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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


The Derivational Complexity (full) 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), 304 ms]
(4) CpxRelTRS
(5) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms]
(6) CpxRelTRS
(7) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
(8) CpxWeightedTrs
(9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
(10) CpxTypedWeightedTrs
(11) CompletionProof [UPPER BOUND(ID), 0 ms]
(12) CpxTypedWeightedCompleteTrs
(13) NarrowingProof [BOTH BOUNDS(ID, ID), 474 ms]
(14) CpxTypedWeightedCompleteTrs
(15) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
(16) CpxRNTS
(17) SimplificationProof [BOTH BOUNDS(ID, ID), 2 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), 52 ms]
(24) CpxRNTS
(25) IntTrsBoundProof [UPPER BOUND(ID), 24 ms]
(26) CpxRNTS
(27) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(28) CpxRNTS
(29) IntTrsBoundProof [UPPER BOUND(ID), 43 ms]
(30) CpxRNTS
(31) IntTrsBoundProof [UPPER BOUND(ID), 2 ms]
(32) CpxRNTS
(33) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(34) CpxRNTS
(35) IntTrsBoundProof [UPPER BOUND(ID), 26 ms]
(36) CpxRNTS
(37) IntTrsBoundProof [UPPER BOUND(ID), 2 ms]
(38) CpxRNTS
(39) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(40) CpxRNTS
(41) IntTrsBoundProof [UPPER BOUND(ID), 1274 ms]
(42) CpxRNTS
(43) IntTrsBoundProof [UPPER BOUND(ID), 320 ms]
(44) CpxRNTS
(45) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(46) CpxRNTS
(47) IntTrsBoundProof [UPPER BOUND(ID), 1759 ms]
(48) CpxRNTS
(49) IntTrsBoundProof [UPPER BOUND(ID), 655 ms]
(50) CpxRNTS
(51) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(52) CpxRNTS
(53) IntTrsBoundProof [UPPER BOUND(ID), 559 ms]
(54) CpxRNTS
(55) IntTrsBoundProof [UPPER BOUND(ID), 139 ms]
(56) CpxRNTS
(57) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(58) CpxRNTS
(59) IntTrsBoundProof [UPPER BOUND(ID), 261 ms]
(60) CpxRNTS
(61) IntTrsBoundProof [UPPER BOUND(ID), 73 ms]
(62) CpxRNTS
(63) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(64) CpxRNTS
(65) IntTrsBoundProof [UPPER BOUND(ID), 538 ms]
(66) CpxRNTS
(67) IntTrsBoundProof [UPPER BOUND(ID), 128 ms]
(68) CpxRNTS
(69) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(70) CpxRNTS
(71) IntTrsBoundProof [UPPER BOUND(ID), 178 ms]
(72) CpxRNTS
(73) IntTrsBoundProof [UPPER BOUND(ID), 52 ms]
(74) CpxRNTS
(75) FinalProof [FINISHED, 0 ms]
(76) BOUNDS(1, n^1)


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

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


The TRS R consists of the following rules:

   f(X) -> if(X, c, n__f(true))
   if(true, X, Y) -> X
   if(false, X, Y) -> activate(Y)
   f(X) -> n__f(X)
   activate(n__f(X)) -> f(X)
   activate(X) -> X

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

(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(c) -> c
   encArg(n__f(x_1)) -> n__f(encArg(x_1))
   encArg(true) -> true
   encArg(false) -> false
   encArg(cons_f(x_1)) -> f(encArg(x_1))
   encArg(cons_if(x_1, x_2, x_3)) -> if(encArg(x_1), encArg(x_2), encArg(x_3))
   encArg(cons_activate(x_1)) -> activate(encArg(x_1))
   encode_f(x_1) -> f(encArg(x_1))
   encode_if(x_1, x_2, x_3) -> if(encArg(x_1), encArg(x_2), encArg(x_3))
   encode_c -> c
   encode_n__f(x_1) -> n__f(encArg(x_1))
   encode_true -> true
   encode_false -> false
   encode_activate(x_1) -> activate(encArg(x_1))


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

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


The TRS R consists of the following rules:

   f(X) -> if(X, c, n__f(true))
   if(true, X, Y) -> X
   if(false, X, Y) -> activate(Y)
   f(X) -> n__f(X)
   activate(n__f(X)) -> f(X)
   activate(X) -> X

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

   encArg(c) -> c
   encArg(n__f(x_1)) -> n__f(encArg(x_1))
   encArg(true) -> true
   encArg(false) -> false
   encArg(cons_f(x_1)) -> f(encArg(x_1))
   encArg(cons_if(x_1, x_2, x_3)) -> if(encArg(x_1), encArg(x_2), encArg(x_3))
   encArg(cons_activate(x_1)) -> activate(encArg(x_1))
   encode_f(x_1) -> f(encArg(x_1))
   encode_if(x_1, x_2, x_3) -> if(encArg(x_1), encArg(x_2), encArg(x_3))
   encode_c -> c
   encode_n__f(x_1) -> n__f(encArg(x_1))
   encode_true -> true
   encode_false -> false
   encode_activate(x_1) -> activate(encArg(x_1))

Rewrite Strategy: FULL
----------------------------------------

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

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


The TRS R consists of the following rules:

   f(X) -> if(X, c, n__f(true))
   if(true, X, Y) -> X
   if(false, X, Y) -> activate(Y)
   f(X) -> n__f(X)
   activate(n__f(X)) -> f(X)
   activate(X) -> X

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

   encArg(c) -> c
   encArg(n__f(x_1)) -> n__f(encArg(x_1))
   encArg(true) -> true
   encArg(false) -> false
   encArg(cons_f(x_1)) -> f(encArg(x_1))
   encArg(cons_if(x_1, x_2, x_3)) -> if(encArg(x_1), encArg(x_2), encArg(x_3))
   encArg(cons_activate(x_1)) -> activate(encArg(x_1))
   encode_f(x_1) -> f(encArg(x_1))
   encode_if(x_1, x_2, x_3) -> if(encArg(x_1), encArg(x_2), encArg(x_3))
   encode_c -> c
   encode_n__f(x_1) -> n__f(encArg(x_1))
   encode_true -> true
   encode_false -> false
   encode_activate(x_1) -> activate(encArg(x_1))

Rewrite Strategy: FULL
----------------------------------------

(5) RcToIrcProof (BOTH BOUNDS(ID, ID))
Converted rc-obligation to irc-obligation.

As the TRS is a non-duplicating overlay system, we have rc = irc.
----------------------------------------

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


The TRS R consists of the following rules:

   f(X) -> if(X, c, n__f(true))
   if(true, X, Y) -> X
   if(false, X, Y) -> activate(Y)
   f(X) -> n__f(X)
   activate(n__f(X)) -> f(X)
   activate(X) -> X

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

   encArg(c) -> c
   encArg(n__f(x_1)) -> n__f(encArg(x_1))
   encArg(true) -> true
   encArg(false) -> false
   encArg(cons_f(x_1)) -> f(encArg(x_1))
   encArg(cons_if(x_1, x_2, x_3)) -> if(encArg(x_1), encArg(x_2), encArg(x_3))
   encArg(cons_activate(x_1)) -> activate(encArg(x_1))
   encode_f(x_1) -> f(encArg(x_1))
   encode_if(x_1, x_2, x_3) -> if(encArg(x_1), encArg(x_2), encArg(x_3))
   encode_c -> c
   encode_n__f(x_1) -> n__f(encArg(x_1))
   encode_true -> true
   encode_false -> false
   encode_activate(x_1) -> activate(encArg(x_1))

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

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

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


The TRS R consists of the following rules:

   f(X) -> if(X, c, n__f(true)) [1]
   if(true, X, Y) -> X [1]
   if(false, X, Y) -> activate(Y) [1]
   f(X) -> n__f(X) [1]
   activate(n__f(X)) -> f(X) [1]
   activate(X) -> X [1]
   encArg(c) -> c [0]
   encArg(n__f(x_1)) -> n__f(encArg(x_1)) [0]
   encArg(true) -> true [0]
   encArg(false) -> false [0]
   encArg(cons_f(x_1)) -> f(encArg(x_1)) [0]
   encArg(cons_if(x_1, x_2, x_3)) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encArg(cons_activate(x_1)) -> activate(encArg(x_1)) [0]
   encode_f(x_1) -> f(encArg(x_1)) [0]
   encode_if(x_1, x_2, x_3) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encode_c -> c [0]
   encode_n__f(x_1) -> n__f(encArg(x_1)) [0]
   encode_true -> true [0]
   encode_false -> false [0]
   encode_activate(x_1) -> activate(encArg(x_1)) [0]

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

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

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

   f(X) -> if(X, c, n__f(true)) [1]
   if(true, X, Y) -> X [1]
   if(false, X, Y) -> activate(Y) [1]
   f(X) -> n__f(X) [1]
   activate(n__f(X)) -> f(X) [1]
   activate(X) -> X [1]
   encArg(c) -> c [0]
   encArg(n__f(x_1)) -> n__f(encArg(x_1)) [0]
   encArg(true) -> true [0]
   encArg(false) -> false [0]
   encArg(cons_f(x_1)) -> f(encArg(x_1)) [0]
   encArg(cons_if(x_1, x_2, x_3)) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encArg(cons_activate(x_1)) -> activate(encArg(x_1)) [0]
   encode_f(x_1) -> f(encArg(x_1)) [0]
   encode_if(x_1, x_2, x_3) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encode_c -> c [0]
   encode_n__f(x_1) -> n__f(encArg(x_1)) [0]
   encode_true -> true [0]
   encode_false -> false [0]
   encode_activate(x_1) -> activate(encArg(x_1)) [0]

The TRS has the following type information:
f :: c:true:n__f:false:cons_f:cons_if:cons_activate -> c:true:n__f:false:cons_f:cons_if:cons_activate
if :: c:true:n__f:false:cons_f:cons_if:cons_activate -> c:true:n__f:false:cons_f:cons_if:cons_activate -> c:true:n__f:false:cons_f:cons_if:cons_activate -> c:true:n__f:false:cons_f:cons_if:cons_activate
c :: c:true:n__f:false:cons_f:cons_if:cons_activate
n__f :: c:true:n__f:false:cons_f:cons_if:cons_activate -> c:true:n__f:false:cons_f:cons_if:cons_activate
true :: c:true:n__f:false:cons_f:cons_if:cons_activate
false :: c:true:n__f:false:cons_f:cons_if:cons_activate
activate :: c:true:n__f:false:cons_f:cons_if:cons_activate -> c:true:n__f:false:cons_f:cons_if:cons_activate
encArg :: c:true:n__f:false:cons_f:cons_if:cons_activate -> c:true:n__f:false:cons_f:cons_if:cons_activate
cons_f :: c:true:n__f:false:cons_f:cons_if:cons_activate -> c:true:n__f:false:cons_f:cons_if:cons_activate
cons_if :: c:true:n__f:false:cons_f:cons_if:cons_activate -> c:true:n__f:false:cons_f:cons_if:cons_activate -> c:true:n__f:false:cons_f:cons_if:cons_activate -> c:true:n__f:false:cons_f:cons_if:cons_activate
cons_activate :: c:true:n__f:false:cons_f:cons_if:cons_activate -> c:true:n__f:false:cons_f:cons_if:cons_activate
encode_f :: c:true:n__f:false:cons_f:cons_if:cons_activate -> c:true:n__f:false:cons_f:cons_if:cons_activate
encode_if :: c:true:n__f:false:cons_f:cons_if:cons_activate -> c:true:n__f:false:cons_f:cons_if:cons_activate -> c:true:n__f:false:cons_f:cons_if:cons_activate -> c:true:n__f:false:cons_f:cons_if:cons_activate
encode_c :: c:true:n__f:false:cons_f:cons_if:cons_activate
encode_n__f :: c:true:n__f:false:cons_f:cons_if:cons_activate -> c:true:n__f:false:cons_f:cons_if:cons_activate
encode_true :: c:true:n__f:false:cons_f:cons_if:cons_activate
encode_false :: c:true:n__f:false:cons_f:cons_if:cons_activate
encode_activate :: c:true:n__f:false:cons_f:cons_if:cons_activate -> c:true:n__f:false:cons_f:cons_if:cons_activate

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

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

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

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

(c) The following functions are completely defined:

   if_3
   activate_1
   f_1
   encArg_1
   encode_f_1
   encode_if_3
   encode_c
   encode_n__f_1
   encode_true
   encode_false
   encode_activate_1

Due to the following rules being added:

   encArg(v0) -> null_encArg [0]
   encode_f(v0) -> null_encode_f [0]
   encode_if(v0, v1, v2) -> null_encode_if [0]
   encode_c -> null_encode_c [0]
   encode_n__f(v0) -> null_encode_n__f [0]
   encode_true -> null_encode_true [0]
   encode_false -> null_encode_false [0]
   encode_activate(v0) -> null_encode_activate [0]
   if(v0, v1, v2) -> null_if [0]

And the following fresh constants:    null_encArg, null_encode_f, null_encode_if, null_encode_c, null_encode_n__f, null_encode_true, null_encode_false, null_encode_activate, null_if

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

(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) -> if(X, c, n__f(true)) [1]
   if(true, X, Y) -> X [1]
   if(false, X, Y) -> activate(Y) [1]
   f(X) -> n__f(X) [1]
   activate(n__f(X)) -> f(X) [1]
   activate(X) -> X [1]
   encArg(c) -> c [0]
   encArg(n__f(x_1)) -> n__f(encArg(x_1)) [0]
   encArg(true) -> true [0]
   encArg(false) -> false [0]
   encArg(cons_f(x_1)) -> f(encArg(x_1)) [0]
   encArg(cons_if(x_1, x_2, x_3)) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encArg(cons_activate(x_1)) -> activate(encArg(x_1)) [0]
   encode_f(x_1) -> f(encArg(x_1)) [0]
   encode_if(x_1, x_2, x_3) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encode_c -> c [0]
   encode_n__f(x_1) -> n__f(encArg(x_1)) [0]
   encode_true -> true [0]
   encode_false -> false [0]
   encode_activate(x_1) -> activate(encArg(x_1)) [0]
   encArg(v0) -> null_encArg [0]
   encode_f(v0) -> null_encode_f [0]
   encode_if(v0, v1, v2) -> null_encode_if [0]
   encode_c -> null_encode_c [0]
   encode_n__f(v0) -> null_encode_n__f [0]
   encode_true -> null_encode_true [0]
   encode_false -> null_encode_false [0]
   encode_activate(v0) -> null_encode_activate [0]
   if(v0, v1, v2) -> null_if [0]

The TRS has the following type information:
f :: c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if -> c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if
if :: c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if -> c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if -> c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if -> c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if
c :: c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if
n__f :: c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if -> c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if
true :: c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if
false :: c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if
activate :: c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if -> c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if
encArg :: c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if -> c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if
cons_f :: c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if -> c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if
cons_if :: c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if -> c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if -> c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if -> c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if
cons_activate :: c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if -> c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if
encode_f :: c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if -> c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if
encode_if :: c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if -> c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if -> c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if -> c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if
encode_c :: c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if
encode_n__f :: c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if -> c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if
encode_true :: c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if
encode_false :: c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if
encode_activate :: c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if -> c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if
null_encArg :: c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if
null_encode_f :: c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if
null_encode_if :: c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if
null_encode_c :: c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if
null_encode_n__f :: c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if
null_encode_true :: c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if
null_encode_false :: c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if
null_encode_activate :: c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if
null_if :: c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if

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

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

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

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

   f(X) -> if(X, c, n__f(true)) [1]
   if(true, X, Y) -> X [1]
   if(false, X, Y) -> activate(Y) [1]
   f(X) -> n__f(X) [1]
   activate(n__f(X)) -> f(X) [1]
   activate(X) -> X [1]
   encArg(c) -> c [0]
   encArg(n__f(x_1)) -> n__f(encArg(x_1)) [0]
   encArg(true) -> true [0]
   encArg(false) -> false [0]
   encArg(cons_f(c)) -> f(c) [0]
   encArg(cons_f(n__f(x_1'))) -> f(n__f(encArg(x_1'))) [0]
   encArg(cons_f(true)) -> f(true) [0]
   encArg(cons_f(false)) -> f(false) [0]
   encArg(cons_f(cons_f(x_1''))) -> f(f(encArg(x_1''))) [0]
   encArg(cons_f(cons_if(x_11, x_2', x_3'))) -> f(if(encArg(x_11), encArg(x_2'), encArg(x_3'))) [0]
   encArg(cons_f(cons_activate(x_12))) -> f(activate(encArg(x_12))) [0]
   encArg(cons_f(x_1)) -> f(null_encArg) [0]
   encArg(cons_if(x_1, x_2, x_3)) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encArg(cons_activate(c)) -> activate(c) [0]
   encArg(cons_activate(n__f(x_1295))) -> activate(n__f(encArg(x_1295))) [0]
   encArg(cons_activate(true)) -> activate(true) [0]
   encArg(cons_activate(false)) -> activate(false) [0]
   encArg(cons_activate(cons_f(x_1296))) -> activate(f(encArg(x_1296))) [0]
   encArg(cons_activate(cons_if(x_1297, x_273, x_373))) -> activate(if(encArg(x_1297), encArg(x_273), encArg(x_373))) [0]
   encArg(cons_activate(cons_activate(x_1298))) -> activate(activate(encArg(x_1298))) [0]
   encArg(cons_activate(x_1)) -> activate(null_encArg) [0]
   encode_f(c) -> f(c) [0]
   encode_f(n__f(x_1299)) -> f(n__f(encArg(x_1299))) [0]
   encode_f(true) -> f(true) [0]
   encode_f(false) -> f(false) [0]
   encode_f(cons_f(x_1300)) -> f(f(encArg(x_1300))) [0]
   encode_f(cons_if(x_1301, x_274, x_374)) -> f(if(encArg(x_1301), encArg(x_274), encArg(x_374))) [0]
   encode_f(cons_activate(x_1302)) -> f(activate(encArg(x_1302))) [0]
   encode_f(x_1) -> f(null_encArg) [0]
   encode_if(x_1, x_2, x_3) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encode_c -> c [0]
   encode_n__f(x_1) -> n__f(encArg(x_1)) [0]
   encode_true -> true [0]
   encode_false -> false [0]
   encode_activate(c) -> activate(c) [0]
   encode_activate(n__f(x_1595)) -> activate(n__f(encArg(x_1595))) [0]
   encode_activate(true) -> activate(true) [0]
   encode_activate(false) -> activate(false) [0]
   encode_activate(cons_f(x_1596)) -> activate(f(encArg(x_1596))) [0]
   encode_activate(cons_if(x_1597, x_2148, x_3148)) -> activate(if(encArg(x_1597), encArg(x_2148), encArg(x_3148))) [0]
   encode_activate(cons_activate(x_1598)) -> activate(activate(encArg(x_1598))) [0]
   encode_activate(x_1) -> activate(null_encArg) [0]
   encArg(v0) -> null_encArg [0]
   encode_f(v0) -> null_encode_f [0]
   encode_if(v0, v1, v2) -> null_encode_if [0]
   encode_c -> null_encode_c [0]
   encode_n__f(v0) -> null_encode_n__f [0]
   encode_true -> null_encode_true [0]
   encode_false -> null_encode_false [0]
   encode_activate(v0) -> null_encode_activate [0]
   if(v0, v1, v2) -> null_if [0]

The TRS has the following type information:
f :: c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if -> c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if
if :: c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if -> c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if -> c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if -> c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if
c :: c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if
n__f :: c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if -> c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if
true :: c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if
false :: c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if
activate :: c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if -> c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if
encArg :: c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if -> c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if
cons_f :: c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if -> c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if
cons_if :: c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if -> c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if -> c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if -> c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if
cons_activate :: c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if -> c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if
encode_f :: c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if -> c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if
encode_if :: c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if -> c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if -> c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if -> c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if
encode_c :: c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if
encode_n__f :: c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if -> c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if
encode_true :: c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if
encode_false :: c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if
encode_activate :: c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if -> c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if
null_encArg :: c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if
null_encode_f :: c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if
null_encode_if :: c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if
null_encode_c :: c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if
null_encode_n__f :: c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if
null_encode_true :: c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if
null_encode_false :: c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if
null_encode_activate :: c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if
null_if :: c:true:n__f:false:cons_f:cons_if:cons_activate:null_encArg:null_encode_f:null_encode_if:null_encode_c:null_encode_n__f:null_encode_true:null_encode_false:null_encode_activate:null_if

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

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

   c => 0
   true => 2
   false => 1
   null_encArg => 0
   null_encode_f => 0
   null_encode_if => 0
   null_encode_c => 0
   null_encode_n__f => 0
   null_encode_true => 0
   null_encode_false => 0
   null_encode_activate => 0
   null_if => 0

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

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

   activate(z) -{ 1 }-> X :|: X >= 0, z = X
   activate(z) -{ 1 }-> f(X) :|: z = 1 + X, X >= 0
   encArg(z) -{ 0 }-> if(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> f(if(encArg(x_11), encArg(x_2'), encArg(x_3'))) :|: x_11 >= 0, x_3' >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2' + x_3')
   encArg(z) -{ 0 }-> f(f(encArg(x_1''))) :|: z = 1 + (1 + x_1''), x_1'' >= 0
   encArg(z) -{ 0 }-> f(activate(encArg(x_12))) :|: z = 1 + (1 + x_12), x_12 >= 0
   encArg(z) -{ 0 }-> f(2) :|: z = 1 + 2
   encArg(z) -{ 0 }-> f(1) :|: z = 1 + 1
   encArg(z) -{ 0 }-> f(0) :|: z = 1 + 0
   encArg(z) -{ 0 }-> f(0) :|: z = 1 + x_1, x_1 >= 0
   encArg(z) -{ 0 }-> f(1 + encArg(x_1')) :|: z = 1 + (1 + x_1'), x_1' >= 0
   encArg(z) -{ 0 }-> activate(if(encArg(x_1297), encArg(x_273), encArg(x_373))) :|: z = 1 + (1 + x_1297 + x_273 + x_373), x_373 >= 0, x_273 >= 0, x_1297 >= 0
   encArg(z) -{ 0 }-> activate(f(encArg(x_1296))) :|: z = 1 + (1 + x_1296), x_1296 >= 0
   encArg(z) -{ 0 }-> activate(activate(encArg(x_1298))) :|: z = 1 + (1 + x_1298), x_1298 >= 0
   encArg(z) -{ 0 }-> activate(2) :|: z = 1 + 2
   encArg(z) -{ 0 }-> activate(1) :|: z = 1 + 1
   encArg(z) -{ 0 }-> activate(0) :|: z = 1 + 0
   encArg(z) -{ 0 }-> activate(0) :|: z = 1 + x_1, x_1 >= 0
   encArg(z) -{ 0 }-> activate(1 + encArg(x_1295)) :|: x_1295 >= 0, z = 1 + (1 + x_1295)
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encArg(z) -{ 0 }-> 1 + encArg(x_1) :|: z = 1 + x_1, x_1 >= 0
   encode_activate(z) -{ 0 }-> activate(if(encArg(x_1597), encArg(x_2148), encArg(x_3148))) :|: z = 1 + x_1597 + x_2148 + x_3148, x_3148 >= 0, x_2148 >= 0, x_1597 >= 0
   encode_activate(z) -{ 0 }-> activate(f(encArg(x_1596))) :|: z = 1 + x_1596, x_1596 >= 0
   encode_activate(z) -{ 0 }-> activate(activate(encArg(x_1598))) :|: z = 1 + x_1598, x_1598 >= 0
   encode_activate(z) -{ 0 }-> activate(2) :|: z = 2
   encode_activate(z) -{ 0 }-> activate(1) :|: z = 1
   encode_activate(z) -{ 0 }-> activate(0) :|: z = 0
   encode_activate(z) -{ 0 }-> activate(0) :|: x_1 >= 0, z = x_1
   encode_activate(z) -{ 0 }-> activate(1 + encArg(x_1595)) :|: x_1595 >= 0, z = 1 + x_1595
   encode_activate(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z) -{ 0 }-> f(if(encArg(x_1301), encArg(x_274), encArg(x_374))) :|: x_374 >= 0, x_274 >= 0, z = 1 + x_1301 + x_274 + x_374, x_1301 >= 0
   encode_f(z) -{ 0 }-> f(f(encArg(x_1300))) :|: x_1300 >= 0, z = 1 + x_1300
   encode_f(z) -{ 0 }-> f(activate(encArg(x_1302))) :|: z = 1 + x_1302, x_1302 >= 0
   encode_f(z) -{ 0 }-> f(2) :|: z = 2
   encode_f(z) -{ 0 }-> f(1) :|: z = 1
   encode_f(z) -{ 0 }-> f(0) :|: z = 0
   encode_f(z) -{ 0 }-> f(0) :|: x_1 >= 0, z = x_1
   encode_f(z) -{ 0 }-> f(1 + encArg(x_1299)) :|: x_1299 >= 0, z = 1 + x_1299
   encode_f(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_if(z, z', z'') -{ 0 }-> if(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, x_3 >= 0, x_2 >= 0, z = x_1, z' = x_2, z'' = x_3
   encode_if(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   encode_n__f(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_n__f(z) -{ 0 }-> 1 + encArg(x_1) :|: x_1 >= 0, z = x_1
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   f(z) -{ 1 }-> if(X, 0, 1 + 2) :|: X >= 0, z = X
   f(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   if(z, z', z'') -{ 1 }-> X :|: z = 2, z' = X, Y >= 0, z'' = Y, X >= 0
   if(z, z', z'') -{ 1 }-> activate(Y) :|: z' = X, Y >= 0, z = 1, z'' = Y, X >= 0
   if(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0


