/export/starexec/sandbox2/solver/bin/starexec_run_rcdcRelativeAlsoLower /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


--------------------------------------------------------------------------------


WORST_CASE(Omega(n^1), ?)
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF).

(0) DCpxTrs
(1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms]
(2) CpxRelTRS
(3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 698 ms]
(4) CpxRelTRS
(5) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(6) CpxRelTRS
(7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
(8) typed CpxTrs
(9) OrderProof [LOWER BOUND(ID), 0 ms]
(10) typed CpxTrs
(11) RewriteLemmaProof [LOWER BOUND(ID), 283 ms]
(12) BEST
    (13) proven lower bound
        (14) LowerBoundPropagationProof [FINISHED, 0 ms]
        (15) BOUNDS(n^1, INF)
    (16) typed CpxTrs


----------------------------------------

(0)
Obligation:
The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF).


The TRS R consists of the following rules:

   fstsplit(0, x) -> nil
   fstsplit(s(n), nil) -> nil
   fstsplit(s(n), cons(h, t)) -> cons(h, fstsplit(n, t))
   sndsplit(0, x) -> x
   sndsplit(s(n), nil) -> nil
   sndsplit(s(n), cons(h, t)) -> sndsplit(n, t)
   empty(nil) -> true
   empty(cons(h, t)) -> false
   leq(0, m) -> true
   leq(s(n), 0) -> false
   leq(s(n), s(m)) -> leq(n, m)
   length(nil) -> 0
   length(cons(h, t)) -> s(length(t))
   app(nil, x) -> x
   app(cons(h, t), x) -> cons(h, app(t, x))
   map_f(pid, nil) -> nil
   map_f(pid, cons(h, t)) -> app(f(pid, h), map_f(pid, t))
   process(store, m) -> if1(store, m, leq(m, length(store)))
   if1(store, m, true) -> if2(store, m, empty(fstsplit(m, store)))
   if1(store, m, false) -> if3(store, m, empty(fstsplit(m, app(map_f(self, nil), store))))
   if2(store, m, false) -> process(app(map_f(self, nil), sndsplit(m, store)), m)
   if3(store, m, false) -> process(sndsplit(m, app(map_f(self, nil), store)), m)

S is empty.
Rewrite Strategy: INNERMOST
----------------------------------------

(1) DerivationalComplexityToRuntimeComplexityProof (BOTH BOUNDS(ID, ID))
The following rules have been added to S to convert the given derivational complexity problem to a runtime complexity problem:

   encArg(0) -> 0
   encArg(nil) -> nil
   encArg(s(x_1)) -> s(encArg(x_1))
   encArg(cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2))
   encArg(true) -> true
   encArg(false) -> false
   encArg(f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2))
   encArg(self) -> self
   encArg(cons_fstsplit(x_1, x_2)) -> fstsplit(encArg(x_1), encArg(x_2))
   encArg(cons_sndsplit(x_1, x_2)) -> sndsplit(encArg(x_1), encArg(x_2))
   encArg(cons_empty(x_1)) -> empty(encArg(x_1))
   encArg(cons_leq(x_1, x_2)) -> leq(encArg(x_1), encArg(x_2))
   encArg(cons_length(x_1)) -> length(encArg(x_1))
   encArg(cons_app(x_1, x_2)) -> app(encArg(x_1), encArg(x_2))
   encArg(cons_map_f(x_1, x_2)) -> map_f(encArg(x_1), encArg(x_2))
   encArg(cons_process(x_1, x_2)) -> process(encArg(x_1), encArg(x_2))
   encArg(cons_if1(x_1, x_2, x_3)) -> if1(encArg(x_1), encArg(x_2), encArg(x_3))
   encArg(cons_if2(x_1, x_2, x_3)) -> if2(encArg(x_1), encArg(x_2), encArg(x_3))
   encArg(cons_if3(x_1, x_2, x_3)) -> if3(encArg(x_1), encArg(x_2), encArg(x_3))
   encode_fstsplit(x_1, x_2) -> fstsplit(encArg(x_1), encArg(x_2))
   encode_0 -> 0
   encode_nil -> nil
   encode_s(x_1) -> s(encArg(x_1))
   encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2))
   encode_sndsplit(x_1, x_2) -> sndsplit(encArg(x_1), encArg(x_2))
   encode_empty(x_1) -> empty(encArg(x_1))
   encode_true -> true
   encode_false -> false
   encode_leq(x_1, x_2) -> leq(encArg(x_1), encArg(x_2))
   encode_length(x_1) -> length(encArg(x_1))
   encode_app(x_1, x_2) -> app(encArg(x_1), encArg(x_2))
   encode_map_f(x_1, x_2) -> map_f(encArg(x_1), encArg(x_2))
   encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2))
   encode_process(x_1, x_2) -> process(encArg(x_1), encArg(x_2))
   encode_if1(x_1, x_2, x_3) -> if1(encArg(x_1), encArg(x_2), encArg(x_3))
   encode_if2(x_1, x_2, x_3) -> if2(encArg(x_1), encArg(x_2), encArg(x_3))
   encode_if3(x_1, x_2, x_3) -> if3(encArg(x_1), encArg(x_2), encArg(x_3))
   encode_self -> self


----------------------------------------

(2)
Obligation:
The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF).


