MAYBE

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

Strict Trs:
  { le(s(x), s(y)) -> le(x, y)
  , le(s(x), 0()) -> false()
  , le(0(), y) -> true()
  , double(s(x)) -> s(s(double(x)))
  , double(0()) -> 0()
  , log(s(x)) -> loop(s(x), s(0()), 0())
  , log(0()) -> logError()
  , loop(x, s(y), z) -> if(le(x, s(y)), x, s(y), z)
  , if(false(), x, y, z) -> loop(x, double(y), s(z))
  , if(true(), x, y, z) -> z
  , maplog(xs) -> mapIter(xs, nil())
  , mapIter(xs, ys) -> ifmap(isempty(xs), xs, ys)
  , ifmap(false(), xs, ys) ->
    mapIter(droplast(xs), cons(log(last(xs)), ys))
  , ifmap(true(), xs, ys) -> ys
  , isempty(nil()) -> true()
  , isempty(cons(x, xs)) -> false()
  , droplast(nil()) -> nil()
  , droplast(cons(x, nil())) -> nil()
  , droplast(cons(x, cons(y, xs))) -> cons(x, droplast(cons(y, xs)))
  , last(nil()) -> error()
  , last(cons(x, nil())) -> x
  , last(cons(x, cons(y, xs))) -> last(cons(y, xs))
  , a() -> b()
  , a() -> c() }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We add following dependency tuples:

Strict DPs:
  { le^#(s(x), s(y)) -> c_1(le^#(x, y))
  , le^#(s(x), 0()) -> c_2()
  , le^#(0(), y) -> c_3()
  , double^#(s(x)) -> c_4(double^#(x))
  , double^#(0()) -> c_5()
  , log^#(s(x)) -> c_6(loop^#(s(x), s(0()), 0()))
  , log^#(0()) -> c_7()
  , loop^#(x, s(y), z) ->
    c_8(if^#(le(x, s(y)), x, s(y), z), le^#(x, s(y)))
  , if^#(false(), x, y, z) ->
    c_9(loop^#(x, double(y), s(z)), double^#(y))
  , if^#(true(), x, y, z) -> c_10()
  , maplog^#(xs) -> c_11(mapIter^#(xs, nil()))
  , mapIter^#(xs, ys) ->
    c_12(ifmap^#(isempty(xs), xs, ys), isempty^#(xs))
  , ifmap^#(false(), xs, ys) ->
    c_13(mapIter^#(droplast(xs), cons(log(last(xs)), ys)),
         droplast^#(xs),
         log^#(last(xs)),
         last^#(xs))
  , ifmap^#(true(), xs, ys) -> c_14()
  , isempty^#(nil()) -> c_15()
  , isempty^#(cons(x, xs)) -> c_16()
  , droplast^#(nil()) -> c_17()
  , droplast^#(cons(x, nil())) -> c_18()
  , droplast^#(cons(x, cons(y, xs))) -> c_19(droplast^#(cons(y, xs)))
  , last^#(nil()) -> c_20()
  , last^#(cons(x, nil())) -> c_21()
  , last^#(cons(x, cons(y, xs))) -> c_22(last^#(cons(y, xs)))
  , a^#() -> c_23()
  , a^#() -> c_24() }

and mark the set of starting terms.

