Input TRS:
    1: table() -> gen(s(0()))
    2: gen(x) -> if1(le(x,10()),x)
    3: if1(false(),x) -> nil()
    4: if1(true(),x) -> if2(x,x)
    5: if2(x,y) -> if3(le(y,10()),x,y)
    6: if3(true(),x,y) -> cons(entry(x,y,times(x,y)),if2(x,s(y)))
    7: if3(false(),x,y) -> gen(s(x))
    8: le(0(),y) -> true()
    9: le(s(x),0()) -> false()
    10: le(s(x),s(y)) -> le(x,y)
    11: plus(0(),y) -> y
    12: plus(s(x),y) -> s(plus(x,y))
    13: times(0(),y) -> 0()
    14: times(s(x),y) -> plus(y,times(x,y))
    15: 10() -> s(s(s(s(s(s(s(s(s(s(0()))))))))))
Number of strict rules: 15
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #gen(x) -> #if1(le(x,10()),x)
   #2: #gen(x) -> #le(x,10())
   #3: #gen(x) -> #10()
   #4: #if3(true(),x,y) -> #times(x,y)
   #5: #if3(true(),x,y) -> #if2(x,s(y))
   #6: #plus(s(x),y) -> #plus(x,y)
   #7: #times(s(x),y) -> #plus(y,times(x,y))
   #8: #times(s(x),y) -> #times(x,y)
   #9: #if3(false(),x,y) -> #gen(s(x))
   #10: #le(s(x),s(y)) -> #le(x,y)
   #11: #if2(x,y) -> #if3(le(y,10()),x,y)
   #12: #if2(x,y) -> #le(y,10())
   #13: #if2(x,y) -> #10()
   #14: #table() -> #gen(s(0()))
   #15: #if1(true(),x) -> #if2(x,x)
Number of SCCs: 4, DPs: 8, edges: 9
	SCC { #6 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
    10()	weight: 0
    le(x1,x2)	weight: 0
     s(x1)	weight: (/ 1 2) + x1
  #le(x1,x2)	weight: 0
#plus(x1,x2)	weight: x1
   if1(x1,x2)	weight: 0
 false()	weight: 0
  true()	weight: 0
 #if1(x1,x2)	weight: 0
 table()	weight: 0
#table()	weight: 0
   if2(x1,x2)	weight: 0
 entry(x1,x2,x3)	weight: 0
 #if3(x1,x2,x3)	weight: 0
#times(x1,x2)	weight: 0
     0()	weight: 0
 times(x1,x2)	weight: 0
  #10()	weight: 0
   nil()	weight: 0
 #gen(x1)	weight: 0
   gen(x1)	weight: 0
  plus(x1,x2)	weight: 0
   if3(x1,x2,x3)	weight: 0
  cons(x1,x2)	weight: 0
 #if2(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #6
Number of SCCs: 3, DPs: 7, edges: 8
	SCC { #8 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
    10()	weight: 0
    le(x1,x2)	weight: 0
     s(x1)	weight: (/ 1 2) + x1
  #le(x1,x2)	weight: 0
#plus(x1,x2)	weight: 0
   if1(x1,x2)	weight: 0
 false()	weight: 0
  true()	weight: 0
 #if1(x1,x2)	weight: 0
 table()	weight: 0
#table()	weight: 0
   if2(x1,x2)	weight: 0
 entry(x1,x2,x3)	weight: 0
 #if3(x1,x2,x3)	weight: 0
#times(x1,x2)	weight: x1
     0()	weight: 0
 times(x1,x2)	weight: 0
  #10()	weight: 0
   nil()	weight: 0
 #gen(x1)	weight: 0
   gen(x1)	weight: 0
  plus(x1,x2)	weight: 0
   if3(x1,x2,x3)	weight: 0
  cons(x1,x2)	weight: 0
 #if2(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #8
Number of SCCs: 2, DPs: 6, edges: 7
	SCC { #10 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
    10()	weight: 0
    le(x1,x2)	weight: 0
     s(x1)	weight: (/ 1 2) + x1
  #le(x1,x2)	weight: x2
#plus(x1,x2)	weight: 0
   if1(x1,x2)	weight: 0
 false()	weight: 0
  true()	weight: 0
 #if1(x1,x2)	weight: 0
 table()	weight: 0
#table()	weight: 0
   if2(x1,x2)	weight: 0
 entry(x1,x2,x3)	weight: 0
 #if3(x1,x2,x3)	weight: 0
#times(x1,x2)	weight: 0
     0()	weight: 0
 times(x1,x2)	weight: 0
  #10()	weight: 0
   nil()	weight: 0
 #gen(x1)	weight: 0
   gen(x1)	weight: 0
  plus(x1,x2)	weight: 0
   if3(x1,x2,x3)	weight: 0
  cons(x1,x2)	weight: 0
 #if2(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #10
Number of SCCs: 1, DPs: 5, edges: 6
	SCC { #1 #5 #9 #11 #15 }
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)... succeeded.
