Input TRS:
    1: a__f(X) -> cons(mark(X),f(g(X)))
    2: a__g(0()) -> s(0())
    3: a__g(s(X)) -> s(s(a__g(mark(X))))
    4: a__sel(0(),cons(X,Y)) -> mark(X)
    5: a__sel(s(X),cons(Y,Z)) -> a__sel(mark(X),mark(Z))
    6: mark(f(X)) -> a__f(mark(X))
    7: mark(g(X)) -> a__g(mark(X))
    8: mark(sel(X1,X2)) -> a__sel(mark(X1),mark(X2))
    9: mark(cons(X1,X2)) -> cons(mark(X1),X2)
    10: mark(0()) -> 0()
    11: mark(s(X)) -> s(mark(X))
    12: a__f(X) -> f(X)
    13: a__g(X) -> g(X)
    14: a__sel(X1,X2) -> sel(X1,X2)
Number of strict rules: 14
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #mark(f(X)) -> #a__f(mark(X))
   #2: #mark(f(X)) -> #mark(X)
   #3: #mark(cons(X1,X2)) -> #mark(X1)
   #4: #mark(s(X)) -> #mark(X)
   #5: #mark(g(X)) -> #a__g(mark(X))
   #6: #mark(g(X)) -> #mark(X)
   #7: #a__sel(s(X),cons(Y,Z)) -> #a__sel(mark(X),mark(Z))
   #8: #a__sel(s(X),cons(Y,Z)) -> #mark(X)
   #9: #a__sel(s(X),cons(Y,Z)) -> #mark(Z)
   #10: #a__g(s(X)) -> #a__g(mark(X))
   #11: #a__g(s(X)) -> #mark(X)
   #12: #a__f(X) -> #mark(X)
   #13: #mark(sel(X1,X2)) -> #a__sel(mark(X1),mark(X2))
   #14: #mark(sel(X1,X2)) -> #mark(X1)
   #15: #mark(sel(X1,X2)) -> #mark(X2)
   #16: #a__sel(0(),cons(X,Y)) -> #mark(X)
Number of SCCs: 1, DPs: 16, edges: 112
	SCC { #1..16 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... succeeded.
  a__g(x1)	weight: x1
     s(x1)	weight: x1
#a__g(x1)	weight: (/ 1 4) + x1
  a__f(x1)	weight: x1
     f(x1)	weight: x1
#mark(x1)	weight: (/ 1 4) + x1
     0()	weight: 0
   sel(x1,x2)	weight: max{x2, (/ 1 4) + x1}
#a__sel(x1,x2)	weight: max{(/ 1 4) + x2, (/ 1 2) + x1}
  mark(x1)	weight: x1
a__sel(x1,x2)	weight: max{x2, (/ 1 4) + x1}
  cons(x1,x2)	weight: max{x2, x1}
#a__f(x1)	weight: (/ 1 4) + x1
     g(x1)	weight: x1
    Usable rules: { 1..14 }
    Removed DPs: #8 #14
Number of SCCs: 1, DPs: 14, edges: 83
	SCC { #1..7 #9..13 #15 #16 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... succeeded.
  a__g(x1)	weight: x1
     s(x1)	weight: x1
#a__g(x1)	weight: (/ 1 4) + x1
  a__f(x1)	weight: x1
     f(x1)	weight: x1
#mark(x1)	weight: (/ 1 4) + x1
     0()	weight: 0
   sel(x1,x2)	weight: max{(/ 3 4) + x2, (/ 1 2) + x1}
#a__sel(x1,x2)	weight: max{(/ 1 4) + x2, (/ 1 2) + x1}
  mark(x1)	weight: x1
a__sel(x1,x2)	weight: max{(/ 3 4) + x2, (/ 1 2) + x1}
  cons(x1,x2)	weight: max{x2, x1}
#a__f(x1)	weight: (/ 1 4) + x1
     g(x1)	weight: x1
    Usable rules: { 1..14 }
    Removed DPs: #13 #15
Number of SCCs: 2, DPs: 10, edges: 42
	SCC { #7 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... QWPOpS(PosReal,>,MaxSum)... succeeded.
