/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(x,a()),f(a(),a())),a())
Number of strict rules: 1
Direct POLO(bPol) ... failed.
Uncurrying f
1: f^2_a(x,a()) -> f(f(f(x,a()),f^1_a(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 POLO(bPol) ... failed.
Dependency Pairs:
   #1: #f(f^1_a(_1),_2) ->? #f^2_a(_1,_2)
   #2: #f^2_a(x,a()) -> #f(f(f(x,a()),f^1_a(a())),a())
   #3: #f^2_a(x,a()) -> #f(f(x,a()),f^1_a(a()))
   #4: #f^2_a(x,a()) -> #f(x,a())
Number of SCCs: 1, DPs: 4
  SCC { #1..4 }
POLO(Sum)... succeeded.
      a 	w: 3
      f 	w: 1
      #f^2_a	w: x2
      f^1_a	w: 2
      #f 	w: x2
      f^2_a	w: 1
    USABLE RULES: { }
    Removed DPs: #3
Number of SCCs: 1, DPs: 3
  SCC { #1 #2 #4 }
POLO(Sum)... POLO(max)... succeeded.
      a 	w: 1
      f 	w: 0
      #f^2_a	w: max(x1 + 4, x2 + 1)
      f^1_a	w: x1 + 4
      #f 	w: max(x1 + 1, x2 + 2)
      f^2_a	w: 0
    USABLE RULES: { 1 3 }
    Removed DPs: #1 #2 #4
Number of SCCs: 0, DPs: 0