Input TRS:
    1: p(a(x0),p(a(a(a(x1))),x2)) -> p(a(x2),p(a(a(b(x0))),x2))
Number of strict rules: 1
Direct Order(PosReal,>,Poly) ... failed.
Freezing p
1: p❆1_a(x0,p❆1_a(a(a(x1)),x2)) -> p❆1_a(x2,p❆1_a(a(b(x0)),x2))
2: p(a(_1),_2) ->= p❆1_a(_1,_2)
Number of strict rules: 1
Direct Order(PosReal,>,Poly) ... failed.
Dependency Pairs:
   #1: #p(a(_1),_2) ->? #p❆1_a(_1,_2)
   #2: #p❆1_a(x0,p❆1_a(a(a(x1)),x2)) -> #p❆1_a(x2,p❆1_a(a(b(x0)),x2))
   #3: #p❆1_a(x0,p❆1_a(a(a(x1)),x2)) -> #p❆1_a(a(b(x0)),x2)
Number of SCCs: 1, DPs: 2, edges: 4
	SCC { #2 #3 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     a(x1)	weight: (/ 1 4) + x1
     b(x1)	weight: (/ 94701 4)
   #p(x1,x2)	weight: 0
     p(x1,x2)	weight: 0
#p❆1_a(x1,x2)	weight: x2
p❆1_a(x1,x2)	weight: (/ 1 4) + x2
    Usable rules: { 1 }
    Removed DPs: #3
Number of SCCs: 1, DPs: 1, edges: 1
	SCC { #2 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... succeeded.
     a(x1)	status: [x1]	precedence above: b p❆1_a
     b(x1)	status: []	precedence above: a p❆1_a
   #p(x1,x2)	status: []	precedence above:
     p(x1,x2)	status: [x2,x1]	precedence above:
#p❆1_a(x1,x2)	status: [x2]	precedence above: a b p❆1_a
p❆1_a(x1,x2)	status: [x2,x1]	precedence above: a b
    Usable rules: { 1 }
    Removed DPs: #2
Number of SCCs: 0, DPs: 0, edges: 0
YES