Input TRS:
    1: a__f(0()) -> cons(0(),f(s(0())))
    2: a__f(s(0())) -> a__f(a__p(s(0())))
    3: a__p(s(0())) -> 0()
    4: mark(f(X)) -> a__f(mark(X))
    5: mark(p(X)) -> a__p(mark(X))
    6: mark(0()) -> 0()
    7: mark(cons(X1,X2)) -> cons(mark(X1),X2)
    8: mark(s(X)) -> s(mark(X))
    9: a__f(X) -> f(X)
    10: a__p(X) -> p(X)
Number of strict rules: 10
Direct Order(PosReal,>,Poly) ... removes: 4 8 1 3 7 9 6
     s(x1)	weight: (/ 61225 2) + 2 * x1
  a__f(x1)	weight: (/ 244905 4) + x1
  a__p(x1)	weight: x1
     f(x1)	weight: (/ 122453 4) + x1
     p(x1)	weight: x1
     0()	weight: 0
  mark(x1)	weight: (/ 1 4) + 2 * x1
  cons(x1,x2)	weight: (/ 1 4) + x1 + x2
Number of strict rules: 3
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #a__f(s(0())) -> #a__f(a__p(s(0())))
   #2: #a__f(s(0())) -> #a__p(s(0()))
   #3: #mark(p(X)) -> #a__p(mark(X))
   #4: #mark(p(X)) -> #mark(X)
Number of SCCs: 1, DPs: 1, edges: 1
	SCC { #4 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: 0
  a__f(x1)	weight: 0
  a__p(x1)	weight: 0
     f(x1)	weight: 0
     p(x1)	weight: (/ 1 2) + x1
#mark(x1)	weight: x1
     0()	weight: 0
  mark(x1)	weight: 0
#a__p(x1)	weight: 0
  cons(x1,x2)	weight: 0
#a__f(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #4
Number of SCCs: 0, DPs: 0, edges: 0
YES