MAYBE

We are left with following problem, upon which TcT provides the
certificate MAYBE.

Strict Trs:
  { from(X) -> cons(X, n__from(s(X)))
  , from(X) -> n__from(X)
  , 2ndspos(s(N), cons(X, Z)) -> 2ndspos(s(N), cons2(X, activate(Z)))
  , 2ndspos(s(N), cons2(X, cons(Y, Z))) ->
    rcons(posrecip(Y), 2ndsneg(N, activate(Z)))
  , 2ndspos(0(), Z) -> rnil()
  , activate(X) -> X
  , activate(n__from(X)) -> from(X)
  , 2ndsneg(s(N), cons(X, Z)) -> 2ndsneg(s(N), cons2(X, activate(Z)))
  , 2ndsneg(s(N), cons2(X, cons(Y, Z))) ->
    rcons(negrecip(Y), 2ndspos(N, activate(Z)))
  , 2ndsneg(0(), Z) -> rnil()
  , pi(X) -> 2ndspos(X, from(0()))
  , plus(s(X), Y) -> s(plus(X, Y))
  , plus(0(), Y) -> Y
  , times(s(X), Y) -> plus(Y, times(X, Y))
  , times(0(), Y) -> 0()
  , square(X) -> times(X, X) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We add following dependency tuples:

Strict DPs:
  { from^#(X) -> c_1()
  , from^#(X) -> c_2()
  , 2ndspos^#(s(N), cons(X, Z)) ->
    c_3(2ndspos^#(s(N), cons2(X, activate(Z))), activate^#(Z))
  , 2ndspos^#(s(N), cons2(X, cons(Y, Z))) ->
    c_4(2ndsneg^#(N, activate(Z)), activate^#(Z))
  , 2ndspos^#(0(), Z) -> c_5()
  , activate^#(X) -> c_6()
  , activate^#(n__from(X)) -> c_7(from^#(X))
  , 2ndsneg^#(s(N), cons(X, Z)) ->
    c_8(2ndsneg^#(s(N), cons2(X, activate(Z))), activate^#(Z))
  , 2ndsneg^#(s(N), cons2(X, cons(Y, Z))) ->
    c_9(2ndspos^#(N, activate(Z)), activate^#(Z))
  , 2ndsneg^#(0(), Z) -> c_10()
  , pi^#(X) -> c_11(2ndspos^#(X, from(0())), from^#(0()))
  , plus^#(s(X), Y) -> c_12(plus^#(X, Y))
  , plus^#(0(), Y) -> c_13()
  , times^#(s(X), Y) -> c_14(plus^#(Y, times(X, Y)), times^#(X, Y))
  , times^#(0(), Y) -> c_15()
  , square^#(X) -> c_16(times^#(X, X)) }

and mark the set of starting terms.

We are left with following problem, upon which TcT provides the
certificate MAYBE.

Strict DPs:
  { from^#(X) -> c_1()
  , from^#(X) -> c_2()
  , 2ndspos^#(s(N), cons(X, Z)) ->
    c_3(2ndspos^#(s(N), cons2(X, activate(Z))), activate^#(Z))
  , 2ndspos^#(s(N), cons2(X, cons(Y, Z))) ->
    c_4(2ndsneg^#(N, activate(Z)), activate^#(Z))
  , 2ndspos^#(0(), Z) -> c_5()
  , activate^#(X) -> c_6()
  , activate^#(n__from(X)) -> c_7(from^#(X))
  , 2ndsneg^#(s(N), cons(X, Z)) ->
    c_8(2ndsneg^#(s(N), cons2(X, activate(Z))), activate^#(Z))
  , 2ndsneg^#(s(N), cons2(X, cons(Y, Z))) ->
    c_9(2ndspos^#(N, activate(Z)), activate^#(Z))
  , 2ndsneg^#(0(), Z) -> c_10()
  , pi^#(X) -> c_11(2ndspos^#(X, from(0())), from^#(0()))
  , plus^#(s(X), Y) -> c_12(plus^#(X, Y))
  , plus^#(0(), Y) -> c_13()
  , times^#(s(X), Y) -> c_14(plus^#(Y, times(X, Y)), times^#(X, Y))
  , times^#(0(), Y) -> c_15()
  , square^#(X) -> c_16(times^#(X, X)) }
Weak Trs:
  { from(X) -> cons(X, n__from(s(X)))
  , from(X) -> n__from(X)
  , 2ndspos(s(N), cons(X, Z)) -> 2ndspos(s(N), cons2(X, activate(Z)))
  , 2ndspos(s(N), cons2(X, cons(Y, Z))) ->
    rcons(posrecip(Y), 2ndsneg(N, activate(Z)))
  , 2ndspos(0(), Z) -> rnil()
  , activate(X) -> X
  , activate(n__from(X)) -> from(X)
  , 2ndsneg(s(N), cons(X, Z)) -> 2ndsneg(s(N), cons2(X, activate(Z)))
  , 2ndsneg(s(N), cons2(X, cons(Y, Z))) ->
    rcons(negrecip(Y), 2ndspos(N, activate(Z)))
  , 2ndsneg(0(), Z) -> rnil()
  , pi(X) -> 2ndspos(X, from(0()))
  , plus(s(X), Y) -> s(plus(X, Y))
  , plus(0(), Y) -> Y
  , times(s(X), Y) -> plus(Y, times(X, Y))
  , times(0(), Y) -> 0()
  , square(X) -> times(X, X) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We estimate the number of application of {1,2,5,6,10,13,15} by
applications of Pre({1,2,5,6,10,13,15}) = {3,4,7,8,9,11,12,14,16}.
Here rules are labeled as follows:

  DPs:
    { 1: from^#(X) -> c_1()
    , 2: from^#(X) -> c_2()
    , 3: 2ndspos^#(s(N), cons(X, Z)) ->
         c_3(2ndspos^#(s(N), cons2(X, activate(Z))), activate^#(Z))
    , 4: 2ndspos^#(s(N), cons2(X, cons(Y, Z))) ->
         c_4(2ndsneg^#(N, activate(Z)), activate^#(Z))
    , 5: 2ndspos^#(0(), Z) -> c_5()
    , 6: activate^#(X) -> c_6()
    , 7: activate^#(n__from(X)) -> c_7(from^#(X))
    , 8: 2ndsneg^#(s(N), cons(X, Z)) ->
         c_8(2ndsneg^#(s(N), cons2(X, activate(Z))), activate^#(Z))
    , 9: 2ndsneg^#(s(N), cons2(X, cons(Y, Z))) ->
         c_9(2ndspos^#(N, activate(Z)), activate^#(Z))
    , 10: 2ndsneg^#(0(), Z) -> c_10()
    , 11: pi^#(X) -> c_11(2ndspos^#(X, from(0())), from^#(0()))
    , 12: plus^#(s(X), Y) -> c_12(plus^#(X, Y))
    , 13: plus^#(0(), Y) -> c_13()
    , 14: times^#(s(X), Y) ->
          c_14(plus^#(Y, times(X, Y)), times^#(X, Y))
    , 15: times^#(0(), Y) -> c_15()
    , 16: square^#(X) -> c_16(times^#(X, X)) }

We are left with following problem, upon which TcT provides the
certificate MAYBE.

Strict DPs:
  { 2ndspos^#(s(N), cons(X, Z)) ->
    c_3(2ndspos^#(s(N), cons2(X, activate(Z))), activate^#(Z))
  , 2ndspos^#(s(N), cons2(X, cons(Y, Z))) ->
    c_4(2ndsneg^#(N, activate(Z)), activate^#(Z))
  , activate^#(n__from(X)) -> c_7(from^#(X))
  , 2ndsneg^#(s(N), cons(X, Z)) ->
    c_8(2ndsneg^#(s(N), cons2(X, activate(Z))), activate^#(Z))
  , 2ndsneg^#(s(N), cons2(X, cons(Y, Z))) ->
    c_9(2ndspos^#(N, activate(Z)), activate^#(Z))
  , pi^#(X) -> c_11(2ndspos^#(X, from(0())), from^#(0()))
  , plus^#(s(X), Y) -> c_12(plus^#(X, Y))
  , times^#(s(X), Y) -> c_14(plus^#(Y, times(X, Y)), times^#(X, Y))
  , square^#(X) -> c_16(times^#(X, X)) }
Weak DPs:
  { from^#(X) -> c_1()
  , from^#(X) -> c_2()
  , 2ndspos^#(0(), Z) -> c_5()
  , activate^#(X) -> c_6()
  , 2ndsneg^#(0(), Z) -> c_10()
  , plus^#(0(), Y) -> c_13()
  , times^#(0(), Y) -> c_15() }
Weak Trs:
  { from(X) -> cons(X, n__from(s(X)))
  , from(X) -> n__from(X)
  , 2ndspos(s(N), cons(X, Z)) -> 2ndspos(s(N), cons2(X, activate(Z)))
  , 2ndspos(s(N), cons2(X, cons(Y, Z))) ->
    rcons(posrecip(Y), 2ndsneg(N, activate(Z)))
  , 2ndspos(0(), Z) -> rnil()
  , activate(X) -> X
  , activate(n__from(X)) -> from(X)
  , 2ndsneg(s(N), cons(X, Z)) -> 2ndsneg(s(N), cons2(X, activate(Z)))
  , 2ndsneg(s(N), cons2(X, cons(Y, Z))) ->
    rcons(negrecip(Y), 2ndspos(N, activate(Z)))
  , 2ndsneg(0(), Z) -> rnil()
  , pi(X) -> 2ndspos(X, from(0()))
  , plus(s(X), Y) -> s(plus(X, Y))
  , plus(0(), Y) -> Y
  , times(s(X), Y) -> plus(Y, times(X, Y))
  , times(0(), Y) -> 0()
  , square(X) -> times(X, X) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We estimate the number of application of {3} by applications of
Pre({3}) = {1,2,4,5}. Here rules are labeled as follows:

  DPs:
    { 1: 2ndspos^#(s(N), cons(X, Z)) ->
         c_3(2ndspos^#(s(N), cons2(X, activate(Z))), activate^#(Z))
    , 2: 2ndspos^#(s(N), cons2(X, cons(Y, Z))) ->
         c_4(2ndsneg^#(N, activate(Z)), activate^#(Z))
    , 3: activate^#(n__from(X)) -> c_7(from^#(X))
    , 4: 2ndsneg^#(s(N), cons(X, Z)) ->
         c_8(2ndsneg^#(s(N), cons2(X, activate(Z))), activate^#(Z))
    , 5: 2ndsneg^#(s(N), cons2(X, cons(Y, Z))) ->
         c_9(2ndspos^#(N, activate(Z)), activate^#(Z))
    , 6: pi^#(X) -> c_11(2ndspos^#(X, from(0())), from^#(0()))
    , 7: plus^#(s(X), Y) -> c_12(plus^#(X, Y))
    , 8: times^#(s(X), Y) ->
         c_14(plus^#(Y, times(X, Y)), times^#(X, Y))
    , 9: square^#(X) -> c_16(times^#(X, X))
    , 10: from^#(X) -> c_1()
    , 11: from^#(X) -> c_2()
    , 12: 2ndspos^#(0(), Z) -> c_5()
    , 13: activate^#(X) -> c_6()
    , 14: 2ndsneg^#(0(), Z) -> c_10()
    , 15: plus^#(0(), Y) -> c_13()
    , 16: times^#(0(), Y) -> c_15() }

We are left with following problem, upon which TcT provides the
certificate MAYBE.

Strict DPs:
  { 2ndspos^#(s(N), cons(X, Z)) ->
    c_3(2ndspos^#(s(N), cons2(X, activate(Z))), activate^#(Z))
  , 2ndspos^#(s(N), cons2(X, cons(Y, Z))) ->
    c_4(2ndsneg^#(N, activate(Z)), activate^#(Z))
  , 2ndsneg^#(s(N), cons(X, Z)) ->
    c_8(2ndsneg^#(s(N), cons2(X, activate(Z))), activate^#(Z))
  , 2ndsneg^#(s(N), cons2(X, cons(Y, Z))) ->
    c_9(2ndspos^#(N, activate(Z)), activate^#(Z))
  , pi^#(X) -> c_11(2ndspos^#(X, from(0())), from^#(0()))
  , plus^#(s(X), Y) -> c_12(plus^#(X, Y))
  , times^#(s(X), Y) -> c_14(plus^#(Y, times(X, Y)), times^#(X, Y))
  , square^#(X) -> c_16(times^#(X, X)) }
Weak DPs:
  { from^#(X) -> c_1()
  , from^#(X) -> c_2()
  , 2ndspos^#(0(), Z) -> c_5()
  , activate^#(X) -> c_6()
  , activate^#(n__from(X)) -> c_7(from^#(X))
  , 2ndsneg^#(0(), Z) -> c_10()
  , plus^#(0(), Y) -> c_13()
  , times^#(0(), Y) -> c_15() }
Weak Trs:
  { from(X) -> cons(X, n__from(s(X)))
  , from(X) -> n__from(X)
  , 2ndspos(s(N), cons(X, Z)) -> 2ndspos(s(N), cons2(X, activate(Z)))
  , 2ndspos(s(N), cons2(X, cons(Y, Z))) ->
    rcons(posrecip(Y), 2ndsneg(N, activate(Z)))
  , 2ndspos(0(), Z) -> rnil()
  , activate(X) -> X
  , activate(n__from(X)) -> from(X)
  , 2ndsneg(s(N), cons(X, Z)) -> 2ndsneg(s(N), cons2(X, activate(Z)))
  , 2ndsneg(s(N), cons2(X, cons(Y, Z))) ->
    rcons(negrecip(Y), 2ndspos(N, activate(Z)))
  , 2ndsneg(0(), Z) -> rnil()
  , pi(X) -> 2ndspos(X, from(0()))
  , plus(s(X), Y) -> s(plus(X, Y))
  , plus(0(), Y) -> Y
  , times(s(X), Y) -> plus(Y, times(X, Y))
  , times(0(), Y) -> 0()
  , square(X) -> times(X, X) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

