Input TRS:
    1: f(f(s(x),0()),f(y,z)) -> f(f(y,z),f(y,s(z)))
    2: f(f(s(x),s(y)),f(z,w)) -> f(f(x,y),f(z,w))
Number of strict rules: 2
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #f(f(s(x),s(y)),f(z,w)) -> #f(f(x,y),f(z,w))
   #2: #f(f(s(x),s(y)),f(z,w)) -> #f(x,y)
   #3: #f(f(s(x),0()),f(y,z)) -> #f(f(y,z),f(y,s(z)))
   #4: #f(f(s(x),0()),f(y,z)) -> #f(y,s(z))
Number of SCCs: 1, DPs: 3, edges: 9
	SCC { #1..3 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... succeeded.
     s(x1)	weight: x1
     f(x1,x2)	weight: max{(/ 307 8) + x2, (/ 305 8) + x1}
     0()	weight: (/ 1 8)
   #f(x1,x2)	weight: max{(/ 1 8) + x2, (/ 1 8) + x1}
    Usable rules: { 1 2 }
    Removed DPs: #2
Number of SCCs: 1, DPs: 2, edges: 4
	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