Input TRS:
    1: zeros() -> cons(0(),n__zeros())
    2: U11(tt(),V1) -> U12(isNatList(activate(V1)))
    3: U12(tt()) -> tt()
    4: U21(tt(),V1) -> U22(isNat(activate(V1)))
    5: U22(tt()) -> tt()
    6: U31(tt(),V) -> U32(isNatList(activate(V)))
    7: U32(tt()) -> tt()
    8: U41(tt(),V1,V2) -> U42(isNat(activate(V1)),activate(V2))
    9: U42(tt(),V2) -> U43(isNatIList(activate(V2)))
    10: U43(tt()) -> tt()
    11: U51(tt(),V1,V2) -> U52(isNat(activate(V1)),activate(V2))
    12: U52(tt(),V2) -> U53(isNatList(activate(V2)))
    13: U53(tt()) -> tt()
    14: U61(tt(),V1,V2) -> U62(isNat(activate(V1)),activate(V2))
    15: U62(tt(),V2) -> U63(isNatIList(activate(V2)))
    16: U63(tt()) -> tt()
    17: U71(tt(),L) -> s(length(activate(L)))
    18: U81(tt()) -> nil()
    19: U91(tt(),IL,M,N) -> cons(activate(N),n__take(activate(M),activate(IL)))
    20: and(tt(),X) -> activate(X)
    21: isNat(n__0()) -> tt()
    22: isNat(n__length(V1)) -> U11(isNatIListKind(activate(V1)),activate(V1))
    23: isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1))
    24: isNatIList(V) -> U31(isNatIListKind(activate(V)),activate(V))
    25: isNatIList(n__zeros()) -> tt()
    26: isNatIList(n__cons(V1,V2)) -> U41(and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))),activate(V1),activate(V2))
    27: isNatIListKind(n__nil()) -> tt()
    28: isNatIListKind(n__zeros()) -> tt()
    29: isNatIListKind(n__cons(V1,V2)) -> and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2)))
    30: isNatIListKind(n__take(V1,V2)) -> and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2)))
    31: isNatKind(n__0()) -> tt()
    32: isNatKind(n__length(V1)) -> isNatIListKind(activate(V1))
    33: isNatKind(n__s(V1)) -> isNatKind(activate(V1))
    34: isNatList(n__nil()) -> tt()
    35: isNatList(n__cons(V1,V2)) -> U51(and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))),activate(V1),activate(V2))
    36: isNatList(n__take(V1,V2)) -> U61(and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))),activate(V1),activate(V2))
    37: length(nil()) -> 0()
    38: length(cons(N,L)) -> U71(and(and(isNatList(activate(L)),n__isNatIListKind(activate(L))),n__and(n__isNat(N),n__isNatKind(N))),activate(L))
    39: take(0(),IL) -> U81(and(isNatIList(IL),n__isNatIListKind(IL)))
    40: take(s(M),cons(N,IL)) -> U91(and(and(isNatIList(activate(IL)),n__isNatIListKind(activate(IL))),n__and(n__and(n__isNat(M),n__isNatKind(M)),n__and(n__isNat(N),n__isNatKind(N)))),activate(IL),M,N)
    41: zeros() -> n__zeros()
    42: take(X1,X2) -> n__take(X1,X2)
    43: 0() -> n__0()
    44: length(X) -> n__length(X)
    45: s(X) -> n__s(X)
    46: cons(X1,X2) -> n__cons(X1,X2)
    47: isNatIListKind(X) -> n__isNatIListKind(X)
    48: nil() -> n__nil()
    49: and(X1,X2) -> n__and(X1,X2)
    50: isNat(X) -> n__isNat(X)
    51: isNatKind(X) -> n__isNatKind(X)
