/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 143 ms]
(4) CpxRelTRS
(5) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
(6) CpxWeightedTrs
(7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
(8) CpxTypedWeightedTrs
(9) CompletionProof [UPPER BOUND(ID), 0 ms]
(10) CpxTypedWeightedCompleteTrs
(11) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
(12) CpxTypedWeightedCompleteTrs
(13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
(14) CpxRNTS
(15) InliningProof [UPPER BOUND(ID), 439 ms]
(16) CpxRNTS
(17) SimplificationProof [BOTH BOUNDS(ID, ID), 3 ms]
(18) CpxRNTS
(19) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms]
(20) CpxRNTS
(21) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(22) CpxRNTS
(23) IntTrsBoundProof [UPPER BOUND(ID), 29 ms]
(24) CpxRNTS
(25) IntTrsBoundProof [UPPER BOUND(ID), 5 ms]
(26) CpxRNTS
(27) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(28) CpxRNTS
(29) IntTrsBoundProof [UPPER BOUND(ID), 158 ms]
(30) CpxRNTS
(31) IntTrsBoundProof [UPPER BOUND(ID), 62 ms]
(32) CpxRNTS
(33) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(34) CpxRNTS
(35) IntTrsBoundProof [UPPER BOUND(ID), 106 ms]
(36) CpxRNTS
(37) IntTrsBoundProof [UPPER BOUND(ID), 33 ms]
(38) CpxRNTS
(39) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(40) CpxRNTS
(41) IntTrsBoundProof [UPPER BOUND(ID), 148 ms]
(42) CpxRNTS
(43) IntTrsBoundProof [UPPER BOUND(ID), 54 ms]
(44) CpxRNTS
(45) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(46) CpxRNTS
(47) IntTrsBoundProof [UPPER BOUND(ID), 118 ms]
(48) CpxRNTS
(49) IntTrsBoundProof [UPPER BOUND(ID), 31 ms]
(50) CpxRNTS
(51) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(52) CpxRNTS
(53) IntTrsBoundProof [UPPER BOUND(ID), 106 ms]
(54) CpxRNTS
(55) IntTrsBoundProof [UPPER BOUND(ID), 0 ms]
(56) CpxRNTS
(57) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(58) CpxRNTS
(59) IntTrsBoundProof [UPPER BOUND(ID), 610 ms]
(60) CpxRNTS
(61) IntTrsBoundProof [UPPER BOUND(ID), 280 ms]
(62) CpxRNTS
(63) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(64) CpxRNTS
(65) IntTrsBoundProof [UPPER BOUND(ID), 427 ms]
(66) CpxRNTS
(67) IntTrsBoundProof [UPPER BOUND(ID), 97 ms]
(68) CpxRNTS
(69) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(70) CpxRNTS
(71) IntTrsBoundProof [UPPER BOUND(ID), 169 ms]
(72) CpxRNTS
(73) IntTrsBoundProof [UPPER BOUND(ID), 65 ms]
(74) CpxRNTS
(75) FinalProof [FINISHED, 0 ms]
(76) 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, X) -> f(a, n__b)
   b -> a
   b -> n__b
   activate(n__b) -> b
   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(a) -> a
   encArg(n__b) -> n__b
   encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2))
   encArg(cons_b) -> b
   encArg(cons_activate(x_1)) -> activate(encArg(x_1))
   encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2))
   encode_a -> a
   encode_n__b -> n__b
   encode_b -> b
   encode_activate(x_1) -> activate(encArg(x_1))


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

(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, X) -> f(a, n__b)
   b -> a
   b -> n__b
   activate(n__b) -> b
   activate(X) -> X

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

   encArg(a) -> a
   encArg(n__b) -> n__b
   encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2))
   encArg(cons_b) -> b
   encArg(cons_activate(x_1)) -> activate(encArg(x_1))
   encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2))
   encode_a -> a
   encode_n__b -> n__b
   encode_b -> b
   encode_activate(x_1) -> activate(encArg(x_1))

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, X) -> f(a, n__b)
   b -> a
   b -> n__b
   activate(n__b) -> b
   activate(X) -> X

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

   encArg(a) -> a
   encArg(n__b) -> n__b
   encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2))
   encArg(cons_b) -> b
   encArg(cons_activate(x_1)) -> activate(encArg(x_1))
   encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2))
   encode_a -> a
   encode_n__b -> n__b
   encode_b -> b
   encode_activate(x_1) -> activate(encArg(x_1))

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

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

(6)
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, X) -> f(a, n__b) [1]
   b -> a [1]
   b -> n__b [1]
   activate(n__b) -> b [1]
   activate(X) -> X [1]
   encArg(a) -> a [0]
   encArg(n__b) -> n__b [0]
   encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2)) [0]
   encArg(cons_b) -> b [0]
   encArg(cons_activate(x_1)) -> activate(encArg(x_1)) [0]
   encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2)) [0]
   encode_a -> a [0]
   encode_n__b -> n__b [0]
   encode_b -> b [0]
   encode_activate(x_1) -> activate(encArg(x_1)) [0]

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

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

(8)
Obligation:
Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   f(X, X) -> f(a, n__b) [1]
   b -> a [1]
   b -> n__b [1]
   activate(n__b) -> b [1]
   activate(X) -> X [1]
   encArg(a) -> a [0]
   encArg(n__b) -> n__b [0]
   encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2)) [0]
   encArg(cons_b) -> b [0]
   encArg(cons_activate(x_1)) -> activate(encArg(x_1)) [0]
   encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2)) [0]
   encode_a -> a [0]
   encode_n__b -> n__b [0]
   encode_b -> b [0]
   encode_activate(x_1) -> activate(encArg(x_1)) [0]

The TRS has the following type information:
f :: a:n__b:cons_f:cons_b:cons_activate -> a:n__b:cons_f:cons_b:cons_activate -> a:n__b:cons_f:cons_b:cons_activate
a :: a:n__b:cons_f:cons_b:cons_activate
n__b :: a:n__b:cons_f:cons_b:cons_activate
b :: a:n__b:cons_f:cons_b:cons_activate
activate :: a:n__b:cons_f:cons_b:cons_activate -> a:n__b:cons_f:cons_b:cons_activate
encArg :: a:n__b:cons_f:cons_b:cons_activate -> a:n__b:cons_f:cons_b:cons_activate
cons_f :: a:n__b:cons_f:cons_b:cons_activate -> a:n__b:cons_f:cons_b:cons_activate -> a:n__b:cons_f:cons_b:cons_activate
cons_b :: a:n__b:cons_f:cons_b:cons_activate
cons_activate :: a:n__b:cons_f:cons_b:cons_activate -> a:n__b:cons_f:cons_b:cons_activate
encode_f :: a:n__b:cons_f:cons_b:cons_activate -> a:n__b:cons_f:cons_b:cons_activate -> a:n__b:cons_f:cons_b:cons_activate
encode_a :: a:n__b:cons_f:cons_b:cons_activate
encode_n__b :: a:n__b:cons_f:cons_b:cons_activate
encode_b :: a:n__b:cons_f:cons_b:cons_activate
encode_activate :: a:n__b:cons_f:cons_b:cons_activate -> a:n__b:cons_f:cons_b:cons_activate

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

(9) 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:

   b
   f_2
   activate_1
   encArg_1
   encode_f_2
   encode_a
   encode_n__b
   encode_b
   encode_activate_1

Due to the following rules being added:

   encArg(v0) -> null_encArg [0]
   encode_f(v0, v1) -> null_encode_f [0]
   encode_a -> null_encode_a [0]
   encode_n__b -> null_encode_n__b [0]
   encode_b -> null_encode_b [0]
   encode_activate(v0) -> null_encode_activate [0]
   f(v0, v1) -> null_f [0]

And the following fresh constants:    null_encArg, null_encode_f, null_encode_a, null_encode_n__b, null_encode_b, null_encode_activate, null_f

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

(10)
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, X) -> f(a, n__b) [1]
   b -> a [1]
   b -> n__b [1]
   activate(n__b) -> b [1]
   activate(X) -> X [1]
   encArg(a) -> a [0]
   encArg(n__b) -> n__b [0]
   encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2)) [0]
   encArg(cons_b) -> b [0]
   encArg(cons_activate(x_1)) -> activate(encArg(x_1)) [0]
   encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2)) [0]
   encode_a -> a [0]
   encode_n__b -> n__b [0]
   encode_b -> b [0]
   encode_activate(x_1) -> activate(encArg(x_1)) [0]
   encArg(v0) -> null_encArg [0]
   encode_f(v0, v1) -> null_encode_f [0]
   encode_a -> null_encode_a [0]
   encode_n__b -> null_encode_n__b [0]
   encode_b -> null_encode_b [0]
   encode_activate(v0) -> null_encode_activate [0]
   f(v0, v1) -> null_f [0]

The TRS has the following type information:
f :: a:n__b:cons_f:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_a:null_encode_n__b:null_encode_b:null_encode_activate:null_f -> a:n__b:cons_f:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_a:null_encode_n__b:null_encode_b:null_encode_activate:null_f -> a:n__b:cons_f:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_a:null_encode_n__b:null_encode_b:null_encode_activate:null_f
a :: a:n__b:cons_f:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_a:null_encode_n__b:null_encode_b:null_encode_activate:null_f
n__b :: a:n__b:cons_f:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_a:null_encode_n__b:null_encode_b:null_encode_activate:null_f
b :: a:n__b:cons_f:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_a:null_encode_n__b:null_encode_b:null_encode_activate:null_f
activate :: a:n__b:cons_f:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_a:null_encode_n__b:null_encode_b:null_encode_activate:null_f -> a:n__b:cons_f:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_a:null_encode_n__b:null_encode_b:null_encode_activate:null_f
encArg :: a:n__b:cons_f:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_a:null_encode_n__b:null_encode_b:null_encode_activate:null_f -> a:n__b:cons_f:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_a:null_encode_n__b:null_encode_b:null_encode_activate:null_f
cons_f :: a:n__b:cons_f:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_a:null_encode_n__b:null_encode_b:null_encode_activate:null_f -> a:n__b:cons_f:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_a:null_encode_n__b:null_encode_b:null_encode_activate:null_f -> a:n__b:cons_f:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_a:null_encode_n__b:null_encode_b:null_encode_activate:null_f
cons_b :: a:n__b:cons_f:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_a:null_encode_n__b:null_encode_b:null_encode_activate:null_f
cons_activate :: a:n__b:cons_f:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_a:null_encode_n__b:null_encode_b:null_encode_activate:null_f -> a:n__b:cons_f:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_a:null_encode_n__b:null_encode_b:null_encode_activate:null_f
encode_f :: a:n__b:cons_f:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_a:null_encode_n__b:null_encode_b:null_encode_activate:null_f -> a:n__b:cons_f:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_a:null_encode_n__b:null_encode_b:null_encode_activate:null_f -> a:n__b:cons_f:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_a:null_encode_n__b:null_encode_b:null_encode_activate:null_f
encode_a :: a:n__b:cons_f:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_a:null_encode_n__b:null_encode_b:null_encode_activate:null_f
encode_n__b :: a:n__b:cons_f:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_a:null_encode_n__b:null_encode_b:null_encode_activate:null_f
encode_b :: a:n__b:cons_f:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_a:null_encode_n__b:null_encode_b:null_encode_activate:null_f
encode_activate :: a:n__b:cons_f:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_a:null_encode_n__b:null_encode_b:null_encode_activate:null_f -> a:n__b:cons_f:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_a:null_encode_n__b:null_encode_b:null_encode_activate:null_f
null_encArg :: a:n__b:cons_f:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_a:null_encode_n__b:null_encode_b:null_encode_activate:null_f
null_encode_f :: a:n__b:cons_f:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_a:null_encode_n__b:null_encode_b:null_encode_activate:null_f
null_encode_a :: a:n__b:cons_f:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_a:null_encode_n__b:null_encode_b:null_encode_activate:null_f
null_encode_n__b :: a:n__b:cons_f:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_a:null_encode_n__b:null_encode_b:null_encode_activate:null_f
null_encode_b :: a:n__b:cons_f:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_a:null_encode_n__b:null_encode_b:null_encode_activate:null_f
null_encode_activate :: a:n__b:cons_f:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_a:null_encode_n__b:null_encode_b:null_encode_activate:null_f
null_f :: a:n__b:cons_f:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_a:null_encode_n__b:null_encode_b:null_encode_activate:null_f

