/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: active(zeros()) -> mark(cons(0(),zeros()))
    2: active(tail(cons(X,XS))) -> mark(XS)
    3: active(cons(X1,X2)) -> cons(active(X1),X2)
    4: active(tail(X)) -> tail(active(X))
    5: cons(mark(X1),X2) -> mark(cons(X1,X2))
    6: tail(mark(X)) -> mark(tail(X))
    7: proper(zeros()) -> ok(zeros())
    8: proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
    9: proper(0()) -> ok(0())
    10: proper(tail(X)) -> tail(proper(X))
    11: cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
    12: tail(ok(X)) -> ok(tail(X))
    13: top(mark(X)) -> top(proper(X))
    14: top(ok(X)) -> top(active(X))
Number of strict rules: 14
Direct POLO(bPol) ... removes: 2
      top	w: x1
      zeros	w: 1
      tail	w: x1 + 1
      proper	w: x1
      ok	w: x1
      0 	w: 0
      mark	w: x1
      active	w: x1
      cons	w: x1 + x2
Number of strict rules: 13
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
   #1: #tail(mark(X)) -> #tail(X)
   #2: #top(mark(X)) -> #top(proper(X))
   #3: #top(mark(X)) -> #proper(X)
   #4: #cons(ok(X1),ok(X2)) -> #cons(X1,X2)
   #5: #tail(ok(X)) -> #tail(X)
   #6: #top(ok(X)) -> #top(active(X))
   #7: #top(ok(X)) -> #active(X)
   #8: #proper(tail(X)) -> #tail(proper(X))
   #9: #proper(tail(X)) -> #proper(X)
   #10: #cons(mark(X1),X2) -> #cons(X1,X2)
   #11: #active(cons(X1,X2)) -> #cons(active(X1),X2)
   #12: #active(cons(X1,X2)) -> #active(X1)
   #13: #active(zeros()) -> #cons(0(),zeros())
   #14: #proper(cons(X1,X2)) -> #cons(proper(X1),proper(X2))
   #15: #proper(cons(X1,X2)) -> #proper(X1)
   #16: #proper(cons(X1,X2)) -> #proper(X2)
   #17: #active(tail(X)) -> #tail(active(X))
   #18: #active(tail(X)) -> #active(X)
Number of SCCs: 5, DPs: 11
  SCC { #1 #5 }
POLO(Sum)... succeeded.
      #cons	w: 0
      top	w: 0
      #top	w: 0
      zeros	w: 0
      tail	w: 0
      proper	w: 0
      ok	w: x1 + 1
      0 	w: 0
      #tail	w: x1
      mark	w: x1 + 1
      #proper	w: 0
      active	w: 0
      cons	w: 0
      #active	w: 0
    USABLE RULES: { }
    Removed DPs: #1 #5
Number of SCCs: 4, DPs: 9
  SCC { #12 #18 }
POLO(Sum)... succeeded.
      #cons	w: 0
      top	w: 0
      #top	w: 0
      zeros	w: 0
      tail	w: x1 + 1
      proper	w: 0
      ok	w: 1
      0 	w: 0
      #tail	w: 0
      mark	w: 1
      #proper	w: 0
      active	w: 0
      cons	w: x1 + 1
      #active	w: x1
    USABLE RULES: { }
    Removed DPs: #12 #18
Number of SCCs: 3, DPs: 7
  SCC { #2 #6 }
POLO(Sum)... succeeded.
      #cons	w: 0
      top	w: 0
      #top	w: x1
      zeros	w: 4
      tail	w: x1 + 1
      proper	w: x1 + 2
      ok	w: x1 + 2
      0 	w: 1
      #tail	w: 0
      mark	w: x1 + 3
      #proper	w: 0
      active	w: x1 + 1
      cons	w: x1 + 1
      #active	w: 0
    USABLE RULES: { 1 3..12 }
    Removed DPs: #2 #6
Number of SCCs: 2, DPs: 5
  SCC { #4 #10 }
POLO(Sum)... succeeded.
      #cons	w: x2
      top	w: 0
      #top	w: x1
      zeros	w: 4
      tail	w: x1 + 1
      proper	w: x1 + 2
      ok	w: x1 + 2
      0 	w: 1
      #tail	w: 0
      mark	w: 3
      #proper	w: 0
      active	w: x1 + 1
      cons	w: x1
      #active	w: 0
    USABLE RULES: { 1 3..12 }
    Removed DPs: #4
Number of SCCs: 2, DPs: 4
  SCC { #10 }
POLO(Sum)... succeeded.
      #cons	w: x1
      top	w: 0
      #top	w: x1
      zeros	w: 4
      tail	w: x1 + 1
      proper	w: x1 + 2
      ok	w: x1 + 2
      0 	w: 1
      #tail	w: 0
      mark	w: x1 + 3
      #proper	w: 0
      active	w: x1 + 3
      cons	w: x1 + 1
      #active	w: 0
    USABLE RULES: { 1 3..12 }
    Removed DPs: #10
Number of SCCs: 1, DPs: 3
  SCC { #9 #15 #16 }
POLO(Sum)... succeeded.
      #cons	w: 0
      top	w: 0
      #top	w: x1
      zeros	w: 4
      tail	w: x1 + 1
      proper	w: x1
      ok	w: x1
      0 	w: 1
      #tail	w: 0
      mark	w: x1 + 3
      #proper	w: x1
      active	w: x1 + 7
      cons	w: x1 + x2 + 1
      #active	w: 0
    USABLE RULES: { 1 3..12 }
    Removed DPs: #9 #15 #16
Number of SCCs: 0, DPs: 0