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)
    12: -(x,0()) -> x
    13: -(0(),x) -> 0()
    14: -(O(x),O(y)) -> O(-(x,y))
    15: -(O(x),I(y)) -> I(-(-(x,y),I(1())))
    16: -(I(x),O(y)) -> I(-(x,y))
    17: -(I(x),I(y)) -> O(-(x,y))
Number of strict rules: 17
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: #-(O(x),O(y)) -> #O(-(x,y))
   #6: #-(O(x),O(y)) -> #-(x,y)
   #7: #+(I(x),I(y)) -> #O(+(+(x,y),I(0())))
   #8: #+(I(x),I(y)) -> #+(+(x,y),I(0()))
   #9: #+(I(x),I(y)) -> #+(x,y)
   #10: #*(O(x),y) -> #O(*(x,y))
   #11: #*(O(x),y) -> #*(x,y)
   #12: #+(O(x),I(y)) -> #+(x,y)
   #13: #-(I(x),I(y)) -> #O(-(x,y))
   #14: #-(I(x),I(y)) -> #-(x,y)
   #15: #-(I(x),O(y)) -> #-(x,y)
   #16: #-(O(x),I(y)) -> #-(-(x,y),I(1()))
   #17: #-(O(x),I(y)) -> #-(x,y)
   #18: #+(O(x),O(y)) -> #O(+(x,y))
   #19: #+(O(x),O(y)) -> #+(x,y)
Number of SCCs: 3, DPs: 12, edges: 50
	SCC { #4 #11 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     1()	weight: 0
   #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
   #+(x1,x2)	weight: 0
     *(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #4 #11
Number of SCCs: 2, DPs: 10, edges: 46
	SCC { #1 #8 #9 #12 #19 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     1()	weight: 0
   #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: 0
   #-(x1,x2)	weight: 0
     +(x1,x2)	weight: (/ 1 2)
   #+(x1,x2)	weight: x2
     *(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #1 #9 #12 #19
Number of SCCs: 2, DPs: 6, edges: 24
	SCC { #8 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     1()	weight: 0
   #O(x1)	weight: 0
   #*(x1,x2)	weight: 0
     O(x1)	weight: x1
     I(x1)	weight: (/ 1 4) + x1
     0()	weight: 0
     -(x1,x2)	weight: 0
   #-(x1,x2)	weight: 0
     +(x1,x2)	weight: (/ 1 8) + x1 + x2
   #+(x1,x2)	weight: x1 + x2
     *(x1,x2)	weight: 0
    Usable rules: { 1..7 }
    Removed DPs: #8
Number of SCCs: 1, DPs: 5, edges: 23
	SCC { #6 #14..17 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     1()	weight: 0
   #O(x1)	weight: 0
   #*(x1,x2)	weight: 0
     O(x1)	weight: x1
     I(x1)	weight: (/ 1 2) + x1
     0()	weight: 0
     -(x1,x2)	weight: (/ 1 2)
   #-(x1,x2)	weight: x2
     +(x1,x2)	weight: (/ 1 2) + x1 + x2
   #+(x1,x2)	weight: x1
     *(x1,x2)	weight: 0
    Usable rules: { 1 }
    Removed DPs: #14 #17
Number of SCCs: 3, DPs: 3, edges: 5
	SCC { #16 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     1()	weight: 0
   #O(x1)	weight: 0
   #*(x1,x2)	weight: 0
     O(x1)	weight: (/ 1 2) + x1
     I(x1)	weight: (/ 1 4) + x1
     0()	weight: 0
     -(x1,x2)	weight: (/ 1 4) + x1 + x2
   #-(x1,x2)	weight: x1 + x2
     +(x1,x2)	weight: (/ 1 4) + x2
   #+(x1,x2)	weight: 0
     *(x1,x2)	weight: 0
    Usable rules: { 1 12..17 }
    Removed DPs: #16
Number of SCCs: 2, DPs: 2, edges: 4
	SCC { #6 #15 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     1()	weight: 0
   #O(x1)	weight: 0
   #*(x1,x2)	weight: 0
     O(x1)	weight: (/ 1 4) + x1
     I(x1)	weight: (/ 1 8) + x1
     0()	weight: 0
     -(x1,x2)	weight: (/ 1 8) + x1 + x2
   #-(x1,x2)	weight: x1 + x2
     +(x1,x2)	weight: (/ 1 8) + x2
   #+(x1,x2)	weight: 0
     *(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #6 #15
Number of SCCs: 1, DPs: 0, edges: 0
YES