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


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YES
Input TRS:
    1: terms(N) -> cons(recip(sqr(N)),n__terms(n__s(N)))
    2: sqr(0()) -> 0()
    3: sqr(s(X)) -> s(n__add(n__sqr(activate(X)),n__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: s(X) -> n__s(X)
    12: add(X1,X2) -> n__add(X1,X2)
    13: sqr(X) -> n__sqr(X)
    14: dbl(X) -> n__dbl(X)
    15: first(X1,X2) -> n__first(X1,X2)
    16: activate(n__terms(X)) -> terms(activate(X))
    17: activate(n__s(X)) -> s(X)
    18: activate(n__add(X1,X2)) -> add(activate(X1),activate(X2))
    19: activate(n__sqr(X)) -> sqr(activate(X))
    20: activate(n__dbl(X)) -> dbl(activate(X))
    21: activate(n__first(X1,X2)) -> first(activate(X1),activate(X2))
    22: activate(X) -> X
Number of strict rules: 22
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: #activate(n__dbl(X)) -> #dbl(activate(X))
   #4: #activate(n__dbl(X)) -> #activate(X)
   #5: #add(s(X),Y) -> #s(n__add(activate(X),Y))
   #6: #add(s(X),Y) -> #activate(X)
   #7: #dbl(s(X)) -> #s(n__s(n__dbl(activate(X))))
   #8: #dbl(s(X)) -> #activate(X)
   #9: #activate(n__s(X)) -> #s(X)
   #10: #activate(n__sqr(X)) -> #sqr(activate(X))
   #11: #activate(n__sqr(X)) -> #activate(X)
   #12: #activate(n__first(X1,X2)) -> #first(activate(X1),activate(X2))
   #13: #activate(n__first(X1,X2)) -> #activate(X1)
   #14: #activate(n__first(X1,X2)) -> #activate(X2)
   #15: #activate(n__terms(X)) -> #terms(activate(X))
   #16: #activate(n__terms(X)) -> #activate(X)
   #17: #sqr(s(X)) -> #s(n__add(n__sqr(activate(X)),n__dbl(activate(X))))
   #18: #sqr(s(X)) -> #activate(X)
   #19: #sqr(s(X)) -> #activate(X)
   #20: #terms(N) -> #sqr(N)
   #21: #activate(n__add(X1,X2)) -> #add(activate(X1),activate(X2))
   #22: #activate(n__add(X1,X2)) -> #activate(X1)
   #23: #activate(n__add(X1,X2)) -> #activate(X2)
Number of SCCs: 1, DPs: 19
	SCC { #1..4 #6 #8 #10..16 #18..23 }
Sum... Max... succeeded.
  s(x1)		w: (x1)
  n__sqr(x1)		w: (40654 + x1)
  n__first(x1,x2)		w: (max{10454 + x2, 10452 + x1})
  recip(x1)		w: (0)
  activate(x1)		w: (x1)
  dbl(x1)		w: (8367 + x1)
  #dbl(x1)		w: (44832 + x1)
  #terms(x1)		w: (36468 + x1)
  #activate(x1)		w: (36466 + x1)
  n__add(x1,x2)		w: (max{32287 + x2, x1})
  n__s(x1)		w: (x1)
  #sqr(x1)		w: (36467 + x1)
  n__dbl(x1)		w: (8367 + x1)
  0()		w: (1)
  #s(x1)		w: (0)
  #first(x1,x2)		w: (max{46917 + x2, 46918 + x1})
  nil()		w: (10454)
  first(x1,x2)		w: (max{10454 + x2, 10452 + x1})
  n__terms(x1)		w: (10455 + x1)
  cons(x1,x2)		w: (max{x2, 10455 + x1})
  #add(x1,x2)		w: (max{68752 + x2, 36466 + x1})
  add(x1,x2)		w: (max{32287 + x2, x1})
  sqr(x1)		w: (40654 + x1)
  terms(x1)		w: (10455 + x1)
    USABLE RULES: { 1..22 }
    Removed DPs: #1..4 #8 #10 #11 #13..16 #18..20 #23
Number of SCCs: 1, DPs: 3
	SCC { #6 #21 #22 }
Sum... Max... QLPOpS... succeeded.
  s(x1)	1[x1]
  n__sqr(x1)	3[x1]
  n__first(x1,x2)	4[x1]
  recip(x1)	2[]
  activate(x1)	x1
  dbl(x1)	3[x1]
  #dbl(x1)	0[]
  #terms(x1)	0[]
  #activate(x1)	0[x1]
  n__add(x1,x2)	2[x1,x2]
  n__s(x1)	1[x1]
  #sqr(x1)	0[]
  n__dbl(x1)	3[x1]
  0()	3
  #s(x1)	0[]
  #first(x1,x2)	0[x2]
  nil()	4
  first(x1,x2)	4[x1]
  n__terms(x1)	3[]
  cons(x1,x2)	x2
  #add(x1,x2)	0[x1]
  add(x1,x2)	2[x1,x2]
  sqr(x1)	3[x1]
  terms(x1)	3[]
    USABLE RULES: { 1..22 }
    Removed DPs: #6 #21 #22
Number of SCCs: 0, DPs: 0