Input TRS:
    1: active(U11(tt(),N)) -> mark(N)
    2: active(U21(tt(),M,N)) -> mark(s(plus(N,M)))
    3: active(U31(tt())) -> mark(0())
    4: active(U41(tt(),M,N)) -> mark(plus(x(N,M),N))
    5: active(and(tt(),X)) -> mark(X)
    6: active(isNat(0())) -> mark(tt())
    7: active(isNat(plus(V1,V2))) -> mark(and(isNat(V1),isNat(V2)))
    8: active(isNat(s(V1))) -> mark(isNat(V1))
    9: active(isNat(x(V1,V2))) -> mark(and(isNat(V1),isNat(V2)))
    10: active(plus(N,0())) -> mark(U11(isNat(N),N))
    11: active(plus(N,s(M))) -> mark(U21(and(isNat(M),isNat(N)),M,N))
    12: active(x(N,0())) -> mark(U31(isNat(N)))
    13: active(x(N,s(M))) -> mark(U41(and(isNat(M),isNat(N)),M,N))
    14: active(U11(X1,X2)) -> U11(active(X1),X2)
    15: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
    16: active(s(X)) -> s(active(X))
    17: active(plus(X1,X2)) -> plus(active(X1),X2)
    18: active(plus(X1,X2)) -> plus(X1,active(X2))
    19: active(U31(X)) -> U31(active(X))
    20: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
    21: active(x(X1,X2)) -> x(active(X1),X2)
    22: active(x(X1,X2)) -> x(X1,active(X2))
    23: active(and(X1,X2)) -> and(active(X1),X2)
    24: U11(mark(X1),X2) -> mark(U11(X1,X2))
    25: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
    26: s(mark(X)) -> mark(s(X))
    27: plus(mark(X1),X2) -> mark(plus(X1,X2))
    28: plus(X1,mark(X2)) -> mark(plus(X1,X2))
    29: U31(mark(X)) -> mark(U31(X))
    30: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
    31: x(mark(X1),X2) -> mark(x(X1,X2))
    32: x(X1,mark(X2)) -> mark(x(X1,X2))
    33: and(mark(X1),X2) -> mark(and(X1,X2))
    34: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
    35: proper(tt()) -> ok(tt())
    36: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
    37: proper(s(X)) -> s(proper(X))
    38: proper(plus(X1,X2)) -> plus(proper(X1),proper(X2))
    39: proper(U31(X)) -> U31(proper(X))
    40: proper(0()) -> ok(0())
    41: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
    42: proper(x(X1,X2)) -> x(proper(X1),proper(X2))
    43: proper(and(X1,X2)) -> and(proper(X1),proper(X2))
    44: proper(isNat(X)) -> isNat(proper(X))
    45: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
    46: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
    47: s(ok(X)) -> ok(s(X))
    48: plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
    49: U31(ok(X)) -> ok(U31(X))
    50: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
    51: x(ok(X1),ok(X2)) -> ok(x(X1,X2))
    52: and(ok(X1),ok(X2)) -> ok(and(X1,X2))
    53: isNat(ok(X)) -> ok(isNat(X))
    54: top(mark(X)) -> top(proper(X))
    55: top(ok(X)) -> top(active(X))
Number of strict rules: 55
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #active(U21(tt(),M,N)) -> #s(plus(N,M))
   #2: #active(U21(tt(),M,N)) -> #plus(N,M)
   #3: #proper(and(X1,X2)) -> #and(proper(X1),proper(X2))
   #4: #proper(and(X1,X2)) -> #proper(X1)
   #5: #proper(and(X1,X2)) -> #proper(X2)
   #6: #U31(mark(X)) -> #U31(X)
   #7: #U21(ok(X1),ok(X2),ok(X3)) -> #U21(X1,X2,X3)
   #8: #proper(x(X1,X2)) -> #x(proper(X1),proper(X2))
   #9: #proper(x(X1,X2)) -> #proper(X1)
