/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: a__and(tt(),T) -> mark(T)
    2: a__isNatIList(IL) -> a__isNatList(IL)
    3: a__isNat(0()) -> tt()
    4: a__isNat(s(N)) -> a__isNat(N)
    5: a__isNat(length(L)) -> a__isNatList(L)
    6: a__isNatIList(zeros()) -> tt()
    7: a__isNatIList(cons(N,IL)) -> a__and(a__isNat(N),a__isNatIList(IL))
    8: a__isNatList(nil()) -> tt()
    9: a__isNatList(cons(N,L)) -> a__and(a__isNat(N),a__isNatList(L))
    10: a__isNatList(take(N,IL)) -> a__and(a__isNat(N),a__isNatIList(IL))
    11: a__zeros() -> cons(0(),zeros())
    12: a__take(0(),IL) -> a__uTake1(a__isNatIList(IL))
    13: a__uTake1(tt()) -> nil()
    14: a__take(s(M),cons(N,IL)) -> a__uTake2(a__and(a__isNat(M),a__and(a__isNat(N),a__isNatIList(IL))),M,N,IL)
    15: a__uTake2(tt(),M,N,IL) -> cons(mark(N),take(M,IL))
    16: a__length(cons(N,L)) -> a__uLength(a__and(a__isNat(N),a__isNatList(L)),L)
    17: a__uLength(tt(),L) -> s(a__length(mark(L)))
    18: mark(and(X1,X2)) -> a__and(mark(X1),mark(X2))
    19: mark(isNatIList(X)) -> a__isNatIList(X)
    20: mark(isNatList(X)) -> a__isNatList(X)
    21: mark(isNat(X)) -> a__isNat(X)
    22: mark(length(X)) -> a__length(mark(X))
    23: mark(zeros()) -> a__zeros()
    24: mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
    25: mark(uTake1(X)) -> a__uTake1(mark(X))
    26: mark(uTake2(X1,X2,X3,X4)) -> a__uTake2(mark(X1),X2,X3,X4)
    27: mark(uLength(X1,X2)) -> a__uLength(mark(X1),X2)
    28: mark(tt()) -> tt()
    29: mark(0()) -> 0()
    30: mark(s(X)) -> s(mark(X))
    31: mark(cons(X1,X2)) -> cons(mark(X1),X2)
    32: mark(nil()) -> nil()
    33: a__and(X1,X2) -> and(X1,X2)
    34: a__isNatIList(X) -> isNatIList(X)
    35: a__isNatList(X) -> isNatList(X)
    36: a__isNat(X) -> isNat(X)
    37: a__length(X) -> length(X)
    38: a__zeros() -> zeros()
    39: a__take(X1,X2) -> take(X1,X2)
    40: a__uTake1(X) -> uTake1(X)
    41: a__uTake2(X1,X2,X3,X4) -> uTake2(X1,X2,X3,X4)
    42: a__uLength(X1,X2) -> uLength(X1,X2)
Number of strict rules: 42
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
   #1: #a__isNatIList(IL) -> #a__isNatList(IL)
   #2: #a__isNatList(cons(N,L)) -> #a__and(a__isNat(N),a__isNatList(L))
   #3: #a__isNatList(cons(N,L)) -> #a__isNat(N)
   #4: #a__isNatList(cons(N,L)) -> #a__isNatList(L)
   #5: #mark(take(X1,X2)) -> #a__take(mark(X1),mark(X2))
   #6: #mark(take(X1,X2)) -> #mark(X1)
   #7: #mark(take(X1,X2)) -> #mark(X2)
   #8: #mark(zeros()) -> #a__zeros()
   #9: #a__take(0(),IL) -> #a__uTake1(a__isNatIList(IL))
   #10: #a__take(0(),IL) -> #a__isNatIList(IL)
   #11: #mark(cons(X1,X2)) -> #mark(X1)
   #12: #a__take(s(M),cons(N,IL)) -> #a__uTake2(a__and(a__isNat(M),a__and(a__isNat(N),a__isNatIList(IL))),M,N,IL)
   #13: #a__take(s(M),cons(N,IL)) -> #a__and(a__isNat(M),a__and(a__isNat(N),a__isNatIList(IL)))
   #14: #a__take(s(M),cons(N,IL)) -> #a__isNat(M)
