/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 POLO(bPol) ... failed.
Uncurrying 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 POLO(bPol) ... 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 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... succeeded.
      a 	w: [1;4]
      f 	w: [0,1;0,0] * x1 + [0,1;0,0] * x2
      #f^2_a	w: [0,1;0,0] * x1 + [1,1;0,0] * x2 + [2;0]
      f^1_a	w: [0,1;0,0] * x1 + [2;0]
      #f 	w: [1,0;0,0] * x1 + [1,1;0,0] * x2
      f^2_a	w: [0;0]
    USABLE RULES: { 1..3 }
    Removed DPs: #3
Number of SCCs: 1, DPs: 2
  SCC { #1 #2 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... succeeded.
      a 	w: 6
      f 	w: max(x1 + x2 - 9, 0)
      #f^2_a	w: max(x1 + x2 + 1, 0)
      f^1_a	w: max(x1 - 3, 0)
      #f 	w: max(x1 + x2 + 5, 0)
      f^2_a	w: max(x2 - 12, 0)
    USABLE RULES: { 1..3 }
    Removed DPs: #1 #2
Number of SCCs: 0, DPs: 0