Input TRS:
    1: |app'|(|app'|(eq(),|0|()),|0|()) -> true()
    2: |app'|(|app'|(eq(),|0|()),|app'|(s(),x)) -> false()
    3: |app'|(|app'|(eq(),|app'|(s(),x)),|0|()) -> false()
    4: |app'|(|app'|(eq(),|app'|(s(),x)),|app'|(s(),y)) -> |app'|(|app'|(eq(),x),y)
    5: |app'|(|app'|(le(),|0|()),y) -> true()
    6: |app'|(|app'|(le(),|app'|(s(),x)),|0|()) -> false()
    7: |app'|(|app'|(le(),|app'|(s(),x)),|app'|(s(),y)) -> |app'|(|app'|(le(),x),y)
    8: |app'|(|app'|(app(),nil()),y) -> y
    9: |app'|(|app'|(app(),|app'|(|app'|(add(),n),x)),y) -> |app'|(|app'|(add(),n),|app'|(|app'|(app(),x),y))
    10: |app'|(min(),|app'|(|app'|(add(),n),nil())) -> n
    11: |app'|(min(),|app'|(|app'|(add(),n),|app'|(|app'|(add(),m),x))) -> |app'|(|app'|(if_min(),|app'|(|app'|(le(),n),m)),|app'|(|app'|(add(),n),|app'|(|app'|(add(),m),x)))
    12: |app'|(|app'|(if_min(),true()),|app'|(|app'|(add(),n),|app'|(|app'|(add(),m),x))) -> |app'|(min(),|app'|(|app'|(add(),n),x))
    13: |app'|(|app'|(if_min(),false()),|app'|(|app'|(add(),n),|app'|(|app'|(add(),m),x))) -> |app'|(min(),|app'|(|app'|(add(),m),x))
    14: |app'|(|app'|(rm(),n),nil()) -> nil()
    15: |app'|(|app'|(rm(),n),|app'|(|app'|(add(),m),x)) -> |app'|(|app'|(|app'|(if_rm(),|app'|(|app'|(eq(),n),m)),n),|app'|(|app'|(add(),m),x))
    16: |app'|(|app'|(|app'|(if_rm(),true()),n),|app'|(|app'|(add(),m),x)) -> |app'|(|app'|(rm(),n),x)
    17: |app'|(|app'|(|app'|(if_rm(),false()),n),|app'|(|app'|(add(),m),x)) -> |app'|(|app'|(add(),m),|app'|(|app'|(rm(),n),x))
    18: |app'|(|app'|(minsort(),nil()),nil()) -> nil()
    19: |app'|(|app'|(minsort(),|app'|(|app'|(add(),n),x)),y) -> |app'|(|app'|(|app'|(if_minsort(),|app'|(|app'|(eq(),n),|app'|(min(),|app'|(|app'|(add(),n),x)))),|app'|(|app'|(add(),n),x)),y)
    20: |app'|(|app'|(|app'|(if_minsort(),true()),|app'|(|app'|(add(),n),x)),y) -> |app'|(|app'|(add(),n),|app'|(|app'|(minsort(),|app'|(|app'|(app(),|app'|(|app'|(rm(),n),x)),y)),nil()))
    21: |app'|(|app'|(|app'|(if_minsort(),false()),|app'|(|app'|(add(),n),x)),y) -> |app'|(|app'|(minsort(),x),|app'|(|app'|(add(),n),y))
    22: |app'|(|app'|(map(),f),nil()) -> nil()
    23: |app'|(|app'|(map(),f),|app'|(|app'|(add(),x),xs)) -> |app'|(|app'|(add(),|app'|(f,x)),|app'|(|app'|(map(),f),xs))
    24: |app'|(|app'|(filter(),f),nil()) -> nil()
    25: |app'|(|app'|(filter(),f),|app'|(|app'|(add(),x),xs)) -> |app'|(|app'|(|app'|(|app'|(filter2(),|app'|(f,x)),f),x),xs)
    26: |app'|(|app'|(|app'|(|app'|(filter2(),true()),f),x),xs) -> |app'|(|app'|(add(),x),|app'|(|app'|(filter(),f),xs))
    27: |app'|(|app'|(|app'|(|app'|(filter2(),false()),f),x),xs) -> |app'|(|app'|(filter(),f),xs)
Number of strict rules: 27
Direct Order(PosReal,>,Poly) ... failed.
