/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(from(X)) -> mark(cons(X,from(s(X))))
    2: active(head(cons(X,XS))) -> mark(X)
    3: active(2nd(cons(X,XS))) -> mark(head(XS))
    4: active(take(0(),XS)) -> mark(nil())
    5: active(take(s(N),cons(X,XS))) -> mark(cons(X,take(N,XS)))
    6: active(sel(0(),cons(X,XS))) -> mark(X)
    7: active(sel(s(N),cons(X,XS))) -> mark(sel(N,XS))
    8: active(from(X)) -> from(active(X))
    9: active(cons(X1,X2)) -> cons(active(X1),X2)
    10: active(s(X)) -> s(active(X))
    11: active(head(X)) -> head(active(X))
    12: active(2nd(X)) -> 2nd(active(X))
    13: active(take(X1,X2)) -> take(active(X1),X2)
    14: active(take(X1,X2)) -> take(X1,active(X2))
    15: active(sel(X1,X2)) -> sel(active(X1),X2)
    16: active(sel(X1,X2)) -> sel(X1,active(X2))
    17: from(mark(X)) -> mark(from(X))
    18: cons(mark(X1),X2) -> mark(cons(X1,X2))
    19: s(mark(X)) -> mark(s(X))
    20: head(mark(X)) -> mark(head(X))
    21: 2nd(mark(X)) -> mark(2nd(X))
    22: take(mark(X1),X2) -> mark(take(X1,X2))
    23: take(X1,mark(X2)) -> mark(take(X1,X2))
    24: sel(mark(X1),X2) -> mark(sel(X1,X2))
    25: sel(X1,mark(X2)) -> mark(sel(X1,X2))
    26: proper(from(X)) -> from(proper(X))
    27: proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
    28: proper(s(X)) -> s(proper(X))
    29: proper(head(X)) -> head(proper(X))
    30: proper(2nd(X)) -> 2nd(proper(X))
    31: proper(take(X1,X2)) -> take(proper(X1),proper(X2))
    32: proper(0()) -> ok(0())
    33: proper(nil()) -> ok(nil())
    34: proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
    35: from(ok(X)) -> ok(from(X))
    36: cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
    37: s(ok(X)) -> ok(s(X))
    38: head(ok(X)) -> ok(head(X))
    39: 2nd(ok(X)) -> ok(2nd(X))
    40: take(ok(X1),ok(X2)) -> ok(take(X1,X2))
    41: sel(ok(X1),ok(X2)) -> ok(sel(X1,X2))
    42: top(mark(X)) -> top(proper(X))
    43: top(ok(X)) -> top(active(X))
Number of strict rules: 43
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
   #1: #top(ok(X)) -> #top(active(X))
   #2: #top(ok(X)) -> #active(X)
   #3: #proper(head(X)) -> #head(proper(X))
   #4: #proper(head(X)) -> #proper(X)
   #5: #from(ok(X)) -> #from(X)
   #6: #top(mark(X)) -> #top(proper(X))
   #7: #top(mark(X)) -> #proper(X)
   #8: #sel(ok(X1),ok(X2)) -> #sel(X1,X2)
   #9: #s(ok(X)) -> #s(X)
   #10: #head(ok(X)) -> #head(X)
   #11: #take(ok(X1),ok(X2)) -> #take(X1,X2)
   #12: #active(take(X1,X2)) -> #take(active(X1),X2)
   #13: #active(take(X1,X2)) -> #active(X1)
   #14: #active(cons(X1,X2)) -> #cons(active(X1),X2)
   #15: #active(cons(X1,X2)) -> #active(X1)
   #16: #active(head(X)) -> #head(active(X))
   #17: #active(head(X)) -> #active(X)
   #18: #sel(mark(X1),X2) -> #sel(X1,X2)
   #19: #take(X1,mark(X2)) -> #take(X1,X2)
   #20: #active(2nd(X)) -> #2nd(active(X))
   #21: #active(2nd(X)) -> #active(X)
   #22: #proper(take(X1,X2)) -> #take(proper(X1),proper(X2))
   #23: #proper(take(X1,X2)) -> #proper(X1)
   #24: #proper(take(X1,X2)) -> #proper(X2)
   #25: #active(take(X1,X2)) -> #take(X1,active(X2))
   #26: #active(take(X1,X2)) -> #active(X2)
   #27: #proper(2nd(X)) -> #2nd(proper(X))
   #28: #proper(2nd(X)) -> #proper(X)
   #29: #sel(X1,mark(X2)) -> #sel(X1,X2)
   #30: #head(mark(X)) -> #head(X)
   #31: #active(sel(s(N),cons(X,XS))) -> #sel(N,XS)
   #32: #2nd(ok(X)) -> #2nd(X)
   #33: #active(s(X)) -> #s(active(X))
