Input TRS:
    1: :(x,x) -> e()
    2: :(x,e()) -> x
    3: i(:(x,y)) -> :(y,x)
    4: :(:(x,y),z) -> :(x,:(z,i(y)))
    5: :(e(),x) -> i(x)
    6: i(i(x)) -> x
    7: i(e()) -> e()
    8: :(x,:(y,i(x))) -> i(y)
    9: :(x,:(y,:(i(x),z))) -> :(i(z),y)
    10: :(i(x),:(y,x)) -> i(y)
    11: :(i(x),:(y,:(x,z))) -> :(i(z),y)
Number of strict rules: 11
Direct Order(PosReal,>,Poly) ... removes: 8 1 5 10 11 9 2
     :(x1,x2)	weight: 8856 + x1 + x2
     i(x1)	weight: x1
     e()	weight: 0
Number of strict rules: 4
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #i(:(x,y)) -> #:(y,x)
   #2: #:(:(x,y),z) -> #:(x,:(z,i(y)))
   #3: #:(:(x,y),z) -> #:(z,i(y))
   #4: #:(:(x,y),z) -> #i(y)
Number of SCCs: 1, DPs: 4, edges: 10
	SCC { #1..4 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   #:(x1,x2)	weight: x1 + x2
     :(x1,x2)	weight: (/ 1 2) + x1 + x2
     i(x1)	weight: x1
     e()	weight: 0
   #i(x1)	weight: x1
    Usable rules: { 3 4 6 7 }
    Removed DPs: #1 #3 #4
Number of SCCs: 1, DPs: 1, edges: 1
	SCC { #2 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   #:(x1,x2)	weight: x1
     :(x1,x2)	weight: (/ 1 2) + x1
     i(x1)	weight: (/ 1 4)
     e()	weight: 0
   #i(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #2
Number of SCCs: 0, DPs: 0, edges: 0
YES