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

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

(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, X) -> f(a, n__b) [1]
   b -> a [1]
   b -> n__b [1]
   activate(n__b) -> b [1]
   activate(X) -> X [1]
   encArg(a) -> a [0]
   encArg(n__b) -> n__b [0]
   encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2)) [0]
   encArg(cons_b) -> b [0]
   encArg(cons_activate(a)) -> activate(a) [0]
   encArg(cons_activate(n__b)) -> activate(n__b) [0]
   encArg(cons_activate(cons_f(x_113, x_26))) -> activate(f(encArg(x_113), encArg(x_26))) [0]
   encArg(cons_activate(cons_b)) -> activate(b) [0]
   encArg(cons_activate(cons_activate(x_114))) -> activate(activate(encArg(x_114))) [0]
   encArg(cons_activate(x_1)) -> activate(null_encArg) [0]
   encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2)) [0]
   encode_a -> a [0]
   encode_n__b -> n__b [0]
   encode_b -> b [0]
   encode_activate(a) -> activate(a) [0]
   encode_activate(n__b) -> activate(n__b) [0]
   encode_activate(cons_f(x_129, x_214)) -> activate(f(encArg(x_129), encArg(x_214))) [0]
   encode_activate(cons_b) -> activate(b) [0]
   encode_activate(cons_activate(x_130)) -> activate(activate(encArg(x_130))) [0]
   encode_activate(x_1) -> activate(null_encArg) [0]
   encArg(v0) -> null_encArg [0]
   encode_f(v0, v1) -> null_encode_f [0]
   encode_a -> null_encode_a [0]
   encode_n__b -> null_encode_n__b [0]
   encode_b -> null_encode_b [0]
   encode_activate(v0) -> null_encode_activate [0]
   f(v0, v1) -> null_f [0]

The TRS has the following type information:
f :: a:n__b:cons_f:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_a:null_encode_n__b:null_encode_b:null_encode_activate:null_f -> a:n__b:cons_f:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_a:null_encode_n__b:null_encode_b:null_encode_activate:null_f -> a:n__b:cons_f:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_a:null_encode_n__b:null_encode_b:null_encode_activate:null_f
a :: a:n__b:cons_f:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_a:null_encode_n__b:null_encode_b:null_encode_activate:null_f
n__b :: a:n__b:cons_f:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_a:null_encode_n__b:null_encode_b:null_encode_activate:null_f
b :: a:n__b:cons_f:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_a:null_encode_n__b:null_encode_b:null_encode_activate:null_f
activate :: a:n__b:cons_f:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_a:null_encode_n__b:null_encode_b:null_encode_activate:null_f -> a:n__b:cons_f:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_a:null_encode_n__b:null_encode_b:null_encode_activate:null_f
encArg :: a:n__b:cons_f:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_a:null_encode_n__b:null_encode_b:null_encode_activate:null_f -> a:n__b:cons_f:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_a:null_encode_n__b:null_encode_b:null_encode_activate:null_f
cons_f :: a:n__b:cons_f:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_a:null_encode_n__b:null_encode_b:null_encode_activate:null_f -> a:n__b:cons_f:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_a:null_encode_n__b:null_encode_b:null_encode_activate:null_f -> a:n__b:cons_f:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_a:null_encode_n__b:null_encode_b:null_encode_activate:null_f
cons_b :: a:n__b:cons_f:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_a:null_encode_n__b:null_encode_b:null_encode_activate:null_f
cons_activate :: a:n__b:cons_f:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_a:null_encode_n__b:null_encode_b:null_encode_activate:null_f -> a:n__b:cons_f:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_a:null_encode_n__b:null_encode_b:null_encode_activate:null_f
encode_f :: a:n__b:cons_f:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_a:null_encode_n__b:null_encode_b:null_encode_activate:null_f -> a:n__b:cons_f:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_a:null_encode_n__b:null_encode_b:null_encode_activate:null_f -> a:n__b:cons_f:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_a:null_encode_n__b:null_encode_b:null_encode_activate:null_f
encode_a :: a:n__b:cons_f:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_a:null_encode_n__b:null_encode_b:null_encode_activate:null_f
encode_n__b :: a:n__b:cons_f:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_a:null_encode_n__b:null_encode_b:null_encode_activate:null_f
encode_b :: a:n__b:cons_f:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_a:null_encode_n__b:null_encode_b:null_encode_activate:null_f
encode_activate :: a:n__b:cons_f:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_a:null_encode_n__b:null_encode_b:null_encode_activate:null_f -> a:n__b:cons_f:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_a:null_encode_n__b:null_encode_b:null_encode_activate:null_f
null_encArg :: a:n__b:cons_f:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_a:null_encode_n__b:null_encode_b:null_encode_activate:null_f
null_encode_f :: a:n__b:cons_f:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_a:null_encode_n__b:null_encode_b:null_encode_activate:null_f
null_encode_a :: a:n__b:cons_f:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_a:null_encode_n__b:null_encode_b:null_encode_activate:null_f
null_encode_n__b :: a:n__b:cons_f:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_a:null_encode_n__b:null_encode_b:null_encode_activate:null_f
null_encode_b :: a:n__b:cons_f:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_a:null_encode_n__b:null_encode_b:null_encode_activate:null_f
null_encode_activate :: a:n__b:cons_f:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_a:null_encode_n__b:null_encode_b:null_encode_activate:null_f
null_f :: a:n__b:cons_f:cons_b:cons_activate:null_encArg:null_encode_f:null_encode_a:null_encode_n__b:null_encode_b:null_encode_activate:null_f

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

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

   a => 0
   n__b => 2
   cons_b => 1
   null_encArg => 0
   null_encode_f => 0
   null_encode_a => 0
   null_encode_n__b => 0
   null_encode_b => 0
   null_encode_activate => 0
   null_f => 0

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

(14)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 1 }-> X :|: X >= 0, z = X
   activate(z) -{ 1 }-> b :|: z = 2
   b -{ 1 }-> 2 :|: 
   b -{ 1 }-> 0 :|: 
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> b :|: z = 1
   encArg(z) -{ 0 }-> activate(f(encArg(x_113), encArg(x_26))) :|: x_113 >= 0, z = 1 + (1 + x_113 + x_26), x_26 >= 0
   encArg(z) -{ 0 }-> activate(b) :|: z = 1 + 1
   encArg(z) -{ 0 }-> activate(activate(encArg(x_114))) :|: z = 1 + (1 + x_114), x_114 >= 0
   encArg(z) -{ 0 }-> activate(2) :|: z = 1 + 2
   encArg(z) -{ 0 }-> activate(0) :|: z = 1 + 0
   encArg(z) -{ 0 }-> activate(0) :|: z = 1 + x_1, x_1 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_a -{ 0 }-> 0 :|: 
   encode_activate(z) -{ 0 }-> activate(f(encArg(x_129), encArg(x_214))) :|: z = 1 + x_129 + x_214, x_214 >= 0, x_129 >= 0
   encode_activate(z) -{ 0 }-> activate(b) :|: z = 1
   encode_activate(z) -{ 0 }-> activate(activate(encArg(x_130))) :|: x_130 >= 0, z = 1 + x_130
   encode_activate(z) -{ 0 }-> activate(2) :|: z = 2
   encode_activate(z) -{ 0 }-> activate(0) :|: z = 0
   encode_activate(z) -{ 0 }-> activate(0) :|: x_1 >= 0, z = x_1
   encode_activate(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_b -{ 0 }-> b :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_f(z, z') -{ 0 }-> f(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2
   encode_f(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   encode_n__b -{ 0 }-> 2 :|: 
   encode_n__b -{ 0 }-> 0 :|: 
   f(z, z') -{ 1 }-> f(0, 2) :|: z' = X, X >= 0, z = X
   f(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1


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

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

   b -{ 1 }-> 2 :|: 
   b -{ 1 }-> 0 :|: 
   activate(z) -{ 1 }-> b :|: z = 2
   activate(z) -{ 1 }-> X :|: X >= 0, z = X

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

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

   activate(z) -{ 1 }-> X :|: X >= 0, z = X
   activate(z) -{ 2 }-> 2 :|: z = 2
   activate(z) -{ 2 }-> 0 :|: z = 2
   b -{ 1 }-> 2 :|: 
   b -{ 1 }-> 0 :|: 
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 2 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + x_1, x_1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 1, X >= 0, 2 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 1, X >= 0, 0 = X
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 1 }-> b :|: z = 1 + 2, 2 = 2
   encArg(z) -{ 2 }-> b :|: z = 1 + 1, 2 = 2
   encArg(z) -{ 0 }-> activate(f(encArg(x_113), encArg(x_26))) :|: x_113 >= 0, z = 1 + (1 + x_113 + x_26), x_26 >= 0
   encArg(z) -{ 0 }-> activate(activate(encArg(x_114))) :|: z = 1 + (1 + x_114), x_114 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 1 }-> 2 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1
   encode_a -{ 0 }-> 0 :|: 
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 2 = X
   encode_activate(z) -{ 1 }-> X :|: x_1 >= 0, z = x_1, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> X :|: z = 1, X >= 0, 2 = X
   encode_activate(z) -{ 2 }-> X :|: z = 1, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> b :|: z = 2, 2 = 2
   encode_activate(z) -{ 2 }-> b :|: z = 1, 2 = 2
   encode_activate(z) -{ 0 }-> activate(f(encArg(x_129), encArg(x_214))) :|: z = 1 + x_129 + x_214, x_214 >= 0, x_129 >= 0
   encode_activate(z) -{ 0 }-> activate(activate(encArg(x_130))) :|: x_130 >= 0, z = 1 + x_130
   encode_activate(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_b -{ 1 }-> 2 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_f(z, z') -{ 0 }-> f(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2
   encode_f(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   encode_n__b -{ 0 }-> 2 :|: 
   encode_n__b -{ 0 }-> 0 :|: 
   f(z, z') -{ 1 }-> f(0, 2) :|: z' = X, X >= 0, z = X
   f(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1