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

Strict DPs:
  { le^#(s(x), s(y)) -> c_1(le^#(x, y))
  , le^#(s(x), 0()) -> c_2()
  , le^#(0(), y) -> c_3()
  , double^#(s(x)) -> c_4(double^#(x))
  , double^#(0()) -> c_5()
  , log^#(s(x)) -> c_6(loop^#(s(x), s(0()), 0()))
  , log^#(0()) -> c_7()
  , loop^#(x, s(y), z) ->
    c_8(if^#(le(x, s(y)), x, s(y), z), le^#(x, s(y)))
  , if^#(false(), x, y, z) ->
    c_9(loop^#(x, double(y), s(z)), double^#(y))
  , if^#(true(), x, y, z) -> c_10()
  , maplog^#(xs) -> c_11(mapIter^#(xs, nil()))
  , mapIter^#(xs, ys) ->
    c_12(ifmap^#(isempty(xs), xs, ys), isempty^#(xs))
  , ifmap^#(false(), xs, ys) ->
    c_13(mapIter^#(droplast(xs), cons(log(last(xs)), ys)),
         droplast^#(xs),
         log^#(last(xs)),
         last^#(xs))
  , ifmap^#(true(), xs, ys) -> c_14()
  , isempty^#(nil()) -> c_15()
  , isempty^#(cons(x, xs)) -> c_16()
  , droplast^#(nil()) -> c_17()
  , droplast^#(cons(x, nil())) -> c_18()
  , droplast^#(cons(x, cons(y, xs))) -> c_19(droplast^#(cons(y, xs)))
  , last^#(nil()) -> c_20()
  , last^#(cons(x, nil())) -> c_21()
  , last^#(cons(x, cons(y, xs))) -> c_22(last^#(cons(y, xs)))
  , a^#() -> c_23()
  , a^#() -> c_24() }
Weak Trs:
  { le(s(x), s(y)) -> le(x, y)
  , le(s(x), 0()) -> false()
  , le(0(), y) -> true()
  , double(s(x)) -> s(s(double(x)))
  , double(0()) -> 0()
  , log(s(x)) -> loop(s(x), s(0()), 0())
  , log(0()) -> logError()
  , loop(x, s(y), z) -> if(le(x, s(y)), x, s(y), z)
  , if(false(), x, y, z) -> loop(x, double(y), s(z))
  , if(true(), x, y, z) -> z
  , maplog(xs) -> mapIter(xs, nil())
  , mapIter(xs, ys) -> ifmap(isempty(xs), xs, ys)
  , ifmap(false(), xs, ys) ->
    mapIter(droplast(xs), cons(log(last(xs)), ys))
  , ifmap(true(), xs, ys) -> ys
  , isempty(nil()) -> true()
  , isempty(cons(x, xs)) -> false()
  , droplast(nil()) -> nil()
  , droplast(cons(x, nil())) -> nil()
  , droplast(cons(x, cons(y, xs))) -> cons(x, droplast(cons(y, xs)))
  , last(nil()) -> error()
  , last(cons(x, nil())) -> x
  , last(cons(x, cons(y, xs))) -> last(cons(y, xs))
  , a() -> b()
  , a() -> c() }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We estimate the number of application of
{2,3,5,7,10,14,15,16,17,18,20,21,23,24} by applications of
Pre({2,3,5,7,10,14,15,16,17,18,20,21,23,24}) =
{1,4,8,9,12,13,19,22}. Here rules are labeled as follows:

  DPs:
    { 1: le^#(s(x), s(y)) -> c_1(le^#(x, y))
    , 2: le^#(s(x), 0()) -> c_2()
    , 3: le^#(0(), y) -> c_3()
    , 4: double^#(s(x)) -> c_4(double^#(x))
    , 5: double^#(0()) -> c_5()
    , 6: log^#(s(x)) -> c_6(loop^#(s(x), s(0()), 0()))
    , 7: log^#(0()) -> c_7()
    , 8: loop^#(x, s(y), z) ->
         c_8(if^#(le(x, s(y)), x, s(y), z), le^#(x, s(y)))
    , 9: if^#(false(), x, y, z) ->
         c_9(loop^#(x, double(y), s(z)), double^#(y))
    , 10: if^#(true(), x, y, z) -> c_10()
    , 11: maplog^#(xs) -> c_11(mapIter^#(xs, nil()))
    , 12: mapIter^#(xs, ys) ->
          c_12(ifmap^#(isempty(xs), xs, ys), isempty^#(xs))
    , 13: ifmap^#(false(), xs, ys) ->
          c_13(mapIter^#(droplast(xs), cons(log(last(xs)), ys)),
               droplast^#(xs),
               log^#(last(xs)),
               last^#(xs))
    , 14: ifmap^#(true(), xs, ys) -> c_14()
    , 15: isempty^#(nil()) -> c_15()
    , 16: isempty^#(cons(x, xs)) -> c_16()
    , 17: droplast^#(nil()) -> c_17()
    , 18: droplast^#(cons(x, nil())) -> c_18()
    , 19: droplast^#(cons(x, cons(y, xs))) ->
          c_19(droplast^#(cons(y, xs)))
    , 20: last^#(nil()) -> c_20()
    , 21: last^#(cons(x, nil())) -> c_21()
    , 22: last^#(cons(x, cons(y, xs))) -> c_22(last^#(cons(y, xs)))
    , 23: a^#() -> c_23()
    , 24: a^#() -> c_24() }

