Input TRS:
    1: eq(|0|(),|0|()) -> true()
    2: eq(|0|(),s(x)) -> false()
    3: eq(s(x),|0|()) -> false()
    4: eq(s(x),s(y)) -> eq(x,y)
    5: rm(n,nil()) -> nil()
    6: rm(n,cons(m,x)) -> ifrm(eq(n,m),n,cons(m,x))
    7: ifrm(true(),n,cons(m,x)) -> rm(n,x)
    8: ifrm(false(),n,cons(m,x)) -> cons(m,rm(n,x))
    9: purge(nil()) -> nil()
    10: purge(cons(n,x)) -> cons(n,purge(rm(n,x)))
    11: purge(cons(x,xs())) ->= purge(consSwap(x,xs()))
    12: consSwap(x,xs()) ->= cons(x,xs())
    13: consSwap(x,cons(y,xs())) ->= cons(y,consSwap(x,xs()))
Number of strict rules: 10
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #rm(n,cons(m,x)) -> #ifrm(eq(n,m),n,cons(m,x))
   #2: #rm(n,cons(m,x)) -> #eq(n,m)
   #3: #purge(cons(x,xs())) ->? #purge(consSwap(x,xs()))
   #4: #ifrm(true(),n,cons(m,x)) -> #rm(n,x)
   #5: #purge(cons(n,x)) -> #purge(rm(n,x))
   #6: #purge(cons(n,x)) -> #rm(n,x)
   #7: #ifrm(false(),n,cons(m,x)) -> #rm(n,x)
   #8: #eq(s(x),s(y)) -> #eq(x,y)
Number of SCCs: 3, DPs: 6, edges: 9
	SCC { #8 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   |0|()	weight: 0
#ifrm(x1,x2,x3)	weight: 0
     s(x1)	weight: (/ 1 2) + x1
#purge(x1)	weight: 0
    eq(x1,x2)	weight: 0
 false()	weight: 0
  true()	weight: 0
 purge(x1)	weight: 0
  #eq(x1,x2)	weight: x2
consSwap(x1,x2)	weight: 0
  ifrm(x1,x2,x3)	weight: 0
   nil()	weight: 0
  cons(x1,x2)	weight: 0
    xs()	weight: 0
    rm(x1,x2)	weight: 0
  #rm(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #8
Number of SCCs: 2, DPs: 5, edges: 8
	SCC { #3 #5 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   |0|()	weight: 0
#ifrm(x1,x2,x3)	weight: 0
     s(x1)	weight: (/ 1 4)
#purge(x1)	weight: x1
    eq(x1,x2)	weight: (/ 1 4)
 false()	weight: 0
  true()	weight: 0
 purge(x1)	weight: 0
  #eq(x1,x2)	weight: 0
consSwap(x1,x2)	weight: (/ 1 2) + x1
  ifrm(x1,x2,x3)	weight: (/ 1 4) + x3
   nil()	weight: 0
  cons(x1,x2)	weight: (/ 1 2) + x1 + x2
    xs()	weight: 0
    rm(x1,x2)	weight: (/ 1 4) + x2
  #rm(x1,x2)	weight: 0
    Usable rules: { 5..8 12 }
    Removed DPs: #5
Number of SCCs: 2, DPs: 4, edges: 5
	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