Input TRS:
    1: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z)))
    2: a____(X,nil()) -> mark(X)
    3: a____(nil(),X) -> mark(X)
    4: a__U11(tt()) -> tt()
    5: a__U21(tt(),V2) -> a__U22(a__isList(V2))
    6: a__U22(tt()) -> tt()
    7: a__U31(tt()) -> tt()
    8: a__U41(tt(),V2) -> a__U42(a__isNeList(V2))
    9: a__U42(tt()) -> tt()
    10: a__U51(tt(),V2) -> a__U52(a__isList(V2))
    11: a__U52(tt()) -> tt()
    12: a__U61(tt()) -> tt()
    13: a__U71(tt(),P) -> a__U72(a__isPal(P))
    14: a__U72(tt()) -> tt()
    15: a__U81(tt()) -> tt()
    16: a__isList(V) -> a__U11(a__isNeList(V))
    17: a__isList(nil()) -> tt()
    18: a__isList(__(V1,V2)) -> a__U21(a__isList(V1),V2)
    19: a__isNeList(V) -> a__U31(a__isQid(V))
    20: a__isNeList(__(V1,V2)) -> a__U41(a__isList(V1),V2)
    21: a__isNeList(__(V1,V2)) -> a__U51(a__isNeList(V1),V2)
    22: a__isNePal(V) -> a__U61(a__isQid(V))
    23: a__isNePal(__(I,__(P,I))) -> a__U71(a__isQid(I),P)
    24: a__isPal(V) -> a__U81(a__isNePal(V))
    25: a__isPal(nil()) -> tt()
    26: a__isQid(a()) -> tt()
    27: a__isQid(e()) -> tt()
    28: a__isQid(i()) -> tt()
    29: a__isQid(o()) -> tt()
    30: a__isQid(u()) -> tt()
    31: mark(__(X1,X2)) -> a____(mark(X1),mark(X2))
    32: mark(U11(X)) -> a__U11(mark(X))
    33: mark(U21(X1,X2)) -> a__U21(mark(X1),X2)
    34: mark(U22(X)) -> a__U22(mark(X))
    35: mark(isList(X)) -> a__isList(X)
    36: mark(U31(X)) -> a__U31(mark(X))
    37: mark(U41(X1,X2)) -> a__U41(mark(X1),X2)
    38: mark(U42(X)) -> a__U42(mark(X))
    39: mark(isNeList(X)) -> a__isNeList(X)
    40: mark(U51(X1,X2)) -> a__U51(mark(X1),X2)
    41: mark(U52(X)) -> a__U52(mark(X))
    42: mark(U61(X)) -> a__U61(mark(X))
    43: mark(U71(X1,X2)) -> a__U71(mark(X1),X2)
    44: mark(U72(X)) -> a__U72(mark(X))
    45: mark(isPal(X)) -> a__isPal(X)
    46: mark(U81(X)) -> a__U81(mark(X))
    47: mark(isQid(X)) -> a__isQid(X)
    48: mark(isNePal(X)) -> a__isNePal(X)
    49: mark(nil()) -> nil()
    50: mark(tt()) -> tt()
    51: mark(a()) -> a()
    52: mark(e()) -> e()
    53: mark(i()) -> i()
    54: mark(o()) -> o()
    55: mark(u()) -> u()
    56: a____(X1,X2) -> __(X1,X2)
    57: a__U11(X) -> U11(X)
    58: a__U21(X1,X2) -> U21(X1,X2)
    59: a__U22(X) -> U22(X)
    60: a__isList(X) -> isList(X)
    61: a__U31(X) -> U31(X)
    62: a__U41(X1,X2) -> U41(X1,X2)
    63: a__U42(X) -> U42(X)
    64: a__isNeList(X) -> isNeList(X)
    65: a__U51(X1,X2) -> U51(X1,X2)
    66: a__U52(X) -> U52(X)