   #10: #proper(x(X1,X2)) -> #proper(X2)
   #11: #proper(U41(X1,X2,X3)) -> #U41(proper(X1),proper(X2),proper(X3))
   #12: #proper(U41(X1,X2,X3)) -> #proper(X1)
   #13: #proper(U41(X1,X2,X3)) -> #proper(X2)
   #14: #proper(U41(X1,X2,X3)) -> #proper(X3)
   #15: #proper(s(X)) -> #s(proper(X))
   #16: #proper(s(X)) -> #proper(X)
   #17: #s(ok(X)) -> #s(X)
   #18: #isNat(ok(X)) -> #isNat(X)
   #19: #plus(ok(X1),ok(X2)) -> #plus(X1,X2)
   #20: #proper(plus(X1,X2)) -> #plus(proper(X1),proper(X2))
   #21: #proper(plus(X1,X2)) -> #proper(X1)
   #22: #proper(plus(X1,X2)) -> #proper(X2)
   #23: #top(ok(X)) -> #top(active(X))
   #24: #top(ok(X)) -> #active(X)
   #25: #x(ok(X1),ok(X2)) -> #x(X1,X2)
   #26: #active(x(N,s(M))) -> #U41(and(isNat(M),isNat(N)),M,N)
   #27: #active(x(N,s(M))) -> #and(isNat(M),isNat(N))
   #28: #active(x(N,s(M))) -> #isNat(M)
   #29: #active(x(N,s(M))) -> #isNat(N)
   #30: #active(isNat(x(V1,V2))) -> #and(isNat(V1),isNat(V2))
   #31: #active(isNat(x(V1,V2))) -> #isNat(V1)
   #32: #active(isNat(x(V1,V2))) -> #isNat(V2)
   #33: #active(plus(N,s(M))) -> #U21(and(isNat(M),isNat(N)),M,N)
   #34: #active(plus(N,s(M))) -> #and(isNat(M),isNat(N))
   #35: #active(plus(N,s(M))) -> #isNat(M)
   #36: #active(plus(N,s(M))) -> #isNat(N)
   #37: #U11(mark(X1),X2) -> #U11(X1,X2)
   #38: #active(and(X1,X2)) -> #and(active(X1),X2)
   #39: #active(and(X1,X2)) -> #active(X1)
   #40: #U11(ok(X1),ok(X2)) -> #U11(X1,X2)
   #41: #active(x(N,0())) -> #U31(isNat(N))
   #42: #active(x(N,0())) -> #isNat(N)
   #43: #x(mark(X1),X2) -> #x(X1,X2)
   #44: #active(U11(X1,X2)) -> #U11(active(X1),X2)
   #45: #active(U11(X1,X2)) -> #active(X1)
   #46: #U41(mark(X1),X2,X3) -> #U41(X1,X2,X3)
   #47: #and(ok(X1),ok(X2)) -> #and(X1,X2)
   #48: #U31(ok(X)) -> #U31(X)
   #49: #U21(mark(X1),X2,X3) -> #U21(X1,X2,X3)
   #50: #active(U41(X1,X2,X3)) -> #U41(active(X1),X2,X3)
   #51: #active(U41(X1,X2,X3)) -> #active(X1)
   #52: #active(isNat(plus(V1,V2))) -> #and(isNat(V1),isNat(V2))
   #53: #active(isNat(plus(V1,V2))) -> #isNat(V1)
   #54: #active(isNat(plus(V1,V2))) -> #isNat(V2)
   #55: #proper(U31(X)) -> #U31(proper(X))
   #56: #proper(U31(X)) -> #proper(X)
   #57: #active(plus(N,0())) -> #U11(isNat(N),N)
   #58: #active(plus(N,0())) -> #isNat(N)
   #59: #and(mark(X1),X2) -> #and(X1,X2)
   #60: #proper(isNat(X)) -> #isNat(proper(X))
   #61: #proper(isNat(X)) -> #proper(X)
   #62: #plus(X1,mark(X2)) -> #plus(X1,X2)
   #63: #active(x(X1,X2)) -> #x(X1,active(X2))
   #64: #active(x(X1,X2)) -> #active(X2)
   #65: #proper(U11(X1,X2)) -> #U11(proper(X1),proper(X2))
   #66: #proper(U11(X1,X2)) -> #proper(X1)
   #67: #proper(U11(X1,X2)) -> #proper(X2)
   #68: #plus(mark(X1),X2) -> #plus(X1,X2)
   #69: #active(plus(X1,X2)) -> #plus(active(X1),X2)
   #70: #active(plus(X1,X2)) -> #active(X1)
   #71: #x(X1,mark(X2)) -> #x(X1,X2)
   #72: #active(U31(X)) -> #U31(active(X))
   #73: #active(U31(X)) -> #active(X)
   #74: #s(mark(X)) -> #s(X)
   #75: #proper(U21(X1,X2,X3)) -> #U21(proper(X1),proper(X2),proper(X3))
   #76: #proper(U21(X1,X2,X3)) -> #proper(X1)
   #77: #proper(U21(X1,X2,X3)) -> #proper(X2)
   #78: #proper(U21(X1,X2,X3)) -> #proper(X3)
