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__and(tt(),X) -> mark(X)
    5: a__isList(V) -> a__isNeList(V)
    6: a__isList(nil()) -> tt()
    7: a__isList(__(V1,V2)) -> a__and(a__isList(V1),isList(V2))
    8: a__isNeList(V) -> a__isQid(V)
    9: a__isNeList(__(V1,V2)) -> a__and(a__isList(V1),isNeList(V2))
    10: a__isNeList(__(V1,V2)) -> a__and(a__isNeList(V1),isList(V2))
    11: a__isNePal(V) -> a__isQid(V)
    12: a__isNePal(__(I,__(P,I))) -> a__and(a__isQid(I),isPal(P))
    13: a__isPal(V) -> a__isNePal(V)
    14: a__isPal(nil()) -> tt()
    15: a__isQid(a()) -> tt()
    16: a__isQid(e()) -> tt()
    17: a__isQid(i()) -> tt()
    18: a__isQid(o()) -> tt()
    19: a__isQid(u()) -> tt()
    20: mark(__(X1,X2)) -> a____(mark(X1),mark(X2))
    21: mark(and(X1,X2)) -> a__and(mark(X1),X2)
    22: mark(isList(X)) -> a__isList(X)
    23: mark(isNeList(X)) -> a__isNeList(X)
    24: mark(isQid(X)) -> a__isQid(X)
    25: mark(isNePal(X)) -> a__isNePal(X)
    26: mark(isPal(X)) -> a__isPal(X)
    27: mark(nil()) -> nil()
    28: mark(tt()) -> tt()
    29: mark(a()) -> a()
    30: mark(e()) -> e()
    31: mark(i()) -> i()
    32: mark(o()) -> o()
    33: mark(u()) -> u()
    34: a____(X1,X2) -> __(X1,X2)
    35: a__and(X1,X2) -> and(X1,X2)
    36: a__isList(X) -> isList(X)
    37: a__isNeList(X) -> isNeList(X)
    38: a__isQid(X) -> isQid(X)
    39: a__isNePal(X) -> isNePal(X)
    40: a__isPal(X) -> isPal(X)
Number of strict rules: 40
Direct Order(PosReal,>,Poly) ... removes: 18 4 15 8 3 16 19 17 5 10 7 14 12 11 9 13 6 2
     a()	weight: 0
isNeList(x1)	weight: (/ 1 4) + 2 * x1
 isPal(x1)	weight: (/ 17923 8) + x1
     u()	weight: 0
   and(x1,x2)	weight: (/ 1 8) + x1 + x2
isNePal(x1)	weight: (/ 8961 4) + x1
 isQid(x1)	weight: (/ 1 8) + x1
 a____(x1,x2)	weight: (/ 5 16) + x1 + x2
a__isList(x1)	weight: (/ 3 8) + 2 * x1
a__isNeList(x1)	weight: (/ 1 4) + 2 * x1
     o()	weight: 0
isList(x1)	weight: (/ 3 8) + 2 * x1
   nil()	weight: 0
  mark(x1)	weight: x1
a__isNePal(x1)	weight: (/ 8961 4) + x1
     i()	weight: 0
     e()	weight: 0
a__isPal(x1)	weight: (/ 17923 8) + x1
    tt()	weight: 0
a__isQid(x1)	weight: (/ 1 8) + x1
a__and(x1,x2)	weight: (/ 1 8) + x1 + x2
    __(x1,x2)	weight: (/ 5 16) + x1 + x2
Number of strict rules: 22
Direct Order(PosReal,>,Poly) ... removes: 1
     a()	weight: 0
isNeList(x1)	weight: (/ 1 4) + 2 * x1
 isPal(x1)	weight: (/ 17923 8) + x1
     u()	weight: 0
   and(x1,x2)	weight: (/ 1 8) + x1 + x2
isNePal(x1)	weight: (/ 8961 4) + x1
 isQid(x1)	weight: (/ 1 8) + x1
 a____(x1,x2)	weight: (/ 13445 16) + 2 * x1 + x2
a__isList(x1)	weight: (/ 3 8) + 2 * x1
a__isNeList(x1)	weight: (/ 1 4) + 2 * x1
     o()	weight: 0
isList(x1)	weight: (/ 3 8) + 2 * x1