    67: a__U61(X) -> U61(X)
    68: a__U71(X1,X2) -> U71(X1,X2)
    69: a__U72(X) -> U72(X)
    70: a__isPal(X) -> isPal(X)
    71: a__U81(X) -> U81(X)
    72: a__isQid(X) -> isQid(X)
    73: a__isNePal(X) -> isNePal(X)
Number of strict rules: 73
Direct Order(PosReal,>,Poly) ... removes: 22 25 12
     a()	weight: 0
   U21(x1,x2)	weight: x1 + x2
   U11(x1)	weight: x1
isNeList(x1)	weight: x1
 isPal(x1)	weight: (/ 1 4) + x1
   U42(x1)	weight: x1
     u()	weight: 0
   U71(x1,x2)	weight: (/ 1 4) + x1 + 2 * x2
a__U22(x1)	weight: x1
isNePal(x1)	weight: (/ 1 4) + x1
   U72(x1)	weight: x1
a__U31(x1)	weight: x1
a__U51(x1,x2)	weight: x1 + x2
a__U81(x1)	weight: x1
 isQid(x1)	weight: x1
 a____(x1,x2)	weight: 2 * x1 + x2
a__U41(x1,x2)	weight: x1 + x2
a__isList(x1)	weight: x1
a__isNeList(x1)	weight: x1
     o()	weight: 0
isList(x1)	weight: x1
a__U21(x1,x2)	weight: x1 + x2
   nil()	weight: 0
  mark(x1)	weight: x1
a__U72(x1)	weight: x1
a__isNePal(x1)	weight: (/ 1 4) + x1
a__U11(x1)	weight: x1
a__U42(x1)	weight: x1
a__U52(x1)	weight: x1
     i()	weight: 0
   U52(x1)	weight: x1
   U61(x1)	weight: (/ 1 8) + x1
     e()	weight: 0
   U31(x1)	weight: x1
a__U71(x1,x2)	weight: (/ 1 4) + x1 + 2 * x2
a__isPal(x1)	weight: (/ 1 4) + x1
a__U61(x1)	weight: (/ 1 8) + x1
   U81(x1)	weight: x1
    tt()	weight: 0
a__isQid(x1)	weight: x1
   U22(x1)	weight: x1
   U51(x1,x2)	weight: x1 + x2
   U41(x1,x2)	weight: x1 + x2
    __(x1,x2)	weight: 2 * x1 + x2
Number of strict rules: 70
Direct Order(PosReal,>,Poly) ... removes: 18 4 15 8 3 16 26 19 17 27 28 5 10 7 20 30 14 23 24 11 9 13 6 29 2
     a()	weight: 0
   U21(x1,x2)	weight: (/ 314083 4) + x1 + 2 * x2
   U11(x1)	weight: (/ 119293 4) + x1
isNeList(x1)	weight: (/ 128095 4) + 2 * x1
 isPal(x1)	weight: 31562 + 2 * x1
   U42(x1)	weight: (/ 957 4) + x1
     u()	weight: 0
   U71(x1,x2)	weight: (/ 63125 2) + 2 * x1 + 2 * x2
a__U22(x1)	weight: (/ 66693 4) + x1
isNePal(x1)	weight: (/ 63123 2) + 2 * x1
   U72(x1)	weight: (/ 1 4) + x1
a__U31(x1)	weight: (/ 128093 4) + x1
a__U51(x1,x2)	weight: 78521 + x1 + 2 * x2
a__U81(x1)	weight: (/ 1 4) + x1
 isQid(x1)	weight: (/ 1 4) + x1
 a____(x1,x2)	weight: (/ 78521 2) + x1 + x2
a__U41(x1,x2)	weight: (/ 129053 4) + x1 + 2 * x2
a__isList(x1)	weight: (/ 247389 4) + 2 * x1
a__isNeList(x1)	weight: (/ 128095 4) + 2 * x1
     o()	weight: 0
isList(x1)	weight: (/ 247389 4) + 2 * x1
a__U21(x1,x2)	weight: (/ 314083 4) + x1 + 2 * x2
   nil()	weight: 0
  mark(x1)	weight: x1
a__U72(x1)	weight: (/ 1 4) + x1