   #34: #active(s(X)) -> #active(X)
   #35: #active(take(s(N),cons(X,XS))) -> #cons(X,take(N,XS))
   #36: #active(take(s(N),cons(X,XS))) -> #take(N,XS)
   #37: #proper(s(X)) -> #s(proper(X))
   #38: #proper(s(X)) -> #proper(X)
   #39: #take(mark(X1),X2) -> #take(X1,X2)
   #40: #proper(sel(X1,X2)) -> #sel(proper(X1),proper(X2))
   #41: #proper(sel(X1,X2)) -> #proper(X1)
   #42: #proper(sel(X1,X2)) -> #proper(X2)
   #43: #proper(cons(X1,X2)) -> #cons(proper(X1),proper(X2))
   #44: #proper(cons(X1,X2)) -> #proper(X1)
   #45: #proper(cons(X1,X2)) -> #proper(X2)
   #46: #from(mark(X)) -> #from(X)
   #47: #s(mark(X)) -> #s(X)
   #48: #proper(from(X)) -> #from(proper(X))
   #49: #proper(from(X)) -> #proper(X)
   #50: #cons(ok(X1),ok(X2)) -> #cons(X1,X2)
   #51: #2nd(mark(X)) -> #2nd(X)
   #52: #active(sel(X1,X2)) -> #sel(X1,active(X2))
   #53: #active(sel(X1,X2)) -> #active(X2)
   #54: #active(2nd(cons(X,XS))) -> #head(XS)
   #55: #active(from(X)) -> #cons(X,from(s(X)))
   #56: #active(from(X)) -> #from(s(X))
   #57: #active(from(X)) -> #s(X)
   #58: #active(from(X)) -> #from(active(X))
   #59: #active(from(X)) -> #active(X)
   #60: #active(sel(X1,X2)) -> #sel(active(X1),X2)
   #61: #active(sel(X1,X2)) -> #active(X1)
   #62: #cons(mark(X1),X2) -> #cons(X1,X2)
Number of SCCs: 10, DPs: 37
  SCC { #10 #30 }
POLO(Sum)... succeeded.
      #cons	w: 0
      s 	w: 0
      #take	w: 0
      take	w: 0
      top	w: 0
      2nd	w: 0
      #top	w: 0
      #head	w: x1
      proper	w: 0
      ok	w: x1 + 1
      0 	w: 0
      #sel	w: 0
      from	w: 0
      sel	w: 0
      #s 	w: 0
      nil	w: 0
      #2nd	w: 0
      mark	w: x1 + 1
      #proper	w: 0
      #from	w: 0
      active	w: 0
      head	w: 0
      cons	w: 0
      #active	w: 0
    USABLE RULES: { }
    Removed DPs: #10 #30
Number of SCCs: 9, DPs: 35
  SCC { #9 #47 }
POLO(Sum)... succeeded.
      #cons	w: 0
      s 	w: 0
      #take	w: 0
      take	w: 0
      top	w: 0
      2nd	w: 0
      #top	w: 0
      #head	w: 0
      proper	w: 0
      ok	w: x1 + 1
      0 	w: 0
      #sel	w: 0
      from	w: 0
      sel	w: 0
      #s 	w: x1
      nil	w: 0
      #2nd	w: 0
      mark	w: x1 + 1
      #proper	w: 0
      #from	w: 0
      active	w: 0
      head	w: 0
      cons	w: 0
      #active	w: 0
    USABLE RULES: { }
    Removed DPs: #9 #47
Number of SCCs: 8, DPs: 33
  SCC { #5 #46 }
POLO(Sum)... succeeded.
      #cons	w: 0
      s 	w: 0
      #take	w: 0
      take	w: 0
      top	w: 0
      2nd	w: 0
      #top	w: 0
      #head	w: 0
      proper	w: 0
      ok	w: x1 + 1
      0 	w: 0
      #sel	w: 0
      from	w: 0
      sel	w: 0
      #s 	w: 0
      nil	w: 0
      #2nd	w: 0
      mark	w: x1 + 1
      #proper	w: 0
      #from	w: x1
      active	w: 0
      head	w: 0
      cons	w: 0
      #active	w: 0
    USABLE RULES: { }
    Removed DPs: #5 #46
Number of SCCs: 7, DPs: 31
  SCC { #32 #51 }
POLO(Sum)... succeeded.
      #cons	w: 0
      s 	w: 0
      #take	w: 0
      take	w: 0
      top	w: 0
      2nd	w: 0
      #top	w: 0
      #head	w: 0
      proper	w: 0
      ok	w: x1 + 1
      0 	w: 0
      #sel	w: 0
      from	w: 0
      sel	w: 0
      #s 	w: 0
      nil	w: 0
      #2nd	w: x1
      mark	w: x1 + 1
      #proper	w: 0
      #from	w: 0
      active	w: 0
      head	w: 0
      cons	w: 0
      #active	w: 0
    USABLE RULES: { }
    Removed DPs: #32 #51
Number of SCCs: 6, DPs: 29
  SCC { #1 #6 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded.
