/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES
Input TRS:
    1: app(app(le(),0()),y) -> true()
    2: app(app(le(),app(s(),x)),0()) -> false()
    3: app(app(le(),app(s(),x)),app(s(),y)) -> app(app(le(),x),y)
    4: app(pred(),app(s(),x)) -> x
    5: app(app(minus(),x),0()) -> x
    6: app(app(minus(),x),app(s(),y)) -> app(pred(),app(app(minus(),x),y))
    7: app(app(gcd(),0()),y) -> y
    8: app(app(gcd(),app(s(),x)),0()) -> app(s(),x)
    9: app(app(gcd(),app(s(),x)),app(s(),y)) -> app(app(app(if_gcd(),app(app(le(),y),x)),app(s(),x)),app(s(),y))
    10: app(app(app(if_gcd(),true()),app(s(),x)),app(s(),y)) -> app(app(gcd(),app(app(minus(),x),y)),app(s(),y))
    11: app(app(app(if_gcd(),false()),app(s(),x)),app(s(),y)) -> app(app(gcd(),app(app(minus(),y),x)),app(s(),x))
    12: app(app(map(),f),nil()) -> nil()
    13: app(app(map(),f),app(app(cons(),x),xs)) -> app(app(cons(),app(f,x)),app(app(map(),f),xs))
    14: app(app(filter(),f),nil()) -> nil()
    15: app(app(filter(),f),app(app(cons(),x),xs)) -> app(app(app(app(filter2(),app(f,x)),f),x),xs)
    16: app(app(app(app(filter2(),true()),f),x),xs) -> app(app(cons(),x),app(app(filter(),f),xs))
    17: app(app(app(app(filter2(),false()),f),x),xs) -> app(app(filter(),f),xs)
Number of strict rules: 17
Direct poly ... failed.
Freezing app
1: app❆2_le(0(),y) -> true()
2: app❆2_le(app❆1_s(x),0()) -> false()
3: app❆2_le(app❆1_s(x),app❆1_s(y)) -> app❆2_le(x,y)
4: app❆1_pred(app❆1_s(x)) -> x
5: app❆2_minus(x,0()) -> x
6: app❆2_minus(x,app❆1_s(y)) -> app❆1_pred(app❆2_minus(x,y))
7: app❆2_gcd(0(),y) -> y
8: app❆2_gcd(app❆1_s(x),0()) -> app❆1_s(x)
9: app❆2_gcd(app❆1_s(x),app❆1_s(y)) -> app❆3_if_gcd(app❆2_le(y,x),app❆1_s(x),app❆1_s(y))
10: app❆3_if_gcd(true(),app❆1_s(x),app❆1_s(y)) -> app❆2_gcd(app❆2_minus(x,y),app❆1_s(y))
11: app❆3_if_gcd(false(),app❆1_s(x),app❆1_s(y)) -> app❆2_gcd(app❆2_minus(y,x),app❆1_s(x))
12: app❆2_map(f,nil()) -> nil()
13: app❆2_map(f,app❆2_cons(x,xs)) -> app❆2_cons(app(f,x),app❆2_map(f,xs))
14: app❆2_filter(f,nil()) -> nil()
15: app❆2_filter(f,app❆2_cons(x,xs)) -> app❆4_filter2(app(f,x),f,x,xs)
16: app❆4_filter2(true(),f,x,xs) -> app❆2_cons(x,app❆2_filter(f,xs))
17: app❆4_filter2(false(),f,x,xs) -> app❆2_filter(f,xs)
18: app(le(),_1) ->= app❆1_le(_1)
19: app(app❆1_le(_1),_2) ->= app❆2_le(_1,_2)
20: app(cons(),_1) ->= app❆1_cons(_1)
21: app(app❆1_cons(_1),_2) ->= app❆2_cons(_1,_2)
22: app(if_gcd(),_1) ->= app❆1_if_gcd(_1)
23: app(app❆1_if_gcd(_1),_2) ->= app❆2_if_gcd(_1,_2)
24: app(app❆2_if_gcd(_1,_2),_3) ->= app❆3_if_gcd(_1,_2,_3)
25: app(s(),_1) ->= app❆1_s(_1)
26: app(filter(),_1) ->= app❆1_filter(_1)
27: app(app❆1_filter(_1),_2) ->= app❆2_filter(_1,_2)
28: app(map(),_1) ->= app❆1_map(_1)
29: app(app❆1_map(_1),_2) ->= app❆2_map(_1,_2)
30: app(minus(),_1) ->= app❆1_minus(_1)
31: app(app❆1_minus(_1),_2) ->= app❆2_minus(_1,_2)
32: app(gcd(),_1) ->= app❆1_gcd(_1)
33: app(app❆1_gcd(_1),_2) ->= app❆2_gcd(_1,_2)
34: app(pred(),_1) ->= app❆1_pred(_1)
35: app(filter2(),_1) ->= app❆1_filter2(_1)
36: app(app❆1_filter2(_1),_2) ->= app❆2_filter2(_1,_2)
37: app(app❆2_filter2(_1,_2),_3) ->= app❆3_filter2(_1,_2,_3)
38: app(app❆3_filter2(_1,_2,_3),_4) ->= app❆4_filter2(_1,_2,_3,_4)
Number of strict rules: 17
Direct poly ... failed.