    52: activate(n__zeros()) -> zeros()
    53: activate(n__take(X1,X2)) -> take(activate(X1),activate(X2))
    54: activate(n__0()) -> 0()
    55: activate(n__length(X)) -> length(activate(X))
    56: activate(n__s(X)) -> s(activate(X))
    57: activate(n__cons(X1,X2)) -> cons(activate(X1),X2)
    58: activate(n__isNatIListKind(X)) -> isNatIListKind(X)
    59: activate(n__nil()) -> nil()
    60: activate(n__and(X1,X2)) -> and(activate(X1),X2)
    61: activate(n__isNat(X)) -> isNat(X)
    62: activate(n__isNatKind(X)) -> isNatKind(X)
    63: activate(X) -> X
Number of strict rules: 63
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #U11(tt(),V1) -> #U12(isNatList(activate(V1)))
   #2: #U11(tt(),V1) -> #isNatList(activate(V1))
   #3: #U11(tt(),V1) -> #activate(V1)
   #4: #isNatIListKind(n__cons(V1,V2)) -> #and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2)))
   #5: #isNatIListKind(n__cons(V1,V2)) -> #isNatKind(activate(V1))
   #6: #isNatIListKind(n__cons(V1,V2)) -> #activate(V1)
   #7: #isNatIListKind(n__cons(V1,V2)) -> #activate(V2)
   #8: #isNatList(n__cons(V1,V2)) -> #U51(and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))),activate(V1),activate(V2))
   #9: #isNatList(n__cons(V1,V2)) -> #and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2)))
   #10: #isNatList(n__cons(V1,V2)) -> #isNatKind(activate(V1))
   #11: #isNatList(n__cons(V1,V2)) -> #activate(V1)
   #12: #isNatList(n__cons(V1,V2)) -> #activate(V2)
   #13: #isNatList(n__cons(V1,V2)) -> #activate(V1)
   #14: #isNatList(n__cons(V1,V2)) -> #activate(V2)
   #15: #length(nil()) -> #0()
   #16: #activate(n__take(X1,X2)) -> #take(activate(X1),activate(X2))
   #17: #activate(n__take(X1,X2)) -> #activate(X1)
   #18: #activate(n__take(X1,X2)) -> #activate(X2)
   #19: #activate(n__isNatIListKind(X)) -> #isNatIListKind(X)
   #20: #activate(n__isNat(X)) -> #isNat(X)
   #21: #length(cons(N,L)) -> #U71(and(and(isNatList(activate(L)),n__isNatIListKind(activate(L))),n__and(n__isNat(N),n__isNatKind(N))),activate(L))
   #22: #length(cons(N,L)) -> #and(and(isNatList(activate(L)),n__isNatIListKind(activate(L))),n__and(n__isNat(N),n__isNatKind(N)))
   #23: #length(cons(N,L)) -> #and(isNatList(activate(L)),n__isNatIListKind(activate(L)))
   #24: #length(cons(N,L)) -> #isNatList(activate(L))
   #25: #length(cons(N,L)) -> #activate(L)
   #26: #length(cons(N,L)) -> #activate(L)
   #27: #length(cons(N,L)) -> #activate(L)
   #28: #U31(tt(),V) -> #U32(isNatList(activate(V)))
   #29: #U31(tt(),V) -> #isNatList(activate(V))
   #30: #U31(tt(),V) -> #activate(V)
   #31: #activate(n__nil()) -> #nil()
   #32: #activate(n__length(X)) -> #length(activate(X))
   #33: #activate(n__length(X)) -> #activate(X)
   #34: #take(s(M),cons(N,IL)) -> #U91(and(and(isNatIList(activate(IL)),n__isNatIListKind(activate(IL))),n__and(n__and(n__isNat(M),n__isNatKind(M)),n__and(n__isNat(N),n__isNatKind(N)))),activate(IL),M,N)