      #cons	s: [2]	p: 0	w: max(x2 + 1)
      s 	s: [1]	p: 2	w: x1
      #take	s: [1]	p: 0	w: x1
      take	s: [2,1]	p: 8	w: x1 + x2 + 1
      top	s: []	p: 0	w: 1
      2nd	s: [1]	p: 1	w: x1 + 4
      #top	s: [1]	p: 0	w: x1
      #head	s: []	p: 0	w: 1
      proper	s: 1
      ok	s: 1
      0 	s: []	p: 8	w: 3
      #sel	s: [2]	p: 0	w: x2 + 1
      from	s: [1]	p: 4	w: x1 + 3
      sel	s: [1,2]	p: 6	w: x1 + x2 + 3
      #s 	s: []	p: 0	w: 0
      nil	s: []	p: 9	w: 2
      #2nd	s: []	p: 0	w: 1
      mark	s: [1]	p: 0	w: x1
      #proper	s: []	p: 0	w: 0
      #from	s: []	p: 0	w: 0
      active	s: 1
      head	s: [1]	p: 2	w: x1 + 3
      cons	s: [1]	p: 3	w: max(x1 + 2, x2)
      #active	s: []	p: 0	w: 1
    USABLE RULES: { 1..41 }
    Removed DPs: #6
Number of SCCs: 6, DPs: 28
  SCC { #1 }
POLO(Sum)... succeeded.
      #cons	w: 0
      s 	w: x1 + 1
      #take	w: 0
      take	w: x1 + 1
      top	w: 0
      2nd	w: x1 + 1
      #top	w: x1
      #head	w: 0
      proper	w: x1 + 2
      ok	w: x1 + 2
      0 	w: 1
      #sel	w: 0
      from	w: x1 + 1
      sel	w: x2 + 1
      #s 	w: 0
      nil	w: 1
      #2nd	w: 0
      mark	w: 1
      #proper	w: 0
      #from	w: 0
      active	w: x1 + 1
      head	w: x1 + 1
      cons	w: x2 + 1
      #active	w: 0
    USABLE RULES: { 1..41 }
    Removed DPs: #1
Number of SCCs: 5, DPs: 27
  SCC { #50 #62 }
POLO(Sum)... succeeded.
      #cons	w: x2
      s 	w: x1 + 1
      #take	w: 0
      take	w: x1 + 1
      top	w: 0
      2nd	w: x1 + 1
      #top	w: x1
      #head	w: 0
      proper	w: x1 + 2
      ok	w: x1 + 2
      0 	w: 1
      #sel	w: 0
      from	w: x1 + 1
      sel	w: x2 + 1
      #s 	w: 0
      nil	w: 1
      #2nd	w: 0
      mark	w: 1
      #proper	w: 0
      #from	w: 0
      active	w: x1 + 1
      head	w: x1 + 1
      cons	w: x2 + 1
      #active	w: 0
    USABLE RULES: { 1..41 }
    Removed DPs: #50
Number of SCCs: 5, DPs: 26
  SCC { #62 }
POLO(Sum)... succeeded.
      #cons	w: x1
      s 	w: x1 + 1
      #take	w: 0
      take	w: x2 + 1
      top	w: 0
      2nd	w: 1
      #top	w: 0
      #head	w: 0
      proper	w: x1 + 1
      ok	w: x1 + 1
      0 	w: 1
      #sel	w: 0
      from	w: x1 + 1
      sel	w: x2 + 1
      #s 	w: 0
      nil	w: 3
      #2nd	w: 0
      mark	w: x1 + 1
      #proper	w: 0
      #from	w: 0
      active	w: x1 + 3
      head	w: x1 + 1
      cons	w: x1 + x2 + 1
      #active	w: 0
    USABLE RULES: { 4 17..20 32 33 35..38 }
    Removed DPs: #62
Number of SCCs: 4, DPs: 25
  SCC { #11 #19 #39 }
POLO(Sum)... succeeded.
      #cons	w: 0
      s 	w: x1 + 1
      #take	w: x2
      take	w: x2 + 1
      top	w: 0
      2nd	w: 1
      #top	w: 0
      #head	w: 0
      proper	w: x1 + 1
      ok	w: x1 + 1
      0 	w: 1
      #sel	w: 0
      from	w: x1 + 1
      sel	w: x2 + 1
      #s 	w: 0
      nil	w: 3
      #2nd	w: 0
      mark	w: x1 + 1
      #proper	w: 0
      #from	w: 0
      active	w: x1 + 3
      head	w: x1 + 1
      cons	w: x1 + x2 + 1
      #active	w: 0
    USABLE RULES: { 4 17..20 32 33 35..38 }
    Removed DPs: #11 #19
Number of SCCs: 4, DPs: 23
  SCC { #39 }
POLO(Sum)... succeeded.
