Input TRS:
    1: b(f(b(x,z)),y) -> f(f(f(b(z,b(y,z)))))
    2: c(f(f(c(x,a(),z))),a(),y) -> b(y,f(b(a(),z)))
    3: b(b(c(b(a(),a()),a(),z),f(a())),y) -> z
Number of strict rules: 3
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #c(f(f(c(x,a(),z))),a(),y) -> #b(y,f(b(a(),z)))
   #2: #c(f(f(c(x,a(),z))),a(),y) -> #b(a(),z)
   #3: #b(f(b(x,z)),y) -> #b(z,b(y,z))
   #4: #b(f(b(x,z)),y) -> #b(y,z)
Number of SCCs: 1, DPs: 2, edges: 4
	SCC { #3 #4 }
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(x1,x2)	weight: (/ 1 8) + x2_2 + x1_1; x1_2
     c(x1,x2,x3)	weight: x3_1 + x3_2; x3_1 + x3_2
     f(x1)	weight: (/ 1 8); x1_1
   #c(x1,x2,x3)	weight: 0; 0
   #b(x1,x2)	weight: x2_2 + x1_2; 0
    Usable rules: { 1 3 }
    Removed DPs: #3 #4
Number of SCCs: 0, DPs: 0, edges: 0
YES