   #79: #active(x(X1,X2)) -> #x(active(X1),X2)
   #80: #active(x(X1,X2)) -> #active(X1)
   #81: #active(s(X)) -> #s(active(X))
   #82: #active(s(X)) -> #active(X)
   #83: #top(mark(X)) -> #top(proper(X))
   #84: #top(mark(X)) -> #proper(X)
   #85: #active(isNat(s(V1))) -> #isNat(V1)
   #86: #active(U21(X1,X2,X3)) -> #U21(active(X1),X2,X3)
   #87: #active(U21(X1,X2,X3)) -> #active(X1)
   #88: #active(U41(tt(),M,N)) -> #plus(x(N,M),N)
   #89: #active(U41(tt(),M,N)) -> #x(N,M)
   #90: #U41(ok(X1),ok(X2),ok(X3)) -> #U41(X1,X2,X3)
   #91: #active(plus(X1,X2)) -> #plus(X1,active(X2))
   #92: #active(plus(X1,X2)) -> #active(X2)
Number of SCCs: 12, DPs: 48, edges: 436
	SCC { #18 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   U21(x1,x2,x3)	weight: 0
   U11(x1,x2)	weight: 0
     s(x1)	weight: 0
#isNat(x1)	weight: x1
   top(x1)	weight: 0
   and(x1,x2)	weight: 0
#plus(x1,x2)	weight: 0
 #top(x1)	weight: 0
     x(x1,x2)	weight: 0
proper(x1)	weight: 0
    ok(x1)	weight: (/ 1 2) + x1
     0()	weight: 0
   #x(x1,x2)	weight: 0
   #s(x1)	weight: 0
  mark(x1)	weight: 0
#proper(x1)	weight: 0
 isNat(x1)	weight: 0
  plus(x1,x2)	weight: 0
 #U11(x1,x2)	weight: 0
active(x1)	weight: 0
   U31(x1)	weight: 0
 #U41(x1,x2,x3)	weight: 0
#active(x1)	weight: 0
 #U21(x1,x2,x3)	weight: 0
    tt()	weight: 0
   U41(x1,x2,x3)	weight: 0
 #U31(x1)	weight: 0
 #and(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #18
Number of SCCs: 11, DPs: 47, edges: 435
	SCC { #17 #74 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   U21(x1,x2,x3)	weight: 0
   U11(x1,x2)	weight: 0
     s(x1)	weight: 0
#isNat(x1)	weight: 0
   top(x1)	weight: 0
   and(x1,x2)	weight: 0
#plus(x1,x2)	weight: 0
 #top(x1)	weight: 0
     x(x1,x2)	weight: 0
proper(x1)	weight: 0
    ok(x1)	weight: (/ 1 2) + x1
     0()	weight: 0
   #x(x1,x2)	weight: 0
   #s(x1)	weight: x1
  mark(x1)	weight: (/ 1 2) + x1
#proper(x1)	weight: 0
 isNat(x1)	weight: 0
  plus(x1,x2)	weight: 0
 #U11(x1,x2)	weight: 0
active(x1)	weight: 0
   U31(x1)	weight: 0
 #U41(x1,x2,x3)	weight: 0
#active(x1)	weight: 0
 #U21(x1,x2,x3)	weight: 0
    tt()	weight: 0
   U41(x1,x2,x3)	weight: 0
 #U31(x1)	weight: 0
 #and(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #17 #74
Number of SCCs: 10, DPs: 45, edges: 431
	SCC { #6 #48 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   U21(x1,x2,x3)	weight: 0
   U11(x1,x2)	weight: 0
     s(x1)	weight: 0
#isNat(x1)	weight: 0
   top(x1)	weight: 0
   and(x1,x2)	weight: 0
#plus(x1,x2)	weight: 0
 #top(x1)	weight: 0
     x(x1,x2)	weight: 0
proper(x1)	weight: 0
    ok(x1)	weight: (/ 1 2) + x1
     0()	weight: 0
   #x(x1,x2)	weight: 0
   #s(x1)	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
#proper(x1)	weight: 0
 isNat(x1)	weight: 0
  plus(x1,x2)	weight: 0
 #U11(x1,x2)	weight: 0
active(x1)	weight: 0
   U31(x1)	weight: 0
 #U41(x1,x2,x3)	weight: 0
#active(x1)	weight: 0
 #U21(x1,x2,x3)	weight: 0
    tt()	weight: 0
   U41(x1,x2,x3)	weight: 0
 #U31(x1)	weight: x1
 #and(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #6 #48
Number of SCCs: 9, DPs: 43, edges: 427
	SCC { #23 #83 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... succeeded.
