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


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


WORST_CASE(?, O(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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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(1, n^1).

(0) DCpxTrs
(1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms]
(2) CpxRelTRS
(3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 239 ms]
(4) CpxRelTRS
(5) NonCtorToCtorProof [UPPER BOUND(ID), 0 ms]
(6) CpxRelTRS
(7) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
(8) CpxWeightedTrs
(9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
(10) CpxTypedWeightedTrs
(11) CompletionProof [UPPER BOUND(ID), 0 ms]
(12) CpxTypedWeightedCompleteTrs
(13) NarrowingProof [BOTH BOUNDS(ID, ID), 321 ms]
(14) CpxTypedWeightedCompleteTrs
(15) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
(16) CpxRNTS
(17) InliningProof [UPPER BOUND(ID), 1473 ms]
(18) CpxRNTS
(19) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
(20) CpxRNTS
(21) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms]
(22) CpxRNTS
(23) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(24) CpxRNTS
(25) IntTrsBoundProof [UPPER BOUND(ID), 2191 ms]
(26) CpxRNTS
(27) IntTrsBoundProof [UPPER BOUND(ID), 1038 ms]
(28) CpxRNTS
(29) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(30) CpxRNTS
(31) IntTrsBoundProof [UPPER BOUND(ID), 107 ms]
(32) CpxRNTS
(33) IntTrsBoundProof [UPPER BOUND(ID), 32 ms]
(34) CpxRNTS
(35) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(36) CpxRNTS
(37) IntTrsBoundProof [UPPER BOUND(ID), 143 ms]
(38) CpxRNTS
(39) IntTrsBoundProof [UPPER BOUND(ID), 52 ms]
(40) CpxRNTS
(41) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(42) CpxRNTS
(43) IntTrsBoundProof [UPPER BOUND(ID), 53 ms]
(44) CpxRNTS
(45) IntTrsBoundProof [UPPER BOUND(ID), 1 ms]
(46) CpxRNTS
(47) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(48) CpxRNTS
(49) IntTrsBoundProof [UPPER BOUND(ID), 7 ms]
(50) CpxRNTS
(51) IntTrsBoundProof [UPPER BOUND(ID), 22 ms]
(52) CpxRNTS
(53) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(54) CpxRNTS
(55) IntTrsBoundProof [UPPER BOUND(ID), 116 ms]
(56) CpxRNTS
(57) IntTrsBoundProof [UPPER BOUND(ID), 1 ms]
(58) CpxRNTS
(59) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(60) CpxRNTS
(61) IntTrsBoundProof [UPPER BOUND(ID), 1223 ms]
(62) CpxRNTS
(63) IntTrsBoundProof [UPPER BOUND(ID), 610 ms]
(64) CpxRNTS
(65) ResultPropagationProof [UPPER BOUND(ID), 1 ms]
(66) CpxRNTS
(67) IntTrsBoundProof [UPPER BOUND(ID), 525 ms]
(68) CpxRNTS
(69) IntTrsBoundProof [UPPER BOUND(ID), 158 ms]
(70) CpxRNTS
(71) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(72) CpxRNTS
(73) IntTrsBoundProof [UPPER BOUND(ID), 526 ms]
(74) CpxRNTS
(75) IntTrsBoundProof [UPPER BOUND(ID), 138 ms]
(76) CpxRNTS
(77) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(78) CpxRNTS
(79) IntTrsBoundProof [UPPER BOUND(ID), 186 ms]
(80) CpxRNTS
(81) IntTrsBoundProof [UPPER BOUND(ID), 63 ms]
(82) CpxRNTS
(83) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(84) CpxRNTS
(85) IntTrsBoundProof [UPPER BOUND(ID), 188 ms]
(86) CpxRNTS
(87) IntTrsBoundProof [UPPER BOUND(ID), 82 ms]
(88) CpxRNTS
(89) FinalProof [FINISHED, 0 ms]
(90) BOUNDS(1, n^1)


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

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


The TRS R consists of the following rules:

   f(X, n__g(X), Y) -> f(activate(Y), activate(Y), activate(Y))
   g(b) -> c
   b -> c
   g(X) -> n__g(X)
   activate(n__g(X)) -> g(X)
   activate(X) -> X

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(n__g(x_1)) -> n__g(encArg(x_1))
   encArg(c) -> c
   encArg(cons_f(x_1, x_2, x_3)) -> f(encArg(x_1), encArg(x_2), encArg(x_3))
   encArg(cons_g(x_1)) -> g(encArg(x_1))
   encArg(cons_b) -> b
   encArg(cons_activate(x_1)) -> activate(encArg(x_1))
   encode_f(x_1, x_2, x_3) -> f(encArg(x_1), encArg(x_2), encArg(x_3))
   encode_n__g(x_1) -> n__g(encArg(x_1))
   encode_activate(x_1) -> activate(encArg(x_1))
   encode_g(x_1) -> g(encArg(x_1))
   encode_b -> b
   encode_c -> c


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

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


The TRS R consists of the following rules:

   f(X, n__g(X), Y) -> f(activate(Y), activate(Y), activate(Y))
   g(b) -> c
   b -> c
   g(X) -> n__g(X)
   activate(n__g(X)) -> g(X)
   activate(X) -> X

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

   encArg(n__g(x_1)) -> n__g(encArg(x_1))
   encArg(c) -> c
   encArg(cons_f(x_1, x_2, x_3)) -> f(encArg(x_1), encArg(x_2), encArg(x_3))
   encArg(cons_g(x_1)) -> g(encArg(x_1))
   encArg(cons_b) -> b
   encArg(cons_activate(x_1)) -> activate(encArg(x_1))
   encode_f(x_1, x_2, x_3) -> f(encArg(x_1), encArg(x_2), encArg(x_3))
   encode_n__g(x_1) -> n__g(encArg(x_1))
   encode_activate(x_1) -> activate(encArg(x_1))
   encode_g(x_1) -> g(encArg(x_1))
   encode_b -> b
   encode_c -> c

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(1, n^1).


The TRS R consists of the following rules:

   f(X, n__g(X), Y) -> f(activate(Y), activate(Y), activate(Y))
   g(b) -> c
   b -> c
   g(X) -> n__g(X)
   activate(n__g(X)) -> g(X)
   activate(X) -> X

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

   encArg(n__g(x_1)) -> n__g(encArg(x_1))
   encArg(c) -> c
   encArg(cons_f(x_1, x_2, x_3)) -> f(encArg(x_1), encArg(x_2), encArg(x_3))
   encArg(cons_g(x_1)) -> g(encArg(x_1))
   encArg(cons_b) -> b
   encArg(cons_activate(x_1)) -> activate(encArg(x_1))
   encode_f(x_1, x_2, x_3) -> f(encArg(x_1), encArg(x_2), encArg(x_3))
   encode_n__g(x_1) -> n__g(encArg(x_1))
   encode_activate(x_1) -> activate(encArg(x_1))
   encode_g(x_1) -> g(encArg(x_1))
   encode_b -> b
   encode_c -> c

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

(5) NonCtorToCtorProof (UPPER BOUND(ID))
transformed non-ctor to ctor-system
----------------------------------------

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


The TRS R consists of the following rules:

   f(X, n__g(X), Y) -> f(activate(Y), activate(Y), activate(Y))
   b -> c
   g(X) -> n__g(X)
   activate(n__g(X)) -> g(X)
   activate(X) -> X
   g(c_b) -> c

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

   encArg(n__g(x_1)) -> n__g(encArg(x_1))
   encArg(c) -> c
   encArg(cons_f(x_1, x_2, x_3)) -> f(encArg(x_1), encArg(x_2), encArg(x_3))
   encArg(cons_g(x_1)) -> g(encArg(x_1))
   encArg(cons_b) -> b
   encArg(cons_activate(x_1)) -> activate(encArg(x_1))
   encode_f(x_1, x_2, x_3) -> f(encArg(x_1), encArg(x_2), encArg(x_3))
   encode_n__g(x_1) -> n__g(encArg(x_1))
   encode_activate(x_1) -> activate(encArg(x_1))
   encode_g(x_1) -> g(encArg(x_1))
   encode_b -> b
   encode_c -> c
   b -> c_b

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

(7) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID))
Transformed relative TRS to weighted TRS
----------------------------------------

(8)
Obligation:
The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1).


The TRS R consists of the following rules:

   f(X, n__g(X), Y) -> f(activate(Y), activate(Y), activate(Y)) [1]
   b -> c [1]
   g(X) -> n__g(X) [1]
   activate(n__g(X)) -> g(X) [1]
   activate(X) -> X [1]
   g(c_b) -> c [1]
   encArg(n__g(x_1)) -> n__g(encArg(x_1)) [0]
   encArg(c) -> c [0]
   encArg(cons_f(x_1, x_2, x_3)) -> f(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encArg(cons_g(x_1)) -> g(encArg(x_1)) [0]
   encArg(cons_b) -> b [0]
   encArg(cons_activate(x_1)) -> activate(encArg(x_1)) [0]
   encode_f(x_1, x_2, x_3) -> f(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encode_n__g(x_1) -> n__g(encArg(x_1)) [0]
   encode_activate(x_1) -> activate(encArg(x_1)) [0]
   encode_g(x_1) -> g(encArg(x_1)) [0]
   encode_b -> b [0]
   encode_c -> c [0]
   b -> c_b [0]

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

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

(10)
Obligation:
Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   f(X, n__g(X), Y) -> f(activate(Y), activate(Y), activate(Y)) [1]
   b -> c [1]
   g(X) -> n__g(X) [1]
   activate(n__g(X)) -> g(X) [1]
   activate(X) -> X [1]
   g(c_b) -> c [1]
   encArg(n__g(x_1)) -> n__g(encArg(x_1)) [0]
   encArg(c) -> c [0]
   encArg(cons_f(x_1, x_2, x_3)) -> f(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encArg(cons_g(x_1)) -> g(encArg(x_1)) [0]
   encArg(cons_b) -> b [0]
   encArg(cons_activate(x_1)) -> activate(encArg(x_1)) [0]
   encode_f(x_1, x_2, x_3) -> f(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encode_n__g(x_1) -> n__g(encArg(x_1)) [0]
   encode_activate(x_1) -> activate(encArg(x_1)) [0]
   encode_g(x_1) -> g(encArg(x_1)) [0]
   encode_b -> b [0]
   encode_c -> c [0]
   b -> c_b [0]

The TRS has the following type information:
f :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate -> n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate -> n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate -> n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate
n__g :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate -> n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate
activate :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate -> n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate
b :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate
c :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate
g :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate -> n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate
c_b :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate
encArg :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate -> n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate
cons_f :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate -> n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate -> n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate -> n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate
cons_g :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate -> n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate
cons_b :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate
cons_activate :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate -> n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate
encode_f :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate -> n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate -> n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate -> n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate
encode_n__g :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate -> n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate
encode_activate :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate -> n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate
encode_g :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate -> n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate
encode_b :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate
encode_c :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate

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

(11) CompletionProof (UPPER BOUND(ID))
The transformation into a RNTS is sound, since:

(a) The obligation is a constructor system where every type has a constant constructor,

(b) The following defined symbols do not have to be completely defined, as they can never occur inside other defined symbols:
none

(c) The following functions are completely defined:

   activate_1
   f_3
   g_1
   encArg_1
   encode_f_3
   encode_n__g_1
   encode_activate_1
   encode_g_1
   encode_b
   encode_c
   b

Due to the following rules being added:

   encArg(v0) -> null_encArg [0]
   encode_f(v0, v1, v2) -> null_encode_f [0]
   encode_n__g(v0) -> null_encode_n__g [0]
   encode_activate(v0) -> null_encode_activate [0]
   encode_g(v0) -> null_encode_g [0]
   encode_b -> null_encode_b [0]
   encode_c -> null_encode_c [0]
   b -> null_b [0]
   f(v0, v1, v2) -> null_f [0]

And the following fresh constants:    null_encArg, null_encode_f, null_encode_n__g, null_encode_activate, null_encode_g, null_encode_b, null_encode_c, null_b, null_f

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

(12)
Obligation:
Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is:

Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   f(X, n__g(X), Y) -> f(activate(Y), activate(Y), activate(Y)) [1]
   b -> c [1]
   g(X) -> n__g(X) [1]
   activate(n__g(X)) -> g(X) [1]
   activate(X) -> X [1]
   g(c_b) -> c [1]
   encArg(n__g(x_1)) -> n__g(encArg(x_1)) [0]
   encArg(c) -> c [0]
   encArg(cons_f(x_1, x_2, x_3)) -> f(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encArg(cons_g(x_1)) -> g(encArg(x_1)) [0]
   encArg(cons_b) -> b [0]
   encArg(cons_activate(x_1)) -> activate(encArg(x_1)) [0]
   encode_f(x_1, x_2, x_3) -> f(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encode_n__g(x_1) -> n__g(encArg(x_1)) [0]
   encode_activate(x_1) -> activate(encArg(x_1)) [0]
   encode_g(x_1) -> g(encArg(x_1)) [0]
   encode_b -> b [0]
   encode_c -> c [0]
   b -> c_b [0]
   encArg(v0) -> null_encArg [0]
   encode_f(v0, v1, v2) -> null_encode_f [0]
   encode_n__g(v0) -> null_encode_n__g [0]
   encode_activate(v0) -> null_encode_activate [0]
   encode_g(v0) -> null_encode_g [0]
   encode_b -> null_encode_b [0]
   encode_c -> null_encode_c [0]
   b -> null_b [0]
   f(v0, v1, v2) -> null_f [0]

The TRS has the following type information:
f :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f -> n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f -> n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f -> n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f
n__g :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f -> n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f
activate :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f -> n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f
b :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f
c :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f
g :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f -> n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f
c_b :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f
encArg :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f -> n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f
cons_f :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f -> n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f -> n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f -> n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f
cons_g :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f -> n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f
cons_b :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f
cons_activate :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f -> n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f
encode_f :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f -> n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f -> n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f -> n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f
encode_n__g :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f -> n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f
encode_activate :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f -> n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f
encode_g :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f -> n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f
encode_b :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f
encode_c :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f
null_encArg :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f
null_encode_f :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f
null_encode_n__g :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f
null_encode_activate :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f
null_encode_g :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f
null_encode_b :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f
null_encode_c :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f
null_b :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f
null_f :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f

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

(13) NarrowingProof (BOTH BOUNDS(ID, ID))
Narrowed the inner basic terms of all right-hand sides by a single narrowing step.
----------------------------------------

(14)
Obligation:
Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is:

Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   f(X, n__g(X), n__g(X')) -> f(g(X'), g(X'), g(X')) [4]
   f(X, n__g(X), n__g(X')) -> f(g(X'), g(X'), n__g(X')) [4]
   f(X, n__g(X), n__g(X')) -> f(g(X'), n__g(X'), g(X')) [4]
   f(X, n__g(X), n__g(X')) -> f(g(X'), n__g(X'), n__g(X')) [4]
   f(X, n__g(X), n__g(X'')) -> f(n__g(X''), g(X''), g(X'')) [4]
   f(X, n__g(X), n__g(X'')) -> f(n__g(X''), g(X''), n__g(X'')) [4]
   f(X, n__g(X), n__g(X1)) -> f(n__g(X1), n__g(X1), g(X1)) [4]
   f(X, n__g(X), Y) -> f(Y, Y, Y) [4]
   b -> c [1]
   g(X) -> n__g(X) [1]
   activate(n__g(X)) -> g(X) [1]
   activate(X) -> X [1]
   g(c_b) -> c [1]
   encArg(n__g(x_1)) -> n__g(encArg(x_1)) [0]
   encArg(c) -> c [0]
   encArg(cons_f(x_1, x_2, x_3)) -> f(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encArg(cons_g(n__g(x_1227))) -> g(n__g(encArg(x_1227))) [0]
   encArg(cons_g(c)) -> g(c) [0]
   encArg(cons_g(cons_f(x_1228, x_256, x_356))) -> g(f(encArg(x_1228), encArg(x_256), encArg(x_356))) [0]
   encArg(cons_g(cons_g(x_1229))) -> g(g(encArg(x_1229))) [0]
   encArg(cons_g(cons_b)) -> g(b) [0]
   encArg(cons_g(cons_activate(x_1230))) -> g(activate(encArg(x_1230))) [0]
   encArg(cons_g(x_1)) -> g(null_encArg) [0]
   encArg(cons_b) -> b [0]
   encArg(cons_activate(n__g(x_1231))) -> activate(n__g(encArg(x_1231))) [0]
   encArg(cons_activate(c)) -> activate(c) [0]
   encArg(cons_activate(cons_f(x_1232, x_257, x_357))) -> activate(f(encArg(x_1232), encArg(x_257), encArg(x_357))) [0]
   encArg(cons_activate(cons_g(x_1233))) -> activate(g(encArg(x_1233))) [0]
   encArg(cons_activate(cons_b)) -> activate(b) [0]
   encArg(cons_activate(cons_activate(x_1234))) -> activate(activate(encArg(x_1234))) [0]
   encArg(cons_activate(x_1)) -> activate(null_encArg) [0]
   encode_f(x_1, x_2, x_3) -> f(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encode_n__g(x_1) -> n__g(encArg(x_1)) [0]
   encode_activate(n__g(x_1463)) -> activate(n__g(encArg(x_1463))) [0]
   encode_activate(c) -> activate(c) [0]
   encode_activate(cons_f(x_1464, x_2115, x_3115)) -> activate(f(encArg(x_1464), encArg(x_2115), encArg(x_3115))) [0]
   encode_activate(cons_g(x_1465)) -> activate(g(encArg(x_1465))) [0]
   encode_activate(cons_b) -> activate(b) [0]
   encode_activate(cons_activate(x_1466)) -> activate(activate(encArg(x_1466))) [0]
   encode_activate(x_1) -> activate(null_encArg) [0]
   encode_g(n__g(x_1467)) -> g(n__g(encArg(x_1467))) [0]
   encode_g(c) -> g(c) [0]
   encode_g(cons_f(x_1468, x_2116, x_3116)) -> g(f(encArg(x_1468), encArg(x_2116), encArg(x_3116))) [0]
   encode_g(cons_g(x_1469)) -> g(g(encArg(x_1469))) [0]
   encode_g(cons_b) -> g(b) [0]
   encode_g(cons_activate(x_1470)) -> g(activate(encArg(x_1470))) [0]
   encode_g(x_1) -> g(null_encArg) [0]
   encode_b -> b [0]
   encode_c -> c [0]
   b -> c_b [0]
   encArg(v0) -> null_encArg [0]
   encode_f(v0, v1, v2) -> null_encode_f [0]
   encode_n__g(v0) -> null_encode_n__g [0]
   encode_activate(v0) -> null_encode_activate [0]
   encode_g(v0) -> null_encode_g [0]
   encode_b -> null_encode_b [0]
   encode_c -> null_encode_c [0]
   b -> null_b [0]
   f(v0, v1, v2) -> null_f [0]

The TRS has the following type information:
f :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f -> n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f -> n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f -> n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f
n__g :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f -> n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f
activate :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f -> n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f
b :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f
c :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f
g :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f -> n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f
c_b :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f
encArg :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f -> n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f
cons_f :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f -> n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f -> n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f -> n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f
cons_g :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f -> n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f
cons_b :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f
cons_activate :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f -> n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f
encode_f :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f -> n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f -> n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f -> n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f
encode_n__g :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f -> n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f
encode_activate :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f -> n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f
encode_g :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f -> n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f
encode_b :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f
encode_c :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f
null_encArg :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f
null_encode_f :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f
null_encode_n__g :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f
null_encode_activate :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f
null_encode_g :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f
null_encode_b :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f
null_encode_c :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f
null_b :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f
null_f :: n__g:c:c_b:cons_f:cons_g:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_n__g:null_encode_activate:null_encode_g:null_encode_b:null_encode_c:null_b:null_f

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

(15) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID))
Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction.
The constant constructors are abstracted as follows:

   c => 0
   c_b => 1
   cons_b => 2
   null_encArg => 0
   null_encode_f => 0
   null_encode_n__g => 0
   null_encode_activate => 0
   null_encode_g => 0
   null_encode_b => 0
   null_encode_c => 0
   null_b => 0
   null_f => 0

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

(16)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 1 }-> X :|: X >= 0, z = X
   activate(z) -{ 1 }-> g(X) :|: z = 1 + X, X >= 0
   b -{ 0 }-> 1 :|: 
   b -{ 1 }-> 0 :|: 
   b -{ 0 }-> 0 :|: 
   encArg(z) -{ 0 }-> g(g(encArg(x_1229))) :|: x_1229 >= 0, z = 1 + (1 + x_1229)
   encArg(z) -{ 0 }-> g(f(encArg(x_1228), encArg(x_256), encArg(x_356))) :|: z = 1 + (1 + x_1228 + x_256 + x_356), x_256 >= 0, x_1228 >= 0, x_356 >= 0
   encArg(z) -{ 0 }-> g(b) :|: z = 1 + 2
   encArg(z) -{ 0 }-> g(activate(encArg(x_1230))) :|: z = 1 + (1 + x_1230), x_1230 >= 0
   encArg(z) -{ 0 }-> g(0) :|: z = 1 + 0
   encArg(z) -{ 0 }-> g(0) :|: z = 1 + x_1, x_1 >= 0
   encArg(z) -{ 0 }-> g(1 + encArg(x_1227)) :|: z = 1 + (1 + x_1227), x_1227 >= 0
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> b :|: z = 2
   encArg(z) -{ 0 }-> activate(g(encArg(x_1233))) :|: z = 1 + (1 + x_1233), x_1233 >= 0
   encArg(z) -{ 0 }-> activate(f(encArg(x_1232), encArg(x_257), encArg(x_357))) :|: x_1232 >= 0, x_357 >= 0, z = 1 + (1 + x_1232 + x_257 + x_357), x_257 >= 0
   encArg(z) -{ 0 }-> activate(b) :|: z = 1 + 2
   encArg(z) -{ 0 }-> activate(activate(encArg(x_1234))) :|: z = 1 + (1 + x_1234), x_1234 >= 0
   encArg(z) -{ 0 }-> activate(0) :|: z = 1 + 0
   encArg(z) -{ 0 }-> activate(0) :|: z = 1 + x_1, x_1 >= 0
   encArg(z) -{ 0 }-> activate(1 + encArg(x_1231)) :|: z = 1 + (1 + x_1231), x_1231 >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encArg(z) -{ 0 }-> 1 + encArg(x_1) :|: z = 1 + x_1, x_1 >= 0
   encode_activate(z) -{ 0 }-> activate(g(encArg(x_1465))) :|: x_1465 >= 0, z = 1 + x_1465
   encode_activate(z) -{ 0 }-> activate(f(encArg(x_1464), encArg(x_2115), encArg(x_3115))) :|: x_3115 >= 0, x_1464 >= 0, x_2115 >= 0, z = 1 + x_1464 + x_2115 + x_3115
   encode_activate(z) -{ 0 }-> activate(b) :|: z = 2
   encode_activate(z) -{ 0 }-> activate(activate(encArg(x_1466))) :|: x_1466 >= 0, z = 1 + x_1466
   encode_activate(z) -{ 0 }-> activate(0) :|: z = 0
   encode_activate(z) -{ 0 }-> activate(0) :|: x_1 >= 0, z = x_1
   encode_activate(z) -{ 0 }-> activate(1 + encArg(x_1463)) :|: x_1463 >= 0, z = 1 + x_1463
   encode_activate(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_b -{ 0 }-> b :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z, z', z'') -{ 0 }-> f(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, x_3 >= 0, x_2 >= 0, z = x_1, z' = x_2, z'' = x_3
   encode_f(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   encode_g(z) -{ 0 }-> g(g(encArg(x_1469))) :|: x_1469 >= 0, z = 1 + x_1469
   encode_g(z) -{ 0 }-> g(f(encArg(x_1468), encArg(x_2116), encArg(x_3116))) :|: x_3116 >= 0, z = 1 + x_1468 + x_2116 + x_3116, x_2116 >= 0, x_1468 >= 0
   encode_g(z) -{ 0 }-> g(b) :|: z = 2
   encode_g(z) -{ 0 }-> g(activate(encArg(x_1470))) :|: z = 1 + x_1470, x_1470 >= 0
   encode_g(z) -{ 0 }-> g(0) :|: z = 0
   encode_g(z) -{ 0 }-> g(0) :|: x_1 >= 0, z = x_1
   encode_g(z) -{ 0 }-> g(1 + encArg(x_1467)) :|: x_1467 >= 0, z = 1 + x_1467
   encode_g(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_n__g(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_n__g(z) -{ 0 }-> 1 + encArg(x_1) :|: x_1 >= 0, z = x_1
   f(z, z', z'') -{ 4 }-> f(Y, Y, Y) :|: Y >= 0, z'' = Y, z' = 1 + X, X >= 0, z = X
   f(z, z', z'') -{ 4 }-> f(g(X'), g(X'), g(X')) :|: z' = 1 + X, X >= 0, X' >= 0, z = X, z'' = 1 + X'
   f(z, z', z'') -{ 4 }-> f(g(X'), g(X'), 1 + X') :|: z' = 1 + X, X >= 0, X' >= 0, z = X, z'' = 1 + X'
   f(z, z', z'') -{ 4 }-> f(g(X'), 1 + X', g(X')) :|: z' = 1 + X, X >= 0, X' >= 0, z = X, z'' = 1 + X'
   f(z, z', z'') -{ 4 }-> f(g(X'), 1 + X', 1 + X') :|: z' = 1 + X, X >= 0, X' >= 0, z = X, z'' = 1 + X'
   f(z, z', z'') -{ 4 }-> f(1 + X'', g(X''), g(X'')) :|: z' = 1 + X, X >= 0, z'' = 1 + X'', z = X, X'' >= 0
   f(z, z', z'') -{ 4 }-> f(1 + X'', g(X''), 1 + X'') :|: z' = 1 + X, X >= 0, z'' = 1 + X'', z = X, X'' >= 0
   f(z, z', z'') -{ 4 }-> f(1 + X1, 1 + X1, g(X1)) :|: X1 >= 0, z' = 1 + X, X >= 0, z = X, z'' = 1 + X1
   f(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   g(z) -{ 1 }-> 0 :|: z = 1
   g(z) -{ 1 }-> 1 + X :|: X >= 0, z = X


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

(17) InliningProof (UPPER BOUND(ID))
Inlined the following terminating rules on right-hand sides where appropriate:

   b -{ 0 }-> 1 :|: 
   b -{ 0 }-> 0 :|: 
   b -{ 1 }-> 0 :|: 
   g(z) -{ 1 }-> 0 :|: z = 1
   g(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   activate(z) -{ 1 }-> g(X) :|: z = 1 + X, X >= 0
   activate(z) -{ 1 }-> X :|: X >= 0, z = X

