Input TRS:
    1: f(s(x)) -> s(f(f(p(s(x)))))
    2: f(0()) -> 0()
    3: p(s(x)) -> x
Number of strict rules: 3
Direct Order(PosReal,>,Poly) ... failed.
Freezing p
1: f(s(x)) -> s(f(f(p❆1_s(x))))
2: f(0()) -> 0()
3: p❆1_s(x) -> x
4: p(s(_1)) ->= p❆1_s(_1)
Number of strict rules: 3
Direct Order(PosReal,>,Poly) ... removes: 4
     s(x1)	weight: (/ 1 4) + x1
p❆1_s(x1)	weight: x1
     f(x1)	weight: x1
     p(x1)	weight: 2 * x1
     0()	weight: 0
Number of strict rules: 3
Direct Order(PosReal,>,Poly) ... failed.
Dependency Pairs:
   #1: #f(s(x)) -> #f(f(p❆1_s(x)))
   #2: #f(s(x)) -> #f(p❆1_s(x))
   #3: #f(s(x)) -> #p❆1_s(x)
Number of SCCs: 1, DPs: 2, edges: 4
	SCC { #1 #2 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 2) + x1
p❆1_s(x1)	weight: x1
#p❆1_s(x1)	weight: 0
     f(x1)	weight: x1
     p(x1)	weight: 0
     0()	weight: 0
   #f(x1)	weight: x1
    Usable rules: { 1..3 }
    Removed DPs: #1 #2
Number of SCCs: 0, DPs: 0, edges: 0
YES