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


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WORST_CASE(Omega(n^1), O(n^2))
proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^2).

(0) DCpxTrs
(1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms]
(2) CpxRelTRS
(3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 159 ms]
(4) CpxRelTRS
(5) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
(6) CpxWeightedTrs
    (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (8) CpxTypedWeightedTrs
    (9) CompletionProof [UPPER BOUND(ID), 0 ms]
    (10) CpxTypedWeightedCompleteTrs
    (11) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (12) CpxTypedWeightedCompleteTrs
    (13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 10 ms]
    (14) CpxRNTS
    (15) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (16) CpxRNTS
    (17) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 6 ms]
    (18) CpxRNTS
    (19) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (20) CpxRNTS
    (21) IntTrsBoundProof [UPPER BOUND(ID), 455 ms]
    (22) CpxRNTS
    (23) IntTrsBoundProof [UPPER BOUND(ID), 151 ms]
    (24) CpxRNTS
    (25) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (26) CpxRNTS
    (27) IntTrsBoundProof [UPPER BOUND(ID), 2774 ms]
    (28) CpxRNTS
    (29) IntTrsBoundProof [UPPER BOUND(ID), 5343 ms]
    (30) CpxRNTS
    (31) ResultPropagationProof [UPPER BOUND(ID), 18 ms]
    (32) CpxRNTS
    (33) IntTrsBoundProof [UPPER BOUND(ID), 140 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), 1244 ms]
    (40) CpxRNTS
    (41) IntTrsBoundProof [UPPER BOUND(ID), 827 ms]
    (42) CpxRNTS
    (43) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (44) CpxRNTS
    (45) IntTrsBoundProof [UPPER BOUND(ID), 1204 ms]
    (46) CpxRNTS
    (47) IntTrsBoundProof [UPPER BOUND(ID), 745 ms]
    (48) CpxRNTS
    (49) FinalProof [FINISHED, 0 ms]
    (50) BOUNDS(1, n^2)
(51) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(52) CpxRelTRS
    (53) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (54) typed CpxTrs
    (55) OrderProof [LOWER BOUND(ID), 0 ms]
    (56) typed CpxTrs
    (57) RewriteLemmaProof [LOWER BOUND(ID), 416 ms]
    (58) BEST
        (59) proven lower bound
            (60) LowerBoundPropagationProof [FINISHED, 0 ms]
            (61) BOUNDS(n^1, INF)
        (62) typed CpxTrs
            (63) RewriteLemmaProof [LOWER BOUND(ID), 104 ms]
            (64) typed CpxTrs
            (65) RewriteLemmaProof [LOWER BOUND(ID), 55 ms]
            (66) typed CpxTrs
            (67) RewriteLemmaProof [LOWER BOUND(ID), 103 ms]
            (68) BOUNDS(1, INF)


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

(0)
Obligation:
The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^2).


The TRS R consists of the following rules:

   h(f(x), y) -> f(g(x, y))
   g(x, y) -> h(x, y)

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(f(x_1)) -> f(encArg(x_1))
   encArg(cons_h(x_1, x_2)) -> h(encArg(x_1), encArg(x_2))
   encArg(cons_g(x_1, x_2)) -> g(encArg(x_1), encArg(x_2))
   encode_h(x_1, x_2) -> h(encArg(x_1), encArg(x_2))
   encode_f(x_1) -> f(encArg(x_1))
   encode_g(x_1, x_2) -> g(encArg(x_1), encArg(x_2))


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

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


The TRS R consists of the following rules:

   h(f(x), y) -> f(g(x, y))
   g(x, y) -> h(x, y)

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

   encArg(f(x_1)) -> f(encArg(x_1))
   encArg(cons_h(x_1, x_2)) -> h(encArg(x_1), encArg(x_2))
   encArg(cons_g(x_1, x_2)) -> g(encArg(x_1), encArg(x_2))
   encode_h(x_1, x_2) -> h(encArg(x_1), encArg(x_2))
   encode_f(x_1) -> f(encArg(x_1))
   encode_g(x_1, x_2) -> g(encArg(x_1), encArg(x_2))

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

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

(4)
Obligation:
The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2).


The TRS R consists of the following rules:

   h(f(x), y) -> f(g(x, y))
   g(x, y) -> h(x, y)

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

   encArg(f(x_1)) -> f(encArg(x_1))
   encArg(cons_h(x_1, x_2)) -> h(encArg(x_1), encArg(x_2))
   encArg(cons_g(x_1, x_2)) -> g(encArg(x_1), encArg(x_2))
   encode_h(x_1, x_2) -> h(encArg(x_1), encArg(x_2))
   encode_f(x_1) -> f(encArg(x_1))
   encode_g(x_1, x_2) -> g(encArg(x_1), encArg(x_2))

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

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

(6)
Obligation:
The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2).


The TRS R consists of the following rules:

   h(f(x), y) -> f(g(x, y)) [1]
   g(x, y) -> h(x, y) [1]
   encArg(f(x_1)) -> f(encArg(x_1)) [0]
   encArg(cons_h(x_1, x_2)) -> h(encArg(x_1), encArg(x_2)) [0]
   encArg(cons_g(x_1, x_2)) -> g(encArg(x_1), encArg(x_2)) [0]
   encode_h(x_1, x_2) -> h(encArg(x_1), encArg(x_2)) [0]
   encode_f(x_1) -> f(encArg(x_1)) [0]
   encode_g(x_1, x_2) -> g(encArg(x_1), encArg(x_2)) [0]

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

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

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

   h(f(x), y) -> f(g(x, y)) [1]
   g(x, y) -> h(x, y) [1]
   encArg(f(x_1)) -> f(encArg(x_1)) [0]
   encArg(cons_h(x_1, x_2)) -> h(encArg(x_1), encArg(x_2)) [0]
   encArg(cons_g(x_1, x_2)) -> g(encArg(x_1), encArg(x_2)) [0]
   encode_h(x_1, x_2) -> h(encArg(x_1), encArg(x_2)) [0]
   encode_f(x_1) -> f(encArg(x_1)) [0]
   encode_g(x_1, x_2) -> g(encArg(x_1), encArg(x_2)) [0]

The TRS has the following type information:
h :: f:cons_h:cons_g -> f:cons_h:cons_g -> f:cons_h:cons_g
f :: f:cons_h:cons_g -> f:cons_h:cons_g
g :: f:cons_h:cons_g -> f:cons_h:cons_g -> f:cons_h:cons_g
encArg :: f:cons_h:cons_g -> f:cons_h:cons_g
cons_h :: f:cons_h:cons_g -> f:cons_h:cons_g -> f:cons_h:cons_g
cons_g :: f:cons_h:cons_g -> f:cons_h:cons_g -> f:cons_h:cons_g
encode_h :: f:cons_h:cons_g -> f:cons_h:cons_g -> f:cons_h:cons_g
encode_f :: f:cons_h:cons_g -> f:cons_h:cons_g
encode_g :: f:cons_h:cons_g -> f:cons_h:cons_g -> f:cons_h:cons_g

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

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

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

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

(c) The following functions are completely defined:

   h_2
   g_2
   encArg_1
   encode_h_2
   encode_f_1
   encode_g_2

Due to the following rules being added:

   encArg(v0) -> const [0]
   encode_h(v0, v1) -> const [0]
   encode_f(v0) -> const [0]
   encode_g(v0, v1) -> const [0]
   h(v0, v1) -> const [0]

And the following fresh constants:    const

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

(10)
Obligation:
Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is:

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

   h(f(x), y) -> f(g(x, y)) [1]
   g(x, y) -> h(x, y) [1]
   encArg(f(x_1)) -> f(encArg(x_1)) [0]
   encArg(cons_h(x_1, x_2)) -> h(encArg(x_1), encArg(x_2)) [0]
   encArg(cons_g(x_1, x_2)) -> g(encArg(x_1), encArg(x_2)) [0]
   encode_h(x_1, x_2) -> h(encArg(x_1), encArg(x_2)) [0]
   encode_f(x_1) -> f(encArg(x_1)) [0]
   encode_g(x_1, x_2) -> g(encArg(x_1), encArg(x_2)) [0]
   encArg(v0) -> const [0]
   encode_h(v0, v1) -> const [0]
   encode_f(v0) -> const [0]
   encode_g(v0, v1) -> const [0]
   h(v0, v1) -> const [0]

The TRS has the following type information:
h :: f:cons_h:cons_g:const -> f:cons_h:cons_g:const -> f:cons_h:cons_g:const
f :: f:cons_h:cons_g:const -> f:cons_h:cons_g:const
g :: f:cons_h:cons_g:const -> f:cons_h:cons_g:const -> f:cons_h:cons_g:const
encArg :: f:cons_h:cons_g:const -> f:cons_h:cons_g:const
cons_h :: f:cons_h:cons_g:const -> f:cons_h:cons_g:const -> f:cons_h:cons_g:const
cons_g :: f:cons_h:cons_g:const -> f:cons_h:cons_g:const -> f:cons_h:cons_g:const
encode_h :: f:cons_h:cons_g:const -> f:cons_h:cons_g:const -> f:cons_h:cons_g:const
encode_f :: f:cons_h:cons_g:const -> f:cons_h:cons_g:const
encode_g :: f:cons_h:cons_g:const -> f:cons_h:cons_g:const -> f:cons_h:cons_g:const
const :: f:cons_h:cons_g:const

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

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

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

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

   h(f(x), y) -> f(g(x, y)) [1]
   g(x, y) -> h(x, y) [1]
   encArg(f(x_1)) -> f(encArg(x_1)) [0]
   encArg(cons_h(f(x_1'), f(x_12))) -> h(f(encArg(x_1')), f(encArg(x_12))) [0]
   encArg(cons_h(f(x_1'), cons_h(x_13, x_21))) -> h(f(encArg(x_1')), h(encArg(x_13), encArg(x_21))) [0]
   encArg(cons_h(f(x_1'), cons_g(x_14, x_22))) -> h(f(encArg(x_1')), g(encArg(x_14), encArg(x_22))) [0]
   encArg(cons_h(f(x_1'), x_2)) -> h(f(encArg(x_1')), const) [0]
   encArg(cons_h(cons_h(x_1'', x_2'), f(x_15))) -> h(h(encArg(x_1''), encArg(x_2')), f(encArg(x_15))) [0]
   encArg(cons_h(cons_h(x_1'', x_2'), cons_h(x_16, x_23))) -> h(h(encArg(x_1''), encArg(x_2')), h(encArg(x_16), encArg(x_23))) [0]
   encArg(cons_h(cons_h(x_1'', x_2'), cons_g(x_17, x_24))) -> h(h(encArg(x_1''), encArg(x_2')), g(encArg(x_17), encArg(x_24))) [0]
   encArg(cons_h(cons_h(x_1'', x_2'), x_2)) -> h(h(encArg(x_1''), encArg(x_2')), const) [0]
   encArg(cons_h(cons_g(x_11, x_2''), f(x_18))) -> h(g(encArg(x_11), encArg(x_2'')), f(encArg(x_18))) [0]
   encArg(cons_h(cons_g(x_11, x_2''), cons_h(x_19, x_25))) -> h(g(encArg(x_11), encArg(x_2'')), h(encArg(x_19), encArg(x_25))) [0]
   encArg(cons_h(cons_g(x_11, x_2''), cons_g(x_110, x_26))) -> h(g(encArg(x_11), encArg(x_2'')), g(encArg(x_110), encArg(x_26))) [0]
   encArg(cons_h(cons_g(x_11, x_2''), x_2)) -> h(g(encArg(x_11), encArg(x_2'')), const) [0]
   encArg(cons_h(x_1, f(x_111))) -> h(const, f(encArg(x_111))) [0]
   encArg(cons_h(x_1, cons_h(x_112, x_27))) -> h(const, h(encArg(x_112), encArg(x_27))) [0]
   encArg(cons_h(x_1, cons_g(x_113, x_28))) -> h(const, g(encArg(x_113), encArg(x_28))) [0]
   encArg(cons_h(x_1, x_2)) -> h(const, const) [0]
   encArg(cons_g(f(x_114), f(x_117))) -> g(f(encArg(x_114)), f(encArg(x_117))) [0]
   encArg(cons_g(f(x_114), cons_h(x_118, x_211))) -> g(f(encArg(x_114)), h(encArg(x_118), encArg(x_211))) [0]
   encArg(cons_g(f(x_114), cons_g(x_119, x_212))) -> g(f(encArg(x_114)), g(encArg(x_119), encArg(x_212))) [0]
   encArg(cons_g(f(x_114), x_2)) -> g(f(encArg(x_114)), const) [0]
   encArg(cons_g(cons_h(x_115, x_29), f(x_120))) -> g(h(encArg(x_115), encArg(x_29)), f(encArg(x_120))) [0]
   encArg(cons_g(cons_h(x_115, x_29), cons_h(x_121, x_213))) -> g(h(encArg(x_115), encArg(x_29)), h(encArg(x_121), encArg(x_213))) [0]
   encArg(cons_g(cons_h(x_115, x_29), cons_g(x_122, x_214))) -> g(h(encArg(x_115), encArg(x_29)), g(encArg(x_122), encArg(x_214))) [0]
   encArg(cons_g(cons_h(x_115, x_29), x_2)) -> g(h(encArg(x_115), encArg(x_29)), const) [0]
   encArg(cons_g(cons_g(x_116, x_210), f(x_123))) -> g(g(encArg(x_116), encArg(x_210)), f(encArg(x_123))) [0]
   encArg(cons_g(cons_g(x_116, x_210), cons_h(x_124, x_215))) -> g(g(encArg(x_116), encArg(x_210)), h(encArg(x_124), encArg(x_215))) [0]
   encArg(cons_g(cons_g(x_116, x_210), cons_g(x_125, x_216))) -> g(g(encArg(x_116), encArg(x_210)), g(encArg(x_125), encArg(x_216))) [0]
   encArg(cons_g(cons_g(x_116, x_210), x_2)) -> g(g(encArg(x_116), encArg(x_210)), const) [0]
   encArg(cons_g(x_1, f(x_126))) -> g(const, f(encArg(x_126))) [0]
   encArg(cons_g(x_1, cons_h(x_127, x_217))) -> g(const, h(encArg(x_127), encArg(x_217))) [0]
   encArg(cons_g(x_1, cons_g(x_128, x_218))) -> g(const, g(encArg(x_128), encArg(x_218))) [0]
   encArg(cons_g(x_1, x_2)) -> g(const, const) [0]
   encode_h(f(x_129), f(x_132)) -> h(f(encArg(x_129)), f(encArg(x_132))) [0]
   encode_h(f(x_129), cons_h(x_133, x_221)) -> h(f(encArg(x_129)), h(encArg(x_133), encArg(x_221))) [0]
   encode_h(f(x_129), cons_g(x_134, x_222)) -> h(f(encArg(x_129)), g(encArg(x_134), encArg(x_222))) [0]
   encode_h(f(x_129), x_2) -> h(f(encArg(x_129)), const) [0]
   encode_h(cons_h(x_130, x_219), f(x_135)) -> h(h(encArg(x_130), encArg(x_219)), f(encArg(x_135))) [0]
   encode_h(cons_h(x_130, x_219), cons_h(x_136, x_223)) -> h(h(encArg(x_130), encArg(x_219)), h(encArg(x_136), encArg(x_223))) [0]
   encode_h(cons_h(x_130, x_219), cons_g(x_137, x_224)) -> h(h(encArg(x_130), encArg(x_219)), g(encArg(x_137), encArg(x_224))) [0]
   encode_h(cons_h(x_130, x_219), x_2) -> h(h(encArg(x_130), encArg(x_219)), const) [0]
   encode_h(cons_g(x_131, x_220), f(x_138)) -> h(g(encArg(x_131), encArg(x_220)), f(encArg(x_138))) [0]
   encode_h(cons_g(x_131, x_220), cons_h(x_139, x_225)) -> h(g(encArg(x_131), encArg(x_220)), h(encArg(x_139), encArg(x_225))) [0]
   encode_h(cons_g(x_131, x_220), cons_g(x_140, x_226)) -> h(g(encArg(x_131), encArg(x_220)), g(encArg(x_140), encArg(x_226))) [0]
   encode_h(cons_g(x_131, x_220), x_2) -> h(g(encArg(x_131), encArg(x_220)), const) [0]
   encode_h(x_1, f(x_141)) -> h(const, f(encArg(x_141))) [0]
   encode_h(x_1, cons_h(x_142, x_227)) -> h(const, h(encArg(x_142), encArg(x_227))) [0]
   encode_h(x_1, cons_g(x_143, x_228)) -> h(const, g(encArg(x_143), encArg(x_228))) [0]
   encode_h(x_1, x_2) -> h(const, const) [0]
   encode_f(x_1) -> f(encArg(x_1)) [0]
   encode_g(f(x_144), f(x_147)) -> g(f(encArg(x_144)), f(encArg(x_147))) [0]
   encode_g(f(x_144), cons_h(x_148, x_231)) -> g(f(encArg(x_144)), h(encArg(x_148), encArg(x_231))) [0]
   encode_g(f(x_144), cons_g(x_149, x_232)) -> g(f(encArg(x_144)), g(encArg(x_149), encArg(x_232))) [0]
   encode_g(f(x_144), x_2) -> g(f(encArg(x_144)), const) [0]
   encode_g(cons_h(x_145, x_229), f(x_150)) -> g(h(encArg(x_145), encArg(x_229)), f(encArg(x_150))) [0]
   encode_g(cons_h(x_145, x_229), cons_h(x_151, x_233)) -> g(h(encArg(x_145), encArg(x_229)), h(encArg(x_151), encArg(x_233))) [0]
   encode_g(cons_h(x_145, x_229), cons_g(x_152, x_234)) -> g(h(encArg(x_145), encArg(x_229)), g(encArg(x_152), encArg(x_234))) [0]
   encode_g(cons_h(x_145, x_229), x_2) -> g(h(encArg(x_145), encArg(x_229)), const) [0]
   encode_g(cons_g(x_146, x_230), f(x_153)) -> g(g(encArg(x_146), encArg(x_230)), f(encArg(x_153))) [0]
   encode_g(cons_g(x_146, x_230), cons_h(x_154, x_235)) -> g(g(encArg(x_146), encArg(x_230)), h(encArg(x_154), encArg(x_235))) [0]
   encode_g(cons_g(x_146, x_230), cons_g(x_155, x_236)) -> g(g(encArg(x_146), encArg(x_230)), g(encArg(x_155), encArg(x_236))) [0]
   encode_g(cons_g(x_146, x_230), x_2) -> g(g(encArg(x_146), encArg(x_230)), const) [0]
   encode_g(x_1, f(x_156)) -> g(const, f(encArg(x_156))) [0]
   encode_g(x_1, cons_h(x_157, x_237)) -> g(const, h(encArg(x_157), encArg(x_237))) [0]
   encode_g(x_1, cons_g(x_158, x_238)) -> g(const, g(encArg(x_158), encArg(x_238))) [0]
   encode_g(x_1, x_2) -> g(const, const) [0]
   encArg(v0) -> const [0]
   encode_h(v0, v1) -> const [0]
   encode_f(v0) -> const [0]
   encode_g(v0, v1) -> const [0]
   h(v0, v1) -> const [0]

The TRS has the following type information:
h :: f:cons_h:cons_g:const -> f:cons_h:cons_g:const -> f:cons_h:cons_g:const
f :: f:cons_h:cons_g:const -> f:cons_h:cons_g:const
g :: f:cons_h:cons_g:const -> f:cons_h:cons_g:const -> f:cons_h:cons_g:const
encArg :: f:cons_h:cons_g:const -> f:cons_h:cons_g:const
cons_h :: f:cons_h:cons_g:const -> f:cons_h:cons_g:const -> f:cons_h:cons_g:const
cons_g :: f:cons_h:cons_g:const -> f:cons_h:cons_g:const -> f:cons_h:cons_g:const
encode_h :: f:cons_h:cons_g:const -> f:cons_h:cons_g:const -> f:cons_h:cons_g:const
encode_f :: f:cons_h:cons_g:const -> f:cons_h:cons_g:const
encode_g :: f:cons_h:cons_g:const -> f:cons_h:cons_g:const -> f:cons_h:cons_g:const
const :: f:cons_h:cons_g:const