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

(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) -{ 1 }-> f(z - 1) :|: z - 1 >= 0
   encArg(z) -{ 0 }-> if(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> f(if(encArg(x_11), encArg(x_2'), encArg(x_3'))) :|: x_11 >= 0, x_3' >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2' + x_3')
   encArg(z) -{ 0 }-> f(f(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(2) :|: z = 1 + 2
   encArg(z) -{ 0 }-> f(1) :|: z = 1 + 1
   encArg(z) -{ 0 }-> f(0) :|: z = 1 + 0
   encArg(z) -{ 0 }-> f(0) :|: z - 1 >= 0
   encArg(z) -{ 0 }-> f(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(if(encArg(x_1297), encArg(x_273), encArg(x_373))) :|: z = 1 + (1 + x_1297 + x_273 + x_373), x_373 >= 0, x_273 >= 0, x_1297 >= 0
   encArg(z) -{ 0 }-> activate(f(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(2) :|: z = 1 + 2
   encArg(z) -{ 0 }-> activate(1) :|: z = 1 + 1
   encArg(z) -{ 0 }-> activate(0) :|: z = 1 + 0
   encArg(z) -{ 0 }-> activate(0) :|: z - 1 >= 0
   encArg(z) -{ 0 }-> activate(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(if(encArg(x_1597), encArg(x_2148), encArg(x_3148))) :|: z = 1 + x_1597 + x_2148 + x_3148, x_3148 >= 0, x_2148 >= 0, x_1597 >= 0
   encode_activate(z) -{ 0 }-> activate(f(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(2) :|: z = 2
   encode_activate(z) -{ 0 }-> activate(1) :|: z = 1
   encode_activate(z) -{ 0 }-> activate(0) :|: z = 0
   encode_activate(z) -{ 0 }-> activate(0) :|: z >= 0
   encode_activate(z) -{ 0 }-> activate(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z) -{ 0 }-> f(if(encArg(x_1301), encArg(x_274), encArg(x_374))) :|: x_374 >= 0, x_274 >= 0, z = 1 + x_1301 + x_274 + x_374, x_1301 >= 0
   encode_f(z) -{ 0 }-> f(f(encArg(z - 1))) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> f(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> f(2) :|: z = 2
   encode_f(z) -{ 0 }-> f(1) :|: z = 1
   encode_f(z) -{ 0 }-> f(0) :|: z = 0
   encode_f(z) -{ 0 }-> f(0) :|: z >= 0
   encode_f(z) -{ 0 }-> f(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> 0 :|: z >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_if(z, z', z'') -{ 0 }-> if(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_n__f(z) -{ 0 }-> 0 :|: z >= 0
   encode_n__f(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   f(z) -{ 1 }-> if(z, 0, 1 + 2) :|: z >= 0
   f(z) -{ 1 }-> 1 + z :|: z >= 0
   if(z, z', z'') -{ 1 }-> z' :|: z = 2, z'' >= 0, z' >= 0
   if(z, z', z'') -{ 1 }-> activate(z'') :|: z'' >= 0, z = 1, z' >= 0
   if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0


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

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

   { encode_false }
   { encode_c }
   { encode_true }
   { f, if, activate }
   { encArg }
   { encode_activate }
   { encode_if }
   { encode_f }
   { encode_n__f }

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 1 }-> f(z - 1) :|: z - 1 >= 0
   encArg(z) -{ 0 }-> if(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> f(if(encArg(x_11), encArg(x_2'), encArg(x_3'))) :|: x_11 >= 0, x_3' >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2' + x_3')
   encArg(z) -{ 0 }-> f(f(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(2) :|: z = 1 + 2
   encArg(z) -{ 0 }-> f(1) :|: z = 1 + 1
   encArg(z) -{ 0 }-> f(0) :|: z = 1 + 0
   encArg(z) -{ 0 }-> f(0) :|: z - 1 >= 0
   encArg(z) -{ 0 }-> f(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(if(encArg(x_1297), encArg(x_273), encArg(x_373))) :|: z = 1 + (1 + x_1297 + x_273 + x_373), x_373 >= 0, x_273 >= 0, x_1297 >= 0
   encArg(z) -{ 0 }-> activate(f(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(2) :|: z = 1 + 2
   encArg(z) -{ 0 }-> activate(1) :|: z = 1 + 1
   encArg(z) -{ 0 }-> activate(0) :|: z = 1 + 0
   encArg(z) -{ 0 }-> activate(0) :|: z - 1 >= 0
   encArg(z) -{ 0 }-> activate(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(if(encArg(x_1597), encArg(x_2148), encArg(x_3148))) :|: z = 1 + x_1597 + x_2148 + x_3148, x_3148 >= 0, x_2148 >= 0, x_1597 >= 0
   encode_activate(z) -{ 0 }-> activate(f(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(2) :|: z = 2
   encode_activate(z) -{ 0 }-> activate(1) :|: z = 1
   encode_activate(z) -{ 0 }-> activate(0) :|: z = 0
   encode_activate(z) -{ 0 }-> activate(0) :|: z >= 0
   encode_activate(z) -{ 0 }-> activate(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z) -{ 0 }-> f(if(encArg(x_1301), encArg(x_274), encArg(x_374))) :|: x_374 >= 0, x_274 >= 0, z = 1 + x_1301 + x_274 + x_374, x_1301 >= 0
   encode_f(z) -{ 0 }-> f(f(encArg(z - 1))) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> f(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> f(2) :|: z = 2
   encode_f(z) -{ 0 }-> f(1) :|: z = 1
   encode_f(z) -{ 0 }-> f(0) :|: z = 0
   encode_f(z) -{ 0 }-> f(0) :|: z >= 0
   encode_f(z) -{ 0 }-> f(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> 0 :|: z >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_if(z, z', z'') -{ 0 }-> if(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_n__f(z) -{ 0 }-> 0 :|: z >= 0
   encode_n__f(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   f(z) -{ 1 }-> if(z, 0, 1 + 2) :|: z >= 0
   f(z) -{ 1 }-> 1 + z :|: z >= 0
   if(z, z', z'') -{ 1 }-> z' :|: z = 2, z'' >= 0, z' >= 0
   if(z, z', z'') -{ 1 }-> activate(z'') :|: z'' >= 0, z = 1, z' >= 0
   if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0

Function symbols to be analyzed: {encode_false}, {encode_c}, {encode_true}, {f,if,activate}, {encArg}, {encode_activate}, {encode_if}, {encode_f}, {encode_n__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) -{ 1 }-> f(z - 1) :|: z - 1 >= 0
   encArg(z) -{ 0 }-> if(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> f(if(encArg(x_11), encArg(x_2'), encArg(x_3'))) :|: x_11 >= 0, x_3' >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2' + x_3')
   encArg(z) -{ 0 }-> f(f(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(2) :|: z = 1 + 2
   encArg(z) -{ 0 }-> f(1) :|: z = 1 + 1
   encArg(z) -{ 0 }-> f(0) :|: z = 1 + 0
   encArg(z) -{ 0 }-> f(0) :|: z - 1 >= 0
   encArg(z) -{ 0 }-> f(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(if(encArg(x_1297), encArg(x_273), encArg(x_373))) :|: z = 1 + (1 + x_1297 + x_273 + x_373), x_373 >= 0, x_273 >= 0, x_1297 >= 0
   encArg(z) -{ 0 }-> activate(f(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(2) :|: z = 1 + 2
   encArg(z) -{ 0 }-> activate(1) :|: z = 1 + 1
   encArg(z) -{ 0 }-> activate(0) :|: z = 1 + 0
   encArg(z) -{ 0 }-> activate(0) :|: z - 1 >= 0
   encArg(z) -{ 0 }-> activate(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(if(encArg(x_1597), encArg(x_2148), encArg(x_3148))) :|: z = 1 + x_1597 + x_2148 + x_3148, x_3148 >= 0, x_2148 >= 0, x_1597 >= 0
   encode_activate(z) -{ 0 }-> activate(f(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(2) :|: z = 2
   encode_activate(z) -{ 0 }-> activate(1) :|: z = 1
   encode_activate(z) -{ 0 }-> activate(0) :|: z = 0
   encode_activate(z) -{ 0 }-> activate(0) :|: z >= 0
   encode_activate(z) -{ 0 }-> activate(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z) -{ 0 }-> f(if(encArg(x_1301), encArg(x_274), encArg(x_374))) :|: x_374 >= 0, x_274 >= 0, z = 1 + x_1301 + x_274 + x_374, x_1301 >= 0
   encode_f(z) -{ 0 }-> f(f(encArg(z - 1))) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> f(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> f(2) :|: z = 2
   encode_f(z) -{ 0 }-> f(1) :|: z = 1
   encode_f(z) -{ 0 }-> f(0) :|: z = 0
   encode_f(z) -{ 0 }-> f(0) :|: z >= 0
   encode_f(z) -{ 0 }-> f(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> 0 :|: z >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_if(z, z', z'') -{ 0 }-> if(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_n__f(z) -{ 0 }-> 0 :|: z >= 0
   encode_n__f(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   f(z) -{ 1 }-> if(z, 0, 1 + 2) :|: z >= 0
   f(z) -{ 1 }-> 1 + z :|: z >= 0
   if(z, z', z'') -{ 1 }-> z' :|: z = 2, z'' >= 0, z' >= 0
   if(z, z', z'') -{ 1 }-> activate(z'') :|: z'' >= 0, z = 1, z' >= 0
   if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0

Function symbols to be analyzed: {encode_false}, {encode_c}, {encode_true}, {f,if,activate}, {encArg}, {encode_activate}, {encode_if}, {encode_f}, {encode_n__f}

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

(23) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 1 }-> f(z - 1) :|: z - 1 >= 0
   encArg(z) -{ 0 }-> if(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> f(if(encArg(x_11), encArg(x_2'), encArg(x_3'))) :|: x_11 >= 0, x_3' >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2' + x_3')
   encArg(z) -{ 0 }-> f(f(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(2) :|: z = 1 + 2
   encArg(z) -{ 0 }-> f(1) :|: z = 1 + 1
   encArg(z) -{ 0 }-> f(0) :|: z = 1 + 0
   encArg(z) -{ 0 }-> f(0) :|: z - 1 >= 0
   encArg(z) -{ 0 }-> f(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(if(encArg(x_1297), encArg(x_273), encArg(x_373))) :|: z = 1 + (1 + x_1297 + x_273 + x_373), x_373 >= 0, x_273 >= 0, x_1297 >= 0
   encArg(z) -{ 0 }-> activate(f(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(2) :|: z = 1 + 2
   encArg(z) -{ 0 }-> activate(1) :|: z = 1 + 1
   encArg(z) -{ 0 }-> activate(0) :|: z = 1 + 0
   encArg(z) -{ 0 }-> activate(0) :|: z - 1 >= 0
   encArg(z) -{ 0 }-> activate(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(if(encArg(x_1597), encArg(x_2148), encArg(x_3148))) :|: z = 1 + x_1597 + x_2148 + x_3148, x_3148 >= 0, x_2148 >= 0, x_1597 >= 0
   encode_activate(z) -{ 0 }-> activate(f(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(2) :|: z = 2
   encode_activate(z) -{ 0 }-> activate(1) :|: z = 1
   encode_activate(z) -{ 0 }-> activate(0) :|: z = 0
   encode_activate(z) -{ 0 }-> activate(0) :|: z >= 0
   encode_activate(z) -{ 0 }-> activate(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z) -{ 0 }-> f(if(encArg(x_1301), encArg(x_274), encArg(x_374))) :|: x_374 >= 0, x_274 >= 0, z = 1 + x_1301 + x_274 + x_374, x_1301 >= 0
   encode_f(z) -{ 0 }-> f(f(encArg(z - 1))) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> f(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> f(2) :|: z = 2
   encode_f(z) -{ 0 }-> f(1) :|: z = 1
   encode_f(z) -{ 0 }-> f(0) :|: z = 0
   encode_f(z) -{ 0 }-> f(0) :|: z >= 0
   encode_f(z) -{ 0 }-> f(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> 0 :|: z >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_if(z, z', z'') -{ 0 }-> if(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_n__f(z) -{ 0 }-> 0 :|: z >= 0
   encode_n__f(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   f(z) -{ 1 }-> if(z, 0, 1 + 2) :|: z >= 0
   f(z) -{ 1 }-> 1 + z :|: z >= 0
   if(z, z', z'') -{ 1 }-> z' :|: z = 2, z'' >= 0, z' >= 0
   if(z, z', z'') -{ 1 }-> activate(z'') :|: z'' >= 0, z = 1, z' >= 0
   if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0

Function symbols to be analyzed: {encode_false}, {encode_c}, {encode_true}, {f,if,activate}, {encArg}, {encode_activate}, {encode_if}, {encode_f}, {encode_n__f}
Previous analysis results are:
  encode_false: runtime: ?, size: O(1) [1]

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

(25) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: encode_false
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) -{ 1 }-> f(z - 1) :|: z - 1 >= 0
   encArg(z) -{ 0 }-> if(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> f(if(encArg(x_11), encArg(x_2'), encArg(x_3'))) :|: x_11 >= 0, x_3' >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2' + x_3')
   encArg(z) -{ 0 }-> f(f(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(2) :|: z = 1 + 2
   encArg(z) -{ 0 }-> f(1) :|: z = 1 + 1
   encArg(z) -{ 0 }-> f(0) :|: z = 1 + 0
   encArg(z) -{ 0 }-> f(0) :|: z - 1 >= 0
   encArg(z) -{ 0 }-> f(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(if(encArg(x_1297), encArg(x_273), encArg(x_373))) :|: z = 1 + (1 + x_1297 + x_273 + x_373), x_373 >= 0, x_273 >= 0, x_1297 >= 0
   encArg(z) -{ 0 }-> activate(f(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(2) :|: z = 1 + 2
   encArg(z) -{ 0 }-> activate(1) :|: z = 1 + 1
   encArg(z) -{ 0 }-> activate(0) :|: z = 1 + 0
   encArg(z) -{ 0 }-> activate(0) :|: z - 1 >= 0
   encArg(z) -{ 0 }-> activate(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(if(encArg(x_1597), encArg(x_2148), encArg(x_3148))) :|: z = 1 + x_1597 + x_2148 + x_3148, x_3148 >= 0, x_2148 >= 0, x_1597 >= 0
   encode_activate(z) -{ 0 }-> activate(f(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(2) :|: z = 2
   encode_activate(z) -{ 0 }-> activate(1) :|: z = 1
   encode_activate(z) -{ 0 }-> activate(0) :|: z = 0
   encode_activate(z) -{ 0 }-> activate(0) :|: z >= 0
   encode_activate(z) -{ 0 }-> activate(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z) -{ 0 }-> f(if(encArg(x_1301), encArg(x_274), encArg(x_374))) :|: x_374 >= 0, x_274 >= 0, z = 1 + x_1301 + x_274 + x_374, x_1301 >= 0
   encode_f(z) -{ 0 }-> f(f(encArg(z - 1))) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> f(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> f(2) :|: z = 2
   encode_f(z) -{ 0 }-> f(1) :|: z = 1
   encode_f(z) -{ 0 }-> f(0) :|: z = 0
   encode_f(z) -{ 0 }-> f(0) :|: z >= 0
   encode_f(z) -{ 0 }-> f(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> 0 :|: z >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_if(z, z', z'') -{ 0 }-> if(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_n__f(z) -{ 0 }-> 0 :|: z >= 0
   encode_n__f(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   f(z) -{ 1 }-> if(z, 0, 1 + 2) :|: z >= 0
   f(z) -{ 1 }-> 1 + z :|: z >= 0
   if(z, z', z'') -{ 1 }-> z' :|: z = 2, z'' >= 0, z' >= 0
   if(z, z', z'') -{ 1 }-> activate(z'') :|: z'' >= 0, z = 1, z' >= 0
   if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0

Function symbols to be analyzed: {encode_c}, {encode_true}, {f,if,activate}, {encArg}, {encode_activate}, {encode_if}, {encode_f}, {encode_n__f}
Previous analysis results are:
  encode_false: runtime: O(1) [0], size: O(1) [1]

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

(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) -{ 1 }-> f(z - 1) :|: z - 1 >= 0
   encArg(z) -{ 0 }-> if(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> f(if(encArg(x_11), encArg(x_2'), encArg(x_3'))) :|: x_11 >= 0, x_3' >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2' + x_3')
   encArg(z) -{ 0 }-> f(f(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(2) :|: z = 1 + 2
   encArg(z) -{ 0 }-> f(1) :|: z = 1 + 1
   encArg(z) -{ 0 }-> f(0) :|: z = 1 + 0
   encArg(z) -{ 0 }-> f(0) :|: z - 1 >= 0
   encArg(z) -{ 0 }-> f(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(if(encArg(x_1297), encArg(x_273), encArg(x_373))) :|: z = 1 + (1 + x_1297 + x_273 + x_373), x_373 >= 0, x_273 >= 0, x_1297 >= 0
   encArg(z) -{ 0 }-> activate(f(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(2) :|: z = 1 + 2
   encArg(z) -{ 0 }-> activate(1) :|: z = 1 + 1
   encArg(z) -{ 0 }-> activate(0) :|: z = 1 + 0
   encArg(z) -{ 0 }-> activate(0) :|: z - 1 >= 0
   encArg(z) -{ 0 }-> activate(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(if(encArg(x_1597), encArg(x_2148), encArg(x_3148))) :|: z = 1 + x_1597 + x_2148 + x_3148, x_3148 >= 0, x_2148 >= 0, x_1597 >= 0
   encode_activate(z) -{ 0 }-> activate(f(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(2) :|: z = 2
   encode_activate(z) -{ 0 }-> activate(1) :|: z = 1
   encode_activate(z) -{ 0 }-> activate(0) :|: z = 0
   encode_activate(z) -{ 0 }-> activate(0) :|: z >= 0
   encode_activate(z) -{ 0 }-> activate(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z) -{ 0 }-> f(if(encArg(x_1301), encArg(x_274), encArg(x_374))) :|: x_374 >= 0, x_274 >= 0, z = 1 + x_1301 + x_274 + x_374, x_1301 >= 0
   encode_f(z) -{ 0 }-> f(f(encArg(z - 1))) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> f(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> f(2) :|: z = 2
   encode_f(z) -{ 0 }-> f(1) :|: z = 1
   encode_f(z) -{ 0 }-> f(0) :|: z = 0
   encode_f(z) -{ 0 }-> f(0) :|: z >= 0
   encode_f(z) -{ 0 }-> f(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> 0 :|: z >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_if(z, z', z'') -{ 0 }-> if(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_n__f(z) -{ 0 }-> 0 :|: z >= 0
   encode_n__f(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   f(z) -{ 1 }-> if(z, 0, 1 + 2) :|: z >= 0
   f(z) -{ 1 }-> 1 + z :|: z >= 0
   if(z, z', z'') -{ 1 }-> z' :|: z = 2, z'' >= 0, z' >= 0
   if(z, z', z'') -{ 1 }-> activate(z'') :|: z'' >= 0, z = 1, z' >= 0
   if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0

Function symbols to be analyzed: {encode_c}, {encode_true}, {f,if,activate}, {encArg}, {encode_activate}, {encode_if}, {encode_f}, {encode_n__f}
Previous analysis results are:
  encode_false: runtime: O(1) [0], size: O(1) [1]

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

(29) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 1 }-> f(z - 1) :|: z - 1 >= 0
   encArg(z) -{ 0 }-> if(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> f(if(encArg(x_11), encArg(x_2'), encArg(x_3'))) :|: x_11 >= 0, x_3' >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2' + x_3')
   encArg(z) -{ 0 }-> f(f(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(2) :|: z = 1 + 2
   encArg(z) -{ 0 }-> f(1) :|: z = 1 + 1
   encArg(z) -{ 0 }-> f(0) :|: z = 1 + 0
   encArg(z) -{ 0 }-> f(0) :|: z - 1 >= 0
   encArg(z) -{ 0 }-> f(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(if(encArg(x_1297), encArg(x_273), encArg(x_373))) :|: z = 1 + (1 + x_1297 + x_273 + x_373), x_373 >= 0, x_273 >= 0, x_1297 >= 0
   encArg(z) -{ 0 }-> activate(f(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(2) :|: z = 1 + 2
   encArg(z) -{ 0 }-> activate(1) :|: z = 1 + 1
   encArg(z) -{ 0 }-> activate(0) :|: z = 1 + 0
   encArg(z) -{ 0 }-> activate(0) :|: z - 1 >= 0
   encArg(z) -{ 0 }-> activate(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(if(encArg(x_1597), encArg(x_2148), encArg(x_3148))) :|: z = 1 + x_1597 + x_2148 + x_3148, x_3148 >= 0, x_2148 >= 0, x_1597 >= 0
   encode_activate(z) -{ 0 }-> activate(f(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(2) :|: z = 2
   encode_activate(z) -{ 0 }-> activate(1) :|: z = 1
   encode_activate(z) -{ 0 }-> activate(0) :|: z = 0
   encode_activate(z) -{ 0 }-> activate(0) :|: z >= 0
   encode_activate(z) -{ 0 }-> activate(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z) -{ 0 }-> f(if(encArg(x_1301), encArg(x_274), encArg(x_374))) :|: x_374 >= 0, x_274 >= 0, z = 1 + x_1301 + x_274 + x_374, x_1301 >= 0
   encode_f(z) -{ 0 }-> f(f(encArg(z - 1))) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> f(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> f(2) :|: z = 2
   encode_f(z) -{ 0 }-> f(1) :|: z = 1
   encode_f(z) -{ 0 }-> f(0) :|: z = 0
   encode_f(z) -{ 0 }-> f(0) :|: z >= 0
   encode_f(z) -{ 0 }-> f(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> 0 :|: z >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_if(z, z', z'') -{ 0 }-> if(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_n__f(z) -{ 0 }-> 0 :|: z >= 0
   encode_n__f(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   f(z) -{ 1 }-> if(z, 0, 1 + 2) :|: z >= 0
   f(z) -{ 1 }-> 1 + z :|: z >= 0
   if(z, z', z'') -{ 1 }-> z' :|: z = 2, z'' >= 0, z' >= 0
   if(z, z', z'') -{ 1 }-> activate(z'') :|: z'' >= 0, z = 1, z' >= 0
   if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0

Function symbols to be analyzed: {encode_c}, {encode_true}, {f,if,activate}, {encArg}, {encode_activate}, {encode_if}, {encode_f}, {encode_n__f}
Previous analysis results are:
  encode_false: runtime: O(1) [0], size: O(1) [1]
  encode_c: runtime: ?, size: O(1) [0]

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

(31) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 1 }-> f(z - 1) :|: z - 1 >= 0
   encArg(z) -{ 0 }-> if(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> f(if(encArg(x_11), encArg(x_2'), encArg(x_3'))) :|: x_11 >= 0, x_3' >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2' + x_3')
   encArg(z) -{ 0 }-> f(f(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(2) :|: z = 1 + 2
   encArg(z) -{ 0 }-> f(1) :|: z = 1 + 1
   encArg(z) -{ 0 }-> f(0) :|: z = 1 + 0
   encArg(z) -{ 0 }-> f(0) :|: z - 1 >= 0
   encArg(z) -{ 0 }-> f(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(if(encArg(x_1297), encArg(x_273), encArg(x_373))) :|: z = 1 + (1 + x_1297 + x_273 + x_373), x_373 >= 0, x_273 >= 0, x_1297 >= 0
   encArg(z) -{ 0 }-> activate(f(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(2) :|: z = 1 + 2
   encArg(z) -{ 0 }-> activate(1) :|: z = 1 + 1
   encArg(z) -{ 0 }-> activate(0) :|: z = 1 + 0
   encArg(z) -{ 0 }-> activate(0) :|: z - 1 >= 0
   encArg(z) -{ 0 }-> activate(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(if(encArg(x_1597), encArg(x_2148), encArg(x_3148))) :|: z = 1 + x_1597 + x_2148 + x_3148, x_3148 >= 0, x_2148 >= 0, x_1597 >= 0
   encode_activate(z) -{ 0 }-> activate(f(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(2) :|: z = 2
   encode_activate(z) -{ 0 }-> activate(1) :|: z = 1
   encode_activate(z) -{ 0 }-> activate(0) :|: z = 0
   encode_activate(z) -{ 0 }-> activate(0) :|: z >= 0
   encode_activate(z) -{ 0 }-> activate(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z) -{ 0 }-> f(if(encArg(x_1301), encArg(x_274), encArg(x_374))) :|: x_374 >= 0, x_274 >= 0, z = 1 + x_1301 + x_274 + x_374, x_1301 >= 0
   encode_f(z) -{ 0 }-> f(f(encArg(z - 1))) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> f(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> f(2) :|: z = 2
   encode_f(z) -{ 0 }-> f(1) :|: z = 1
   encode_f(z) -{ 0 }-> f(0) :|: z = 0
   encode_f(z) -{ 0 }-> f(0) :|: z >= 0
   encode_f(z) -{ 0 }-> f(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> 0 :|: z >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_if(z, z', z'') -{ 0 }-> if(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_n__f(z) -{ 0 }-> 0 :|: z >= 0
   encode_n__f(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   f(z) -{ 1 }-> if(z, 0, 1 + 2) :|: z >= 0
   f(z) -{ 1 }-> 1 + z :|: z >= 0
   if(z, z', z'') -{ 1 }-> z' :|: z = 2, z'' >= 0, z' >= 0
   if(z, z', z'') -{ 1 }-> activate(z'') :|: z'' >= 0, z = 1, z' >= 0
   if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0

