Input TRS:
    1: zeros() -> cons(0(),n__zeros())
    2: U11(tt(),L) -> s(length(activate(L)))
    3: and(tt(),X) -> activate(X)
    4: isNat(n__0()) -> tt()
    5: isNat(n__length(V1)) -> isNatList(activate(V1))
    6: isNat(n__s(V1)) -> isNat(activate(V1))
    7: isNatIList(V) -> isNatList(activate(V))
    8: isNatIList(n__zeros()) -> tt()
    9: isNatIList(n__cons(V1,V2)) -> and(isNat(activate(V1)),n__isNatIList(activate(V2)))
    10: isNatList(n__nil()) -> tt()
    11: isNatList(n__cons(V1,V2)) -> and(isNat(activate(V1)),n__isNatList(activate(V2)))
    12: length(nil()) -> 0()
    13: length(cons(N,L)) -> U11(and(isNatList(activate(L)),n__isNat(N)),activate(L))
    14: zeros() -> n__zeros()
    15: 0() -> n__0()
    16: length(X) -> n__length(X)
    17: s(X) -> n__s(X)
    18: cons(X1,X2) -> n__cons(X1,X2)
    19: isNatIList(X) -> n__isNatIList(X)
    20: nil() -> n__nil()
    21: isNatList(X) -> n__isNatList(X)
    22: isNat(X) -> n__isNat(X)
    23: activate(n__zeros()) -> zeros()
    24: activate(n__0()) -> 0()
    25: activate(n__length(X)) -> length(activate(X))
    26: activate(n__s(X)) -> s(activate(X))
    27: activate(n__cons(X1,X2)) -> cons(activate(X1),X2)
    28: activate(n__isNatIList(X)) -> isNatIList(X)
    29: activate(n__nil()) -> nil()
    30: activate(n__isNatList(X)) -> isNatList(X)
    31: activate(n__isNat(X)) -> isNat(X)
    32: activate(X) -> X
Number of strict rules: 32
Direct Order(PosReal,>,Poly) ... removes: 8 5 7 12
isNatList(x1)	weight: x1
   U11(x1,x2)	weight: (/ 58721 4) + x1 + x2
     s(x1)	weight: x1
activate(x1)	weight: x1
   and(x1,x2)	weight: x1 + x2
n__zeros()	weight: 0
isNatIList(x1)	weight: (/ 1 4) + 2 * x1
 zeros()	weight: 0
n__nil()	weight: 0
  n__s(x1)	weight: x1
     0()	weight: 0
n__isNatList(x1)	weight: x1
n__cons(x1,x2)	weight: x1 + 2 * x2
   nil()	weight: 0
n__isNat(x1)	weight: x1
  n__0()	weight: 0
n__length(x1)	weight: (/ 58721 4) + x1
 isNat(x1)	weight: x1
  cons(x1,x2)	weight: x1 + 2 * x2
n__isNatIList(x1)	weight: (/ 1 4) + 2 * x1
    tt()	weight: 0
length(x1)	weight: (/ 58721 4) + x1
Number of strict rules: 28
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #U11(tt(),L) -> #s(length(activate(L)))
   #2: #U11(tt(),L) -> #length(activate(L))
   #3: #U11(tt(),L) -> #activate(L)
   #4: #activate(n__nil()) -> #nil()
   #5: #isNat(n__s(V1)) -> #isNat(activate(V1))
   #6: #isNat(n__s(V1)) -> #activate(V1)
   #7: #length(cons(N,L)) -> #U11(and(isNatList(activate(L)),n__isNat(N)),activate(L))
   #8: #length(cons(N,L)) -> #and(isNatList(activate(L)),n__isNat(N))
   #9: #length(cons(N,L)) -> #isNatList(activate(L))
