Input TRS:
    1: a(b(x)) -> b(a(a(x)))
    2: b(c(x)) -> c(b(b(x)))
    3: c(a(x)) -> a(c(c(x)))
    4: u(a(x)) -> x
    5: v(b(x)) -> x
    6: w(c(x)) -> x
    7: a(u(x)) -> x
    8: b(v(x)) -> x
    9: c(w(x)) -> x
Number of strict rules: 9
Direct Order(PosReal,>,Poly) ... removes: 4 8 5 7 9 6
     a(x1)	weight: x1
     v(x1)	weight: (/ 120373 4) + x1
     b(x1)	weight: x1
     u(x1)	weight: (/ 56937 4) + x1
     w(x1)	weight: (/ 1 4) + x1
     c(x1)	weight: x1
Number of strict rules: 3
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #b(c(x)) -> #c(b(b(x)))
   #2: #b(c(x)) -> #b(b(x))
   #3: #b(c(x)) -> #b(x)
   #4: #c(a(x)) -> #a(c(c(x)))
   #5: #c(a(x)) -> #c(c(x))
   #6: #c(a(x)) -> #c(x)
   #7: #a(b(x)) -> #b(a(a(x)))
   #8: #a(b(x)) -> #a(a(x))
   #9: #a(b(x)) -> #a(x)
Number of SCCs: 1, DPs: 9, edges: 27
	SCC { #1..9 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     a(x1)	weight: (/ 1 4) + x1
     v(x1)	weight: 0
     b(x1)	weight: (/ 1 16)
     u(x1)	weight: 0
     w(x1)	weight: 0
     c(x1)	weight: x1
   #c(x1)	weight: x1
   #a(x1)	weight: (/ 3 16)
   #b(x1)	weight: (/ 1 8)
    Usable rules: { 1..3 }
    Removed DPs: #1 #4..7
Number of SCCs: 2, DPs: 4, edges: 8
	SCC { #2 #3 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     a(x1)	weight: (/ 1 4)
     v(x1)	weight: 0
     b(x1)	weight: x1
     u(x1)	weight: 0
     w(x1)	weight: 0
     c(x1)	weight: (/ 1 4) + x1
   #c(x1)	weight: x1
   #a(x1)	weight: (/ 3 4)
   #b(x1)	weight: (/ 1 2) + x1
    Usable rules: { 1..3 }
    Removed DPs: #2 #3
Number of SCCs: 1, DPs: 2, edges: 4
	SCC { #8 #9 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     a(x1)	weight: x1
     v(x1)	weight: 0
     b(x1)	weight: (/ 1 4) + x1
     u(x1)	weight: 0
     w(x1)	weight: 0
     c(x1)	weight: 0
   #c(x1)	weight: x1
   #a(x1)	weight: (/ 3 4) + x1
   #b(x1)	weight: (/ 1 2) + x1
    Usable rules: { 1..3 }
    Removed DPs: #8 #9
Number of SCCs: 0, DPs: 0, edges: 0
YES