Input TRS:
    1: from(X) -> cons(X,from(s(X)))
    2: |2ndspos|(|0|(),Z) -> rnil()
    3: |2ndspos|(s(N),cons(X,Z)) -> |2ndspos|(s(N),cons2(X,Z))
    4: |2ndspos|(s(N),cons2(X,cons(Y,Z))) -> rcons(posrecip(Y),|2ndsneg|(N,Z))
    5: |2ndsneg|(|0|(),Z) -> rnil()
    6: |2ndsneg|(s(N),cons(X,Z)) -> |2ndsneg|(s(N),cons2(X,Z))
    7: |2ndsneg|(s(N),cons2(X,cons(Y,Z))) -> rcons(negrecip(Y),|2ndspos|(N,Z))
    8: pi(X) -> |2ndspos|(X,from(|0|()))
    9: plus(|0|(),Y) -> Y
    10: plus(s(X),Y) -> s(plus(X,Y))
    11: times(|0|(),Y) -> |0|()
    12: times(s(X),Y) -> plus(Y,times(X,Y))
    13: square(X) -> times(X,X)
Number of strict rules: 13
Direct Order(PosReal,>,Poly) ... failed.
Freezing |2ndspos| |2ndsneg|
1: from(X) -> cons(X,from(s(X)))
2: |2ndspos|❆1_|0|(Z) -> rnil()
3: |2ndspos|❆1_s(N,cons(X,Z)) -> |2ndspos|❆1_s(N,cons2(X,Z))
4: |2ndspos|❆1_s(N,cons2(X,cons(Y,Z))) -> rcons(posrecip(Y),|2ndsneg|(N,Z))
5: |2ndsneg|❆1_|0|(Z) -> rnil()
6: |2ndsneg|❆1_s(N,cons(X,Z)) -> |2ndsneg|❆1_s(N,cons2(X,Z))
7: |2ndsneg|❆1_s(N,cons2(X,cons(Y,Z))) -> rcons(negrecip(Y),|2ndspos|(N,Z))
8: pi(X) -> |2ndspos|(X,from(|0|()))
9: plus(|0|(),Y) -> Y
10: plus(s(X),Y) -> s(plus(X,Y))
11: times(|0|(),Y) -> |0|()
12: times(s(X),Y) -> plus(Y,times(X,Y))
13: square(X) -> times(X,X)
14: |2ndsneg|(|0|(),_1) ->= |2ndsneg|❆1_|0|(_1)
15: |2ndsneg|(s(_1),_2) ->= |2ndsneg|❆1_s(_1,_2)
16: |2ndspos|(|0|(),_1) ->= |2ndspos|❆1_|0|(_1)
17: |2ndspos|(s(_1),_2) ->= |2ndspos|❆1_s(_1,_2)
Number of strict rules: 13
Direct Order(PosReal,>,Poly) ... failed.
Dependency Pairs:
   #1: #|2ndsneg|❆1_s(N,cons(X,Z)) -> #|2ndsneg|❆1_s(N,cons2(X,Z))
   #2: #square(X) -> #times(X,X)
   #3: #times(s(X),Y) -> #plus(Y,times(X,Y))
   #4: #times(s(X),Y) -> #times(X,Y)
   #5: #|2ndsneg|(|0|(),_1) ->? #|2ndsneg|❆1_|0|(_1)
   #6: #|2ndsneg|❆1_s(N,cons2(X,cons(Y,Z))) -> #|2ndspos|(N,Z)
   #7: #plus(s(X),Y) -> #plus(X,Y)
   #8: #|2ndspos|(s(_1),_2) ->? #|2ndspos|❆1_s(_1,_2)
   #9: #|2ndspos|(|0|(),_1) ->? #|2ndspos|❆1_|0|(_1)
   #10: #|2ndspos|❆1_s(N,cons(X,Z)) -> #|2ndspos|❆1_s(N,cons2(X,Z))
   #11: #from(X) -> #from(s(X))
   #12: #pi(X) -> #|2ndspos|(X,from(|0|()))
   #13: #pi(X) -> #from(|0|())
   #14: #|2ndsneg|(s(_1),_2) ->? #|2ndsneg|❆1_s(_1,_2)
   #15: #|2ndspos|❆1_s(N,cons2(X,cons(Y,Z))) -> #|2ndsneg|(N,Z)
Number of SCCs: 4, DPs: 9, edges: 11
	SCC { #11 }
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...  found.
  #from(X)	-#11->
  #from(s(X))	--->*
  #from(s(X))
  Looping with: [ X := s(X); ]
NO