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

(18)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 1 }-> X :|: X >= 0, z = X
   activate(z) -{ 2 }-> 0 :|: z = 1 + X, X >= 0, X = 1
   activate(z) -{ 2 }-> 1 + X' :|: z = 1 + X, X >= 0, X' >= 0, X = X'
   b -{ 0 }-> 1 :|: 
   b -{ 1 }-> 0 :|: 
   b -{ 0 }-> 0 :|: 
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + x_1, x_1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 1 }-> g(X) :|: z = 1 + 2, 1 = 1 + X, X >= 0
   encArg(z) -{ 0 }-> g(g(encArg(x_1229))) :|: x_1229 >= 0, z = 1 + (1 + x_1229)
   encArg(z) -{ 0 }-> g(f(encArg(x_1228), encArg(x_256), encArg(x_356))) :|: z = 1 + (1 + x_1228 + x_256 + x_356), x_256 >= 0, x_1228 >= 0, x_356 >= 0
   encArg(z) -{ 0 }-> g(activate(encArg(x_1230))) :|: z = 1 + (1 + x_1230), x_1230 >= 0
   encArg(z) -{ 0 }-> g(1 + encArg(x_1227)) :|: z = 1 + (1 + x_1227), x_1227 >= 0
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> activate(g(encArg(x_1233))) :|: z = 1 + (1 + x_1233), x_1233 >= 0
   encArg(z) -{ 0 }-> activate(f(encArg(x_1232), encArg(x_257), encArg(x_357))) :|: x_1232 >= 0, x_357 >= 0, z = 1 + (1 + x_1232 + x_257 + x_357), x_257 >= 0
   encArg(z) -{ 0 }-> activate(activate(encArg(x_1234))) :|: z = 1 + (1 + x_1234), x_1234 >= 0
   encArg(z) -{ 0 }-> activate(1 + encArg(x_1231)) :|: z = 1 + (1 + x_1231), x_1231 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, 1 = 1
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + x_1, x_1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 0 }-> 1 + encArg(x_1) :|: z = 1 + x_1, x_1 >= 0
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: x_1 >= 0, z = x_1, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 1 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> g(X) :|: z = 2, 1 = 1 + X, X >= 0
   encode_activate(z) -{ 0 }-> activate(g(encArg(x_1465))) :|: x_1465 >= 0, z = 1 + x_1465
   encode_activate(z) -{ 0 }-> activate(f(encArg(x_1464), encArg(x_2115), encArg(x_3115))) :|: x_3115 >= 0, x_1464 >= 0, x_2115 >= 0, z = 1 + x_1464 + x_2115 + x_3115
   encode_activate(z) -{ 0 }-> activate(activate(encArg(x_1466))) :|: x_1466 >= 0, z = 1 + x_1466
   encode_activate(z) -{ 0 }-> activate(1 + encArg(x_1463)) :|: x_1463 >= 0, z = 1 + x_1463
   encode_activate(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_b -{ 0 }-> 1 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z, z', z'') -{ 0 }-> f(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, x_3 >= 0, x_2 >= 0, z = x_1, z' = x_2, z'' = x_3
   encode_f(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   encode_g(z) -{ 0 }-> g(g(encArg(x_1469))) :|: x_1469 >= 0, z = 1 + x_1469
   encode_g(z) -{ 0 }-> g(f(encArg(x_1468), encArg(x_2116), encArg(x_3116))) :|: x_3116 >= 0, z = 1 + x_1468 + x_2116 + x_3116, x_2116 >= 0, x_1468 >= 0
   encode_g(z) -{ 0 }-> g(activate(encArg(x_1470))) :|: z = 1 + x_1470, x_1470 >= 0
   encode_g(z) -{ 0 }-> g(1 + encArg(x_1467)) :|: x_1467 >= 0, z = 1 + x_1467
   encode_g(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, 1 = 1
   encode_g(z) -{ 1 }-> 1 + X :|: z = 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: x_1 >= 0, z = x_1, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 1 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_g(z) -{ 2 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_n__g(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_n__g(z) -{ 0 }-> 1 + encArg(x_1) :|: x_1 >= 0, z = x_1
   f(z, z', z'') -{ 4 }-> f(Y, Y, Y) :|: Y >= 0, z'' = Y, z' = 1 + X, X >= 0, z = X
   f(z, z', z'') -{ 7 }-> f(0, 0, 0) :|: z' = 1 + X, X >= 0, X' >= 0, z = X, z'' = 1 + X', X' = 1
   f(z, z', z'') -{ 6 }-> f(0, 0, 1 + X') :|: z' = 1 + X, X >= 0, X' >= 0, z = X, z'' = 1 + X', X' = 1
   f(z, z', z'') -{ 7 }-> f(0, 0, 1 + X'') :|: z' = 1 + X, X >= 0, X' >= 0, z = X, z'' = 1 + X', X' = 1, X'' >= 0, X' = X''
   f(z, z', z'') -{ 6 }-> f(0, 1 + X', 0) :|: z' = 1 + X, X >= 0, X' >= 0, z = X, z'' = 1 + X', X' = 1
   f(z, z', z'') -{ 5 }-> f(0, 1 + X', 1 + X') :|: z' = 1 + X, X >= 0, X' >= 0, z = X, z'' = 1 + X', X' = 1
   f(z, z', z'') -{ 6 }-> f(0, 1 + X', 1 + X'') :|: z' = 1 + X, X >= 0, X' >= 0, z = X, z'' = 1 + X', X' = 1, X'' >= 0, X' = X''
   f(z, z', z'') -{ 7 }-> f(0, 1 + X'', 0) :|: z' = 1 + X, X >= 0, X' >= 0, z = X, z'' = 1 + X', X' = 1, X'' >= 0, X' = X''
   f(z, z', z'') -{ 6 }-> f(0, 1 + X'', 1 + X') :|: z' = 1 + X, X >= 0, X' >= 0, z = X, z'' = 1 + X', X' = 1, X'' >= 0, X' = X''
   f(z, z', z'') -{ 7 }-> f(0, 1 + X'', 1 + X1) :|: z' = 1 + X, X >= 0, X' >= 0, z = X, z'' = 1 + X', X' = 1, X'' >= 0, X' = X'', X1 >= 0, X' = X1
   f(z, z', z'') -{ 7 }-> f(1 + X'', 0, 0) :|: z' = 1 + X, X >= 0, X' >= 0, z = X, z'' = 1 + X', X'' >= 0, X' = X'', X' = 1
   f(z, z', z'') -{ 6 }-> f(1 + X'', 0, 0) :|: z' = 1 + X, X >= 0, z'' = 1 + X'', z = X, X'' >= 0, X'' = 1
   f(z, z', z'') -{ 6 }-> f(1 + X'', 0, 1 + X') :|: z' = 1 + X, X >= 0, X' >= 0, z = X, z'' = 1 + X', X'' >= 0, X' = X'', X' = 1
   f(z, z', z'') -{ 6 }-> f(1 + X'', 0, 1 + X') :|: z' = 1 + X, X >= 0, z'' = 1 + X'', z = X, X'' >= 0, X'' = 1, X' >= 0, X'' = X'
   f(z, z', z'') -{ 5 }-> f(1 + X'', 0, 1 + X'') :|: z' = 1 + X, X >= 0, z'' = 1 + X'', z = X, X'' >= 0, X'' = 1
   f(z, z', z'') -{ 7 }-> f(1 + X'', 0, 1 + X1) :|: z' = 1 + X, X >= 0, X' >= 0, z = X, z'' = 1 + X', X'' >= 0, X' = X'', X' = 1, X1 >= 0, X' = X1
   f(z, z', z'') -{ 6 }-> f(1 + X'', 1 + X', 0) :|: z' = 1 + X, X >= 0, X' >= 0, z = X, z'' = 1 + X', X'' >= 0, X' = X'', X' = 1
   f(z, z', z'') -{ 6 }-> f(1 + X'', 1 + X', 0) :|: z' = 1 + X, X >= 0, z'' = 1 + X'', z = X, X'' >= 0, X' >= 0, X'' = X', X'' = 1
   f(z, z', z'') -{ 5 }-> f(1 + X'', 1 + X', 1 + X') :|: z' = 1 + X, X >= 0, X' >= 0, z = X, z'' = 1 + X', X'' >= 0, X' = X''
   f(z, z', z'') -{ 5 }-> f(1 + X'', 1 + X', 1 + X'') :|: z' = 1 + X, X >= 0, z'' = 1 + X'', z = X, X'' >= 0, X' >= 0, X'' = X'
   f(z, z', z'') -{ 6 }-> f(1 + X'', 1 + X', 1 + X1) :|: z' = 1 + X, X >= 0, X' >= 0, z = X, z'' = 1 + X', X'' >= 0, X' = X'', X1 >= 0, X' = X1
   f(z, z', z'') -{ 6 }-> f(1 + X'', 1 + X', 1 + X1) :|: z' = 1 + X, X >= 0, z'' = 1 + X'', z = X, X'' >= 0, X' >= 0, X'' = X', X1 >= 0, X'' = X1
   f(z, z', z'') -{ 7 }-> f(1 + X'', 1 + X1, 0) :|: z' = 1 + X, X >= 0, X' >= 0, z = X, z'' = 1 + X', X'' >= 0, X' = X'', X1 >= 0, X' = X1, X' = 1
   f(z, z', z'') -{ 6 }-> f(1 + X'', 1 + X1, 1 + X') :|: z' = 1 + X, X >= 0, X' >= 0, z = X, z'' = 1 + X', X'' >= 0, X' = X'', X1 >= 0, X' = X1
   f(z, z', z'') -{ 7 }-> f(1 + X'', 1 + X1, 1 + X2) :|: z' = 1 + X, X >= 0, X' >= 0, z = X, z'' = 1 + X', X'' >= 0, X' = X'', X1 >= 0, X' = X1, X2 >= 0, X' = X2
   f(z, z', z'') -{ 5 }-> f(1 + X1, 1 + X1, 0) :|: X1 >= 0, z' = 1 + X, X >= 0, z = X, z'' = 1 + X1, X1 = 1
   f(z, z', z'') -{ 5 }-> f(1 + X1, 1 + X1, 1 + X') :|: X1 >= 0, z' = 1 + X, X >= 0, z = X, z'' = 1 + X1, X' >= 0, X1 = X'
   f(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   g(z) -{ 1 }-> 0 :|: z = 1
   g(z) -{ 1 }-> 1 + X :|: X >= 0, z = X


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

(19) SimplificationProof (BOTH BOUNDS(ID, ID))
Simplified the RNTS by moving equalities from the constraints into the right-hand sides.
----------------------------------------

(20)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 0 :|: z - 1 >= 0, z - 1 = 1
   activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   b -{ 0 }-> 1 :|: 
   b -{ 1 }-> 0 :|: 
   b -{ 0 }-> 0 :|: 
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 1 }-> g(X) :|: z = 1 + 2, 1 = 1 + X, X >= 0
   encArg(z) -{ 0 }-> g(g(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> g(f(encArg(x_1228), encArg(x_256), encArg(x_356))) :|: z = 1 + (1 + x_1228 + x_256 + x_356), x_256 >= 0, x_1228 >= 0, x_356 >= 0
   encArg(z) -{ 0 }-> g(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> g(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> activate(g(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(f(encArg(x_1232), encArg(x_257), encArg(x_357))) :|: x_1232 >= 0, x_357 >= 0, z = 1 + (1 + x_1232 + x_257 + x_357), x_257 >= 0
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, 1 = 1
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 1 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> g(X) :|: z = 2, 1 = 1 + X, X >= 0
   encode_activate(z) -{ 0 }-> activate(g(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(f(encArg(x_1464), encArg(x_2115), encArg(x_3115))) :|: x_3115 >= 0, x_1464 >= 0, x_2115 >= 0, z = 1 + x_1464 + x_2115 + x_3115
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_b -{ 0 }-> 1 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z, z', z'') -{ 0 }-> f(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g(z) -{ 0 }-> g(g(encArg(z - 1))) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> g(f(encArg(x_1468), encArg(x_2116), encArg(x_3116))) :|: x_3116 >= 0, z = 1 + x_1468 + x_2116 + x_3116, x_2116 >= 0, x_1468 >= 0
   encode_g(z) -{ 0 }-> g(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> g(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, 1 = 1
   encode_g(z) -{ 1 }-> 1 + X :|: z = 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z >= 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 1 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_g(z) -{ 2 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_n__g(z) -{ 0 }-> 0 :|: z >= 0
   encode_n__g(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   f(z, z', z'') -{ 4 }-> f(z'', z'', z'') :|: z'' >= 0, z' - 1 >= 0, z = z' - 1
   f(z, z', z'') -{ 7 }-> f(0, 0, 0) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 7 }-> f(0, 0, 1 + X'') :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 6 }-> f(0, 0, 1 + (z'' - 1)) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 7 }-> f(0, 1 + X'', 0) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 7 }-> f(0, 1 + X'', 1 + X1) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 6 }-> f(0, 1 + X'', 1 + (z'' - 1)) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 6 }-> f(0, 1 + (z'' - 1), 0) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 6 }-> f(0, 1 + (z'' - 1), 1 + X'') :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 5 }-> f(0, 1 + (z'' - 1), 1 + (z'' - 1)) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 7 }-> f(1 + X'', 0, 0) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 7 }-> f(1 + X'', 0, 1 + X1) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1, X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 6 }-> f(1 + X'', 0, 1 + (z'' - 1)) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 7 }-> f(1 + X'', 1 + X1, 0) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1, z'' - 1 = 1
   f(z, z', z'') -{ 7 }-> f(1 + X'', 1 + X1, 1 + X2) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1, X2 >= 0, z'' - 1 = X2
   f(z, z', z'') -{ 6 }-> f(1 + X'', 1 + X1, 1 + (z'' - 1)) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 6 }-> f(1 + X'', 1 + (z'' - 1), 0) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 6 }-> f(1 + X'', 1 + (z'' - 1), 1 + X1) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 5 }-> f(1 + X'', 1 + (z'' - 1), 1 + (z'' - 1)) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 6 }-> f(1 + (z'' - 1), 0, 0) :|: z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1
   f(z, z', z'') -{ 6 }-> f(1 + (z'' - 1), 0, 1 + X') :|: z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 5 }-> f(1 + (z'' - 1), 0, 1 + (z'' - 1)) :|: z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1
   f(z, z', z'') -{ 6 }-> f(1 + (z'' - 1), 1 + X', 0) :|: z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X', z'' - 1 = 1
   f(z, z', z'') -{ 6 }-> f(1 + (z'' - 1), 1 + X', 1 + X1) :|: z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 5 }-> f(1 + (z'' - 1), 1 + X', 1 + (z'' - 1)) :|: z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 5 }-> f(1 + (z'' - 1), 1 + (z'' - 1), 0) :|: z'' - 1 >= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 5 }-> f(1 + (z'' - 1), 1 + (z'' - 1), 1 + X') :|: z'' - 1 >= 0, z' - 1 >= 0, z = z' - 1, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g(z) -{ 1 }-> 0 :|: z = 1
   g(z) -{ 1 }-> 1 + z :|: z >= 0


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

(21) CpxRntsAnalysisOrderProof (BOTH BOUNDS(ID, ID))
Found the following analysis order by SCC decomposition:

   { f }
   { b }
   { g }
   { encode_c }
   { activate }
   { encode_b }
   { encArg }
   { encode_activate }
   { encode_g }
   { encode_n__g }
   { encode_f }

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

(22)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 0 :|: z - 1 >= 0, z - 1 = 1
   activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   b -{ 0 }-> 1 :|: 
   b -{ 1 }-> 0 :|: 
   b -{ 0 }-> 0 :|: 
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 1 }-> g(X) :|: z = 1 + 2, 1 = 1 + X, X >= 0
   encArg(z) -{ 0 }-> g(g(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> g(f(encArg(x_1228), encArg(x_256), encArg(x_356))) :|: z = 1 + (1 + x_1228 + x_256 + x_356), x_256 >= 0, x_1228 >= 0, x_356 >= 0
   encArg(z) -{ 0 }-> g(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> g(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> activate(g(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(f(encArg(x_1232), encArg(x_257), encArg(x_357))) :|: x_1232 >= 0, x_357 >= 0, z = 1 + (1 + x_1232 + x_257 + x_357), x_257 >= 0
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, 1 = 1
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 1 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> g(X) :|: z = 2, 1 = 1 + X, X >= 0
   encode_activate(z) -{ 0 }-> activate(g(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(f(encArg(x_1464), encArg(x_2115), encArg(x_3115))) :|: x_3115 >= 0, x_1464 >= 0, x_2115 >= 0, z = 1 + x_1464 + x_2115 + x_3115
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_b -{ 0 }-> 1 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z, z', z'') -{ 0 }-> f(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g(z) -{ 0 }-> g(g(encArg(z - 1))) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> g(f(encArg(x_1468), encArg(x_2116), encArg(x_3116))) :|: x_3116 >= 0, z = 1 + x_1468 + x_2116 + x_3116, x_2116 >= 0, x_1468 >= 0
   encode_g(z) -{ 0 }-> g(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> g(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, 1 = 1
   encode_g(z) -{ 1 }-> 1 + X :|: z = 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z >= 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 1 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_g(z) -{ 2 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_n__g(z) -{ 0 }-> 0 :|: z >= 0
   encode_n__g(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   f(z, z', z'') -{ 4 }-> f(z'', z'', z'') :|: z'' >= 0, z' - 1 >= 0, z = z' - 1
   f(z, z', z'') -{ 7 }-> f(0, 0, 0) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 7 }-> f(0, 0, 1 + X'') :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 6 }-> f(0, 0, 1 + (z'' - 1)) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 7 }-> f(0, 1 + X'', 0) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 7 }-> f(0, 1 + X'', 1 + X1) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 6 }-> f(0, 1 + X'', 1 + (z'' - 1)) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 6 }-> f(0, 1 + (z'' - 1), 0) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 6 }-> f(0, 1 + (z'' - 1), 1 + X'') :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 5 }-> f(0, 1 + (z'' - 1), 1 + (z'' - 1)) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 7 }-> f(1 + X'', 0, 0) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 7 }-> f(1 + X'', 0, 1 + X1) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1, X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 6 }-> f(1 + X'', 0, 1 + (z'' - 1)) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 7 }-> f(1 + X'', 1 + X1, 0) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1, z'' - 1 = 1
   f(z, z', z'') -{ 7 }-> f(1 + X'', 1 + X1, 1 + X2) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1, X2 >= 0, z'' - 1 = X2
   f(z, z', z'') -{ 6 }-> f(1 + X'', 1 + X1, 1 + (z'' - 1)) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 6 }-> f(1 + X'', 1 + (z'' - 1), 0) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 6 }-> f(1 + X'', 1 + (z'' - 1), 1 + X1) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 5 }-> f(1 + X'', 1 + (z'' - 1), 1 + (z'' - 1)) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 6 }-> f(1 + (z'' - 1), 0, 0) :|: z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1
   f(z, z', z'') -{ 6 }-> f(1 + (z'' - 1), 0, 1 + X') :|: z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 5 }-> f(1 + (z'' - 1), 0, 1 + (z'' - 1)) :|: z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1
   f(z, z', z'') -{ 6 }-> f(1 + (z'' - 1), 1 + X', 0) :|: z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X', z'' - 1 = 1
   f(z, z', z'') -{ 6 }-> f(1 + (z'' - 1), 1 + X', 1 + X1) :|: z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 5 }-> f(1 + (z'' - 1), 1 + X', 1 + (z'' - 1)) :|: z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 5 }-> f(1 + (z'' - 1), 1 + (z'' - 1), 0) :|: z'' - 1 >= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 5 }-> f(1 + (z'' - 1), 1 + (z'' - 1), 1 + X') :|: z'' - 1 >= 0, z' - 1 >= 0, z = z' - 1, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g(z) -{ 1 }-> 0 :|: z = 1
   g(z) -{ 1 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {f}, {b}, {g}, {encode_c}, {activate}, {encode_b}, {encArg}, {encode_activate}, {encode_g}, {encode_n__g}, {encode_f}

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

(23) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(24)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 0 :|: z - 1 >= 0, z - 1 = 1
   activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   b -{ 0 }-> 1 :|: 
   b -{ 1 }-> 0 :|: 
   b -{ 0 }-> 0 :|: 
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 1 }-> g(X) :|: z = 1 + 2, 1 = 1 + X, X >= 0
   encArg(z) -{ 0 }-> g(g(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> g(f(encArg(x_1228), encArg(x_256), encArg(x_356))) :|: z = 1 + (1 + x_1228 + x_256 + x_356), x_256 >= 0, x_1228 >= 0, x_356 >= 0
   encArg(z) -{ 0 }-> g(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> g(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> activate(g(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(f(encArg(x_1232), encArg(x_257), encArg(x_357))) :|: x_1232 >= 0, x_357 >= 0, z = 1 + (1 + x_1232 + x_257 + x_357), x_257 >= 0
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, 1 = 1
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 1 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> g(X) :|: z = 2, 1 = 1 + X, X >= 0
   encode_activate(z) -{ 0 }-> activate(g(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(f(encArg(x_1464), encArg(x_2115), encArg(x_3115))) :|: x_3115 >= 0, x_1464 >= 0, x_2115 >= 0, z = 1 + x_1464 + x_2115 + x_3115
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_b -{ 0 }-> 1 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z, z', z'') -{ 0 }-> f(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g(z) -{ 0 }-> g(g(encArg(z - 1))) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> g(f(encArg(x_1468), encArg(x_2116), encArg(x_3116))) :|: x_3116 >= 0, z = 1 + x_1468 + x_2116 + x_3116, x_2116 >= 0, x_1468 >= 0
   encode_g(z) -{ 0 }-> g(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> g(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, 1 = 1
   encode_g(z) -{ 1 }-> 1 + X :|: z = 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z >= 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 1 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_g(z) -{ 2 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_n__g(z) -{ 0 }-> 0 :|: z >= 0
   encode_n__g(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   f(z, z', z'') -{ 4 }-> f(z'', z'', z'') :|: z'' >= 0, z' - 1 >= 0, z = z' - 1
   f(z, z', z'') -{ 7 }-> f(0, 0, 0) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 7 }-> f(0, 0, 1 + X'') :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 6 }-> f(0, 0, 1 + (z'' - 1)) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 7 }-> f(0, 1 + X'', 0) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 7 }-> f(0, 1 + X'', 1 + X1) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 6 }-> f(0, 1 + X'', 1 + (z'' - 1)) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 6 }-> f(0, 1 + (z'' - 1), 0) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 6 }-> f(0, 1 + (z'' - 1), 1 + X'') :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 5 }-> f(0, 1 + (z'' - 1), 1 + (z'' - 1)) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 7 }-> f(1 + X'', 0, 0) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 7 }-> f(1 + X'', 0, 1 + X1) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1, X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 6 }-> f(1 + X'', 0, 1 + (z'' - 1)) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 7 }-> f(1 + X'', 1 + X1, 0) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1, z'' - 1 = 1
   f(z, z', z'') -{ 7 }-> f(1 + X'', 1 + X1, 1 + X2) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1, X2 >= 0, z'' - 1 = X2
   f(z, z', z'') -{ 6 }-> f(1 + X'', 1 + X1, 1 + (z'' - 1)) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 6 }-> f(1 + X'', 1 + (z'' - 1), 0) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 6 }-> f(1 + X'', 1 + (z'' - 1), 1 + X1) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 5 }-> f(1 + X'', 1 + (z'' - 1), 1 + (z'' - 1)) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 6 }-> f(1 + (z'' - 1), 0, 0) :|: z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1
   f(z, z', z'') -{ 6 }-> f(1 + (z'' - 1), 0, 1 + X') :|: z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 5 }-> f(1 + (z'' - 1), 0, 1 + (z'' - 1)) :|: z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1
   f(z, z', z'') -{ 6 }-> f(1 + (z'' - 1), 1 + X', 0) :|: z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X', z'' - 1 = 1
   f(z, z', z'') -{ 6 }-> f(1 + (z'' - 1), 1 + X', 1 + X1) :|: z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 5 }-> f(1 + (z'' - 1), 1 + X', 1 + (z'' - 1)) :|: z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 5 }-> f(1 + (z'' - 1), 1 + (z'' - 1), 0) :|: z'' - 1 >= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 5 }-> f(1 + (z'' - 1), 1 + (z'' - 1), 1 + X') :|: z'' - 1 >= 0, z' - 1 >= 0, z = z' - 1, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g(z) -{ 1 }-> 0 :|: z = 1
   g(z) -{ 1 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {f}, {b}, {g}, {encode_c}, {activate}, {encode_b}, {encArg}, {encode_activate}, {encode_g}, {encode_n__g}, {encode_f}

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

(25) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using KoAT for: f
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 0

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

(26)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 0 :|: z - 1 >= 0, z - 1 = 1
   activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   b -{ 0 }-> 1 :|: 
   b -{ 1 }-> 0 :|: 
   b -{ 0 }-> 0 :|: 
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 1 }-> g(X) :|: z = 1 + 2, 1 = 1 + X, X >= 0
   encArg(z) -{ 0 }-> g(g(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> g(f(encArg(x_1228), encArg(x_256), encArg(x_356))) :|: z = 1 + (1 + x_1228 + x_256 + x_356), x_256 >= 0, x_1228 >= 0, x_356 >= 0
   encArg(z) -{ 0 }-> g(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> g(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> activate(g(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(f(encArg(x_1232), encArg(x_257), encArg(x_357))) :|: x_1232 >= 0, x_357 >= 0, z = 1 + (1 + x_1232 + x_257 + x_357), x_257 >= 0
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, 1 = 1
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 1 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> g(X) :|: z = 2, 1 = 1 + X, X >= 0
   encode_activate(z) -{ 0 }-> activate(g(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(f(encArg(x_1464), encArg(x_2115), encArg(x_3115))) :|: x_3115 >= 0, x_1464 >= 0, x_2115 >= 0, z = 1 + x_1464 + x_2115 + x_3115
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_b -{ 0 }-> 1 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z, z', z'') -{ 0 }-> f(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g(z) -{ 0 }-> g(g(encArg(z - 1))) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> g(f(encArg(x_1468), encArg(x_2116), encArg(x_3116))) :|: x_3116 >= 0, z = 1 + x_1468 + x_2116 + x_3116, x_2116 >= 0, x_1468 >= 0
   encode_g(z) -{ 0 }-> g(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> g(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, 1 = 1
   encode_g(z) -{ 1 }-> 1 + X :|: z = 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z >= 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 1 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_g(z) -{ 2 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_n__g(z) -{ 0 }-> 0 :|: z >= 0
   encode_n__g(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   f(z, z', z'') -{ 4 }-> f(z'', z'', z'') :|: z'' >= 0, z' - 1 >= 0, z = z' - 1
   f(z, z', z'') -{ 7 }-> f(0, 0, 0) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 7 }-> f(0, 0, 1 + X'') :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 6 }-> f(0, 0, 1 + (z'' - 1)) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 7 }-> f(0, 1 + X'', 0) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 7 }-> f(0, 1 + X'', 1 + X1) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 6 }-> f(0, 1 + X'', 1 + (z'' - 1)) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 6 }-> f(0, 1 + (z'' - 1), 0) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 6 }-> f(0, 1 + (z'' - 1), 1 + X'') :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 5 }-> f(0, 1 + (z'' - 1), 1 + (z'' - 1)) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 7 }-> f(1 + X'', 0, 0) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 7 }-> f(1 + X'', 0, 1 + X1) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1, X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 6 }-> f(1 + X'', 0, 1 + (z'' - 1)) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 7 }-> f(1 + X'', 1 + X1, 0) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1, z'' - 1 = 1
   f(z, z', z'') -{ 7 }-> f(1 + X'', 1 + X1, 1 + X2) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1, X2 >= 0, z'' - 1 = X2
   f(z, z', z'') -{ 6 }-> f(1 + X'', 1 + X1, 1 + (z'' - 1)) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 6 }-> f(1 + X'', 1 + (z'' - 1), 0) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 6 }-> f(1 + X'', 1 + (z'' - 1), 1 + X1) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 5 }-> f(1 + X'', 1 + (z'' - 1), 1 + (z'' - 1)) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 6 }-> f(1 + (z'' - 1), 0, 0) :|: z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1
   f(z, z', z'') -{ 6 }-> f(1 + (z'' - 1), 0, 1 + X') :|: z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 5 }-> f(1 + (z'' - 1), 0, 1 + (z'' - 1)) :|: z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1
   f(z, z', z'') -{ 6 }-> f(1 + (z'' - 1), 1 + X', 0) :|: z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X', z'' - 1 = 1
   f(z, z', z'') -{ 6 }-> f(1 + (z'' - 1), 1 + X', 1 + X1) :|: z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 5 }-> f(1 + (z'' - 1), 1 + X', 1 + (z'' - 1)) :|: z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 5 }-> f(1 + (z'' - 1), 1 + (z'' - 1), 0) :|: z'' - 1 >= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 5 }-> f(1 + (z'' - 1), 1 + (z'' - 1), 1 + X') :|: z'' - 1 >= 0, z' - 1 >= 0, z = z' - 1, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g(z) -{ 1 }-> 0 :|: z = 1
   g(z) -{ 1 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {f}, {b}, {g}, {encode_c}, {activate}, {encode_b}, {encArg}, {encode_activate}, {encode_g}, {encode_n__g}, {encode_f}
Previous analysis results are:
  f: runtime: ?, size: O(1) [0]

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

(27) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using KoAT for: f
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 162

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

(28)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 0 :|: z - 1 >= 0, z - 1 = 1
   activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   b -{ 0 }-> 1 :|: 
   b -{ 1 }-> 0 :|: 
   b -{ 0 }-> 0 :|: 
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 1 }-> g(X) :|: z = 1 + 2, 1 = 1 + X, X >= 0
   encArg(z) -{ 0 }-> g(g(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> g(f(encArg(x_1228), encArg(x_256), encArg(x_356))) :|: z = 1 + (1 + x_1228 + x_256 + x_356), x_256 >= 0, x_1228 >= 0, x_356 >= 0
   encArg(z) -{ 0 }-> g(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> g(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> activate(g(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(f(encArg(x_1232), encArg(x_257), encArg(x_357))) :|: x_1232 >= 0, x_357 >= 0, z = 1 + (1 + x_1232 + x_257 + x_357), x_257 >= 0
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, 1 = 1
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 1 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> g(X) :|: z = 2, 1 = 1 + X, X >= 0
   encode_activate(z) -{ 0 }-> activate(g(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(f(encArg(x_1464), encArg(x_2115), encArg(x_3115))) :|: x_3115 >= 0, x_1464 >= 0, x_2115 >= 0, z = 1 + x_1464 + x_2115 + x_3115
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_b -{ 0 }-> 1 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z, z', z'') -{ 0 }-> f(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g(z) -{ 0 }-> g(g(encArg(z - 1))) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> g(f(encArg(x_1468), encArg(x_2116), encArg(x_3116))) :|: x_3116 >= 0, z = 1 + x_1468 + x_2116 + x_3116, x_2116 >= 0, x_1468 >= 0
   encode_g(z) -{ 0 }-> g(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> g(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, 1 = 1
   encode_g(z) -{ 1 }-> 1 + X :|: z = 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z >= 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 1 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_g(z) -{ 2 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_n__g(z) -{ 0 }-> 0 :|: z >= 0
   encode_n__g(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   f(z, z', z'') -{ 4 }-> f(z'', z'', z'') :|: z'' >= 0, z' - 1 >= 0, z = z' - 1
   f(z, z', z'') -{ 7 }-> f(0, 0, 0) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 7 }-> f(0, 0, 1 + X'') :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 6 }-> f(0, 0, 1 + (z'' - 1)) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 7 }-> f(0, 1 + X'', 0) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 7 }-> f(0, 1 + X'', 1 + X1) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 6 }-> f(0, 1 + X'', 1 + (z'' - 1)) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 6 }-> f(0, 1 + (z'' - 1), 0) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 6 }-> f(0, 1 + (z'' - 1), 1 + X'') :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 5 }-> f(0, 1 + (z'' - 1), 1 + (z'' - 1)) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 7 }-> f(1 + X'', 0, 0) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 7 }-> f(1 + X'', 0, 1 + X1) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1, X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 6 }-> f(1 + X'', 0, 1 + (z'' - 1)) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 7 }-> f(1 + X'', 1 + X1, 0) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1, z'' - 1 = 1
   f(z, z', z'') -{ 7 }-> f(1 + X'', 1 + X1, 1 + X2) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1, X2 >= 0, z'' - 1 = X2
   f(z, z', z'') -{ 6 }-> f(1 + X'', 1 + X1, 1 + (z'' - 1)) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 6 }-> f(1 + X'', 1 + (z'' - 1), 0) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 6 }-> f(1 + X'', 1 + (z'' - 1), 1 + X1) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 5 }-> f(1 + X'', 1 + (z'' - 1), 1 + (z'' - 1)) :|: z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 6 }-> f(1 + (z'' - 1), 0, 0) :|: z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1
   f(z, z', z'') -{ 6 }-> f(1 + (z'' - 1), 0, 1 + X') :|: z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 5 }-> f(1 + (z'' - 1), 0, 1 + (z'' - 1)) :|: z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1
   f(z, z', z'') -{ 6 }-> f(1 + (z'' - 1), 1 + X', 0) :|: z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X', z'' - 1 = 1
   f(z, z', z'') -{ 6 }-> f(1 + (z'' - 1), 1 + X', 1 + X1) :|: z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 5 }-> f(1 + (z'' - 1), 1 + X', 1 + (z'' - 1)) :|: z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 5 }-> f(1 + (z'' - 1), 1 + (z'' - 1), 0) :|: z'' - 1 >= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 5 }-> f(1 + (z'' - 1), 1 + (z'' - 1), 1 + X') :|: z'' - 1 >= 0, z' - 1 >= 0, z = z' - 1, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g(z) -{ 1 }-> 0 :|: z = 1
   g(z) -{ 1 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {b}, {g}, {encode_c}, {activate}, {encode_b}, {encArg}, {encode_activate}, {encode_g}, {encode_n__g}, {encode_f}
Previous analysis results are:
  f: runtime: O(1) [162], size: O(1) [0]