Function symbols to be analyzed: {encode_true}, {f,if,activate}, {encArg}, {encode_activate}, {encode_if}, {encode_f}, {encode_n__f}
Previous analysis results are:
  encode_false: runtime: O(1) [0], size: O(1) [1]
  encode_c: runtime: O(1) [0], 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) -{ 1 }-> f(z - 1) :|: z - 1 >= 0
   encArg(z) -{ 0 }-> if(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> f(if(encArg(x_11), encArg(x_2'), encArg(x_3'))) :|: x_11 >= 0, x_3' >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2' + x_3')
   encArg(z) -{ 0 }-> f(f(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(2) :|: z = 1 + 2
   encArg(z) -{ 0 }-> f(1) :|: z = 1 + 1
   encArg(z) -{ 0 }-> f(0) :|: z = 1 + 0
   encArg(z) -{ 0 }-> f(0) :|: z - 1 >= 0
   encArg(z) -{ 0 }-> f(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(if(encArg(x_1297), encArg(x_273), encArg(x_373))) :|: z = 1 + (1 + x_1297 + x_273 + x_373), x_373 >= 0, x_273 >= 0, x_1297 >= 0
   encArg(z) -{ 0 }-> activate(f(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(2) :|: z = 1 + 2
   encArg(z) -{ 0 }-> activate(1) :|: z = 1 + 1
   encArg(z) -{ 0 }-> activate(0) :|: z = 1 + 0
   encArg(z) -{ 0 }-> activate(0) :|: z - 1 >= 0
   encArg(z) -{ 0 }-> activate(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(if(encArg(x_1597), encArg(x_2148), encArg(x_3148))) :|: z = 1 + x_1597 + x_2148 + x_3148, x_3148 >= 0, x_2148 >= 0, x_1597 >= 0
   encode_activate(z) -{ 0 }-> activate(f(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(2) :|: z = 2
   encode_activate(z) -{ 0 }-> activate(1) :|: z = 1
   encode_activate(z) -{ 0 }-> activate(0) :|: z = 0
   encode_activate(z) -{ 0 }-> activate(0) :|: z >= 0
   encode_activate(z) -{ 0 }-> activate(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z) -{ 0 }-> f(if(encArg(x_1301), encArg(x_274), encArg(x_374))) :|: x_374 >= 0, x_274 >= 0, z = 1 + x_1301 + x_274 + x_374, x_1301 >= 0
   encode_f(z) -{ 0 }-> f(f(encArg(z - 1))) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> f(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> f(2) :|: z = 2
   encode_f(z) -{ 0 }-> f(1) :|: z = 1
   encode_f(z) -{ 0 }-> f(0) :|: z = 0
   encode_f(z) -{ 0 }-> f(0) :|: z >= 0
   encode_f(z) -{ 0 }-> f(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> 0 :|: z >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_if(z, z', z'') -{ 0 }-> if(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_n__f(z) -{ 0 }-> 0 :|: z >= 0
   encode_n__f(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   f(z) -{ 1 }-> if(z, 0, 1 + 2) :|: z >= 0
   f(z) -{ 1 }-> 1 + z :|: z >= 0
   if(z, z', z'') -{ 1 }-> z' :|: z = 2, z'' >= 0, z' >= 0
   if(z, z', z'') -{ 1 }-> activate(z'') :|: z'' >= 0, z = 1, z' >= 0
   if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0

Function symbols to be analyzed: {encode_true}, {f,if,activate}, {encArg}, {encode_activate}, {encode_if}, {encode_f}, {encode_n__f}
Previous analysis results are:
  encode_false: runtime: O(1) [0], size: O(1) [1]
  encode_c: runtime: O(1) [0], size: O(1) [0]

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

(35) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: encode_true
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) -{ 1 }-> f(z - 1) :|: z - 1 >= 0
   encArg(z) -{ 0 }-> if(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> f(if(encArg(x_11), encArg(x_2'), encArg(x_3'))) :|: x_11 >= 0, x_3' >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2' + x_3')
   encArg(z) -{ 0 }-> f(f(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(2) :|: z = 1 + 2
   encArg(z) -{ 0 }-> f(1) :|: z = 1 + 1
   encArg(z) -{ 0 }-> f(0) :|: z = 1 + 0
   encArg(z) -{ 0 }-> f(0) :|: z - 1 >= 0
   encArg(z) -{ 0 }-> f(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(if(encArg(x_1297), encArg(x_273), encArg(x_373))) :|: z = 1 + (1 + x_1297 + x_273 + x_373), x_373 >= 0, x_273 >= 0, x_1297 >= 0
   encArg(z) -{ 0 }-> activate(f(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(2) :|: z = 1 + 2
   encArg(z) -{ 0 }-> activate(1) :|: z = 1 + 1
   encArg(z) -{ 0 }-> activate(0) :|: z = 1 + 0
   encArg(z) -{ 0 }-> activate(0) :|: z - 1 >= 0
   encArg(z) -{ 0 }-> activate(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(if(encArg(x_1597), encArg(x_2148), encArg(x_3148))) :|: z = 1 + x_1597 + x_2148 + x_3148, x_3148 >= 0, x_2148 >= 0, x_1597 >= 0
   encode_activate(z) -{ 0 }-> activate(f(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(2) :|: z = 2
   encode_activate(z) -{ 0 }-> activate(1) :|: z = 1
   encode_activate(z) -{ 0 }-> activate(0) :|: z = 0
   encode_activate(z) -{ 0 }-> activate(0) :|: z >= 0
   encode_activate(z) -{ 0 }-> activate(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z) -{ 0 }-> f(if(encArg(x_1301), encArg(x_274), encArg(x_374))) :|: x_374 >= 0, x_274 >= 0, z = 1 + x_1301 + x_274 + x_374, x_1301 >= 0
   encode_f(z) -{ 0 }-> f(f(encArg(z - 1))) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> f(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> f(2) :|: z = 2
   encode_f(z) -{ 0 }-> f(1) :|: z = 1
   encode_f(z) -{ 0 }-> f(0) :|: z = 0
   encode_f(z) -{ 0 }-> f(0) :|: z >= 0
   encode_f(z) -{ 0 }-> f(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> 0 :|: z >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_if(z, z', z'') -{ 0 }-> if(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_n__f(z) -{ 0 }-> 0 :|: z >= 0
   encode_n__f(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   f(z) -{ 1 }-> if(z, 0, 1 + 2) :|: z >= 0
   f(z) -{ 1 }-> 1 + z :|: z >= 0
   if(z, z', z'') -{ 1 }-> z' :|: z = 2, z'' >= 0, z' >= 0
   if(z, z', z'') -{ 1 }-> activate(z'') :|: z'' >= 0, z = 1, z' >= 0
   if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0

Function symbols to be analyzed: {encode_true}, {f,if,activate}, {encArg}, {encode_activate}, {encode_if}, {encode_f}, {encode_n__f}
Previous analysis results are:
  encode_false: runtime: O(1) [0], size: O(1) [1]
  encode_c: runtime: O(1) [0], size: O(1) [0]
  encode_true: runtime: ?, size: O(1) [2]

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

(37) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 1 }-> f(z - 1) :|: z - 1 >= 0
   encArg(z) -{ 0 }-> if(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> f(if(encArg(x_11), encArg(x_2'), encArg(x_3'))) :|: x_11 >= 0, x_3' >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2' + x_3')
   encArg(z) -{ 0 }-> f(f(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(2) :|: z = 1 + 2
   encArg(z) -{ 0 }-> f(1) :|: z = 1 + 1
   encArg(z) -{ 0 }-> f(0) :|: z = 1 + 0
   encArg(z) -{ 0 }-> f(0) :|: z - 1 >= 0
   encArg(z) -{ 0 }-> f(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(if(encArg(x_1297), encArg(x_273), encArg(x_373))) :|: z = 1 + (1 + x_1297 + x_273 + x_373), x_373 >= 0, x_273 >= 0, x_1297 >= 0
   encArg(z) -{ 0 }-> activate(f(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(2) :|: z = 1 + 2
   encArg(z) -{ 0 }-> activate(1) :|: z = 1 + 1
   encArg(z) -{ 0 }-> activate(0) :|: z = 1 + 0
   encArg(z) -{ 0 }-> activate(0) :|: z - 1 >= 0
   encArg(z) -{ 0 }-> activate(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(if(encArg(x_1597), encArg(x_2148), encArg(x_3148))) :|: z = 1 + x_1597 + x_2148 + x_3148, x_3148 >= 0, x_2148 >= 0, x_1597 >= 0
   encode_activate(z) -{ 0 }-> activate(f(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(2) :|: z = 2
   encode_activate(z) -{ 0 }-> activate(1) :|: z = 1
   encode_activate(z) -{ 0 }-> activate(0) :|: z = 0
   encode_activate(z) -{ 0 }-> activate(0) :|: z >= 0
   encode_activate(z) -{ 0 }-> activate(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z) -{ 0 }-> f(if(encArg(x_1301), encArg(x_274), encArg(x_374))) :|: x_374 >= 0, x_274 >= 0, z = 1 + x_1301 + x_274 + x_374, x_1301 >= 0
   encode_f(z) -{ 0 }-> f(f(encArg(z - 1))) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> f(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> f(2) :|: z = 2
   encode_f(z) -{ 0 }-> f(1) :|: z = 1
   encode_f(z) -{ 0 }-> f(0) :|: z = 0
   encode_f(z) -{ 0 }-> f(0) :|: z >= 0
   encode_f(z) -{ 0 }-> f(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> 0 :|: z >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_if(z, z', z'') -{ 0 }-> if(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_n__f(z) -{ 0 }-> 0 :|: z >= 0
   encode_n__f(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   f(z) -{ 1 }-> if(z, 0, 1 + 2) :|: z >= 0
   f(z) -{ 1 }-> 1 + z :|: z >= 0
   if(z, z', z'') -{ 1 }-> z' :|: z = 2, z'' >= 0, z' >= 0
   if(z, z', z'') -{ 1 }-> activate(z'') :|: z'' >= 0, z = 1, z' >= 0
   if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0

Function symbols to be analyzed: {f,if,activate}, {encArg}, {encode_activate}, {encode_if}, {encode_f}, {encode_n__f}
Previous analysis results are:
  encode_false: runtime: O(1) [0], size: O(1) [1]
  encode_c: runtime: O(1) [0], size: O(1) [0]
  encode_true: runtime: O(1) [0], 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) -{ 1 }-> f(z - 1) :|: z - 1 >= 0
   encArg(z) -{ 0 }-> if(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> f(if(encArg(x_11), encArg(x_2'), encArg(x_3'))) :|: x_11 >= 0, x_3' >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2' + x_3')
   encArg(z) -{ 0 }-> f(f(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(2) :|: z = 1 + 2
   encArg(z) -{ 0 }-> f(1) :|: z = 1 + 1
   encArg(z) -{ 0 }-> f(0) :|: z = 1 + 0
   encArg(z) -{ 0 }-> f(0) :|: z - 1 >= 0
   encArg(z) -{ 0 }-> f(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(if(encArg(x_1297), encArg(x_273), encArg(x_373))) :|: z = 1 + (1 + x_1297 + x_273 + x_373), x_373 >= 0, x_273 >= 0, x_1297 >= 0
   encArg(z) -{ 0 }-> activate(f(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(2) :|: z = 1 + 2
   encArg(z) -{ 0 }-> activate(1) :|: z = 1 + 1
   encArg(z) -{ 0 }-> activate(0) :|: z = 1 + 0
   encArg(z) -{ 0 }-> activate(0) :|: z - 1 >= 0
   encArg(z) -{ 0 }-> activate(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(if(encArg(x_1597), encArg(x_2148), encArg(x_3148))) :|: z = 1 + x_1597 + x_2148 + x_3148, x_3148 >= 0, x_2148 >= 0, x_1597 >= 0
   encode_activate(z) -{ 0 }-> activate(f(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(2) :|: z = 2
   encode_activate(z) -{ 0 }-> activate(1) :|: z = 1
   encode_activate(z) -{ 0 }-> activate(0) :|: z = 0
   encode_activate(z) -{ 0 }-> activate(0) :|: z >= 0
   encode_activate(z) -{ 0 }-> activate(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z) -{ 0 }-> f(if(encArg(x_1301), encArg(x_274), encArg(x_374))) :|: x_374 >= 0, x_274 >= 0, z = 1 + x_1301 + x_274 + x_374, x_1301 >= 0
   encode_f(z) -{ 0 }-> f(f(encArg(z - 1))) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> f(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> f(2) :|: z = 2
   encode_f(z) -{ 0 }-> f(1) :|: z = 1
   encode_f(z) -{ 0 }-> f(0) :|: z = 0
   encode_f(z) -{ 0 }-> f(0) :|: z >= 0
   encode_f(z) -{ 0 }-> f(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> 0 :|: z >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_if(z, z', z'') -{ 0 }-> if(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_n__f(z) -{ 0 }-> 0 :|: z >= 0
   encode_n__f(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   f(z) -{ 1 }-> if(z, 0, 1 + 2) :|: z >= 0
   f(z) -{ 1 }-> 1 + z :|: z >= 0
   if(z, z', z'') -{ 1 }-> z' :|: z = 2, z'' >= 0, z' >= 0
   if(z, z', z'') -{ 1 }-> activate(z'') :|: z'' >= 0, z = 1, z' >= 0
   if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0

Function symbols to be analyzed: {f,if,activate}, {encArg}, {encode_activate}, {encode_if}, {encode_f}, {encode_n__f}
Previous analysis results are:
  encode_false: runtime: O(1) [0], size: O(1) [1]
  encode_c: runtime: O(1) [0], size: O(1) [0]
  encode_true: runtime: O(1) [0], size: O(1) [2]

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

(41) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: f
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 3 + z

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

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

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 1 }-> f(z - 1) :|: z - 1 >= 0
   encArg(z) -{ 0 }-> if(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> f(if(encArg(x_11), encArg(x_2'), encArg(x_3'))) :|: x_11 >= 0, x_3' >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2' + x_3')
   encArg(z) -{ 0 }-> f(f(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(2) :|: z = 1 + 2
   encArg(z) -{ 0 }-> f(1) :|: z = 1 + 1
   encArg(z) -{ 0 }-> f(0) :|: z = 1 + 0
   encArg(z) -{ 0 }-> f(0) :|: z - 1 >= 0
   encArg(z) -{ 0 }-> f(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(if(encArg(x_1297), encArg(x_273), encArg(x_373))) :|: z = 1 + (1 + x_1297 + x_273 + x_373), x_373 >= 0, x_273 >= 0, x_1297 >= 0
   encArg(z) -{ 0 }-> activate(f(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(2) :|: z = 1 + 2
   encArg(z) -{ 0 }-> activate(1) :|: z = 1 + 1
   encArg(z) -{ 0 }-> activate(0) :|: z = 1 + 0
   encArg(z) -{ 0 }-> activate(0) :|: z - 1 >= 0
   encArg(z) -{ 0 }-> activate(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(if(encArg(x_1597), encArg(x_2148), encArg(x_3148))) :|: z = 1 + x_1597 + x_2148 + x_3148, x_3148 >= 0, x_2148 >= 0, x_1597 >= 0
   encode_activate(z) -{ 0 }-> activate(f(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(2) :|: z = 2
   encode_activate(z) -{ 0 }-> activate(1) :|: z = 1
   encode_activate(z) -{ 0 }-> activate(0) :|: z = 0
   encode_activate(z) -{ 0 }-> activate(0) :|: z >= 0
   encode_activate(z) -{ 0 }-> activate(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z) -{ 0 }-> f(if(encArg(x_1301), encArg(x_274), encArg(x_374))) :|: x_374 >= 0, x_274 >= 0, z = 1 + x_1301 + x_274 + x_374, x_1301 >= 0
   encode_f(z) -{ 0 }-> f(f(encArg(z - 1))) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> f(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> f(2) :|: z = 2
   encode_f(z) -{ 0 }-> f(1) :|: z = 1
   encode_f(z) -{ 0 }-> f(0) :|: z = 0
   encode_f(z) -{ 0 }-> f(0) :|: z >= 0
   encode_f(z) -{ 0 }-> f(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> 0 :|: z >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_if(z, z', z'') -{ 0 }-> if(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_n__f(z) -{ 0 }-> 0 :|: z >= 0
   encode_n__f(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   f(z) -{ 1 }-> if(z, 0, 1 + 2) :|: z >= 0
   f(z) -{ 1 }-> 1 + z :|: z >= 0
   if(z, z', z'') -{ 1 }-> z' :|: z = 2, z'' >= 0, z' >= 0
   if(z, z', z'') -{ 1 }-> activate(z'') :|: z'' >= 0, z = 1, z' >= 0
   if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0

Function symbols to be analyzed: {f,if,activate}, {encArg}, {encode_activate}, {encode_if}, {encode_f}, {encode_n__f}
Previous analysis results are:
  encode_false: runtime: O(1) [0], size: O(1) [1]
  encode_c: runtime: O(1) [0], size: O(1) [0]
  encode_true: runtime: O(1) [0], size: O(1) [2]
  f: runtime: ?, size: O(n^1) [3 + z]
  if: runtime: ?, size: O(n^1) [2 + z' + z'']
  activate: runtime: ?, size: O(n^1) [2 + z]

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

(43) 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: 5

Computed RUNTIME bound using CoFloCo for: if
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 7

Computed RUNTIME bound using CoFloCo for: activate
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 6

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 1 }-> f(z - 1) :|: z - 1 >= 0
   encArg(z) -{ 0 }-> if(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> f(if(encArg(x_11), encArg(x_2'), encArg(x_3'))) :|: x_11 >= 0, x_3' >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2' + x_3')
   encArg(z) -{ 0 }-> f(f(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(2) :|: z = 1 + 2
   encArg(z) -{ 0 }-> f(1) :|: z = 1 + 1
   encArg(z) -{ 0 }-> f(0) :|: z = 1 + 0
   encArg(z) -{ 0 }-> f(0) :|: z - 1 >= 0
   encArg(z) -{ 0 }-> f(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(if(encArg(x_1297), encArg(x_273), encArg(x_373))) :|: z = 1 + (1 + x_1297 + x_273 + x_373), x_373 >= 0, x_273 >= 0, x_1297 >= 0
   encArg(z) -{ 0 }-> activate(f(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(2) :|: z = 1 + 2
   encArg(z) -{ 0 }-> activate(1) :|: z = 1 + 1
   encArg(z) -{ 0 }-> activate(0) :|: z = 1 + 0
   encArg(z) -{ 0 }-> activate(0) :|: z - 1 >= 0
   encArg(z) -{ 0 }-> activate(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(if(encArg(x_1597), encArg(x_2148), encArg(x_3148))) :|: z = 1 + x_1597 + x_2148 + x_3148, x_3148 >= 0, x_2148 >= 0, x_1597 >= 0
   encode_activate(z) -{ 0 }-> activate(f(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(2) :|: z = 2
   encode_activate(z) -{ 0 }-> activate(1) :|: z = 1
   encode_activate(z) -{ 0 }-> activate(0) :|: z = 0
   encode_activate(z) -{ 0 }-> activate(0) :|: z >= 0
   encode_activate(z) -{ 0 }-> activate(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z) -{ 0 }-> f(if(encArg(x_1301), encArg(x_274), encArg(x_374))) :|: x_374 >= 0, x_274 >= 0, z = 1 + x_1301 + x_274 + x_374, x_1301 >= 0
   encode_f(z) -{ 0 }-> f(f(encArg(z - 1))) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> f(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> f(2) :|: z = 2
   encode_f(z) -{ 0 }-> f(1) :|: z = 1
   encode_f(z) -{ 0 }-> f(0) :|: z = 0
   encode_f(z) -{ 0 }-> f(0) :|: z >= 0
   encode_f(z) -{ 0 }-> f(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> 0 :|: z >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_if(z, z', z'') -{ 0 }-> if(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_n__f(z) -{ 0 }-> 0 :|: z >= 0
   encode_n__f(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   f(z) -{ 1 }-> if(z, 0, 1 + 2) :|: z >= 0
   f(z) -{ 1 }-> 1 + z :|: z >= 0
   if(z, z', z'') -{ 1 }-> z' :|: z = 2, z'' >= 0, z' >= 0
   if(z, z', z'') -{ 1 }-> activate(z'') :|: z'' >= 0, z = 1, z' >= 0
   if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0

Function symbols to be analyzed: {encArg}, {encode_activate}, {encode_if}, {encode_f}, {encode_n__f}
Previous analysis results are:
  encode_false: runtime: O(1) [0], size: O(1) [1]
  encode_c: runtime: O(1) [0], size: O(1) [0]
  encode_true: runtime: O(1) [0], size: O(1) [2]
  f: runtime: O(1) [5], size: O(n^1) [3 + z]
  if: runtime: O(1) [7], size: O(n^1) [2 + z' + z'']
  activate: runtime: O(1) [6], size: O(n^1) [2 + 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) -{ 6 }-> s'' :|: s'' >= 0, s'' <= z - 1 + 3, z - 1 >= 0
   activate(z) -{ 1 }-> z :|: z >= 0
   encArg(z) -{ 5 }-> s1 :|: s1 >= 0, s1 <= 0 + 3, z = 1 + 0
   encArg(z) -{ 5 }-> s2 :|: s2 >= 0, s2 <= 2 + 3, z = 1 + 2
   encArg(z) -{ 5 }-> s3 :|: s3 >= 0, s3 <= 1 + 3, z = 1 + 1
   encArg(z) -{ 5 }-> s4 :|: s4 >= 0, s4 <= 0 + 3, z - 1 >= 0
   encArg(z) -{ 6 }-> s5 :|: s5 >= 0, s5 <= 0 + 2, z = 1 + 0
   encArg(z) -{ 6 }-> s6 :|: s6 >= 0, s6 <= 2 + 2, z = 1 + 2
   encArg(z) -{ 6 }-> s7 :|: s7 >= 0, s7 <= 1 + 2, z = 1 + 1
   encArg(z) -{ 6 }-> s8 :|: s8 >= 0, s8 <= 0 + 2, z - 1 >= 0
   encArg(z) -{ 0 }-> if(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> f(if(encArg(x_11), encArg(x_2'), encArg(x_3'))) :|: x_11 >= 0, x_3' >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2' + x_3')
   encArg(z) -{ 0 }-> f(f(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(if(encArg(x_1297), encArg(x_273), encArg(x_373))) :|: z = 1 + (1 + x_1297 + x_273 + x_373), x_373 >= 0, x_273 >= 0, x_1297 >= 0
   encArg(z) -{ 0 }-> activate(f(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_activate(z) -{ 6 }-> s13 :|: s13 >= 0, s13 <= 0 + 2, z = 0
   encode_activate(z) -{ 6 }-> s14 :|: s14 >= 0, s14 <= 2 + 2, z = 2
   encode_activate(z) -{ 6 }-> s15 :|: s15 >= 0, s15 <= 1 + 2, z = 1
   encode_activate(z) -{ 6 }-> s16 :|: s16 >= 0, s16 <= 0 + 2, z >= 0
   encode_activate(z) -{ 0 }-> activate(if(encArg(x_1597), encArg(x_2148), encArg(x_3148))) :|: z = 1 + x_1597 + x_2148 + x_3148, x_3148 >= 0, x_2148 >= 0, x_1597 >= 0
   encode_activate(z) -{ 0 }-> activate(f(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z) -{ 5 }-> s10 :|: s10 >= 0, s10 <= 2 + 3, z = 2
   encode_f(z) -{ 5 }-> s11 :|: s11 >= 0, s11 <= 1 + 3, z = 1
   encode_f(z) -{ 5 }-> s12 :|: s12 >= 0, s12 <= 0 + 3, z >= 0
   encode_f(z) -{ 5 }-> s9 :|: s9 >= 0, s9 <= 0 + 3, z = 0
   encode_f(z) -{ 0 }-> f(if(encArg(x_1301), encArg(x_274), encArg(x_374))) :|: x_374 >= 0, x_274 >= 0, z = 1 + x_1301 + x_274 + x_374, x_1301 >= 0
   encode_f(z) -{ 0 }-> f(f(encArg(z - 1))) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> f(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> f(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> 0 :|: z >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_if(z, z', z'') -{ 0 }-> if(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_n__f(z) -{ 0 }-> 0 :|: z >= 0
   encode_n__f(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   f(z) -{ 8 }-> s :|: s >= 0, s <= 1 + 2 + 2 + 0, z >= 0
   f(z) -{ 1 }-> 1 + z :|: z >= 0
   if(z, z', z'') -{ 7 }-> s' :|: s' >= 0, s' <= z'' + 2, z'' >= 0, z = 1, z' >= 0
   if(z, z', z'') -{ 1 }-> z' :|: z = 2, z'' >= 0, z' >= 0
   if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0

