Input TRS:
    1: o(lambda(x),y) -> lambda(o(x,d(1(),o(y,p()))))
    2: o(d(x,y),z) -> d(o(x,z),o(y,z))
    3: o(o(x,y),z) -> o(x,o(y,z))
    4: lambda(x) -> x
    5: o(x,y) -> x
    6: o(x,y) -> y
    7: d(x,y) -> x
    8: d(x,y) -> y
    9: o(x,y) ->= d(x,y)
    10: o(x,y) ->= d(y,x)
Number of strict rules: 8
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #o(d(x,y),z) -> #d(o(x,z),o(y,z))
   #2: #o(d(x,y),z) -> #o(x,z)
   #3: #o(d(x,y),z) -> #o(y,z)
   #4: #o(x,y) ->? #d(x,y)
   #5: #o(x,y) ->? #d(y,x)
   #6: #o(o(x,y),z) -> #o(x,o(y,z))
   #7: #o(o(x,y),z) -> #o(y,z)
   #8: #o(lambda(x),y) -> #lambda(o(x,d(1(),o(y,p()))))
   #9: #o(lambda(x),y) -> #o(x,d(1(),o(y,p())))
   #10: #o(lambda(x),y) -> #d(1(),o(y,p()))
   #11: #o(lambda(x),y) -> #o(y,p())
Number of SCCs: 1, DPs: 6, edges: 36
	SCC { #2 #3 #6 #7 #9 #11 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... succeeded.
     1()	weight: 0
     d(x1,x2)	weight: max{0, x1, x2}
#lambda(x1)	weight: 0
lambda(x1)	weight: max{0, (/ 1 4) + x1}
     o(x1,x2)	weight: max{0, x2 + x1}
     p()	weight: 0
   #o(x1,x2)	weight: max{0, (/ 1 4) + x2 + x1}
   #d(x1,x2)	weight: 0
    Usable rules: { 1..10 }
    Removed DPs: #9 #11
Number of SCCs: 1, DPs: 4, edges: 16
	SCC { #2 #3 #6 #7 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     1()	weight: 0
     d(x1,x2)	weight: (/ 1 4) + x1 + x2
#lambda(x1)	weight: 0
lambda(x1)	weight: (/ 1 8)
     o(x1,x2)	weight: (/ 1 8) + x1 + x2
     p()	weight: 0
   #o(x1,x2)	weight: x1
   #d(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #2 #3 #6 #7
Number of SCCs: 0, DPs: 0, edges: 0
YES