Dependency Pairs:
   #1: #app(app❆1_map(_1),_2) ->? #app❆2_map(_1,_2)
   #2: #app(app❆3_filter2(_1,_2,_3),_4) ->? #app❆4_filter2(_1,_2,_3,_4)
   #3: #app❆2_minus(x,app❆1_s(y)) -> #app❆1_pred(app❆2_minus(x,y))
   #4: #app❆2_minus(x,app❆1_s(y)) -> #app❆2_minus(x,y)
   #5: #app❆2_map(f,app❆2_cons(x,xs)) -> #app(f,x)
   #6: #app❆2_map(f,app❆2_cons(x,xs)) -> #app❆2_map(f,xs)
   #7: #app❆2_gcd(app❆1_s(x),app❆1_s(y)) -> #app❆3_if_gcd(app❆2_le(y,x),app❆1_s(x),app❆1_s(y))
   #8: #app❆2_gcd(app❆1_s(x),app❆1_s(y)) -> #app❆2_le(y,x)
   #9: #app❆3_if_gcd(false(),app❆1_s(x),app❆1_s(y)) -> #app❆2_gcd(app❆2_minus(y,x),app❆1_s(x))
   #10: #app❆3_if_gcd(false(),app❆1_s(x),app❆1_s(y)) -> #app❆2_minus(y,x)
   #11: #app(app❆2_if_gcd(_1,_2),_3) ->? #app❆3_if_gcd(_1,_2,_3)
   #12: #app(app❆1_minus(_1),_2) ->? #app❆2_minus(_1,_2)
   #13: #app❆3_if_gcd(true(),app❆1_s(x),app❆1_s(y)) -> #app❆2_gcd(app❆2_minus(x,y),app❆1_s(y))
   #14: #app❆3_if_gcd(true(),app❆1_s(x),app❆1_s(y)) -> #app❆2_minus(x,y)
   #15: #app(app❆1_gcd(_1),_2) ->? #app❆2_gcd(_1,_2)
   #16: #app(pred(),_1) ->? #app❆1_pred(_1)
   #17: #app(app❆1_filter(_1),_2) ->? #app❆2_filter(_1,_2)
   #18: #app❆4_filter2(false(),f,x,xs) -> #app❆2_filter(f,xs)
   #19: #app(app❆1_le(_1),_2) ->? #app❆2_le(_1,_2)
   #20: #app❆4_filter2(true(),f,x,xs) -> #app❆2_filter(f,xs)
   #21: #app❆2_le(app❆1_s(x),app❆1_s(y)) -> #app❆2_le(x,y)
   #22: #app❆2_filter(f,app❆2_cons(x,xs)) -> #app❆4_filter2(app(f,x),f,x,xs)
   #23: #app❆2_filter(f,app❆2_cons(x,xs)) -> #app(f,x)
Number of SCCs: 4, DPs: 14
	SCC { #4 }
Sum... succeeded.
