Input TRS:
    1: f(true(),x,y) -> f(gt(x,y),plus2(x),plus1(y))
    2: gt(s(x),0()) -> true()
    3: gt(0(),y) -> false()
    4: gt(s(x),s(y)) -> gt(x,y)
    5: plus1(x) -> plus(x,s(0()))
    6: plus2(x) -> plus(x,s(s(0())))
    7: plus(0(),y) -> y
    8: plus(s(x),y) -> s(plus(x,y))
Number of strict rules: 8
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #plus2(x) -> #plus(x,s(s(0())))
   #2: #plus1(x) -> #plus(x,s(0()))
   #3: #f(true(),x,y) -> #f(gt(x,y),plus2(x),plus1(y))
   #4: #f(true(),x,y) -> #gt(x,y)
   #5: #f(true(),x,y) -> #plus2(x)
   #6: #f(true(),x,y) -> #plus1(y)
   #7: #plus(s(x),y) -> #plus(x,y)
   #8: #gt(s(x),s(y)) -> #gt(x,y)
Number of SCCs: 3, DPs: 3, edges: 3
	SCC { #7 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 2) + x1
    gt(x1,x2)	weight: 0
 plus1(x1)	weight: 0
#plus(x1,x2)	weight: x1
 false()	weight: 0
#plus2(x1)	weight: 0
  true()	weight: 0
     f(x1,x2,x3)	weight: 0
     0()	weight: 0
  #gt(x1,x2)	weight: 0
   #f(x1,x2,x3)	weight: 0
  plus(x1,x2)	weight: 0
#plus1(x1)	weight: 0
 plus2(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #7
Number of SCCs: 2, DPs: 2, edges: 2
	SCC { #8 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 2) + x1
    gt(x1,x2)	weight: 0
 plus1(x1)	weight: 0
#plus(x1,x2)	weight: 0
 false()	weight: 0
#plus2(x1)	weight: 0
  true()	weight: 0
     f(x1,x2,x3)	weight: 0
     0()	weight: 0
  #gt(x1,x2)	weight: x2
   #f(x1,x2,x3)	weight: 0
  plus(x1,x2)	weight: 0
#plus1(x1)	weight: 0
 plus2(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #8
Number of SCCs: 1, DPs: 1, edges: 1
	SCC { #3 }
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