   #10: #length(cons(N,L)) -> #activate(L)
   #11: #length(cons(N,L)) -> #activate(L)
   #12: #isNatIList(n__cons(V1,V2)) -> #and(isNat(activate(V1)),n__isNatIList(activate(V2)))
   #13: #isNatIList(n__cons(V1,V2)) -> #isNat(activate(V1))
   #14: #isNatIList(n__cons(V1,V2)) -> #activate(V1)
   #15: #isNatIList(n__cons(V1,V2)) -> #activate(V2)
   #16: #isNatList(n__cons(V1,V2)) -> #and(isNat(activate(V1)),n__isNatList(activate(V2)))
   #17: #isNatList(n__cons(V1,V2)) -> #isNat(activate(V1))
   #18: #isNatList(n__cons(V1,V2)) -> #activate(V1)
   #19: #isNatList(n__cons(V1,V2)) -> #activate(V2)
   #20: #activate(n__0()) -> #0()
   #21: #activate(n__zeros()) -> #zeros()
   #22: #activate(n__isNat(X)) -> #isNat(X)
   #23: #activate(n__isNatList(X)) -> #isNatList(X)
   #24: #activate(n__length(X)) -> #length(activate(X))
   #25: #activate(n__length(X)) -> #activate(X)
   #26: #activate(n__isNatIList(X)) -> #isNatIList(X)
   #27: #activate(n__cons(X1,X2)) -> #cons(activate(X1),X2)
   #28: #activate(n__cons(X1,X2)) -> #activate(X1)
   #29: #activate(n__s(X)) -> #s(activate(X))
   #30: #activate(n__s(X)) -> #activate(X)
   #31: #and(tt(),X) -> #activate(X)
   #32: #zeros() -> #cons(0(),n__zeros())
   #33: #zeros() -> #0()
Number of SCCs: 1, DPs: 25, edges: 119
	SCC { #2 #3 #5..19 #22..26 #28 #30 #31 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   #0()	weight: 0
isNatList(x1)	weight: (/ 1 4) + x1
   U11(x1,x2)	weight: (/ 1 2) + x2
#cons(x1,x2)	weight: 0
     s(x1)	weight: x1
#isNat(x1)	weight: (/ 1 8) + x1
activate(x1)	weight: x1
   and(x1,x2)	weight: x2
n__zeros()	weight: 0
isNatIList(x1)	weight: (/ 1 4) + x1
#activate(x1)	weight: x1
 zeros()	weight: 0
n__nil()	weight: 0
  n__s(x1)	weight: x1
     0()	weight: 0
#zeros()	weight: 0
n__isNatList(x1)	weight: (/ 1 4) + x1
#isNatList(x1)	weight: (/ 1 4) + x1
   #s(x1)	weight: 0
n__cons(x1,x2)	weight: x1 + x2
   nil()	weight: 0
n__isNat(x1)	weight: (/ 1 4) + x1
 #nil()	weight: 0
  n__0()	weight: 0
n__length(x1)	weight: (/ 1 2) + x1
 isNat(x1)	weight: (/ 1 4) + x1
 #U11(x1,x2)	weight: (/ 3 8) + x2
  cons(x1,x2)	weight: x1 + x2
n__isNatIList(x1)	weight: (/ 1 4) + x1
#isNatIList(x1)	weight: (/ 1 4) + x1
    tt()	weight: 0
length(x1)	weight: (/ 1 2) + x1
#length(x1)	weight: (/ 3 8) + x1
 #and(x1,x2)	weight: x2
    Usable rules: { 1..4 6 9..11 13..32 }
    Removed DPs: #3 #6 #8..11 #13..15 #17..19 #22 #24 #25
Number of SCCs: 3, DPs: 10, edges: 19
	SCC { #5 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... QWPOpS(PosReal,>,MaxSum)... Order(PosReal,>,Sum-Sum; PosReal,≥,Sum-Sum)... Order(PosReal,>,Sum-Sum; NegReal,≥,Sum)... succeeded.
