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