   #15: #a__take(s(M),cons(N,IL)) -> #a__and(a__isNat(N),a__isNatIList(IL))
   #16: #a__take(s(M),cons(N,IL)) -> #a__isNat(N)
   #17: #a__take(s(M),cons(N,IL)) -> #a__isNatIList(IL)
   #18: #mark(s(X)) -> #mark(X)
   #19: #mark(uTake1(X)) -> #a__uTake1(mark(X))
   #20: #mark(uTake1(X)) -> #mark(X)
   #21: #mark(isNatList(X)) -> #a__isNatList(X)
   #22: #a__isNatIList(cons(N,IL)) -> #a__and(a__isNat(N),a__isNatIList(IL))
   #23: #a__isNatIList(cons(N,IL)) -> #a__isNat(N)
   #24: #a__isNatIList(cons(N,IL)) -> #a__isNatIList(IL)
   #25: #a__isNatList(take(N,IL)) -> #a__and(a__isNat(N),a__isNatIList(IL))
   #26: #a__isNatList(take(N,IL)) -> #a__isNat(N)
   #27: #a__isNatList(take(N,IL)) -> #a__isNatIList(IL)
   #28: #a__isNat(length(L)) -> #a__isNatList(L)
   #29: #mark(length(X)) -> #a__length(mark(X))
   #30: #mark(length(X)) -> #mark(X)
   #31: #mark(uLength(X1,X2)) -> #a__uLength(mark(X1),X2)
   #32: #mark(uLength(X1,X2)) -> #mark(X1)
   #33: #a__uLength(tt(),L) -> #a__length(mark(L))
   #34: #a__uLength(tt(),L) -> #mark(L)
   #35: #mark(isNatIList(X)) -> #a__isNatIList(X)
   #36: #mark(uTake2(X1,X2,X3,X4)) -> #a__uTake2(mark(X1),X2,X3,X4)
   #37: #mark(uTake2(X1,X2,X3,X4)) -> #mark(X1)
   #38: #mark(isNat(X)) -> #a__isNat(X)
   #39: #a__length(cons(N,L)) -> #a__uLength(a__and(a__isNat(N),a__isNatList(L)),L)
   #40: #a__length(cons(N,L)) -> #a__and(a__isNat(N),a__isNatList(L))
   #41: #a__length(cons(N,L)) -> #a__isNat(N)
   #42: #a__length(cons(N,L)) -> #a__isNatList(L)
   #43: #a__and(tt(),T) -> #mark(T)
   #44: #a__uTake2(tt(),M,N,IL) -> #mark(N)
   #45: #a__isNat(s(N)) -> #a__isNat(N)
   #46: #mark(and(X1,X2)) -> #a__and(mark(X1),mark(X2))
   #47: #mark(and(X1,X2)) -> #mark(X1)
   #48: #mark(and(X1,X2)) -> #mark(X2)
Number of SCCs: 1, DPs: 45
  SCC { #1..7 #10..18 #20..48 }
POLO(Sum)... succeeded.
      #a__uLength	w: x2 + 1
      #a__uTake2	w: x3 + x4 + 2
      isNatList	w: 0
      s 	w: x1
      a__isNatIList	w: 0
      #a__isNat	w: 0
      take	w: x1 + x2 + 4
      and	w: x1 + x2
      isNatIList	w: 0
      zeros	w: 1
      #a__take	w: x2 + 3
      uTake2	w: x1 + x2 + x3 + x4 + 4
      a__isNatList	w: 0
      #a__isNatIList	w: 0
      uLength	w: x1 + x2 + 2
      #mark	w: x1
      #a__uTake1	w: 0
      0 	w: 0
      a__uTake2	w: x1 + x2 + x3 + x4 + 4
      #a__and	w: x2
      #a__zeros	w: 0
      nil	w: 1
      mark	w: x1
      #a__length	w: x1 + 1
      isNat	w: 0
      a__uLength	w: x1 + x2 + 2
      a__uTake1	w: x1 + 1
      #a__isNatList	w: 0
      cons	w: x1 + x2
      a__take	w: x1 + x2 + 4
      tt	w: 0
      uTake1	w: x1 + 1
      a__isNat	w: 0
      a__and	w: x1 + x2
      length	w: x1 + 2
      a__zeros	w: 1
      a__length	w: x1 + 2
    USABLE RULES: { 1..42 }
    Removed DPs: #5..7 #10 #12..17 #20 #29..32 #34 #36 #37 #40..42 #44
Number of SCCs: 2, DPs: 23
  SCC { #33 #39 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... succeeded.
