/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: a__terms(N) -> cons(recip(a__sqr(mark(N))),terms(s(N)))
    2: a__sqr(0()) -> 0()
    3: a__sqr(s(X)) -> s(a__add(a__sqr(mark(X)),a__dbl(mark(X))))
    4: a__dbl(0()) -> 0()
    5: a__dbl(s(X)) -> s(s(a__dbl(mark(X))))
    6: a__add(0(),X) -> mark(X)
    7: a__add(s(X),Y) -> s(a__add(mark(X),mark(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(mark(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)
Number of strict rules: 24
Direct poly ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #a__add(0(),X) -> #mark(X)
   #2: #mark(dbl(X)) -> #a__dbl(mark(X))
   #3: #mark(dbl(X)) -> #mark(X)
   #4: #a__first(s(X),cons(Y,Z)) -> #mark(Y)
   #5: #mark(sqr(X)) -> #a__sqr(mark(X))
   #6: #mark(sqr(X)) -> #mark(X)
   #7: #mark(add(X1,X2)) -> #a__add(mark(X1),mark(X2))
   #8: #mark(add(X1,X2)) -> #mark(X1)
   #9: #mark(add(X1,X2)) -> #mark(X2)
   #10: #mark(first(X1,X2)) -> #a__first(mark(X1),mark(X2))
   #11: #mark(first(X1,X2)) -> #mark(X1)
   #12: #mark(first(X1,X2)) -> #mark(X2)
   #13: #a__add(s(X),Y) -> #a__add(mark(X),mark(Y))
   #14: #a__add(s(X),Y) -> #mark(X)
   #15: #a__add(s(X),Y) -> #mark(Y)
   #16: #mark(terms(X)) -> #a__terms(mark(X))
   #17: #mark(terms(X)) -> #mark(X)
   #18: #a__dbl(s(X)) -> #a__dbl(mark(X))
   #19: #a__dbl(s(X)) -> #mark(X)
   #20: #mark(s(X)) -> #mark(X)
   #21: #mark(recip(X)) -> #mark(X)
   #22: #a__sqr(s(X)) -> #a__add(a__sqr(mark(X)),a__dbl(mark(X)))
   #23: #a__sqr(s(X)) -> #a__sqr(mark(X))
   #24: #a__sqr(s(X)) -> #mark(X)
   #25: #a__sqr(s(X)) -> #a__dbl(mark(X))
   #26: #a__sqr(s(X)) -> #mark(X)
   #27: #a__terms(N) -> #a__sqr(mark(N))
   #28: #a__terms(N) -> #mark(N)
   #29: #mark(cons(X1,X2)) -> #mark(X1)
Number of SCCs: 1, DPs: 29
	SCC { #1..29 }
Sum... Max... succeeded.
  s(x1)		w: (x1)
  #a__first(x1,x2)		w: (max{51580 + x2, 35657 + x1})
  recip(x1)		w: (1 + x1)
  dbl(x1)		w: (x1)
  #a__add(x1,x2)		w: (max{51580 + x2, 51579 + x1})
  a__add(x1,x2)		w: (max{8947 + x2, x1})
  a__dbl(x1)		w: (x1)
  a__sqr(x1)		w: (8947 + x1)
  #a__terms(x1)		w: (60527 + x1)
  #mark(x1)		w: (51579 + x1)
  0()		w: (1)
  nil()		w: (26289)
  #a__dbl(x1)		w: (51579 + x1)
  mark(x1)		w: (x1)
  first(x1,x2)		w: (max{2 + x2, 26288 + x1})
  a__first(x1,x2)		w: (max{2 + x2, 26288 + x1})
  cons(x1,x2)		w: (max{0, 26289 + x1})
  add(x1,x2)		w: (max{8947 + x2, x1})
  sqr(x1)		w: (8947 + x1)
  a__terms(x1)		w: (35237 + x1)
  #a__sqr(x1)		w: (60526 + x1)
  terms(x1)		w: (35237 + x1)
    USABLE RULES: { 1..24 }
    Removed DPs: #1 #4 #6 #9..12 #15..17 #21 #24..29
Number of SCCs: 1, DPs: 12
	SCC { #2 #3 #5 #7 #8 #13 #14 #18..20 #22 #23 }
Sum... Max... succeeded.
