Input TRS:
    1: h(X,Z) -> f(X,s(X),Z)
    2: f(X,Y,g(X,Y)) -> h(|0|(),g(X,Y))
    3: g(|0|(),Y) -> |0|()
    4: g(X,s(Y)) -> g(X,Y)
Number of strict rules: 4
Direct Order(PosReal,>,Poly) ... removes: 3
   |0|()	weight: 0
     h(x1,x2)	weight: 2 * x1 + x2
     s(x1)	weight: x1
     f(x1,x2,x3)	weight: x1 + x2 + x3
     g(x1,x2)	weight: (/ 1 4) + 2 * x1 + x2
Number of strict rules: 3
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #f(X,Y,g(X,Y)) -> #h(|0|(),g(X,Y))
   #2: #h(X,Z) -> #f(X,s(X),Z)
   #3: #g(X,s(Y)) -> #g(X,Y)
Number of SCCs: 2, DPs: 3, edges: 3
	SCC { #3 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   |0|()	weight: 0
     h(x1,x2)	weight: 0
     s(x1)	weight: (/ 1 2) + x1
     f(x1,x2,x3)	weight: 0
   #h(x1,x2)	weight: 0
   #f(x1,x2,x3)	weight: 0
   #g(x1,x2)	weight: x2
     g(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #3
Number of SCCs: 1, DPs: 2, edges: 2
	SCC { #1 #2 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... QWPOpS(PosReal,>,MaxSum)... Order(PosReal,>,Sum-Sum; PosReal,≥,Sum-Sum)... Order(PosReal,>,Sum-Sum; NegReal,≥,Sum)... Order(PosReal,>,MaxSum-Sum; NegReal,≥,Sum)... failed.
Removing edges: failed.
Finding a loop...  found.
  #f(|0|(),s(|0|()),g(|0|(),s(|0|())))	-#1->
  #h(|0|(),g(|0|(),s(|0|())))	--->*
  #h(|0|(),g(|0|(),s(|0|())))	-#2->
  #f(|0|(),s(|0|()),g(|0|(),s(|0|())))	--->*
  #f(|0|(),s(|0|()),g(|0|(),s(|0|())))
  Looping with: [ ]
NO