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

(29) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(30)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 0 :|: z - 1 >= 0, z - 1 = 1
   activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   b -{ 0 }-> 1 :|: 
   b -{ 1 }-> 0 :|: 
   b -{ 0 }-> 0 :|: 
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 1 }-> g(X) :|: z = 1 + 2, 1 = 1 + X, X >= 0
   encArg(z) -{ 0 }-> g(g(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> g(f(encArg(x_1228), encArg(x_256), encArg(x_356))) :|: z = 1 + (1 + x_1228 + x_256 + x_356), x_256 >= 0, x_1228 >= 0, x_356 >= 0
   encArg(z) -{ 0 }-> g(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> g(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> activate(g(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(f(encArg(x_1232), encArg(x_257), encArg(x_357))) :|: x_1232 >= 0, x_357 >= 0, z = 1 + (1 + x_1232 + x_257 + x_357), x_257 >= 0
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, 1 = 1
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 1 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> g(X) :|: z = 2, 1 = 1 + X, X >= 0
   encode_activate(z) -{ 0 }-> activate(g(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(f(encArg(x_1464), encArg(x_2115), encArg(x_3115))) :|: x_3115 >= 0, x_1464 >= 0, x_2115 >= 0, z = 1 + x_1464 + x_2115 + x_3115
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_b -{ 0 }-> 1 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z, z', z'') -{ 0 }-> f(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g(z) -{ 0 }-> g(g(encArg(z - 1))) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> g(f(encArg(x_1468), encArg(x_2116), encArg(x_3116))) :|: x_3116 >= 0, z = 1 + x_1468 + x_2116 + x_3116, x_2116 >= 0, x_1468 >= 0
   encode_g(z) -{ 0 }-> g(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> g(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, 1 = 1
   encode_g(z) -{ 1 }-> 1 + X :|: z = 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z >= 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 1 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_g(z) -{ 2 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_n__g(z) -{ 0 }-> 0 :|: z >= 0
   encode_n__g(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   f(z, z', z'') -{ 166 }-> s :|: s >= 0, s <= 0, z'' >= 0, z' - 1 >= 0, z = z' - 1
   f(z, z', z'') -{ 169 }-> s' :|: s' >= 0, s' <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s'' :|: s'' >= 0, s'' <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 169 }-> s1 :|: s1 >= 0, s1 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s10 :|: s10 >= 0, s10 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 168 }-> s11 :|: s11 >= 0, s11 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s12 :|: s12 >= 0, s12 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s13 :|: s13 >= 0, s13 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s14 :|: s14 >= 0, s14 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 167 }-> s15 :|: s15 >= 0, s15 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s16 :|: s16 >= 0, s16 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s17 :|: s17 >= 0, s17 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s18 :|: s18 >= 0, s18 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 168 }-> s19 :|: s19 >= 0, s19 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X', z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s2 :|: s2 >= 0, s2 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 168 }-> s20 :|: s20 >= 0, s20 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 167 }-> s21 :|: s21 >= 0, s21 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s22 :|: s22 >= 0, s22 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 167 }-> s23 :|: s23 >= 0, s23 <= 0, z'' - 1 >= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s24 :|: s24 >= 0, s24 <= 0, z'' - 1 >= 0, z' - 1 >= 0, z = z' - 1, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 169 }-> s3 :|: s3 >= 0, s3 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s4 :|: s4 >= 0, s4 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1, X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 169 }-> s5 :|: s5 >= 0, s5 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1, z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s6 :|: s6 >= 0, s6 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1, X2 >= 0, z'' - 1 = X2
   f(z, z', z'') -{ 168 }-> s7 :|: s7 >= 0, s7 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s8 :|: s8 >= 0, s8 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s9 :|: s9 >= 0, s9 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g(z) -{ 1 }-> 0 :|: z = 1
   g(z) -{ 1 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {b}, {g}, {encode_c}, {activate}, {encode_b}, {encArg}, {encode_activate}, {encode_g}, {encode_n__g}, {encode_f}
Previous analysis results are:
  f: runtime: O(1) [162], size: O(1) [0]

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

(31) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: b
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 1

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

(32)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 0 :|: z - 1 >= 0, z - 1 = 1
   activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   b -{ 0 }-> 1 :|: 
   b -{ 1 }-> 0 :|: 
   b -{ 0 }-> 0 :|: 
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 1 }-> g(X) :|: z = 1 + 2, 1 = 1 + X, X >= 0
   encArg(z) -{ 0 }-> g(g(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> g(f(encArg(x_1228), encArg(x_256), encArg(x_356))) :|: z = 1 + (1 + x_1228 + x_256 + x_356), x_256 >= 0, x_1228 >= 0, x_356 >= 0
   encArg(z) -{ 0 }-> g(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> g(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> activate(g(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(f(encArg(x_1232), encArg(x_257), encArg(x_357))) :|: x_1232 >= 0, x_357 >= 0, z = 1 + (1 + x_1232 + x_257 + x_357), x_257 >= 0
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, 1 = 1
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 1 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> g(X) :|: z = 2, 1 = 1 + X, X >= 0
   encode_activate(z) -{ 0 }-> activate(g(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(f(encArg(x_1464), encArg(x_2115), encArg(x_3115))) :|: x_3115 >= 0, x_1464 >= 0, x_2115 >= 0, z = 1 + x_1464 + x_2115 + x_3115
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_b -{ 0 }-> 1 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z, z', z'') -{ 0 }-> f(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g(z) -{ 0 }-> g(g(encArg(z - 1))) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> g(f(encArg(x_1468), encArg(x_2116), encArg(x_3116))) :|: x_3116 >= 0, z = 1 + x_1468 + x_2116 + x_3116, x_2116 >= 0, x_1468 >= 0
   encode_g(z) -{ 0 }-> g(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> g(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, 1 = 1
   encode_g(z) -{ 1 }-> 1 + X :|: z = 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z >= 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 1 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_g(z) -{ 2 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_n__g(z) -{ 0 }-> 0 :|: z >= 0
   encode_n__g(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   f(z, z', z'') -{ 166 }-> s :|: s >= 0, s <= 0, z'' >= 0, z' - 1 >= 0, z = z' - 1
   f(z, z', z'') -{ 169 }-> s' :|: s' >= 0, s' <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s'' :|: s'' >= 0, s'' <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 169 }-> s1 :|: s1 >= 0, s1 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s10 :|: s10 >= 0, s10 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 168 }-> s11 :|: s11 >= 0, s11 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s12 :|: s12 >= 0, s12 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s13 :|: s13 >= 0, s13 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s14 :|: s14 >= 0, s14 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 167 }-> s15 :|: s15 >= 0, s15 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s16 :|: s16 >= 0, s16 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s17 :|: s17 >= 0, s17 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s18 :|: s18 >= 0, s18 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 168 }-> s19 :|: s19 >= 0, s19 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X', z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s2 :|: s2 >= 0, s2 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 168 }-> s20 :|: s20 >= 0, s20 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 167 }-> s21 :|: s21 >= 0, s21 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s22 :|: s22 >= 0, s22 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 167 }-> s23 :|: s23 >= 0, s23 <= 0, z'' - 1 >= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s24 :|: s24 >= 0, s24 <= 0, z'' - 1 >= 0, z' - 1 >= 0, z = z' - 1, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 169 }-> s3 :|: s3 >= 0, s3 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s4 :|: s4 >= 0, s4 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1, X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 169 }-> s5 :|: s5 >= 0, s5 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1, z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s6 :|: s6 >= 0, s6 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1, X2 >= 0, z'' - 1 = X2
   f(z, z', z'') -{ 168 }-> s7 :|: s7 >= 0, s7 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s8 :|: s8 >= 0, s8 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s9 :|: s9 >= 0, s9 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g(z) -{ 1 }-> 0 :|: z = 1
   g(z) -{ 1 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {b}, {g}, {encode_c}, {activate}, {encode_b}, {encArg}, {encode_activate}, {encode_g}, {encode_n__g}, {encode_f}
Previous analysis results are:
  f: runtime: O(1) [162], size: O(1) [0]
  b: runtime: ?, size: O(1) [1]

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

(33) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: b
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 1

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

(34)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 0 :|: z - 1 >= 0, z - 1 = 1
   activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   b -{ 0 }-> 1 :|: 
   b -{ 1 }-> 0 :|: 
   b -{ 0 }-> 0 :|: 
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 1 }-> g(X) :|: z = 1 + 2, 1 = 1 + X, X >= 0
   encArg(z) -{ 0 }-> g(g(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> g(f(encArg(x_1228), encArg(x_256), encArg(x_356))) :|: z = 1 + (1 + x_1228 + x_256 + x_356), x_256 >= 0, x_1228 >= 0, x_356 >= 0
   encArg(z) -{ 0 }-> g(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> g(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> activate(g(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(f(encArg(x_1232), encArg(x_257), encArg(x_357))) :|: x_1232 >= 0, x_357 >= 0, z = 1 + (1 + x_1232 + x_257 + x_357), x_257 >= 0
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, 1 = 1
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 1 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> g(X) :|: z = 2, 1 = 1 + X, X >= 0
   encode_activate(z) -{ 0 }-> activate(g(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(f(encArg(x_1464), encArg(x_2115), encArg(x_3115))) :|: x_3115 >= 0, x_1464 >= 0, x_2115 >= 0, z = 1 + x_1464 + x_2115 + x_3115
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_b -{ 0 }-> 1 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z, z', z'') -{ 0 }-> f(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g(z) -{ 0 }-> g(g(encArg(z - 1))) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> g(f(encArg(x_1468), encArg(x_2116), encArg(x_3116))) :|: x_3116 >= 0, z = 1 + x_1468 + x_2116 + x_3116, x_2116 >= 0, x_1468 >= 0
   encode_g(z) -{ 0 }-> g(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> g(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, 1 = 1
   encode_g(z) -{ 1 }-> 1 + X :|: z = 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z >= 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 1 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_g(z) -{ 2 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_n__g(z) -{ 0 }-> 0 :|: z >= 0
   encode_n__g(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   f(z, z', z'') -{ 166 }-> s :|: s >= 0, s <= 0, z'' >= 0, z' - 1 >= 0, z = z' - 1
   f(z, z', z'') -{ 169 }-> s' :|: s' >= 0, s' <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s'' :|: s'' >= 0, s'' <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 169 }-> s1 :|: s1 >= 0, s1 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s10 :|: s10 >= 0, s10 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 168 }-> s11 :|: s11 >= 0, s11 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s12 :|: s12 >= 0, s12 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s13 :|: s13 >= 0, s13 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s14 :|: s14 >= 0, s14 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 167 }-> s15 :|: s15 >= 0, s15 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s16 :|: s16 >= 0, s16 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s17 :|: s17 >= 0, s17 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s18 :|: s18 >= 0, s18 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 168 }-> s19 :|: s19 >= 0, s19 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X', z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s2 :|: s2 >= 0, s2 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 168 }-> s20 :|: s20 >= 0, s20 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 167 }-> s21 :|: s21 >= 0, s21 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s22 :|: s22 >= 0, s22 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 167 }-> s23 :|: s23 >= 0, s23 <= 0, z'' - 1 >= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s24 :|: s24 >= 0, s24 <= 0, z'' - 1 >= 0, z' - 1 >= 0, z = z' - 1, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 169 }-> s3 :|: s3 >= 0, s3 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s4 :|: s4 >= 0, s4 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1, X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 169 }-> s5 :|: s5 >= 0, s5 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1, z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s6 :|: s6 >= 0, s6 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1, X2 >= 0, z'' - 1 = X2
   f(z, z', z'') -{ 168 }-> s7 :|: s7 >= 0, s7 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s8 :|: s8 >= 0, s8 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s9 :|: s9 >= 0, s9 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g(z) -{ 1 }-> 0 :|: z = 1
   g(z) -{ 1 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {g}, {encode_c}, {activate}, {encode_b}, {encArg}, {encode_activate}, {encode_g}, {encode_n__g}, {encode_f}
Previous analysis results are:
  f: runtime: O(1) [162], size: O(1) [0]
  b: runtime: O(1) [1], size: O(1) [1]

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

(35) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(36)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 0 :|: z - 1 >= 0, z - 1 = 1
   activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   b -{ 0 }-> 1 :|: 
   b -{ 1 }-> 0 :|: 
   b -{ 0 }-> 0 :|: 
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 1 }-> g(X) :|: z = 1 + 2, 1 = 1 + X, X >= 0
   encArg(z) -{ 0 }-> g(g(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> g(f(encArg(x_1228), encArg(x_256), encArg(x_356))) :|: z = 1 + (1 + x_1228 + x_256 + x_356), x_256 >= 0, x_1228 >= 0, x_356 >= 0
   encArg(z) -{ 0 }-> g(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> g(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> activate(g(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(f(encArg(x_1232), encArg(x_257), encArg(x_357))) :|: x_1232 >= 0, x_357 >= 0, z = 1 + (1 + x_1232 + x_257 + x_357), x_257 >= 0
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, 1 = 1
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 1 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> g(X) :|: z = 2, 1 = 1 + X, X >= 0
   encode_activate(z) -{ 0 }-> activate(g(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(f(encArg(x_1464), encArg(x_2115), encArg(x_3115))) :|: x_3115 >= 0, x_1464 >= 0, x_2115 >= 0, z = 1 + x_1464 + x_2115 + x_3115
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_b -{ 0 }-> 1 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z, z', z'') -{ 0 }-> f(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g(z) -{ 0 }-> g(g(encArg(z - 1))) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> g(f(encArg(x_1468), encArg(x_2116), encArg(x_3116))) :|: x_3116 >= 0, z = 1 + x_1468 + x_2116 + x_3116, x_2116 >= 0, x_1468 >= 0
   encode_g(z) -{ 0 }-> g(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> g(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, 1 = 1
   encode_g(z) -{ 1 }-> 1 + X :|: z = 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z >= 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 1 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_g(z) -{ 2 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_n__g(z) -{ 0 }-> 0 :|: z >= 0
   encode_n__g(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   f(z, z', z'') -{ 166 }-> s :|: s >= 0, s <= 0, z'' >= 0, z' - 1 >= 0, z = z' - 1
   f(z, z', z'') -{ 169 }-> s' :|: s' >= 0, s' <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s'' :|: s'' >= 0, s'' <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 169 }-> s1 :|: s1 >= 0, s1 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s10 :|: s10 >= 0, s10 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 168 }-> s11 :|: s11 >= 0, s11 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s12 :|: s12 >= 0, s12 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s13 :|: s13 >= 0, s13 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s14 :|: s14 >= 0, s14 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 167 }-> s15 :|: s15 >= 0, s15 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s16 :|: s16 >= 0, s16 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s17 :|: s17 >= 0, s17 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s18 :|: s18 >= 0, s18 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 168 }-> s19 :|: s19 >= 0, s19 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X', z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s2 :|: s2 >= 0, s2 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 168 }-> s20 :|: s20 >= 0, s20 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 167 }-> s21 :|: s21 >= 0, s21 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s22 :|: s22 >= 0, s22 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 167 }-> s23 :|: s23 >= 0, s23 <= 0, z'' - 1 >= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s24 :|: s24 >= 0, s24 <= 0, z'' - 1 >= 0, z' - 1 >= 0, z = z' - 1, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 169 }-> s3 :|: s3 >= 0, s3 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s4 :|: s4 >= 0, s4 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1, X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 169 }-> s5 :|: s5 >= 0, s5 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1, z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s6 :|: s6 >= 0, s6 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1, X2 >= 0, z'' - 1 = X2
   f(z, z', z'') -{ 168 }-> s7 :|: s7 >= 0, s7 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s8 :|: s8 >= 0, s8 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s9 :|: s9 >= 0, s9 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g(z) -{ 1 }-> 0 :|: z = 1
   g(z) -{ 1 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {g}, {encode_c}, {activate}, {encode_b}, {encArg}, {encode_activate}, {encode_g}, {encode_n__g}, {encode_f}
Previous analysis results are:
  f: runtime: O(1) [162], size: O(1) [0]
  b: runtime: O(1) [1], size: O(1) [1]

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

(37) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: g
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 1 + z

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

(38)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 0 :|: z - 1 >= 0, z - 1 = 1
   activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   b -{ 0 }-> 1 :|: 
   b -{ 1 }-> 0 :|: 
   b -{ 0 }-> 0 :|: 
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 1 }-> g(X) :|: z = 1 + 2, 1 = 1 + X, X >= 0
   encArg(z) -{ 0 }-> g(g(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> g(f(encArg(x_1228), encArg(x_256), encArg(x_356))) :|: z = 1 + (1 + x_1228 + x_256 + x_356), x_256 >= 0, x_1228 >= 0, x_356 >= 0
   encArg(z) -{ 0 }-> g(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> g(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> activate(g(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(f(encArg(x_1232), encArg(x_257), encArg(x_357))) :|: x_1232 >= 0, x_357 >= 0, z = 1 + (1 + x_1232 + x_257 + x_357), x_257 >= 0
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, 1 = 1
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 1 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> g(X) :|: z = 2, 1 = 1 + X, X >= 0
   encode_activate(z) -{ 0 }-> activate(g(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(f(encArg(x_1464), encArg(x_2115), encArg(x_3115))) :|: x_3115 >= 0, x_1464 >= 0, x_2115 >= 0, z = 1 + x_1464 + x_2115 + x_3115
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_b -{ 0 }-> 1 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z, z', z'') -{ 0 }-> f(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g(z) -{ 0 }-> g(g(encArg(z - 1))) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> g(f(encArg(x_1468), encArg(x_2116), encArg(x_3116))) :|: x_3116 >= 0, z = 1 + x_1468 + x_2116 + x_3116, x_2116 >= 0, x_1468 >= 0
   encode_g(z) -{ 0 }-> g(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> g(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, 1 = 1
   encode_g(z) -{ 1 }-> 1 + X :|: z = 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z >= 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 1 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_g(z) -{ 2 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_n__g(z) -{ 0 }-> 0 :|: z >= 0
   encode_n__g(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   f(z, z', z'') -{ 166 }-> s :|: s >= 0, s <= 0, z'' >= 0, z' - 1 >= 0, z = z' - 1
   f(z, z', z'') -{ 169 }-> s' :|: s' >= 0, s' <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s'' :|: s'' >= 0, s'' <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 169 }-> s1 :|: s1 >= 0, s1 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s10 :|: s10 >= 0, s10 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 168 }-> s11 :|: s11 >= 0, s11 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s12 :|: s12 >= 0, s12 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s13 :|: s13 >= 0, s13 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s14 :|: s14 >= 0, s14 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 167 }-> s15 :|: s15 >= 0, s15 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s16 :|: s16 >= 0, s16 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s17 :|: s17 >= 0, s17 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s18 :|: s18 >= 0, s18 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 168 }-> s19 :|: s19 >= 0, s19 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X', z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s2 :|: s2 >= 0, s2 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 168 }-> s20 :|: s20 >= 0, s20 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 167 }-> s21 :|: s21 >= 0, s21 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s22 :|: s22 >= 0, s22 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 167 }-> s23 :|: s23 >= 0, s23 <= 0, z'' - 1 >= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s24 :|: s24 >= 0, s24 <= 0, z'' - 1 >= 0, z' - 1 >= 0, z = z' - 1, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 169 }-> s3 :|: s3 >= 0, s3 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s4 :|: s4 >= 0, s4 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1, X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 169 }-> s5 :|: s5 >= 0, s5 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1, z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s6 :|: s6 >= 0, s6 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1, X2 >= 0, z'' - 1 = X2
   f(z, z', z'') -{ 168 }-> s7 :|: s7 >= 0, s7 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s8 :|: s8 >= 0, s8 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s9 :|: s9 >= 0, s9 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g(z) -{ 1 }-> 0 :|: z = 1
   g(z) -{ 1 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {g}, {encode_c}, {activate}, {encode_b}, {encArg}, {encode_activate}, {encode_g}, {encode_n__g}, {encode_f}
Previous analysis results are:
  f: runtime: O(1) [162], size: O(1) [0]
  b: runtime: O(1) [1], size: O(1) [1]
  g: runtime: ?, size: O(n^1) [1 + z]

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

(39) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: g
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 1

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

(40)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 0 :|: z - 1 >= 0, z - 1 = 1
   activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   b -{ 0 }-> 1 :|: 
   b -{ 1 }-> 0 :|: 
   b -{ 0 }-> 0 :|: 
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 1 }-> g(X) :|: z = 1 + 2, 1 = 1 + X, X >= 0
   encArg(z) -{ 0 }-> g(g(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> g(f(encArg(x_1228), encArg(x_256), encArg(x_356))) :|: z = 1 + (1 + x_1228 + x_256 + x_356), x_256 >= 0, x_1228 >= 0, x_356 >= 0
   encArg(z) -{ 0 }-> g(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> g(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> activate(g(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(f(encArg(x_1232), encArg(x_257), encArg(x_357))) :|: x_1232 >= 0, x_357 >= 0, z = 1 + (1 + x_1232 + x_257 + x_357), x_257 >= 0
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, 1 = 1
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 1 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> g(X) :|: z = 2, 1 = 1 + X, X >= 0
   encode_activate(z) -{ 0 }-> activate(g(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(f(encArg(x_1464), encArg(x_2115), encArg(x_3115))) :|: x_3115 >= 0, x_1464 >= 0, x_2115 >= 0, z = 1 + x_1464 + x_2115 + x_3115
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_b -{ 0 }-> 1 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z, z', z'') -{ 0 }-> f(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g(z) -{ 0 }-> g(g(encArg(z - 1))) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> g(f(encArg(x_1468), encArg(x_2116), encArg(x_3116))) :|: x_3116 >= 0, z = 1 + x_1468 + x_2116 + x_3116, x_2116 >= 0, x_1468 >= 0
   encode_g(z) -{ 0 }-> g(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> g(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, 1 = 1
   encode_g(z) -{ 1 }-> 1 + X :|: z = 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z >= 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 1 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_g(z) -{ 2 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_n__g(z) -{ 0 }-> 0 :|: z >= 0
   encode_n__g(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   f(z, z', z'') -{ 166 }-> s :|: s >= 0, s <= 0, z'' >= 0, z' - 1 >= 0, z = z' - 1
   f(z, z', z'') -{ 169 }-> s' :|: s' >= 0, s' <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s'' :|: s'' >= 0, s'' <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 169 }-> s1 :|: s1 >= 0, s1 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s10 :|: s10 >= 0, s10 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 168 }-> s11 :|: s11 >= 0, s11 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s12 :|: s12 >= 0, s12 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s13 :|: s13 >= 0, s13 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s14 :|: s14 >= 0, s14 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 167 }-> s15 :|: s15 >= 0, s15 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s16 :|: s16 >= 0, s16 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s17 :|: s17 >= 0, s17 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s18 :|: s18 >= 0, s18 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 168 }-> s19 :|: s19 >= 0, s19 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X', z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s2 :|: s2 >= 0, s2 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 168 }-> s20 :|: s20 >= 0, s20 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 167 }-> s21 :|: s21 >= 0, s21 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s22 :|: s22 >= 0, s22 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 167 }-> s23 :|: s23 >= 0, s23 <= 0, z'' - 1 >= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s24 :|: s24 >= 0, s24 <= 0, z'' - 1 >= 0, z' - 1 >= 0, z = z' - 1, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 169 }-> s3 :|: s3 >= 0, s3 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s4 :|: s4 >= 0, s4 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1, X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 169 }-> s5 :|: s5 >= 0, s5 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1, z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s6 :|: s6 >= 0, s6 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1, X2 >= 0, z'' - 1 = X2
   f(z, z', z'') -{ 168 }-> s7 :|: s7 >= 0, s7 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s8 :|: s8 >= 0, s8 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s9 :|: s9 >= 0, s9 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g(z) -{ 1 }-> 0 :|: z = 1
   g(z) -{ 1 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {encode_c}, {activate}, {encode_b}, {encArg}, {encode_activate}, {encode_g}, {encode_n__g}, {encode_f}
Previous analysis results are:
  f: runtime: O(1) [162], size: O(1) [0]
  b: runtime: O(1) [1], size: O(1) [1]
  g: runtime: O(1) [1], size: O(n^1) [1 + z]

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

(41) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(42)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 0 :|: z - 1 >= 0, z - 1 = 1
   activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   b -{ 0 }-> 1 :|: 
   b -{ 1 }-> 0 :|: 
   b -{ 0 }-> 0 :|: 
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> s25 :|: s25 >= 0, s25 <= X + 1, z = 1 + 2, 1 = 1 + X, X >= 0
   encArg(z) -{ 0 }-> g(g(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> g(f(encArg(x_1228), encArg(x_256), encArg(x_356))) :|: z = 1 + (1 + x_1228 + x_256 + x_356), x_256 >= 0, x_1228 >= 0, x_356 >= 0
   encArg(z) -{ 0 }-> g(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> g(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> activate(g(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(f(encArg(x_1232), encArg(x_257), encArg(x_357))) :|: x_1232 >= 0, x_357 >= 0, z = 1 + (1 + x_1232 + x_257 + x_357), x_257 >= 0
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, 1 = 1
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 1 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> s26 :|: s26 >= 0, s26 <= X + 1, z = 2, 1 = 1 + X, X >= 0
   encode_activate(z) -{ 0 }-> activate(g(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(f(encArg(x_1464), encArg(x_2115), encArg(x_3115))) :|: x_3115 >= 0, x_1464 >= 0, x_2115 >= 0, z = 1 + x_1464 + x_2115 + x_3115
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_b -{ 0 }-> 1 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z, z', z'') -{ 0 }-> f(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g(z) -{ 0 }-> g(g(encArg(z - 1))) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> g(f(encArg(x_1468), encArg(x_2116), encArg(x_3116))) :|: x_3116 >= 0, z = 1 + x_1468 + x_2116 + x_3116, x_2116 >= 0, x_1468 >= 0
   encode_g(z) -{ 0 }-> g(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> g(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, 1 = 1
   encode_g(z) -{ 1 }-> 1 + X :|: z = 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z >= 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 1 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_g(z) -{ 2 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_n__g(z) -{ 0 }-> 0 :|: z >= 0
   encode_n__g(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   f(z, z', z'') -{ 166 }-> s :|: s >= 0, s <= 0, z'' >= 0, z' - 1 >= 0, z = z' - 1
   f(z, z', z'') -{ 169 }-> s' :|: s' >= 0, s' <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s'' :|: s'' >= 0, s'' <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 169 }-> s1 :|: s1 >= 0, s1 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s10 :|: s10 >= 0, s10 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 168 }-> s11 :|: s11 >= 0, s11 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s12 :|: s12 >= 0, s12 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s13 :|: s13 >= 0, s13 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s14 :|: s14 >= 0, s14 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 167 }-> s15 :|: s15 >= 0, s15 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s16 :|: s16 >= 0, s16 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s17 :|: s17 >= 0, s17 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s18 :|: s18 >= 0, s18 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 168 }-> s19 :|: s19 >= 0, s19 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X', z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s2 :|: s2 >= 0, s2 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 168 }-> s20 :|: s20 >= 0, s20 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 167 }-> s21 :|: s21 >= 0, s21 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s22 :|: s22 >= 0, s22 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 167 }-> s23 :|: s23 >= 0, s23 <= 0, z'' - 1 >= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s24 :|: s24 >= 0, s24 <= 0, z'' - 1 >= 0, z' - 1 >= 0, z = z' - 1, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 169 }-> s3 :|: s3 >= 0, s3 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s4 :|: s4 >= 0, s4 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1, X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 169 }-> s5 :|: s5 >= 0, s5 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1, z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s6 :|: s6 >= 0, s6 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1, X2 >= 0, z'' - 1 = X2
   f(z, z', z'') -{ 168 }-> s7 :|: s7 >= 0, s7 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s8 :|: s8 >= 0, s8 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s9 :|: s9 >= 0, s9 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g(z) -{ 1 }-> 0 :|: z = 1
   g(z) -{ 1 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {encode_c}, {activate}, {encode_b}, {encArg}, {encode_activate}, {encode_g}, {encode_n__g}, {encode_f}
Previous analysis results are:
  f: runtime: O(1) [162], size: O(1) [0]
  b: runtime: O(1) [1], size: O(1) [1]
  g: runtime: O(1) [1], size: O(n^1) [1 + z]

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

(43) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: encode_c
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 0