Freezing |app'|❆1_min |app'|
1: |app'|❆2_eq(|0|(),|0|()) -> true()
2: |app'|❆2_eq(|0|(),|app'|❆1_s(x)) -> false()
3: |app'|❆2_eq(|app'|❆1_s(x),|0|()) -> false()
4: |app'|❆2_eq(|app'|❆1_s(x),|app'|❆1_s(y)) -> |app'|❆2_eq(x,y)
5: |app'|❆2_le(|0|(),y) -> true()
6: |app'|❆2_le(|app'|❆1_s(x),|0|()) -> false()
7: |app'|❆2_le(|app'|❆1_s(x),|app'|❆1_s(y)) -> |app'|❆2_le(x,y)
8: |app'|❆2_app(nil(),y) -> y
9: |app'|❆2_app(|app'|❆2_add(n,x),y) -> |app'|❆2_add(n,|app'|❆2_app(x,y))
10: |app'|❆1_min❆1_|app'|❆2_add(n,nil()) -> n
11: |app'|❆1_min❆1_|app'|❆2_add(n,|app'|❆2_add(m,x)) -> |app'|❆2_if_min(|app'|❆2_le(n,m),|app'|❆2_add(n,|app'|❆2_add(m,x)))
12: |app'|❆2_if_min(true(),|app'|❆2_add(n,|app'|❆2_add(m,x))) -> |app'|❆1_min❆1_|app'|❆2_add(n,x)
13: |app'|❆2_if_min(false(),|app'|❆2_add(n,|app'|❆2_add(m,x))) -> |app'|❆1_min❆1_|app'|❆2_add(m,x)
14: |app'|❆2_rm(n,nil()) -> nil()
15: |app'|❆2_rm(n,|app'|❆2_add(m,x)) -> |app'|❆3_if_rm(|app'|❆2_eq(n,m),n,|app'|❆2_add(m,x))
16: |app'|❆3_if_rm(true(),n,|app'|❆2_add(m,x)) -> |app'|❆2_rm(n,x)
17: |app'|❆3_if_rm(false(),n,|app'|❆2_add(m,x)) -> |app'|❆2_add(m,|app'|❆2_rm(n,x))
18: |app'|❆2_minsort(nil(),nil()) -> nil()
19: |app'|❆2_minsort(|app'|❆2_add(n,x),y) -> |app'|❆3_if_minsort(|app'|❆2_eq(n,|app'|❆1_min❆1_|app'|❆2_add(n,x)),|app'|❆2_add(n,x),y)
20: |app'|❆3_if_minsort(true(),|app'|❆2_add(n,x),y) -> |app'|❆2_add(n,|app'|❆2_minsort(|app'|❆2_app(|app'|❆2_rm(n,x),y),nil()))
21: |app'|❆3_if_minsort(false(),|app'|❆2_add(n,x),y) -> |app'|❆2_minsort(x,|app'|❆2_add(n,y))
22: |app'|❆2_map(f,nil()) -> nil()
23: |app'|❆2_map(f,|app'|❆2_add(x,xs)) -> |app'|❆2_add(|app'|(f,x),|app'|❆2_map(f,xs))
24: |app'|❆2_filter(f,nil()) -> nil()
25: |app'|❆2_filter(f,|app'|❆2_add(x,xs)) -> |app'|❆4_filter2(|app'|(f,x),f,x,xs)
26: |app'|❆4_filter2(true(),f,x,xs) -> |app'|❆2_add(x,|app'|❆2_filter(f,xs))
27: |app'|❆4_filter2(false(),f,x,xs) -> |app'|❆2_filter(f,xs)
28: |app'|(eq(),_1) ->= |app'|❆1_eq(_1)
29: |app'|(|app'|❆1_eq(_1),_2) ->= |app'|❆2_eq(_1,_2)
30: |app'|(min(),_1) ->= |app'|❆1_min(_1)
31: |app'|(le(),_1) ->= |app'|❆1_le(_1)
32: |app'|(|app'|❆1_le(_1),_2) ->= |app'|❆2_le(_1,_2)
33: |app'|(if_rm(),_1) ->= |app'|❆1_if_rm(_1)
34: |app'|(|app'|❆1_if_rm(_1),_2) ->= |app'|❆2_if_rm(_1,_2)
35: |app'|(|app'|❆2_if_rm(_1,_2),_3) ->= |app'|❆3_if_rm(_1,_2,_3)
36: |app'|(add(),_1) ->= |app'|❆1_add(_1)
37: |app'|(|app'|❆1_add(_1),_2) ->= |app'|❆2_add(_1,_2)
38: |app'|(if_min(),_1) ->= |app'|❆1_if_min(_1)
39: |app'|(|app'|❆1_if_min(_1),_2) ->= |app'|❆2_if_min(_1,_2)
40: |app'|(s(),_1) ->= |app'|❆1_s(_1)
41: |app'|(if_minsort(),_1) ->= |app'|❆1_if_minsort(_1)
42: |app'|(|app'|❆1_if_minsort(_1),_2) ->= |app'|❆2_if_minsort(_1,_2)
43: |app'|(|app'|❆2_if_minsort(_1,_2),_3) ->= |app'|❆3_if_minsort(_1,_2,_3)
44: |app'|(filter(),_1) ->= |app'|❆1_filter(_1)
45: |app'|(|app'|❆1_filter(_1),_2) ->= |app'|❆2_filter(_1,_2)
46: |app'|(minsort(),_1) ->= |app'|❆1_minsort(_1)
47: |app'|(|app'|❆1_minsort(_1),_2) ->= |app'|❆2_minsort(_1,_2)
48: |app'|(map(),_1) ->= |app'|❆1_map(_1)
49: |app'|(|app'|❆1_map(_1),_2) ->= |app'|❆2_map(_1,_2)
50: |app'|(filter2(),_1) ->= |app'|❆1_filter2(_1)
51: |app'|(|app'|❆1_filter2(_1),_2) ->= |app'|❆2_filter2(_1,_2)
52: |app'|(|app'|❆2_filter2(_1,_2),_3) ->= |app'|❆3_filter2(_1,_2,_3)
53: |app'|(|app'|❆3_filter2(_1,_2,_3),_4) ->= |app'|❆4_filter2(_1,_2,_3,_4)
54: |app'|(rm(),_1) ->= |app'|❆1_rm(_1)
55: |app'|(|app'|❆1_rm(_1),_2) ->= |app'|❆2_rm(_1,_2)
56: |app'|(app(),_1) ->= |app'|❆1_app(_1)
57: |app'|(|app'|❆1_app(_1),_2) ->= |app'|❆2_app(_1,_2)
58: |app'|❆1_min(|app'|❆2_add(_1,_2)) ->= |app'|❆1_min❆1_|app'|❆2_add(_1,_2)
Number of strict rules: 27
Direct Order(PosReal,>,Poly) ... failed.