      #cons	w: 0
      s 	w: x1 + 1
      #take	w: x1
      take	w: x2 + 1
      top	w: 0
      2nd	w: 1
      #top	w: 0
      #head	w: 0
      proper	w: x1 + 1
      ok	w: x1 + 1
      0 	w: 1
      #sel	w: 0
      from	w: x1 + 1
      sel	w: x2 + 1
      #s 	w: 0
      nil	w: 3
      #2nd	w: 0
      mark	w: x1 + 1
      #proper	w: 0
      #from	w: 0
      active	w: x1 + 3
      head	w: x1 + 1
      cons	w: x1 + x2 + 1
      #active	w: 0
    USABLE RULES: { 4 17..20 32 33 35..38 }
    Removed DPs: #39
Number of SCCs: 3, DPs: 22
  SCC { #8 #18 #29 }
POLO(Sum)... succeeded.
      #cons	w: 0
      s 	w: x1 + 1
      #take	w: 0
      take	w: x2 + 1
      top	w: 0
      2nd	w: 1
      #top	w: 0
      #head	w: 0
      proper	w: x1 + 1
      ok	w: x1 + 1
      0 	w: 1
      #sel	w: x1
      from	w: x1 + 1
      sel	w: x2 + 1
      #s 	w: 0
      nil	w: 3
      #2nd	w: 0
      mark	w: x1 + 1
      #proper	w: 0
      #from	w: 0
      active	w: x1 + 3
      head	w: x1 + 1
      cons	w: x1 + x2 + 1
      #active	w: 0
    USABLE RULES: { 4 17..20 32 33 35..38 }
    Removed DPs: #8 #18
Number of SCCs: 3, DPs: 20
  SCC { #29 }
POLO(Sum)... succeeded.
      #cons	w: 0
      s 	w: x1 + 1
      #take	w: 0
      take	w: x2 + 1
      top	w: 0
      2nd	w: 1
      #top	w: 0
      #head	w: 0
      proper	w: x1 + 1
      ok	w: x1 + 1
      0 	w: 1
      #sel	w: x2
      from	w: x1 + 1
      sel	w: x2 + 1
      #s 	w: 0
      nil	w: 3
      #2nd	w: 0
      mark	w: x1 + 1
      #proper	w: 0
      #from	w: 0
      active	w: x1 + 3
      head	w: x1 + 1
      cons	w: x1 + x2 + 1
      #active	w: 0
    USABLE RULES: { 4 17..20 32 33 35..38 }
    Removed DPs: #29
Number of SCCs: 2, DPs: 19
  SCC { #13 #15 #17 #21 #26 #34 #53 #59 #61 }
POLO(Sum)... succeeded.
      #cons	w: 0
      s 	w: x1 + 1
      #take	w: 0
      take	w: x1 + x2 + 1
      top	w: 0
      2nd	w: x1 + 1
      #top	w: 0
      #head	w: 0
      proper	w: x1 + 1
      ok	w: x1 + 1
      0 	w: 1
      #sel	w: 0
      from	w: x1 + 1
      sel	w: x1 + x2 + 1
      #s 	w: 0
      nil	w: 3
      #2nd	w: 0
      mark	w: x1
      #proper	w: 0
      #from	w: 0
      active	w: 3
      head	w: x1 + 1
      cons	w: x1 + x2 + 1
      #active	w: x1
    USABLE RULES: { 4 17..20 32 33 35..38 }
    Removed DPs: #13 #15 #17 #21 #26 #34 #53 #59 #61
Number of SCCs: 1, DPs: 10
  SCC { #4 #23 #24 #28 #38 #41 #42 #44 #45 #49 }
POLO(Sum)... succeeded.
      #cons	w: 0
      s 	w: x1 + 1
      #take	w: 0
      take	w: x1 + x2 + 1
      top	w: 0
      2nd	w: x1 + 1
      #top	w: 0
      #head	w: 0
      proper	w: x1 + 1
      ok	w: x1 + 1
      0 	w: 1
      #sel	w: 0
      from	w: x1 + 1
      sel	w: x1 + x2 + 1
      #s 	w: 0
      nil	w: 3
      #2nd	w: 0
      mark	w: x1
      #proper	w: x1
      #from	w: 0
      active	w: 3
      head	w: x1 + 1
      cons	w: x1 + x2 + 1
      #active	w: 0
    USABLE RULES: { 4 17..20 32 33 35..38 }
    Removed DPs: #4 #23 #24 #28 #38 #41 #42 #44 #45 #49
Number of SCCs: 0, DPs: 0