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

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 2 :|: z = 2
   activate(z) -{ 2 }-> 0 :|: z = 2
   b -{ 1 }-> 2 :|: 
   b -{ 1 }-> 0 :|: 
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 2 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 1, X >= 0, 2 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 1, X >= 0, 0 = X
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 1 }-> b :|: z = 1 + 2, 2 = 2
   encArg(z) -{ 2 }-> b :|: z = 1 + 1, 2 = 2
   encArg(z) -{ 0 }-> activate(f(encArg(x_113), encArg(x_26))) :|: x_113 >= 0, z = 1 + (1 + x_113 + x_26), x_26 >= 0
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 1 }-> 2 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 1 }-> 0 :|: z = 1
   encode_a -{ 0 }-> 0 :|: 
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 2 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> X :|: z = 1, X >= 0, 2 = X
   encode_activate(z) -{ 2 }-> X :|: z = 1, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> b :|: z = 2, 2 = 2
   encode_activate(z) -{ 2 }-> b :|: z = 1, 2 = 2
   encode_activate(z) -{ 0 }-> activate(f(encArg(x_129), encArg(x_214))) :|: z = 1 + x_129 + x_214, x_214 >= 0, x_129 >= 0
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_b -{ 1 }-> 2 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_f(z, z') -{ 0 }-> f(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_n__b -{ 0 }-> 2 :|: 
   encode_n__b -{ 0 }-> 0 :|: 
   f(z, z') -{ 1 }-> f(0, 2) :|: z' >= 0, z = z'
   f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0


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

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

   { encode_a }
   { f }
   { b }
   { activate }
   { encode_b }
   { encode_n__b }
   { encArg }
   { encode_activate }
   { encode_f }

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 2 :|: z = 2
   activate(z) -{ 2 }-> 0 :|: z = 2
   b -{ 1 }-> 2 :|: 
   b -{ 1 }-> 0 :|: 
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 2 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 1, X >= 0, 2 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 1, X >= 0, 0 = X
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 1 }-> b :|: z = 1 + 2, 2 = 2
   encArg(z) -{ 2 }-> b :|: z = 1 + 1, 2 = 2
   encArg(z) -{ 0 }-> activate(f(encArg(x_113), encArg(x_26))) :|: x_113 >= 0, z = 1 + (1 + x_113 + x_26), x_26 >= 0
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 1 }-> 2 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 1 }-> 0 :|: z = 1
   encode_a -{ 0 }-> 0 :|: 
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 2 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> X :|: z = 1, X >= 0, 2 = X
   encode_activate(z) -{ 2 }-> X :|: z = 1, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> b :|: z = 2, 2 = 2
   encode_activate(z) -{ 2 }-> b :|: z = 1, 2 = 2
   encode_activate(z) -{ 0 }-> activate(f(encArg(x_129), encArg(x_214))) :|: z = 1 + x_129 + x_214, x_214 >= 0, x_129 >= 0
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_b -{ 1 }-> 2 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_f(z, z') -{ 0 }-> f(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_n__b -{ 0 }-> 2 :|: 
   encode_n__b -{ 0 }-> 0 :|: 
   f(z, z') -{ 1 }-> f(0, 2) :|: z' >= 0, z = z'
   f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0

Function symbols to be analyzed: {encode_a}, {f}, {b}, {activate}, {encode_b}, {encode_n__b}, {encArg}, {encode_activate}, {encode_f}

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

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 2 :|: z = 2
   activate(z) -{ 2 }-> 0 :|: z = 2
   b -{ 1 }-> 2 :|: 
   b -{ 1 }-> 0 :|: 
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 2 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 1, X >= 0, 2 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 1, X >= 0, 0 = X
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 1 }-> b :|: z = 1 + 2, 2 = 2
   encArg(z) -{ 2 }-> b :|: z = 1 + 1, 2 = 2
   encArg(z) -{ 0 }-> activate(f(encArg(x_113), encArg(x_26))) :|: x_113 >= 0, z = 1 + (1 + x_113 + x_26), x_26 >= 0
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 1 }-> 2 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 1 }-> 0 :|: z = 1
   encode_a -{ 0 }-> 0 :|: 
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 2 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> X :|: z = 1, X >= 0, 2 = X
   encode_activate(z) -{ 2 }-> X :|: z = 1, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> b :|: z = 2, 2 = 2
   encode_activate(z) -{ 2 }-> b :|: z = 1, 2 = 2
   encode_activate(z) -{ 0 }-> activate(f(encArg(x_129), encArg(x_214))) :|: z = 1 + x_129 + x_214, x_214 >= 0, x_129 >= 0
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_b -{ 1 }-> 2 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_f(z, z') -{ 0 }-> f(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_n__b -{ 0 }-> 2 :|: 
   encode_n__b -{ 0 }-> 0 :|: 
   f(z, z') -{ 1 }-> f(0, 2) :|: z' >= 0, z = z'
   f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0

Function symbols to be analyzed: {encode_a}, {f}, {b}, {activate}, {encode_b}, {encode_n__b}, {encArg}, {encode_activate}, {encode_f}

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

(23) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 2 :|: z = 2
   activate(z) -{ 2 }-> 0 :|: z = 2
   b -{ 1 }-> 2 :|: 
   b -{ 1 }-> 0 :|: 
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 2 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 1, X >= 0, 2 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 1, X >= 0, 0 = X
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 1 }-> b :|: z = 1 + 2, 2 = 2
   encArg(z) -{ 2 }-> b :|: z = 1 + 1, 2 = 2
   encArg(z) -{ 0 }-> activate(f(encArg(x_113), encArg(x_26))) :|: x_113 >= 0, z = 1 + (1 + x_113 + x_26), x_26 >= 0
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 1 }-> 2 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 1 }-> 0 :|: z = 1
   encode_a -{ 0 }-> 0 :|: 
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 2 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> X :|: z = 1, X >= 0, 2 = X
   encode_activate(z) -{ 2 }-> X :|: z = 1, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> b :|: z = 2, 2 = 2
   encode_activate(z) -{ 2 }-> b :|: z = 1, 2 = 2
   encode_activate(z) -{ 0 }-> activate(f(encArg(x_129), encArg(x_214))) :|: z = 1 + x_129 + x_214, x_214 >= 0, x_129 >= 0
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_b -{ 1 }-> 2 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_f(z, z') -{ 0 }-> f(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_n__b -{ 0 }-> 2 :|: 
   encode_n__b -{ 0 }-> 0 :|: 
   f(z, z') -{ 1 }-> f(0, 2) :|: z' >= 0, z = z'
   f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0

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

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

(25) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: encode_a
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 }-> 2 :|: z = 2
   activate(z) -{ 2 }-> 0 :|: z = 2
   b -{ 1 }-> 2 :|: 
   b -{ 1 }-> 0 :|: 
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 2 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 1, X >= 0, 2 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 1, X >= 0, 0 = X
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 1 }-> b :|: z = 1 + 2, 2 = 2
   encArg(z) -{ 2 }-> b :|: z = 1 + 1, 2 = 2
   encArg(z) -{ 0 }-> activate(f(encArg(x_113), encArg(x_26))) :|: x_113 >= 0, z = 1 + (1 + x_113 + x_26), x_26 >= 0
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 1 }-> 2 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 1 }-> 0 :|: z = 1
   encode_a -{ 0 }-> 0 :|: 
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 2 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> X :|: z = 1, X >= 0, 2 = X
   encode_activate(z) -{ 2 }-> X :|: z = 1, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> b :|: z = 2, 2 = 2
   encode_activate(z) -{ 2 }-> b :|: z = 1, 2 = 2
   encode_activate(z) -{ 0 }-> activate(f(encArg(x_129), encArg(x_214))) :|: z = 1 + x_129 + x_214, x_214 >= 0, x_129 >= 0
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_b -{ 1 }-> 2 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_f(z, z') -{ 0 }-> f(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_n__b -{ 0 }-> 2 :|: 
   encode_n__b -{ 0 }-> 0 :|: 
   f(z, z') -{ 1 }-> f(0, 2) :|: z' >= 0, z = z'
   f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0

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

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

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 2 :|: z = 2
   activate(z) -{ 2 }-> 0 :|: z = 2
   b -{ 1 }-> 2 :|: 
   b -{ 1 }-> 0 :|: 
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 2 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 1, X >= 0, 2 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 1, X >= 0, 0 = X
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 1 }-> b :|: z = 1 + 2, 2 = 2
   encArg(z) -{ 2 }-> b :|: z = 1 + 1, 2 = 2
   encArg(z) -{ 0 }-> activate(f(encArg(x_113), encArg(x_26))) :|: x_113 >= 0, z = 1 + (1 + x_113 + x_26), x_26 >= 0
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 1 }-> 2 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 1 }-> 0 :|: z = 1
   encode_a -{ 0 }-> 0 :|: 
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 2 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> X :|: z = 1, X >= 0, 2 = X
   encode_activate(z) -{ 2 }-> X :|: z = 1, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> b :|: z = 2, 2 = 2
   encode_activate(z) -{ 2 }-> b :|: z = 1, 2 = 2
   encode_activate(z) -{ 0 }-> activate(f(encArg(x_129), encArg(x_214))) :|: z = 1 + x_129 + x_214, x_214 >= 0, x_129 >= 0
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_b -{ 1 }-> 2 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_f(z, z') -{ 0 }-> f(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_n__b -{ 0 }-> 2 :|: 
   encode_n__b -{ 0 }-> 0 :|: 
   f(z, z') -{ 1 }-> f(0, 2) :|: z' >= 0, z = z'
   f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0

