Input TRS:
    1: le(0(),y) -> true()
    2: le(s(x),0()) -> false()
    3: le(s(x),s(y)) -> le(x,y)
    4: minus(x,0()) -> x
    5: minus(s(x),s(y)) -> minus(x,y)
    6: gcd(0(),y) -> y
    7: gcd(s(x),0()) -> s(x)
    8: gcd(s(x),s(y)) -> if_gcd(le(y,x),s(x),s(y))
    9: if_gcd(true(),s(x),s(y)) -> gcd(minus(x,y),s(y))
    10: if_gcd(false(),s(x),s(y)) -> gcd(minus(y,x),s(x))
    11: rand(x) ->= x
    12: rand(x) ->= rand(s(x))
Number of strict rules: 10
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #if_gcd(true(),s(x),s(y)) -> #gcd(minus(x,y),s(y))
   #2: #if_gcd(true(),s(x),s(y)) -> #minus(x,y)
   #3: #if_gcd(false(),s(x),s(y)) -> #gcd(minus(y,x),s(x))
   #4: #if_gcd(false(),s(x),s(y)) -> #minus(y,x)
   #5: #minus(s(x),s(y)) -> #minus(x,y)
   #6: #le(s(x),s(y)) -> #le(x,y)
   #7: #gcd(s(x),s(y)) -> #if_gcd(le(y,x),s(x),s(y))
   #8: #gcd(s(x),s(y)) -> #le(y,x)
Number of SCCs: 3, DPs: 5, edges: 6
	SCC { #5 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... QWPOpS(PosReal,>,MaxSum)... succeeded.
    le(x1,x2)	weight: max{0, (/ 1 4) + x2}	status: [x2]	precedence above: gcd false true if_gcd
     s(x1)	weight: x1	status: [x1]	precedence above: le gcd false true #minus if_gcd
  #le(x1,x2)	weight: (/ 1 8) + x2 + x1	status: [x1,x2]	precedence above:
 minus(x1,x2)	weight: max{0, x1}	status: x1
   gcd(x1,x2)	weight: max{(/ 5 8) + x2, (/ 5 8) + x1}	status: []	precedence above: if_gcd
 false()	weight: (/ 1 2)	status: []	precedence above:
  true()	weight: (/ 1 8)	status: []	precedence above:
  rand(x1)	weight: (/ 1 8) + x1	status: []	precedence above:
     0()	weight: (/ 5 8)	status: []	precedence above: false true
#minus(x1,x2)	weight: (/ 1 8) + x1	status: [x1]	precedence above:
if_gcd(x1,x2,x3)	weight: max{(/ 5 8) + x3, (/ 5 8) + x2, (/ 1 4) + x1}	status: []	precedence above: gcd
#if_gcd(x1,x2,x3)	weight: max{0, (/ 1 8) + x3}	status: [x3]	precedence above:
 #gcd(x1,x2)	weight: max{(/ 1 8) + x2, (/ 1 8) + x1}	status: [x1,x2]	precedence above:
    Removed DPs: #5
Number of SCCs: 2, DPs: 4, edges: 5
	SCC { #6 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... QWPOpS(PosReal,>,MaxSum)... succeeded.
    le(x1,x2)	weight: max{0, (/ 1 4) + x2}	status: [x2]	precedence above: gcd false true if_gcd
     s(x1)	weight: x1	status: [x1]	precedence above: le gcd false true #minus if_gcd
  #le(x1,x2)	weight: x1	status: x1
 minus(x1,x2)	weight: max{0, x1}	status: x1
   gcd(x1,x2)	weight: max{(/ 5 8) + x2, (/ 5 8) + x1}	status: []	precedence above: if_gcd
 false()	weight: (/ 1 2)	status: []	precedence above:
  true()	weight: (/ 1 8)	status: []	precedence above:
  rand(x1)	weight: (/ 1 8) + x1	status: []	precedence above:
     0()	weight: (/ 5 8)	status: []	precedence above: false true
#minus(x1,x2)	weight: (/ 1 8) + x1	status: [x1]	precedence above:
if_gcd(x1,x2,x3)	weight: max{(/ 5 8) + x3, (/ 5 8) + x2, (/ 1 4) + x1}	status: []	precedence above: gcd
#if_gcd(x1,x2,x3)	weight: max{0, (/ 1 8) + x3}	status: [x3]	precedence above:
 #gcd(x1,x2)	weight: max{(/ 1 8) + x2, (/ 1 8) + x1}	status: [x1,x2]	precedence above:
    Removed DPs: #6
Number of SCCs: 1, DPs: 3, edges: 4
	SCC { #1 #3 #7 }
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