Input TRS:
    1: active(nats()) -> mark(cons(0(),incr(nats())))
    2: active(pairs()) -> mark(cons(0(),incr(odds())))
    3: active(odds()) -> mark(incr(pairs()))
    4: active(incr(cons(X,XS))) -> mark(cons(s(X),incr(XS)))
    5: active(head(cons(X,XS))) -> mark(X)
    6: active(tail(cons(X,XS))) -> mark(XS)
    7: mark(nats()) -> active(nats())
    8: mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
    9: mark(0()) -> active(0())
    10: mark(incr(X)) -> active(incr(mark(X)))
    11: mark(pairs()) -> active(pairs())
    12: mark(odds()) -> active(odds())
    13: mark(s(X)) -> active(s(mark(X)))
    14: mark(head(X)) -> active(head(mark(X)))
    15: mark(tail(X)) -> active(tail(mark(X)))
    16: cons(mark(X1),X2) -> cons(X1,X2)
    17: cons(X1,mark(X2)) -> cons(X1,X2)
    18: cons(active(X1),X2) -> cons(X1,X2)
    19: cons(X1,active(X2)) -> cons(X1,X2)
    20: incr(mark(X)) -> incr(X)
    21: incr(active(X)) -> incr(X)
    22: s(mark(X)) -> s(X)
    23: s(active(X)) -> s(X)
    24: head(mark(X)) -> head(X)
    25: head(active(X)) -> head(X)
    26: tail(mark(X)) -> tail(X)
    27: tail(active(X)) -> tail(X)
Number of strict rules: 27
Direct Order(PosReal,>,Poly) ... removes: 5 6
  incr(x1)	weight: x1
     s(x1)	weight: x1
 pairs()	weight: 0
  tail(x1)	weight: 14681 + x1
     0()	weight: 0
  odds()	weight: 0
  mark(x1)	weight: x1
  nats()	weight: 0
active(x1)	weight: x1
  head(x1)	weight: (/ 5997 2) + 2 * x1
  cons(x1,x2)	weight: x1 + x2
Number of strict rules: 25
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #active(pairs()) -> #mark(cons(0(),incr(odds())))
   #2: #active(pairs()) -> #cons(0(),incr(odds()))
   #3: #active(pairs()) -> #incr(odds())
   #4: #mark(s(X)) -> #active(s(mark(X)))
   #5: #mark(s(X)) -> #s(mark(X))
   #6: #mark(s(X)) -> #mark(X)
   #7: #mark(0()) -> #active(0())
   #8: #mark(pairs()) -> #active(pairs())
   #9: #head(mark(X)) -> #head(X)
   #10: #s(active(X)) -> #s(X)
   #11: #mark(odds()) -> #active(odds())
   #12: #mark(head(X)) -> #active(head(mark(X)))
   #13: #mark(head(X)) -> #head(mark(X))
   #14: #mark(head(X)) -> #mark(X)
   #15: #head(active(X)) -> #head(X)
   #16: #incr(mark(X)) -> #incr(X)
   #17: #mark(nats()) -> #active(nats())
   #18: #mark(incr(X)) -> #active(incr(mark(X)))
   #19: #mark(incr(X)) -> #incr(mark(X))
   #20: #mark(incr(X)) -> #mark(X)
   #21: #s(mark(X)) -> #s(X)
   #22: #tail(active(X)) -> #tail(X)
   #23: #cons(X1,mark(X2)) -> #cons(X1,X2)
   #24: #cons(X1,active(X2)) -> #cons(X1,X2)
   #25: #tail(mark(X)) -> #tail(X)
   #26: #incr(active(X)) -> #incr(X)
   #27: #cons(mark(X1),X2) -> #cons(X1,X2)
   #28: #active(odds()) -> #mark(incr(pairs()))
   #29: #active(odds()) -> #incr(pairs())
   #30: #active(nats()) -> #mark(cons(0(),incr(nats())))
   #31: #active(nats()) -> #cons(0(),incr(nats()))
   #32: #active(nats()) -> #incr(nats())
   #33: #mark(cons(X1,X2)) -> #active(cons(mark(X1),X2))
   #34: #mark(cons(X1,X2)) -> #cons(mark(X1),X2)
   #35: #mark(cons(X1,X2)) -> #mark(X1)
   #36: #mark(tail(X)) -> #active(tail(mark(X)))
   #37: #mark(tail(X)) -> #tail(mark(X))
   #38: #mark(tail(X)) -> #mark(X)
   #39: #active(incr(cons(X,XS))) -> #mark(cons(s(X),incr(XS)))
   #40: #active(incr(cons(X,XS))) -> #cons(s(X),incr(XS))
   #41: #active(incr(cons(X,XS))) -> #s(X)
   #42: #active(incr(cons(X,XS))) -> #incr(XS)
   #43: #cons(active(X1),X2) -> #cons(X1,X2)
