Input TRS:
    1: -(x,0()) -> x
    2: -(s(x),s(y)) -> -(x,y)
    3: +(0(),y) -> y
    4: +(s(x),y) -> s(+(x,y))
    5: *(x,0()) -> 0()
    6: *(x,s(y)) -> +(x,*(x,y))
    7: p(s(x)) -> x
    8: f(s(x)) -> f(-(p(*(s(x),s(x))),*(s(x),s(x))))
Number of strict rules: 8
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #-(s(x),s(y)) -> #-(x,y)
   #2: #*(x,s(y)) -> #+(x,*(x,y))
   #3: #*(x,s(y)) -> #*(x,y)
   #4: #f(s(x)) -> #f(-(p(*(s(x),s(x))),*(s(x),s(x))))
   #5: #f(s(x)) -> #-(p(*(s(x),s(x))),*(s(x),s(x)))
   #6: #f(s(x)) -> #p(*(s(x),s(x)))
   #7: #f(s(x)) -> #*(s(x),s(x))
   #8: #f(s(x)) -> #*(s(x),s(x))
   #9: #+(s(x),y) -> #+(x,y)
Number of SCCs: 4, DPs: 4, edges: 4
	SCC { #9 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 2) + x1
   #*(x1,x2)	weight: 0
   #p(x1)	weight: 0
     f(x1)	weight: 0
     p(x1)	weight: 0
     0()	weight: 0
     -(x1,x2)	weight: 0
   #f(x1)	weight: 0
   #-(x1,x2)	weight: 0
     +(x1,x2)	weight: 0
   #+(x1,x2)	weight: x1
     *(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #9
Number of SCCs: 3, DPs: 3, edges: 3
	SCC { #3 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 2) + x1
   #*(x1,x2)	weight: x2
   #p(x1)	weight: 0
     f(x1)	weight: 0
     p(x1)	weight: 0
     0()	weight: 0
     -(x1,x2)	weight: 0
   #f(x1)	weight: 0
   #-(x1,x2)	weight: 0
     +(x1,x2)	weight: 0
   #+(x1,x2)	weight: 0
     *(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #3
Number of SCCs: 2, DPs: 2, edges: 2
	SCC { #1 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 2) + x1
   #*(x1,x2)	weight: 0
   #p(x1)	weight: 0
     f(x1)	weight: 0
     p(x1)	weight: 0
     0()	weight: 0
     -(x1,x2)	weight: 0
   #f(x1)	weight: 0
   #-(x1,x2)	weight: x2
     +(x1,x2)	weight: 0
   #+(x1,x2)	weight: 0
     *(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #1
Number of SCCs: 1, DPs: 1, edges: 1
	SCC { #4 }
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