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

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

(29) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 2 :|: z = 2
   activate(z) -{ 2 }-> 0 :|: z = 2
   b -{ 1 }-> 2 :|: 
   b -{ 1 }-> 0 :|: 
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 2 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 1, X >= 0, 2 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 1, X >= 0, 0 = X
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 1 }-> b :|: z = 1 + 2, 2 = 2
   encArg(z) -{ 2 }-> b :|: z = 1 + 1, 2 = 2
   encArg(z) -{ 0 }-> activate(f(encArg(x_113), encArg(x_26))) :|: x_113 >= 0, z = 1 + (1 + x_113 + x_26), x_26 >= 0
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 1 }-> 2 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 1 }-> 0 :|: z = 1
   encode_a -{ 0 }-> 0 :|: 
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 2 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> X :|: z = 1, X >= 0, 2 = X
   encode_activate(z) -{ 2 }-> X :|: z = 1, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> b :|: z = 2, 2 = 2
   encode_activate(z) -{ 2 }-> b :|: z = 1, 2 = 2
   encode_activate(z) -{ 0 }-> activate(f(encArg(x_129), encArg(x_214))) :|: z = 1 + x_129 + x_214, x_214 >= 0, x_129 >= 0
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_b -{ 1 }-> 2 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_f(z, z') -{ 0 }-> f(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_n__b -{ 0 }-> 2 :|: 
   encode_n__b -{ 0 }-> 0 :|: 
   f(z, z') -{ 1 }-> f(0, 2) :|: z' >= 0, z = z'
   f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0

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

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

(31) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: f
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 }-> 2 :|: z = 2
   activate(z) -{ 2 }-> 0 :|: z = 2
   b -{ 1 }-> 2 :|: 
   b -{ 1 }-> 0 :|: 
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 2 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 1, X >= 0, 2 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 1, X >= 0, 0 = X
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 1 }-> b :|: z = 1 + 2, 2 = 2
   encArg(z) -{ 2 }-> b :|: z = 1 + 1, 2 = 2
   encArg(z) -{ 0 }-> activate(f(encArg(x_113), encArg(x_26))) :|: x_113 >= 0, z = 1 + (1 + x_113 + x_26), x_26 >= 0
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 1 }-> 2 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 1 }-> 0 :|: z = 1
   encode_a -{ 0 }-> 0 :|: 
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 2 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> X :|: z = 1, X >= 0, 2 = X
   encode_activate(z) -{ 2 }-> X :|: z = 1, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> b :|: z = 2, 2 = 2
   encode_activate(z) -{ 2 }-> b :|: z = 1, 2 = 2
   encode_activate(z) -{ 0 }-> activate(f(encArg(x_129), encArg(x_214))) :|: z = 1 + x_129 + x_214, x_214 >= 0, x_129 >= 0
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_b -{ 1 }-> 2 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_f(z, z') -{ 0 }-> f(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_n__b -{ 0 }-> 2 :|: 
   encode_n__b -{ 0 }-> 0 :|: 
   f(z, z') -{ 1 }-> f(0, 2) :|: z' >= 0, z = z'
   f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0

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

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

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 2 :|: z = 2
   activate(z) -{ 2 }-> 0 :|: z = 2
   b -{ 1 }-> 2 :|: 
   b -{ 1 }-> 0 :|: 
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 2 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 1, X >= 0, 2 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 1, X >= 0, 0 = X
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 1 }-> b :|: z = 1 + 2, 2 = 2
   encArg(z) -{ 2 }-> b :|: z = 1 + 1, 2 = 2
   encArg(z) -{ 0 }-> activate(f(encArg(x_113), encArg(x_26))) :|: x_113 >= 0, z = 1 + (1 + x_113 + x_26), x_26 >= 0
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 1 }-> 2 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 1 }-> 0 :|: z = 1
   encode_a -{ 0 }-> 0 :|: 
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 2 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> X :|: z = 1, X >= 0, 2 = X
   encode_activate(z) -{ 2 }-> X :|: z = 1, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> b :|: z = 2, 2 = 2
   encode_activate(z) -{ 2 }-> b :|: z = 1, 2 = 2
   encode_activate(z) -{ 0 }-> activate(f(encArg(x_129), encArg(x_214))) :|: z = 1 + x_129 + x_214, x_214 >= 0, x_129 >= 0
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_b -{ 1 }-> 2 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_f(z, z') -{ 0 }-> f(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_n__b -{ 0 }-> 2 :|: 
   encode_n__b -{ 0 }-> 0 :|: 
   f(z, z') -{ 2 }-> s :|: s >= 0, s <= 0, z' >= 0, z = z'
   f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0

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

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

(35) 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: 2

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 2 :|: z = 2
   activate(z) -{ 2 }-> 0 :|: z = 2
   b -{ 1 }-> 2 :|: 
   b -{ 1 }-> 0 :|: 
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 2 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 1, X >= 0, 2 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 1, X >= 0, 0 = X
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 1 }-> b :|: z = 1 + 2, 2 = 2
   encArg(z) -{ 2 }-> b :|: z = 1 + 1, 2 = 2
   encArg(z) -{ 0 }-> activate(f(encArg(x_113), encArg(x_26))) :|: x_113 >= 0, z = 1 + (1 + x_113 + x_26), x_26 >= 0
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 1 }-> 2 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 1 }-> 0 :|: z = 1
   encode_a -{ 0 }-> 0 :|: 
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 2 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> X :|: z = 1, X >= 0, 2 = X
   encode_activate(z) -{ 2 }-> X :|: z = 1, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> b :|: z = 2, 2 = 2
   encode_activate(z) -{ 2 }-> b :|: z = 1, 2 = 2
   encode_activate(z) -{ 0 }-> activate(f(encArg(x_129), encArg(x_214))) :|: z = 1 + x_129 + x_214, x_214 >= 0, x_129 >= 0
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_b -{ 1 }-> 2 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_f(z, z') -{ 0 }-> f(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_n__b -{ 0 }-> 2 :|: 
   encode_n__b -{ 0 }-> 0 :|: 
   f(z, z') -{ 2 }-> s :|: s >= 0, s <= 0, z' >= 0, z = z'
   f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0

Function symbols to be analyzed: {b}, {activate}, {encode_b}, {encode_n__b}, {encArg}, {encode_activate}, {encode_f}
Previous analysis results are:
  encode_a: runtime: O(1) [0], size: O(1) [0]
  f: runtime: O(1) [1], size: O(1) [0]
  b: runtime: ?, size: O(1) [2]

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

(37) 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

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 2 :|: z = 2
   activate(z) -{ 2 }-> 0 :|: z = 2
   b -{ 1 }-> 2 :|: 
   b -{ 1 }-> 0 :|: 
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 2 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 1, X >= 0, 2 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 1, X >= 0, 0 = X
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 1 }-> b :|: z = 1 + 2, 2 = 2
   encArg(z) -{ 2 }-> b :|: z = 1 + 1, 2 = 2
   encArg(z) -{ 0 }-> activate(f(encArg(x_113), encArg(x_26))) :|: x_113 >= 0, z = 1 + (1 + x_113 + x_26), x_26 >= 0
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 1 }-> 2 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 1 }-> 0 :|: z = 1
   encode_a -{ 0 }-> 0 :|: 
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 2 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> X :|: z = 1, X >= 0, 2 = X
   encode_activate(z) -{ 2 }-> X :|: z = 1, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> b :|: z = 2, 2 = 2
   encode_activate(z) -{ 2 }-> b :|: z = 1, 2 = 2
   encode_activate(z) -{ 0 }-> activate(f(encArg(x_129), encArg(x_214))) :|: z = 1 + x_129 + x_214, x_214 >= 0, x_129 >= 0
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_b -{ 1 }-> 2 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_f(z, z') -{ 0 }-> f(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_n__b -{ 0 }-> 2 :|: 
   encode_n__b -{ 0 }-> 0 :|: 
   f(z, z') -{ 2 }-> s :|: s >= 0, s <= 0, z' >= 0, z = z'
   f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0

Function symbols to be analyzed: {activate}, {encode_b}, {encode_n__b}, {encArg}, {encode_activate}, {encode_f}
Previous analysis results are:
  encode_a: runtime: O(1) [0], size: O(1) [0]
  f: runtime: O(1) [1], size: O(1) [0]
  b: runtime: O(1) [1], size: O(1) [2]

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

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 2 :|: z = 2
   activate(z) -{ 2 }-> 0 :|: z = 2
   b -{ 1 }-> 2 :|: 
   b -{ 1 }-> 0 :|: 
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 2 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 1, X >= 0, 2 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 1, X >= 0, 0 = X
   encArg(z) -{ 2 }-> s' :|: s' >= 0, s' <= 2, z = 1 + 2, 2 = 2
   encArg(z) -{ 3 }-> s1 :|: s1 >= 0, s1 <= 2, z = 1 + 1, 2 = 2
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> activate(f(encArg(x_113), encArg(x_26))) :|: x_113 >= 0, z = 1 + (1 + x_113 + x_26), x_26 >= 0
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 1 }-> 2 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 1 }-> 0 :|: z = 1
   encode_a -{ 0 }-> 0 :|: 
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 2 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> X :|: z = 1, X >= 0, 2 = X
   encode_activate(z) -{ 2 }-> X :|: z = 1, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> s'' :|: s'' >= 0, s'' <= 2, z = 2, 2 = 2
   encode_activate(z) -{ 3 }-> s2 :|: s2 >= 0, s2 <= 2, z = 1, 2 = 2
   encode_activate(z) -{ 0 }-> activate(f(encArg(x_129), encArg(x_214))) :|: z = 1 + x_129 + x_214, x_214 >= 0, x_129 >= 0
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_b -{ 1 }-> 2 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_f(z, z') -{ 0 }-> f(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_n__b -{ 0 }-> 2 :|: 
   encode_n__b -{ 0 }-> 0 :|: 
   f(z, z') -{ 2 }-> s :|: s >= 0, s <= 0, z' >= 0, z = z'
   f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0

Function symbols to be analyzed: {activate}, {encode_b}, {encode_n__b}, {encArg}, {encode_activate}, {encode_f}
Previous analysis results are:
  encode_a: runtime: O(1) [0], size: O(1) [0]
  f: runtime: O(1) [1], size: O(1) [0]
  b: runtime: O(1) [1], size: O(1) [2]

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

(41) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 2 :|: z = 2
   activate(z) -{ 2 }-> 0 :|: z = 2
   b -{ 1 }-> 2 :|: 
   b -{ 1 }-> 0 :|: 
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 2 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 1, X >= 0, 2 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 1, X >= 0, 0 = X
   encArg(z) -{ 2 }-> s' :|: s' >= 0, s' <= 2, z = 1 + 2, 2 = 2
   encArg(z) -{ 3 }-> s1 :|: s1 >= 0, s1 <= 2, z = 1 + 1, 2 = 2
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> activate(f(encArg(x_113), encArg(x_26))) :|: x_113 >= 0, z = 1 + (1 + x_113 + x_26), x_26 >= 0
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 1 }-> 2 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 1 }-> 0 :|: z = 1
   encode_a -{ 0 }-> 0 :|: 
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 2 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> X :|: z = 1, X >= 0, 2 = X
   encode_activate(z) -{ 2 }-> X :|: z = 1, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> s'' :|: s'' >= 0, s'' <= 2, z = 2, 2 = 2
   encode_activate(z) -{ 3 }-> s2 :|: s2 >= 0, s2 <= 2, z = 1, 2 = 2
   encode_activate(z) -{ 0 }-> activate(f(encArg(x_129), encArg(x_214))) :|: z = 1 + x_129 + x_214, x_214 >= 0, x_129 >= 0
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_b -{ 1 }-> 2 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_f(z, z') -{ 0 }-> f(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_n__b -{ 0 }-> 2 :|: 
   encode_n__b -{ 0 }-> 0 :|: 
   f(z, z') -{ 2 }-> s :|: s >= 0, s <= 0, z' >= 0, z = z'
   f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0