   #0()	weight: 0; 0
isNatList(x1)	weight: (max (/ 1 8) 0); x1_2
   U11(x1,x2)	weight: max{0, (/ 5 16) + x2_1 + x1_2}; (- (/ 1 16)) + x1_2
#cons(x1,x2)	weight: 0; 0
     s(x1)	weight: max{0, (/ 1 4) + x1_1}; (- (/ 1 16))
#isNat(x1)	weight: max{0, (- (/ 3 16)) + x1_1}; 0
activate(x1)	weight: max{0, (/ 1 8) + x1_1}; x1_2
   and(x1,x2)	weight: max{0, (/ 1 8) + x2_1}; x2_2 + x1_2
n__zeros()	weight: (/ 1 16); (- (/ 3 8))
isNatIList(x1)	weight: (max (/ 1 8) 0); (- (/ 1 16))
#activate(x1)	weight: 0; 0
 zeros()	weight: (/ 3 16); (- (/ 3 8))
n__nil()	weight: (/ 1 16); 0
  n__s(x1)	weight: max{0, (/ 1 4) + x1_1}; (- (/ 1 16))
     0()	weight: (/ 1 16); (- (/ 1 16))
#zeros()	weight: 0; 0
n__isNatList(x1)	weight: max{0, (- (/ 1 8)) + x1_2}; x1_2
#isNatList(x1)	weight: 0; 0
   #s(x1)	weight: 0; 0
n__cons(x1,x2)	weight: max{0, (/ 3 8) + x2_1 + x2_2}; x2_2
   nil()	weight: (/ 1 16); 0
n__isNat(x1)	weight: max{0, (- (/ 1 16)) + x1_1}; 0
 #nil()	weight: 0; 0
  n__0()	weight: (/ 1 16); (- (/ 1 16))
n__length(x1)	weight: max{0, (- (/ 1 16)) + x1_1}; (- (/ 1 16)) + x1_2
 isNat(x1)	weight: max{0, (/ 1 16) + x1_1}; 0
 #U11(x1,x2)	weight: 0; 0
  cons(x1,x2)	weight: max{0, (/ 1 2) + x2_1 + x2_2}; x2_2
n__isNatIList(x1)	weight: 0; (- (/ 1 16))
#isNatIList(x1)	weight: 0; 0
    tt()	weight: (/ 1 16); 0
length(x1)	weight: max{0, (- (/ 1 16)) + x1_1}; (- (/ 1 16)) + x1_2
#length(x1)	weight: 0; 0
 #and(x1,x2)	weight: 0; 0
    Usable rules: { 1..4 6 9..11 13..32 }
    Removed DPs: #5
Number of SCCs: 2, DPs: 9, edges: 18
	SCC { #2 #7 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... QWPOpS(PosReal,>,MaxSum)... Order(PosReal,>,Sum-Sum; PosReal,≥,Sum-Sum)... Order(PosReal,>,Sum-Sum; NegReal,≥,Sum)... succeeded.