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

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

   const => 0

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

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

   encArg(z) -{ 0 }-> h(h(encArg(x_1''), encArg(x_2')), h(encArg(x_16), encArg(x_23))) :|: x_1'' >= 0, x_16 >= 0, x_2' >= 0, x_23 >= 0, z = 1 + (1 + x_1'' + x_2') + (1 + x_16 + x_23)
   encArg(z) -{ 0 }-> h(h(encArg(x_1''), encArg(x_2')), g(encArg(x_17), encArg(x_24))) :|: x_1'' >= 0, x_2' >= 0, x_17 >= 0, x_24 >= 0, z = 1 + (1 + x_1'' + x_2') + (1 + x_17 + x_24)
   encArg(z) -{ 0 }-> h(h(encArg(x_1''), encArg(x_2')), 0) :|: x_1'' >= 0, x_2' >= 0, z = 1 + (1 + x_1'' + x_2') + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> h(h(encArg(x_1''), encArg(x_2')), 1 + encArg(x_15)) :|: x_15 >= 0, z = 1 + (1 + x_1'' + x_2') + (1 + x_15), x_1'' >= 0, x_2' >= 0
   encArg(z) -{ 0 }-> h(g(encArg(x_11), encArg(x_2'')), h(encArg(x_19), encArg(x_25))) :|: x_11 >= 0, z = 1 + (1 + x_11 + x_2'') + (1 + x_19 + x_25), x_25 >= 0, x_2'' >= 0, x_19 >= 0
   encArg(z) -{ 0 }-> h(g(encArg(x_11), encArg(x_2'')), g(encArg(x_110), encArg(x_26))) :|: x_11 >= 0, x_26 >= 0, x_2'' >= 0, z = 1 + (1 + x_11 + x_2'') + (1 + x_110 + x_26), x_110 >= 0
   encArg(z) -{ 0 }-> h(g(encArg(x_11), encArg(x_2'')), 0) :|: x_11 >= 0, x_2'' >= 0, x_2 >= 0, z = 1 + (1 + x_11 + x_2'') + x_2
   encArg(z) -{ 0 }-> h(g(encArg(x_11), encArg(x_2'')), 1 + encArg(x_18)) :|: x_11 >= 0, z = 1 + (1 + x_11 + x_2'') + (1 + x_18), x_2'' >= 0, x_18 >= 0
   encArg(z) -{ 0 }-> h(0, h(encArg(x_112), encArg(x_27))) :|: x_1 >= 0, x_27 >= 0, z = 1 + x_1 + (1 + x_112 + x_27), x_112 >= 0
   encArg(z) -{ 0 }-> h(0, g(encArg(x_113), encArg(x_28))) :|: x_1 >= 0, x_113 >= 0, x_28 >= 0, z = 1 + x_1 + (1 + x_113 + x_28)
   encArg(z) -{ 0 }-> h(0, 0) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> h(0, 1 + encArg(x_111)) :|: x_1 >= 0, z = 1 + x_1 + (1 + x_111), x_111 >= 0
   encArg(z) -{ 0 }-> h(1 + encArg(x_1'), h(encArg(x_13), encArg(x_21))) :|: x_13 >= 0, x_1' >= 0, z = 1 + (1 + x_1') + (1 + x_13 + x_21), x_21 >= 0
   encArg(z) -{ 0 }-> h(1 + encArg(x_1'), g(encArg(x_14), encArg(x_22))) :|: z = 1 + (1 + x_1') + (1 + x_14 + x_22), x_14 >= 0, x_1' >= 0, x_22 >= 0
   encArg(z) -{ 0 }-> h(1 + encArg(x_1'), 0) :|: x_1' >= 0, x_2 >= 0, z = 1 + (1 + x_1') + x_2
   encArg(z) -{ 0 }-> h(1 + encArg(x_1'), 1 + encArg(x_12)) :|: z = 1 + (1 + x_1') + (1 + x_12), x_1' >= 0, x_12 >= 0
   encArg(z) -{ 0 }-> g(h(encArg(x_115), encArg(x_29)), h(encArg(x_121), encArg(x_213))) :|: x_213 >= 0, x_115 >= 0, z = 1 + (1 + x_115 + x_29) + (1 + x_121 + x_213), x_29 >= 0, x_121 >= 0
   encArg(z) -{ 0 }-> g(h(encArg(x_115), encArg(x_29)), g(encArg(x_122), encArg(x_214))) :|: z = 1 + (1 + x_115 + x_29) + (1 + x_122 + x_214), x_115 >= 0, x_214 >= 0, x_122 >= 0, x_29 >= 0
   encArg(z) -{ 0 }-> g(h(encArg(x_115), encArg(x_29)), 0) :|: x_115 >= 0, x_2 >= 0, z = 1 + (1 + x_115 + x_29) + x_2, x_29 >= 0
   encArg(z) -{ 0 }-> g(h(encArg(x_115), encArg(x_29)), 1 + encArg(x_120)) :|: x_120 >= 0, x_115 >= 0, z = 1 + (1 + x_115 + x_29) + (1 + x_120), x_29 >= 0
   encArg(z) -{ 0 }-> g(g(encArg(x_116), encArg(x_210)), h(encArg(x_124), encArg(x_215))) :|: x_124 >= 0, x_215 >= 0, x_116 >= 0, z = 1 + (1 + x_116 + x_210) + (1 + x_124 + x_215), x_210 >= 0
   encArg(z) -{ 0 }-> g(g(encArg(x_116), encArg(x_210)), g(encArg(x_125), encArg(x_216))) :|: x_216 >= 0, z = 1 + (1 + x_116 + x_210) + (1 + x_125 + x_216), x_116 >= 0, x_125 >= 0, x_210 >= 0
   encArg(z) -{ 0 }-> g(g(encArg(x_116), encArg(x_210)), 0) :|: x_116 >= 0, x_2 >= 0, z = 1 + (1 + x_116 + x_210) + x_2, x_210 >= 0
   encArg(z) -{ 0 }-> g(g(encArg(x_116), encArg(x_210)), 1 + encArg(x_123)) :|: x_123 >= 0, z = 1 + (1 + x_116 + x_210) + (1 + x_123), x_116 >= 0, x_210 >= 0
   encArg(z) -{ 0 }-> g(0, h(encArg(x_127), encArg(x_217))) :|: x_1 >= 0, x_127 >= 0, z = 1 + x_1 + (1 + x_127 + x_217), x_217 >= 0
   encArg(z) -{ 0 }-> g(0, g(encArg(x_128), encArg(x_218))) :|: x_1 >= 0, x_128 >= 0, z = 1 + x_1 + (1 + x_128 + x_218), x_218 >= 0
   encArg(z) -{ 0 }-> g(0, 0) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> g(0, 1 + encArg(x_126)) :|: x_1 >= 0, z = 1 + x_1 + (1 + x_126), x_126 >= 0
   encArg(z) -{ 0 }-> g(1 + encArg(x_114), h(encArg(x_118), encArg(x_211))) :|: z = 1 + (1 + x_114) + (1 + x_118 + x_211), x_114 >= 0, x_118 >= 0, x_211 >= 0
   encArg(z) -{ 0 }-> g(1 + encArg(x_114), g(encArg(x_119), encArg(x_212))) :|: x_212 >= 0, x_114 >= 0, z = 1 + (1 + x_114) + (1 + x_119 + x_212), x_119 >= 0
   encArg(z) -{ 0 }-> g(1 + encArg(x_114), 0) :|: z = 1 + (1 + x_114) + x_2, x_114 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> g(1 + encArg(x_114), 1 + encArg(x_117)) :|: z = 1 + (1 + x_114) + (1 + x_117), x_117 >= 0, x_114 >= 0
   encArg(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encArg(z) -{ 0 }-> 1 + encArg(x_1) :|: z = 1 + x_1, x_1 >= 0
   encode_f(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_f(z) -{ 0 }-> 1 + encArg(x_1) :|: x_1 >= 0, z = x_1
   encode_g(z, z') -{ 0 }-> g(h(encArg(x_145), encArg(x_229)), h(encArg(x_151), encArg(x_233))) :|: x_233 >= 0, z = 1 + x_145 + x_229, x_145 >= 0, x_229 >= 0, z' = 1 + x_151 + x_233, x_151 >= 0
   encode_g(z, z') -{ 0 }-> g(h(encArg(x_145), encArg(x_229)), g(encArg(x_152), encArg(x_234))) :|: z = 1 + x_145 + x_229, x_234 >= 0, x_145 >= 0, z' = 1 + x_152 + x_234, x_229 >= 0, x_152 >= 0
   encode_g(z, z') -{ 0 }-> g(h(encArg(x_145), encArg(x_229)), 0) :|: z = 1 + x_145 + x_229, x_145 >= 0, x_229 >= 0, x_2 >= 0, z' = x_2
   encode_g(z, z') -{ 0 }-> g(h(encArg(x_145), encArg(x_229)), 1 + encArg(x_150)) :|: z = 1 + x_145 + x_229, x_145 >= 0, x_229 >= 0, x_150 >= 0, z' = 1 + x_150
   encode_g(z, z') -{ 0 }-> g(g(encArg(x_146), encArg(x_230)), h(encArg(x_154), encArg(x_235))) :|: z = 1 + x_146 + x_230, x_146 >= 0, x_154 >= 0, z' = 1 + x_154 + x_235, x_235 >= 0, x_230 >= 0
   encode_g(z, z') -{ 0 }-> g(g(encArg(x_146), encArg(x_230)), g(encArg(x_155), encArg(x_236))) :|: z = 1 + x_146 + x_230, x_146 >= 0, x_155 >= 0, z' = 1 + x_155 + x_236, x_236 >= 0, x_230 >= 0
   encode_g(z, z') -{ 0 }-> g(g(encArg(x_146), encArg(x_230)), 0) :|: z = 1 + x_146 + x_230, x_146 >= 0, x_2 >= 0, z' = x_2, x_230 >= 0
   encode_g(z, z') -{ 0 }-> g(g(encArg(x_146), encArg(x_230)), 1 + encArg(x_153)) :|: z = 1 + x_146 + x_230, x_146 >= 0, z' = 1 + x_153, x_153 >= 0, x_230 >= 0
   encode_g(z, z') -{ 0 }-> g(0, h(encArg(x_157), encArg(x_237))) :|: x_237 >= 0, x_1 >= 0, x_157 >= 0, z' = 1 + x_157 + x_237, z = x_1
   encode_g(z, z') -{ 0 }-> g(0, g(encArg(x_158), encArg(x_238))) :|: x_1 >= 0, z' = 1 + x_158 + x_238, z = x_1, x_158 >= 0, x_238 >= 0
   encode_g(z, z') -{ 0 }-> g(0, 0) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2
   encode_g(z, z') -{ 0 }-> g(0, 1 + encArg(x_156)) :|: x_1 >= 0, x_156 >= 0, z' = 1 + x_156, z = x_1
   encode_g(z, z') -{ 0 }-> g(1 + encArg(x_144), h(encArg(x_148), encArg(x_231))) :|: z' = 1 + x_148 + x_231, x_144 >= 0, x_231 >= 0, z = 1 + x_144, x_148 >= 0
   encode_g(z, z') -{ 0 }-> g(1 + encArg(x_144), g(encArg(x_149), encArg(x_232))) :|: x_232 >= 0, x_144 >= 0, z' = 1 + x_149 + x_232, z = 1 + x_144, x_149 >= 0
   encode_g(z, z') -{ 0 }-> g(1 + encArg(x_144), 0) :|: x_144 >= 0, x_2 >= 0, z' = x_2, z = 1 + x_144
   encode_g(z, z') -{ 0 }-> g(1 + encArg(x_144), 1 + encArg(x_147)) :|: z' = 1 + x_147, x_144 >= 0, x_147 >= 0, z = 1 + x_144
   encode_g(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   encode_h(z, z') -{ 0 }-> h(h(encArg(x_130), encArg(x_219)), h(encArg(x_136), encArg(x_223))) :|: z' = 1 + x_136 + x_223, x_130 >= 0, z = 1 + x_130 + x_219, x_223 >= 0, x_136 >= 0, x_219 >= 0
   encode_h(z, z') -{ 0 }-> h(h(encArg(x_130), encArg(x_219)), g(encArg(x_137), encArg(x_224))) :|: z' = 1 + x_137 + x_224, x_130 >= 0, z = 1 + x_130 + x_219, x_224 >= 0, x_137 >= 0, x_219 >= 0
   encode_h(z, z') -{ 0 }-> h(h(encArg(x_130), encArg(x_219)), 0) :|: x_130 >= 0, z = 1 + x_130 + x_219, x_2 >= 0, z' = x_2, x_219 >= 0
   encode_h(z, z') -{ 0 }-> h(h(encArg(x_130), encArg(x_219)), 1 + encArg(x_135)) :|: x_130 >= 0, z = 1 + x_130 + x_219, x_135 >= 0, z' = 1 + x_135, x_219 >= 0
   encode_h(z, z') -{ 0 }-> h(g(encArg(x_131), encArg(x_220)), h(encArg(x_139), encArg(x_225))) :|: z = 1 + x_131 + x_220, z' = 1 + x_139 + x_225, x_225 >= 0, x_139 >= 0, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ 0 }-> h(g(encArg(x_131), encArg(x_220)), g(encArg(x_140), encArg(x_226))) :|: z = 1 + x_131 + x_220, x_226 >= 0, z' = 1 + x_140 + x_226, x_140 >= 0, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ 0 }-> h(g(encArg(x_131), encArg(x_220)), 0) :|: z = 1 + x_131 + x_220, x_2 >= 0, z' = x_2, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ 0 }-> h(g(encArg(x_131), encArg(x_220)), 1 + encArg(x_138)) :|: x_138 >= 0, z = 1 + x_131 + x_220, z' = 1 + x_138, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ 0 }-> h(0, h(encArg(x_142), encArg(x_227))) :|: x_1 >= 0, z = x_1, z' = 1 + x_142 + x_227, x_142 >= 0, x_227 >= 0
   encode_h(z, z') -{ 0 }-> h(0, g(encArg(x_143), encArg(x_228))) :|: x_1 >= 0, z' = 1 + x_143 + x_228, x_143 >= 0, z = x_1, x_228 >= 0
   encode_h(z, z') -{ 0 }-> h(0, 0) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2
   encode_h(z, z') -{ 0 }-> h(0, 1 + encArg(x_141)) :|: x_1 >= 0, z' = 1 + x_141, z = x_1, x_141 >= 0
   encode_h(z, z') -{ 0 }-> h(1 + encArg(x_129), h(encArg(x_133), encArg(x_221))) :|: z = 1 + x_129, z' = 1 + x_133 + x_221, x_221 >= 0, x_133 >= 0, x_129 >= 0
   encode_h(z, z') -{ 0 }-> h(1 + encArg(x_129), g(encArg(x_134), encArg(x_222))) :|: z = 1 + x_129, z' = 1 + x_134 + x_222, x_134 >= 0, x_222 >= 0, x_129 >= 0
   encode_h(z, z') -{ 0 }-> h(1 + encArg(x_129), 0) :|: z = 1 + x_129, x_2 >= 0, z' = x_2, x_129 >= 0
   encode_h(z, z') -{ 0 }-> h(1 + encArg(x_129), 1 + encArg(x_132)) :|: z = 1 + x_129, z' = 1 + x_132, x_132 >= 0, x_129 >= 0
   encode_h(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   g(z, z') -{ 1 }-> h(x, y) :|: x >= 0, y >= 0, z = x, z' = y
   h(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   h(z, z') -{ 1 }-> 1 + g(x, y) :|: x >= 0, y >= 0, z = 1 + x, z' = y


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

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

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

   encArg(z) -{ 0 }-> h(h(encArg(x_1''), encArg(x_2')), h(encArg(x_16), encArg(x_23))) :|: x_1'' >= 0, x_16 >= 0, x_2' >= 0, x_23 >= 0, z = 1 + (1 + x_1'' + x_2') + (1 + x_16 + x_23)
   encArg(z) -{ 0 }-> h(h(encArg(x_1''), encArg(x_2')), g(encArg(x_17), encArg(x_24))) :|: x_1'' >= 0, x_2' >= 0, x_17 >= 0, x_24 >= 0, z = 1 + (1 + x_1'' + x_2') + (1 + x_17 + x_24)
   encArg(z) -{ 0 }-> h(h(encArg(x_1''), encArg(x_2')), 0) :|: x_1'' >= 0, x_2' >= 0, z = 1 + (1 + x_1'' + x_2') + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> h(h(encArg(x_1''), encArg(x_2')), 1 + encArg(x_15)) :|: x_15 >= 0, z = 1 + (1 + x_1'' + x_2') + (1 + x_15), x_1'' >= 0, x_2' >= 0
   encArg(z) -{ 0 }-> h(g(encArg(x_11), encArg(x_2'')), h(encArg(x_19), encArg(x_25))) :|: x_11 >= 0, z = 1 + (1 + x_11 + x_2'') + (1 + x_19 + x_25), x_25 >= 0, x_2'' >= 0, x_19 >= 0
   encArg(z) -{ 0 }-> h(g(encArg(x_11), encArg(x_2'')), g(encArg(x_110), encArg(x_26))) :|: x_11 >= 0, x_26 >= 0, x_2'' >= 0, z = 1 + (1 + x_11 + x_2'') + (1 + x_110 + x_26), x_110 >= 0
   encArg(z) -{ 0 }-> h(g(encArg(x_11), encArg(x_2'')), 0) :|: x_11 >= 0, x_2'' >= 0, x_2 >= 0, z = 1 + (1 + x_11 + x_2'') + x_2
   encArg(z) -{ 0 }-> h(g(encArg(x_11), encArg(x_2'')), 1 + encArg(x_18)) :|: x_11 >= 0, z = 1 + (1 + x_11 + x_2'') + (1 + x_18), x_2'' >= 0, x_18 >= 0
   encArg(z) -{ 0 }-> h(0, h(encArg(x_112), encArg(x_27))) :|: x_1 >= 0, x_27 >= 0, z = 1 + x_1 + (1 + x_112 + x_27), x_112 >= 0
   encArg(z) -{ 0 }-> h(0, g(encArg(x_113), encArg(x_28))) :|: x_1 >= 0, x_113 >= 0, x_28 >= 0, z = 1 + x_1 + (1 + x_113 + x_28)
   encArg(z) -{ 0 }-> h(0, 0) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> h(0, 1 + encArg(x_111)) :|: x_1 >= 0, z = 1 + x_1 + (1 + x_111), x_111 >= 0
   encArg(z) -{ 0 }-> h(1 + encArg(x_1'), h(encArg(x_13), encArg(x_21))) :|: x_13 >= 0, x_1' >= 0, z = 1 + (1 + x_1') + (1 + x_13 + x_21), x_21 >= 0
   encArg(z) -{ 0 }-> h(1 + encArg(x_1'), g(encArg(x_14), encArg(x_22))) :|: z = 1 + (1 + x_1') + (1 + x_14 + x_22), x_14 >= 0, x_1' >= 0, x_22 >= 0
   encArg(z) -{ 0 }-> h(1 + encArg(x_1'), 0) :|: x_1' >= 0, x_2 >= 0, z = 1 + (1 + x_1') + x_2
   encArg(z) -{ 0 }-> h(1 + encArg(x_1'), 1 + encArg(x_12)) :|: z = 1 + (1 + x_1') + (1 + x_12), x_1' >= 0, x_12 >= 0
   encArg(z) -{ 0 }-> g(h(encArg(x_115), encArg(x_29)), h(encArg(x_121), encArg(x_213))) :|: x_213 >= 0, x_115 >= 0, z = 1 + (1 + x_115 + x_29) + (1 + x_121 + x_213), x_29 >= 0, x_121 >= 0
   encArg(z) -{ 0 }-> g(h(encArg(x_115), encArg(x_29)), g(encArg(x_122), encArg(x_214))) :|: z = 1 + (1 + x_115 + x_29) + (1 + x_122 + x_214), x_115 >= 0, x_214 >= 0, x_122 >= 0, x_29 >= 0
   encArg(z) -{ 0 }-> g(h(encArg(x_115), encArg(x_29)), 0) :|: x_115 >= 0, x_2 >= 0, z = 1 + (1 + x_115 + x_29) + x_2, x_29 >= 0
   encArg(z) -{ 0 }-> g(h(encArg(x_115), encArg(x_29)), 1 + encArg(x_120)) :|: x_120 >= 0, x_115 >= 0, z = 1 + (1 + x_115 + x_29) + (1 + x_120), x_29 >= 0
   encArg(z) -{ 0 }-> g(g(encArg(x_116), encArg(x_210)), h(encArg(x_124), encArg(x_215))) :|: x_124 >= 0, x_215 >= 0, x_116 >= 0, z = 1 + (1 + x_116 + x_210) + (1 + x_124 + x_215), x_210 >= 0
   encArg(z) -{ 0 }-> g(g(encArg(x_116), encArg(x_210)), g(encArg(x_125), encArg(x_216))) :|: x_216 >= 0, z = 1 + (1 + x_116 + x_210) + (1 + x_125 + x_216), x_116 >= 0, x_125 >= 0, x_210 >= 0
   encArg(z) -{ 0 }-> g(g(encArg(x_116), encArg(x_210)), 0) :|: x_116 >= 0, x_2 >= 0, z = 1 + (1 + x_116 + x_210) + x_2, x_210 >= 0
   encArg(z) -{ 0 }-> g(g(encArg(x_116), encArg(x_210)), 1 + encArg(x_123)) :|: x_123 >= 0, z = 1 + (1 + x_116 + x_210) + (1 + x_123), x_116 >= 0, x_210 >= 0
   encArg(z) -{ 0 }-> g(0, h(encArg(x_127), encArg(x_217))) :|: x_1 >= 0, x_127 >= 0, z = 1 + x_1 + (1 + x_127 + x_217), x_217 >= 0
   encArg(z) -{ 0 }-> g(0, g(encArg(x_128), encArg(x_218))) :|: x_1 >= 0, x_128 >= 0, z = 1 + x_1 + (1 + x_128 + x_218), x_218 >= 0
   encArg(z) -{ 0 }-> g(0, 0) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> g(0, 1 + encArg(x_126)) :|: x_1 >= 0, z = 1 + x_1 + (1 + x_126), x_126 >= 0
   encArg(z) -{ 0 }-> g(1 + encArg(x_114), h(encArg(x_118), encArg(x_211))) :|: z = 1 + (1 + x_114) + (1 + x_118 + x_211), x_114 >= 0, x_118 >= 0, x_211 >= 0
   encArg(z) -{ 0 }-> g(1 + encArg(x_114), g(encArg(x_119), encArg(x_212))) :|: x_212 >= 0, x_114 >= 0, z = 1 + (1 + x_114) + (1 + x_119 + x_212), x_119 >= 0
   encArg(z) -{ 0 }-> g(1 + encArg(x_114), 0) :|: z = 1 + (1 + x_114) + x_2, x_114 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> g(1 + encArg(x_114), 1 + encArg(x_117)) :|: z = 1 + (1 + x_114) + (1 + x_117), x_117 >= 0, x_114 >= 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> 0 :|: z >= 0
   encode_f(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   encode_g(z, z') -{ 0 }-> g(h(encArg(x_145), encArg(x_229)), h(encArg(x_151), encArg(x_233))) :|: x_233 >= 0, z = 1 + x_145 + x_229, x_145 >= 0, x_229 >= 0, z' = 1 + x_151 + x_233, x_151 >= 0
   encode_g(z, z') -{ 0 }-> g(h(encArg(x_145), encArg(x_229)), g(encArg(x_152), encArg(x_234))) :|: z = 1 + x_145 + x_229, x_234 >= 0, x_145 >= 0, z' = 1 + x_152 + x_234, x_229 >= 0, x_152 >= 0
   encode_g(z, z') -{ 0 }-> g(h(encArg(x_145), encArg(x_229)), 0) :|: z = 1 + x_145 + x_229, x_145 >= 0, x_229 >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> g(h(encArg(x_145), encArg(x_229)), 1 + encArg(z' - 1)) :|: z = 1 + x_145 + x_229, x_145 >= 0, x_229 >= 0, z' - 1 >= 0
   encode_g(z, z') -{ 0 }-> g(g(encArg(x_146), encArg(x_230)), h(encArg(x_154), encArg(x_235))) :|: z = 1 + x_146 + x_230, x_146 >= 0, x_154 >= 0, z' = 1 + x_154 + x_235, x_235 >= 0, x_230 >= 0
   encode_g(z, z') -{ 0 }-> g(g(encArg(x_146), encArg(x_230)), g(encArg(x_155), encArg(x_236))) :|: z = 1 + x_146 + x_230, x_146 >= 0, x_155 >= 0, z' = 1 + x_155 + x_236, x_236 >= 0, x_230 >= 0
   encode_g(z, z') -{ 0 }-> g(g(encArg(x_146), encArg(x_230)), 0) :|: z = 1 + x_146 + x_230, x_146 >= 0, z' >= 0, x_230 >= 0
   encode_g(z, z') -{ 0 }-> g(g(encArg(x_146), encArg(x_230)), 1 + encArg(z' - 1)) :|: z = 1 + x_146 + x_230, x_146 >= 0, z' - 1 >= 0, x_230 >= 0
   encode_g(z, z') -{ 0 }-> g(0, h(encArg(x_157), encArg(x_237))) :|: x_237 >= 0, z >= 0, x_157 >= 0, z' = 1 + x_157 + x_237
   encode_g(z, z') -{ 0 }-> g(0, g(encArg(x_158), encArg(x_238))) :|: z >= 0, z' = 1 + x_158 + x_238, x_158 >= 0, x_238 >= 0
   encode_g(z, z') -{ 0 }-> g(0, 0) :|: z >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> g(0, 1 + encArg(z' - 1)) :|: z >= 0, z' - 1 >= 0
   encode_g(z, z') -{ 0 }-> g(1 + encArg(z - 1), h(encArg(x_148), encArg(x_231))) :|: z' = 1 + x_148 + x_231, z - 1 >= 0, x_231 >= 0, x_148 >= 0
   encode_g(z, z') -{ 0 }-> g(1 + encArg(z - 1), g(encArg(x_149), encArg(x_232))) :|: x_232 >= 0, z - 1 >= 0, z' = 1 + x_149 + x_232, x_149 >= 0
   encode_g(z, z') -{ 0 }-> g(1 + encArg(z - 1), 0) :|: z - 1 >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> g(1 + encArg(z - 1), 1 + encArg(z' - 1)) :|: z - 1 >= 0, z' - 1 >= 0
   encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_h(z, z') -{ 0 }-> h(h(encArg(x_130), encArg(x_219)), h(encArg(x_136), encArg(x_223))) :|: z' = 1 + x_136 + x_223, x_130 >= 0, z = 1 + x_130 + x_219, x_223 >= 0, x_136 >= 0, x_219 >= 0
   encode_h(z, z') -{ 0 }-> h(h(encArg(x_130), encArg(x_219)), g(encArg(x_137), encArg(x_224))) :|: z' = 1 + x_137 + x_224, x_130 >= 0, z = 1 + x_130 + x_219, x_224 >= 0, x_137 >= 0, x_219 >= 0
   encode_h(z, z') -{ 0 }-> h(h(encArg(x_130), encArg(x_219)), 0) :|: x_130 >= 0, z = 1 + x_130 + x_219, z' >= 0, x_219 >= 0
   encode_h(z, z') -{ 0 }-> h(h(encArg(x_130), encArg(x_219)), 1 + encArg(z' - 1)) :|: x_130 >= 0, z = 1 + x_130 + x_219, z' - 1 >= 0, x_219 >= 0
   encode_h(z, z') -{ 0 }-> h(g(encArg(x_131), encArg(x_220)), h(encArg(x_139), encArg(x_225))) :|: z = 1 + x_131 + x_220, z' = 1 + x_139 + x_225, x_225 >= 0, x_139 >= 0, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ 0 }-> h(g(encArg(x_131), encArg(x_220)), g(encArg(x_140), encArg(x_226))) :|: z = 1 + x_131 + x_220, x_226 >= 0, z' = 1 + x_140 + x_226, x_140 >= 0, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ 0 }-> h(g(encArg(x_131), encArg(x_220)), 0) :|: z = 1 + x_131 + x_220, z' >= 0, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ 0 }-> h(g(encArg(x_131), encArg(x_220)), 1 + encArg(z' - 1)) :|: z' - 1 >= 0, z = 1 + x_131 + x_220, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ 0 }-> h(0, h(encArg(x_142), encArg(x_227))) :|: z >= 0, z' = 1 + x_142 + x_227, x_142 >= 0, x_227 >= 0
   encode_h(z, z') -{ 0 }-> h(0, g(encArg(x_143), encArg(x_228))) :|: z >= 0, z' = 1 + x_143 + x_228, x_143 >= 0, x_228 >= 0
   encode_h(z, z') -{ 0 }-> h(0, 0) :|: z >= 0, z' >= 0
   encode_h(z, z') -{ 0 }-> h(0, 1 + encArg(z' - 1)) :|: z >= 0, z' - 1 >= 0
   encode_h(z, z') -{ 0 }-> h(1 + encArg(z - 1), h(encArg(x_133), encArg(x_221))) :|: z' = 1 + x_133 + x_221, x_221 >= 0, x_133 >= 0, z - 1 >= 0
   encode_h(z, z') -{ 0 }-> h(1 + encArg(z - 1), g(encArg(x_134), encArg(x_222))) :|: z' = 1 + x_134 + x_222, x_134 >= 0, x_222 >= 0, z - 1 >= 0
   encode_h(z, z') -{ 0 }-> h(1 + encArg(z - 1), 0) :|: z' >= 0, z - 1 >= 0
   encode_h(z, z') -{ 0 }-> h(1 + encArg(z - 1), 1 + encArg(z' - 1)) :|: z' - 1 >= 0, z - 1 >= 0
   encode_h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   g(z, z') -{ 1 }-> h(z, z') :|: z >= 0, z' >= 0
   h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   h(z, z') -{ 1 }-> 1 + g(z - 1, z') :|: z - 1 >= 0, z' >= 0