  app❆2_minus(x1,x2)		w: (0)
  app❆1_pred(x1)		w: (0)
  le()		w: (0)
  app❆1_le(x1)		w: (0)
  app❆1_gcd(x1)		w: (0)
  #app❆2_map(x1,x2)		w: (0)
  s()		w: (0)
  app❆1_map(x1)		w: (0)
  app❆1_minus(x1)		w: (0)
  minus()		w: (0)
  gcd()		w: (0)
  app❆2_if_gcd(x1,x2)		w: (0)
  app❆4_filter2(x1,x2,x3,x4)		w: (0)
  app❆2_map(x1,x2)		w: (0)
  #app❆2_minus(x1,x2)		w: (x2)
  false()		w: (0)
  app❆1_if_gcd(x1)		w: (0)
  true()		w: (0)
  #app❆1_pred(x1)		w: (0)
  pred()		w: (0)
  filter2()		w: (0)
  app❆2_filter(x1,x2)		w: (0)
  app❆3_if_gcd(x1,x2,x3)		w: (0)
  app❆2_le(x1,x2)		w: (0)
  0()		w: (0)
  nil()		w: (0)
  app❆1_filter(x1)		w: (0)
  #app(x1,x2)		w: (0)
  map()		w: (0)
  #app❆2_gcd(x1,x2)		w: (0)
  #app❆4_filter2(x1,x2,x3,x4)		w: (0)
  #app❆3_if_gcd(x1,x2,x3)		w: (0)
  app❆2_filter2(x1,x2)		w: (0)
  #app❆2_filter(x1,x2)		w: (0)
  cons()		w: (0)
  app❆2_cons(x1,x2)		w: (0)
  if_gcd()		w: (0)
  filter()		w: (0)
  app❆1_s(x1)		w: (1 + x1)
  app❆1_filter2(x1)		w: (0)
  app❆2_gcd(x1,x2)		w: (0)
  app❆1_cons(x1)		w: (0)
  app❆3_filter2(x1,x2,x3)		w: (0)
  #app❆2_le(x1,x2)		w: (0)
  app(x1,x2)		w: (0)
    USABLE RULES: { }
    Removed DPs: #4
Number of SCCs: 3, DPs: 13
	SCC { #21 }
Sum... succeeded.
  app❆2_minus(x1,x2)		w: (0)
  app❆1_pred(x1)		w: (0)
  le()		w: (0)
  app❆1_le(x1)		w: (0)
  app❆1_gcd(x1)		w: (0)
  #app❆2_map(x1,x2)		w: (0)
  s()		w: (0)
  app❆1_map(x1)		w: (0)
  app❆1_minus(x1)		w: (0)
  minus()		w: (0)
  gcd()		w: (0)
  app❆2_if_gcd(x1,x2)		w: (0)
  app❆4_filter2(x1,x2,x3,x4)		w: (0)
  app❆2_map(x1,x2)		w: (0)
  #app❆2_minus(x1,x2)		w: (0)
  false()		w: (0)
  app❆1_if_gcd(x1)		w: (0)
  true()		w: (0)
  #app❆1_pred(x1)		w: (0)
  pred()		w: (0)
  filter2()		w: (0)
  app❆2_filter(x1,x2)		w: (0)
  app❆3_if_gcd(x1,x2,x3)		w: (0)
  app❆2_le(x1,x2)		w: (0)
  0()		w: (0)
  nil()		w: (0)
  app❆1_filter(x1)		w: (0)
  #app(x1,x2)		w: (0)
  map()		w: (0)
  #app❆2_gcd(x1,x2)		w: (0)
  #app❆4_filter2(x1,x2,x3,x4)		w: (0)
  #app❆3_if_gcd(x1,x2,x3)		w: (0)
  app❆2_filter2(x1,x2)		w: (0)
  #app❆2_filter(x1,x2)		w: (0)
  cons()		w: (0)
  app❆2_cons(x1,x2)		w: (0)
  if_gcd()		w: (0)
  filter()		w: (0)
  app❆1_s(x1)		w: (1 + x1)
  app❆1_filter2(x1)		w: (0)
  app❆2_gcd(x1,x2)		w: (0)
  app❆1_cons(x1)		w: (0)
  app❆3_filter2(x1,x2,x3)		w: (0)
  #app❆2_le(x1,x2)		w: (x2)
  app(x1,x2)		w: (0)
    USABLE RULES: { }
    Removed DPs: #21
Number of SCCs: 2, DPs: 12
	SCC { #7 #9 #13 }
Sum... succeeded.
