Input TRS:
    1: f(true(),x) -> f(eq(|0|(),minus(x,x)),plus1(x))
    2: plus1(x) -> plus(s(|0|()),x)
    3: plus(|0|(),y) -> y
    4: plus(s(x),y) -> s(plus(x,y))
    5: minus(x,|0|()) -> x
    6: minus(|0|(),y) -> |0|()
    7: minus(s(x),s(y)) -> minus(x,y)
    8: eq(|0|(),|0|()) -> true()
    9: eq(s(x),|0|()) -> false()
    10: eq(|0|(),s(y)) -> false()
    11: eq(s(x),s(y)) -> eq(x,y)
Number of strict rules: 11
Direct Order(PosReal,>,Poly) ... failed.
Freezing plus eq
1: f(true(),x) -> f(eq❆1_|0|(minus(x,x)),plus1(x))
2: plus1(x) -> plus❆1_s(|0|(),x)
3: plus❆1_|0|(y) -> y
4: plus❆1_s(x,y) -> s(plus(x,y))
5: minus(x,|0|()) -> x
6: minus(|0|(),y) -> |0|()
7: minus(s(x),s(y)) -> minus(x,y)
8: eq❆1_|0|(|0|()) -> true()
9: eq❆1_s(x,|0|()) -> false()
10: eq❆1_|0|(s(y)) -> false()
11: eq❆1_s(x,s(y)) -> eq(x,y)
12: eq(|0|(),_1) ->= eq❆1_|0|(_1)
13: eq(s(_1),_2) ->= eq❆1_s(_1,_2)
14: plus(|0|(),_1) ->= plus❆1_|0|(_1)
15: plus(s(_1),_2) ->= plus❆1_s(_1,_2)
Number of strict rules: 11
Direct Order(PosReal,>,Poly) ... failed.
Dependency Pairs:
   #1: #plus1(x) -> #plus❆1_s(|0|(),x)
   #2: #eq(s(_1),_2) ->? #eq❆1_s(_1,_2)
   #3: #eq❆1_s(x,s(y)) -> #eq(x,y)
   #4: #eq(|0|(),_1) ->? #eq❆1_|0|(_1)
   #5: #plus(|0|(),_1) ->? #plus❆1_|0|(_1)
   #6: #minus(s(x),s(y)) -> #minus(x,y)
   #7: #f(true(),x) -> #f(eq❆1_|0|(minus(x,x)),plus1(x))
   #8: #f(true(),x) -> #eq❆1_|0|(minus(x,x))
   #9: #f(true(),x) -> #minus(x,x)
   #10: #f(true(),x) -> #plus1(x)
   #11: #plus(s(_1),_2) ->? #plus❆1_s(_1,_2)
   #12: #plus❆1_s(x,y) -> #plus(x,y)
Number of SCCs: 4, DPs: 6, edges: 6
	SCC { #6 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   |0|()	weight: 0
#eq❆1_|0|(x1)	weight: 0
     s(x1)	weight: (/ 1 2) + x1
 minus(x1,x2)	weight: 0
 plus1(x1)	weight: 0
#plus(x1,x2)	weight: 0
#plus❆1_|0|(x1)	weight: 0
    eq(x1,x2)	weight: 0
 false()	weight: 0
plus❆1_|0|(x1)	weight: 0
eq❆1_|0|(x1)	weight: 0
  true()	weight: 0
     f(x1,x2)	weight: 0
  #eq(x1,x2)	weight: 0
eq❆1_s(x1,x2)	weight: 0
#eq❆1_s(x1,x2)	weight: 0
   #f(x1,x2)	weight: 0
#minus(x1,x2)	weight: x2
  plus(x1,x2)	weight: 0
#plus1(x1)	weight: 0
plus❆1_s(x1,x2)	weight: 0
#plus❆1_s(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #6
Number of SCCs: 3, DPs: 5, edges: 5
	SCC { #7 }
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