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

   { h, g }
   { encArg }
   { encode_f }
   { encode_h }
   { encode_g }

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

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

   encArg(z) -{ 0 }-> h(h(encArg(x_1''), encArg(x_2')), h(encArg(x_16), encArg(x_23))) :|: x_1'' >= 0, x_16 >= 0, x_2' >= 0, x_23 >= 0, z = 1 + (1 + x_1'' + x_2') + (1 + x_16 + x_23)
   encArg(z) -{ 0 }-> h(h(encArg(x_1''), encArg(x_2')), g(encArg(x_17), encArg(x_24))) :|: x_1'' >= 0, x_2' >= 0, x_17 >= 0, x_24 >= 0, z = 1 + (1 + x_1'' + x_2') + (1 + x_17 + x_24)
   encArg(z) -{ 0 }-> h(h(encArg(x_1''), encArg(x_2')), 0) :|: x_1'' >= 0, x_2' >= 0, z = 1 + (1 + x_1'' + x_2') + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> h(h(encArg(x_1''), encArg(x_2')), 1 + encArg(x_15)) :|: x_15 >= 0, z = 1 + (1 + x_1'' + x_2') + (1 + x_15), x_1'' >= 0, x_2' >= 0
   encArg(z) -{ 0 }-> h(g(encArg(x_11), encArg(x_2'')), h(encArg(x_19), encArg(x_25))) :|: x_11 >= 0, z = 1 + (1 + x_11 + x_2'') + (1 + x_19 + x_25), x_25 >= 0, x_2'' >= 0, x_19 >= 0
   encArg(z) -{ 0 }-> h(g(encArg(x_11), encArg(x_2'')), g(encArg(x_110), encArg(x_26))) :|: x_11 >= 0, x_26 >= 0, x_2'' >= 0, z = 1 + (1 + x_11 + x_2'') + (1 + x_110 + x_26), x_110 >= 0
   encArg(z) -{ 0 }-> h(g(encArg(x_11), encArg(x_2'')), 0) :|: x_11 >= 0, x_2'' >= 0, x_2 >= 0, z = 1 + (1 + x_11 + x_2'') + x_2
   encArg(z) -{ 0 }-> h(g(encArg(x_11), encArg(x_2'')), 1 + encArg(x_18)) :|: x_11 >= 0, z = 1 + (1 + x_11 + x_2'') + (1 + x_18), x_2'' >= 0, x_18 >= 0
   encArg(z) -{ 0 }-> h(0, h(encArg(x_112), encArg(x_27))) :|: x_1 >= 0, x_27 >= 0, z = 1 + x_1 + (1 + x_112 + x_27), x_112 >= 0
   encArg(z) -{ 0 }-> h(0, g(encArg(x_113), encArg(x_28))) :|: x_1 >= 0, x_113 >= 0, x_28 >= 0, z = 1 + x_1 + (1 + x_113 + x_28)
   encArg(z) -{ 0 }-> h(0, 0) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> h(0, 1 + encArg(x_111)) :|: x_1 >= 0, z = 1 + x_1 + (1 + x_111), x_111 >= 0
   encArg(z) -{ 0 }-> h(1 + encArg(x_1'), h(encArg(x_13), encArg(x_21))) :|: x_13 >= 0, x_1' >= 0, z = 1 + (1 + x_1') + (1 + x_13 + x_21), x_21 >= 0
   encArg(z) -{ 0 }-> h(1 + encArg(x_1'), g(encArg(x_14), encArg(x_22))) :|: z = 1 + (1 + x_1') + (1 + x_14 + x_22), x_14 >= 0, x_1' >= 0, x_22 >= 0
   encArg(z) -{ 0 }-> h(1 + encArg(x_1'), 0) :|: x_1' >= 0, x_2 >= 0, z = 1 + (1 + x_1') + x_2
   encArg(z) -{ 0 }-> h(1 + encArg(x_1'), 1 + encArg(x_12)) :|: z = 1 + (1 + x_1') + (1 + x_12), x_1' >= 0, x_12 >= 0
   encArg(z) -{ 0 }-> g(h(encArg(x_115), encArg(x_29)), h(encArg(x_121), encArg(x_213))) :|: x_213 >= 0, x_115 >= 0, z = 1 + (1 + x_115 + x_29) + (1 + x_121 + x_213), x_29 >= 0, x_121 >= 0
   encArg(z) -{ 0 }-> g(h(encArg(x_115), encArg(x_29)), g(encArg(x_122), encArg(x_214))) :|: z = 1 + (1 + x_115 + x_29) + (1 + x_122 + x_214), x_115 >= 0, x_214 >= 0, x_122 >= 0, x_29 >= 0
   encArg(z) -{ 0 }-> g(h(encArg(x_115), encArg(x_29)), 0) :|: x_115 >= 0, x_2 >= 0, z = 1 + (1 + x_115 + x_29) + x_2, x_29 >= 0
   encArg(z) -{ 0 }-> g(h(encArg(x_115), encArg(x_29)), 1 + encArg(x_120)) :|: x_120 >= 0, x_115 >= 0, z = 1 + (1 + x_115 + x_29) + (1 + x_120), x_29 >= 0
   encArg(z) -{ 0 }-> g(g(encArg(x_116), encArg(x_210)), h(encArg(x_124), encArg(x_215))) :|: x_124 >= 0, x_215 >= 0, x_116 >= 0, z = 1 + (1 + x_116 + x_210) + (1 + x_124 + x_215), x_210 >= 0
   encArg(z) -{ 0 }-> g(g(encArg(x_116), encArg(x_210)), g(encArg(x_125), encArg(x_216))) :|: x_216 >= 0, z = 1 + (1 + x_116 + x_210) + (1 + x_125 + x_216), x_116 >= 0, x_125 >= 0, x_210 >= 0
   encArg(z) -{ 0 }-> g(g(encArg(x_116), encArg(x_210)), 0) :|: x_116 >= 0, x_2 >= 0, z = 1 + (1 + x_116 + x_210) + x_2, x_210 >= 0
   encArg(z) -{ 0 }-> g(g(encArg(x_116), encArg(x_210)), 1 + encArg(x_123)) :|: x_123 >= 0, z = 1 + (1 + x_116 + x_210) + (1 + x_123), x_116 >= 0, x_210 >= 0
   encArg(z) -{ 0 }-> g(0, h(encArg(x_127), encArg(x_217))) :|: x_1 >= 0, x_127 >= 0, z = 1 + x_1 + (1 + x_127 + x_217), x_217 >= 0
   encArg(z) -{ 0 }-> g(0, g(encArg(x_128), encArg(x_218))) :|: x_1 >= 0, x_128 >= 0, z = 1 + x_1 + (1 + x_128 + x_218), x_218 >= 0
   encArg(z) -{ 0 }-> g(0, 0) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> g(0, 1 + encArg(x_126)) :|: x_1 >= 0, z = 1 + x_1 + (1 + x_126), x_126 >= 0
   encArg(z) -{ 0 }-> g(1 + encArg(x_114), h(encArg(x_118), encArg(x_211))) :|: z = 1 + (1 + x_114) + (1 + x_118 + x_211), x_114 >= 0, x_118 >= 0, x_211 >= 0
   encArg(z) -{ 0 }-> g(1 + encArg(x_114), g(encArg(x_119), encArg(x_212))) :|: x_212 >= 0, x_114 >= 0, z = 1 + (1 + x_114) + (1 + x_119 + x_212), x_119 >= 0
   encArg(z) -{ 0 }-> g(1 + encArg(x_114), 0) :|: z = 1 + (1 + x_114) + x_2, x_114 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> g(1 + encArg(x_114), 1 + encArg(x_117)) :|: z = 1 + (1 + x_114) + (1 + x_117), x_117 >= 0, x_114 >= 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> 0 :|: z >= 0
   encode_f(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   encode_g(z, z') -{ 0 }-> g(h(encArg(x_145), encArg(x_229)), h(encArg(x_151), encArg(x_233))) :|: x_233 >= 0, z = 1 + x_145 + x_229, x_145 >= 0, x_229 >= 0, z' = 1 + x_151 + x_233, x_151 >= 0
   encode_g(z, z') -{ 0 }-> g(h(encArg(x_145), encArg(x_229)), g(encArg(x_152), encArg(x_234))) :|: z = 1 + x_145 + x_229, x_234 >= 0, x_145 >= 0, z' = 1 + x_152 + x_234, x_229 >= 0, x_152 >= 0
   encode_g(z, z') -{ 0 }-> g(h(encArg(x_145), encArg(x_229)), 0) :|: z = 1 + x_145 + x_229, x_145 >= 0, x_229 >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> g(h(encArg(x_145), encArg(x_229)), 1 + encArg(z' - 1)) :|: z = 1 + x_145 + x_229, x_145 >= 0, x_229 >= 0, z' - 1 >= 0
   encode_g(z, z') -{ 0 }-> g(g(encArg(x_146), encArg(x_230)), h(encArg(x_154), encArg(x_235))) :|: z = 1 + x_146 + x_230, x_146 >= 0, x_154 >= 0, z' = 1 + x_154 + x_235, x_235 >= 0, x_230 >= 0
   encode_g(z, z') -{ 0 }-> g(g(encArg(x_146), encArg(x_230)), g(encArg(x_155), encArg(x_236))) :|: z = 1 + x_146 + x_230, x_146 >= 0, x_155 >= 0, z' = 1 + x_155 + x_236, x_236 >= 0, x_230 >= 0
   encode_g(z, z') -{ 0 }-> g(g(encArg(x_146), encArg(x_230)), 0) :|: z = 1 + x_146 + x_230, x_146 >= 0, z' >= 0, x_230 >= 0
   encode_g(z, z') -{ 0 }-> g(g(encArg(x_146), encArg(x_230)), 1 + encArg(z' - 1)) :|: z = 1 + x_146 + x_230, x_146 >= 0, z' - 1 >= 0, x_230 >= 0
   encode_g(z, z') -{ 0 }-> g(0, h(encArg(x_157), encArg(x_237))) :|: x_237 >= 0, z >= 0, x_157 >= 0, z' = 1 + x_157 + x_237
   encode_g(z, z') -{ 0 }-> g(0, g(encArg(x_158), encArg(x_238))) :|: z >= 0, z' = 1 + x_158 + x_238, x_158 >= 0, x_238 >= 0
   encode_g(z, z') -{ 0 }-> g(0, 0) :|: z >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> g(0, 1 + encArg(z' - 1)) :|: z >= 0, z' - 1 >= 0
   encode_g(z, z') -{ 0 }-> g(1 + encArg(z - 1), h(encArg(x_148), encArg(x_231))) :|: z' = 1 + x_148 + x_231, z - 1 >= 0, x_231 >= 0, x_148 >= 0
   encode_g(z, z') -{ 0 }-> g(1 + encArg(z - 1), g(encArg(x_149), encArg(x_232))) :|: x_232 >= 0, z - 1 >= 0, z' = 1 + x_149 + x_232, x_149 >= 0
   encode_g(z, z') -{ 0 }-> g(1 + encArg(z - 1), 0) :|: z - 1 >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> g(1 + encArg(z - 1), 1 + encArg(z' - 1)) :|: z - 1 >= 0, z' - 1 >= 0
   encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_h(z, z') -{ 0 }-> h(h(encArg(x_130), encArg(x_219)), h(encArg(x_136), encArg(x_223))) :|: z' = 1 + x_136 + x_223, x_130 >= 0, z = 1 + x_130 + x_219, x_223 >= 0, x_136 >= 0, x_219 >= 0
   encode_h(z, z') -{ 0 }-> h(h(encArg(x_130), encArg(x_219)), g(encArg(x_137), encArg(x_224))) :|: z' = 1 + x_137 + x_224, x_130 >= 0, z = 1 + x_130 + x_219, x_224 >= 0, x_137 >= 0, x_219 >= 0
   encode_h(z, z') -{ 0 }-> h(h(encArg(x_130), encArg(x_219)), 0) :|: x_130 >= 0, z = 1 + x_130 + x_219, z' >= 0, x_219 >= 0
   encode_h(z, z') -{ 0 }-> h(h(encArg(x_130), encArg(x_219)), 1 + encArg(z' - 1)) :|: x_130 >= 0, z = 1 + x_130 + x_219, z' - 1 >= 0, x_219 >= 0
   encode_h(z, z') -{ 0 }-> h(g(encArg(x_131), encArg(x_220)), h(encArg(x_139), encArg(x_225))) :|: z = 1 + x_131 + x_220, z' = 1 + x_139 + x_225, x_225 >= 0, x_139 >= 0, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ 0 }-> h(g(encArg(x_131), encArg(x_220)), g(encArg(x_140), encArg(x_226))) :|: z = 1 + x_131 + x_220, x_226 >= 0, z' = 1 + x_140 + x_226, x_140 >= 0, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ 0 }-> h(g(encArg(x_131), encArg(x_220)), 0) :|: z = 1 + x_131 + x_220, z' >= 0, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ 0 }-> h(g(encArg(x_131), encArg(x_220)), 1 + encArg(z' - 1)) :|: z' - 1 >= 0, z = 1 + x_131 + x_220, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ 0 }-> h(0, h(encArg(x_142), encArg(x_227))) :|: z >= 0, z' = 1 + x_142 + x_227, x_142 >= 0, x_227 >= 0
   encode_h(z, z') -{ 0 }-> h(0, g(encArg(x_143), encArg(x_228))) :|: z >= 0, z' = 1 + x_143 + x_228, x_143 >= 0, x_228 >= 0
   encode_h(z, z') -{ 0 }-> h(0, 0) :|: z >= 0, z' >= 0
   encode_h(z, z') -{ 0 }-> h(0, 1 + encArg(z' - 1)) :|: z >= 0, z' - 1 >= 0
   encode_h(z, z') -{ 0 }-> h(1 + encArg(z - 1), h(encArg(x_133), encArg(x_221))) :|: z' = 1 + x_133 + x_221, x_221 >= 0, x_133 >= 0, z - 1 >= 0
   encode_h(z, z') -{ 0 }-> h(1 + encArg(z - 1), g(encArg(x_134), encArg(x_222))) :|: z' = 1 + x_134 + x_222, x_134 >= 0, x_222 >= 0, z - 1 >= 0
   encode_h(z, z') -{ 0 }-> h(1 + encArg(z - 1), 0) :|: z' >= 0, z - 1 >= 0
   encode_h(z, z') -{ 0 }-> h(1 + encArg(z - 1), 1 + encArg(z' - 1)) :|: z' - 1 >= 0, z - 1 >= 0
   encode_h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   g(z, z') -{ 1 }-> h(z, z') :|: z >= 0, z' >= 0
   h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   h(z, z') -{ 1 }-> 1 + g(z - 1, z') :|: z - 1 >= 0, z' >= 0

Function symbols to be analyzed: {h,g}, {encArg}, {encode_f}, {encode_h}, {encode_g}