Function symbols to be analyzed: {encArg}, {encode_activate}, {encode_if}, {encode_f}, {encode_n__f}
Previous analysis results are:
  encode_false: runtime: O(1) [0], size: O(1) [1]
  encode_c: runtime: O(1) [0], size: O(1) [0]
  encode_true: runtime: O(1) [0], size: O(1) [2]
  f: runtime: O(1) [5], size: O(n^1) [3 + z]
  if: runtime: O(1) [7], size: O(n^1) [2 + z' + z'']
  activate: runtime: O(1) [6], size: O(n^1) [2 + z]

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

(47) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: encArg
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 5 + 16*z

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

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

   activate(z) -{ 6 }-> s'' :|: s'' >= 0, s'' <= z - 1 + 3, z - 1 >= 0
   activate(z) -{ 1 }-> z :|: z >= 0
   encArg(z) -{ 5 }-> s1 :|: s1 >= 0, s1 <= 0 + 3, z = 1 + 0
   encArg(z) -{ 5 }-> s2 :|: s2 >= 0, s2 <= 2 + 3, z = 1 + 2
   encArg(z) -{ 5 }-> s3 :|: s3 >= 0, s3 <= 1 + 3, z = 1 + 1
   encArg(z) -{ 5 }-> s4 :|: s4 >= 0, s4 <= 0 + 3, z - 1 >= 0
   encArg(z) -{ 6 }-> s5 :|: s5 >= 0, s5 <= 0 + 2, z = 1 + 0
   encArg(z) -{ 6 }-> s6 :|: s6 >= 0, s6 <= 2 + 2, z = 1 + 2
   encArg(z) -{ 6 }-> s7 :|: s7 >= 0, s7 <= 1 + 2, z = 1 + 1
   encArg(z) -{ 6 }-> s8 :|: s8 >= 0, s8 <= 0 + 2, z - 1 >= 0
   encArg(z) -{ 0 }-> if(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> f(if(encArg(x_11), encArg(x_2'), encArg(x_3'))) :|: x_11 >= 0, x_3' >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2' + x_3')
   encArg(z) -{ 0 }-> f(f(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(if(encArg(x_1297), encArg(x_273), encArg(x_373))) :|: z = 1 + (1 + x_1297 + x_273 + x_373), x_373 >= 0, x_273 >= 0, x_1297 >= 0
   encArg(z) -{ 0 }-> activate(f(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_activate(z) -{ 6 }-> s13 :|: s13 >= 0, s13 <= 0 + 2, z = 0
   encode_activate(z) -{ 6 }-> s14 :|: s14 >= 0, s14 <= 2 + 2, z = 2
   encode_activate(z) -{ 6 }-> s15 :|: s15 >= 0, s15 <= 1 + 2, z = 1
   encode_activate(z) -{ 6 }-> s16 :|: s16 >= 0, s16 <= 0 + 2, z >= 0
   encode_activate(z) -{ 0 }-> activate(if(encArg(x_1597), encArg(x_2148), encArg(x_3148))) :|: z = 1 + x_1597 + x_2148 + x_3148, x_3148 >= 0, x_2148 >= 0, x_1597 >= 0
   encode_activate(z) -{ 0 }-> activate(f(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z) -{ 5 }-> s10 :|: s10 >= 0, s10 <= 2 + 3, z = 2
   encode_f(z) -{ 5 }-> s11 :|: s11 >= 0, s11 <= 1 + 3, z = 1
   encode_f(z) -{ 5 }-> s12 :|: s12 >= 0, s12 <= 0 + 3, z >= 0
   encode_f(z) -{ 5 }-> s9 :|: s9 >= 0, s9 <= 0 + 3, z = 0
   encode_f(z) -{ 0 }-> f(if(encArg(x_1301), encArg(x_274), encArg(x_374))) :|: x_374 >= 0, x_274 >= 0, z = 1 + x_1301 + x_274 + x_374, x_1301 >= 0
   encode_f(z) -{ 0 }-> f(f(encArg(z - 1))) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> f(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> f(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> 0 :|: z >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_if(z, z', z'') -{ 0 }-> if(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_n__f(z) -{ 0 }-> 0 :|: z >= 0
   encode_n__f(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   f(z) -{ 8 }-> s :|: s >= 0, s <= 1 + 2 + 2 + 0, z >= 0
   f(z) -{ 1 }-> 1 + z :|: z >= 0
   if(z, z', z'') -{ 7 }-> s' :|: s' >= 0, s' <= z'' + 2, z'' >= 0, z = 1, z' >= 0
   if(z, z', z'') -{ 1 }-> z' :|: z = 2, z'' >= 0, z' >= 0
   if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0

Function symbols to be analyzed: {encArg}, {encode_activate}, {encode_if}, {encode_f}, {encode_n__f}
Previous analysis results are:
  encode_false: runtime: O(1) [0], size: O(1) [1]
  encode_c: runtime: O(1) [0], size: O(1) [0]
  encode_true: runtime: O(1) [0], size: O(1) [2]
  f: runtime: O(1) [5], size: O(n^1) [3 + z]
  if: runtime: O(1) [7], size: O(n^1) [2 + z' + z'']
  activate: runtime: O(1) [6], size: O(n^1) [2 + z]
  encArg: runtime: ?, size: O(n^1) [5 + 16*z]

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

(49) 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: 6 + 13*z

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

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

   activate(z) -{ 6 }-> s'' :|: s'' >= 0, s'' <= z - 1 + 3, z - 1 >= 0
   activate(z) -{ 1 }-> z :|: z >= 0
   encArg(z) -{ 5 }-> s1 :|: s1 >= 0, s1 <= 0 + 3, z = 1 + 0
   encArg(z) -{ 5 }-> s2 :|: s2 >= 0, s2 <= 2 + 3, z = 1 + 2
   encArg(z) -{ 5 }-> s3 :|: s3 >= 0, s3 <= 1 + 3, z = 1 + 1
   encArg(z) -{ 5 }-> s4 :|: s4 >= 0, s4 <= 0 + 3, z - 1 >= 0
   encArg(z) -{ 6 }-> s5 :|: s5 >= 0, s5 <= 0 + 2, z = 1 + 0
   encArg(z) -{ 6 }-> s6 :|: s6 >= 0, s6 <= 2 + 2, z = 1 + 2
   encArg(z) -{ 6 }-> s7 :|: s7 >= 0, s7 <= 1 + 2, z = 1 + 1
   encArg(z) -{ 6 }-> s8 :|: s8 >= 0, s8 <= 0 + 2, z - 1 >= 0
   encArg(z) -{ 0 }-> if(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> f(if(encArg(x_11), encArg(x_2'), encArg(x_3'))) :|: x_11 >= 0, x_3' >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2' + x_3')
   encArg(z) -{ 0 }-> f(f(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(if(encArg(x_1297), encArg(x_273), encArg(x_373))) :|: z = 1 + (1 + x_1297 + x_273 + x_373), x_373 >= 0, x_273 >= 0, x_1297 >= 0
   encArg(z) -{ 0 }-> activate(f(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_activate(z) -{ 6 }-> s13 :|: s13 >= 0, s13 <= 0 + 2, z = 0
   encode_activate(z) -{ 6 }-> s14 :|: s14 >= 0, s14 <= 2 + 2, z = 2
   encode_activate(z) -{ 6 }-> s15 :|: s15 >= 0, s15 <= 1 + 2, z = 1
   encode_activate(z) -{ 6 }-> s16 :|: s16 >= 0, s16 <= 0 + 2, z >= 0
   encode_activate(z) -{ 0 }-> activate(if(encArg(x_1597), encArg(x_2148), encArg(x_3148))) :|: z = 1 + x_1597 + x_2148 + x_3148, x_3148 >= 0, x_2148 >= 0, x_1597 >= 0
   encode_activate(z) -{ 0 }-> activate(f(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z) -{ 5 }-> s10 :|: s10 >= 0, s10 <= 2 + 3, z = 2
   encode_f(z) -{ 5 }-> s11 :|: s11 >= 0, s11 <= 1 + 3, z = 1
   encode_f(z) -{ 5 }-> s12 :|: s12 >= 0, s12 <= 0 + 3, z >= 0
   encode_f(z) -{ 5 }-> s9 :|: s9 >= 0, s9 <= 0 + 3, z = 0
   encode_f(z) -{ 0 }-> f(if(encArg(x_1301), encArg(x_274), encArg(x_374))) :|: x_374 >= 0, x_274 >= 0, z = 1 + x_1301 + x_274 + x_374, x_1301 >= 0
   encode_f(z) -{ 0 }-> f(f(encArg(z - 1))) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> f(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> f(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> 0 :|: z >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_if(z, z', z'') -{ 0 }-> if(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_n__f(z) -{ 0 }-> 0 :|: z >= 0
   encode_n__f(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   f(z) -{ 8 }-> s :|: s >= 0, s <= 1 + 2 + 2 + 0, z >= 0
   f(z) -{ 1 }-> 1 + z :|: z >= 0
   if(z, z', z'') -{ 7 }-> s' :|: s' >= 0, s' <= z'' + 2, z'' >= 0, z = 1, z' >= 0
   if(z, z', z'') -{ 1 }-> z' :|: z = 2, z'' >= 0, z' >= 0
   if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0

Function symbols to be analyzed: {encode_activate}, {encode_if}, {encode_f}, {encode_n__f}
Previous analysis results are:
  encode_false: runtime: O(1) [0], size: O(1) [1]
  encode_c: runtime: O(1) [0], size: O(1) [0]
  encode_true: runtime: O(1) [0], size: O(1) [2]
  f: runtime: O(1) [5], size: O(n^1) [3 + z]
  if: runtime: O(1) [7], size: O(n^1) [2 + z' + z'']
  activate: runtime: O(1) [6], size: O(n^1) [2 + z]
  encArg: runtime: O(n^1) [6 + 13*z], size: O(n^1) [5 + 16*z]

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

(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) -{ 6 }-> s'' :|: s'' >= 0, s'' <= z - 1 + 3, z - 1 >= 0
   activate(z) -{ 1 }-> z :|: z >= 0
   encArg(z) -{ 5 }-> s1 :|: s1 >= 0, s1 <= 0 + 3, z = 1 + 0
   encArg(z) -{ -15 + 13*z }-> s19 :|: s18 >= 0, s18 <= 16 * (z - 2) + 5, s19 >= 0, s19 <= 1 + s18 + 3, z - 2 >= 0
   encArg(z) -{ 5 }-> s2 :|: s2 >= 0, s2 <= 2 + 3, z = 1 + 2
   encArg(z) -{ -10 + 13*z }-> s22 :|: s20 >= 0, s20 <= 16 * (z - 2) + 5, s21 >= 0, s21 <= s20 + 3, s22 >= 0, s22 <= s21 + 3, z - 2 >= 0
   encArg(z) -{ 30 + 13*x_11 + 13*x_2' + 13*x_3' }-> s27 :|: s23 >= 0, s23 <= 16 * x_11 + 5, s24 >= 0, s24 <= 16 * x_2' + 5, s25 >= 0, s25 <= 16 * x_3' + 5, s26 >= 0, s26 <= s25 + 2 + s24, s27 >= 0, s27 <= s26 + 3, x_11 >= 0, x_3' >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2' + x_3')
   encArg(z) -{ 5 }-> s3 :|: s3 >= 0, s3 <= 1 + 3, z = 1 + 1
   encArg(z) -{ -9 + 13*z }-> s30 :|: s28 >= 0, s28 <= 16 * (z - 2) + 5, s29 >= 0, s29 <= s28 + 2, s30 >= 0, s30 <= s29 + 3, z - 2 >= 0
   encArg(z) -{ 25 + 13*x_1 + 13*x_2 + 13*x_3 }-> s34 :|: s31 >= 0, s31 <= 16 * x_1 + 5, s32 >= 0, s32 <= 16 * x_2 + 5, s33 >= 0, s33 <= 16 * x_3 + 5, s34 >= 0, s34 <= s33 + 2 + s32, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ -14 + 13*z }-> s36 :|: s35 >= 0, s35 <= 16 * (z - 2) + 5, s36 >= 0, s36 <= 1 + s35 + 2, z - 2 >= 0
   encArg(z) -{ -9 + 13*z }-> s39 :|: s37 >= 0, s37 <= 16 * (z - 2) + 5, s38 >= 0, s38 <= s37 + 3, s39 >= 0, s39 <= s38 + 2, z - 2 >= 0
   encArg(z) -{ 5 }-> s4 :|: s4 >= 0, s4 <= 0 + 3, z - 1 >= 0
   encArg(z) -{ 31 + 13*x_1297 + 13*x_273 + 13*x_373 }-> s44 :|: s40 >= 0, s40 <= 16 * x_1297 + 5, s41 >= 0, s41 <= 16 * x_273 + 5, s42 >= 0, s42 <= 16 * x_373 + 5, s43 >= 0, s43 <= s42 + 2 + s41, s44 >= 0, s44 <= s43 + 2, z = 1 + (1 + x_1297 + x_273 + x_373), x_373 >= 0, x_273 >= 0, x_1297 >= 0
   encArg(z) -{ -8 + 13*z }-> s47 :|: s45 >= 0, s45 <= 16 * (z - 2) + 5, s46 >= 0, s46 <= s45 + 2, s47 >= 0, s47 <= s46 + 2, z - 2 >= 0
   encArg(z) -{ 6 }-> s5 :|: s5 >= 0, s5 <= 0 + 2, z = 1 + 0
   encArg(z) -{ 6 }-> s6 :|: s6 >= 0, s6 <= 2 + 2, z = 1 + 2
   encArg(z) -{ 6 }-> s7 :|: s7 >= 0, s7 <= 1 + 2, z = 1 + 1
   encArg(z) -{ 6 }-> s8 :|: s8 >= 0, s8 <= 0 + 2, z - 1 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ -7 + 13*z }-> 1 + s17 :|: s17 >= 0, s17 <= 16 * (z - 1) + 5, z - 1 >= 0
   encode_activate(z) -{ 6 }-> s13 :|: s13 >= 0, s13 <= 0 + 2, z = 0
   encode_activate(z) -{ 6 }-> s14 :|: s14 >= 0, s14 <= 2 + 2, z = 2
   encode_activate(z) -{ 6 }-> s15 :|: s15 >= 0, s15 <= 1 + 2, z = 1
   encode_activate(z) -{ 6 }-> s16 :|: s16 >= 0, s16 <= 0 + 2, z >= 0
   encode_activate(z) -{ -1 + 13*z }-> s67 :|: s66 >= 0, s66 <= 16 * (z - 1) + 5, s67 >= 0, s67 <= 1 + s66 + 2, z - 1 >= 0
   encode_activate(z) -{ 4 + 13*z }-> s70 :|: s68 >= 0, s68 <= 16 * (z - 1) + 5, s69 >= 0, s69 <= s68 + 3, s70 >= 0, s70 <= s69 + 2, z - 1 >= 0
   encode_activate(z) -{ 31 + 13*x_1597 + 13*x_2148 + 13*x_3148 }-> s75 :|: s71 >= 0, s71 <= 16 * x_1597 + 5, s72 >= 0, s72 <= 16 * x_2148 + 5, s73 >= 0, s73 <= 16 * x_3148 + 5, s74 >= 0, s74 <= s73 + 2 + s72, s75 >= 0, s75 <= s74 + 2, z = 1 + x_1597 + x_2148 + x_3148, x_3148 >= 0, x_2148 >= 0, x_1597 >= 0
   encode_activate(z) -{ 5 + 13*z }-> s78 :|: s76 >= 0, s76 <= 16 * (z - 1) + 5, s77 >= 0, s77 <= s76 + 2, s78 >= 0, s78 <= s77 + 2, z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z) -{ 5 }-> s10 :|: s10 >= 0, s10 <= 2 + 3, z = 2
   encode_f(z) -{ 5 }-> s11 :|: s11 >= 0, s11 <= 1 + 3, z = 1
   encode_f(z) -{ 5 }-> s12 :|: s12 >= 0, s12 <= 0 + 3, z >= 0
   encode_f(z) -{ -2 + 13*z }-> s49 :|: s48 >= 0, s48 <= 16 * (z - 1) + 5, s49 >= 0, s49 <= 1 + s48 + 3, z - 1 >= 0
   encode_f(z) -{ 3 + 13*z }-> s52 :|: s50 >= 0, s50 <= 16 * (z - 1) + 5, s51 >= 0, s51 <= s50 + 3, s52 >= 0, s52 <= s51 + 3, z - 1 >= 0
   encode_f(z) -{ 30 + 13*x_1301 + 13*x_274 + 13*x_374 }-> s57 :|: s53 >= 0, s53 <= 16 * x_1301 + 5, s54 >= 0, s54 <= 16 * x_274 + 5, s55 >= 0, s55 <= 16 * x_374 + 5, s56 >= 0, s56 <= s55 + 2 + s54, s57 >= 0, s57 <= s56 + 3, x_374 >= 0, x_274 >= 0, z = 1 + x_1301 + x_274 + x_374, x_1301 >= 0
   encode_f(z) -{ 4 + 13*z }-> s60 :|: s58 >= 0, s58 <= 16 * (z - 1) + 5, s59 >= 0, s59 <= s58 + 2, s60 >= 0, s60 <= s59 + 3, z - 1 >= 0
   encode_f(z) -{ 5 }-> s9 :|: s9 >= 0, s9 <= 0 + 3, z = 0
   encode_f(z) -{ 0 }-> 0 :|: z >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_if(z, z', z'') -{ 25 + 13*z + 13*z' + 13*z'' }-> s64 :|: s61 >= 0, s61 <= 16 * z + 5, s62 >= 0, s62 <= 16 * z' + 5, s63 >= 0, s63 <= 16 * z'' + 5, s64 >= 0, s64 <= s63 + 2 + s62, z >= 0, z'' >= 0, z' >= 0
   encode_if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_n__f(z) -{ 0 }-> 0 :|: z >= 0
   encode_n__f(z) -{ 6 + 13*z }-> 1 + s65 :|: s65 >= 0, s65 <= 16 * z + 5, z >= 0
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   f(z) -{ 8 }-> s :|: s >= 0, s <= 1 + 2 + 2 + 0, z >= 0
   f(z) -{ 1 }-> 1 + z :|: z >= 0
   if(z, z', z'') -{ 7 }-> s' :|: s' >= 0, s' <= z'' + 2, z'' >= 0, z = 1, z' >= 0
   if(z, z', z'') -{ 1 }-> z' :|: z = 2, z'' >= 0, z' >= 0
   if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0

Function symbols to be analyzed: {encode_activate}, {encode_if}, {encode_f}, {encode_n__f}
Previous analysis results are:
  encode_false: runtime: O(1) [0], size: O(1) [1]
  encode_c: runtime: O(1) [0], size: O(1) [0]
  encode_true: runtime: O(1) [0], size: O(1) [2]
  f: runtime: O(1) [5], size: O(n^1) [3 + z]
  if: runtime: O(1) [7], size: O(n^1) [2 + z' + z'']
  activate: runtime: O(1) [6], size: O(n^1) [2 + z]
  encArg: runtime: O(n^1) [6 + 13*z], size: O(n^1) [5 + 16*z]

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

(53) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: encode_activate
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 2 + 16*z

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

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

   activate(z) -{ 6 }-> s'' :|: s'' >= 0, s'' <= z - 1 + 3, z - 1 >= 0
   activate(z) -{ 1 }-> z :|: z >= 0
   encArg(z) -{ 5 }-> s1 :|: s1 >= 0, s1 <= 0 + 3, z = 1 + 0
   encArg(z) -{ -15 + 13*z }-> s19 :|: s18 >= 0, s18 <= 16 * (z - 2) + 5, s19 >= 0, s19 <= 1 + s18 + 3, z - 2 >= 0
   encArg(z) -{ 5 }-> s2 :|: s2 >= 0, s2 <= 2 + 3, z = 1 + 2
   encArg(z) -{ -10 + 13*z }-> s22 :|: s20 >= 0, s20 <= 16 * (z - 2) + 5, s21 >= 0, s21 <= s20 + 3, s22 >= 0, s22 <= s21 + 3, z - 2 >= 0
   encArg(z) -{ 30 + 13*x_11 + 13*x_2' + 13*x_3' }-> s27 :|: s23 >= 0, s23 <= 16 * x_11 + 5, s24 >= 0, s24 <= 16 * x_2' + 5, s25 >= 0, s25 <= 16 * x_3' + 5, s26 >= 0, s26 <= s25 + 2 + s24, s27 >= 0, s27 <= s26 + 3, x_11 >= 0, x_3' >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2' + x_3')
   encArg(z) -{ 5 }-> s3 :|: s3 >= 0, s3 <= 1 + 3, z = 1 + 1
   encArg(z) -{ -9 + 13*z }-> s30 :|: s28 >= 0, s28 <= 16 * (z - 2) + 5, s29 >= 0, s29 <= s28 + 2, s30 >= 0, s30 <= s29 + 3, z - 2 >= 0
   encArg(z) -{ 25 + 13*x_1 + 13*x_2 + 13*x_3 }-> s34 :|: s31 >= 0, s31 <= 16 * x_1 + 5, s32 >= 0, s32 <= 16 * x_2 + 5, s33 >= 0, s33 <= 16 * x_3 + 5, s34 >= 0, s34 <= s33 + 2 + s32, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ -14 + 13*z }-> s36 :|: s35 >= 0, s35 <= 16 * (z - 2) + 5, s36 >= 0, s36 <= 1 + s35 + 2, z - 2 >= 0
   encArg(z) -{ -9 + 13*z }-> s39 :|: s37 >= 0, s37 <= 16 * (z - 2) + 5, s38 >= 0, s38 <= s37 + 3, s39 >= 0, s39 <= s38 + 2, z - 2 >= 0
   encArg(z) -{ 5 }-> s4 :|: s4 >= 0, s4 <= 0 + 3, z - 1 >= 0
   encArg(z) -{ 31 + 13*x_1297 + 13*x_273 + 13*x_373 }-> s44 :|: s40 >= 0, s40 <= 16 * x_1297 + 5, s41 >= 0, s41 <= 16 * x_273 + 5, s42 >= 0, s42 <= 16 * x_373 + 5, s43 >= 0, s43 <= s42 + 2 + s41, s44 >= 0, s44 <= s43 + 2, z = 1 + (1 + x_1297 + x_273 + x_373), x_373 >= 0, x_273 >= 0, x_1297 >= 0
   encArg(z) -{ -8 + 13*z }-> s47 :|: s45 >= 0, s45 <= 16 * (z - 2) + 5, s46 >= 0, s46 <= s45 + 2, s47 >= 0, s47 <= s46 + 2, z - 2 >= 0
   encArg(z) -{ 6 }-> s5 :|: s5 >= 0, s5 <= 0 + 2, z = 1 + 0
   encArg(z) -{ 6 }-> s6 :|: s6 >= 0, s6 <= 2 + 2, z = 1 + 2
   encArg(z) -{ 6 }-> s7 :|: s7 >= 0, s7 <= 1 + 2, z = 1 + 1
   encArg(z) -{ 6 }-> s8 :|: s8 >= 0, s8 <= 0 + 2, z - 1 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ -7 + 13*z }-> 1 + s17 :|: s17 >= 0, s17 <= 16 * (z - 1) + 5, z - 1 >= 0
   encode_activate(z) -{ 6 }-> s13 :|: s13 >= 0, s13 <= 0 + 2, z = 0
   encode_activate(z) -{ 6 }-> s14 :|: s14 >= 0, s14 <= 2 + 2, z = 2
   encode_activate(z) -{ 6 }-> s15 :|: s15 >= 0, s15 <= 1 + 2, z = 1
   encode_activate(z) -{ 6 }-> s16 :|: s16 >= 0, s16 <= 0 + 2, z >= 0
   encode_activate(z) -{ -1 + 13*z }-> s67 :|: s66 >= 0, s66 <= 16 * (z - 1) + 5, s67 >= 0, s67 <= 1 + s66 + 2, z - 1 >= 0
   encode_activate(z) -{ 4 + 13*z }-> s70 :|: s68 >= 0, s68 <= 16 * (z - 1) + 5, s69 >= 0, s69 <= s68 + 3, s70 >= 0, s70 <= s69 + 2, z - 1 >= 0
   encode_activate(z) -{ 31 + 13*x_1597 + 13*x_2148 + 13*x_3148 }-> s75 :|: s71 >= 0, s71 <= 16 * x_1597 + 5, s72 >= 0, s72 <= 16 * x_2148 + 5, s73 >= 0, s73 <= 16 * x_3148 + 5, s74 >= 0, s74 <= s73 + 2 + s72, s75 >= 0, s75 <= s74 + 2, z = 1 + x_1597 + x_2148 + x_3148, x_3148 >= 0, x_2148 >= 0, x_1597 >= 0
   encode_activate(z) -{ 5 + 13*z }-> s78 :|: s76 >= 0, s76 <= 16 * (z - 1) + 5, s77 >= 0, s77 <= s76 + 2, s78 >= 0, s78 <= s77 + 2, z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z) -{ 5 }-> s10 :|: s10 >= 0, s10 <= 2 + 3, z = 2
   encode_f(z) -{ 5 }-> s11 :|: s11 >= 0, s11 <= 1 + 3, z = 1
   encode_f(z) -{ 5 }-> s12 :|: s12 >= 0, s12 <= 0 + 3, z >= 0
   encode_f(z) -{ -2 + 13*z }-> s49 :|: s48 >= 0, s48 <= 16 * (z - 1) + 5, s49 >= 0, s49 <= 1 + s48 + 3, z - 1 >= 0
   encode_f(z) -{ 3 + 13*z }-> s52 :|: s50 >= 0, s50 <= 16 * (z - 1) + 5, s51 >= 0, s51 <= s50 + 3, s52 >= 0, s52 <= s51 + 3, z - 1 >= 0
   encode_f(z) -{ 30 + 13*x_1301 + 13*x_274 + 13*x_374 }-> s57 :|: s53 >= 0, s53 <= 16 * x_1301 + 5, s54 >= 0, s54 <= 16 * x_274 + 5, s55 >= 0, s55 <= 16 * x_374 + 5, s56 >= 0, s56 <= s55 + 2 + s54, s57 >= 0, s57 <= s56 + 3, x_374 >= 0, x_274 >= 0, z = 1 + x_1301 + x_274 + x_374, x_1301 >= 0
   encode_f(z) -{ 4 + 13*z }-> s60 :|: s58 >= 0, s58 <= 16 * (z - 1) + 5, s59 >= 0, s59 <= s58 + 2, s60 >= 0, s60 <= s59 + 3, z - 1 >= 0
   encode_f(z) -{ 5 }-> s9 :|: s9 >= 0, s9 <= 0 + 3, z = 0
   encode_f(z) -{ 0 }-> 0 :|: z >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_if(z, z', z'') -{ 25 + 13*z + 13*z' + 13*z'' }-> s64 :|: s61 >= 0, s61 <= 16 * z + 5, s62 >= 0, s62 <= 16 * z' + 5, s63 >= 0, s63 <= 16 * z'' + 5, s64 >= 0, s64 <= s63 + 2 + s62, z >= 0, z'' >= 0, z' >= 0
   encode_if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_n__f(z) -{ 0 }-> 0 :|: z >= 0
   encode_n__f(z) -{ 6 + 13*z }-> 1 + s65 :|: s65 >= 0, s65 <= 16 * z + 5, z >= 0
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   f(z) -{ 8 }-> s :|: s >= 0, s <= 1 + 2 + 2 + 0, z >= 0
   f(z) -{ 1 }-> 1 + z :|: z >= 0
   if(z, z', z'') -{ 7 }-> s' :|: s' >= 0, s' <= z'' + 2, z'' >= 0, z = 1, z' >= 0
   if(z, z', z'') -{ 1 }-> z' :|: z = 2, z'' >= 0, z' >= 0
   if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0