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

Strict DPs:
  { le^#(s(x), s(y)) -> c_1(le^#(x, y))
  , double^#(s(x)) -> c_4(double^#(x))
  , log^#(s(x)) -> c_6(loop^#(s(x), s(0()), 0()))
  , loop^#(x, s(y), z) ->
    c_8(if^#(le(x, s(y)), x, s(y), z), le^#(x, s(y)))
  , if^#(false(), x, y, z) ->
    c_9(loop^#(x, double(y), s(z)), double^#(y))
  , maplog^#(xs) -> c_11(mapIter^#(xs, nil()))
  , mapIter^#(xs, ys) ->
    c_12(ifmap^#(isempty(xs), xs, ys), isempty^#(xs))
  , ifmap^#(false(), xs, ys) ->
    c_13(mapIter^#(droplast(xs), cons(log(last(xs)), ys)),
         droplast^#(xs),
         log^#(last(xs)),
         last^#(xs))
  , droplast^#(cons(x, cons(y, xs))) -> c_19(droplast^#(cons(y, xs)))
  , last^#(cons(x, cons(y, xs))) -> c_22(last^#(cons(y, xs))) }
Weak DPs:
  { le^#(s(x), 0()) -> c_2()
  , le^#(0(), y) -> c_3()
  , double^#(0()) -> c_5()
  , log^#(0()) -> c_7()
  , if^#(true(), x, y, z) -> c_10()
  , ifmap^#(true(), xs, ys) -> c_14()
  , isempty^#(nil()) -> c_15()
  , isempty^#(cons(x, xs)) -> c_16()
  , droplast^#(nil()) -> c_17()
  , droplast^#(cons(x, nil())) -> c_18()
  , last^#(nil()) -> c_20()
  , last^#(cons(x, nil())) -> c_21()
  , a^#() -> c_23()
  , a^#() -> c_24() }
Weak Trs:
  { le(s(x), s(y)) -> le(x, y)
  , le(s(x), 0()) -> false()
  , le(0(), y) -> true()
  , double(s(x)) -> s(s(double(x)))
  , double(0()) -> 0()
  , log(s(x)) -> loop(s(x), s(0()), 0())
  , log(0()) -> logError()
  , loop(x, s(y), z) -> if(le(x, s(y)), x, s(y), z)
  , if(false(), x, y, z) -> loop(x, double(y), s(z))
  , if(true(), x, y, z) -> z
  , maplog(xs) -> mapIter(xs, nil())
  , mapIter(xs, ys) -> ifmap(isempty(xs), xs, ys)
  , ifmap(false(), xs, ys) ->
    mapIter(droplast(xs), cons(log(last(xs)), ys))
  , ifmap(true(), xs, ys) -> ys
  , isempty(nil()) -> true()
  , isempty(cons(x, xs)) -> false()
  , droplast(nil()) -> nil()
  , droplast(cons(x, nil())) -> nil()
  , droplast(cons(x, cons(y, xs))) -> cons(x, droplast(cons(y, xs)))
  , last(nil()) -> error()
  , last(cons(x, nil())) -> x
  , last(cons(x, cons(y, xs))) -> last(cons(y, xs))
  , a() -> b()
  , a() -> c() }
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.

