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