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


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


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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


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

(0) DCpxTrs
(1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms]
(2) CpxRelTRS
(3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 177 ms]
(4) CpxRelTRS
(5) NonCtorToCtorProof [UPPER BOUND(ID), 0 ms]
(6) CpxRelTRS
(7) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
(8) CpxWeightedTrs
(9) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(10) CpxWeightedTrs
(11) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
(12) CpxTypedWeightedTrs
(13) CompletionProof [UPPER BOUND(ID), 0 ms]
(14) CpxTypedWeightedCompleteTrs
(15) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
(16) CpxTypedWeightedCompleteTrs
(17) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
(18) CpxRNTS
(19) InliningProof [UPPER BOUND(ID), 228 ms]
(20) CpxRNTS
(21) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
(22) CpxRNTS
(23) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms]
(24) CpxRNTS
(25) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(26) CpxRNTS
(27) IntTrsBoundProof [UPPER BOUND(ID), 111 ms]
(28) CpxRNTS
(29) IntTrsBoundProof [UPPER BOUND(ID), 33 ms]
(30) CpxRNTS
(31) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(32) CpxRNTS
(33) IntTrsBoundProof [UPPER BOUND(ID), 66 ms]
(34) CpxRNTS
(35) IntTrsBoundProof [UPPER BOUND(ID), 0 ms]
(36) CpxRNTS
(37) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(38) CpxRNTS
(39) IntTrsBoundProof [UPPER BOUND(ID), 148 ms]
(40) CpxRNTS
(41) IntTrsBoundProof [UPPER BOUND(ID), 52 ms]
(42) CpxRNTS
(43) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(44) CpxRNTS
(45) IntTrsBoundProof [UPPER BOUND(ID), 180 ms]
(46) CpxRNTS
(47) IntTrsBoundProof [UPPER BOUND(ID), 63 ms]
(48) CpxRNTS
(49) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(50) CpxRNTS
(51) IntTrsBoundProof [UPPER BOUND(ID), 106 ms]
(52) CpxRNTS
(53) IntTrsBoundProof [UPPER BOUND(ID), 31 ms]
(54) CpxRNTS
(55) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(56) CpxRNTS
(57) IntTrsBoundProof [UPPER BOUND(ID), 664 ms]
(58) CpxRNTS
(59) IntTrsBoundProof [UPPER BOUND(ID), 361 ms]
(60) CpxRNTS
(61) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(62) CpxRNTS
(63) IntTrsBoundProof [UPPER BOUND(ID), 148 ms]
(64) CpxRNTS
(65) IntTrsBoundProof [UPPER BOUND(ID), 63 ms]
(66) CpxRNTS
(67) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(68) CpxRNTS
(69) IntTrsBoundProof [UPPER BOUND(ID), 300 ms]
(70) CpxRNTS
(71) IntTrsBoundProof [UPPER BOUND(ID), 108 ms]
(72) CpxRNTS
(73) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(74) CpxRNTS
(75) IntTrsBoundProof [UPPER BOUND(ID), 138 ms]
(76) CpxRNTS
(77) IntTrsBoundProof [UPPER BOUND(ID), 53 ms]
(78) CpxRNTS
(79) FinalProof [FINISHED, 0 ms]
(80) BOUNDS(1, n^1)


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

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


The TRS R consists of the following rules:

   f(s(x)) -> f(g(x, x))
   g(0, 1) -> s(0)
   0 -> 1

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

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

   encArg(s(x_1)) -> s(encArg(x_1))
   encArg(1) -> 1
   encArg(cons_f(x_1)) -> f(encArg(x_1))
   encArg(cons_g(x_1, x_2)) -> g(encArg(x_1), encArg(x_2))
   encArg(cons_0) -> 0
   encode_f(x_1) -> f(encArg(x_1))
   encode_s(x_1) -> s(encArg(x_1))
   encode_g(x_1, x_2) -> g(encArg(x_1), encArg(x_2))
   encode_0 -> 0
   encode_1 -> 1


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

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


The TRS R consists of the following rules:

   f(s(x)) -> f(g(x, x))
   g(0, 1) -> s(0)
   0 -> 1

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

   encArg(s(x_1)) -> s(encArg(x_1))
   encArg(1) -> 1
   encArg(cons_f(x_1)) -> f(encArg(x_1))
   encArg(cons_g(x_1, x_2)) -> g(encArg(x_1), encArg(x_2))
   encArg(cons_0) -> 0
   encode_f(x_1) -> f(encArg(x_1))
   encode_s(x_1) -> s(encArg(x_1))
   encode_g(x_1, x_2) -> g(encArg(x_1), encArg(x_2))
   encode_0 -> 0
   encode_1 -> 1

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

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

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


The TRS R consists of the following rules:

   f(s(x)) -> f(g(x, x))
   g(0, 1) -> s(0)
   0 -> 1

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

   encArg(s(x_1)) -> s(encArg(x_1))
   encArg(1) -> 1
   encArg(cons_f(x_1)) -> f(encArg(x_1))
   encArg(cons_g(x_1, x_2)) -> g(encArg(x_1), encArg(x_2))
   encArg(cons_0) -> 0
   encode_f(x_1) -> f(encArg(x_1))
   encode_s(x_1) -> s(encArg(x_1))
   encode_g(x_1, x_2) -> g(encArg(x_1), encArg(x_2))
   encode_0 -> 0
   encode_1 -> 1

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

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

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


The TRS R consists of the following rules:

   f(s(x)) -> f(g(x, x))
   0 -> 1
   g(c_0, 1) -> s(0)

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

   encArg(s(x_1)) -> s(encArg(x_1))
   encArg(1) -> 1
   encArg(cons_f(x_1)) -> f(encArg(x_1))
   encArg(cons_g(x_1, x_2)) -> g(encArg(x_1), encArg(x_2))
   encArg(cons_0) -> 0
   encode_f(x_1) -> f(encArg(x_1))
   encode_s(x_1) -> s(encArg(x_1))
   encode_g(x_1, x_2) -> g(encArg(x_1), encArg(x_2))
   encode_0 -> 0
   encode_1 -> 1
   0 -> c_0

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(s(x)) -> f(g(x, x)) [1]
   0 -> 1 [1]
   g(c_0, 1) -> s(0) [1]
   encArg(s(x_1)) -> s(encArg(x_1)) [0]
   encArg(1) -> 1 [0]
   encArg(cons_f(x_1)) -> f(encArg(x_1)) [0]
   encArg(cons_g(x_1, x_2)) -> g(encArg(x_1), encArg(x_2)) [0]
   encArg(cons_0) -> 0 [0]
   encode_f(x_1) -> f(encArg(x_1)) [0]
   encode_s(x_1) -> s(encArg(x_1)) [0]
   encode_g(x_1, x_2) -> g(encArg(x_1), encArg(x_2)) [0]
   encode_0 -> 0 [0]
   encode_1 -> 1 [0]
   0 -> c_0 [0]

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

(9) CpxWeightedTrsRenamingProof (BOTH BOUNDS(ID, ID))
Renamed defined symbols to avoid conflicts with arithmetic symbols:

0 => 0'

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

(10)
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(s(x)) -> f(g(x, x)) [1]
   0' -> 1 [1]
   g(c_0, 1) -> s(0') [1]
   encArg(s(x_1)) -> s(encArg(x_1)) [0]
   encArg(1) -> 1 [0]
   encArg(cons_f(x_1)) -> f(encArg(x_1)) [0]
   encArg(cons_g(x_1, x_2)) -> g(encArg(x_1), encArg(x_2)) [0]
   encArg(cons_0) -> 0' [0]
   encode_f(x_1) -> f(encArg(x_1)) [0]
   encode_s(x_1) -> s(encArg(x_1)) [0]
   encode_g(x_1, x_2) -> g(encArg(x_1), encArg(x_2)) [0]
   encode_0 -> 0' [0]
   encode_1 -> 1 [0]
   0' -> c_0 [0]

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

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

(12)
Obligation:
Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   f(s(x)) -> f(g(x, x)) [1]
   0' -> 1 [1]
   g(c_0, 1) -> s(0') [1]
   encArg(s(x_1)) -> s(encArg(x_1)) [0]
   encArg(1) -> 1 [0]
   encArg(cons_f(x_1)) -> f(encArg(x_1)) [0]
   encArg(cons_g(x_1, x_2)) -> g(encArg(x_1), encArg(x_2)) [0]
   encArg(cons_0) -> 0' [0]
   encode_f(x_1) -> f(encArg(x_1)) [0]
   encode_s(x_1) -> s(encArg(x_1)) [0]
   encode_g(x_1, x_2) -> g(encArg(x_1), encArg(x_2)) [0]
   encode_0 -> 0' [0]
   encode_1 -> 1 [0]
   0' -> c_0 [0]

The TRS has the following type information:
f :: s:1:c_0:cons_f:cons_g:cons_0 -> s:1:c_0:cons_f:cons_g:cons_0
s :: s:1:c_0:cons_f:cons_g:cons_0 -> s:1:c_0:cons_f:cons_g:cons_0
g :: s:1:c_0:cons_f:cons_g:cons_0 -> s:1:c_0:cons_f:cons_g:cons_0 -> s:1:c_0:cons_f:cons_g:cons_0
0' :: s:1:c_0:cons_f:cons_g:cons_0
1 :: s:1:c_0:cons_f:cons_g:cons_0
c_0 :: s:1:c_0:cons_f:cons_g:cons_0
encArg :: s:1:c_0:cons_f:cons_g:cons_0 -> s:1:c_0:cons_f:cons_g:cons_0
cons_f :: s:1:c_0:cons_f:cons_g:cons_0 -> s:1:c_0:cons_f:cons_g:cons_0
cons_g :: s:1:c_0:cons_f:cons_g:cons_0 -> s:1:c_0:cons_f:cons_g:cons_0 -> s:1:c_0:cons_f:cons_g:cons_0
cons_0 :: s:1:c_0:cons_f:cons_g:cons_0
encode_f :: s:1:c_0:cons_f:cons_g:cons_0 -> s:1:c_0:cons_f:cons_g:cons_0
encode_s :: s:1:c_0:cons_f:cons_g:cons_0 -> s:1:c_0:cons_f:cons_g:cons_0
encode_g :: s:1:c_0:cons_f:cons_g:cons_0 -> s:1:c_0:cons_f:cons_g:cons_0 -> s:1:c_0:cons_f:cons_g:cons_0
encode_0 :: s:1:c_0:cons_f:cons_g:cons_0
encode_1 :: s:1:c_0:cons_f:cons_g:cons_0

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

(13) 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:

   g_2
   f_1
   encArg_1
   encode_f_1
   encode_s_1
   encode_g_2
   encode_0
   encode_1
   0'

Due to the following rules being added:

   encArg(v0) -> null_encArg [0]
   encode_f(v0) -> null_encode_f [0]
   encode_s(v0) -> null_encode_s [0]
   encode_g(v0, v1) -> null_encode_g [0]
   encode_0 -> null_encode_0 [0]
   encode_1 -> null_encode_1 [0]
   0' -> null_0' [0]
   g(v0, v1) -> null_g [0]
   f(v0) -> null_f [0]

And the following fresh constants:    null_encArg, null_encode_f, null_encode_s, null_encode_g, null_encode_0, null_encode_1, null_0', null_g, null_f

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

(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(s(x)) -> f(g(x, x)) [1]
   0' -> 1 [1]
   g(c_0, 1) -> s(0') [1]
   encArg(s(x_1)) -> s(encArg(x_1)) [0]
   encArg(1) -> 1 [0]
   encArg(cons_f(x_1)) -> f(encArg(x_1)) [0]
   encArg(cons_g(x_1, x_2)) -> g(encArg(x_1), encArg(x_2)) [0]
   encArg(cons_0) -> 0' [0]
   encode_f(x_1) -> f(encArg(x_1)) [0]
   encode_s(x_1) -> s(encArg(x_1)) [0]
   encode_g(x_1, x_2) -> g(encArg(x_1), encArg(x_2)) [0]
   encode_0 -> 0' [0]
   encode_1 -> 1 [0]
   0' -> c_0 [0]
   encArg(v0) -> null_encArg [0]
   encode_f(v0) -> null_encode_f [0]
   encode_s(v0) -> null_encode_s [0]
   encode_g(v0, v1) -> null_encode_g [0]
   encode_0 -> null_encode_0 [0]
   encode_1 -> null_encode_1 [0]
   0' -> null_0' [0]
   g(v0, v1) -> null_g [0]
   f(v0) -> null_f [0]

The TRS has the following type information:
f :: s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f -> s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f
s :: s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f -> s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f
g :: s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f -> s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f -> s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f
0' :: s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f
1 :: s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f
c_0 :: s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f
encArg :: s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f -> s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f
cons_f :: s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f -> s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f
cons_g :: s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f -> s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f -> s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f
cons_0 :: s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f
encode_f :: s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f -> s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f
encode_s :: s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f -> s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f
encode_g :: s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f -> s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f -> s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f
encode_0 :: s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f
encode_1 :: s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f
null_encArg :: s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f
null_encode_f :: s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f
null_encode_s :: s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f
null_encode_g :: s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f
null_encode_0 :: s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f
null_encode_1 :: s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f
null_0' :: s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f
null_g :: s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f
null_f :: s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f

