/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(a(),f(a(),x)) -> f(x,f(a(),f(f(a(),a()),a())))
Number of strict rules: 1
Direct poly ... failed.
Freezing f
1: f❆1_a(f❆1_a(x)) -> f(x,f❆1_a(f(f❆1_a(a()),a())))
2: f(a(),_1) ->= f❆1_a(_1)
Number of strict rules: 1
Direct poly ... failed.
Dependency Pairs:
   #1: #f(a(),_1) ->? #f❆1_a(_1)
   #2: #f❆1_a(f❆1_a(x)) -> #f(x,f❆1_a(f(f❆1_a(a()),a())))
   #3: #f❆1_a(f❆1_a(x)) -> #f❆1_a(f(f❆1_a(a()),a()))
   #4: #f❆1_a(f❆1_a(x)) -> #f(f❆1_a(a()),a())
   #5: #f❆1_a(f❆1_a(x)) -> #f❆1_a(a())
Number of SCCs: 1, DPs: 2
	SCC { #1 #2 }
Sum... Max... QLPOpS... NegMaxSum... succeeded.
  a()		w: (56203)
  f(x1,x2)		w: (max{0, -56203 + x2 + x1})
  #f❆1_a(x1)		w: (max{0, 57627 + x1})
  #f(x1,x2)		w: (max{0, 29525 + x2 + x1})
  f❆1_a(x1)		w: (max{0, -28101 + x1})
    USABLE RULES: { 1 2 }
    Removed DPs: #1
Number of SCCs: 0, DPs: 0