  a__g(x1)	weight: x1	status: [x1]	precedence above: s 0 sel mark a__sel cons g
     s(x1)	weight: x1	status: [x1]	precedence above: sel mark a__sel cons
#a__g(x1)	weight: x1	status: []	precedence above:
  a__f(x1)	weight: (/ 3 4) + x1	status: []	precedence above: f sel a__sel cons
     f(x1)	weight: (/ 3 4) + x1	status: []	precedence above: a__f sel a__sel cons
#mark(x1)	weight: x1	status: []	precedence above:
     0()	weight: (/ 1 4)	status: []	precedence above: s sel mark a__sel cons
   sel(x1,x2)	weight: (/ 1 4) + x2	status: []	precedence above: a__sel
#a__sel(x1,x2)	weight: (/ 1 4) + x2 + x1	status: [x1,x2]	precedence above: a__f f sel mark a__sel cons
  mark(x1)	weight: x1	status: x1
a__sel(x1,x2)	weight: (/ 1 4) + x2	status: []	precedence above: sel
  cons(x1,x2)	weight: max{x2, (/ 1 2) + x1}	status: []	precedence above: sel a__sel
#a__f(x1)	weight: (/ 1 4)	status: []	precedence above:
     g(x1)	weight: x1	status: [x1]	precedence above: a__g s 0 sel mark a__sel cons
    Usable rules: { 1..14 }
    Removed DPs: #7
Number of SCCs: 1, DPs: 9, edges: 41
	SCC { #1..6 #10..12 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... succeeded.
  a__g(x1)	weight: x1
     s(x1)	weight: x1
#a__g(x1)	weight: (/ 1 4) + x1
  a__f(x1)	weight: (/ 1 4) + x1
     f(x1)	weight: (/ 1 4) + x1
#mark(x1)	weight: (/ 1 4) + x1
     0()	weight: 0
   sel(x1,x2)	weight: max{(/ 1 4) + x2, (/ 3 4) + x1}
#a__sel(x1,x2)	weight: 0
  mark(x1)	weight: x1
a__sel(x1,x2)	weight: max{(/ 1 4) + x2, (/ 3 4) + x1}
  cons(x1,x2)	weight: max{x2, (/ 1 4) + x1}
#a__f(x1)	weight: (/ 1 2) + x1
     g(x1)	weight: x1
    Usable rules: { 1..14 }
    Removed DPs: #2 #3 #12
Number of SCCs: 1, DPs: 5, edges: 13
	SCC { #4..6 #10 #11 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... QWPOpS(PosReal,>,MaxSum)... succeeded.
  a__g(x1)	weight: x1	status: [x1]	precedence above: s #a__g 0 sel mark a__sel cons g
     s(x1)	weight: x1	status: [x1]	precedence above: sel mark a__sel cons
#a__g(x1)	weight: x1	status: [x1]	precedence above: a__g s 0 sel mark a__sel cons g
  a__f(x1)	weight: (/ 3 4) + x1	status: []	precedence above: f sel a__sel cons
     f(x1)	weight: (/ 3 4) + x1	status: []	precedence above: a__f sel a__sel cons
#mark(x1)	weight: x1	status: x1
     0()	weight: (/ 1 4)	status: []	precedence above: s sel mark a__sel cons
   sel(x1,x2)	weight: (/ 1 4) + x2	status: []	precedence above: a__sel
#a__sel(x1,x2)	weight: (/ 1 4) + x2 + x1	status: [x1,x2]	precedence above: a__f f sel mark a__sel cons
  mark(x1)	weight: x1	status: x1
a__sel(x1,x2)	weight: (/ 1 4) + x2	status: []	precedence above: sel
  cons(x1,x2)	weight: max{x2, (/ 1 2) + x1}	status: []	precedence above: sel a__sel
#a__f(x1)	weight: (/ 1 4)	status: []	precedence above:
     g(x1)	weight: x1	status: [x1]	precedence above: a__g s #a__g 0 sel mark a__sel cons
    Usable rules: { 1..14 }
    Removed DPs: #4 #6 #10 #11
Number of SCCs: 0, DPs: 0, edges: 0
YES