   U21(x1,x2,x3)	status: [x3,x2,x1]	precedence above: U11 s and proper 0 mark isNat plus active tt
   U11(x1,x2)	status: [x2,x1]	precedence above: mark active
     s(x1)	status: [x1]	precedence above: 0 mark isNat active tt
#isNat(x1)	status: []	precedence above:
   top(x1)	status: []	precedence above:
   and(x1,x2)	status: [x2,x1]	precedence above: mark active
#plus(x1,x2)	status: []	precedence above:
 #top(x1)	status: [x1]	precedence above:
     x(x1,x2)	status: [x1,x2]	precedence above: U21 U11 s and proper 0 mark isNat plus active U31 tt U41
proper(x1)	status: x1
    ok(x1)	status: x1
     0()	status: []	precedence above: mark active tt
   #x(x1,x2)	status: [x2]	precedence above:
   #s(x1)	status: []	precedence above:
  mark(x1)	status: [x1]	precedence above: active
#proper(x1)	status: []	precedence above:
 isNat(x1)	status: [x1]	precedence above: mark active tt
  plus(x1,x2)	status: [x1,x2]	precedence above: U21 U11 s and proper 0 mark isNat active tt
 #U11(x1,x2)	status: [x2,x1]	precedence above:
active(x1)	status: x1
   U31(x1)	status: [x1]	precedence above: s proper 0 mark isNat active tt
 #U41(x1,x2,x3)	status: [x1]	precedence above:
#active(x1)	status: []	precedence above:
 #U21(x1,x2,x3)	status: [x2,x1]	precedence above:
    tt()	status: []	precedence above:
   U41(x1,x2,x3)	status: [x3,x2,x1]	precedence above: U21 U11 s and x proper 0 mark isNat plus active U31 tt
 #U31(x1)	status: []	precedence above:
 #and(x1,x2)	status: [x2]	precedence above:
    Usable rules: { 1..53 }
    Removed DPs: #83
Number of SCCs: 9, DPs: 42, edges: 424
	SCC { #23 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   U21(x1,x2,x3)	weight: (/ 1 4) + x2
   U11(x1,x2)	weight: (/ 1 4) + x1
     s(x1)	weight: (/ 1 4) + x1
#isNat(x1)	weight: 0
   top(x1)	weight: 0
   and(x1,x2)	weight: x1
#plus(x1,x2)	weight: 0
 #top(x1)	weight: x1
     x(x1,x2)	weight: (/ 1 4) + x2
proper(x1)	weight: (/ 1 2) + x1
    ok(x1)	weight: (/ 1 2) + x1
     0()	weight: 0
   #x(x1,x2)	weight: 0
   #s(x1)	weight: 0
  mark(x1)	weight: 0
#proper(x1)	weight: 0
 isNat(x1)	weight: (/ 1 4) + x1
  plus(x1,x2)	weight: x2
 #U11(x1,x2)	weight: 0
active(x1)	weight: (/ 1 4) + x1
   U31(x1)	weight: (/ 1 4) + x1
 #U41(x1,x2,x3)	weight: 0
#active(x1)	weight: 0
 #U21(x1,x2,x3)	weight: 0
    tt()	weight: 0
   U41(x1,x2,x3)	weight: (/ 1 4) + x3
 #U31(x1)	weight: 0
 #and(x1,x2)	weight: 0
    Usable rules: { 1..33 45..53 }
    Removed DPs: #23
Number of SCCs: 8, DPs: 41, edges: 423
	SCC { #37 #40 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   U21(x1,x2,x3)	weight: (/ 1 4) + x2
   U11(x1,x2)	weight: (/ 1 4) + x1
     s(x1)	weight: (/ 1 4) + x1
