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.
   |0|()	weight: 0
     s(x1)	weight: (/ 1 4) + x1
     f(x1,x2,x3)	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.
   |0|()	weight: 0
     s(x1)	weight: (/ 1 4) + x1
     f(x1,x2,x3)	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.
   |0|()	weight: 0
     s(x1)	weight: (/ 1 4) + x1
     f(x1,x2,x3)	weight: (/ 1 2) + x3
   #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.
   |0|()	weight: (/ 1 4)
     s(x1)	weight: (/ 1 4) + x1
     f(x1,x2,x3)	weight: 0
   #f(x1,x2,x3)	weight: max{0, x3}
    Usable rules: { }
    Removed DPs: #4
Number of SCCs: 1, DPs: 4, edges: 12
	SCC { #1 #6..8 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   |0|()	weight: 0
     s(x1)	weight: (/ 1 4) + x1
     f(x1,x2,x3)	weight: (/ 1 2) + x1 + x3
   #f(x1,x2,x3)	weight: x1 + x2
    Usable rules: { }
    Removed DPs: #6 #7
Number of SCCs: 2, DPs: 1, edges: 1
	SCC { #8 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... succeeded.
   |0|()	weight: (/ 1 4)
     s(x1)	weight: (/ 1 4) + x1
     f(x1,x2,x3)	weight: 0
   #f(x1,x2,x3)	weight: max{0, (/ 1 4) + x3}
    Usable rules: { }
    Removed DPs: #8
Number of SCCs: 1, DPs: 0, edges: 0
YES