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

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

   encArg(z) -{ 0 }-> h(h(encArg(x_1''), encArg(x_2')), h(encArg(x_16), encArg(x_23))) :|: x_1'' >= 0, x_16 >= 0, x_2' >= 0, x_23 >= 0, z = 1 + (1 + x_1'' + x_2') + (1 + x_16 + x_23)
   encArg(z) -{ 0 }-> h(h(encArg(x_1''), encArg(x_2')), g(encArg(x_17), encArg(x_24))) :|: x_1'' >= 0, x_2' >= 0, x_17 >= 0, x_24 >= 0, z = 1 + (1 + x_1'' + x_2') + (1 + x_17 + x_24)
   encArg(z) -{ 0 }-> h(h(encArg(x_1''), encArg(x_2')), 0) :|: x_1'' >= 0, x_2' >= 0, z = 1 + (1 + x_1'' + x_2') + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> h(h(encArg(x_1''), encArg(x_2')), 1 + encArg(x_15)) :|: x_15 >= 0, z = 1 + (1 + x_1'' + x_2') + (1 + x_15), x_1'' >= 0, x_2' >= 0
   encArg(z) -{ 0 }-> h(g(encArg(x_11), encArg(x_2'')), h(encArg(x_19), encArg(x_25))) :|: x_11 >= 0, z = 1 + (1 + x_11 + x_2'') + (1 + x_19 + x_25), x_25 >= 0, x_2'' >= 0, x_19 >= 0
   encArg(z) -{ 0 }-> h(g(encArg(x_11), encArg(x_2'')), g(encArg(x_110), encArg(x_26))) :|: x_11 >= 0, x_26 >= 0, x_2'' >= 0, z = 1 + (1 + x_11 + x_2'') + (1 + x_110 + x_26), x_110 >= 0
   encArg(z) -{ 0 }-> h(g(encArg(x_11), encArg(x_2'')), 0) :|: x_11 >= 0, x_2'' >= 0, x_2 >= 0, z = 1 + (1 + x_11 + x_2'') + x_2
   encArg(z) -{ 0 }-> h(g(encArg(x_11), encArg(x_2'')), 1 + encArg(x_18)) :|: x_11 >= 0, z = 1 + (1 + x_11 + x_2'') + (1 + x_18), x_2'' >= 0, x_18 >= 0
   encArg(z) -{ 0 }-> h(0, h(encArg(x_112), encArg(x_27))) :|: x_1 >= 0, x_27 >= 0, z = 1 + x_1 + (1 + x_112 + x_27), x_112 >= 0
   encArg(z) -{ 0 }-> h(0, g(encArg(x_113), encArg(x_28))) :|: x_1 >= 0, x_113 >= 0, x_28 >= 0, z = 1 + x_1 + (1 + x_113 + x_28)
   encArg(z) -{ 0 }-> h(0, 0) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> h(0, 1 + encArg(x_111)) :|: x_1 >= 0, z = 1 + x_1 + (1 + x_111), x_111 >= 0
   encArg(z) -{ 0 }-> h(1 + encArg(x_1'), h(encArg(x_13), encArg(x_21))) :|: x_13 >= 0, x_1' >= 0, z = 1 + (1 + x_1') + (1 + x_13 + x_21), x_21 >= 0
   encArg(z) -{ 0 }-> h(1 + encArg(x_1'), g(encArg(x_14), encArg(x_22))) :|: z = 1 + (1 + x_1') + (1 + x_14 + x_22), x_14 >= 0, x_1' >= 0, x_22 >= 0
   encArg(z) -{ 0 }-> h(1 + encArg(x_1'), 0) :|: x_1' >= 0, x_2 >= 0, z = 1 + (1 + x_1') + x_2
   encArg(z) -{ 0 }-> h(1 + encArg(x_1'), 1 + encArg(x_12)) :|: z = 1 + (1 + x_1') + (1 + x_12), x_1' >= 0, x_12 >= 0
   encArg(z) -{ 0 }-> g(h(encArg(x_115), encArg(x_29)), h(encArg(x_121), encArg(x_213))) :|: x_213 >= 0, x_115 >= 0, z = 1 + (1 + x_115 + x_29) + (1 + x_121 + x_213), x_29 >= 0, x_121 >= 0
   encArg(z) -{ 0 }-> g(h(encArg(x_115), encArg(x_29)), g(encArg(x_122), encArg(x_214))) :|: z = 1 + (1 + x_115 + x_29) + (1 + x_122 + x_214), x_115 >= 0, x_214 >= 0, x_122 >= 0, x_29 >= 0
   encArg(z) -{ 0 }-> g(h(encArg(x_115), encArg(x_29)), 0) :|: x_115 >= 0, x_2 >= 0, z = 1 + (1 + x_115 + x_29) + x_2, x_29 >= 0
   encArg(z) -{ 0 }-> g(h(encArg(x_115), encArg(x_29)), 1 + encArg(x_120)) :|: x_120 >= 0, x_115 >= 0, z = 1 + (1 + x_115 + x_29) + (1 + x_120), x_29 >= 0
   encArg(z) -{ 0 }-> g(g(encArg(x_116), encArg(x_210)), h(encArg(x_124), encArg(x_215))) :|: x_124 >= 0, x_215 >= 0, x_116 >= 0, z = 1 + (1 + x_116 + x_210) + (1 + x_124 + x_215), x_210 >= 0
   encArg(z) -{ 0 }-> g(g(encArg(x_116), encArg(x_210)), g(encArg(x_125), encArg(x_216))) :|: x_216 >= 0, z = 1 + (1 + x_116 + x_210) + (1 + x_125 + x_216), x_116 >= 0, x_125 >= 0, x_210 >= 0
   encArg(z) -{ 0 }-> g(g(encArg(x_116), encArg(x_210)), 0) :|: x_116 >= 0, x_2 >= 0, z = 1 + (1 + x_116 + x_210) + x_2, x_210 >= 0
   encArg(z) -{ 0 }-> g(g(encArg(x_116), encArg(x_210)), 1 + encArg(x_123)) :|: x_123 >= 0, z = 1 + (1 + x_116 + x_210) + (1 + x_123), x_116 >= 0, x_210 >= 0
   encArg(z) -{ 0 }-> g(0, h(encArg(x_127), encArg(x_217))) :|: x_1 >= 0, x_127 >= 0, z = 1 + x_1 + (1 + x_127 + x_217), x_217 >= 0
   encArg(z) -{ 0 }-> g(0, g(encArg(x_128), encArg(x_218))) :|: x_1 >= 0, x_128 >= 0, z = 1 + x_1 + (1 + x_128 + x_218), x_218 >= 0
   encArg(z) -{ 0 }-> g(0, 0) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> g(0, 1 + encArg(x_126)) :|: x_1 >= 0, z = 1 + x_1 + (1 + x_126), x_126 >= 0
   encArg(z) -{ 0 }-> g(1 + encArg(x_114), h(encArg(x_118), encArg(x_211))) :|: z = 1 + (1 + x_114) + (1 + x_118 + x_211), x_114 >= 0, x_118 >= 0, x_211 >= 0
   encArg(z) -{ 0 }-> g(1 + encArg(x_114), g(encArg(x_119), encArg(x_212))) :|: x_212 >= 0, x_114 >= 0, z = 1 + (1 + x_114) + (1 + x_119 + x_212), x_119 >= 0
   encArg(z) -{ 0 }-> g(1 + encArg(x_114), 0) :|: z = 1 + (1 + x_114) + x_2, x_114 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> g(1 + encArg(x_114), 1 + encArg(x_117)) :|: z = 1 + (1 + x_114) + (1 + x_117), x_117 >= 0, x_114 >= 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> 0 :|: z >= 0
   encode_f(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   encode_g(z, z') -{ 0 }-> g(h(encArg(x_145), encArg(x_229)), h(encArg(x_151), encArg(x_233))) :|: x_233 >= 0, z = 1 + x_145 + x_229, x_145 >= 0, x_229 >= 0, z' = 1 + x_151 + x_233, x_151 >= 0
   encode_g(z, z') -{ 0 }-> g(h(encArg(x_145), encArg(x_229)), g(encArg(x_152), encArg(x_234))) :|: z = 1 + x_145 + x_229, x_234 >= 0, x_145 >= 0, z' = 1 + x_152 + x_234, x_229 >= 0, x_152 >= 0
   encode_g(z, z') -{ 0 }-> g(h(encArg(x_145), encArg(x_229)), 0) :|: z = 1 + x_145 + x_229, x_145 >= 0, x_229 >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> g(h(encArg(x_145), encArg(x_229)), 1 + encArg(z' - 1)) :|: z = 1 + x_145 + x_229, x_145 >= 0, x_229 >= 0, z' - 1 >= 0
   encode_g(z, z') -{ 0 }-> g(g(encArg(x_146), encArg(x_230)), h(encArg(x_154), encArg(x_235))) :|: z = 1 + x_146 + x_230, x_146 >= 0, x_154 >= 0, z' = 1 + x_154 + x_235, x_235 >= 0, x_230 >= 0
   encode_g(z, z') -{ 0 }-> g(g(encArg(x_146), encArg(x_230)), g(encArg(x_155), encArg(x_236))) :|: z = 1 + x_146 + x_230, x_146 >= 0, x_155 >= 0, z' = 1 + x_155 + x_236, x_236 >= 0, x_230 >= 0
   encode_g(z, z') -{ 0 }-> g(g(encArg(x_146), encArg(x_230)), 0) :|: z = 1 + x_146 + x_230, x_146 >= 0, z' >= 0, x_230 >= 0
   encode_g(z, z') -{ 0 }-> g(g(encArg(x_146), encArg(x_230)), 1 + encArg(z' - 1)) :|: z = 1 + x_146 + x_230, x_146 >= 0, z' - 1 >= 0, x_230 >= 0
   encode_g(z, z') -{ 0 }-> g(0, h(encArg(x_157), encArg(x_237))) :|: x_237 >= 0, z >= 0, x_157 >= 0, z' = 1 + x_157 + x_237
   encode_g(z, z') -{ 0 }-> g(0, g(encArg(x_158), encArg(x_238))) :|: z >= 0, z' = 1 + x_158 + x_238, x_158 >= 0, x_238 >= 0
   encode_g(z, z') -{ 0 }-> g(0, 0) :|: z >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> g(0, 1 + encArg(z' - 1)) :|: z >= 0, z' - 1 >= 0
   encode_g(z, z') -{ 0 }-> g(1 + encArg(z - 1), h(encArg(x_148), encArg(x_231))) :|: z' = 1 + x_148 + x_231, z - 1 >= 0, x_231 >= 0, x_148 >= 0
   encode_g(z, z') -{ 0 }-> g(1 + encArg(z - 1), g(encArg(x_149), encArg(x_232))) :|: x_232 >= 0, z - 1 >= 0, z' = 1 + x_149 + x_232, x_149 >= 0
   encode_g(z, z') -{ 0 }-> g(1 + encArg(z - 1), 0) :|: z - 1 >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> g(1 + encArg(z - 1), 1 + encArg(z' - 1)) :|: z - 1 >= 0, z' - 1 >= 0
   encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_h(z, z') -{ 0 }-> h(h(encArg(x_130), encArg(x_219)), h(encArg(x_136), encArg(x_223))) :|: z' = 1 + x_136 + x_223, x_130 >= 0, z = 1 + x_130 + x_219, x_223 >= 0, x_136 >= 0, x_219 >= 0
   encode_h(z, z') -{ 0 }-> h(h(encArg(x_130), encArg(x_219)), g(encArg(x_137), encArg(x_224))) :|: z' = 1 + x_137 + x_224, x_130 >= 0, z = 1 + x_130 + x_219, x_224 >= 0, x_137 >= 0, x_219 >= 0
   encode_h(z, z') -{ 0 }-> h(h(encArg(x_130), encArg(x_219)), 0) :|: x_130 >= 0, z = 1 + x_130 + x_219, z' >= 0, x_219 >= 0
   encode_h(z, z') -{ 0 }-> h(h(encArg(x_130), encArg(x_219)), 1 + encArg(z' - 1)) :|: x_130 >= 0, z = 1 + x_130 + x_219, z' - 1 >= 0, x_219 >= 0
   encode_h(z, z') -{ 0 }-> h(g(encArg(x_131), encArg(x_220)), h(encArg(x_139), encArg(x_225))) :|: z = 1 + x_131 + x_220, z' = 1 + x_139 + x_225, x_225 >= 0, x_139 >= 0, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ 0 }-> h(g(encArg(x_131), encArg(x_220)), g(encArg(x_140), encArg(x_226))) :|: z = 1 + x_131 + x_220, x_226 >= 0, z' = 1 + x_140 + x_226, x_140 >= 0, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ 0 }-> h(g(encArg(x_131), encArg(x_220)), 0) :|: z = 1 + x_131 + x_220, z' >= 0, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ 0 }-> h(g(encArg(x_131), encArg(x_220)), 1 + encArg(z' - 1)) :|: z' - 1 >= 0, z = 1 + x_131 + x_220, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ 0 }-> h(0, h(encArg(x_142), encArg(x_227))) :|: z >= 0, z' = 1 + x_142 + x_227, x_142 >= 0, x_227 >= 0
   encode_h(z, z') -{ 0 }-> h(0, g(encArg(x_143), encArg(x_228))) :|: z >= 0, z' = 1 + x_143 + x_228, x_143 >= 0, x_228 >= 0
   encode_h(z, z') -{ 0 }-> h(0, 0) :|: z >= 0, z' >= 0
   encode_h(z, z') -{ 0 }-> h(0, 1 + encArg(z' - 1)) :|: z >= 0, z' - 1 >= 0
   encode_h(z, z') -{ 0 }-> h(1 + encArg(z - 1), h(encArg(x_133), encArg(x_221))) :|: z' = 1 + x_133 + x_221, x_221 >= 0, x_133 >= 0, z - 1 >= 0
   encode_h(z, z') -{ 0 }-> h(1 + encArg(z - 1), g(encArg(x_134), encArg(x_222))) :|: z' = 1 + x_134 + x_222, x_134 >= 0, x_222 >= 0, z - 1 >= 0
   encode_h(z, z') -{ 0 }-> h(1 + encArg(z - 1), 0) :|: z' >= 0, z - 1 >= 0
   encode_h(z, z') -{ 0 }-> h(1 + encArg(z - 1), 1 + encArg(z' - 1)) :|: z' - 1 >= 0, z - 1 >= 0
   encode_h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   g(z, z') -{ 1 }-> h(z, z') :|: z >= 0, z' >= 0
   h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   h(z, z') -{ 1 }-> 1 + g(z - 1, z') :|: z - 1 >= 0, z' >= 0

Function symbols to be analyzed: {h,g}, {encArg}, {encode_f}, {encode_h}, {encode_g}

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

(21) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

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

   encArg(z) -{ 0 }-> h(h(encArg(x_1''), encArg(x_2')), h(encArg(x_16), encArg(x_23))) :|: x_1'' >= 0, x_16 >= 0, x_2' >= 0, x_23 >= 0, z = 1 + (1 + x_1'' + x_2') + (1 + x_16 + x_23)
   encArg(z) -{ 0 }-> h(h(encArg(x_1''), encArg(x_2')), g(encArg(x_17), encArg(x_24))) :|: x_1'' >= 0, x_2' >= 0, x_17 >= 0, x_24 >= 0, z = 1 + (1 + x_1'' + x_2') + (1 + x_17 + x_24)
   encArg(z) -{ 0 }-> h(h(encArg(x_1''), encArg(x_2')), 0) :|: x_1'' >= 0, x_2' >= 0, z = 1 + (1 + x_1'' + x_2') + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> h(h(encArg(x_1''), encArg(x_2')), 1 + encArg(x_15)) :|: x_15 >= 0, z = 1 + (1 + x_1'' + x_2') + (1 + x_15), x_1'' >= 0, x_2' >= 0
   encArg(z) -{ 0 }-> h(g(encArg(x_11), encArg(x_2'')), h(encArg(x_19), encArg(x_25))) :|: x_11 >= 0, z = 1 + (1 + x_11 + x_2'') + (1 + x_19 + x_25), x_25 >= 0, x_2'' >= 0, x_19 >= 0
   encArg(z) -{ 0 }-> h(g(encArg(x_11), encArg(x_2'')), g(encArg(x_110), encArg(x_26))) :|: x_11 >= 0, x_26 >= 0, x_2'' >= 0, z = 1 + (1 + x_11 + x_2'') + (1 + x_110 + x_26), x_110 >= 0
   encArg(z) -{ 0 }-> h(g(encArg(x_11), encArg(x_2'')), 0) :|: x_11 >= 0, x_2'' >= 0, x_2 >= 0, z = 1 + (1 + x_11 + x_2'') + x_2
   encArg(z) -{ 0 }-> h(g(encArg(x_11), encArg(x_2'')), 1 + encArg(x_18)) :|: x_11 >= 0, z = 1 + (1 + x_11 + x_2'') + (1 + x_18), x_2'' >= 0, x_18 >= 0
   encArg(z) -{ 0 }-> h(0, h(encArg(x_112), encArg(x_27))) :|: x_1 >= 0, x_27 >= 0, z = 1 + x_1 + (1 + x_112 + x_27), x_112 >= 0
   encArg(z) -{ 0 }-> h(0, g(encArg(x_113), encArg(x_28))) :|: x_1 >= 0, x_113 >= 0, x_28 >= 0, z = 1 + x_1 + (1 + x_113 + x_28)
   encArg(z) -{ 0 }-> h(0, 0) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> h(0, 1 + encArg(x_111)) :|: x_1 >= 0, z = 1 + x_1 + (1 + x_111), x_111 >= 0
   encArg(z) -{ 0 }-> h(1 + encArg(x_1'), h(encArg(x_13), encArg(x_21))) :|: x_13 >= 0, x_1' >= 0, z = 1 + (1 + x_1') + (1 + x_13 + x_21), x_21 >= 0
   encArg(z) -{ 0 }-> h(1 + encArg(x_1'), g(encArg(x_14), encArg(x_22))) :|: z = 1 + (1 + x_1') + (1 + x_14 + x_22), x_14 >= 0, x_1' >= 0, x_22 >= 0
   encArg(z) -{ 0 }-> h(1 + encArg(x_1'), 0) :|: x_1' >= 0, x_2 >= 0, z = 1 + (1 + x_1') + x_2
   encArg(z) -{ 0 }-> h(1 + encArg(x_1'), 1 + encArg(x_12)) :|: z = 1 + (1 + x_1') + (1 + x_12), x_1' >= 0, x_12 >= 0
   encArg(z) -{ 0 }-> g(h(encArg(x_115), encArg(x_29)), h(encArg(x_121), encArg(x_213))) :|: x_213 >= 0, x_115 >= 0, z = 1 + (1 + x_115 + x_29) + (1 + x_121 + x_213), x_29 >= 0, x_121 >= 0
   encArg(z) -{ 0 }-> g(h(encArg(x_115), encArg(x_29)), g(encArg(x_122), encArg(x_214))) :|: z = 1 + (1 + x_115 + x_29) + (1 + x_122 + x_214), x_115 >= 0, x_214 >= 0, x_122 >= 0, x_29 >= 0
   encArg(z) -{ 0 }-> g(h(encArg(x_115), encArg(x_29)), 0) :|: x_115 >= 0, x_2 >= 0, z = 1 + (1 + x_115 + x_29) + x_2, x_29 >= 0
   encArg(z) -{ 0 }-> g(h(encArg(x_115), encArg(x_29)), 1 + encArg(x_120)) :|: x_120 >= 0, x_115 >= 0, z = 1 + (1 + x_115 + x_29) + (1 + x_120), x_29 >= 0
   encArg(z) -{ 0 }-> g(g(encArg(x_116), encArg(x_210)), h(encArg(x_124), encArg(x_215))) :|: x_124 >= 0, x_215 >= 0, x_116 >= 0, z = 1 + (1 + x_116 + x_210) + (1 + x_124 + x_215), x_210 >= 0
   encArg(z) -{ 0 }-> g(g(encArg(x_116), encArg(x_210)), g(encArg(x_125), encArg(x_216))) :|: x_216 >= 0, z = 1 + (1 + x_116 + x_210) + (1 + x_125 + x_216), x_116 >= 0, x_125 >= 0, x_210 >= 0
   encArg(z) -{ 0 }-> g(g(encArg(x_116), encArg(x_210)), 0) :|: x_116 >= 0, x_2 >= 0, z = 1 + (1 + x_116 + x_210) + x_2, x_210 >= 0
   encArg(z) -{ 0 }-> g(g(encArg(x_116), encArg(x_210)), 1 + encArg(x_123)) :|: x_123 >= 0, z = 1 + (1 + x_116 + x_210) + (1 + x_123), x_116 >= 0, x_210 >= 0
   encArg(z) -{ 0 }-> g(0, h(encArg(x_127), encArg(x_217))) :|: x_1 >= 0, x_127 >= 0, z = 1 + x_1 + (1 + x_127 + x_217), x_217 >= 0
   encArg(z) -{ 0 }-> g(0, g(encArg(x_128), encArg(x_218))) :|: x_1 >= 0, x_128 >= 0, z = 1 + x_1 + (1 + x_128 + x_218), x_218 >= 0
   encArg(z) -{ 0 }-> g(0, 0) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> g(0, 1 + encArg(x_126)) :|: x_1 >= 0, z = 1 + x_1 + (1 + x_126), x_126 >= 0
   encArg(z) -{ 0 }-> g(1 + encArg(x_114), h(encArg(x_118), encArg(x_211))) :|: z = 1 + (1 + x_114) + (1 + x_118 + x_211), x_114 >= 0, x_118 >= 0, x_211 >= 0
   encArg(z) -{ 0 }-> g(1 + encArg(x_114), g(encArg(x_119), encArg(x_212))) :|: x_212 >= 0, x_114 >= 0, z = 1 + (1 + x_114) + (1 + x_119 + x_212), x_119 >= 0
   encArg(z) -{ 0 }-> g(1 + encArg(x_114), 0) :|: z = 1 + (1 + x_114) + x_2, x_114 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> g(1 + encArg(x_114), 1 + encArg(x_117)) :|: z = 1 + (1 + x_114) + (1 + x_117), x_117 >= 0, x_114 >= 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> 0 :|: z >= 0
   encode_f(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   encode_g(z, z') -{ 0 }-> g(h(encArg(x_145), encArg(x_229)), h(encArg(x_151), encArg(x_233))) :|: x_233 >= 0, z = 1 + x_145 + x_229, x_145 >= 0, x_229 >= 0, z' = 1 + x_151 + x_233, x_151 >= 0
   encode_g(z, z') -{ 0 }-> g(h(encArg(x_145), encArg(x_229)), g(encArg(x_152), encArg(x_234))) :|: z = 1 + x_145 + x_229, x_234 >= 0, x_145 >= 0, z' = 1 + x_152 + x_234, x_229 >= 0, x_152 >= 0
   encode_g(z, z') -{ 0 }-> g(h(encArg(x_145), encArg(x_229)), 0) :|: z = 1 + x_145 + x_229, x_145 >= 0, x_229 >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> g(h(encArg(x_145), encArg(x_229)), 1 + encArg(z' - 1)) :|: z = 1 + x_145 + x_229, x_145 >= 0, x_229 >= 0, z' - 1 >= 0
   encode_g(z, z') -{ 0 }-> g(g(encArg(x_146), encArg(x_230)), h(encArg(x_154), encArg(x_235))) :|: z = 1 + x_146 + x_230, x_146 >= 0, x_154 >= 0, z' = 1 + x_154 + x_235, x_235 >= 0, x_230 >= 0
   encode_g(z, z') -{ 0 }-> g(g(encArg(x_146), encArg(x_230)), g(encArg(x_155), encArg(x_236))) :|: z = 1 + x_146 + x_230, x_146 >= 0, x_155 >= 0, z' = 1 + x_155 + x_236, x_236 >= 0, x_230 >= 0
   encode_g(z, z') -{ 0 }-> g(g(encArg(x_146), encArg(x_230)), 0) :|: z = 1 + x_146 + x_230, x_146 >= 0, z' >= 0, x_230 >= 0
   encode_g(z, z') -{ 0 }-> g(g(encArg(x_146), encArg(x_230)), 1 + encArg(z' - 1)) :|: z = 1 + x_146 + x_230, x_146 >= 0, z' - 1 >= 0, x_230 >= 0
   encode_g(z, z') -{ 0 }-> g(0, h(encArg(x_157), encArg(x_237))) :|: x_237 >= 0, z >= 0, x_157 >= 0, z' = 1 + x_157 + x_237
   encode_g(z, z') -{ 0 }-> g(0, g(encArg(x_158), encArg(x_238))) :|: z >= 0, z' = 1 + x_158 + x_238, x_158 >= 0, x_238 >= 0
   encode_g(z, z') -{ 0 }-> g(0, 0) :|: z >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> g(0, 1 + encArg(z' - 1)) :|: z >= 0, z' - 1 >= 0
   encode_g(z, z') -{ 0 }-> g(1 + encArg(z - 1), h(encArg(x_148), encArg(x_231))) :|: z' = 1 + x_148 + x_231, z - 1 >= 0, x_231 >= 0, x_148 >= 0
   encode_g(z, z') -{ 0 }-> g(1 + encArg(z - 1), g(encArg(x_149), encArg(x_232))) :|: x_232 >= 0, z - 1 >= 0, z' = 1 + x_149 + x_232, x_149 >= 0
   encode_g(z, z') -{ 0 }-> g(1 + encArg(z - 1), 0) :|: z - 1 >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> g(1 + encArg(z - 1), 1 + encArg(z' - 1)) :|: z - 1 >= 0, z' - 1 >= 0
   encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_h(z, z') -{ 0 }-> h(h(encArg(x_130), encArg(x_219)), h(encArg(x_136), encArg(x_223))) :|: z' = 1 + x_136 + x_223, x_130 >= 0, z = 1 + x_130 + x_219, x_223 >= 0, x_136 >= 0, x_219 >= 0
   encode_h(z, z') -{ 0 }-> h(h(encArg(x_130), encArg(x_219)), g(encArg(x_137), encArg(x_224))) :|: z' = 1 + x_137 + x_224, x_130 >= 0, z = 1 + x_130 + x_219, x_224 >= 0, x_137 >= 0, x_219 >= 0
   encode_h(z, z') -{ 0 }-> h(h(encArg(x_130), encArg(x_219)), 0) :|: x_130 >= 0, z = 1 + x_130 + x_219, z' >= 0, x_219 >= 0
   encode_h(z, z') -{ 0 }-> h(h(encArg(x_130), encArg(x_219)), 1 + encArg(z' - 1)) :|: x_130 >= 0, z = 1 + x_130 + x_219, z' - 1 >= 0, x_219 >= 0
   encode_h(z, z') -{ 0 }-> h(g(encArg(x_131), encArg(x_220)), h(encArg(x_139), encArg(x_225))) :|: z = 1 + x_131 + x_220, z' = 1 + x_139 + x_225, x_225 >= 0, x_139 >= 0, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ 0 }-> h(g(encArg(x_131), encArg(x_220)), g(encArg(x_140), encArg(x_226))) :|: z = 1 + x_131 + x_220, x_226 >= 0, z' = 1 + x_140 + x_226, x_140 >= 0, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ 0 }-> h(g(encArg(x_131), encArg(x_220)), 0) :|: z = 1 + x_131 + x_220, z' >= 0, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ 0 }-> h(g(encArg(x_131), encArg(x_220)), 1 + encArg(z' - 1)) :|: z' - 1 >= 0, z = 1 + x_131 + x_220, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ 0 }-> h(0, h(encArg(x_142), encArg(x_227))) :|: z >= 0, z' = 1 + x_142 + x_227, x_142 >= 0, x_227 >= 0
   encode_h(z, z') -{ 0 }-> h(0, g(encArg(x_143), encArg(x_228))) :|: z >= 0, z' = 1 + x_143 + x_228, x_143 >= 0, x_228 >= 0
   encode_h(z, z') -{ 0 }-> h(0, 0) :|: z >= 0, z' >= 0
   encode_h(z, z') -{ 0 }-> h(0, 1 + encArg(z' - 1)) :|: z >= 0, z' - 1 >= 0
   encode_h(z, z') -{ 0 }-> h(1 + encArg(z - 1), h(encArg(x_133), encArg(x_221))) :|: z' = 1 + x_133 + x_221, x_221 >= 0, x_133 >= 0, z - 1 >= 0
   encode_h(z, z') -{ 0 }-> h(1 + encArg(z - 1), g(encArg(x_134), encArg(x_222))) :|: z' = 1 + x_134 + x_222, x_134 >= 0, x_222 >= 0, z - 1 >= 0
   encode_h(z, z') -{ 0 }-> h(1 + encArg(z - 1), 0) :|: z' >= 0, z - 1 >= 0
   encode_h(z, z') -{ 0 }-> h(1 + encArg(z - 1), 1 + encArg(z' - 1)) :|: z' - 1 >= 0, z - 1 >= 0
   encode_h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   g(z, z') -{ 1 }-> h(z, z') :|: z >= 0, z' >= 0
   h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   h(z, z') -{ 1 }-> 1 + g(z - 1, z') :|: z - 1 >= 0, z' >= 0

