Input TRS:
    1: f(s(x1),x2,x3,x4,x5) -> f(x1,x2,x3,x4,x5)
    2: f(|0|(),s(x2),x3,x4,x5) -> f(x2,x2,x3,x4,x5)
    3: f(|0|(),|0|(),s(x3),x4,x5) -> f(x3,x3,x3,x4,x5)
    4: f(|0|(),|0|(),|0|(),s(x4),x5) -> f(x4,x4,x4,x4,x5)
    5: f(|0|(),|0|(),|0|(),|0|(),s(x5)) -> f(x5,x5,x5,x5,x5)
    6: f(|0|(),|0|(),|0|(),|0|(),|0|()) -> |0|()
Number of strict rules: 6
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #f(|0|(),s(x2),x3,x4,x5) -> #f(x2,x2,x3,x4,x5)
   #2: #f(|0|(),|0|(),|0|(),|0|(),s(x5)) -> #f(x5,x5,x5,x5,x5)
   #3: #f(|0|(),|0|(),s(x3),x4,x5) -> #f(x3,x3,x3,x4,x5)
   #4: #f(s(x1),x2,x3,x4,x5) -> #f(x1,x2,x3,x4,x5)
   #5: #f(|0|(),|0|(),|0|(),s(x4),x5) -> #f(x4,x4,x4,x4,x5)
Number of SCCs: 1, DPs: 5, edges: 25
	SCC { #1..5 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   |0|()	weight: 0
     s(x1)	weight: (/ 1 2) + x1
     f(x1,x2,x3,x4,x5)	weight: 0
   #f(x1,x2,x3,x4,x5)	weight: x5
    Usable rules: { }
    Removed DPs: #2
Number of SCCs: 1, DPs: 4, edges: 16
	SCC { #1 #3..5 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   |0|()	weight: 0
     s(x1)	weight: (/ 1 2) + x1
     f(x1,x2,x3,x4,x5)	weight: 0
   #f(x1,x2,x3,x4,x5)	weight: x4
    Usable rules: { }
    Removed DPs: #5
Number of SCCs: 1, DPs: 3, edges: 9
	SCC { #1 #3 #4 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   |0|()	weight: 0
     s(x1)	weight: (/ 1 2) + x1
     f(x1,x2,x3,x4,x5)	weight: 0
   #f(x1,x2,x3,x4,x5)	weight: x3
    Usable rules: { }
    Removed DPs: #3
Number of SCCs: 1, DPs: 2, edges: 4
	SCC { #1 #4 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   |0|()	weight: 0
     s(x1)	weight: (/ 1 2) + x1
     f(x1,x2,x3,x4,x5)	weight: 0
   #f(x1,x2,x3,x4,x5)	weight: x2
    Usable rules: { }
    Removed DPs: #1
Number of SCCs: 1, DPs: 1, edges: 1
	SCC { #4 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   |0|()	weight: 0
     s(x1)	weight: (/ 1 2) + x1
     f(x1,x2,x3,x4,x5)	weight: 0
   #f(x1,x2,x3,x4,x5)	weight: x1
    Usable rules: { }
    Removed DPs: #4
Number of SCCs: 0, DPs: 0, edges: 0
YES