The TRS R consists of the following rules:

   fstsplit(0, x) -> nil
   fstsplit(s(n), nil) -> nil
   fstsplit(s(n), cons(h, t)) -> cons(h, fstsplit(n, t))
   sndsplit(0, x) -> x
   sndsplit(s(n), nil) -> nil
   sndsplit(s(n), cons(h, t)) -> sndsplit(n, t)
   empty(nil) -> true
   empty(cons(h, t)) -> false
   leq(0, m) -> true
   leq(s(n), 0) -> false
   leq(s(n), s(m)) -> leq(n, m)
   length(nil) -> 0
   length(cons(h, t)) -> s(length(t))
   app(nil, x) -> x
   app(cons(h, t), x) -> cons(h, app(t, x))
   map_f(pid, nil) -> nil
   map_f(pid, cons(h, t)) -> app(f(pid, h), map_f(pid, t))
   process(store, m) -> if1(store, m, leq(m, length(store)))
   if1(store, m, true) -> if2(store, m, empty(fstsplit(m, store)))
   if1(store, m, false) -> if3(store, m, empty(fstsplit(m, app(map_f(self, nil), store))))
   if2(store, m, false) -> process(app(map_f(self, nil), sndsplit(m, store)), m)
   if3(store, m, false) -> process(sndsplit(m, app(map_f(self, nil), store)), m)

The (relative) TRS S consists of the following rules:

   encArg(0) -> 0
   encArg(nil) -> nil
   encArg(s(x_1)) -> s(encArg(x_1))
   encArg(cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2))
   encArg(true) -> true
   encArg(false) -> false
   encArg(f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2))
   encArg(self) -> self
   encArg(cons_fstsplit(x_1, x_2)) -> fstsplit(encArg(x_1), encArg(x_2))
   encArg(cons_sndsplit(x_1, x_2)) -> sndsplit(encArg(x_1), encArg(x_2))
   encArg(cons_empty(x_1)) -> empty(encArg(x_1))
   encArg(cons_leq(x_1, x_2)) -> leq(encArg(x_1), encArg(x_2))
   encArg(cons_length(x_1)) -> length(encArg(x_1))
   encArg(cons_app(x_1, x_2)) -> app(encArg(x_1), encArg(x_2))
   encArg(cons_map_f(x_1, x_2)) -> map_f(encArg(x_1), encArg(x_2))
   encArg(cons_process(x_1, x_2)) -> process(encArg(x_1), encArg(x_2))
   encArg(cons_if1(x_1, x_2, x_3)) -> if1(encArg(x_1), encArg(x_2), encArg(x_3))
   encArg(cons_if2(x_1, x_2, x_3)) -> if2(encArg(x_1), encArg(x_2), encArg(x_3))
   encArg(cons_if3(x_1, x_2, x_3)) -> if3(encArg(x_1), encArg(x_2), encArg(x_3))
   encode_fstsplit(x_1, x_2) -> fstsplit(encArg(x_1), encArg(x_2))
   encode_0 -> 0
   encode_nil -> nil
   encode_s(x_1) -> s(encArg(x_1))
   encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2))
   encode_sndsplit(x_1, x_2) -> sndsplit(encArg(x_1), encArg(x_2))
   encode_empty(x_1) -> empty(encArg(x_1))
   encode_true -> true
   encode_false -> false
   encode_leq(x_1, x_2) -> leq(encArg(x_1), encArg(x_2))
   encode_length(x_1) -> length(encArg(x_1))
   encode_app(x_1, x_2) -> app(encArg(x_1), encArg(x_2))
   encode_map_f(x_1, x_2) -> map_f(encArg(x_1), encArg(x_2))
   encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2))
   encode_process(x_1, x_2) -> process(encArg(x_1), encArg(x_2))
   encode_if1(x_1, x_2, x_3) -> if1(encArg(x_1), encArg(x_2), encArg(x_3))
   encode_if2(x_1, x_2, x_3) -> if2(encArg(x_1), encArg(x_2), encArg(x_3))
   encode_if3(x_1, x_2, x_3) -> if3(encArg(x_1), encArg(x_2), encArg(x_3))
   encode_self -> self

Rewrite Strategy: INNERMOST
----------------------------------------

(3) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID))
proved innermost termination of relative rules
----------------------------------------

(4)
Obligation:
The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF).


The TRS R consists of the following rules:

   fstsplit(0, x) -> nil
   fstsplit(s(n), nil) -> nil
   fstsplit(s(n), cons(h, t)) -> cons(h, fstsplit(n, t))
   sndsplit(0, x) -> x
   sndsplit(s(n), nil) -> nil
   sndsplit(s(n), cons(h, t)) -> sndsplit(n, t)
   empty(nil) -> true
   empty(cons(h, t)) -> false
   leq(0, m) -> true
   leq(s(n), 0) -> false
   leq(s(n), s(m)) -> leq(n, m)
   length(nil) -> 0
   length(cons(h, t)) -> s(length(t))
   app(nil, x) -> x
   app(cons(h, t), x) -> cons(h, app(t, x))
   map_f(pid, nil) -> nil
   map_f(pid, cons(h, t)) -> app(f(pid, h), map_f(pid, t))
   process(store, m) -> if1(store, m, leq(m, length(store)))
   if1(store, m, true) -> if2(store, m, empty(fstsplit(m, store)))
   if1(store, m, false) -> if3(store, m, empty(fstsplit(m, app(map_f(self, nil), store))))
   if2(store, m, false) -> process(app(map_f(self, nil), sndsplit(m, store)), m)
   if3(store, m, false) -> process(sndsplit(m, app(map_f(self, nil), store)), m)