a__isNePal(x1)	weight: (/ 63123 2) + 2 * x1
a__U11(x1)	weight: (/ 119293 4) + x1
a__U42(x1)	weight: (/ 957 4) + x1
a__U52(x1)	weight: (/ 1 4) + x1
     i()	weight: 0
   U52(x1)	weight: (/ 1 4) + x1
   U61(x1)	weight: (/ 126245 4) + x1
     e()	weight: 0
   U31(x1)	weight: (/ 128093 4) + x1
a__U71(x1,x2)	weight: (/ 63125 2) + 2 * x1 + 2 * x2
a__isPal(x1)	weight: 31562 + 2 * x1
a__U61(x1)	weight: (/ 126245 4) + x1
   U81(x1)	weight: (/ 1 4) + x1
    tt()	weight: 0
a__isQid(x1)	weight: (/ 1 4) + x1
   U22(x1)	weight: (/ 66693 4) + x1
   U51(x1,x2)	weight: 78521 + x1 + 2 * x2
   U41(x1,x2)	weight: (/ 129053 4) + x1 + 2 * x2
    __(x1,x2)	weight: (/ 78521 2) + x1 + x2
Number of strict rules: 45
Direct Order(PosReal,>,Poly) ... removes: 21
     a()	weight: 0
   U21(x1,x2)	weight: (/ 314083 4) + x1 + 2 * x2
   U11(x1)	weight: (/ 119293 4) + x1
isNeList(x1)	weight: (/ 128095 4) + 2 * x1
 isPal(x1)	weight: 31562 + 2 * x1
   U42(x1)	weight: (/ 957 4) + x1
     u()	weight: 0
   U71(x1,x2)	weight: (/ 63125 2) + 2 * x1 + 2 * x2
a__U22(x1)	weight: (/ 66693 4) + x1
isNePal(x1)	weight: (/ 63123 2) + 2 * x1
   U72(x1)	weight: (/ 1 4) + x1
a__U31(x1)	weight: (/ 128093 4) + x1
a__U51(x1,x2)	weight: (/ 314083 4) + x1 + 2 * x2
a__U81(x1)	weight: (/ 1 4) + x1
 isQid(x1)	weight: (/ 1 4) + x1
 a____(x1,x2)	weight: (/ 78521 2) + x1 + x2
a__U41(x1,x2)	weight: (/ 129053 4) + x1 + 2 * x2
a__isList(x1)	weight: (/ 247389 4) + 2 * x1
a__isNeList(x1)	weight: (/ 128095 4) + 2 * x1
     o()	weight: 0
isList(x1)	weight: (/ 247389 4) + 2 * x1
a__U21(x1,x2)	weight: (/ 314083 4) + x1 + 2 * x2
   nil()	weight: 0
  mark(x1)	weight: x1
a__U72(x1)	weight: (/ 1 4) + x1
a__isNePal(x1)	weight: (/ 63123 2) + 2 * x1
a__U11(x1)	weight: (/ 119293 4) + x1
a__U42(x1)	weight: (/ 957 4) + x1
a__U52(x1)	weight: (/ 1 4) + x1
     i()	weight: 0
   U52(x1)	weight: (/ 1 4) + x1
   U61(x1)	weight: (/ 126245 4) + x1
     e()	weight: 0
   U31(x1)	weight: (/ 128093 4) + x1
a__U71(x1,x2)	weight: (/ 63125 2) + 2 * x1 + 2 * x2
a__isPal(x1)	weight: 31562 + 2 * x1
a__U61(x1)	weight: (/ 126245 4) + x1
   U81(x1)	weight: (/ 1 4) + x1
    tt()	weight: 0
a__isQid(x1)	weight: (/ 1 4) + x1
   U22(x1)	weight: (/ 66693 4) + x1
   U51(x1,x2)	weight: (/ 314083 4) + x1 + 2 * x2
   U41(x1,x2)	weight: (/ 129053 4) + x1 + 2 * x2
    __(x1,x2)	weight: (/ 78521 2) + x1 + x2
Number of strict rules: 44
Direct Order(PosReal,>,Poly) ... removes: 1
     a()	weight: 0
   U21(x1,x2)	weight: 120518 + x1 + 2 * x2
   U11(x1)	weight: (/ 236445 4) + x1
