Input TRS:
    1: f(0()) -> 0()
    2: f(s(0())) -> s(0())
    3: f(s(s(x))) -> p(h(g(x)))
    4: g(0()) -> pair(s(0()),s(0()))
    5: g(s(x)) -> h(g(x))
    6: h(x) -> pair(+(p(x),q(x)),p(x))
    7: p(pair(x,y)) -> x
    8: q(pair(x,y)) -> y
    9: +(x,0()) -> x
    10: +(x,s(y)) -> s(+(x,y))
    11: f(s(s(x))) -> +(p(g(x)),q(g(x)))
    12: g(s(x)) -> pair(+(p(g(x)),q(g(x))),p(g(x)))
Number of strict rules: 12
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #h(x) -> #+(p(x),q(x))
   #2: #h(x) -> #p(x)
   #3: #h(x) -> #q(x)
   #4: #h(x) -> #p(x)
   #5: #f(s(s(x))) -> #+(p(g(x)),q(g(x)))
   #6: #f(s(s(x))) -> #p(g(x))
   #7: #f(s(s(x))) -> #g(x)
   #8: #f(s(s(x))) -> #q(g(x))
   #9: #f(s(s(x))) -> #g(x)
   #10: #g(s(x)) -> #+(p(g(x)),q(g(x)))
   #11: #g(s(x)) -> #p(g(x))
   #12: #g(s(x)) -> #g(x)
   #13: #g(s(x)) -> #q(g(x))
   #14: #g(s(x)) -> #g(x)
   #15: #g(s(x)) -> #p(g(x))
   #16: #g(s(x)) -> #g(x)
   #17: #+(x,s(y)) -> #+(x,y)
   #18: #g(s(x)) -> #h(g(x))
   #19: #g(s(x)) -> #g(x)
   #20: #f(s(s(x))) -> #p(h(g(x)))
   #21: #f(s(s(x))) -> #h(g(x))
   #22: #f(s(s(x))) -> #g(x)
Number of SCCs: 2, DPs: 5, edges: 17
	SCC { #17 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     h(x1)	weight: 0
     q(x1)	weight: 0
     s(x1)	weight: (/ 1 2) + x1
  pair(x1,x2)	weight: 0
   #p(x1)	weight: 0
     f(x1)	weight: 0
     p(x1)	weight: 0
     0()	weight: 0
   #h(x1)	weight: 0
   #f(x1)	weight: 0
   #g(x1)	weight: 0
   #q(x1)	weight: 0
     +(x1,x2)	weight: 0
     g(x1)	weight: 0
   #+(x1,x2)	weight: x2
    Usable rules: { }
    Removed DPs: #17
Number of SCCs: 1, DPs: 4, edges: 16
	SCC { #12 #14 #16 #19 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     h(x1)	weight: 0
     q(x1)	weight: 0
     s(x1)	weight: (/ 1 2) + x1
  pair(x1,x2)	weight: 0
   #p(x1)	weight: 0
     f(x1)	weight: 0
     p(x1)	weight: 0
     0()	weight: 0
   #h(x1)	weight: 0
   #f(x1)	weight: 0
   #g(x1)	weight: x1
   #q(x1)	weight: 0
     +(x1,x2)	weight: 0
     g(x1)	weight: 0
   #+(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #12 #14 #16 #19
Number of SCCs: 0, DPs: 0, edges: 0
YES