    10()	weight: (/ 51 8); (- (/ 51 8))
    le(x1,x2)	weight: max{0, (/ 3 8) + x2_1 + x1_2}; (- (/ 1 8))
     s(x1)	weight: max{0, (/ 5 8) + x1_1}; (- (/ 5 8)) + x1_2
  #le(x1,x2)	weight: 0; 0
#plus(x1,x2)	weight: 0; 0
   if1(x1,x2)	weight: 0; 0
 false()	weight: 0; (- (/ 3 8))
  true()	weight: (/ 1 4); (- (/ 3 8))
 #if1(x1,x2)	weight: max{0, (- (/ 1 8)) + x1_1, (/ 27 4) + x2_2}; 0
 table()	weight: 0; 0
#table()	weight: 0; 0
   if2(x1,x2)	weight: 0; 0
 entry(x1,x2,x3)	weight: 0; 0
 #if3(x1,x2,x3)	weight: max{0, (- (/ 55 8)) + x1_1, (/ 25 4) + x2_2}; 0
#times(x1,x2)	weight: 0; 0
     0()	weight: (/ 1 8); (- (/ 1 8))
 times(x1,x2)	weight: 0; 0
  #10()	weight: 0; 0
   nil()	weight: 0; 0
 #gen(x1)	weight: max{0, (/ 27 4) + x1_2}; 0
   gen(x1)	weight: 0; 0
  plus(x1,x2)	weight: 0; 0
   if3(x1,x2,x3)	weight: 0; 0
  cons(x1,x2)	weight: 0; 0
 #if2(x1,x2)	weight: max{0, (/ 25 4) + x1_2}; 0
    Usable rules: { 8..10 15 }
    Removed DPs: #15
Number of SCCs: 1, DPs: 2, edges: 2
	SCC { #5 #11 }
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)... succeeded.
    10()	weight: (/ 5 8); 0
    le(x1,x2)	weight: max{0, (/ 3 16) + x2_1 + x1_2}; 0
     s(x1)	weight: max{0, (/ 1 16) + x1_1}; (- (/ 1 16)) + x1_2
  #le(x1,x2)	weight: 0; 0
#plus(x1,x2)	weight: 0; 0
   if1(x1,x2)	weight: 0; 0
 false()	weight: 0; (- (/ 1 8))
  true()	weight: (/ 3 16); 0
 #if1(x1,x2)	weight: 0; 0
 table()	weight: 0; 0
#table()	weight: 0; 0
   if2(x1,x2)	weight: 0; 0
 entry(x1,x2,x3)	weight: 0; 0
 #if3(x1,x2,x3)	weight: max{0, (- (/ 1 16)) + x1_1, (/ 3 4) + x3_2}; 0
#times(x1,x2)	weight: 0; 0
     0()	weight: 0; 0
 times(x1,x2)	weight: 0; 0
  #10()	weight: 0; 0
   nil()	weight: 0; 0
 #gen(x1)	weight: 0; 0
   gen(x1)	weight: 0; 0
  plus(x1,x2)	weight: 0; 0
   if3(x1,x2,x3)	weight: 0; 0
  cons(x1,x2)	weight: 0; 0
 #if2(x1,x2)	weight: max{0, (/ 1 16) + x1_2, (/ 3 4) + x2_2}; 0
    Usable rules: { 8..10 15 }
    Removed DPs: #5
Number of SCCs: 0, DPs: 0, edges: 0
YES