Input TRS:
    1: active(f(X)) -> mark(cons(X,f(g(X))))
    2: active(g(0())) -> mark(s(0()))
    3: active(g(s(X))) -> mark(s(s(g(X))))
    4: active(sel(0(),cons(X,Y))) -> mark(X)
    5: active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z))
    6: mark(f(X)) -> active(f(mark(X)))
    7: mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
    8: mark(g(X)) -> active(g(mark(X)))
    9: mark(0()) -> active(0())
    10: mark(s(X)) -> active(s(mark(X)))
    11: mark(sel(X1,X2)) -> active(sel(mark(X1),mark(X2)))
    12: f(mark(X)) -> f(X)
    13: f(active(X)) -> f(X)
    14: cons(mark(X1),X2) -> cons(X1,X2)
    15: cons(X1,mark(X2)) -> cons(X1,X2)
    16: cons(active(X1),X2) -> cons(X1,X2)
    17: cons(X1,active(X2)) -> cons(X1,X2)
    18: g(mark(X)) -> g(X)
    19: g(active(X)) -> g(X)
    20: s(mark(X)) -> s(X)
    21: s(active(X)) -> s(X)
    22: sel(mark(X1),X2) -> sel(X1,X2)
    23: sel(X1,mark(X2)) -> sel(X1,X2)
    24: sel(active(X1),X2) -> sel(X1,X2)
    25: sel(X1,active(X2)) -> sel(X1,X2)
Number of strict rules: 25
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #active(g(0())) -> #mark(s(0()))
   #2: #active(g(0())) -> #s(0())
   #3: #mark(f(X)) -> #active(f(mark(X)))
   #4: #mark(f(X)) -> #f(mark(X))
   #5: #mark(f(X)) -> #mark(X)
   #6: #f(active(X)) -> #f(X)
   #7: #mark(0()) -> #active(0())
   #8: #mark(sel(X1,X2)) -> #active(sel(mark(X1),mark(X2)))
   #9: #mark(sel(X1,X2)) -> #sel(mark(X1),mark(X2))
   #10: #mark(sel(X1,X2)) -> #mark(X1)
   #11: #mark(sel(X1,X2)) -> #mark(X2)
   #12: #sel(active(X1),X2) -> #sel(X1,X2)
   #13: #sel(X1,mark(X2)) -> #sel(X1,X2)
   #14: #f(mark(X)) -> #f(X)
   #15: #cons(mark(X1),X2) -> #cons(X1,X2)
   #16: #sel(X1,active(X2)) -> #sel(X1,X2)
   #17: #s(mark(X)) -> #s(X)
   #18: #mark(cons(X1,X2)) -> #active(cons(mark(X1),X2))
   #19: #mark(cons(X1,X2)) -> #cons(mark(X1),X2)
   #20: #mark(cons(X1,X2)) -> #mark(X1)
   #21: #mark(s(X)) -> #active(s(mark(X)))
   #22: #mark(s(X)) -> #s(mark(X))
   #23: #mark(s(X)) -> #mark(X)
   #24: #active(sel(s(X),cons(Y,Z))) -> #mark(sel(X,Z))
   #25: #active(sel(s(X),cons(Y,Z))) -> #sel(X,Z)
   #26: #sel(mark(X1),X2) -> #sel(X1,X2)
   #27: #cons(X1,active(X2)) -> #cons(X1,X2)
   #28: #g(active(X)) -> #g(X)
   #29: #s(active(X)) -> #s(X)
   #30: #cons(active(X1),X2) -> #cons(X1,X2)
   #31: #active(g(s(X))) -> #mark(s(s(g(X))))
   #32: #active(g(s(X))) -> #s(s(g(X)))
   #33: #active(g(s(X))) -> #s(g(X))
   #34: #active(g(s(X))) -> #g(X)
   #35: #active(f(X)) -> #mark(cons(X,f(g(X))))
   #36: #active(f(X)) -> #cons(X,f(g(X)))
   #37: #active(f(X)) -> #f(g(X))
   #38: #active(f(X)) -> #g(X)
   #39: #mark(g(X)) -> #active(g(mark(X)))
   #40: #mark(g(X)) -> #g(mark(X))
   #41: #mark(g(X)) -> #mark(X)
   #42: #cons(X1,mark(X2)) -> #cons(X1,X2)
   #43: #active(sel(0(),cons(X,Y))) -> #mark(X)
   #44: #g(mark(X)) -> #g(X)
Number of SCCs: 6, DPs: 28, edges: 118
	SCC { #28 #44 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: 0
     s(x1)	weight: 0
     f(x1)	weight: 0
#mark(x1)	weight: 0
     0()	weight: 0
 #sel(x1,x2)	weight: 0
   sel(x1,x2)	weight: 0
   #s(x1)	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
   #f(x1)	weight: 0
   #g(x1)	weight: x1
active(x1)	weight: (/ 1 2) + x1
