/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: f(0()) -> 1()
    2: f(s(x)) -> g(x,s(x))
    3: g(0(),y) -> y
    4: g(s(x),y) -> g(x,+(y,s(x)))
    5: +(x,0()) -> x
    6: +(x,s(y)) -> s(+(x,y))
    7: g(s(x),y) -> g(x,s(+(y,x)))
Number of strict rules: 7
Direct poly ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #f(s(x)) -> #g(x,s(x))
   #2: #+(x,s(y)) -> #+(x,y)
   #3: #g(s(x),y) -> #g(x,s(+(y,x)))
   #4: #g(s(x),y) -> #+(y,x)
   #5: #g(s(x),y) -> #g(x,+(y,s(x)))
   #6: #g(s(x),y) -> #+(y,s(x))
Number of SCCs: 2, DPs: 3
	SCC { #2 }
Sum... succeeded.
  1()		w: (0)
  s(x1)		w: (1 + x1)
  f(x1)		w: (0)
  0()		w: (0)
  #f(x1)		w: (0)
  #g(x1,x2)		w: (0)
  +(x1,x2)		w: (0)
  g(x1,x2)		w: (0)
  #+(x1,x2)		w: (x2)
    USABLE RULES: { }
    Removed DPs: #2
Number of SCCs: 1, DPs: 2
	SCC { #3 #5 }
Sum... succeeded.
  1()		w: (0)
  s(x1)		w: (1 + x1)
  f(x1)		w: (0)
  0()		w: (1)
  #f(x1)		w: (0)
  #g(x1,x2)		w: (20653 + x1)
  +(x1,x2)		w: (2438 + x2)
  g(x1,x2)		w: (0)
  #+(x1,x2)		w: (0)
    USABLE RULES: { }
    Removed DPs: #3 #5
Number of SCCs: 0, DPs: 0