#isNat(x1)	weight: 0
   top(x1)	weight: 0
   and(x1,x2)	weight: x1
#plus(x1,x2)	weight: 0
 #top(x1)	weight: x1
     x(x1,x2)	weight: (/ 1 4) + x2
proper(x1)	weight: (/ 1 2) + x1
    ok(x1)	weight: (/ 1 2) + x1
     0()	weight: 0
   #x(x1,x2)	weight: 0
   #s(x1)	weight: 0
  mark(x1)	weight: 0
#proper(x1)	weight: 0
 isNat(x1)	weight: (/ 1 4) + x1
  plus(x1,x2)	weight: x2
 #U11(x1,x2)	weight: x2
active(x1)	weight: (/ 1 4) + x1
   U31(x1)	weight: (/ 1 4) + x1
 #U41(x1,x2,x3)	weight: 0
#active(x1)	weight: 0
 #U21(x1,x2,x3)	weight: 0
    tt()	weight: 0
   U41(x1,x2,x3)	weight: (/ 1 4) + x3
 #U31(x1)	weight: 0
 #and(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #40
Number of SCCs: 9, DPs: 40, edges: 420
	SCC { #37 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   U21(x1,x2,x3)	weight: 0
   U11(x1,x2)	weight: (/ 1 4)
     s(x1)	weight: (/ 1 4) + x1
#isNat(x1)	weight: 0
   top(x1)	weight: 0
   and(x1,x2)	weight: x1
#plus(x1,x2)	weight: 0
 #top(x1)	weight: 0
     x(x1,x2)	weight: x2
proper(x1)	weight: (/ 1 2) + x1
    ok(x1)	weight: (/ 1 4) + x1
     0()	weight: 0
   #x(x1,x2)	weight: 0
   #s(x1)	weight: 0
  mark(x1)	weight: (/ 1 4) + x1
#proper(x1)	weight: 0
 isNat(x1)	weight: (/ 1 4) + x1
  plus(x1,x2)	weight: 0
 #U11(x1,x2)	weight: x1
active(x1)	weight: (/ 3 4) + x1
   U31(x1)	weight: (/ 1 4) + x1
 #U41(x1,x2,x3)	weight: 0
#active(x1)	weight: 0
 #U21(x1,x2,x3)	weight: 0
    tt()	weight: 0
   U41(x1,x2,x3)	weight: x3
 #U31(x1)	weight: 0
 #and(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #37
Number of SCCs: 8, DPs: 39, edges: 419
	SCC { #47 #59 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   U21(x1,x2,x3)	weight: 0
   U11(x1,x2)	weight: (/ 1 4)
     s(x1)	weight: (/ 1 4) + x1
#isNat(x1)	weight: 0
   top(x1)	weight: 0
   and(x1,x2)	weight: x1
#plus(x1,x2)	weight: 0
 #top(x1)	weight: 0
     x(x1,x2)	weight: x2
proper(x1)	weight: (/ 1 2) + x1
    ok(x1)	weight: (/ 1 4) + x1
     0()	weight: 0
   #x(x1,x2)	weight: 0
   #s(x1)	weight: 0
  mark(x1)	weight: (/ 1 4) + x1
#proper(x1)	weight: 0
 isNat(x1)	weight: (/ 1 4) + x1
  plus(x1,x2)	weight: 0
 #U11(x1,x2)	weight: 0
active(x1)	weight: (/ 3 4) + x1
   U31(x1)	weight: (/ 1 4) + x1
 #U41(x1,x2,x3)	weight: 0
#active(x1)	weight: 0
 #U21(x1,x2,x3)	weight: 0
    tt()	weight: 0
   U41(x1,x2,x3)	weight: x3
 #U31(x1)	weight: 0
 #and(x1,x2)	weight: x1
    Usable rules: { }
    Removed DPs: #47 #59
Number of SCCs: 8, DPs: 37, edges: 415
	SCC { #7 #49 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   U21(x1,x2,x3)	weight: 0
   U11(x1,x2)	weight: (/ 1 4)
     s(x1)	weight: (/ 1 4) + x1
#isNat(x1)	weight: 0
