Input TRS:
    1: min(x,0()) -> 0()
    2: min(0(),y) -> 0()
    3: min(s(x),s(y)) -> s(min(x,y))
    4: max(x,0()) -> x
    5: max(0(),y) -> y
    6: max(s(x),s(y)) -> s(max(x,y))
    7: -(x,0()) -> x
    8: -(s(x),s(y)) -> -(x,y)
    9: gcd(nil()) -> 0()
    10: gcd(cons(x,nil())) -> x
    11: gcd(cons(0(),y)) -> gcd(y)
    12: gcd(cons(x,cons(y,z))) -> gcd(cons(-(x,y),cons(y,z)))
    13: gcd(cons(x,cons(y,z))) ->= gcd(cons(max(x,y),cons(min(x,y),z)))
Number of strict rules: 12
Direct Order(PosReal,>,Poly) ... failed.
Freezing gcd
1: min(x,0()) -> 0()
2: min(0(),y) -> 0()
3: min(s(x),s(y)) -> s(min(x,y))
4: max(x,0()) -> x
5: max(0(),y) -> y
6: max(s(x),s(y)) -> s(max(x,y))
7: -(x,0()) -> x
8: -(s(x),s(y)) -> -(x,y)
9: gcd❆1_nil() -> 0()
10: gcd❆1_cons(x,nil()) -> x
11: gcd❆1_cons(0(),y) -> gcd(y)
12: gcd❆1_cons(x,cons(y,z)) -> gcd❆1_cons(-(x,y),cons(y,z))
13: gcd❆1_cons(x,cons(y,z)) ->= gcd❆1_cons(max(x,y),cons(min(x,y),z))
14: gcd(cons(_1,_2)) ->= gcd❆1_cons(_1,_2)
15: gcd(nil()) ->= gcd❆1_nil()
Number of strict rules: 12
Direct Order(PosReal,>,Poly) ... failed.
Dependency Pairs:
   #1: #max(s(x),s(y)) -> #max(x,y)
   #2: #gcd❆1_cons(x,cons(y,z)) ->? #gcd❆1_cons(max(x,y),cons(min(x,y),z))
   #3: #gcd❆1_cons(x,cons(y,z)) ->? #max(x,y)
   #4: #gcd❆1_cons(x,cons(y,z)) ->? #min(x,y)
   #5: #gcd❆1_cons(0(),y) -> #gcd(y)
   #6: #gcd❆1_cons(x,cons(y,z)) -> #gcd❆1_cons(-(x,y),cons(y,z))
   #7: #gcd❆1_cons(x,cons(y,z)) -> #-(x,y)
   #8: #gcd(cons(_1,_2)) ->? #gcd❆1_cons(_1,_2)
   #9: #min(s(x),s(y)) -> #min(x,y)
   #10: #-(s(x),s(y)) -> #-(x,y)
   #11: #gcd(nil()) ->? #gcd❆1_nil()
Number of SCCs: 4, DPs: 7, edges: 13
	SCC { #10 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 2) + x1
   gcd(x1)	weight: 0
 #min(x1,x2)	weight: 0
#gcd❆1_cons(x1,x2)	weight: 0
     0()	weight: 0
   max(x1,x2)	weight: 0
   nil()	weight: 0
 #max(x1,x2)	weight: 0
     -(x1,x2)	weight: 0
#gcd❆1_nil()	weight: 0
   min(x1,x2)	weight: 0
   #-(x1,x2)	weight: x2
  cons(x1,x2)	weight: 0
gcd❆1_cons(x1,x2)	weight: 0
gcd❆1_nil()	weight: 0
 #gcd(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #10
Number of SCCs: 3, DPs: 6, edges: 12
	SCC { #9 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 2) + x1
   gcd(x1)	weight: 0
 #min(x1,x2)	weight: x2
#gcd❆1_cons(x1,x2)	weight: 0
     0()	weight: 0
   max(x1,x2)	weight: 0
   nil()	weight: 0
 #max(x1,x2)	weight: 0
     -(x1,x2)	weight: 0
#gcd❆1_nil()	weight: 0
   min(x1,x2)	weight: 0
   #-(x1,x2)	weight: 0
  cons(x1,x2)	weight: 0
gcd❆1_cons(x1,x2)	weight: 0
gcd❆1_nil()	weight: 0
 #gcd(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #9
Number of SCCs: 2, DPs: 5, edges: 11
	SCC { #1 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 2) + x1
   gcd(x1)	weight: 0
 #min(x1,x2)	weight: 0
#gcd❆1_cons(x1,x2)	weight: 0
     0()	weight: 0
   max(x1,x2)	weight: 0
   nil()	weight: 0
 #max(x1,x2)	weight: x1
     -(x1,x2)	weight: 0
#gcd❆1_nil()	weight: 0
   min(x1,x2)	weight: 0
   #-(x1,x2)	weight: 0
  cons(x1,x2)	weight: 0
gcd❆1_cons(x1,x2)	weight: 0
gcd❆1_nil()	weight: 0
 #gcd(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #1
Number of SCCs: 1, DPs: 4, edges: 10
	SCC { #2 #5 #6 #8 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 2)
   gcd(x1)	weight: 0
 #min(x1,x2)	weight: 0
#gcd❆1_cons(x1,x2)	weight: (/ 1 4) + x2
     0()	weight: 0
   max(x1,x2)	weight: (/ 1 4)
   nil()	weight: 0
 #max(x1,x2)	weight: 0
     -(x1,x2)	weight: (/ 1 4)
#gcd❆1_nil()	weight: 0
   min(x1,x2)	weight: (/ 1 4) + x2
   #-(x1,x2)	weight: 0
  cons(x1,x2)	weight: (/ 1 2) + x2
gcd❆1_cons(x1,x2)	weight: 0
gcd❆1_nil()	weight: 0
 #gcd(x1)	weight: x1
    Usable rules: { 1..3 }
    Removed DPs: #5 #8
Number of SCCs: 1, DPs: 2, edges: 4
	SCC { #2 #6 }
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...  found.
  #gcd❆1_cons(x,cons(y_{1},z_{1}))	-#6->
  #gcd❆1_cons(-(x,y_{1}),cons(y_{1},z_{1}))	--->*
  #gcd❆1_cons(-(x,y_{1}),cons(y_{1},z_{1}))
  Looping with: [ x := -(x,y_{1}); y_{1} := y_{1}; z_{1} := z_{1}; ]
NO