/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 POLO(bPol) ... failed.
Uncurrying ... 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 }
POLO(Sum)... POLO(max)... succeeded.
      s 	w: x1
      n__sqr	w: x1 + 3
      n__first	w: max(x1 + 2, x2 + 4)
      recip	w: x1
      activate	w: x1
      dbl	w: x1 + 2
      #dbl	w: x1 + 2
      #terms	w: x1 + 3
      #activate	w: x1 + 1
      n__add	w: max(x1, x2 + 1)
      n__s	w: x1
      #sqr	w: x1 + 2
      n__dbl	w: x1 + 2
      0 	w: 1
      #s 	w: 0
      #first	w: max(x1 + 2, x2 + 2)
      nil	w: 4
      first	w: max(x1 + 2, x2 + 4)
      n__terms	w: x1 + 3
      cons	w: max(x2)
      #add	w: max(x1 + 1, x2 + 2)
      add	w: max(x1, x2 + 1)
      sqr	w: x1 + 3
      terms	w: x1 + 3
    USABLE RULES: { 1..22 }
    Removed DPs: #1..4 #8 #10..16 #18..20 #23
Number of SCCs: 1, DPs: 3
  SCC { #6 #21 #22 }
POLO(Sum)... POLO(max)... QLPOS... succeeded.
      s 	s: [1]	p: 2
      n__sqr	s: [1]	p: 4
      n__first	s: []	p: 4
      recip	s: [1]	p: 2
      activate	s: 1
      dbl	s: [1]	p: 4
      #dbl	s: []	p: 0
      #terms	s: []	p: 0
      #activate	s: [1]	p: 0
      n__add	s: [1,2]	p: 3
      n__s	s: [1]	p: 2
      #sqr	s: []	p: 0
      n__dbl	s: [1]	p: 4
      0 	s: []	p: 4
      #s 	s: []	p: 0
      #first	s: [1,2]	p: 0
      nil	s: []	p: 4
      first	s: []	p: 4
      n__terms	s: []	p: 1
      cons	s: 2
      #add	s: [1,2]	p: 0
      add	s: [1,2]	p: 3
      sqr	s: [1]	p: 4
      terms	s: []	p: 1
    USABLE RULES: { 1..22 }
    Removed DPs: #6 #21 #22
Number of SCCs: 0, DPs: 0