Function symbols to be analyzed: {activate}, {encode_b}, {encode_n__b}, {encArg}, {encode_activate}, {encode_f}
Previous analysis results are:
  encode_a: runtime: O(1) [0], size: O(1) [0]
  f: runtime: O(1) [1], size: O(1) [0]
  b: runtime: O(1) [1], size: O(1) [2]
  activate: runtime: ?, size: O(n^1) [z]

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

(43) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: activate
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 2

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 2 :|: z = 2
   activate(z) -{ 2 }-> 0 :|: z = 2
   b -{ 1 }-> 2 :|: 
   b -{ 1 }-> 0 :|: 
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 2 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 1, X >= 0, 2 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 1, X >= 0, 0 = X
   encArg(z) -{ 2 }-> s' :|: s' >= 0, s' <= 2, z = 1 + 2, 2 = 2
   encArg(z) -{ 3 }-> s1 :|: s1 >= 0, s1 <= 2, z = 1 + 1, 2 = 2
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> activate(f(encArg(x_113), encArg(x_26))) :|: x_113 >= 0, z = 1 + (1 + x_113 + x_26), x_26 >= 0
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 1 }-> 2 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 1 }-> 0 :|: z = 1
   encode_a -{ 0 }-> 0 :|: 
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 2 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> X :|: z = 1, X >= 0, 2 = X
   encode_activate(z) -{ 2 }-> X :|: z = 1, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> s'' :|: s'' >= 0, s'' <= 2, z = 2, 2 = 2
   encode_activate(z) -{ 3 }-> s2 :|: s2 >= 0, s2 <= 2, z = 1, 2 = 2
   encode_activate(z) -{ 0 }-> activate(f(encArg(x_129), encArg(x_214))) :|: z = 1 + x_129 + x_214, x_214 >= 0, x_129 >= 0
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_b -{ 1 }-> 2 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_f(z, z') -{ 0 }-> f(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_n__b -{ 0 }-> 2 :|: 
   encode_n__b -{ 0 }-> 0 :|: 
   f(z, z') -{ 2 }-> s :|: s >= 0, s <= 0, z' >= 0, z = z'
   f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0

Function symbols to be analyzed: {encode_b}, {encode_n__b}, {encArg}, {encode_activate}, {encode_f}
Previous analysis results are:
  encode_a: runtime: O(1) [0], size: O(1) [0]
  f: runtime: O(1) [1], size: O(1) [0]
  b: runtime: O(1) [1], size: O(1) [2]
  activate: runtime: O(1) [2], size: O(n^1) [z]

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

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 2 :|: z = 2
   activate(z) -{ 2 }-> 0 :|: z = 2
   b -{ 1 }-> 2 :|: 
   b -{ 1 }-> 0 :|: 
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 2 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 1, X >= 0, 2 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 1, X >= 0, 0 = X
   encArg(z) -{ 2 }-> s' :|: s' >= 0, s' <= 2, z = 1 + 2, 2 = 2
   encArg(z) -{ 3 }-> s1 :|: s1 >= 0, s1 <= 2, z = 1 + 1, 2 = 2
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> activate(f(encArg(x_113), encArg(x_26))) :|: x_113 >= 0, z = 1 + (1 + x_113 + x_26), x_26 >= 0
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 1 }-> 2 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 1 }-> 0 :|: z = 1
   encode_a -{ 0 }-> 0 :|: 
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 2 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> X :|: z = 1, X >= 0, 2 = X
   encode_activate(z) -{ 2 }-> X :|: z = 1, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> s'' :|: s'' >= 0, s'' <= 2, z = 2, 2 = 2
   encode_activate(z) -{ 3 }-> s2 :|: s2 >= 0, s2 <= 2, z = 1, 2 = 2
   encode_activate(z) -{ 0 }-> activate(f(encArg(x_129), encArg(x_214))) :|: z = 1 + x_129 + x_214, x_214 >= 0, x_129 >= 0
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_b -{ 1 }-> 2 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_f(z, z') -{ 0 }-> f(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_n__b -{ 0 }-> 2 :|: 
   encode_n__b -{ 0 }-> 0 :|: 
   f(z, z') -{ 2 }-> s :|: s >= 0, s <= 0, z' >= 0, z = z'
   f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0

Function symbols to be analyzed: {encode_b}, {encode_n__b}, {encArg}, {encode_activate}, {encode_f}
Previous analysis results are:
  encode_a: runtime: O(1) [0], size: O(1) [0]
  f: runtime: O(1) [1], size: O(1) [0]
  b: runtime: O(1) [1], size: O(1) [2]
  activate: runtime: O(1) [2], size: O(n^1) [z]

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

(47) 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: 2

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 2 :|: z = 2
   activate(z) -{ 2 }-> 0 :|: z = 2
   b -{ 1 }-> 2 :|: 
   b -{ 1 }-> 0 :|: 
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 2 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 1, X >= 0, 2 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 1, X >= 0, 0 = X
   encArg(z) -{ 2 }-> s' :|: s' >= 0, s' <= 2, z = 1 + 2, 2 = 2
   encArg(z) -{ 3 }-> s1 :|: s1 >= 0, s1 <= 2, z = 1 + 1, 2 = 2
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> activate(f(encArg(x_113), encArg(x_26))) :|: x_113 >= 0, z = 1 + (1 + x_113 + x_26), x_26 >= 0
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 1 }-> 2 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 1 }-> 0 :|: z = 1
   encode_a -{ 0 }-> 0 :|: 
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 2 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> X :|: z = 1, X >= 0, 2 = X
   encode_activate(z) -{ 2 }-> X :|: z = 1, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> s'' :|: s'' >= 0, s'' <= 2, z = 2, 2 = 2
   encode_activate(z) -{ 3 }-> s2 :|: s2 >= 0, s2 <= 2, z = 1, 2 = 2
   encode_activate(z) -{ 0 }-> activate(f(encArg(x_129), encArg(x_214))) :|: z = 1 + x_129 + x_214, x_214 >= 0, x_129 >= 0
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_b -{ 1 }-> 2 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_f(z, z') -{ 0 }-> f(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_n__b -{ 0 }-> 2 :|: 
   encode_n__b -{ 0 }-> 0 :|: 
   f(z, z') -{ 2 }-> s :|: s >= 0, s <= 0, z' >= 0, z = z'
   f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0

Function symbols to be analyzed: {encode_b}, {encode_n__b}, {encArg}, {encode_activate}, {encode_f}
Previous analysis results are:
  encode_a: runtime: O(1) [0], size: O(1) [0]
  f: runtime: O(1) [1], size: O(1) [0]
  b: runtime: O(1) [1], size: O(1) [2]
  activate: runtime: O(1) [2], size: O(n^1) [z]
  encode_b: runtime: ?, size: O(1) [2]

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

(49) 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

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 2 :|: z = 2
   activate(z) -{ 2 }-> 0 :|: z = 2
   b -{ 1 }-> 2 :|: 
   b -{ 1 }-> 0 :|: 
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 2 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 1, X >= 0, 2 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 1, X >= 0, 0 = X
   encArg(z) -{ 2 }-> s' :|: s' >= 0, s' <= 2, z = 1 + 2, 2 = 2
   encArg(z) -{ 3 }-> s1 :|: s1 >= 0, s1 <= 2, z = 1 + 1, 2 = 2
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> activate(f(encArg(x_113), encArg(x_26))) :|: x_113 >= 0, z = 1 + (1 + x_113 + x_26), x_26 >= 0
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 1 }-> 2 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 1 }-> 0 :|: z = 1
   encode_a -{ 0 }-> 0 :|: 
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 2 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> X :|: z = 1, X >= 0, 2 = X
   encode_activate(z) -{ 2 }-> X :|: z = 1, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> s'' :|: s'' >= 0, s'' <= 2, z = 2, 2 = 2
   encode_activate(z) -{ 3 }-> s2 :|: s2 >= 0, s2 <= 2, z = 1, 2 = 2
   encode_activate(z) -{ 0 }-> activate(f(encArg(x_129), encArg(x_214))) :|: z = 1 + x_129 + x_214, x_214 >= 0, x_129 >= 0
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_b -{ 1 }-> 2 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_f(z, z') -{ 0 }-> f(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_n__b -{ 0 }-> 2 :|: 
   encode_n__b -{ 0 }-> 0 :|: 
   f(z, z') -{ 2 }-> s :|: s >= 0, s <= 0, z' >= 0, z = z'
   f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0

Function symbols to be analyzed: {encode_n__b}, {encArg}, {encode_activate}, {encode_f}
Previous analysis results are:
  encode_a: runtime: O(1) [0], size: O(1) [0]
  f: runtime: O(1) [1], size: O(1) [0]
  b: runtime: O(1) [1], size: O(1) [2]
  activate: runtime: O(1) [2], size: O(n^1) [z]
  encode_b: runtime: O(1) [1], size: O(1) [2]

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

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 2 :|: z = 2
   activate(z) -{ 2 }-> 0 :|: z = 2
   b -{ 1 }-> 2 :|: 
   b -{ 1 }-> 0 :|: 
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 2 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 1, X >= 0, 2 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 1, X >= 0, 0 = X
   encArg(z) -{ 2 }-> s' :|: s' >= 0, s' <= 2, z = 1 + 2, 2 = 2
   encArg(z) -{ 3 }-> s1 :|: s1 >= 0, s1 <= 2, z = 1 + 1, 2 = 2
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> activate(f(encArg(x_113), encArg(x_26))) :|: x_113 >= 0, z = 1 + (1 + x_113 + x_26), x_26 >= 0
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 1 }-> 2 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 1 }-> 0 :|: z = 1
   encode_a -{ 0 }-> 0 :|: 
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 2 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> X :|: z = 1, X >= 0, 2 = X
   encode_activate(z) -{ 2 }-> X :|: z = 1, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> s'' :|: s'' >= 0, s'' <= 2, z = 2, 2 = 2
   encode_activate(z) -{ 3 }-> s2 :|: s2 >= 0, s2 <= 2, z = 1, 2 = 2
   encode_activate(z) -{ 0 }-> activate(f(encArg(x_129), encArg(x_214))) :|: z = 1 + x_129 + x_214, x_214 >= 0, x_129 >= 0
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_b -{ 1 }-> 2 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_f(z, z') -{ 0 }-> f(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_n__b -{ 0 }-> 2 :|: 
   encode_n__b -{ 0 }-> 0 :|: 
   f(z, z') -{ 2 }-> s :|: s >= 0, s <= 0, z' >= 0, z = z'
   f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0