Dependency Pairs:
   #1: #|app'|(|app'|❆2_if_minsort(_1,_2),_3) ->? #|app'|❆3_if_minsort(_1,_2,_3)
   #2: #|app'|(|app'|❆1_eq(_1),_2) ->? #|app'|❆2_eq(_1,_2)
   #3: #|app'|(|app'|❆2_if_rm(_1,_2),_3) ->? #|app'|❆3_if_rm(_1,_2,_3)
   #4: #|app'|(|app'|❆1_minsort(_1),_2) ->? #|app'|❆2_minsort(_1,_2)
   #5: #|app'|(|app'|❆3_filter2(_1,_2,_3),_4) ->? #|app'|❆4_filter2(_1,_2,_3,_4)
   #6: #|app'|❆1_min(|app'|❆2_add(_1,_2)) ->? #|app'|❆1_min❆1_|app'|❆2_add(_1,_2)
   #7: #|app'|(|app'|❆1_rm(_1),_2) ->? #|app'|❆2_rm(_1,_2)
   #8: #|app'|❆2_if_min(false(),|app'|❆2_add(n,|app'|❆2_add(m,x))) -> #|app'|❆1_min❆1_|app'|❆2_add(m,x)
   #9: #|app'|❆2_app(|app'|❆2_add(n,x),y) -> #|app'|❆2_app(x,y)
   #10: #|app'|❆1_min❆1_|app'|❆2_add(n,|app'|❆2_add(m,x)) -> #|app'|❆2_if_min(|app'|❆2_le(n,m),|app'|❆2_add(n,|app'|❆2_add(m,x)))
   #11: #|app'|❆1_min❆1_|app'|❆2_add(n,|app'|❆2_add(m,x)) -> #|app'|❆2_le(n,m)
   #12: #|app'|(|app'|❆1_app(_1),_2) ->? #|app'|❆2_app(_1,_2)
   #13: #|app'|❆2_map(f,|app'|❆2_add(x,xs)) -> #|app'|(f,x)
   #14: #|app'|❆2_map(f,|app'|❆2_add(x,xs)) -> #|app'|❆2_map(f,xs)
   #15: #|app'|(|app'|❆1_filter(_1),_2) ->? #|app'|❆2_filter(_1,_2)
   #16: #|app'|❆2_if_min(true(),|app'|❆2_add(n,|app'|❆2_add(m,x))) -> #|app'|❆1_min❆1_|app'|❆2_add(n,x)
   #17: #|app'|(min(),_1) ->? #|app'|❆1_min(_1)
   #18: #|app'|(|app'|❆1_map(_1),_2) ->? #|app'|❆2_map(_1,_2)
   #19: #|app'|❆2_filter(f,|app'|❆2_add(x,xs)) -> #|app'|❆4_filter2(|app'|(f,x),f,x,xs)
   #20: #|app'|❆2_filter(f,|app'|❆2_add(x,xs)) -> #|app'|(f,x)
   #21: #|app'|❆3_if_minsort(true(),|app'|❆2_add(n,x),y) -> #|app'|❆2_minsort(|app'|❆2_app(|app'|❆2_rm(n,x),y),nil())
   #22: #|app'|❆3_if_minsort(true(),|app'|❆2_add(n,x),y) -> #|app'|❆2_app(|app'|❆2_rm(n,x),y)
   #23: #|app'|❆3_if_minsort(true(),|app'|❆2_add(n,x),y) -> #|app'|❆2_rm(n,x)
   #24: #|app'|❆2_le(|app'|❆1_s(x),|app'|❆1_s(y)) -> #|app'|❆2_le(x,y)
   #25: #|app'|(|app'|❆1_if_min(_1),_2) ->? #|app'|❆2_if_min(_1,_2)
   #26: #|app'|❆4_filter2(false(),f,x,xs) -> #|app'|❆2_filter(f,xs)
   #27: #|app'|❆3_if_rm(false(),n,|app'|❆2_add(m,x)) -> #|app'|❆2_rm(n,x)
   #28: #|app'|(|app'|❆1_le(_1),_2) ->? #|app'|❆2_le(_1,_2)
   #29: #|app'|❆2_minsort(|app'|❆2_add(n,x),y) -> #|app'|❆3_if_minsort(|app'|❆2_eq(n,|app'|❆1_min❆1_|app'|❆2_add(n,x)),|app'|❆2_add(n,x),y)
   #30: #|app'|❆2_minsort(|app'|❆2_add(n,x),y) -> #|app'|❆2_eq(n,|app'|❆1_min❆1_|app'|❆2_add(n,x))
   #31: #|app'|❆2_minsort(|app'|❆2_add(n,x),y) -> #|app'|❆1_min❆1_|app'|❆2_add(n,x)
   #32: #|app'|❆4_filter2(true(),f,x,xs) -> #|app'|❆2_filter(f,xs)
   #33: #|app'|❆3_if_minsort(false(),|app'|❆2_add(n,x),y) -> #|app'|❆2_minsort(x,|app'|❆2_add(n,y))
   #34: #|app'|❆3_if_rm(true(),n,|app'|❆2_add(m,x)) -> #|app'|❆2_rm(n,x)
   #35: #|app'|❆2_rm(n,|app'|❆2_add(m,x)) -> #|app'|❆3_if_rm(|app'|❆2_eq(n,m),n,|app'|❆2_add(m,x))
   #36: #|app'|❆2_rm(n,|app'|❆2_add(m,x)) -> #|app'|❆2_eq(n,m)
   #37: #|app'|❆2_eq(|app'|❆1_s(x),|app'|❆1_s(y)) -> #|app'|❆2_eq(x,y)
Number of SCCs: 7, DPs: 21, edges: 35
	SCC { #24 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   |0|()	weight: 0
#|app'|(x1,x2)	weight: 0
    le()	weight: 0
|app'|❆3_filter2(x1,x2,x3)	weight: 0
 if_rm()	weight: 0
|app'|❆4_filter2(x1,x2,x3,x4)	weight: 0
|app'|❆2_eq(x1,x2)	weight: 0
     s()	weight: 0
