/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: g(x,0()) -> 0()
    2: g(d(),s(x)) -> s(s(g(d(),x)))
    3: g(h(),s(0())) -> 0()
    4: g(h(),s(s(x))) -> s(g(h(),x))
    5: double(x) -> g(d(),x)
    6: half(x) -> g(h(),x)
    7: f(s(x),y) -> f(half(s(x)),double(y))
    8: f(s(0()),y) -> y
    9: id(x) -> f(x,s(0()))
Number of strict rules: 9
Direct poly ... removes: 8 9
  h()		w: (0)
  d()		w: (0)
  s(x1)		w: (x1)
  f(x1,x2)		w: (1142 + x2 + x1)
  half(x1)		w: (x1)
  0()		w: (282)
  double(x1)		w: (x1)
  id(x1)		w: (1425 + x1)
  g(x1,x2)		w: (x2 + x1)
Number of strict rules: 7
Direct poly ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #g(d(),s(x)) -> #g(d(),x)
   #2: #half(x) -> #g(h(),x)
   #3: #f(s(x),y) -> #f(half(s(x)),double(y))
   #4: #f(s(x),y) -> #half(s(x))
   #5: #f(s(x),y) -> #double(y)
   #6: #double(x) -> #g(d(),x)
   #7: #g(h(),s(s(x))) -> #g(h(),x)
Number of SCCs: 3, DPs: 3
	SCC { #1 }
Sum... succeeded.
  h()		w: (0)
  d()		w: (1)
  s(x1)		w: (1 + x1)
  #half(x1)		w: (0)
  f(x1,x2)		w: (0)
  half(x1)		w: (0)
  0()		w: (0)
  #double(x1)		w: (0)
  double(x1)		w: (0)
  #f(x1,x2)		w: (0)
  #g(x1,x2)		w: (x2 + x1)
  id(x1)		w: (0)
  g(x1,x2)		w: (0)
    USABLE RULES: { }
    Removed DPs: #1
Number of SCCs: 2, DPs: 2
	SCC { #7 }
Sum... succeeded.
  h()		w: (1)
  d()		w: (1)
  s(x1)		w: (1 + x1)
  #half(x1)		w: (0)
  f(x1,x2)		w: (0)
  half(x1)		w: (0)
  0()		w: (0)
  #double(x1)		w: (0)
  double(x1)		w: (0)
  #f(x1,x2)		w: (0)
  #g(x1,x2)		w: (x2 + x1)
  id(x1)		w: (0)
  g(x1,x2)		w: (0)
    USABLE RULES: { }
    Removed DPs: #7
Number of SCCs: 1, DPs: 1
	SCC { #3 }
Sum... Max... QLPOpS... NegMaxSum... succeeded.
  h()		w: (1)
  d()		w: (4)
  s(x1)		w: (max{0, 21241 + x1})
  #half(x1)		w: (0)
  f(x1,x2)		w: (0)
  half(x1)		w: (max{0, -2 + x1})
  0()		w: (0)
  #double(x1)		w: (0)
  double(x1)		w: (0)
  #f(x1,x2)		w: (max{0, -21240 + x1})
  #g(x1,x2)		w: (0)
  id(x1)		w: (0)
  g(x1,x2)		w: (max{0, -3 + x2 + x1})
    USABLE RULES: { 1 3 4 6 }
    Removed DPs: #3
Number of SCCs: 0, DPs: 0