Input TRS:
    1: b(y,z) -> f(c(c(y,z,z),a(),a()))
    2: b(b(z,y),a()) -> z
    3: c(f(z),f(c(a(),x,a())),y) -> c(f(b(x,z)),c(z,y,a()),a())
Number of strict rules: 3
Direct Order(PosReal,>,Poly) ... failed.
Freezing c
1: b(y,z) -> f(c(c(y,z,z),a(),a()))
2: b(b(z,y),a()) -> z
3: c❆1_f(z,f(c❆1_a(x,a())),y) -> c❆1_f(b(x,z),c(z,y,a()),a())
4: c(a(),_2,_3) ->= c❆1_a(_2,_3)
5: c(f(_1),_3,_4) ->= c❆1_f(_1,_3,_4)
Number of strict rules: 3
Direct Order(PosReal,>,Poly) ... failed.
Dependency Pairs:
   #1: #c(f(_1),_3,_4) ->? #c❆1_f(_1,_3,_4)
   #2: #c❆1_f(z,f(c❆1_a(x,a())),y) -> #c❆1_f(b(x,z),c(z,y,a()),a())
   #3: #c❆1_f(z,f(c❆1_a(x,a())),y) -> #b(x,z)
   #4: #c❆1_f(z,f(c❆1_a(x,a())),y) -> #c(z,y,a())
   #5: #b(y,z) -> #c(c(y,z,z),a(),a())
   #6: #b(y,z) -> #c(y,z,z)
Number of SCCs: 1, DPs: 4, edges: 5
	SCC { #1 #3 #4 #6 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... succeeded.
     a()	weight: (/ 1 16)
c❆1_f(x1,x2,x3)	weight: 0
     b(x1,x2)	weight: 0
c❆1_a(x1,x2)	weight: max{x2, (/ 1 16) + x1}
#c❆1_f(x1,x2,x3)	weight: max{(/ 7 16) + x3, (/ 1 16) + x2, (/ 11 16) + x1}
     c(x1,x2,x3)	weight: 0
     f(x1)	weight: (/ 7 16) + x1
   #c(x1,x2,x3)	weight: max{(/ 7 16) + x3, (/ 1 16) + x2, (/ 5 16) + x1}
   #b(x1,x2)	weight: max{(/ 5 8) + x2, (/ 3 8) + x1}
    Usable rules: { }
    Removed DPs: #3 #4 #6
Number of SCCs: 0, DPs: 0, edges: 0
YES