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

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

(16)
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(s(x)) -> f(null_g) [1]
   0' -> 1 [1]
   g(c_0, 1) -> s(0') [1]
   encArg(s(x_1)) -> s(encArg(x_1)) [0]
   encArg(1) -> 1 [0]
   encArg(cons_f(s(x_1'))) -> f(s(encArg(x_1'))) [0]
   encArg(cons_f(1)) -> f(1) [0]
   encArg(cons_f(cons_f(x_1''))) -> f(f(encArg(x_1''))) [0]
   encArg(cons_f(cons_g(x_11, x_2'))) -> f(g(encArg(x_11), encArg(x_2'))) [0]
   encArg(cons_f(cons_0)) -> f(0') [0]
   encArg(cons_f(x_1)) -> f(null_encArg) [0]
   encArg(cons_g(x_1, x_2)) -> g(encArg(x_1), encArg(x_2)) [0]
   encArg(cons_0) -> 0' [0]
   encode_f(s(x_123)) -> f(s(encArg(x_123))) [0]
   encode_f(1) -> f(1) [0]
   encode_f(cons_f(x_124)) -> f(f(encArg(x_124))) [0]
   encode_f(cons_g(x_125, x_27)) -> f(g(encArg(x_125), encArg(x_27))) [0]
   encode_f(cons_0) -> f(0') [0]
   encode_f(x_1) -> f(null_encArg) [0]
   encode_s(x_1) -> s(encArg(x_1)) [0]
   encode_g(x_1, x_2) -> g(encArg(x_1), encArg(x_2)) [0]
   encode_0 -> 0' [0]
   encode_1 -> 1 [0]
   0' -> c_0 [0]
   encArg(v0) -> null_encArg [0]
   encode_f(v0) -> null_encode_f [0]
   encode_s(v0) -> null_encode_s [0]
   encode_g(v0, v1) -> null_encode_g [0]
   encode_0 -> null_encode_0 [0]
   encode_1 -> null_encode_1 [0]
   0' -> null_0' [0]
   g(v0, v1) -> null_g [0]
   f(v0) -> null_f [0]

The TRS has the following type information:
f :: s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f -> s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f
s :: s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f -> s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f
g :: s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f -> s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f -> s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f
0' :: s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f
1 :: s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f
c_0 :: s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f
encArg :: s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f -> s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f
cons_f :: s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f -> s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f
cons_g :: s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f -> s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f -> s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f
cons_0 :: s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f
encode_f :: s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f -> s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f
encode_s :: s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f -> s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f
encode_g :: s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f -> s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f -> s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f
encode_0 :: s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f
encode_1 :: s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f
null_encArg :: s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f
null_encode_f :: s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f
null_encode_s :: s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f
null_encode_g :: s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f
null_encode_0 :: s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f
null_encode_1 :: s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f
null_0' :: s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f
null_g :: s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f
null_f :: s:1:c_0:cons_f:cons_g:cons_0:null_encArg:null_encode_f:null_encode_s:null_encode_g:null_encode_0:null_encode_1:null_0':null_g:null_f

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

   1 => 0
   c_0 => 1
   cons_0 => 2
   null_encArg => 0
   null_encode_f => 0
   null_encode_s => 0
   null_encode_g => 0
   null_encode_0 => 0
   null_encode_1 => 0
   null_0' => 0
   null_g => 0
   null_f => 0

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

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

   0' -{ 0 }-> 1 :|: 
   0' -{ 1 }-> 0 :|: 
   0' -{ 0 }-> 0 :|: 
   encArg(z) -{ 0 }-> g(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> f(g(encArg(x_11), encArg(x_2'))) :|: x_11 >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2')
   encArg(z) -{ 0 }-> f(f(encArg(x_1''))) :|: z = 1 + (1 + x_1''), x_1'' >= 0
   encArg(z) -{ 0 }-> f(0') :|: z = 1 + 2
   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 }-> 0' :|: z = 2
   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_0 -{ 0 }-> 0' :|: 
   encode_0 -{ 0 }-> 0 :|: 
   encode_1 -{ 0 }-> 0 :|: 
   encode_f(z) -{ 0 }-> f(g(encArg(x_125), encArg(x_27))) :|: x_125 >= 0, x_27 >= 0, z = 1 + x_125 + x_27
   encode_f(z) -{ 0 }-> f(f(encArg(x_124))) :|: x_124 >= 0, z = 1 + x_124
   encode_f(z) -{ 0 }-> f(0') :|: z = 2
   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_123)) :|: x_123 >= 0, z = 1 + x_123
   encode_f(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_g(z, z') -{ 0 }-> g(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2
   encode_g(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   encode_s(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_s(z) -{ 0 }-> 1 + encArg(x_1) :|: x_1 >= 0, z = x_1
   f(z) -{ 1 }-> f(0) :|: x >= 0, z = 1 + x
   f(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   g(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   g(z, z') -{ 1 }-> 1 + 0' :|: z = 1, z' = 0


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

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

   0' -{ 0 }-> 1 :|: 
   0' -{ 0 }-> 0 :|: 
   0' -{ 1 }-> 0 :|: 
   g(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   g(z, z') -{ 1 }-> 1 + 0' :|: z = 1, z' = 0

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

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

   0' -{ 0 }-> 1 :|: 
   0' -{ 1 }-> 0 :|: 
   0' -{ 0 }-> 0 :|: 
   encArg(z) -{ 0 }-> g(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> f(g(encArg(x_11), encArg(x_2'))) :|: x_11 >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2')
   encArg(z) -{ 0 }-> f(f(encArg(x_1''))) :|: z = 1 + (1 + x_1''), x_1'' >= 0
   encArg(z) -{ 0 }-> f(1) :|: z = 1 + 2
   encArg(z) -{ 0 }-> f(0) :|: z = 1 + 0
   encArg(z) -{ 0 }-> f(0) :|: z = 1 + x_1, x_1 >= 0
   encArg(z) -{ 0 }-> f(0) :|: z = 1 + 2
   encArg(z) -{ 1 }-> f(0) :|: z = 1 + 2
   encArg(z) -{ 0 }-> f(1 + encArg(x_1')) :|: z = 1 + (1 + x_1'), x_1' >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 0 }-> 1 + encArg(x_1) :|: z = 1 + x_1, x_1 >= 0
   encode_0 -{ 0 }-> 1 :|: 
   encode_0 -{ 0 }-> 0 :|: 
   encode_0 -{ 1 }-> 0 :|: 
   encode_1 -{ 0 }-> 0 :|: 
   encode_f(z) -{ 0 }-> f(g(encArg(x_125), encArg(x_27))) :|: x_125 >= 0, x_27 >= 0, z = 1 + x_125 + x_27
   encode_f(z) -{ 0 }-> f(f(encArg(x_124))) :|: x_124 >= 0, z = 1 + x_124
   encode_f(z) -{ 0 }-> f(1) :|: z = 2
   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(0) :|: z = 2
   encode_f(z) -{ 1 }-> f(0) :|: z = 2
   encode_f(z) -{ 0 }-> f(1 + encArg(x_123)) :|: x_123 >= 0, z = 1 + x_123
   encode_f(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_g(z, z') -{ 0 }-> g(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2
   encode_g(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   encode_s(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_s(z) -{ 0 }-> 1 + encArg(x_1) :|: x_1 >= 0, z = x_1
   f(z) -{ 1 }-> f(0) :|: x >= 0, z = 1 + x
   f(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   g(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   g(z, z') -{ 1 }-> 1 + 1 :|: z = 1, z' = 0
   g(z, z') -{ 1 }-> 1 + 0 :|: z = 1, z' = 0
   g(z, z') -{ 2 }-> 1 + 0 :|: z = 1, z' = 0


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

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

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

   0' -{ 0 }-> 1 :|: 
   0' -{ 1 }-> 0 :|: 
   0' -{ 0 }-> 0 :|: 
   encArg(z) -{ 0 }-> g(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> f(g(encArg(x_11), encArg(x_2'))) :|: x_11 >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2')
   encArg(z) -{ 0 }-> f(f(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(1) :|: z = 1 + 2
   encArg(z) -{ 0 }-> f(0) :|: z = 1 + 0
   encArg(z) -{ 0 }-> f(0) :|: z - 1 >= 0
   encArg(z) -{ 0 }-> f(0) :|: z = 1 + 2
   encArg(z) -{ 1 }-> f(0) :|: z = 1 + 2
   encArg(z) -{ 0 }-> f(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_0 -{ 0 }-> 1 :|: 
   encode_0 -{ 0 }-> 0 :|: 
   encode_0 -{ 1 }-> 0 :|: 
   encode_1 -{ 0 }-> 0 :|: 
   encode_f(z) -{ 0 }-> f(g(encArg(x_125), encArg(x_27))) :|: x_125 >= 0, x_27 >= 0, z = 1 + x_125 + x_27
   encode_f(z) -{ 0 }-> f(f(encArg(z - 1))) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> f(1) :|: z = 2
   encode_f(z) -{ 0 }-> f(0) :|: z = 0
   encode_f(z) -{ 0 }-> f(0) :|: z >= 0
   encode_f(z) -{ 0 }-> f(0) :|: z = 2
   encode_f(z) -{ 1 }-> f(0) :|: z = 2
   encode_f(z) -{ 0 }-> f(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z, z') -{ 0 }-> g(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   f(z) -{ 1 }-> f(0) :|: z - 1 >= 0
   f(z) -{ 0 }-> 0 :|: z >= 0
   g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   g(z, z') -{ 1 }-> 1 + 1 :|: z = 1, z' = 0
   g(z, z') -{ 1 }-> 1 + 0 :|: z = 1, z' = 0
   g(z, z') -{ 2 }-> 1 + 0 :|: z = 1, z' = 0


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

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

   { encode_0 }
   { encode_1 }
   { f }
   { g }
   { 0' }
   { encArg }
   { encode_g }
   { encode_f }
   { encode_s }

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

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

   0' -{ 0 }-> 1 :|: 
   0' -{ 1 }-> 0 :|: 
   0' -{ 0 }-> 0 :|: 
   encArg(z) -{ 0 }-> g(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> f(g(encArg(x_11), encArg(x_2'))) :|: x_11 >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2')
   encArg(z) -{ 0 }-> f(f(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(1) :|: z = 1 + 2
   encArg(z) -{ 0 }-> f(0) :|: z = 1 + 0
   encArg(z) -{ 0 }-> f(0) :|: z - 1 >= 0
   encArg(z) -{ 0 }-> f(0) :|: z = 1 + 2
   encArg(z) -{ 1 }-> f(0) :|: z = 1 + 2
   encArg(z) -{ 0 }-> f(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_0 -{ 0 }-> 1 :|: 
   encode_0 -{ 0 }-> 0 :|: 
   encode_0 -{ 1 }-> 0 :|: 
   encode_1 -{ 0 }-> 0 :|: 
   encode_f(z) -{ 0 }-> f(g(encArg(x_125), encArg(x_27))) :|: x_125 >= 0, x_27 >= 0, z = 1 + x_125 + x_27
   encode_f(z) -{ 0 }-> f(f(encArg(z - 1))) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> f(1) :|: z = 2
   encode_f(z) -{ 0 }-> f(0) :|: z = 0
   encode_f(z) -{ 0 }-> f(0) :|: z >= 0
   encode_f(z) -{ 0 }-> f(0) :|: z = 2
   encode_f(z) -{ 1 }-> f(0) :|: z = 2
   encode_f(z) -{ 0 }-> f(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z, z') -{ 0 }-> g(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   f(z) -{ 1 }-> f(0) :|: z - 1 >= 0
   f(z) -{ 0 }-> 0 :|: z >= 0
   g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   g(z, z') -{ 1 }-> 1 + 1 :|: z = 1, z' = 0
   g(z, z') -{ 1 }-> 1 + 0 :|: z = 1, z' = 0
   g(z, z') -{ 2 }-> 1 + 0 :|: z = 1, z' = 0

Function symbols to be analyzed: {encode_0}, {encode_1}, {f}, {g}, {0'}, {encArg}, {encode_g}, {encode_f}, {encode_s}

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

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

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

   0' -{ 0 }-> 1 :|: 
   0' -{ 1 }-> 0 :|: 
   0' -{ 0 }-> 0 :|: 
   encArg(z) -{ 0 }-> g(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> f(g(encArg(x_11), encArg(x_2'))) :|: x_11 >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2')
   encArg(z) -{ 0 }-> f(f(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(1) :|: z = 1 + 2
   encArg(z) -{ 0 }-> f(0) :|: z = 1 + 0
   encArg(z) -{ 0 }-> f(0) :|: z - 1 >= 0
   encArg(z) -{ 0 }-> f(0) :|: z = 1 + 2
   encArg(z) -{ 1 }-> f(0) :|: z = 1 + 2
   encArg(z) -{ 0 }-> f(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_0 -{ 0 }-> 1 :|: 
   encode_0 -{ 0 }-> 0 :|: 
   encode_0 -{ 1 }-> 0 :|: 
   encode_1 -{ 0 }-> 0 :|: 
   encode_f(z) -{ 0 }-> f(g(encArg(x_125), encArg(x_27))) :|: x_125 >= 0, x_27 >= 0, z = 1 + x_125 + x_27
   encode_f(z) -{ 0 }-> f(f(encArg(z - 1))) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> f(1) :|: z = 2
   encode_f(z) -{ 0 }-> f(0) :|: z = 0
   encode_f(z) -{ 0 }-> f(0) :|: z >= 0
   encode_f(z) -{ 0 }-> f(0) :|: z = 2
   encode_f(z) -{ 1 }-> f(0) :|: z = 2
   encode_f(z) -{ 0 }-> f(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z, z') -{ 0 }-> g(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   f(z) -{ 1 }-> f(0) :|: z - 1 >= 0
   f(z) -{ 0 }-> 0 :|: z >= 0
   g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   g(z, z') -{ 1 }-> 1 + 1 :|: z = 1, z' = 0
   g(z, z') -{ 1 }-> 1 + 0 :|: z = 1, z' = 0
   g(z, z') -{ 2 }-> 1 + 0 :|: z = 1, z' = 0

Function symbols to be analyzed: {encode_0}, {encode_1}, {f}, {g}, {0'}, {encArg}, {encode_g}, {encode_f}, {encode_s}

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

(27) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: encode_0
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 1