Function symbols to be analyzed: {h,g}, {encArg}, {encode_f}, {encode_h}, {encode_g}
Previous analysis results are:
  h: runtime: ?, size: O(n^1) [z]
  g: runtime: ?, size: O(n^1) [z]

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

(23) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using KoAT for: h
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 4*z

Computed RUNTIME bound using CoFloCo for: g
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 1 + 4*z

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

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

   encArg(z) -{ 0 }-> h(h(encArg(x_1''), encArg(x_2')), h(encArg(x_16), encArg(x_23))) :|: x_1'' >= 0, x_16 >= 0, x_2' >= 0, x_23 >= 0, z = 1 + (1 + x_1'' + x_2') + (1 + x_16 + x_23)
   encArg(z) -{ 0 }-> h(h(encArg(x_1''), encArg(x_2')), g(encArg(x_17), encArg(x_24))) :|: x_1'' >= 0, x_2' >= 0, x_17 >= 0, x_24 >= 0, z = 1 + (1 + x_1'' + x_2') + (1 + x_17 + x_24)
   encArg(z) -{ 0 }-> h(h(encArg(x_1''), encArg(x_2')), 0) :|: x_1'' >= 0, x_2' >= 0, z = 1 + (1 + x_1'' + x_2') + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> h(h(encArg(x_1''), encArg(x_2')), 1 + encArg(x_15)) :|: x_15 >= 0, z = 1 + (1 + x_1'' + x_2') + (1 + x_15), x_1'' >= 0, x_2' >= 0
   encArg(z) -{ 0 }-> h(g(encArg(x_11), encArg(x_2'')), h(encArg(x_19), encArg(x_25))) :|: x_11 >= 0, z = 1 + (1 + x_11 + x_2'') + (1 + x_19 + x_25), x_25 >= 0, x_2'' >= 0, x_19 >= 0
   encArg(z) -{ 0 }-> h(g(encArg(x_11), encArg(x_2'')), g(encArg(x_110), encArg(x_26))) :|: x_11 >= 0, x_26 >= 0, x_2'' >= 0, z = 1 + (1 + x_11 + x_2'') + (1 + x_110 + x_26), x_110 >= 0
   encArg(z) -{ 0 }-> h(g(encArg(x_11), encArg(x_2'')), 0) :|: x_11 >= 0, x_2'' >= 0, x_2 >= 0, z = 1 + (1 + x_11 + x_2'') + x_2
   encArg(z) -{ 0 }-> h(g(encArg(x_11), encArg(x_2'')), 1 + encArg(x_18)) :|: x_11 >= 0, z = 1 + (1 + x_11 + x_2'') + (1 + x_18), x_2'' >= 0, x_18 >= 0
   encArg(z) -{ 0 }-> h(0, h(encArg(x_112), encArg(x_27))) :|: x_1 >= 0, x_27 >= 0, z = 1 + x_1 + (1 + x_112 + x_27), x_112 >= 0
   encArg(z) -{ 0 }-> h(0, g(encArg(x_113), encArg(x_28))) :|: x_1 >= 0, x_113 >= 0, x_28 >= 0, z = 1 + x_1 + (1 + x_113 + x_28)
   encArg(z) -{ 0 }-> h(0, 0) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> h(0, 1 + encArg(x_111)) :|: x_1 >= 0, z = 1 + x_1 + (1 + x_111), x_111 >= 0
   encArg(z) -{ 0 }-> h(1 + encArg(x_1'), h(encArg(x_13), encArg(x_21))) :|: x_13 >= 0, x_1' >= 0, z = 1 + (1 + x_1') + (1 + x_13 + x_21), x_21 >= 0
   encArg(z) -{ 0 }-> h(1 + encArg(x_1'), g(encArg(x_14), encArg(x_22))) :|: z = 1 + (1 + x_1') + (1 + x_14 + x_22), x_14 >= 0, x_1' >= 0, x_22 >= 0
   encArg(z) -{ 0 }-> h(1 + encArg(x_1'), 0) :|: x_1' >= 0, x_2 >= 0, z = 1 + (1 + x_1') + x_2
   encArg(z) -{ 0 }-> h(1 + encArg(x_1'), 1 + encArg(x_12)) :|: z = 1 + (1 + x_1') + (1 + x_12), x_1' >= 0, x_12 >= 0
   encArg(z) -{ 0 }-> g(h(encArg(x_115), encArg(x_29)), h(encArg(x_121), encArg(x_213))) :|: x_213 >= 0, x_115 >= 0, z = 1 + (1 + x_115 + x_29) + (1 + x_121 + x_213), x_29 >= 0, x_121 >= 0
   encArg(z) -{ 0 }-> g(h(encArg(x_115), encArg(x_29)), g(encArg(x_122), encArg(x_214))) :|: z = 1 + (1 + x_115 + x_29) + (1 + x_122 + x_214), x_115 >= 0, x_214 >= 0, x_122 >= 0, x_29 >= 0
   encArg(z) -{ 0 }-> g(h(encArg(x_115), encArg(x_29)), 0) :|: x_115 >= 0, x_2 >= 0, z = 1 + (1 + x_115 + x_29) + x_2, x_29 >= 0
   encArg(z) -{ 0 }-> g(h(encArg(x_115), encArg(x_29)), 1 + encArg(x_120)) :|: x_120 >= 0, x_115 >= 0, z = 1 + (1 + x_115 + x_29) + (1 + x_120), x_29 >= 0
   encArg(z) -{ 0 }-> g(g(encArg(x_116), encArg(x_210)), h(encArg(x_124), encArg(x_215))) :|: x_124 >= 0, x_215 >= 0, x_116 >= 0, z = 1 + (1 + x_116 + x_210) + (1 + x_124 + x_215), x_210 >= 0
   encArg(z) -{ 0 }-> g(g(encArg(x_116), encArg(x_210)), g(encArg(x_125), encArg(x_216))) :|: x_216 >= 0, z = 1 + (1 + x_116 + x_210) + (1 + x_125 + x_216), x_116 >= 0, x_125 >= 0, x_210 >= 0
   encArg(z) -{ 0 }-> g(g(encArg(x_116), encArg(x_210)), 0) :|: x_116 >= 0, x_2 >= 0, z = 1 + (1 + x_116 + x_210) + x_2, x_210 >= 0
   encArg(z) -{ 0 }-> g(g(encArg(x_116), encArg(x_210)), 1 + encArg(x_123)) :|: x_123 >= 0, z = 1 + (1 + x_116 + x_210) + (1 + x_123), x_116 >= 0, x_210 >= 0
   encArg(z) -{ 0 }-> g(0, h(encArg(x_127), encArg(x_217))) :|: x_1 >= 0, x_127 >= 0, z = 1 + x_1 + (1 + x_127 + x_217), x_217 >= 0
   encArg(z) -{ 0 }-> g(0, g(encArg(x_128), encArg(x_218))) :|: x_1 >= 0, x_128 >= 0, z = 1 + x_1 + (1 + x_128 + x_218), x_218 >= 0
   encArg(z) -{ 0 }-> g(0, 0) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> g(0, 1 + encArg(x_126)) :|: x_1 >= 0, z = 1 + x_1 + (1 + x_126), x_126 >= 0
   encArg(z) -{ 0 }-> g(1 + encArg(x_114), h(encArg(x_118), encArg(x_211))) :|: z = 1 + (1 + x_114) + (1 + x_118 + x_211), x_114 >= 0, x_118 >= 0, x_211 >= 0
   encArg(z) -{ 0 }-> g(1 + encArg(x_114), g(encArg(x_119), encArg(x_212))) :|: x_212 >= 0, x_114 >= 0, z = 1 + (1 + x_114) + (1 + x_119 + x_212), x_119 >= 0
   encArg(z) -{ 0 }-> g(1 + encArg(x_114), 0) :|: z = 1 + (1 + x_114) + x_2, x_114 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> g(1 + encArg(x_114), 1 + encArg(x_117)) :|: z = 1 + (1 + x_114) + (1 + x_117), x_117 >= 0, x_114 >= 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> 0 :|: z >= 0
   encode_f(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   encode_g(z, z') -{ 0 }-> g(h(encArg(x_145), encArg(x_229)), h(encArg(x_151), encArg(x_233))) :|: x_233 >= 0, z = 1 + x_145 + x_229, x_145 >= 0, x_229 >= 0, z' = 1 + x_151 + x_233, x_151 >= 0
   encode_g(z, z') -{ 0 }-> g(h(encArg(x_145), encArg(x_229)), g(encArg(x_152), encArg(x_234))) :|: z = 1 + x_145 + x_229, x_234 >= 0, x_145 >= 0, z' = 1 + x_152 + x_234, x_229 >= 0, x_152 >= 0
   encode_g(z, z') -{ 0 }-> g(h(encArg(x_145), encArg(x_229)), 0) :|: z = 1 + x_145 + x_229, x_145 >= 0, x_229 >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> g(h(encArg(x_145), encArg(x_229)), 1 + encArg(z' - 1)) :|: z = 1 + x_145 + x_229, x_145 >= 0, x_229 >= 0, z' - 1 >= 0
   encode_g(z, z') -{ 0 }-> g(g(encArg(x_146), encArg(x_230)), h(encArg(x_154), encArg(x_235))) :|: z = 1 + x_146 + x_230, x_146 >= 0, x_154 >= 0, z' = 1 + x_154 + x_235, x_235 >= 0, x_230 >= 0
   encode_g(z, z') -{ 0 }-> g(g(encArg(x_146), encArg(x_230)), g(encArg(x_155), encArg(x_236))) :|: z = 1 + x_146 + x_230, x_146 >= 0, x_155 >= 0, z' = 1 + x_155 + x_236, x_236 >= 0, x_230 >= 0
   encode_g(z, z') -{ 0 }-> g(g(encArg(x_146), encArg(x_230)), 0) :|: z = 1 + x_146 + x_230, x_146 >= 0, z' >= 0, x_230 >= 0
   encode_g(z, z') -{ 0 }-> g(g(encArg(x_146), encArg(x_230)), 1 + encArg(z' - 1)) :|: z = 1 + x_146 + x_230, x_146 >= 0, z' - 1 >= 0, x_230 >= 0
   encode_g(z, z') -{ 0 }-> g(0, h(encArg(x_157), encArg(x_237))) :|: x_237 >= 0, z >= 0, x_157 >= 0, z' = 1 + x_157 + x_237
   encode_g(z, z') -{ 0 }-> g(0, g(encArg(x_158), encArg(x_238))) :|: z >= 0, z' = 1 + x_158 + x_238, x_158 >= 0, x_238 >= 0
   encode_g(z, z') -{ 0 }-> g(0, 0) :|: z >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> g(0, 1 + encArg(z' - 1)) :|: z >= 0, z' - 1 >= 0
   encode_g(z, z') -{ 0 }-> g(1 + encArg(z - 1), h(encArg(x_148), encArg(x_231))) :|: z' = 1 + x_148 + x_231, z - 1 >= 0, x_231 >= 0, x_148 >= 0
   encode_g(z, z') -{ 0 }-> g(1 + encArg(z - 1), g(encArg(x_149), encArg(x_232))) :|: x_232 >= 0, z - 1 >= 0, z' = 1 + x_149 + x_232, x_149 >= 0
   encode_g(z, z') -{ 0 }-> g(1 + encArg(z - 1), 0) :|: z - 1 >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> g(1 + encArg(z - 1), 1 + encArg(z' - 1)) :|: z - 1 >= 0, z' - 1 >= 0
   encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_h(z, z') -{ 0 }-> h(h(encArg(x_130), encArg(x_219)), h(encArg(x_136), encArg(x_223))) :|: z' = 1 + x_136 + x_223, x_130 >= 0, z = 1 + x_130 + x_219, x_223 >= 0, x_136 >= 0, x_219 >= 0
   encode_h(z, z') -{ 0 }-> h(h(encArg(x_130), encArg(x_219)), g(encArg(x_137), encArg(x_224))) :|: z' = 1 + x_137 + x_224, x_130 >= 0, z = 1 + x_130 + x_219, x_224 >= 0, x_137 >= 0, x_219 >= 0
   encode_h(z, z') -{ 0 }-> h(h(encArg(x_130), encArg(x_219)), 0) :|: x_130 >= 0, z = 1 + x_130 + x_219, z' >= 0, x_219 >= 0
   encode_h(z, z') -{ 0 }-> h(h(encArg(x_130), encArg(x_219)), 1 + encArg(z' - 1)) :|: x_130 >= 0, z = 1 + x_130 + x_219, z' - 1 >= 0, x_219 >= 0
   encode_h(z, z') -{ 0 }-> h(g(encArg(x_131), encArg(x_220)), h(encArg(x_139), encArg(x_225))) :|: z = 1 + x_131 + x_220, z' = 1 + x_139 + x_225, x_225 >= 0, x_139 >= 0, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ 0 }-> h(g(encArg(x_131), encArg(x_220)), g(encArg(x_140), encArg(x_226))) :|: z = 1 + x_131 + x_220, x_226 >= 0, z' = 1 + x_140 + x_226, x_140 >= 0, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ 0 }-> h(g(encArg(x_131), encArg(x_220)), 0) :|: z = 1 + x_131 + x_220, z' >= 0, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ 0 }-> h(g(encArg(x_131), encArg(x_220)), 1 + encArg(z' - 1)) :|: z' - 1 >= 0, z = 1 + x_131 + x_220, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ 0 }-> h(0, h(encArg(x_142), encArg(x_227))) :|: z >= 0, z' = 1 + x_142 + x_227, x_142 >= 0, x_227 >= 0
   encode_h(z, z') -{ 0 }-> h(0, g(encArg(x_143), encArg(x_228))) :|: z >= 0, z' = 1 + x_143 + x_228, x_143 >= 0, x_228 >= 0
   encode_h(z, z') -{ 0 }-> h(0, 0) :|: z >= 0, z' >= 0
   encode_h(z, z') -{ 0 }-> h(0, 1 + encArg(z' - 1)) :|: z >= 0, z' - 1 >= 0
   encode_h(z, z') -{ 0 }-> h(1 + encArg(z - 1), h(encArg(x_133), encArg(x_221))) :|: z' = 1 + x_133 + x_221, x_221 >= 0, x_133 >= 0, z - 1 >= 0
   encode_h(z, z') -{ 0 }-> h(1 + encArg(z - 1), g(encArg(x_134), encArg(x_222))) :|: z' = 1 + x_134 + x_222, x_134 >= 0, x_222 >= 0, z - 1 >= 0
   encode_h(z, z') -{ 0 }-> h(1 + encArg(z - 1), 0) :|: z' >= 0, z - 1 >= 0
   encode_h(z, z') -{ 0 }-> h(1 + encArg(z - 1), 1 + encArg(z' - 1)) :|: z' - 1 >= 0, z - 1 >= 0
   encode_h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   g(z, z') -{ 1 }-> h(z, z') :|: z >= 0, z' >= 0
   h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   h(z, z') -{ 1 }-> 1 + g(z - 1, z') :|: z - 1 >= 0, z' >= 0

Function symbols to be analyzed: {encArg}, {encode_f}, {encode_h}, {encode_g}
Previous analysis results are:
  h: runtime: O(n^1) [4*z], size: O(n^1) [z]
  g: runtime: O(n^1) [1 + 4*z], size: O(n^1) [z]

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

(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:

