/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: b(a(a(x1))) -> a(b(c(x1)))
    2: c(a(x1)) -> a(c(x1))
    3: c(b(x1)) -> b(a(x1))
    4: L(a(a(x1))) -> L(a(b(c(x1))))
    5: c(R(x1)) -> b(a(R(x1)))
Number of strict rules: 5
Direct poly ... failed.
Freezing L
1: b(a(a(x1))) -> a(b(c(x1)))
2: c(a(x1)) -> a(c(x1))
3: c(b(x1)) -> b(a(x1))
4: L❆1_a(a(x1)) -> L❆1_a(b(c(x1)))
5: c(R(x1)) -> b(a(R(x1)))
6: L(a(_1)) ->= L❆1_a(_1)
Number of strict rules: 5
Direct poly ... removes: 6
  a(x1)		w: (1 + x1)
  b(x1)		w: (x1)
  L❆1_a(x1)		w: (2 * x1)
  c(x1)		w: (1 + x1)
  R(x1)		w: (28101 + 2 * x1)
  L(x1)		w: (2 * x1)
Number of strict rules: 5
Direct poly ... failed.
Dependency Pairs:
   #1: #c(a(x1)) -> #c(x1)
   #2: #c(R(x1)) -> #b(a(R(x1)))
   #3: #c(b(x1)) -> #b(a(x1))
   #4: #b(a(a(x1))) -> #b(c(x1))
   #5: #b(a(a(x1))) -> #c(x1)
   #6: #L❆1_a(a(x1)) -> #L❆1_a(b(c(x1)))
   #7: #L❆1_a(a(x1)) -> #b(c(x1))
   #8: #L❆1_a(a(x1)) -> #c(x1)
Number of SCCs: 2, DPs: 5
	SCC { #6 }
Sum... Max... QLPOpS... NegMaxSum... succeeded.
  a(x1)		w: (max{0, 3 + x1})
  b(x1)		w: (max{0, -1 + x1})
  L❆1_a(x1)		w: (0)
  c(x1)		w: (max{0, 3 + x1})
  #L❆1_a(x1)		w: (max{0, -1 + x1})
  R(x1)		w: (max{0, 2 + x1})
  L(x1)		w: (0)
  #c(x1)		w: (0)
  #b(x1)		w: (0)
    USABLE RULES: { 1..3 5 }
    Removed DPs: #6
Number of SCCs: 1, DPs: 4
	SCC { #1 #3..5 }
Sum... succeeded.
  a(x1)		w: (1144 + x1)
  b(x1)		w: (x1)
  L❆1_a(x1)		w: (0)
  c(x1)		w: (1144 + x1)
  #L❆1_a(x1)		w: (0)
  R(x1)		w: (1)
  L(x1)		w: (0)
  #c(x1)		w: (1145 + x1)
  #b(x1)		w: (x1)
    USABLE RULES: { 1..3 5 }
    Removed DPs: #1 #3..5
Number of SCCs: 0, DPs: 0