The (relative) TRS S consists of the following rules:

   encArg(0) -> 0
   encArg(nil) -> nil
   encArg(s(x_1)) -> s(encArg(x_1))
   encArg(cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2))
   encArg(true) -> true
   encArg(false) -> false
   encArg(f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2))
   encArg(self) -> self
   encArg(cons_fstsplit(x_1, x_2)) -> fstsplit(encArg(x_1), encArg(x_2))
   encArg(cons_sndsplit(x_1, x_2)) -> sndsplit(encArg(x_1), encArg(x_2))
   encArg(cons_empty(x_1)) -> empty(encArg(x_1))
   encArg(cons_leq(x_1, x_2)) -> leq(encArg(x_1), encArg(x_2))
   encArg(cons_length(x_1)) -> length(encArg(x_1))
   encArg(cons_app(x_1, x_2)) -> app(encArg(x_1), encArg(x_2))
   encArg(cons_map_f(x_1, x_2)) -> map_f(encArg(x_1), encArg(x_2))
   encArg(cons_process(x_1, x_2)) -> process(encArg(x_1), encArg(x_2))
   encArg(cons_if1(x_1, x_2, x_3)) -> if1(encArg(x_1), encArg(x_2), encArg(x_3))
   encArg(cons_if2(x_1, x_2, x_3)) -> if2(encArg(x_1), encArg(x_2), encArg(x_3))
   encArg(cons_if3(x_1, x_2, x_3)) -> if3(encArg(x_1), encArg(x_2), encArg(x_3))
   encode_fstsplit(x_1, x_2) -> fstsplit(encArg(x_1), encArg(x_2))
   encode_0 -> 0
   encode_nil -> nil
   encode_s(x_1) -> s(encArg(x_1))
   encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2))
   encode_sndsplit(x_1, x_2) -> sndsplit(encArg(x_1), encArg(x_2))
   encode_empty(x_1) -> empty(encArg(x_1))
   encode_true -> true
   encode_false -> false
   encode_leq(x_1, x_2) -> leq(encArg(x_1), encArg(x_2))
   encode_length(x_1) -> length(encArg(x_1))
   encode_app(x_1, x_2) -> app(encArg(x_1), encArg(x_2))
   encode_map_f(x_1, x_2) -> map_f(encArg(x_1), encArg(x_2))
   encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2))
   encode_process(x_1, x_2) -> process(encArg(x_1), encArg(x_2))
   encode_if1(x_1, x_2, x_3) -> if1(encArg(x_1), encArg(x_2), encArg(x_3))
   encode_if2(x_1, x_2, x_3) -> if2(encArg(x_1), encArg(x_2), encArg(x_3))
   encode_if3(x_1, x_2, x_3) -> if3(encArg(x_1), encArg(x_2), encArg(x_3))
   encode_self -> self

Rewrite Strategy: INNERMOST
----------------------------------------

(5) RenamingProof (BOTH BOUNDS(ID, ID))
Renamed function symbols to avoid clashes with predefined symbol.
----------------------------------------

(6)
Obligation:
The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF).


The TRS R consists of the following rules:

   fstsplit(0', x) -> nil
   fstsplit(s(n), nil) -> nil
   fstsplit(s(n), cons(h, t)) -> cons(h, fstsplit(n, t))
   sndsplit(0', x) -> x
   sndsplit(s(n), nil) -> nil
   sndsplit(s(n), cons(h, t)) -> sndsplit(n, t)
   empty(nil) -> true
   empty(cons(h, t)) -> false
   leq(0', m) -> true
   leq(s(n), 0') -> false
   leq(s(n), s(m)) -> leq(n, m)
   length(nil) -> 0'
   length(cons(h, t)) -> s(length(t))
   app(nil, x) -> x
   app(cons(h, t), x) -> cons(h, app(t, x))
   map_f(pid, nil) -> nil
   map_f(pid, cons(h, t)) -> app(f(pid, h), map_f(pid, t))
   process(store, m) -> if1(store, m, leq(m, length(store)))
   if1(store, m, true) -> if2(store, m, empty(fstsplit(m, store)))
   if1(store, m, false) -> if3(store, m, empty(fstsplit(m, app(map_f(self, nil), store))))
   if2(store, m, false) -> process(app(map_f(self, nil), sndsplit(m, store)), m)
   if3(store, m, false) -> process(sndsplit(m, app(map_f(self, nil), store)), m)