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

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

   0' -{ 0 }-> 1 :|: 
   0' -{ 1 }-> 0 :|: 
   0' -{ 0 }-> 0 :|: 
   encArg(z) -{ 0 }-> g(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> f(g(encArg(x_11), encArg(x_2'))) :|: x_11 >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2')
   encArg(z) -{ 0 }-> f(f(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(1) :|: z = 1 + 2
   encArg(z) -{ 0 }-> f(0) :|: z = 1 + 0
   encArg(z) -{ 0 }-> f(0) :|: z - 1 >= 0
   encArg(z) -{ 0 }-> f(0) :|: z = 1 + 2
   encArg(z) -{ 1 }-> f(0) :|: z = 1 + 2
   encArg(z) -{ 0 }-> f(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_0 -{ 0 }-> 1 :|: 
   encode_0 -{ 0 }-> 0 :|: 
   encode_0 -{ 1 }-> 0 :|: 
   encode_1 -{ 0 }-> 0 :|: 
   encode_f(z) -{ 0 }-> f(g(encArg(x_125), encArg(x_27))) :|: x_125 >= 0, x_27 >= 0, z = 1 + x_125 + x_27
   encode_f(z) -{ 0 }-> f(f(encArg(z - 1))) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> f(1) :|: z = 2
   encode_f(z) -{ 0 }-> f(0) :|: z = 0
   encode_f(z) -{ 0 }-> f(0) :|: z >= 0
   encode_f(z) -{ 0 }-> f(0) :|: z = 2
   encode_f(z) -{ 1 }-> f(0) :|: z = 2
   encode_f(z) -{ 0 }-> f(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z, z') -{ 0 }-> g(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   f(z) -{ 1 }-> f(0) :|: z - 1 >= 0
   f(z) -{ 0 }-> 0 :|: z >= 0
   g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   g(z, z') -{ 1 }-> 1 + 1 :|: z = 1, z' = 0
   g(z, z') -{ 1 }-> 1 + 0 :|: z = 1, z' = 0
   g(z, z') -{ 2 }-> 1 + 0 :|: z = 1, z' = 0

Function symbols to be analyzed: {encode_0}, {encode_1}, {f}, {g}, {0'}, {encArg}, {encode_g}, {encode_f}, {encode_s}
Previous analysis results are:
  encode_0: runtime: ?, size: O(1) [1]

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

(29) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: encode_0
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 1

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

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

   0' -{ 0 }-> 1 :|: 
   0' -{ 1 }-> 0 :|: 
   0' -{ 0 }-> 0 :|: 
   encArg(z) -{ 0 }-> g(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> f(g(encArg(x_11), encArg(x_2'))) :|: x_11 >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2')
   encArg(z) -{ 0 }-> f(f(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(1) :|: z = 1 + 2
   encArg(z) -{ 0 }-> f(0) :|: z = 1 + 0
   encArg(z) -{ 0 }-> f(0) :|: z - 1 >= 0
   encArg(z) -{ 0 }-> f(0) :|: z = 1 + 2
   encArg(z) -{ 1 }-> f(0) :|: z = 1 + 2
   encArg(z) -{ 0 }-> f(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_0 -{ 0 }-> 1 :|: 
   encode_0 -{ 0 }-> 0 :|: 
   encode_0 -{ 1 }-> 0 :|: 
   encode_1 -{ 0 }-> 0 :|: 
   encode_f(z) -{ 0 }-> f(g(encArg(x_125), encArg(x_27))) :|: x_125 >= 0, x_27 >= 0, z = 1 + x_125 + x_27
   encode_f(z) -{ 0 }-> f(f(encArg(z - 1))) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> f(1) :|: z = 2
   encode_f(z) -{ 0 }-> f(0) :|: z = 0
   encode_f(z) -{ 0 }-> f(0) :|: z >= 0
   encode_f(z) -{ 0 }-> f(0) :|: z = 2
   encode_f(z) -{ 1 }-> f(0) :|: z = 2
   encode_f(z) -{ 0 }-> f(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z, z') -{ 0 }-> g(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   f(z) -{ 1 }-> f(0) :|: z - 1 >= 0
   f(z) -{ 0 }-> 0 :|: z >= 0
   g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   g(z, z') -{ 1 }-> 1 + 1 :|: z = 1, z' = 0
   g(z, z') -{ 1 }-> 1 + 0 :|: z = 1, z' = 0
   g(z, z') -{ 2 }-> 1 + 0 :|: z = 1, z' = 0

Function symbols to be analyzed: {encode_1}, {f}, {g}, {0'}, {encArg}, {encode_g}, {encode_f}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [1], size: O(1) [1]

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

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

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

   0' -{ 0 }-> 1 :|: 
   0' -{ 1 }-> 0 :|: 
   0' -{ 0 }-> 0 :|: 
   encArg(z) -{ 0 }-> g(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> f(g(encArg(x_11), encArg(x_2'))) :|: x_11 >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2')
   encArg(z) -{ 0 }-> f(f(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(1) :|: z = 1 + 2
   encArg(z) -{ 0 }-> f(0) :|: z = 1 + 0
   encArg(z) -{ 0 }-> f(0) :|: z - 1 >= 0
   encArg(z) -{ 0 }-> f(0) :|: z = 1 + 2
   encArg(z) -{ 1 }-> f(0) :|: z = 1 + 2
   encArg(z) -{ 0 }-> f(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_0 -{ 0 }-> 1 :|: 
   encode_0 -{ 0 }-> 0 :|: 
   encode_0 -{ 1 }-> 0 :|: 
   encode_1 -{ 0 }-> 0 :|: 
   encode_f(z) -{ 0 }-> f(g(encArg(x_125), encArg(x_27))) :|: x_125 >= 0, x_27 >= 0, z = 1 + x_125 + x_27
   encode_f(z) -{ 0 }-> f(f(encArg(z - 1))) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> f(1) :|: z = 2
   encode_f(z) -{ 0 }-> f(0) :|: z = 0
   encode_f(z) -{ 0 }-> f(0) :|: z >= 0
   encode_f(z) -{ 0 }-> f(0) :|: z = 2
   encode_f(z) -{ 1 }-> f(0) :|: z = 2
   encode_f(z) -{ 0 }-> f(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z, z') -{ 0 }-> g(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   f(z) -{ 1 }-> f(0) :|: z - 1 >= 0
   f(z) -{ 0 }-> 0 :|: z >= 0
   g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   g(z, z') -{ 1 }-> 1 + 1 :|: z = 1, z' = 0
   g(z, z') -{ 1 }-> 1 + 0 :|: z = 1, z' = 0
   g(z, z') -{ 2 }-> 1 + 0 :|: z = 1, z' = 0

Function symbols to be analyzed: {encode_1}, {f}, {g}, {0'}, {encArg}, {encode_g}, {encode_f}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [1], size: O(1) [1]

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

(33) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: encode_1
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 0

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

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

   0' -{ 0 }-> 1 :|: 
   0' -{ 1 }-> 0 :|: 
   0' -{ 0 }-> 0 :|: 
   encArg(z) -{ 0 }-> g(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> f(g(encArg(x_11), encArg(x_2'))) :|: x_11 >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2')
   encArg(z) -{ 0 }-> f(f(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(1) :|: z = 1 + 2
   encArg(z) -{ 0 }-> f(0) :|: z = 1 + 0
   encArg(z) -{ 0 }-> f(0) :|: z - 1 >= 0
   encArg(z) -{ 0 }-> f(0) :|: z = 1 + 2
   encArg(z) -{ 1 }-> f(0) :|: z = 1 + 2
   encArg(z) -{ 0 }-> f(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_0 -{ 0 }-> 1 :|: 
   encode_0 -{ 0 }-> 0 :|: 
   encode_0 -{ 1 }-> 0 :|: 
   encode_1 -{ 0 }-> 0 :|: 
   encode_f(z) -{ 0 }-> f(g(encArg(x_125), encArg(x_27))) :|: x_125 >= 0, x_27 >= 0, z = 1 + x_125 + x_27
   encode_f(z) -{ 0 }-> f(f(encArg(z - 1))) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> f(1) :|: z = 2
   encode_f(z) -{ 0 }-> f(0) :|: z = 0
   encode_f(z) -{ 0 }-> f(0) :|: z >= 0
   encode_f(z) -{ 0 }-> f(0) :|: z = 2
   encode_f(z) -{ 1 }-> f(0) :|: z = 2
   encode_f(z) -{ 0 }-> f(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z, z') -{ 0 }-> g(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   f(z) -{ 1 }-> f(0) :|: z - 1 >= 0
   f(z) -{ 0 }-> 0 :|: z >= 0
   g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   g(z, z') -{ 1 }-> 1 + 1 :|: z = 1, z' = 0
   g(z, z') -{ 1 }-> 1 + 0 :|: z = 1, z' = 0
   g(z, z') -{ 2 }-> 1 + 0 :|: z = 1, z' = 0

Function symbols to be analyzed: {encode_1}, {f}, {g}, {0'}, {encArg}, {encode_g}, {encode_f}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [1], size: O(1) [1]
  encode_1: runtime: ?, size: O(1) [0]

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

(35) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: encode_1
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 0

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

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

   0' -{ 0 }-> 1 :|: 
   0' -{ 1 }-> 0 :|: 
   0' -{ 0 }-> 0 :|: 
   encArg(z) -{ 0 }-> g(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> f(g(encArg(x_11), encArg(x_2'))) :|: x_11 >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2')
   encArg(z) -{ 0 }-> f(f(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(1) :|: z = 1 + 2
   encArg(z) -{ 0 }-> f(0) :|: z = 1 + 0
   encArg(z) -{ 0 }-> f(0) :|: z - 1 >= 0
   encArg(z) -{ 0 }-> f(0) :|: z = 1 + 2
   encArg(z) -{ 1 }-> f(0) :|: z = 1 + 2
   encArg(z) -{ 0 }-> f(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_0 -{ 0 }-> 1 :|: 
   encode_0 -{ 0 }-> 0 :|: 
   encode_0 -{ 1 }-> 0 :|: 
   encode_1 -{ 0 }-> 0 :|: 
   encode_f(z) -{ 0 }-> f(g(encArg(x_125), encArg(x_27))) :|: x_125 >= 0, x_27 >= 0, z = 1 + x_125 + x_27
   encode_f(z) -{ 0 }-> f(f(encArg(z - 1))) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> f(1) :|: z = 2
   encode_f(z) -{ 0 }-> f(0) :|: z = 0
   encode_f(z) -{ 0 }-> f(0) :|: z >= 0
   encode_f(z) -{ 0 }-> f(0) :|: z = 2
   encode_f(z) -{ 1 }-> f(0) :|: z = 2
   encode_f(z) -{ 0 }-> f(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z, z') -{ 0 }-> g(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   f(z) -{ 1 }-> f(0) :|: z - 1 >= 0
   f(z) -{ 0 }-> 0 :|: z >= 0
   g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   g(z, z') -{ 1 }-> 1 + 1 :|: z = 1, z' = 0
   g(z, z') -{ 1 }-> 1 + 0 :|: z = 1, z' = 0
   g(z, z') -{ 2 }-> 1 + 0 :|: z = 1, z' = 0

Function symbols to be analyzed: {f}, {g}, {0'}, {encArg}, {encode_g}, {encode_f}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [1], size: O(1) [1]
  encode_1: runtime: O(1) [0], size: O(1) [0]

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

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

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

   0' -{ 0 }-> 1 :|: 
   0' -{ 1 }-> 0 :|: 
   0' -{ 0 }-> 0 :|: 
   encArg(z) -{ 0 }-> g(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> f(g(encArg(x_11), encArg(x_2'))) :|: x_11 >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2')
   encArg(z) -{ 0 }-> f(f(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(1) :|: z = 1 + 2
   encArg(z) -{ 0 }-> f(0) :|: z = 1 + 0
   encArg(z) -{ 0 }-> f(0) :|: z - 1 >= 0
   encArg(z) -{ 0 }-> f(0) :|: z = 1 + 2
   encArg(z) -{ 1 }-> f(0) :|: z = 1 + 2
   encArg(z) -{ 0 }-> f(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_0 -{ 0 }-> 1 :|: 
   encode_0 -{ 0 }-> 0 :|: 
   encode_0 -{ 1 }-> 0 :|: 
   encode_1 -{ 0 }-> 0 :|: 
   encode_f(z) -{ 0 }-> f(g(encArg(x_125), encArg(x_27))) :|: x_125 >= 0, x_27 >= 0, z = 1 + x_125 + x_27
   encode_f(z) -{ 0 }-> f(f(encArg(z - 1))) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> f(1) :|: z = 2
   encode_f(z) -{ 0 }-> f(0) :|: z = 0
   encode_f(z) -{ 0 }-> f(0) :|: z >= 0
   encode_f(z) -{ 0 }-> f(0) :|: z = 2
   encode_f(z) -{ 1 }-> f(0) :|: z = 2
   encode_f(z) -{ 0 }-> f(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z, z') -{ 0 }-> g(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   f(z) -{ 1 }-> f(0) :|: z - 1 >= 0
   f(z) -{ 0 }-> 0 :|: z >= 0
   g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   g(z, z') -{ 1 }-> 1 + 1 :|: z = 1, z' = 0
   g(z, z') -{ 1 }-> 1 + 0 :|: z = 1, z' = 0
   g(z, z') -{ 2 }-> 1 + 0 :|: z = 1, z' = 0

Function symbols to be analyzed: {f}, {g}, {0'}, {encArg}, {encode_g}, {encode_f}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [1], size: O(1) [1]
  encode_1: runtime: O(1) [0], size: O(1) [0]

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

(39) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   0' -{ 0 }-> 1 :|: 
   0' -{ 1 }-> 0 :|: 
   0' -{ 0 }-> 0 :|: 
   encArg(z) -{ 0 }-> g(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> f(g(encArg(x_11), encArg(x_2'))) :|: x_11 >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2')
   encArg(z) -{ 0 }-> f(f(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(1) :|: z = 1 + 2
   encArg(z) -{ 0 }-> f(0) :|: z = 1 + 0
   encArg(z) -{ 0 }-> f(0) :|: z - 1 >= 0
   encArg(z) -{ 0 }-> f(0) :|: z = 1 + 2
   encArg(z) -{ 1 }-> f(0) :|: z = 1 + 2
   encArg(z) -{ 0 }-> f(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_0 -{ 0 }-> 1 :|: 
   encode_0 -{ 0 }-> 0 :|: 
   encode_0 -{ 1 }-> 0 :|: 
   encode_1 -{ 0 }-> 0 :|: 
   encode_f(z) -{ 0 }-> f(g(encArg(x_125), encArg(x_27))) :|: x_125 >= 0, x_27 >= 0, z = 1 + x_125 + x_27
   encode_f(z) -{ 0 }-> f(f(encArg(z - 1))) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> f(1) :|: z = 2
   encode_f(z) -{ 0 }-> f(0) :|: z = 0
   encode_f(z) -{ 0 }-> f(0) :|: z >= 0
   encode_f(z) -{ 0 }-> f(0) :|: z = 2
   encode_f(z) -{ 1 }-> f(0) :|: z = 2
   encode_f(z) -{ 0 }-> f(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z, z') -{ 0 }-> g(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   f(z) -{ 1 }-> f(0) :|: z - 1 >= 0
   f(z) -{ 0 }-> 0 :|: z >= 0
   g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   g(z, z') -{ 1 }-> 1 + 1 :|: z = 1, z' = 0
   g(z, z') -{ 1 }-> 1 + 0 :|: z = 1, z' = 0
   g(z, z') -{ 2 }-> 1 + 0 :|: z = 1, z' = 0