   #35: #take(s(M),cons(N,IL)) -> #and(and(isNatIList(activate(IL)),n__isNatIListKind(activate(IL))),n__and(n__and(n__isNat(M),n__isNatKind(M)),n__and(n__isNat(N),n__isNatKind(N))))
   #36: #take(s(M),cons(N,IL)) -> #and(isNatIList(activate(IL)),n__isNatIListKind(activate(IL)))
   #37: #take(s(M),cons(N,IL)) -> #isNatIList(activate(IL))
   #38: #take(s(M),cons(N,IL)) -> #activate(IL)
   #39: #take(s(M),cons(N,IL)) -> #activate(IL)
   #40: #take(s(M),cons(N,IL)) -> #activate(IL)
   #41: #U42(tt(),V2) -> #U43(isNatIList(activate(V2)))
   #42: #U42(tt(),V2) -> #isNatIList(activate(V2))
   #43: #U42(tt(),V2) -> #activate(V2)
   #44: #U51(tt(),V1,V2) -> #U52(isNat(activate(V1)),activate(V2))
   #45: #U51(tt(),V1,V2) -> #isNat(activate(V1))
   #46: #U51(tt(),V1,V2) -> #activate(V1)
   #47: #U51(tt(),V1,V2) -> #activate(V2)
   #48: #activate(n__cons(X1,X2)) -> #cons(activate(X1),X2)
   #49: #activate(n__cons(X1,X2)) -> #activate(X1)
   #50: #isNatIList(V) -> #U31(isNatIListKind(activate(V)),activate(V))
   #51: #isNatIList(V) -> #isNatIListKind(activate(V))
   #52: #isNatIList(V) -> #activate(V)
   #53: #isNatIList(V) -> #activate(V)
   #54: #isNat(n__s(V1)) -> #U21(isNatKind(activate(V1)),activate(V1))
   #55: #isNat(n__s(V1)) -> #isNatKind(activate(V1))
   #56: #isNat(n__s(V1)) -> #activate(V1)
   #57: #isNat(n__s(V1)) -> #activate(V1)
   #58: #U52(tt(),V2) -> #U53(isNatList(activate(V2)))
   #59: #U52(tt(),V2) -> #isNatList(activate(V2))
   #60: #U52(tt(),V2) -> #activate(V2)
   #61: #activate(n__s(X)) -> #s(activate(X))
   #62: #activate(n__s(X)) -> #activate(X)
   #63: #U61(tt(),V1,V2) -> #U62(isNat(activate(V1)),activate(V2))
   #64: #U61(tt(),V1,V2) -> #isNat(activate(V1))
   #65: #U61(tt(),V1,V2) -> #activate(V1)
   #66: #U61(tt(),V1,V2) -> #activate(V2)
   #67: #activate(n__isNatKind(X)) -> #isNatKind(X)
   #68: #isNatIListKind(n__take(V1,V2)) -> #and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2)))
   #69: #isNatIListKind(n__take(V1,V2)) -> #isNatKind(activate(V1))
   #70: #isNatIListKind(n__take(V1,V2)) -> #activate(V1)
   #71: #isNatIListKind(n__take(V1,V2)) -> #activate(V2)
   #72: #activate(n__zeros()) -> #zeros()
   #73: #and(tt(),X) -> #activate(X)
   #74: #take(0(),IL) -> #U81(and(isNatIList(IL),n__isNatIListKind(IL)))
   #75: #take(0(),IL) -> #and(isNatIList(IL),n__isNatIListKind(IL))
   #76: #take(0(),IL) -> #isNatIList(IL)
   #77: #isNatKind(n__s(V1)) -> #isNatKind(activate(V1))
   #78: #isNatKind(n__s(V1)) -> #activate(V1)
   #79: #isNat(n__length(V1)) -> #U11(isNatIListKind(activate(V1)),activate(V1))
   #80: #isNat(n__length(V1)) -> #isNatIListKind(activate(V1))
   #81: #isNat(n__length(V1)) -> #activate(V1)
   #82: #isNat(n__length(V1)) -> #activate(V1)
   #83: #activate(n__and(X1,X2)) -> #and(activate(X1),X2)