The following weak DPs constitute a sub-graph of the DG that is
closed under successors. The DPs are removed.

{ from^#(X) -> c_1()
, from^#(X) -> c_2()
, 2ndspos^#(0(), Z) -> c_5()
, activate^#(X) -> c_6()
, activate^#(n__from(X)) -> c_7(from^#(X))
, 2ndsneg^#(0(), Z) -> c_10()
, plus^#(0(), Y) -> c_13()
, times^#(0(), Y) -> c_15() }

We are left with following problem, upon which TcT provides the
certificate MAYBE.

Strict DPs:
  { 2ndspos^#(s(N), cons(X, Z)) ->
    c_3(2ndspos^#(s(N), cons2(X, activate(Z))), activate^#(Z))
  , 2ndspos^#(s(N), cons2(X, cons(Y, Z))) ->
    c_4(2ndsneg^#(N, activate(Z)), activate^#(Z))
  , 2ndsneg^#(s(N), cons(X, Z)) ->
    c_8(2ndsneg^#(s(N), cons2(X, activate(Z))), activate^#(Z))
  , 2ndsneg^#(s(N), cons2(X, cons(Y, Z))) ->
    c_9(2ndspos^#(N, activate(Z)), activate^#(Z))
  , pi^#(X) -> c_11(2ndspos^#(X, from(0())), from^#(0()))
  , plus^#(s(X), Y) -> c_12(plus^#(X, Y))
  , times^#(s(X), Y) -> c_14(plus^#(Y, times(X, Y)), times^#(X, Y))
  , square^#(X) -> c_16(times^#(X, X)) }
Weak Trs:
  { from(X) -> cons(X, n__from(s(X)))
  , from(X) -> n__from(X)
  , 2ndspos(s(N), cons(X, Z)) -> 2ndspos(s(N), cons2(X, activate(Z)))
  , 2ndspos(s(N), cons2(X, cons(Y, Z))) ->
    rcons(posrecip(Y), 2ndsneg(N, activate(Z)))
  , 2ndspos(0(), Z) -> rnil()
  , activate(X) -> X
  , activate(n__from(X)) -> from(X)
  , 2ndsneg(s(N), cons(X, Z)) -> 2ndsneg(s(N), cons2(X, activate(Z)))
  , 2ndsneg(s(N), cons2(X, cons(Y, Z))) ->
    rcons(negrecip(Y), 2ndspos(N, activate(Z)))
  , 2ndsneg(0(), Z) -> rnil()
  , pi(X) -> 2ndspos(X, from(0()))
  , plus(s(X), Y) -> s(plus(X, Y))
  , plus(0(), Y) -> Y
  , times(s(X), Y) -> plus(Y, times(X, Y))
  , times(0(), Y) -> 0()
  , square(X) -> times(X, X) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

Due to missing edges in the dependency-graph, the right-hand sides
of following rules could be simplified:

  { 2ndspos^#(s(N), cons(X, Z)) ->
    c_3(2ndspos^#(s(N), cons2(X, activate(Z))), activate^#(Z))
  , 2ndspos^#(s(N), cons2(X, cons(Y, Z))) ->
    c_4(2ndsneg^#(N, activate(Z)), activate^#(Z))
  , 2ndsneg^#(s(N), cons(X, Z)) ->
    c_8(2ndsneg^#(s(N), cons2(X, activate(Z))), activate^#(Z))
  , 2ndsneg^#(s(N), cons2(X, cons(Y, Z))) ->
    c_9(2ndspos^#(N, activate(Z)), activate^#(Z))
  , pi^#(X) -> c_11(2ndspos^#(X, from(0())), from^#(0())) }

We are left with following problem, upon which TcT provides the
certificate MAYBE.

