Input TRS:
    1: f(f(a(),a()),x) -> f(a(),f(b(),f(a(),x)))
    2: f(x,f(y,z)) -> f(f(x,y),z)
Number of strict rules: 2
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #f(x,f(y,z)) -> #f(f(x,y),z)
   #2: #f(x,f(y,z)) -> #f(x,y)
   #3: #f(f(a(),a()),x) -> #f(a(),f(b(),f(a(),x)))
   #4: #f(f(a(),a()),x) -> #f(b(),f(a(),x))
   #5: #f(f(a(),a()),x) -> #f(a(),x)
Number of SCCs: 1, DPs: 5, edges: 16
	SCC { #1..5 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... succeeded.
     a()	weight: (/ 1 4)
     b()	weight: (/ 1 8)
     f(x1,x2)	weight: max{0, x1}
   #f(x1,x2)	weight: max{0, (/ 1 8) + x1}
    Usable rules: { 1 2 }
    Removed DPs: #4
Number of SCCs: 1, DPs: 4, edges: 12
	SCC { #1..3 #5 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... succeeded.
     a()	weight: (/ 1 4)
     b()	weight: 0
     f(x1,x2)	weight: max{0, x2 + x1}
   #f(x1,x2)	weight: max{0, (/ 1 4) + x2 + x1}
    Usable rules: { 1 2 }
    Removed DPs: #5
Number of SCCs: 1, DPs: 3, edges: 8
	SCC { #1..3 }
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