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