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

(44)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 0 :|: z - 1 >= 0, z - 1 = 1
   activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   b -{ 0 }-> 1 :|: 
   b -{ 1 }-> 0 :|: 
   b -{ 0 }-> 0 :|: 
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> s25 :|: s25 >= 0, s25 <= X + 1, z = 1 + 2, 1 = 1 + X, X >= 0
   encArg(z) -{ 0 }-> g(g(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> g(f(encArg(x_1228), encArg(x_256), encArg(x_356))) :|: z = 1 + (1 + x_1228 + x_256 + x_356), x_256 >= 0, x_1228 >= 0, x_356 >= 0
   encArg(z) -{ 0 }-> g(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> g(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> activate(g(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(f(encArg(x_1232), encArg(x_257), encArg(x_357))) :|: x_1232 >= 0, x_357 >= 0, z = 1 + (1 + x_1232 + x_257 + x_357), x_257 >= 0
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, 1 = 1
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 1 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> s26 :|: s26 >= 0, s26 <= X + 1, z = 2, 1 = 1 + X, X >= 0
   encode_activate(z) -{ 0 }-> activate(g(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(f(encArg(x_1464), encArg(x_2115), encArg(x_3115))) :|: x_3115 >= 0, x_1464 >= 0, x_2115 >= 0, z = 1 + x_1464 + x_2115 + x_3115
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_b -{ 0 }-> 1 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z, z', z'') -{ 0 }-> f(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g(z) -{ 0 }-> g(g(encArg(z - 1))) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> g(f(encArg(x_1468), encArg(x_2116), encArg(x_3116))) :|: x_3116 >= 0, z = 1 + x_1468 + x_2116 + x_3116, x_2116 >= 0, x_1468 >= 0
   encode_g(z) -{ 0 }-> g(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> g(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, 1 = 1
   encode_g(z) -{ 1 }-> 1 + X :|: z = 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z >= 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 1 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_g(z) -{ 2 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_n__g(z) -{ 0 }-> 0 :|: z >= 0
   encode_n__g(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   f(z, z', z'') -{ 166 }-> s :|: s >= 0, s <= 0, z'' >= 0, z' - 1 >= 0, z = z' - 1
   f(z, z', z'') -{ 169 }-> s' :|: s' >= 0, s' <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s'' :|: s'' >= 0, s'' <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 169 }-> s1 :|: s1 >= 0, s1 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s10 :|: s10 >= 0, s10 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 168 }-> s11 :|: s11 >= 0, s11 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s12 :|: s12 >= 0, s12 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s13 :|: s13 >= 0, s13 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s14 :|: s14 >= 0, s14 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 167 }-> s15 :|: s15 >= 0, s15 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s16 :|: s16 >= 0, s16 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s17 :|: s17 >= 0, s17 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s18 :|: s18 >= 0, s18 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 168 }-> s19 :|: s19 >= 0, s19 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X', z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s2 :|: s2 >= 0, s2 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 168 }-> s20 :|: s20 >= 0, s20 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 167 }-> s21 :|: s21 >= 0, s21 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s22 :|: s22 >= 0, s22 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 167 }-> s23 :|: s23 >= 0, s23 <= 0, z'' - 1 >= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s24 :|: s24 >= 0, s24 <= 0, z'' - 1 >= 0, z' - 1 >= 0, z = z' - 1, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 169 }-> s3 :|: s3 >= 0, s3 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s4 :|: s4 >= 0, s4 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1, X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 169 }-> s5 :|: s5 >= 0, s5 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1, z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s6 :|: s6 >= 0, s6 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1, X2 >= 0, z'' - 1 = X2
   f(z, z', z'') -{ 168 }-> s7 :|: s7 >= 0, s7 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s8 :|: s8 >= 0, s8 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s9 :|: s9 >= 0, s9 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g(z) -{ 1 }-> 0 :|: z = 1
   g(z) -{ 1 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {encode_c}, {activate}, {encode_b}, {encArg}, {encode_activate}, {encode_g}, {encode_n__g}, {encode_f}
Previous analysis results are:
  f: runtime: O(1) [162], size: O(1) [0]
  b: runtime: O(1) [1], size: O(1) [1]
  g: runtime: O(1) [1], size: O(n^1) [1 + z]
  encode_c: runtime: ?, size: O(1) [0]

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

(45) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: encode_c
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 0

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

(46)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 0 :|: z - 1 >= 0, z - 1 = 1
   activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   b -{ 0 }-> 1 :|: 
   b -{ 1 }-> 0 :|: 
   b -{ 0 }-> 0 :|: 
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> s25 :|: s25 >= 0, s25 <= X + 1, z = 1 + 2, 1 = 1 + X, X >= 0
   encArg(z) -{ 0 }-> g(g(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> g(f(encArg(x_1228), encArg(x_256), encArg(x_356))) :|: z = 1 + (1 + x_1228 + x_256 + x_356), x_256 >= 0, x_1228 >= 0, x_356 >= 0
   encArg(z) -{ 0 }-> g(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> g(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> activate(g(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(f(encArg(x_1232), encArg(x_257), encArg(x_357))) :|: x_1232 >= 0, x_357 >= 0, z = 1 + (1 + x_1232 + x_257 + x_357), x_257 >= 0
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, 1 = 1
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 1 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> s26 :|: s26 >= 0, s26 <= X + 1, z = 2, 1 = 1 + X, X >= 0
   encode_activate(z) -{ 0 }-> activate(g(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(f(encArg(x_1464), encArg(x_2115), encArg(x_3115))) :|: x_3115 >= 0, x_1464 >= 0, x_2115 >= 0, z = 1 + x_1464 + x_2115 + x_3115
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_b -{ 0 }-> 1 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z, z', z'') -{ 0 }-> f(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g(z) -{ 0 }-> g(g(encArg(z - 1))) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> g(f(encArg(x_1468), encArg(x_2116), encArg(x_3116))) :|: x_3116 >= 0, z = 1 + x_1468 + x_2116 + x_3116, x_2116 >= 0, x_1468 >= 0
   encode_g(z) -{ 0 }-> g(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> g(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, 1 = 1
   encode_g(z) -{ 1 }-> 1 + X :|: z = 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z >= 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 1 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_g(z) -{ 2 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_n__g(z) -{ 0 }-> 0 :|: z >= 0
   encode_n__g(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   f(z, z', z'') -{ 166 }-> s :|: s >= 0, s <= 0, z'' >= 0, z' - 1 >= 0, z = z' - 1
   f(z, z', z'') -{ 169 }-> s' :|: s' >= 0, s' <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s'' :|: s'' >= 0, s'' <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 169 }-> s1 :|: s1 >= 0, s1 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s10 :|: s10 >= 0, s10 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 168 }-> s11 :|: s11 >= 0, s11 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s12 :|: s12 >= 0, s12 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s13 :|: s13 >= 0, s13 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s14 :|: s14 >= 0, s14 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 167 }-> s15 :|: s15 >= 0, s15 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s16 :|: s16 >= 0, s16 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s17 :|: s17 >= 0, s17 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s18 :|: s18 >= 0, s18 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 168 }-> s19 :|: s19 >= 0, s19 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X', z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s2 :|: s2 >= 0, s2 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 168 }-> s20 :|: s20 >= 0, s20 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 167 }-> s21 :|: s21 >= 0, s21 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s22 :|: s22 >= 0, s22 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 167 }-> s23 :|: s23 >= 0, s23 <= 0, z'' - 1 >= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s24 :|: s24 >= 0, s24 <= 0, z'' - 1 >= 0, z' - 1 >= 0, z = z' - 1, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 169 }-> s3 :|: s3 >= 0, s3 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s4 :|: s4 >= 0, s4 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1, X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 169 }-> s5 :|: s5 >= 0, s5 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1, z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s6 :|: s6 >= 0, s6 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1, X2 >= 0, z'' - 1 = X2
   f(z, z', z'') -{ 168 }-> s7 :|: s7 >= 0, s7 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s8 :|: s8 >= 0, s8 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s9 :|: s9 >= 0, s9 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g(z) -{ 1 }-> 0 :|: z = 1
   g(z) -{ 1 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {activate}, {encode_b}, {encArg}, {encode_activate}, {encode_g}, {encode_n__g}, {encode_f}
Previous analysis results are:
  f: runtime: O(1) [162], size: O(1) [0]
  b: runtime: O(1) [1], size: O(1) [1]
  g: runtime: O(1) [1], size: O(n^1) [1 + z]
  encode_c: runtime: O(1) [0], size: O(1) [0]

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

(47) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(48)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 0 :|: z - 1 >= 0, z - 1 = 1
   activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   b -{ 0 }-> 1 :|: 
   b -{ 1 }-> 0 :|: 
   b -{ 0 }-> 0 :|: 
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> s25 :|: s25 >= 0, s25 <= X + 1, z = 1 + 2, 1 = 1 + X, X >= 0
   encArg(z) -{ 0 }-> g(g(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> g(f(encArg(x_1228), encArg(x_256), encArg(x_356))) :|: z = 1 + (1 + x_1228 + x_256 + x_356), x_256 >= 0, x_1228 >= 0, x_356 >= 0
   encArg(z) -{ 0 }-> g(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> g(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> activate(g(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(f(encArg(x_1232), encArg(x_257), encArg(x_357))) :|: x_1232 >= 0, x_357 >= 0, z = 1 + (1 + x_1232 + x_257 + x_357), x_257 >= 0
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, 1 = 1
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 1 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> s26 :|: s26 >= 0, s26 <= X + 1, z = 2, 1 = 1 + X, X >= 0
   encode_activate(z) -{ 0 }-> activate(g(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(f(encArg(x_1464), encArg(x_2115), encArg(x_3115))) :|: x_3115 >= 0, x_1464 >= 0, x_2115 >= 0, z = 1 + x_1464 + x_2115 + x_3115
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_b -{ 0 }-> 1 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z, z', z'') -{ 0 }-> f(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g(z) -{ 0 }-> g(g(encArg(z - 1))) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> g(f(encArg(x_1468), encArg(x_2116), encArg(x_3116))) :|: x_3116 >= 0, z = 1 + x_1468 + x_2116 + x_3116, x_2116 >= 0, x_1468 >= 0
   encode_g(z) -{ 0 }-> g(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> g(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, 1 = 1
   encode_g(z) -{ 1 }-> 1 + X :|: z = 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z >= 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 1 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_g(z) -{ 2 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_n__g(z) -{ 0 }-> 0 :|: z >= 0
   encode_n__g(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   f(z, z', z'') -{ 166 }-> s :|: s >= 0, s <= 0, z'' >= 0, z' - 1 >= 0, z = z' - 1
   f(z, z', z'') -{ 169 }-> s' :|: s' >= 0, s' <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s'' :|: s'' >= 0, s'' <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 169 }-> s1 :|: s1 >= 0, s1 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s10 :|: s10 >= 0, s10 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 168 }-> s11 :|: s11 >= 0, s11 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s12 :|: s12 >= 0, s12 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s13 :|: s13 >= 0, s13 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s14 :|: s14 >= 0, s14 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 167 }-> s15 :|: s15 >= 0, s15 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s16 :|: s16 >= 0, s16 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s17 :|: s17 >= 0, s17 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s18 :|: s18 >= 0, s18 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 168 }-> s19 :|: s19 >= 0, s19 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X', z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s2 :|: s2 >= 0, s2 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 168 }-> s20 :|: s20 >= 0, s20 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 167 }-> s21 :|: s21 >= 0, s21 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s22 :|: s22 >= 0, s22 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 167 }-> s23 :|: s23 >= 0, s23 <= 0, z'' - 1 >= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s24 :|: s24 >= 0, s24 <= 0, z'' - 1 >= 0, z' - 1 >= 0, z = z' - 1, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 169 }-> s3 :|: s3 >= 0, s3 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s4 :|: s4 >= 0, s4 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1, X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 169 }-> s5 :|: s5 >= 0, s5 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1, z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s6 :|: s6 >= 0, s6 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1, X2 >= 0, z'' - 1 = X2
   f(z, z', z'') -{ 168 }-> s7 :|: s7 >= 0, s7 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s8 :|: s8 >= 0, s8 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s9 :|: s9 >= 0, s9 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g(z) -{ 1 }-> 0 :|: z = 1
   g(z) -{ 1 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {activate}, {encode_b}, {encArg}, {encode_activate}, {encode_g}, {encode_n__g}, {encode_f}
Previous analysis results are:
  f: runtime: O(1) [162], size: O(1) [0]
  b: runtime: O(1) [1], size: O(1) [1]
  g: runtime: O(1) [1], size: O(n^1) [1 + z]
  encode_c: runtime: O(1) [0], size: O(1) [0]

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

(49) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using KoAT for: activate
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: z

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

(50)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 0 :|: z - 1 >= 0, z - 1 = 1
   activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   b -{ 0 }-> 1 :|: 
   b -{ 1 }-> 0 :|: 
   b -{ 0 }-> 0 :|: 
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> s25 :|: s25 >= 0, s25 <= X + 1, z = 1 + 2, 1 = 1 + X, X >= 0
   encArg(z) -{ 0 }-> g(g(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> g(f(encArg(x_1228), encArg(x_256), encArg(x_356))) :|: z = 1 + (1 + x_1228 + x_256 + x_356), x_256 >= 0, x_1228 >= 0, x_356 >= 0
   encArg(z) -{ 0 }-> g(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> g(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> activate(g(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(f(encArg(x_1232), encArg(x_257), encArg(x_357))) :|: x_1232 >= 0, x_357 >= 0, z = 1 + (1 + x_1232 + x_257 + x_357), x_257 >= 0
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, 1 = 1
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 1 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> s26 :|: s26 >= 0, s26 <= X + 1, z = 2, 1 = 1 + X, X >= 0
   encode_activate(z) -{ 0 }-> activate(g(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(f(encArg(x_1464), encArg(x_2115), encArg(x_3115))) :|: x_3115 >= 0, x_1464 >= 0, x_2115 >= 0, z = 1 + x_1464 + x_2115 + x_3115
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_b -{ 0 }-> 1 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z, z', z'') -{ 0 }-> f(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g(z) -{ 0 }-> g(g(encArg(z - 1))) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> g(f(encArg(x_1468), encArg(x_2116), encArg(x_3116))) :|: x_3116 >= 0, z = 1 + x_1468 + x_2116 + x_3116, x_2116 >= 0, x_1468 >= 0
   encode_g(z) -{ 0 }-> g(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> g(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, 1 = 1
   encode_g(z) -{ 1 }-> 1 + X :|: z = 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z >= 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 1 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_g(z) -{ 2 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_n__g(z) -{ 0 }-> 0 :|: z >= 0
   encode_n__g(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   f(z, z', z'') -{ 166 }-> s :|: s >= 0, s <= 0, z'' >= 0, z' - 1 >= 0, z = z' - 1
   f(z, z', z'') -{ 169 }-> s' :|: s' >= 0, s' <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s'' :|: s'' >= 0, s'' <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 169 }-> s1 :|: s1 >= 0, s1 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s10 :|: s10 >= 0, s10 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 168 }-> s11 :|: s11 >= 0, s11 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s12 :|: s12 >= 0, s12 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s13 :|: s13 >= 0, s13 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s14 :|: s14 >= 0, s14 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 167 }-> s15 :|: s15 >= 0, s15 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s16 :|: s16 >= 0, s16 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s17 :|: s17 >= 0, s17 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s18 :|: s18 >= 0, s18 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 168 }-> s19 :|: s19 >= 0, s19 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X', z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s2 :|: s2 >= 0, s2 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 168 }-> s20 :|: s20 >= 0, s20 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 167 }-> s21 :|: s21 >= 0, s21 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s22 :|: s22 >= 0, s22 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 167 }-> s23 :|: s23 >= 0, s23 <= 0, z'' - 1 >= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s24 :|: s24 >= 0, s24 <= 0, z'' - 1 >= 0, z' - 1 >= 0, z = z' - 1, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 169 }-> s3 :|: s3 >= 0, s3 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s4 :|: s4 >= 0, s4 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1, X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 169 }-> s5 :|: s5 >= 0, s5 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1, z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s6 :|: s6 >= 0, s6 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1, X2 >= 0, z'' - 1 = X2
   f(z, z', z'') -{ 168 }-> s7 :|: s7 >= 0, s7 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s8 :|: s8 >= 0, s8 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s9 :|: s9 >= 0, s9 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g(z) -{ 1 }-> 0 :|: z = 1
   g(z) -{ 1 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {activate}, {encode_b}, {encArg}, {encode_activate}, {encode_g}, {encode_n__g}, {encode_f}
Previous analysis results are:
  f: runtime: O(1) [162], size: O(1) [0]
  b: runtime: O(1) [1], size: O(1) [1]
  g: runtime: O(1) [1], size: O(n^1) [1 + z]
  encode_c: runtime: O(1) [0], size: O(1) [0]
  activate: runtime: ?, size: O(n^1) [z]

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

(51) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using KoAT for: activate
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 5

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

(52)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 0 :|: z - 1 >= 0, z - 1 = 1
   activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   b -{ 0 }-> 1 :|: 
   b -{ 1 }-> 0 :|: 
   b -{ 0 }-> 0 :|: 
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> s25 :|: s25 >= 0, s25 <= X + 1, z = 1 + 2, 1 = 1 + X, X >= 0
   encArg(z) -{ 0 }-> g(g(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> g(f(encArg(x_1228), encArg(x_256), encArg(x_356))) :|: z = 1 + (1 + x_1228 + x_256 + x_356), x_256 >= 0, x_1228 >= 0, x_356 >= 0
   encArg(z) -{ 0 }-> g(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> g(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> activate(g(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(f(encArg(x_1232), encArg(x_257), encArg(x_357))) :|: x_1232 >= 0, x_357 >= 0, z = 1 + (1 + x_1232 + x_257 + x_357), x_257 >= 0
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, 1 = 1
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 1 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> s26 :|: s26 >= 0, s26 <= X + 1, z = 2, 1 = 1 + X, X >= 0
   encode_activate(z) -{ 0 }-> activate(g(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(f(encArg(x_1464), encArg(x_2115), encArg(x_3115))) :|: x_3115 >= 0, x_1464 >= 0, x_2115 >= 0, z = 1 + x_1464 + x_2115 + x_3115
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_b -{ 0 }-> 1 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z, z', z'') -{ 0 }-> f(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g(z) -{ 0 }-> g(g(encArg(z - 1))) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> g(f(encArg(x_1468), encArg(x_2116), encArg(x_3116))) :|: x_3116 >= 0, z = 1 + x_1468 + x_2116 + x_3116, x_2116 >= 0, x_1468 >= 0
   encode_g(z) -{ 0 }-> g(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> g(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, 1 = 1
   encode_g(z) -{ 1 }-> 1 + X :|: z = 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z >= 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 1 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_g(z) -{ 2 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_n__g(z) -{ 0 }-> 0 :|: z >= 0
   encode_n__g(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   f(z, z', z'') -{ 166 }-> s :|: s >= 0, s <= 0, z'' >= 0, z' - 1 >= 0, z = z' - 1
   f(z, z', z'') -{ 169 }-> s' :|: s' >= 0, s' <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s'' :|: s'' >= 0, s'' <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 169 }-> s1 :|: s1 >= 0, s1 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s10 :|: s10 >= 0, s10 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 168 }-> s11 :|: s11 >= 0, s11 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s12 :|: s12 >= 0, s12 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s13 :|: s13 >= 0, s13 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s14 :|: s14 >= 0, s14 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 167 }-> s15 :|: s15 >= 0, s15 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s16 :|: s16 >= 0, s16 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s17 :|: s17 >= 0, s17 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s18 :|: s18 >= 0, s18 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 168 }-> s19 :|: s19 >= 0, s19 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X', z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s2 :|: s2 >= 0, s2 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 168 }-> s20 :|: s20 >= 0, s20 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 167 }-> s21 :|: s21 >= 0, s21 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s22 :|: s22 >= 0, s22 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 167 }-> s23 :|: s23 >= 0, s23 <= 0, z'' - 1 >= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s24 :|: s24 >= 0, s24 <= 0, z'' - 1 >= 0, z' - 1 >= 0, z = z' - 1, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 169 }-> s3 :|: s3 >= 0, s3 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s4 :|: s4 >= 0, s4 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1, X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 169 }-> s5 :|: s5 >= 0, s5 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1, z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s6 :|: s6 >= 0, s6 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1, X2 >= 0, z'' - 1 = X2
   f(z, z', z'') -{ 168 }-> s7 :|: s7 >= 0, s7 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s8 :|: s8 >= 0, s8 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s9 :|: s9 >= 0, s9 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g(z) -{ 1 }-> 0 :|: z = 1
   g(z) -{ 1 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {encode_b}, {encArg}, {encode_activate}, {encode_g}, {encode_n__g}, {encode_f}
Previous analysis results are:
  f: runtime: O(1) [162], size: O(1) [0]
  b: runtime: O(1) [1], size: O(1) [1]
  g: runtime: O(1) [1], size: O(n^1) [1 + z]
  encode_c: runtime: O(1) [0], size: O(1) [0]
  activate: runtime: O(1) [5], size: O(n^1) [z]

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

(53) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(54)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 0 :|: z - 1 >= 0, z - 1 = 1
   activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   b -{ 0 }-> 1 :|: 
   b -{ 1 }-> 0 :|: 
   b -{ 0 }-> 0 :|: 
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> s25 :|: s25 >= 0, s25 <= X + 1, z = 1 + 2, 1 = 1 + X, X >= 0
   encArg(z) -{ 0 }-> g(g(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> g(f(encArg(x_1228), encArg(x_256), encArg(x_356))) :|: z = 1 + (1 + x_1228 + x_256 + x_356), x_256 >= 0, x_1228 >= 0, x_356 >= 0
   encArg(z) -{ 0 }-> g(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> g(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> activate(g(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(f(encArg(x_1232), encArg(x_257), encArg(x_357))) :|: x_1232 >= 0, x_357 >= 0, z = 1 + (1 + x_1232 + x_257 + x_357), x_257 >= 0
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, 1 = 1
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 1 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> s26 :|: s26 >= 0, s26 <= X + 1, z = 2, 1 = 1 + X, X >= 0
   encode_activate(z) -{ 0 }-> activate(g(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(f(encArg(x_1464), encArg(x_2115), encArg(x_3115))) :|: x_3115 >= 0, x_1464 >= 0, x_2115 >= 0, z = 1 + x_1464 + x_2115 + x_3115
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_b -{ 0 }-> 1 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z, z', z'') -{ 0 }-> f(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g(z) -{ 0 }-> g(g(encArg(z - 1))) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> g(f(encArg(x_1468), encArg(x_2116), encArg(x_3116))) :|: x_3116 >= 0, z = 1 + x_1468 + x_2116 + x_3116, x_2116 >= 0, x_1468 >= 0
   encode_g(z) -{ 0 }-> g(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> g(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, 1 = 1
   encode_g(z) -{ 1 }-> 1 + X :|: z = 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z >= 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 1 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_g(z) -{ 2 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_n__g(z) -{ 0 }-> 0 :|: z >= 0
   encode_n__g(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   f(z, z', z'') -{ 166 }-> s :|: s >= 0, s <= 0, z'' >= 0, z' - 1 >= 0, z = z' - 1
   f(z, z', z'') -{ 169 }-> s' :|: s' >= 0, s' <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s'' :|: s'' >= 0, s'' <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 169 }-> s1 :|: s1 >= 0, s1 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s10 :|: s10 >= 0, s10 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 168 }-> s11 :|: s11 >= 0, s11 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s12 :|: s12 >= 0, s12 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s13 :|: s13 >= 0, s13 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s14 :|: s14 >= 0, s14 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 167 }-> s15 :|: s15 >= 0, s15 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s16 :|: s16 >= 0, s16 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s17 :|: s17 >= 0, s17 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s18 :|: s18 >= 0, s18 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 168 }-> s19 :|: s19 >= 0, s19 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X', z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s2 :|: s2 >= 0, s2 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 168 }-> s20 :|: s20 >= 0, s20 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 167 }-> s21 :|: s21 >= 0, s21 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s22 :|: s22 >= 0, s22 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 167 }-> s23 :|: s23 >= 0, s23 <= 0, z'' - 1 >= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s24 :|: s24 >= 0, s24 <= 0, z'' - 1 >= 0, z' - 1 >= 0, z = z' - 1, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 169 }-> s3 :|: s3 >= 0, s3 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s4 :|: s4 >= 0, s4 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1, X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 169 }-> s5 :|: s5 >= 0, s5 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1, z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s6 :|: s6 >= 0, s6 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1, X2 >= 0, z'' - 1 = X2
   f(z, z', z'') -{ 168 }-> s7 :|: s7 >= 0, s7 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s8 :|: s8 >= 0, s8 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s9 :|: s9 >= 0, s9 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g(z) -{ 1 }-> 0 :|: z = 1
   g(z) -{ 1 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {encode_b}, {encArg}, {encode_activate}, {encode_g}, {encode_n__g}, {encode_f}
Previous analysis results are:
  f: runtime: O(1) [162], size: O(1) [0]
  b: runtime: O(1) [1], size: O(1) [1]
  g: runtime: O(1) [1], size: O(n^1) [1 + z]
  encode_c: runtime: O(1) [0], size: O(1) [0]
  activate: runtime: O(1) [5], size: O(n^1) [z]

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

(55) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: encode_b
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 1

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

(56)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 0 :|: z - 1 >= 0, z - 1 = 1
   activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   b -{ 0 }-> 1 :|: 
   b -{ 1 }-> 0 :|: 
   b -{ 0 }-> 0 :|: 
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> s25 :|: s25 >= 0, s25 <= X + 1, z = 1 + 2, 1 = 1 + X, X >= 0
   encArg(z) -{ 0 }-> g(g(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> g(f(encArg(x_1228), encArg(x_256), encArg(x_356))) :|: z = 1 + (1 + x_1228 + x_256 + x_356), x_256 >= 0, x_1228 >= 0, x_356 >= 0
   encArg(z) -{ 0 }-> g(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> g(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> activate(g(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(f(encArg(x_1232), encArg(x_257), encArg(x_357))) :|: x_1232 >= 0, x_357 >= 0, z = 1 + (1 + x_1232 + x_257 + x_357), x_257 >= 0
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, 1 = 1
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 1 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> s26 :|: s26 >= 0, s26 <= X + 1, z = 2, 1 = 1 + X, X >= 0
   encode_activate(z) -{ 0 }-> activate(g(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(f(encArg(x_1464), encArg(x_2115), encArg(x_3115))) :|: x_3115 >= 0, x_1464 >= 0, x_2115 >= 0, z = 1 + x_1464 + x_2115 + x_3115
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_b -{ 0 }-> 1 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z, z', z'') -{ 0 }-> f(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g(z) -{ 0 }-> g(g(encArg(z - 1))) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> g(f(encArg(x_1468), encArg(x_2116), encArg(x_3116))) :|: x_3116 >= 0, z = 1 + x_1468 + x_2116 + x_3116, x_2116 >= 0, x_1468 >= 0
   encode_g(z) -{ 0 }-> g(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> g(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, 1 = 1
   encode_g(z) -{ 1 }-> 1 + X :|: z = 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z >= 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 1 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_g(z) -{ 2 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_n__g(z) -{ 0 }-> 0 :|: z >= 0
   encode_n__g(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   f(z, z', z'') -{ 166 }-> s :|: s >= 0, s <= 0, z'' >= 0, z' - 1 >= 0, z = z' - 1
   f(z, z', z'') -{ 169 }-> s' :|: s' >= 0, s' <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s'' :|: s'' >= 0, s'' <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 169 }-> s1 :|: s1 >= 0, s1 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s10 :|: s10 >= 0, s10 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 168 }-> s11 :|: s11 >= 0, s11 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s12 :|: s12 >= 0, s12 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s13 :|: s13 >= 0, s13 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s14 :|: s14 >= 0, s14 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 167 }-> s15 :|: s15 >= 0, s15 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s16 :|: s16 >= 0, s16 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s17 :|: s17 >= 0, s17 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s18 :|: s18 >= 0, s18 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 168 }-> s19 :|: s19 >= 0, s19 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X', z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s2 :|: s2 >= 0, s2 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 168 }-> s20 :|: s20 >= 0, s20 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 167 }-> s21 :|: s21 >= 0, s21 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s22 :|: s22 >= 0, s22 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 167 }-> s23 :|: s23 >= 0, s23 <= 0, z'' - 1 >= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s24 :|: s24 >= 0, s24 <= 0, z'' - 1 >= 0, z' - 1 >= 0, z = z' - 1, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 169 }-> s3 :|: s3 >= 0, s3 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s4 :|: s4 >= 0, s4 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1, X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 169 }-> s5 :|: s5 >= 0, s5 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1, z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s6 :|: s6 >= 0, s6 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1, X2 >= 0, z'' - 1 = X2
   f(z, z', z'') -{ 168 }-> s7 :|: s7 >= 0, s7 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s8 :|: s8 >= 0, s8 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s9 :|: s9 >= 0, s9 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g(z) -{ 1 }-> 0 :|: z = 1
   g(z) -{ 1 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {encode_b}, {encArg}, {encode_activate}, {encode_g}, {encode_n__g}, {encode_f}
Previous analysis results are:
  f: runtime: O(1) [162], size: O(1) [0]
  b: runtime: O(1) [1], size: O(1) [1]
  g: runtime: O(1) [1], size: O(n^1) [1 + z]
  encode_c: runtime: O(1) [0], size: O(1) [0]
  activate: runtime: O(1) [5], size: O(n^1) [z]
  encode_b: runtime: ?, size: O(1) [1]

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

(57) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: encode_b
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 1

