/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 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: #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 }
POLO(Sum)... succeeded.
      s 	w: x1 + 1
      n__first	w: x1 + x2 + 1
      recip	w: x1
      activate	w: x1 + 1
      dbl	w: x1 + 2
      #dbl	w: x1
      #terms	w: x1 + 1
      #activate	w: x1
      n__add	w: x1 + x2 + 1
      n__s	w: x1
      #sqr	w: x1 + 1
      n__dbl	w: x1 + 1
      0 	w: 1
      #s 	w: 0
      #first	w: x1 + x2
      nil	w: 0
      first	w: x1 + x2 + 2
      n__terms	w: x1 + 2
      cons	w: x2
      #add	w: x1
      add	w: x1 + x2 + 2
      sqr	w: x1 + 1
      terms	w: x1 + 3
    USABLE RULES: { 1 4..20 }
    Removed DPs: #1 #2 #4 #6 #8 #9 #12..14 #17 #18
Number of SCCs: 1, DPs: 1
  SCC { #11 }
POLO(Sum)... POLO(max)... QLPOS... succeeded.
      s 	s: [1]	p: 5
      n__first	s: 1
      recip	s: []	p: 1
      activate	s: [1]	p: 4
      dbl	s: [1]	p: 6
      #dbl	s: []	p: 0
      #terms	s: []	p: 0
      #activate	s: []	p: 0
      n__add	s: [1,2]	p: 6
      n__s	s: [1]	p: 5
      #sqr	s: [1]	p: 0
      n__dbl	s: [1]	p: 6
      0 	s: []	p: 0
      #s 	s: []	p: 0
      #first	s: []	p: 0
      nil	s: []	p: 0
      first	s: 1
      n__terms	s: []	p: 0
      cons	s: 2
      #add	s: [2]	p: 0
      add	s: [1,2]	p: 6
      sqr	s: []	p: 0
      terms	s: []	p: 1
    USABLE RULES: { 1 2 4..20 }
    Removed DPs: #11
Number of SCCs: 0, DPs: 0