Strict DPs:
  { 2ndspos^#(s(N), cons(X, Z)) ->
    c_1(2ndspos^#(s(N), cons2(X, activate(Z))))
  , 2ndspos^#(s(N), cons2(X, cons(Y, Z))) ->
    c_2(2ndsneg^#(N, activate(Z)))
  , 2ndsneg^#(s(N), cons(X, Z)) ->
    c_3(2ndsneg^#(s(N), cons2(X, activate(Z))))
  , 2ndsneg^#(s(N), cons2(X, cons(Y, Z))) ->
    c_4(2ndspos^#(N, activate(Z)))
  , pi^#(X) -> c_5(2ndspos^#(X, from(0())))
  , plus^#(s(X), Y) -> c_6(plus^#(X, Y))
  , times^#(s(X), Y) -> c_7(plus^#(Y, times(X, Y)), times^#(X, Y))
  , square^#(X) -> c_8(times^#(X, X)) }
Weak Trs:
  { from(X) -> cons(X, n__from(s(X)))
  , from(X) -> n__from(X)
  , 2ndspos(s(N), cons(X, Z)) -> 2ndspos(s(N), cons2(X, activate(Z)))
  , 2ndspos(s(N), cons2(X, cons(Y, Z))) ->
    rcons(posrecip(Y), 2ndsneg(N, activate(Z)))
  , 2ndspos(0(), Z) -> rnil()
  , activate(X) -> X
  , activate(n__from(X)) -> from(X)
  , 2ndsneg(s(N), cons(X, Z)) -> 2ndsneg(s(N), cons2(X, activate(Z)))
  , 2ndsneg(s(N), cons2(X, cons(Y, Z))) ->
    rcons(negrecip(Y), 2ndspos(N, activate(Z)))
  , 2ndsneg(0(), Z) -> rnil()
  , pi(X) -> 2ndspos(X, from(0()))
  , plus(s(X), Y) -> s(plus(X, Y))
  , plus(0(), Y) -> Y
  , times(s(X), Y) -> plus(Y, times(X, Y))
  , times(0(), Y) -> 0()
  , square(X) -> times(X, X) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We replace rewrite rules by usable rules:

  Weak Usable Rules:
    { from(X) -> cons(X, n__from(s(X)))
    , from(X) -> n__from(X)
    , activate(X) -> X
    , activate(n__from(X)) -> from(X)
    , plus(s(X), Y) -> s(plus(X, Y))
    , plus(0(), Y) -> Y
    , times(s(X), Y) -> plus(Y, times(X, Y))
    , times(0(), Y) -> 0() }

We are left with following problem, upon which TcT provides the
certificate MAYBE.

Strict DPs:
  { 2ndspos^#(s(N), cons(X, Z)) ->
    c_1(2ndspos^#(s(N), cons2(X, activate(Z))))
  , 2ndspos^#(s(N), cons2(X, cons(Y, Z))) ->
    c_2(2ndsneg^#(N, activate(Z)))
  , 2ndsneg^#(s(N), cons(X, Z)) ->
    c_3(2ndsneg^#(s(N), cons2(X, activate(Z))))
  , 2ndsneg^#(s(N), cons2(X, cons(Y, Z))) ->
    c_4(2ndspos^#(N, activate(Z)))
  , pi^#(X) -> c_5(2ndspos^#(X, from(0())))
  , plus^#(s(X), Y) -> c_6(plus^#(X, Y))
  , times^#(s(X), Y) -> c_7(plus^#(Y, times(X, Y)), times^#(X, Y))
  , square^#(X) -> c_8(times^#(X, X)) }
Weak Trs:
  { from(X) -> cons(X, n__from(s(X)))
  , from(X) -> n__from(X)
  , activate(X) -> X
  , activate(n__from(X)) -> from(X)
  , plus(s(X), Y) -> s(plus(X, Y))
  , plus(0(), Y) -> Y
  , times(s(X), Y) -> plus(Y, times(X, Y))
  , times(0(), Y) -> 0() }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