   #84: #activate(n__and(X1,X2)) -> #activate(X1)
   #85: #U71(tt(),L) -> #s(length(activate(L)))
   #86: #U71(tt(),L) -> #length(activate(L))
   #87: #U71(tt(),L) -> #activate(L)
   #88: #isNatKind(n__length(V1)) -> #isNatIListKind(activate(V1))
   #89: #isNatKind(n__length(V1)) -> #activate(V1)
   #90: #U91(tt(),IL,M,N) -> #cons(activate(N),n__take(activate(M),activate(IL)))
   #91: #U91(tt(),IL,M,N) -> #activate(N)
   #92: #U91(tt(),IL,M,N) -> #activate(M)
   #93: #U91(tt(),IL,M,N) -> #activate(IL)
   #94: #isNatIList(n__cons(V1,V2)) -> #U41(and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))),activate(V1),activate(V2))
   #95: #isNatIList(n__cons(V1,V2)) -> #and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2)))
   #96: #isNatIList(n__cons(V1,V2)) -> #isNatKind(activate(V1))
   #97: #isNatIList(n__cons(V1,V2)) -> #activate(V1)
   #98: #isNatIList(n__cons(V1,V2)) -> #activate(V2)
   #99: #isNatIList(n__cons(V1,V2)) -> #activate(V1)
   #100: #isNatIList(n__cons(V1,V2)) -> #activate(V2)
   #101: #isNatList(n__take(V1,V2)) -> #U61(and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))),activate(V1),activate(V2))
   #102: #isNatList(n__take(V1,V2)) -> #and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2)))
   #103: #isNatList(n__take(V1,V2)) -> #isNatKind(activate(V1))
   #104: #isNatList(n__take(V1,V2)) -> #activate(V1)
   #105: #isNatList(n__take(V1,V2)) -> #activate(V2)
   #106: #isNatList(n__take(V1,V2)) -> #activate(V1)
   #107: #isNatList(n__take(V1,V2)) -> #activate(V2)
   #108: #zeros() -> #cons(0(),n__zeros())
   #109: #zeros() -> #0()
   #110: #activate(n__0()) -> #0()
   #111: #U41(tt(),V1,V2) -> #U42(isNat(activate(V1)),activate(V2))
   #112: #U41(tt(),V1,V2) -> #isNat(activate(V1))
   #113: #U41(tt(),V1,V2) -> #activate(V1)
   #114: #U41(tt(),V1,V2) -> #activate(V2)
   #115: #U62(tt(),V2) -> #U63(isNatIList(activate(V2)))
   #116: #U62(tt(),V2) -> #isNatIList(activate(V2))
   #117: #U62(tt(),V2) -> #activate(V2)
   #118: #U21(tt(),V1) -> #U22(isNat(activate(V1)))
   #119: #U21(tt(),V1) -> #isNat(activate(V1))
   #120: #U21(tt(),V1) -> #activate(V1)
   #121: #U81(tt()) -> #nil()
Number of SCCs: 1, DPs: 103, edges: 903
	SCC { #2..14 #16..27 #29 #30 #32..40 #42..47 #49..57 #59 #60 #62..71 #73 #75..84 #86..89 #91..107 #111..114 #116 #117 #119 #120 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... succeeded.
   #0()	weight: 0
 #U32(x1)	weight: 0
#isNatIListKind(x1)	weight: x1
isNatKind(x1)	weight: x1
   U21(x1,x2)	weight: max{(/ 1 32) + x2, (/ 1 32) + x1}
isNatList(x1)	weight: (/ 1 32)
   U11(x1,x2)	weight: max{(/ 1 32) + x2, (/ 1 32) + x1}
#cons(x1,x2)	weight: 0
     s(x1)	weight: x1
#isNat(x1)	weight: (/ 1 16) + x1
#take(x1,x2)	weight: max{(/ 1 16) + x2, (/ 9 32) + x1}
   U42(x1,x2)	weight: max{(/ 3 16) + x2, (/ 1 16) + x1}
   U91(x1,x2,x3,x4)	weight: max{0, (/ 3 8) + x4, (/ 5 16) + x3, (/ 11 32) + x2}
