Input TRS:
    1: le(0(),y) -> true()
    2: le(s(x),0()) -> false()
    3: le(s(x),s(y)) -> le(x,y)
    4: eq(0(),0()) -> true()
    5: eq(0(),s(y)) -> false()
    6: eq(s(x),0()) -> false()
    7: eq(s(x),s(y)) -> eq(x,y)
    8: minsort(nil()) -> nil()
    9: minsort(cons(x,xs)) -> cons(min(cons(x,xs)),minsort(rm(min(cons(x,xs)),cons(x,xs))))
    10: min(nil()) -> 0()
    11: min(cons(x,nil())) -> x
    12: min(cons(x,cons(y,xs))) -> if1(le(x,y),x,y,xs)
    13: if1(true(),x,y,xs) -> min(cons(x,xs))
    14: if1(false(),x,y,xs) -> min(cons(y,xs))
    15: rm(x,nil()) -> nil()
    16: rm(x,cons(y,xs)) -> if2(eq(x,y),x,y,xs)
    17: if2(true(),x,y,xs) -> rm(x,xs)
    18: if2(false(),x,y,xs) -> cons(y,rm(x,xs))
Number of strict rules: 18
Direct Order(PosReal,>,Poly) ... failed.
Freezing min
1: le(0(),y) -> true()
2: le(s(x),0()) -> false()
3: le(s(x),s(y)) -> le(x,y)
4: eq(0(),0()) -> true()
5: eq(0(),s(y)) -> false()
6: eq(s(x),0()) -> false()
7: eq(s(x),s(y)) -> eq(x,y)
8: minsort(nil()) -> nil()
9: minsort(cons(x,xs)) -> cons(min❆1_cons(x,xs),minsort(rm(min❆1_cons(x,xs),cons(x,xs))))
10: min❆1_nil() -> 0()
11: min❆1_cons(x,nil()) -> x
12: min❆1_cons(x,cons(y,xs)) -> if1(le(x,y),x,y,xs)
13: if1(true(),x,y,xs) -> min❆1_cons(x,xs)
14: if1(false(),x,y,xs) -> min❆1_cons(y,xs)
15: rm(x,nil()) -> nil()
16: rm(x,cons(y,xs)) -> if2(eq(x,y),x,y,xs)
17: if2(true(),x,y,xs) -> rm(x,xs)
18: if2(false(),x,y,xs) -> cons(y,rm(x,xs))
19: min(cons(_1,_2)) ->= min❆1_cons(_1,_2)
20: min(nil()) ->= min❆1_nil()
Number of strict rules: 18
Direct Order(PosReal,>,Poly) ... failed.
Dependency Pairs:
   #1: #if1(true(),x,y,xs) -> #min❆1_cons(x,xs)
   #2: #minsort(cons(x,xs)) -> #min❆1_cons(x,xs)
   #3: #minsort(cons(x,xs)) -> #minsort(rm(min❆1_cons(x,xs),cons(x,xs)))
   #4: #minsort(cons(x,xs)) -> #rm(min❆1_cons(x,xs),cons(x,xs))
   #5: #minsort(cons(x,xs)) -> #min❆1_cons(x,xs)
   #6: #min❆1_cons(x,cons(y,xs)) -> #if1(le(x,y),x,y,xs)
   #7: #min❆1_cons(x,cons(y,xs)) -> #le(x,y)
   #8: #if1(false(),x,y,xs) -> #min❆1_cons(y,xs)
   #9: #min(nil()) ->? #min❆1_nil()
   #10: #eq(s(x),s(y)) -> #eq(x,y)
   #11: #if2(true(),x,y,xs) -> #rm(x,xs)
   #12: #min(cons(_1,_2)) ->? #min❆1_cons(_1,_2)
   #13: #rm(x,cons(y,xs)) -> #if2(eq(x,y),x,y,xs)
   #14: #rm(x,cons(y,xs)) -> #eq(x,y)
   #15: #le(s(x),s(y)) -> #le(x,y)
   #16: #if2(false(),x,y,xs) -> #rm(x,xs)
Number of SCCs: 5, DPs: 9, edges: 11
	SCC { #15 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
    le(x1,x2)	weight: 0
     s(x1)	weight: (/ 1 2) + x1
  #le(x1,x2)	weight: x2
    eq(x1,x2)	weight: 0
   if1(x1,x2,x3,x4)	weight: 0
 false()	weight: 0
 #min(x1)	weight: 0
min❆1_cons(x1,x2)	weight: 0
#min❆1_nil()	weight: 0
  true()	weight: 0
  #eq(x1,x2)	weight: 0
 #if1(x1,x2,x3,x4)	weight: 0
   if2(x1,x2,x3,x4)	weight: 0
     0()	weight: 0
   nil()	weight: 0
min❆1_nil()	weight: 0
   min(x1)	weight: 0
#min❆1_cons(x1,x2)	weight: 0
  cons(x1,x2)	weight: 0
#minsort(x1)	weight: 0
minsort(x1)	weight: 0
 #if2(x1,x2,x3,x4)	weight: 0
    rm(x1,x2)	weight: 0
  #rm(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #15
Number of SCCs: 4, DPs: 8, edges: 10
	SCC { #10 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
    le(x1,x2)	weight: 0
     s(x1)	weight: (/ 1 2) + x1
  #le(x1,x2)	weight: 0
    eq(x1,x2)	weight: 0
   if1(x1,x2,x3,x4)	weight: 0
 false()	weight: 0
 #min(x1)	weight: 0
min❆1_cons(x1,x2)	weight: 0
#min❆1_nil()	weight: 0
  true()	weight: 0
  #eq(x1,x2)	weight: x2
 #if1(x1,x2,x3,x4)	weight: 0
   if2(x1,x2,x3,x4)	weight: 0
     0()	weight: 0
   nil()	weight: 0
min❆1_nil()	weight: 0
   min(x1)	weight: 0
#min❆1_cons(x1,x2)	weight: 0
  cons(x1,x2)	weight: 0
#minsort(x1)	weight: 0
minsort(x1)	weight: 0
 #if2(x1,x2,x3,x4)	weight: 0
    rm(x1,x2)	weight: 0
  #rm(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #10
Number of SCCs: 3, DPs: 7, edges: 9
	SCC { #3 }
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