/export/starexec/sandbox2/solver/bin/starexec_run_Default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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