/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(),a()),x) -> f(f(x,a()),f(a(),f(a(),a())))
Number of strict rules: 1
Direct poly ... failed.
Freezing f
1: f❆2_a(a(),x) -> f(f(x,a()),f❆1_a(f❆1_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(a(),x) -> #f(f(x,a()),f❆1_a(f❆1_a(a())))
   #3: #f❆2_a(a(),x) -> #f(x,a())
Number of SCCs: 1, DPs: 3
	SCC { #1..3 }
Sum... Max... QLPOpS... NegMaxSum... QWPOpSMaxSum... 2D-Mat... succeeded.
  a()		w: (12239, 1)
  f❆2_a(x1,x2)		w: (12240, 0)
  #f❆2_a(x1,x2)		w: (31251 + x2_2 + x1_1, 24170)
  f(x1,x2)		w: (12240, x2_1)
  #f(x1,x2)		w: (31251 + x2_2 + x1_2, 24170)
  f❆1_a(x1)		w: (0, x1_1)
    USABLE RULES: { 1..3 }
    Removed DPs: #3
Number of SCCs: 1, DPs: 2
	SCC { #1 #2 }
Sum... Max... QLPOpS... NegMaxSum... succeeded.
  a()		w: (96013)
  f❆2_a(x1,x2)		w: (max{0, -220129 + x2})
  #f❆2_a(x1,x2)		w: (max{0, 1 + x2 + x1})
  f(x1,x2)		w: (max{0, -158071 + x2 + x1})
  #f(x1,x2)		w: (max{0, 90160 + x2 + x1})
  f❆1_a(x1)		w: (max{0, -62058 + x1})
    USABLE RULES: { 1..3 }
    Removed DPs: #1 #2
Number of SCCs: 0, DPs: 0