  app❆2_minus(x1,x2)		w: (1 + x1)
  app❆1_pred(x1)		w: (x1)
  le()		w: (0)
  app❆1_le(x1)		w: (0)
  app❆1_gcd(x1)		w: (0)
  #app❆2_map(x1,x2)		w: (0)
  s()		w: (0)
  app❆1_map(x1)		w: (0)
  app❆1_minus(x1)		w: (0)
  minus()		w: (0)
  gcd()		w: (0)
  app❆2_if_gcd(x1,x2)		w: (0)
  app❆4_filter2(x1,x2,x3,x4)		w: (0)
  app❆2_map(x1,x2)		w: (0)
  #app❆2_minus(x1,x2)		w: (0)
  false()		w: (9)
  app❆1_if_gcd(x1)		w: (0)
  true()		w: (6)
  #app❆1_pred(x1)		w: (0)
  pred()		w: (0)
  filter2()		w: (0)
  app❆2_filter(x1,x2)		w: (0)
  app❆3_if_gcd(x1,x2,x3)		w: (0)
  app❆2_le(x1,x2)		w: (4 + x2 + x1)
  0()		w: (1)
  nil()		w: (0)
  app❆1_filter(x1)		w: (0)
  #app(x1,x2)		w: (0)
  map()		w: (0)
  #app❆2_gcd(x1,x2)		w: (15922 + x2 + x1)
  #app❆4_filter2(x1,x2,x3,x4)		w: (0)
  #app❆3_if_gcd(x1,x2,x3)		w: (15921 + x3 + x2)
  app❆2_filter2(x1,x2)		w: (0)
  #app❆2_filter(x1,x2)		w: (0)
  cons()		w: (0)
  app❆2_cons(x1,x2)		w: (0)
  if_gcd()		w: (0)
  filter()		w: (0)
  app❆1_s(x1)		w: (3 + x1)
  app❆1_filter2(x1)		w: (0)
  app❆2_gcd(x1,x2)		w: (0)
  app❆1_cons(x1)		w: (0)
  app❆3_filter2(x1,x2,x3)		w: (0)
  #app❆2_le(x1,x2)		w: (0)
  app(x1,x2)		w: (0)
    USABLE RULES: { 4..6 }
    Removed DPs: #7 #9 #13
Number of SCCs: 1, DPs: 9
	SCC { #1 #2 #5 #6 #17 #18 #20 #22 #23 }
Sum... succeeded.
  app❆2_minus(x1,x2)		w: (14301 + x2 + x1)
  app❆1_pred(x1)		w: (842 + x1)
  le()		w: (591)
  app❆1_le(x1)		w: (592)
  app❆1_gcd(x1)		w: (4)
  #app❆2_map(x1,x2)		w: (32279 + x2)
  s()		w: (841)
  app❆1_map(x1)		w: (12458)
  app❆1_minus(x1)		w: (2)
  minus()		w: (1)
  gcd()		w: (2)
  app❆2_if_gcd(x1,x2)		w: (12620 + x1)
  app❆4_filter2(x1,x2,x3,x4)		w: (48891 + x4 + x1)
  app❆2_map(x1,x2)		w: (x2 + x1)
  #app❆2_minus(x1,x2)		w: (0)
  false()		w: (1437)
  app❆1_if_gcd(x1)		w: (12619)
  true()		w: (595)
  #app❆1_pred(x1)		w: (0)
  pred()		w: (841)
  filter2()		w: (29534)
  app❆2_filter(x1,x2)		w: (50329 + x1)
  app❆3_if_gcd(x1,x2,x3)		w: (12621 + x3 + x2)
  app❆2_le(x1,x2)		w: (593 + x2 + x1)
  0()		w: (1)
  nil()		w: (19929)
  app❆1_filter(x1)		w: (2819)
  #app(x1,x2)		w: (32280 + x2)
  map()		w: (12457)
  #app❆2_gcd(x1,x2)		w: (15922 + x1)
  #app❆4_filter2(x1,x2,x3,x4)		w: (32279 + x4)
  #app❆3_if_gcd(x1,x2,x3)		w: (15921)
  app❆2_filter2(x1,x2)		w: (46443)
  #app❆2_filter(x1,x2)		w: (32278 + x2)
  cons()		w: (18588)
  app❆2_cons(x1,x2)		w: (18590 + x2 + x1)
  if_gcd()		w: (12618)
  filter()		w: (2818)
  app❆1_s(x1)		w: (842 + x1)
  app❆1_filter2(x1)		w: (46442 + x1)
  app❆2_gcd(x1,x2)		w: (5 + x1)
  app❆1_cons(x1)		w: (18589 + x1)
  app❆3_filter2(x1,x2,x3)		w: (46444 + x3 + x2 + x1)
  #app❆2_le(x1,x2)		w: (0)
  app(x1,x2)		w: (x1)
    USABLE RULES: { 4..6 12 }
    Removed DPs: #1 #2 #5 #6 #17 #18 #20 #22 #23
Number of SCCs: 0, DPs: 0