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

(58)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 0 :|: z - 1 >= 0, z - 1 = 1
   activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   b -{ 0 }-> 1 :|: 
   b -{ 1 }-> 0 :|: 
   b -{ 0 }-> 0 :|: 
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> s25 :|: s25 >= 0, s25 <= X + 1, z = 1 + 2, 1 = 1 + X, X >= 0
   encArg(z) -{ 0 }-> g(g(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> g(f(encArg(x_1228), encArg(x_256), encArg(x_356))) :|: z = 1 + (1 + x_1228 + x_256 + x_356), x_256 >= 0, x_1228 >= 0, x_356 >= 0
   encArg(z) -{ 0 }-> g(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> g(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> activate(g(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(f(encArg(x_1232), encArg(x_257), encArg(x_357))) :|: x_1232 >= 0, x_357 >= 0, z = 1 + (1 + x_1232 + x_257 + x_357), x_257 >= 0
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, 1 = 1
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 1 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> s26 :|: s26 >= 0, s26 <= X + 1, z = 2, 1 = 1 + X, X >= 0
   encode_activate(z) -{ 0 }-> activate(g(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(f(encArg(x_1464), encArg(x_2115), encArg(x_3115))) :|: x_3115 >= 0, x_1464 >= 0, x_2115 >= 0, z = 1 + x_1464 + x_2115 + x_3115
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_b -{ 0 }-> 1 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z, z', z'') -{ 0 }-> f(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g(z) -{ 0 }-> g(g(encArg(z - 1))) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> g(f(encArg(x_1468), encArg(x_2116), encArg(x_3116))) :|: x_3116 >= 0, z = 1 + x_1468 + x_2116 + x_3116, x_2116 >= 0, x_1468 >= 0
   encode_g(z) -{ 0 }-> g(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> g(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, 1 = 1
   encode_g(z) -{ 1 }-> 1 + X :|: z = 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z >= 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 1 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_g(z) -{ 2 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_n__g(z) -{ 0 }-> 0 :|: z >= 0
   encode_n__g(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   f(z, z', z'') -{ 166 }-> s :|: s >= 0, s <= 0, z'' >= 0, z' - 1 >= 0, z = z' - 1
   f(z, z', z'') -{ 169 }-> s' :|: s' >= 0, s' <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s'' :|: s'' >= 0, s'' <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 169 }-> s1 :|: s1 >= 0, s1 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s10 :|: s10 >= 0, s10 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 168 }-> s11 :|: s11 >= 0, s11 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s12 :|: s12 >= 0, s12 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s13 :|: s13 >= 0, s13 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s14 :|: s14 >= 0, s14 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 167 }-> s15 :|: s15 >= 0, s15 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s16 :|: s16 >= 0, s16 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s17 :|: s17 >= 0, s17 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s18 :|: s18 >= 0, s18 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 168 }-> s19 :|: s19 >= 0, s19 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X', z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s2 :|: s2 >= 0, s2 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 168 }-> s20 :|: s20 >= 0, s20 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 167 }-> s21 :|: s21 >= 0, s21 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s22 :|: s22 >= 0, s22 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 167 }-> s23 :|: s23 >= 0, s23 <= 0, z'' - 1 >= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s24 :|: s24 >= 0, s24 <= 0, z'' - 1 >= 0, z' - 1 >= 0, z = z' - 1, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 169 }-> s3 :|: s3 >= 0, s3 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s4 :|: s4 >= 0, s4 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1, X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 169 }-> s5 :|: s5 >= 0, s5 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1, z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s6 :|: s6 >= 0, s6 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1, X2 >= 0, z'' - 1 = X2
   f(z, z', z'') -{ 168 }-> s7 :|: s7 >= 0, s7 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s8 :|: s8 >= 0, s8 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s9 :|: s9 >= 0, s9 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g(z) -{ 1 }-> 0 :|: z = 1
   g(z) -{ 1 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {encArg}, {encode_activate}, {encode_g}, {encode_n__g}, {encode_f}
Previous analysis results are:
  f: runtime: O(1) [162], size: O(1) [0]
  b: runtime: O(1) [1], size: O(1) [1]
  g: runtime: O(1) [1], size: O(n^1) [1 + z]
  encode_c: runtime: O(1) [0], size: O(1) [0]
  activate: runtime: O(1) [5], size: O(n^1) [z]
  encode_b: runtime: O(1) [1], size: O(1) [1]

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

(59) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(60)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 0 :|: z - 1 >= 0, z - 1 = 1
   activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   b -{ 0 }-> 1 :|: 
   b -{ 1 }-> 0 :|: 
   b -{ 0 }-> 0 :|: 
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> s25 :|: s25 >= 0, s25 <= X + 1, z = 1 + 2, 1 = 1 + X, X >= 0
   encArg(z) -{ 0 }-> g(g(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> g(f(encArg(x_1228), encArg(x_256), encArg(x_356))) :|: z = 1 + (1 + x_1228 + x_256 + x_356), x_256 >= 0, x_1228 >= 0, x_356 >= 0
   encArg(z) -{ 0 }-> g(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> g(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> activate(g(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(f(encArg(x_1232), encArg(x_257), encArg(x_357))) :|: x_1232 >= 0, x_357 >= 0, z = 1 + (1 + x_1232 + x_257 + x_357), x_257 >= 0
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, 1 = 1
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 1 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> s26 :|: s26 >= 0, s26 <= X + 1, z = 2, 1 = 1 + X, X >= 0
   encode_activate(z) -{ 0 }-> activate(g(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(f(encArg(x_1464), encArg(x_2115), encArg(x_3115))) :|: x_3115 >= 0, x_1464 >= 0, x_2115 >= 0, z = 1 + x_1464 + x_2115 + x_3115
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_b -{ 0 }-> 1 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z, z', z'') -{ 0 }-> f(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g(z) -{ 0 }-> g(g(encArg(z - 1))) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> g(f(encArg(x_1468), encArg(x_2116), encArg(x_3116))) :|: x_3116 >= 0, z = 1 + x_1468 + x_2116 + x_3116, x_2116 >= 0, x_1468 >= 0
   encode_g(z) -{ 0 }-> g(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> g(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, 1 = 1
   encode_g(z) -{ 1 }-> 1 + X :|: z = 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z >= 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 1 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_g(z) -{ 2 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_n__g(z) -{ 0 }-> 0 :|: z >= 0
   encode_n__g(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   f(z, z', z'') -{ 166 }-> s :|: s >= 0, s <= 0, z'' >= 0, z' - 1 >= 0, z = z' - 1
   f(z, z', z'') -{ 169 }-> s' :|: s' >= 0, s' <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s'' :|: s'' >= 0, s'' <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 169 }-> s1 :|: s1 >= 0, s1 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s10 :|: s10 >= 0, s10 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 168 }-> s11 :|: s11 >= 0, s11 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s12 :|: s12 >= 0, s12 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s13 :|: s13 >= 0, s13 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s14 :|: s14 >= 0, s14 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 167 }-> s15 :|: s15 >= 0, s15 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s16 :|: s16 >= 0, s16 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s17 :|: s17 >= 0, s17 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s18 :|: s18 >= 0, s18 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 168 }-> s19 :|: s19 >= 0, s19 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X', z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s2 :|: s2 >= 0, s2 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 168 }-> s20 :|: s20 >= 0, s20 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 167 }-> s21 :|: s21 >= 0, s21 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s22 :|: s22 >= 0, s22 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 167 }-> s23 :|: s23 >= 0, s23 <= 0, z'' - 1 >= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s24 :|: s24 >= 0, s24 <= 0, z'' - 1 >= 0, z' - 1 >= 0, z = z' - 1, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 169 }-> s3 :|: s3 >= 0, s3 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s4 :|: s4 >= 0, s4 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1, X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 169 }-> s5 :|: s5 >= 0, s5 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1, z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s6 :|: s6 >= 0, s6 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1, X2 >= 0, z'' - 1 = X2
   f(z, z', z'') -{ 168 }-> s7 :|: s7 >= 0, s7 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s8 :|: s8 >= 0, s8 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s9 :|: s9 >= 0, s9 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g(z) -{ 1 }-> 0 :|: z = 1
   g(z) -{ 1 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {encArg}, {encode_activate}, {encode_g}, {encode_n__g}, {encode_f}
Previous analysis results are:
  f: runtime: O(1) [162], size: O(1) [0]
  b: runtime: O(1) [1], size: O(1) [1]
  g: runtime: O(1) [1], size: O(n^1) [1 + z]
  encode_c: runtime: O(1) [0], size: O(1) [0]
  activate: runtime: O(1) [5], size: O(n^1) [z]
  encode_b: runtime: O(1) [1], size: O(1) [1]

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

(61) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using KoAT for: encArg
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: z

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

(62)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 0 :|: z - 1 >= 0, z - 1 = 1
   activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   b -{ 0 }-> 1 :|: 
   b -{ 1 }-> 0 :|: 
   b -{ 0 }-> 0 :|: 
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> s25 :|: s25 >= 0, s25 <= X + 1, z = 1 + 2, 1 = 1 + X, X >= 0
   encArg(z) -{ 0 }-> g(g(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> g(f(encArg(x_1228), encArg(x_256), encArg(x_356))) :|: z = 1 + (1 + x_1228 + x_256 + x_356), x_256 >= 0, x_1228 >= 0, x_356 >= 0
   encArg(z) -{ 0 }-> g(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> g(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> activate(g(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(f(encArg(x_1232), encArg(x_257), encArg(x_357))) :|: x_1232 >= 0, x_357 >= 0, z = 1 + (1 + x_1232 + x_257 + x_357), x_257 >= 0
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, 1 = 1
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 1 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> s26 :|: s26 >= 0, s26 <= X + 1, z = 2, 1 = 1 + X, X >= 0
   encode_activate(z) -{ 0 }-> activate(g(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(f(encArg(x_1464), encArg(x_2115), encArg(x_3115))) :|: x_3115 >= 0, x_1464 >= 0, x_2115 >= 0, z = 1 + x_1464 + x_2115 + x_3115
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_b -{ 0 }-> 1 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z, z', z'') -{ 0 }-> f(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g(z) -{ 0 }-> g(g(encArg(z - 1))) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> g(f(encArg(x_1468), encArg(x_2116), encArg(x_3116))) :|: x_3116 >= 0, z = 1 + x_1468 + x_2116 + x_3116, x_2116 >= 0, x_1468 >= 0
   encode_g(z) -{ 0 }-> g(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> g(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, 1 = 1
   encode_g(z) -{ 1 }-> 1 + X :|: z = 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z >= 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 1 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_g(z) -{ 2 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_n__g(z) -{ 0 }-> 0 :|: z >= 0
   encode_n__g(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   f(z, z', z'') -{ 166 }-> s :|: s >= 0, s <= 0, z'' >= 0, z' - 1 >= 0, z = z' - 1
   f(z, z', z'') -{ 169 }-> s' :|: s' >= 0, s' <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s'' :|: s'' >= 0, s'' <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 169 }-> s1 :|: s1 >= 0, s1 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s10 :|: s10 >= 0, s10 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 168 }-> s11 :|: s11 >= 0, s11 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s12 :|: s12 >= 0, s12 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s13 :|: s13 >= 0, s13 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s14 :|: s14 >= 0, s14 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 167 }-> s15 :|: s15 >= 0, s15 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s16 :|: s16 >= 0, s16 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s17 :|: s17 >= 0, s17 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s18 :|: s18 >= 0, s18 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 168 }-> s19 :|: s19 >= 0, s19 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X', z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s2 :|: s2 >= 0, s2 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 168 }-> s20 :|: s20 >= 0, s20 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 167 }-> s21 :|: s21 >= 0, s21 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s22 :|: s22 >= 0, s22 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 167 }-> s23 :|: s23 >= 0, s23 <= 0, z'' - 1 >= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s24 :|: s24 >= 0, s24 <= 0, z'' - 1 >= 0, z' - 1 >= 0, z = z' - 1, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 169 }-> s3 :|: s3 >= 0, s3 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s4 :|: s4 >= 0, s4 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1, X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 169 }-> s5 :|: s5 >= 0, s5 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1, z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s6 :|: s6 >= 0, s6 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1, X2 >= 0, z'' - 1 = X2
   f(z, z', z'') -{ 168 }-> s7 :|: s7 >= 0, s7 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s8 :|: s8 >= 0, s8 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s9 :|: s9 >= 0, s9 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g(z) -{ 1 }-> 0 :|: z = 1
   g(z) -{ 1 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {encArg}, {encode_activate}, {encode_g}, {encode_n__g}, {encode_f}
Previous analysis results are:
  f: runtime: O(1) [162], size: O(1) [0]
  b: runtime: O(1) [1], size: O(1) [1]
  g: runtime: O(1) [1], size: O(n^1) [1 + z]
  encode_c: runtime: O(1) [0], size: O(1) [0]
  activate: runtime: O(1) [5], size: O(n^1) [z]
  encode_b: runtime: O(1) [1], size: O(1) [1]
  encArg: runtime: ?, size: O(n^1) [z]

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

(63) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: encArg
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 2 + 167*z

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

(64)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 0 :|: z - 1 >= 0, z - 1 = 1
   activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   b -{ 0 }-> 1 :|: 
   b -{ 1 }-> 0 :|: 
   b -{ 0 }-> 0 :|: 
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> s25 :|: s25 >= 0, s25 <= X + 1, z = 1 + 2, 1 = 1 + X, X >= 0
   encArg(z) -{ 0 }-> g(g(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> g(f(encArg(x_1228), encArg(x_256), encArg(x_356))) :|: z = 1 + (1 + x_1228 + x_256 + x_356), x_256 >= 0, x_1228 >= 0, x_356 >= 0
   encArg(z) -{ 0 }-> g(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> g(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> activate(g(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(f(encArg(x_1232), encArg(x_257), encArg(x_357))) :|: x_1232 >= 0, x_357 >= 0, z = 1 + (1 + x_1232 + x_257 + x_357), x_257 >= 0
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, 1 = 1
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 1 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> s26 :|: s26 >= 0, s26 <= X + 1, z = 2, 1 = 1 + X, X >= 0
   encode_activate(z) -{ 0 }-> activate(g(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(f(encArg(x_1464), encArg(x_2115), encArg(x_3115))) :|: x_3115 >= 0, x_1464 >= 0, x_2115 >= 0, z = 1 + x_1464 + x_2115 + x_3115
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_b -{ 0 }-> 1 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z, z', z'') -{ 0 }-> f(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g(z) -{ 0 }-> g(g(encArg(z - 1))) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> g(f(encArg(x_1468), encArg(x_2116), encArg(x_3116))) :|: x_3116 >= 0, z = 1 + x_1468 + x_2116 + x_3116, x_2116 >= 0, x_1468 >= 0
   encode_g(z) -{ 0 }-> g(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> g(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, 1 = 1
   encode_g(z) -{ 1 }-> 1 + X :|: z = 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z >= 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 1 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_g(z) -{ 2 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_n__g(z) -{ 0 }-> 0 :|: z >= 0
   encode_n__g(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   f(z, z', z'') -{ 166 }-> s :|: s >= 0, s <= 0, z'' >= 0, z' - 1 >= 0, z = z' - 1
   f(z, z', z'') -{ 169 }-> s' :|: s' >= 0, s' <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s'' :|: s'' >= 0, s'' <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 169 }-> s1 :|: s1 >= 0, s1 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s10 :|: s10 >= 0, s10 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 168 }-> s11 :|: s11 >= 0, s11 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s12 :|: s12 >= 0, s12 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s13 :|: s13 >= 0, s13 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s14 :|: s14 >= 0, s14 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 167 }-> s15 :|: s15 >= 0, s15 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s16 :|: s16 >= 0, s16 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s17 :|: s17 >= 0, s17 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s18 :|: s18 >= 0, s18 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 168 }-> s19 :|: s19 >= 0, s19 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X', z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s2 :|: s2 >= 0, s2 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 168 }-> s20 :|: s20 >= 0, s20 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 167 }-> s21 :|: s21 >= 0, s21 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s22 :|: s22 >= 0, s22 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 167 }-> s23 :|: s23 >= 0, s23 <= 0, z'' - 1 >= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s24 :|: s24 >= 0, s24 <= 0, z'' - 1 >= 0, z' - 1 >= 0, z = z' - 1, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 169 }-> s3 :|: s3 >= 0, s3 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s4 :|: s4 >= 0, s4 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1, X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 169 }-> s5 :|: s5 >= 0, s5 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1, z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s6 :|: s6 >= 0, s6 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1, X2 >= 0, z'' - 1 = X2
   f(z, z', z'') -{ 168 }-> s7 :|: s7 >= 0, s7 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s8 :|: s8 >= 0, s8 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s9 :|: s9 >= 0, s9 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g(z) -{ 1 }-> 0 :|: z = 1
   g(z) -{ 1 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {encode_activate}, {encode_g}, {encode_n__g}, {encode_f}
Previous analysis results are:
  f: runtime: O(1) [162], size: O(1) [0]
  b: runtime: O(1) [1], size: O(1) [1]
  g: runtime: O(1) [1], size: O(n^1) [1 + z]
  encode_c: runtime: O(1) [0], size: O(1) [0]
  activate: runtime: O(1) [5], size: O(n^1) [z]
  encode_b: runtime: O(1) [1], size: O(1) [1]
  encArg: runtime: O(n^1) [2 + 167*z], size: O(n^1) [z]

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

(65) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(66)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 0 :|: z - 1 >= 0, z - 1 = 1
   activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   b -{ 0 }-> 1 :|: 
   b -{ 1 }-> 0 :|: 
   b -{ 0 }-> 0 :|: 
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> s25 :|: s25 >= 0, s25 <= X + 1, z = 1 + 2, 1 = 1 + X, X >= 0
   encArg(z) -{ 168 + 167*x_1 + 167*x_2 + 167*x_3 }-> s31 :|: s28 >= 0, s28 <= x_1, s29 >= 0, s29 <= x_2, s30 >= 0, s30 <= x_3, s31 >= 0, s31 <= 0, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ -331 + 167*z }-> s38 :|: s37 >= 0, s37 <= z - 2, s38 >= 0, s38 <= 1 + s37 + 1, z - 2 >= 0
   encArg(z) -{ 169 + 167*x_1228 + 167*x_256 + 167*x_356 }-> s43 :|: s39 >= 0, s39 <= x_1228, s40 >= 0, s40 <= x_256, s41 >= 0, s41 <= x_356, s42 >= 0, s42 <= 0, s43 >= 0, s43 <= s42 + 1, z = 1 + (1 + x_1228 + x_256 + x_356), x_256 >= 0, x_1228 >= 0, x_356 >= 0
   encArg(z) -{ -330 + 167*z }-> s46 :|: s44 >= 0, s44 <= z - 2, s45 >= 0, s45 <= s44 + 1, s46 >= 0, s46 <= s45 + 1, z - 2 >= 0
   encArg(z) -{ -327 + 167*z }-> s58 :|: s57 >= 0, s57 <= z - 2, s58 >= 0, s58 <= 1 + s57, z - 2 >= 0
   encArg(z) -{ 173 + 167*x_1232 + 167*x_257 + 167*x_357 }-> s63 :|: s59 >= 0, s59 <= x_1232, s60 >= 0, s60 <= x_257, s61 >= 0, s61 <= x_357, s62 >= 0, s62 <= 0, s63 >= 0, s63 <= s62, x_1232 >= 0, x_357 >= 0, z = 1 + (1 + x_1232 + x_257 + x_357), x_257 >= 0
   encArg(z) -{ -322 + 167*z }-> s66 :|: s64 >= 0, s64 <= z - 2, s65 >= 0, s65 <= s64, s66 >= 0, s66 <= s65, z - 2 >= 0
   encArg(z) -{ -326 + 167*z }-> s79 :|: s77 >= 0, s77 <= z - 2, s78 >= 0, s78 <= s77, s79 >= 0, s79 <= s78 + 1, z - 2 >= 0
   encArg(z) -{ -326 + 167*z }-> s82 :|: s80 >= 0, s80 <= z - 2, s81 >= 0, s81 <= s80 + 1, s82 >= 0, s82 <= s81, z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, 1 = 1
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ -165 + 167*z }-> 1 + s27 :|: s27 >= 0, s27 <= z - 1, z - 1 >= 0
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 1 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> s26 :|: s26 >= 0, s26 <= X + 1, z = 2, 1 = 1 + X, X >= 0
   encode_activate(z) -{ -160 + 167*z }-> s68 :|: s67 >= 0, s67 <= z - 1, s68 >= 0, s68 <= 1 + s67, z - 1 >= 0
   encode_activate(z) -{ 173 + 167*x_1464 + 167*x_2115 + 167*x_3115 }-> s73 :|: s69 >= 0, s69 <= x_1464, s70 >= 0, s70 <= x_2115, s71 >= 0, s71 <= x_3115, s72 >= 0, s72 <= 0, s73 >= 0, s73 <= s72, x_3115 >= 0, x_1464 >= 0, x_2115 >= 0, z = 1 + x_1464 + x_2115 + x_3115
   encode_activate(z) -{ -155 + 167*z }-> s76 :|: s74 >= 0, s74 <= z - 1, s75 >= 0, s75 <= s74, s76 >= 0, s76 <= s75, z - 1 >= 0
   encode_activate(z) -{ -159 + 167*z }-> s85 :|: s83 >= 0, s83 <= z - 1, s84 >= 0, s84 <= s83 + 1, s85 >= 0, s85 <= s84, z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_b -{ 0 }-> 1 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z, z', z'') -{ 168 + 167*z + 167*z' + 167*z'' }-> s35 :|: s32 >= 0, s32 <= z, s33 >= 0, s33 <= z', s34 >= 0, s34 <= z'', s35 >= 0, s35 <= 0, z >= 0, z'' >= 0, z' >= 0
   encode_f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g(z) -{ -164 + 167*z }-> s48 :|: s47 >= 0, s47 <= z - 1, s48 >= 0, s48 <= 1 + s47 + 1, z - 1 >= 0
   encode_g(z) -{ 169 + 167*x_1468 + 167*x_2116 + 167*x_3116 }-> s53 :|: s49 >= 0, s49 <= x_1468, s50 >= 0, s50 <= x_2116, s51 >= 0, s51 <= x_3116, s52 >= 0, s52 <= 0, s53 >= 0, s53 <= s52 + 1, x_3116 >= 0, z = 1 + x_1468 + x_2116 + x_3116, x_2116 >= 0, x_1468 >= 0
   encode_g(z) -{ -163 + 167*z }-> s56 :|: s54 >= 0, s54 <= z - 1, s55 >= 0, s55 <= s54 + 1, s56 >= 0, s56 <= s55 + 1, z - 1 >= 0
   encode_g(z) -{ -159 + 167*z }-> s88 :|: s86 >= 0, s86 <= z - 1, s87 >= 0, s87 <= s86, s88 >= 0, s88 <= s87 + 1, z - 1 >= 0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, 1 = 1
   encode_g(z) -{ 1 }-> 1 + X :|: z = 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z >= 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 1 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_g(z) -{ 2 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_n__g(z) -{ 0 }-> 0 :|: z >= 0
   encode_n__g(z) -{ 2 + 167*z }-> 1 + s36 :|: s36 >= 0, s36 <= z, z >= 0
   f(z, z', z'') -{ 166 }-> s :|: s >= 0, s <= 0, z'' >= 0, z' - 1 >= 0, z = z' - 1
   f(z, z', z'') -{ 169 }-> s' :|: s' >= 0, s' <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s'' :|: s'' >= 0, s'' <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 169 }-> s1 :|: s1 >= 0, s1 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s10 :|: s10 >= 0, s10 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 168 }-> s11 :|: s11 >= 0, s11 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s12 :|: s12 >= 0, s12 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s13 :|: s13 >= 0, s13 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s14 :|: s14 >= 0, s14 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 167 }-> s15 :|: s15 >= 0, s15 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s16 :|: s16 >= 0, s16 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s17 :|: s17 >= 0, s17 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s18 :|: s18 >= 0, s18 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 168 }-> s19 :|: s19 >= 0, s19 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X', z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s2 :|: s2 >= 0, s2 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 168 }-> s20 :|: s20 >= 0, s20 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 167 }-> s21 :|: s21 >= 0, s21 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s22 :|: s22 >= 0, s22 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 167 }-> s23 :|: s23 >= 0, s23 <= 0, z'' - 1 >= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s24 :|: s24 >= 0, s24 <= 0, z'' - 1 >= 0, z' - 1 >= 0, z = z' - 1, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 169 }-> s3 :|: s3 >= 0, s3 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s4 :|: s4 >= 0, s4 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1, X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 169 }-> s5 :|: s5 >= 0, s5 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1, z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s6 :|: s6 >= 0, s6 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1, X2 >= 0, z'' - 1 = X2
   f(z, z', z'') -{ 168 }-> s7 :|: s7 >= 0, s7 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s8 :|: s8 >= 0, s8 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s9 :|: s9 >= 0, s9 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g(z) -{ 1 }-> 0 :|: z = 1
   g(z) -{ 1 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {encode_activate}, {encode_g}, {encode_n__g}, {encode_f}
Previous analysis results are:
  f: runtime: O(1) [162], size: O(1) [0]
  b: runtime: O(1) [1], size: O(1) [1]
  g: runtime: O(1) [1], size: O(n^1) [1 + z]
  encode_c: runtime: O(1) [0], size: O(1) [0]
  activate: runtime: O(1) [5], size: O(n^1) [z]
  encode_b: runtime: O(1) [1], size: O(1) [1]
  encArg: runtime: O(n^1) [2 + 167*z], size: O(n^1) [z]

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

(67) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: encode_activate
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: z

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

(68)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 0 :|: z - 1 >= 0, z - 1 = 1
   activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   b -{ 0 }-> 1 :|: 
   b -{ 1 }-> 0 :|: 
   b -{ 0 }-> 0 :|: 
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> s25 :|: s25 >= 0, s25 <= X + 1, z = 1 + 2, 1 = 1 + X, X >= 0
   encArg(z) -{ 168 + 167*x_1 + 167*x_2 + 167*x_3 }-> s31 :|: s28 >= 0, s28 <= x_1, s29 >= 0, s29 <= x_2, s30 >= 0, s30 <= x_3, s31 >= 0, s31 <= 0, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ -331 + 167*z }-> s38 :|: s37 >= 0, s37 <= z - 2, s38 >= 0, s38 <= 1 + s37 + 1, z - 2 >= 0
   encArg(z) -{ 169 + 167*x_1228 + 167*x_256 + 167*x_356 }-> s43 :|: s39 >= 0, s39 <= x_1228, s40 >= 0, s40 <= x_256, s41 >= 0, s41 <= x_356, s42 >= 0, s42 <= 0, s43 >= 0, s43 <= s42 + 1, z = 1 + (1 + x_1228 + x_256 + x_356), x_256 >= 0, x_1228 >= 0, x_356 >= 0
   encArg(z) -{ -330 + 167*z }-> s46 :|: s44 >= 0, s44 <= z - 2, s45 >= 0, s45 <= s44 + 1, s46 >= 0, s46 <= s45 + 1, z - 2 >= 0
   encArg(z) -{ -327 + 167*z }-> s58 :|: s57 >= 0, s57 <= z - 2, s58 >= 0, s58 <= 1 + s57, z - 2 >= 0
   encArg(z) -{ 173 + 167*x_1232 + 167*x_257 + 167*x_357 }-> s63 :|: s59 >= 0, s59 <= x_1232, s60 >= 0, s60 <= x_257, s61 >= 0, s61 <= x_357, s62 >= 0, s62 <= 0, s63 >= 0, s63 <= s62, x_1232 >= 0, x_357 >= 0, z = 1 + (1 + x_1232 + x_257 + x_357), x_257 >= 0
   encArg(z) -{ -322 + 167*z }-> s66 :|: s64 >= 0, s64 <= z - 2, s65 >= 0, s65 <= s64, s66 >= 0, s66 <= s65, z - 2 >= 0
   encArg(z) -{ -326 + 167*z }-> s79 :|: s77 >= 0, s77 <= z - 2, s78 >= 0, s78 <= s77, s79 >= 0, s79 <= s78 + 1, z - 2 >= 0
   encArg(z) -{ -326 + 167*z }-> s82 :|: s80 >= 0, s80 <= z - 2, s81 >= 0, s81 <= s80 + 1, s82 >= 0, s82 <= s81, z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, 1 = 1
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ -165 + 167*z }-> 1 + s27 :|: s27 >= 0, s27 <= z - 1, z - 1 >= 0
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 1 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> s26 :|: s26 >= 0, s26 <= X + 1, z = 2, 1 = 1 + X, X >= 0
   encode_activate(z) -{ -160 + 167*z }-> s68 :|: s67 >= 0, s67 <= z - 1, s68 >= 0, s68 <= 1 + s67, z - 1 >= 0
   encode_activate(z) -{ 173 + 167*x_1464 + 167*x_2115 + 167*x_3115 }-> s73 :|: s69 >= 0, s69 <= x_1464, s70 >= 0, s70 <= x_2115, s71 >= 0, s71 <= x_3115, s72 >= 0, s72 <= 0, s73 >= 0, s73 <= s72, x_3115 >= 0, x_1464 >= 0, x_2115 >= 0, z = 1 + x_1464 + x_2115 + x_3115
   encode_activate(z) -{ -155 + 167*z }-> s76 :|: s74 >= 0, s74 <= z - 1, s75 >= 0, s75 <= s74, s76 >= 0, s76 <= s75, z - 1 >= 0
   encode_activate(z) -{ -159 + 167*z }-> s85 :|: s83 >= 0, s83 <= z - 1, s84 >= 0, s84 <= s83 + 1, s85 >= 0, s85 <= s84, z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_b -{ 0 }-> 1 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z, z', z'') -{ 168 + 167*z + 167*z' + 167*z'' }-> s35 :|: s32 >= 0, s32 <= z, s33 >= 0, s33 <= z', s34 >= 0, s34 <= z'', s35 >= 0, s35 <= 0, z >= 0, z'' >= 0, z' >= 0
   encode_f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g(z) -{ -164 + 167*z }-> s48 :|: s47 >= 0, s47 <= z - 1, s48 >= 0, s48 <= 1 + s47 + 1, z - 1 >= 0
   encode_g(z) -{ 169 + 167*x_1468 + 167*x_2116 + 167*x_3116 }-> s53 :|: s49 >= 0, s49 <= x_1468, s50 >= 0, s50 <= x_2116, s51 >= 0, s51 <= x_3116, s52 >= 0, s52 <= 0, s53 >= 0, s53 <= s52 + 1, x_3116 >= 0, z = 1 + x_1468 + x_2116 + x_3116, x_2116 >= 0, x_1468 >= 0
   encode_g(z) -{ -163 + 167*z }-> s56 :|: s54 >= 0, s54 <= z - 1, s55 >= 0, s55 <= s54 + 1, s56 >= 0, s56 <= s55 + 1, z - 1 >= 0
   encode_g(z) -{ -159 + 167*z }-> s88 :|: s86 >= 0, s86 <= z - 1, s87 >= 0, s87 <= s86, s88 >= 0, s88 <= s87 + 1, z - 1 >= 0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, 1 = 1
   encode_g(z) -{ 1 }-> 1 + X :|: z = 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z >= 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 1 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_g(z) -{ 2 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_n__g(z) -{ 0 }-> 0 :|: z >= 0
   encode_n__g(z) -{ 2 + 167*z }-> 1 + s36 :|: s36 >= 0, s36 <= z, z >= 0
   f(z, z', z'') -{ 166 }-> s :|: s >= 0, s <= 0, z'' >= 0, z' - 1 >= 0, z = z' - 1
   f(z, z', z'') -{ 169 }-> s' :|: s' >= 0, s' <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s'' :|: s'' >= 0, s'' <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 169 }-> s1 :|: s1 >= 0, s1 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s10 :|: s10 >= 0, s10 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 168 }-> s11 :|: s11 >= 0, s11 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s12 :|: s12 >= 0, s12 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s13 :|: s13 >= 0, s13 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s14 :|: s14 >= 0, s14 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 167 }-> s15 :|: s15 >= 0, s15 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s16 :|: s16 >= 0, s16 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s17 :|: s17 >= 0, s17 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s18 :|: s18 >= 0, s18 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 168 }-> s19 :|: s19 >= 0, s19 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X', z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s2 :|: s2 >= 0, s2 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 168 }-> s20 :|: s20 >= 0, s20 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 167 }-> s21 :|: s21 >= 0, s21 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s22 :|: s22 >= 0, s22 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 167 }-> s23 :|: s23 >= 0, s23 <= 0, z'' - 1 >= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s24 :|: s24 >= 0, s24 <= 0, z'' - 1 >= 0, z' - 1 >= 0, z = z' - 1, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 169 }-> s3 :|: s3 >= 0, s3 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s4 :|: s4 >= 0, s4 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1, X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 169 }-> s5 :|: s5 >= 0, s5 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1, z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s6 :|: s6 >= 0, s6 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1, X2 >= 0, z'' - 1 = X2
   f(z, z', z'') -{ 168 }-> s7 :|: s7 >= 0, s7 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s8 :|: s8 >= 0, s8 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s9 :|: s9 >= 0, s9 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g(z) -{ 1 }-> 0 :|: z = 1
   g(z) -{ 1 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {encode_activate}, {encode_g}, {encode_n__g}, {encode_f}
Previous analysis results are:
  f: runtime: O(1) [162], size: O(1) [0]
  b: runtime: O(1) [1], size: O(1) [1]
  g: runtime: O(1) [1], size: O(n^1) [1 + z]
  encode_c: runtime: O(1) [0], size: O(1) [0]
  activate: runtime: O(1) [5], size: O(n^1) [z]
  encode_b: runtime: O(1) [1], size: O(1) [1]
  encArg: runtime: O(n^1) [2 + 167*z], size: O(n^1) [z]
  encode_activate: runtime: ?, size: O(n^1) [z]