   top(x1)	weight: 0
   and(x1,x2)	weight: x1
#plus(x1,x2)	weight: 0
 #top(x1)	weight: 0
     x(x1,x2)	weight: x2
proper(x1)	weight: (/ 1 2) + x1
    ok(x1)	weight: (/ 1 4) + x1
     0()	weight: 0
   #x(x1,x2)	weight: 0
   #s(x1)	weight: 0
  mark(x1)	weight: (/ 1 4) + x1
#proper(x1)	weight: 0
 isNat(x1)	weight: (/ 1 4) + x1
  plus(x1,x2)	weight: 0
 #U11(x1,x2)	weight: 0
active(x1)	weight: (/ 3 4) + x1
   U31(x1)	weight: (/ 1 4) + x1
 #U41(x1,x2,x3)	weight: 0
#active(x1)	weight: 0
 #U21(x1,x2,x3)	weight: x2
    tt()	weight: 0
   U41(x1,x2,x3)	weight: x3
 #U31(x1)	weight: 0
 #and(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #7
Number of SCCs: 8, DPs: 36, edges: 412
	SCC { #49 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   U21(x1,x2,x3)	weight: 0
   U11(x1,x2)	weight: (/ 1 4)
     s(x1)	weight: (/ 1 4) + x1
#isNat(x1)	weight: 0
   top(x1)	weight: 0
   and(x1,x2)	weight: x1
#plus(x1,x2)	weight: 0
 #top(x1)	weight: 0
     x(x1,x2)	weight: x2
proper(x1)	weight: (/ 1 2) + x1
    ok(x1)	weight: (/ 1 4) + x1
     0()	weight: 0
   #x(x1,x2)	weight: 0
   #s(x1)	weight: 0
  mark(x1)	weight: (/ 1 4) + x1
#proper(x1)	weight: 0
 isNat(x1)	weight: (/ 1 4) + x1
  plus(x1,x2)	weight: 0
 #U11(x1,x2)	weight: 0
active(x1)	weight: (/ 3 4) + x1
   U31(x1)	weight: (/ 1 4) + x1
 #U41(x1,x2,x3)	weight: 0
#active(x1)	weight: 0
 #U21(x1,x2,x3)	weight: x1
    tt()	weight: 0
   U41(x1,x2,x3)	weight: x3
 #U31(x1)	weight: 0
 #and(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #49
Number of SCCs: 7, DPs: 35, edges: 411
	SCC { #46 #90 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   U21(x1,x2,x3)	weight: 0
   U11(x1,x2)	weight: (/ 1 4)
     s(x1)	weight: (/ 1 4) + x1
#isNat(x1)	weight: 0
   top(x1)	weight: 0
   and(x1,x2)	weight: x1
#plus(x1,x2)	weight: 0
 #top(x1)	weight: 0
     x(x1,x2)	weight: x2
proper(x1)	weight: (/ 1 2) + x1
    ok(x1)	weight: (/ 1 4) + x1
     0()	weight: 0
   #x(x1,x2)	weight: 0
   #s(x1)	weight: 0
  mark(x1)	weight: (/ 1 4) + x1
#proper(x1)	weight: 0
 isNat(x1)	weight: (/ 1 4) + x1
  plus(x1,x2)	weight: 0
 #U11(x1,x2)	weight: 0
active(x1)	weight: (/ 3 4) + x1
   U31(x1)	weight: (/ 1 4) + x1
 #U41(x1,x2,x3)	weight: x1
#active(x1)	weight: 0
 #U21(x1,x2,x3)	weight: 0
    tt()	weight: 0
   U41(x1,x2,x3)	weight: x3
 #U31(x1)	weight: 0
 #and(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #46 #90
Number of SCCs: 7, DPs: 33, edges: 407
	SCC { #19 #62 #68 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   U21(x1,x2,x3)	weight: 0
   U11(x1,x2)	weight: (/ 1 4)
     s(x1)	weight: (/ 1 4) + x1
#isNat(x1)	weight: 0
   top(x1)	weight: 0
   and(x1,x2)	weight: x1
