Input TRS:
    1: b(B(x)) -> B(b(x))
    2: b(c(d(x))) -> B(c(D(x)))
    3: D(d(x)) -> d(D(x))
    4: a(P(x)) -> a(b(b(x)))
    5: B(P(x)) -> P(b(x))
    6: b(c(d(x))) -> P(c(Q(x)))
    7: Q(D(x)) -> d(Q(x))
    8: Q(e(x)) -> d(d(e(x)))
Number of strict rules: 8
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #b(c(d(x))) -> #B(c(D(x)))
   #2: #b(c(d(x))) -> #D(x)
   #3: #b(c(d(x))) -> #Q(x)
   #4: #Q(D(x)) -> #Q(x)
   #5: #B(P(x)) -> #b(x)
   #6: #D(d(x)) -> #D(x)
   #7: #b(B(x)) -> #B(b(x))
   #8: #b(B(x)) -> #b(x)
   #9: #a(P(x)) -> #a(b(b(x)))
   #10: #a(P(x)) -> #b(b(x))
   #11: #a(P(x)) -> #b(x)
Number of SCCs: 4, DPs: 6, edges: 8
	SCC { #6 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     a(x1)	weight: 0
     Q(x1)	weight: 0
     d(x1)	weight: (/ 1 2) + x1
     b(x1)	weight: 0
   #B(x1)	weight: 0
   #Q(x1)	weight: 0
     c(x1)	weight: 0
     D(x1)	weight: 0
     B(x1)	weight: 0
   #D(x1)	weight: x1
     e(x1)	weight: 0
     P(x1)	weight: 0
   #a(x1)	weight: 0
   #b(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #6
Number of SCCs: 3, DPs: 5, edges: 7
	SCC { #4 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     a(x1)	weight: 0
     Q(x1)	weight: 0
     d(x1)	weight: (/ 1 2)
     b(x1)	weight: 0
   #B(x1)	weight: 0
   #Q(x1)	weight: x1
     c(x1)	weight: 0
     D(x1)	weight: (/ 1 2) + x1
     B(x1)	weight: 0
   #D(x1)	weight: 0
     e(x1)	weight: 0
     P(x1)	weight: 0
   #a(x1)	weight: 0
   #b(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #4
Number of SCCs: 2, DPs: 4, edges: 6
	SCC { #9 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... QWPOpS(PosReal,>,MaxSum)... Order(PosReal,>,Sum-Sum; PosReal,≥,Sum-Sum)... Order(PosReal,>,Sum-Sum; NegReal,≥,Sum)... Order(PosReal,>,MaxSum-Sum; NegReal,≥,Sum)... failed.
Removing edges: failed.
Finding a loop...  failed.
MAYBE