Input TRS:
    1: f(a(),f(b(),x)) -> f(b(),f(a(),x))
    2: f(b(),f(c(),x)) -> f(c(),f(b(),x))
    3: f(c(),f(a(),x)) -> f(a(),f(c(),x))
Number of strict rules: 3
Direct Order(PosReal,>,Poly) ... failed.
Freezing f
1: f❆1_a(f❆1_b(x)) -> f❆1_b(f❆1_a(x))
2: f❆1_b(f❆1_c(x)) -> f❆1_c(f❆1_b(x))
3: f❆1_c(f❆1_a(x)) -> f❆1_a(f❆1_c(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 1 5 6
     a()	weight: 0
     b()	weight: 0
     c()	weight: 0
f❆1_c(x1)	weight: x1
     f(x1,x2)	weight: (/ 3 8) + x1 + 2 * x2
f❆1_b(x1)	weight: (/ 1 4) + 2 * x1
f❆1_a(x1)	weight: (/ 1 8) + 2 * x1
Number of strict rules: 2
Direct Order(PosReal,>,Poly) ... removes: 3
     a()	weight: 0
     b()	weight: 0
     c()	weight: 0
f❆1_c(x1)	weight: (/ 1 8) + 2 * x1
     f(x1,x2)	weight: (/ 1 4) + x1 + 2 * x2
f❆1_b(x1)	weight: x1
f❆1_a(x1)	weight: (/ 1 4) + 2 * x1
Number of strict rules: 1
Direct Order(PosReal,>,Poly) ... removes: 2
     a()	weight: 0
     b()	weight: 0
     c()	weight: 0
f❆1_c(x1)	weight: (/ 1 4) + 2 * x1
     f(x1,x2)	weight: (/ 1 4) + x1 + 2 * x2
f❆1_b(x1)	weight: (/ 1 8) + 2 * x1
f❆1_a(x1)	weight: (/ 1 8) + 2 * x1
Number of strict rules: 0
YES