Input TRS:
    1: f(x,0(),0()) -> s(x)
    2: f(0(),y,0()) -> s(y)
    3: f(0(),0(),z) -> s(z)
    4: f(s(0()),y,z) -> f(0(),s(y),s(z))
    5: f(s(x),s(y),0()) -> f(x,y,s(0()))
    6: f(s(x),0(),s(z)) -> f(x,s(0()),z)
    7: f(0(),s(0()),s(0())) -> s(s(0()))
    8: f(s(x),s(y),s(z)) -> f(x,y,f(s(x),s(y),z))
    9: f(0(),s(s(y)),s(0())) -> f(0(),y,s(0()))
    10: f(0(),s(0()),s(s(z))) -> f(0(),s(0()),z)
    11: f(0(),s(s(y)),s(s(z))) -> f(0(),y,f(0(),s(s(y)),s(z)))
Number of strict rules: 11
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #f(s(x),0(),s(z)) -> #f(x,s(0()),z)
   #2: #f(0(),s(s(y)),s(0())) -> #f(0(),y,s(0()))
   #3: #f(0(),s(s(y)),s(s(z))) -> #f(0(),y,f(0(),s(s(y)),s(z)))
   #4: #f(0(),s(s(y)),s(s(z))) -> #f(0(),s(s(y)),s(z))
   #5: #f(0(),s(0()),s(s(z))) -> #f(0(),s(0()),z)
   #6: #f(s(x),s(y),0()) -> #f(x,y,s(0()))
   #7: #f(s(x),s(y),s(z)) -> #f(x,y,f(s(x),s(y),z))
   #8: #f(s(x),s(y),s(z)) -> #f(s(x),s(y),z)
   #9: #f(s(0()),y,z) -> #f(0(),s(y),s(z))
Number of SCCs: 4, DPs: 8, edges: 18
	SCC { #2 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 4) + x1
     f(x1,x2,x3)	weight: 0
     0()	weight: 0
   #f(x1,x2,x3)	weight: x2
    Usable rules: { }
    Removed DPs: #2
Number of SCCs: 3, DPs: 7, edges: 17
	SCC { #5 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 4) + x1
     f(x1,x2,x3)	weight: 0
     0()	weight: 0
   #f(x1,x2,x3)	weight: x3
    Usable rules: { }
    Removed DPs: #5
Number of SCCs: 2, DPs: 6, edges: 16
	SCC { #3 #4 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 4) + x1
     f(x1,x2,x3)	weight: (/ 1 2) + x3
     0()	weight: 0
   #f(x1,x2,x3)	weight: x2
    Usable rules: { }
    Removed DPs: #3
Number of SCCs: 2, DPs: 5, edges: 13
	SCC { #4 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... succeeded.
     s(x1)	weight: (/ 1 4) + x1
     f(x1,x2,x3)	weight: 0
     0()	weight: (/ 3 8)
   #f(x1,x2,x3)	weight: max{0, x3, x1}
    Usable rules: { }
    Removed DPs: #4
Number of SCCs: 1, DPs: 4, edges: 12
	SCC { #1 #6..8 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 4) + x1
     f(x1,x2,x3)	weight: (/ 1 8)
     0()	weight: 0
   #f(x1,x2,x3)	weight: x1
    Usable rules: { }
    Removed DPs: #1 #6 #7
Number of SCCs: 2, DPs: 1, edges: 1
	SCC { #8 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... succeeded.
     s(x1)	weight: (/ 1 4) + x1
     f(x1,x2,x3)	weight: 0
     0()	weight: (/ 3 4)
   #f(x1,x2,x3)	weight: max{0, (/ 1 4) + x3}
    Usable rules: { }
    Removed DPs: #8
Number of SCCs: 1, DPs: 0, edges: 0
YES