isNeList(x1)	weight: (/ 122813 2) + 2 * x1
 isPal(x1)	weight: 14894 + 2 * x1
   U42(x1)	weight: (/ 1 4) + x1
     u()	weight: 0
   U71(x1,x2)	weight: (/ 1023717 4) + x1 + 2 * x2
a__U22(x1)	weight: (/ 1 4) + x1
isNePal(x1)	weight: (/ 29787 2) + 2 * x1
   U72(x1)	weight: (/ 1 4) + x1
a__U31(x1)	weight: (/ 245625 4) + x1
a__U51(x1,x2)	weight: 120518 + x1 + 2 * x2
a__U81(x1)	weight: (/ 1 4) + x1
 isQid(x1)	weight: (/ 1 4) + x1
 a____(x1,x2)	weight: 60259 + 2 * x1 + x2
a__U41(x1,x2)	weight: (/ 245627 4) + x1 + 2 * x2
a__isList(x1)	weight: (/ 482071 4) + 2 * x1
a__isNeList(x1)	weight: (/ 122813 2) + 2 * x1
     o()	weight: 0
isList(x1)	weight: (/ 482071 4) + 2 * x1
a__U21(x1,x2)	weight: 120518 + x1 + 2 * x2
   nil()	weight: 0
  mark(x1)	weight: x1
a__U72(x1)	weight: (/ 1 4) + x1
a__isNePal(x1)	weight: (/ 29787 2) + 2 * x1
a__U11(x1)	weight: (/ 236445 4) + x1
a__U42(x1)	weight: (/ 1 4) + x1
a__U52(x1)	weight: (/ 1 4) + x1
     i()	weight: 0
   U52(x1)	weight: (/ 1 4) + x1
   U61(x1)	weight: (/ 59573 4) + x1
     e()	weight: 0
   U31(x1)	weight: (/ 245625 4) + x1
a__U71(x1,x2)	weight: (/ 1023717 4) + x1 + 2 * x2
a__isPal(x1)	weight: 14894 + 2 * x1
a__U61(x1)	weight: (/ 59573 4) + x1
   U81(x1)	weight: (/ 1 4) + x1
    tt()	weight: 0
a__isQid(x1)	weight: (/ 1 4) + x1
   U22(x1)	weight: (/ 1 4) + x1
   U51(x1,x2)	weight: 120518 + x1 + 2 * x2
   U41(x1,x2)	weight: (/ 245627 4) + x1 + 2 * x2
    __(x1,x2)	weight: 60259 + 2 * x1 + x2
Number of strict rules: 43
Direct Order(PosReal,>,Poly) ... removes: 36 68 63 32 60 34 65 44 72 33 64 39 62 56 31 69 45 70 57 40 67 59 38 61 58 48 71 47 73 37 41 42 46 66 35 43
     a()	weight: 0
   U21(x1,x2)	weight: (/ 1202443 8) + x1 + 2 * x2
   U11(x1)	weight: (/ 116641 4) + x1
isNeList(x1)	weight: (/ 215445 8) + 2 * x1
 isPal(x1)	weight: (/ 368793 8) + 2 * x1
   U42(x1)	weight: (/ 45733 4) + x1
     u()	weight: 0
   U71(x1,x2)	weight: (/ 360143 2) + x1 + 2 * x2
a__U22(x1)	weight: (/ 520435 8) + x1
isNePal(x1)	weight: (/ 368791 16) + 2 * x1
   U72(x1)	weight: (/ 267945 4) + x1
a__U31(x1)	weight: (/ 61171 8) + x1
a__U51(x1,x2)	weight: (/ 300611 2) + x1 + 2 * x2
a__U81(x1)	weight: (/ 3 8) + x1
 isQid(x1)	weight: (/ 38569 4) + x1
 a____(x1,x2)	weight: (/ 1202443 8) + 2 * x1 + x2
a__U41(x1,x2)	weight: (/ 398377 8) + x1 + 2 * x2
a__isList(x1)	weight: (/ 682009 8) + 2 * x1
a__isNeList(x1)	weight: (/ 107723 4) + 2 * x1
     o()	weight: 0
isList(x1)	weight: (/ 341005 8) + 2 * x1
a__U21(x1,x2)	weight: (/ 300611 2) + x1 + 2 * x2
