Input TRS:
    1: D(t()) -> 1()
    2: D(constant()) -> 0()
    3: D(+(x,y)) -> +(D(x),D(y))
    4: D(*(x,y)) -> +(*(y,D(x)),*(x,D(y)))
    5: D(-(x,y)) -> -(D(x),D(y))
    6: D(minus(x)) -> minus(D(x))
    7: D(div(x,y)) -> -(div(D(x),y),div(*(x,D(y)),pow(y,2())))
    8: D(ln(x)) -> div(D(x),x)
    9: D(pow(x,y)) -> +(*(*(y,pow(x,-(y,1()))),D(x)),*(*(pow(x,y),ln(x)),D(y)))
Number of strict rules: 9
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #D(minus(x)) -> #D(x)
   #2: #D(pow(x,y)) -> #D(x)
   #3: #D(pow(x,y)) -> #D(y)
   #4: #D(div(x,y)) -> #D(x)
   #5: #D(div(x,y)) -> #D(y)
   #6: #D(-(x,y)) -> #D(x)
   #7: #D(-(x,y)) -> #D(y)
   #8: #D(+(x,y)) -> #D(x)
   #9: #D(+(x,y)) -> #D(y)
   #10: #D(ln(x)) -> #D(x)
   #11: #D(*(x,y)) -> #D(x)
   #12: #D(*(x,y)) -> #D(y)
Number of SCCs: 1, DPs: 12, edges: 144
	SCC { #1..12 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     1()	weight: 0
    ln(x1)	weight: (/ 1 2) + x1
constant()	weight: 0
 minus(x1)	weight: (/ 1 2) + x1
   pow(x1,x2)	weight: (/ 1 2) + x1 + x2
     t()	weight: 0
   div(x1,x2)	weight: (/ 1 2) + x1 + x2
     D(x1)	weight: 0
     0()	weight: 0
   #D(x1)	weight: x1
     -(x1,x2)	weight: (/ 1 2) + x1 + x2
     2()	weight: 0
     +(x1,x2)	weight: (/ 1 2) + x1 + x2
     *(x1,x2)	weight: (/ 1 2) + x1 + x2
    Usable rules: { }
    Removed DPs: #1..12
Number of SCCs: 0, DPs: 0, edges: 0
YES