Input TRS:
    1: f(true(),xs) -> f(eq(s(length(xs)),length(cons(a(),xs))),append(cons(a(),nil()),xs))
    2: length(nil()) -> 0()
    3: length(cons(x,xs)) -> s(length(xs))
    4: eq(0(),0()) -> true()
    5: eq(s(x),0()) -> false()
    6: eq(0(),s(y)) -> false()
    7: eq(s(x),s(y)) -> eq(x,y)
    8: append(xs,ys) -> appendAkk(reverse(xs),ys)
    9: appendAkk(nil(),ys) -> ys
    10: appendAkk(cons(x,xs),ys) -> appendAkk(xs,cons(x,ys))
    11: reverse(nil()) -> nil()
    12: reverse(cons(x,xs)) -> append(reverse(xs),cons(x,nil()))
Number of strict rules: 12
Direct Order(PosReal,>,Poly) ... failed.
Freezing length eq
1: f(true(),xs) -> f(eq❆1_s(length(xs),length❆1_cons(a(),xs)),append(cons(a(),nil()),xs))
2: length❆1_nil() -> 0()
3: length❆1_cons(x,xs) -> s(length(xs))
4: eq❆1_0(0()) -> true()
5: eq❆1_s(x,0()) -> false()
6: eq❆1_0(s(y)) -> false()
7: eq❆1_s(x,s(y)) -> eq(x,y)
8: append(xs,ys) -> appendAkk(reverse(xs),ys)
9: appendAkk(nil(),ys) -> ys
10: appendAkk(cons(x,xs),ys) -> appendAkk(xs,cons(x,ys))
11: reverse(nil()) -> nil()
12: reverse(cons(x,xs)) -> append(reverse(xs),cons(x,nil()))
13: eq(0(),_1) ->= eq❆1_0(_1)
14: eq(s(_1),_2) ->= eq❆1_s(_1,_2)
15: length(cons(_1,_2)) ->= length❆1_cons(_1,_2)
16: length(nil()) ->= length❆1_nil()
Number of strict rules: 12
Direct Order(PosReal,>,Poly) ... failed.
Dependency Pairs:
   #1: #eq(0(),_1) ->? #eq❆1_0(_1)
   #2: #reverse(cons(x,xs)) -> #append(reverse(xs),cons(x,nil()))
   #3: #reverse(cons(x,xs)) -> #reverse(xs)
   #4: #eq(s(_1),_2) ->? #eq❆1_s(_1,_2)
   #5: #eq❆1_s(x,s(y)) -> #eq(x,y)
   #6: #appendAkk(cons(x,xs),ys) -> #appendAkk(xs,cons(x,ys))
   #7: #length(nil()) ->? #length❆1_nil()
   #8: #length❆1_cons(x,xs) -> #length(xs)
   #9: #f(true(),xs) -> #f(eq❆1_s(length(xs),length❆1_cons(a(),xs)),append(cons(a(),nil()),xs))
   #10: #f(true(),xs) -> #eq❆1_s(length(xs),length❆1_cons(a(),xs))
   #11: #f(true(),xs) -> #length(xs)
   #12: #f(true(),xs) -> #length❆1_cons(a(),xs)
   #13: #f(true(),xs) -> #append(cons(a(),nil()),xs)
   #14: #append(xs,ys) -> #appendAkk(reverse(xs),ys)
   #15: #append(xs,ys) -> #reverse(xs)
   #16: #length(cons(_1,_2)) ->? #length❆1_cons(_1,_2)
Number of SCCs: 5, DPs: 9, edges: 11
	SCC { #6 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     a()	weight: 0
     s(x1)	weight: 0
#append(x1,x2)	weight: 0
#reverse(x1)	weight: 0
length❆1_nil()	weight: 0
    eq(x1,x2)	weight: 0
#length❆1_nil()	weight: 0
 false()	weight: 0
appendAkk(x1,x2)	weight: 0
reverse(x1)	weight: 0
  true()	weight: 0
#eq❆1_0(x1)	weight: 0
     f(x1,x2)	weight: 0
  #eq(x1,x2)	weight: 0
eq❆1_s(x1,x2)	weight: 0
append(x1,x2)	weight: 0
     0()	weight: 0
   nil()	weight: 0
#eq❆1_s(x1,x2)	weight: 0
eq❆1_0(x1)	weight: 0
   #f(x1,x2)	weight: 0
  cons(x1,x2)	weight: (/ 1 2) + x1 + x2
length❆1_cons(x1,x2)	weight: 0
length(x1)	weight: 0
#length(x1)	weight: 0
#appendAkk(x1,x2)	weight: x1
#length❆1_cons(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #6
Number of SCCs: 4, DPs: 8, edges: 10
	SCC { #8 #16 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     a()	weight: 0
     s(x1)	weight: 0
#append(x1,x2)	weight: 0
#reverse(x1)	weight: 0
length❆1_nil()	weight: 0
    eq(x1,x2)	weight: 0
#length❆1_nil()	weight: 0
 false()	weight: 0
appendAkk(x1,x2)	weight: 0
reverse(x1)	weight: 0
  true()	weight: 0
#eq❆1_0(x1)	weight: 0
     f(x1,x2)	weight: 0
  #eq(x1,x2)	weight: 0
eq❆1_s(x1,x2)	weight: 0
append(x1,x2)	weight: 0
     0()	weight: 0
   nil()	weight: 0
#eq❆1_s(x1,x2)	weight: 0
eq❆1_0(x1)	weight: 0
   #f(x1,x2)	weight: 0
  cons(x1,x2)	weight: (/ 1 2) + x2
length❆1_cons(x1,x2)	weight: 0
length(x1)	weight: 0
#length(x1)	weight: x1
#appendAkk(x1,x2)	weight: 0
#length❆1_cons(x1,x2)	weight: (/ 1 4) + x2
    Usable rules: { }
    Removed DPs: #8 #16
Number of SCCs: 3, DPs: 6, edges: 8
	SCC { #4 #5 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     a()	weight: 0
     s(x1)	weight: (/ 1 2) + x1
#append(x1,x2)	weight: 0
#reverse(x1)	weight: 0
length❆1_nil()	weight: 0
    eq(x1,x2)	weight: 0
#length❆1_nil()	weight: 0
 false()	weight: 0
appendAkk(x1,x2)	weight: 0
reverse(x1)	weight: 0
  true()	weight: 0
#eq❆1_0(x1)	weight: 0
     f(x1,x2)	weight: 0
  #eq(x1,x2)	weight: (/ 1 4) + x2
eq❆1_s(x1,x2)	weight: 0
append(x1,x2)	weight: 0
     0()	weight: 0
   nil()	weight: 0
#eq❆1_s(x1,x2)	weight: x2
eq❆1_0(x1)	weight: 0
   #f(x1,x2)	weight: 0
  cons(x1,x2)	weight: (/ 1 2)
length❆1_cons(x1,x2)	weight: 0
length(x1)	weight: 0
#length(x1)	weight: 0
#appendAkk(x1,x2)	weight: 0
#length❆1_cons(x1,x2)	weight: (/ 1 4)
    Usable rules: { }
    Removed DPs: #4 #5
Number of SCCs: 2, DPs: 4, edges: 6
	SCC { #9 }
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