Input TRS:
    1: f_0(x) -> a()
    2: f_1(x) -> g_1(x,x)
    3: g_1(s(x),y) -> b(f_0(y),g_1(x,y))
    4: f_2(x) -> g_2(x,x)
    5: g_2(s(x),y) -> b(f_1(y),g_2(x,y))
    6: f_3(x) -> g_3(x,x)
    7: g_3(s(x),y) -> b(f_2(y),g_3(x,y))
    8: f_4(x) -> g_4(x,x)
    9: g_4(s(x),y) -> b(f_3(y),g_4(x,y))
    10: f_5(x) -> g_5(x,x)
    11: g_5(s(x),y) -> b(f_4(y),g_5(x,y))
Number of strict rules: 11
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #f_1(x) -> #g_1(x,x)
   #2: #f_3(x) -> #g_3(x,x)
   #3: #g_4(s(x),y) -> #f_3(y)
   #4: #g_4(s(x),y) -> #g_4(x,y)
   #5: #g_5(s(x),y) -> #f_4(y)
   #6: #g_5(s(x),y) -> #g_5(x,y)
   #7: #g_3(s(x),y) -> #f_2(y)
   #8: #g_3(s(x),y) -> #g_3(x,y)
   #9: #f_5(x) -> #g_5(x,x)
   #10: #g_2(s(x),y) -> #f_1(y)
   #11: #g_2(s(x),y) -> #g_2(x,y)
   #12: #g_1(s(x),y) -> #f_0(y)
   #13: #g_1(s(x),y) -> #g_1(x,y)
   #14: #f_4(x) -> #g_4(x,x)
   #15: #f_2(x) -> #g_2(x,x)
Number of SCCs: 5, DPs: 5, edges: 5
	SCC { #13 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     a()	weight: 0
   g_5(x1,x2)	weight: 0
 #g_1(x1,x2)	weight: x1
     s(x1)	weight: (/ 1 2) + x1
 #g_4(x1,x2)	weight: 0
 #f_4(x1)	weight: 0
     b(x1,x2)	weight: 0
   g_3(x1,x2)	weight: 0
   f_5(x1)	weight: 0
   f_2(x1)	weight: 0
 #g_3(x1,x2)	weight: 0
 #f_2(x1)	weight: 0
   g_1(x1,x2)	weight: 0
   g_2(x1,x2)	weight: 0
 #g_2(x1,x2)	weight: 0
   f_1(x1)	weight: 0
 #g_5(x1,x2)	weight: 0
   g_4(x1,x2)	weight: 0
 #f_0(x1)	weight: 0
   f_0(x1)	weight: 0
 #f_3(x1)	weight: 0
   f_4(x1)	weight: 0
 #f_1(x1)	weight: 0
 #f_5(x1)	weight: 0
   f_3(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #13
Number of SCCs: 4, DPs: 4, edges: 4
	SCC { #11 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     a()	weight: 0
   g_5(x1,x2)	weight: 0
 #g_1(x1,x2)	weight: 0
     s(x1)	weight: (/ 1 2) + x1
 #g_4(x1,x2)	weight: 0
 #f_4(x1)	weight: 0
     b(x1,x2)	weight: 0
   g_3(x1,x2)	weight: 0
   f_5(x1)	weight: 0
   f_2(x1)	weight: 0
 #g_3(x1,x2)	weight: 0
 #f_2(x1)	weight: 0
   g_1(x1,x2)	weight: 0
   g_2(x1,x2)	weight: 0
 #g_2(x1,x2)	weight: x1
   f_1(x1)	weight: 0
 #g_5(x1,x2)	weight: 0
   g_4(x1,x2)	weight: 0
 #f_0(x1)	weight: 0
   f_0(x1)	weight: 0
 #f_3(x1)	weight: 0
   f_4(x1)	weight: 0
 #f_1(x1)	weight: 0
 #f_5(x1)	weight: 0
   f_3(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #11
Number of SCCs: 3, DPs: 3, edges: 3
	SCC { #8 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     a()	weight: 0
   g_5(x1,x2)	weight: 0
 #g_1(x1,x2)	weight: 0
     s(x1)	weight: (/ 1 2) + x1
 #g_4(x1,x2)	weight: 0
 #f_4(x1)	weight: 0
     b(x1,x2)	weight: 0
   g_3(x1,x2)	weight: 0
   f_5(x1)	weight: 0
   f_2(x1)	weight: 0
 #g_3(x1,x2)	weight: x1
 #f_2(x1)	weight: 0
   g_1(x1,x2)	weight: 0
   g_2(x1,x2)	weight: 0
 #g_2(x1,x2)	weight: 0
   f_1(x1)	weight: 0
 #g_5(x1,x2)	weight: 0
   g_4(x1,x2)	weight: 0
 #f_0(x1)	weight: 0
   f_0(x1)	weight: 0
 #f_3(x1)	weight: 0
   f_4(x1)	weight: 0
 #f_1(x1)	weight: 0
 #f_5(x1)	weight: 0
   f_3(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #8
Number of SCCs: 2, DPs: 2, edges: 2
	SCC { #4 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     a()	weight: 0
   g_5(x1,x2)	weight: 0
 #g_1(x1,x2)	weight: 0
     s(x1)	weight: (/ 1 2) + x1
 #g_4(x1,x2)	weight: x1
 #f_4(x1)	weight: 0
     b(x1,x2)	weight: 0
   g_3(x1,x2)	weight: 0
   f_5(x1)	weight: 0
   f_2(x1)	weight: 0
 #g_3(x1,x2)	weight: 0
 #f_2(x1)	weight: 0
   g_1(x1,x2)	weight: 0
   g_2(x1,x2)	weight: 0
 #g_2(x1,x2)	weight: 0
   f_1(x1)	weight: 0
 #g_5(x1,x2)	weight: 0
   g_4(x1,x2)	weight: 0
 #f_0(x1)	weight: 0
   f_0(x1)	weight: 0
 #f_3(x1)	weight: 0
   f_4(x1)	weight: 0
 #f_1(x1)	weight: 0
 #f_5(x1)	weight: 0
   f_3(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #4
Number of SCCs: 1, DPs: 1, edges: 1
	SCC { #6 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     a()	weight: 0
   g_5(x1,x2)	weight: 0
 #g_1(x1,x2)	weight: 0
     s(x1)	weight: (/ 1 2) + x1
 #g_4(x1,x2)	weight: 0
 #f_4(x1)	weight: 0
     b(x1,x2)	weight: 0
   g_3(x1,x2)	weight: 0
   f_5(x1)	weight: 0
   f_2(x1)	weight: 0
 #g_3(x1,x2)	weight: 0
 #f_2(x1)	weight: 0
   g_1(x1,x2)	weight: 0
   g_2(x1,x2)	weight: 0
 #g_2(x1,x2)	weight: 0
   f_1(x1)	weight: 0
 #g_5(x1,x2)	weight: x1
   g_4(x1,x2)	weight: 0
 #f_0(x1)	weight: 0
   f_0(x1)	weight: 0
 #f_3(x1)	weight: 0
   f_4(x1)	weight: 0
 #f_1(x1)	weight: 0
 #f_5(x1)	weight: 0
   f_3(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #6
Number of SCCs: 0, DPs: 0, edges: 0
YES