Input TRS:
    1: a__f(a(),X,X) -> a__f(X,a__b(),b())
    2: a__b() -> a()
    3: mark(f(X1,X2,X3)) -> a__f(X1,mark(X2),X3)
    4: mark(b()) -> a__b()
    5: mark(a()) -> a()
    6: a__f(X1,X2,X3) -> f(X1,X2,X3)
    7: a__b() -> b()
Number of strict rules: 7
Direct Order(PosReal,>,Poly) ... removes: 4 3 5 6
     a()	weight: 0
     b()	weight: 0
  a__b()	weight: 0
  a__f(x1,x2,x3)	weight: (/ 3 8) + x1 + x2 + 2 * x3
     f(x1,x2,x3)	weight: (/ 1 4) + x1 + x2 + x3
  mark(x1)	weight: (/ 1 8) + 2 * x1
Number of strict rules: 3
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #a__f(a(),X,X) -> #a__f(X,a__b(),b())
   #2: #a__f(a(),X,X) -> #a__b()
Number of SCCs: 1, DPs: 1, edges: 1
	SCC { #1 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... succeeded.
     a()	weight: (/ 1 2)
     b()	weight: (/ 1 4)
  a__b()	weight: (/ 1 8)
  a__f(x1,x2,x3)	weight: 0
#a__b()	weight: 0
     f(x1,x2,x3)	weight: 0
  mark(x1)	weight: 0
#a__f(x1,x2,x3)	weight: max{0, (/ 1 8) + x3, x1}
    Usable rules: { }
    Removed DPs: #1
Number of SCCs: 0, DPs: 0, edges: 0
YES