Function symbols to be analyzed: {encode_activate}, {encode_if}, {encode_f}, {encode_n__f}
Previous analysis results are:
  encode_false: runtime: O(1) [0], size: O(1) [1]
  encode_c: runtime: O(1) [0], size: O(1) [0]
  encode_true: runtime: O(1) [0], size: O(1) [2]
  f: runtime: O(1) [5], size: O(n^1) [3 + z]
  if: runtime: O(1) [7], size: O(n^1) [2 + z' + z'']
  activate: runtime: O(1) [6], size: O(n^1) [2 + z]
  encArg: runtime: O(n^1) [6 + 13*z], size: O(n^1) [5 + 16*z]
  encode_activate: runtime: ?, size: O(n^1) [2 + 16*z]

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

(55) 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: 18 + 13*z

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

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

   activate(z) -{ 6 }-> s'' :|: s'' >= 0, s'' <= z - 1 + 3, z - 1 >= 0
   activate(z) -{ 1 }-> z :|: z >= 0
   encArg(z) -{ 5 }-> s1 :|: s1 >= 0, s1 <= 0 + 3, z = 1 + 0
   encArg(z) -{ -15 + 13*z }-> s19 :|: s18 >= 0, s18 <= 16 * (z - 2) + 5, s19 >= 0, s19 <= 1 + s18 + 3, z - 2 >= 0
   encArg(z) -{ 5 }-> s2 :|: s2 >= 0, s2 <= 2 + 3, z = 1 + 2
   encArg(z) -{ -10 + 13*z }-> s22 :|: s20 >= 0, s20 <= 16 * (z - 2) + 5, s21 >= 0, s21 <= s20 + 3, s22 >= 0, s22 <= s21 + 3, z - 2 >= 0
   encArg(z) -{ 30 + 13*x_11 + 13*x_2' + 13*x_3' }-> s27 :|: s23 >= 0, s23 <= 16 * x_11 + 5, s24 >= 0, s24 <= 16 * x_2' + 5, s25 >= 0, s25 <= 16 * x_3' + 5, s26 >= 0, s26 <= s25 + 2 + s24, s27 >= 0, s27 <= s26 + 3, x_11 >= 0, x_3' >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2' + x_3')
   encArg(z) -{ 5 }-> s3 :|: s3 >= 0, s3 <= 1 + 3, z = 1 + 1
   encArg(z) -{ -9 + 13*z }-> s30 :|: s28 >= 0, s28 <= 16 * (z - 2) + 5, s29 >= 0, s29 <= s28 + 2, s30 >= 0, s30 <= s29 + 3, z - 2 >= 0
   encArg(z) -{ 25 + 13*x_1 + 13*x_2 + 13*x_3 }-> s34 :|: s31 >= 0, s31 <= 16 * x_1 + 5, s32 >= 0, s32 <= 16 * x_2 + 5, s33 >= 0, s33 <= 16 * x_3 + 5, s34 >= 0, s34 <= s33 + 2 + s32, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ -14 + 13*z }-> s36 :|: s35 >= 0, s35 <= 16 * (z - 2) + 5, s36 >= 0, s36 <= 1 + s35 + 2, z - 2 >= 0
   encArg(z) -{ -9 + 13*z }-> s39 :|: s37 >= 0, s37 <= 16 * (z - 2) + 5, s38 >= 0, s38 <= s37 + 3, s39 >= 0, s39 <= s38 + 2, z - 2 >= 0
   encArg(z) -{ 5 }-> s4 :|: s4 >= 0, s4 <= 0 + 3, z - 1 >= 0
   encArg(z) -{ 31 + 13*x_1297 + 13*x_273 + 13*x_373 }-> s44 :|: s40 >= 0, s40 <= 16 * x_1297 + 5, s41 >= 0, s41 <= 16 * x_273 + 5, s42 >= 0, s42 <= 16 * x_373 + 5, s43 >= 0, s43 <= s42 + 2 + s41, s44 >= 0, s44 <= s43 + 2, z = 1 + (1 + x_1297 + x_273 + x_373), x_373 >= 0, x_273 >= 0, x_1297 >= 0
   encArg(z) -{ -8 + 13*z }-> s47 :|: s45 >= 0, s45 <= 16 * (z - 2) + 5, s46 >= 0, s46 <= s45 + 2, s47 >= 0, s47 <= s46 + 2, z - 2 >= 0
   encArg(z) -{ 6 }-> s5 :|: s5 >= 0, s5 <= 0 + 2, z = 1 + 0
   encArg(z) -{ 6 }-> s6 :|: s6 >= 0, s6 <= 2 + 2, z = 1 + 2
   encArg(z) -{ 6 }-> s7 :|: s7 >= 0, s7 <= 1 + 2, z = 1 + 1
   encArg(z) -{ 6 }-> s8 :|: s8 >= 0, s8 <= 0 + 2, z - 1 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ -7 + 13*z }-> 1 + s17 :|: s17 >= 0, s17 <= 16 * (z - 1) + 5, z - 1 >= 0
   encode_activate(z) -{ 6 }-> s13 :|: s13 >= 0, s13 <= 0 + 2, z = 0
   encode_activate(z) -{ 6 }-> s14 :|: s14 >= 0, s14 <= 2 + 2, z = 2
   encode_activate(z) -{ 6 }-> s15 :|: s15 >= 0, s15 <= 1 + 2, z = 1
   encode_activate(z) -{ 6 }-> s16 :|: s16 >= 0, s16 <= 0 + 2, z >= 0
   encode_activate(z) -{ -1 + 13*z }-> s67 :|: s66 >= 0, s66 <= 16 * (z - 1) + 5, s67 >= 0, s67 <= 1 + s66 + 2, z - 1 >= 0
   encode_activate(z) -{ 4 + 13*z }-> s70 :|: s68 >= 0, s68 <= 16 * (z - 1) + 5, s69 >= 0, s69 <= s68 + 3, s70 >= 0, s70 <= s69 + 2, z - 1 >= 0
   encode_activate(z) -{ 31 + 13*x_1597 + 13*x_2148 + 13*x_3148 }-> s75 :|: s71 >= 0, s71 <= 16 * x_1597 + 5, s72 >= 0, s72 <= 16 * x_2148 + 5, s73 >= 0, s73 <= 16 * x_3148 + 5, s74 >= 0, s74 <= s73 + 2 + s72, s75 >= 0, s75 <= s74 + 2, z = 1 + x_1597 + x_2148 + x_3148, x_3148 >= 0, x_2148 >= 0, x_1597 >= 0
   encode_activate(z) -{ 5 + 13*z }-> s78 :|: s76 >= 0, s76 <= 16 * (z - 1) + 5, s77 >= 0, s77 <= s76 + 2, s78 >= 0, s78 <= s77 + 2, z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z) -{ 5 }-> s10 :|: s10 >= 0, s10 <= 2 + 3, z = 2
   encode_f(z) -{ 5 }-> s11 :|: s11 >= 0, s11 <= 1 + 3, z = 1
   encode_f(z) -{ 5 }-> s12 :|: s12 >= 0, s12 <= 0 + 3, z >= 0
   encode_f(z) -{ -2 + 13*z }-> s49 :|: s48 >= 0, s48 <= 16 * (z - 1) + 5, s49 >= 0, s49 <= 1 + s48 + 3, z - 1 >= 0
   encode_f(z) -{ 3 + 13*z }-> s52 :|: s50 >= 0, s50 <= 16 * (z - 1) + 5, s51 >= 0, s51 <= s50 + 3, s52 >= 0, s52 <= s51 + 3, z - 1 >= 0
   encode_f(z) -{ 30 + 13*x_1301 + 13*x_274 + 13*x_374 }-> s57 :|: s53 >= 0, s53 <= 16 * x_1301 + 5, s54 >= 0, s54 <= 16 * x_274 + 5, s55 >= 0, s55 <= 16 * x_374 + 5, s56 >= 0, s56 <= s55 + 2 + s54, s57 >= 0, s57 <= s56 + 3, x_374 >= 0, x_274 >= 0, z = 1 + x_1301 + x_274 + x_374, x_1301 >= 0
   encode_f(z) -{ 4 + 13*z }-> s60 :|: s58 >= 0, s58 <= 16 * (z - 1) + 5, s59 >= 0, s59 <= s58 + 2, s60 >= 0, s60 <= s59 + 3, z - 1 >= 0
   encode_f(z) -{ 5 }-> s9 :|: s9 >= 0, s9 <= 0 + 3, z = 0
   encode_f(z) -{ 0 }-> 0 :|: z >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_if(z, z', z'') -{ 25 + 13*z + 13*z' + 13*z'' }-> s64 :|: s61 >= 0, s61 <= 16 * z + 5, s62 >= 0, s62 <= 16 * z' + 5, s63 >= 0, s63 <= 16 * z'' + 5, s64 >= 0, s64 <= s63 + 2 + s62, z >= 0, z'' >= 0, z' >= 0
   encode_if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_n__f(z) -{ 0 }-> 0 :|: z >= 0
   encode_n__f(z) -{ 6 + 13*z }-> 1 + s65 :|: s65 >= 0, s65 <= 16 * z + 5, z >= 0
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   f(z) -{ 8 }-> s :|: s >= 0, s <= 1 + 2 + 2 + 0, z >= 0
   f(z) -{ 1 }-> 1 + z :|: z >= 0
   if(z, z', z'') -{ 7 }-> s' :|: s' >= 0, s' <= z'' + 2, z'' >= 0, z = 1, z' >= 0
   if(z, z', z'') -{ 1 }-> z' :|: z = 2, z'' >= 0, z' >= 0
   if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0

Function symbols to be analyzed: {encode_if}, {encode_f}, {encode_n__f}
Previous analysis results are:
  encode_false: runtime: O(1) [0], size: O(1) [1]
  encode_c: runtime: O(1) [0], size: O(1) [0]
  encode_true: runtime: O(1) [0], size: O(1) [2]
  f: runtime: O(1) [5], size: O(n^1) [3 + z]
  if: runtime: O(1) [7], size: O(n^1) [2 + z' + z'']
  activate: runtime: O(1) [6], size: O(n^1) [2 + z]
  encArg: runtime: O(n^1) [6 + 13*z], size: O(n^1) [5 + 16*z]
  encode_activate: runtime: O(n^1) [18 + 13*z], size: O(n^1) [2 + 16*z]

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

(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) -{ 6 }-> s'' :|: s'' >= 0, s'' <= z - 1 + 3, z - 1 >= 0
   activate(z) -{ 1 }-> z :|: z >= 0
   encArg(z) -{ 5 }-> s1 :|: s1 >= 0, s1 <= 0 + 3, z = 1 + 0
   encArg(z) -{ -15 + 13*z }-> s19 :|: s18 >= 0, s18 <= 16 * (z - 2) + 5, s19 >= 0, s19 <= 1 + s18 + 3, z - 2 >= 0
   encArg(z) -{ 5 }-> s2 :|: s2 >= 0, s2 <= 2 + 3, z = 1 + 2
   encArg(z) -{ -10 + 13*z }-> s22 :|: s20 >= 0, s20 <= 16 * (z - 2) + 5, s21 >= 0, s21 <= s20 + 3, s22 >= 0, s22 <= s21 + 3, z - 2 >= 0
   encArg(z) -{ 30 + 13*x_11 + 13*x_2' + 13*x_3' }-> s27 :|: s23 >= 0, s23 <= 16 * x_11 + 5, s24 >= 0, s24 <= 16 * x_2' + 5, s25 >= 0, s25 <= 16 * x_3' + 5, s26 >= 0, s26 <= s25 + 2 + s24, s27 >= 0, s27 <= s26 + 3, x_11 >= 0, x_3' >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2' + x_3')
   encArg(z) -{ 5 }-> s3 :|: s3 >= 0, s3 <= 1 + 3, z = 1 + 1
   encArg(z) -{ -9 + 13*z }-> s30 :|: s28 >= 0, s28 <= 16 * (z - 2) + 5, s29 >= 0, s29 <= s28 + 2, s30 >= 0, s30 <= s29 + 3, z - 2 >= 0
   encArg(z) -{ 25 + 13*x_1 + 13*x_2 + 13*x_3 }-> s34 :|: s31 >= 0, s31 <= 16 * x_1 + 5, s32 >= 0, s32 <= 16 * x_2 + 5, s33 >= 0, s33 <= 16 * x_3 + 5, s34 >= 0, s34 <= s33 + 2 + s32, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ -14 + 13*z }-> s36 :|: s35 >= 0, s35 <= 16 * (z - 2) + 5, s36 >= 0, s36 <= 1 + s35 + 2, z - 2 >= 0
   encArg(z) -{ -9 + 13*z }-> s39 :|: s37 >= 0, s37 <= 16 * (z - 2) + 5, s38 >= 0, s38 <= s37 + 3, s39 >= 0, s39 <= s38 + 2, z - 2 >= 0
   encArg(z) -{ 5 }-> s4 :|: s4 >= 0, s4 <= 0 + 3, z - 1 >= 0
   encArg(z) -{ 31 + 13*x_1297 + 13*x_273 + 13*x_373 }-> s44 :|: s40 >= 0, s40 <= 16 * x_1297 + 5, s41 >= 0, s41 <= 16 * x_273 + 5, s42 >= 0, s42 <= 16 * x_373 + 5, s43 >= 0, s43 <= s42 + 2 + s41, s44 >= 0, s44 <= s43 + 2, z = 1 + (1 + x_1297 + x_273 + x_373), x_373 >= 0, x_273 >= 0, x_1297 >= 0
   encArg(z) -{ -8 + 13*z }-> s47 :|: s45 >= 0, s45 <= 16 * (z - 2) + 5, s46 >= 0, s46 <= s45 + 2, s47 >= 0, s47 <= s46 + 2, z - 2 >= 0
   encArg(z) -{ 6 }-> s5 :|: s5 >= 0, s5 <= 0 + 2, z = 1 + 0
   encArg(z) -{ 6 }-> s6 :|: s6 >= 0, s6 <= 2 + 2, z = 1 + 2
   encArg(z) -{ 6 }-> s7 :|: s7 >= 0, s7 <= 1 + 2, z = 1 + 1
   encArg(z) -{ 6 }-> s8 :|: s8 >= 0, s8 <= 0 + 2, z - 1 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ -7 + 13*z }-> 1 + s17 :|: s17 >= 0, s17 <= 16 * (z - 1) + 5, z - 1 >= 0
   encode_activate(z) -{ 6 }-> s13 :|: s13 >= 0, s13 <= 0 + 2, z = 0
   encode_activate(z) -{ 6 }-> s14 :|: s14 >= 0, s14 <= 2 + 2, z = 2
   encode_activate(z) -{ 6 }-> s15 :|: s15 >= 0, s15 <= 1 + 2, z = 1
   encode_activate(z) -{ 6 }-> s16 :|: s16 >= 0, s16 <= 0 + 2, z >= 0
   encode_activate(z) -{ -1 + 13*z }-> s67 :|: s66 >= 0, s66 <= 16 * (z - 1) + 5, s67 >= 0, s67 <= 1 + s66 + 2, z - 1 >= 0
   encode_activate(z) -{ 4 + 13*z }-> s70 :|: s68 >= 0, s68 <= 16 * (z - 1) + 5, s69 >= 0, s69 <= s68 + 3, s70 >= 0, s70 <= s69 + 2, z - 1 >= 0
   encode_activate(z) -{ 31 + 13*x_1597 + 13*x_2148 + 13*x_3148 }-> s75 :|: s71 >= 0, s71 <= 16 * x_1597 + 5, s72 >= 0, s72 <= 16 * x_2148 + 5, s73 >= 0, s73 <= 16 * x_3148 + 5, s74 >= 0, s74 <= s73 + 2 + s72, s75 >= 0, s75 <= s74 + 2, z = 1 + x_1597 + x_2148 + x_3148, x_3148 >= 0, x_2148 >= 0, x_1597 >= 0
   encode_activate(z) -{ 5 + 13*z }-> s78 :|: s76 >= 0, s76 <= 16 * (z - 1) + 5, s77 >= 0, s77 <= s76 + 2, s78 >= 0, s78 <= s77 + 2, z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z) -{ 5 }-> s10 :|: s10 >= 0, s10 <= 2 + 3, z = 2
   encode_f(z) -{ 5 }-> s11 :|: s11 >= 0, s11 <= 1 + 3, z = 1
   encode_f(z) -{ 5 }-> s12 :|: s12 >= 0, s12 <= 0 + 3, z >= 0
   encode_f(z) -{ -2 + 13*z }-> s49 :|: s48 >= 0, s48 <= 16 * (z - 1) + 5, s49 >= 0, s49 <= 1 + s48 + 3, z - 1 >= 0
   encode_f(z) -{ 3 + 13*z }-> s52 :|: s50 >= 0, s50 <= 16 * (z - 1) + 5, s51 >= 0, s51 <= s50 + 3, s52 >= 0, s52 <= s51 + 3, z - 1 >= 0
   encode_f(z) -{ 30 + 13*x_1301 + 13*x_274 + 13*x_374 }-> s57 :|: s53 >= 0, s53 <= 16 * x_1301 + 5, s54 >= 0, s54 <= 16 * x_274 + 5, s55 >= 0, s55 <= 16 * x_374 + 5, s56 >= 0, s56 <= s55 + 2 + s54, s57 >= 0, s57 <= s56 + 3, x_374 >= 0, x_274 >= 0, z = 1 + x_1301 + x_274 + x_374, x_1301 >= 0
   encode_f(z) -{ 4 + 13*z }-> s60 :|: s58 >= 0, s58 <= 16 * (z - 1) + 5, s59 >= 0, s59 <= s58 + 2, s60 >= 0, s60 <= s59 + 3, z - 1 >= 0
   encode_f(z) -{ 5 }-> s9 :|: s9 >= 0, s9 <= 0 + 3, z = 0
   encode_f(z) -{ 0 }-> 0 :|: z >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_if(z, z', z'') -{ 25 + 13*z + 13*z' + 13*z'' }-> s64 :|: s61 >= 0, s61 <= 16 * z + 5, s62 >= 0, s62 <= 16 * z' + 5, s63 >= 0, s63 <= 16 * z'' + 5, s64 >= 0, s64 <= s63 + 2 + s62, z >= 0, z'' >= 0, z' >= 0
   encode_if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_n__f(z) -{ 0 }-> 0 :|: z >= 0
   encode_n__f(z) -{ 6 + 13*z }-> 1 + s65 :|: s65 >= 0, s65 <= 16 * z + 5, z >= 0
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   f(z) -{ 8 }-> s :|: s >= 0, s <= 1 + 2 + 2 + 0, z >= 0
   f(z) -{ 1 }-> 1 + z :|: z >= 0
   if(z, z', z'') -{ 7 }-> s' :|: s' >= 0, s' <= z'' + 2, z'' >= 0, z = 1, z' >= 0
   if(z, z', z'') -{ 1 }-> z' :|: z = 2, z'' >= 0, z' >= 0
   if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0

Function symbols to be analyzed: {encode_if}, {encode_f}, {encode_n__f}
Previous analysis results are:
  encode_false: runtime: O(1) [0], size: O(1) [1]
  encode_c: runtime: O(1) [0], size: O(1) [0]
  encode_true: runtime: O(1) [0], size: O(1) [2]
  f: runtime: O(1) [5], size: O(n^1) [3 + z]
  if: runtime: O(1) [7], size: O(n^1) [2 + z' + z'']
  activate: runtime: O(1) [6], size: O(n^1) [2 + z]
  encArg: runtime: O(n^1) [6 + 13*z], size: O(n^1) [5 + 16*z]
  encode_activate: runtime: O(n^1) [18 + 13*z], size: O(n^1) [2 + 16*z]

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

(59) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: encode_if
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 12 + 16*z' + 16*z''