   encArg(z) -{ 0 }-> s'' :|: s'' >= 0, s'' <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 1 }-> s1 :|: s1 >= 0, s1 <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> h(h(encArg(x_1''), encArg(x_2')), h(encArg(x_16), encArg(x_23))) :|: x_1'' >= 0, x_16 >= 0, x_2' >= 0, x_23 >= 0, z = 1 + (1 + x_1'' + x_2') + (1 + x_16 + x_23)
   encArg(z) -{ 0 }-> h(h(encArg(x_1''), encArg(x_2')), g(encArg(x_17), encArg(x_24))) :|: x_1'' >= 0, x_2' >= 0, x_17 >= 0, x_24 >= 0, z = 1 + (1 + x_1'' + x_2') + (1 + x_17 + x_24)
   encArg(z) -{ 0 }-> h(h(encArg(x_1''), encArg(x_2')), 0) :|: x_1'' >= 0, x_2' >= 0, z = 1 + (1 + x_1'' + x_2') + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> h(h(encArg(x_1''), encArg(x_2')), 1 + encArg(x_15)) :|: x_15 >= 0, z = 1 + (1 + x_1'' + x_2') + (1 + x_15), x_1'' >= 0, x_2' >= 0
   encArg(z) -{ 0 }-> h(g(encArg(x_11), encArg(x_2'')), h(encArg(x_19), encArg(x_25))) :|: x_11 >= 0, z = 1 + (1 + x_11 + x_2'') + (1 + x_19 + x_25), x_25 >= 0, x_2'' >= 0, x_19 >= 0
   encArg(z) -{ 0 }-> h(g(encArg(x_11), encArg(x_2'')), g(encArg(x_110), encArg(x_26))) :|: x_11 >= 0, x_26 >= 0, x_2'' >= 0, z = 1 + (1 + x_11 + x_2'') + (1 + x_110 + x_26), x_110 >= 0
   encArg(z) -{ 0 }-> h(g(encArg(x_11), encArg(x_2'')), 0) :|: x_11 >= 0, x_2'' >= 0, x_2 >= 0, z = 1 + (1 + x_11 + x_2'') + x_2
   encArg(z) -{ 0 }-> h(g(encArg(x_11), encArg(x_2'')), 1 + encArg(x_18)) :|: x_11 >= 0, z = 1 + (1 + x_11 + x_2'') + (1 + x_18), x_2'' >= 0, x_18 >= 0
   encArg(z) -{ 0 }-> h(0, h(encArg(x_112), encArg(x_27))) :|: x_1 >= 0, x_27 >= 0, z = 1 + x_1 + (1 + x_112 + x_27), x_112 >= 0
   encArg(z) -{ 0 }-> h(0, g(encArg(x_113), encArg(x_28))) :|: x_1 >= 0, x_113 >= 0, x_28 >= 0, z = 1 + x_1 + (1 + x_113 + x_28)
   encArg(z) -{ 0 }-> h(0, 1 + encArg(x_111)) :|: x_1 >= 0, z = 1 + x_1 + (1 + x_111), x_111 >= 0
   encArg(z) -{ 0 }-> h(1 + encArg(x_1'), h(encArg(x_13), encArg(x_21))) :|: x_13 >= 0, x_1' >= 0, z = 1 + (1 + x_1') + (1 + x_13 + x_21), x_21 >= 0
   encArg(z) -{ 0 }-> h(1 + encArg(x_1'), g(encArg(x_14), encArg(x_22))) :|: z = 1 + (1 + x_1') + (1 + x_14 + x_22), x_14 >= 0, x_1' >= 0, x_22 >= 0
   encArg(z) -{ 0 }-> h(1 + encArg(x_1'), 0) :|: x_1' >= 0, x_2 >= 0, z = 1 + (1 + x_1') + x_2
   encArg(z) -{ 0 }-> h(1 + encArg(x_1'), 1 + encArg(x_12)) :|: z = 1 + (1 + x_1') + (1 + x_12), x_1' >= 0, x_12 >= 0
   encArg(z) -{ 0 }-> g(h(encArg(x_115), encArg(x_29)), h(encArg(x_121), encArg(x_213))) :|: x_213 >= 0, x_115 >= 0, z = 1 + (1 + x_115 + x_29) + (1 + x_121 + x_213), x_29 >= 0, x_121 >= 0
   encArg(z) -{ 0 }-> g(h(encArg(x_115), encArg(x_29)), g(encArg(x_122), encArg(x_214))) :|: z = 1 + (1 + x_115 + x_29) + (1 + x_122 + x_214), x_115 >= 0, x_214 >= 0, x_122 >= 0, x_29 >= 0
   encArg(z) -{ 0 }-> g(h(encArg(x_115), encArg(x_29)), 0) :|: x_115 >= 0, x_2 >= 0, z = 1 + (1 + x_115 + x_29) + x_2, x_29 >= 0
   encArg(z) -{ 0 }-> g(h(encArg(x_115), encArg(x_29)), 1 + encArg(x_120)) :|: x_120 >= 0, x_115 >= 0, z = 1 + (1 + x_115 + x_29) + (1 + x_120), x_29 >= 0
   encArg(z) -{ 0 }-> g(g(encArg(x_116), encArg(x_210)), h(encArg(x_124), encArg(x_215))) :|: x_124 >= 0, x_215 >= 0, x_116 >= 0, z = 1 + (1 + x_116 + x_210) + (1 + x_124 + x_215), x_210 >= 0
   encArg(z) -{ 0 }-> g(g(encArg(x_116), encArg(x_210)), g(encArg(x_125), encArg(x_216))) :|: x_216 >= 0, z = 1 + (1 + x_116 + x_210) + (1 + x_125 + x_216), x_116 >= 0, x_125 >= 0, x_210 >= 0
   encArg(z) -{ 0 }-> g(g(encArg(x_116), encArg(x_210)), 0) :|: x_116 >= 0, x_2 >= 0, z = 1 + (1 + x_116 + x_210) + x_2, x_210 >= 0
   encArg(z) -{ 0 }-> g(g(encArg(x_116), encArg(x_210)), 1 + encArg(x_123)) :|: x_123 >= 0, z = 1 + (1 + x_116 + x_210) + (1 + x_123), x_116 >= 0, x_210 >= 0
   encArg(z) -{ 0 }-> g(0, h(encArg(x_127), encArg(x_217))) :|: x_1 >= 0, x_127 >= 0, z = 1 + x_1 + (1 + x_127 + x_217), x_217 >= 0
   encArg(z) -{ 0 }-> g(0, g(encArg(x_128), encArg(x_218))) :|: x_1 >= 0, x_128 >= 0, z = 1 + x_1 + (1 + x_128 + x_218), x_218 >= 0
   encArg(z) -{ 0 }-> g(0, 1 + encArg(x_126)) :|: x_1 >= 0, z = 1 + x_1 + (1 + x_126), x_126 >= 0
   encArg(z) -{ 0 }-> g(1 + encArg(x_114), h(encArg(x_118), encArg(x_211))) :|: z = 1 + (1 + x_114) + (1 + x_118 + x_211), x_114 >= 0, x_118 >= 0, x_211 >= 0
   encArg(z) -{ 0 }-> g(1 + encArg(x_114), g(encArg(x_119), encArg(x_212))) :|: x_212 >= 0, x_114 >= 0, z = 1 + (1 + x_114) + (1 + x_119 + x_212), x_119 >= 0
   encArg(z) -{ 0 }-> g(1 + encArg(x_114), 0) :|: z = 1 + (1 + x_114) + x_2, x_114 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> g(1 + encArg(x_114), 1 + encArg(x_117)) :|: z = 1 + (1 + x_114) + (1 + x_117), x_117 >= 0, x_114 >= 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> 0 :|: z >= 0
   encode_f(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   encode_g(z, z') -{ 1 }-> s3 :|: s3 >= 0, s3 <= 0, z >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> g(h(encArg(x_145), encArg(x_229)), h(encArg(x_151), encArg(x_233))) :|: x_233 >= 0, z = 1 + x_145 + x_229, x_145 >= 0, x_229 >= 0, z' = 1 + x_151 + x_233, x_151 >= 0
   encode_g(z, z') -{ 0 }-> g(h(encArg(x_145), encArg(x_229)), g(encArg(x_152), encArg(x_234))) :|: z = 1 + x_145 + x_229, x_234 >= 0, x_145 >= 0, z' = 1 + x_152 + x_234, x_229 >= 0, x_152 >= 0
   encode_g(z, z') -{ 0 }-> g(h(encArg(x_145), encArg(x_229)), 0) :|: z = 1 + x_145 + x_229, x_145 >= 0, x_229 >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> g(h(encArg(x_145), encArg(x_229)), 1 + encArg(z' - 1)) :|: z = 1 + x_145 + x_229, x_145 >= 0, x_229 >= 0, z' - 1 >= 0
   encode_g(z, z') -{ 0 }-> g(g(encArg(x_146), encArg(x_230)), h(encArg(x_154), encArg(x_235))) :|: z = 1 + x_146 + x_230, x_146 >= 0, x_154 >= 0, z' = 1 + x_154 + x_235, x_235 >= 0, x_230 >= 0
   encode_g(z, z') -{ 0 }-> g(g(encArg(x_146), encArg(x_230)), g(encArg(x_155), encArg(x_236))) :|: z = 1 + x_146 + x_230, x_146 >= 0, x_155 >= 0, z' = 1 + x_155 + x_236, x_236 >= 0, x_230 >= 0
   encode_g(z, z') -{ 0 }-> g(g(encArg(x_146), encArg(x_230)), 0) :|: z = 1 + x_146 + x_230, x_146 >= 0, z' >= 0, x_230 >= 0
   encode_g(z, z') -{ 0 }-> g(g(encArg(x_146), encArg(x_230)), 1 + encArg(z' - 1)) :|: z = 1 + x_146 + x_230, x_146 >= 0, z' - 1 >= 0, x_230 >= 0
   encode_g(z, z') -{ 0 }-> g(0, h(encArg(x_157), encArg(x_237))) :|: x_237 >= 0, z >= 0, x_157 >= 0, z' = 1 + x_157 + x_237
   encode_g(z, z') -{ 0 }-> g(0, g(encArg(x_158), encArg(x_238))) :|: z >= 0, z' = 1 + x_158 + x_238, x_158 >= 0, x_238 >= 0
   encode_g(z, z') -{ 0 }-> g(0, 1 + encArg(z' - 1)) :|: z >= 0, z' - 1 >= 0
   encode_g(z, z') -{ 0 }-> g(1 + encArg(z - 1), h(encArg(x_148), encArg(x_231))) :|: z' = 1 + x_148 + x_231, z - 1 >= 0, x_231 >= 0, x_148 >= 0
   encode_g(z, z') -{ 0 }-> g(1 + encArg(z - 1), g(encArg(x_149), encArg(x_232))) :|: x_232 >= 0, z - 1 >= 0, z' = 1 + x_149 + x_232, x_149 >= 0
   encode_g(z, z') -{ 0 }-> g(1 + encArg(z - 1), 0) :|: z - 1 >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> g(1 + encArg(z - 1), 1 + encArg(z' - 1)) :|: z - 1 >= 0, z' - 1 >= 0
   encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_h(z, z') -{ 0 }-> s2 :|: s2 >= 0, s2 <= 0, z >= 0, z' >= 0
   encode_h(z, z') -{ 0 }-> h(h(encArg(x_130), encArg(x_219)), h(encArg(x_136), encArg(x_223))) :|: z' = 1 + x_136 + x_223, x_130 >= 0, z = 1 + x_130 + x_219, x_223 >= 0, x_136 >= 0, x_219 >= 0
   encode_h(z, z') -{ 0 }-> h(h(encArg(x_130), encArg(x_219)), g(encArg(x_137), encArg(x_224))) :|: z' = 1 + x_137 + x_224, x_130 >= 0, z = 1 + x_130 + x_219, x_224 >= 0, x_137 >= 0, x_219 >= 0
   encode_h(z, z') -{ 0 }-> h(h(encArg(x_130), encArg(x_219)), 0) :|: x_130 >= 0, z = 1 + x_130 + x_219, z' >= 0, x_219 >= 0
   encode_h(z, z') -{ 0 }-> h(h(encArg(x_130), encArg(x_219)), 1 + encArg(z' - 1)) :|: x_130 >= 0, z = 1 + x_130 + x_219, z' - 1 >= 0, x_219 >= 0
   encode_h(z, z') -{ 0 }-> h(g(encArg(x_131), encArg(x_220)), h(encArg(x_139), encArg(x_225))) :|: z = 1 + x_131 + x_220, z' = 1 + x_139 + x_225, x_225 >= 0, x_139 >= 0, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ 0 }-> h(g(encArg(x_131), encArg(x_220)), g(encArg(x_140), encArg(x_226))) :|: z = 1 + x_131 + x_220, x_226 >= 0, z' = 1 + x_140 + x_226, x_140 >= 0, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ 0 }-> h(g(encArg(x_131), encArg(x_220)), 0) :|: z = 1 + x_131 + x_220, z' >= 0, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ 0 }-> h(g(encArg(x_131), encArg(x_220)), 1 + encArg(z' - 1)) :|: z' - 1 >= 0, z = 1 + x_131 + x_220, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ 0 }-> h(0, h(encArg(x_142), encArg(x_227))) :|: z >= 0, z' = 1 + x_142 + x_227, x_142 >= 0, x_227 >= 0
   encode_h(z, z') -{ 0 }-> h(0, g(encArg(x_143), encArg(x_228))) :|: z >= 0, z' = 1 + x_143 + x_228, x_143 >= 0, x_228 >= 0
   encode_h(z, z') -{ 0 }-> h(0, 1 + encArg(z' - 1)) :|: z >= 0, z' - 1 >= 0
   encode_h(z, z') -{ 0 }-> h(1 + encArg(z - 1), h(encArg(x_133), encArg(x_221))) :|: z' = 1 + x_133 + x_221, x_221 >= 0, x_133 >= 0, z - 1 >= 0
   encode_h(z, z') -{ 0 }-> h(1 + encArg(z - 1), g(encArg(x_134), encArg(x_222))) :|: z' = 1 + x_134 + x_222, x_134 >= 0, x_222 >= 0, z - 1 >= 0
   encode_h(z, z') -{ 0 }-> h(1 + encArg(z - 1), 0) :|: z' >= 0, z - 1 >= 0
   encode_h(z, z') -{ 0 }-> h(1 + encArg(z - 1), 1 + encArg(z' - 1)) :|: z' - 1 >= 0, z - 1 >= 0
   encode_h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   g(z, z') -{ 1 + 4*z }-> s' :|: s' >= 0, s' <= z, z >= 0, z' >= 0
   h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   h(z, z') -{ -2 + 4*z }-> 1 + s :|: s >= 0, s <= z - 1, z - 1 >= 0, z' >= 0

Function symbols to be analyzed: {encArg}, {encode_f}, {encode_h}, {encode_g}
Previous analysis results are:
  h: runtime: O(n^1) [4*z], size: O(n^1) [z]
  g: runtime: O(n^1) [1 + 4*z], size: O(n^1) [z]

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

(27) 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: z

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

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

   encArg(z) -{ 0 }-> s'' :|: s'' >= 0, s'' <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 1 }-> s1 :|: s1 >= 0, s1 <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> h(h(encArg(x_1''), encArg(x_2')), h(encArg(x_16), encArg(x_23))) :|: x_1'' >= 0, x_16 >= 0, x_2' >= 0, x_23 >= 0, z = 1 + (1 + x_1'' + x_2') + (1 + x_16 + x_23)
   encArg(z) -{ 0 }-> h(h(encArg(x_1''), encArg(x_2')), g(encArg(x_17), encArg(x_24))) :|: x_1'' >= 0, x_2' >= 0, x_17 >= 0, x_24 >= 0, z = 1 + (1 + x_1'' + x_2') + (1 + x_17 + x_24)
   encArg(z) -{ 0 }-> h(h(encArg(x_1''), encArg(x_2')), 0) :|: x_1'' >= 0, x_2' >= 0, z = 1 + (1 + x_1'' + x_2') + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> h(h(encArg(x_1''), encArg(x_2')), 1 + encArg(x_15)) :|: x_15 >= 0, z = 1 + (1 + x_1'' + x_2') + (1 + x_15), x_1'' >= 0, x_2' >= 0
   encArg(z) -{ 0 }-> h(g(encArg(x_11), encArg(x_2'')), h(encArg(x_19), encArg(x_25))) :|: x_11 >= 0, z = 1 + (1 + x_11 + x_2'') + (1 + x_19 + x_25), x_25 >= 0, x_2'' >= 0, x_19 >= 0
   encArg(z) -{ 0 }-> h(g(encArg(x_11), encArg(x_2'')), g(encArg(x_110), encArg(x_26))) :|: x_11 >= 0, x_26 >= 0, x_2'' >= 0, z = 1 + (1 + x_11 + x_2'') + (1 + x_110 + x_26), x_110 >= 0
   encArg(z) -{ 0 }-> h(g(encArg(x_11), encArg(x_2'')), 0) :|: x_11 >= 0, x_2'' >= 0, x_2 >= 0, z = 1 + (1 + x_11 + x_2'') + x_2
   encArg(z) -{ 0 }-> h(g(encArg(x_11), encArg(x_2'')), 1 + encArg(x_18)) :|: x_11 >= 0, z = 1 + (1 + x_11 + x_2'') + (1 + x_18), x_2'' >= 0, x_18 >= 0
   encArg(z) -{ 0 }-> h(0, h(encArg(x_112), encArg(x_27))) :|: x_1 >= 0, x_27 >= 0, z = 1 + x_1 + (1 + x_112 + x_27), x_112 >= 0
   encArg(z) -{ 0 }-> h(0, g(encArg(x_113), encArg(x_28))) :|: x_1 >= 0, x_113 >= 0, x_28 >= 0, z = 1 + x_1 + (1 + x_113 + x_28)
   encArg(z) -{ 0 }-> h(0, 1 + encArg(x_111)) :|: x_1 >= 0, z = 1 + x_1 + (1 + x_111), x_111 >= 0
   encArg(z) -{ 0 }-> h(1 + encArg(x_1'), h(encArg(x_13), encArg(x_21))) :|: x_13 >= 0, x_1' >= 0, z = 1 + (1 + x_1') + (1 + x_13 + x_21), x_21 >= 0
   encArg(z) -{ 0 }-> h(1 + encArg(x_1'), g(encArg(x_14), encArg(x_22))) :|: z = 1 + (1 + x_1') + (1 + x_14 + x_22), x_14 >= 0, x_1' >= 0, x_22 >= 0
   encArg(z) -{ 0 }-> h(1 + encArg(x_1'), 0) :|: x_1' >= 0, x_2 >= 0, z = 1 + (1 + x_1') + x_2
   encArg(z) -{ 0 }-> h(1 + encArg(x_1'), 1 + encArg(x_12)) :|: z = 1 + (1 + x_1') + (1 + x_12), x_1' >= 0, x_12 >= 0
   encArg(z) -{ 0 }-> g(h(encArg(x_115), encArg(x_29)), h(encArg(x_121), encArg(x_213))) :|: x_213 >= 0, x_115 >= 0, z = 1 + (1 + x_115 + x_29) + (1 + x_121 + x_213), x_29 >= 0, x_121 >= 0
   encArg(z) -{ 0 }-> g(h(encArg(x_115), encArg(x_29)), g(encArg(x_122), encArg(x_214))) :|: z = 1 + (1 + x_115 + x_29) + (1 + x_122 + x_214), x_115 >= 0, x_214 >= 0, x_122 >= 0, x_29 >= 0
   encArg(z) -{ 0 }-> g(h(encArg(x_115), encArg(x_29)), 0) :|: x_115 >= 0, x_2 >= 0, z = 1 + (1 + x_115 + x_29) + x_2, x_29 >= 0
   encArg(z) -{ 0 }-> g(h(encArg(x_115), encArg(x_29)), 1 + encArg(x_120)) :|: x_120 >= 0, x_115 >= 0, z = 1 + (1 + x_115 + x_29) + (1 + x_120), x_29 >= 0
   encArg(z) -{ 0 }-> g(g(encArg(x_116), encArg(x_210)), h(encArg(x_124), encArg(x_215))) :|: x_124 >= 0, x_215 >= 0, x_116 >= 0, z = 1 + (1 + x_116 + x_210) + (1 + x_124 + x_215), x_210 >= 0
   encArg(z) -{ 0 }-> g(g(encArg(x_116), encArg(x_210)), g(encArg(x_125), encArg(x_216))) :|: x_216 >= 0, z = 1 + (1 + x_116 + x_210) + (1 + x_125 + x_216), x_116 >= 0, x_125 >= 0, x_210 >= 0
   encArg(z) -{ 0 }-> g(g(encArg(x_116), encArg(x_210)), 0) :|: x_116 >= 0, x_2 >= 0, z = 1 + (1 + x_116 + x_210) + x_2, x_210 >= 0
   encArg(z) -{ 0 }-> g(g(encArg(x_116), encArg(x_210)), 1 + encArg(x_123)) :|: x_123 >= 0, z = 1 + (1 + x_116 + x_210) + (1 + x_123), x_116 >= 0, x_210 >= 0
   encArg(z) -{ 0 }-> g(0, h(encArg(x_127), encArg(x_217))) :|: x_1 >= 0, x_127 >= 0, z = 1 + x_1 + (1 + x_127 + x_217), x_217 >= 0
   encArg(z) -{ 0 }-> g(0, g(encArg(x_128), encArg(x_218))) :|: x_1 >= 0, x_128 >= 0, z = 1 + x_1 + (1 + x_128 + x_218), x_218 >= 0
   encArg(z) -{ 0 }-> g(0, 1 + encArg(x_126)) :|: x_1 >= 0, z = 1 + x_1 + (1 + x_126), x_126 >= 0
   encArg(z) -{ 0 }-> g(1 + encArg(x_114), h(encArg(x_118), encArg(x_211))) :|: z = 1 + (1 + x_114) + (1 + x_118 + x_211), x_114 >= 0, x_118 >= 0, x_211 >= 0
   encArg(z) -{ 0 }-> g(1 + encArg(x_114), g(encArg(x_119), encArg(x_212))) :|: x_212 >= 0, x_114 >= 0, z = 1 + (1 + x_114) + (1 + x_119 + x_212), x_119 >= 0
   encArg(z) -{ 0 }-> g(1 + encArg(x_114), 0) :|: z = 1 + (1 + x_114) + x_2, x_114 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> g(1 + encArg(x_114), 1 + encArg(x_117)) :|: z = 1 + (1 + x_114) + (1 + x_117), x_117 >= 0, x_114 >= 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> 0 :|: z >= 0
   encode_f(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   encode_g(z, z') -{ 1 }-> s3 :|: s3 >= 0, s3 <= 0, z >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> g(h(encArg(x_145), encArg(x_229)), h(encArg(x_151), encArg(x_233))) :|: x_233 >= 0, z = 1 + x_145 + x_229, x_145 >= 0, x_229 >= 0, z' = 1 + x_151 + x_233, x_151 >= 0
   encode_g(z, z') -{ 0 }-> g(h(encArg(x_145), encArg(x_229)), g(encArg(x_152), encArg(x_234))) :|: z = 1 + x_145 + x_229, x_234 >= 0, x_145 >= 0, z' = 1 + x_152 + x_234, x_229 >= 0, x_152 >= 0
   encode_g(z, z') -{ 0 }-> g(h(encArg(x_145), encArg(x_229)), 0) :|: z = 1 + x_145 + x_229, x_145 >= 0, x_229 >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> g(h(encArg(x_145), encArg(x_229)), 1 + encArg(z' - 1)) :|: z = 1 + x_145 + x_229, x_145 >= 0, x_229 >= 0, z' - 1 >= 0
   encode_g(z, z') -{ 0 }-> g(g(encArg(x_146), encArg(x_230)), h(encArg(x_154), encArg(x_235))) :|: z = 1 + x_146 + x_230, x_146 >= 0, x_154 >= 0, z' = 1 + x_154 + x_235, x_235 >= 0, x_230 >= 0
   encode_g(z, z') -{ 0 }-> g(g(encArg(x_146), encArg(x_230)), g(encArg(x_155), encArg(x_236))) :|: z = 1 + x_146 + x_230, x_146 >= 0, x_155 >= 0, z' = 1 + x_155 + x_236, x_236 >= 0, x_230 >= 0
   encode_g(z, z') -{ 0 }-> g(g(encArg(x_146), encArg(x_230)), 0) :|: z = 1 + x_146 + x_230, x_146 >= 0, z' >= 0, x_230 >= 0
   encode_g(z, z') -{ 0 }-> g(g(encArg(x_146), encArg(x_230)), 1 + encArg(z' - 1)) :|: z = 1 + x_146 + x_230, x_146 >= 0, z' - 1 >= 0, x_230 >= 0
   encode_g(z, z') -{ 0 }-> g(0, h(encArg(x_157), encArg(x_237))) :|: x_237 >= 0, z >= 0, x_157 >= 0, z' = 1 + x_157 + x_237
   encode_g(z, z') -{ 0 }-> g(0, g(encArg(x_158), encArg(x_238))) :|: z >= 0, z' = 1 + x_158 + x_238, x_158 >= 0, x_238 >= 0
   encode_g(z, z') -{ 0 }-> g(0, 1 + encArg(z' - 1)) :|: z >= 0, z' - 1 >= 0
   encode_g(z, z') -{ 0 }-> g(1 + encArg(z - 1), h(encArg(x_148), encArg(x_231))) :|: z' = 1 + x_148 + x_231, z - 1 >= 0, x_231 >= 0, x_148 >= 0
   encode_g(z, z') -{ 0 }-> g(1 + encArg(z - 1), g(encArg(x_149), encArg(x_232))) :|: x_232 >= 0, z - 1 >= 0, z' = 1 + x_149 + x_232, x_149 >= 0
   encode_g(z, z') -{ 0 }-> g(1 + encArg(z - 1), 0) :|: z - 1 >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> g(1 + encArg(z - 1), 1 + encArg(z' - 1)) :|: z - 1 >= 0, z' - 1 >= 0
   encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_h(z, z') -{ 0 }-> s2 :|: s2 >= 0, s2 <= 0, z >= 0, z' >= 0
   encode_h(z, z') -{ 0 }-> h(h(encArg(x_130), encArg(x_219)), h(encArg(x_136), encArg(x_223))) :|: z' = 1 + x_136 + x_223, x_130 >= 0, z = 1 + x_130 + x_219, x_223 >= 0, x_136 >= 0, x_219 >= 0
   encode_h(z, z') -{ 0 }-> h(h(encArg(x_130), encArg(x_219)), g(encArg(x_137), encArg(x_224))) :|: z' = 1 + x_137 + x_224, x_130 >= 0, z = 1 + x_130 + x_219, x_224 >= 0, x_137 >= 0, x_219 >= 0
   encode_h(z, z') -{ 0 }-> h(h(encArg(x_130), encArg(x_219)), 0) :|: x_130 >= 0, z = 1 + x_130 + x_219, z' >= 0, x_219 >= 0
   encode_h(z, z') -{ 0 }-> h(h(encArg(x_130), encArg(x_219)), 1 + encArg(z' - 1)) :|: x_130 >= 0, z = 1 + x_130 + x_219, z' - 1 >= 0, x_219 >= 0
   encode_h(z, z') -{ 0 }-> h(g(encArg(x_131), encArg(x_220)), h(encArg(x_139), encArg(x_225))) :|: z = 1 + x_131 + x_220, z' = 1 + x_139 + x_225, x_225 >= 0, x_139 >= 0, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ 0 }-> h(g(encArg(x_131), encArg(x_220)), g(encArg(x_140), encArg(x_226))) :|: z = 1 + x_131 + x_220, x_226 >= 0, z' = 1 + x_140 + x_226, x_140 >= 0, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ 0 }-> h(g(encArg(x_131), encArg(x_220)), 0) :|: z = 1 + x_131 + x_220, z' >= 0, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ 0 }-> h(g(encArg(x_131), encArg(x_220)), 1 + encArg(z' - 1)) :|: z' - 1 >= 0, z = 1 + x_131 + x_220, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ 0 }-> h(0, h(encArg(x_142), encArg(x_227))) :|: z >= 0, z' = 1 + x_142 + x_227, x_142 >= 0, x_227 >= 0
   encode_h(z, z') -{ 0 }-> h(0, g(encArg(x_143), encArg(x_228))) :|: z >= 0, z' = 1 + x_143 + x_228, x_143 >= 0, x_228 >= 0
   encode_h(z, z') -{ 0 }-> h(0, 1 + encArg(z' - 1)) :|: z >= 0, z' - 1 >= 0
   encode_h(z, z') -{ 0 }-> h(1 + encArg(z - 1), h(encArg(x_133), encArg(x_221))) :|: z' = 1 + x_133 + x_221, x_221 >= 0, x_133 >= 0, z - 1 >= 0
   encode_h(z, z') -{ 0 }-> h(1 + encArg(z - 1), g(encArg(x_134), encArg(x_222))) :|: z' = 1 + x_134 + x_222, x_134 >= 0, x_222 >= 0, z - 1 >= 0
   encode_h(z, z') -{ 0 }-> h(1 + encArg(z - 1), 0) :|: z' >= 0, z - 1 >= 0
   encode_h(z, z') -{ 0 }-> h(1 + encArg(z - 1), 1 + encArg(z' - 1)) :|: z' - 1 >= 0, z - 1 >= 0
   encode_h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   g(z, z') -{ 1 + 4*z }-> s' :|: s' >= 0, s' <= z, z >= 0, z' >= 0
   h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   h(z, z') -{ -2 + 4*z }-> 1 + s :|: s >= 0, s <= z - 1, z - 1 >= 0, z' >= 0

