Input TRS:
    1: __(__(X,Y),Z) -> __(X,__(Y,Z))
    2: __(X,nil()) -> X
    3: __(nil(),X) -> X
    4: and(tt(),X) -> activate(X)
    5: isList(V) -> isNeList(activate(V))
    6: isList(n__nil()) -> tt()
    7: isList(n____(V1,V2)) -> and(isList(activate(V1)),n__isList(activate(V2)))
    8: isNeList(V) -> isQid(activate(V))
    9: isNeList(n____(V1,V2)) -> and(isList(activate(V1)),n__isNeList(activate(V2)))
    10: isNeList(n____(V1,V2)) -> and(isNeList(activate(V1)),n__isList(activate(V2)))
    11: isNePal(V) -> isQid(activate(V))
    12: isNePal(n____(I,n____(P,I))) -> and(isQid(activate(I)),n__isPal(activate(P)))
    13: isPal(V) -> isNePal(activate(V))
    14: isPal(n__nil()) -> tt()
    15: isQid(n__a()) -> tt()
    16: isQid(n__e()) -> tt()
    17: isQid(n__i()) -> tt()
    18: isQid(n__o()) -> tt()
    19: isQid(n__u()) -> tt()
    20: nil() -> n__nil()
    21: __(X1,X2) -> n____(X1,X2)
    22: isList(X) -> n__isList(X)
    23: isNeList(X) -> n__isNeList(X)
    24: isPal(X) -> n__isPal(X)
    25: a() -> n__a()
    26: e() -> n__e()
    27: i() -> n__i()
    28: o() -> n__o()
    29: u() -> n__u()
    30: activate(n__nil()) -> nil()
    31: activate(n____(X1,X2)) -> __(activate(X1),activate(X2))
    32: activate(n__isList(X)) -> isList(X)
    33: activate(n__isNeList(X)) -> isNeList(X)
    34: activate(n__isPal(X)) -> isPal(X)
    35: activate(n__a()) -> a()
    36: activate(n__e()) -> e()
    37: activate(n__i()) -> i()
    38: activate(n__o()) -> o()
    39: activate(n__u()) -> u()
    40: activate(X) -> 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
  n__a()	weight: 0
  n__o()	weight: 0
isNeList(x1)	weight: 19781 + 2 * x1
 isPal(x1)	weight: 19782 + x1
     u()	weight: 0
activate(x1)	weight: x1
   and(x1,x2)	weight: (/ 1 2) + x1 + x2
n__isNeList(x1)	weight: 19781 + 2 * x1
  n__i()	weight: 0
n__isList(x1)	weight: (/ 39563 2) + 2 * x1
isNePal(x1)	weight: 1324 + x1
n__isPal(x1)	weight: 19782 + x1
n__nil()	weight: 0
 isQid(x1)	weight: (/ 2647 2) + x1
 n____(x1,x2)	weight: (/ 39565 4) + x1 + x2
  n__e()	weight: 0
     o()	weight: 0
isList(x1)	weight: (/ 39563 2) + 2 * x1
   nil()	weight: 0
  n__u()	weight: 0
     i()	weight: 0
     e()	weight: 0
    tt()	weight: 0
    __(x1,x2)	weight: (/ 39565 4) + x1 + x2
Number of strict rules: 22
Direct Order(PosReal,>,Poly) ... removes: 34 33 23 24
     a()	weight: 0
  n__a()	weight: 0
  n__o()	weight: 0
isNeList(x1)	weight: (/ 39563 2) + 2 * x1
 isPal(x1)	weight: (/ 39563 2) + 2 * x1
     u()	weight: 0
activate(x1)	weight: 2 * x1
   and(x1,x2)	weight: x1 + x2
n__isNeList(x1)	weight: 19781 + 2 * x1
  n__i()	weight: 0
n__isList(x1)	weight: 2 * x1
isNePal(x1)	weight: (/ 22429 2) + x1
n__isPal(x1)	weight: 9891 + x1
n__nil()	weight: 0
 isQid(x1)	weight: (/ 2647 2) + x1
 n____(x1,x2)	weight: x1 + x2
  n__e()	weight: 0
     o()	weight: 0
isList(x1)	weight: 2 * x1
   nil()	weight: 0
  n__u()	weight: 0
     i()	weight: 0
     e()	weight: 0
    tt()	weight: 0
    __(x1,x2)	weight: x1 + x2
Number of strict rules: 18
Direct Order(PosReal,>,Poly) ... removes: 21 31
     a()	weight: 0
  n__a()	weight: 0
  n__o()	weight: 0
isNeList(x1)	weight: (/ 316483 16) + 2 * x1
 isPal(x1)	weight: (/ 316483 16) + 2 * x1
     u()	weight: 0
activate(x1)	weight: 2 * x1
   and(x1,x2)	weight: x1 + x2
n__isNeList(x1)	weight: (/ 158241 8) + 2 * x1
  n__i()	weight: 0
n__isList(x1)	weight: 2 * x1
isNePal(x1)	weight: (/ 179407 16) + x1
n__isPal(x1)	weight: (/ 79121 8) + x1
n__nil()	weight: 0
 isQid(x1)	weight: (/ 21169 16) + x1
 n____(x1,x2)	weight: (/ 1 8) + x1 + x2
  n__e()	weight: 0
     o()	weight: 0
isList(x1)	weight: 2 * x1
   nil()	weight: 0
  n__u()	weight: 0
     i()	weight: 0
     e()	weight: 0
    tt()	weight: 0
    __(x1,x2)	weight: (/ 3 16) + x1 + x2
Number of strict rules: 16
Direct Order(PosReal,>,Poly) ... removes: 1 36 32 22 39 30 40 38 37 35
     a()	weight: 0
  n__a()	weight: 0
  n__o()	weight: 0
isNeList(x1)	weight: (/ 632963 32) + 2 * x1
 isPal(x1)	weight: (/ 632963 32) + 2 * x1
     u()	weight: 0
activate(x1)	weight: (/ 1 16) + 2 * x1
   and(x1,x2)	weight: x1 + x2
n__isNeList(x1)	weight: (/ 316481 16) + x1
  n__i()	weight: 0
n__isList(x1)	weight: x1
isNePal(x1)	weight: (/ 358813 32) + x1
n__isPal(x1)	weight: (/ 158241 16) + x1
n__nil()	weight: 0
 isQid(x1)	weight: (/ 42335 32) + x1
 n____(x1,x2)	weight: (/ 1 8) + x1 + x2
  n__e()	weight: 0
     o()	weight: 0
isList(x1)	weight: (/ 1 32) + 2 * x1
   nil()	weight: 0
  n__u()	weight: 0
     i()	weight: 0
     e()	weight: 0
    tt()	weight: 0
    __(x1,x2)	weight: (/ 1 8) + 2 * x1 + x2
Number of strict rules: 6
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
Number of SCCs: 0, DPs: 0, edges: 0
YES