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: f(s(x)) -> f(-(max(*(s(x),s(x)),+(s(x),s(s(s(0()))))),max(s(*(s(x),s(x))),+(s(x),s(s(s(s(0()))))))))
Number of strict rules: 13
Direct Order(PosReal,>,Poly) ... failed.
Freezing +
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: +❆1_0(y) -> y
8: +❆1_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: f(s(x)) -> f(-(max(*(s(x),s(x)),+❆1_s(x,s(s(s(0()))))),max(s(*(s(x),s(x))),+❆1_s(x,s(s(s(s(0()))))))))
14: +(0(),_1) ->= +❆1_0(_1)
15: +(s(_1),_2) ->= +❆1_s(_1,_2)
Number of strict rules: 13
Direct Order(PosReal,>,Poly) ... failed.
Dependency Pairs:
   #1: #max(s(x),s(y)) -> #max(x,y)
   #2: #f(s(x)) -> #f(-(max(*(s(x),s(x)),+❆1_s(x,s(s(s(0()))))),max(s(*(s(x),s(x))),+❆1_s(x,s(s(s(s(0()))))))))
   #3: #f(s(x)) -> #-(max(*(s(x),s(x)),+❆1_s(x,s(s(s(0()))))),max(s(*(s(x),s(x))),+❆1_s(x,s(s(s(s(0())))))))
   #4: #f(s(x)) -> #max(*(s(x),s(x)),+❆1_s(x,s(s(s(0())))))
   #5: #f(s(x)) -> #*(s(x),s(x))
   #6: #f(s(x)) -> #+❆1_s(x,s(s(s(0()))))
   #7: #f(s(x)) -> #max(s(*(s(x),s(x))),+❆1_s(x,s(s(s(s(0()))))))
   #8: #f(s(x)) -> #*(s(x),s(x))
   #9: #f(s(x)) -> #+❆1_s(x,s(s(s(s(0())))))
   #10: #*(x,s(y)) -> #+(x,*(x,y))
   #11: #*(x,s(y)) -> #*(x,y)
   #12: #+(0(),_1) ->? #+❆1_0(_1)
   #13: #-(s(x),s(y)) -> #-(x,y)
   #14: #min(s(x),s(y)) -> #min(x,y)
   #15: #+❆1_s(x,y) -> #+(x,y)
   #16: #+(s(_1),_2) ->? #+❆1_s(_1,_2)
Number of SCCs: 6, DPs: 7, edges: 7
	SCC { #11 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#+❆1_0(x1)	weight: 0
+❆1_0(x1)	weight: 0
     s(x1)	weight: (/ 1 2) + x1
+❆1_s(x1,x2)	weight: 0
 #min(x1,x2)	weight: 0
   #*(x1,x2)	weight: x2
     f(x1)	weight: 0
#+❆1_s(x1,x2)	weight: 0
     0()	weight: 0
   max(x1,x2)	weight: 0
 #max(x1,x2)	weight: 0
     -(x1,x2)	weight: 0
   #f(x1)	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: #11
Number of SCCs: 5, DPs: 6, edges: 6
	SCC { #1 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#+❆1_0(x1)	weight: 0
+❆1_0(x1)	weight: 0
     s(x1)	weight: (/ 1 2) + x1
+❆1_s(x1,x2)	weight: 0
 #min(x1,x2)	weight: 0
   #*(x1,x2)	weight: 0
     f(x1)	weight: 0
#+❆1_s(x1,x2)	weight: 0
     0()	weight: 0
   max(x1,x2)	weight: 0
 #max(x1,x2)	weight: x2
     -(x1,x2)	weight: 0
   #f(x1)	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: 4, DPs: 5, edges: 5
	SCC { #13 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#+❆1_0(x1)	weight: 0
+❆1_0(x1)	weight: 0
     s(x1)	weight: (/ 1 2) + x1
+❆1_s(x1,x2)	weight: 0
 #min(x1,x2)	weight: 0
   #*(x1,x2)	weight: 0
     f(x1)	weight: 0
#+❆1_s(x1,x2)	weight: 0
     0()	weight: 0
   max(x1,x2)	weight: 0
 #max(x1,x2)	weight: 0
     -(x1,x2)	weight: 0
   #f(x1)	weight: 0
   min(x1,x2)	weight: 0
   #-(x1,x2)	weight: x2
     +(x1,x2)	weight: 0
   #+(x1,x2)	weight: 0
     *(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #13
Number of SCCs: 3, DPs: 4, edges: 4
	SCC { #14 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#+❆1_0(x1)	weight: 0
+❆1_0(x1)	weight: 0
     s(x1)	weight: (/ 1 2) + x1
+❆1_s(x1,x2)	weight: 0
 #min(x1,x2)	weight: x2
   #*(x1,x2)	weight: 0
     f(x1)	weight: 0
#+❆1_s(x1,x2)	weight: 0
     0()	weight: 0
   max(x1,x2)	weight: 0
 #max(x1,x2)	weight: 0
     -(x1,x2)	weight: 0
   #f(x1)	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: #14
Number of SCCs: 2, DPs: 3, edges: 3
	SCC { #15 #16 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#+❆1_0(x1)	weight: 0
+❆1_0(x1)	weight: 0
     s(x1)	weight: (/ 1 2) + x1
+❆1_s(x1,x2)	weight: 0
 #min(x1,x2)	weight: 0
   #*(x1,x2)	weight: 0
     f(x1)	weight: 0
#+❆1_s(x1,x2)	weight: (/ 1 4) + x1
     0()	weight: 0
   max(x1,x2)	weight: 0
 #max(x1,x2)	weight: 0
     -(x1,x2)	weight: 0
   #f(x1)	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: #15 #16
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