      #a__uLength	w: [1,0;0,0] * x1 + [1,0;0,0] * x2 + [0;1]
      #a__uTake2	w: [0;0]
      isNatList	w: [0,1;0,0] * x1 + [1;0]
      s 	w: [1,1;0,1] * x1 + [2;0]
      a__isNatIList	w: [0,1;0,0] * x1 + [3;0]
      #a__isNat	w: [0;0]
      take	w: x1 + x2 + [1;2]
      and	w: [0,1;0,0] * x1 + x2
      isNatIList	w: [0,1;0,0] * x1 + [3;0]
      zeros	w: [1;0]
      #a__take	w: [0;0]
      uTake2	w: [1,1;0,1] * x2 + [0,1;1,1] * x3 + [1,1;0,1] * x4 + [3;2]
      a__isNatList	w: [0,1;0,0] * x1 + [1;0]
      #a__isNatIList	w: [0;0]
      uLength	w: [1,0;0,0] * x1 + [1,1;0,0] * x2 + [1;0]
      #mark	w: [0;0]
      #a__uTake1	w: [0;0]
      0 	w: [0;0]
      a__uTake2	w: [1,1;0,1] * x2 + [0,1;1,1] * x3 + [1,1;0,1] * x4 + [3;2]
      #a__and	w: [0;0]
      #a__zeros	w: [0;0]
      nil	w: [1;2]
      mark	w: x1
      #a__length	w: [1,0;0,0] * x1 + [2;1]
      isNat	w: x1 + [3;0]
      a__uLength	w: [1,0;0,0] * x1 + [1,1;0,0] * x2 + [1;0]
      a__uTake1	w: [1;2]
      #a__isNatList	w: [0;0]
      cons	w: [0,1;1,1] * x1 + [1,1;0,1] * x2
      a__take	w: x1 + x2 + [1;2]
      tt	w: [3;0]
      uTake1	w: [1;2]
      a__isNat	w: x1 + [3;0]
      a__and	w: [0,1;0,0] * x1 + x2
      length	w: [1,1;0,0] * x1 + [2;0]
      a__zeros	w: [1;0]
      a__length	w: [1,1;0,0] * x1 + [2;0]
    USABLE RULES: { 1..42 }
    Removed DPs: #33 #39
Number of SCCs: 1, DPs: 21
  SCC { #1..4 #11 #18 #21..28 #35 #38 #43 #45..48 }
POLO(Sum)... succeeded.
      #a__uLength	w: 4
      #a__uTake2	w: 2
      isNatList	w: x1 + 1
      s 	w: x1
      a__isNatIList	w: x1 + 2
      #a__isNat	w: x1 + 2
      take	w: x1 + x2 + 2
      and	w: x1 + x2
      isNatIList	w: x1 + 2
      zeros	w: 1
      #a__take	w: 3
      uTake2	w: x2 + x3 + x4 + 2
      a__isNatList	w: x1 + 1
      #a__isNatIList	w: x1 + 5
      uLength	w: x2 + 3
      #mark	w: x1 + 3
      #a__uTake1	w: 0
      0 	w: 0
      a__uTake2	w: x2 + x3 + x4 + 2
      #a__and	w: x2 + 3
      #a__zeros	w: 0
      nil	w: 1
      mark	w: x1
      #a__length	w: 4
      isNat	w: x1
      a__uLength	w: x2 + 3
      a__uTake1	w: 1
      #a__isNatList	w: x1 + 4
      cons	w: x1 + x2
      a__take	w: x1 + x2 + 2
      tt	w: 0
      uTake1	w: 1
      a__isNat	w: x1
      a__and	w: x1 + x2
      length	w: x1 + 3
      a__zeros	w: 1
      a__length	w: x1 + 3
    USABLE RULES: { 1..42 }
    Removed DPs: #1 #3 #23 #25..28 #38
Number of SCCs: 2, DPs: 13
  SCC { #45 }
POLO(Sum)... succeeded.
      #a__uLength	w: 4
      #a__uTake2	w: 2
      isNatList	w: 2
      s 	w: x1 + 1
      a__isNatIList	w: x1 + 1
      #a__isNat	w: x1 + 2
      take	w: 3
      and	w: x2
      isNatIList	w: 1
      zeros	w: 1
      #a__take	w: 3
      uTake2	w: x4 + 1
      a__isNatList	w: 2
      #a__isNatIList	w: 5
      uLength	w: 3
      #mark	w: 3
      #a__uTake1	w: 0
      0 	w: 1
      a__uTake2	w: x1 + x3 + 1
      #a__and	w: 3
      #a__zeros	w: 0
      nil	w: 1
      mark	w: x1 + 1
      #a__length	w: 4
      isNat	w: x1
      a__uLength	w: 3
      a__uTake1	w: x1 + 1
      #a__isNatList	w: 4
      cons	w: 2
      a__take	w: 4
      tt	w: 2
      uTake1	w: 1
      a__isNat	w: x1 + 1
      a__and	w: x1 + x2
      length	w: x1 + 1
      a__zeros	w: 2
      a__length	w: x1 + 1
    USABLE RULES: { 3 6 8 11 13 15 23 28 29 31..40 42 }
    Removed DPs: #45
Number of SCCs: 1, DPs: 12
  SCC { #2 #4 #11 #18 #21 #22 #24 #35 #43 #46..48 }
POLO(Sum)... succeeded.