The (relative) TRS S consists of the following rules:

   encArg(0') -> 0'
   encArg(nil) -> nil
   encArg(s(x_1)) -> s(encArg(x_1))
   encArg(cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2))
   encArg(true) -> true
   encArg(false) -> false
   encArg(f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2))
   encArg(self) -> self
   encArg(cons_fstsplit(x_1, x_2)) -> fstsplit(encArg(x_1), encArg(x_2))
   encArg(cons_sndsplit(x_1, x_2)) -> sndsplit(encArg(x_1), encArg(x_2))
   encArg(cons_empty(x_1)) -> empty(encArg(x_1))
   encArg(cons_leq(x_1, x_2)) -> leq(encArg(x_1), encArg(x_2))
   encArg(cons_length(x_1)) -> length(encArg(x_1))
   encArg(cons_app(x_1, x_2)) -> app(encArg(x_1), encArg(x_2))
   encArg(cons_map_f(x_1, x_2)) -> map_f(encArg(x_1), encArg(x_2))
   encArg(cons_process(x_1, x_2)) -> process(encArg(x_1), encArg(x_2))
   encArg(cons_if1(x_1, x_2, x_3)) -> if1(encArg(x_1), encArg(x_2), encArg(x_3))
   encArg(cons_if2(x_1, x_2, x_3)) -> if2(encArg(x_1), encArg(x_2), encArg(x_3))
   encArg(cons_if3(x_1, x_2, x_3)) -> if3(encArg(x_1), encArg(x_2), encArg(x_3))
   encode_fstsplit(x_1, x_2) -> fstsplit(encArg(x_1), encArg(x_2))
   encode_0 -> 0'
   encode_nil -> nil
   encode_s(x_1) -> s(encArg(x_1))
   encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2))
   encode_sndsplit(x_1, x_2) -> sndsplit(encArg(x_1), encArg(x_2))
   encode_empty(x_1) -> empty(encArg(x_1))
   encode_true -> true
   encode_false -> false
   encode_leq(x_1, x_2) -> leq(encArg(x_1), encArg(x_2))
   encode_length(x_1) -> length(encArg(x_1))
   encode_app(x_1, x_2) -> app(encArg(x_1), encArg(x_2))
   encode_map_f(x_1, x_2) -> map_f(encArg(x_1), encArg(x_2))
   encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2))
   encode_process(x_1, x_2) -> process(encArg(x_1), encArg(x_2))
   encode_if1(x_1, x_2, x_3) -> if1(encArg(x_1), encArg(x_2), encArg(x_3))
   encode_if2(x_1, x_2, x_3) -> if2(encArg(x_1), encArg(x_2), encArg(x_3))
   encode_if3(x_1, x_2, x_3) -> if3(encArg(x_1), encArg(x_2), encArg(x_3))
   encode_self -> self

Rewrite Strategy: INNERMOST
----------------------------------------

(7) TypeInferenceProof (BOTH BOUNDS(ID, ID))
Infered types.
----------------------------------------

(8)
Obligation:
Innermost TRS:
Rules:
fstsplit(0', x) -> nil
fstsplit(s(n), nil) -> nil
fstsplit(s(n), cons(h, t)) -> cons(h, fstsplit(n, t))
sndsplit(0', x) -> x
sndsplit(s(n), nil) -> nil
sndsplit(s(n), cons(h, t)) -> sndsplit(n, t)
empty(nil) -> true
empty(cons(h, t)) -> false
leq(0', m) -> true
leq(s(n), 0') -> false
leq(s(n), s(m)) -> leq(n, m)
length(nil) -> 0'
length(cons(h, t)) -> s(length(t))
app(nil, x) -> x
app(cons(h, t), x) -> cons(h, app(t, x))
map_f(pid, nil) -> nil
map_f(pid, cons(h, t)) -> app(f(pid, h), map_f(pid, t))
process(store, m) -> if1(store, m, leq(m, length(store)))
if1(store, m, true) -> if2(store, m, empty(fstsplit(m, store)))
if1(store, m, false) -> if3(store, m, empty(fstsplit(m, app(map_f(self, nil), store))))
if2(store, m, false) -> process(app(map_f(self, nil), sndsplit(m, store)), m)
if3(store, m, false) -> process(sndsplit(m, app(map_f(self, nil), store)), m)
encArg(0') -> 0'
encArg(nil) -> nil
encArg(s(x_1)) -> s(encArg(x_1))
encArg(cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2))
encArg(true) -> true
encArg(false) -> false
encArg(f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2))
encArg(self) -> self
encArg(cons_fstsplit(x_1, x_2)) -> fstsplit(encArg(x_1), encArg(x_2))
encArg(cons_sndsplit(x_1, x_2)) -> sndsplit(encArg(x_1), encArg(x_2))
encArg(cons_empty(x_1)) -> empty(encArg(x_1))
encArg(cons_leq(x_1, x_2)) -> leq(encArg(x_1), encArg(x_2))
encArg(cons_length(x_1)) -> length(encArg(x_1))
encArg(cons_app(x_1, x_2)) -> app(encArg(x_1), encArg(x_2))
encArg(cons_map_f(x_1, x_2)) -> map_f(encArg(x_1), encArg(x_2))
encArg(cons_process(x_1, x_2)) -> process(encArg(x_1), encArg(x_2))
encArg(cons_if1(x_1, x_2, x_3)) -> if1(encArg(x_1), encArg(x_2), encArg(x_3))
encArg(cons_if2(x_1, x_2, x_3)) -> if2(encArg(x_1), encArg(x_2), encArg(x_3))
encArg(cons_if3(x_1, x_2, x_3)) -> if3(encArg(x_1), encArg(x_2), encArg(x_3))
encode_fstsplit(x_1, x_2) -> fstsplit(encArg(x_1), encArg(x_2))
encode_0 -> 0'
encode_nil -> nil
encode_s(x_1) -> s(encArg(x_1))
encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2))
encode_sndsplit(x_1, x_2) -> sndsplit(encArg(x_1), encArg(x_2))
encode_empty(x_1) -> empty(encArg(x_1))
encode_true -> true
encode_false -> false
encode_leq(x_1, x_2) -> leq(encArg(x_1), encArg(x_2))
encode_length(x_1) -> length(encArg(x_1))
encode_app(x_1, x_2) -> app(encArg(x_1), encArg(x_2))
encode_map_f(x_1, x_2) -> map_f(encArg(x_1), encArg(x_2))
encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2))
encode_process(x_1, x_2) -> process(encArg(x_1), encArg(x_2))
encode_if1(x_1, x_2, x_3) -> if1(encArg(x_1), encArg(x_2), encArg(x_3))
encode_if2(x_1, x_2, x_3) -> if2(encArg(x_1), encArg(x_2), encArg(x_3))
encode_if3(x_1, x_2, x_3) -> if3(encArg(x_1), encArg(x_2), encArg(x_3))
encode_self -> self

