Input TRS:
    1: a__h(X) -> a__g(mark(X),X)
    2: a__g(a(),X) -> a__f(b(),X)
    3: a__f(X,X) -> a__h(a__a())
    4: a__a() -> b()
    5: mark(h(X)) -> a__h(mark(X))
    6: mark(g(X1,X2)) -> a__g(mark(X1),X2)
    7: mark(a()) -> a__a()
    8: mark(f(X1,X2)) -> a__f(mark(X1),X2)
    9: mark(b()) -> b()
    10: a__h(X) -> h(X)
    11: a__g(X1,X2) -> g(X1,X2)
    12: a__a() -> a()
    13: a__f(X1,X2) -> f(X1,X2)
Number of strict rules: 13
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #a__g(a(),X) -> #a__f(b(),X)
   #2: #mark(g(X1,X2)) -> #a__g(mark(X1),X2)
   #3: #mark(g(X1,X2)) -> #mark(X1)
   #4: #mark(a()) -> #a__a()
   #5: #mark(h(X)) -> #a__h(mark(X))
   #6: #mark(h(X)) -> #mark(X)
   #7: #a__f(X,X) -> #a__h(a__a())
   #8: #a__f(X,X) -> #a__a()
   #9: #a__h(X) -> #a__g(mark(X),X)
   #10: #a__h(X) -> #mark(X)
   #11: #mark(f(X1,X2)) -> #a__f(mark(X1),X2)
   #12: #mark(f(X1,X2)) -> #mark(X1)
Number of SCCs: 1, DPs: 10, edges: 32
	SCC { #1..3 #5..7 #9..12 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     a()	weight: 0
     h(x1)	weight: (/ 1 2) + x1
  a__g(x1,x2)	weight: (/ 1 2) + x1
  a__h(x1)	weight: (/ 1 2) + x1
     b()	weight: 0
#a__g(x1,x2)	weight: (/ 1 4)
  a__a()	weight: 0
  a__f(x1,x2)	weight: (/ 1 2) + x1
#a__h(x1)	weight: (/ 1 4) + x1
     f(x1,x2)	weight: (/ 1 2) + x1
#mark(x1)	weight: x1
#a__a()	weight: 0
  mark(x1)	weight: x1
#a__f(x1,x2)	weight: (/ 1 4)
     g(x1,x2)	weight: (/ 1 2) + x1
    Usable rules: { 1..13 }
    Removed DPs: #2 #3 #5 #6 #10..12
Number of SCCs: 1, DPs: 3, edges: 3
	SCC { #1 #7 #9 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... QWPOpS(PosReal,>,MaxSum)... Order(PosReal,>,Sum-Sum; PosReal,≥,Sum-Sum)... Order(PosReal,>,Sum-Sum; NegReal,≥,Sum)... Order(PosReal,>,MaxSum-Sum; NegReal,≥,Sum)... failed.
Removing edges: failed.
Finding a loop...  failed.
MAYBE