Input TRS:
    1: f(x,a(b(y))) -> f(a(a(x)),y)
    2: f(x,b(a(y))) -> f(b(b(x)),y)
    3: f(a(x),y) -> f(x,a(y))
    4: f(b(x),y) -> f(x,b(y))
Number of strict rules: 4
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #f(x,b(a(y))) -> #f(b(b(x)),y)
   #2: #f(a(x),y) -> #f(x,a(y))
   #3: #f(x,a(b(y))) -> #f(a(a(x)),y)
   #4: #f(b(x),y) -> #f(x,b(y))
Number of SCCs: 1, DPs: 4, edges: 12
	SCC { #1..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