Input TRS:
    1: minus(x,x) -> 0()
    2: minus(s(x),s(y)) -> minus(x,y)
    3: minus(0(),x) -> 0()
    4: minus(x,0()) -> x
    5: div(s(x),s(y)) -> s(div(minus(x,y),s(y)))
    6: div(0(),s(y)) -> 0()
    7: f(x,0(),b) -> x
    8: f(x,s(y),b) -> div(f(x,minus(s(y),s(0())),b),b)
Number of strict rules: 8
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #minus(s(x),s(y)) -> #minus(x,y)
   #2: #div(s(x),s(y)) -> #div(minus(x,y),s(y))
   #3: #div(s(x),s(y)) -> #minus(x,y)
   #4: #f(x,s(y),b) -> #div(f(x,minus(s(y),s(0())),b),b)
   #5: #f(x,s(y),b) -> #f(x,minus(s(y),s(0())),b)
   #6: #f(x,s(y),b) -> #minus(s(y),s(0()))
Number of SCCs: 3, DPs: 3, edges: 3
	SCC { #1 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
 #div(x1,x2)	weight: 0
     s(x1)	weight: (/ 1 2) + x1
 minus(x1,x2)	weight: 0
   div(x1,x2)	weight: 0
     f(x1,x2,x3)	weight: 0
     0()	weight: 0
   #f(x1,x2,x3)	weight: 0
#minus(x1,x2)	weight: x2
    Usable rules: { }
    Removed DPs: #1
Number of SCCs: 2, DPs: 2, edges: 2
	SCC { #2 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
 #div(x1,x2)	weight: x1
     s(x1)	weight: (/ 1 2) + x1
 minus(x1,x2)	weight: (/ 1 4) + x1
   div(x1,x2)	weight: 0
     f(x1,x2,x3)	weight: 0
     0()	weight: 0
   #f(x1,x2,x3)	weight: 0
#minus(x1,x2)	weight: 0
    Usable rules: { 1..4 }
    Removed DPs: #2
Number of SCCs: 1, DPs: 1, edges: 1
	SCC { #5 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... QWPOpS(PosReal,>,MaxSum)... Order(PosReal,>,Sum-Sum; PosReal,≥,Sum-Sum)... Order(PosReal,>,Sum-Sum; NegReal,≥,Sum)... succeeded.
 #div(x1,x2)	weight: 0; 0
     s(x1)	weight: max{0, (/ 1 2) + x1_1}; (- (/ 1 2)) + x1_2
 minus(x1,x2)	weight: max{0, (/ 1 4) + x2_2 + x1_1}; 0
   div(x1,x2)	weight: 0; 0
     f(x1,x2,x3)	weight: 0; 0
     0()	weight: 0; (- (/ 1 4))
   #f(x1,x2,x3)	weight: max{0, (- (/ 1 4)) + x2_1}; 0
#minus(x1,x2)	weight: 0; 0
    Usable rules: { 1..4 }
    Removed DPs: #5
Number of SCCs: 0, DPs: 0, edges: 0
YES