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

(69) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: encode_activate
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 160 + 167*z

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

(70)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 0 :|: z - 1 >= 0, z - 1 = 1
   activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   b -{ 0 }-> 1 :|: 
   b -{ 1 }-> 0 :|: 
   b -{ 0 }-> 0 :|: 
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> s25 :|: s25 >= 0, s25 <= X + 1, z = 1 + 2, 1 = 1 + X, X >= 0
   encArg(z) -{ 168 + 167*x_1 + 167*x_2 + 167*x_3 }-> s31 :|: s28 >= 0, s28 <= x_1, s29 >= 0, s29 <= x_2, s30 >= 0, s30 <= x_3, s31 >= 0, s31 <= 0, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ -331 + 167*z }-> s38 :|: s37 >= 0, s37 <= z - 2, s38 >= 0, s38 <= 1 + s37 + 1, z - 2 >= 0
   encArg(z) -{ 169 + 167*x_1228 + 167*x_256 + 167*x_356 }-> s43 :|: s39 >= 0, s39 <= x_1228, s40 >= 0, s40 <= x_256, s41 >= 0, s41 <= x_356, s42 >= 0, s42 <= 0, s43 >= 0, s43 <= s42 + 1, z = 1 + (1 + x_1228 + x_256 + x_356), x_256 >= 0, x_1228 >= 0, x_356 >= 0
   encArg(z) -{ -330 + 167*z }-> s46 :|: s44 >= 0, s44 <= z - 2, s45 >= 0, s45 <= s44 + 1, s46 >= 0, s46 <= s45 + 1, z - 2 >= 0
   encArg(z) -{ -327 + 167*z }-> s58 :|: s57 >= 0, s57 <= z - 2, s58 >= 0, s58 <= 1 + s57, z - 2 >= 0
   encArg(z) -{ 173 + 167*x_1232 + 167*x_257 + 167*x_357 }-> s63 :|: s59 >= 0, s59 <= x_1232, s60 >= 0, s60 <= x_257, s61 >= 0, s61 <= x_357, s62 >= 0, s62 <= 0, s63 >= 0, s63 <= s62, x_1232 >= 0, x_357 >= 0, z = 1 + (1 + x_1232 + x_257 + x_357), x_257 >= 0
   encArg(z) -{ -322 + 167*z }-> s66 :|: s64 >= 0, s64 <= z - 2, s65 >= 0, s65 <= s64, s66 >= 0, s66 <= s65, z - 2 >= 0
   encArg(z) -{ -326 + 167*z }-> s79 :|: s77 >= 0, s77 <= z - 2, s78 >= 0, s78 <= s77, s79 >= 0, s79 <= s78 + 1, z - 2 >= 0
   encArg(z) -{ -326 + 167*z }-> s82 :|: s80 >= 0, s80 <= z - 2, s81 >= 0, s81 <= s80 + 1, s82 >= 0, s82 <= s81, z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, 1 = 1
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ -165 + 167*z }-> 1 + s27 :|: s27 >= 0, s27 <= z - 1, z - 1 >= 0
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 1 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> s26 :|: s26 >= 0, s26 <= X + 1, z = 2, 1 = 1 + X, X >= 0
   encode_activate(z) -{ -160 + 167*z }-> s68 :|: s67 >= 0, s67 <= z - 1, s68 >= 0, s68 <= 1 + s67, z - 1 >= 0
   encode_activate(z) -{ 173 + 167*x_1464 + 167*x_2115 + 167*x_3115 }-> s73 :|: s69 >= 0, s69 <= x_1464, s70 >= 0, s70 <= x_2115, s71 >= 0, s71 <= x_3115, s72 >= 0, s72 <= 0, s73 >= 0, s73 <= s72, x_3115 >= 0, x_1464 >= 0, x_2115 >= 0, z = 1 + x_1464 + x_2115 + x_3115
   encode_activate(z) -{ -155 + 167*z }-> s76 :|: s74 >= 0, s74 <= z - 1, s75 >= 0, s75 <= s74, s76 >= 0, s76 <= s75, z - 1 >= 0
   encode_activate(z) -{ -159 + 167*z }-> s85 :|: s83 >= 0, s83 <= z - 1, s84 >= 0, s84 <= s83 + 1, s85 >= 0, s85 <= s84, z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_b -{ 0 }-> 1 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z, z', z'') -{ 168 + 167*z + 167*z' + 167*z'' }-> s35 :|: s32 >= 0, s32 <= z, s33 >= 0, s33 <= z', s34 >= 0, s34 <= z'', s35 >= 0, s35 <= 0, z >= 0, z'' >= 0, z' >= 0
   encode_f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g(z) -{ -164 + 167*z }-> s48 :|: s47 >= 0, s47 <= z - 1, s48 >= 0, s48 <= 1 + s47 + 1, z - 1 >= 0
   encode_g(z) -{ 169 + 167*x_1468 + 167*x_2116 + 167*x_3116 }-> s53 :|: s49 >= 0, s49 <= x_1468, s50 >= 0, s50 <= x_2116, s51 >= 0, s51 <= x_3116, s52 >= 0, s52 <= 0, s53 >= 0, s53 <= s52 + 1, x_3116 >= 0, z = 1 + x_1468 + x_2116 + x_3116, x_2116 >= 0, x_1468 >= 0
   encode_g(z) -{ -163 + 167*z }-> s56 :|: s54 >= 0, s54 <= z - 1, s55 >= 0, s55 <= s54 + 1, s56 >= 0, s56 <= s55 + 1, z - 1 >= 0
   encode_g(z) -{ -159 + 167*z }-> s88 :|: s86 >= 0, s86 <= z - 1, s87 >= 0, s87 <= s86, s88 >= 0, s88 <= s87 + 1, z - 1 >= 0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, 1 = 1
   encode_g(z) -{ 1 }-> 1 + X :|: z = 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z >= 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 1 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_g(z) -{ 2 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_n__g(z) -{ 0 }-> 0 :|: z >= 0
   encode_n__g(z) -{ 2 + 167*z }-> 1 + s36 :|: s36 >= 0, s36 <= z, z >= 0
   f(z, z', z'') -{ 166 }-> s :|: s >= 0, s <= 0, z'' >= 0, z' - 1 >= 0, z = z' - 1
   f(z, z', z'') -{ 169 }-> s' :|: s' >= 0, s' <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s'' :|: s'' >= 0, s'' <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 169 }-> s1 :|: s1 >= 0, s1 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s10 :|: s10 >= 0, s10 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 168 }-> s11 :|: s11 >= 0, s11 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s12 :|: s12 >= 0, s12 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s13 :|: s13 >= 0, s13 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s14 :|: s14 >= 0, s14 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 167 }-> s15 :|: s15 >= 0, s15 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s16 :|: s16 >= 0, s16 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s17 :|: s17 >= 0, s17 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s18 :|: s18 >= 0, s18 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 168 }-> s19 :|: s19 >= 0, s19 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X', z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s2 :|: s2 >= 0, s2 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 168 }-> s20 :|: s20 >= 0, s20 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 167 }-> s21 :|: s21 >= 0, s21 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s22 :|: s22 >= 0, s22 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 167 }-> s23 :|: s23 >= 0, s23 <= 0, z'' - 1 >= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s24 :|: s24 >= 0, s24 <= 0, z'' - 1 >= 0, z' - 1 >= 0, z = z' - 1, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 169 }-> s3 :|: s3 >= 0, s3 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s4 :|: s4 >= 0, s4 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1, X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 169 }-> s5 :|: s5 >= 0, s5 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1, z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s6 :|: s6 >= 0, s6 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1, X2 >= 0, z'' - 1 = X2
   f(z, z', z'') -{ 168 }-> s7 :|: s7 >= 0, s7 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s8 :|: s8 >= 0, s8 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s9 :|: s9 >= 0, s9 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g(z) -{ 1 }-> 0 :|: z = 1
   g(z) -{ 1 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {encode_g}, {encode_n__g}, {encode_f}
Previous analysis results are:
  f: runtime: O(1) [162], size: O(1) [0]
  b: runtime: O(1) [1], size: O(1) [1]
  g: runtime: O(1) [1], size: O(n^1) [1 + z]
  encode_c: runtime: O(1) [0], size: O(1) [0]
  activate: runtime: O(1) [5], size: O(n^1) [z]
  encode_b: runtime: O(1) [1], size: O(1) [1]
  encArg: runtime: O(n^1) [2 + 167*z], size: O(n^1) [z]
  encode_activate: runtime: O(n^1) [160 + 167*z], size: O(n^1) [z]

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

(71) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(72)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 0 :|: z - 1 >= 0, z - 1 = 1
   activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   b -{ 0 }-> 1 :|: 
   b -{ 1 }-> 0 :|: 
   b -{ 0 }-> 0 :|: 
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> s25 :|: s25 >= 0, s25 <= X + 1, z = 1 + 2, 1 = 1 + X, X >= 0
   encArg(z) -{ 168 + 167*x_1 + 167*x_2 + 167*x_3 }-> s31 :|: s28 >= 0, s28 <= x_1, s29 >= 0, s29 <= x_2, s30 >= 0, s30 <= x_3, s31 >= 0, s31 <= 0, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ -331 + 167*z }-> s38 :|: s37 >= 0, s37 <= z - 2, s38 >= 0, s38 <= 1 + s37 + 1, z - 2 >= 0
   encArg(z) -{ 169 + 167*x_1228 + 167*x_256 + 167*x_356 }-> s43 :|: s39 >= 0, s39 <= x_1228, s40 >= 0, s40 <= x_256, s41 >= 0, s41 <= x_356, s42 >= 0, s42 <= 0, s43 >= 0, s43 <= s42 + 1, z = 1 + (1 + x_1228 + x_256 + x_356), x_256 >= 0, x_1228 >= 0, x_356 >= 0
   encArg(z) -{ -330 + 167*z }-> s46 :|: s44 >= 0, s44 <= z - 2, s45 >= 0, s45 <= s44 + 1, s46 >= 0, s46 <= s45 + 1, z - 2 >= 0
   encArg(z) -{ -327 + 167*z }-> s58 :|: s57 >= 0, s57 <= z - 2, s58 >= 0, s58 <= 1 + s57, z - 2 >= 0
   encArg(z) -{ 173 + 167*x_1232 + 167*x_257 + 167*x_357 }-> s63 :|: s59 >= 0, s59 <= x_1232, s60 >= 0, s60 <= x_257, s61 >= 0, s61 <= x_357, s62 >= 0, s62 <= 0, s63 >= 0, s63 <= s62, x_1232 >= 0, x_357 >= 0, z = 1 + (1 + x_1232 + x_257 + x_357), x_257 >= 0
   encArg(z) -{ -322 + 167*z }-> s66 :|: s64 >= 0, s64 <= z - 2, s65 >= 0, s65 <= s64, s66 >= 0, s66 <= s65, z - 2 >= 0
   encArg(z) -{ -326 + 167*z }-> s79 :|: s77 >= 0, s77 <= z - 2, s78 >= 0, s78 <= s77, s79 >= 0, s79 <= s78 + 1, z - 2 >= 0
   encArg(z) -{ -326 + 167*z }-> s82 :|: s80 >= 0, s80 <= z - 2, s81 >= 0, s81 <= s80 + 1, s82 >= 0, s82 <= s81, z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, 1 = 1
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ -165 + 167*z }-> 1 + s27 :|: s27 >= 0, s27 <= z - 1, z - 1 >= 0
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 1 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> s26 :|: s26 >= 0, s26 <= X + 1, z = 2, 1 = 1 + X, X >= 0
   encode_activate(z) -{ -160 + 167*z }-> s68 :|: s67 >= 0, s67 <= z - 1, s68 >= 0, s68 <= 1 + s67, z - 1 >= 0
   encode_activate(z) -{ 173 + 167*x_1464 + 167*x_2115 + 167*x_3115 }-> s73 :|: s69 >= 0, s69 <= x_1464, s70 >= 0, s70 <= x_2115, s71 >= 0, s71 <= x_3115, s72 >= 0, s72 <= 0, s73 >= 0, s73 <= s72, x_3115 >= 0, x_1464 >= 0, x_2115 >= 0, z = 1 + x_1464 + x_2115 + x_3115
   encode_activate(z) -{ -155 + 167*z }-> s76 :|: s74 >= 0, s74 <= z - 1, s75 >= 0, s75 <= s74, s76 >= 0, s76 <= s75, z - 1 >= 0
   encode_activate(z) -{ -159 + 167*z }-> s85 :|: s83 >= 0, s83 <= z - 1, s84 >= 0, s84 <= s83 + 1, s85 >= 0, s85 <= s84, z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_b -{ 0 }-> 1 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z, z', z'') -{ 168 + 167*z + 167*z' + 167*z'' }-> s35 :|: s32 >= 0, s32 <= z, s33 >= 0, s33 <= z', s34 >= 0, s34 <= z'', s35 >= 0, s35 <= 0, z >= 0, z'' >= 0, z' >= 0
   encode_f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g(z) -{ -164 + 167*z }-> s48 :|: s47 >= 0, s47 <= z - 1, s48 >= 0, s48 <= 1 + s47 + 1, z - 1 >= 0
   encode_g(z) -{ 169 + 167*x_1468 + 167*x_2116 + 167*x_3116 }-> s53 :|: s49 >= 0, s49 <= x_1468, s50 >= 0, s50 <= x_2116, s51 >= 0, s51 <= x_3116, s52 >= 0, s52 <= 0, s53 >= 0, s53 <= s52 + 1, x_3116 >= 0, z = 1 + x_1468 + x_2116 + x_3116, x_2116 >= 0, x_1468 >= 0
   encode_g(z) -{ -163 + 167*z }-> s56 :|: s54 >= 0, s54 <= z - 1, s55 >= 0, s55 <= s54 + 1, s56 >= 0, s56 <= s55 + 1, z - 1 >= 0
   encode_g(z) -{ -159 + 167*z }-> s88 :|: s86 >= 0, s86 <= z - 1, s87 >= 0, s87 <= s86, s88 >= 0, s88 <= s87 + 1, z - 1 >= 0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, 1 = 1
   encode_g(z) -{ 1 }-> 1 + X :|: z = 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z >= 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 1 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_g(z) -{ 2 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_n__g(z) -{ 0 }-> 0 :|: z >= 0
   encode_n__g(z) -{ 2 + 167*z }-> 1 + s36 :|: s36 >= 0, s36 <= z, z >= 0
   f(z, z', z'') -{ 166 }-> s :|: s >= 0, s <= 0, z'' >= 0, z' - 1 >= 0, z = z' - 1
   f(z, z', z'') -{ 169 }-> s' :|: s' >= 0, s' <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s'' :|: s'' >= 0, s'' <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 169 }-> s1 :|: s1 >= 0, s1 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s10 :|: s10 >= 0, s10 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 168 }-> s11 :|: s11 >= 0, s11 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s12 :|: s12 >= 0, s12 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s13 :|: s13 >= 0, s13 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s14 :|: s14 >= 0, s14 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 167 }-> s15 :|: s15 >= 0, s15 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s16 :|: s16 >= 0, s16 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s17 :|: s17 >= 0, s17 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s18 :|: s18 >= 0, s18 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 168 }-> s19 :|: s19 >= 0, s19 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X', z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s2 :|: s2 >= 0, s2 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 168 }-> s20 :|: s20 >= 0, s20 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 167 }-> s21 :|: s21 >= 0, s21 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s22 :|: s22 >= 0, s22 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 167 }-> s23 :|: s23 >= 0, s23 <= 0, z'' - 1 >= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s24 :|: s24 >= 0, s24 <= 0, z'' - 1 >= 0, z' - 1 >= 0, z = z' - 1, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 169 }-> s3 :|: s3 >= 0, s3 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s4 :|: s4 >= 0, s4 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1, X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 169 }-> s5 :|: s5 >= 0, s5 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1, z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s6 :|: s6 >= 0, s6 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1, X2 >= 0, z'' - 1 = X2
   f(z, z', z'') -{ 168 }-> s7 :|: s7 >= 0, s7 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s8 :|: s8 >= 0, s8 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s9 :|: s9 >= 0, s9 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g(z) -{ 1 }-> 0 :|: z = 1
   g(z) -{ 1 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {encode_g}, {encode_n__g}, {encode_f}
Previous analysis results are:
  f: runtime: O(1) [162], size: O(1) [0]
  b: runtime: O(1) [1], size: O(1) [1]
  g: runtime: O(1) [1], size: O(n^1) [1 + z]
  encode_c: runtime: O(1) [0], size: O(1) [0]
  activate: runtime: O(1) [5], size: O(n^1) [z]
  encode_b: runtime: O(1) [1], size: O(1) [1]
  encArg: runtime: O(n^1) [2 + 167*z], size: O(n^1) [z]
  encode_activate: runtime: O(n^1) [160 + 167*z], size: O(n^1) [z]

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

(73) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: encode_g
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 1 + z

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

(74)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 0 :|: z - 1 >= 0, z - 1 = 1
   activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   b -{ 0 }-> 1 :|: 
   b -{ 1 }-> 0 :|: 
   b -{ 0 }-> 0 :|: 
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> s25 :|: s25 >= 0, s25 <= X + 1, z = 1 + 2, 1 = 1 + X, X >= 0
   encArg(z) -{ 168 + 167*x_1 + 167*x_2 + 167*x_3 }-> s31 :|: s28 >= 0, s28 <= x_1, s29 >= 0, s29 <= x_2, s30 >= 0, s30 <= x_3, s31 >= 0, s31 <= 0, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ -331 + 167*z }-> s38 :|: s37 >= 0, s37 <= z - 2, s38 >= 0, s38 <= 1 + s37 + 1, z - 2 >= 0
   encArg(z) -{ 169 + 167*x_1228 + 167*x_256 + 167*x_356 }-> s43 :|: s39 >= 0, s39 <= x_1228, s40 >= 0, s40 <= x_256, s41 >= 0, s41 <= x_356, s42 >= 0, s42 <= 0, s43 >= 0, s43 <= s42 + 1, z = 1 + (1 + x_1228 + x_256 + x_356), x_256 >= 0, x_1228 >= 0, x_356 >= 0
   encArg(z) -{ -330 + 167*z }-> s46 :|: s44 >= 0, s44 <= z - 2, s45 >= 0, s45 <= s44 + 1, s46 >= 0, s46 <= s45 + 1, z - 2 >= 0
   encArg(z) -{ -327 + 167*z }-> s58 :|: s57 >= 0, s57 <= z - 2, s58 >= 0, s58 <= 1 + s57, z - 2 >= 0
   encArg(z) -{ 173 + 167*x_1232 + 167*x_257 + 167*x_357 }-> s63 :|: s59 >= 0, s59 <= x_1232, s60 >= 0, s60 <= x_257, s61 >= 0, s61 <= x_357, s62 >= 0, s62 <= 0, s63 >= 0, s63 <= s62, x_1232 >= 0, x_357 >= 0, z = 1 + (1 + x_1232 + x_257 + x_357), x_257 >= 0
   encArg(z) -{ -322 + 167*z }-> s66 :|: s64 >= 0, s64 <= z - 2, s65 >= 0, s65 <= s64, s66 >= 0, s66 <= s65, z - 2 >= 0
   encArg(z) -{ -326 + 167*z }-> s79 :|: s77 >= 0, s77 <= z - 2, s78 >= 0, s78 <= s77, s79 >= 0, s79 <= s78 + 1, z - 2 >= 0
   encArg(z) -{ -326 + 167*z }-> s82 :|: s80 >= 0, s80 <= z - 2, s81 >= 0, s81 <= s80 + 1, s82 >= 0, s82 <= s81, z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, 1 = 1
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ -165 + 167*z }-> 1 + s27 :|: s27 >= 0, s27 <= z - 1, z - 1 >= 0
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 1 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> s26 :|: s26 >= 0, s26 <= X + 1, z = 2, 1 = 1 + X, X >= 0
   encode_activate(z) -{ -160 + 167*z }-> s68 :|: s67 >= 0, s67 <= z - 1, s68 >= 0, s68 <= 1 + s67, z - 1 >= 0
   encode_activate(z) -{ 173 + 167*x_1464 + 167*x_2115 + 167*x_3115 }-> s73 :|: s69 >= 0, s69 <= x_1464, s70 >= 0, s70 <= x_2115, s71 >= 0, s71 <= x_3115, s72 >= 0, s72 <= 0, s73 >= 0, s73 <= s72, x_3115 >= 0, x_1464 >= 0, x_2115 >= 0, z = 1 + x_1464 + x_2115 + x_3115
   encode_activate(z) -{ -155 + 167*z }-> s76 :|: s74 >= 0, s74 <= z - 1, s75 >= 0, s75 <= s74, s76 >= 0, s76 <= s75, z - 1 >= 0
   encode_activate(z) -{ -159 + 167*z }-> s85 :|: s83 >= 0, s83 <= z - 1, s84 >= 0, s84 <= s83 + 1, s85 >= 0, s85 <= s84, z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_b -{ 0 }-> 1 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z, z', z'') -{ 168 + 167*z + 167*z' + 167*z'' }-> s35 :|: s32 >= 0, s32 <= z, s33 >= 0, s33 <= z', s34 >= 0, s34 <= z'', s35 >= 0, s35 <= 0, z >= 0, z'' >= 0, z' >= 0
   encode_f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g(z) -{ -164 + 167*z }-> s48 :|: s47 >= 0, s47 <= z - 1, s48 >= 0, s48 <= 1 + s47 + 1, z - 1 >= 0
   encode_g(z) -{ 169 + 167*x_1468 + 167*x_2116 + 167*x_3116 }-> s53 :|: s49 >= 0, s49 <= x_1468, s50 >= 0, s50 <= x_2116, s51 >= 0, s51 <= x_3116, s52 >= 0, s52 <= 0, s53 >= 0, s53 <= s52 + 1, x_3116 >= 0, z = 1 + x_1468 + x_2116 + x_3116, x_2116 >= 0, x_1468 >= 0
   encode_g(z) -{ -163 + 167*z }-> s56 :|: s54 >= 0, s54 <= z - 1, s55 >= 0, s55 <= s54 + 1, s56 >= 0, s56 <= s55 + 1, z - 1 >= 0
   encode_g(z) -{ -159 + 167*z }-> s88 :|: s86 >= 0, s86 <= z - 1, s87 >= 0, s87 <= s86, s88 >= 0, s88 <= s87 + 1, z - 1 >= 0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, 1 = 1
   encode_g(z) -{ 1 }-> 1 + X :|: z = 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z >= 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 1 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_g(z) -{ 2 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_n__g(z) -{ 0 }-> 0 :|: z >= 0
   encode_n__g(z) -{ 2 + 167*z }-> 1 + s36 :|: s36 >= 0, s36 <= z, z >= 0
   f(z, z', z'') -{ 166 }-> s :|: s >= 0, s <= 0, z'' >= 0, z' - 1 >= 0, z = z' - 1
   f(z, z', z'') -{ 169 }-> s' :|: s' >= 0, s' <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s'' :|: s'' >= 0, s'' <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 169 }-> s1 :|: s1 >= 0, s1 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s10 :|: s10 >= 0, s10 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 168 }-> s11 :|: s11 >= 0, s11 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s12 :|: s12 >= 0, s12 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s13 :|: s13 >= 0, s13 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s14 :|: s14 >= 0, s14 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 167 }-> s15 :|: s15 >= 0, s15 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s16 :|: s16 >= 0, s16 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s17 :|: s17 >= 0, s17 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s18 :|: s18 >= 0, s18 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 168 }-> s19 :|: s19 >= 0, s19 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X', z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s2 :|: s2 >= 0, s2 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 168 }-> s20 :|: s20 >= 0, s20 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 167 }-> s21 :|: s21 >= 0, s21 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s22 :|: s22 >= 0, s22 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 167 }-> s23 :|: s23 >= 0, s23 <= 0, z'' - 1 >= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s24 :|: s24 >= 0, s24 <= 0, z'' - 1 >= 0, z' - 1 >= 0, z = z' - 1, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 169 }-> s3 :|: s3 >= 0, s3 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s4 :|: s4 >= 0, s4 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1, X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 169 }-> s5 :|: s5 >= 0, s5 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1, z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s6 :|: s6 >= 0, s6 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1, X2 >= 0, z'' - 1 = X2
   f(z, z', z'') -{ 168 }-> s7 :|: s7 >= 0, s7 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s8 :|: s8 >= 0, s8 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s9 :|: s9 >= 0, s9 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g(z) -{ 1 }-> 0 :|: z = 1
   g(z) -{ 1 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {encode_g}, {encode_n__g}, {encode_f}
Previous analysis results are:
  f: runtime: O(1) [162], size: O(1) [0]
  b: runtime: O(1) [1], size: O(1) [1]
  g: runtime: O(1) [1], size: O(n^1) [1 + z]
  encode_c: runtime: O(1) [0], size: O(1) [0]
  activate: runtime: O(1) [5], size: O(n^1) [z]
  encode_b: runtime: O(1) [1], size: O(1) [1]
  encArg: runtime: O(n^1) [2 + 167*z], size: O(n^1) [z]
  encode_activate: runtime: O(n^1) [160 + 167*z], size: O(n^1) [z]
  encode_g: runtime: ?, size: O(n^1) [1 + z]

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

(75) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: encode_g
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 164 + 167*z