Function symbols to be analyzed: {encode_n__b}, {encArg}, {encode_activate}, {encode_f}
Previous analysis results are:
  encode_a: runtime: O(1) [0], size: O(1) [0]
  f: runtime: O(1) [1], size: O(1) [0]
  b: runtime: O(1) [1], size: O(1) [2]
  activate: runtime: O(1) [2], size: O(n^1) [z]
  encode_b: runtime: O(1) [1], size: O(1) [2]

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

(53) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: encode_n__b
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 2

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 2 :|: z = 2
   activate(z) -{ 2 }-> 0 :|: z = 2
   b -{ 1 }-> 2 :|: 
   b -{ 1 }-> 0 :|: 
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 2 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 1, X >= 0, 2 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 1, X >= 0, 0 = X
   encArg(z) -{ 2 }-> s' :|: s' >= 0, s' <= 2, z = 1 + 2, 2 = 2
   encArg(z) -{ 3 }-> s1 :|: s1 >= 0, s1 <= 2, z = 1 + 1, 2 = 2
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> activate(f(encArg(x_113), encArg(x_26))) :|: x_113 >= 0, z = 1 + (1 + x_113 + x_26), x_26 >= 0
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 1 }-> 2 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 1 }-> 0 :|: z = 1
   encode_a -{ 0 }-> 0 :|: 
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 2 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> X :|: z = 1, X >= 0, 2 = X
   encode_activate(z) -{ 2 }-> X :|: z = 1, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> s'' :|: s'' >= 0, s'' <= 2, z = 2, 2 = 2
   encode_activate(z) -{ 3 }-> s2 :|: s2 >= 0, s2 <= 2, z = 1, 2 = 2
   encode_activate(z) -{ 0 }-> activate(f(encArg(x_129), encArg(x_214))) :|: z = 1 + x_129 + x_214, x_214 >= 0, x_129 >= 0
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_b -{ 1 }-> 2 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_f(z, z') -{ 0 }-> f(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_n__b -{ 0 }-> 2 :|: 
   encode_n__b -{ 0 }-> 0 :|: 
   f(z, z') -{ 2 }-> s :|: s >= 0, s <= 0, z' >= 0, z = z'
   f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0

Function symbols to be analyzed: {encode_n__b}, {encArg}, {encode_activate}, {encode_f}
Previous analysis results are:
  encode_a: runtime: O(1) [0], size: O(1) [0]
  f: runtime: O(1) [1], size: O(1) [0]
  b: runtime: O(1) [1], size: O(1) [2]
  activate: runtime: O(1) [2], size: O(n^1) [z]
  encode_b: runtime: O(1) [1], size: O(1) [2]
  encode_n__b: runtime: ?, size: O(1) [2]

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

(55) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 2 :|: z = 2
   activate(z) -{ 2 }-> 0 :|: z = 2
   b -{ 1 }-> 2 :|: 
   b -{ 1 }-> 0 :|: 
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 2 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 1, X >= 0, 2 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 1, X >= 0, 0 = X
   encArg(z) -{ 2 }-> s' :|: s' >= 0, s' <= 2, z = 1 + 2, 2 = 2
   encArg(z) -{ 3 }-> s1 :|: s1 >= 0, s1 <= 2, z = 1 + 1, 2 = 2
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> activate(f(encArg(x_113), encArg(x_26))) :|: x_113 >= 0, z = 1 + (1 + x_113 + x_26), x_26 >= 0
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 1 }-> 2 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 1 }-> 0 :|: z = 1
   encode_a -{ 0 }-> 0 :|: 
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 2 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> X :|: z = 1, X >= 0, 2 = X
   encode_activate(z) -{ 2 }-> X :|: z = 1, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> s'' :|: s'' >= 0, s'' <= 2, z = 2, 2 = 2
   encode_activate(z) -{ 3 }-> s2 :|: s2 >= 0, s2 <= 2, z = 1, 2 = 2
   encode_activate(z) -{ 0 }-> activate(f(encArg(x_129), encArg(x_214))) :|: z = 1 + x_129 + x_214, x_214 >= 0, x_129 >= 0
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_b -{ 1 }-> 2 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_f(z, z') -{ 0 }-> f(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_n__b -{ 0 }-> 2 :|: 
   encode_n__b -{ 0 }-> 0 :|: 
   f(z, z') -{ 2 }-> s :|: s >= 0, s <= 0, z' >= 0, z = z'
   f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0

Function symbols to be analyzed: {encArg}, {encode_activate}, {encode_f}
Previous analysis results are:
  encode_a: runtime: O(1) [0], size: O(1) [0]
  f: runtime: O(1) [1], size: O(1) [0]
  b: runtime: O(1) [1], size: O(1) [2]
  activate: runtime: O(1) [2], size: O(n^1) [z]
  encode_b: runtime: O(1) [1], size: O(1) [2]
  encode_n__b: runtime: O(1) [0], size: O(1) [2]

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

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 2 :|: z = 2
   activate(z) -{ 2 }-> 0 :|: z = 2
   b -{ 1 }-> 2 :|: 
   b -{ 1 }-> 0 :|: 
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 2 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 1, X >= 0, 2 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 1, X >= 0, 0 = X
   encArg(z) -{ 2 }-> s' :|: s' >= 0, s' <= 2, z = 1 + 2, 2 = 2
   encArg(z) -{ 3 }-> s1 :|: s1 >= 0, s1 <= 2, z = 1 + 1, 2 = 2
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> activate(f(encArg(x_113), encArg(x_26))) :|: x_113 >= 0, z = 1 + (1 + x_113 + x_26), x_26 >= 0
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 1 }-> 2 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 1 }-> 0 :|: z = 1
   encode_a -{ 0 }-> 0 :|: 
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 2 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> X :|: z = 1, X >= 0, 2 = X
   encode_activate(z) -{ 2 }-> X :|: z = 1, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> s'' :|: s'' >= 0, s'' <= 2, z = 2, 2 = 2
   encode_activate(z) -{ 3 }-> s2 :|: s2 >= 0, s2 <= 2, z = 1, 2 = 2
   encode_activate(z) -{ 0 }-> activate(f(encArg(x_129), encArg(x_214))) :|: z = 1 + x_129 + x_214, x_214 >= 0, x_129 >= 0
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_b -{ 1 }-> 2 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_f(z, z') -{ 0 }-> f(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_n__b -{ 0 }-> 2 :|: 
   encode_n__b -{ 0 }-> 0 :|: 
   f(z, z') -{ 2 }-> s :|: s >= 0, s <= 0, z' >= 0, z = z'
   f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0

Function symbols to be analyzed: {encArg}, {encode_activate}, {encode_f}
Previous analysis results are:
  encode_a: runtime: O(1) [0], size: O(1) [0]
  f: runtime: O(1) [1], size: O(1) [0]
  b: runtime: O(1) [1], size: O(1) [2]
  activate: runtime: O(1) [2], size: O(n^1) [z]
  encode_b: runtime: O(1) [1], size: O(1) [2]
  encode_n__b: runtime: O(1) [0], size: O(1) [2]

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

(59) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: encArg
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 2

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 2 :|: z = 2
   activate(z) -{ 2 }-> 0 :|: z = 2
   b -{ 1 }-> 2 :|: 
   b -{ 1 }-> 0 :|: 
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 2 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 1, X >= 0, 2 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 1, X >= 0, 0 = X
   encArg(z) -{ 2 }-> s' :|: s' >= 0, s' <= 2, z = 1 + 2, 2 = 2
   encArg(z) -{ 3 }-> s1 :|: s1 >= 0, s1 <= 2, z = 1 + 1, 2 = 2
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> activate(f(encArg(x_113), encArg(x_26))) :|: x_113 >= 0, z = 1 + (1 + x_113 + x_26), x_26 >= 0
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 1 }-> 2 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 1 }-> 0 :|: z = 1
   encode_a -{ 0 }-> 0 :|: 
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 2 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> X :|: z = 1, X >= 0, 2 = X
   encode_activate(z) -{ 2 }-> X :|: z = 1, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> s'' :|: s'' >= 0, s'' <= 2, z = 2, 2 = 2
   encode_activate(z) -{ 3 }-> s2 :|: s2 >= 0, s2 <= 2, z = 1, 2 = 2
   encode_activate(z) -{ 0 }-> activate(f(encArg(x_129), encArg(x_214))) :|: z = 1 + x_129 + x_214, x_214 >= 0, x_129 >= 0
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_b -{ 1 }-> 2 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_f(z, z') -{ 0 }-> f(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_n__b -{ 0 }-> 2 :|: 
   encode_n__b -{ 0 }-> 0 :|: 
   f(z, z') -{ 2 }-> s :|: s >= 0, s <= 0, z' >= 0, z = z'
   f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0

Function symbols to be analyzed: {encArg}, {encode_activate}, {encode_f}
Previous analysis results are:
  encode_a: runtime: O(1) [0], size: O(1) [0]
  f: runtime: O(1) [1], size: O(1) [0]
  b: runtime: O(1) [1], size: O(1) [2]
  activate: runtime: O(1) [2], size: O(n^1) [z]
  encode_b: runtime: O(1) [1], size: O(1) [2]
  encode_n__b: runtime: O(1) [0], size: O(1) [2]
  encArg: runtime: ?, size: O(1) [2]

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

(61) 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: 3 + 4*z

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 2 :|: z = 2
   activate(z) -{ 2 }-> 0 :|: z = 2
   b -{ 1 }-> 2 :|: 
   b -{ 1 }-> 0 :|: 
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 2 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 1, X >= 0, 2 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 1, X >= 0, 0 = X
   encArg(z) -{ 2 }-> s' :|: s' >= 0, s' <= 2, z = 1 + 2, 2 = 2
   encArg(z) -{ 3 }-> s1 :|: s1 >= 0, s1 <= 2, z = 1 + 1, 2 = 2
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> activate(f(encArg(x_113), encArg(x_26))) :|: x_113 >= 0, z = 1 + (1 + x_113 + x_26), x_26 >= 0
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 1 }-> 2 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 1 }-> 0 :|: z = 1
   encode_a -{ 0 }-> 0 :|: 
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 2 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> X :|: z = 1, X >= 0, 2 = X
   encode_activate(z) -{ 2 }-> X :|: z = 1, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> s'' :|: s'' >= 0, s'' <= 2, z = 2, 2 = 2
   encode_activate(z) -{ 3 }-> s2 :|: s2 >= 0, s2 <= 2, z = 1, 2 = 2
   encode_activate(z) -{ 0 }-> activate(f(encArg(x_129), encArg(x_214))) :|: z = 1 + x_129 + x_214, x_214 >= 0, x_129 >= 0
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_b -{ 1 }-> 2 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_f(z, z') -{ 0 }-> f(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_n__b -{ 0 }-> 2 :|: 
   encode_n__b -{ 0 }-> 0 :|: 
   f(z, z') -{ 2 }-> s :|: s >= 0, s <= 0, z' >= 0, z = z'
   f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0