{ le^#(s(x), 0()) -> c_2()
, le^#(0(), y) -> c_3()
, double^#(0()) -> c_5()
, log^#(0()) -> c_7()
, if^#(true(), x, y, z) -> c_10()
, ifmap^#(true(), xs, ys) -> c_14()
, isempty^#(nil()) -> c_15()
, isempty^#(cons(x, xs)) -> c_16()
, droplast^#(nil()) -> c_17()
, droplast^#(cons(x, nil())) -> c_18()
, last^#(nil()) -> c_20()
, last^#(cons(x, nil())) -> c_21()
, a^#() -> c_23()
, a^#() -> c_24() }

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

Strict DPs:
  { le^#(s(x), s(y)) -> c_1(le^#(x, y))
  , double^#(s(x)) -> c_4(double^#(x))
  , log^#(s(x)) -> c_6(loop^#(s(x), s(0()), 0()))
  , loop^#(x, s(y), z) ->
    c_8(if^#(le(x, s(y)), x, s(y), z), le^#(x, s(y)))
  , if^#(false(), x, y, z) ->
    c_9(loop^#(x, double(y), s(z)), double^#(y))
  , maplog^#(xs) -> c_11(mapIter^#(xs, nil()))
  , mapIter^#(xs, ys) ->
    c_12(ifmap^#(isempty(xs), xs, ys), isempty^#(xs))
  , ifmap^#(false(), xs, ys) ->
    c_13(mapIter^#(droplast(xs), cons(log(last(xs)), ys)),
         droplast^#(xs),
         log^#(last(xs)),
         last^#(xs))
  , droplast^#(cons(x, cons(y, xs))) -> c_19(droplast^#(cons(y, xs)))
  , last^#(cons(x, cons(y, xs))) -> c_22(last^#(cons(y, xs))) }
Weak Trs:
  { le(s(x), s(y)) -> le(x, y)
  , le(s(x), 0()) -> false()
  , le(0(), y) -> true()
  , double(s(x)) -> s(s(double(x)))
  , double(0()) -> 0()
  , log(s(x)) -> loop(s(x), s(0()), 0())
  , log(0()) -> logError()
  , loop(x, s(y), z) -> if(le(x, s(y)), x, s(y), z)
  , if(false(), x, y, z) -> loop(x, double(y), s(z))
  , if(true(), x, y, z) -> z
  , maplog(xs) -> mapIter(xs, nil())
  , mapIter(xs, ys) -> ifmap(isempty(xs), xs, ys)
  , ifmap(false(), xs, ys) ->
    mapIter(droplast(xs), cons(log(last(xs)), ys))
  , ifmap(true(), xs, ys) -> ys
  , isempty(nil()) -> true()
  , isempty(cons(x, xs)) -> false()
  , droplast(nil()) -> nil()
  , droplast(cons(x, nil())) -> nil()
  , droplast(cons(x, cons(y, xs))) -> cons(x, droplast(cons(y, xs)))
  , last(nil()) -> error()
  , last(cons(x, nil())) -> x
  , last(cons(x, cons(y, xs))) -> last(cons(y, xs))
  , a() -> b()
  , a() -> c() }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