|app'|❆1_min❆1_|app'|❆2_add(x1,x2)	weight: 0
|app'|❆1_map(x1)	weight: 0
|app'|❆2_add(x1,x2)	weight: 0
|app'|❆2_if_minsort(x1,x2)	weight: 0
#|app'|❆2_le(x1,x2)	weight: x2
|app'|❆1_eq(x1)	weight: 0
|app'|❆2_if_min(x1,x2)	weight: 0
    eq()	weight: 0
|app'|❆2_filter(x1,x2)	weight: 0
|app'|❆3_if_minsort(x1,x2,x3)	weight: 0
 false()	weight: 0
#|app'|❆1_min❆1_|app'|❆2_add(x1,x2)	weight: 0
|app'|(x1,x2)	weight: 0
#|app'|❆2_if_min(x1,x2)	weight: 0
|app'|❆1_filter2(x1)	weight: 0
#|app'|❆2_app(x1,x2)	weight: 0
|app'|❆1_if_minsort(x1)	weight: 0
|app'|❆3_if_rm(x1,x2,x3)	weight: 0
|app'|❆1_min(x1)	weight: 0
#|app'|❆4_filter2(x1,x2,x3,x4)	weight: 0
  true()	weight: 0
filter2()	weight: 0
|app'|❆2_le(x1,x2)	weight: 0
#|app'|❆3_if_rm(x1,x2,x3)	weight: 0
|app'|❆1_rm(x1)	weight: 0
|app'|❆2_minsort(x1,x2)	weight: 0
|app'|❆1_minsort(x1)	weight: 0
#|app'|❆3_if_minsort(x1,x2,x3)	weight: 0
|app'|❆2_filter2(x1,x2)	weight: 0
|app'|❆1_le(x1)	weight: 0
|app'|❆2_map(x1,x2)	weight: 0
   nil()	weight: 0
#|app'|❆2_filter(x1,x2)	weight: 0
#|app'|❆2_rm(x1,x2)	weight: 0
|app'|❆1_app(x1)	weight: 0
   map()	weight: 0
#|app'|❆2_eq(x1,x2)	weight: 0
|app'|❆1_filter(x1)	weight: 0
   min()	weight: 0
|app'|❆1_s(x1)	weight: (/ 1 2) + x1
|app'|❆2_if_rm(x1,x2)	weight: 0
#|app'|❆2_minsort(x1,x2)	weight: 0
   add()	weight: 0
if_min()	weight: 0
if_minsort()	weight: 0
filter()	weight: 0
#|app'|❆1_min(x1)	weight: 0
|app'|❆2_app(x1,x2)	weight: 0
|app'|❆2_rm(x1,x2)	weight: 0
|app'|❆1_if_rm(x1)	weight: 0
minsort()	weight: 0
|app'|❆1_add(x1)	weight: 0
|app'|❆1_if_min(x1)	weight: 0
    rm()	weight: 0
#|app'|❆2_map(x1,x2)	weight: 0
   app()	weight: 0
    Usable rules: { }
    Removed DPs: #24
Number of SCCs: 6, DPs: 20, edges: 34
	SCC { #9 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   |0|()	weight: 0
#|app'|(x1,x2)	weight: 0
    le()	weight: 0
|app'|❆3_filter2(x1,x2,x3)	weight: 0
 if_rm()	weight: 0
|app'|❆4_filter2(x1,x2,x3,x4)	weight: 0
|app'|❆2_eq(x1,x2)	weight: 0
     s()	weight: 0
|app'|❆1_min❆1_|app'|❆2_add(x1,x2)	weight: 0
|app'|❆1_map(x1)	weight: 0
|app'|❆2_add(x1,x2)	weight: (/ 1 2) + x2
|app'|❆2_if_minsort(x1,x2)	weight: 0
#|app'|❆2_le(x1,x2)	weight: 0
|app'|❆1_eq(x1)	weight: 0
|app'|❆2_if_min(x1,x2)	weight: 0
    eq()	weight: 0
|app'|❆2_filter(x1,x2)	weight: 0
|app'|❆3_if_minsort(x1,x2,x3)	weight: 0
 false()	weight: 0
#|app'|❆1_min❆1_|app'|❆2_add(x1,x2)	weight: 0
|app'|(x1,x2)	weight: 0
#|app'|❆2_if_min(x1,x2)	weight: 0
|app'|❆1_filter2(x1)	weight: 0
#|app'|❆2_app(x1,x2)	weight: x1
|app'|❆1_if_minsort(x1)	weight: 0
|app'|❆3_if_rm(x1,x2,x3)	weight: 0
|app'|❆1_min(x1)	weight: 0
#|app'|❆4_filter2(x1,x2,x3,x4)	weight: 0
  true()	weight: 0
filter2()	weight: 0
|app'|❆2_le(x1,x2)	weight: 0
#|app'|❆3_if_rm(x1,x2,x3)	weight: 0
|app'|❆1_rm(x1)	weight: 0
|app'|❆2_minsort(x1,x2)	weight: 0
|app'|❆1_minsort(x1)	weight: 0
#|app'|❆3_if_minsort(x1,x2,x3)	weight: 0
|app'|❆2_filter2(x1,x2)	weight: 0
|app'|❆1_le(x1)	weight: 0
|app'|❆2_map(x1,x2)	weight: 0
   nil()	weight: 0
#|app'|❆2_filter(x1,x2)	weight: 0
#|app'|❆2_rm(x1,x2)	weight: 0
|app'|❆1_app(x1)	weight: 0
   map()	weight: 0
#|app'|❆2_eq(x1,x2)	weight: 0
|app'|❆1_filter(x1)	weight: 0
   min()	weight: 0
|app'|❆1_s(x1)	weight: (/ 1 2)
|app'|❆2_if_rm(x1,x2)	weight: 0
#|app'|❆2_minsort(x1,x2)	weight: 0
   add()	weight: 0
