Input TRS:
    1: plus(0(),Y) -> Y
    2: plus(s(X),Y) -> s(plus(X,Y))
    3: min(X,0()) -> X
    4: min(s(X),s(Y)) -> min(X,Y)
    5: min(min(X,Y),Z()) -> min(X,plus(Y,Z()))
    6: quot(0(),s(Y)) -> 0()
    7: quot(s(X),s(Y)) -> s(quot(min(X,Y),s(Y)))
Number of strict rules: 7
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #plus(s(X),Y) -> #plus(X,Y)
   #2: #quot(s(X),s(Y)) -> #quot(min(X,Y),s(Y))
   #3: #quot(s(X),s(Y)) -> #min(X,Y)
   #4: #min(min(X,Y),Z()) -> #min(X,plus(Y,Z()))
   #5: #min(min(X,Y),Z()) -> #plus(Y,Z())
   #6: #min(s(X),s(Y)) -> #min(X,Y)
Number of SCCs: 3, DPs: 4, edges: 6
	SCC { #1 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     Z()	weight: 0
     s(x1)	weight: (/ 1 2) + x1
#plus(x1,x2)	weight: x1
 #min(x1,x2)	weight: 0
     0()	weight: 0
  quot(x1,x2)	weight: 0
  plus(x1,x2)	weight: 0
   min(x1,x2)	weight: 0
#quot(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #1
Number of SCCs: 2, DPs: 3, edges: 5
	SCC { #2 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     Z()	weight: 0
     s(x1)	weight: (/ 1 2) + x1
#plus(x1,x2)	weight: 0
 #min(x1,x2)	weight: 0
     0()	weight: 0
  quot(x1,x2)	weight: 0
  plus(x1,x2)	weight: (/ 1 4)
   min(x1,x2)	weight: (/ 1 4) + x1
#quot(x1,x2)	weight: x1
    Usable rules: { 3..5 }
    Removed DPs: #2
Number of SCCs: 1, DPs: 2, edges: 4
	SCC { #4 #6 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     Z()	weight: 0
     s(x1)	weight: x1
#plus(x1,x2)	weight: 0
 #min(x1,x2)	weight: x1 + x2
     0()	weight: 0
  quot(x1,x2)	weight: 0
  plus(x1,x2)	weight: (/ 1 4) + x2
   min(x1,x2)	weight: (/ 1 2) + x1 + x2
#quot(x1,x2)	weight: x1
    Usable rules: { 1 2 }
    Removed DPs: #4
Number of SCCs: 1, DPs: 1, edges: 1
	SCC { #6 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     Z()	weight: 0
     s(x1)	weight: (/ 1 4) + x1
#plus(x1,x2)	weight: 0
 #min(x1,x2)	weight: x2
     0()	weight: 0
  quot(x1,x2)	weight: 0
  plus(x1,x2)	weight: (/ 1 4) + x1 + x2
   min(x1,x2)	weight: (/ 1 2) + x1 + x2
#quot(x1,x2)	weight: x1
    Usable rules: { }
    Removed DPs: #6
Number of SCCs: 0, DPs: 0, edges: 0
YES