Input TRS:
    1: active(incr(nil())) -> mark(nil())
    2: active(incr(cons(X,L))) -> mark(cons(s(X),incr(L)))
    3: active(adx(nil())) -> mark(nil())
    4: active(adx(cons(X,L))) -> mark(incr(cons(X,adx(L))))
    5: active(nats()) -> mark(adx(zeros()))
    6: active(zeros()) -> mark(cons(0(),zeros()))
    7: active(head(cons(X,L))) -> mark(X)
    8: active(tail(cons(X,L))) -> mark(L)
    9: mark(incr(X)) -> active(incr(mark(X)))
    10: mark(nil()) -> active(nil())
    11: mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
    12: mark(s(X)) -> active(s(mark(X)))
    13: mark(adx(X)) -> active(adx(mark(X)))
    14: mark(nats()) -> active(nats())
    15: mark(zeros()) -> active(zeros())
    16: mark(0()) -> active(0())
    17: mark(head(X)) -> active(head(mark(X)))
    18: mark(tail(X)) -> active(tail(mark(X)))
    19: incr(mark(X)) -> incr(X)
    20: incr(active(X)) -> incr(X)
    21: cons(mark(X1),X2) -> cons(X1,X2)
    22: cons(X1,mark(X2)) -> cons(X1,X2)
    23: cons(active(X1),X2) -> cons(X1,X2)
    24: cons(X1,active(X2)) -> cons(X1,X2)
    25: s(mark(X)) -> s(X)
    26: s(active(X)) -> s(X)
    27: adx(mark(X)) -> adx(X)
    28: adx(active(X)) -> adx(X)
    29: head(mark(X)) -> head(X)
    30: head(active(X)) -> head(X)
    31: tail(mark(X)) -> tail(X)
    32: tail(active(X)) -> tail(X)
Number of strict rules: 32
Direct Order(PosReal,>,Poly) ... removes: 8 7
  incr(x1)	weight: x1
     s(x1)	weight: x1
   adx(x1)	weight: x1
 zeros()	weight: 0
  tail(x1)	weight: 17888 + x1
     0()	weight: 0
   nil()	weight: 0
  mark(x1)	weight: x1
  nats()	weight: 0
active(x1)	weight: x1
  head(x1)	weight: 35102 + 2 * x1
  cons(x1,x2)	weight: x1 + x2
Number of strict rules: 30
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #active(incr(cons(X,L))) -> #mark(cons(s(X),incr(L)))
   #2: #active(incr(cons(X,L))) -> #cons(s(X),incr(L))
   #3: #active(incr(cons(X,L))) -> #s(X)
   #4: #active(incr(cons(X,L))) -> #incr(L)
   #5: #head(mark(X)) -> #head(X)
   #6: #active(zeros()) -> #mark(cons(0(),zeros()))
   #7: #active(zeros()) -> #cons(0(),zeros())
   #8: #mark(adx(X)) -> #active(adx(mark(X)))
   #9: #mark(adx(X)) -> #adx(mark(X))
   #10: #mark(adx(X)) -> #mark(X)
   #11: #mark(incr(X)) -> #active(incr(mark(X)))
   #12: #mark(incr(X)) -> #incr(mark(X))
   #13: #mark(incr(X)) -> #mark(X)
   #14: #mark(cons(X1,X2)) -> #active(cons(mark(X1),X2))
   #15: #mark(cons(X1,X2)) -> #cons(mark(X1),X2)
   #16: #mark(cons(X1,X2)) -> #mark(X1)
   #17: #cons(X1,active(X2)) -> #cons(X1,X2)
   #18: #cons(active(X1),X2) -> #cons(X1,X2)
   #19: #mark(s(X)) -> #active(s(mark(X)))
   #20: #mark(s(X)) -> #s(mark(X))
   #21: #mark(s(X)) -> #mark(X)
   #22: #tail(mark(X)) -> #tail(X)
   #23: #mark(nats()) -> #active(nats())
   #24: #head(active(X)) -> #head(X)
   #25: #s(mark(X)) -> #s(X)
   #26: #incr(active(X)) -> #incr(X)
   #27: #mark(nil()) -> #active(nil())
   #28: #active(nats()) -> #mark(adx(zeros()))
   #29: #active(nats()) -> #adx(zeros())
   #30: #adx(active(X)) -> #adx(X)
   #31: #cons(X1,mark(X2)) -> #cons(X1,X2)
   #32: #adx(mark(X)) -> #adx(X)
   #33: #mark(head(X)) -> #active(head(mark(X)))
   #34: #mark(head(X)) -> #head(mark(X))
