Input TRS:
    1: f(b(x),y) -> f(x,b(y))
    2: f(x,a(y)) -> f(a(x),y)
    3: f(x,y) ->= f(a(x),y)
    4: f(x,y) ->= f(x,b(y))
Number of strict rules: 2
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #f(x,a(y)) -> #f(a(x),y)
   #2: #f(x,y) ->? #f(a(x),y)
   #3: #f(b(x),y) -> #f(x,b(y))
   #4: #f(x,y) ->? #f(x,b(y))
Number of SCCs: 1, DPs: 4, edges: 12
	SCC { #1..4 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     a(x1)	weight: (/ 1 2) + x1
     b(x1)	weight: 0
     f(x1,x2)	weight: 0
   #f(x1,x2)	weight: x2
    Usable rules: { }
    Removed DPs: #1
Number of SCCs: 1, DPs: 3, edges: 8
	SCC { #2..4 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     a(x1)	weight: 0
     b(x1)	weight: (/ 1 2) + x1
     f(x1,x2)	weight: 0
   #f(x1,x2)	weight: x1
    Usable rules: { }
    Removed DPs: #3
Number of SCCs: 1, DPs: 2, edges: 4
	SCC { #2 #4 }
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