Input TRS:
    1: f(true(),x,y) -> f(gt(x,y),trunc(x),s(y))
    2: trunc(0()) -> 0()
    3: trunc(s(0())) -> 0()
    4: trunc(s(s(x))) -> s(s(trunc(x)))
    5: gt(0(),v) -> false()
    6: gt(s(u),0()) -> true()
    7: gt(s(u),s(v)) -> gt(u,v)
Number of strict rules: 7
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #gt(s(u),s(v)) -> #gt(u,v)
   #2: #f(true(),x,y) -> #f(gt(x,y),trunc(x),s(y))
   #3: #f(true(),x,y) -> #gt(x,y)
   #4: #f(true(),x,y) -> #trunc(x)
   #5: #trunc(s(s(x))) -> #trunc(x)
Number of SCCs: 3, DPs: 3, edges: 3
	SCC { #5 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 4) + x1
    gt(x1,x2)	weight: 0
 false()	weight: 0
  true()	weight: 0
     f(x1,x2,x3)	weight: 0
#trunc(x1)	weight: x1
     0()	weight: 0
  #gt(x1,x2)	weight: 0
   #f(x1,x2,x3)	weight: 0
 trunc(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #5
Number of SCCs: 2, DPs: 2, edges: 2
	SCC { #1 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 2) + x1
    gt(x1,x2)	weight: 0
 false()	weight: 0
  true()	weight: 0
     f(x1,x2,x3)	weight: 0
#trunc(x1)	weight: 0
     0()	weight: 0
  #gt(x1,x2)	weight: x2
   #f(x1,x2,x3)	weight: 0
 trunc(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #1
Number of SCCs: 1, DPs: 1, edges: 1
	SCC { #2 }
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