   #35: #mark(head(X)) -> #mark(X)
   #36: #tail(active(X)) -> #tail(X)
   #37: #incr(mark(X)) -> #incr(X)
   #38: #s(active(X)) -> #s(X)
   #39: #cons(mark(X1),X2) -> #cons(X1,X2)
   #40: #mark(0()) -> #active(0())
   #41: #active(adx(nil())) -> #mark(nil())
   #42: #active(incr(nil())) -> #mark(nil())
   #43: #mark(zeros()) -> #active(zeros())
   #44: #active(adx(cons(X,L))) -> #mark(incr(cons(X,adx(L))))
   #45: #active(adx(cons(X,L))) -> #incr(cons(X,adx(L)))
   #46: #active(adx(cons(X,L))) -> #cons(X,adx(L))
   #47: #active(adx(cons(X,L))) -> #adx(L)
   #48: #mark(tail(X)) -> #active(tail(mark(X)))
   #49: #mark(tail(X)) -> #tail(mark(X))
   #50: #mark(tail(X)) -> #mark(X)
Number of SCCs: 7, DPs: 28, edges: 106
	SCC { #25 #38 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
 #adx(x1)	weight: 0
  incr(x1)	weight: 0
#cons(x1,x2)	weight: 0
     s(x1)	weight: 0
#head(x1)	weight: 0
   adx(x1)	weight: 0
 zeros()	weight: 0
  tail(x1)	weight: 0
#mark(x1)	weight: 0
     0()	weight: 0
   #s(x1)	weight: x1
   nil()	weight: 0
#tail(x1)	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
#incr(x1)	weight: 0
  nats()	weight: 0
active(x1)	weight: (/ 1 2) + x1
  head(x1)	weight: 0
  cons(x1,x2)	weight: 0
#active(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #25 #38
Number of SCCs: 6, DPs: 26, edges: 102
	SCC { #22 #36 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
 #adx(x1)	weight: 0
  incr(x1)	weight: 0
#cons(x1,x2)	weight: 0
     s(x1)	weight: 0
#head(x1)	weight: 0
   adx(x1)	weight: 0
 zeros()	weight: 0
  tail(x1)	weight: 0
#mark(x1)	weight: 0
     0()	weight: 0
   #s(x1)	weight: 0
   nil()	weight: 0
#tail(x1)	weight: x1
  mark(x1)	weight: (/ 1 2) + x1
#incr(x1)	weight: 0
  nats()	weight: 0
active(x1)	weight: (/ 1 2) + x1
  head(x1)	weight: 0
  cons(x1,x2)	weight: 0
#active(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #22 #36
Number of SCCs: 5, DPs: 24, edges: 98
	SCC { #5 #24 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
 #adx(x1)	weight: 0
  incr(x1)	weight: 0
#cons(x1,x2)	weight: 0
     s(x1)	weight: 0
#head(x1)	weight: x1
   adx(x1)	weight: 0
 zeros()	weight: 0
  tail(x1)	weight: 0
#mark(x1)	weight: 0
     0()	weight: 0
   #s(x1)	weight: 0
   nil()	weight: 0
#tail(x1)	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
#incr(x1)	weight: 0
  nats()	weight: 0
active(x1)	weight: (/ 1 2) + x1
  head(x1)	weight: 0
  cons(x1,x2)	weight: 0
#active(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #5 #24
Number of SCCs: 4, DPs: 22, edges: 94
	SCC { #26 #37 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
 #adx(x1)	weight: 0
  incr(x1)	weight: 0
#cons(x1,x2)	weight: 0
     s(x1)	weight: 0
#head(x1)	weight: 0
   adx(x1)	weight: 0
 zeros()	weight: 0
  tail(x1)	weight: 0
#mark(x1)	weight: 0
     0()	weight: 0
   #s(x1)	weight: 0
   nil()	weight: 0
#tail(x1)	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
#incr(x1)	weight: x1
  nats()	weight: 0
active(x1)	weight: (/ 1 2) + x1
  head(x1)	weight: 0
  cons(x1,x2)	weight: 0
#active(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #26 #37
Number of SCCs: 3, DPs: 20, edges: 90
	SCC { #30 #32 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
 #adx(x1)	weight: x1
