Input TRS:
    1: f(a(),x) -> f(b(),f(c(),x))
    2: f(a(),f(b(),x)) -> f(b(),f(a(),x))
    3: f(d(),f(c(),x)) -> f(d(),f(a(),x))
    4: f(a(),f(c(),x)) -> f(c(),f(a(),x))
Number of strict rules: 4
Direct Order(PosReal,>,Poly) ... failed.
Freezing f
1: f❆1_a(x) -> f❆1_b(f❆1_c(x))
2: f❆1_a(f❆1_b(x)) -> f❆1_b(f❆1_a(x))
3: f❆1_d(f❆1_c(x)) -> f❆1_d(f❆1_a(x))
4: f❆1_a(f❆1_c(x)) -> f❆1_c(f❆1_a(x))
5: f(a(),_1) ->= f❆1_a(_1)
6: f(d(),_1) ->= f❆1_d(_1)
7: f(c(),_1) ->= f❆1_c(_1)
8: f(b(),_1) ->= f❆1_b(_1)
Number of strict rules: 4
Direct Order(PosReal,>,Poly) ... removes: 8 5 7 6
     a()	weight: 0
     d()	weight: 0
     b()	weight: 0
     c()	weight: 0
f❆1_c(x1)	weight: (/ 1 4) + 2 * x1
     f(x1,x2)	weight: (/ 1 2) + x1 + 2 * x2
f❆1_b(x1)	weight: x1
f❆1_d(x1)	weight: x1
f❆1_a(x1)	weight: (/ 1 4) + 2 * x1
Number of strict rules: 4
Direct Order(PosReal,>,Poly) ... failed.
Dependency Pairs:
   #1: #f❆1_a(f❆1_b(x)) -> #f❆1_a(x)
   #2: #f❆1_d(f❆1_c(x)) -> #f❆1_d(f❆1_a(x))
   #3: #f❆1_d(f❆1_c(x)) -> #f❆1_a(x)
   #4: #f❆1_a(f❆1_c(x)) -> #f❆1_a(x)
Number of SCCs: 2, DPs: 3, edges: 5
	SCC { #2 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     a()	weight: 0
     d()	weight: 0
     b()	weight: 0
     c()	weight: 0
#f❆1_d(x1)	weight: x1
f❆1_c(x1)	weight: (/ 1 2) + x1
     f(x1,x2)	weight: 0
#f❆1_a(x1)	weight: 0
f❆1_b(x1)	weight: (/ 1 4)
f❆1_d(x1)	weight: 0
f❆1_a(x1)	weight: (/ 1 4) + x1
    Usable rules: { 1 2 4 }
    Removed DPs: #2
Number of SCCs: 1, DPs: 2, edges: 4
	SCC { #1 #4 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     a()	weight: 0
     d()	weight: 0
     b()	weight: 0
     c()	weight: 0
#f❆1_d(x1)	weight: x1
f❆1_c(x1)	weight: (/ 1 4) + x1
     f(x1,x2)	weight: 0
#f❆1_a(x1)	weight: x1
f❆1_b(x1)	weight: (/ 1 4) + x1
f❆1_d(x1)	weight: 0
f❆1_a(x1)	weight: (/ 1 2) + x1
    Usable rules: { }
    Removed DPs: #1 #4
Number of SCCs: 0, DPs: 0, edges: 0
YES