/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(0(x1)) -> s(0(x1))
    2: d(0(x1)) -> 0(x1)
    3: d(s(x1)) -> s(s(d(p(s(x1)))))
    4: f(s(x1)) -> d(f(p(s(x1))))
    5: p(s(x1)) -> x1
Number of strict rules: 5
Direct poly ... removes: 1
  d(x1)		w: (x1)
  s(x1)		w: (x1)
  f(x1)		w: (32287 + x1)
  p(x1)		w: (x1)
  0(x1)		w: (10451 + 2 * x1)
Number of strict rules: 4
Direct poly ... failed.
Freezing p
2: d(0(x1)) -> 0(x1)
3: d(s(x1)) -> s(s(d(p❆1_s(x1))))
4: f(s(x1)) -> d(f(p❆1_s(x1)))
5: p❆1_s(x1) -> x1
6: p(s(_1)) ->= p❆1_s(_1)
Number of strict rules: 4
Direct poly ... removes: 6
  d(x1)		w: (x1)
  s(x1)		w: (x1)
  p❆1_s(x1)		w: (x1)
  f(x1)		w: (20819 + x1)
  p(x1)		w: (5 + x1)
  0(x1)		w: (15922 + x1)
Number of strict rules: 4
Direct poly ... failed.
Dependency Pairs:
   #1: #d(s(x1)) -> #d(p❆1_s(x1))
   #2: #d(s(x1)) -> #p❆1_s(x1)
   #3: #f(s(x1)) -> #d(f(p❆1_s(x1)))
   #4: #f(s(x1)) -> #f(p❆1_s(x1))
   #5: #f(s(x1)) -> #p❆1_s(x1)
Number of SCCs: 2, DPs: 2
	SCC { #4 }
Sum... succeeded.
  d(x1)		w: (0)
  s(x1)		w: (1 + x1)
  p❆1_s(x1)		w: (x1)
  #p❆1_s(x1)		w: (0)
  f(x1)		w: (0)
  p(x1)		w: (0)
  0(x1)		w: (0)
  #d(x1)		w: (0)
  #f(x1)		w: (x1)
    USABLE RULES: { 5 }
    Removed DPs: #4
Number of SCCs: 1, DPs: 1
	SCC { #1 }
Sum... succeeded.
  d(x1)		w: (0)
  s(x1)		w: (1 + x1)
  p❆1_s(x1)		w: (x1)
  #p❆1_s(x1)		w: (0)
  f(x1)		w: (0)
  p(x1)		w: (0)
  0(x1)		w: (0)
  #d(x1)		w: (x1)
  #f(x1)		w: (x1)
    USABLE RULES: { 5 }
    Removed DPs: #1
Number of SCCs: 0, DPs: 0