Input TRS:
    1: f(f(a(),x),y) -> f(y,f(x,f(a(),f(h(a()),a()))))
Number of strict rules: 1
Direct Order(PosReal,>,Poly) ... failed.
Freezing f
1: f❆2_a(x,y) -> f(y,f(x,f❆1_a(f❆1_h(a(),a()))))
2: f(h(_1),_2) ->= f❆1_h(_1,_2)
3: f(a(),_1) ->= f❆1_a(_1)
4: f(f❆1_a(_1),_2) ->= f❆2_a(_1,_2)
Number of strict rules: 1
Direct Order(PosReal,>,Poly) ... removes: 2
     a()	weight: 0
     h(x1)	weight: (/ 1 4) + x1
f❆2_a(x1,x2)	weight: x1 + x2
     f(x1,x2)	weight: x1 + x2
f❆1_h(x1,x2)	weight: x1 + x2
f❆1_a(x1)	weight: x1
Number of strict rules: 1
Direct Order(PosReal,>,Poly) ... failed.
Dependency Pairs:
   #1: #f❆2_a(x,y) -> #f(y,f(x,f❆1_a(f❆1_h(a(),a()))))
   #2: #f❆2_a(x,y) -> #f(x,f❆1_a(f❆1_h(a(),a())))
   #3: #f(f❆1_a(_1),_2) ->? #f❆2_a(_1,_2)
Number of SCCs: 1, DPs: 3, edges: 4
	SCC { #1..3 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... succeeded.
     a()	weight: (/ 1 2)
     h(x1)	weight: 0
f❆2_a(x1,x2)	weight: max{0, (- (/ 1 4)) + x2 + x1}
#f❆2_a(x1,x2)	weight: max{0, (/ 1 4) + x2 + x1}
     f(x1,x2)	weight: max{0, (- (/ 3 8)) + x2 + x1}
f❆1_h(x1,x2)	weight: 0
   #f(x1,x2)	weight: max{0, (/ 1 8) + x2 + x1}
f❆1_a(x1)	weight: max{0, (/ 1 8) + x1}
    Usable rules: { 1 3 4 }
    Removed DPs: #1
Number of SCCs: 1, DPs: 2, edges: 2
	SCC { #2 #3 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     a()	weight: 0
     h(x1)	weight: 0
f❆2_a(x1,x2)	weight: (/ 3 4)
#f❆2_a(x1,x2)	weight: (/ 1 4) + x1
     f(x1,x2)	weight: x1
f❆1_h(x1,x2)	weight: (/ 1 4)
   #f(x1,x2)	weight: x1
f❆1_a(x1)	weight: (/ 1 2) + x1
    Usable rules: { }
    Removed DPs: #2 #3
Number of SCCs: 0, DPs: 0, edges: 0
YES