Function symbols to be analyzed: {encode_activate}, {encode_f}
Previous analysis results are:
  encode_a: runtime: O(1) [0], size: O(1) [0]
  f: runtime: O(1) [1], size: O(1) [0]
  b: runtime: O(1) [1], size: O(1) [2]
  activate: runtime: O(1) [2], size: O(n^1) [z]
  encode_b: runtime: O(1) [1], size: O(1) [2]
  encode_n__b: runtime: O(1) [0], size: O(1) [2]
  encArg: runtime: O(n^1) [3 + 4*z], size: O(1) [2]

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

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 2 :|: z = 2
   activate(z) -{ 2 }-> 0 :|: z = 2
   b -{ 1 }-> 2 :|: 
   b -{ 1 }-> 0 :|: 
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 2 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 1, X >= 0, 2 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 1, X >= 0, 0 = X
   encArg(z) -{ 2 }-> s' :|: s' >= 0, s' <= 2, z = 1 + 2, 2 = 2
   encArg(z) -{ 3 }-> s1 :|: s1 >= 0, s1 <= 2, z = 1 + 1, 2 = 2
   encArg(z) -{ 9 + 4*x_113 + 4*x_26 }-> s12 :|: s9 >= 0, s9 <= 2, s10 >= 0, s10 <= 2, s11 >= 0, s11 <= 0, s12 >= 0, s12 <= s11, x_113 >= 0, z = 1 + (1 + x_113 + x_26), x_26 >= 0
   encArg(z) -{ -1 + 4*z }-> s15 :|: s13 >= 0, s13 <= 2, s14 >= 0, s14 <= s13, s15 >= 0, s15 <= s14, z - 2 >= 0
   encArg(z) -{ 7 + 4*x_1 + 4*x_2 }-> s5 :|: s3 >= 0, s3 <= 2, s4 >= 0, s4 <= 2, s5 >= 0, s5 <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 1 }-> 2 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 1 }-> 0 :|: z = 1
   encode_a -{ 0 }-> 0 :|: 
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 2 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> X :|: z = 1, X >= 0, 2 = X
   encode_activate(z) -{ 2 }-> X :|: z = 1, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> s'' :|: s'' >= 0, s'' <= 2, z = 2, 2 = 2
   encode_activate(z) -{ 9 + 4*x_129 + 4*x_214 }-> s19 :|: s16 >= 0, s16 <= 2, s17 >= 0, s17 <= 2, s18 >= 0, s18 <= 0, s19 >= 0, s19 <= s18, z = 1 + x_129 + x_214, x_214 >= 0, x_129 >= 0
   encode_activate(z) -{ 3 }-> s2 :|: s2 >= 0, s2 <= 2, z = 1, 2 = 2
   encode_activate(z) -{ 3 + 4*z }-> s22 :|: s20 >= 0, s20 <= 2, s21 >= 0, s21 <= s20, s22 >= 0, s22 <= s21, z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_b -{ 1 }-> 2 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_f(z, z') -{ 7 + 4*z + 4*z' }-> s8 :|: s6 >= 0, s6 <= 2, s7 >= 0, s7 <= 2, s8 >= 0, s8 <= 0, z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_n__b -{ 0 }-> 2 :|: 
   encode_n__b -{ 0 }-> 0 :|: 
   f(z, z') -{ 2 }-> s :|: s >= 0, s <= 0, z' >= 0, z = z'
   f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0

Function symbols to be analyzed: {encode_activate}, {encode_f}
Previous analysis results are:
  encode_a: runtime: O(1) [0], size: O(1) [0]
  f: runtime: O(1) [1], size: O(1) [0]
  b: runtime: O(1) [1], size: O(1) [2]
  activate: runtime: O(1) [2], size: O(n^1) [z]
  encode_b: runtime: O(1) [1], size: O(1) [2]
  encode_n__b: runtime: O(1) [0], size: O(1) [2]
  encArg: runtime: O(n^1) [3 + 4*z], size: O(1) [2]

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

(65) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: encode_activate
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 2

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 2 :|: z = 2
   activate(z) -{ 2 }-> 0 :|: z = 2
   b -{ 1 }-> 2 :|: 
   b -{ 1 }-> 0 :|: 
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 2 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 1, X >= 0, 2 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 1, X >= 0, 0 = X
   encArg(z) -{ 2 }-> s' :|: s' >= 0, s' <= 2, z = 1 + 2, 2 = 2
   encArg(z) -{ 3 }-> s1 :|: s1 >= 0, s1 <= 2, z = 1 + 1, 2 = 2
   encArg(z) -{ 9 + 4*x_113 + 4*x_26 }-> s12 :|: s9 >= 0, s9 <= 2, s10 >= 0, s10 <= 2, s11 >= 0, s11 <= 0, s12 >= 0, s12 <= s11, x_113 >= 0, z = 1 + (1 + x_113 + x_26), x_26 >= 0
   encArg(z) -{ -1 + 4*z }-> s15 :|: s13 >= 0, s13 <= 2, s14 >= 0, s14 <= s13, s15 >= 0, s15 <= s14, z - 2 >= 0
   encArg(z) -{ 7 + 4*x_1 + 4*x_2 }-> s5 :|: s3 >= 0, s3 <= 2, s4 >= 0, s4 <= 2, s5 >= 0, s5 <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 1 }-> 2 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 1 }-> 0 :|: z = 1
   encode_a -{ 0 }-> 0 :|: 
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 2 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> X :|: z = 1, X >= 0, 2 = X
   encode_activate(z) -{ 2 }-> X :|: z = 1, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> s'' :|: s'' >= 0, s'' <= 2, z = 2, 2 = 2
   encode_activate(z) -{ 9 + 4*x_129 + 4*x_214 }-> s19 :|: s16 >= 0, s16 <= 2, s17 >= 0, s17 <= 2, s18 >= 0, s18 <= 0, s19 >= 0, s19 <= s18, z = 1 + x_129 + x_214, x_214 >= 0, x_129 >= 0
   encode_activate(z) -{ 3 }-> s2 :|: s2 >= 0, s2 <= 2, z = 1, 2 = 2
   encode_activate(z) -{ 3 + 4*z }-> s22 :|: s20 >= 0, s20 <= 2, s21 >= 0, s21 <= s20, s22 >= 0, s22 <= s21, z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_b -{ 1 }-> 2 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_f(z, z') -{ 7 + 4*z + 4*z' }-> s8 :|: s6 >= 0, s6 <= 2, s7 >= 0, s7 <= 2, s8 >= 0, s8 <= 0, z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_n__b -{ 0 }-> 2 :|: 
   encode_n__b -{ 0 }-> 0 :|: 
   f(z, z') -{ 2 }-> s :|: s >= 0, s <= 0, z' >= 0, z = z'
   f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0

Function symbols to be analyzed: {encode_activate}, {encode_f}
Previous analysis results are:
  encode_a: runtime: O(1) [0], size: O(1) [0]
  f: runtime: O(1) [1], size: O(1) [0]
  b: runtime: O(1) [1], size: O(1) [2]
  activate: runtime: O(1) [2], size: O(n^1) [z]
  encode_b: runtime: O(1) [1], size: O(1) [2]
  encode_n__b: runtime: O(1) [0], size: O(1) [2]
  encArg: runtime: O(n^1) [3 + 4*z], size: O(1) [2]
  encode_activate: runtime: ?, size: O(1) [2]

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

(67) 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: 5 + 4*z

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 2 :|: z = 2
   activate(z) -{ 2 }-> 0 :|: z = 2
   b -{ 1 }-> 2 :|: 
   b -{ 1 }-> 0 :|: 
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 2 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 1, X >= 0, 2 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 1, X >= 0, 0 = X
   encArg(z) -{ 2 }-> s' :|: s' >= 0, s' <= 2, z = 1 + 2, 2 = 2
   encArg(z) -{ 3 }-> s1 :|: s1 >= 0, s1 <= 2, z = 1 + 1, 2 = 2
   encArg(z) -{ 9 + 4*x_113 + 4*x_26 }-> s12 :|: s9 >= 0, s9 <= 2, s10 >= 0, s10 <= 2, s11 >= 0, s11 <= 0, s12 >= 0, s12 <= s11, x_113 >= 0, z = 1 + (1 + x_113 + x_26), x_26 >= 0
   encArg(z) -{ -1 + 4*z }-> s15 :|: s13 >= 0, s13 <= 2, s14 >= 0, s14 <= s13, s15 >= 0, s15 <= s14, z - 2 >= 0
   encArg(z) -{ 7 + 4*x_1 + 4*x_2 }-> s5 :|: s3 >= 0, s3 <= 2, s4 >= 0, s4 <= 2, s5 >= 0, s5 <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 1 }-> 2 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 1 }-> 0 :|: z = 1
   encode_a -{ 0 }-> 0 :|: 
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 2 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> X :|: z = 1, X >= 0, 2 = X
   encode_activate(z) -{ 2 }-> X :|: z = 1, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> s'' :|: s'' >= 0, s'' <= 2, z = 2, 2 = 2
   encode_activate(z) -{ 9 + 4*x_129 + 4*x_214 }-> s19 :|: s16 >= 0, s16 <= 2, s17 >= 0, s17 <= 2, s18 >= 0, s18 <= 0, s19 >= 0, s19 <= s18, z = 1 + x_129 + x_214, x_214 >= 0, x_129 >= 0
   encode_activate(z) -{ 3 }-> s2 :|: s2 >= 0, s2 <= 2, z = 1, 2 = 2
   encode_activate(z) -{ 3 + 4*z }-> s22 :|: s20 >= 0, s20 <= 2, s21 >= 0, s21 <= s20, s22 >= 0, s22 <= s21, z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_b -{ 1 }-> 2 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_f(z, z') -{ 7 + 4*z + 4*z' }-> s8 :|: s6 >= 0, s6 <= 2, s7 >= 0, s7 <= 2, s8 >= 0, s8 <= 0, z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_n__b -{ 0 }-> 2 :|: 
   encode_n__b -{ 0 }-> 0 :|: 
   f(z, z') -{ 2 }-> s :|: s >= 0, s <= 0, z' >= 0, z = z'
   f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0

Function symbols to be analyzed: {encode_f}
Previous analysis results are:
  encode_a: runtime: O(1) [0], size: O(1) [0]
  f: runtime: O(1) [1], size: O(1) [0]
  b: runtime: O(1) [1], size: O(1) [2]
  activate: runtime: O(1) [2], size: O(n^1) [z]
  encode_b: runtime: O(1) [1], size: O(1) [2]
  encode_n__b: runtime: O(1) [0], size: O(1) [2]
  encArg: runtime: O(n^1) [3 + 4*z], size: O(1) [2]
  encode_activate: runtime: O(n^1) [5 + 4*z], size: O(1) [2]