Consider the dependency graph

  1: 2ndspos^#(s(N), cons(X, Z)) ->
     c_1(2ndspos^#(s(N), cons2(X, activate(Z))))
     -->_1 2ndspos^#(s(N), cons2(X, cons(Y, Z))) ->
           c_2(2ndsneg^#(N, activate(Z))) :2
  
  2: 2ndspos^#(s(N), cons2(X, cons(Y, Z))) ->
     c_2(2ndsneg^#(N, activate(Z)))
     -->_1 2ndsneg^#(s(N), cons2(X, cons(Y, Z))) ->
           c_4(2ndspos^#(N, activate(Z))) :4
     -->_1 2ndsneg^#(s(N), cons(X, Z)) ->
           c_3(2ndsneg^#(s(N), cons2(X, activate(Z)))) :3
  
  3: 2ndsneg^#(s(N), cons(X, Z)) ->
     c_3(2ndsneg^#(s(N), cons2(X, activate(Z))))
     -->_1 2ndsneg^#(s(N), cons2(X, cons(Y, Z))) ->
           c_4(2ndspos^#(N, activate(Z))) :4
  
  4: 2ndsneg^#(s(N), cons2(X, cons(Y, Z))) ->
     c_4(2ndspos^#(N, activate(Z)))
     -->_1 2ndspos^#(s(N), cons2(X, cons(Y, Z))) ->
           c_2(2ndsneg^#(N, activate(Z))) :2
     -->_1 2ndspos^#(s(N), cons(X, Z)) ->
           c_1(2ndspos^#(s(N), cons2(X, activate(Z)))) :1
  
  5: pi^#(X) -> c_5(2ndspos^#(X, from(0())))
     -->_1 2ndspos^#(s(N), cons2(X, cons(Y, Z))) ->
           c_2(2ndsneg^#(N, activate(Z))) :2
     -->_1 2ndspos^#(s(N), cons(X, Z)) ->
           c_1(2ndspos^#(s(N), cons2(X, activate(Z)))) :1
  
  6: plus^#(s(X), Y) -> c_6(plus^#(X, Y))
     -->_1 plus^#(s(X), Y) -> c_6(plus^#(X, Y)) :6
  
  7: times^#(s(X), Y) -> c_7(plus^#(Y, times(X, Y)), times^#(X, Y))
     -->_2 times^#(s(X), Y) ->
           c_7(plus^#(Y, times(X, Y)), times^#(X, Y)) :7
     -->_1 plus^#(s(X), Y) -> c_6(plus^#(X, Y)) :6
  
  8: square^#(X) -> c_8(times^#(X, X))
     -->_1 times^#(s(X), Y) ->
           c_7(plus^#(Y, times(X, Y)), times^#(X, Y)) :7
  

Following roots of the dependency graph are removed, as the
considered set of starting terms is closed under reduction with
respect to these rules (modulo compound contexts).

  { square^#(X) -> c_8(times^#(X, X)) }


We are left with following problem, upon which TcT provides the
certificate MAYBE.

Strict DPs:
  { 2ndspos^#(s(N), cons(X, Z)) ->
    c_1(2ndspos^#(s(N), cons2(X, activate(Z))))
  , 2ndspos^#(s(N), cons2(X, cons(Y, Z))) ->
    c_2(2ndsneg^#(N, activate(Z)))
  , 2ndsneg^#(s(N), cons(X, Z)) ->
    c_3(2ndsneg^#(s(N), cons2(X, activate(Z))))
  , 2ndsneg^#(s(N), cons2(X, cons(Y, Z))) ->
    c_4(2ndspos^#(N, activate(Z)))
  , pi^#(X) -> c_5(2ndspos^#(X, from(0())))
  , plus^#(s(X), Y) -> c_6(plus^#(X, Y))
  , times^#(s(X), Y) -> c_7(plus^#(Y, times(X, Y)), times^#(X, Y)) }
Weak Trs:
  { from(X) -> cons(X, n__from(s(X)))
  , from(X) -> n__from(X)
  , activate(X) -> X
  , activate(n__from(X)) -> from(X)
  , plus(s(X), Y) -> s(plus(X, Y))
  , plus(0(), Y) -> Y
  , times(s(X), Y) -> plus(Y, times(X, Y))
  , times(0(), Y) -> 0() }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

The input cannot be shown compatible

Arrrr..