Input TRS:
    1: quot(0(),s(y),s(z)) -> 0()
    2: quot(s(x),s(y),z) -> quot(x,y,z)
    3: plus(0(),y) -> y
    4: plus(s(x),y) -> s(plus(x,y))
    5: quot(x,0(),s(z)) -> s(quot(x,plus(z,s(0())),s(z)))
Number of strict rules: 5
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #quot(s(x),s(y),z) -> #quot(x,y,z)
   #2: #quot(x,0(),s(z)) -> #quot(x,plus(z,s(0())),s(z))
   #3: #quot(x,0(),s(z)) -> #plus(z,s(0()))
   #4: #plus(s(x),y) -> #plus(x,y)
Number of SCCs: 2, DPs: 3, edges: 5
	SCC { #4 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 2) + x1
#plus(x1,x2)	weight: x1
     0()	weight: 0
  quot(x1,x2,x3)	weight: 0
  plus(x1,x2)	weight: 0
#quot(x1,x2,x3)	weight: 0
    Usable rules: { }
    Removed DPs: #4
Number of SCCs: 1, DPs: 2, edges: 4
	SCC { #1 #2 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 2) + x1
#plus(x1,x2)	weight: 0
     0()	weight: 0
  quot(x1,x2,x3)	weight: 0
  plus(x1,x2)	weight: (/ 1 2) + x1
#quot(x1,x2,x3)	weight: x1
    Usable rules: { }
    Removed DPs: #1
Number of SCCs: 1, DPs: 1, edges: 1
	SCC { #2 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... succeeded.
     s(x1)	weight: (/ 1 4)
#plus(x1,x2)	weight: 0
     0()	weight: (/ 3 4)
  quot(x1,x2,x3)	weight: 0
  plus(x1,x2)	weight: max{0, (/ 1 4) + x2}
#quot(x1,x2,x3)	weight: max{0, x2}
    Usable rules: { 3 4 }
    Removed DPs: #2
Number of SCCs: 0, DPs: 0, edges: 0
YES