Number of SCCs: 6, DPs: 25, edges: 86
	SCC { #22 #25 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
  incr(x1)	weight: 0
#cons(x1,x2)	weight: 0
     s(x1)	weight: 0
 pairs()	weight: 0
#head(x1)	weight: 0
  tail(x1)	weight: 0
#mark(x1)	weight: 0
     0()	weight: 0
   #s(x1)	weight: 0
  odds()	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 #25
Number of SCCs: 5, DPs: 23, edges: 82
	SCC { #16 #26 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
  incr(x1)	weight: 0
#cons(x1,x2)	weight: 0
     s(x1)	weight: 0
 pairs()	weight: 0
#head(x1)	weight: 0
  tail(x1)	weight: 0
#mark(x1)	weight: 0
     0()	weight: 0
   #s(x1)	weight: 0
  odds()	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: #16 #26
Number of SCCs: 4, DPs: 21, edges: 78
	SCC { #10 #21 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
  incr(x1)	weight: 0
#cons(x1,x2)	weight: 0
     s(x1)	weight: 0
 pairs()	weight: 0
#head(x1)	weight: 0
  tail(x1)	weight: 0
#mark(x1)	weight: 0
     0()	weight: 0
   #s(x1)	weight: x1
  odds()	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: #10 #21
Number of SCCs: 3, DPs: 19, edges: 74
	SCC { #9 #15 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
  incr(x1)	weight: 0
#cons(x1,x2)	weight: 0
     s(x1)	weight: 0
 pairs()	weight: 0
#head(x1)	weight: x1
  tail(x1)	weight: 0
#mark(x1)	weight: 0
     0()	weight: 0
   #s(x1)	weight: 0
  odds()	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: #9 #15
Number of SCCs: 2, DPs: 17, edges: 70
	SCC { #23 #24 #27 #43 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
  incr(x1)	weight: 0
#cons(x1,x2)	weight: x2
     s(x1)	weight: 0
 pairs()	weight: 0
#head(x1)	weight: 0
  tail(x1)	weight: 0
#mark(x1)	weight: 0
     0()	weight: 0
   #s(x1)	weight: 0
  odds()	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: #23 #24
Number of SCCs: 2, DPs: 15, edges: 58
	SCC { #27 #43 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
  incr(x1)	weight: 0
#cons(x1,x2)	weight: x1
     s(x1)	weight: 0
 pairs()	weight: 0
#head(x1)	weight: 0
  tail(x1)	weight: 0
#mark(x1)	weight: 0
     0()	weight: 0
   #s(x1)	weight: 0
  odds()	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: #27 #43
Number of SCCs: 1, DPs: 13, edges: 54
	SCC { #1 #6 #8 #11 #14 #17 #18 #20 #28 #30 #35 #38 #39 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
  incr(x1)	weight: x1
#cons(x1,x2)	weight: 0
     s(x1)	weight: x1
 pairs()	weight: 0
#head(x1)	weight: 0
  tail(x1)	weight: (/ 1 2) + x1
#mark(x1)	weight: x1
     0()	weight: 0
   #s(x1)	weight: 0
  odds()	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..4 7..27 }
    Removed DPs: #14 #38
Number of SCCs: 2, DPs: 11, edges: 30
	SCC { #1 #6 #8 #11 #17 #18 #20 #28 #30 #35 #39 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... succeeded.
  incr(x1)	weight: (/ 325203 8) + x1
#cons(x1,x2)	weight: 0
     s(x1)	weight: (/ 1 8) + x1
 pairs()	weight: (/ 325205 8)
#head(x1)	weight: 0
  tail(x1)	weight: (/ 1 8) + x1
#mark(x1)	weight: (/ 162601 4) + x1
     0()	weight: (/ 1 8)
   #s(x1)	weight: 0
  odds()	weight: (/ 975611 8)
#tail(x1)	weight: 0
  mark(x1)	weight: (/ 325201 8) + x1
#incr(x1)	weight: 0
  nats()	weight: (/ 325205 8)
active(x1)	weight: x1
  head(x1)	weight: (/ 1 8)
  cons(x1,x2)	weight: max{0, (/ 1 8) + x1}
#active(x1)	weight: x1
    Usable rules: { 1..4 7..27 }
    Removed DPs: #1 #6 #8 #11 #17 #18 #20 #28 #30 #35
Number of SCCs: 1, DPs: 0, edges: 0
YES