if_min()	weight: 0
if_minsort()	weight: 0
filter()	weight: 0
#|app'|❆1_min(x1)	weight: 0
|app'|❆2_app(x1,x2)	weight: 0
|app'|❆2_rm(x1,x2)	weight: 0
|app'|❆1_if_rm(x1)	weight: 0
minsort()	weight: 0
|app'|❆1_add(x1)	weight: 0
|app'|❆1_if_min(x1)	weight: 0
    rm()	weight: 0
#|app'|❆2_map(x1,x2)	weight: 0
   app()	weight: 0
    Usable rules: { }
    Removed DPs: #9
Number of SCCs: 5, DPs: 19, edges: 33
	SCC { #37 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   |0|()	weight: 0
#|app'|(x1,x2)	weight: 0
    le()	weight: 0
|app'|❆3_filter2(x1,x2,x3)	weight: 0
 if_rm()	weight: 0
|app'|❆4_filter2(x1,x2,x3,x4)	weight: 0
|app'|❆2_eq(x1,x2)	weight: 0
     s()	weight: 0
|app'|❆1_min❆1_|app'|❆2_add(x1,x2)	weight: 0
|app'|❆1_map(x1)	weight: 0
|app'|❆2_add(x1,x2)	weight: (/ 1 2)
|app'|❆2_if_minsort(x1,x2)	weight: 0
#|app'|❆2_le(x1,x2)	weight: 0
|app'|❆1_eq(x1)	weight: 0
|app'|❆2_if_min(x1,x2)	weight: 0
    eq()	weight: 0
|app'|❆2_filter(x1,x2)	weight: 0
|app'|❆3_if_minsort(x1,x2,x3)	weight: 0
 false()	weight: 0
#|app'|❆1_min❆1_|app'|❆2_add(x1,x2)	weight: 0
|app'|(x1,x2)	weight: 0
#|app'|❆2_if_min(x1,x2)	weight: 0
|app'|❆1_filter2(x1)	weight: 0
#|app'|❆2_app(x1,x2)	weight: 0
|app'|❆1_if_minsort(x1)	weight: 0
|app'|❆3_if_rm(x1,x2,x3)	weight: 0
|app'|❆1_min(x1)	weight: 0
#|app'|❆4_filter2(x1,x2,x3,x4)	weight: 0
  true()	weight: 0
filter2()	weight: 0
|app'|❆2_le(x1,x2)	weight: 0
#|app'|❆3_if_rm(x1,x2,x3)	weight: 0
|app'|❆1_rm(x1)	weight: 0
|app'|❆2_minsort(x1,x2)	weight: 0
|app'|❆1_minsort(x1)	weight: 0
#|app'|❆3_if_minsort(x1,x2,x3)	weight: 0
|app'|❆2_filter2(x1,x2)	weight: 0
|app'|❆1_le(x1)	weight: 0
|app'|❆2_map(x1,x2)	weight: 0
   nil()	weight: 0
#|app'|❆2_filter(x1,x2)	weight: 0
#|app'|❆2_rm(x1,x2)	weight: 0
|app'|❆1_app(x1)	weight: 0
   map()	weight: 0
#|app'|❆2_eq(x1,x2)	weight: x2
|app'|❆1_filter(x1)	weight: 0
   min()	weight: 0
|app'|❆1_s(x1)	weight: (/ 1 2) + x1
|app'|❆2_if_rm(x1,x2)	weight: 0
#|app'|❆2_minsort(x1,x2)	weight: 0
   add()	weight: 0
if_min()	weight: 0
if_minsort()	weight: 0
filter()	weight: 0
#|app'|❆1_min(x1)	weight: 0
|app'|❆2_app(x1,x2)	weight: 0
|app'|❆2_rm(x1,x2)	weight: 0
|app'|❆1_if_rm(x1)	weight: 0
minsort()	weight: 0
|app'|❆1_add(x1)	weight: 0
|app'|❆1_if_min(x1)	weight: 0
    rm()	weight: 0
#|app'|❆2_map(x1,x2)	weight: 0
   app()	weight: 0
    Usable rules: { }
    Removed DPs: #37
Number of SCCs: 4, DPs: 18, edges: 32
	SCC { #27 #34 #35 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   |0|()	weight: 0
#|app'|(x1,x2)	weight: 0
    le()	weight: 0
|app'|❆3_filter2(x1,x2,x3)	weight: 0
 if_rm()	weight: 0
|app'|❆4_filter2(x1,x2,x3,x4)	weight: 0
|app'|❆2_eq(x1,x2)	weight: (/ 1 4) + x1
     s()	weight: 0
|app'|❆1_min❆1_|app'|❆2_add(x1,x2)	weight: 0
|app'|❆1_map(x1)	weight: 0
|app'|❆2_add(x1,x2)	weight: (/ 1 2) + x1 + x2
|app'|❆2_if_minsort(x1,x2)	weight: 0
#|app'|❆2_le(x1,x2)	weight: 0
|app'|❆1_eq(x1)	weight: 0
|app'|❆2_if_min(x1,x2)	weight: 0
    eq()	weight: 0
|app'|❆2_filter(x1,x2)	weight: 0
|app'|❆3_if_minsort(x1,x2,x3)	weight: 0
 false()	weight: 0
#|app'|❆1_min❆1_|app'|❆2_add(x1,x2)	weight: 0
|app'|(x1,x2)	weight: 0
#|app'|❆2_if_min(x1,x2)	weight: 0
|app'|❆1_filter2(x1)	weight: 0
#|app'|❆2_app(x1,x2)	weight: 0
|app'|❆1_if_minsort(x1)	weight: 0
|app'|❆3_if_rm(x1,x2,x3)	weight: 0