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

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

   activate(z) -{ 6 }-> s'' :|: s'' >= 0, s'' <= z - 1 + 3, z - 1 >= 0
   activate(z) -{ 1 }-> z :|: z >= 0
   encArg(z) -{ 5 }-> s1 :|: s1 >= 0, s1 <= 0 + 3, z = 1 + 0
   encArg(z) -{ -15 + 13*z }-> s19 :|: s18 >= 0, s18 <= 16 * (z - 2) + 5, s19 >= 0, s19 <= 1 + s18 + 3, z - 2 >= 0
   encArg(z) -{ 5 }-> s2 :|: s2 >= 0, s2 <= 2 + 3, z = 1 + 2
   encArg(z) -{ -10 + 13*z }-> s22 :|: s20 >= 0, s20 <= 16 * (z - 2) + 5, s21 >= 0, s21 <= s20 + 3, s22 >= 0, s22 <= s21 + 3, z - 2 >= 0
   encArg(z) -{ 30 + 13*x_11 + 13*x_2' + 13*x_3' }-> s27 :|: s23 >= 0, s23 <= 16 * x_11 + 5, s24 >= 0, s24 <= 16 * x_2' + 5, s25 >= 0, s25 <= 16 * x_3' + 5, s26 >= 0, s26 <= s25 + 2 + s24, s27 >= 0, s27 <= s26 + 3, x_11 >= 0, x_3' >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2' + x_3')
   encArg(z) -{ 5 }-> s3 :|: s3 >= 0, s3 <= 1 + 3, z = 1 + 1
   encArg(z) -{ -9 + 13*z }-> s30 :|: s28 >= 0, s28 <= 16 * (z - 2) + 5, s29 >= 0, s29 <= s28 + 2, s30 >= 0, s30 <= s29 + 3, z - 2 >= 0
   encArg(z) -{ 25 + 13*x_1 + 13*x_2 + 13*x_3 }-> s34 :|: s31 >= 0, s31 <= 16 * x_1 + 5, s32 >= 0, s32 <= 16 * x_2 + 5, s33 >= 0, s33 <= 16 * x_3 + 5, s34 >= 0, s34 <= s33 + 2 + s32, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ -14 + 13*z }-> s36 :|: s35 >= 0, s35 <= 16 * (z - 2) + 5, s36 >= 0, s36 <= 1 + s35 + 2, z - 2 >= 0
   encArg(z) -{ -9 + 13*z }-> s39 :|: s37 >= 0, s37 <= 16 * (z - 2) + 5, s38 >= 0, s38 <= s37 + 3, s39 >= 0, s39 <= s38 + 2, z - 2 >= 0
   encArg(z) -{ 5 }-> s4 :|: s4 >= 0, s4 <= 0 + 3, z - 1 >= 0
   encArg(z) -{ 31 + 13*x_1297 + 13*x_273 + 13*x_373 }-> s44 :|: s40 >= 0, s40 <= 16 * x_1297 + 5, s41 >= 0, s41 <= 16 * x_273 + 5, s42 >= 0, s42 <= 16 * x_373 + 5, s43 >= 0, s43 <= s42 + 2 + s41, s44 >= 0, s44 <= s43 + 2, z = 1 + (1 + x_1297 + x_273 + x_373), x_373 >= 0, x_273 >= 0, x_1297 >= 0
   encArg(z) -{ -8 + 13*z }-> s47 :|: s45 >= 0, s45 <= 16 * (z - 2) + 5, s46 >= 0, s46 <= s45 + 2, s47 >= 0, s47 <= s46 + 2, z - 2 >= 0
   encArg(z) -{ 6 }-> s5 :|: s5 >= 0, s5 <= 0 + 2, z = 1 + 0
   encArg(z) -{ 6 }-> s6 :|: s6 >= 0, s6 <= 2 + 2, z = 1 + 2
   encArg(z) -{ 6 }-> s7 :|: s7 >= 0, s7 <= 1 + 2, z = 1 + 1
   encArg(z) -{ 6 }-> s8 :|: s8 >= 0, s8 <= 0 + 2, z - 1 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ -7 + 13*z }-> 1 + s17 :|: s17 >= 0, s17 <= 16 * (z - 1) + 5, z - 1 >= 0
   encode_activate(z) -{ 6 }-> s13 :|: s13 >= 0, s13 <= 0 + 2, z = 0
   encode_activate(z) -{ 6 }-> s14 :|: s14 >= 0, s14 <= 2 + 2, z = 2
   encode_activate(z) -{ 6 }-> s15 :|: s15 >= 0, s15 <= 1 + 2, z = 1
   encode_activate(z) -{ 6 }-> s16 :|: s16 >= 0, s16 <= 0 + 2, z >= 0
   encode_activate(z) -{ -1 + 13*z }-> s67 :|: s66 >= 0, s66 <= 16 * (z - 1) + 5, s67 >= 0, s67 <= 1 + s66 + 2, z - 1 >= 0
   encode_activate(z) -{ 4 + 13*z }-> s70 :|: s68 >= 0, s68 <= 16 * (z - 1) + 5, s69 >= 0, s69 <= s68 + 3, s70 >= 0, s70 <= s69 + 2, z - 1 >= 0
   encode_activate(z) -{ 31 + 13*x_1597 + 13*x_2148 + 13*x_3148 }-> s75 :|: s71 >= 0, s71 <= 16 * x_1597 + 5, s72 >= 0, s72 <= 16 * x_2148 + 5, s73 >= 0, s73 <= 16 * x_3148 + 5, s74 >= 0, s74 <= s73 + 2 + s72, s75 >= 0, s75 <= s74 + 2, z = 1 + x_1597 + x_2148 + x_3148, x_3148 >= 0, x_2148 >= 0, x_1597 >= 0
   encode_activate(z) -{ 5 + 13*z }-> s78 :|: s76 >= 0, s76 <= 16 * (z - 1) + 5, s77 >= 0, s77 <= s76 + 2, s78 >= 0, s78 <= s77 + 2, z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z) -{ 5 }-> s10 :|: s10 >= 0, s10 <= 2 + 3, z = 2
   encode_f(z) -{ 5 }-> s11 :|: s11 >= 0, s11 <= 1 + 3, z = 1
   encode_f(z) -{ 5 }-> s12 :|: s12 >= 0, s12 <= 0 + 3, z >= 0
   encode_f(z) -{ -2 + 13*z }-> s49 :|: s48 >= 0, s48 <= 16 * (z - 1) + 5, s49 >= 0, s49 <= 1 + s48 + 3, z - 1 >= 0
   encode_f(z) -{ 3 + 13*z }-> s52 :|: s50 >= 0, s50 <= 16 * (z - 1) + 5, s51 >= 0, s51 <= s50 + 3, s52 >= 0, s52 <= s51 + 3, z - 1 >= 0
   encode_f(z) -{ 30 + 13*x_1301 + 13*x_274 + 13*x_374 }-> s57 :|: s53 >= 0, s53 <= 16 * x_1301 + 5, s54 >= 0, s54 <= 16 * x_274 + 5, s55 >= 0, s55 <= 16 * x_374 + 5, s56 >= 0, s56 <= s55 + 2 + s54, s57 >= 0, s57 <= s56 + 3, x_374 >= 0, x_274 >= 0, z = 1 + x_1301 + x_274 + x_374, x_1301 >= 0
   encode_f(z) -{ 4 + 13*z }-> s60 :|: s58 >= 0, s58 <= 16 * (z - 1) + 5, s59 >= 0, s59 <= s58 + 2, s60 >= 0, s60 <= s59 + 3, z - 1 >= 0
   encode_f(z) -{ 5 }-> s9 :|: s9 >= 0, s9 <= 0 + 3, z = 0
   encode_f(z) -{ 0 }-> 0 :|: z >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_if(z, z', z'') -{ 25 + 13*z + 13*z' + 13*z'' }-> s64 :|: s61 >= 0, s61 <= 16 * z + 5, s62 >= 0, s62 <= 16 * z' + 5, s63 >= 0, s63 <= 16 * z'' + 5, s64 >= 0, s64 <= s63 + 2 + s62, z >= 0, z'' >= 0, z' >= 0
   encode_if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_n__f(z) -{ 0 }-> 0 :|: z >= 0
   encode_n__f(z) -{ 6 + 13*z }-> 1 + s65 :|: s65 >= 0, s65 <= 16 * z + 5, z >= 0
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   f(z) -{ 8 }-> s :|: s >= 0, s <= 1 + 2 + 2 + 0, z >= 0
   f(z) -{ 1 }-> 1 + z :|: z >= 0
   if(z, z', z'') -{ 7 }-> s' :|: s' >= 0, s' <= z'' + 2, z'' >= 0, z = 1, z' >= 0
   if(z, z', z'') -{ 1 }-> z' :|: z = 2, z'' >= 0, z' >= 0
   if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0

Function symbols to be analyzed: {encode_if}, {encode_f}, {encode_n__f}
Previous analysis results are:
  encode_false: runtime: O(1) [0], size: O(1) [1]
  encode_c: runtime: O(1) [0], size: O(1) [0]
  encode_true: runtime: O(1) [0], size: O(1) [2]
  f: runtime: O(1) [5], size: O(n^1) [3 + z]
  if: runtime: O(1) [7], size: O(n^1) [2 + z' + z'']
  activate: runtime: O(1) [6], size: O(n^1) [2 + z]
  encArg: runtime: O(n^1) [6 + 13*z], size: O(n^1) [5 + 16*z]
  encode_activate: runtime: O(n^1) [18 + 13*z], size: O(n^1) [2 + 16*z]
  encode_if: runtime: ?, size: O(n^1) [12 + 16*z' + 16*z'']

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

(61) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: encode_if
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 25 + 13*z + 13*z' + 13*z''

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

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

   activate(z) -{ 6 }-> s'' :|: s'' >= 0, s'' <= z - 1 + 3, z - 1 >= 0
   activate(z) -{ 1 }-> z :|: z >= 0
   encArg(z) -{ 5 }-> s1 :|: s1 >= 0, s1 <= 0 + 3, z = 1 + 0
   encArg(z) -{ -15 + 13*z }-> s19 :|: s18 >= 0, s18 <= 16 * (z - 2) + 5, s19 >= 0, s19 <= 1 + s18 + 3, z - 2 >= 0
   encArg(z) -{ 5 }-> s2 :|: s2 >= 0, s2 <= 2 + 3, z = 1 + 2
   encArg(z) -{ -10 + 13*z }-> s22 :|: s20 >= 0, s20 <= 16 * (z - 2) + 5, s21 >= 0, s21 <= s20 + 3, s22 >= 0, s22 <= s21 + 3, z - 2 >= 0
   encArg(z) -{ 30 + 13*x_11 + 13*x_2' + 13*x_3' }-> s27 :|: s23 >= 0, s23 <= 16 * x_11 + 5, s24 >= 0, s24 <= 16 * x_2' + 5, s25 >= 0, s25 <= 16 * x_3' + 5, s26 >= 0, s26 <= s25 + 2 + s24, s27 >= 0, s27 <= s26 + 3, x_11 >= 0, x_3' >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2' + x_3')
   encArg(z) -{ 5 }-> s3 :|: s3 >= 0, s3 <= 1 + 3, z = 1 + 1
   encArg(z) -{ -9 + 13*z }-> s30 :|: s28 >= 0, s28 <= 16 * (z - 2) + 5, s29 >= 0, s29 <= s28 + 2, s30 >= 0, s30 <= s29 + 3, z - 2 >= 0
   encArg(z) -{ 25 + 13*x_1 + 13*x_2 + 13*x_3 }-> s34 :|: s31 >= 0, s31 <= 16 * x_1 + 5, s32 >= 0, s32 <= 16 * x_2 + 5, s33 >= 0, s33 <= 16 * x_3 + 5, s34 >= 0, s34 <= s33 + 2 + s32, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ -14 + 13*z }-> s36 :|: s35 >= 0, s35 <= 16 * (z - 2) + 5, s36 >= 0, s36 <= 1 + s35 + 2, z - 2 >= 0
   encArg(z) -{ -9 + 13*z }-> s39 :|: s37 >= 0, s37 <= 16 * (z - 2) + 5, s38 >= 0, s38 <= s37 + 3, s39 >= 0, s39 <= s38 + 2, z - 2 >= 0
   encArg(z) -{ 5 }-> s4 :|: s4 >= 0, s4 <= 0 + 3, z - 1 >= 0
   encArg(z) -{ 31 + 13*x_1297 + 13*x_273 + 13*x_373 }-> s44 :|: s40 >= 0, s40 <= 16 * x_1297 + 5, s41 >= 0, s41 <= 16 * x_273 + 5, s42 >= 0, s42 <= 16 * x_373 + 5, s43 >= 0, s43 <= s42 + 2 + s41, s44 >= 0, s44 <= s43 + 2, z = 1 + (1 + x_1297 + x_273 + x_373), x_373 >= 0, x_273 >= 0, x_1297 >= 0
   encArg(z) -{ -8 + 13*z }-> s47 :|: s45 >= 0, s45 <= 16 * (z - 2) + 5, s46 >= 0, s46 <= s45 + 2, s47 >= 0, s47 <= s46 + 2, z - 2 >= 0
   encArg(z) -{ 6 }-> s5 :|: s5 >= 0, s5 <= 0 + 2, z = 1 + 0
   encArg(z) -{ 6 }-> s6 :|: s6 >= 0, s6 <= 2 + 2, z = 1 + 2
   encArg(z) -{ 6 }-> s7 :|: s7 >= 0, s7 <= 1 + 2, z = 1 + 1
   encArg(z) -{ 6 }-> s8 :|: s8 >= 0, s8 <= 0 + 2, z - 1 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ -7 + 13*z }-> 1 + s17 :|: s17 >= 0, s17 <= 16 * (z - 1) + 5, z - 1 >= 0
   encode_activate(z) -{ 6 }-> s13 :|: s13 >= 0, s13 <= 0 + 2, z = 0
   encode_activate(z) -{ 6 }-> s14 :|: s14 >= 0, s14 <= 2 + 2, z = 2
   encode_activate(z) -{ 6 }-> s15 :|: s15 >= 0, s15 <= 1 + 2, z = 1
   encode_activate(z) -{ 6 }-> s16 :|: s16 >= 0, s16 <= 0 + 2, z >= 0
   encode_activate(z) -{ -1 + 13*z }-> s67 :|: s66 >= 0, s66 <= 16 * (z - 1) + 5, s67 >= 0, s67 <= 1 + s66 + 2, z - 1 >= 0
   encode_activate(z) -{ 4 + 13*z }-> s70 :|: s68 >= 0, s68 <= 16 * (z - 1) + 5, s69 >= 0, s69 <= s68 + 3, s70 >= 0, s70 <= s69 + 2, z - 1 >= 0
   encode_activate(z) -{ 31 + 13*x_1597 + 13*x_2148 + 13*x_3148 }-> s75 :|: s71 >= 0, s71 <= 16 * x_1597 + 5, s72 >= 0, s72 <= 16 * x_2148 + 5, s73 >= 0, s73 <= 16 * x_3148 + 5, s74 >= 0, s74 <= s73 + 2 + s72, s75 >= 0, s75 <= s74 + 2, z = 1 + x_1597 + x_2148 + x_3148, x_3148 >= 0, x_2148 >= 0, x_1597 >= 0
   encode_activate(z) -{ 5 + 13*z }-> s78 :|: s76 >= 0, s76 <= 16 * (z - 1) + 5, s77 >= 0, s77 <= s76 + 2, s78 >= 0, s78 <= s77 + 2, z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z) -{ 5 }-> s10 :|: s10 >= 0, s10 <= 2 + 3, z = 2
   encode_f(z) -{ 5 }-> s11 :|: s11 >= 0, s11 <= 1 + 3, z = 1
   encode_f(z) -{ 5 }-> s12 :|: s12 >= 0, s12 <= 0 + 3, z >= 0
   encode_f(z) -{ -2 + 13*z }-> s49 :|: s48 >= 0, s48 <= 16 * (z - 1) + 5, s49 >= 0, s49 <= 1 + s48 + 3, z - 1 >= 0
   encode_f(z) -{ 3 + 13*z }-> s52 :|: s50 >= 0, s50 <= 16 * (z - 1) + 5, s51 >= 0, s51 <= s50 + 3, s52 >= 0, s52 <= s51 + 3, z - 1 >= 0
   encode_f(z) -{ 30 + 13*x_1301 + 13*x_274 + 13*x_374 }-> s57 :|: s53 >= 0, s53 <= 16 * x_1301 + 5, s54 >= 0, s54 <= 16 * x_274 + 5, s55 >= 0, s55 <= 16 * x_374 + 5, s56 >= 0, s56 <= s55 + 2 + s54, s57 >= 0, s57 <= s56 + 3, x_374 >= 0, x_274 >= 0, z = 1 + x_1301 + x_274 + x_374, x_1301 >= 0
   encode_f(z) -{ 4 + 13*z }-> s60 :|: s58 >= 0, s58 <= 16 * (z - 1) + 5, s59 >= 0, s59 <= s58 + 2, s60 >= 0, s60 <= s59 + 3, z - 1 >= 0
   encode_f(z) -{ 5 }-> s9 :|: s9 >= 0, s9 <= 0 + 3, z = 0
   encode_f(z) -{ 0 }-> 0 :|: z >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_if(z, z', z'') -{ 25 + 13*z + 13*z' + 13*z'' }-> s64 :|: s61 >= 0, s61 <= 16 * z + 5, s62 >= 0, s62 <= 16 * z' + 5, s63 >= 0, s63 <= 16 * z'' + 5, s64 >= 0, s64 <= s63 + 2 + s62, z >= 0, z'' >= 0, z' >= 0
   encode_if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_n__f(z) -{ 0 }-> 0 :|: z >= 0
   encode_n__f(z) -{ 6 + 13*z }-> 1 + s65 :|: s65 >= 0, s65 <= 16 * z + 5, z >= 0
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   f(z) -{ 8 }-> s :|: s >= 0, s <= 1 + 2 + 2 + 0, z >= 0
   f(z) -{ 1 }-> 1 + z :|: z >= 0
   if(z, z', z'') -{ 7 }-> s' :|: s' >= 0, s' <= z'' + 2, z'' >= 0, z = 1, z' >= 0
   if(z, z', z'') -{ 1 }-> z' :|: z = 2, z'' >= 0, z' >= 0
   if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0

Function symbols to be analyzed: {encode_f}, {encode_n__f}
Previous analysis results are:
  encode_false: runtime: O(1) [0], size: O(1) [1]
  encode_c: runtime: O(1) [0], size: O(1) [0]
  encode_true: runtime: O(1) [0], size: O(1) [2]
  f: runtime: O(1) [5], size: O(n^1) [3 + z]
  if: runtime: O(1) [7], size: O(n^1) [2 + z' + z'']
  activate: runtime: O(1) [6], size: O(n^1) [2 + z]
  encArg: runtime: O(n^1) [6 + 13*z], size: O(n^1) [5 + 16*z]
  encode_activate: runtime: O(n^1) [18 + 13*z], size: O(n^1) [2 + 16*z]
  encode_if: runtime: O(n^1) [25 + 13*z + 13*z' + 13*z''], size: O(n^1) [12 + 16*z' + 16*z'']

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

(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) -{ 6 }-> s'' :|: s'' >= 0, s'' <= z - 1 + 3, z - 1 >= 0
   activate(z) -{ 1 }-> z :|: z >= 0
   encArg(z) -{ 5 }-> s1 :|: s1 >= 0, s1 <= 0 + 3, z = 1 + 0
   encArg(z) -{ -15 + 13*z }-> s19 :|: s18 >= 0, s18 <= 16 * (z - 2) + 5, s19 >= 0, s19 <= 1 + s18 + 3, z - 2 >= 0
   encArg(z) -{ 5 }-> s2 :|: s2 >= 0, s2 <= 2 + 3, z = 1 + 2
   encArg(z) -{ -10 + 13*z }-> s22 :|: s20 >= 0, s20 <= 16 * (z - 2) + 5, s21 >= 0, s21 <= s20 + 3, s22 >= 0, s22 <= s21 + 3, z - 2 >= 0
   encArg(z) -{ 30 + 13*x_11 + 13*x_2' + 13*x_3' }-> s27 :|: s23 >= 0, s23 <= 16 * x_11 + 5, s24 >= 0, s24 <= 16 * x_2' + 5, s25 >= 0, s25 <= 16 * x_3' + 5, s26 >= 0, s26 <= s25 + 2 + s24, s27 >= 0, s27 <= s26 + 3, x_11 >= 0, x_3' >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2' + x_3')
   encArg(z) -{ 5 }-> s3 :|: s3 >= 0, s3 <= 1 + 3, z = 1 + 1
   encArg(z) -{ -9 + 13*z }-> s30 :|: s28 >= 0, s28 <= 16 * (z - 2) + 5, s29 >= 0, s29 <= s28 + 2, s30 >= 0, s30 <= s29 + 3, z - 2 >= 0
   encArg(z) -{ 25 + 13*x_1 + 13*x_2 + 13*x_3 }-> s34 :|: s31 >= 0, s31 <= 16 * x_1 + 5, s32 >= 0, s32 <= 16 * x_2 + 5, s33 >= 0, s33 <= 16 * x_3 + 5, s34 >= 0, s34 <= s33 + 2 + s32, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ -14 + 13*z }-> s36 :|: s35 >= 0, s35 <= 16 * (z - 2) + 5, s36 >= 0, s36 <= 1 + s35 + 2, z - 2 >= 0
   encArg(z) -{ -9 + 13*z }-> s39 :|: s37 >= 0, s37 <= 16 * (z - 2) + 5, s38 >= 0, s38 <= s37 + 3, s39 >= 0, s39 <= s38 + 2, z - 2 >= 0
   encArg(z) -{ 5 }-> s4 :|: s4 >= 0, s4 <= 0 + 3, z - 1 >= 0
   encArg(z) -{ 31 + 13*x_1297 + 13*x_273 + 13*x_373 }-> s44 :|: s40 >= 0, s40 <= 16 * x_1297 + 5, s41 >= 0, s41 <= 16 * x_273 + 5, s42 >= 0, s42 <= 16 * x_373 + 5, s43 >= 0, s43 <= s42 + 2 + s41, s44 >= 0, s44 <= s43 + 2, z = 1 + (1 + x_1297 + x_273 + x_373), x_373 >= 0, x_273 >= 0, x_1297 >= 0
   encArg(z) -{ -8 + 13*z }-> s47 :|: s45 >= 0, s45 <= 16 * (z - 2) + 5, s46 >= 0, s46 <= s45 + 2, s47 >= 0, s47 <= s46 + 2, z - 2 >= 0
   encArg(z) -{ 6 }-> s5 :|: s5 >= 0, s5 <= 0 + 2, z = 1 + 0
   encArg(z) -{ 6 }-> s6 :|: s6 >= 0, s6 <= 2 + 2, z = 1 + 2
   encArg(z) -{ 6 }-> s7 :|: s7 >= 0, s7 <= 1 + 2, z = 1 + 1
   encArg(z) -{ 6 }-> s8 :|: s8 >= 0, s8 <= 0 + 2, z - 1 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ -7 + 13*z }-> 1 + s17 :|: s17 >= 0, s17 <= 16 * (z - 1) + 5, z - 1 >= 0
   encode_activate(z) -{ 6 }-> s13 :|: s13 >= 0, s13 <= 0 + 2, z = 0
   encode_activate(z) -{ 6 }-> s14 :|: s14 >= 0, s14 <= 2 + 2, z = 2
   encode_activate(z) -{ 6 }-> s15 :|: s15 >= 0, s15 <= 1 + 2, z = 1
   encode_activate(z) -{ 6 }-> s16 :|: s16 >= 0, s16 <= 0 + 2, z >= 0
   encode_activate(z) -{ -1 + 13*z }-> s67 :|: s66 >= 0, s66 <= 16 * (z - 1) + 5, s67 >= 0, s67 <= 1 + s66 + 2, z - 1 >= 0
   encode_activate(z) -{ 4 + 13*z }-> s70 :|: s68 >= 0, s68 <= 16 * (z - 1) + 5, s69 >= 0, s69 <= s68 + 3, s70 >= 0, s70 <= s69 + 2, z - 1 >= 0
   encode_activate(z) -{ 31 + 13*x_1597 + 13*x_2148 + 13*x_3148 }-> s75 :|: s71 >= 0, s71 <= 16 * x_1597 + 5, s72 >= 0, s72 <= 16 * x_2148 + 5, s73 >= 0, s73 <= 16 * x_3148 + 5, s74 >= 0, s74 <= s73 + 2 + s72, s75 >= 0, s75 <= s74 + 2, z = 1 + x_1597 + x_2148 + x_3148, x_3148 >= 0, x_2148 >= 0, x_1597 >= 0
   encode_activate(z) -{ 5 + 13*z }-> s78 :|: s76 >= 0, s76 <= 16 * (z - 1) + 5, s77 >= 0, s77 <= s76 + 2, s78 >= 0, s78 <= s77 + 2, z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z) -{ 5 }-> s10 :|: s10 >= 0, s10 <= 2 + 3, z = 2
   encode_f(z) -{ 5 }-> s11 :|: s11 >= 0, s11 <= 1 + 3, z = 1
   encode_f(z) -{ 5 }-> s12 :|: s12 >= 0, s12 <= 0 + 3, z >= 0
   encode_f(z) -{ -2 + 13*z }-> s49 :|: s48 >= 0, s48 <= 16 * (z - 1) + 5, s49 >= 0, s49 <= 1 + s48 + 3, z - 1 >= 0
   encode_f(z) -{ 3 + 13*z }-> s52 :|: s50 >= 0, s50 <= 16 * (z - 1) + 5, s51 >= 0, s51 <= s50 + 3, s52 >= 0, s52 <= s51 + 3, z - 1 >= 0
   encode_f(z) -{ 30 + 13*x_1301 + 13*x_274 + 13*x_374 }-> s57 :|: s53 >= 0, s53 <= 16 * x_1301 + 5, s54 >= 0, s54 <= 16 * x_274 + 5, s55 >= 0, s55 <= 16 * x_374 + 5, s56 >= 0, s56 <= s55 + 2 + s54, s57 >= 0, s57 <= s56 + 3, x_374 >= 0, x_274 >= 0, z = 1 + x_1301 + x_274 + x_374, x_1301 >= 0
   encode_f(z) -{ 4 + 13*z }-> s60 :|: s58 >= 0, s58 <= 16 * (z - 1) + 5, s59 >= 0, s59 <= s58 + 2, s60 >= 0, s60 <= s59 + 3, z - 1 >= 0
   encode_f(z) -{ 5 }-> s9 :|: s9 >= 0, s9 <= 0 + 3, z = 0
   encode_f(z) -{ 0 }-> 0 :|: z >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_if(z, z', z'') -{ 25 + 13*z + 13*z' + 13*z'' }-> s64 :|: s61 >= 0, s61 <= 16 * z + 5, s62 >= 0, s62 <= 16 * z' + 5, s63 >= 0, s63 <= 16 * z'' + 5, s64 >= 0, s64 <= s63 + 2 + s62, z >= 0, z'' >= 0, z' >= 0
   encode_if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_n__f(z) -{ 0 }-> 0 :|: z >= 0
   encode_n__f(z) -{ 6 + 13*z }-> 1 + s65 :|: s65 >= 0, s65 <= 16 * z + 5, z >= 0
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   f(z) -{ 8 }-> s :|: s >= 0, s <= 1 + 2 + 2 + 0, z >= 0
   f(z) -{ 1 }-> 1 + z :|: z >= 0
   if(z, z', z'') -{ 7 }-> s' :|: s' >= 0, s' <= z'' + 2, z'' >= 0, z = 1, z' >= 0
   if(z, z', z'') -{ 1 }-> z' :|: z = 2, z'' >= 0, z' >= 0
   if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0

