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(X)) -> mark(X)
    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: 9 6
   |0|()	weight: 0
     s(x1)	weight: (/ 1 16) + 2 * x1
  a__f(x1)	weight: (/ 5 16) + 2 * x1
  a__p(x1)	weight: x1
     f(x1)	weight: (/ 3 16) + 2 * x1
     p(x1)	weight: x1
  mark(x1)	weight: (/ 1 16) + 2 * x1
  cons(x1,x2)	weight: x1 + x2
Number of strict rules: 8
Direct Order(PosReal,>,Poly) ... removes: 4 8 1 3
   |0|()	weight: 0
     s(x1)	weight: (/ 64571 2) + 2 * x1
  a__f(x1)	weight: 129143 + 2 * x1
  a__p(x1)	weight: x1
     f(x1)	weight: (/ 258287 4) + 2 * x1
     p(x1)	weight: x1
  mark(x1)	weight: (/ 1 4) + 2 * x1
  cons(x1,x2)	weight: x1 + x2
Number of strict rules: 4
Direct Order(PosReal,>,Poly) ... removes: 7
   |0|()	weight: 0
     s(x1)	weight: 42554 + 2 * x1
  a__f(x1)	weight: (/ 340433 2) + x1
  a__p(x1)	weight: x1
     f(x1)	weight: (/ 340433 4) + 2 * x1
     p(x1)	weight: x1
  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.
   |0|()	weight: 0
     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
  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