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

(76)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 0 :|: z - 1 >= 0, z - 1 = 1
   activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   b -{ 0 }-> 1 :|: 
   b -{ 1 }-> 0 :|: 
   b -{ 0 }-> 0 :|: 
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> s25 :|: s25 >= 0, s25 <= X + 1, z = 1 + 2, 1 = 1 + X, X >= 0
   encArg(z) -{ 168 + 167*x_1 + 167*x_2 + 167*x_3 }-> s31 :|: s28 >= 0, s28 <= x_1, s29 >= 0, s29 <= x_2, s30 >= 0, s30 <= x_3, s31 >= 0, s31 <= 0, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ -331 + 167*z }-> s38 :|: s37 >= 0, s37 <= z - 2, s38 >= 0, s38 <= 1 + s37 + 1, z - 2 >= 0
   encArg(z) -{ 169 + 167*x_1228 + 167*x_256 + 167*x_356 }-> s43 :|: s39 >= 0, s39 <= x_1228, s40 >= 0, s40 <= x_256, s41 >= 0, s41 <= x_356, s42 >= 0, s42 <= 0, s43 >= 0, s43 <= s42 + 1, z = 1 + (1 + x_1228 + x_256 + x_356), x_256 >= 0, x_1228 >= 0, x_356 >= 0
   encArg(z) -{ -330 + 167*z }-> s46 :|: s44 >= 0, s44 <= z - 2, s45 >= 0, s45 <= s44 + 1, s46 >= 0, s46 <= s45 + 1, z - 2 >= 0
   encArg(z) -{ -327 + 167*z }-> s58 :|: s57 >= 0, s57 <= z - 2, s58 >= 0, s58 <= 1 + s57, z - 2 >= 0
   encArg(z) -{ 173 + 167*x_1232 + 167*x_257 + 167*x_357 }-> s63 :|: s59 >= 0, s59 <= x_1232, s60 >= 0, s60 <= x_257, s61 >= 0, s61 <= x_357, s62 >= 0, s62 <= 0, s63 >= 0, s63 <= s62, x_1232 >= 0, x_357 >= 0, z = 1 + (1 + x_1232 + x_257 + x_357), x_257 >= 0
   encArg(z) -{ -322 + 167*z }-> s66 :|: s64 >= 0, s64 <= z - 2, s65 >= 0, s65 <= s64, s66 >= 0, s66 <= s65, z - 2 >= 0
   encArg(z) -{ -326 + 167*z }-> s79 :|: s77 >= 0, s77 <= z - 2, s78 >= 0, s78 <= s77, s79 >= 0, s79 <= s78 + 1, z - 2 >= 0
   encArg(z) -{ -326 + 167*z }-> s82 :|: s80 >= 0, s80 <= z - 2, s81 >= 0, s81 <= s80 + 1, s82 >= 0, s82 <= s81, z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, 1 = 1
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ -165 + 167*z }-> 1 + s27 :|: s27 >= 0, s27 <= z - 1, z - 1 >= 0
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 1 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> s26 :|: s26 >= 0, s26 <= X + 1, z = 2, 1 = 1 + X, X >= 0
   encode_activate(z) -{ -160 + 167*z }-> s68 :|: s67 >= 0, s67 <= z - 1, s68 >= 0, s68 <= 1 + s67, z - 1 >= 0
   encode_activate(z) -{ 173 + 167*x_1464 + 167*x_2115 + 167*x_3115 }-> s73 :|: s69 >= 0, s69 <= x_1464, s70 >= 0, s70 <= x_2115, s71 >= 0, s71 <= x_3115, s72 >= 0, s72 <= 0, s73 >= 0, s73 <= s72, x_3115 >= 0, x_1464 >= 0, x_2115 >= 0, z = 1 + x_1464 + x_2115 + x_3115
   encode_activate(z) -{ -155 + 167*z }-> s76 :|: s74 >= 0, s74 <= z - 1, s75 >= 0, s75 <= s74, s76 >= 0, s76 <= s75, z - 1 >= 0
   encode_activate(z) -{ -159 + 167*z }-> s85 :|: s83 >= 0, s83 <= z - 1, s84 >= 0, s84 <= s83 + 1, s85 >= 0, s85 <= s84, z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_b -{ 0 }-> 1 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z, z', z'') -{ 168 + 167*z + 167*z' + 167*z'' }-> s35 :|: s32 >= 0, s32 <= z, s33 >= 0, s33 <= z', s34 >= 0, s34 <= z'', s35 >= 0, s35 <= 0, z >= 0, z'' >= 0, z' >= 0
   encode_f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g(z) -{ -164 + 167*z }-> s48 :|: s47 >= 0, s47 <= z - 1, s48 >= 0, s48 <= 1 + s47 + 1, z - 1 >= 0
   encode_g(z) -{ 169 + 167*x_1468 + 167*x_2116 + 167*x_3116 }-> s53 :|: s49 >= 0, s49 <= x_1468, s50 >= 0, s50 <= x_2116, s51 >= 0, s51 <= x_3116, s52 >= 0, s52 <= 0, s53 >= 0, s53 <= s52 + 1, x_3116 >= 0, z = 1 + x_1468 + x_2116 + x_3116, x_2116 >= 0, x_1468 >= 0
   encode_g(z) -{ -163 + 167*z }-> s56 :|: s54 >= 0, s54 <= z - 1, s55 >= 0, s55 <= s54 + 1, s56 >= 0, s56 <= s55 + 1, z - 1 >= 0
   encode_g(z) -{ -159 + 167*z }-> s88 :|: s86 >= 0, s86 <= z - 1, s87 >= 0, s87 <= s86, s88 >= 0, s88 <= s87 + 1, z - 1 >= 0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, 1 = 1
   encode_g(z) -{ 1 }-> 1 + X :|: z = 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z >= 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 1 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_g(z) -{ 2 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_n__g(z) -{ 0 }-> 0 :|: z >= 0
   encode_n__g(z) -{ 2 + 167*z }-> 1 + s36 :|: s36 >= 0, s36 <= z, z >= 0
   f(z, z', z'') -{ 166 }-> s :|: s >= 0, s <= 0, z'' >= 0, z' - 1 >= 0, z = z' - 1
   f(z, z', z'') -{ 169 }-> s' :|: s' >= 0, s' <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s'' :|: s'' >= 0, s'' <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 169 }-> s1 :|: s1 >= 0, s1 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s10 :|: s10 >= 0, s10 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 168 }-> s11 :|: s11 >= 0, s11 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s12 :|: s12 >= 0, s12 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s13 :|: s13 >= 0, s13 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s14 :|: s14 >= 0, s14 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 167 }-> s15 :|: s15 >= 0, s15 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s16 :|: s16 >= 0, s16 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s17 :|: s17 >= 0, s17 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s18 :|: s18 >= 0, s18 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 168 }-> s19 :|: s19 >= 0, s19 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X', z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s2 :|: s2 >= 0, s2 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 168 }-> s20 :|: s20 >= 0, s20 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 167 }-> s21 :|: s21 >= 0, s21 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s22 :|: s22 >= 0, s22 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 167 }-> s23 :|: s23 >= 0, s23 <= 0, z'' - 1 >= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s24 :|: s24 >= 0, s24 <= 0, z'' - 1 >= 0, z' - 1 >= 0, z = z' - 1, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 169 }-> s3 :|: s3 >= 0, s3 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s4 :|: s4 >= 0, s4 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1, X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 169 }-> s5 :|: s5 >= 0, s5 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1, z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s6 :|: s6 >= 0, s6 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1, X2 >= 0, z'' - 1 = X2
   f(z, z', z'') -{ 168 }-> s7 :|: s7 >= 0, s7 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s8 :|: s8 >= 0, s8 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s9 :|: s9 >= 0, s9 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g(z) -{ 1 }-> 0 :|: z = 1
   g(z) -{ 1 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {encode_n__g}, {encode_f}
Previous analysis results are:
  f: runtime: O(1) [162], size: O(1) [0]
  b: runtime: O(1) [1], size: O(1) [1]
  g: runtime: O(1) [1], size: O(n^1) [1 + z]
  encode_c: runtime: O(1) [0], size: O(1) [0]
  activate: runtime: O(1) [5], size: O(n^1) [z]
  encode_b: runtime: O(1) [1], size: O(1) [1]
  encArg: runtime: O(n^1) [2 + 167*z], size: O(n^1) [z]
  encode_activate: runtime: O(n^1) [160 + 167*z], size: O(n^1) [z]
  encode_g: runtime: O(n^1) [164 + 167*z], size: O(n^1) [1 + z]

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

(77) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(78)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 0 :|: z - 1 >= 0, z - 1 = 1
   activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   b -{ 0 }-> 1 :|: 
   b -{ 1 }-> 0 :|: 
   b -{ 0 }-> 0 :|: 
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> s25 :|: s25 >= 0, s25 <= X + 1, z = 1 + 2, 1 = 1 + X, X >= 0
   encArg(z) -{ 168 + 167*x_1 + 167*x_2 + 167*x_3 }-> s31 :|: s28 >= 0, s28 <= x_1, s29 >= 0, s29 <= x_2, s30 >= 0, s30 <= x_3, s31 >= 0, s31 <= 0, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ -331 + 167*z }-> s38 :|: s37 >= 0, s37 <= z - 2, s38 >= 0, s38 <= 1 + s37 + 1, z - 2 >= 0
   encArg(z) -{ 169 + 167*x_1228 + 167*x_256 + 167*x_356 }-> s43 :|: s39 >= 0, s39 <= x_1228, s40 >= 0, s40 <= x_256, s41 >= 0, s41 <= x_356, s42 >= 0, s42 <= 0, s43 >= 0, s43 <= s42 + 1, z = 1 + (1 + x_1228 + x_256 + x_356), x_256 >= 0, x_1228 >= 0, x_356 >= 0
   encArg(z) -{ -330 + 167*z }-> s46 :|: s44 >= 0, s44 <= z - 2, s45 >= 0, s45 <= s44 + 1, s46 >= 0, s46 <= s45 + 1, z - 2 >= 0
   encArg(z) -{ -327 + 167*z }-> s58 :|: s57 >= 0, s57 <= z - 2, s58 >= 0, s58 <= 1 + s57, z - 2 >= 0
   encArg(z) -{ 173 + 167*x_1232 + 167*x_257 + 167*x_357 }-> s63 :|: s59 >= 0, s59 <= x_1232, s60 >= 0, s60 <= x_257, s61 >= 0, s61 <= x_357, s62 >= 0, s62 <= 0, s63 >= 0, s63 <= s62, x_1232 >= 0, x_357 >= 0, z = 1 + (1 + x_1232 + x_257 + x_357), x_257 >= 0
   encArg(z) -{ -322 + 167*z }-> s66 :|: s64 >= 0, s64 <= z - 2, s65 >= 0, s65 <= s64, s66 >= 0, s66 <= s65, z - 2 >= 0
   encArg(z) -{ -326 + 167*z }-> s79 :|: s77 >= 0, s77 <= z - 2, s78 >= 0, s78 <= s77, s79 >= 0, s79 <= s78 + 1, z - 2 >= 0
   encArg(z) -{ -326 + 167*z }-> s82 :|: s80 >= 0, s80 <= z - 2, s81 >= 0, s81 <= s80 + 1, s82 >= 0, s82 <= s81, z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, 1 = 1
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ -165 + 167*z }-> 1 + s27 :|: s27 >= 0, s27 <= z - 1, z - 1 >= 0
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 1 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> s26 :|: s26 >= 0, s26 <= X + 1, z = 2, 1 = 1 + X, X >= 0
   encode_activate(z) -{ -160 + 167*z }-> s68 :|: s67 >= 0, s67 <= z - 1, s68 >= 0, s68 <= 1 + s67, z - 1 >= 0
   encode_activate(z) -{ 173 + 167*x_1464 + 167*x_2115 + 167*x_3115 }-> s73 :|: s69 >= 0, s69 <= x_1464, s70 >= 0, s70 <= x_2115, s71 >= 0, s71 <= x_3115, s72 >= 0, s72 <= 0, s73 >= 0, s73 <= s72, x_3115 >= 0, x_1464 >= 0, x_2115 >= 0, z = 1 + x_1464 + x_2115 + x_3115
   encode_activate(z) -{ -155 + 167*z }-> s76 :|: s74 >= 0, s74 <= z - 1, s75 >= 0, s75 <= s74, s76 >= 0, s76 <= s75, z - 1 >= 0
   encode_activate(z) -{ -159 + 167*z }-> s85 :|: s83 >= 0, s83 <= z - 1, s84 >= 0, s84 <= s83 + 1, s85 >= 0, s85 <= s84, z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_b -{ 0 }-> 1 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z, z', z'') -{ 168 + 167*z + 167*z' + 167*z'' }-> s35 :|: s32 >= 0, s32 <= z, s33 >= 0, s33 <= z', s34 >= 0, s34 <= z'', s35 >= 0, s35 <= 0, z >= 0, z'' >= 0, z' >= 0
   encode_f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g(z) -{ -164 + 167*z }-> s48 :|: s47 >= 0, s47 <= z - 1, s48 >= 0, s48 <= 1 + s47 + 1, z - 1 >= 0
   encode_g(z) -{ 169 + 167*x_1468 + 167*x_2116 + 167*x_3116 }-> s53 :|: s49 >= 0, s49 <= x_1468, s50 >= 0, s50 <= x_2116, s51 >= 0, s51 <= x_3116, s52 >= 0, s52 <= 0, s53 >= 0, s53 <= s52 + 1, x_3116 >= 0, z = 1 + x_1468 + x_2116 + x_3116, x_2116 >= 0, x_1468 >= 0
   encode_g(z) -{ -163 + 167*z }-> s56 :|: s54 >= 0, s54 <= z - 1, s55 >= 0, s55 <= s54 + 1, s56 >= 0, s56 <= s55 + 1, z - 1 >= 0
   encode_g(z) -{ -159 + 167*z }-> s88 :|: s86 >= 0, s86 <= z - 1, s87 >= 0, s87 <= s86, s88 >= 0, s88 <= s87 + 1, z - 1 >= 0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, 1 = 1
   encode_g(z) -{ 1 }-> 1 + X :|: z = 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z >= 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 1 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_g(z) -{ 2 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_n__g(z) -{ 0 }-> 0 :|: z >= 0
   encode_n__g(z) -{ 2 + 167*z }-> 1 + s36 :|: s36 >= 0, s36 <= z, z >= 0
   f(z, z', z'') -{ 166 }-> s :|: s >= 0, s <= 0, z'' >= 0, z' - 1 >= 0, z = z' - 1
   f(z, z', z'') -{ 169 }-> s' :|: s' >= 0, s' <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s'' :|: s'' >= 0, s'' <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 169 }-> s1 :|: s1 >= 0, s1 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s10 :|: s10 >= 0, s10 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 168 }-> s11 :|: s11 >= 0, s11 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s12 :|: s12 >= 0, s12 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s13 :|: s13 >= 0, s13 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s14 :|: s14 >= 0, s14 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 167 }-> s15 :|: s15 >= 0, s15 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s16 :|: s16 >= 0, s16 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s17 :|: s17 >= 0, s17 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s18 :|: s18 >= 0, s18 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 168 }-> s19 :|: s19 >= 0, s19 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X', z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s2 :|: s2 >= 0, s2 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 168 }-> s20 :|: s20 >= 0, s20 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 167 }-> s21 :|: s21 >= 0, s21 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s22 :|: s22 >= 0, s22 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 167 }-> s23 :|: s23 >= 0, s23 <= 0, z'' - 1 >= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s24 :|: s24 >= 0, s24 <= 0, z'' - 1 >= 0, z' - 1 >= 0, z = z' - 1, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 169 }-> s3 :|: s3 >= 0, s3 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s4 :|: s4 >= 0, s4 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1, X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 169 }-> s5 :|: s5 >= 0, s5 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1, z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s6 :|: s6 >= 0, s6 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1, X2 >= 0, z'' - 1 = X2
   f(z, z', z'') -{ 168 }-> s7 :|: s7 >= 0, s7 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s8 :|: s8 >= 0, s8 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s9 :|: s9 >= 0, s9 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g(z) -{ 1 }-> 0 :|: z = 1
   g(z) -{ 1 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {encode_n__g}, {encode_f}
Previous analysis results are:
  f: runtime: O(1) [162], size: O(1) [0]
  b: runtime: O(1) [1], size: O(1) [1]
  g: runtime: O(1) [1], size: O(n^1) [1 + z]
  encode_c: runtime: O(1) [0], size: O(1) [0]
  activate: runtime: O(1) [5], size: O(n^1) [z]
  encode_b: runtime: O(1) [1], size: O(1) [1]
  encArg: runtime: O(n^1) [2 + 167*z], size: O(n^1) [z]
  encode_activate: runtime: O(n^1) [160 + 167*z], size: O(n^1) [z]
  encode_g: runtime: O(n^1) [164 + 167*z], size: O(n^1) [1 + z]

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

(79) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: encode_n__g
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 1 + z

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

(80)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 0 :|: z - 1 >= 0, z - 1 = 1
   activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   b -{ 0 }-> 1 :|: 
   b -{ 1 }-> 0 :|: 
   b -{ 0 }-> 0 :|: 
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> s25 :|: s25 >= 0, s25 <= X + 1, z = 1 + 2, 1 = 1 + X, X >= 0
   encArg(z) -{ 168 + 167*x_1 + 167*x_2 + 167*x_3 }-> s31 :|: s28 >= 0, s28 <= x_1, s29 >= 0, s29 <= x_2, s30 >= 0, s30 <= x_3, s31 >= 0, s31 <= 0, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ -331 + 167*z }-> s38 :|: s37 >= 0, s37 <= z - 2, s38 >= 0, s38 <= 1 + s37 + 1, z - 2 >= 0
   encArg(z) -{ 169 + 167*x_1228 + 167*x_256 + 167*x_356 }-> s43 :|: s39 >= 0, s39 <= x_1228, s40 >= 0, s40 <= x_256, s41 >= 0, s41 <= x_356, s42 >= 0, s42 <= 0, s43 >= 0, s43 <= s42 + 1, z = 1 + (1 + x_1228 + x_256 + x_356), x_256 >= 0, x_1228 >= 0, x_356 >= 0
   encArg(z) -{ -330 + 167*z }-> s46 :|: s44 >= 0, s44 <= z - 2, s45 >= 0, s45 <= s44 + 1, s46 >= 0, s46 <= s45 + 1, z - 2 >= 0
   encArg(z) -{ -327 + 167*z }-> s58 :|: s57 >= 0, s57 <= z - 2, s58 >= 0, s58 <= 1 + s57, z - 2 >= 0
   encArg(z) -{ 173 + 167*x_1232 + 167*x_257 + 167*x_357 }-> s63 :|: s59 >= 0, s59 <= x_1232, s60 >= 0, s60 <= x_257, s61 >= 0, s61 <= x_357, s62 >= 0, s62 <= 0, s63 >= 0, s63 <= s62, x_1232 >= 0, x_357 >= 0, z = 1 + (1 + x_1232 + x_257 + x_357), x_257 >= 0
   encArg(z) -{ -322 + 167*z }-> s66 :|: s64 >= 0, s64 <= z - 2, s65 >= 0, s65 <= s64, s66 >= 0, s66 <= s65, z - 2 >= 0
   encArg(z) -{ -326 + 167*z }-> s79 :|: s77 >= 0, s77 <= z - 2, s78 >= 0, s78 <= s77, s79 >= 0, s79 <= s78 + 1, z - 2 >= 0
   encArg(z) -{ -326 + 167*z }-> s82 :|: s80 >= 0, s80 <= z - 2, s81 >= 0, s81 <= s80 + 1, s82 >= 0, s82 <= s81, z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, 1 = 1
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ -165 + 167*z }-> 1 + s27 :|: s27 >= 0, s27 <= z - 1, z - 1 >= 0
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 1 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> s26 :|: s26 >= 0, s26 <= X + 1, z = 2, 1 = 1 + X, X >= 0
   encode_activate(z) -{ -160 + 167*z }-> s68 :|: s67 >= 0, s67 <= z - 1, s68 >= 0, s68 <= 1 + s67, z - 1 >= 0
   encode_activate(z) -{ 173 + 167*x_1464 + 167*x_2115 + 167*x_3115 }-> s73 :|: s69 >= 0, s69 <= x_1464, s70 >= 0, s70 <= x_2115, s71 >= 0, s71 <= x_3115, s72 >= 0, s72 <= 0, s73 >= 0, s73 <= s72, x_3115 >= 0, x_1464 >= 0, x_2115 >= 0, z = 1 + x_1464 + x_2115 + x_3115
   encode_activate(z) -{ -155 + 167*z }-> s76 :|: s74 >= 0, s74 <= z - 1, s75 >= 0, s75 <= s74, s76 >= 0, s76 <= s75, z - 1 >= 0
   encode_activate(z) -{ -159 + 167*z }-> s85 :|: s83 >= 0, s83 <= z - 1, s84 >= 0, s84 <= s83 + 1, s85 >= 0, s85 <= s84, z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_b -{ 0 }-> 1 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z, z', z'') -{ 168 + 167*z + 167*z' + 167*z'' }-> s35 :|: s32 >= 0, s32 <= z, s33 >= 0, s33 <= z', s34 >= 0, s34 <= z'', s35 >= 0, s35 <= 0, z >= 0, z'' >= 0, z' >= 0
   encode_f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g(z) -{ -164 + 167*z }-> s48 :|: s47 >= 0, s47 <= z - 1, s48 >= 0, s48 <= 1 + s47 + 1, z - 1 >= 0
   encode_g(z) -{ 169 + 167*x_1468 + 167*x_2116 + 167*x_3116 }-> s53 :|: s49 >= 0, s49 <= x_1468, s50 >= 0, s50 <= x_2116, s51 >= 0, s51 <= x_3116, s52 >= 0, s52 <= 0, s53 >= 0, s53 <= s52 + 1, x_3116 >= 0, z = 1 + x_1468 + x_2116 + x_3116, x_2116 >= 0, x_1468 >= 0
   encode_g(z) -{ -163 + 167*z }-> s56 :|: s54 >= 0, s54 <= z - 1, s55 >= 0, s55 <= s54 + 1, s56 >= 0, s56 <= s55 + 1, z - 1 >= 0
   encode_g(z) -{ -159 + 167*z }-> s88 :|: s86 >= 0, s86 <= z - 1, s87 >= 0, s87 <= s86, s88 >= 0, s88 <= s87 + 1, z - 1 >= 0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, 1 = 1
   encode_g(z) -{ 1 }-> 1 + X :|: z = 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z >= 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 1 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_g(z) -{ 2 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_n__g(z) -{ 0 }-> 0 :|: z >= 0
   encode_n__g(z) -{ 2 + 167*z }-> 1 + s36 :|: s36 >= 0, s36 <= z, z >= 0
   f(z, z', z'') -{ 166 }-> s :|: s >= 0, s <= 0, z'' >= 0, z' - 1 >= 0, z = z' - 1
   f(z, z', z'') -{ 169 }-> s' :|: s' >= 0, s' <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s'' :|: s'' >= 0, s'' <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 169 }-> s1 :|: s1 >= 0, s1 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s10 :|: s10 >= 0, s10 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 168 }-> s11 :|: s11 >= 0, s11 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s12 :|: s12 >= 0, s12 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s13 :|: s13 >= 0, s13 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s14 :|: s14 >= 0, s14 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 167 }-> s15 :|: s15 >= 0, s15 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s16 :|: s16 >= 0, s16 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s17 :|: s17 >= 0, s17 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s18 :|: s18 >= 0, s18 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 168 }-> s19 :|: s19 >= 0, s19 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X', z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s2 :|: s2 >= 0, s2 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 168 }-> s20 :|: s20 >= 0, s20 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 167 }-> s21 :|: s21 >= 0, s21 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s22 :|: s22 >= 0, s22 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 167 }-> s23 :|: s23 >= 0, s23 <= 0, z'' - 1 >= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s24 :|: s24 >= 0, s24 <= 0, z'' - 1 >= 0, z' - 1 >= 0, z = z' - 1, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 169 }-> s3 :|: s3 >= 0, s3 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s4 :|: s4 >= 0, s4 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1, X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 169 }-> s5 :|: s5 >= 0, s5 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1, z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s6 :|: s6 >= 0, s6 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1, X2 >= 0, z'' - 1 = X2
   f(z, z', z'') -{ 168 }-> s7 :|: s7 >= 0, s7 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s8 :|: s8 >= 0, s8 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s9 :|: s9 >= 0, s9 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g(z) -{ 1 }-> 0 :|: z = 1
   g(z) -{ 1 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {encode_n__g}, {encode_f}
Previous analysis results are:
  f: runtime: O(1) [162], size: O(1) [0]
  b: runtime: O(1) [1], size: O(1) [1]
  g: runtime: O(1) [1], size: O(n^1) [1 + z]
  encode_c: runtime: O(1) [0], size: O(1) [0]
  activate: runtime: O(1) [5], size: O(n^1) [z]
  encode_b: runtime: O(1) [1], size: O(1) [1]
  encArg: runtime: O(n^1) [2 + 167*z], size: O(n^1) [z]
  encode_activate: runtime: O(n^1) [160 + 167*z], size: O(n^1) [z]
  encode_g: runtime: O(n^1) [164 + 167*z], size: O(n^1) [1 + z]
  encode_n__g: runtime: ?, size: O(n^1) [1 + z]

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

(81) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: encode_n__g
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 2 + 167*z

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

(82)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 0 :|: z - 1 >= 0, z - 1 = 1
   activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   b -{ 0 }-> 1 :|: 
   b -{ 1 }-> 0 :|: 
   b -{ 0 }-> 0 :|: 
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> s25 :|: s25 >= 0, s25 <= X + 1, z = 1 + 2, 1 = 1 + X, X >= 0
   encArg(z) -{ 168 + 167*x_1 + 167*x_2 + 167*x_3 }-> s31 :|: s28 >= 0, s28 <= x_1, s29 >= 0, s29 <= x_2, s30 >= 0, s30 <= x_3, s31 >= 0, s31 <= 0, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ -331 + 167*z }-> s38 :|: s37 >= 0, s37 <= z - 2, s38 >= 0, s38 <= 1 + s37 + 1, z - 2 >= 0
   encArg(z) -{ 169 + 167*x_1228 + 167*x_256 + 167*x_356 }-> s43 :|: s39 >= 0, s39 <= x_1228, s40 >= 0, s40 <= x_256, s41 >= 0, s41 <= x_356, s42 >= 0, s42 <= 0, s43 >= 0, s43 <= s42 + 1, z = 1 + (1 + x_1228 + x_256 + x_356), x_256 >= 0, x_1228 >= 0, x_356 >= 0
   encArg(z) -{ -330 + 167*z }-> s46 :|: s44 >= 0, s44 <= z - 2, s45 >= 0, s45 <= s44 + 1, s46 >= 0, s46 <= s45 + 1, z - 2 >= 0
   encArg(z) -{ -327 + 167*z }-> s58 :|: s57 >= 0, s57 <= z - 2, s58 >= 0, s58 <= 1 + s57, z - 2 >= 0
   encArg(z) -{ 173 + 167*x_1232 + 167*x_257 + 167*x_357 }-> s63 :|: s59 >= 0, s59 <= x_1232, s60 >= 0, s60 <= x_257, s61 >= 0, s61 <= x_357, s62 >= 0, s62 <= 0, s63 >= 0, s63 <= s62, x_1232 >= 0, x_357 >= 0, z = 1 + (1 + x_1232 + x_257 + x_357), x_257 >= 0
   encArg(z) -{ -322 + 167*z }-> s66 :|: s64 >= 0, s64 <= z - 2, s65 >= 0, s65 <= s64, s66 >= 0, s66 <= s65, z - 2 >= 0
   encArg(z) -{ -326 + 167*z }-> s79 :|: s77 >= 0, s77 <= z - 2, s78 >= 0, s78 <= s77, s79 >= 0, s79 <= s78 + 1, z - 2 >= 0
   encArg(z) -{ -326 + 167*z }-> s82 :|: s80 >= 0, s80 <= z - 2, s81 >= 0, s81 <= s80 + 1, s82 >= 0, s82 <= s81, z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, 1 = 1
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ -165 + 167*z }-> 1 + s27 :|: s27 >= 0, s27 <= z - 1, z - 1 >= 0
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 1 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> s26 :|: s26 >= 0, s26 <= X + 1, z = 2, 1 = 1 + X, X >= 0
   encode_activate(z) -{ -160 + 167*z }-> s68 :|: s67 >= 0, s67 <= z - 1, s68 >= 0, s68 <= 1 + s67, z - 1 >= 0
   encode_activate(z) -{ 173 + 167*x_1464 + 167*x_2115 + 167*x_3115 }-> s73 :|: s69 >= 0, s69 <= x_1464, s70 >= 0, s70 <= x_2115, s71 >= 0, s71 <= x_3115, s72 >= 0, s72 <= 0, s73 >= 0, s73 <= s72, x_3115 >= 0, x_1464 >= 0, x_2115 >= 0, z = 1 + x_1464 + x_2115 + x_3115
   encode_activate(z) -{ -155 + 167*z }-> s76 :|: s74 >= 0, s74 <= z - 1, s75 >= 0, s75 <= s74, s76 >= 0, s76 <= s75, z - 1 >= 0
   encode_activate(z) -{ -159 + 167*z }-> s85 :|: s83 >= 0, s83 <= z - 1, s84 >= 0, s84 <= s83 + 1, s85 >= 0, s85 <= s84, z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_b -{ 0 }-> 1 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z, z', z'') -{ 168 + 167*z + 167*z' + 167*z'' }-> s35 :|: s32 >= 0, s32 <= z, s33 >= 0, s33 <= z', s34 >= 0, s34 <= z'', s35 >= 0, s35 <= 0, z >= 0, z'' >= 0, z' >= 0
   encode_f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g(z) -{ -164 + 167*z }-> s48 :|: s47 >= 0, s47 <= z - 1, s48 >= 0, s48 <= 1 + s47 + 1, z - 1 >= 0
   encode_g(z) -{ 169 + 167*x_1468 + 167*x_2116 + 167*x_3116 }-> s53 :|: s49 >= 0, s49 <= x_1468, s50 >= 0, s50 <= x_2116, s51 >= 0, s51 <= x_3116, s52 >= 0, s52 <= 0, s53 >= 0, s53 <= s52 + 1, x_3116 >= 0, z = 1 + x_1468 + x_2116 + x_3116, x_2116 >= 0, x_1468 >= 0
   encode_g(z) -{ -163 + 167*z }-> s56 :|: s54 >= 0, s54 <= z - 1, s55 >= 0, s55 <= s54 + 1, s56 >= 0, s56 <= s55 + 1, z - 1 >= 0
   encode_g(z) -{ -159 + 167*z }-> s88 :|: s86 >= 0, s86 <= z - 1, s87 >= 0, s87 <= s86, s88 >= 0, s88 <= s87 + 1, z - 1 >= 0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, 1 = 1
   encode_g(z) -{ 1 }-> 1 + X :|: z = 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z >= 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 1 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_g(z) -{ 2 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_n__g(z) -{ 0 }-> 0 :|: z >= 0
   encode_n__g(z) -{ 2 + 167*z }-> 1 + s36 :|: s36 >= 0, s36 <= z, z >= 0
   f(z, z', z'') -{ 166 }-> s :|: s >= 0, s <= 0, z'' >= 0, z' - 1 >= 0, z = z' - 1
   f(z, z', z'') -{ 169 }-> s' :|: s' >= 0, s' <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s'' :|: s'' >= 0, s'' <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 169 }-> s1 :|: s1 >= 0, s1 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s10 :|: s10 >= 0, s10 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 168 }-> s11 :|: s11 >= 0, s11 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s12 :|: s12 >= 0, s12 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s13 :|: s13 >= 0, s13 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s14 :|: s14 >= 0, s14 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 167 }-> s15 :|: s15 >= 0, s15 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s16 :|: s16 >= 0, s16 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s17 :|: s17 >= 0, s17 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s18 :|: s18 >= 0, s18 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 168 }-> s19 :|: s19 >= 0, s19 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X', z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s2 :|: s2 >= 0, s2 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 168 }-> s20 :|: s20 >= 0, s20 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 167 }-> s21 :|: s21 >= 0, s21 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s22 :|: s22 >= 0, s22 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 167 }-> s23 :|: s23 >= 0, s23 <= 0, z'' - 1 >= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s24 :|: s24 >= 0, s24 <= 0, z'' - 1 >= 0, z' - 1 >= 0, z = z' - 1, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 169 }-> s3 :|: s3 >= 0, s3 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s4 :|: s4 >= 0, s4 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1, X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 169 }-> s5 :|: s5 >= 0, s5 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1, z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s6 :|: s6 >= 0, s6 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1, X2 >= 0, z'' - 1 = X2
   f(z, z', z'') -{ 168 }-> s7 :|: s7 >= 0, s7 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s8 :|: s8 >= 0, s8 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s9 :|: s9 >= 0, s9 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g(z) -{ 1 }-> 0 :|: z = 1
   g(z) -{ 1 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {encode_f}
Previous analysis results are:
  f: runtime: O(1) [162], size: O(1) [0]
  b: runtime: O(1) [1], size: O(1) [1]
  g: runtime: O(1) [1], size: O(n^1) [1 + z]
  encode_c: runtime: O(1) [0], size: O(1) [0]
  activate: runtime: O(1) [5], size: O(n^1) [z]
  encode_b: runtime: O(1) [1], size: O(1) [1]
  encArg: runtime: O(n^1) [2 + 167*z], size: O(n^1) [z]
  encode_activate: runtime: O(n^1) [160 + 167*z], size: O(n^1) [z]
  encode_g: runtime: O(n^1) [164 + 167*z], size: O(n^1) [1 + z]
  encode_n__g: runtime: O(n^1) [2 + 167*z], size: O(n^1) [1 + z]

