Input TRS:
    1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
    2: active(__(X,nil())) -> mark(X)
    3: active(__(nil(),X)) -> mark(X)
    4: active(U11(tt())) -> mark(tt())
    5: active(U21(tt(),V2)) -> mark(U22(isList(V2)))
    6: active(U22(tt())) -> mark(tt())
    7: active(U31(tt())) -> mark(tt())
    8: active(U41(tt(),V2)) -> mark(U42(isNeList(V2)))
    9: active(U42(tt())) -> mark(tt())
    10: active(U51(tt(),V2)) -> mark(U52(isList(V2)))
    11: active(U52(tt())) -> mark(tt())
    12: active(U61(tt())) -> mark(tt())
    13: active(U71(tt(),P)) -> mark(U72(isPal(P)))
    14: active(U72(tt())) -> mark(tt())
    15: active(U81(tt())) -> mark(tt())
    16: active(isList(V)) -> mark(U11(isNeList(V)))
    17: active(isList(nil())) -> mark(tt())
    18: active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2))
    19: active(isNeList(V)) -> mark(U31(isQid(V)))
    20: active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2))
    21: active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2))
    22: active(isNePal(V)) -> mark(U61(isQid(V)))
    23: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P))
    24: active(isPal(V)) -> mark(U81(isNePal(V)))
    25: active(isPal(nil())) -> mark(tt())
    26: active(isQid(a())) -> mark(tt())
    27: active(isQid(e())) -> mark(tt())
    28: active(isQid(i())) -> mark(tt())
    29: active(isQid(o())) -> mark(tt())
    30: active(isQid(u())) -> mark(tt())
    31: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
    32: mark(nil()) -> active(nil())
    33: mark(U11(X)) -> active(U11(mark(X)))
    34: mark(tt()) -> active(tt())
    35: mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
    36: mark(U22(X)) -> active(U22(mark(X)))
    37: mark(isList(X)) -> active(isList(X))
    38: mark(U31(X)) -> active(U31(mark(X)))
    39: mark(U41(X1,X2)) -> active(U41(mark(X1),X2))
    40: mark(U42(X)) -> active(U42(mark(X)))
    41: mark(isNeList(X)) -> active(isNeList(X))
    42: mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
    43: mark(U52(X)) -> active(U52(mark(X)))
    44: mark(U61(X)) -> active(U61(mark(X)))
    45: mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
    46: mark(U72(X)) -> active(U72(mark(X)))
    47: mark(isPal(X)) -> active(isPal(X))
    48: mark(U81(X)) -> active(U81(mark(X)))
    49: mark(isQid(X)) -> active(isQid(X))
    50: mark(isNePal(X)) -> active(isNePal(X))
    51: mark(a()) -> active(a())
    52: mark(e()) -> active(e())
    53: mark(i()) -> active(i())
    54: mark(o()) -> active(o())
    55: mark(u()) -> active(u())
    56: __(mark(X1),X2) -> __(X1,X2)
    57: __(X1,mark(X2)) -> __(X1,X2)
    58: __(active(X1),X2) -> __(X1,X2)
    59: __(X1,active(X2)) -> __(X1,X2)
    60: U11(mark(X)) -> U11(X)
    61: U11(active(X)) -> U11(X)
