Input TRS:
    1: :(:(:(:(C(),x),y),z),u) -> :(:(x,z),:(:(:(x,y),z),u))
Number of strict rules: 1
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #:(:(:(:(C(),x),y),z),u) -> #:(:(x,z),:(:(:(x,y),z),u))
   #2: #:(:(:(:(C(),x),y),z),u) -> #:(x,z)
   #3: #:(:(:(:(C(),x),y),z),u) -> #:(:(:(x,y),z),u)
   #4: #:(:(:(:(C(),x),y),z),u) -> #:(:(x,y),z)
   #5: #:(:(:(:(C(),x),y),z),u) -> #:(x,y)
Number of SCCs: 1, DPs: 5, edges: 25
	SCC { #1..5 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... succeeded.
   #:(x1,x2)	weight: max{(/ 1 8) + x2, (/ 1 4) + x1}
     C()	weight: 0
     :(x1,x2)	weight: max{x2, (/ 1 8) + x1}
    Usable rules: { 1 }
    Removed DPs: #2 #4 #5
Number of SCCs: 1, DPs: 2, edges: 4
	SCC { #1 #3 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... succeeded.
   #:(x1,x2)	status: [x1]	precedence above: :
     C()	status: []	precedence above:
     :(x1,x2)	status: [x1,x2]	precedence above: #:
    Usable rules: { 1 }
    Removed DPs: #1
Number of SCCs: 1, DPs: 1, edges: 1
	SCC { #3 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... succeeded.
   #:(x1,x2)	status: x1
     C()	status: []	precedence above:
     :(x1,x2)	status: [x1,x2]	precedence above: #:
    Usable rules: { 1 }
    Removed DPs: #3
Number of SCCs: 0, DPs: 0, edges: 0
YES