|app'|❆1_min(x1)	weight: 0
#|app'|❆4_filter2(x1,x2,x3,x4)	weight: 0
  true()	weight: 0
filter2()	weight: 0
|app'|❆2_le(x1,x2)	weight: 0
#|app'|❆3_if_rm(x1,x2,x3)	weight: x3
|app'|❆1_rm(x1)	weight: 0
|app'|❆2_minsort(x1,x2)	weight: 0
|app'|❆1_minsort(x1)	weight: 0
#|app'|❆3_if_minsort(x1,x2,x3)	weight: 0
|app'|❆2_filter2(x1,x2)	weight: 0
|app'|❆1_le(x1)	weight: 0
|app'|❆2_map(x1,x2)	weight: 0
   nil()	weight: 0
#|app'|❆2_filter(x1,x2)	weight: 0
#|app'|❆2_rm(x1,x2)	weight: (/ 1 4) + x2
|app'|❆1_app(x1)	weight: 0
   map()	weight: 0
#|app'|❆2_eq(x1,x2)	weight: 0
|app'|❆1_filter(x1)	weight: 0
   min()	weight: 0
|app'|❆1_s(x1)	weight: (/ 1 4)
|app'|❆2_if_rm(x1,x2)	weight: 0
#|app'|❆2_minsort(x1,x2)	weight: 0
   add()	weight: 0
if_min()	weight: 0
if_minsort()	weight: 0
filter()	weight: 0
#|app'|❆1_min(x1)	weight: 0
|app'|❆2_app(x1,x2)	weight: 0
|app'|❆2_rm(x1,x2)	weight: 0
|app'|❆1_if_rm(x1)	weight: 0
minsort()	weight: 0
|app'|❆1_add(x1)	weight: 0
|app'|❆1_if_min(x1)	weight: 0
    rm()	weight: 0
#|app'|❆2_map(x1,x2)	weight: 0
   app()	weight: 0
    Usable rules: { }
    Removed DPs: #27 #34 #35
Number of SCCs: 3, DPs: 15, edges: 28
	SCC { #8 #10 #16 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   |0|()	weight: 0
#|app'|(x1,x2)	weight: 0
    le()	weight: 0
|app'|❆3_filter2(x1,x2,x3)	weight: 0
 if_rm()	weight: 0
|app'|❆4_filter2(x1,x2,x3,x4)	weight: 0
|app'|❆2_eq(x1,x2)	weight: (/ 1 8) + x1
     s()	weight: 0
|app'|❆1_min❆1_|app'|❆2_add(x1,x2)	weight: 0
|app'|❆1_map(x1)	weight: 0
|app'|❆2_add(x1,x2)	weight: (/ 1 4) + x2
|app'|❆2_if_minsort(x1,x2)	weight: 0
#|app'|❆2_le(x1,x2)	weight: 0
|app'|❆1_eq(x1)	weight: 0
|app'|❆2_if_min(x1,x2)	weight: 0
    eq()	weight: 0
|app'|❆2_filter(x1,x2)	weight: 0
|app'|❆3_if_minsort(x1,x2,x3)	weight: 0
 false()	weight: 0
#|app'|❆1_min❆1_|app'|❆2_add(x1,x2)	weight: (/ 3 8) + x2
|app'|(x1,x2)	weight: 0
#|app'|❆2_if_min(x1,x2)	weight: x2
|app'|❆1_filter2(x1)	weight: 0
#|app'|❆2_app(x1,x2)	weight: 0
|app'|❆1_if_minsort(x1)	weight: 0
|app'|❆3_if_rm(x1,x2,x3)	weight: 0
|app'|❆1_min(x1)	weight: 0
#|app'|❆4_filter2(x1,x2,x3,x4)	weight: 0
  true()	weight: 0
filter2()	weight: 0
|app'|❆2_le(x1,x2)	weight: (/ 1 8)
#|app'|❆3_if_rm(x1,x2,x3)	weight: 0
|app'|❆1_rm(x1)	weight: 0
|app'|❆2_minsort(x1,x2)	weight: 0
|app'|❆1_minsort(x1)	weight: 0
#|app'|❆3_if_minsort(x1,x2,x3)	weight: 0
|app'|❆2_filter2(x1,x2)	weight: 0
|app'|❆1_le(x1)	weight: 0
|app'|❆2_map(x1,x2)	weight: 0
   nil()	weight: 0
#|app'|❆2_filter(x1,x2)	weight: 0
#|app'|❆2_rm(x1,x2)	weight: (/ 1 8)
|app'|❆1_app(x1)	weight: 0
   map()	weight: 0
#|app'|❆2_eq(x1,x2)	weight: 0
|app'|❆1_filter(x1)	weight: 0
   min()	weight: 0
|app'|❆1_s(x1)	weight: (/ 1 8)
|app'|❆2_if_rm(x1,x2)	weight: 0
#|app'|❆2_minsort(x1,x2)	weight: 0
   add()	weight: 0
if_min()	weight: 0
if_minsort()	weight: 0
filter()	weight: 0
#|app'|❆1_min(x1)	weight: 0
|app'|❆2_app(x1,x2)	weight: 0
|app'|❆2_rm(x1,x2)	weight: 0
|app'|❆1_if_rm(x1)	weight: 0
minsort()	weight: 0
|app'|❆1_add(x1)	weight: 0
|app'|❆1_if_min(x1)	weight: 0
    rm()	weight: 0
#|app'|❆2_map(x1,x2)	weight: 0
   app()	weight: 0
    Usable rules: { }
    Removed DPs: #8 #10 #16
Number of SCCs: 2, DPs: 12, edges: 24
	SCC { #21 #29 #33 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   |0|()	weight: 0
#|app'|(x1,x2)	weight: 0