   #0()	weight: 0; 0
isNatList(x1)	weight: (max (/ 9 32) 0); x1_2
   U11(x1,x2)	weight: max{0, (- (/ 1 32)) + x2_2}; x2_2 + x1_2
#cons(x1,x2)	weight: 0; 0
     s(x1)	weight: max{0, (- (/ 1 32)) + x1_2}; (- (/ 1 32)) + x1_2
#isNat(x1)	weight: 0; 0
activate(x1)	weight: max{0, (/ 3 32) + x1_1}; x1_2
   and(x1,x2)	weight: max{0, (- (/ 3 16)) + x2_1 + x1_1}; x2_2 + x1_2
n__zeros()	weight: (/ 1 32); (- (/ 1 4))
isNatIList(x1)	weight: (max (/ 3 32) 0); 0
#activate(x1)	weight: 0; 0
 zeros()	weight: (/ 1 8); (- (/ 1 4))
n__nil()	weight: (/ 1 32); 0
  n__s(x1)	weight: max{0, (- (/ 1 32)) + x1_2}; (- (/ 1 32)) + x1_2
     0()	weight: (/ 1 32); (- (/ 1 32))
#zeros()	weight: 0; 0
n__isNatList(x1)	weight: (max (/ 3 16) 0); x1_2
#isNatList(x1)	weight: 0; 0
   #s(x1)	weight: 0; 0
n__cons(x1,x2)	weight: max{0, (/ 1 4) + x2_1 + x2_2}; x2_2
   nil()	weight: (/ 1 32); 0
n__isNat(x1)	weight: (max (/ 9 32) 0); 0
 #nil()	weight: 0; 0
  n__0()	weight: (/ 1 32); (- (/ 1 32))
n__length(x1)	weight: (max (- (/ 1 32)) 0); x1_2
 isNat(x1)	weight: (max (/ 9 32) 0); 0
 #U11(x1,x2)	weight: max{0, (- (/ 7 32)) + x2_1 + x1_1 + x1_2}; x1_2
  cons(x1,x2)	weight: max{0, (/ 11 32) + x2_1 + x2_2}; x2_2
n__isNatIList(x1)	weight: 0; 0
#isNatIList(x1)	weight: 0; 0
    tt()	weight: (/ 9 32); 0
length(x1)	weight: (max (- (/ 1 32)) 0); x1_2
#length(x1)	weight: max{0, (- (/ 1 16)) + x1_1}; 0
 #and(x1,x2)	weight: 0; 0
    Usable rules: { 1..4 6 9..11 13..32 }
    Removed DPs: #2
Number of SCCs: 1, DPs: 7, edges: 16
	SCC { #12 #16 #23 #26 #28 #30 #31 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   #0()	weight: 0
isNatList(x1)	weight: (/ 1 8)
   U11(x1,x2)	weight: (/ 5 8)
#cons(x1,x2)	weight: 0
     s(x1)	weight: (/ 3 4)
#isNat(x1)	weight: (/ 1 8)
activate(x1)	weight: (/ 3 8)
   and(x1,x2)	weight: (/ 1 4)
n__zeros()	weight: 0
isNatIList(x1)	weight: 0
#activate(x1)	weight: x1
 zeros()	weight: 0
n__nil()	weight: 0
  n__s(x1)	weight: (/ 7 8) + x1
     0()	weight: 0
#zeros()	weight: 0
n__isNatList(x1)	weight: (/ 1 4)
#isNatList(x1)	weight: (/ 1 4)
   #s(x1)	weight: 0
n__cons(x1,x2)	weight: (/ 1 4) + x1
   nil()	weight: 0
n__isNat(x1)	weight: (/ 5 8)
 #nil()	weight: 0
  n__0()	weight: 0
n__length(x1)	weight: (/ 5 8)
 isNat(x1)	weight: (/ 1 2)
 #U11(x1,x2)	weight: (/ 3 8)
  cons(x1,x2)	weight: (/ 1 8) + x1
n__isNatIList(x1)	weight: (/ 1 8)
#isNatIList(x1)	weight: (/ 1 8)
    tt()	weight: 0
length(x1)	weight: (/ 1 2)
#length(x1)	weight: (/ 1 4)
 #and(x1,x2)	weight: x2
    Usable rules: { }
    Removed DPs: #28 #30
Number of SCCs: 1, DPs: 5, edges: 6
	SCC { #12 #16 #23 #26 #31 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... QWPOpS(PosReal,>,MaxSum)... Order(PosReal,>,Sum-Sum; PosReal,≥,Sum-Sum)... Order(PosReal,>,Sum-Sum; NegReal,≥,Sum)... Order(PosReal,>,MaxSum-Sum; NegReal,≥,Sum)... failed.
Removing edges: failed.
Finding a loop...  failed.
MAYBE