/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: f(a(),f(b(),x)) -> f(a(),f(a(),f(a(),x)))
    2: f(b(),f(a(),x)) -> f(b(),f(b(),f(b(),x)))
Number of strict rules: 2
Direct poly ... failed.
Freezing f
1: f❆1_a(f❆1_b(x)) -> f❆1_a(f❆1_a(f❆1_a(x)))
2: f❆1_b(f❆1_a(x)) -> f❆1_b(f❆1_b(f❆1_b(x)))
3: f(a(),_1) ->= f❆1_a(_1)
4: f(b(),_1) ->= f❆1_b(_1)
Number of strict rules: 2
Direct poly ... removes: 4 3
  a()		w: (0)
  b()		w: (1)
  f(x1,x2)		w: (1 + x2 + x1)
  f❆1_b(x1)		w: (x1)
  f❆1_a(x1)		w: (x1)
Number of strict rules: 2
Direct poly ... failed.
Dependency Pairs:
   #1: #f❆1_b(f❆1_a(x)) -> #f❆1_b(f❆1_b(f❆1_b(x)))
   #2: #f❆1_b(f❆1_a(x)) -> #f❆1_b(f❆1_b(x))
   #3: #f❆1_b(f❆1_a(x)) -> #f❆1_b(x)
   #4: #f❆1_a(f❆1_b(x)) -> #f❆1_a(f❆1_a(f❆1_a(x)))
   #5: #f❆1_a(f❆1_b(x)) -> #f❆1_a(f❆1_a(x))
   #6: #f❆1_a(f❆1_b(x)) -> #f❆1_a(x)
Number of SCCs: 2, DPs: 2
	SCC { #3 }
Sum... succeeded.
  a()		w: (0)
  b()		w: (0)
  #f❆1_b(x1)		w: (x1)
  f(x1,x2)		w: (0)
  #f❆1_a(x1)		w: (0)
  f❆1_b(x1)		w: (0)
  f❆1_a(x1)		w: (1 + x1)
    USABLE RULES: { }
    Removed DPs: #3
Number of SCCs: 1, DPs: 1
	SCC { #6 }
Sum... succeeded.
  a()		w: (0)
  b()		w: (0)
  #f❆1_b(x1)		w: (0)
  f(x1,x2)		w: (0)
  #f❆1_a(x1)		w: (x1)
  f❆1_b(x1)		w: (1 + x1)
  f❆1_a(x1)		w: (1)
    USABLE RULES: { }
    Removed DPs: #6
Number of SCCs: 0, DPs: 0