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