/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: fib(0()) -> 0()
    2: fib(s(0())) -> s(0())
    3: fib(s(s(x))) -> +(fib(s(x)),fib(x))
    4: +(x,0()) -> x
    5: +(x,s(y)) -> s(+(x,y))
Number of strict rules: 5
Direct poly ... failed.
Freezing fib
1: fib❆1_0() -> 0()
2: fib❆1_s(0()) -> s(0())
3: fib❆1_s(s(x)) -> +(fib❆1_s(x),fib(x))
4: +(x,0()) -> x
5: +(x,s(y)) -> s(+(x,y))
6: fib(0()) ->= fib❆1_0()
7: fib(s(_1)) ->= fib❆1_s(_1)
Number of strict rules: 5
Direct poly ... failed.
Dependency Pairs:
   #1: #fib(0()) ->? #fib❆1_0()
   #2: #fib(s(_1)) ->? #fib❆1_s(_1)
   #3: #+(x,s(y)) -> #+(x,y)
   #4: #fib❆1_s(s(x)) -> #+(fib❆1_s(x),fib(x))
   #5: #fib❆1_s(s(x)) -> #fib❆1_s(x)
   #6: #fib❆1_s(s(x)) -> #fib(x)
Number of SCCs: 2, DPs: 4
	SCC { #3 }
Sum... succeeded.
  s(x1)		w: (1 + x1)
  #fib❆1_s(x1)		w: (0)
  fib❆1_0()		w: (0)
  fib(x1)		w: (0)
  0()		w: (0)
  #fib❆1_0()		w: (0)
  fib❆1_s(x1)		w: (0)
  +(x1,x2)		w: (0)
  #fib(x1)		w: (0)
  #+(x1,x2)		w: (x2)
    USABLE RULES: { }
    Removed DPs: #3
Number of SCCs: 1, DPs: 3
	SCC { #2 #5 #6 }
Sum... succeeded.
  s(x1)		w: (39 + x1)
  #fib❆1_s(x1)		w: (x1)
  fib❆1_0()		w: (0)
  fib(x1)		w: (0)
  0()		w: (0)
  #fib❆1_0()		w: (0)
  fib❆1_s(x1)		w: (0)
  +(x1,x2)		w: (0)
  #fib(x1)		w: (x1)
  #+(x1,x2)		w: (0)
    USABLE RULES: { }
    Removed DPs: #2 #5 #6
Number of SCCs: 0, DPs: 0