Input TRS:
    1: a(a(b(b(x)))) -> b(b(b(a(a(a(x))))))
    2: a(c(x)) -> c(a(x))
    3: c(b(x)) -> b(c(x))
    4: dup(A'(a(b(b(x))))) -> collapse(A'(a(x)),A'(a(x)))
    5: collapse(x,y) -> dup(x)
    6: collapse(x,y) -> dup(y)
Number of strict rules: 6
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #a(c(x)) -> #c(a(x))
   #2: #a(c(x)) -> #a(x)
   #3: #collapse(x,y) -> #dup(y)
   #4: #collapse(x,y) -> #dup(x)
   #5: #c(b(x)) -> #c(x)
   #6: #a(a(b(b(x)))) -> #a(a(a(x)))
   #7: #a(a(b(b(x)))) -> #a(a(x))
   #8: #a(a(b(b(x)))) -> #a(x)
   #9: #dup(A'(a(b(b(x))))) -> #collapse(A'(a(x)),A'(a(x)))
   #10: #dup(A'(a(b(b(x))))) -> #a(x)
   #11: #dup(A'(a(b(b(x))))) -> #a(x)
Number of SCCs: 3, DPs: 8, edges: 21
	SCC { #5 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     a(x1)	weight: 0
   dup(x1)	weight: 0
     b(x1)	weight: (/ 1 2) + x1
#collapse(x1,x2)	weight: 0
     c(x1)	weight: 0
    A'(x1)	weight: 0
collapse(x1,x2)	weight: 0
   #c(x1)	weight: x1
   #a(x1)	weight: 0
 #dup(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #5
Number of SCCs: 2, DPs: 7, edges: 20
	SCC { #3 #4 #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