#plus(x1,x2)	weight: x2
 #top(x1)	weight: 0
     x(x1,x2)	weight: x2
proper(x1)	weight: (/ 1 2) + x1
    ok(x1)	weight: (/ 1 4) + x1
     0()	weight: 0
   #x(x1,x2)	weight: 0
   #s(x1)	weight: 0
  mark(x1)	weight: (/ 1 4) + x1
#proper(x1)	weight: 0
 isNat(x1)	weight: (/ 1 4) + x1
  plus(x1,x2)	weight: 0
 #U11(x1,x2)	weight: 0
active(x1)	weight: (/ 3 4) + x1
   U31(x1)	weight: (/ 1 4) + x1
 #U41(x1,x2,x3)	weight: 0
#active(x1)	weight: 0
 #U21(x1,x2,x3)	weight: 0
    tt()	weight: 0
   U41(x1,x2,x3)	weight: x3
 #U31(x1)	weight: 0
 #and(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #19 #62
Number of SCCs: 7, DPs: 31, edges: 399
	SCC { #68 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   U21(x1,x2,x3)	weight: 0
   U11(x1,x2)	weight: (/ 1 4)
     s(x1)	weight: (/ 1 4) + x1
#isNat(x1)	weight: 0
   top(x1)	weight: 0
   and(x1,x2)	weight: x1
#plus(x1,x2)	weight: x1
 #top(x1)	weight: 0
     x(x1,x2)	weight: x2
proper(x1)	weight: (/ 1 2) + x1
    ok(x1)	weight: (/ 1 4) + x1
     0()	weight: 0
   #x(x1,x2)	weight: 0
   #s(x1)	weight: 0
  mark(x1)	weight: (/ 1 4) + x1
#proper(x1)	weight: 0
 isNat(x1)	weight: (/ 1 4) + x1
  plus(x1,x2)	weight: 0
 #U11(x1,x2)	weight: 0
active(x1)	weight: (/ 3 4) + x1
   U31(x1)	weight: (/ 1 4) + x1
 #U41(x1,x2,x3)	weight: 0
#active(x1)	weight: 0
 #U21(x1,x2,x3)	weight: 0
    tt()	weight: 0
   U41(x1,x2,x3)	weight: x3
 #U31(x1)	weight: 0
 #and(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #68
Number of SCCs: 6, DPs: 30, edges: 398
	SCC { #25 #43 #71 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   U21(x1,x2,x3)	weight: 0
   U11(x1,x2)	weight: (/ 1 4)
     s(x1)	weight: (/ 1 4) + x1
#isNat(x1)	weight: 0
   top(x1)	weight: 0
   and(x1,x2)	weight: x1
#plus(x1,x2)	weight: 0
 #top(x1)	weight: 0
     x(x1,x2)	weight: x2
proper(x1)	weight: (/ 1 2) + x1
    ok(x1)	weight: (/ 1 4) + x1
     0()	weight: 0
   #x(x1,x2)	weight: x2
   #s(x1)	weight: 0
  mark(x1)	weight: (/ 1 4) + x1
#proper(x1)	weight: 0
 isNat(x1)	weight: (/ 1 4) + x1
  plus(x1,x2)	weight: 0
 #U11(x1,x2)	weight: 0
active(x1)	weight: (/ 3 4) + x1
   U31(x1)	weight: (/ 1 4) + x1
 #U41(x1,x2,x3)	weight: 0
#active(x1)	weight: 0
 #U21(x1,x2,x3)	weight: 0
    tt()	weight: 0
   U41(x1,x2,x3)	weight: x3
 #U31(x1)	weight: 0
 #and(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #25 #71
Number of SCCs: 7, DPs: 28, edges: 390
	SCC { #43 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   U21(x1,x2,x3)	weight: 0
   U11(x1,x2)	weight: (/ 1 4)
     s(x1)	weight: (/ 1 4) + x1
#isNat(x1)	weight: 0
   top(x1)	weight: 0
   and(x1,x2)	weight: x1
#plus(x1,x2)	weight: 0
 #top(x1)	weight: 0
     x(x1,x2)	weight: x2
