Input TRS:
    1: a(lambda(x),y) -> lambda(a(x,p(1(),a(y,t()))))
    2: a(p(x,y),z) -> p(a(x,z),a(y,z))
    3: a(a(x,y),z) -> a(x,a(y,z))
    4: a(id(),x) -> x
    5: a(1(),id()) -> 1()
    6: a(t(),id()) -> t()
    7: a(1(),p(x,y)) -> x
    8: a(t(),p(x,y)) -> y
Number of strict rules: 8
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #a(p(x,y),z) -> #a(x,z)
   #2: #a(p(x,y),z) -> #a(y,z)
   #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,p(1(),a(y,t())))
   #6: #a(lambda(x),y) -> #a(y,t())
Number of SCCs: 1, DPs: 6, edges: 36
	SCC { #1..6 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... succeeded.
     a(x1,x2)	weight: max{0, x2 + x1}
     1()	weight: 0
     t()	weight: 0
lambda(x1)	weight: max{0, (/ 1 2) + x1}
     p(x1,x2)	weight: max{0, x1, x2}
    id()	weight: (/ 1 4)
   #a(x1,x2)	weight: max{0, (- (/ 1 4)) + x2 + x1}
    Usable rules: { 1..8 }
    Removed DPs: #5 #6
Number of SCCs: 1, DPs: 4, edges: 16
	SCC { #1..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)
     p(x1,x2)	weight: (/ 1 4) + x1 + x2
    id()	weight: 0
   #a(x1,x2)	weight: x1
    Usable rules: { }
    Removed DPs: #1..4
Number of SCCs: 0, DPs: 0, edges: 0
YES