/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(f(a(),x),a()) -> f(f(f(a(),a()),f(x,a())),a())
Number of strict rules: 1
Direct poly ... failed.
Freezing f
1: f❆2_a(x,a()) -> f(f❆2_a(a(),f(x,a())),a())
2: f(a(),_1) ->= f❆1_a(_1)
3: f(f❆1_a(_1),_2) ->= f❆2_a(_1,_2)
Number of strict rules: 1
Direct poly ... failed.
Dependency Pairs:
   #1: #f(f❆1_a(_1),_2) ->? #f❆2_a(_1,_2)
   #2: #f❆2_a(x,a()) -> #f(f❆2_a(a(),f(x,a())),a())
   #3: #f❆2_a(x,a()) -> #f❆2_a(a(),f(x,a()))
   #4: #f❆2_a(x,a()) -> #f(x,a())
Number of SCCs: 1, DPs: 2
	SCC { #1 #4 }
Sum... succeeded.
  a()		w: (1)
  f❆2_a(x1,x2)		w: (0)
  #f❆2_a(x1,x2)		w: (7720 + x2 + x1)
  f(x1,x2)		w: (0)
  #f(x1,x2)		w: (x2 + x1)
  f❆1_a(x1)		w: (7721 + x1)
    USABLE RULES: { }
    Removed DPs: #1 #4
Number of SCCs: 0, DPs: 0