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(0(),y))) -> gcd(cons(x,y))
    13: gcd(cons(s(x),cons(s(y),z))) -> gcd(cons(-(max(x,y),min(x,y)),cons(s(min(x,y)),z)))
    14: cons(x,cons(y,z)) ->= cons(y,cons(x,z))
Number of strict rules: 13
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #max(s(x),s(y)) -> #max(x,y)
   #2: #gcd(cons(s(x),cons(s(y),z))) -> #gcd(cons(-(max(x,y),min(x,y)),cons(s(min(x,y)),z)))
   #3: #gcd(cons(s(x),cons(s(y),z))) -> #-(max(x,y),min(x,y))
   #4: #gcd(cons(s(x),cons(s(y),z))) -> #max(x,y)
   #5: #gcd(cons(s(x),cons(s(y),z))) -> #min(x,y)
   #6: #gcd(cons(s(x),cons(s(y),z))) -> #min(x,y)
   #7: #gcd(cons(0(),y)) -> #gcd(y)
   #8: #gcd(cons(x,cons(0(),y))) -> #gcd(cons(x,y))
   #9: #min(s(x),s(y)) -> #min(x,y)
   #10: #-(s(x),s(y)) -> #-(x,y)
Number of SCCs: 4, 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
     0()	weight: 0
   max(x1,x2)	weight: 0
   nil()	weight: 0
 #max(x1,x2)	weight: 0
     -(x1,x2)	weight: 0
   min(x1,x2)	weight: 0
   #-(x1,x2)	weight: 0
  cons(x1,x2)	weight: 0
 #gcd(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #9
Number of SCCs: 3, 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
     0()	weight: 0
   max(x1,x2)	weight: 0
   nil()	weight: 0
 #max(x1,x2)	weight: x2
     -(x1,x2)	weight: 0
   min(x1,x2)	weight: 0
   #-(x1,x2)	weight: 0
  cons(x1,x2)	weight: 0
 #gcd(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #1
Number of SCCs: 2, DPs: 4, edges: 10
	SCC { #10 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 2) + x1
   gcd(x1)	weight: 0
 #min(x1,x2)	weight: 0
     0()	weight: 0
   max(x1,x2)	weight: 0
   nil()	weight: 0
 #max(x1,x2)	weight: 0
     -(x1,x2)	weight: 0
   min(x1,x2)	weight: 0
   #-(x1,x2)	weight: x1
  cons(x1,x2)	weight: 0
 #gcd(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #10
Number of SCCs: 1, DPs: 3, edges: 9
	SCC { #2 #7 #8 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 2)
   gcd(x1)	weight: 0
 #min(x1,x2)	weight: 0
     0()	weight: 0
   max(x1,x2)	weight: (/ 1 4) + x1 + x2
   nil()	weight: 0
 #max(x1,x2)	weight: 0
     -(x1,x2)	weight: (/ 1 4)
   min(x1,x2)	weight: (/ 1 4)
   #-(x1,x2)	weight: 0
  cons(x1,x2)	weight: (/ 1 4) + x2
 #gcd(x1)	weight: x1
    Usable rules: { 4..6 14 }
    Removed DPs: #7 #8
Number of SCCs: 1, DPs: 1, edges: 1
	SCC { #2 }
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