proper(x1)	weight: (/ 1 2) + x1
    ok(x1)	weight: (/ 1 4) + x1
     0()	weight: 0
   #x(x1,x2)	weight: x1
   #s(x1)	weight: 0
  mark(x1)	weight: (/ 1 4) + x1
#proper(x1)	weight: 0
 isNat(x1)	weight: (/ 1 4) + x1
  plus(x1,x2)	weight: 0
 #U11(x1,x2)	weight: 0
active(x1)	weight: (/ 3 4) + x1
   U31(x1)	weight: (/ 1 4) + x1
 #U41(x1,x2,x3)	weight: 0
#active(x1)	weight: 0
 #U21(x1,x2,x3)	weight: 0
    tt()	weight: 0
   U41(x1,x2,x3)	weight: x3
 #U31(x1)	weight: 0
 #and(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #43
Number of SCCs: 6, DPs: 27, edges: 389
	SCC { #39 #45 #51 #64 #70 #73 #80 #82 #87 #92 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   U21(x1,x2,x3)	weight: (/ 1 4) + x1
   U11(x1,x2)	weight: (/ 1 4) + x1
     s(x1)	weight: (/ 1 4) + x1
#isNat(x1)	weight: 0
   top(x1)	weight: 0
   and(x1,x2)	weight: (/ 1 4) + x1
#plus(x1,x2)	weight: 0
 #top(x1)	weight: 0
     x(x1,x2)	weight: (/ 1 4) + x1 + x2
proper(x1)	weight: (/ 1 2) + x1
    ok(x1)	weight: (/ 1 4) + x1
     0()	weight: 0
   #x(x1,x2)	weight: 0
   #s(x1)	weight: 0
  mark(x1)	weight: (/ 1 4) + x1
#proper(x1)	weight: 0
 isNat(x1)	weight: (/ 1 4) + x1
  plus(x1,x2)	weight: (/ 1 4) + x1 + x2
 #U11(x1,x2)	weight: 0
active(x1)	weight: (/ 1 2) + x1
   U31(x1)	weight: (/ 1 4) + x1
 #U41(x1,x2,x3)	weight: 0
#active(x1)	weight: x1
 #U21(x1,x2,x3)	weight: 0
    tt()	weight: 0
   U41(x1,x2,x3)	weight: (/ 1 4) + x1
 #U31(x1)	weight: 0
 #and(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #39 #45 #51 #64 #70 #73 #80 #82 #87 #92
Number of SCCs: 6, DPs: 17, edges: 289
	SCC { #4 #5 #9 #10 #12..14 #16 #21 #22 #56 #61 #66 #67 #76..78 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   U21(x1,x2,x3)	weight: (/ 1 8) + x1 + x2 + x3
   U11(x1,x2)	weight: (/ 1 8) + x1 + x2
     s(x1)	weight: (/ 3 16) + x1
#isNat(x1)	weight: 0
   top(x1)	weight: 0
   and(x1,x2)	weight: (/ 1 8) + x1 + x2
#plus(x1,x2)	weight: 0
 #top(x1)	weight: 0
     x(x1,x2)	weight: (/ 1 8) + x1 + x2
proper(x1)	weight: (/ 1 4) + x1
    ok(x1)	weight: (/ 1 8) + x1
     0()	weight: 0
   #x(x1,x2)	weight: 0
   #s(x1)	weight: 0
  mark(x1)	weight: (/ 1 8) + x1
#proper(x1)	weight: x1
 isNat(x1)	weight: (/ 1 8) + x1
  plus(x1,x2)	weight: (/ 1 8) + x1 + x2
 #U11(x1,x2)	weight: 0
active(x1)	weight: (/ 5 16) + x1
   U31(x1)	weight: (/ 1 8) + x1
 #U41(x1,x2,x3)	weight: 0
#active(x1)	weight: 0
 #U21(x1,x2,x3)	weight: 0
    tt()	weight: 0
   U41(x1,x2,x3)	weight: (/ 1 8) + x1 + x2 + x3
 #U31(x1)	weight: 0
 #and(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #4 #5 #9 #10 #12..14 #16 #21 #22 #56 #61 #66 #67 #76..78
Number of SCCs: 5, DPs: 0, edges: 0
YES