   nil()	weight: 0
  mark(x1)	weight: x1
a__isNePal(x1)	weight: (/ 8961 4) + x1
     i()	weight: 0
     e()	weight: 0
a__isPal(x1)	weight: (/ 17923 8) + x1
    tt()	weight: 0
a__isQid(x1)	weight: (/ 1 8) + x1
a__and(x1,x2)	weight: (/ 1 8) + x1 + x2
    __(x1,x2)	weight: (/ 13445 16) + 2 * x1 + x2
Number of strict rules: 21
Direct Order(PosReal,>,Poly) ... removes: 36 26 34 22 39 20 25 23 24 40 38 37
     a()	weight: 0
isNeList(x1)	weight: (/ 3 16) + 2 * x1
 isPal(x1)	weight: (/ 35843 16) + x1
     u()	weight: 0
   and(x1,x2)	weight: x1 + x2
isNePal(x1)	weight: (/ 35843 16) + x1
 isQid(x1)	weight: (/ 1 8) + x1
 a____(x1,x2)	weight: (/ 3 16) + 2 * x1 + x2
a__isList(x1)	weight: (/ 5 16) + 2 * x1
a__isNeList(x1)	weight: (/ 1 4) + 2 * x1
     o()	weight: 0
isList(x1)	weight: (/ 1 4) + 2 * x1
   nil()	weight: 0
  mark(x1)	weight: 2 * x1
a__isNePal(x1)	weight: (/ 8961 4) + x1
     i()	weight: 0
     e()	weight: 0
a__isPal(x1)	weight: (/ 8961 4) + x1
    tt()	weight: 0
a__isQid(x1)	weight: (/ 3 16) + x1
a__and(x1,x2)	weight: x1 + x2
    __(x1,x2)	weight: (/ 1 8) + 2 * x1 + x2
Number of strict rules: 9
Direct Order(PosReal,>,Poly) ... removes: 21 35
     a()	weight: 0
isNeList(x1)	weight: (/ 1 16) + 2 * x1
 isPal(x1)	weight: (/ 35843 16) + x1
     u()	weight: 0
   and(x1,x2)	weight: (/ 1 8) + x1 + x2
isNePal(x1)	weight: (/ 8961 4) + x1
 isQid(x1)	weight: (/ 1 8) + x1
 a____(x1,x2)	weight: (/ 3 16) + 2 * x1 + x2
a__isList(x1)	weight: (/ 1 8) + 2 * x1
a__isNeList(x1)	weight: (/ 1 8) + 2 * x1
     o()	weight: 0
isList(x1)	weight: (/ 1 16) + 2 * x1
   nil()	weight: 0
  mark(x1)	weight: 2 * x1
a__isNePal(x1)	weight: (/ 35845 16) + x1
     i()	weight: 0
     e()	weight: 0
a__isPal(x1)	weight: (/ 35845 16) + x1
    tt()	weight: 0
a__isQid(x1)	weight: (/ 3 16) + x1
a__and(x1,x2)	weight: (/ 3 16) + x1 + x2
    __(x1,x2)	weight: (/ 1 8) + 2 * x1 + x2
Number of strict rules: 7
Direct Order(PosReal,>,Poly) ... removes: 32 27 28 33 30 31 29
     a()	weight: 0
isNeList(x1)	weight: (/ 1 32) + 2 * x1
 isPal(x1)	weight: (/ 71683 32) + x1
     u()	weight: 0
   and(x1,x2)	weight: (/ 1 16) + x1 + x2
isNePal(x1)	weight: (/ 71679 32) + x1
 isQid(x1)	weight: (/ 1 32) + x1
 a____(x1,x2)	weight: (/ 1 32) + x1 + x2
a__isList(x1)	weight: (/ 3 32) + 2 * x1
a__isNeList(x1)	weight: (/ 1 32) + 2 * x1
     o()	weight: 0
isList(x1)	weight: (/ 1 32) + 2 * x1
   nil()	weight: 0
  mark(x1)	weight: (/ 1 32) + 2 * x1
a__isNePal(x1)	weight: 2240 + x1
     i()	weight: 0
     e()	weight: 0
a__isPal(x1)	weight: (/ 71683 32) + x1
    tt()	weight: 0
a__isQid(x1)	weight: (/ 1 16) + x1
a__and(x1,x2)	weight: (/ 3 32) + x1 + x2
    __(x1,x2)	weight: (/ 1 8) + 2 * x1 + x2
Number of strict rules: 0
YES