    62: U21(mark(X1),X2) -> U21(X1,X2)
    63: U21(X1,mark(X2)) -> U21(X1,X2)
    64: U21(active(X1),X2) -> U21(X1,X2)
    65: U21(X1,active(X2)) -> U21(X1,X2)
    66: U22(mark(X)) -> U22(X)
    67: U22(active(X)) -> U22(X)
    68: isList(mark(X)) -> isList(X)
    69: isList(active(X)) -> isList(X)
    70: U31(mark(X)) -> U31(X)
    71: U31(active(X)) -> U31(X)
    72: U41(mark(X1),X2) -> U41(X1,X2)
    73: U41(X1,mark(X2)) -> U41(X1,X2)
    74: U41(active(X1),X2) -> U41(X1,X2)
    75: U41(X1,active(X2)) -> U41(X1,X2)
    76: U42(mark(X)) -> U42(X)
    77: U42(active(X)) -> U42(X)
    78: isNeList(mark(X)) -> isNeList(X)
    79: isNeList(active(X)) -> isNeList(X)
    80: U51(mark(X1),X2) -> U51(X1,X2)
    81: U51(X1,mark(X2)) -> U51(X1,X2)
    82: U51(active(X1),X2) -> U51(X1,X2)
    83: U51(X1,active(X2)) -> U51(X1,X2)
    84: U52(mark(X)) -> U52(X)
    85: U52(active(X)) -> U52(X)
    86: U61(mark(X)) -> U61(X)
    87: U61(active(X)) -> U61(X)
    88: U71(mark(X1),X2) -> U71(X1,X2)
    89: U71(X1,mark(X2)) -> U71(X1,X2)
    90: U71(active(X1),X2) -> U71(X1,X2)
    91: U71(X1,active(X2)) -> U71(X1,X2)
    92: U72(mark(X)) -> U72(X)
    93: U72(active(X)) -> U72(X)
    94: isPal(mark(X)) -> isPal(X)
    95: isPal(active(X)) -> isPal(X)
    96: U81(mark(X)) -> U81(X)
    97: U81(active(X)) -> U81(X)
    98: isQid(mark(X)) -> isQid(X)
    99: isQid(active(X)) -> isQid(X)
    100: isNePal(mark(X)) -> isNePal(X)
    101: isNePal(active(X)) -> isNePal(X)
Number of strict rules: 101
Direct Order(PosReal,>,Poly) ... removes: 18 4 15 8 1 3 16 21 26 19 17 27 22 28 5 10 7 20 25 30 14 12 23 24 11 9 13 6 29 2
     a()	weight: 0
   U21(x1,x2)	weight: (/ 307755 4) + x1 + x2
   U11(x1)	weight: (/ 103933 4) + x1
isNeList(x1)	weight: (/ 201323 4) + x1
 isPal(x1)	weight: (/ 67941 4) + x1
   U42(x1)	weight: (/ 46297 4) + x1
     u()	weight: 0
   U71(x1,x2)	weight: (/ 132023 4) + x1 + x2
isNePal(x1)	weight: (/ 55847 4) + x1
   U72(x1)	weight: (/ 64081 4) + x1
 isQid(x1)	weight: (/ 1 4) + x1
     o()	weight: 0
isList(x1)	weight: (/ 305257 4) + x1
   nil()	weight: 0
  mark(x1)	weight: x1
     i()	weight: 0
   U52(x1)	weight: (/ 1 4) + x1
   U61(x1)	weight: (/ 55845 4) + x1
     e()	weight: 0
active(x1)	weight: x1
   U31(x1)	weight: (/ 201321 4) + x1
   U81(x1)	weight: (/ 12093 4) + x1
    tt()	weight: 0
   U22(x1)	weight: (/ 2497 4) + x1
   U51(x1,x2)	weight: (/ 305259 4) + x1 + x2
   U41(x1,x2)	weight: (/ 247621 4) + 2 * x1 + x2
    __(x1,x2)	weight: (/ 656813 4) + 2 * x1 + x2
Number of strict rules: 71
Direct Order(PosReal,>,Poly) ... removes: 50 36 44 33 39 49 45 40 38 48 47 37 41 42 46 35 43
     a()	weight: 0
   U21(x1,x2)	weight: (/ 48105 2) + x1 + x2
   U11(x1)	weight: (/ 1 8) + x1
isNeList(x1)	weight: (/ 115749 2) + x1