   nil()	weight: 0
  mark(x1)	weight: 2 * x1
a__U72(x1)	weight: (/ 1071779 8) + x1
a__isNePal(x1)	weight: (/ 184395 4) + 2 * x1
a__U11(x1)	weight: (/ 466563 8) + x1
a__U42(x1)	weight: (/ 182931 8) + x1
a__U52(x1)	weight: (/ 3 8) + x1
     i()	weight: 0
   U52(x1)	weight: (/ 1 4) + x1
   U61(x1)	weight: (/ 107257 4) + x1
     e()	weight: 0
   U31(x1)	weight: (/ 15293 4) + x1
a__U71(x1,x2)	weight: (/ 1440573 8) + x1 + 2 * x2
a__isPal(x1)	weight: (/ 184397 4) + 2 * x1
a__U61(x1)	weight: (/ 214515 8) + x1
   U81(x1)	weight: (/ 1 4) + x1
    tt()	weight: 0
a__isQid(x1)	weight: (/ 154275 8) + x1
   U22(x1)	weight: (/ 130109 4) + x1
   U51(x1,x2)	weight: (/ 1202443 8) + x1 + 2 * x2
   U41(x1,x2)	weight: 49797 + x1 + 2 * x2
    __(x1,x2)	weight: (/ 300611 4) + 2 * x1 + x2
Number of strict rules: 7
Direct Order(PosReal,>,Poly) ... removes: 50 54 49 52 51 55 53
     a()	weight: 0
   U21(x1,x2)	weight: (/ 260217 4) + x1 + 2 * x2
   U11(x1)	weight: (/ 116641 4) + x1
isNeList(x1)	weight: (/ 1 8) + 2 * x1
 isPal(x1)	weight: (/ 1 8) + 2 * x1
   U42(x1)	weight: (/ 45733 4) + x1
     u()	weight: 0
   U71(x1,x2)	weight: (/ 1071779 8) + x1 + 2 * x2
a__U22(x1)	weight: (/ 520435 8) + 2 * x1
isNePal(x1)	weight: (/ 368791 16) + 2 * x1
   U72(x1)	weight: (/ 535891 8) + x1
a__U31(x1)	weight: (/ 1 8) + 2 * x1
a__U51(x1,x2)	weight: 65054 + 2 * x1 + 2 * x2
a__U81(x1)	weight: (/ 3 8) + x1
 isQid(x1)	weight: (/ 1 8) + x1
 a____(x1,x2)	weight: (/ 260215 4) + 2 * x1 + x2
a__U41(x1,x2)	weight: (/ 182937 8) + 2 * x1 + 2 * x2
a__isList(x1)	weight: 2 * x1
a__isNeList(x1)	weight: (/ 3 8) + 2 * x1
     o()	weight: 0
isList(x1)	weight: (/ 1 8) + 2 * x1
a__U21(x1,x2)	weight: (/ 520435 8) + x1 + 2 * x2
   nil()	weight: 0
  mark(x1)	weight: (/ 1 8) + 2 * x1
a__U72(x1)	weight: (/ 267945 2) + 2 * x1
a__isNePal(x1)	weight: (/ 214517 8) + 2 * x1
a__U11(x1)	weight: (/ 466563 8) + x1
a__U42(x1)	weight: (/ 182931 8) + 2 * x1
a__U52(x1)	weight: (/ 3 8) + x1
     i()	weight: 0
   U52(x1)	weight: (/ 1 4) + x1
   U61(x1)	weight: (/ 107257 4) + x1
     e()	weight: 0
   U31(x1)	weight: (/ 1 8) + 2 * x1
a__U71(x1,x2)	weight: (/ 267945 2) + x1 + 2 * x2
a__isPal(x1)	weight: 2 * x1
a__U61(x1)	weight: (/ 214515 8) + 2 * x1
   U81(x1)	weight: (/ 1 4) + x1
    tt()	weight: 0
a__isQid(x1)	weight: (/ 1 8) + x1
   U22(x1)	weight: (/ 130109 4) + x1
   U51(x1,x2)	weight: (/ 520431 8) + x1 + 2 * x2
   U41(x1,x2)	weight: 22867 + x1 + 2 * x2
    __(x1,x2)	weight: (/ 520435 16) + 2 * x1 + x2
Number of strict rules: 0
YES