Input TRS:
    1: a__f(g(X),Y) -> a__f(mark(X),f(g(X),Y))
    2: mark(f(X1,X2)) -> a__f(mark(X1),X2)
    3: mark(g(X)) -> g(mark(X))
    4: a__f(X1,X2) -> f(X1,X2)
Number of strict rules: 4
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #mark(f(X1,X2)) -> #a__f(mark(X1),X2)
   #2: #mark(f(X1,X2)) -> #mark(X1)
   #3: #mark(g(X)) -> #mark(X)
   #4: #a__f(g(X),Y) -> #a__f(mark(X),f(g(X),Y))
   #5: #a__f(g(X),Y) -> #mark(X)
Number of SCCs: 1, DPs: 5, edges: 13
	SCC { #1..5 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
  a__f(x1,x2)	weight: (/ 1 4) + x1
     f(x1,x2)	weight: (/ 1 4) + x1
#mark(x1)	weight: (/ 1 4) + x1
  mark(x1)	weight: (/ 1 4) + x1
#a__f(x1,x2)	weight: x1
     g(x1)	weight: (/ 1 2) + x1
    Usable rules: { 1..4 }
    Removed DPs: #1..5
Number of SCCs: 0, DPs: 0, edges: 0
YES