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

  { mapIter^#(xs, ys) ->
    c_12(ifmap^#(isempty(xs), xs, ys), isempty^#(xs)) }

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

Strict DPs:
  { le^#(s(x), s(y)) -> c_1(le^#(x, y))
  , double^#(s(x)) -> c_2(double^#(x))
  , log^#(s(x)) -> c_3(loop^#(s(x), s(0()), 0()))
  , loop^#(x, s(y), z) ->
    c_4(if^#(le(x, s(y)), x, s(y), z), le^#(x, s(y)))
  , if^#(false(), x, y, z) ->
    c_5(loop^#(x, double(y), s(z)), double^#(y))
  , maplog^#(xs) -> c_6(mapIter^#(xs, nil()))
  , mapIter^#(xs, ys) -> c_7(ifmap^#(isempty(xs), xs, ys))
  , ifmap^#(false(), xs, ys) ->
    c_8(mapIter^#(droplast(xs), cons(log(last(xs)), ys)),
        droplast^#(xs),
        log^#(last(xs)),
        last^#(xs))
  , droplast^#(cons(x, cons(y, xs))) -> c_9(droplast^#(cons(y, xs)))
  , last^#(cons(x, cons(y, xs))) -> c_10(last^#(cons(y, xs))) }
Weak Trs:
  { le(s(x), s(y)) -> le(x, y)
  , le(s(x), 0()) -> false()
  , le(0(), y) -> true()
  , double(s(x)) -> s(s(double(x)))
  , double(0()) -> 0()
  , log(s(x)) -> loop(s(x), s(0()), 0())
  , log(0()) -> logError()
  , loop(x, s(y), z) -> if(le(x, s(y)), x, s(y), z)
  , if(false(), x, y, z) -> loop(x, double(y), s(z))
  , if(true(), x, y, z) -> z
  , maplog(xs) -> mapIter(xs, nil())
  , mapIter(xs, ys) -> ifmap(isempty(xs), xs, ys)
  , ifmap(false(), xs, ys) ->
    mapIter(droplast(xs), cons(log(last(xs)), ys))
  , ifmap(true(), xs, ys) -> ys
  , isempty(nil()) -> true()
  , isempty(cons(x, xs)) -> false()
  , droplast(nil()) -> nil()
  , droplast(cons(x, nil())) -> nil()
  , droplast(cons(x, cons(y, xs))) -> cons(x, droplast(cons(y, xs)))
  , last(nil()) -> error()
  , last(cons(x, nil())) -> x
  , last(cons(x, cons(y, xs))) -> last(cons(y, xs))
  , a() -> b()
  , a() -> c() }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We replace rewrite rules by usable rules:

  Weak Usable Rules:
    { le(s(x), s(y)) -> le(x, y)
    , le(s(x), 0()) -> false()
    , le(0(), y) -> true()
    , double(s(x)) -> s(s(double(x)))
    , double(0()) -> 0()
    , log(s(x)) -> loop(s(x), s(0()), 0())
    , log(0()) -> logError()
    , loop(x, s(y), z) -> if(le(x, s(y)), x, s(y), z)
    , if(false(), x, y, z) -> loop(x, double(y), s(z))
    , if(true(), x, y, z) -> z
    , isempty(nil()) -> true()
    , isempty(cons(x, xs)) -> false()
    , droplast(nil()) -> nil()
    , droplast(cons(x, nil())) -> nil()
    , droplast(cons(x, cons(y, xs))) -> cons(x, droplast(cons(y, xs)))
    , last(nil()) -> error()
    , last(cons(x, nil())) -> x
    , last(cons(x, cons(y, xs))) -> last(cons(y, xs)) }

