Input TRS:
    1: f(a(),f(a(),x)) -> f(c(),f(b(),x))
    2: f(b(),f(b(),x)) -> f(a(),f(c(),x))
    3: f(c(),f(c(),x)) -> f(b(),f(a(),x))
Number of strict rules: 3
Direct Order(PosReal,>,Poly) ... failed.
Freezing f
1: f❆1_a(f❆1_a(x)) -> f❆1_c(f❆1_b(x))
2: f❆1_b(f❆1_b(x)) -> f❆1_a(f❆1_c(x))
3: f❆1_c(f❆1_c(x)) -> f❆1_b(f❆1_a(x))
4: f(a(),_1) ->= f❆1_a(_1)
5: f(c(),_1) ->= f❆1_c(_1)
6: f(b(),_1) ->= f❆1_b(_1)
Number of strict rules: 3
Direct Order(PosReal,>,Poly) ... removes: 4 5 6
     a()	weight: 0
     b()	weight: 0
     c()	weight: 0
f❆1_c(x1)	weight: (/ 85471 2) + x1
     f(x1,x2)	weight: 42736 + x1 + x2
f❆1_b(x1)	weight: (/ 85471 2) + x1
f❆1_a(x1)	weight: (/ 85471 2) + x1
Number of strict rules: 3
Direct Order(PosReal,>,Poly) ... failed.
Dependency Pairs:
   #1: #f❆1_b(f❆1_b(x)) -> #f❆1_a(f❆1_c(x))
   #2: #f❆1_b(f❆1_b(x)) -> #f❆1_c(x)
   #3: #f❆1_c(f❆1_c(x)) -> #f❆1_b(f❆1_a(x))
   #4: #f❆1_c(f❆1_c(x)) -> #f❆1_a(x)
   #5: #f❆1_a(f❆1_a(x)) -> #f❆1_c(f❆1_b(x))
   #6: #f❆1_a(f❆1_a(x)) -> #f❆1_b(x)
Number of SCCs: 1, DPs: 6, edges: 12
	SCC { #1..6 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     a()	weight: 0
     b()	weight: 0
     c()	weight: 0
#f❆1_b(x1)	weight: x1
f❆1_c(x1)	weight: (/ 1 2) + x1
     f(x1,x2)	weight: 0
#f❆1_c(x1)	weight: x1
#f❆1_a(x1)	weight: x1
f❆1_b(x1)	weight: (/ 1 2) + x1
f❆1_a(x1)	weight: (/ 1 2) + x1
    Usable rules: { 1..3 }
    Removed DPs: #2 #4 #6
Number of SCCs: 1, DPs: 3, edges: 3
	SCC { #1 #3 #5 }
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