Function symbols to be analyzed: {f}, {g}, {0'}, {encArg}, {encode_g}, {encode_f}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [1], size: O(1) [1]
  encode_1: runtime: O(1) [0], size: O(1) [0]
  f: runtime: ?, size: O(1) [0]

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

(41) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   0' -{ 0 }-> 1 :|: 
   0' -{ 1 }-> 0 :|: 
   0' -{ 0 }-> 0 :|: 
   encArg(z) -{ 0 }-> g(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> f(g(encArg(x_11), encArg(x_2'))) :|: x_11 >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2')
   encArg(z) -{ 0 }-> f(f(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(1) :|: z = 1 + 2
   encArg(z) -{ 0 }-> f(0) :|: z = 1 + 0
   encArg(z) -{ 0 }-> f(0) :|: z - 1 >= 0
   encArg(z) -{ 0 }-> f(0) :|: z = 1 + 2
   encArg(z) -{ 1 }-> f(0) :|: z = 1 + 2
   encArg(z) -{ 0 }-> f(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_0 -{ 0 }-> 1 :|: 
   encode_0 -{ 0 }-> 0 :|: 
   encode_0 -{ 1 }-> 0 :|: 
   encode_1 -{ 0 }-> 0 :|: 
   encode_f(z) -{ 0 }-> f(g(encArg(x_125), encArg(x_27))) :|: x_125 >= 0, x_27 >= 0, z = 1 + x_125 + x_27
   encode_f(z) -{ 0 }-> f(f(encArg(z - 1))) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> f(1) :|: z = 2
   encode_f(z) -{ 0 }-> f(0) :|: z = 0
   encode_f(z) -{ 0 }-> f(0) :|: z >= 0
   encode_f(z) -{ 0 }-> f(0) :|: z = 2
   encode_f(z) -{ 1 }-> f(0) :|: z = 2
   encode_f(z) -{ 0 }-> f(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z, z') -{ 0 }-> g(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   f(z) -{ 1 }-> f(0) :|: z - 1 >= 0
   f(z) -{ 0 }-> 0 :|: z >= 0
   g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   g(z, z') -{ 1 }-> 1 + 1 :|: z = 1, z' = 0
   g(z, z') -{ 1 }-> 1 + 0 :|: z = 1, z' = 0
   g(z, z') -{ 2 }-> 1 + 0 :|: z = 1, z' = 0

Function symbols to be analyzed: {g}, {0'}, {encArg}, {encode_g}, {encode_f}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [1], size: O(1) [1]
  encode_1: runtime: O(1) [0], size: O(1) [0]
  f: runtime: O(1) [1], size: O(1) [0]

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

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

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

   0' -{ 0 }-> 1 :|: 
   0' -{ 1 }-> 0 :|: 
   0' -{ 0 }-> 0 :|: 
   encArg(z) -{ 1 }-> s' :|: s' >= 0, s' <= 0, z = 1 + 0
   encArg(z) -{ 1 }-> s'' :|: s'' >= 0, s'' <= 0, z - 1 >= 0
   encArg(z) -{ 1 }-> s3 :|: s3 >= 0, s3 <= 0, z = 1 + 2
   encArg(z) -{ 1 }-> s4 :|: s4 >= 0, s4 <= 0, z = 1 + 2
   encArg(z) -{ 2 }-> s5 :|: s5 >= 0, s5 <= 0, z = 1 + 2
   encArg(z) -{ 0 }-> g(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> f(g(encArg(x_11), encArg(x_2'))) :|: x_11 >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2')
   encArg(z) -{ 0 }-> f(f(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_0 -{ 0 }-> 1 :|: 
   encode_0 -{ 0 }-> 0 :|: 
   encode_0 -{ 1 }-> 0 :|: 
   encode_1 -{ 0 }-> 0 :|: 
   encode_f(z) -{ 1 }-> s1 :|: s1 >= 0, s1 <= 0, z = 0
   encode_f(z) -{ 1 }-> s2 :|: s2 >= 0, s2 <= 0, z >= 0
   encode_f(z) -{ 1 }-> s6 :|: s6 >= 0, s6 <= 0, z = 2
   encode_f(z) -{ 1 }-> s7 :|: s7 >= 0, s7 <= 0, z = 2
   encode_f(z) -{ 2 }-> s8 :|: s8 >= 0, s8 <= 0, z = 2
   encode_f(z) -{ 0 }-> f(g(encArg(x_125), encArg(x_27))) :|: x_125 >= 0, x_27 >= 0, z = 1 + x_125 + x_27
   encode_f(z) -{ 0 }-> f(f(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_g(z, z') -{ 0 }-> g(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   f(z) -{ 2 }-> s :|: s >= 0, s <= 0, z - 1 >= 0
   f(z) -{ 0 }-> 0 :|: z >= 0
   g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   g(z, z') -{ 1 }-> 1 + 1 :|: z = 1, z' = 0
   g(z, z') -{ 1 }-> 1 + 0 :|: z = 1, z' = 0
   g(z, z') -{ 2 }-> 1 + 0 :|: z = 1, z' = 0

Function symbols to be analyzed: {g}, {0'}, {encArg}, {encode_g}, {encode_f}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [1], size: O(1) [1]
  encode_1: runtime: O(1) [0], size: O(1) [0]
  f: runtime: O(1) [1], size: O(1) [0]

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

(45) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   0' -{ 0 }-> 1 :|: 
   0' -{ 1 }-> 0 :|: 
   0' -{ 0 }-> 0 :|: 
   encArg(z) -{ 1 }-> s' :|: s' >= 0, s' <= 0, z = 1 + 0
   encArg(z) -{ 1 }-> s'' :|: s'' >= 0, s'' <= 0, z - 1 >= 0
   encArg(z) -{ 1 }-> s3 :|: s3 >= 0, s3 <= 0, z = 1 + 2
   encArg(z) -{ 1 }-> s4 :|: s4 >= 0, s4 <= 0, z = 1 + 2
   encArg(z) -{ 2 }-> s5 :|: s5 >= 0, s5 <= 0, z = 1 + 2
   encArg(z) -{ 0 }-> g(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> f(g(encArg(x_11), encArg(x_2'))) :|: x_11 >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2')
   encArg(z) -{ 0 }-> f(f(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_0 -{ 0 }-> 1 :|: 
   encode_0 -{ 0 }-> 0 :|: 
   encode_0 -{ 1 }-> 0 :|: 
   encode_1 -{ 0 }-> 0 :|: 
   encode_f(z) -{ 1 }-> s1 :|: s1 >= 0, s1 <= 0, z = 0
   encode_f(z) -{ 1 }-> s2 :|: s2 >= 0, s2 <= 0, z >= 0
   encode_f(z) -{ 1 }-> s6 :|: s6 >= 0, s6 <= 0, z = 2
   encode_f(z) -{ 1 }-> s7 :|: s7 >= 0, s7 <= 0, z = 2
   encode_f(z) -{ 2 }-> s8 :|: s8 >= 0, s8 <= 0, z = 2
   encode_f(z) -{ 0 }-> f(g(encArg(x_125), encArg(x_27))) :|: x_125 >= 0, x_27 >= 0, z = 1 + x_125 + x_27
   encode_f(z) -{ 0 }-> f(f(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_g(z, z') -{ 0 }-> g(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   f(z) -{ 2 }-> s :|: s >= 0, s <= 0, z - 1 >= 0
   f(z) -{ 0 }-> 0 :|: z >= 0
   g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   g(z, z') -{ 1 }-> 1 + 1 :|: z = 1, z' = 0
   g(z, z') -{ 1 }-> 1 + 0 :|: z = 1, z' = 0
   g(z, z') -{ 2 }-> 1 + 0 :|: z = 1, z' = 0

Function symbols to be analyzed: {g}, {0'}, {encArg}, {encode_g}, {encode_f}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [1], size: O(1) [1]
  encode_1: runtime: O(1) [0], size: O(1) [0]
  f: runtime: O(1) [1], size: O(1) [0]
  g: runtime: ?, size: O(1) [2]

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

(47) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   0' -{ 0 }-> 1 :|: 
   0' -{ 1 }-> 0 :|: 
   0' -{ 0 }-> 0 :|: 
   encArg(z) -{ 1 }-> s' :|: s' >= 0, s' <= 0, z = 1 + 0
   encArg(z) -{ 1 }-> s'' :|: s'' >= 0, s'' <= 0, z - 1 >= 0
   encArg(z) -{ 1 }-> s3 :|: s3 >= 0, s3 <= 0, z = 1 + 2
   encArg(z) -{ 1 }-> s4 :|: s4 >= 0, s4 <= 0, z = 1 + 2
   encArg(z) -{ 2 }-> s5 :|: s5 >= 0, s5 <= 0, z = 1 + 2
   encArg(z) -{ 0 }-> g(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> f(g(encArg(x_11), encArg(x_2'))) :|: x_11 >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2')
   encArg(z) -{ 0 }-> f(f(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_0 -{ 0 }-> 1 :|: 
   encode_0 -{ 0 }-> 0 :|: 
   encode_0 -{ 1 }-> 0 :|: 
   encode_1 -{ 0 }-> 0 :|: 
   encode_f(z) -{ 1 }-> s1 :|: s1 >= 0, s1 <= 0, z = 0
   encode_f(z) -{ 1 }-> s2 :|: s2 >= 0, s2 <= 0, z >= 0
   encode_f(z) -{ 1 }-> s6 :|: s6 >= 0, s6 <= 0, z = 2
   encode_f(z) -{ 1 }-> s7 :|: s7 >= 0, s7 <= 0, z = 2
   encode_f(z) -{ 2 }-> s8 :|: s8 >= 0, s8 <= 0, z = 2
   encode_f(z) -{ 0 }-> f(g(encArg(x_125), encArg(x_27))) :|: x_125 >= 0, x_27 >= 0, z = 1 + x_125 + x_27
   encode_f(z) -{ 0 }-> f(f(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_g(z, z') -{ 0 }-> g(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   f(z) -{ 2 }-> s :|: s >= 0, s <= 0, z - 1 >= 0
   f(z) -{ 0 }-> 0 :|: z >= 0
   g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   g(z, z') -{ 1 }-> 1 + 1 :|: z = 1, z' = 0
   g(z, z') -{ 1 }-> 1 + 0 :|: z = 1, z' = 0
   g(z, z') -{ 2 }-> 1 + 0 :|: z = 1, z' = 0

Function symbols to be analyzed: {0'}, {encArg}, {encode_g}, {encode_f}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [1], size: O(1) [1]
  encode_1: runtime: O(1) [0], size: O(1) [0]
  f: runtime: O(1) [1], size: O(1) [0]
  g: runtime: O(1) [2], size: O(1) [2]

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

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

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

   0' -{ 0 }-> 1 :|: 
   0' -{ 1 }-> 0 :|: 
   0' -{ 0 }-> 0 :|: 
   encArg(z) -{ 1 }-> s' :|: s' >= 0, s' <= 0, z = 1 + 0
   encArg(z) -{ 1 }-> s'' :|: s'' >= 0, s'' <= 0, z - 1 >= 0
   encArg(z) -{ 1 }-> s3 :|: s3 >= 0, s3 <= 0, z = 1 + 2
   encArg(z) -{ 1 }-> s4 :|: s4 >= 0, s4 <= 0, z = 1 + 2
   encArg(z) -{ 2 }-> s5 :|: s5 >= 0, s5 <= 0, z = 1 + 2
   encArg(z) -{ 0 }-> g(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> f(g(encArg(x_11), encArg(x_2'))) :|: x_11 >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2')
   encArg(z) -{ 0 }-> f(f(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_0 -{ 0 }-> 1 :|: 
   encode_0 -{ 0 }-> 0 :|: 
   encode_0 -{ 1 }-> 0 :|: 
   encode_1 -{ 0 }-> 0 :|: 
   encode_f(z) -{ 1 }-> s1 :|: s1 >= 0, s1 <= 0, z = 0
   encode_f(z) -{ 1 }-> s2 :|: s2 >= 0, s2 <= 0, z >= 0
   encode_f(z) -{ 1 }-> s6 :|: s6 >= 0, s6 <= 0, z = 2
   encode_f(z) -{ 1 }-> s7 :|: s7 >= 0, s7 <= 0, z = 2
   encode_f(z) -{ 2 }-> s8 :|: s8 >= 0, s8 <= 0, z = 2
   encode_f(z) -{ 0 }-> f(g(encArg(x_125), encArg(x_27))) :|: x_125 >= 0, x_27 >= 0, z = 1 + x_125 + x_27
   encode_f(z) -{ 0 }-> f(f(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_g(z, z') -{ 0 }-> g(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   f(z) -{ 2 }-> s :|: s >= 0, s <= 0, z - 1 >= 0
   f(z) -{ 0 }-> 0 :|: z >= 0
   g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   g(z, z') -{ 1 }-> 1 + 1 :|: z = 1, z' = 0
   g(z, z') -{ 1 }-> 1 + 0 :|: z = 1, z' = 0
   g(z, z') -{ 2 }-> 1 + 0 :|: z = 1, z' = 0

