Input TRS:
    1: |:|(|:|(x,y),z) -> |:|(x,|:|(y,z))
    2: |:|(+(x,y),z) -> +(|:|(x,z),|:|(y,z))
    3: |:|(z,+(x,f(y))) -> |:|(g(z,y),+(x,a()))
Number of strict rules: 3
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #|:|(+(x,y),z) -> #|:|(x,z)
   #2: #|:|(+(x,y),z) -> #|:|(y,z)
   #3: #|:|(z,+(x,f(y))) -> #|:|(g(z,y),+(x,a()))
   #4: #|:|(|:|(x,y),z) -> #|:|(x,|:|(y,z))
   #5: #|:|(|:|(x,y),z) -> #|:|(y,z)
Number of SCCs: 1, DPs: 4, edges: 16
	SCC { #1 #2 #4 #5 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     a()	weight: 0
 #|:|(x1,x2)	weight: x1
     f(x1)	weight: (/ 1 4)
   |:|(x1,x2)	weight: (/ 1 4) + x1 + x2
     +(x1,x2)	weight: (/ 1 4) + x1 + x2
     g(x1,x2)	weight: (/ 1 2) + x2
    Usable rules: { }
    Removed DPs: #1 #2 #4 #5
Number of SCCs: 0, DPs: 0, edges: 0
YES