/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(),f(a(),a())),x),a())
Number of strict rules: 1
Direct poly ... failed.
Freezing f
1: f❆2_a(x,a()) -> f(f❆2_a(f❆1_a(a()),x),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(f❆1_a(a()),x),a())
   #3: #f❆2_a(x,a()) -> #f❆2_a(f❆1_a(a()),x)
Number of SCCs: 1, DPs: 3
	SCC { #1..3 }
Sum... succeeded.
  a()		w: (1)
  f❆2_a(x1,x2)		w: (11798)
  #f❆2_a(x1,x2)		w: (11799)
  f(x1,x2)		w: (11798)
  #f(x1,x2)		w: (x1)
  f❆1_a(x1)		w: (11800)
    USABLE RULES: { 1 3 }
    Removed DPs: #1 #2
Number of SCCs: 1, DPs: 1
	SCC { #3 }
Sum... succeeded.
  a()		w: (283)
  f❆2_a(x1,x2)		w: (12941)
  #f❆2_a(x1,x2)		w: (11797 + x2 + x1)
  f(x1,x2)		w: (12941)
  #f(x1,x2)		w: (x1)
  f❆1_a(x1)		w: (1)
    USABLE RULES: { 1 3 }
    Removed DPs: #3
Number of SCCs: 0, DPs: 0