Types:
fstsplit :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
0' :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
nil :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
s :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
cons :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
sndsplit :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
empty :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
true :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
false :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
leq :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
length :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
app :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
map_f :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
f :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
process :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
if1 :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
if2 :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
if3 :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
self :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encArg :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
cons_fstsplit :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
cons_sndsplit :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
cons_empty :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
cons_leq :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
cons_length :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
cons_app :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
cons_map_f :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
cons_process :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
cons_if1 :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
cons_if2 :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
cons_if3 :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_fstsplit :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_0 :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_nil :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_s :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_cons :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_sndsplit :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_empty :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_true :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_false :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_leq :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_length :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_app :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_map_f :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_f :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_process :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_if1 :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_if2 :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_if3 :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_self :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
hole_0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if31_4 :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
gen_0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if32_4 :: Nat -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3

----------------------------------------

(9) OrderProof (LOWER BOUND(ID))
Heuristically decided to analyse the following defined symbols:
fstsplit, sndsplit, leq, length, app, map_f, process, if1, if2, if3, encArg

They will be analysed ascendingly in the following order:
fstsplit < if1
fstsplit < encArg
sndsplit < if2
sndsplit < if3
sndsplit < encArg
leq < process
leq < encArg
length < process
length < encArg
app < map_f
app < if1
app < if2
app < if3
app < encArg
map_f < if1
map_f < if2
map_f < if3
map_f < encArg
process = if1
process = if2
process = if3
process < encArg
if1 = if2
if1 = if3
if1 < encArg
if2 = if3
if2 < encArg
if3 < encArg

----------------------------------------

(10)
Obligation:
Innermost TRS:
Rules:
fstsplit(0', x) -> nil
fstsplit(s(n), nil) -> nil
fstsplit(s(n), cons(h, t)) -> cons(h, fstsplit(n, t))
sndsplit(0', x) -> x
sndsplit(s(n), nil) -> nil
sndsplit(s(n), cons(h, t)) -> sndsplit(n, t)
empty(nil) -> true
empty(cons(h, t)) -> false
leq(0', m) -> true
leq(s(n), 0') -> false
leq(s(n), s(m)) -> leq(n, m)
length(nil) -> 0'
length(cons(h, t)) -> s(length(t))
app(nil, x) -> x
app(cons(h, t), x) -> cons(h, app(t, x))
map_f(pid, nil) -> nil
map_f(pid, cons(h, t)) -> app(f(pid, h), map_f(pid, t))
process(store, m) -> if1(store, m, leq(m, length(store)))
if1(store, m, true) -> if2(store, m, empty(fstsplit(m, store)))
if1(store, m, false) -> if3(store, m, empty(fstsplit(m, app(map_f(self, nil), store))))
if2(store, m, false) -> process(app(map_f(self, nil), sndsplit(m, store)), m)
if3(store, m, false) -> process(sndsplit(m, app(map_f(self, nil), store)), m)
encArg(0') -> 0'
encArg(nil) -> nil
encArg(s(x_1)) -> s(encArg(x_1))
encArg(cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2))
encArg(true) -> true
encArg(false) -> false
encArg(f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2))
encArg(self) -> self
encArg(cons_fstsplit(x_1, x_2)) -> fstsplit(encArg(x_1), encArg(x_2))
encArg(cons_sndsplit(x_1, x_2)) -> sndsplit(encArg(x_1), encArg(x_2))
encArg(cons_empty(x_1)) -> empty(encArg(x_1))
encArg(cons_leq(x_1, x_2)) -> leq(encArg(x_1), encArg(x_2))
encArg(cons_length(x_1)) -> length(encArg(x_1))
encArg(cons_app(x_1, x_2)) -> app(encArg(x_1), encArg(x_2))
encArg(cons_map_f(x_1, x_2)) -> map_f(encArg(x_1), encArg(x_2))
encArg(cons_process(x_1, x_2)) -> process(encArg(x_1), encArg(x_2))
encArg(cons_if1(x_1, x_2, x_3)) -> if1(encArg(x_1), encArg(x_2), encArg(x_3))
encArg(cons_if2(x_1, x_2, x_3)) -> if2(encArg(x_1), encArg(x_2), encArg(x_3))
encArg(cons_if3(x_1, x_2, x_3)) -> if3(encArg(x_1), encArg(x_2), encArg(x_3))
encode_fstsplit(x_1, x_2) -> fstsplit(encArg(x_1), encArg(x_2))
encode_0 -> 0'
encode_nil -> nil
encode_s(x_1) -> s(encArg(x_1))
encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2))
encode_sndsplit(x_1, x_2) -> sndsplit(encArg(x_1), encArg(x_2))
encode_empty(x_1) -> empty(encArg(x_1))
encode_true -> true
encode_false -> false
encode_leq(x_1, x_2) -> leq(encArg(x_1), encArg(x_2))
encode_length(x_1) -> length(encArg(x_1))
encode_app(x_1, x_2) -> app(encArg(x_1), encArg(x_2))
encode_map_f(x_1, x_2) -> map_f(encArg(x_1), encArg(x_2))
encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2))
encode_process(x_1, x_2) -> process(encArg(x_1), encArg(x_2))
encode_if1(x_1, x_2, x_3) -> if1(encArg(x_1), encArg(x_2), encArg(x_3))
encode_if2(x_1, x_2, x_3) -> if2(encArg(x_1), encArg(x_2), encArg(x_3))
encode_if3(x_1, x_2, x_3) -> if3(encArg(x_1), encArg(x_2), encArg(x_3))
encode_self -> self

