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())))
   e1: cons(x,cons(y,z())) ->= cons(y,cons(x,z()))	[relative]
Number of Rules: 13
Direct POLO(Sum) ...Direct Mat2b ...Direct Mat3b ... 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
  SCC { #10 }
    POLO(Sum)... removes: #10
	I(s) = max(x1 + 1, 0)
	I(z) = 1
	I(# -) = max(x1 + 1, 0)
	I(cons) = max(x2 - 1, 0)
    USABLE RULES: { }
Number of SCCs: 3
  SCC { #1 }
    POLO(Sum)... removes: #1
	I(s) = max(x1 + 1, 0)
	I(z) = 1
	I(# max) = max(x1 + 1, 0)
	I(cons) = max(x2 - 1, 0)
    USABLE RULES: { }
Number of SCCs: 2
  SCC { #9 }
    POLO(Sum)... removes: #9
	I(s) = max(x1 + 1, 0)
	I(z) = 1
	I(# min) = max(x1 + 1, 0)
	I(cons) = max(x2 - 1, 0)
    USABLE RULES: { }
Number of SCCs: 1
  SCC { #2 #7 #8 }
    POLO(Sum)... removes: #7 #8
	I(s) = max(x1 + 2, 0)
	I(z) = 1
	I(# gcd) = max(x1 + 1, 0)
	I(0) = 2
	I(max) = max(x1 + x2 - 1, 0)
	I(-) = max(x1 + x2 + 1, 0)
	I(min) = max(x1 + 1, 0)
	I(cons) = max(x2 + 1, 0)
    USABLE RULES: { 4 8 5 7 6 2 }
Number of SCCs: 1
  SCC { #2 }
    POLO(Sum)... QLPOS... QWPOpS(mSum)... Mat3b...