Input TRS:
    1: min(0(),y) -> 0()
    2: min(x,0()) -> 0()
    3: min(s(x),s(y)) -> s(min(x,y))
    4: max(0(),y) -> y
    5: max(x,0()) -> x
    6: max(s(x),s(y)) -> s(max(x,y))
    7: +(0(),y) -> y
    8: +(s(x),y) -> s(+(x,y))
    9: -(x,0()) -> x
    10: -(s(x),s(y)) -> -(x,y)
    11: *(x,0()) -> 0()
    12: *(x,s(y)) -> +(x,*(x,y))
    13: p(s(x)) -> x
    14: f(s(x),s(y)) -> f(-(min(s(x),s(y)),max(s(x),s(y))),*(s(x),s(y)))
Number of strict rules: 14
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #max(s(x),s(y)) -> #max(x,y)
   #2: #*(x,s(y)) -> #+(x,*(x,y))
   #3: #*(x,s(y)) -> #*(x,y)
   #4: #f(s(x),s(y)) -> #f(-(min(s(x),s(y)),max(s(x),s(y))),*(s(x),s(y)))
   #5: #f(s(x),s(y)) -> #-(min(s(x),s(y)),max(s(x),s(y)))
   #6: #f(s(x),s(y)) -> #min(s(x),s(y))
   #7: #f(s(x),s(y)) -> #max(s(x),s(y))
   #8: #f(s(x),s(y)) -> #*(s(x),s(y))
   #9: #-(s(x),s(y)) -> #-(x,y)
   #10: #min(s(x),s(y)) -> #min(x,y)
   #11: #+(s(x),y) -> #+(x,y)
Number of SCCs: 6, DPs: 6, edges: 6
	SCC { #11 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 2) + x1
 #min(x1,x2)	weight: 0
   #*(x1,x2)	weight: 0
   #p(x1)	weight: 0
     f(x1,x2)	weight: 0
     p(x1)	weight: 0
     0()	weight: 0
   max(x1,x2)	weight: 0
 #max(x1,x2)	weight: 0
     -(x1,x2)	weight: 0
   #f(x1,x2)	weight: 0
   min(x1,x2)	weight: 0
   #-(x1,x2)	weight: 0
     +(x1,x2)	weight: 0
   #+(x1,x2)	weight: x1
     *(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #11
Number of SCCs: 5, DPs: 5, edges: 5
	SCC { #3 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 2) + x1
 #min(x1,x2)	weight: 0
   #*(x1,x2)	weight: x2
   #p(x1)	weight: 0
     f(x1,x2)	weight: 0
     p(x1)	weight: 0
     0()	weight: 0
   max(x1,x2)	weight: 0
 #max(x1,x2)	weight: 0
     -(x1,x2)	weight: 0
   #f(x1,x2)	weight: 0
   min(x1,x2)	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: 4, DPs: 4, edges: 4
	SCC { #1 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 2) + x1
 #min(x1,x2)	weight: 0
   #*(x1,x2)	weight: 0
   #p(x1)	weight: 0
     f(x1,x2)	weight: 0
     p(x1)	weight: 0
     0()	weight: 0
   max(x1,x2)	weight: 0
 #max(x1,x2)	weight: x2
     -(x1,x2)	weight: 0
   #f(x1,x2)	weight: 0
   min(x1,x2)	weight: 0
   #-(x1,x2)	weight: 0
     +(x1,x2)	weight: 0
   #+(x1,x2)	weight: 0
     *(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #1
Number of SCCs: 3, DPs: 3, edges: 3
	SCC { #10 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 2) + x1
 #min(x1,x2)	weight: x2
   #*(x1,x2)	weight: 0
   #p(x1)	weight: 0
     f(x1,x2)	weight: 0
     p(x1)	weight: 0
     0()	weight: 0
   max(x1,x2)	weight: 0
 #max(x1,x2)	weight: 0
     -(x1,x2)	weight: 0
   #f(x1,x2)	weight: 0
   min(x1,x2)	weight: 0
   #-(x1,x2)	weight: 0
     +(x1,x2)	weight: 0
   #+(x1,x2)	weight: 0
     *(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #10
Number of SCCs: 2, DPs: 2, edges: 2
	SCC { #9 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 2) + x1
 #min(x1,x2)	weight: 0
   #*(x1,x2)	weight: 0
   #p(x1)	weight: 0
     f(x1,x2)	weight: 0
     p(x1)	weight: 0
     0()	weight: 0
   max(x1,x2)	weight: 0
 #max(x1,x2)	weight: 0
     -(x1,x2)	weight: 0
   #f(x1,x2)	weight: 0
   min(x1,x2)	weight: 0
   #-(x1,x2)	weight: x1
     +(x1,x2)	weight: 0
   #+(x1,x2)	weight: 0
     *(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #9
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)... succeeded.
     s(x1)	weight: max{0, (/ 1 4) + x1_1}; (- (/ 1 4))
 #min(x1,x2)	weight: 0; 0
   #*(x1,x2)	weight: 0; 0
   #p(x1)	weight: 0; 0
     f(x1,x2)	weight: 0; 0
     p(x1)	weight: 0; 0
     0()	weight: 0; 0
   max(x1,x2)	weight: max{0, (/ 1 4) + x2_1 + x1_1}; x1_2
 #max(x1,x2)	weight: 0; 0
     -(x1,x2)	weight: max{0, x2_2 + x1_1}; 0
   #f(x1,x2)	weight: max{0, (/ 1 4) + x1_1}; 0
   min(x1,x2)	weight: max{0, x1_1}; 0
   #-(x1,x2)	weight: 0; 0
     +(x1,x2)	weight: max{0, (- (/ 1 16)) + x2_2 + x1_1}; (- (/ 3 16)) + x2_2
   #+(x1,x2)	weight: 0; 0
     *(x1,x2)	weight: max{0, (/ 1 16) + x2_1 + x2_2}; (- (/ 1 16)) + x2_2 + x1_2
    Usable rules: { 1..6 9 10 }
    Removed DPs: #4
Number of SCCs: 0, DPs: 0, edges: 0
YES