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

Strict DPs:
  { le^#(s(x), s(y)) -> c_1(le^#(x, y))
  , double^#(s(x)) -> c_2(double^#(x))
  , log^#(s(x)) -> c_3(loop^#(s(x), s(0()), 0()))
  , loop^#(x, s(y), z) ->
    c_4(if^#(le(x, s(y)), x, s(y), z), le^#(x, s(y)))
  , if^#(false(), x, y, z) ->
    c_5(loop^#(x, double(y), s(z)), double^#(y))
  , maplog^#(xs) -> c_6(mapIter^#(xs, nil()))
  , mapIter^#(xs, ys) -> c_7(ifmap^#(isempty(xs), xs, ys))
  , ifmap^#(false(), xs, ys) ->
    c_8(mapIter^#(droplast(xs), cons(log(last(xs)), ys)),
        droplast^#(xs),
        log^#(last(xs)),
        last^#(xs))
  , droplast^#(cons(x, cons(y, xs))) -> c_9(droplast^#(cons(y, xs)))
  , last^#(cons(x, cons(y, xs))) -> c_10(last^#(cons(y, xs))) }
Weak Trs:
  { le(s(x), s(y)) -> le(x, y)
  , le(s(x), 0()) -> false()
  , le(0(), y) -> true()
  , double(s(x)) -> s(s(double(x)))
  , double(0()) -> 0()
  , log(s(x)) -> loop(s(x), s(0()), 0())
  , log(0()) -> logError()
  , loop(x, s(y), z) -> if(le(x, s(y)), x, s(y), z)
  , if(false(), x, y, z) -> loop(x, double(y), s(z))
  , if(true(), x, y, z) -> z
  , isempty(nil()) -> true()
  , isempty(cons(x, xs)) -> false()
  , droplast(nil()) -> nil()
  , droplast(cons(x, nil())) -> nil()
  , droplast(cons(x, cons(y, xs))) -> cons(x, droplast(cons(y, xs)))
  , last(nil()) -> error()
  , last(cons(x, nil())) -> x
  , last(cons(x, cons(y, xs))) -> last(cons(y, xs)) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

Consider the dependency graph

  1: le^#(s(x), s(y)) -> c_1(le^#(x, y))
     -->_1 le^#(s(x), s(y)) -> c_1(le^#(x, y)) :1
  
  2: double^#(s(x)) -> c_2(double^#(x))
     -->_1 double^#(s(x)) -> c_2(double^#(x)) :2
  
  3: log^#(s(x)) -> c_3(loop^#(s(x), s(0()), 0()))
     -->_1 loop^#(x, s(y), z) ->
           c_4(if^#(le(x, s(y)), x, s(y), z), le^#(x, s(y))) :4
  
  4: loop^#(x, s(y), z) ->
     c_4(if^#(le(x, s(y)), x, s(y), z), le^#(x, s(y)))
     -->_1 if^#(false(), x, y, z) ->
           c_5(loop^#(x, double(y), s(z)), double^#(y)) :5
     -->_2 le^#(s(x), s(y)) -> c_1(le^#(x, y)) :1
  
  5: if^#(false(), x, y, z) ->
     c_5(loop^#(x, double(y), s(z)), double^#(y))
     -->_1 loop^#(x, s(y), z) ->
           c_4(if^#(le(x, s(y)), x, s(y), z), le^#(x, s(y))) :4
     -->_2 double^#(s(x)) -> c_2(double^#(x)) :2
  
  6: maplog^#(xs) -> c_6(mapIter^#(xs, nil()))
     -->_1 mapIter^#(xs, ys) -> c_7(ifmap^#(isempty(xs), xs, ys)) :7
  
  7: mapIter^#(xs, ys) -> c_7(ifmap^#(isempty(xs), xs, ys))
     -->_1 ifmap^#(false(), xs, ys) ->
           c_8(mapIter^#(droplast(xs), cons(log(last(xs)), ys)),
               droplast^#(xs),
               log^#(last(xs)),
               last^#(xs)) :8
  
  8: ifmap^#(false(), xs, ys) ->
     c_8(mapIter^#(droplast(xs), cons(log(last(xs)), ys)),
         droplast^#(xs),
         log^#(last(xs)),
         last^#(xs))
     -->_4 last^#(cons(x, cons(y, xs))) -> c_10(last^#(cons(y, xs))) :10
     -->_2 droplast^#(cons(x, cons(y, xs))) ->
           c_9(droplast^#(cons(y, xs))) :9
     -->_1 mapIter^#(xs, ys) -> c_7(ifmap^#(isempty(xs), xs, ys)) :7
     -->_3 log^#(s(x)) -> c_3(loop^#(s(x), s(0()), 0())) :3
  