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

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 2 :|: z = 2
   activate(z) -{ 2 }-> 0 :|: z = 2
   b -{ 1 }-> 2 :|: 
   b -{ 1 }-> 0 :|: 
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 2 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 1, X >= 0, 2 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 1, X >= 0, 0 = X
   encArg(z) -{ 2 }-> s' :|: s' >= 0, s' <= 2, z = 1 + 2, 2 = 2
   encArg(z) -{ 3 }-> s1 :|: s1 >= 0, s1 <= 2, z = 1 + 1, 2 = 2
   encArg(z) -{ 9 + 4*x_113 + 4*x_26 }-> s12 :|: s9 >= 0, s9 <= 2, s10 >= 0, s10 <= 2, s11 >= 0, s11 <= 0, s12 >= 0, s12 <= s11, x_113 >= 0, z = 1 + (1 + x_113 + x_26), x_26 >= 0
   encArg(z) -{ -1 + 4*z }-> s15 :|: s13 >= 0, s13 <= 2, s14 >= 0, s14 <= s13, s15 >= 0, s15 <= s14, z - 2 >= 0
   encArg(z) -{ 7 + 4*x_1 + 4*x_2 }-> s5 :|: s3 >= 0, s3 <= 2, s4 >= 0, s4 <= 2, s5 >= 0, s5 <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 1 }-> 2 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 1 }-> 0 :|: z = 1
   encode_a -{ 0 }-> 0 :|: 
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 2 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> X :|: z = 1, X >= 0, 2 = X
   encode_activate(z) -{ 2 }-> X :|: z = 1, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> s'' :|: s'' >= 0, s'' <= 2, z = 2, 2 = 2
   encode_activate(z) -{ 9 + 4*x_129 + 4*x_214 }-> s19 :|: s16 >= 0, s16 <= 2, s17 >= 0, s17 <= 2, s18 >= 0, s18 <= 0, s19 >= 0, s19 <= s18, z = 1 + x_129 + x_214, x_214 >= 0, x_129 >= 0
   encode_activate(z) -{ 3 }-> s2 :|: s2 >= 0, s2 <= 2, z = 1, 2 = 2
   encode_activate(z) -{ 3 + 4*z }-> s22 :|: s20 >= 0, s20 <= 2, s21 >= 0, s21 <= s20, s22 >= 0, s22 <= s21, z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_b -{ 1 }-> 2 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_f(z, z') -{ 7 + 4*z + 4*z' }-> s8 :|: s6 >= 0, s6 <= 2, s7 >= 0, s7 <= 2, s8 >= 0, s8 <= 0, z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_n__b -{ 0 }-> 2 :|: 
   encode_n__b -{ 0 }-> 0 :|: 
   f(z, z') -{ 2 }-> s :|: s >= 0, s <= 0, z' >= 0, z = z'
   f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0

Function symbols to be analyzed: {encode_f}
Previous analysis results are:
  encode_a: runtime: O(1) [0], size: O(1) [0]
  f: runtime: O(1) [1], size: O(1) [0]
  b: runtime: O(1) [1], size: O(1) [2]
  activate: runtime: O(1) [2], size: O(n^1) [z]
  encode_b: runtime: O(1) [1], size: O(1) [2]
  encode_n__b: runtime: O(1) [0], size: O(1) [2]
  encArg: runtime: O(n^1) [3 + 4*z], size: O(1) [2]
  encode_activate: runtime: O(n^1) [5 + 4*z], size: O(1) [2]

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

(71) 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

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 2 :|: z = 2
   activate(z) -{ 2 }-> 0 :|: z = 2
   b -{ 1 }-> 2 :|: 
   b -{ 1 }-> 0 :|: 
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 2 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 1, X >= 0, 2 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 1, X >= 0, 0 = X
   encArg(z) -{ 2 }-> s' :|: s' >= 0, s' <= 2, z = 1 + 2, 2 = 2
   encArg(z) -{ 3 }-> s1 :|: s1 >= 0, s1 <= 2, z = 1 + 1, 2 = 2
   encArg(z) -{ 9 + 4*x_113 + 4*x_26 }-> s12 :|: s9 >= 0, s9 <= 2, s10 >= 0, s10 <= 2, s11 >= 0, s11 <= 0, s12 >= 0, s12 <= s11, x_113 >= 0, z = 1 + (1 + x_113 + x_26), x_26 >= 0
   encArg(z) -{ -1 + 4*z }-> s15 :|: s13 >= 0, s13 <= 2, s14 >= 0, s14 <= s13, s15 >= 0, s15 <= s14, z - 2 >= 0
   encArg(z) -{ 7 + 4*x_1 + 4*x_2 }-> s5 :|: s3 >= 0, s3 <= 2, s4 >= 0, s4 <= 2, s5 >= 0, s5 <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 1 }-> 2 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 1 }-> 0 :|: z = 1
   encode_a -{ 0 }-> 0 :|: 
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 2 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> X :|: z = 1, X >= 0, 2 = X
   encode_activate(z) -{ 2 }-> X :|: z = 1, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> s'' :|: s'' >= 0, s'' <= 2, z = 2, 2 = 2
   encode_activate(z) -{ 9 + 4*x_129 + 4*x_214 }-> s19 :|: s16 >= 0, s16 <= 2, s17 >= 0, s17 <= 2, s18 >= 0, s18 <= 0, s19 >= 0, s19 <= s18, z = 1 + x_129 + x_214, x_214 >= 0, x_129 >= 0
   encode_activate(z) -{ 3 }-> s2 :|: s2 >= 0, s2 <= 2, z = 1, 2 = 2
   encode_activate(z) -{ 3 + 4*z }-> s22 :|: s20 >= 0, s20 <= 2, s21 >= 0, s21 <= s20, s22 >= 0, s22 <= s21, z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_b -{ 1 }-> 2 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_f(z, z') -{ 7 + 4*z + 4*z' }-> s8 :|: s6 >= 0, s6 <= 2, s7 >= 0, s7 <= 2, s8 >= 0, s8 <= 0, z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_n__b -{ 0 }-> 2 :|: 
   encode_n__b -{ 0 }-> 0 :|: 
   f(z, z') -{ 2 }-> s :|: s >= 0, s <= 0, z' >= 0, z = z'
   f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0

Function symbols to be analyzed: {encode_f}
Previous analysis results are:
  encode_a: runtime: O(1) [0], size: O(1) [0]
  f: runtime: O(1) [1], size: O(1) [0]
  b: runtime: O(1) [1], size: O(1) [2]
  activate: runtime: O(1) [2], size: O(n^1) [z]
  encode_b: runtime: O(1) [1], size: O(1) [2]
  encode_n__b: runtime: O(1) [0], size: O(1) [2]
  encArg: runtime: O(n^1) [3 + 4*z], size: O(1) [2]
  encode_activate: runtime: O(n^1) [5 + 4*z], size: O(1) [2]
  encode_f: runtime: ?, size: O(1) [0]

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(73) 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: 7 + 4*z + 4*z'

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 2 :|: z = 2
   activate(z) -{ 2 }-> 0 :|: z = 2
   b -{ 1 }-> 2 :|: 
   b -{ 1 }-> 0 :|: 
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 2 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 1, X >= 0, 2 = X
   encArg(z) -{ 2 }-> X :|: z = 1 + 1, X >= 0, 0 = X
   encArg(z) -{ 2 }-> s' :|: s' >= 0, s' <= 2, z = 1 + 2, 2 = 2
   encArg(z) -{ 3 }-> s1 :|: s1 >= 0, s1 <= 2, z = 1 + 1, 2 = 2
   encArg(z) -{ 9 + 4*x_113 + 4*x_26 }-> s12 :|: s9 >= 0, s9 <= 2, s10 >= 0, s10 <= 2, s11 >= 0, s11 <= 0, s12 >= 0, s12 <= s11, x_113 >= 0, z = 1 + (1 + x_113 + x_26), x_26 >= 0
   encArg(z) -{ -1 + 4*z }-> s15 :|: s13 >= 0, s13 <= 2, s14 >= 0, s14 <= s13, s15 >= 0, s15 <= s14, z - 2 >= 0
   encArg(z) -{ 7 + 4*x_1 + 4*x_2 }-> s5 :|: s3 >= 0, s3 <= 2, s4 >= 0, s4 <= 2, s5 >= 0, s5 <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 1 }-> 2 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 1 }-> 0 :|: z = 1
   encode_a -{ 0 }-> 0 :|: 
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 2 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> X :|: z = 1, X >= 0, 2 = X
   encode_activate(z) -{ 2 }-> X :|: z = 1, X >= 0, 0 = X
   encode_activate(z) -{ 2 }-> s'' :|: s'' >= 0, s'' <= 2, z = 2, 2 = 2
   encode_activate(z) -{ 9 + 4*x_129 + 4*x_214 }-> s19 :|: s16 >= 0, s16 <= 2, s17 >= 0, s17 <= 2, s18 >= 0, s18 <= 0, s19 >= 0, s19 <= s18, z = 1 + x_129 + x_214, x_214 >= 0, x_129 >= 0
   encode_activate(z) -{ 3 }-> s2 :|: s2 >= 0, s2 <= 2, z = 1, 2 = 2
   encode_activate(z) -{ 3 + 4*z }-> s22 :|: s20 >= 0, s20 <= 2, s21 >= 0, s21 <= s20, s22 >= 0, s22 <= s21, z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_b -{ 1 }-> 2 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_f(z, z') -{ 7 + 4*z + 4*z' }-> s8 :|: s6 >= 0, s6 <= 2, s7 >= 0, s7 <= 2, s8 >= 0, s8 <= 0, z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_n__b -{ 0 }-> 2 :|: 
   encode_n__b -{ 0 }-> 0 :|: 
   f(z, z') -{ 2 }-> s :|: s >= 0, s <= 0, z' >= 0, z = z'
   f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0

Function symbols to be analyzed: 
Previous analysis results are:
  encode_a: runtime: O(1) [0], size: O(1) [0]
  f: runtime: O(1) [1], size: O(1) [0]
  b: runtime: O(1) [1], size: O(1) [2]
  activate: runtime: O(1) [2], size: O(n^1) [z]
  encode_b: runtime: O(1) [1], size: O(1) [2]
  encode_n__b: runtime: O(1) [0], size: O(1) [2]
  encArg: runtime: O(n^1) [3 + 4*z], size: O(1) [2]
  encode_activate: runtime: O(n^1) [5 + 4*z], size: O(1) [2]
  encode_f: runtime: O(n^1) [7 + 4*z + 4*z'], size: O(1) [0]

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(75) FinalProof (FINISHED)
Computed overall runtime complexity
----------------------------------------

(76)
BOUNDS(1, n^1)