/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(x,f(s(s(y)),f(z,w))) -> f(s(x),f(y,f(s(z),w)))
    2: L(f(s(s(y)),f(z,w))) -> L(f(s(0()),f(y,f(s(z),w))))
    3: f(x,f(s(s(y)),nil())) -> f(s(x),f(y,f(s(0()),nil())))
Number of strict rules: 3
Direct poly ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #L(f(s(s(y)),f(z,w))) -> #L(f(s(0()),f(y,f(s(z),w))))
   #2: #L(f(s(s(y)),f(z,w))) -> #f(s(0()),f(y,f(s(z),w)))
   #3: #L(f(s(s(y)),f(z,w))) -> #f(y,f(s(z),w))
   #4: #L(f(s(s(y)),f(z,w))) -> #f(s(z),w)
   #5: #f(x,f(s(s(y)),nil())) -> #f(s(x),f(y,f(s(0()),nil())))
   #6: #f(x,f(s(s(y)),nil())) -> #f(y,f(s(0()),nil()))
   #7: #f(x,f(s(s(y)),nil())) -> #f(s(0()),nil())
   #8: #f(x,f(s(s(y)),f(z,w))) -> #f(s(x),f(y,f(s(z),w)))
   #9: #f(x,f(s(s(y)),f(z,w))) -> #f(y,f(s(z),w))
   #10: #f(x,f(s(s(y)),f(z,w))) -> #f(s(z),w)
Number of SCCs: 2, DPs: 5
	SCC { #1 }
Sum... Max... QLPOpS... NegMaxSum... succeeded.
  s(x1)		w: (max{0, 47771 + x1})
  #L(x1)		w: (max{0, 15925 + x1})
  f(x1,x2)		w: (max{0, -15924 + x2 + x1})
  0()		w: (15923)
  nil()		w: (47770)
  #f(x1,x2)		w: (0)
  L(x1)		w: (0)
    USABLE RULES: { 1 3 }
    Removed DPs: #1
Number of SCCs: 1, DPs: 4
	SCC { #5 #8..10 }
Sum... succeeded.
  s(x1)		w: (1 + x1)
  #L(x1)		w: (2)
  f(x1,x2)		w: (x2 + x1)
  0()		w: (0)
  nil()		w: (5854)
  #f(x1,x2)		w: (30613 + x2)
  L(x1)		w: (0)
    USABLE RULES: { 1 3 }
    Removed DPs: #5 #8..10
Number of SCCs: 0, DPs: 0