Function symbols to be analyzed: {0'}, {encArg}, {encode_g}, {encode_f}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [1], size: O(1) [1]
  encode_1: runtime: O(1) [0], size: O(1) [0]
  f: runtime: O(1) [1], size: O(1) [0]
  g: runtime: O(1) [2], size: O(1) [2]

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

(51) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   0' -{ 0 }-> 1 :|: 
   0' -{ 1 }-> 0 :|: 
   0' -{ 0 }-> 0 :|: 
   encArg(z) -{ 1 }-> s' :|: s' >= 0, s' <= 0, z = 1 + 0
   encArg(z) -{ 1 }-> s'' :|: s'' >= 0, s'' <= 0, z - 1 >= 0
   encArg(z) -{ 1 }-> s3 :|: s3 >= 0, s3 <= 0, z = 1 + 2
   encArg(z) -{ 1 }-> s4 :|: s4 >= 0, s4 <= 0, z = 1 + 2
   encArg(z) -{ 2 }-> s5 :|: s5 >= 0, s5 <= 0, z = 1 + 2
   encArg(z) -{ 0 }-> g(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> f(g(encArg(x_11), encArg(x_2'))) :|: x_11 >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2')
   encArg(z) -{ 0 }-> f(f(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_0 -{ 0 }-> 1 :|: 
   encode_0 -{ 0 }-> 0 :|: 
   encode_0 -{ 1 }-> 0 :|: 
   encode_1 -{ 0 }-> 0 :|: 
   encode_f(z) -{ 1 }-> s1 :|: s1 >= 0, s1 <= 0, z = 0
   encode_f(z) -{ 1 }-> s2 :|: s2 >= 0, s2 <= 0, z >= 0
   encode_f(z) -{ 1 }-> s6 :|: s6 >= 0, s6 <= 0, z = 2
   encode_f(z) -{ 1 }-> s7 :|: s7 >= 0, s7 <= 0, z = 2
   encode_f(z) -{ 2 }-> s8 :|: s8 >= 0, s8 <= 0, z = 2
   encode_f(z) -{ 0 }-> f(g(encArg(x_125), encArg(x_27))) :|: x_125 >= 0, x_27 >= 0, z = 1 + x_125 + x_27
   encode_f(z) -{ 0 }-> f(f(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_g(z, z') -{ 0 }-> g(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   f(z) -{ 2 }-> s :|: s >= 0, s <= 0, z - 1 >= 0
   f(z) -{ 0 }-> 0 :|: z >= 0
   g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   g(z, z') -{ 1 }-> 1 + 1 :|: z = 1, z' = 0
   g(z, z') -{ 1 }-> 1 + 0 :|: z = 1, z' = 0
   g(z, z') -{ 2 }-> 1 + 0 :|: z = 1, z' = 0

Function symbols to be analyzed: {0'}, {encArg}, {encode_g}, {encode_f}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [1], size: O(1) [1]
  encode_1: runtime: O(1) [0], size: O(1) [0]
  f: runtime: O(1) [1], size: O(1) [0]
  g: runtime: O(1) [2], size: O(1) [2]
  0': runtime: ?, size: O(1) [1]

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

(53) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   0' -{ 0 }-> 1 :|: 
   0' -{ 1 }-> 0 :|: 
   0' -{ 0 }-> 0 :|: 
   encArg(z) -{ 1 }-> s' :|: s' >= 0, s' <= 0, z = 1 + 0
   encArg(z) -{ 1 }-> s'' :|: s'' >= 0, s'' <= 0, z - 1 >= 0
   encArg(z) -{ 1 }-> s3 :|: s3 >= 0, s3 <= 0, z = 1 + 2
   encArg(z) -{ 1 }-> s4 :|: s4 >= 0, s4 <= 0, z = 1 + 2
   encArg(z) -{ 2 }-> s5 :|: s5 >= 0, s5 <= 0, z = 1 + 2
   encArg(z) -{ 0 }-> g(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> f(g(encArg(x_11), encArg(x_2'))) :|: x_11 >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2')
   encArg(z) -{ 0 }-> f(f(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_0 -{ 0 }-> 1 :|: 
   encode_0 -{ 0 }-> 0 :|: 
   encode_0 -{ 1 }-> 0 :|: 
   encode_1 -{ 0 }-> 0 :|: 
   encode_f(z) -{ 1 }-> s1 :|: s1 >= 0, s1 <= 0, z = 0
   encode_f(z) -{ 1 }-> s2 :|: s2 >= 0, s2 <= 0, z >= 0
   encode_f(z) -{ 1 }-> s6 :|: s6 >= 0, s6 <= 0, z = 2
   encode_f(z) -{ 1 }-> s7 :|: s7 >= 0, s7 <= 0, z = 2
   encode_f(z) -{ 2 }-> s8 :|: s8 >= 0, s8 <= 0, z = 2
   encode_f(z) -{ 0 }-> f(g(encArg(x_125), encArg(x_27))) :|: x_125 >= 0, x_27 >= 0, z = 1 + x_125 + x_27
   encode_f(z) -{ 0 }-> f(f(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_g(z, z') -{ 0 }-> g(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   f(z) -{ 2 }-> s :|: s >= 0, s <= 0, z - 1 >= 0
   f(z) -{ 0 }-> 0 :|: z >= 0
   g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   g(z, z') -{ 1 }-> 1 + 1 :|: z = 1, z' = 0
   g(z, z') -{ 1 }-> 1 + 0 :|: z = 1, z' = 0
   g(z, z') -{ 2 }-> 1 + 0 :|: z = 1, z' = 0

Function symbols to be analyzed: {encArg}, {encode_g}, {encode_f}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [1], size: O(1) [1]
  encode_1: runtime: O(1) [0], size: O(1) [0]
  f: runtime: O(1) [1], size: O(1) [0]
  g: runtime: O(1) [2], size: O(1) [2]
  0': runtime: O(1) [1], size: O(1) [1]

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

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

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

   0' -{ 0 }-> 1 :|: 
   0' -{ 1 }-> 0 :|: 
   0' -{ 0 }-> 0 :|: 
   encArg(z) -{ 1 }-> s' :|: s' >= 0, s' <= 0, z = 1 + 0
   encArg(z) -{ 1 }-> s'' :|: s'' >= 0, s'' <= 0, z - 1 >= 0
   encArg(z) -{ 1 }-> s3 :|: s3 >= 0, s3 <= 0, z = 1 + 2
   encArg(z) -{ 1 }-> s4 :|: s4 >= 0, s4 <= 0, z = 1 + 2
   encArg(z) -{ 2 }-> s5 :|: s5 >= 0, s5 <= 0, z = 1 + 2
   encArg(z) -{ 0 }-> g(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> f(g(encArg(x_11), encArg(x_2'))) :|: x_11 >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2')
   encArg(z) -{ 0 }-> f(f(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_0 -{ 0 }-> 1 :|: 
   encode_0 -{ 0 }-> 0 :|: 
   encode_0 -{ 1 }-> 0 :|: 
   encode_1 -{ 0 }-> 0 :|: 
   encode_f(z) -{ 1 }-> s1 :|: s1 >= 0, s1 <= 0, z = 0
   encode_f(z) -{ 1 }-> s2 :|: s2 >= 0, s2 <= 0, z >= 0
   encode_f(z) -{ 1 }-> s6 :|: s6 >= 0, s6 <= 0, z = 2
   encode_f(z) -{ 1 }-> s7 :|: s7 >= 0, s7 <= 0, z = 2
   encode_f(z) -{ 2 }-> s8 :|: s8 >= 0, s8 <= 0, z = 2
   encode_f(z) -{ 0 }-> f(g(encArg(x_125), encArg(x_27))) :|: x_125 >= 0, x_27 >= 0, z = 1 + x_125 + x_27
   encode_f(z) -{ 0 }-> f(f(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_g(z, z') -{ 0 }-> g(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   f(z) -{ 2 }-> s :|: s >= 0, s <= 0, z - 1 >= 0
   f(z) -{ 0 }-> 0 :|: z >= 0
   g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   g(z, z') -{ 1 }-> 1 + 1 :|: z = 1, z' = 0
   g(z, z') -{ 1 }-> 1 + 0 :|: z = 1, z' = 0
   g(z, z') -{ 2 }-> 1 + 0 :|: z = 1, z' = 0

Function symbols to be analyzed: {encArg}, {encode_g}, {encode_f}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [1], size: O(1) [1]
  encode_1: runtime: O(1) [0], size: O(1) [0]
  f: runtime: O(1) [1], size: O(1) [0]
  g: runtime: O(1) [2], size: O(1) [2]
  0': runtime: O(1) [1], size: O(1) [1]

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

(57) 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: 2 + z

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

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

   0' -{ 0 }-> 1 :|: 
   0' -{ 1 }-> 0 :|: 
   0' -{ 0 }-> 0 :|: 
   encArg(z) -{ 1 }-> s' :|: s' >= 0, s' <= 0, z = 1 + 0
   encArg(z) -{ 1 }-> s'' :|: s'' >= 0, s'' <= 0, z - 1 >= 0
   encArg(z) -{ 1 }-> s3 :|: s3 >= 0, s3 <= 0, z = 1 + 2
   encArg(z) -{ 1 }-> s4 :|: s4 >= 0, s4 <= 0, z = 1 + 2
   encArg(z) -{ 2 }-> s5 :|: s5 >= 0, s5 <= 0, z = 1 + 2
   encArg(z) -{ 0 }-> g(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> f(g(encArg(x_11), encArg(x_2'))) :|: x_11 >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2')
   encArg(z) -{ 0 }-> f(f(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_0 -{ 0 }-> 1 :|: 
   encode_0 -{ 0 }-> 0 :|: 
   encode_0 -{ 1 }-> 0 :|: 
   encode_1 -{ 0 }-> 0 :|: 
   encode_f(z) -{ 1 }-> s1 :|: s1 >= 0, s1 <= 0, z = 0
   encode_f(z) -{ 1 }-> s2 :|: s2 >= 0, s2 <= 0, z >= 0
   encode_f(z) -{ 1 }-> s6 :|: s6 >= 0, s6 <= 0, z = 2
   encode_f(z) -{ 1 }-> s7 :|: s7 >= 0, s7 <= 0, z = 2
   encode_f(z) -{ 2 }-> s8 :|: s8 >= 0, s8 <= 0, z = 2
   encode_f(z) -{ 0 }-> f(g(encArg(x_125), encArg(x_27))) :|: x_125 >= 0, x_27 >= 0, z = 1 + x_125 + x_27
   encode_f(z) -{ 0 }-> f(f(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_g(z, z') -{ 0 }-> g(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   f(z) -{ 2 }-> s :|: s >= 0, s <= 0, z - 1 >= 0
   f(z) -{ 0 }-> 0 :|: z >= 0
   g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   g(z, z') -{ 1 }-> 1 + 1 :|: z = 1, z' = 0
   g(z, z') -{ 1 }-> 1 + 0 :|: z = 1, z' = 0
   g(z, z') -{ 2 }-> 1 + 0 :|: z = 1, z' = 0

Function symbols to be analyzed: {encArg}, {encode_g}, {encode_f}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [1], size: O(1) [1]
  encode_1: runtime: O(1) [0], size: O(1) [0]
  f: runtime: O(1) [1], size: O(1) [0]
  g: runtime: O(1) [2], size: O(1) [2]
  0': runtime: O(1) [1], size: O(1) [1]
  encArg: runtime: ?, size: O(n^1) [2 + z]

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

(59) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: encArg
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 2 + 3*z

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

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

   0' -{ 0 }-> 1 :|: 
   0' -{ 1 }-> 0 :|: 
   0' -{ 0 }-> 0 :|: 
   encArg(z) -{ 1 }-> s' :|: s' >= 0, s' <= 0, z = 1 + 0
   encArg(z) -{ 1 }-> s'' :|: s'' >= 0, s'' <= 0, z - 1 >= 0
   encArg(z) -{ 1 }-> s3 :|: s3 >= 0, s3 <= 0, z = 1 + 2
   encArg(z) -{ 1 }-> s4 :|: s4 >= 0, s4 <= 0, z = 1 + 2
   encArg(z) -{ 2 }-> s5 :|: s5 >= 0, s5 <= 0, z = 1 + 2
   encArg(z) -{ 0 }-> g(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> f(g(encArg(x_11), encArg(x_2'))) :|: x_11 >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2')
   encArg(z) -{ 0 }-> f(f(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_0 -{ 0 }-> 1 :|: 
   encode_0 -{ 0 }-> 0 :|: 
   encode_0 -{ 1 }-> 0 :|: 
   encode_1 -{ 0 }-> 0 :|: 
   encode_f(z) -{ 1 }-> s1 :|: s1 >= 0, s1 <= 0, z = 0
   encode_f(z) -{ 1 }-> s2 :|: s2 >= 0, s2 <= 0, z >= 0
   encode_f(z) -{ 1 }-> s6 :|: s6 >= 0, s6 <= 0, z = 2
   encode_f(z) -{ 1 }-> s7 :|: s7 >= 0, s7 <= 0, z = 2
   encode_f(z) -{ 2 }-> s8 :|: s8 >= 0, s8 <= 0, z = 2
   encode_f(z) -{ 0 }-> f(g(encArg(x_125), encArg(x_27))) :|: x_125 >= 0, x_27 >= 0, z = 1 + x_125 + x_27
   encode_f(z) -{ 0 }-> f(f(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_g(z, z') -{ 0 }-> g(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   f(z) -{ 2 }-> s :|: s >= 0, s <= 0, z - 1 >= 0
   f(z) -{ 0 }-> 0 :|: z >= 0
   g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   g(z, z') -{ 1 }-> 1 + 1 :|: z = 1, z' = 0
   g(z, z') -{ 1 }-> 1 + 0 :|: z = 1, z' = 0
   g(z, z') -{ 2 }-> 1 + 0 :|: z = 1, z' = 0

Function symbols to be analyzed: {encode_g}, {encode_f}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [1], size: O(1) [1]
  encode_1: runtime: O(1) [0], size: O(1) [0]
  f: runtime: O(1) [1], size: O(1) [0]
  g: runtime: O(1) [2], size: O(1) [2]
  0': runtime: O(1) [1], size: O(1) [1]
  encArg: runtime: O(n^1) [2 + 3*z], size: O(n^1) [2 + z]