Types:
fstsplit :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
0' :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
nil :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
s :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
cons :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
sndsplit :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
empty :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
true :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
false :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
leq :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
length :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
app :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
map_f :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
f :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
process :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
if1 :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
if2 :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
if3 :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
self :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encArg :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
cons_fstsplit :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
cons_sndsplit :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
cons_empty :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
cons_leq :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
cons_length :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
cons_app :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
cons_map_f :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
cons_process :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
cons_if1 :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
cons_if2 :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
cons_if3 :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_fstsplit :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_0 :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_nil :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_s :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_cons :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_sndsplit :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_empty :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_true :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_false :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_leq :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_length :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_app :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_map_f :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_f :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_process :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_if1 :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_if2 :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_if3 :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_self :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
hole_0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if31_4 :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
gen_0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if32_4 :: Nat -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3


Generator Equations:
gen_0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if32_4(0) <=> 0'
gen_0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if32_4(+(x, 1)) <=> s(gen_0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if32_4(x))


The following defined symbols remain to be analysed:
fstsplit, sndsplit, leq, length, app, map_f, process, if1, if2, if3, encArg

They will be analysed ascendingly in the following order:
fstsplit < if1
fstsplit < encArg
sndsplit < if2
sndsplit < if3
sndsplit < encArg
leq < process
leq < encArg
length < process
length < encArg
app < map_f
app < if1
app < if2
app < if3
app < encArg
map_f < if1
map_f < if2
map_f < if3
map_f < encArg
process = if1
process = if2
process = if3
process < encArg
if1 = if2
if1 = if3
if1 < encArg
if2 = if3
if2 < encArg
if3 < encArg

----------------------------------------

(11) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
leq(gen_0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if32_4(n54_4), gen_0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if32_4(n54_4)) -> true, rt in Omega(1 + n54_4)

Induction Base:
leq(gen_0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if32_4(0), gen_0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if32_4(0)) ->_R^Omega(1)
true

Induction Step:
leq(gen_0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if32_4(+(n54_4, 1)), gen_0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if32_4(+(n54_4, 1))) ->_R^Omega(1)
leq(gen_0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if32_4(n54_4), gen_0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if32_4(n54_4)) ->_IH
true

We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n).
----------------------------------------

(12)
Complex Obligation (BEST)

----------------------------------------

(13)
Obligation:
Proved the lower bound n^1 for the following obligation:

Innermost TRS:
Rules:
fstsplit(0', x) -> nil
fstsplit(s(n), nil) -> nil
fstsplit(s(n), cons(h, t)) -> cons(h, fstsplit(n, t))
sndsplit(0', x) -> x
sndsplit(s(n), nil) -> nil
sndsplit(s(n), cons(h, t)) -> sndsplit(n, t)
empty(nil) -> true
empty(cons(h, t)) -> false
leq(0', m) -> true
leq(s(n), 0') -> false
leq(s(n), s(m)) -> leq(n, m)
length(nil) -> 0'
length(cons(h, t)) -> s(length(t))
app(nil, x) -> x
app(cons(h, t), x) -> cons(h, app(t, x))
map_f(pid, nil) -> nil
map_f(pid, cons(h, t)) -> app(f(pid, h), map_f(pid, t))
process(store, m) -> if1(store, m, leq(m, length(store)))
if1(store, m, true) -> if2(store, m, empty(fstsplit(m, store)))
if1(store, m, false) -> if3(store, m, empty(fstsplit(m, app(map_f(self, nil), store))))
if2(store, m, false) -> process(app(map_f(self, nil), sndsplit(m, store)), m)
if3(store, m, false) -> process(sndsplit(m, app(map_f(self, nil), store)), m)
encArg(0') -> 0'
encArg(nil) -> nil
encArg(s(x_1)) -> s(encArg(x_1))
encArg(cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2))
encArg(true) -> true
encArg(false) -> false
encArg(f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2))
encArg(self) -> self
encArg(cons_fstsplit(x_1, x_2)) -> fstsplit(encArg(x_1), encArg(x_2))
encArg(cons_sndsplit(x_1, x_2)) -> sndsplit(encArg(x_1), encArg(x_2))
encArg(cons_empty(x_1)) -> empty(encArg(x_1))
encArg(cons_leq(x_1, x_2)) -> leq(encArg(x_1), encArg(x_2))
encArg(cons_length(x_1)) -> length(encArg(x_1))
encArg(cons_app(x_1, x_2)) -> app(encArg(x_1), encArg(x_2))
encArg(cons_map_f(x_1, x_2)) -> map_f(encArg(x_1), encArg(x_2))
encArg(cons_process(x_1, x_2)) -> process(encArg(x_1), encArg(x_2))
encArg(cons_if1(x_1, x_2, x_3)) -> if1(encArg(x_1), encArg(x_2), encArg(x_3))
encArg(cons_if2(x_1, x_2, x_3)) -> if2(encArg(x_1), encArg(x_2), encArg(x_3))
encArg(cons_if3(x_1, x_2, x_3)) -> if3(encArg(x_1), encArg(x_2), encArg(x_3))
encode_fstsplit(x_1, x_2) -> fstsplit(encArg(x_1), encArg(x_2))
encode_0 -> 0'
encode_nil -> nil
encode_s(x_1) -> s(encArg(x_1))
encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2))
encode_sndsplit(x_1, x_2) -> sndsplit(encArg(x_1), encArg(x_2))
encode_empty(x_1) -> empty(encArg(x_1))
encode_true -> true
encode_false -> false
encode_leq(x_1, x_2) -> leq(encArg(x_1), encArg(x_2))
encode_length(x_1) -> length(encArg(x_1))
encode_app(x_1, x_2) -> app(encArg(x_1), encArg(x_2))
encode_map_f(x_1, x_2) -> map_f(encArg(x_1), encArg(x_2))
encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2))
encode_process(x_1, x_2) -> process(encArg(x_1), encArg(x_2))
encode_if1(x_1, x_2, x_3) -> if1(encArg(x_1), encArg(x_2), encArg(x_3))
encode_if2(x_1, x_2, x_3) -> if2(encArg(x_1), encArg(x_2), encArg(x_3))
encode_if3(x_1, x_2, x_3) -> if3(encArg(x_1), encArg(x_2), encArg(x_3))
encode_self -> self

Types:
fstsplit :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
0' :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
nil :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
s :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
cons :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
sndsplit :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
empty :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
true :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
false :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
leq :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
length :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
app :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
map_f :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
f :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
process :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
if1 :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
if2 :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
if3 :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
self :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encArg :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
cons_fstsplit :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
cons_sndsplit :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
cons_empty :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
cons_leq :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
cons_length :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
cons_app :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
cons_map_f :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
cons_process :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
cons_if1 :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
cons_if2 :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
cons_if3 :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_fstsplit :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_0 :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_nil :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_s :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_cons :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_sndsplit :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_empty :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_true :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_false :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_leq :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_length :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_app :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_map_f :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_f :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_process :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_if1 :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_if2 :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_if3 :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_self :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
hole_0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if31_4 :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
gen_0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if32_4 :: Nat -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3


Generator Equations:
gen_0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if32_4(0) <=> 0'
gen_0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if32_4(+(x, 1)) <=> s(gen_0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if32_4(x))


The following defined symbols remain to be analysed:
leq, length, app, map_f, process, if1, if2, if3, encArg

They will be analysed ascendingly in the following order:
leq < process
leq < encArg
length < process
length < encArg
app < map_f
app < if1
app < if2
app < if3
app < encArg
map_f < if1
map_f < if2
map_f < if3
map_f < encArg
process = if1
process = if2
process = if3
process < encArg
if1 = if2
if1 = if3
if1 < encArg
if2 = if3
if2 < encArg
if3 < encArg

----------------------------------------

(14) LowerBoundPropagationProof (FINISHED)
Propagated lower bound.
----------------------------------------

(15)
BOUNDS(n^1, INF)

