Input TRS:
    1: f(a(),f(a(),f(a(),f(x,b())))) -> f(f(a(),f(a(),f(a(),x))),b())
    2: f(f(f(a(),x),b()),b()) -> f(f(a(),f(f(x,b()),b())),b())
Number of strict rules: 2
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #f(f(f(a(),x),b()),b()) -> #f(f(a(),f(f(x,b()),b())),b())
   #2: #f(f(f(a(),x),b()),b()) -> #f(a(),f(f(x,b()),b()))
   #3: #f(f(f(a(),x),b()),b()) -> #f(f(x,b()),b())
   #4: #f(f(f(a(),x),b()),b()) -> #f(x,b())
   #5: #f(a(),f(a(),f(a(),f(x,b())))) -> #f(f(a(),f(a(),f(a(),x))),b())
   #6: #f(a(),f(a(),f(a(),f(x,b())))) -> #f(a(),f(a(),f(a(),x)))
   #7: #f(a(),f(a(),f(a(),f(x,b())))) -> #f(a(),f(a(),x))
   #8: #f(a(),f(a(),f(a(),f(x,b())))) -> #f(a(),x)
Number of SCCs: 1, DPs: 8, edges: 32
	SCC { #1..8 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... succeeded.
     a()	weight: (/ 127433 2)
     b()	weight: (/ 42477 2)
     f(x1,x2)	weight: max{21239 + x2, x1}
   #f(x1,x2)	weight: max{(/ 42479 2) + x2, (/ 1 2) + x1}
    Usable rules: { 1 2 }
    Removed DPs: #3 #4 #7 #8
Number of SCCs: 1, DPs: 4, edges: 8
	SCC { #1 #2 #5 #6 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... QWPOpS(PosReal,>,MaxSum)... Order(PosReal,>,Sum-Sum; PosReal,≥,Sum-Sum)... succeeded.
     a()	weight: (/ 1 16); (/ 3 16)
     b()	weight: (/ 3 16); (/ 1 16)
     f(x1,x2)	weight: (/ 1 16) + x1_2; (/ 1 16)
   #f(x1,x2)	weight: x2_1; 0
    Usable rules: { 1 2 }
    Removed DPs: #2 #5
Number of SCCs: 2, DPs: 2, edges: 2
	SCC { #1 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... QWPOpS(PosReal,>,MaxSum)... Order(PosReal,>,Sum-Sum; PosReal,≥,Sum-Sum)... succeeded.
     a()	weight: (/ 1 8); (/ 1 8)
     b()	weight: (/ 1 4); 0
     f(x1,x2)	weight: (/ 1 8) + x2_2; (/ 1 8) + x2_1
   #f(x1,x2)	weight: x1_2; 0
    Usable rules: { 1 2 }
    Removed DPs: #1
Number of SCCs: 1, DPs: 1, edges: 1
	SCC { #6 }
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