      #a__uLength	w: 4
      #a__uTake2	w: 2
      isNatList	w: 0
      s 	w: x1
      a__isNatIList	w: 0
      #a__isNat	w: 2
      take	w: x2 + 1
      and	w: x1 + x2
      isNatIList	w: 0
      zeros	w: 2
      #a__take	w: 3
      uTake2	w: x1 + x3 + 1
      a__isNatList	w: 0
      #a__isNatIList	w: 0
      uLength	w: 1
      #mark	w: x1
      #a__uTake1	w: 0
      0 	w: 1
      a__uTake2	w: x1 + x3 + 1
      #a__and	w: x2
      #a__zeros	w: 0
      nil	w: 1
      mark	w: x1
      #a__length	w: 4
      isNat	w: 0
      a__uLength	w: 1
      a__uTake1	w: x1 + 1
      #a__isNatList	w: 0
      cons	w: x1 + 1
      a__take	w: x2 + 1
      tt	w: 0
      uTake1	w: x1 + 1
      a__isNat	w: 0
      a__and	w: x1 + x2
      length	w: 1
      a__zeros	w: 2
      a__length	w: 1
    USABLE RULES: { 1..42 }
    Removed DPs: #11
Number of SCCs: 1, DPs: 11
  SCC { #2 #4 #18 #21 #22 #24 #35 #43 #46..48 }
POLO(Sum)... POLO(max)... succeeded.
      #a__uLength	w: 0
      #a__uTake2	w: 0
      isNatList	w: x1 + 1
      s 	w: x1
      a__isNatIList	w: x1 + 10
      #a__isNat	w: 0
      take	w: max(x1 + 8, x2 + 13)
      and	w: max(x1 + 1, x2)
      isNatIList	w: x1 + 10
      zeros	w: 5
      #a__take	w: 0
      uTake2	w: max(x1 + 3, x2 + 8, x3 + 8, x4 + 13)
      a__isNatList	w: x1 + 1
      #a__isNatIList	w: x1 + 13
      uLength	w: max(x2 + 1)
      #mark	w: x1 + 3
      #a__uTake1	w: 0
      0 	w: 1
      a__uTake2	w: max(x1 + 3, x2 + 8, x3 + 8, x4 + 13)
      #a__and	w: max(x1 + 1, x2 + 3)
      #a__zeros	w: 0
      nil	w: 1
      mark	w: x1
      #a__length	w: 2
      isNat	w: x1 + 4
      a__uLength	w: max(x2 + 1)
      a__uTake1	w: 10
      #a__isNatList	w: x1 + 4
      cons	w: max(x1 + 4, x2)
      a__take	w: max(x1 + 8, x2 + 13)
      tt	w: 1
      uTake1	w: 10
      a__isNat	w: x1 + 4
      a__and	w: max(x1 + 1, x2)
      length	w: x1 + 1
      a__zeros	w: 5
      a__length	w: x1 + 1
    USABLE RULES: { 1..42 }
    Removed DPs: #47
Number of SCCs: 1, DPs: 10
  SCC { #2 #4 #18 #21 #22 #24 #35 #43 #46 #48 }
POLO(Sum)... succeeded.
      #a__uLength	w: 4
      #a__uTake2	w: 2
      isNatList	w: x1 + 1
      s 	w: x1
      a__isNatIList	w: x1 + 1
      #a__isNat	w: 2
      take	w: x2 + 2
      and	w: x2 + 2
      isNatIList	w: x1 + 1
      zeros	w: 1
      #a__take	w: 3
      uTake2	w: x4 + 2
      a__isNatList	w: x1 + 1
      #a__isNatIList	w: x1
      uLength	w: x2 + 3
      #mark	w: x1
      #a__uTake1	w: 0
      0 	w: 1
      a__uTake2	w: x4 + 4
      #a__and	w: x2
      #a__zeros	w: 0
      nil	w: 1
      mark	w: x1 + 2
      #a__length	w: 4
      isNat	w: x1 + 1
      a__uLength	w: x2 + 3
      a__uTake1	w: x1 + 1
      #a__isNatList	w: x1
      cons	w: x2 + 2
      a__take	w: x2 + 2
      tt	w: 1
      uTake1	w: x1 + 1
      a__isNat	w: x1 + 1
      a__and	w: x2 + 2
      length	w: x1 + 1
      a__zeros	w: 3
      a__length	w: x1 + 1
    USABLE RULES: { 1..42 }
    Removed DPs: #2 #4 #21 #22 #24 #35 #48
Number of SCCs: 1, DPs: 3
  SCC { #18 #43 #46 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded.