  cons(x1,x2)	weight: 0
#active(x1)	weight: 0
     g(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #28 #44
Number of SCCs: 5, DPs: 26, edges: 114
	SCC { #17 #29 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: 0
     s(x1)	weight: 0
     f(x1)	weight: 0
#mark(x1)	weight: 0
     0()	weight: 0
 #sel(x1,x2)	weight: 0
   sel(x1,x2)	weight: 0
   #s(x1)	weight: x1
  mark(x1)	weight: (/ 1 2) + x1
   #f(x1)	weight: 0
   #g(x1)	weight: 0
active(x1)	weight: (/ 1 2) + x1
  cons(x1,x2)	weight: 0
#active(x1)	weight: 0
     g(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #17 #29
Number of SCCs: 4, DPs: 24, edges: 110
	SCC { #6 #14 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: 0
     s(x1)	weight: 0
     f(x1)	weight: 0
#mark(x1)	weight: 0
     0()	weight: 0
 #sel(x1,x2)	weight: 0
   sel(x1,x2)	weight: 0
   #s(x1)	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
   #f(x1)	weight: x1
   #g(x1)	weight: 0
active(x1)	weight: (/ 1 2) + x1
  cons(x1,x2)	weight: 0
#active(x1)	weight: 0
     g(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #6 #14
Number of SCCs: 3, DPs: 22, edges: 106
	SCC { #15 #27 #30 #42 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: x1
     s(x1)	weight: 0
     f(x1)	weight: 0
#mark(x1)	weight: 0
     0()	weight: 0
 #sel(x1,x2)	weight: 0
   sel(x1,x2)	weight: 0
   #s(x1)	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
   #f(x1)	weight: 0
   #g(x1)	weight: 0
active(x1)	weight: (/ 1 2) + x1
  cons(x1,x2)	weight: 0
#active(x1)	weight: 0
     g(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #15 #30
Number of SCCs: 3, DPs: 20, edges: 94
	SCC { #27 #42 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: x2
     s(x1)	weight: 0
     f(x1)	weight: 0
#mark(x1)	weight: 0
     0()	weight: 0
 #sel(x1,x2)	weight: 0
   sel(x1,x2)	weight: 0
   #s(x1)	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
   #f(x1)	weight: 0
   #g(x1)	weight: 0
active(x1)	weight: (/ 1 2) + x1
  cons(x1,x2)	weight: 0
#active(x1)	weight: 0
     g(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #27 #42
Number of SCCs: 2, DPs: 18, edges: 90
	SCC { #12 #13 #16 #26 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: 0
     s(x1)	weight: 0
     f(x1)	weight: 0
#mark(x1)	weight: 0
     0()	weight: 0
 #sel(x1,x2)	weight: x1
   sel(x1,x2)	weight: 0
   #s(x1)	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
   #f(x1)	weight: 0
   #g(x1)	weight: 0
active(x1)	weight: (/ 1 2) + x1
  cons(x1,x2)	weight: 0
#active(x1)	weight: 0
     g(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #12 #26
Number of SCCs: 3, DPs: 16, edges: 78
	SCC { #13 #16 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: 0
     s(x1)	weight: 0
     f(x1)	weight: 0
#mark(x1)	weight: 0
     0()	weight: 0
 #sel(x1,x2)	weight: x2
   sel(x1,x2)	weight: 0
   #s(x1)	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
   #f(x1)	weight: 0
   #g(x1)	weight: 0
active(x1)	weight: (/ 1 2) + x1
  cons(x1,x2)	weight: 0
#active(x1)	weight: 0
     g(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #13 #16
Number of SCCs: 2, DPs: 14, edges: 74
	SCC { #1 #3 #5 #8 #10 #11 #20 #23 #24 #31 #35 #39 #41 #43 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... succeeded.
