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
     i(x1)	weight: x1
     e()	weight: 0
   |:|(x1,x2)	weight: 8856 + x1 + x2
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
     i(x1)	weight: x1
     e()	weight: 0
   |:|(x1,x2)	weight: (/ 1 2) + x1 + x2
   #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
     i(x1)	weight: (/ 1 4)
     e()	weight: 0
   |:|(x1,x2)	weight: (/ 1 2) + x1
   #i(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #2
Number of SCCs: 0, DPs: 0, edges: 0
YES