/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: R(x1) -> r(x1)
    2: r(p(x1)) -> p(p(r(P(x1))))
    3: r(r(x1)) -> x1
    4: r(P(P(x1))) -> P(P(r(x1)))
    5: p(P(x1)) -> x1
    6: P(p(x1)) -> x1
    7: r(R(x1)) -> x1
    8: R(r(x1)) -> x1
Number of strict rules: 8
Direct poly ... removes: 8 1 3 5 7 6
  r(x1)		w: (2438 + 2 * x1)
  p(x1)		w: (8856 + x1)
  R(x1)		w: (2439 + 2 * x1)
  P(x1)		w: (x1)
Number of strict rules: 2
Direct poly ... failed.
Freezing r
2: r❆1_p(x1) -> p(p(r❆1_P(x1)))
4: r❆1_P(P(x1)) -> P(P(r(x1)))
9: r(p(_1)) ->= r❆1_p(_1)
10: r(P(_1)) ->= r❆1_P(_1)
Number of strict rules: 2
Direct poly ... removes: 10
  r(x1)		w: (30613 + 2 * x1)
  r❆1_P(x1)		w: (30613 + 2 * x1)
  r❆1_p(x1)		w: (30615 + 2 * x1)
  p(x1)		w: (1 + x1)
  R(x1)		w: (x1)
  P(x1)		w: (1 + x1)
Number of strict rules: 2
Direct poly ... failed.
Dependency Pairs:
   #1: #r❆1_p(x1) -> #r❆1_P(x1)
   #2: #r(p(_1)) ->? #r❆1_p(_1)
   #3: #r❆1_P(P(x1)) -> #r(x1)
Number of SCCs: 1, DPs: 3
	SCC { #1..3 }
Sum... succeeded.
  #r❆1_P(x1)		w: (x1)
  r(x1)		w: (0)
  r❆1_P(x1)		w: (0)
  r❆1_p(x1)		w: (0)
  p(x1)		w: (1 + x1)
  #r❆1_p(x1)		w: (1 + x1)
  R(x1)		w: (0)
  #r(x1)		w: (3 + x1)
  P(x1)		w: (42 + x1)
    USABLE RULES: { }
    Removed DPs: #1..3
Number of SCCs: 0, DPs: 0