Input TRS:
    1: app(x,y) -> helpa(0(),plus(length(x),length(y)),x,y)
    2: plus(x,0()) -> x
    3: plus(x,s(y)) -> s(plus(x,y))
    4: length(nil()) -> 0()
    5: length(cons(x,y)) -> s(length(y))
    6: helpa(c,l,ys,zs) -> if(ge(c,l),c,l,ys,zs)
    7: ge(x,0()) -> true()
    8: ge(0(),s(x)) -> false()
    9: ge(s(x),s(y)) -> ge(x,y)
    10: if(true(),c,l,ys,zs) -> nil()
    11: if(false(),c,l,ys,zs) -> helpb(c,l,greater(ys,zs),smaller(ys,zs))
    12: greater(ys,zs) -> helpc(ge(length(ys),length(zs)),ys,zs)
    13: smaller(ys,zs) -> helpc(ge(length(ys),length(zs)),zs,ys)
    14: helpc(true(),ys,zs) -> ys
    15: helpc(false(),ys,zs) -> zs
    16: helpb(c,l,cons(y,ys),zs) -> cons(y,helpa(s(c),l,ys,zs))
Number of strict rules: 16
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #helpa(c,l,ys,zs) -> #if(ge(c,l),c,l,ys,zs)
   #2: #helpa(c,l,ys,zs) -> #ge(c,l)
   #3: #smaller(ys,zs) -> #helpc(ge(length(ys),length(zs)),zs,ys)
   #4: #smaller(ys,zs) -> #ge(length(ys),length(zs))
   #5: #smaller(ys,zs) -> #length(ys)
   #6: #smaller(ys,zs) -> #length(zs)
   #7: #ge(s(x),s(y)) -> #ge(x,y)
   #8: #if(false(),c,l,ys,zs) -> #helpb(c,l,greater(ys,zs),smaller(ys,zs))
   #9: #if(false(),c,l,ys,zs) -> #greater(ys,zs)
   #10: #if(false(),c,l,ys,zs) -> #smaller(ys,zs)
   #11: #greater(ys,zs) -> #helpc(ge(length(ys),length(zs)),ys,zs)
   #12: #greater(ys,zs) -> #ge(length(ys),length(zs))
   #13: #greater(ys,zs) -> #length(ys)
   #14: #greater(ys,zs) -> #length(zs)
   #15: #length(cons(x,y)) -> #length(y)
   #16: #helpb(c,l,cons(y,ys),zs) -> #helpa(s(c),l,ys,zs)
   #17: #plus(x,s(y)) -> #plus(x,y)
   #18: #app(x,y) -> #helpa(0(),plus(length(x),length(y)),x,y)
   #19: #app(x,y) -> #plus(length(x),length(y))
   #20: #app(x,y) -> #length(x)
   #21: #app(x,y) -> #length(y)
Number of SCCs: 4, DPs: 6, edges: 6
	SCC { #15 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
smaller(x1,x2)	weight: 0
     s(x1)	weight: 0
greater(x1,x2)	weight: 0
#plus(x1,x2)	weight: 0
#helpa(x1,x2,x3,x4)	weight: 0
 false()	weight: 0
  #ge(x1,x2)	weight: 0
 helpb(x1,x2,x3,x4)	weight: 0
#smaller(x1,x2)	weight: 0
  true()	weight: 0
     0()	weight: 0
    if(x1,x2,x3,x4,x5)	weight: 0
    ge(x1,x2)	weight: 0
#helpc(x1,x2,x3)	weight: 0
   nil()	weight: 0
 helpc(x1,x2,x3)	weight: 0
 #app(x1,x2)	weight: 0
  plus(x1,x2)	weight: 0
#greater(x1,x2)	weight: 0
  cons(x1,x2)	weight: (/ 1 2) + x2
  #if(x1,x2,x3,x4,x5)	weight: 0
 helpa(x1,x2,x3,x4)	weight: 0
length(x1)	weight: 0
#length(x1)	weight: x1
#helpb(x1,x2,x3,x4)	weight: 0
   app(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #15
Number of SCCs: 3, DPs: 5, edges: 5
	SCC { #17 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
smaller(x1,x2)	weight: 0
     s(x1)	weight: (/ 1 2) + x1
greater(x1,x2)	weight: 0
#plus(x1,x2)	weight: x2
#helpa(x1,x2,x3,x4)	weight: 0
 false()	weight: 0
  #ge(x1,x2)	weight: 0
 helpb(x1,x2,x3,x4)	weight: 0
#smaller(x1,x2)	weight: 0
  true()	weight: 0
     0()	weight: 0
    if(x1,x2,x3,x4,x5)	weight: 0
    ge(x1,x2)	weight: 0
#helpc(x1,x2,x3)	weight: 0
   nil()	weight: 0
 helpc(x1,x2,x3)	weight: 0
 #app(x1,x2)	weight: 0
  plus(x1,x2)	weight: 0
#greater(x1,x2)	weight: 0
  cons(x1,x2)	weight: (/ 1 2)
  #if(x1,x2,x3,x4,x5)	weight: 0
 helpa(x1,x2,x3,x4)	weight: 0
length(x1)	weight: 0
#length(x1)	weight: 0
#helpb(x1,x2,x3,x4)	weight: 0
   app(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #17
Number of SCCs: 2, DPs: 4, edges: 4
	SCC { #7 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
smaller(x1,x2)	weight: 0
     s(x1)	weight: (/ 1 2) + x1
greater(x1,x2)	weight: 0
#plus(x1,x2)	weight: 0
#helpa(x1,x2,x3,x4)	weight: 0
 false()	weight: 0
  #ge(x1,x2)	weight: x2
 helpb(x1,x2,x3,x4)	weight: 0
#smaller(x1,x2)	weight: 0
  true()	weight: 0
     0()	weight: 0
    if(x1,x2,x3,x4,x5)	weight: 0
    ge(x1,x2)	weight: 0
#helpc(x1,x2,x3)	weight: 0
   nil()	weight: 0
 helpc(x1,x2,x3)	weight: 0
 #app(x1,x2)	weight: 0
  plus(x1,x2)	weight: 0
#greater(x1,x2)	weight: 0
  cons(x1,x2)	weight: (/ 1 2)
  #if(x1,x2,x3,x4,x5)	weight: 0
 helpa(x1,x2,x3,x4)	weight: 0
length(x1)	weight: 0
#length(x1)	weight: 0
#helpb(x1,x2,x3,x4)	weight: 0
   app(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #7
Number of SCCs: 1, DPs: 3, edges: 3
	SCC { #1 #8 #16 }
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...  failed.
MAYBE