Input TRS:
    1: f(x,f(s(s(y)),f(z,w))) -> f(s(x),f(y,f(s(z),w)))
    2: L(f(s(s(y)),f(z,w))) -> L(f(s(0()),f(y,f(s(z),w))))
    3: f(x,f(s(s(y)),nil())) -> f(s(x),f(y,f(s(0()),nil())))
Number of strict rules: 3
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #L(f(s(s(y)),f(z,w))) -> #L(f(s(0()),f(y,f(s(z),w))))
   #2: #L(f(s(s(y)),f(z,w))) -> #f(s(0()),f(y,f(s(z),w)))
   #3: #L(f(s(s(y)),f(z,w))) -> #f(y,f(s(z),w))
   #4: #L(f(s(s(y)),f(z,w))) -> #f(s(z),w)
   #5: #f(x,f(s(s(y)),nil())) -> #f(s(x),f(y,f(s(0()),nil())))
   #6: #f(x,f(s(s(y)),nil())) -> #f(y,f(s(0()),nil()))
   #7: #f(x,f(s(s(y)),nil())) -> #f(s(0()),nil())
   #8: #f(x,f(s(s(y)),f(z,w))) -> #f(s(x),f(y,f(s(z),w)))
   #9: #f(x,f(s(s(y)),f(z,w))) -> #f(y,f(s(z),w))
   #10: #f(x,f(s(s(y)),f(z,w))) -> #f(s(z),w)
Number of SCCs: 2, DPs: 5, edges: 16
	SCC { #1 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... succeeded.
     s(x1)	weight: max{0, (/ 1 4) + x1}
   #L(x1)	weight: max{0, (/ 13 32) + x1}
     f(x1,x2)	weight: max{0, (- (/ 3 16)) + x2 + x1}
     0()	weight: (/ 3 32)
   nil()	weight: (/ 13 32)
   #f(x1,x2)	weight: 0
     L(x1)	weight: 0
    Usable rules: { 1 3 }
    Removed DPs: #1
Number of SCCs: 1, DPs: 4, edges: 15
	SCC { #5 #8..10 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 4) + x1
   #L(x1)	weight: 0
     f(x1,x2)	weight: x1 + x2
     0()	weight: 0
   nil()	weight: 0
   #f(x1,x2)	weight: x2
     L(x1)	weight: 0
    Usable rules: { 1 3 }
    Removed DPs: #5 #8..10
Number of SCCs: 0, DPs: 0, edges: 0
YES