Input TRS:
    1: __(__(X,Y),Z) -> __(X,__(Y,Z))
    2: __(X,nil()) -> X
    3: __(nil(),X) -> X
    4: U11(tt()) -> tt()
    5: U21(tt(),V2) -> U22(isList(activate(V2)))
    6: U22(tt()) -> tt()
    7: U31(tt()) -> tt()
    8: U41(tt(),V2) -> U42(isNeList(activate(V2)))
    9: U42(tt()) -> tt()
    10: U51(tt(),V2) -> U52(isList(activate(V2)))
    11: U52(tt()) -> tt()
    12: U61(tt()) -> tt()
    13: U71(tt(),P) -> U72(isPal(activate(P)))
    14: U72(tt()) -> tt()
    15: U81(tt()) -> tt()
    16: isList(V) -> U11(isNeList(activate(V)))
    17: isList(n__nil()) -> tt()
    18: isList(n____(V1,V2)) -> U21(isList(activate(V1)),activate(V2))
    19: isNeList(V) -> U31(isQid(activate(V)))
    20: isNeList(n____(V1,V2)) -> U41(isList(activate(V1)),activate(V2))
    21: isNeList(n____(V1,V2)) -> U51(isNeList(activate(V1)),activate(V2))
    22: isNePal(V) -> U61(isQid(activate(V)))
    23: isNePal(n____(I,n____(P,I))) -> U71(isQid(activate(I)),activate(P))
    24: isPal(V) -> U81(isNePal(activate(V)))
    25: isPal(n__nil()) -> tt()
    26: isQid(n__a()) -> tt()
    27: isQid(n__e()) -> tt()
    28: isQid(n__i()) -> tt()
    29: isQid(n__o()) -> tt()
    30: isQid(n__u()) -> tt()
    31: nil() -> n__nil()
    32: __(X1,X2) -> n____(X1,X2)
    33: a() -> n__a()
    34: e() -> n__e()
    35: i() -> n__i()
    36: o() -> n__o()
    37: u() -> n__u()
    38: activate(n__nil()) -> nil()
    39: activate(n____(X1,X2)) -> __(activate(X1),activate(X2))
    40: activate(n__a()) -> a()
    41: activate(n__e()) -> e()
    42: activate(n__i()) -> i()
    43: activate(n__o()) -> o()
    44: activate(n__u()) -> u()
    45: activate(X) -> X
Number of strict rules: 45
Direct Order(PosReal,>,Poly) ... removes: 18 4 15 8 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
  n__a()	weight: 0
   U21(x1,x2)	weight: (/ 120823 4) + x1 + x2
   U11(x1)	weight: (/ 1 4) + x1
  n__o()	weight: 0
isNeList(x1)	weight: (/ 115527 4) + x1
 isPal(x1)	weight: (/ 232677 4) + x1
   U42(x1)	weight: (/ 1 4) + x1
     u()	weight: 0
activate(x1)	weight: x1
   U71(x1,x2)	weight: (/ 241645 4) + x1 + x2
  n__i()	weight: 0
isNePal(x1)	weight: (/ 3 4) + x1
   U72(x1)	weight: (/ 1 4) + x1
n__nil()	weight: 0
 isQid(x1)	weight: (/ 1 4) + x1
 n____(x1,x2)	weight: 30206 + x1 + x2
  n__e()	weight: 0
     o()	weight: 0
isList(x1)	weight: (/ 120821 4) + x1
   nil()	weight: 0
  n__u()	weight: 0
     i()	weight: 0
   U52(x1)	weight: (/ 1 4) + x1
   U61(x1)	weight: (/ 1 4) + x1
     e()	weight: 0
   U31(x1)	weight: (/ 115525 4) + x1
   U81(x1)	weight: (/ 1 4) + x1
    tt()	weight: 0
   U22(x1)	weight: (/ 1 4) + x1
   U51(x1,x2)	weight: (/ 120823 4) + x1 + x2
   U41(x1,x2)	weight: (/ 115529 4) + x1 + x2
    __(x1,x2)	weight: 30206 + x1 + x2
Number of strict rules: 16
Direct Order(PosReal,>,Poly) ... removes: 32 44 39 45 40 38 41 42 43
     a()	weight: 0
  n__a()	weight: 0
   U21(x1,x2)	weight: (/ 3 16) + x1 + x2
   U11(x1)	weight: x1
  n__o()	weight: 0
isNeList(x1)	weight: (/ 1 16) + x1
 isPal(x1)	weight: (/ 5 8) + x1
   U42(x1)	weight: x1
     u()	weight: 0
activate(x1)	weight: (/ 1 16) + 2 * x1
   U71(x1,x2)	weight: (/ 11 16) + x1 + x2
  n__i()	weight: 0
isNePal(x1)	weight: (/ 3 16) + x1
   U72(x1)	weight: x1
n__nil()	weight: 0
 isQid(x1)	weight: x1
 n____(x1,x2)	weight: (/ 5 16) + x1 + x2
  n__e()	weight: 0
     o()	weight: 0
isList(x1)	weight: (/ 1 8) + x1
   nil()	weight: 0
  n__u()	weight: 0
     i()	weight: 0
   U52(x1)	weight: x1
   U61(x1)	weight: (/ 1 16) + x1
     e()	weight: 0
   U31(x1)	weight: x1
   U81(x1)	weight: (/ 1 16) + x1
    tt()	weight: 0
   U22(x1)	weight: x1
   U51(x1,x2)	weight: (/ 3 16) + x1 + x2
   U41(x1,x2)	weight: (/ 1 8) + x1 + x2
    __(x1,x2)	weight: (/ 3 8) + x1 + x2
Number of strict rules: 7
Direct Order(PosReal,>,Poly) ... removes: 1
     a()	weight: 0
  n__a()	weight: 0
   U21(x1,x2)	weight: (/ 3 16) + x1 + x2
   U11(x1)	weight: x1
  n__o()	weight: 0
isNeList(x1)	weight: (/ 1 16) + x1
 isPal(x1)	weight: (/ 5 8) + x1
   U42(x1)	weight: x1
     u()	weight: 0
activate(x1)	weight: (/ 1 16) + 2 * x1
   U71(x1,x2)	weight: (/ 11 16) + x1 + x2
  n__i()	weight: 0
isNePal(x1)	weight: (/ 3 16) + x1
   U72(x1)	weight: x1
n__nil()	weight: 0
 isQid(x1)	weight: x1
 n____(x1,x2)	weight: (/ 5 16) + x1 + x2
  n__e()	weight: 0
     o()	weight: 0
isList(x1)	weight: (/ 1 8) + x1
   nil()	weight: 0
  n__u()	weight: 0
     i()	weight: 0
   U52(x1)	weight: x1
   U61(x1)	weight: (/ 1 16) + x1
     e()	weight: 0
   U31(x1)	weight: x1
   U81(x1)	weight: (/ 1 16) + x1
    tt()	weight: 0
   U22(x1)	weight: x1
   U51(x1,x2)	weight: (/ 3 16) + x1 + x2
   U41(x1,x2)	weight: (/ 1 8) + x1 + x2
    __(x1,x2)	weight: (/ 3 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