  s(x1)		w: (x1)
  #a__first(x1,x2)		w: (max{51580 + x2, 35657 + x1})
  recip(x1)		w: (2447 + x1)
  dbl(x1)		w: (2 + x1)
  #a__add(x1,x2)		w: (max{50867 + x2, 50866 + x1})
  a__add(x1,x2)		w: (max{2 + x2, x1})
  a__dbl(x1)		w: (2 + x1)
  a__sqr(x1)		w: (4 + x1)
  #a__terms(x1)		w: (60527 + x1)
  #mark(x1)		w: (50866 + x1)
  0()		w: (1)
  nil()		w: (2)
  #a__dbl(x1)		w: (50867 + x1)
  mark(x1)		w: (x1)
  first(x1,x2)		w: (max{1 + x2, 2 + x1})
  a__first(x1,x2)		w: (max{1 + x2, 2 + x1})
  cons(x1,x2)		w: (max{0, 593 + x1})
  add(x1,x2)		w: (max{2 + x2, x1})
  sqr(x1)		w: (4 + x1)
  a__terms(x1)		w: (3044 + x1)
  #a__sqr(x1)		w: (50870 + x1)
  terms(x1)		w: (3044 + x1)
    USABLE RULES: { 1..24 }
    Removed DPs: #2 #3 #19
Number of SCCs: 2, DPs: 9
	SCC { #18 }
Sum... Max... QLPOpS... succeeded.
  s(x1)	0[x1]
  #a__first(x1,x2)	0[]
  recip(x1)	0[]
  dbl(x1)	2[x1]
  #a__add(x1,x2)	0[x1,x2]
  a__add(x1,x2)	1[x2,x1]
  a__dbl(x1)	2[x1]
  a__sqr(x1)	2[x1]
  #a__terms(x1)	0[]
  #mark(x1)	0[]
  0()	2
  nil()	3
  #a__dbl(x1)	0[x1]
  mark(x1)	x1
  first(x1,x2)	3[x2]
  a__first(x1,x2)	3[x2]
  cons(x1,x2)	0[x1]
  add(x1,x2)	1[x2,x1]
  sqr(x1)	2[x1]
  a__terms(x1)	3[]
  #a__sqr(x1)	0[]
  terms(x1)	3[]
    USABLE RULES: { 1..24 }
    Removed DPs: #18
Number of SCCs: 1, DPs: 8
	SCC { #5 #7 #8 #13 #14 #20 #22 #23 }
Sum... Max... QLPOpS... succeeded.
  s(x1)	0[x1]
  #a__first(x1,x2)	0[]
  recip(x1)	0[]
  dbl(x1)	1[x1]
  #a__add(x1,x2)	1[x2,x1]
  a__add(x1,x2)	1[x2,x1]
  a__dbl(x1)	1[x1]
  a__sqr(x1)	2[x1]
  #a__terms(x1)	0[]
  #mark(x1)	x1
  0()	2
  nil()	3
  #a__dbl(x1)	0[x1]
  mark(x1)	x1
  first(x1,x2)	3[x2]
  a__first(x1,x2)	3[x2]
  cons(x1,x2)	0[x1]
  add(x1,x2)	1[x2,x1]
  sqr(x1)	2[x1]
  a__terms(x1)	3[]
  #a__sqr(x1)	2[x1]
  terms(x1)	3[]
    USABLE RULES: { 1..24 }
    Removed DPs: #8 #13 #14 #20 #22 #23
Number of SCCs: 0, DPs: 0