)) >= s(add(sqr(X),dbl(X)))
constraint: a__sqr(0) >= 0
constraint: a__sqr(X) >= sqr(X)
constraint: mark(cons(X1,X2)) >= cons(mark(X1),X2)
constraint: mark(recip(X)) >= recip(mark(X))
constraint: mark(terms(X)) >= a__terms(mark(X))
constraint: mark(s(X)) >= s(X)
constraint: mark(0) >= 0
constraint: mark(add(X1,X2)) >= a__add(mark(X1),mark(X2))
constraint: mark(sqr(X)) >= a__sqr(mark(X))
constraint: mark(dbl(X)) >= a__dbl(mark(X))
constraint: mark(nil) >= nil
constraint: mark(first(X1,X2)) >= a__first(mark(X1),mark(X2))
constraint: a__terms(N) >= cons(recip(a__sqr(mark(N))),terms(s(N)))
constraint: a__terms(X) >= terms(X)
constraint: a__dbl(s(X)) >= s(s(dbl(X)))
constraint: a__dbl(0) >= 0
constraint: a__dbl(X) >= dbl(X)
constraint: a__add(s(X),Y) >= s(add(X,Y))
constraint: a__add(0,X) >= mark(X)
constraint: a__add(X1,X2) >= add(X1,X2)
constraint: a__first(s(X),cons(Y,Z)) >= cons(mark(Y),first(X,Z))
constraint: a__first(0,X) >= nil
constraint: a__first(X1,X2) >= first(X1,X2)
constraint: Marked_mark(recip(X)) >= Marked_mark(X)
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] a__terms(N) -> cons(recip(a__sqr(mark(N))),terms(s(N)))
[2] a__sqr(0) -> 0
[3] a__sqr(s(X)) -> s(add(sqr(X),dbl(X)))
[4] a__dbl(0) -> 0
[5] a__dbl(s(X)) -> s(s(dbl(X)))
[6] a__add(0,X) -> mark(X)
[7] a__add(s(X),Y) -> s(add(X,Y))
[8] a__first(0,X) -> nil
[9] a__first(s(X),cons(Y,Z)) -> cons(mark(Y),first(X,Z))
[10] mark(terms(X)) -> a__terms(mark(X))
[11] mark(sqr(X)) -> a__sqr(mark(X))
[12] mark(add(X1,X2)) -> a__add(mark(X1),mark(X2))
[13] mark(dbl(X)) -> a__dbl(mark(X))
[14] mark(first(X1,X2)) -> a__first(mark(X1),mark(X2))
[15] mark(cons(X1,X2)) -> cons(mark(X1),X2)
[16] mark(recip(X)) -> recip(mark(X))
[17] mark(s(X)) -> s(X)
[18] mark(0) -> 0
[19] mark(nil) -> nil
[20] a__terms(X) -> terms(X)
[21] a__sqr(X) -> sqr(X)
[22] a__add(X1,X2) -> add(X1,X2)
[23] a__dbl(X) -> dbl(X)
[24] a__first(X1,X2) -> first(X1,X2)
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_a__terms(N) , Marked_a__sqr(mark(N))>
<Marked_a__terms(N) , Marked_mark(N)>
<Marked_a__add(0,X) , Marked_mark(X)>
<Marked_a__first(s(X),cons(Y,Z)) , Marked_mark(Y)>
<Marked_mark(terms(X)) , Marked_a__terms(mark(X))>
<Marked_mark(terms(X)) , Marked_mark(X)>
<Marked_mark(sqr(X)) , Marked_a__sqr(mark(X))>
<Marked_mark(sqr(X)) , Marked_mark(X)>
<Marked_mark(add(X1,X2)) , Marked_a__add(mark(X1),mark(X2))>
<Marked_mark(add(X1,X2)) , Marked_mark(X1)>
<Marked_mark(add(X1,X2)) , Marked_mark(X2)>
<Marked_mark(dbl(X)) , Marked_a__dbl(mark(X))>
<Marked_mark(dbl(X)) , Marked_mark(X)>
<Marked_mark(first(X1,X2)) , Marked_a__first(mark(X1),mark(X2))>
<Marked_mark(first(X1,X2)) , Marked_mark(X1)>
<Marked_mark(first(X1,X2)) , Marked_mark(X2)>
<Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
<Marked_mark(recip(X)) , Marked_mark(X)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_a__terms(N) , Marked_mark(N)>
<Marked_a__add(0,X) , Marked_mark(X)>
<Marked_a__first(s(X),cons(Y,Z)) , Marked_mark(Y)>
<Marked_mark(terms(X)) , Marked_a__terms(mark(X))>
<Marked_mark(terms(X)) , Marked_mark(X)>
<Marked_mark(sqr(X)) , Marked_mark(X)>
<Marked_mark(add(X1,X2)) , Marked_a__add(mark(X1),mark(X2))>
<Marked_mark(add(X1,X2)) , Marked_mark(X1)>
<Marked_mark(add(X1,X2)) , Marked_mark(X2)>
<Marked_mark(dbl(X)) , Marked_mark(X)>
<Marked_mark(first(X1,X2)) , Marked_a__first(mark(X1),mark(X2))>
<Marked_mark(first(X1,X2)) , Marked_mark(X1)>
<Marked_mark(first(X1,X2)) , Marked_mark(X2)>
<Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
<Marked_mark(recip(X)) , Marked_mark(X)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ cons ] (X0,X1) = 1*X0 + 3; 
 [ Marked_a__first ] (X0,X1) = 2*X1 + 1*X0 + 3; 
 [ add ] (X0,X1) = 2*X1 + 1*X0 + 2; 
 [ terms ] (X0) = 3*X0 + 3; 
 [ Marked_a__terms ] (X0) = 2*X0; 
 [ a__add ] (X0,X1) = 2*X1 + 1*X0 + 2; 
 [ a__sqr ] (X0) = 1*X0; 
 [ Marked_a__add ] (X0,X1) = 2*X1 + 2; 
 [ dbl ] (X0) = 1*X0; 
 [ a__terms ] (X0) = 3*X0 + 3; 
 [ a__first ] (X0,X1) = 3*X1 + 2*X0 + 3; 
 [ recip ] (X0) = 1*X0; 
 [ sqr ] (X0) = 1*X0; 
 [ s ] (X0) = 2; 
 [ Marked_mark ] (X0) = 2*X0; 
 [ nil ] () = 0; 
 [ mark ] (X0) = 2*X0; 
 [ a__dbl ] (X0) = 1*X0; 
 [ 0 ] () = 0; 
 [ first ] (X0,X1) = 3*X1 + 2*X0 + 2; 
 removing <Marked_a__add(0,X),Marked_mark(X)><Marked_a__first(s(X),cons(Y,Z)),
Marked_mark(Y)><Marked_mark(terms(X)),Marked_a__terms(mark(X))><Marked_mark(
                                                                 terms(
                                                                  X)),
Marked_mark(X)><Marked_mark(add(X1,X2)),Marked_a__add(mark(X1),mark(X2))><
Marked_mark(add(X1,X2)),Marked_mark(X1)><Marked_mark(add(X1,X2)),Marked_mark(
                                                                  X2)><
Marked_mark(first(X1,X2)),Marked_a__first(mark(X1),mark(X2))><Marked_mark(
                                                               first(
                                                                X1,X2)),
Marked_mark(X1)><Marked_mark(first(X1,X2)),Marked_mark(X2)><Marked_mark(
                                                             cons(X1,
                                                              X2)),Marked_mark(
                                                                    X1)>
 [ {
      