    le()	weight: 0
|app'|❆3_filter2(x1,x2,x3)	weight: 0
 if_rm()	weight: 0
|app'|❆4_filter2(x1,x2,x3,x4)	weight: 0
|app'|❆2_eq(x1,x2)	weight: (/ 1 8) + x1
     s()	weight: 0
|app'|❆1_min❆1_|app'|❆2_add(x1,x2)	weight: (/ 1 4) + x2
|app'|❆1_map(x1)	weight: 0
|app'|❆2_add(x1,x2)	weight: (/ 3 8) + x1 + x2
|app'|❆2_if_minsort(x1,x2)	weight: 0
#|app'|❆2_le(x1,x2)	weight: 0
|app'|❆1_eq(x1)	weight: 0
|app'|❆2_if_min(x1,x2)	weight: x2
    eq()	weight: 0
|app'|❆2_filter(x1,x2)	weight: 0
|app'|❆3_if_minsort(x1,x2,x3)	weight: 0
 false()	weight: 0
#|app'|❆1_min❆1_|app'|❆2_add(x1,x2)	weight: (/ 3 8)
|app'|(x1,x2)	weight: 0
#|app'|❆2_if_min(x1,x2)	weight: 0
|app'|❆1_filter2(x1)	weight: 0
#|app'|❆2_app(x1,x2)	weight: 0
|app'|❆1_if_minsort(x1)	weight: 0
|app'|❆3_if_rm(x1,x2,x3)	weight: (/ 1 8) + x2 + x3
|app'|❆1_min(x1)	weight: 0
#|app'|❆4_filter2(x1,x2,x3,x4)	weight: 0
  true()	weight: 0
filter2()	weight: 0
|app'|❆2_le(x1,x2)	weight: (/ 1 8)
#|app'|❆3_if_rm(x1,x2,x3)	weight: 0
|app'|❆1_rm(x1)	weight: 0
|app'|❆2_minsort(x1,x2)	weight: 0
|app'|❆1_minsort(x1)	weight: 0
#|app'|❆3_if_minsort(x1,x2,x3)	weight: x2 + x3
|app'|❆2_filter2(x1,x2)	weight: 0
|app'|❆1_le(x1)	weight: 0
|app'|❆2_map(x1,x2)	weight: 0
   nil()	weight: 0
#|app'|❆2_filter(x1,x2)	weight: 0
#|app'|❆2_rm(x1,x2)	weight: (/ 1 8)
|app'|❆1_app(x1)	weight: 0
   map()	weight: 0
#|app'|❆2_eq(x1,x2)	weight: 0
|app'|❆1_filter(x1)	weight: 0
   min()	weight: 0
|app'|❆1_s(x1)	weight: (/ 1 8)
|app'|❆2_if_rm(x1,x2)	weight: 0
#|app'|❆2_minsort(x1,x2)	weight: x1 + x2
   add()	weight: 0
if_min()	weight: 0
if_minsort()	weight: 0
filter()	weight: 0
#|app'|❆1_min(x1)	weight: 0
|app'|❆2_app(x1,x2)	weight: (/ 1 8) + x1 + x2
|app'|❆2_rm(x1,x2)	weight: (/ 1 8) + x1 + x2
|app'|❆1_if_rm(x1)	weight: 0
minsort()	weight: 0
|app'|❆1_add(x1)	weight: 0
|app'|❆1_if_min(x1)	weight: 0
    rm()	weight: 0
#|app'|❆2_map(x1,x2)	weight: 0
   app()	weight: 0
    Usable rules: { 8 9 14..17 }
    Removed DPs: #21
Number of SCCs: 2, DPs: 11, edges: 22
	SCC { #29 #33 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   |0|()	weight: 0
#|app'|(x1,x2)	weight: 0
    le()	weight: 0
|app'|❆3_filter2(x1,x2,x3)	weight: 0
 if_rm()	weight: 0
|app'|❆4_filter2(x1,x2,x3,x4)	weight: 0
|app'|❆2_eq(x1,x2)	weight: (/ 1 8) + x1
     s()	weight: 0
|app'|❆1_min❆1_|app'|❆2_add(x1,x2)	weight: (/ 1 4) + x2
|app'|❆1_map(x1)	weight: 0
|app'|❆2_add(x1,x2)	weight: (/ 1 4) + x1 + x2
|app'|❆2_if_minsort(x1,x2)	weight: 0
#|app'|❆2_le(x1,x2)	weight: 0
|app'|❆1_eq(x1)	weight: 0
|app'|❆2_if_min(x1,x2)	weight: (/ 1 8) + x2
    eq()	weight: 0
|app'|❆2_filter(x1,x2)	weight: 0
|app'|❆3_if_minsort(x1,x2,x3)	weight: 0
 false()	weight: 0
#|app'|❆1_min❆1_|app'|❆2_add(x1,x2)	weight: (/ 3 8)
|app'|(x1,x2)	weight: 0
#|app'|❆2_if_min(x1,x2)	weight: 0
|app'|❆1_filter2(x1)	weight: 0
#|app'|❆2_app(x1,x2)	weight: 0
|app'|❆1_if_minsort(x1)	weight: 0
|app'|❆3_if_rm(x1,x2,x3)	weight: (/ 1 8) + x2 + x3
|app'|❆1_min(x1)	weight: 0
#|app'|❆4_filter2(x1,x2,x3,x4)	weight: 0
  true()	weight: 0
filter2()	weight: 0
|app'|❆2_le(x1,x2)	weight: (/ 1 8)
#|app'|❆3_if_rm(x1,x2,x3)	weight: 0
|app'|❆1_rm(x1)	weight: 0
|app'|❆2_minsort(x1,x2)	weight: 0
|app'|❆1_minsort(x1)	weight: 0
#|app'|❆3_if_minsort(x1,x2,x3)	weight: x2
|app'|❆2_filter2(x1,x2)	weight: 0
