Input TRS:
    1: f(a(),a()) -> f(a(),b())
    2: f(a(),b()) -> f(s(a()),c())
    3: f(s(X),c()) -> f(X,c())
    4: f(c(),c()) -> f(a(),a())
Number of strict rules: 4
Direct Order(PosReal,>,Poly) ... failed.
Freezing f
1: f❆1_a(a()) -> f❆1_a(b())
2: f❆1_a(b()) -> f❆1_s(a(),c())
3: f❆1_s(X,c()) -> f(X,c())
4: f❆1_c(c()) -> f❆1_a(a())
5: f(a(),_1) ->= f❆1_a(_1)
6: f(s(_1),_2) ->= f❆1_s(_1,_2)
7: f(c(),_1) ->= f❆1_c(_1)
Number of strict rules: 4
Direct Order(PosReal,>,Poly) ... removes: 6
     a()	weight: 0
     s(x1)	weight: (/ 1 4) + x1
     b()	weight: 0
     c()	weight: 0
f❆1_s(x1,x2)	weight: 2 * x1 + x2
f❆1_c(x1)	weight: x1
     f(x1,x2)	weight: 2 * x1 + x2
f❆1_a(x1)	weight: x1
Number of strict rules: 4
Direct Order(PosReal,>,Poly) ... failed.
Dependency Pairs:
   #1: #f❆1_a(b()) -> #f❆1_s(a(),c())
   #2: #f(c(),_1) ->? #f❆1_c(_1)
   #3: #f(a(),_1) ->? #f❆1_a(_1)
   #4: #f❆1_s(X,c()) -> #f(X,c())
   #5: #f❆1_a(a()) -> #f❆1_a(b())
   #6: #f❆1_c(c()) -> #f❆1_a(a())
Number of SCCs: 1, DPs: 6, edges: 8
	SCC { #1..6 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... succeeded.
     a()	weight: 0
#f❆1_s(x1,x2)	weight: max{0, x1}
     s(x1)	weight: 0
     b()	weight: (/ 1 4)
     c()	weight: (/ 1 4)
f❆1_s(x1,x2)	weight: 0
f❆1_c(x1)	weight: 0
     f(x1,x2)	weight: 0
#f❆1_c(x1)	weight: 0
#f❆1_a(x1)	weight: 0
   #f(x1,x2)	weight: max{0, x1}
f❆1_a(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #2
Number of SCCs: 1, DPs: 4, edges: 5
	SCC { #1 #3..5 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... succeeded.
     a()	weight: (/ 3 8)
#f❆1_s(x1,x2)	weight: max{0, (/ 1 4) + x2}
     s(x1)	weight: 0
     b()	weight: (/ 1 4)
     c()	weight: 0
f❆1_s(x1,x2)	weight: 0
f❆1_c(x1)	weight: 0
     f(x1,x2)	weight: 0
#f❆1_c(x1)	weight: 0
#f❆1_a(x1)	weight: (/ 1 8) + x1
   #f(x1,x2)	weight: max{0, (/ 1 4) + x2}
f❆1_a(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #1 #3 #5
Number of SCCs: 0, DPs: 0, edges: 0
YES