     DP termination of:
     <Marked_a__terms(N) , Marked_mark(N)>
<Marked_mark(sqr(X)) , Marked_mark(X)>
<Marked_mark(dbl(X)) , Marked_mark(X)>
<Marked_mark(recip(X)) , Marked_mark(X)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_mark(sqr(X)) , Marked_mark(X)>
<Marked_mark(dbl(X)) , Marked_mark(X)>
<Marked_mark(recip(X)) , Marked_mark(X)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ cons ] (X0,X1) = 0; 
 [ add ] (X0,X1) = 1*X1 + 2; 
 [ terms ] (X0) = 0; 
 [ a__add ] (X0,X1) = 1*X1 + 2; 
 [ a__sqr ] (X0) = 2*X0 + 1; 
 [ dbl ] (X0) = 1*X0; 
 [ a__terms ] (X0) = 0; 
 [ a__first ] (X0,X1) = 0; 
 [ recip ] (X0) = 1*X0; 
 [ sqr ] (X0) = 2*X0 + 1; 
 [ s ] (X0) = 0; 
 [ Marked_mark ] (X0) = 3*X0; 
 [ nil ] () = 0; 
 [ mark ] (X0) = 1*X0; 
 [ a__dbl ] (X0) = 1*X0; 
 [ 0 ] () = 0; 
 [ first ] (X0,X1) = 0; 
 removing <Marked_mark(sqr(X)),Marked_mark(X)>
 [ {
      
     DP termination of:
     <Marked_mark(dbl(X)) , Marked_mark(X)>
<Marked_mark(recip(X)) , Marked_mark(X)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_mark(dbl(X)) , Marked_mark(X)>
<Marked_mark(recip(X)) , Marked_mark(X)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ cons ] (X0,X1) = 2*X0 + 2; 
 [ add ] (X0,X1) = 3*X1 + 2; 
 [ terms ] (X0) = 0; 
 [ a__add ] (X0,X1) = 3*X1 + 2; 
 [ a__sqr ] (X0) = 0; 
 [ dbl ] (X0) = 1*X0 + 2; 
 [ a__terms ] (X0) = 2; 
 [ a__first ] (X0,X1) = 3*X1 + 2; 
 [ recip ] (X0) = 1*X0; 
 [ sqr ] (X0) = 0; 
 [ s ] (X0) = 0; 
 [ Marked_mark ] (X0) = 3*X0; 
 [ nil ] () = 0; 
 [ mark ] (X0) = 3*X0 + 2; 
 [ a__dbl ] (X0) = 1*X0 + 2; 
 [ 0 ] () = 0; 
 [ first ] (X0,X1) = 3*X1 + 2; 
 removing <Marked_mark(dbl(X)),Marked_mark(X)>
 [ {
      
     DP termination of:
     <Marked_mark(recip(X)) , Marked_mark(X)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_mark(recip(X)) , Marked_mark(X)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ cons ] (X0,X1) = 0; 
 [ add ] (X0,X1) = 1 + 2*X1 + 0; 
 [ terms ] (X0) = 0; 
 [ a__add ] (X0,X1) = 1 + 2*X1 + 0; 
 [ a__sqr ] (X0) = 0; 
 [ dbl ] (X0) = 0; 
 [ a__terms ] (X0) = 0; 
 [ a__first ] (X0,X1) = 2 + 0; 
 [ recip ] (X0) = 1 + 2*X0 + 0; 
 [ sqr ] (X0) = 0; 
 [ s ] (X0) = 0; 
 [ Marked_mark ] (X0) = 3*X0 + 0; 
 [ nil ] () = 0; 
 [ mark ] (X0) = 2*X0 + 0; 
 [ a__dbl ] (X0) = 0; 
 [ 0 ] () = 0; 
 [ first ] (X0,X1) = 2 + 0; 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 

Cime worked for 0.436220 seconds (real time)
Cime Exit Status: 0