/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(f(a(),x),y) -> f(y,f(x,f(a(),f(h(a()),a()))))
Number of strict rules: 1
Direct poly ... failed.
Freezing f
1: f❆2_a(x,y) -> f(y,f(x,f❆1_a(f❆1_h(a(),a()))))
2: f(h(_1),_2) ->= f❆1_h(_1,_2)
3: f(a(),_1) ->= f❆1_a(_1)
4: f(f❆1_a(_1),_2) ->= f❆2_a(_1,_2)
Number of strict rules: 1
Direct poly ... removes: 2
  a()		w: (0)
  h(x1)		w: (1 + x1)
  f❆2_a(x1,x2)		w: (x2 + x1)
  f(x1,x2)		w: (x2 + x1)
  f❆1_h(x1,x2)		w: (x2 + x1)
  f❆1_a(x1)		w: (x1)
Number of strict rules: 1
Direct poly ... failed.
Dependency Pairs:
   #1: #f❆2_a(x,y) -> #f(y,f(x,f❆1_a(f❆1_h(a(),a()))))
   #2: #f❆2_a(x,y) -> #f(x,f❆1_a(f❆1_h(a(),a())))
   #3: #f(f❆1_a(_1),_2) ->? #f❆2_a(_1,_2)
Number of SCCs: 1, DPs: 3
	SCC { #1..3 }
Sum... Max... QLPOpS... NegMaxSum... succeeded.
  a()		w: (21243)
  h(x1)		w: (0)
  f❆2_a(x1,x2)		w: (max{0, 2 + x2 + x1})
  #f❆2_a(x1,x2)		w: (max{0, 11298 + x2 + x1})
  f(x1,x2)		w: (max{0, -1 + x2 + x1})
  f❆1_h(x1,x2)		w: (max{0, -42487 + x2 + x1})
  #f(x1,x2)		w: (max{0, 11294 + x2 + x1})
  f❆1_a(x1)		w: (max{0, 4 + x1})
    USABLE RULES: { 1 3 4 }
    Removed DPs: #1
Number of SCCs: 1, DPs: 2
	SCC { #2 #3 }
Sum... succeeded.
  a()		w: (1)
  h(x1)		w: (0)
  f❆2_a(x1,x2)		w: (x2 + x1)
  #f❆2_a(x1,x2)		w: (1 + x1)
  f(x1,x2)		w: (1)
  f❆1_h(x1,x2)		w: (10450 + x1)
  #f(x1,x2)		w: (x1)
  f❆1_a(x1)		w: (2 + x1)
    USABLE RULES: { }
    Removed DPs: #2 #3
Number of SCCs: 0, DPs: 0