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

(83) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(84)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 0 :|: z - 1 >= 0, z - 1 = 1
   activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   b -{ 0 }-> 1 :|: 
   b -{ 1 }-> 0 :|: 
   b -{ 0 }-> 0 :|: 
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> s25 :|: s25 >= 0, s25 <= X + 1, z = 1 + 2, 1 = 1 + X, X >= 0
   encArg(z) -{ 168 + 167*x_1 + 167*x_2 + 167*x_3 }-> s31 :|: s28 >= 0, s28 <= x_1, s29 >= 0, s29 <= x_2, s30 >= 0, s30 <= x_3, s31 >= 0, s31 <= 0, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ -331 + 167*z }-> s38 :|: s37 >= 0, s37 <= z - 2, s38 >= 0, s38 <= 1 + s37 + 1, z - 2 >= 0
   encArg(z) -{ 169 + 167*x_1228 + 167*x_256 + 167*x_356 }-> s43 :|: s39 >= 0, s39 <= x_1228, s40 >= 0, s40 <= x_256, s41 >= 0, s41 <= x_356, s42 >= 0, s42 <= 0, s43 >= 0, s43 <= s42 + 1, z = 1 + (1 + x_1228 + x_256 + x_356), x_256 >= 0, x_1228 >= 0, x_356 >= 0
   encArg(z) -{ -330 + 167*z }-> s46 :|: s44 >= 0, s44 <= z - 2, s45 >= 0, s45 <= s44 + 1, s46 >= 0, s46 <= s45 + 1, z - 2 >= 0
   encArg(z) -{ -327 + 167*z }-> s58 :|: s57 >= 0, s57 <= z - 2, s58 >= 0, s58 <= 1 + s57, z - 2 >= 0
   encArg(z) -{ 173 + 167*x_1232 + 167*x_257 + 167*x_357 }-> s63 :|: s59 >= 0, s59 <= x_1232, s60 >= 0, s60 <= x_257, s61 >= 0, s61 <= x_357, s62 >= 0, s62 <= 0, s63 >= 0, s63 <= s62, x_1232 >= 0, x_357 >= 0, z = 1 + (1 + x_1232 + x_257 + x_357), x_257 >= 0
   encArg(z) -{ -322 + 167*z }-> s66 :|: s64 >= 0, s64 <= z - 2, s65 >= 0, s65 <= s64, s66 >= 0, s66 <= s65, z - 2 >= 0
   encArg(z) -{ -326 + 167*z }-> s79 :|: s77 >= 0, s77 <= z - 2, s78 >= 0, s78 <= s77, s79 >= 0, s79 <= s78 + 1, z - 2 >= 0
   encArg(z) -{ -326 + 167*z }-> s82 :|: s80 >= 0, s80 <= z - 2, s81 >= 0, s81 <= s80 + 1, s82 >= 0, s82 <= s81, z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, 1 = 1
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ -165 + 167*z }-> 1 + s27 :|: s27 >= 0, s27 <= z - 1, z - 1 >= 0
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 1 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> s26 :|: s26 >= 0, s26 <= X + 1, z = 2, 1 = 1 + X, X >= 0
   encode_activate(z) -{ -160 + 167*z }-> s68 :|: s67 >= 0, s67 <= z - 1, s68 >= 0, s68 <= 1 + s67, z - 1 >= 0
   encode_activate(z) -{ 173 + 167*x_1464 + 167*x_2115 + 167*x_3115 }-> s73 :|: s69 >= 0, s69 <= x_1464, s70 >= 0, s70 <= x_2115, s71 >= 0, s71 <= x_3115, s72 >= 0, s72 <= 0, s73 >= 0, s73 <= s72, x_3115 >= 0, x_1464 >= 0, x_2115 >= 0, z = 1 + x_1464 + x_2115 + x_3115
   encode_activate(z) -{ -155 + 167*z }-> s76 :|: s74 >= 0, s74 <= z - 1, s75 >= 0, s75 <= s74, s76 >= 0, s76 <= s75, z - 1 >= 0
   encode_activate(z) -{ -159 + 167*z }-> s85 :|: s83 >= 0, s83 <= z - 1, s84 >= 0, s84 <= s83 + 1, s85 >= 0, s85 <= s84, z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_b -{ 0 }-> 1 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z, z', z'') -{ 168 + 167*z + 167*z' + 167*z'' }-> s35 :|: s32 >= 0, s32 <= z, s33 >= 0, s33 <= z', s34 >= 0, s34 <= z'', s35 >= 0, s35 <= 0, z >= 0, z'' >= 0, z' >= 0
   encode_f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g(z) -{ -164 + 167*z }-> s48 :|: s47 >= 0, s47 <= z - 1, s48 >= 0, s48 <= 1 + s47 + 1, z - 1 >= 0
   encode_g(z) -{ 169 + 167*x_1468 + 167*x_2116 + 167*x_3116 }-> s53 :|: s49 >= 0, s49 <= x_1468, s50 >= 0, s50 <= x_2116, s51 >= 0, s51 <= x_3116, s52 >= 0, s52 <= 0, s53 >= 0, s53 <= s52 + 1, x_3116 >= 0, z = 1 + x_1468 + x_2116 + x_3116, x_2116 >= 0, x_1468 >= 0
   encode_g(z) -{ -163 + 167*z }-> s56 :|: s54 >= 0, s54 <= z - 1, s55 >= 0, s55 <= s54 + 1, s56 >= 0, s56 <= s55 + 1, z - 1 >= 0
   encode_g(z) -{ -159 + 167*z }-> s88 :|: s86 >= 0, s86 <= z - 1, s87 >= 0, s87 <= s86, s88 >= 0, s88 <= s87 + 1, z - 1 >= 0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, 1 = 1
   encode_g(z) -{ 1 }-> 1 + X :|: z = 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z >= 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 1 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_g(z) -{ 2 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_n__g(z) -{ 0 }-> 0 :|: z >= 0
   encode_n__g(z) -{ 2 + 167*z }-> 1 + s36 :|: s36 >= 0, s36 <= z, z >= 0
   f(z, z', z'') -{ 166 }-> s :|: s >= 0, s <= 0, z'' >= 0, z' - 1 >= 0, z = z' - 1
   f(z, z', z'') -{ 169 }-> s' :|: s' >= 0, s' <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s'' :|: s'' >= 0, s'' <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 169 }-> s1 :|: s1 >= 0, s1 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s10 :|: s10 >= 0, s10 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 168 }-> s11 :|: s11 >= 0, s11 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s12 :|: s12 >= 0, s12 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s13 :|: s13 >= 0, s13 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s14 :|: s14 >= 0, s14 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 167 }-> s15 :|: s15 >= 0, s15 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s16 :|: s16 >= 0, s16 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s17 :|: s17 >= 0, s17 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s18 :|: s18 >= 0, s18 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 168 }-> s19 :|: s19 >= 0, s19 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X', z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s2 :|: s2 >= 0, s2 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 168 }-> s20 :|: s20 >= 0, s20 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 167 }-> s21 :|: s21 >= 0, s21 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s22 :|: s22 >= 0, s22 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 167 }-> s23 :|: s23 >= 0, s23 <= 0, z'' - 1 >= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s24 :|: s24 >= 0, s24 <= 0, z'' - 1 >= 0, z' - 1 >= 0, z = z' - 1, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 169 }-> s3 :|: s3 >= 0, s3 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s4 :|: s4 >= 0, s4 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1, X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 169 }-> s5 :|: s5 >= 0, s5 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1, z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s6 :|: s6 >= 0, s6 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1, X2 >= 0, z'' - 1 = X2
   f(z, z', z'') -{ 168 }-> s7 :|: s7 >= 0, s7 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s8 :|: s8 >= 0, s8 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s9 :|: s9 >= 0, s9 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g(z) -{ 1 }-> 0 :|: z = 1
   g(z) -{ 1 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {encode_f}
Previous analysis results are:
  f: runtime: O(1) [162], size: O(1) [0]
  b: runtime: O(1) [1], size: O(1) [1]
  g: runtime: O(1) [1], size: O(n^1) [1 + z]
  encode_c: runtime: O(1) [0], size: O(1) [0]
  activate: runtime: O(1) [5], size: O(n^1) [z]
  encode_b: runtime: O(1) [1], size: O(1) [1]
  encArg: runtime: O(n^1) [2 + 167*z], size: O(n^1) [z]
  encode_activate: runtime: O(n^1) [160 + 167*z], size: O(n^1) [z]
  encode_g: runtime: O(n^1) [164 + 167*z], size: O(n^1) [1 + z]
  encode_n__g: runtime: O(n^1) [2 + 167*z], size: O(n^1) [1 + z]

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

(85) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: encode_f
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 0

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

(86)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 0 :|: z - 1 >= 0, z - 1 = 1
   activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   b -{ 0 }-> 1 :|: 
   b -{ 1 }-> 0 :|: 
   b -{ 0 }-> 0 :|: 
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> s25 :|: s25 >= 0, s25 <= X + 1, z = 1 + 2, 1 = 1 + X, X >= 0
   encArg(z) -{ 168 + 167*x_1 + 167*x_2 + 167*x_3 }-> s31 :|: s28 >= 0, s28 <= x_1, s29 >= 0, s29 <= x_2, s30 >= 0, s30 <= x_3, s31 >= 0, s31 <= 0, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ -331 + 167*z }-> s38 :|: s37 >= 0, s37 <= z - 2, s38 >= 0, s38 <= 1 + s37 + 1, z - 2 >= 0
   encArg(z) -{ 169 + 167*x_1228 + 167*x_256 + 167*x_356 }-> s43 :|: s39 >= 0, s39 <= x_1228, s40 >= 0, s40 <= x_256, s41 >= 0, s41 <= x_356, s42 >= 0, s42 <= 0, s43 >= 0, s43 <= s42 + 1, z = 1 + (1 + x_1228 + x_256 + x_356), x_256 >= 0, x_1228 >= 0, x_356 >= 0
   encArg(z) -{ -330 + 167*z }-> s46 :|: s44 >= 0, s44 <= z - 2, s45 >= 0, s45 <= s44 + 1, s46 >= 0, s46 <= s45 + 1, z - 2 >= 0
   encArg(z) -{ -327 + 167*z }-> s58 :|: s57 >= 0, s57 <= z - 2, s58 >= 0, s58 <= 1 + s57, z - 2 >= 0
   encArg(z) -{ 173 + 167*x_1232 + 167*x_257 + 167*x_357 }-> s63 :|: s59 >= 0, s59 <= x_1232, s60 >= 0, s60 <= x_257, s61 >= 0, s61 <= x_357, s62 >= 0, s62 <= 0, s63 >= 0, s63 <= s62, x_1232 >= 0, x_357 >= 0, z = 1 + (1 + x_1232 + x_257 + x_357), x_257 >= 0
   encArg(z) -{ -322 + 167*z }-> s66 :|: s64 >= 0, s64 <= z - 2, s65 >= 0, s65 <= s64, s66 >= 0, s66 <= s65, z - 2 >= 0
   encArg(z) -{ -326 + 167*z }-> s79 :|: s77 >= 0, s77 <= z - 2, s78 >= 0, s78 <= s77, s79 >= 0, s79 <= s78 + 1, z - 2 >= 0
   encArg(z) -{ -326 + 167*z }-> s82 :|: s80 >= 0, s80 <= z - 2, s81 >= 0, s81 <= s80 + 1, s82 >= 0, s82 <= s81, z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, 1 = 1
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ -165 + 167*z }-> 1 + s27 :|: s27 >= 0, s27 <= z - 1, z - 1 >= 0
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 1 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> s26 :|: s26 >= 0, s26 <= X + 1, z = 2, 1 = 1 + X, X >= 0
   encode_activate(z) -{ -160 + 167*z }-> s68 :|: s67 >= 0, s67 <= z - 1, s68 >= 0, s68 <= 1 + s67, z - 1 >= 0
   encode_activate(z) -{ 173 + 167*x_1464 + 167*x_2115 + 167*x_3115 }-> s73 :|: s69 >= 0, s69 <= x_1464, s70 >= 0, s70 <= x_2115, s71 >= 0, s71 <= x_3115, s72 >= 0, s72 <= 0, s73 >= 0, s73 <= s72, x_3115 >= 0, x_1464 >= 0, x_2115 >= 0, z = 1 + x_1464 + x_2115 + x_3115
   encode_activate(z) -{ -155 + 167*z }-> s76 :|: s74 >= 0, s74 <= z - 1, s75 >= 0, s75 <= s74, s76 >= 0, s76 <= s75, z - 1 >= 0
   encode_activate(z) -{ -159 + 167*z }-> s85 :|: s83 >= 0, s83 <= z - 1, s84 >= 0, s84 <= s83 + 1, s85 >= 0, s85 <= s84, z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_b -{ 0 }-> 1 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z, z', z'') -{ 168 + 167*z + 167*z' + 167*z'' }-> s35 :|: s32 >= 0, s32 <= z, s33 >= 0, s33 <= z', s34 >= 0, s34 <= z'', s35 >= 0, s35 <= 0, z >= 0, z'' >= 0, z' >= 0
   encode_f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g(z) -{ -164 + 167*z }-> s48 :|: s47 >= 0, s47 <= z - 1, s48 >= 0, s48 <= 1 + s47 + 1, z - 1 >= 0
   encode_g(z) -{ 169 + 167*x_1468 + 167*x_2116 + 167*x_3116 }-> s53 :|: s49 >= 0, s49 <= x_1468, s50 >= 0, s50 <= x_2116, s51 >= 0, s51 <= x_3116, s52 >= 0, s52 <= 0, s53 >= 0, s53 <= s52 + 1, x_3116 >= 0, z = 1 + x_1468 + x_2116 + x_3116, x_2116 >= 0, x_1468 >= 0
   encode_g(z) -{ -163 + 167*z }-> s56 :|: s54 >= 0, s54 <= z - 1, s55 >= 0, s55 <= s54 + 1, s56 >= 0, s56 <= s55 + 1, z - 1 >= 0
   encode_g(z) -{ -159 + 167*z }-> s88 :|: s86 >= 0, s86 <= z - 1, s87 >= 0, s87 <= s86, s88 >= 0, s88 <= s87 + 1, z - 1 >= 0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, 1 = 1
   encode_g(z) -{ 1 }-> 1 + X :|: z = 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z >= 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 1 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_g(z) -{ 2 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_n__g(z) -{ 0 }-> 0 :|: z >= 0
   encode_n__g(z) -{ 2 + 167*z }-> 1 + s36 :|: s36 >= 0, s36 <= z, z >= 0
   f(z, z', z'') -{ 166 }-> s :|: s >= 0, s <= 0, z'' >= 0, z' - 1 >= 0, z = z' - 1
   f(z, z', z'') -{ 169 }-> s' :|: s' >= 0, s' <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s'' :|: s'' >= 0, s'' <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 169 }-> s1 :|: s1 >= 0, s1 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s10 :|: s10 >= 0, s10 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 168 }-> s11 :|: s11 >= 0, s11 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s12 :|: s12 >= 0, s12 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s13 :|: s13 >= 0, s13 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s14 :|: s14 >= 0, s14 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 167 }-> s15 :|: s15 >= 0, s15 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s16 :|: s16 >= 0, s16 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s17 :|: s17 >= 0, s17 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s18 :|: s18 >= 0, s18 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 168 }-> s19 :|: s19 >= 0, s19 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X', z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s2 :|: s2 >= 0, s2 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 168 }-> s20 :|: s20 >= 0, s20 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 167 }-> s21 :|: s21 >= 0, s21 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s22 :|: s22 >= 0, s22 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 167 }-> s23 :|: s23 >= 0, s23 <= 0, z'' - 1 >= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s24 :|: s24 >= 0, s24 <= 0, z'' - 1 >= 0, z' - 1 >= 0, z = z' - 1, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 169 }-> s3 :|: s3 >= 0, s3 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s4 :|: s4 >= 0, s4 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1, X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 169 }-> s5 :|: s5 >= 0, s5 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1, z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s6 :|: s6 >= 0, s6 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1, X2 >= 0, z'' - 1 = X2
   f(z, z', z'') -{ 168 }-> s7 :|: s7 >= 0, s7 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s8 :|: s8 >= 0, s8 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s9 :|: s9 >= 0, s9 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g(z) -{ 1 }-> 0 :|: z = 1
   g(z) -{ 1 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {encode_f}
Previous analysis results are:
  f: runtime: O(1) [162], size: O(1) [0]
  b: runtime: O(1) [1], size: O(1) [1]
  g: runtime: O(1) [1], size: O(n^1) [1 + z]
  encode_c: runtime: O(1) [0], size: O(1) [0]
  activate: runtime: O(1) [5], size: O(n^1) [z]
  encode_b: runtime: O(1) [1], size: O(1) [1]
  encArg: runtime: O(n^1) [2 + 167*z], size: O(n^1) [z]
  encode_activate: runtime: O(n^1) [160 + 167*z], size: O(n^1) [z]
  encode_g: runtime: O(n^1) [164 + 167*z], size: O(n^1) [1 + z]
  encode_n__g: runtime: O(n^1) [2 + 167*z], size: O(n^1) [1 + z]
  encode_f: runtime: ?, size: O(1) [0]

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

(87) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: encode_f
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 168 + 167*z + 167*z' + 167*z''

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

(88)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 0 :|: z - 1 >= 0, z - 1 = 1
   activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   b -{ 0 }-> 1 :|: 
   b -{ 1 }-> 0 :|: 
   b -{ 0 }-> 0 :|: 
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> s25 :|: s25 >= 0, s25 <= X + 1, z = 1 + 2, 1 = 1 + X, X >= 0
   encArg(z) -{ 168 + 167*x_1 + 167*x_2 + 167*x_3 }-> s31 :|: s28 >= 0, s28 <= x_1, s29 >= 0, s29 <= x_2, s30 >= 0, s30 <= x_3, s31 >= 0, s31 <= 0, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ -331 + 167*z }-> s38 :|: s37 >= 0, s37 <= z - 2, s38 >= 0, s38 <= 1 + s37 + 1, z - 2 >= 0
   encArg(z) -{ 169 + 167*x_1228 + 167*x_256 + 167*x_356 }-> s43 :|: s39 >= 0, s39 <= x_1228, s40 >= 0, s40 <= x_256, s41 >= 0, s41 <= x_356, s42 >= 0, s42 <= 0, s43 >= 0, s43 <= s42 + 1, z = 1 + (1 + x_1228 + x_256 + x_356), x_256 >= 0, x_1228 >= 0, x_356 >= 0
   encArg(z) -{ -330 + 167*z }-> s46 :|: s44 >= 0, s44 <= z - 2, s45 >= 0, s45 <= s44 + 1, s46 >= 0, s46 <= s45 + 1, z - 2 >= 0
   encArg(z) -{ -327 + 167*z }-> s58 :|: s57 >= 0, s57 <= z - 2, s58 >= 0, s58 <= 1 + s57, z - 2 >= 0
   encArg(z) -{ 173 + 167*x_1232 + 167*x_257 + 167*x_357 }-> s63 :|: s59 >= 0, s59 <= x_1232, s60 >= 0, s60 <= x_257, s61 >= 0, s61 <= x_357, s62 >= 0, s62 <= 0, s63 >= 0, s63 <= s62, x_1232 >= 0, x_357 >= 0, z = 1 + (1 + x_1232 + x_257 + x_357), x_257 >= 0
   encArg(z) -{ -322 + 167*z }-> s66 :|: s64 >= 0, s64 <= z - 2, s65 >= 0, s65 <= s64, s66 >= 0, s66 <= s65, z - 2 >= 0
   encArg(z) -{ -326 + 167*z }-> s79 :|: s77 >= 0, s77 <= z - 2, s78 >= 0, s78 <= s77, s79 >= 0, s79 <= s78 + 1, z - 2 >= 0
   encArg(z) -{ -326 + 167*z }-> s82 :|: s80 >= 0, s80 <= z - 2, s81 >= 0, s81 <= s80 + 1, s82 >= 0, s82 <= s81, z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, 1 = 1
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 1 = X
   encArg(z) -{ 1 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ 2 }-> 1 + X :|: z = 1 + 2, X >= 0, 0 = X
   encArg(z) -{ -165 + 167*z }-> 1 + s27 :|: s27 >= 0, s27 <= z - 1, z - 1 >= 0
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 1 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> X :|: z = 2, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> s26 :|: s26 >= 0, s26 <= X + 1, z = 2, 1 = 1 + X, X >= 0
   encode_activate(z) -{ -160 + 167*z }-> s68 :|: s67 >= 0, s67 <= z - 1, s68 >= 0, s68 <= 1 + s67, z - 1 >= 0
   encode_activate(z) -{ 173 + 167*x_1464 + 167*x_2115 + 167*x_3115 }-> s73 :|: s69 >= 0, s69 <= x_1464, s70 >= 0, s70 <= x_2115, s71 >= 0, s71 <= x_3115, s72 >= 0, s72 <= 0, s73 >= 0, s73 <= s72, x_3115 >= 0, x_1464 >= 0, x_2115 >= 0, z = 1 + x_1464 + x_2115 + x_3115
   encode_activate(z) -{ -155 + 167*z }-> s76 :|: s74 >= 0, s74 <= z - 1, s75 >= 0, s75 <= s74, s76 >= 0, s76 <= s75, z - 1 >= 0
   encode_activate(z) -{ -159 + 167*z }-> s85 :|: s83 >= 0, s83 <= z - 1, s84 >= 0, s84 <= s83 + 1, s85 >= 0, s85 <= s84, z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_b -{ 0 }-> 1 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z, z', z'') -{ 168 + 167*z + 167*z' + 167*z'' }-> s35 :|: s32 >= 0, s32 <= z, s33 >= 0, s33 <= z', s34 >= 0, s34 <= z'', s35 >= 0, s35 <= 0, z >= 0, z'' >= 0, z' >= 0
   encode_f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g(z) -{ -164 + 167*z }-> s48 :|: s47 >= 0, s47 <= z - 1, s48 >= 0, s48 <= 1 + s47 + 1, z - 1 >= 0
   encode_g(z) -{ 169 + 167*x_1468 + 167*x_2116 + 167*x_3116 }-> s53 :|: s49 >= 0, s49 <= x_1468, s50 >= 0, s50 <= x_2116, s51 >= 0, s51 <= x_3116, s52 >= 0, s52 <= 0, s53 >= 0, s53 <= s52 + 1, x_3116 >= 0, z = 1 + x_1468 + x_2116 + x_3116, x_2116 >= 0, x_1468 >= 0
   encode_g(z) -{ -163 + 167*z }-> s56 :|: s54 >= 0, s54 <= z - 1, s55 >= 0, s55 <= s54 + 1, s56 >= 0, s56 <= s55 + 1, z - 1 >= 0
   encode_g(z) -{ -159 + 167*z }-> s88 :|: s86 >= 0, s86 <= z - 1, s87 >= 0, s87 <= s86, s88 >= 0, s88 <= s87 + 1, z - 1 >= 0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, 1 = 1
   encode_g(z) -{ 1 }-> 1 + X :|: z = 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z >= 0, X >= 0, 0 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 1 = X
   encode_g(z) -{ 1 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_g(z) -{ 2 }-> 1 + X :|: z = 2, X >= 0, 0 = X
   encode_n__g(z) -{ 0 }-> 0 :|: z >= 0
   encode_n__g(z) -{ 2 + 167*z }-> 1 + s36 :|: s36 >= 0, s36 <= z, z >= 0
   f(z, z', z'') -{ 166 }-> s :|: s >= 0, s <= 0, z'' >= 0, z' - 1 >= 0, z = z' - 1
   f(z, z', z'') -{ 169 }-> s' :|: s' >= 0, s' <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s'' :|: s'' >= 0, s'' <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 169 }-> s1 :|: s1 >= 0, s1 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s10 :|: s10 >= 0, s10 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 168 }-> s11 :|: s11 >= 0, s11 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s12 :|: s12 >= 0, s12 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s13 :|: s13 >= 0, s13 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s14 :|: s14 >= 0, s14 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 167 }-> s15 :|: s15 >= 0, s15 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s16 :|: s16 >= 0, s16 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s17 :|: s17 >= 0, s17 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s18 :|: s18 >= 0, s18 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 168 }-> s19 :|: s19 >= 0, s19 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X', z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s2 :|: s2 >= 0, s2 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 168 }-> s20 :|: s20 >= 0, s20 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X', X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 167 }-> s21 :|: s21 >= 0, s21 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s22 :|: s22 >= 0, s22 <= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 >= 0, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 167 }-> s23 :|: s23 >= 0, s23 <= 0, z'' - 1 >= 0, z' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 167 }-> s24 :|: s24 >= 0, s24 <= 0, z'' - 1 >= 0, z' - 1 >= 0, z = z' - 1, X' >= 0, z'' - 1 = X'
   f(z, z', z'') -{ 169 }-> s3 :|: s3 >= 0, s3 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s4 :|: s4 >= 0, s4 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1, X1 >= 0, z'' - 1 = X1
   f(z, z', z'') -{ 169 }-> s5 :|: s5 >= 0, s5 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1, z'' - 1 = 1
   f(z, z', z'') -{ 169 }-> s6 :|: s6 >= 0, s6 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', X1 >= 0, z'' - 1 = X1, X2 >= 0, z'' - 1 = X2
   f(z, z', z'') -{ 168 }-> s7 :|: s7 >= 0, s7 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1
   f(z, z', z'') -{ 168 }-> s8 :|: s8 >= 0, s8 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, z'' - 1 = 1, X'' >= 0, z'' - 1 = X''
   f(z, z', z'') -{ 168 }-> s9 :|: s9 >= 0, s9 <= 0, z' - 1 >= 0, z'' - 1 >= 0, z = z' - 1, X'' >= 0, z'' - 1 = X'', z'' - 1 = 1
   f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g(z) -{ 1 }-> 0 :|: z = 1
   g(z) -{ 1 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: 
Previous analysis results are:
  f: runtime: O(1) [162], size: O(1) [0]
  b: runtime: O(1) [1], size: O(1) [1]
  g: runtime: O(1) [1], size: O(n^1) [1 + z]
  encode_c: runtime: O(1) [0], size: O(1) [0]
  activate: runtime: O(1) [5], size: O(n^1) [z]
  encode_b: runtime: O(1) [1], size: O(1) [1]
  encArg: runtime: O(n^1) [2 + 167*z], size: O(n^1) [z]
  encode_activate: runtime: O(n^1) [160 + 167*z], size: O(n^1) [z]
  encode_g: runtime: O(n^1) [164 + 167*z], size: O(n^1) [1 + z]
  encode_n__g: runtime: O(n^1) [2 + 167*z], size: O(n^1) [1 + z]
  encode_f: runtime: O(n^1) [168 + 167*z + 167*z' + 167*z''], size: O(1) [0]

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(89) FinalProof (FINISHED)
Computed overall runtime complexity
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(90)
BOUNDS(1, n^1)