Function symbols to be analyzed: {encode_f}, {encode_n__f}
Previous analysis results are:
  encode_false: runtime: O(1) [0], size: O(1) [1]
  encode_c: runtime: O(1) [0], size: O(1) [0]
  encode_true: runtime: O(1) [0], size: O(1) [2]
  f: runtime: O(1) [5], size: O(n^1) [3 + z]
  if: runtime: O(1) [7], size: O(n^1) [2 + z' + z'']
  activate: runtime: O(1) [6], size: O(n^1) [2 + z]
  encArg: runtime: O(n^1) [6 + 13*z], size: O(n^1) [5 + 16*z]
  encode_activate: runtime: O(n^1) [18 + 13*z], size: O(n^1) [2 + 16*z]
  encode_if: runtime: O(n^1) [25 + 13*z + 13*z' + 13*z''], size: O(n^1) [12 + 16*z' + 16*z'']

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

(65) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: encode_f
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 3 + 16*z

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

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

   activate(z) -{ 6 }-> s'' :|: s'' >= 0, s'' <= z - 1 + 3, z - 1 >= 0
   activate(z) -{ 1 }-> z :|: z >= 0
   encArg(z) -{ 5 }-> s1 :|: s1 >= 0, s1 <= 0 + 3, z = 1 + 0
   encArg(z) -{ -15 + 13*z }-> s19 :|: s18 >= 0, s18 <= 16 * (z - 2) + 5, s19 >= 0, s19 <= 1 + s18 + 3, z - 2 >= 0
   encArg(z) -{ 5 }-> s2 :|: s2 >= 0, s2 <= 2 + 3, z = 1 + 2
   encArg(z) -{ -10 + 13*z }-> s22 :|: s20 >= 0, s20 <= 16 * (z - 2) + 5, s21 >= 0, s21 <= s20 + 3, s22 >= 0, s22 <= s21 + 3, z - 2 >= 0
   encArg(z) -{ 30 + 13*x_11 + 13*x_2' + 13*x_3' }-> s27 :|: s23 >= 0, s23 <= 16 * x_11 + 5, s24 >= 0, s24 <= 16 * x_2' + 5, s25 >= 0, s25 <= 16 * x_3' + 5, s26 >= 0, s26 <= s25 + 2 + s24, s27 >= 0, s27 <= s26 + 3, x_11 >= 0, x_3' >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2' + x_3')
   encArg(z) -{ 5 }-> s3 :|: s3 >= 0, s3 <= 1 + 3, z = 1 + 1
   encArg(z) -{ -9 + 13*z }-> s30 :|: s28 >= 0, s28 <= 16 * (z - 2) + 5, s29 >= 0, s29 <= s28 + 2, s30 >= 0, s30 <= s29 + 3, z - 2 >= 0
   encArg(z) -{ 25 + 13*x_1 + 13*x_2 + 13*x_3 }-> s34 :|: s31 >= 0, s31 <= 16 * x_1 + 5, s32 >= 0, s32 <= 16 * x_2 + 5, s33 >= 0, s33 <= 16 * x_3 + 5, s34 >= 0, s34 <= s33 + 2 + s32, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ -14 + 13*z }-> s36 :|: s35 >= 0, s35 <= 16 * (z - 2) + 5, s36 >= 0, s36 <= 1 + s35 + 2, z - 2 >= 0
   encArg(z) -{ -9 + 13*z }-> s39 :|: s37 >= 0, s37 <= 16 * (z - 2) + 5, s38 >= 0, s38 <= s37 + 3, s39 >= 0, s39 <= s38 + 2, z - 2 >= 0
   encArg(z) -{ 5 }-> s4 :|: s4 >= 0, s4 <= 0 + 3, z - 1 >= 0
   encArg(z) -{ 31 + 13*x_1297 + 13*x_273 + 13*x_373 }-> s44 :|: s40 >= 0, s40 <= 16 * x_1297 + 5, s41 >= 0, s41 <= 16 * x_273 + 5, s42 >= 0, s42 <= 16 * x_373 + 5, s43 >= 0, s43 <= s42 + 2 + s41, s44 >= 0, s44 <= s43 + 2, z = 1 + (1 + x_1297 + x_273 + x_373), x_373 >= 0, x_273 >= 0, x_1297 >= 0
   encArg(z) -{ -8 + 13*z }-> s47 :|: s45 >= 0, s45 <= 16 * (z - 2) + 5, s46 >= 0, s46 <= s45 + 2, s47 >= 0, s47 <= s46 + 2, z - 2 >= 0
   encArg(z) -{ 6 }-> s5 :|: s5 >= 0, s5 <= 0 + 2, z = 1 + 0
   encArg(z) -{ 6 }-> s6 :|: s6 >= 0, s6 <= 2 + 2, z = 1 + 2
   encArg(z) -{ 6 }-> s7 :|: s7 >= 0, s7 <= 1 + 2, z = 1 + 1
   encArg(z) -{ 6 }-> s8 :|: s8 >= 0, s8 <= 0 + 2, z - 1 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ -7 + 13*z }-> 1 + s17 :|: s17 >= 0, s17 <= 16 * (z - 1) + 5, z - 1 >= 0
   encode_activate(z) -{ 6 }-> s13 :|: s13 >= 0, s13 <= 0 + 2, z = 0
   encode_activate(z) -{ 6 }-> s14 :|: s14 >= 0, s14 <= 2 + 2, z = 2
   encode_activate(z) -{ 6 }-> s15 :|: s15 >= 0, s15 <= 1 + 2, z = 1
   encode_activate(z) -{ 6 }-> s16 :|: s16 >= 0, s16 <= 0 + 2, z >= 0
   encode_activate(z) -{ -1 + 13*z }-> s67 :|: s66 >= 0, s66 <= 16 * (z - 1) + 5, s67 >= 0, s67 <= 1 + s66 + 2, z - 1 >= 0
   encode_activate(z) -{ 4 + 13*z }-> s70 :|: s68 >= 0, s68 <= 16 * (z - 1) + 5, s69 >= 0, s69 <= s68 + 3, s70 >= 0, s70 <= s69 + 2, z - 1 >= 0
   encode_activate(z) -{ 31 + 13*x_1597 + 13*x_2148 + 13*x_3148 }-> s75 :|: s71 >= 0, s71 <= 16 * x_1597 + 5, s72 >= 0, s72 <= 16 * x_2148 + 5, s73 >= 0, s73 <= 16 * x_3148 + 5, s74 >= 0, s74 <= s73 + 2 + s72, s75 >= 0, s75 <= s74 + 2, z = 1 + x_1597 + x_2148 + x_3148, x_3148 >= 0, x_2148 >= 0, x_1597 >= 0
   encode_activate(z) -{ 5 + 13*z }-> s78 :|: s76 >= 0, s76 <= 16 * (z - 1) + 5, s77 >= 0, s77 <= s76 + 2, s78 >= 0, s78 <= s77 + 2, z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z) -{ 5 }-> s10 :|: s10 >= 0, s10 <= 2 + 3, z = 2
   encode_f(z) -{ 5 }-> s11 :|: s11 >= 0, s11 <= 1 + 3, z = 1
   encode_f(z) -{ 5 }-> s12 :|: s12 >= 0, s12 <= 0 + 3, z >= 0
   encode_f(z) -{ -2 + 13*z }-> s49 :|: s48 >= 0, s48 <= 16 * (z - 1) + 5, s49 >= 0, s49 <= 1 + s48 + 3, z - 1 >= 0
   encode_f(z) -{ 3 + 13*z }-> s52 :|: s50 >= 0, s50 <= 16 * (z - 1) + 5, s51 >= 0, s51 <= s50 + 3, s52 >= 0, s52 <= s51 + 3, z - 1 >= 0
   encode_f(z) -{ 30 + 13*x_1301 + 13*x_274 + 13*x_374 }-> s57 :|: s53 >= 0, s53 <= 16 * x_1301 + 5, s54 >= 0, s54 <= 16 * x_274 + 5, s55 >= 0, s55 <= 16 * x_374 + 5, s56 >= 0, s56 <= s55 + 2 + s54, s57 >= 0, s57 <= s56 + 3, x_374 >= 0, x_274 >= 0, z = 1 + x_1301 + x_274 + x_374, x_1301 >= 0
   encode_f(z) -{ 4 + 13*z }-> s60 :|: s58 >= 0, s58 <= 16 * (z - 1) + 5, s59 >= 0, s59 <= s58 + 2, s60 >= 0, s60 <= s59 + 3, z - 1 >= 0
   encode_f(z) -{ 5 }-> s9 :|: s9 >= 0, s9 <= 0 + 3, z = 0
   encode_f(z) -{ 0 }-> 0 :|: z >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_if(z, z', z'') -{ 25 + 13*z + 13*z' + 13*z'' }-> s64 :|: s61 >= 0, s61 <= 16 * z + 5, s62 >= 0, s62 <= 16 * z' + 5, s63 >= 0, s63 <= 16 * z'' + 5, s64 >= 0, s64 <= s63 + 2 + s62, z >= 0, z'' >= 0, z' >= 0
   encode_if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_n__f(z) -{ 0 }-> 0 :|: z >= 0
   encode_n__f(z) -{ 6 + 13*z }-> 1 + s65 :|: s65 >= 0, s65 <= 16 * z + 5, z >= 0
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   f(z) -{ 8 }-> s :|: s >= 0, s <= 1 + 2 + 2 + 0, z >= 0
   f(z) -{ 1 }-> 1 + z :|: z >= 0
   if(z, z', z'') -{ 7 }-> s' :|: s' >= 0, s' <= z'' + 2, z'' >= 0, z = 1, z' >= 0
   if(z, z', z'') -{ 1 }-> z' :|: z = 2, z'' >= 0, z' >= 0
   if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0

Function symbols to be analyzed: {encode_f}, {encode_n__f}
Previous analysis results are:
  encode_false: runtime: O(1) [0], size: O(1) [1]
  encode_c: runtime: O(1) [0], size: O(1) [0]
  encode_true: runtime: O(1) [0], size: O(1) [2]
  f: runtime: O(1) [5], size: O(n^1) [3 + z]
  if: runtime: O(1) [7], size: O(n^1) [2 + z' + z'']
  activate: runtime: O(1) [6], size: O(n^1) [2 + z]
  encArg: runtime: O(n^1) [6 + 13*z], size: O(n^1) [5 + 16*z]
  encode_activate: runtime: O(n^1) [18 + 13*z], size: O(n^1) [2 + 16*z]
  encode_if: runtime: O(n^1) [25 + 13*z + 13*z' + 13*z''], size: O(n^1) [12 + 16*z' + 16*z'']
  encode_f: runtime: ?, size: O(n^1) [3 + 16*z]

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

(67) 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: 17 + 13*z

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

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

   activate(z) -{ 6 }-> s'' :|: s'' >= 0, s'' <= z - 1 + 3, z - 1 >= 0
   activate(z) -{ 1 }-> z :|: z >= 0
   encArg(z) -{ 5 }-> s1 :|: s1 >= 0, s1 <= 0 + 3, z = 1 + 0
   encArg(z) -{ -15 + 13*z }-> s19 :|: s18 >= 0, s18 <= 16 * (z - 2) + 5, s19 >= 0, s19 <= 1 + s18 + 3, z - 2 >= 0
   encArg(z) -{ 5 }-> s2 :|: s2 >= 0, s2 <= 2 + 3, z = 1 + 2
   encArg(z) -{ -10 + 13*z }-> s22 :|: s20 >= 0, s20 <= 16 * (z - 2) + 5, s21 >= 0, s21 <= s20 + 3, s22 >= 0, s22 <= s21 + 3, z - 2 >= 0
   encArg(z) -{ 30 + 13*x_11 + 13*x_2' + 13*x_3' }-> s27 :|: s23 >= 0, s23 <= 16 * x_11 + 5, s24 >= 0, s24 <= 16 * x_2' + 5, s25 >= 0, s25 <= 16 * x_3' + 5, s26 >= 0, s26 <= s25 + 2 + s24, s27 >= 0, s27 <= s26 + 3, x_11 >= 0, x_3' >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2' + x_3')
   encArg(z) -{ 5 }-> s3 :|: s3 >= 0, s3 <= 1 + 3, z = 1 + 1
   encArg(z) -{ -9 + 13*z }-> s30 :|: s28 >= 0, s28 <= 16 * (z - 2) + 5, s29 >= 0, s29 <= s28 + 2, s30 >= 0, s30 <= s29 + 3, z - 2 >= 0
   encArg(z) -{ 25 + 13*x_1 + 13*x_2 + 13*x_3 }-> s34 :|: s31 >= 0, s31 <= 16 * x_1 + 5, s32 >= 0, s32 <= 16 * x_2 + 5, s33 >= 0, s33 <= 16 * x_3 + 5, s34 >= 0, s34 <= s33 + 2 + s32, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ -14 + 13*z }-> s36 :|: s35 >= 0, s35 <= 16 * (z - 2) + 5, s36 >= 0, s36 <= 1 + s35 + 2, z - 2 >= 0
   encArg(z) -{ -9 + 13*z }-> s39 :|: s37 >= 0, s37 <= 16 * (z - 2) + 5, s38 >= 0, s38 <= s37 + 3, s39 >= 0, s39 <= s38 + 2, z - 2 >= 0
   encArg(z) -{ 5 }-> s4 :|: s4 >= 0, s4 <= 0 + 3, z - 1 >= 0
   encArg(z) -{ 31 + 13*x_1297 + 13*x_273 + 13*x_373 }-> s44 :|: s40 >= 0, s40 <= 16 * x_1297 + 5, s41 >= 0, s41 <= 16 * x_273 + 5, s42 >= 0, s42 <= 16 * x_373 + 5, s43 >= 0, s43 <= s42 + 2 + s41, s44 >= 0, s44 <= s43 + 2, z = 1 + (1 + x_1297 + x_273 + x_373), x_373 >= 0, x_273 >= 0, x_1297 >= 0
   encArg(z) -{ -8 + 13*z }-> s47 :|: s45 >= 0, s45 <= 16 * (z - 2) + 5, s46 >= 0, s46 <= s45 + 2, s47 >= 0, s47 <= s46 + 2, z - 2 >= 0
   encArg(z) -{ 6 }-> s5 :|: s5 >= 0, s5 <= 0 + 2, z = 1 + 0
   encArg(z) -{ 6 }-> s6 :|: s6 >= 0, s6 <= 2 + 2, z = 1 + 2
   encArg(z) -{ 6 }-> s7 :|: s7 >= 0, s7 <= 1 + 2, z = 1 + 1
   encArg(z) -{ 6 }-> s8 :|: s8 >= 0, s8 <= 0 + 2, z - 1 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ -7 + 13*z }-> 1 + s17 :|: s17 >= 0, s17 <= 16 * (z - 1) + 5, z - 1 >= 0
   encode_activate(z) -{ 6 }-> s13 :|: s13 >= 0, s13 <= 0 + 2, z = 0
   encode_activate(z) -{ 6 }-> s14 :|: s14 >= 0, s14 <= 2 + 2, z = 2
   encode_activate(z) -{ 6 }-> s15 :|: s15 >= 0, s15 <= 1 + 2, z = 1
   encode_activate(z) -{ 6 }-> s16 :|: s16 >= 0, s16 <= 0 + 2, z >= 0
   encode_activate(z) -{ -1 + 13*z }-> s67 :|: s66 >= 0, s66 <= 16 * (z - 1) + 5, s67 >= 0, s67 <= 1 + s66 + 2, z - 1 >= 0
   encode_activate(z) -{ 4 + 13*z }-> s70 :|: s68 >= 0, s68 <= 16 * (z - 1) + 5, s69 >= 0, s69 <= s68 + 3, s70 >= 0, s70 <= s69 + 2, z - 1 >= 0
   encode_activate(z) -{ 31 + 13*x_1597 + 13*x_2148 + 13*x_3148 }-> s75 :|: s71 >= 0, s71 <= 16 * x_1597 + 5, s72 >= 0, s72 <= 16 * x_2148 + 5, s73 >= 0, s73 <= 16 * x_3148 + 5, s74 >= 0, s74 <= s73 + 2 + s72, s75 >= 0, s75 <= s74 + 2, z = 1 + x_1597 + x_2148 + x_3148, x_3148 >= 0, x_2148 >= 0, x_1597 >= 0
   encode_activate(z) -{ 5 + 13*z }-> s78 :|: s76 >= 0, s76 <= 16 * (z - 1) + 5, s77 >= 0, s77 <= s76 + 2, s78 >= 0, s78 <= s77 + 2, z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z) -{ 5 }-> s10 :|: s10 >= 0, s10 <= 2 + 3, z = 2
   encode_f(z) -{ 5 }-> s11 :|: s11 >= 0, s11 <= 1 + 3, z = 1
   encode_f(z) -{ 5 }-> s12 :|: s12 >= 0, s12 <= 0 + 3, z >= 0
   encode_f(z) -{ -2 + 13*z }-> s49 :|: s48 >= 0, s48 <= 16 * (z - 1) + 5, s49 >= 0, s49 <= 1 + s48 + 3, z - 1 >= 0
   encode_f(z) -{ 3 + 13*z }-> s52 :|: s50 >= 0, s50 <= 16 * (z - 1) + 5, s51 >= 0, s51 <= s50 + 3, s52 >= 0, s52 <= s51 + 3, z - 1 >= 0
   encode_f(z) -{ 30 + 13*x_1301 + 13*x_274 + 13*x_374 }-> s57 :|: s53 >= 0, s53 <= 16 * x_1301 + 5, s54 >= 0, s54 <= 16 * x_274 + 5, s55 >= 0, s55 <= 16 * x_374 + 5, s56 >= 0, s56 <= s55 + 2 + s54, s57 >= 0, s57 <= s56 + 3, x_374 >= 0, x_274 >= 0, z = 1 + x_1301 + x_274 + x_374, x_1301 >= 0
   encode_f(z) -{ 4 + 13*z }-> s60 :|: s58 >= 0, s58 <= 16 * (z - 1) + 5, s59 >= 0, s59 <= s58 + 2, s60 >= 0, s60 <= s59 + 3, z - 1 >= 0
   encode_f(z) -{ 5 }-> s9 :|: s9 >= 0, s9 <= 0 + 3, z = 0
   encode_f(z) -{ 0 }-> 0 :|: z >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_if(z, z', z'') -{ 25 + 13*z + 13*z' + 13*z'' }-> s64 :|: s61 >= 0, s61 <= 16 * z + 5, s62 >= 0, s62 <= 16 * z' + 5, s63 >= 0, s63 <= 16 * z'' + 5, s64 >= 0, s64 <= s63 + 2 + s62, z >= 0, z'' >= 0, z' >= 0
   encode_if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_n__f(z) -{ 0 }-> 0 :|: z >= 0
   encode_n__f(z) -{ 6 + 13*z }-> 1 + s65 :|: s65 >= 0, s65 <= 16 * z + 5, z >= 0
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   f(z) -{ 8 }-> s :|: s >= 0, s <= 1 + 2 + 2 + 0, z >= 0
   f(z) -{ 1 }-> 1 + z :|: z >= 0
   if(z, z', z'') -{ 7 }-> s' :|: s' >= 0, s' <= z'' + 2, z'' >= 0, z = 1, z' >= 0
   if(z, z', z'') -{ 1 }-> z' :|: z = 2, z'' >= 0, z' >= 0
   if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0

Function symbols to be analyzed: {encode_n__f}
Previous analysis results are:
  encode_false: runtime: O(1) [0], size: O(1) [1]
  encode_c: runtime: O(1) [0], size: O(1) [0]
  encode_true: runtime: O(1) [0], size: O(1) [2]
  f: runtime: O(1) [5], size: O(n^1) [3 + z]
  if: runtime: O(1) [7], size: O(n^1) [2 + z' + z'']
  activate: runtime: O(1) [6], size: O(n^1) [2 + z]
  encArg: runtime: O(n^1) [6 + 13*z], size: O(n^1) [5 + 16*z]
  encode_activate: runtime: O(n^1) [18 + 13*z], size: O(n^1) [2 + 16*z]
  encode_if: runtime: O(n^1) [25 + 13*z + 13*z' + 13*z''], size: O(n^1) [12 + 16*z' + 16*z'']
  encode_f: runtime: O(n^1) [17 + 13*z], size: O(n^1) [3 + 16*z]

