Input TRS:
    1: a(lambda(x),y) -> lambda(a(x,1()))
    2: a(lambda(x),y) -> lambda(a(x,a(y,t())))
    3: a(a(x,y),z) -> a(x,a(y,z))
    4: lambda(x) -> x
    5: a(x,y) -> x
    6: a(x,y) -> y
Number of strict rules: 6
Direct Order(PosReal,>,Poly) ... removes: 4
     a(x1,x2)	weight: x1 + x2
     1()	weight: 0
     t()	weight: 0
lambda(x1)	weight: (/ 1 4) + x1
Number of strict rules: 5
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #a(lambda(x),y) -> #a(x,a(y,t()))
   #2: #a(lambda(x),y) -> #a(y,t())
   #3: #a(a(x,y),z) -> #a(x,a(y,z))
   #4: #a(a(x,y),z) -> #a(y,z)
   #5: #a(lambda(x),y) -> #a(x,1())
Number of SCCs: 1, DPs: 5, edges: 25
	SCC { #1..5 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     a(x1,x2)	weight: x1 + x2
     1()	weight: 0
     t()	weight: 0
lambda(x1)	weight: (/ 1 2) + x1
   #a(x1,x2)	weight: x1 + x2
    Usable rules: { 1..3 5 6 }
    Removed DPs: #1 #2 #5
Number of SCCs: 1, DPs: 2, edges: 4
	SCC { #3 #4 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     a(x1,x2)	weight: (/ 1 4) + x1 + x2
     1()	weight: 0
     t()	weight: 0
lambda(x1)	weight: (/ 1 4) + x1
   #a(x1,x2)	weight: x1
    Usable rules: { }
    Removed DPs: #3 #4
Number of SCCs: 0, DPs: 0, edges: 0
YES