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: minus(x,0()) -> x
    8: minus(s(x),s(y)) -> s(minus(x,y))
    9: gcd(s(x),s(y)) -> gcd(minus(max(x,y),min(x,transform(y))),s(min(x,y)))
    10: transform(x) -> s(s(x))
    11: transform(cons(x,y)) -> cons(cons(x,x),x)
    12: transform(cons(x,y)) -> y
    13: transform(s(x)) -> s(s(transform(x)))
    14: cons(x,y) -> y
    15: cons(x,cons(y,s(z))) -> cons(y,x)
    16: cons(cons(x,z),s(y)) -> transform(x)
Number of strict rules: 16
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #max(s(x),s(y)) -> #max(x,y)
   #2: #transform(s(x)) -> #transform(x)
   #3: #gcd(s(x),s(y)) -> #gcd(minus(max(x,y),min(x,transform(y))),s(min(x,y)))
   #4: #gcd(s(x),s(y)) -> #minus(max(x,y),min(x,transform(y)))
   #5: #gcd(s(x),s(y)) -> #max(x,y)
   #6: #gcd(s(x),s(y)) -> #min(x,transform(y))
   #7: #gcd(s(x),s(y)) -> #transform(y)
   #8: #gcd(s(x),s(y)) -> #min(x,y)
   #9: #transform(cons(x,y)) -> #cons(cons(x,x),x)
   #10: #transform(cons(x,y)) -> #cons(x,x)
   #11: #cons(cons(x,z),s(y)) -> #transform(x)
   #12: #min(s(x),s(y)) -> #min(x,y)
   #13: #minus(s(x),s(y)) -> #minus(x,y)
   #14: #cons(x,cons(y,s(z))) -> #cons(y,x)
Number of SCCs: 5, DPs: 9, edges: 16
	SCC { #1 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: 0
     s(x1)	weight: (/ 1 2) + x1
 minus(x1,x2)	weight: 0
   gcd(x1,x2)	weight: 0
 #min(x1,x2)	weight: 0
#transform(x1)	weight: 0
     0()	weight: 0
transform(x1)	weight: 0
   max(x1,x2)	weight: 0
 #max(x1,x2)	weight: x2
#minus(x1,x2)	weight: 0
   min(x1,x2)	weight: 0
  cons(x1,x2)	weight: 0
 #gcd(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #1
Number of SCCs: 4, DPs: 8, edges: 15
	SCC { #12 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: 0
     s(x1)	weight: (/ 1 2) + x1
 minus(x1,x2)	weight: 0
   gcd(x1,x2)	weight: 0
 #min(x1,x2)	weight: x2
#transform(x1)	weight: 0
     0()	weight: 0
transform(x1)	weight: 0
   max(x1,x2)	weight: 0
 #max(x1,x2)	weight: 0
#minus(x1,x2)	weight: 0
   min(x1,x2)	weight: 0
  cons(x1,x2)	weight: 0
 #gcd(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #12
Number of SCCs: 3, DPs: 7, edges: 14
	SCC { #13 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: 0
     s(x1)	weight: (/ 1 2) + x1
 minus(x1,x2)	weight: 0
   gcd(x1,x2)	weight: 0
 #min(x1,x2)	weight: 0
#transform(x1)	weight: 0
     0()	weight: 0
transform(x1)	weight: 0
   max(x1,x2)	weight: 0
 #max(x1,x2)	weight: 0
#minus(x1,x2)	weight: x1
   min(x1,x2)	weight: 0
  cons(x1,x2)	weight: 0
 #gcd(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #13
Number of SCCs: 2, DPs: 6, edges: 13
	SCC { #3 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... succeeded.
#cons(x1,x2)	weight: 0
     s(x1)	weight: (/ 3 16) + x1
 minus(x1,x2)	weight: max{0, (/ 1 32) + x1}
   gcd(x1,x2)	weight: 0
 #min(x1,x2)	weight: 0
#transform(x1)	weight: 0
     0()	weight: (/ 1 32)
transform(x1)	weight: (/ 7 32)
   max(x1,x2)	weight: max{(/ 1 32) + x2, (/ 1 16) + x1}
 #max(x1,x2)	weight: 0
#minus(x1,x2)	weight: 0
   min(x1,x2)	weight: max{0, (/ 1 32) + x1}
  cons(x1,x2)	weight: max{x2, (/ 1 4) + x1}
 #gcd(x1,x2)	weight: max{x2, (/ 1 16) + x1}
    Usable rules: { 1..8 }
    Removed DPs: #3
Number of SCCs: 1, DPs: 5, edges: 12
	SCC { #2 #9..11 #14 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... succeeded.
#cons(x1,x2)	weight: max{(/ 1 4) + x2, 30613 + x1}
     s(x1)	weight: x1
 minus(x1,x2)	weight: max{0, (/ 1 4) + x1}
   gcd(x1,x2)	weight: 0
 #min(x1,x2)	weight: 0
#transform(x1)	weight: 91838 + x1
     0()	weight: (/ 1 4)
transform(x1)	weight: (/ 244901 4) + x1
   max(x1,x2)	weight: max{(/ 1 4) + x2, (/ 1 2) + x1}
 #max(x1,x2)	weight: 0
#minus(x1,x2)	weight: 0
   min(x1,x2)	weight: max{0, (/ 1 4) + x1}
  cons(x1,x2)	weight: max{(/ 61225 2) + x2, (/ 244901 4) + x1}
 #gcd(x1,x2)	weight: max{x2, (/ 1 2) + x1}
    Usable rules: { 10..16 }
    Removed DPs: #9..11 #14
Number of SCCs: 1, DPs: 1, edges: 1
	SCC { #2 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: 0
     s(x1)	weight: (/ 1 4) + x1
 minus(x1,x2)	weight: (/ 1 4) + x1
   gcd(x1,x2)	weight: 0
 #min(x1,x2)	weight: 0
#transform(x1)	weight: x1
     0()	weight: 0
transform(x1)	weight: 0
   max(x1,x2)	weight: (/ 1 4) + x1 + x2
 #max(x1,x2)	weight: 0
#minus(x1,x2)	weight: 0
   min(x1,x2)	weight: (/ 1 4) + x1
  cons(x1,x2)	weight: (/ 1 4)
 #gcd(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #2
Number of SCCs: 0, DPs: 0, edges: 0
YES