  incr(x1)	weight: 0
#cons(x1,x2)	weight: 0
     s(x1)	weight: 0
#head(x1)	weight: 0
   adx(x1)	weight: 0
 zeros()	weight: 0
  tail(x1)	weight: 0
#mark(x1)	weight: 0
     0()	weight: 0
   #s(x1)	weight: 0
   nil()	weight: 0
#tail(x1)	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
#incr(x1)	weight: 0
  nats()	weight: 0
active(x1)	weight: (/ 1 2) + x1
  head(x1)	weight: 0
  cons(x1,x2)	weight: 0
#active(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #30 #32
Number of SCCs: 2, DPs: 18, edges: 86
	SCC { #17 #18 #31 #39 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
 #adx(x1)	weight: 0
  incr(x1)	weight: 0
#cons(x1,x2)	weight: x2
     s(x1)	weight: 0
#head(x1)	weight: 0
   adx(x1)	weight: 0
 zeros()	weight: 0
  tail(x1)	weight: 0
#mark(x1)	weight: 0
     0()	weight: 0
   #s(x1)	weight: 0
   nil()	weight: 0
#tail(x1)	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
#incr(x1)	weight: 0
  nats()	weight: 0
active(x1)	weight: (/ 1 2) + x1
  head(x1)	weight: 0
  cons(x1,x2)	weight: 0
#active(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #17 #31
Number of SCCs: 2, DPs: 16, edges: 74
	SCC { #18 #39 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
 #adx(x1)	weight: 0
  incr(x1)	weight: 0
#cons(x1,x2)	weight: x1
     s(x1)	weight: 0
#head(x1)	weight: 0
   adx(x1)	weight: 0
 zeros()	weight: 0
  tail(x1)	weight: 0
#mark(x1)	weight: 0
     0()	weight: 0
   #s(x1)	weight: 0
   nil()	weight: 0
#tail(x1)	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
#incr(x1)	weight: 0
  nats()	weight: 0
active(x1)	weight: (/ 1 2) + x1
  head(x1)	weight: 0
  cons(x1,x2)	weight: 0
#active(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #18 #39
Number of SCCs: 1, DPs: 14, edges: 70
	SCC { #1 #6 #8 #10 #11 #13 #16 #21 #23 #28 #35 #43 #44 #50 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
 #adx(x1)	weight: 0
  incr(x1)	weight: x1
#cons(x1,x2)	weight: 0
     s(x1)	weight: x1
#head(x1)	weight: 0
   adx(x1)	weight: x1
 zeros()	weight: 0
  tail(x1)	weight: (/ 1 2) + x1
#mark(x1)	weight: x1
     0()	weight: 0
   #s(x1)	weight: 0
   nil()	weight: 0
#tail(x1)	weight: 0
  mark(x1)	weight: x1
#incr(x1)	weight: 0
  nats()	weight: 0
active(x1)	weight: x1
  head(x1)	weight: (/ 1 2) + x1
  cons(x1,x2)	weight: x1
#active(x1)	weight: x1
    Usable rules: { 1..6 9..32 }
    Removed DPs: #35 #50
Number of SCCs: 2, DPs: 12, edges: 42
	SCC { #1 #6 #8 #10 #11 #13 #16 #21 #23 #28 #43 #44 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... succeeded.
 #adx(x1)	weight: 0
  incr(x1)	weight: (/ 291725 8) + x1
#cons(x1,x2)	weight: 0
     s(x1)	weight: (/ 1 8) + x1
#head(x1)	weight: 0
   adx(x1)	weight: (/ 583449 8) + x1
 zeros()	weight: (/ 291725 8)
  tail(x1)	weight: (/ 1 8)
#mark(x1)	weight: (/ 145861 4) + x1
     0()	weight: (/ 1 8)
   #s(x1)	weight: 0
   nil()	weight: (/ 1 8)
#tail(x1)	weight: 0
  mark(x1)	weight: (/ 291721 8) + x1
#incr(x1)	weight: 0
  nats()	weight: (/ 1166897 8)
active(x1)	weight: x1
  head(x1)	weight: (/ 1 8) + x1
  cons(x1,x2)	weight: max{0, (/ 1 8) + x1}
#active(x1)	weight: x1
    Usable rules: { 1..6 9..32 }
    Removed DPs: #1 #6 #8 #10 #11 #13 #16 #21 #23 #28 #43 #44
Number of SCCs: 1, DPs: 0, edges: 0
YES