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())))
   e1: gcd(cons(x,cons(y,z()))) ->= gcd(cons(max(x,y),cons(min(x,y),z())))	[relative]
Number of Rules: 12
Direct POLO(Sum) ...Direct Mat2b ... failed.
Dependency Pairs:
   #1: # max(s(x),s(y)) -> # max(x,y)
   #2: # gcd(cons(x,cons(y,z()))) -> # gcd(cons(max(x,y),cons(min(x,y),z())))	[relative]
   #3: # gcd(cons(x,cons(y,z()))) -> # max(x,y)	[relative]
   #4: # gcd(cons(x,cons(y,z()))) -> # min(x,y)	[relative]
   #5: # gcd(cons(0(),y)) -> # gcd(y)
   #6: # gcd(cons(x,cons(y,z()))) -> # gcd(cons(-(x,y),cons(y,z())))
   #7: # gcd(cons(x,cons(y,z()))) -> # -(x,y)
   #8: # min(s(x),s(y)) -> # min(x,y)
   #9: # -(s(x),s(y)) -> # -(x,y)
Number of SCCs: 4
  SCC { #1 }
    POLO(Sum)... removes: #1
	I(s) = max(x1 + 2, 0)
	I(# max) = max(x2 - 1, 0)
    USABLE RULES: { }
Number of SCCs: 3
  SCC { #8 }
    POLO(Sum)... removes: #8
	I(s) = max(x1 + 2, 0)
	I(# min) = max(x2 - 1, 0)
    USABLE RULES: { }
Number of SCCs: 2
  SCC { #9 }
    POLO(Sum)... removes: #9
	I(s) = max(x1 + 2, 0)
	I(# -) = max(x2 - 1, 0)
    USABLE RULES: { }
Number of SCCs: 1
  SCC { #2 #5 #6 }
    POLO(Sum)... removes: #5
	I(s) = 0
	I(z) = 1
	I(# gcd) = max(x1 + 1, 0)
	I(0) = 1
	I(max) = 1
	I(-) = 1
	I(min) = max(x2 - 1, 0)
	I(cons) = max(x2 + 1, 0)
    USABLE RULES: { }
Number of SCCs: 1
  SCC { #2 #6 }
    POLO(Sum)... QLPOS... QWPOpS(mSum)... Mat2b... failed.