  9: droplast^#(cons(x, cons(y, xs))) -> c_9(droplast^#(cons(y, xs)))
     -->_1 droplast^#(cons(x, cons(y, xs))) ->
           c_9(droplast^#(cons(y, xs))) :9
  
  10: last^#(cons(x, cons(y, xs))) -> c_10(last^#(cons(y, xs)))
     -->_1 last^#(cons(x, cons(y, xs))) -> c_10(last^#(cons(y, xs))) :10
  

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).

  { maplog^#(xs) -> c_6(mapIter^#(xs, nil())) }


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

Strict DPs:
  { le^#(s(x), s(y)) -> c_1(le^#(x, y))
  , double^#(s(x)) -> c_2(double^#(x))
  , log^#(s(x)) -> c_3(loop^#(s(x), s(0()), 0()))
  , loop^#(x, s(y), z) ->
    c_4(if^#(le(x, s(y)), x, s(y), z), le^#(x, s(y)))
  , if^#(false(), x, y, z) ->
    c_5(loop^#(x, double(y), s(z)), double^#(y))
  , mapIter^#(xs, ys) -> c_7(ifmap^#(isempty(xs), xs, ys))
  , ifmap^#(false(), xs, ys) ->
    c_8(mapIter^#(droplast(xs), cons(log(last(xs)), ys)),
        droplast^#(xs),
        log^#(last(xs)),
        last^#(xs))
  , droplast^#(cons(x, cons(y, xs))) -> c_9(droplast^#(cons(y, xs)))
  , last^#(cons(x, cons(y, xs))) -> c_10(last^#(cons(y, xs))) }
Weak Trs:
  { le(s(x), s(y)) -> le(x, y)
  , le(s(x), 0()) -> false()
  , le(0(), y) -> true()
  , double(s(x)) -> s(s(double(x)))
  , double(0()) -> 0()
  , log(s(x)) -> loop(s(x), s(0()), 0())
  , log(0()) -> logError()
  , loop(x, s(y), z) -> if(le(x, s(y)), x, s(y), z)
  , if(false(), x, y, z) -> loop(x, double(y), s(z))
  , if(true(), x, y, z) -> z
  , isempty(nil()) -> true()
  , isempty(cons(x, xs)) -> false()
  , droplast(nil()) -> nil()
  , droplast(cons(x, nil())) -> nil()
  , droplast(cons(x, cons(y, xs))) -> cons(x, droplast(cons(y, xs)))
  , last(nil()) -> error()
  , last(cons(x, nil())) -> x
  , last(cons(x, cons(y, xs))) -> last(cons(y, xs)) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

None of the processors succeeded.

Details of failed attempt(s):
-----------------------------
1) 'matrices' failed due to the following reason:
   
   None of the processors succeeded.
   
   Details of failed attempt(s):
   -----------------------------
   1) 'matrix interpretation of dimension 4' failed due to the
      following reason:
      
      Following exception was raised:
        stack overflow
   
   2) 'matrix interpretation of dimension 3' failed due to the
      following reason:
      
      The input cannot be shown compatible
   
   3) 'matrix interpretation of dimension 3' failed due to the
      following reason:
      
      The input cannot be shown compatible
   
   4) 'matrix interpretation of dimension 2' failed due to the
      following reason:
      
      The input cannot be shown compatible
   
   5) 'matrix interpretation of dimension 2' failed due to the
      following reason:
      
      The input cannot be shown compatible
   
   6) 'matrix interpretation of dimension 1' failed due to the
      following reason:
      
      The input cannot be shown compatible
   

2) 'empty' failed due to the following reason:
   
   Empty strict component of the problem is NOT empty.


Arrrr..