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

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

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

   0' -{ 0 }-> 1 :|: 
   0' -{ 1 }-> 0 :|: 
   0' -{ 0 }-> 0 :|: 
   encArg(z) -{ 1 }-> s' :|: s' >= 0, s' <= 0, z = 1 + 0
   encArg(z) -{ 1 }-> s'' :|: s'' >= 0, s'' <= 0, z - 1 >= 0
   encArg(z) -{ -3 + 3*z }-> s11 :|: s10 >= 0, s10 <= z - 2 + 2, s11 >= 0, s11 <= 0, z - 2 >= 0
   encArg(z) -{ -2 + 3*z }-> s14 :|: s12 >= 0, s12 <= z - 2 + 2, s13 >= 0, s13 <= 0, s14 >= 0, s14 <= 0, z - 2 >= 0
   encArg(z) -{ 7 + 3*x_11 + 3*x_2' }-> s24 :|: s21 >= 0, s21 <= x_11 + 2, s22 >= 0, s22 <= x_2' + 2, s23 >= 0, s23 <= 2, s24 >= 0, s24 <= 0, x_11 >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2')
   encArg(z) -{ 6 + 3*x_1 + 3*x_2 }-> s27 :|: s25 >= 0, s25 <= x_1 + 2, s26 >= 0, s26 <= x_2 + 2, s27 >= 0, s27 <= 2, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 1 }-> s3 :|: s3 >= 0, s3 <= 0, z = 1 + 2
   encArg(z) -{ 1 }-> s4 :|: s4 >= 0, s4 <= 0, z = 1 + 2
   encArg(z) -{ 2 }-> s5 :|: s5 >= 0, s5 <= 0, z = 1 + 2
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ -1 + 3*z }-> 1 + s9 :|: s9 >= 0, s9 <= z - 1 + 2, z - 1 >= 0
   encode_0 -{ 0 }-> 1 :|: 
   encode_0 -{ 0 }-> 0 :|: 
   encode_0 -{ 1 }-> 0 :|: 
   encode_1 -{ 0 }-> 0 :|: 
   encode_f(z) -{ 1 }-> s1 :|: s1 >= 0, s1 <= 0, z = 0
   encode_f(z) -{ 3*z }-> s16 :|: s15 >= 0, s15 <= z - 1 + 2, s16 >= 0, s16 <= 0, z - 1 >= 0
   encode_f(z) -{ 1 + 3*z }-> s19 :|: s17 >= 0, s17 <= z - 1 + 2, s18 >= 0, s18 <= 0, s19 >= 0, s19 <= 0, z - 1 >= 0
   encode_f(z) -{ 1 }-> s2 :|: s2 >= 0, s2 <= 0, z >= 0
   encode_f(z) -{ 7 + 3*x_125 + 3*x_27 }-> s31 :|: s28 >= 0, s28 <= x_125 + 2, s29 >= 0, s29 <= x_27 + 2, s30 >= 0, s30 <= 2, s31 >= 0, s31 <= 0, x_125 >= 0, x_27 >= 0, z = 1 + x_125 + x_27
   encode_f(z) -{ 1 }-> s6 :|: s6 >= 0, s6 <= 0, z = 2
   encode_f(z) -{ 1 }-> s7 :|: s7 >= 0, s7 <= 0, z = 2
   encode_f(z) -{ 2 }-> s8 :|: s8 >= 0, s8 <= 0, z = 2
   encode_f(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z, z') -{ 6 + 3*z + 3*z' }-> s34 :|: s32 >= 0, s32 <= z + 2, s33 >= 0, s33 <= z' + 2, s34 >= 0, s34 <= 2, z >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 2 + 3*z }-> 1 + s20 :|: s20 >= 0, s20 <= z + 2, z >= 0
   f(z) -{ 2 }-> s :|: s >= 0, s <= 0, z - 1 >= 0
   f(z) -{ 0 }-> 0 :|: z >= 0
   g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   g(z, z') -{ 1 }-> 1 + 1 :|: z = 1, z' = 0
   g(z, z') -{ 1 }-> 1 + 0 :|: z = 1, z' = 0
   g(z, z') -{ 2 }-> 1 + 0 :|: z = 1, z' = 0

Function symbols to be analyzed: {encode_g}, {encode_f}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [1], size: O(1) [1]
  encode_1: runtime: O(1) [0], size: O(1) [0]
  f: runtime: O(1) [1], size: O(1) [0]
  g: runtime: O(1) [2], size: O(1) [2]
  0': runtime: O(1) [1], size: O(1) [1]
  encArg: runtime: O(n^1) [2 + 3*z], size: O(n^1) [2 + z]

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

(63) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   0' -{ 0 }-> 1 :|: 
   0' -{ 1 }-> 0 :|: 
   0' -{ 0 }-> 0 :|: 
   encArg(z) -{ 1 }-> s' :|: s' >= 0, s' <= 0, z = 1 + 0
   encArg(z) -{ 1 }-> s'' :|: s'' >= 0, s'' <= 0, z - 1 >= 0
   encArg(z) -{ -3 + 3*z }-> s11 :|: s10 >= 0, s10 <= z - 2 + 2, s11 >= 0, s11 <= 0, z - 2 >= 0
   encArg(z) -{ -2 + 3*z }-> s14 :|: s12 >= 0, s12 <= z - 2 + 2, s13 >= 0, s13 <= 0, s14 >= 0, s14 <= 0, z - 2 >= 0
   encArg(z) -{ 7 + 3*x_11 + 3*x_2' }-> s24 :|: s21 >= 0, s21 <= x_11 + 2, s22 >= 0, s22 <= x_2' + 2, s23 >= 0, s23 <= 2, s24 >= 0, s24 <= 0, x_11 >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2')
   encArg(z) -{ 6 + 3*x_1 + 3*x_2 }-> s27 :|: s25 >= 0, s25 <= x_1 + 2, s26 >= 0, s26 <= x_2 + 2, s27 >= 0, s27 <= 2, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 1 }-> s3 :|: s3 >= 0, s3 <= 0, z = 1 + 2
   encArg(z) -{ 1 }-> s4 :|: s4 >= 0, s4 <= 0, z = 1 + 2
   encArg(z) -{ 2 }-> s5 :|: s5 >= 0, s5 <= 0, z = 1 + 2
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ -1 + 3*z }-> 1 + s9 :|: s9 >= 0, s9 <= z - 1 + 2, z - 1 >= 0
   encode_0 -{ 0 }-> 1 :|: 
   encode_0 -{ 0 }-> 0 :|: 
   encode_0 -{ 1 }-> 0 :|: 
   encode_1 -{ 0 }-> 0 :|: 
   encode_f(z) -{ 1 }-> s1 :|: s1 >= 0, s1 <= 0, z = 0
   encode_f(z) -{ 3*z }-> s16 :|: s15 >= 0, s15 <= z - 1 + 2, s16 >= 0, s16 <= 0, z - 1 >= 0
   encode_f(z) -{ 1 + 3*z }-> s19 :|: s17 >= 0, s17 <= z - 1 + 2, s18 >= 0, s18 <= 0, s19 >= 0, s19 <= 0, z - 1 >= 0
   encode_f(z) -{ 1 }-> s2 :|: s2 >= 0, s2 <= 0, z >= 0
   encode_f(z) -{ 7 + 3*x_125 + 3*x_27 }-> s31 :|: s28 >= 0, s28 <= x_125 + 2, s29 >= 0, s29 <= x_27 + 2, s30 >= 0, s30 <= 2, s31 >= 0, s31 <= 0, x_125 >= 0, x_27 >= 0, z = 1 + x_125 + x_27
   encode_f(z) -{ 1 }-> s6 :|: s6 >= 0, s6 <= 0, z = 2
   encode_f(z) -{ 1 }-> s7 :|: s7 >= 0, s7 <= 0, z = 2
   encode_f(z) -{ 2 }-> s8 :|: s8 >= 0, s8 <= 0, z = 2
   encode_f(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z, z') -{ 6 + 3*z + 3*z' }-> s34 :|: s32 >= 0, s32 <= z + 2, s33 >= 0, s33 <= z' + 2, s34 >= 0, s34 <= 2, z >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 2 + 3*z }-> 1 + s20 :|: s20 >= 0, s20 <= z + 2, z >= 0
   f(z) -{ 2 }-> s :|: s >= 0, s <= 0, z - 1 >= 0
   f(z) -{ 0 }-> 0 :|: z >= 0
   g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   g(z, z') -{ 1 }-> 1 + 1 :|: z = 1, z' = 0
   g(z, z') -{ 1 }-> 1 + 0 :|: z = 1, z' = 0
   g(z, z') -{ 2 }-> 1 + 0 :|: z = 1, z' = 0

Function symbols to be analyzed: {encode_g}, {encode_f}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [1], size: O(1) [1]
  encode_1: runtime: O(1) [0], size: O(1) [0]
  f: runtime: O(1) [1], size: O(1) [0]
  g: runtime: O(1) [2], size: O(1) [2]
  0': runtime: O(1) [1], size: O(1) [1]
  encArg: runtime: O(n^1) [2 + 3*z], size: O(n^1) [2 + z]
  encode_g: runtime: ?, size: O(1) [2]

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

(65) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: encode_g
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 6 + 3*z + 3*z'

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

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

   0' -{ 0 }-> 1 :|: 
   0' -{ 1 }-> 0 :|: 
   0' -{ 0 }-> 0 :|: 
   encArg(z) -{ 1 }-> s' :|: s' >= 0, s' <= 0, z = 1 + 0
   encArg(z) -{ 1 }-> s'' :|: s'' >= 0, s'' <= 0, z - 1 >= 0
   encArg(z) -{ -3 + 3*z }-> s11 :|: s10 >= 0, s10 <= z - 2 + 2, s11 >= 0, s11 <= 0, z - 2 >= 0
   encArg(z) -{ -2 + 3*z }-> s14 :|: s12 >= 0, s12 <= z - 2 + 2, s13 >= 0, s13 <= 0, s14 >= 0, s14 <= 0, z - 2 >= 0
   encArg(z) -{ 7 + 3*x_11 + 3*x_2' }-> s24 :|: s21 >= 0, s21 <= x_11 + 2, s22 >= 0, s22 <= x_2' + 2, s23 >= 0, s23 <= 2, s24 >= 0, s24 <= 0, x_11 >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2')
   encArg(z) -{ 6 + 3*x_1 + 3*x_2 }-> s27 :|: s25 >= 0, s25 <= x_1 + 2, s26 >= 0, s26 <= x_2 + 2, s27 >= 0, s27 <= 2, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 1 }-> s3 :|: s3 >= 0, s3 <= 0, z = 1 + 2
   encArg(z) -{ 1 }-> s4 :|: s4 >= 0, s4 <= 0, z = 1 + 2
   encArg(z) -{ 2 }-> s5 :|: s5 >= 0, s5 <= 0, z = 1 + 2
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ -1 + 3*z }-> 1 + s9 :|: s9 >= 0, s9 <= z - 1 + 2, z - 1 >= 0
   encode_0 -{ 0 }-> 1 :|: 
   encode_0 -{ 0 }-> 0 :|: 
   encode_0 -{ 1 }-> 0 :|: 
   encode_1 -{ 0 }-> 0 :|: 
   encode_f(z) -{ 1 }-> s1 :|: s1 >= 0, s1 <= 0, z = 0
   encode_f(z) -{ 3*z }-> s16 :|: s15 >= 0, s15 <= z - 1 + 2, s16 >= 0, s16 <= 0, z - 1 >= 0
   encode_f(z) -{ 1 + 3*z }-> s19 :|: s17 >= 0, s17 <= z - 1 + 2, s18 >= 0, s18 <= 0, s19 >= 0, s19 <= 0, z - 1 >= 0
   encode_f(z) -{ 1 }-> s2 :|: s2 >= 0, s2 <= 0, z >= 0
   encode_f(z) -{ 7 + 3*x_125 + 3*x_27 }-> s31 :|: s28 >= 0, s28 <= x_125 + 2, s29 >= 0, s29 <= x_27 + 2, s30 >= 0, s30 <= 2, s31 >= 0, s31 <= 0, x_125 >= 0, x_27 >= 0, z = 1 + x_125 + x_27
   encode_f(z) -{ 1 }-> s6 :|: s6 >= 0, s6 <= 0, z = 2
   encode_f(z) -{ 1 }-> s7 :|: s7 >= 0, s7 <= 0, z = 2
   encode_f(z) -{ 2 }-> s8 :|: s8 >= 0, s8 <= 0, z = 2
   encode_f(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z, z') -{ 6 + 3*z + 3*z' }-> s34 :|: s32 >= 0, s32 <= z + 2, s33 >= 0, s33 <= z' + 2, s34 >= 0, s34 <= 2, z >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 2 + 3*z }-> 1 + s20 :|: s20 >= 0, s20 <= z + 2, z >= 0
   f(z) -{ 2 }-> s :|: s >= 0, s <= 0, z - 1 >= 0
   f(z) -{ 0 }-> 0 :|: z >= 0
   g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   g(z, z') -{ 1 }-> 1 + 1 :|: z = 1, z' = 0
   g(z, z') -{ 1 }-> 1 + 0 :|: z = 1, z' = 0
   g(z, z') -{ 2 }-> 1 + 0 :|: z = 1, z' = 0

Function symbols to be analyzed: {encode_f}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [1], size: O(1) [1]
  encode_1: runtime: O(1) [0], size: O(1) [0]
  f: runtime: O(1) [1], size: O(1) [0]
  g: runtime: O(1) [2], size: O(1) [2]
  0': runtime: O(1) [1], size: O(1) [1]
  encArg: runtime: O(n^1) [2 + 3*z], size: O(n^1) [2 + z]
  encode_g: runtime: O(n^1) [6 + 3*z + 3*z'], size: O(1) [2]