activate(x1)	weight: x1
n__isNatIListKind(x1)	weight: x1
  take(x1,x2)	weight: max{(/ 11 32) + x2, (/ 5 16) + x1}
   U71(x1,x2)	weight: max{0, x2}
n__isNatKind(x1)	weight: x1
 #U81(x1)	weight: 0
   and(x1,x2)	weight: max{x2, x1}
n__zeros()	weight: (/ 7 32)
isNatIList(x1)	weight: (/ 1 32)
   U43(x1)	weight: x1
#activate(x1)	weight: x1
 #U53(x1)	weight: 0
 #U43(x1)	weight: 0
   U63(x1)	weight: 0
 zeros()	weight: (/ 7 32)
n__nil()	weight: (/ 1 16)
 #U52(x1,x2)	weight: max{x2, x1}
   U12(x1)	weight: (/ 1 16)
  n__s(x1)	weight: x1
 #U42(x1,x2)	weight: max{x2, x1}
 #U12(x1)	weight: 0
 #U62(x1,x2)	weight: max{0, (/ 1 32) + x2}
     0()	weight: (/ 1 16)
#zeros()	weight: 0
n__take(x1,x2)	weight: max{(/ 11 32) + x2, (/ 5 16) + x1}
#isNatList(x1)	weight: x1
   #s(x1)	weight: 0
n__cons(x1,x2)	weight: max{x2, (/ 5 32) + x1}
   nil()	weight: (/ 1 16)
isNatIListKind(x1)	weight: x1
n__isNat(x1)	weight: (/ 3 32) + x1
   U62(x1,x2)	weight: 0
 #U63(x1)	weight: 0
 #nil()	weight: 0
   U32(x1)	weight: x1
  n__0()	weight: (/ 1 16)
n__length(x1)	weight: x1
 isNat(x1)	weight: (/ 3 32) + x1
   U52(x1,x2)	weight: max{0, (/ 1 16) + x1}
   U61(x1,x2,x3)	weight: max{0, (/ 1 16) + x3}
 #U51(x1,x2,x3)	weight: max{0, x3, (/ 5 32) + x2}
 #U11(x1,x2)	weight: max{(/ 1 32) + x2, (/ 1 32) + x1}
   U31(x1,x2)	weight: 0
 #U41(x1,x2,x3)	weight: max{0, x3, (/ 1 8) + x2}
  cons(x1,x2)	weight: max{x2, (/ 5 32) + x1}
#isNatIList(x1)	weight: x1
 #U21(x1,x2)	weight: max{(/ 1 16) + x2, (/ 1 32) + x1}
   U81(x1)	weight: (/ 3 8)
 #U22(x1)	weight: 0
    tt()	weight: (/ 1 16)
n__and(x1,x2)	weight: max{x2, x1}
 #U71(x1,x2)	weight: max{0, x2}
   U22(x1)	weight: (/ 1 16)
   U51(x1,x2,x3)	weight: max{0, (/ 1 16) + x1}
#isNatKind(x1)	weight: x1
   U53(x1)	weight: 0
length(x1)	weight: x1
#length(x1)	weight: x1
   U41(x1,x2,x3)	weight: max{0, (/ 5 32) + x2, (/ 1 16) + x1}
 #U31(x1,x2)	weight: max{x2, x1}
 #and(x1,x2)	weight: max{0, x2}
 #U91(x1,x2,x3,x4)	weight: max{0, (/ 1 32) + x4, (/ 1 4) + x3, (/ 1 32) + x2}
 #U61(x1,x2,x3)	weight: max{(/ 9 32) + x3, (/ 9 32) + x2, (/ 9 32) + x1}
    Usable rules: { 1..5 17..23 27..33 37..63 }
    Removed DPs: #2 #3 #5 #6 #10 #11 #13 #16..18 #20 #22 #34..40 #45 #46 #49 #55..57 #63..66 #68..71 #75 #76 #79..82 #91..93 #96 #97 #99 #101..107 #112 #113 #116 #117 #120
Number of SCCs: 3, DPs: 35, edges: 152
	SCC { #54 #119 }
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
 #U32(x1)	weight: 0; 0
#isNatIListKind(x1)	weight: 0; 0
isNatKind(x1)	weight: (max (/ 5 32) 0); 0
   U21(x1,x2)	weight: (max (/ 3 16) 0); 0
isNatList(x1)	weight: max{0, (/ 1 2) + x1_1 + x1_2}; x1_2
   U11(x1,x2)	weight: max{0, (/ 17 32) + x2_1}; 0
#cons(x1,x2)	weight: 0; 0
     s(x1)	weight: max{0, (/ 3 32) + x1_1}; 0
#isNat(x1)	weight: max{0, (- (/ 1 32)) + x1_1 + x1_2}; 0
#take(x1,x2)	weight: 0; 0
   U42(x1,x2)	weight: max{0, (- (/ 3 16)) + x2_2 + x1_1}; (- (/ 5 32)) + x1_2