|app'|❆1_le(x1)	weight: 0
|app'|❆2_map(x1,x2)	weight: 0
   nil()	weight: 0
#|app'|❆2_filter(x1,x2)	weight: 0
#|app'|❆2_rm(x1,x2)	weight: (/ 1 8)
|app'|❆1_app(x1)	weight: 0
   map()	weight: 0
#|app'|❆2_eq(x1,x2)	weight: 0
|app'|❆1_filter(x1)	weight: 0
   min()	weight: 0
|app'|❆1_s(x1)	weight: (/ 1 8)
|app'|❆2_if_rm(x1,x2)	weight: 0
#|app'|❆2_minsort(x1,x2)	weight: (/ 1 8) + x1
   add()	weight: 0
if_min()	weight: 0
if_minsort()	weight: 0
filter()	weight: 0
#|app'|❆1_min(x1)	weight: 0
|app'|❆2_app(x1,x2)	weight: (/ 1 8) + x1 + x2
|app'|❆2_rm(x1,x2)	weight: (/ 1 8) + x1 + x2
|app'|❆1_if_rm(x1)	weight: 0
minsort()	weight: 0
|app'|❆1_add(x1)	weight: 0
|app'|❆1_if_min(x1)	weight: 0
    rm()	weight: 0
#|app'|❆2_map(x1,x2)	weight: 0
   app()	weight: 0
    Usable rules: { }
    Removed DPs: #29 #33
Number of SCCs: 1, DPs: 9, edges: 20
	SCC { #5 #13..15 #18..20 #26 #32 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   |0|()	weight: 0
#|app'|(x1,x2)	weight: x1 + x2
    le()	weight: 0
|app'|❆3_filter2(x1,x2,x3)	weight: (/ 3 8) + x2 + x3
 if_rm()	weight: 0
|app'|❆4_filter2(x1,x2,x3,x4)	weight: (/ 5 8) + x1 + x3 + x4
|app'|❆2_eq(x1,x2)	weight: (/ 3 8) + x1
     s()	weight: 0
|app'|❆1_min❆1_|app'|❆2_add(x1,x2)	weight: (/ 5 8) + x2
|app'|❆1_map(x1)	weight: (/ 3 8) + x1
|app'|❆2_add(x1,x2)	weight: (/ 3 8) + x1 + x2
|app'|❆2_if_minsort(x1,x2)	weight: (/ 3 8) + x1 + x2
#|app'|❆2_le(x1,x2)	weight: 0
|app'|❆1_eq(x1)	weight: (/ 3 8) + x1
|app'|❆2_if_min(x1,x2)	weight: (/ 3 8) + x2
    eq()	weight: 0
|app'|❆2_filter(x1,x2)	weight: (/ 3 8) + x2
|app'|❆3_if_minsort(x1,x2,x3)	weight: (/ 7 8)
 false()	weight: 0
#|app'|❆1_min❆1_|app'|❆2_add(x1,x2)	weight: (/ 3 8)
|app'|(x1,x2)	weight: (/ 1 4)
#|app'|❆2_if_min(x1,x2)	weight: 0
|app'|❆1_filter2(x1)	weight: (/ 3 8) + x1
#|app'|❆2_app(x1,x2)	weight: 0
|app'|❆1_if_minsort(x1)	weight: (/ 3 8) + x1
|app'|❆3_if_rm(x1,x2,x3)	weight: (/ 3 8) + x2 + x3
|app'|❆1_min(x1)	weight: (/ 3 8)
#|app'|❆4_filter2(x1,x2,x3,x4)	weight: (/ 1 8) + x2 + x3 + x4
  true()	weight: 0
filter2()	weight: 0
|app'|❆2_le(x1,x2)	weight: (/ 3 8)
#|app'|❆3_if_rm(x1,x2,x3)	weight: 0
|app'|❆1_rm(x1)	weight: (/ 3 8) + x1
|app'|❆2_minsort(x1,x2)	weight: (/ 3 8) + x1 + x2
|app'|❆1_minsort(x1)	weight: (/ 3 8) + x1
#|app'|❆3_if_minsort(x1,x2,x3)	weight: 0
|app'|❆2_filter2(x1,x2)	weight: (/ 3 8)
|app'|❆1_le(x1)	weight: (/ 3 8)
|app'|❆2_map(x1,x2)	weight: (/ 3 8) + x1
   nil()	weight: 0
#|app'|❆2_filter(x1,x2)	weight: x1 + x2
#|app'|❆2_rm(x1,x2)	weight: (/ 1 8)
|app'|❆1_app(x1)	weight: (/ 3 8)
   map()	weight: 0
#|app'|❆2_eq(x1,x2)	weight: 0
|app'|❆1_filter(x1)	weight: (/ 3 8) + x1
   min()	weight: 0
|app'|❆1_s(x1)	weight: (/ 3 8) + x1
|app'|❆2_if_rm(x1,x2)	weight: (/ 3 8) + x1
#|app'|❆2_minsort(x1,x2)	weight: (/ 1 8) + x1
   add()	weight: 0
if_min()	weight: 0
if_minsort()	weight: 0
filter()	weight: 0
#|app'|❆1_min(x1)	weight: 0
|app'|❆2_app(x1,x2)	weight: (/ 3 8) + x1 + x2
|app'|❆2_rm(x1,x2)	weight: (/ 3 8) + x1 + x2
|app'|❆1_if_rm(x1)	weight: (/ 3 8) + x1
minsort()	weight: 0
|app'|❆1_add(x1)	weight: (/ 3 8) + x1
|app'|❆1_if_min(x1)	weight: (/ 3 8) + x1
    rm()	weight: 0
#|app'|❆2_map(x1,x2)	weight: x1 + x2
   app()	weight: 0
    Usable rules: { 8 9 14..17 }
    Removed DPs: #5 #13..15 #18..20 #26 #32
Number of SCCs: 1, DPs: 0, edges: 0
YES