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

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

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

   0' -{ 0 }-> 1 :|: 
   0' -{ 1 }-> 0 :|: 
   0' -{ 0 }-> 0 :|: 
   encArg(z) -{ 1 }-> s' :|: s' >= 0, s' <= 0, z = 1 + 0
   encArg(z) -{ 1 }-> s'' :|: s'' >= 0, s'' <= 0, z - 1 >= 0
   encArg(z) -{ -3 + 3*z }-> s11 :|: s10 >= 0, s10 <= z - 2 + 2, s11 >= 0, s11 <= 0, z - 2 >= 0
   encArg(z) -{ -2 + 3*z }-> s14 :|: s12 >= 0, s12 <= z - 2 + 2, s13 >= 0, s13 <= 0, s14 >= 0, s14 <= 0, z - 2 >= 0
   encArg(z) -{ 7 + 3*x_11 + 3*x_2' }-> s24 :|: s21 >= 0, s21 <= x_11 + 2, s22 >= 0, s22 <= x_2' + 2, s23 >= 0, s23 <= 2, s24 >= 0, s24 <= 0, x_11 >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2')
   encArg(z) -{ 6 + 3*x_1 + 3*x_2 }-> s27 :|: s25 >= 0, s25 <= x_1 + 2, s26 >= 0, s26 <= x_2 + 2, s27 >= 0, s27 <= 2, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 1 }-> s3 :|: s3 >= 0, s3 <= 0, z = 1 + 2
   encArg(z) -{ 1 }-> s4 :|: s4 >= 0, s4 <= 0, z = 1 + 2
   encArg(z) -{ 2 }-> s5 :|: s5 >= 0, s5 <= 0, z = 1 + 2
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ -1 + 3*z }-> 1 + s9 :|: s9 >= 0, s9 <= z - 1 + 2, z - 1 >= 0
   encode_0 -{ 0 }-> 1 :|: 
   encode_0 -{ 0 }-> 0 :|: 
   encode_0 -{ 1 }-> 0 :|: 
   encode_1 -{ 0 }-> 0 :|: 
   encode_f(z) -{ 1 }-> s1 :|: s1 >= 0, s1 <= 0, z = 0
   encode_f(z) -{ 3*z }-> s16 :|: s15 >= 0, s15 <= z - 1 + 2, s16 >= 0, s16 <= 0, z - 1 >= 0
   encode_f(z) -{ 1 + 3*z }-> s19 :|: s17 >= 0, s17 <= z - 1 + 2, s18 >= 0, s18 <= 0, s19 >= 0, s19 <= 0, z - 1 >= 0
   encode_f(z) -{ 1 }-> s2 :|: s2 >= 0, s2 <= 0, z >= 0
   encode_f(z) -{ 7 + 3*x_125 + 3*x_27 }-> s31 :|: s28 >= 0, s28 <= x_125 + 2, s29 >= 0, s29 <= x_27 + 2, s30 >= 0, s30 <= 2, s31 >= 0, s31 <= 0, x_125 >= 0, x_27 >= 0, z = 1 + x_125 + x_27
   encode_f(z) -{ 1 }-> s6 :|: s6 >= 0, s6 <= 0, z = 2
   encode_f(z) -{ 1 }-> s7 :|: s7 >= 0, s7 <= 0, z = 2
   encode_f(z) -{ 2 }-> s8 :|: s8 >= 0, s8 <= 0, z = 2
   encode_f(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z, z') -{ 6 + 3*z + 3*z' }-> s34 :|: s32 >= 0, s32 <= z + 2, s33 >= 0, s33 <= z' + 2, s34 >= 0, s34 <= 2, z >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 2 + 3*z }-> 1 + s20 :|: s20 >= 0, s20 <= z + 2, z >= 0
   f(z) -{ 2 }-> s :|: s >= 0, s <= 0, z - 1 >= 0
   f(z) -{ 0 }-> 0 :|: z >= 0
   g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   g(z, z') -{ 1 }-> 1 + 1 :|: z = 1, z' = 0
   g(z, z') -{ 1 }-> 1 + 0 :|: z = 1, z' = 0
   g(z, z') -{ 2 }-> 1 + 0 :|: z = 1, z' = 0

Function symbols to be analyzed: {encode_f}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [1], size: O(1) [1]
  encode_1: runtime: O(1) [0], size: O(1) [0]
  f: runtime: O(1) [1], size: O(1) [0]
  g: runtime: O(1) [2], size: O(1) [2]
  0': runtime: O(1) [1], size: O(1) [1]
  encArg: runtime: O(n^1) [2 + 3*z], size: O(n^1) [2 + z]
  encode_g: runtime: O(n^1) [6 + 3*z + 3*z'], size: O(1) [2]

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

(69) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   0' -{ 0 }-> 1 :|: 
   0' -{ 1 }-> 0 :|: 
   0' -{ 0 }-> 0 :|: 
   encArg(z) -{ 1 }-> s' :|: s' >= 0, s' <= 0, z = 1 + 0
   encArg(z) -{ 1 }-> s'' :|: s'' >= 0, s'' <= 0, z - 1 >= 0
   encArg(z) -{ -3 + 3*z }-> s11 :|: s10 >= 0, s10 <= z - 2 + 2, s11 >= 0, s11 <= 0, z - 2 >= 0
   encArg(z) -{ -2 + 3*z }-> s14 :|: s12 >= 0, s12 <= z - 2 + 2, s13 >= 0, s13 <= 0, s14 >= 0, s14 <= 0, z - 2 >= 0
   encArg(z) -{ 7 + 3*x_11 + 3*x_2' }-> s24 :|: s21 >= 0, s21 <= x_11 + 2, s22 >= 0, s22 <= x_2' + 2, s23 >= 0, s23 <= 2, s24 >= 0, s24 <= 0, x_11 >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2')
   encArg(z) -{ 6 + 3*x_1 + 3*x_2 }-> s27 :|: s25 >= 0, s25 <= x_1 + 2, s26 >= 0, s26 <= x_2 + 2, s27 >= 0, s27 <= 2, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 1 }-> s3 :|: s3 >= 0, s3 <= 0, z = 1 + 2
   encArg(z) -{ 1 }-> s4 :|: s4 >= 0, s4 <= 0, z = 1 + 2
   encArg(z) -{ 2 }-> s5 :|: s5 >= 0, s5 <= 0, z = 1 + 2
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ -1 + 3*z }-> 1 + s9 :|: s9 >= 0, s9 <= z - 1 + 2, z - 1 >= 0
   encode_0 -{ 0 }-> 1 :|: 
   encode_0 -{ 0 }-> 0 :|: 
   encode_0 -{ 1 }-> 0 :|: 
   encode_1 -{ 0 }-> 0 :|: 
   encode_f(z) -{ 1 }-> s1 :|: s1 >= 0, s1 <= 0, z = 0
   encode_f(z) -{ 3*z }-> s16 :|: s15 >= 0, s15 <= z - 1 + 2, s16 >= 0, s16 <= 0, z - 1 >= 0
   encode_f(z) -{ 1 + 3*z }-> s19 :|: s17 >= 0, s17 <= z - 1 + 2, s18 >= 0, s18 <= 0, s19 >= 0, s19 <= 0, z - 1 >= 0
   encode_f(z) -{ 1 }-> s2 :|: s2 >= 0, s2 <= 0, z >= 0
   encode_f(z) -{ 7 + 3*x_125 + 3*x_27 }-> s31 :|: s28 >= 0, s28 <= x_125 + 2, s29 >= 0, s29 <= x_27 + 2, s30 >= 0, s30 <= 2, s31 >= 0, s31 <= 0, x_125 >= 0, x_27 >= 0, z = 1 + x_125 + x_27
   encode_f(z) -{ 1 }-> s6 :|: s6 >= 0, s6 <= 0, z = 2
   encode_f(z) -{ 1 }-> s7 :|: s7 >= 0, s7 <= 0, z = 2
   encode_f(z) -{ 2 }-> s8 :|: s8 >= 0, s8 <= 0, z = 2
   encode_f(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z, z') -{ 6 + 3*z + 3*z' }-> s34 :|: s32 >= 0, s32 <= z + 2, s33 >= 0, s33 <= z' + 2, s34 >= 0, s34 <= 2, z >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 2 + 3*z }-> 1 + s20 :|: s20 >= 0, s20 <= z + 2, z >= 0
   f(z) -{ 2 }-> s :|: s >= 0, s <= 0, z - 1 >= 0
   f(z) -{ 0 }-> 0 :|: z >= 0
   g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   g(z, z') -{ 1 }-> 1 + 1 :|: z = 1, z' = 0
   g(z, z') -{ 1 }-> 1 + 0 :|: z = 1, z' = 0
   g(z, z') -{ 2 }-> 1 + 0 :|: z = 1, z' = 0

Function symbols to be analyzed: {encode_f}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [1], size: O(1) [1]
  encode_1: runtime: O(1) [0], size: O(1) [0]
  f: runtime: O(1) [1], size: O(1) [0]
  g: runtime: O(1) [2], size: O(1) [2]
  0': runtime: O(1) [1], size: O(1) [1]
  encArg: runtime: O(n^1) [2 + 3*z], size: O(n^1) [2 + z]
  encode_g: runtime: O(n^1) [6 + 3*z + 3*z'], size: O(1) [2]
  encode_f: runtime: ?, size: O(1) [0]

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

(71) 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: 4 + 3*z

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

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

   0' -{ 0 }-> 1 :|: 
   0' -{ 1 }-> 0 :|: 
   0' -{ 0 }-> 0 :|: 
   encArg(z) -{ 1 }-> s' :|: s' >= 0, s' <= 0, z = 1 + 0
   encArg(z) -{ 1 }-> s'' :|: s'' >= 0, s'' <= 0, z - 1 >= 0
   encArg(z) -{ -3 + 3*z }-> s11 :|: s10 >= 0, s10 <= z - 2 + 2, s11 >= 0, s11 <= 0, z - 2 >= 0
   encArg(z) -{ -2 + 3*z }-> s14 :|: s12 >= 0, s12 <= z - 2 + 2, s13 >= 0, s13 <= 0, s14 >= 0, s14 <= 0, z - 2 >= 0
   encArg(z) -{ 7 + 3*x_11 + 3*x_2' }-> s24 :|: s21 >= 0, s21 <= x_11 + 2, s22 >= 0, s22 <= x_2' + 2, s23 >= 0, s23 <= 2, s24 >= 0, s24 <= 0, x_11 >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2')
   encArg(z) -{ 6 + 3*x_1 + 3*x_2 }-> s27 :|: s25 >= 0, s25 <= x_1 + 2, s26 >= 0, s26 <= x_2 + 2, s27 >= 0, s27 <= 2, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 1 }-> s3 :|: s3 >= 0, s3 <= 0, z = 1 + 2
   encArg(z) -{ 1 }-> s4 :|: s4 >= 0, s4 <= 0, z = 1 + 2
   encArg(z) -{ 2 }-> s5 :|: s5 >= 0, s5 <= 0, z = 1 + 2
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ -1 + 3*z }-> 1 + s9 :|: s9 >= 0, s9 <= z - 1 + 2, z - 1 >= 0
   encode_0 -{ 0 }-> 1 :|: 
   encode_0 -{ 0 }-> 0 :|: 
   encode_0 -{ 1 }-> 0 :|: 
   encode_1 -{ 0 }-> 0 :|: 
   encode_f(z) -{ 1 }-> s1 :|: s1 >= 0, s1 <= 0, z = 0
   encode_f(z) -{ 3*z }-> s16 :|: s15 >= 0, s15 <= z - 1 + 2, s16 >= 0, s16 <= 0, z - 1 >= 0
   encode_f(z) -{ 1 + 3*z }-> s19 :|: s17 >= 0, s17 <= z - 1 + 2, s18 >= 0, s18 <= 0, s19 >= 0, s19 <= 0, z - 1 >= 0
   encode_f(z) -{ 1 }-> s2 :|: s2 >= 0, s2 <= 0, z >= 0
   encode_f(z) -{ 7 + 3*x_125 + 3*x_27 }-> s31 :|: s28 >= 0, s28 <= x_125 + 2, s29 >= 0, s29 <= x_27 + 2, s30 >= 0, s30 <= 2, s31 >= 0, s31 <= 0, x_125 >= 0, x_27 >= 0, z = 1 + x_125 + x_27
   encode_f(z) -{ 1 }-> s6 :|: s6 >= 0, s6 <= 0, z = 2
   encode_f(z) -{ 1 }-> s7 :|: s7 >= 0, s7 <= 0, z = 2
   encode_f(z) -{ 2 }-> s8 :|: s8 >= 0, s8 <= 0, z = 2
   encode_f(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z, z') -{ 6 + 3*z + 3*z' }-> s34 :|: s32 >= 0, s32 <= z + 2, s33 >= 0, s33 <= z' + 2, s34 >= 0, s34 <= 2, z >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 2 + 3*z }-> 1 + s20 :|: s20 >= 0, s20 <= z + 2, z >= 0
   f(z) -{ 2 }-> s :|: s >= 0, s <= 0, z - 1 >= 0
   f(z) -{ 0 }-> 0 :|: z >= 0
   g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   g(z, z') -{ 1 }-> 1 + 1 :|: z = 1, z' = 0
   g(z, z') -{ 1 }-> 1 + 0 :|: z = 1, z' = 0
   g(z, z') -{ 2 }-> 1 + 0 :|: z = 1, z' = 0

Function symbols to be analyzed: {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [1], size: O(1) [1]
  encode_1: runtime: O(1) [0], size: O(1) [0]
  f: runtime: O(1) [1], size: O(1) [0]
  g: runtime: O(1) [2], size: O(1) [2]
  0': runtime: O(1) [1], size: O(1) [1]
  encArg: runtime: O(n^1) [2 + 3*z], size: O(n^1) [2 + z]
  encode_g: runtime: O(n^1) [6 + 3*z + 3*z'], size: O(1) [2]
  encode_f: runtime: O(n^1) [4 + 3*z], size: O(1) [0]

