Input TRS:
    1: O(0()) -> 0()
    2: +(0(),x) -> x
    3: +(x,0()) -> x
    4: +(O(x),O(y)) -> O(+(x,y))
    5: +(O(x),I(y)) -> I(+(x,y))
    6: +(I(x),O(y)) -> I(+(x,y))
    7: +(I(x),I(y)) -> O(+(+(x,y),I(0())))
    8: *(0(),x) -> 0()
    9: *(x,0()) -> 0()
    10: *(O(x),y) -> O(*(x,y))
    11: *(I(x),y) -> +(O(*(x,y)),y)
Number of strict rules: 11
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #+(I(x),O(y)) -> #+(x,y)
   #2: #*(I(x),y) -> #+(O(*(x,y)),y)
   #3: #*(I(x),y) -> #O(*(x,y))
   #4: #*(I(x),y) -> #*(x,y)
   #5: #+(I(x),I(y)) -> #O(+(+(x,y),I(0())))
   #6: #+(I(x),I(y)) -> #+(+(x,y),I(0()))
   #7: #+(I(x),I(y)) -> #+(x,y)
   #8: #*(O(x),y) -> #O(*(x,y))
   #9: #*(O(x),y) -> #*(x,y)
   #10: #+(O(x),I(y)) -> #+(x,y)
   #11: #+(O(x),O(y)) -> #O(+(x,y))
   #12: #+(O(x),O(y)) -> #+(x,y)
Number of SCCs: 2, DPs: 7, edges: 27
	SCC { #4 #9 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   #O(x1)	weight: 0
   #*(x1,x2)	weight: x1
     O(x1)	weight: (/ 1 2) + x1
     I(x1)	weight: (/ 1 2) + x1
     0()	weight: 0
     +(x1,x2)	weight: 0
   #+(x1,x2)	weight: 0
     *(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #4 #9
Number of SCCs: 1, DPs: 5, edges: 23
	SCC { #1 #6 #7 #10 #12 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   #O(x1)	weight: 0
   #*(x1,x2)	weight: 0
     O(x1)	weight: (/ 1 2) + x1
     I(x1)	weight: (/ 1 2) + x1
     0()	weight: 0
     +(x1,x2)	weight: (/ 1 2)
   #+(x1,x2)	weight: x2
     *(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #1 #7 #10 #12
Number of SCCs: 1, DPs: 1, edges: 1
	SCC { #6 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   #O(x1)	weight: 0
   #*(x1,x2)	weight: 0
     O(x1)	weight: x1
     I(x1)	weight: (/ 1 4) + x1
     0()	weight: 0
     +(x1,x2)	weight: (/ 1 8) + x1 + x2
   #+(x1,x2)	weight: x1 + x2
     *(x1,x2)	weight: 0
    Usable rules: { 1..7 }
    Removed DPs: #6
Number of SCCs: 0, DPs: 0, edges: 0
YES