Input TRS:
    1: c(c(b(c(x)))) -> b(a(|0|(),c(x)))
    2: c(c(x)) -> b(c(b(c(x))))
    3: a(|0|(),x) -> c(c(x))
Number of strict rules: 3
Direct Order(PosReal,>,Poly) ... failed.
Freezing a
1: c(c(b(c(x)))) -> b(a❆1_|0|(c(x)))
2: c(c(x)) -> b(c(b(c(x))))
3: a❆1_|0|(x) -> c(c(x))
4: a(|0|(),_1) ->= a❆1_|0|(_1)
Number of strict rules: 3
Direct Order(PosReal,>,Poly) ... removes: 4
   |0|()	weight: 0
     a(x1,x2)	weight: (/ 35423 2) + x1 + x2
a❆1_|0|(x1)	weight: 17711 + x1
     b(x1)	weight: x1
     c(x1)	weight: (/ 17711 2) + x1
Number of strict rules: 3
Direct Order(PosReal,>,Poly) ... failed.
Dependency Pairs:
   #1: #c(c(x)) -> #c(b(c(x)))
   #2: #a❆1_|0|(x) -> #c(c(x))
   #3: #a❆1_|0|(x) -> #c(x)
   #4: #c(c(b(c(x)))) -> #a❆1_|0|(c(x))
Number of SCCs: 1, DPs: 3, edges: 4
	SCC { #2..4 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   |0|()	weight: 0
     a(x1,x2)	weight: 0
a❆1_|0|(x1)	weight: (/ 1 2) + x1
     b(x1)	weight: x1
     c(x1)	weight: (/ 1 4) + x1
#a❆1_|0|(x1)	weight: (/ 1 4) + x1
   #c(x1)	weight: x1
    Usable rules: { 1..3 }
    Removed DPs: #3
Number of SCCs: 1, DPs: 2, edges: 2
	SCC { #2 #4 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... QWPOpS(PosReal,>,MaxSum)... Order(PosReal,>,Sum-Sum; PosReal,≥,Sum-Sum)... succeeded.
   |0|()	weight: 0; 0
     a(x1,x2)	weight: 0; 0
a❆1_|0|(x1)	weight: (/ 1 2) + x1_1; (/ 1 2) + x1_2
     b(x1)	weight: (/ 1 4) + x1_1; (/ 1 8)
     c(x1)	weight: (/ 1 8) + x1_2; (/ 3 8) + x1_1
#a❆1_|0|(x1)	weight: (/ 1 2) + x1_1; 0
   #c(x1)	weight: x1_2; 0
    Usable rules: { 1..3 }
    Removed DPs: #2 #4
Number of SCCs: 0, DPs: 0, edges: 0
YES