   U91(x1,x2,x3,x4)	weight: max{0, (/ 1 8) + x3_1 + x3_2}; x3_2
activate(x1)	weight: max{0, x1_1}; x1_2
n__isNatIListKind(x1)	weight: (max (/ 5 32) 0); 0
  take(x1,x2)	weight: max{0, (/ 1 32) + x1_1}; x1_2
   U71(x1,x2)	weight: max{0, (/ 7 16) + x2_1 + x1_2}; x1_2
n__isNatKind(x1)	weight: (max (/ 5 32) 0); 0
 #U81(x1)	weight: 0; 0
   and(x1,x2)	weight: max{0, (- (/ 5 32)) + x2_1 + x1_1}; x1_2
n__zeros()	weight: (/ 1 32); (- (/ 23 32))
isNatIList(x1)	weight: max{0, (/ 13 16) + x1_1 + x1_2}; (- (/ 3 32)) + x1_2
   U43(x1)	weight: max{0, (/ 1 8) + x1_2}; (- (/ 1 32)) + x1_2
#activate(x1)	weight: 0; 0
 #U53(x1)	weight: 0; 0
 #U43(x1)	weight: 0; 0
   U63(x1)	weight: (max (/ 5 32) 0); 0
 zeros()	weight: (/ 1 32); (- (/ 23 32))
n__nil()	weight: (/ 1 32); 0
 #U52(x1,x2)	weight: 0; 0
   U12(x1)	weight: max{0, (/ 1 32) + x1_1}; x1_2
  n__s(x1)	weight: max{0, (/ 3 32) + x1_1}; 0
 #U42(x1,x2)	weight: 0; 0
 #U12(x1)	weight: 0; 0
 #U62(x1,x2)	weight: 0; 0
     0()	weight: (/ 1 32); 0
#zeros()	weight: 0; 0
n__take(x1,x2)	weight: max{0, (/ 1 32) + x1_1}; x1_2
#isNatList(x1)	weight: 0; 0
   #s(x1)	weight: 0; 0
n__cons(x1,x2)	weight: max{0, (/ 3 32) + x2_1 + x2_2}; x2_2
   nil()	weight: (/ 1 32); 0
isNatIListKind(x1)	weight: (max (/ 5 32) 0); 0
n__isNat(x1)	weight: max{0, (/ 3 16) + x1_1}; x1_2
   U62(x1,x2)	weight: max{0, (/ 5 32) + x1_2}; x1_2
 #U63(x1)	weight: 0; 0
 #nil()	weight: 0; 0
   U32(x1)	weight: (max (/ 1 8) 0); (- (/ 1 32))
  n__0()	weight: (/ 1 32); 0
n__length(x1)	weight: max{0, (/ 11 32) + x1_1}; 0
 isNat(x1)	weight: max{0, (/ 3 16) + x1_1}; x1_2
   U52(x1,x2)	weight: max{0, (/ 5 32) + x2_2}; x2_2
   U61(x1,x2,x3)	weight: max{0, (/ 5 32) + x2_2}; x2_2
 #U51(x1,x2,x3)	weight: 0; 0
 #U11(x1,x2)	weight: 0; 0
   U31(x1,x2)	weight: max{0, (/ 27 32) + x2_2}; (- (/ 1 16))
 #U41(x1,x2,x3)	weight: 0; 0
  cons(x1,x2)	weight: max{0, (/ 3 32) + x2_1 + x2_2}; x2_2
#isNatIList(x1)	weight: 0; 0
 #U21(x1,x2)	weight: max{0, (/ 1 32) + x2_1 + x2_2}; 0
   U81(x1)	weight: (max (/ 1 32) 0); 0
 #U22(x1)	weight: 0; 0
    tt()	weight: (/ 5 32); 0
n__and(x1,x2)	weight: max{0, (- (/ 5 32)) + x2_1 + x1_1}; x1_2
 #U71(x1,x2)	weight: 0; 0
   U22(x1)	weight: max{0, (/ 5 32) + x1_2}; 0
   U51(x1,x2,x3)	weight: max{0, x3_2 + x1_1}; x3_2
#isNatKind(x1)	weight: 0; 0
   U53(x1)	weight: max{0, (/ 5 32) + x1_2}; x1_2
length(x1)	weight: max{0, (/ 11 32) + x1_1}; 0
#length(x1)	weight: 0; 0
   U41(x1,x2,x3)	weight: max{0, (/ 15 16) + x3_2 + x2_2}; (- (/ 1 16)) + x2_2
 #U31(x1,x2)	weight: 0; 0
 #and(x1,x2)	weight: 0; 0
 #U91(x1,x2,x3,x4)	weight: 0; 0
 #U61(x1,x2,x3)	weight: 0; 0
    Usable rules: { 1..5 11..23 27..63 }
    Removed DPs: #54
Number of SCCs: 2, DPs: 33, edges: 150
	SCC { #42 #94 #111 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... QWPOpS(PosReal,>,MaxSum)... Order(PosReal,>,Sum-Sum; PosReal,≥,Sum-Sum)...