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