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

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

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

   0' -{ 0 }-> 1 :|: 
   0' -{ 1 }-> 0 :|: 
   0' -{ 0 }-> 0 :|: 
   encArg(z) -{ 1 }-> s' :|: s' >= 0, s' <= 0, z = 1 + 0
   encArg(z) -{ 1 }-> s'' :|: s'' >= 0, s'' <= 0, z - 1 >= 0
   encArg(z) -{ -3 + 3*z }-> s11 :|: s10 >= 0, s10 <= z - 2 + 2, s11 >= 0, s11 <= 0, z - 2 >= 0
   encArg(z) -{ -2 + 3*z }-> s14 :|: s12 >= 0, s12 <= z - 2 + 2, s13 >= 0, s13 <= 0, s14 >= 0, s14 <= 0, z - 2 >= 0
   encArg(z) -{ 7 + 3*x_11 + 3*x_2' }-> s24 :|: s21 >= 0, s21 <= x_11 + 2, s22 >= 0, s22 <= x_2' + 2, s23 >= 0, s23 <= 2, s24 >= 0, s24 <= 0, x_11 >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2')
   encArg(z) -{ 6 + 3*x_1 + 3*x_2 }-> s27 :|: s25 >= 0, s25 <= x_1 + 2, s26 >= 0, s26 <= x_2 + 2, s27 >= 0, s27 <= 2, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 1 }-> s3 :|: s3 >= 0, s3 <= 0, z = 1 + 2
   encArg(z) -{ 1 }-> s4 :|: s4 >= 0, s4 <= 0, z = 1 + 2
   encArg(z) -{ 2 }-> s5 :|: s5 >= 0, s5 <= 0, z = 1 + 2
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ -1 + 3*z }-> 1 + s9 :|: s9 >= 0, s9 <= z - 1 + 2, z - 1 >= 0
   encode_0 -{ 0 }-> 1 :|: 
   encode_0 -{ 0 }-> 0 :|: 
   encode_0 -{ 1 }-> 0 :|: 
   encode_1 -{ 0 }-> 0 :|: 
   encode_f(z) -{ 1 }-> s1 :|: s1 >= 0, s1 <= 0, z = 0
   encode_f(z) -{ 3*z }-> s16 :|: s15 >= 0, s15 <= z - 1 + 2, s16 >= 0, s16 <= 0, z - 1 >= 0
   encode_f(z) -{ 1 + 3*z }-> s19 :|: s17 >= 0, s17 <= z - 1 + 2, s18 >= 0, s18 <= 0, s19 >= 0, s19 <= 0, z - 1 >= 0
   encode_f(z) -{ 1 }-> s2 :|: s2 >= 0, s2 <= 0, z >= 0
   encode_f(z) -{ 7 + 3*x_125 + 3*x_27 }-> s31 :|: s28 >= 0, s28 <= x_125 + 2, s29 >= 0, s29 <= x_27 + 2, s30 >= 0, s30 <= 2, s31 >= 0, s31 <= 0, x_125 >= 0, x_27 >= 0, z = 1 + x_125 + x_27
   encode_f(z) -{ 1 }-> s6 :|: s6 >= 0, s6 <= 0, z = 2
   encode_f(z) -{ 1 }-> s7 :|: s7 >= 0, s7 <= 0, z = 2
   encode_f(z) -{ 2 }-> s8 :|: s8 >= 0, s8 <= 0, z = 2
   encode_f(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z, z') -{ 6 + 3*z + 3*z' }-> s34 :|: s32 >= 0, s32 <= z + 2, s33 >= 0, s33 <= z' + 2, s34 >= 0, s34 <= 2, z >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 2 + 3*z }-> 1 + s20 :|: s20 >= 0, s20 <= z + 2, z >= 0
   f(z) -{ 2 }-> s :|: s >= 0, s <= 0, z - 1 >= 0
   f(z) -{ 0 }-> 0 :|: z >= 0
   g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   g(z, z') -{ 1 }-> 1 + 1 :|: z = 1, z' = 0
   g(z, z') -{ 1 }-> 1 + 0 :|: z = 1, z' = 0
   g(z, z') -{ 2 }-> 1 + 0 :|: z = 1, z' = 0

Function symbols to be analyzed: {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [1], size: O(1) [1]
  encode_1: runtime: O(1) [0], size: O(1) [0]
  f: runtime: O(1) [1], size: O(1) [0]
  g: runtime: O(1) [2], size: O(1) [2]
  0': runtime: O(1) [1], size: O(1) [1]
  encArg: runtime: O(n^1) [2 + 3*z], size: O(n^1) [2 + z]
  encode_g: runtime: O(n^1) [6 + 3*z + 3*z'], size: O(1) [2]
  encode_f: runtime: O(n^1) [4 + 3*z], size: O(1) [0]

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

(75) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   0' -{ 0 }-> 1 :|: 
   0' -{ 1 }-> 0 :|: 
   0' -{ 0 }-> 0 :|: 
   encArg(z) -{ 1 }-> s' :|: s' >= 0, s' <= 0, z = 1 + 0
   encArg(z) -{ 1 }-> s'' :|: s'' >= 0, s'' <= 0, z - 1 >= 0
   encArg(z) -{ -3 + 3*z }-> s11 :|: s10 >= 0, s10 <= z - 2 + 2, s11 >= 0, s11 <= 0, z - 2 >= 0
   encArg(z) -{ -2 + 3*z }-> s14 :|: s12 >= 0, s12 <= z - 2 + 2, s13 >= 0, s13 <= 0, s14 >= 0, s14 <= 0, z - 2 >= 0
   encArg(z) -{ 7 + 3*x_11 + 3*x_2' }-> s24 :|: s21 >= 0, s21 <= x_11 + 2, s22 >= 0, s22 <= x_2' + 2, s23 >= 0, s23 <= 2, s24 >= 0, s24 <= 0, x_11 >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2')
   encArg(z) -{ 6 + 3*x_1 + 3*x_2 }-> s27 :|: s25 >= 0, s25 <= x_1 + 2, s26 >= 0, s26 <= x_2 + 2, s27 >= 0, s27 <= 2, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 1 }-> s3 :|: s3 >= 0, s3 <= 0, z = 1 + 2
   encArg(z) -{ 1 }-> s4 :|: s4 >= 0, s4 <= 0, z = 1 + 2
   encArg(z) -{ 2 }-> s5 :|: s5 >= 0, s5 <= 0, z = 1 + 2
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ -1 + 3*z }-> 1 + s9 :|: s9 >= 0, s9 <= z - 1 + 2, z - 1 >= 0
   encode_0 -{ 0 }-> 1 :|: 
   encode_0 -{ 0 }-> 0 :|: 
   encode_0 -{ 1 }-> 0 :|: 
   encode_1 -{ 0 }-> 0 :|: 
   encode_f(z) -{ 1 }-> s1 :|: s1 >= 0, s1 <= 0, z = 0
   encode_f(z) -{ 3*z }-> s16 :|: s15 >= 0, s15 <= z - 1 + 2, s16 >= 0, s16 <= 0, z - 1 >= 0
   encode_f(z) -{ 1 + 3*z }-> s19 :|: s17 >= 0, s17 <= z - 1 + 2, s18 >= 0, s18 <= 0, s19 >= 0, s19 <= 0, z - 1 >= 0
   encode_f(z) -{ 1 }-> s2 :|: s2 >= 0, s2 <= 0, z >= 0
   encode_f(z) -{ 7 + 3*x_125 + 3*x_27 }-> s31 :|: s28 >= 0, s28 <= x_125 + 2, s29 >= 0, s29 <= x_27 + 2, s30 >= 0, s30 <= 2, s31 >= 0, s31 <= 0, x_125 >= 0, x_27 >= 0, z = 1 + x_125 + x_27
   encode_f(z) -{ 1 }-> s6 :|: s6 >= 0, s6 <= 0, z = 2
   encode_f(z) -{ 1 }-> s7 :|: s7 >= 0, s7 <= 0, z = 2
   encode_f(z) -{ 2 }-> s8 :|: s8 >= 0, s8 <= 0, z = 2
   encode_f(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z, z') -{ 6 + 3*z + 3*z' }-> s34 :|: s32 >= 0, s32 <= z + 2, s33 >= 0, s33 <= z' + 2, s34 >= 0, s34 <= 2, z >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 2 + 3*z }-> 1 + s20 :|: s20 >= 0, s20 <= z + 2, z >= 0
   f(z) -{ 2 }-> s :|: s >= 0, s <= 0, z - 1 >= 0
   f(z) -{ 0 }-> 0 :|: z >= 0
   g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   g(z, z') -{ 1 }-> 1 + 1 :|: z = 1, z' = 0
   g(z, z') -{ 1 }-> 1 + 0 :|: z = 1, z' = 0
   g(z, z') -{ 2 }-> 1 + 0 :|: z = 1, z' = 0

Function symbols to be analyzed: {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [1], size: O(1) [1]
  encode_1: runtime: O(1) [0], size: O(1) [0]
  f: runtime: O(1) [1], size: O(1) [0]
  g: runtime: O(1) [2], size: O(1) [2]
  0': runtime: O(1) [1], size: O(1) [1]
  encArg: runtime: O(n^1) [2 + 3*z], size: O(n^1) [2 + z]
  encode_g: runtime: O(n^1) [6 + 3*z + 3*z'], size: O(1) [2]
  encode_f: runtime: O(n^1) [4 + 3*z], size: O(1) [0]
  encode_s: runtime: ?, size: O(n^1) [3 + z]

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

(77) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: encode_s
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 2 + 3*z

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

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

   0' -{ 0 }-> 1 :|: 
   0' -{ 1 }-> 0 :|: 
   0' -{ 0 }-> 0 :|: 
   encArg(z) -{ 1 }-> s' :|: s' >= 0, s' <= 0, z = 1 + 0
   encArg(z) -{ 1 }-> s'' :|: s'' >= 0, s'' <= 0, z - 1 >= 0
   encArg(z) -{ -3 + 3*z }-> s11 :|: s10 >= 0, s10 <= z - 2 + 2, s11 >= 0, s11 <= 0, z - 2 >= 0
   encArg(z) -{ -2 + 3*z }-> s14 :|: s12 >= 0, s12 <= z - 2 + 2, s13 >= 0, s13 <= 0, s14 >= 0, s14 <= 0, z - 2 >= 0
   encArg(z) -{ 7 + 3*x_11 + 3*x_2' }-> s24 :|: s21 >= 0, s21 <= x_11 + 2, s22 >= 0, s22 <= x_2' + 2, s23 >= 0, s23 <= 2, s24 >= 0, s24 <= 0, x_11 >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2')
   encArg(z) -{ 6 + 3*x_1 + 3*x_2 }-> s27 :|: s25 >= 0, s25 <= x_1 + 2, s26 >= 0, s26 <= x_2 + 2, s27 >= 0, s27 <= 2, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 1 }-> s3 :|: s3 >= 0, s3 <= 0, z = 1 + 2
   encArg(z) -{ 1 }-> s4 :|: s4 >= 0, s4 <= 0, z = 1 + 2
   encArg(z) -{ 2 }-> s5 :|: s5 >= 0, s5 <= 0, z = 1 + 2
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ -1 + 3*z }-> 1 + s9 :|: s9 >= 0, s9 <= z - 1 + 2, z - 1 >= 0
   encode_0 -{ 0 }-> 1 :|: 
   encode_0 -{ 0 }-> 0 :|: 
   encode_0 -{ 1 }-> 0 :|: 
   encode_1 -{ 0 }-> 0 :|: 
   encode_f(z) -{ 1 }-> s1 :|: s1 >= 0, s1 <= 0, z = 0
   encode_f(z) -{ 3*z }-> s16 :|: s15 >= 0, s15 <= z - 1 + 2, s16 >= 0, s16 <= 0, z - 1 >= 0
   encode_f(z) -{ 1 + 3*z }-> s19 :|: s17 >= 0, s17 <= z - 1 + 2, s18 >= 0, s18 <= 0, s19 >= 0, s19 <= 0, z - 1 >= 0
   encode_f(z) -{ 1 }-> s2 :|: s2 >= 0, s2 <= 0, z >= 0
   encode_f(z) -{ 7 + 3*x_125 + 3*x_27 }-> s31 :|: s28 >= 0, s28 <= x_125 + 2, s29 >= 0, s29 <= x_27 + 2, s30 >= 0, s30 <= 2, s31 >= 0, s31 <= 0, x_125 >= 0, x_27 >= 0, z = 1 + x_125 + x_27
   encode_f(z) -{ 1 }-> s6 :|: s6 >= 0, s6 <= 0, z = 2
   encode_f(z) -{ 1 }-> s7 :|: s7 >= 0, s7 <= 0, z = 2
   encode_f(z) -{ 2 }-> s8 :|: s8 >= 0, s8 <= 0, z = 2
   encode_f(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z, z') -{ 6 + 3*z + 3*z' }-> s34 :|: s32 >= 0, s32 <= z + 2, s33 >= 0, s33 <= z' + 2, s34 >= 0, s34 <= 2, z >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 2 + 3*z }-> 1 + s20 :|: s20 >= 0, s20 <= z + 2, z >= 0
   f(z) -{ 2 }-> s :|: s >= 0, s <= 0, z - 1 >= 0
   f(z) -{ 0 }-> 0 :|: z >= 0
   g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   g(z, z') -{ 1 }-> 1 + 1 :|: z = 1, z' = 0
   g(z, z') -{ 1 }-> 1 + 0 :|: z = 1, z' = 0
   g(z, z') -{ 2 }-> 1 + 0 :|: z = 1, z' = 0

Function symbols to be analyzed: 
Previous analysis results are:
  encode_0: runtime: O(1) [1], size: O(1) [1]
  encode_1: runtime: O(1) [0], size: O(1) [0]
  f: runtime: O(1) [1], size: O(1) [0]
  g: runtime: O(1) [2], size: O(1) [2]
  0': runtime: O(1) [1], size: O(1) [1]
  encArg: runtime: O(n^1) [2 + 3*z], size: O(n^1) [2 + z]
  encode_g: runtime: O(n^1) [6 + 3*z + 3*z'], size: O(1) [2]
  encode_f: runtime: O(n^1) [4 + 3*z], size: O(1) [0]
  encode_s: runtime: O(n^1) [2 + 3*z], size: O(n^1) [3 + z]

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

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

(80)
BOUNDS(1, n^1)