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

(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) -{ 6 }-> s'' :|: s'' >= 0, s'' <= z - 1 + 3, z - 1 >= 0
   activate(z) -{ 1 }-> z :|: z >= 0
   encArg(z) -{ 5 }-> s1 :|: s1 >= 0, s1 <= 0 + 3, z = 1 + 0
   encArg(z) -{ -15 + 13*z }-> s19 :|: s18 >= 0, s18 <= 16 * (z - 2) + 5, s19 >= 0, s19 <= 1 + s18 + 3, z - 2 >= 0
   encArg(z) -{ 5 }-> s2 :|: s2 >= 0, s2 <= 2 + 3, z = 1 + 2
   encArg(z) -{ -10 + 13*z }-> s22 :|: s20 >= 0, s20 <= 16 * (z - 2) + 5, s21 >= 0, s21 <= s20 + 3, s22 >= 0, s22 <= s21 + 3, z - 2 >= 0
   encArg(z) -{ 30 + 13*x_11 + 13*x_2' + 13*x_3' }-> s27 :|: s23 >= 0, s23 <= 16 * x_11 + 5, s24 >= 0, s24 <= 16 * x_2' + 5, s25 >= 0, s25 <= 16 * x_3' + 5, s26 >= 0, s26 <= s25 + 2 + s24, s27 >= 0, s27 <= s26 + 3, x_11 >= 0, x_3' >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2' + x_3')
   encArg(z) -{ 5 }-> s3 :|: s3 >= 0, s3 <= 1 + 3, z = 1 + 1
   encArg(z) -{ -9 + 13*z }-> s30 :|: s28 >= 0, s28 <= 16 * (z - 2) + 5, s29 >= 0, s29 <= s28 + 2, s30 >= 0, s30 <= s29 + 3, z - 2 >= 0
   encArg(z) -{ 25 + 13*x_1 + 13*x_2 + 13*x_3 }-> s34 :|: s31 >= 0, s31 <= 16 * x_1 + 5, s32 >= 0, s32 <= 16 * x_2 + 5, s33 >= 0, s33 <= 16 * x_3 + 5, s34 >= 0, s34 <= s33 + 2 + s32, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ -14 + 13*z }-> s36 :|: s35 >= 0, s35 <= 16 * (z - 2) + 5, s36 >= 0, s36 <= 1 + s35 + 2, z - 2 >= 0
   encArg(z) -{ -9 + 13*z }-> s39 :|: s37 >= 0, s37 <= 16 * (z - 2) + 5, s38 >= 0, s38 <= s37 + 3, s39 >= 0, s39 <= s38 + 2, z - 2 >= 0
   encArg(z) -{ 5 }-> s4 :|: s4 >= 0, s4 <= 0 + 3, z - 1 >= 0
   encArg(z) -{ 31 + 13*x_1297 + 13*x_273 + 13*x_373 }-> s44 :|: s40 >= 0, s40 <= 16 * x_1297 + 5, s41 >= 0, s41 <= 16 * x_273 + 5, s42 >= 0, s42 <= 16 * x_373 + 5, s43 >= 0, s43 <= s42 + 2 + s41, s44 >= 0, s44 <= s43 + 2, z = 1 + (1 + x_1297 + x_273 + x_373), x_373 >= 0, x_273 >= 0, x_1297 >= 0
   encArg(z) -{ -8 + 13*z }-> s47 :|: s45 >= 0, s45 <= 16 * (z - 2) + 5, s46 >= 0, s46 <= s45 + 2, s47 >= 0, s47 <= s46 + 2, z - 2 >= 0
   encArg(z) -{ 6 }-> s5 :|: s5 >= 0, s5 <= 0 + 2, z = 1 + 0
   encArg(z) -{ 6 }-> s6 :|: s6 >= 0, s6 <= 2 + 2, z = 1 + 2
   encArg(z) -{ 6 }-> s7 :|: s7 >= 0, s7 <= 1 + 2, z = 1 + 1
   encArg(z) -{ 6 }-> s8 :|: s8 >= 0, s8 <= 0 + 2, z - 1 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ -7 + 13*z }-> 1 + s17 :|: s17 >= 0, s17 <= 16 * (z - 1) + 5, z - 1 >= 0
   encode_activate(z) -{ 6 }-> s13 :|: s13 >= 0, s13 <= 0 + 2, z = 0
   encode_activate(z) -{ 6 }-> s14 :|: s14 >= 0, s14 <= 2 + 2, z = 2
   encode_activate(z) -{ 6 }-> s15 :|: s15 >= 0, s15 <= 1 + 2, z = 1
   encode_activate(z) -{ 6 }-> s16 :|: s16 >= 0, s16 <= 0 + 2, z >= 0
   encode_activate(z) -{ -1 + 13*z }-> s67 :|: s66 >= 0, s66 <= 16 * (z - 1) + 5, s67 >= 0, s67 <= 1 + s66 + 2, z - 1 >= 0
   encode_activate(z) -{ 4 + 13*z }-> s70 :|: s68 >= 0, s68 <= 16 * (z - 1) + 5, s69 >= 0, s69 <= s68 + 3, s70 >= 0, s70 <= s69 + 2, z - 1 >= 0
   encode_activate(z) -{ 31 + 13*x_1597 + 13*x_2148 + 13*x_3148 }-> s75 :|: s71 >= 0, s71 <= 16 * x_1597 + 5, s72 >= 0, s72 <= 16 * x_2148 + 5, s73 >= 0, s73 <= 16 * x_3148 + 5, s74 >= 0, s74 <= s73 + 2 + s72, s75 >= 0, s75 <= s74 + 2, z = 1 + x_1597 + x_2148 + x_3148, x_3148 >= 0, x_2148 >= 0, x_1597 >= 0
   encode_activate(z) -{ 5 + 13*z }-> s78 :|: s76 >= 0, s76 <= 16 * (z - 1) + 5, s77 >= 0, s77 <= s76 + 2, s78 >= 0, s78 <= s77 + 2, z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z) -{ 5 }-> s10 :|: s10 >= 0, s10 <= 2 + 3, z = 2
   encode_f(z) -{ 5 }-> s11 :|: s11 >= 0, s11 <= 1 + 3, z = 1
   encode_f(z) -{ 5 }-> s12 :|: s12 >= 0, s12 <= 0 + 3, z >= 0
   encode_f(z) -{ -2 + 13*z }-> s49 :|: s48 >= 0, s48 <= 16 * (z - 1) + 5, s49 >= 0, s49 <= 1 + s48 + 3, z - 1 >= 0
   encode_f(z) -{ 3 + 13*z }-> s52 :|: s50 >= 0, s50 <= 16 * (z - 1) + 5, s51 >= 0, s51 <= s50 + 3, s52 >= 0, s52 <= s51 + 3, z - 1 >= 0
   encode_f(z) -{ 30 + 13*x_1301 + 13*x_274 + 13*x_374 }-> s57 :|: s53 >= 0, s53 <= 16 * x_1301 + 5, s54 >= 0, s54 <= 16 * x_274 + 5, s55 >= 0, s55 <= 16 * x_374 + 5, s56 >= 0, s56 <= s55 + 2 + s54, s57 >= 0, s57 <= s56 + 3, x_374 >= 0, x_274 >= 0, z = 1 + x_1301 + x_274 + x_374, x_1301 >= 0
   encode_f(z) -{ 4 + 13*z }-> s60 :|: s58 >= 0, s58 <= 16 * (z - 1) + 5, s59 >= 0, s59 <= s58 + 2, s60 >= 0, s60 <= s59 + 3, z - 1 >= 0
   encode_f(z) -{ 5 }-> s9 :|: s9 >= 0, s9 <= 0 + 3, z = 0
   encode_f(z) -{ 0 }-> 0 :|: z >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_if(z, z', z'') -{ 25 + 13*z + 13*z' + 13*z'' }-> s64 :|: s61 >= 0, s61 <= 16 * z + 5, s62 >= 0, s62 <= 16 * z' + 5, s63 >= 0, s63 <= 16 * z'' + 5, s64 >= 0, s64 <= s63 + 2 + s62, z >= 0, z'' >= 0, z' >= 0
   encode_if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_n__f(z) -{ 0 }-> 0 :|: z >= 0
   encode_n__f(z) -{ 6 + 13*z }-> 1 + s65 :|: s65 >= 0, s65 <= 16 * z + 5, z >= 0
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   f(z) -{ 8 }-> s :|: s >= 0, s <= 1 + 2 + 2 + 0, z >= 0
   f(z) -{ 1 }-> 1 + z :|: z >= 0
   if(z, z', z'') -{ 7 }-> s' :|: s' >= 0, s' <= z'' + 2, z'' >= 0, z = 1, z' >= 0
   if(z, z', z'') -{ 1 }-> z' :|: z = 2, z'' >= 0, z' >= 0
   if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0

Function symbols to be analyzed: {encode_n__f}
Previous analysis results are:
  encode_false: runtime: O(1) [0], size: O(1) [1]
  encode_c: runtime: O(1) [0], size: O(1) [0]
  encode_true: runtime: O(1) [0], size: O(1) [2]
  f: runtime: O(1) [5], size: O(n^1) [3 + z]
  if: runtime: O(1) [7], size: O(n^1) [2 + z' + z'']
  activate: runtime: O(1) [6], size: O(n^1) [2 + z]
  encArg: runtime: O(n^1) [6 + 13*z], size: O(n^1) [5 + 16*z]
  encode_activate: runtime: O(n^1) [18 + 13*z], size: O(n^1) [2 + 16*z]
  encode_if: runtime: O(n^1) [25 + 13*z + 13*z' + 13*z''], size: O(n^1) [12 + 16*z' + 16*z'']
  encode_f: runtime: O(n^1) [17 + 13*z], size: O(n^1) [3 + 16*z]

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

(71) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: encode_n__f
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 6 + 16*z

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

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

   activate(z) -{ 6 }-> s'' :|: s'' >= 0, s'' <= z - 1 + 3, z - 1 >= 0
   activate(z) -{ 1 }-> z :|: z >= 0
   encArg(z) -{ 5 }-> s1 :|: s1 >= 0, s1 <= 0 + 3, z = 1 + 0
   encArg(z) -{ -15 + 13*z }-> s19 :|: s18 >= 0, s18 <= 16 * (z - 2) + 5, s19 >= 0, s19 <= 1 + s18 + 3, z - 2 >= 0
   encArg(z) -{ 5 }-> s2 :|: s2 >= 0, s2 <= 2 + 3, z = 1 + 2
   encArg(z) -{ -10 + 13*z }-> s22 :|: s20 >= 0, s20 <= 16 * (z - 2) + 5, s21 >= 0, s21 <= s20 + 3, s22 >= 0, s22 <= s21 + 3, z - 2 >= 0
   encArg(z) -{ 30 + 13*x_11 + 13*x_2' + 13*x_3' }-> s27 :|: s23 >= 0, s23 <= 16 * x_11 + 5, s24 >= 0, s24 <= 16 * x_2' + 5, s25 >= 0, s25 <= 16 * x_3' + 5, s26 >= 0, s26 <= s25 + 2 + s24, s27 >= 0, s27 <= s26 + 3, x_11 >= 0, x_3' >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2' + x_3')
   encArg(z) -{ 5 }-> s3 :|: s3 >= 0, s3 <= 1 + 3, z = 1 + 1
   encArg(z) -{ -9 + 13*z }-> s30 :|: s28 >= 0, s28 <= 16 * (z - 2) + 5, s29 >= 0, s29 <= s28 + 2, s30 >= 0, s30 <= s29 + 3, z - 2 >= 0
   encArg(z) -{ 25 + 13*x_1 + 13*x_2 + 13*x_3 }-> s34 :|: s31 >= 0, s31 <= 16 * x_1 + 5, s32 >= 0, s32 <= 16 * x_2 + 5, s33 >= 0, s33 <= 16 * x_3 + 5, s34 >= 0, s34 <= s33 + 2 + s32, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ -14 + 13*z }-> s36 :|: s35 >= 0, s35 <= 16 * (z - 2) + 5, s36 >= 0, s36 <= 1 + s35 + 2, z - 2 >= 0
   encArg(z) -{ -9 + 13*z }-> s39 :|: s37 >= 0, s37 <= 16 * (z - 2) + 5, s38 >= 0, s38 <= s37 + 3, s39 >= 0, s39 <= s38 + 2, z - 2 >= 0
   encArg(z) -{ 5 }-> s4 :|: s4 >= 0, s4 <= 0 + 3, z - 1 >= 0
   encArg(z) -{ 31 + 13*x_1297 + 13*x_273 + 13*x_373 }-> s44 :|: s40 >= 0, s40 <= 16 * x_1297 + 5, s41 >= 0, s41 <= 16 * x_273 + 5, s42 >= 0, s42 <= 16 * x_373 + 5, s43 >= 0, s43 <= s42 + 2 + s41, s44 >= 0, s44 <= s43 + 2, z = 1 + (1 + x_1297 + x_273 + x_373), x_373 >= 0, x_273 >= 0, x_1297 >= 0
   encArg(z) -{ -8 + 13*z }-> s47 :|: s45 >= 0, s45 <= 16 * (z - 2) + 5, s46 >= 0, s46 <= s45 + 2, s47 >= 0, s47 <= s46 + 2, z - 2 >= 0
   encArg(z) -{ 6 }-> s5 :|: s5 >= 0, s5 <= 0 + 2, z = 1 + 0
   encArg(z) -{ 6 }-> s6 :|: s6 >= 0, s6 <= 2 + 2, z = 1 + 2
   encArg(z) -{ 6 }-> s7 :|: s7 >= 0, s7 <= 1 + 2, z = 1 + 1
   encArg(z) -{ 6 }-> s8 :|: s8 >= 0, s8 <= 0 + 2, z - 1 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ -7 + 13*z }-> 1 + s17 :|: s17 >= 0, s17 <= 16 * (z - 1) + 5, z - 1 >= 0
   encode_activate(z) -{ 6 }-> s13 :|: s13 >= 0, s13 <= 0 + 2, z = 0
   encode_activate(z) -{ 6 }-> s14 :|: s14 >= 0, s14 <= 2 + 2, z = 2
   encode_activate(z) -{ 6 }-> s15 :|: s15 >= 0, s15 <= 1 + 2, z = 1
   encode_activate(z) -{ 6 }-> s16 :|: s16 >= 0, s16 <= 0 + 2, z >= 0
   encode_activate(z) -{ -1 + 13*z }-> s67 :|: s66 >= 0, s66 <= 16 * (z - 1) + 5, s67 >= 0, s67 <= 1 + s66 + 2, z - 1 >= 0
   encode_activate(z) -{ 4 + 13*z }-> s70 :|: s68 >= 0, s68 <= 16 * (z - 1) + 5, s69 >= 0, s69 <= s68 + 3, s70 >= 0, s70 <= s69 + 2, z - 1 >= 0
   encode_activate(z) -{ 31 + 13*x_1597 + 13*x_2148 + 13*x_3148 }-> s75 :|: s71 >= 0, s71 <= 16 * x_1597 + 5, s72 >= 0, s72 <= 16 * x_2148 + 5, s73 >= 0, s73 <= 16 * x_3148 + 5, s74 >= 0, s74 <= s73 + 2 + s72, s75 >= 0, s75 <= s74 + 2, z = 1 + x_1597 + x_2148 + x_3148, x_3148 >= 0, x_2148 >= 0, x_1597 >= 0
   encode_activate(z) -{ 5 + 13*z }-> s78 :|: s76 >= 0, s76 <= 16 * (z - 1) + 5, s77 >= 0, s77 <= s76 + 2, s78 >= 0, s78 <= s77 + 2, z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z) -{ 5 }-> s10 :|: s10 >= 0, s10 <= 2 + 3, z = 2
   encode_f(z) -{ 5 }-> s11 :|: s11 >= 0, s11 <= 1 + 3, z = 1
   encode_f(z) -{ 5 }-> s12 :|: s12 >= 0, s12 <= 0 + 3, z >= 0
   encode_f(z) -{ -2 + 13*z }-> s49 :|: s48 >= 0, s48 <= 16 * (z - 1) + 5, s49 >= 0, s49 <= 1 + s48 + 3, z - 1 >= 0
   encode_f(z) -{ 3 + 13*z }-> s52 :|: s50 >= 0, s50 <= 16 * (z - 1) + 5, s51 >= 0, s51 <= s50 + 3, s52 >= 0, s52 <= s51 + 3, z - 1 >= 0
   encode_f(z) -{ 30 + 13*x_1301 + 13*x_274 + 13*x_374 }-> s57 :|: s53 >= 0, s53 <= 16 * x_1301 + 5, s54 >= 0, s54 <= 16 * x_274 + 5, s55 >= 0, s55 <= 16 * x_374 + 5, s56 >= 0, s56 <= s55 + 2 + s54, s57 >= 0, s57 <= s56 + 3, x_374 >= 0, x_274 >= 0, z = 1 + x_1301 + x_274 + x_374, x_1301 >= 0
   encode_f(z) -{ 4 + 13*z }-> s60 :|: s58 >= 0, s58 <= 16 * (z - 1) + 5, s59 >= 0, s59 <= s58 + 2, s60 >= 0, s60 <= s59 + 3, z - 1 >= 0
   encode_f(z) -{ 5 }-> s9 :|: s9 >= 0, s9 <= 0 + 3, z = 0
   encode_f(z) -{ 0 }-> 0 :|: z >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_if(z, z', z'') -{ 25 + 13*z + 13*z' + 13*z'' }-> s64 :|: s61 >= 0, s61 <= 16 * z + 5, s62 >= 0, s62 <= 16 * z' + 5, s63 >= 0, s63 <= 16 * z'' + 5, s64 >= 0, s64 <= s63 + 2 + s62, z >= 0, z'' >= 0, z' >= 0
   encode_if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_n__f(z) -{ 0 }-> 0 :|: z >= 0
   encode_n__f(z) -{ 6 + 13*z }-> 1 + s65 :|: s65 >= 0, s65 <= 16 * z + 5, z >= 0
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   f(z) -{ 8 }-> s :|: s >= 0, s <= 1 + 2 + 2 + 0, z >= 0
   f(z) -{ 1 }-> 1 + z :|: z >= 0
   if(z, z', z'') -{ 7 }-> s' :|: s' >= 0, s' <= z'' + 2, z'' >= 0, z = 1, z' >= 0
   if(z, z', z'') -{ 1 }-> z' :|: z = 2, z'' >= 0, z' >= 0
   if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0

Function symbols to be analyzed: {encode_n__f}
Previous analysis results are:
  encode_false: runtime: O(1) [0], size: O(1) [1]
  encode_c: runtime: O(1) [0], size: O(1) [0]
  encode_true: runtime: O(1) [0], size: O(1) [2]
  f: runtime: O(1) [5], size: O(n^1) [3 + z]
  if: runtime: O(1) [7], size: O(n^1) [2 + z' + z'']
  activate: runtime: O(1) [6], size: O(n^1) [2 + z]
  encArg: runtime: O(n^1) [6 + 13*z], size: O(n^1) [5 + 16*z]
  encode_activate: runtime: O(n^1) [18 + 13*z], size: O(n^1) [2 + 16*z]
  encode_if: runtime: O(n^1) [25 + 13*z + 13*z' + 13*z''], size: O(n^1) [12 + 16*z' + 16*z'']
  encode_f: runtime: O(n^1) [17 + 13*z], size: O(n^1) [3 + 16*z]
  encode_n__f: runtime: ?, size: O(n^1) [6 + 16*z]

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

(73) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: encode_n__f
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 6 + 13*z

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

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

   activate(z) -{ 6 }-> s'' :|: s'' >= 0, s'' <= z - 1 + 3, z - 1 >= 0
   activate(z) -{ 1 }-> z :|: z >= 0
   encArg(z) -{ 5 }-> s1 :|: s1 >= 0, s1 <= 0 + 3, z = 1 + 0
   encArg(z) -{ -15 + 13*z }-> s19 :|: s18 >= 0, s18 <= 16 * (z - 2) + 5, s19 >= 0, s19 <= 1 + s18 + 3, z - 2 >= 0
   encArg(z) -{ 5 }-> s2 :|: s2 >= 0, s2 <= 2 + 3, z = 1 + 2
   encArg(z) -{ -10 + 13*z }-> s22 :|: s20 >= 0, s20 <= 16 * (z - 2) + 5, s21 >= 0, s21 <= s20 + 3, s22 >= 0, s22 <= s21 + 3, z - 2 >= 0
   encArg(z) -{ 30 + 13*x_11 + 13*x_2' + 13*x_3' }-> s27 :|: s23 >= 0, s23 <= 16 * x_11 + 5, s24 >= 0, s24 <= 16 * x_2' + 5, s25 >= 0, s25 <= 16 * x_3' + 5, s26 >= 0, s26 <= s25 + 2 + s24, s27 >= 0, s27 <= s26 + 3, x_11 >= 0, x_3' >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2' + x_3')
   encArg(z) -{ 5 }-> s3 :|: s3 >= 0, s3 <= 1 + 3, z = 1 + 1
   encArg(z) -{ -9 + 13*z }-> s30 :|: s28 >= 0, s28 <= 16 * (z - 2) + 5, s29 >= 0, s29 <= s28 + 2, s30 >= 0, s30 <= s29 + 3, z - 2 >= 0
   encArg(z) -{ 25 + 13*x_1 + 13*x_2 + 13*x_3 }-> s34 :|: s31 >= 0, s31 <= 16 * x_1 + 5, s32 >= 0, s32 <= 16 * x_2 + 5, s33 >= 0, s33 <= 16 * x_3 + 5, s34 >= 0, s34 <= s33 + 2 + s32, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ -14 + 13*z }-> s36 :|: s35 >= 0, s35 <= 16 * (z - 2) + 5, s36 >= 0, s36 <= 1 + s35 + 2, z - 2 >= 0
   encArg(z) -{ -9 + 13*z }-> s39 :|: s37 >= 0, s37 <= 16 * (z - 2) + 5, s38 >= 0, s38 <= s37 + 3, s39 >= 0, s39 <= s38 + 2, z - 2 >= 0
   encArg(z) -{ 5 }-> s4 :|: s4 >= 0, s4 <= 0 + 3, z - 1 >= 0
   encArg(z) -{ 31 + 13*x_1297 + 13*x_273 + 13*x_373 }-> s44 :|: s40 >= 0, s40 <= 16 * x_1297 + 5, s41 >= 0, s41 <= 16 * x_273 + 5, s42 >= 0, s42 <= 16 * x_373 + 5, s43 >= 0, s43 <= s42 + 2 + s41, s44 >= 0, s44 <= s43 + 2, z = 1 + (1 + x_1297 + x_273 + x_373), x_373 >= 0, x_273 >= 0, x_1297 >= 0
   encArg(z) -{ -8 + 13*z }-> s47 :|: s45 >= 0, s45 <= 16 * (z - 2) + 5, s46 >= 0, s46 <= s45 + 2, s47 >= 0, s47 <= s46 + 2, z - 2 >= 0
   encArg(z) -{ 6 }-> s5 :|: s5 >= 0, s5 <= 0 + 2, z = 1 + 0
   encArg(z) -{ 6 }-> s6 :|: s6 >= 0, s6 <= 2 + 2, z = 1 + 2
   encArg(z) -{ 6 }-> s7 :|: s7 >= 0, s7 <= 1 + 2, z = 1 + 1
   encArg(z) -{ 6 }-> s8 :|: s8 >= 0, s8 <= 0 + 2, z - 1 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ -7 + 13*z }-> 1 + s17 :|: s17 >= 0, s17 <= 16 * (z - 1) + 5, z - 1 >= 0
   encode_activate(z) -{ 6 }-> s13 :|: s13 >= 0, s13 <= 0 + 2, z = 0
   encode_activate(z) -{ 6 }-> s14 :|: s14 >= 0, s14 <= 2 + 2, z = 2
   encode_activate(z) -{ 6 }-> s15 :|: s15 >= 0, s15 <= 1 + 2, z = 1
   encode_activate(z) -{ 6 }-> s16 :|: s16 >= 0, s16 <= 0 + 2, z >= 0
   encode_activate(z) -{ -1 + 13*z }-> s67 :|: s66 >= 0, s66 <= 16 * (z - 1) + 5, s67 >= 0, s67 <= 1 + s66 + 2, z - 1 >= 0
   encode_activate(z) -{ 4 + 13*z }-> s70 :|: s68 >= 0, s68 <= 16 * (z - 1) + 5, s69 >= 0, s69 <= s68 + 3, s70 >= 0, s70 <= s69 + 2, z - 1 >= 0
   encode_activate(z) -{ 31 + 13*x_1597 + 13*x_2148 + 13*x_3148 }-> s75 :|: s71 >= 0, s71 <= 16 * x_1597 + 5, s72 >= 0, s72 <= 16 * x_2148 + 5, s73 >= 0, s73 <= 16 * x_3148 + 5, s74 >= 0, s74 <= s73 + 2 + s72, s75 >= 0, s75 <= s74 + 2, z = 1 + x_1597 + x_2148 + x_3148, x_3148 >= 0, x_2148 >= 0, x_1597 >= 0
   encode_activate(z) -{ 5 + 13*z }-> s78 :|: s76 >= 0, s76 <= 16 * (z - 1) + 5, s77 >= 0, s77 <= s76 + 2, s78 >= 0, s78 <= s77 + 2, z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z) -{ 5 }-> s10 :|: s10 >= 0, s10 <= 2 + 3, z = 2
   encode_f(z) -{ 5 }-> s11 :|: s11 >= 0, s11 <= 1 + 3, z = 1
   encode_f(z) -{ 5 }-> s12 :|: s12 >= 0, s12 <= 0 + 3, z >= 0
   encode_f(z) -{ -2 + 13*z }-> s49 :|: s48 >= 0, s48 <= 16 * (z - 1) + 5, s49 >= 0, s49 <= 1 + s48 + 3, z - 1 >= 0
   encode_f(z) -{ 3 + 13*z }-> s52 :|: s50 >= 0, s50 <= 16 * (z - 1) + 5, s51 >= 0, s51 <= s50 + 3, s52 >= 0, s52 <= s51 + 3, z - 1 >= 0
   encode_f(z) -{ 30 + 13*x_1301 + 13*x_274 + 13*x_374 }-> s57 :|: s53 >= 0, s53 <= 16 * x_1301 + 5, s54 >= 0, s54 <= 16 * x_274 + 5, s55 >= 0, s55 <= 16 * x_374 + 5, s56 >= 0, s56 <= s55 + 2 + s54, s57 >= 0, s57 <= s56 + 3, x_374 >= 0, x_274 >= 0, z = 1 + x_1301 + x_274 + x_374, x_1301 >= 0
   encode_f(z) -{ 4 + 13*z }-> s60 :|: s58 >= 0, s58 <= 16 * (z - 1) + 5, s59 >= 0, s59 <= s58 + 2, s60 >= 0, s60 <= s59 + 3, z - 1 >= 0
   encode_f(z) -{ 5 }-> s9 :|: s9 >= 0, s9 <= 0 + 3, z = 0
   encode_f(z) -{ 0 }-> 0 :|: z >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_if(z, z', z'') -{ 25 + 13*z + 13*z' + 13*z'' }-> s64 :|: s61 >= 0, s61 <= 16 * z + 5, s62 >= 0, s62 <= 16 * z' + 5, s63 >= 0, s63 <= 16 * z'' + 5, s64 >= 0, s64 <= s63 + 2 + s62, z >= 0, z'' >= 0, z' >= 0
   encode_if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_n__f(z) -{ 0 }-> 0 :|: z >= 0
   encode_n__f(z) -{ 6 + 13*z }-> 1 + s65 :|: s65 >= 0, s65 <= 16 * z + 5, z >= 0
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   f(z) -{ 8 }-> s :|: s >= 0, s <= 1 + 2 + 2 + 0, z >= 0
   f(z) -{ 1 }-> 1 + z :|: z >= 0
   if(z, z', z'') -{ 7 }-> s' :|: s' >= 0, s' <= z'' + 2, z'' >= 0, z = 1, z' >= 0
   if(z, z', z'') -{ 1 }-> z' :|: z = 2, z'' >= 0, z' >= 0
   if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0

Function symbols to be analyzed: 
Previous analysis results are:
  encode_false: runtime: O(1) [0], size: O(1) [1]
  encode_c: runtime: O(1) [0], size: O(1) [0]
  encode_true: runtime: O(1) [0], size: O(1) [2]
  f: runtime: O(1) [5], size: O(n^1) [3 + z]
  if: runtime: O(1) [7], size: O(n^1) [2 + z' + z'']
  activate: runtime: O(1) [6], size: O(n^1) [2 + z]
  encArg: runtime: O(n^1) [6 + 13*z], size: O(n^1) [5 + 16*z]
  encode_activate: runtime: O(n^1) [18 + 13*z], size: O(n^1) [2 + 16*z]
  encode_if: runtime: O(n^1) [25 + 13*z + 13*z' + 13*z''], size: O(n^1) [12 + 16*z' + 16*z'']
  encode_f: runtime: O(n^1) [17 + 13*z], size: O(n^1) [3 + 16*z]
  encode_n__f: runtime: O(n^1) [6 + 13*z], size: O(n^1) [6 + 16*z]

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

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

(76)
BOUNDS(1, n^1)