      #a__uLength	s: []	p: 2	w: max(x1 + 1)
      #a__uTake2	s: [4,3,1]	p: 0	w: x1 + x3 + x4 + 1
      isNatList	s: [1]	p: 6	w: x1 + 2
      s 	s: 1
      a__isNatIList	s: [1]	p: 7	w: x1 + 7
      #a__isNat	s: []	p: 0	w: 0
      take	s: [1]	p: 0	w: max(x1 + 10, x2 + 14)
      and	s: [2,1]	p: 3	w: max(x1 + 2, x2)
      isNatIList	s: [1]	p: 7	w: x1 + 7
      zeros	s: []	p: 2	w: 12
      #a__take	s: [1,2]	p: 0	w: x1 + x2
      uTake2	s: [3,1,2]	p: 0	w: max(x1 + 4, x2 + 10, x3 + 5, x4 + 14)
      a__isNatList	s: [1]	p: 6	w: x1 + 2
      #a__isNatIList	s: []	p: 0	w: 0
      uLength	s: []	p: 9	w: max(x2 + 6)
      #mark	s: [1]	p: 1	w: x1
      #a__uTake1	s: []	p: 0	w: 1
      0 	s: []	p: 1	w: 8
      a__uTake2	s: [3]	p: 1	w: max(x1 + 4, x2 + 10, x3 + 5, x4 + 14)
      #a__and	s: [1,2]	p: 2	w: max(x1 + 2, x2)
      #a__zeros	s: []	p: 0	w: 0
      nil	s: []	p: 2	w: 13
      mark	s: [1]	p: 3	w: x1
      #a__length	s: []	p: 1	w: 1
      isNat	s: []	p: 5	w: x1 + 3
      a__uLength	s: []	p: 9	w: max(x2 + 6)
      a__uTake1	s: []	p: 2	w: 13
      #a__isNatList	s: []	p: 0	w: 0
      cons	s: [1,2]	p: 0	w: max(x1 + 4, x2)
      a__take	s: []	p: 2	w: max(x1 + 10, x2 + 14)
      tt	s: []	p: 8	w: 9
      uTake1	s: []	p: 2	w: 13
      a__isNat	s: []	p: 5	w: x1 + 3
      a__and	s: [2,1]	p: 3	w: max(x1 + 2, x2)
      length	s: []	p: 9	w: x1 + 6
      a__zeros	s: []	p: 3	w: 12
      a__length	s: []	p: 9	w: x1 + 6
    USABLE RULES: { 1..42 }
    Removed DPs: #43 #46
Number of SCCs: 1, DPs: 1
  SCC { #18 }
POLO(Sum)... succeeded.
      #a__uLength	w: 4
      #a__uTake2	w: 2
      isNatList	w: 3
      s 	w: x1 + 2
      a__isNatIList	w: 1
      #a__isNat	w: 2
      take	w: 4
      and	w: 4
      isNatIList	w: 1
      zeros	w: 4
      #a__take	w: 3
      uTake2	w: x2 + 5
      a__isNatList	w: 2
      #a__isNatIList	w: 0
      uLength	w: x1 + 2
      #mark	w: x1
      #a__uTake1	w: 0
      0 	w: 3
      a__uTake2	w: x1 + x3 + x4 + 4
      #a__and	w: 0
      #a__zeros	w: 0
      nil	w: 5
      mark	w: 2
      #a__length	w: 4
      isNat	w: 3
      a__uLength	w: x1 + 1
      a__uTake1	w: 4
      #a__isNatList	w: 0
      cons	w: 4
      a__take	w: 3
      tt	w: 3
      uTake1	w: 5
      a__isNat	w: 2
      a__and	w: 3
      length	w: 3
      a__zeros	w: 3
      a__length	w: 3
    USABLE RULES: { }
    Removed DPs: #18
Number of SCCs: 0, DPs: 0