Input TRS:
    1: a__from(X) -> cons(mark(X),from(s(X)))
    2: a__after(0(),XS) -> mark(XS)
    3: a__after(s(N),cons(X,XS)) -> a__after(mark(N),mark(XS))
    4: mark(from(X)) -> a__from(mark(X))
    5: mark(after(X1,X2)) -> a__after(mark(X1),mark(X2))
    6: mark(cons(X1,X2)) -> cons(mark(X1),X2)
    7: mark(s(X)) -> s(mark(X))
    8: mark(0()) -> 0()
    9: a__from(X) -> from(X)
    10: a__after(X1,X2) -> after(X1,X2)
Number of strict rules: 10
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #a__after(0(),XS) -> #mark(XS)
   #2: #mark(cons(X1,X2)) -> #mark(X1)
   #3: #mark(s(X)) -> #mark(X)
   #4: #mark(after(X1,X2)) -> #a__after(mark(X1),mark(X2))
   #5: #mark(after(X1,X2)) -> #mark(X1)
   #6: #mark(after(X1,X2)) -> #mark(X2)
   #7: #a__after(s(N),cons(X,XS)) -> #a__after(mark(N),mark(XS))
   #8: #a__after(s(N),cons(X,XS)) -> #mark(N)
   #9: #a__after(s(N),cons(X,XS)) -> #mark(XS)
   #10: #a__from(X) -> #mark(X)
   #11: #mark(from(X)) -> #a__from(mark(X))
   #12: #mark(from(X)) -> #mark(X)
Number of SCCs: 1, DPs: 12, edges: 72
	SCC { #1..12 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... succeeded.
     s(x1)	weight: x1
#a__from(x1)	weight: (/ 1 8) + x1
a__from(x1)	weight: (/ 1 4) + x1
 after(x1,x2)	weight: max{(/ 3 8) + x2, (/ 3 4) + x1}
#a__after(x1,x2)	weight: max{(/ 1 8) + x2, (/ 1 4) + x1}
a__after(x1,x2)	weight: max{(/ 3 8) + x2, (/ 3 4) + x1}
#mark(x1)	weight: x1
     0()	weight: (/ 1 8)
  from(x1)	weight: (/ 1 4) + x1
  mark(x1)	weight: x1
  cons(x1,x2)	weight: max{x2, (/ 1 4) + x1}
    Usable rules: { 1..10 }
    Removed DPs: #1 #2 #4..6 #8..12
Number of SCCs: 2, DPs: 2, edges: 2
	SCC { #3 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 2) + x1
#a__from(x1)	weight: 0
a__from(x1)	weight: 2
 after(x1,x2)	weight: (/ 1 2)
#a__after(x1,x2)	weight: 0
a__after(x1,x2)	weight: x1 + x2
#mark(x1)	weight: x1
     0()	weight: 0
  from(x1)	weight: (/ 5 2) + x1
  mark(x1)	weight: (/ 3 2)
  cons(x1,x2)	weight: 2 + x2
    Usable rules: { }
    Removed DPs: #3
Number of SCCs: 1, DPs: 1, edges: 1
	SCC { #7 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 2) + x1
#a__from(x1)	weight: 0
a__from(x1)	weight: (/ 1 2)
 after(x1,x2)	weight: (/ 1 4) + x2
#a__after(x1,x2)	weight: x1
a__after(x1,x2)	weight: (/ 1 4) + x2
#mark(x1)	weight: 0
     0()	weight: 0
  from(x1)	weight: (/ 1 4)
  mark(x1)	weight: (/ 1 4) + x1
  cons(x1,x2)	weight: (/ 1 4) + x2
    Usable rules: { 1..10 }
    Removed DPs: #7
Number of SCCs: 0, DPs: 0, edges: 0
YES