Input TRS:
    1: top(sent(x)) -> top(check(rest(x)))
    2: rest(nil()) -> sent(nil())
    3: rest(cons(x,y)) -> sent(y)
    4: check(sent(x)) -> sent(check(x))
    5: check(rest(x)) -> rest(check(x))
    6: check(cons(x,y)) -> cons(check(x),y)
    7: check(cons(x,y)) -> cons(x,check(y))
    8: check(cons(x,y)) -> cons(x,y)
Number of strict rules: 8
Direct Order(PosReal,>,Poly) ... removes: 3
   top(x1)	weight: 2 * x1
 check(x1)	weight: x1
   nil()	weight: 0
  rest(x1)	weight: 11798 + x1
  sent(x1)	weight: 11798 + x1
  cons(x1,x2)	weight: 17221 + x1 + x2
Number of strict rules: 7
Direct Order(PosReal,>,Poly) ... removes: 8 7 6
   top(x1)	weight: x1
 check(x1)	weight: 2 * x1
   nil()	weight: 0
  rest(x1)	weight: x1
  sent(x1)	weight: 2 * x1
  cons(x1,x2)	weight: (/ 1 4) + x1 + x2
Number of strict rules: 4
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #check(rest(x)) -> #rest(check(x))
   #2: #check(rest(x)) -> #check(x)
   #3: #top(sent(x)) -> #top(check(rest(x)))
   #4: #top(sent(x)) -> #check(rest(x))
   #5: #top(sent(x)) -> #rest(x)
   #6: #check(sent(x)) -> #check(x)
Number of SCCs: 2, DPs: 3, edges: 5
	SCC { #3 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... QWPOpS(PosReal,>,MaxSum)... Order(PosReal,>,Sum-Sum; PosReal,≥,Sum-Sum)... succeeded.
#rest(x1)	weight: 0; 0
   top(x1)	weight: 0; 0
#check(x1)	weight: 0; 0
 #top(x1)	weight: x1_1 + x1_2; 0
 check(x1)	weight: (/ 1 8) + x1_1; (/ 1 8)
   nil()	weight: (/ 1 8); (/ 3 8)
  rest(x1)	weight: (/ 1 8) + x1_2; x1_2
  sent(x1)	weight: (/ 1 2); x1_2
  cons(x1,x2)	weight: 0; 0
    Usable rules: { 2 4 5 }
    Removed DPs: #3
Number of SCCs: 1, DPs: 2, edges: 4
	SCC { #2 #6 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#rest(x1)	weight: 0
   top(x1)	weight: 0
#check(x1)	weight: x1
 #top(x1)	weight: 0
 check(x1)	weight: (/ 1 4)
   nil()	weight: 0
  rest(x1)	weight: (/ 1 4) + x1
  sent(x1)	weight: (/ 1 2) + x1
  cons(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #2 #6
Number of SCCs: 0, DPs: 0, edges: 0
YES