 isPal(x1)	weight: (/ 549791 4) + x1
   U42(x1)	weight: (/ 157673 8) + x1
     u()	weight: 0
   U71(x1,x2)	weight: (/ 170641 8) + 2 * x1 + x2
isNePal(x1)	weight: (/ 170643 4) + x1
   U72(x1)	weight: (/ 180881 8) + x1
 isQid(x1)	weight: (/ 1 8) + x1
     o()	weight: 0
isList(x1)	weight: (/ 1 8) + x1
   nil()	weight: 0
  mark(x1)	weight: 2 * x1
     i()	weight: 0
   U52(x1)	weight: (/ 62409 8) + x1
   U61(x1)	weight: (/ 1 8) + x1
     e()	weight: 0
active(x1)	weight: x1
   U31(x1)	weight: (/ 231497 8) + x1
   U81(x1)	weight: (/ 208505 8) + x1
    tt()	weight: 0
   U22(x1)	weight: (/ 96209 8) + x1
   U51(x1,x2)	weight: (/ 81877 2) + x1 + x2
   U41(x1,x2)	weight: (/ 620669 4) + x1 + x2
    __(x1,x2)	weight: x1 + x2
Number of strict rules: 54
Direct Order(PosReal,>,Poly) ... removes: 31
     a()	weight: 0
   U21(x1,x2)	weight: (/ 48105 2) + x1 + x2
   U11(x1)	weight: (/ 1 8) + x1
isNeList(x1)	weight: (/ 115749 2) + x1
 isPal(x1)	weight: (/ 347725 4) + x1
   U42(x1)	weight: (/ 157673 8) + x1
     u()	weight: 0
   U71(x1,x2)	weight: (/ 170641 8) + 2 * x1 + x2
isNePal(x1)	weight: (/ 34805 2) + x1
   U72(x1)	weight: (/ 180881 8) + x1
 isQid(x1)	weight: (/ 1 8) + x1
     o()	weight: 0
isList(x1)	weight: (/ 1 8) + x1
   nil()	weight: 0
  mark(x1)	weight: 2 * x1
     i()	weight: 0
   U52(x1)	weight: (/ 62409 8) + x1
   U61(x1)	weight: (/ 1 8) + x1
     e()	weight: 0
active(x1)	weight: x1
   U31(x1)	weight: (/ 231497 8) + x1
   U81(x1)	weight: (/ 208505 8) + x1
    tt()	weight: 0
   U22(x1)	weight: (/ 96209 8) + x1
   U51(x1,x2)	weight: (/ 124819 8) + x1 + x2
   U41(x1,x2)	weight: (/ 620669 4) + x1 + x2
    __(x1,x2)	weight: (/ 101033 8) + x1 + x2
Number of strict rules: 53
Direct Order(PosReal,>,Poly) ... removes: 80 54 77 68 85 100 63 32 60 87 84 34 65 72 64 93 92 88 52 62 82 89 56 79 101 69 96 78 81 70 94 76 57 98 51 90 67 55 59 61 58 74 75 71 53 73 91 97 99 95 66 83 86
     a()	weight: 0
   U21(x1,x2)	weight: (/ 769669 32) + x1 + x2
   U11(x1)	weight: (/ 1 32) + x1
isNeList(x1)	weight: (/ 5 32) + x1
 isPal(x1)	weight: (/ 13 32) + x1
   U42(x1)	weight: (/ 630689 32) + x1
     u()	weight: 0
   U71(x1,x2)	weight: (/ 1 8) + x1 + x2
isNePal(x1)	weight: (/ 5 32) + x1
   U72(x1)	weight: (/ 723521 32) + x1
 isQid(x1)	weight: (/ 1 32) + x1
     o()	weight: 0
isList(x1)	weight: (/ 1 32) + x1
   nil()	weight: 0
  mark(x1)	weight: (/ 1 16) + 2 * x1
     i()	weight: 0
   U52(x1)	weight: (/ 249633 32) + x1
   U61(x1)	weight: (/ 1 32) + x1
     e()	weight: 0
active(x1)	weight: (/ 1 32) + x1
   U31(x1)	weight: (/ 1 32) + x1
   U81(x1)	weight: (/ 1 32) + x1
    tt()	weight: 0
   U22(x1)	weight: (/ 384833 32) + x1
   U51(x1,x2)	weight: (/ 124817 8) + x1 + x2
   U41(x1,x2)	weight: (/ 1261389 32) + x1 + x2
    __(x1,x2)	weight: (/ 3 32) + x1 + x2
Number of strict rules: 0
YES