#cons(x1,x2)	weight: 0
     s(x1)	weight: x1
     f(x1)	weight: (/ 1 2) + x1
#mark(x1)	weight: x1
     0()	weight: (/ 1 4)
 #sel(x1,x2)	weight: 0
   sel(x1,x2)	weight: max{(/ 1 2) + x2, (/ 1 4) + x1}
   #s(x1)	weight: 0
  mark(x1)	weight: x1
   #f(x1)	weight: 0
   #g(x1)	weight: 0
active(x1)	weight: x1
  cons(x1,x2)	weight: max{x2, (/ 1 4) + x1}
#active(x1)	weight: x1
     g(x1)	weight: x1
    Usable rules: { 1..25 }
    Removed DPs: #5 #10 #11 #20 #43
Number of SCCs: 4, DPs: 7, edges: 12
	SCC { #8 #24 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... QWPOpS(PosReal,>,MaxSum)... succeeded.
#cons(x1,x2)	weight: (/ 1 2) + x2	status: [x2]	precedence above:
     s(x1)	weight: x1	status: [x1]	precedence above: #mark sel cons
     f(x1)	weight: 2 + x1	status: []	precedence above: s #mark 0 sel cons g
#mark(x1)	weight: x1	status: [x1]	precedence above:
     0()	weight: (/ 1 2)	status: []	precedence above:
 #sel(x1,x2)	weight: (/ 1 2) + x2 + x1	status: [x2,x1]	precedence above:
   sel(x1,x2)	weight: 2 + x2 + x1	status: [x1]	precedence above: s #mark cons
   #s(x1)	weight: (/ 1 2)	status: []	precedence above:
  mark(x1)	weight: x1	status: x1
   #f(x1)	weight: (/ 1 2)	status: []	precedence above:
   #g(x1)	weight: (/ 1 2)	status: []	precedence above:
active(x1)	weight: x1	status: x1
  cons(x1,x2)	weight: max{x2, (/ 3 2) + x1}	status: [x1]	precedence above: s #mark sel
#active(x1)	weight: x1	status: x1
     g(x1)	weight: x1	status: [x1]	precedence above: s #mark 0 sel cons
    Usable rules: { 1..25 }
    Removed DPs: #8 #24
Number of SCCs: 3, DPs: 5, edges: 10
	SCC { #1 #23 #31 #39 #41 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... QWPOpS(PosReal,>,MaxSum)... succeeded.
#cons(x1,x2)	weight: (/ 1 2) + x2	status: [x2]	precedence above:
     s(x1)	weight: x1	status: [x1]	precedence above: #mark sel cons
     f(x1)	weight: 2 + x1	status: []	precedence above: s #mark 0 sel cons #active g
#mark(x1)	weight: x1	status: [x1]	precedence above:
     0()	weight: (/ 1 2)	status: []	precedence above:
 #sel(x1,x2)	weight: (/ 1 2) + x2 + x1	status: [x2,x1]	precedence above:
   sel(x1,x2)	weight: 2 + x2 + x1	status: [x1]	precedence above: s #mark cons
   #s(x1)	weight: (/ 1 2)	status: []	precedence above:
  mark(x1)	weight: x1	status: x1
   #f(x1)	weight: (/ 1 2)	status: []	precedence above:
   #g(x1)	weight: (/ 1 2)	status: []	precedence above:
active(x1)	weight: x1	status: x1
  cons(x1,x2)	weight: max{x2, (/ 3 2) + x1}	status: [x1]	precedence above: s #mark sel
#active(x1)	weight: x1	status: x1
     g(x1)	weight: x1	status: [x1]	precedence above: s #mark 0 sel cons #active
    Usable rules: { 1..25 }
    Removed DPs: #1 #23 #31 #39 #41
Number of SCCs: 2, DPs: 0, edges: 0
YES