----------------------------------------

(16)
Obligation:
Innermost TRS:
Rules:
fstsplit(0', x) -> nil
fstsplit(s(n), nil) -> nil
fstsplit(s(n), cons(h, t)) -> cons(h, fstsplit(n, t))
sndsplit(0', x) -> x
sndsplit(s(n), nil) -> nil
sndsplit(s(n), cons(h, t)) -> sndsplit(n, t)
empty(nil) -> true
empty(cons(h, t)) -> false
leq(0', m) -> true
leq(s(n), 0') -> false
leq(s(n), s(m)) -> leq(n, m)
length(nil) -> 0'
length(cons(h, t)) -> s(length(t))
app(nil, x) -> x
app(cons(h, t), x) -> cons(h, app(t, x))
map_f(pid, nil) -> nil
map_f(pid, cons(h, t)) -> app(f(pid, h), map_f(pid, t))
process(store, m) -> if1(store, m, leq(m, length(store)))
if1(store, m, true) -> if2(store, m, empty(fstsplit(m, store)))
if1(store, m, false) -> if3(store, m, empty(fstsplit(m, app(map_f(self, nil), store))))
if2(store, m, false) -> process(app(map_f(self, nil), sndsplit(m, store)), m)
if3(store, m, false) -> process(sndsplit(m, app(map_f(self, nil), store)), m)
encArg(0') -> 0'
encArg(nil) -> nil
encArg(s(x_1)) -> s(encArg(x_1))
encArg(cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2))
encArg(true) -> true
encArg(false) -> false
encArg(f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2))
encArg(self) -> self
encArg(cons_fstsplit(x_1, x_2)) -> fstsplit(encArg(x_1), encArg(x_2))
encArg(cons_sndsplit(x_1, x_2)) -> sndsplit(encArg(x_1), encArg(x_2))
encArg(cons_empty(x_1)) -> empty(encArg(x_1))
encArg(cons_leq(x_1, x_2)) -> leq(encArg(x_1), encArg(x_2))
encArg(cons_length(x_1)) -> length(encArg(x_1))
encArg(cons_app(x_1, x_2)) -> app(encArg(x_1), encArg(x_2))
encArg(cons_map_f(x_1, x_2)) -> map_f(encArg(x_1), encArg(x_2))
encArg(cons_process(x_1, x_2)) -> process(encArg(x_1), encArg(x_2))
encArg(cons_if1(x_1, x_2, x_3)) -> if1(encArg(x_1), encArg(x_2), encArg(x_3))
encArg(cons_if2(x_1, x_2, x_3)) -> if2(encArg(x_1), encArg(x_2), encArg(x_3))
encArg(cons_if3(x_1, x_2, x_3)) -> if3(encArg(x_1), encArg(x_2), encArg(x_3))
encode_fstsplit(x_1, x_2) -> fstsplit(encArg(x_1), encArg(x_2))
encode_0 -> 0'
encode_nil -> nil
encode_s(x_1) -> s(encArg(x_1))
encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2))
encode_sndsplit(x_1, x_2) -> sndsplit(encArg(x_1), encArg(x_2))
encode_empty(x_1) -> empty(encArg(x_1))
encode_true -> true
encode_false -> false
encode_leq(x_1, x_2) -> leq(encArg(x_1), encArg(x_2))
encode_length(x_1) -> length(encArg(x_1))
encode_app(x_1, x_2) -> app(encArg(x_1), encArg(x_2))
encode_map_f(x_1, x_2) -> map_f(encArg(x_1), encArg(x_2))
encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2))
encode_process(x_1, x_2) -> process(encArg(x_1), encArg(x_2))
encode_if1(x_1, x_2, x_3) -> if1(encArg(x_1), encArg(x_2), encArg(x_3))
encode_if2(x_1, x_2, x_3) -> if2(encArg(x_1), encArg(x_2), encArg(x_3))
encode_if3(x_1, x_2, x_3) -> if3(encArg(x_1), encArg(x_2), encArg(x_3))
encode_self -> self

Types:
fstsplit :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
0' :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
nil :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
s :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
cons :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
sndsplit :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
empty :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
true :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
false :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
leq :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
length :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
app :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
map_f :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
f :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
process :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
if1 :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
if2 :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
if3 :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
self :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encArg :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
cons_fstsplit :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
cons_sndsplit :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
cons_empty :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
cons_leq :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
cons_length :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
cons_app :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
cons_map_f :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
cons_process :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
cons_if1 :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
cons_if2 :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
cons_if3 :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_fstsplit :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_0 :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_nil :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_s :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_cons :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_sndsplit :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_empty :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_true :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_false :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_leq :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_length :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_app :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_map_f :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_f :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_process :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_if1 :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_if2 :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_if3 :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3 -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
encode_self :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
hole_0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if31_4 :: 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3
gen_0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if32_4 :: Nat -> 0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if3


Lemmas:
leq(gen_0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if32_4(n54_4), gen_0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if32_4(n54_4)) -> true, rt in Omega(1 + n54_4)


Generator Equations:
gen_0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if32_4(0) <=> 0'
gen_0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if32_4(+(x, 1)) <=> s(gen_0':nil:s:cons:true:false:f:self:cons_fstsplit:cons_sndsplit:cons_empty:cons_leq:cons_length:cons_app:cons_map_f:cons_process:cons_if1:cons_if2:cons_if32_4(x))


The following defined symbols remain to be analysed:
length, app, map_f, process, if1, if2, if3, encArg

They will be analysed ascendingly in the following order:
length < process
length < encArg
app < map_f
app < if1
app < if2
app < if3
app < encArg
map_f < if1
map_f < if2
map_f < if3
map_f < encArg
process = if1
process = if2
process = if3
process < encArg
if1 = if2
if1 = if3
if1 < encArg
if2 = if3
if2 < encArg
if3 < encArg