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


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YES
Input TRS:
    1: terms(N) -> cons(recip(sqr(N)),n__terms(s(N)))
    2: sqr(0()) -> 0()
    3: sqr(s(X)) -> s(n__add(sqr(activate(X)),dbl(activate(X))))
    4: dbl(0()) -> 0()
    5: dbl(s(X)) -> s(n__s(n__dbl(activate(X))))
    6: add(0(),X) -> X
    7: add(s(X),Y) -> s(n__add(activate(X),Y))
    8: first(0(),X) -> nil()
    9: first(s(X),cons(Y,Z)) -> cons(Y,n__first(activate(X),activate(Z)))
    10: terms(X) -> n__terms(X)
    11: add(X1,X2) -> n__add(X1,X2)
    12: s(X) -> n__s(X)
    13: dbl(X) -> n__dbl(X)
    14: first(X1,X2) -> n__first(X1,X2)
    15: activate(n__terms(X)) -> terms(X)
    16: activate(n__add(X1,X2)) -> add(X1,X2)
    17: activate(n__s(X)) -> s(X)
    18: activate(n__dbl(X)) -> dbl(X)
    19: activate(n__first(X1,X2)) -> first(X1,X2)
    20: activate(X) -> X
Number of strict rules: 20
Direct poly ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #first(s(X),cons(Y,Z)) -> #activate(X)
   #2: #first(s(X),cons(Y,Z)) -> #activate(Z)
   #3: #add(s(X),Y) -> #s(n__add(activate(X),Y))
   #4: #add(s(X),Y) -> #activate(X)
   #5: #dbl(s(X)) -> #s(n__s(n__dbl(activate(X))))
   #6: #dbl(s(X)) -> #activate(X)
   #7: #activate(n__s(X)) -> #s(X)
   #8: #activate(n__first(X1,X2)) -> #first(X1,X2)
   #9: #activate(n__add(X1,X2)) -> #add(X1,X2)
   #10: #sqr(s(X)) -> #s(n__add(sqr(activate(X)),dbl(activate(X))))
   #11: #sqr(s(X)) -> #sqr(activate(X))
   #12: #sqr(s(X)) -> #activate(X)
   #13: #sqr(s(X)) -> #dbl(activate(X))
   #14: #sqr(s(X)) -> #activate(X)
   #15: #terms(N) -> #sqr(N)
   #16: #terms(N) -> #s(N)
   #17: #activate(n__terms(X)) -> #terms(X)
   #18: #activate(n__dbl(X)) -> #dbl(X)
Number of SCCs: 1, DPs: 13
	SCC { #1 #2 #4 #6 #8 #9 #11..15 #17 #18 }
Sum... succeeded.
  s(x1)		w: (7079 + x1)
  n__first(x1,x2)		w: (8856 + x2 + x1)
  recip(x1)		w: (0)
  activate(x1)		w: (7079 + x1)
  dbl(x1)		w: (11799 + x1)
  #dbl(x1)		w: (x1)
  #terms(x1)		w: (7721 + x1)
  #activate(x1)		w: (7078 + x1)
  n__add(x1,x2)		w: (2438 + x2 + x1)
  n__s(x1)		w: (x1)
  #sqr(x1)		w: (7720 + x1)
  n__dbl(x1)		w: (4720 + x1)
  0()		w: (39)
  #s(x1)		w: (0)
  #first(x1,x2)		w: (x2 + x1)
  nil()		w: (0)
  first(x1,x2)		w: (15935 + x2 + x1)
  n__terms(x1)		w: (644 + x1)
  cons(x1,x2)		w: (x2 + x1)
  #add(x1,x2)		w: (x1)
  add(x1,x2)		w: (9517 + x2 + x1)
  sqr(x1)		w: (21239 + x1)
  terms(x1)		w: (7723 + x1)
    USABLE RULES: { 1 2 4..20 }
    Removed DPs: #1 #2 #4 #6 #8 #9 #12..15 #17 #18
Number of SCCs: 1, DPs: 1
	SCC { #11 }
Sum... Max... QLPOpS... succeeded.
  s(x1)	2[x1]
  n__first(x1,x2)	x1
  recip(x1)	1[]
  activate(x1)	1[x1]
  dbl(x1)	3[x1]
  #dbl(x1)	0[]
  #terms(x1)	0[]
  #activate(x1)	0[]
  n__add(x1,x2)	3[x1,x2]
  n__s(x1)	2[x1]
  #sqr(x1)	0[x1]
  n__dbl(x1)	3[x1]
  0()	0
  #s(x1)	0[]
  #first(x1,x2)	0[x2,x1]
  nil()	0
  first(x1,x2)	1[x1]
  n__terms(x1)	1[x1]
  cons(x1,x2)	0[]
  #add(x1,x2)	0[x2]
  add(x1,x2)	3[x1,x2]
  sqr(x1)	2[]
  terms(x1)	1[x1]
    USABLE RULES: { 1 4..20 }
    Removed DPs: #11
Number of SCCs: 0, DPs: 0