Function symbols to be analyzed: {encArg}, {encode_f}, {encode_h}, {encode_g}
Previous analysis results are:
  h: runtime: O(n^1) [4*z], size: O(n^1) [z]
  g: runtime: O(n^1) [1 + 4*z], size: O(n^1) [z]
  encArg: runtime: ?, size: O(n^1) [z]

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

(29) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: encArg
after applying outer abstraction to obtain an ITS,
resulting in: O(n^2) with polynomial bound: 1 + 107*z + 32*z^2

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

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

   encArg(z) -{ 0 }-> s'' :|: s'' >= 0, s'' <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 1 }-> s1 :|: s1 >= 0, s1 <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> h(h(encArg(x_1''), encArg(x_2')), h(encArg(x_16), encArg(x_23))) :|: x_1'' >= 0, x_16 >= 0, x_2' >= 0, x_23 >= 0, z = 1 + (1 + x_1'' + x_2') + (1 + x_16 + x_23)
   encArg(z) -{ 0 }-> h(h(encArg(x_1''), encArg(x_2')), g(encArg(x_17), encArg(x_24))) :|: x_1'' >= 0, x_2' >= 0, x_17 >= 0, x_24 >= 0, z = 1 + (1 + x_1'' + x_2') + (1 + x_17 + x_24)
   encArg(z) -{ 0 }-> h(h(encArg(x_1''), encArg(x_2')), 0) :|: x_1'' >= 0, x_2' >= 0, z = 1 + (1 + x_1'' + x_2') + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> h(h(encArg(x_1''), encArg(x_2')), 1 + encArg(x_15)) :|: x_15 >= 0, z = 1 + (1 + x_1'' + x_2') + (1 + x_15), x_1'' >= 0, x_2' >= 0
   encArg(z) -{ 0 }-> h(g(encArg(x_11), encArg(x_2'')), h(encArg(x_19), encArg(x_25))) :|: x_11 >= 0, z = 1 + (1 + x_11 + x_2'') + (1 + x_19 + x_25), x_25 >= 0, x_2'' >= 0, x_19 >= 0
   encArg(z) -{ 0 }-> h(g(encArg(x_11), encArg(x_2'')), g(encArg(x_110), encArg(x_26))) :|: x_11 >= 0, x_26 >= 0, x_2'' >= 0, z = 1 + (1 + x_11 + x_2'') + (1 + x_110 + x_26), x_110 >= 0
   encArg(z) -{ 0 }-> h(g(encArg(x_11), encArg(x_2'')), 0) :|: x_11 >= 0, x_2'' >= 0, x_2 >= 0, z = 1 + (1 + x_11 + x_2'') + x_2
   encArg(z) -{ 0 }-> h(g(encArg(x_11), encArg(x_2'')), 1 + encArg(x_18)) :|: x_11 >= 0, z = 1 + (1 + x_11 + x_2'') + (1 + x_18), x_2'' >= 0, x_18 >= 0
   encArg(z) -{ 0 }-> h(0, h(encArg(x_112), encArg(x_27))) :|: x_1 >= 0, x_27 >= 0, z = 1 + x_1 + (1 + x_112 + x_27), x_112 >= 0
   encArg(z) -{ 0 }-> h(0, g(encArg(x_113), encArg(x_28))) :|: x_1 >= 0, x_113 >= 0, x_28 >= 0, z = 1 + x_1 + (1 + x_113 + x_28)
   encArg(z) -{ 0 }-> h(0, 1 + encArg(x_111)) :|: x_1 >= 0, z = 1 + x_1 + (1 + x_111), x_111 >= 0
   encArg(z) -{ 0 }-> h(1 + encArg(x_1'), h(encArg(x_13), encArg(x_21))) :|: x_13 >= 0, x_1' >= 0, z = 1 + (1 + x_1') + (1 + x_13 + x_21), x_21 >= 0
   encArg(z) -{ 0 }-> h(1 + encArg(x_1'), g(encArg(x_14), encArg(x_22))) :|: z = 1 + (1 + x_1') + (1 + x_14 + x_22), x_14 >= 0, x_1' >= 0, x_22 >= 0
   encArg(z) -{ 0 }-> h(1 + encArg(x_1'), 0) :|: x_1' >= 0, x_2 >= 0, z = 1 + (1 + x_1') + x_2
   encArg(z) -{ 0 }-> h(1 + encArg(x_1'), 1 + encArg(x_12)) :|: z = 1 + (1 + x_1') + (1 + x_12), x_1' >= 0, x_12 >= 0
   encArg(z) -{ 0 }-> g(h(encArg(x_115), encArg(x_29)), h(encArg(x_121), encArg(x_213))) :|: x_213 >= 0, x_115 >= 0, z = 1 + (1 + x_115 + x_29) + (1 + x_121 + x_213), x_29 >= 0, x_121 >= 0
   encArg(z) -{ 0 }-> g(h(encArg(x_115), encArg(x_29)), g(encArg(x_122), encArg(x_214))) :|: z = 1 + (1 + x_115 + x_29) + (1 + x_122 + x_214), x_115 >= 0, x_214 >= 0, x_122 >= 0, x_29 >= 0
   encArg(z) -{ 0 }-> g(h(encArg(x_115), encArg(x_29)), 0) :|: x_115 >= 0, x_2 >= 0, z = 1 + (1 + x_115 + x_29) + x_2, x_29 >= 0
   encArg(z) -{ 0 }-> g(h(encArg(x_115), encArg(x_29)), 1 + encArg(x_120)) :|: x_120 >= 0, x_115 >= 0, z = 1 + (1 + x_115 + x_29) + (1 + x_120), x_29 >= 0
   encArg(z) -{ 0 }-> g(g(encArg(x_116), encArg(x_210)), h(encArg(x_124), encArg(x_215))) :|: x_124 >= 0, x_215 >= 0, x_116 >= 0, z = 1 + (1 + x_116 + x_210) + (1 + x_124 + x_215), x_210 >= 0
   encArg(z) -{ 0 }-> g(g(encArg(x_116), encArg(x_210)), g(encArg(x_125), encArg(x_216))) :|: x_216 >= 0, z = 1 + (1 + x_116 + x_210) + (1 + x_125 + x_216), x_116 >= 0, x_125 >= 0, x_210 >= 0
   encArg(z) -{ 0 }-> g(g(encArg(x_116), encArg(x_210)), 0) :|: x_116 >= 0, x_2 >= 0, z = 1 + (1 + x_116 + x_210) + x_2, x_210 >= 0
   encArg(z) -{ 0 }-> g(g(encArg(x_116), encArg(x_210)), 1 + encArg(x_123)) :|: x_123 >= 0, z = 1 + (1 + x_116 + x_210) + (1 + x_123), x_116 >= 0, x_210 >= 0
   encArg(z) -{ 0 }-> g(0, h(encArg(x_127), encArg(x_217))) :|: x_1 >= 0, x_127 >= 0, z = 1 + x_1 + (1 + x_127 + x_217), x_217 >= 0
   encArg(z) -{ 0 }-> g(0, g(encArg(x_128), encArg(x_218))) :|: x_1 >= 0, x_128 >= 0, z = 1 + x_1 + (1 + x_128 + x_218), x_218 >= 0
   encArg(z) -{ 0 }-> g(0, 1 + encArg(x_126)) :|: x_1 >= 0, z = 1 + x_1 + (1 + x_126), x_126 >= 0
   encArg(z) -{ 0 }-> g(1 + encArg(x_114), h(encArg(x_118), encArg(x_211))) :|: z = 1 + (1 + x_114) + (1 + x_118 + x_211), x_114 >= 0, x_118 >= 0, x_211 >= 0
   encArg(z) -{ 0 }-> g(1 + encArg(x_114), g(encArg(x_119), encArg(x_212))) :|: x_212 >= 0, x_114 >= 0, z = 1 + (1 + x_114) + (1 + x_119 + x_212), x_119 >= 0
   encArg(z) -{ 0 }-> g(1 + encArg(x_114), 0) :|: z = 1 + (1 + x_114) + x_2, x_114 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> g(1 + encArg(x_114), 1 + encArg(x_117)) :|: z = 1 + (1 + x_114) + (1 + x_117), x_117 >= 0, x_114 >= 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> 0 :|: z >= 0
   encode_f(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   encode_g(z, z') -{ 1 }-> s3 :|: s3 >= 0, s3 <= 0, z >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> g(h(encArg(x_145), encArg(x_229)), h(encArg(x_151), encArg(x_233))) :|: x_233 >= 0, z = 1 + x_145 + x_229, x_145 >= 0, x_229 >= 0, z' = 1 + x_151 + x_233, x_151 >= 0
   encode_g(z, z') -{ 0 }-> g(h(encArg(x_145), encArg(x_229)), g(encArg(x_152), encArg(x_234))) :|: z = 1 + x_145 + x_229, x_234 >= 0, x_145 >= 0, z' = 1 + x_152 + x_234, x_229 >= 0, x_152 >= 0
   encode_g(z, z') -{ 0 }-> g(h(encArg(x_145), encArg(x_229)), 0) :|: z = 1 + x_145 + x_229, x_145 >= 0, x_229 >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> g(h(encArg(x_145), encArg(x_229)), 1 + encArg(z' - 1)) :|: z = 1 + x_145 + x_229, x_145 >= 0, x_229 >= 0, z' - 1 >= 0
   encode_g(z, z') -{ 0 }-> g(g(encArg(x_146), encArg(x_230)), h(encArg(x_154), encArg(x_235))) :|: z = 1 + x_146 + x_230, x_146 >= 0, x_154 >= 0, z' = 1 + x_154 + x_235, x_235 >= 0, x_230 >= 0
   encode_g(z, z') -{ 0 }-> g(g(encArg(x_146), encArg(x_230)), g(encArg(x_155), encArg(x_236))) :|: z = 1 + x_146 + x_230, x_146 >= 0, x_155 >= 0, z' = 1 + x_155 + x_236, x_236 >= 0, x_230 >= 0
   encode_g(z, z') -{ 0 }-> g(g(encArg(x_146), encArg(x_230)), 0) :|: z = 1 + x_146 + x_230, x_146 >= 0, z' >= 0, x_230 >= 0
   encode_g(z, z') -{ 0 }-> g(g(encArg(x_146), encArg(x_230)), 1 + encArg(z' - 1)) :|: z = 1 + x_146 + x_230, x_146 >= 0, z' - 1 >= 0, x_230 >= 0
   encode_g(z, z') -{ 0 }-> g(0, h(encArg(x_157), encArg(x_237))) :|: x_237 >= 0, z >= 0, x_157 >= 0, z' = 1 + x_157 + x_237
   encode_g(z, z') -{ 0 }-> g(0, g(encArg(x_158), encArg(x_238))) :|: z >= 0, z' = 1 + x_158 + x_238, x_158 >= 0, x_238 >= 0
   encode_g(z, z') -{ 0 }-> g(0, 1 + encArg(z' - 1)) :|: z >= 0, z' - 1 >= 0
   encode_g(z, z') -{ 0 }-> g(1 + encArg(z - 1), h(encArg(x_148), encArg(x_231))) :|: z' = 1 + x_148 + x_231, z - 1 >= 0, x_231 >= 0, x_148 >= 0
   encode_g(z, z') -{ 0 }-> g(1 + encArg(z - 1), g(encArg(x_149), encArg(x_232))) :|: x_232 >= 0, z - 1 >= 0, z' = 1 + x_149 + x_232, x_149 >= 0
   encode_g(z, z') -{ 0 }-> g(1 + encArg(z - 1), 0) :|: z - 1 >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> g(1 + encArg(z - 1), 1 + encArg(z' - 1)) :|: z - 1 >= 0, z' - 1 >= 0
   encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_h(z, z') -{ 0 }-> s2 :|: s2 >= 0, s2 <= 0, z >= 0, z' >= 0
   encode_h(z, z') -{ 0 }-> h(h(encArg(x_130), encArg(x_219)), h(encArg(x_136), encArg(x_223))) :|: z' = 1 + x_136 + x_223, x_130 >= 0, z = 1 + x_130 + x_219, x_223 >= 0, x_136 >= 0, x_219 >= 0
   encode_h(z, z') -{ 0 }-> h(h(encArg(x_130), encArg(x_219)), g(encArg(x_137), encArg(x_224))) :|: z' = 1 + x_137 + x_224, x_130 >= 0, z = 1 + x_130 + x_219, x_224 >= 0, x_137 >= 0, x_219 >= 0
   encode_h(z, z') -{ 0 }-> h(h(encArg(x_130), encArg(x_219)), 0) :|: x_130 >= 0, z = 1 + x_130 + x_219, z' >= 0, x_219 >= 0
   encode_h(z, z') -{ 0 }-> h(h(encArg(x_130), encArg(x_219)), 1 + encArg(z' - 1)) :|: x_130 >= 0, z = 1 + x_130 + x_219, z' - 1 >= 0, x_219 >= 0
   encode_h(z, z') -{ 0 }-> h(g(encArg(x_131), encArg(x_220)), h(encArg(x_139), encArg(x_225))) :|: z = 1 + x_131 + x_220, z' = 1 + x_139 + x_225, x_225 >= 0, x_139 >= 0, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ 0 }-> h(g(encArg(x_131), encArg(x_220)), g(encArg(x_140), encArg(x_226))) :|: z = 1 + x_131 + x_220, x_226 >= 0, z' = 1 + x_140 + x_226, x_140 >= 0, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ 0 }-> h(g(encArg(x_131), encArg(x_220)), 0) :|: z = 1 + x_131 + x_220, z' >= 0, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ 0 }-> h(g(encArg(x_131), encArg(x_220)), 1 + encArg(z' - 1)) :|: z' - 1 >= 0, z = 1 + x_131 + x_220, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ 0 }-> h(0, h(encArg(x_142), encArg(x_227))) :|: z >= 0, z' = 1 + x_142 + x_227, x_142 >= 0, x_227 >= 0
   encode_h(z, z') -{ 0 }-> h(0, g(encArg(x_143), encArg(x_228))) :|: z >= 0, z' = 1 + x_143 + x_228, x_143 >= 0, x_228 >= 0
   encode_h(z, z') -{ 0 }-> h(0, 1 + encArg(z' - 1)) :|: z >= 0, z' - 1 >= 0
   encode_h(z, z') -{ 0 }-> h(1 + encArg(z - 1), h(encArg(x_133), encArg(x_221))) :|: z' = 1 + x_133 + x_221, x_221 >= 0, x_133 >= 0, z - 1 >= 0
   encode_h(z, z') -{ 0 }-> h(1 + encArg(z - 1), g(encArg(x_134), encArg(x_222))) :|: z' = 1 + x_134 + x_222, x_134 >= 0, x_222 >= 0, z - 1 >= 0
   encode_h(z, z') -{ 0 }-> h(1 + encArg(z - 1), 0) :|: z' >= 0, z - 1 >= 0
   encode_h(z, z') -{ 0 }-> h(1 + encArg(z - 1), 1 + encArg(z' - 1)) :|: z' - 1 >= 0, z - 1 >= 0
   encode_h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   g(z, z') -{ 1 + 4*z }-> s' :|: s' >= 0, s' <= z, z >= 0, z' >= 0
   h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   h(z, z') -{ -2 + 4*z }-> 1 + s :|: s >= 0, s <= z - 1, z - 1 >= 0, z' >= 0

Function symbols to be analyzed: {encode_f}, {encode_h}, {encode_g}
Previous analysis results are:
  h: runtime: O(n^1) [4*z], size: O(n^1) [z]
  g: runtime: O(n^1) [1 + 4*z], size: O(n^1) [z]
  encArg: runtime: O(n^2) [1 + 107*z + 32*z^2], size: O(n^1) [z]

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

(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:

   encArg(z) -{ 0 }-> s'' :|: s'' >= 0, s'' <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 1 }-> s1 :|: s1 >= 0, s1 <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 5 + 4*s96 + 4*s98 + 4*s99 + 107*x_115 + 32*x_115^2 + 107*x_121 + 32*x_121^2 + 107*x_213 + 32*x_213^2 + 107*x_29 + 32*x_29^2 }-> s102 :|: s96 >= 0, s96 <= x_115, s97 >= 0, s97 <= x_29, s98 >= 0, s98 <= s96, s99 >= 0, s99 <= x_121, s100 >= 0, s100 <= x_213, s101 >= 0, s101 <= s99, s102 >= 0, s102 <= s98, x_213 >= 0, x_115 >= 0, z = 1 + (1 + x_115 + x_29) + (1 + x_121 + x_213), x_29 >= 0, x_121 >= 0
   encArg(z) -{ 6 + 4*s103 + 4*s105 + 4*s106 + 107*x_115 + 32*x_115^2 + 107*x_122 + 32*x_122^2 + 107*x_214 + 32*x_214^2 + 107*x_29 + 32*x_29^2 }-> s109 :|: s103 >= 0, s103 <= x_115, s104 >= 0, s104 <= x_29, s105 >= 0, s105 <= s103, s106 >= 0, s106 <= x_122, s107 >= 0, s107 <= x_214, s108 >= 0, s108 <= s106, s109 >= 0, s109 <= s105, z = 1 + (1 + x_115 + x_29) + (1 + x_122 + x_214), x_115 >= 0, x_214 >= 0, x_122 >= 0, x_29 >= 0
   encArg(z) -{ 3 + 4*s110 + 4*s112 + 107*x_115 + 32*x_115^2 + 107*x_29 + 32*x_29^2 }-> s113 :|: s110 >= 0, s110 <= x_115, s111 >= 0, s111 <= x_29, s112 >= 0, s112 <= s110, s113 >= 0, s113 <= s112, x_115 >= 0, x_2 >= 0, z = 1 + (1 + x_115 + x_29) + x_2, x_29 >= 0
   encArg(z) -{ 5 + 4*s114 + 4*s116 + 107*x_116 + 32*x_116^2 + 107*x_123 + 32*x_123^2 + 107*x_210 + 32*x_210^2 }-> s118 :|: s114 >= 0, s114 <= x_116, s115 >= 0, s115 <= x_210, s116 >= 0, s116 <= s114, s117 >= 0, s117 <= x_123, s118 >= 0, s118 <= s116, x_123 >= 0, z = 1 + (1 + x_116 + x_210) + (1 + x_123), x_116 >= 0, x_210 >= 0
   encArg(z) -{ 7 + 4*s8 + 4*s9 + 107*x_1' + 32*x_1'^2 + 107*x_13 + 32*x_13^2 + 107*x_21 + 32*x_21^2 }-> s12 :|: s8 >= 0, s8 <= x_1', s9 >= 0, s9 <= x_13, s10 >= 0, s10 <= x_21, s11 >= 0, s11 <= s9, s12 >= 0, s12 <= 1 + s8, x_13 >= 0, x_1' >= 0, z = 1 + (1 + x_1') + (1 + x_13 + x_21), x_21 >= 0
   encArg(z) -{ 6 + 4*s119 + 4*s121 + 4*s122 + 107*x_116 + 32*x_116^2 + 107*x_124 + 32*x_124^2 + 107*x_210 + 32*x_210^2 + 107*x_215 + 32*x_215^2 }-> s125 :|: s119 >= 0, s119 <= x_116, s120 >= 0, s120 <= x_210, s121 >= 0, s121 <= s119, s122 >= 0, s122 <= x_124, s123 >= 0, s123 <= x_215, s124 >= 0, s124 <= s122, s125 >= 0, s125 <= s121, x_124 >= 0, x_215 >= 0, x_116 >= 0, z = 1 + (1 + x_116 + x_210) + (1 + x_124 + x_215), x_210 >= 0
   encArg(z) -{ 7 + 4*s126 + 4*s128 + 4*s129 + 107*x_116 + 32*x_116^2 + 107*x_125 + 32*x_125^2 + 107*x_210 + 32*x_210^2 + 107*x_216 + 32*x_216^2 }-> s132 :|: s126 >= 0, s126 <= x_116, s127 >= 0, s127 <= x_210, s128 >= 0, s128 <= s126, s129 >= 0, s129 <= x_125, s130 >= 0, s130 <= x_216, s131 >= 0, s131 <= s129, s132 >= 0, s132 <= s128, x_216 >= 0, z = 1 + (1 + x_116 + x_210) + (1 + x_125 + x_216), x_116 >= 0, x_125 >= 0, x_210 >= 0
   encArg(z) -{ 4 + 4*s133 + 4*s135 + 107*x_116 + 32*x_116^2 + 107*x_210 + 32*x_210^2 }-> s136 :|: s133 >= 0, s133 <= x_116, s134 >= 0, s134 <= x_210, s135 >= 0, s135 <= s133, s136 >= 0, s136 <= s135, x_116 >= 0, x_2 >= 0, z = 1 + (1 + x_116 + x_210) + x_2, x_210 >= 0
   encArg(z) -{ 2 + 107*x_126 + 32*x_126^2 }-> s138 :|: s137 >= 0, s137 <= x_126, s138 >= 0, s138 <= 0, x_1 >= 0, z = 1 + x_1 + (1 + x_126), x_126 >= 0
   encArg(z) -{ 3 + 4*s139 + 107*x_127 + 32*x_127^2 + 107*x_217 + 32*x_217^2 }-> s142 :|: s139 >= 0, s139 <= x_127, s140 >= 0, s140 <= x_217, s141 >= 0, s141 <= s139, s142 >= 0, s142 <= 0, x_1 >= 0, x_127 >= 0, z = 1 + x_1 + (1 + x_127 + x_217), x_217 >= 0
   encArg(z) -{ 4 + 4*s143 + 107*x_128 + 32*x_128^2 + 107*x_218 + 32*x_218^2 }-> s146 :|: s143 >= 0, s143 <= x_128, s144 >= 0, s144 <= x_218, s145 >= 0, s145 <= s143, s146 >= 0, s146 <= 0, x_1 >= 0, x_128 >= 0, z = 1 + x_1 + (1 + x_128 + x_218), x_218 >= 0
   encArg(z) -{ 8 + 4*s13 + 4*s14 + 107*x_1' + 32*x_1'^2 + 107*x_14 + 32*x_14^2 + 107*x_22 + 32*x_22^2 }-> s17 :|: s13 >= 0, s13 <= x_1', s14 >= 0, s14 <= x_14, s15 >= 0, s15 <= x_22, s16 >= 0, s16 <= s14, s17 >= 0, s17 <= 1 + s13, z = 1 + (1 + x_1') + (1 + x_14 + x_22), x_14 >= 0, x_1' >= 0, x_22 >= 0
   encArg(z) -{ 5 + 4*s18 + 107*x_1' + 32*x_1'^2 }-> s19 :|: s18 >= 0, s18 <= x_1', s19 >= 0, s19 <= 1 + s18, x_1' >= 0, x_2 >= 0, z = 1 + (1 + x_1') + x_2
   encArg(z) -{ 3 + 4*s20 + 4*s22 + 107*x_1'' + 32*x_1''^2 + 107*x_15 + 32*x_15^2 + 107*x_2' + 32*x_2'^2 }-> s24 :|: s20 >= 0, s20 <= x_1'', s21 >= 0, s21 <= x_2', s22 >= 0, s22 <= s20, s23 >= 0, s23 <= x_15, s24 >= 0, s24 <= s22, x_15 >= 0, z = 1 + (1 + x_1'' + x_2') + (1 + x_15), x_1'' >= 0, x_2' >= 0
   encArg(z) -{ 4 + 4*s25 + 4*s27 + 4*s28 + 107*x_1'' + 32*x_1''^2 + 107*x_16 + 32*x_16^2 + 107*x_2' + 32*x_2'^2 + 107*x_23 + 32*x_23^2 }-> s31 :|: s25 >= 0, s25 <= x_1'', s26 >= 0, s26 <= x_2', s27 >= 0, s27 <= s25, s28 >= 0, s28 <= x_16, s29 >= 0, s29 <= x_23, s30 >= 0, s30 <= s28, s31 >= 0, s31 <= s27, x_1'' >= 0, x_16 >= 0, x_2' >= 0, x_23 >= 0, z = 1 + (1 + x_1'' + x_2') + (1 + x_16 + x_23)
   encArg(z) -{ 5 + 4*s32 + 4*s34 + 4*s35 + 107*x_1'' + 32*x_1''^2 + 107*x_17 + 32*x_17^2 + 107*x_2' + 32*x_2'^2 + 107*x_24 + 32*x_24^2 }-> s38 :|: s32 >= 0, s32 <= x_1'', s33 >= 0, s33 <= x_2', s34 >= 0, s34 <= s32, s35 >= 0, s35 <= x_17, s36 >= 0, s36 <= x_24, s37 >= 0, s37 <= s35, s38 >= 0, s38 <= s34, x_1'' >= 0, x_2' >= 0, x_17 >= 0, x_24 >= 0, z = 1 + (1 + x_1'' + x_2') + (1 + x_17 + x_24)
   encArg(z) -{ 2 + 4*s39 + 4*s41 + 107*x_1'' + 32*x_1''^2 + 107*x_2' + 32*x_2'^2 }-> s42 :|: s39 >= 0, s39 <= x_1'', s40 >= 0, s40 <= x_2', s41 >= 0, s41 <= s39, s42 >= 0, s42 <= s41, x_1'' >= 0, x_2' >= 0, z = 1 + (1 + x_1'' + x_2') + x_2, x_2 >= 0
   encArg(z) -{ 4 + 4*s43 + 4*s45 + 107*x_11 + 32*x_11^2 + 107*x_18 + 32*x_18^2 + 107*x_2'' + 32*x_2''^2 }-> s47 :|: s43 >= 0, s43 <= x_11, s44 >= 0, s44 <= x_2'', s45 >= 0, s45 <= s43, s46 >= 0, s46 <= x_18, s47 >= 0, s47 <= s45, x_11 >= 0, z = 1 + (1 + x_11 + x_2'') + (1 + x_18), x_2'' >= 0, x_18 >= 0
   encArg(z) -{ 5 + 4*s48 + 4*s50 + 4*s51 + 107*x_11 + 32*x_11^2 + 107*x_19 + 32*x_19^2 + 107*x_2'' + 32*x_2''^2 + 107*x_25 + 32*x_25^2 }-> s54 :|: s48 >= 0, s48 <= x_11, s49 >= 0, s49 <= x_2'', s50 >= 0, s50 <= s48, s51 >= 0, s51 <= x_19, s52 >= 0, s52 <= x_25, s53 >= 0, s53 <= s51, s54 >= 0, s54 <= s50, x_11 >= 0, z = 1 + (1 + x_11 + x_2'') + (1 + x_19 + x_25), x_25 >= 0, x_2'' >= 0, x_19 >= 0
   encArg(z) -{ 6 + 4*s55 + 4*s57 + 4*s58 + 107*x_11 + 32*x_11^2 + 107*x_110 + 32*x_110^2 + 107*x_2'' + 32*x_2''^2 + 107*x_26 + 32*x_26^2 }-> s61 :|: s55 >= 0, s55 <= x_11, s56 >= 0, s56 <= x_2'', s57 >= 0, s57 <= s55, s58 >= 0, s58 <= x_110, s59 >= 0, s59 <= x_26, s60 >= 0, s60 <= s58, s61 >= 0, s61 <= s57, x_11 >= 0, x_26 >= 0, x_2'' >= 0, z = 1 + (1 + x_11 + x_2'') + (1 + x_110 + x_26), x_110 >= 0
   encArg(z) -{ 3 + 4*s62 + 4*s64 + 107*x_11 + 32*x_11^2 + 107*x_2'' + 32*x_2''^2 }-> s65 :|: s62 >= 0, s62 <= x_11, s63 >= 0, s63 <= x_2'', s64 >= 0, s64 <= s62, s65 >= 0, s65 <= s64, x_11 >= 0, x_2'' >= 0, x_2 >= 0, z = 1 + (1 + x_11 + x_2'') + x_2
   encArg(z) -{ 1 + 107*x_111 + 32*x_111^2 }-> s67 :|: s66 >= 0, s66 <= x_111, s67 >= 0, s67 <= 0, x_1 >= 0, z = 1 + x_1 + (1 + x_111), x_111 >= 0
   encArg(z) -{ 6 + 4*s5 + 107*x_1' + 32*x_1'^2 + 107*x_12 + 32*x_12^2 }-> s7 :|: s5 >= 0, s5 <= x_1', s6 >= 0, s6 <= x_12, s7 >= 0, s7 <= 1 + s5, z = 1 + (1 + x_1') + (1 + x_12), x_1' >= 0, x_12 >= 0
   encArg(z) -{ 2 + 4*s68 + 107*x_112 + 32*x_112^2 + 107*x_27 + 32*x_27^2 }-> s71 :|: s68 >= 0, s68 <= x_112, s69 >= 0, s69 <= x_27, s70 >= 0, s70 <= s68, s71 >= 0, s71 <= 0, x_1 >= 0, x_27 >= 0, z = 1 + x_1 + (1 + x_112 + x_27), x_112 >= 0
   encArg(z) -{ 3 + 4*s72 + 107*x_113 + 32*x_113^2 + 107*x_28 + 32*x_28^2 }-> s75 :|: s72 >= 0, s72 <= x_113, s73 >= 0, s73 <= x_28, s74 >= 0, s74 <= s72, s75 >= 0, s75 <= 0, x_1 >= 0, x_113 >= 0, x_28 >= 0, z = 1 + x_1 + (1 + x_113 + x_28)
   encArg(z) -{ 7 + 4*s76 + 107*x_114 + 32*x_114^2 + 107*x_117 + 32*x_117^2 }-> s78 :|: s76 >= 0, s76 <= x_114, s77 >= 0, s77 <= x_117, s78 >= 0, s78 <= 1 + s76, z = 1 + (1 + x_114) + (1 + x_117), x_117 >= 0, x_114 >= 0
   encArg(z) -{ 8 + 4*s79 + 4*s80 + 107*x_114 + 32*x_114^2 + 107*x_118 + 32*x_118^2 + 107*x_211 + 32*x_211^2 }-> s83 :|: s79 >= 0, s79 <= x_114, s80 >= 0, s80 <= x_118, s81 >= 0, s81 <= x_211, s82 >= 0, s82 <= s80, s83 >= 0, s83 <= 1 + s79, z = 1 + (1 + x_114) + (1 + x_118 + x_211), x_114 >= 0, x_118 >= 0, x_211 >= 0
   encArg(z) -{ 9 + 4*s84 + 4*s85 + 107*x_114 + 32*x_114^2 + 107*x_119 + 32*x_119^2 + 107*x_212 + 32*x_212^2 }-> s88 :|: s84 >= 0, s84 <= x_114, s85 >= 0, s85 <= x_119, s86 >= 0, s86 <= x_212, s87 >= 0, s87 <= s85, s88 >= 0, s88 <= 1 + s84, x_212 >= 0, x_114 >= 0, z = 1 + (1 + x_114) + (1 + x_119 + x_212), x_119 >= 0
   encArg(z) -{ 6 + 4*s89 + 107*x_114 + 32*x_114^2 }-> s90 :|: s89 >= 0, s89 <= x_114, s90 >= 0, s90 <= 1 + s89, z = 1 + (1 + x_114) + x_2, x_114 >= 0, x_2 >= 0
   encArg(z) -{ 4 + 4*s91 + 4*s93 + 107*x_115 + 32*x_115^2 + 107*x_120 + 32*x_120^2 + 107*x_29 + 32*x_29^2 }-> s95 :|: s91 >= 0, s91 <= x_115, s92 >= 0, s92 <= x_29, s93 >= 0, s93 <= s91, s94 >= 0, s94 <= x_120, s95 >= 0, s95 <= s93, x_120 >= 0, x_115 >= 0, z = 1 + (1 + x_115 + x_29) + (1 + x_120), x_29 >= 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ -74 + 43*z + 32*z^2 }-> 1 + s4 :|: s4 >= 0, s4 <= z - 1, z - 1 >= 0
   encode_f(z) -{ 0 }-> 0 :|: z >= 0
   encode_f(z) -{ 1 + 107*z + 32*z^2 }-> 1 + s218 :|: s218 >= 0, s218 <= z, z >= 0
   encode_g(z, z') -{ -143 + 4*s219 + 43*z + 32*z^2 + 43*z' + 32*z'^2 }-> s221 :|: s219 >= 0, s219 <= z - 1, s220 >= 0, s220 <= z' - 1, s221 >= 0, s221 <= 1 + s219, z - 1 >= 0, z' - 1 >= 0
   encode_g(z, z') -{ -67 + 4*s222 + 4*s223 + 107*x_148 + 32*x_148^2 + 107*x_231 + 32*x_231^2 + 43*z + 32*z^2 }-> s226 :|: s222 >= 0, s222 <= z - 1, s223 >= 0, s223 <= x_148, s224 >= 0, s224 <= x_231, s225 >= 0, s225 <= s223, s226 >= 0, s226 <= 1 + s222, z' = 1 + x_148 + x_231, z - 1 >= 0, x_231 >= 0, x_148 >= 0
   encode_g(z, z') -{ -66 + 4*s227 + 4*s228 + 107*x_149 + 32*x_149^2 + 107*x_232 + 32*x_232^2 + 43*z + 32*z^2 }-> s231 :|: s227 >= 0, s227 <= z - 1, s228 >= 0, s228 <= x_149, s229 >= 0, s229 <= x_232, s230 >= 0, s230 <= s228, s231 >= 0, s231 <= 1 + s227, x_232 >= 0, z - 1 >= 0, z' = 1 + x_149 + x_232, x_149 >= 0
   encode_g(z, z') -{ -69 + 4*s232 + 43*z + 32*z^2 }-> s233 :|: s232 >= 0, s232 <= z - 1, s233 >= 0, s233 <= 1 + s232, z - 1 >= 0, z' >= 0
   encode_g(z, z') -{ -71 + 4*s234 + 4*s236 + 107*x_145 + 32*x_145^2 + 107*x_229 + 32*x_229^2 + 43*z' + 32*z'^2 }-> s238 :|: s234 >= 0, s234 <= x_145, s235 >= 0, s235 <= x_229, s236 >= 0, s236 <= s234, s237 >= 0, s237 <= z' - 1, s238 >= 0, s238 <= s236, z = 1 + x_145 + x_229, x_145 >= 0, x_229 >= 0, z' - 1 >= 0
   encode_g(z, z') -{ 5 + 4*s239 + 4*s241 + 4*s242 + 107*x_145 + 32*x_145^2 + 107*x_151 + 32*x_151^2 + 107*x_229 + 32*x_229^2 + 107*x_233 + 32*x_233^2 }-> s245 :|: s239 >= 0, s239 <= x_145, s240 >= 0, s240 <= x_229, s241 >= 0, s241 <= s239, s242 >= 0, s242 <= x_151, s243 >= 0, s243 <= x_233, s244 >= 0, s244 <= s242, s245 >= 0, s245 <= s241, x_233 >= 0, z = 1 + x_145 + x_229, x_145 >= 0, x_229 >= 0, z' = 1 + x_151 + x_233, x_151 >= 0
   encode_g(z, z') -{ 6 + 4*s246 + 4*s248 + 4*s249 + 107*x_145 + 32*x_145^2 + 107*x_152 + 32*x_152^2 + 107*x_229 + 32*x_229^2 + 107*x_234 + 32*x_234^2 }-> s252 :|: s246 >= 0, s246 <= x_145, s247 >= 0, s247 <= x_229, s248 >= 0, s248 <= s246, s249 >= 0, s249 <= x_152, s250 >= 0, s250 <= x_234, s251 >= 0, s251 <= s249, s252 >= 0, s252 <= s248, z = 1 + x_145 + x_229, x_234 >= 0, x_145 >= 0, z' = 1 + x_152 + x_234, x_229 >= 0, x_152 >= 0
   encode_g(z, z') -{ 3 + 4*s253 + 4*s255 + 107*x_145 + 32*x_145^2 + 107*x_229 + 32*x_229^2 }-> s256 :|: s253 >= 0, s253 <= x_145, s254 >= 0, s254 <= x_229, s255 >= 0, s255 <= s253, s256 >= 0, s256 <= s255, z = 1 + x_145 + x_229, x_145 >= 0, x_229 >= 0, z' >= 0
   encode_g(z, z') -{ -70 + 4*s257 + 4*s259 + 107*x_146 + 32*x_146^2 + 107*x_230 + 32*x_230^2 + 43*z' + 32*z'^2 }-> s261 :|: s257 >= 0, s257 <= x_146, s258 >= 0, s258 <= x_230, s259 >= 0, s259 <= s257, s260 >= 0, s260 <= z' - 1, s261 >= 0, s261 <= s259, z = 1 + x_146 + x_230, x_146 >= 0, z' - 1 >= 0, x_230 >= 0
   encode_g(z, z') -{ 6 + 4*s262 + 4*s264 + 4*s265 + 107*x_146 + 32*x_146^2 + 107*x_154 + 32*x_154^2 + 107*x_230 + 32*x_230^2 + 107*x_235 + 32*x_235^2 }-> s268 :|: s262 >= 0, s262 <= x_146, s263 >= 0, s263 <= x_230, s264 >= 0, s264 <= s262, s265 >= 0, s265 <= x_154, s266 >= 0, s266 <= x_235, s267 >= 0, s267 <= s265, s268 >= 0, s268 <= s264, z = 1 + x_146 + x_230, x_146 >= 0, x_154 >= 0, z' = 1 + x_154 + x_235, x_235 >= 0, x_230 >= 0
   encode_g(z, z') -{ 7 + 4*s269 + 4*s271 + 4*s272 + 107*x_146 + 32*x_146^2 + 107*x_155 + 32*x_155^2 + 107*x_230 + 32*x_230^2 + 107*x_236 + 32*x_236^2 }-> s275 :|: s269 >= 0, s269 <= x_146, s270 >= 0, s270 <= x_230, s271 >= 0, s271 <= s269, s272 >= 0, s272 <= x_155, s273 >= 0, s273 <= x_236, s274 >= 0, s274 <= s272, s275 >= 0, s275 <= s271, z = 1 + x_146 + x_230, x_146 >= 0, x_155 >= 0, z' = 1 + x_155 + x_236, x_236 >= 0, x_230 >= 0
   encode_g(z, z') -{ 4 + 4*s276 + 4*s278 + 107*x_146 + 32*x_146^2 + 107*x_230 + 32*x_230^2 }-> s279 :|: s276 >= 0, s276 <= x_146, s277 >= 0, s277 <= x_230, s278 >= 0, s278 <= s276, s279 >= 0, s279 <= s278, z = 1 + x_146 + x_230, x_146 >= 0, z' >= 0, x_230 >= 0
   encode_g(z, z') -{ -73 + 43*z' + 32*z'^2 }-> s281 :|: s280 >= 0, s280 <= z' - 1, s281 >= 0, s281 <= 0, z >= 0, z' - 1 >= 0
   encode_g(z, z') -{ 3 + 4*s282 + 107*x_157 + 32*x_157^2 + 107*x_237 + 32*x_237^2 }-> s285 :|: s282 >= 0, s282 <= x_157, s283 >= 0, s283 <= x_237, s284 >= 0, s284 <= s282, s285 >= 0, s285 <= 0, x_237 >= 0, z >= 0, x_157 >= 0, z' = 1 + x_157 + x_237
   encode_g(z, z') -{ 4 + 4*s286 + 107*x_158 + 32*x_158^2 + 107*x_238 + 32*x_238^2 }-> s289 :|: s286 >= 0, s286 <= x_158, s287 >= 0, s287 <= x_238, s288 >= 0, s288 <= s286, s289 >= 0, s289 <= 0, z >= 0, z' = 1 + x_158 + x_238, x_158 >= 0, x_238 >= 0
   encode_g(z, z') -{ 1 }-> s3 :|: s3 >= 0, s3 <= 0, z >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_h(z, z') -{ -144 + 4*s147 + 43*z + 32*z^2 + 43*z' + 32*z'^2 }-> s149 :|: s147 >= 0, s147 <= z - 1, s148 >= 0, s148 <= z' - 1, s149 >= 0, s149 <= 1 + s147, z' - 1 >= 0, z - 1 >= 0
   encode_h(z, z') -{ -68 + 4*s150 + 4*s151 + 107*x_133 + 32*x_133^2 + 107*x_221 + 32*x_221^2 + 43*z + 32*z^2 }-> s154 :|: s150 >= 0, s150 <= z - 1, s151 >= 0, s151 <= x_133, s152 >= 0, s152 <= x_221, s153 >= 0, s153 <= s151, s154 >= 0, s154 <= 1 + s150, z' = 1 + x_133 + x_221, x_221 >= 0, x_133 >= 0, z - 1 >= 0
   encode_h(z, z') -{ -67 + 4*s155 + 4*s156 + 107*x_134 + 32*x_134^2 + 107*x_222 + 32*x_222^2 + 43*z + 32*z^2 }-> s159 :|: s155 >= 0, s155 <= z - 1, s156 >= 0, s156 <= x_134, s157 >= 0, s157 <= x_222, s158 >= 0, s158 <= s156, s159 >= 0, s159 <= 1 + s155, z' = 1 + x_134 + x_222, x_134 >= 0, x_222 >= 0, z - 1 >= 0
   encode_h(z, z') -{ -70 + 4*s160 + 43*z + 32*z^2 }-> s161 :|: s160 >= 0, s160 <= z - 1, s161 >= 0, s161 <= 1 + s160, z' >= 0, z - 1 >= 0
   encode_h(z, z') -{ -72 + 4*s162 + 4*s164 + 107*x_130 + 32*x_130^2 + 107*x_219 + 32*x_219^2 + 43*z' + 32*z'^2 }-> s166 :|: s162 >= 0, s162 <= x_130, s163 >= 0, s163 <= x_219, s164 >= 0, s164 <= s162, s165 >= 0, s165 <= z' - 1, s166 >= 0, s166 <= s164, x_130 >= 0, z = 1 + x_130 + x_219, z' - 1 >= 0, x_219 >= 0
   encode_h(z, z') -{ 4 + 4*s167 + 4*s169 + 4*s170 + 107*x_130 + 32*x_130^2 + 107*x_136 + 32*x_136^2 + 107*x_219 + 32*x_219^2 + 107*x_223 + 32*x_223^2 }-> s173 :|: s167 >= 0, s167 <= x_130, s168 >= 0, s168 <= x_219, s169 >= 0, s169 <= s167, s170 >= 0, s170 <= x_136, s171 >= 0, s171 <= x_223, s172 >= 0, s172 <= s170, s173 >= 0, s173 <= s169, z' = 1 + x_136 + x_223, x_130 >= 0, z = 1 + x_130 + x_219, x_223 >= 0, x_136 >= 0, x_219 >= 0
   encode_h(z, z') -{ 5 + 4*s174 + 4*s176 + 4*s177 + 107*x_130 + 32*x_130^2 + 107*x_137 + 32*x_137^2 + 107*x_219 + 32*x_219^2 + 107*x_224 + 32*x_224^2 }-> s180 :|: s174 >= 0, s174 <= x_130, s175 >= 0, s175 <= x_219, s176 >= 0, s176 <= s174, s177 >= 0, s177 <= x_137, s178 >= 0, s178 <= x_224, s179 >= 0, s179 <= s177, s180 >= 0, s180 <= s176, z' = 1 + x_137 + x_224, x_130 >= 0, z = 1 + x_130 + x_219, x_224 >= 0, x_137 >= 0, x_219 >= 0
   encode_h(z, z') -{ 2 + 4*s181 + 4*s183 + 107*x_130 + 32*x_130^2 + 107*x_219 + 32*x_219^2 }-> s184 :|: s181 >= 0, s181 <= x_130, s182 >= 0, s182 <= x_219, s183 >= 0, s183 <= s181, s184 >= 0, s184 <= s183, x_130 >= 0, z = 1 + x_130 + x_219, z' >= 0, x_219 >= 0
   encode_h(z, z') -{ -71 + 4*s185 + 4*s187 + 107*x_131 + 32*x_131^2 + 107*x_220 + 32*x_220^2 + 43*z' + 32*z'^2 }-> s189 :|: s185 >= 0, s185 <= x_131, s186 >= 0, s186 <= x_220, s187 >= 0, s187 <= s185, s188 >= 0, s188 <= z' - 1, s189 >= 0, s189 <= s187, z' - 1 >= 0, z = 1 + x_131 + x_220, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ 5 + 4*s190 + 4*s192 + 4*s193 + 107*x_131 + 32*x_131^2 + 107*x_139 + 32*x_139^2 + 107*x_220 + 32*x_220^2 + 107*x_225 + 32*x_225^2 }-> s196 :|: s190 >= 0, s190 <= x_131, s191 >= 0, s191 <= x_220, s192 >= 0, s192 <= s190, s193 >= 0, s193 <= x_139, s194 >= 0, s194 <= x_225, s195 >= 0, s195 <= s193, s196 >= 0, s196 <= s192, z = 1 + x_131 + x_220, z' = 1 + x_139 + x_225, x_225 >= 0, x_139 >= 0, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ 0 }-> s2 :|: s2 >= 0, s2 <= 0, z >= 0, z' >= 0
   encode_h(z, z') -{ 6 + 4*s197 + 4*s199 + 4*s200 + 107*x_131 + 32*x_131^2 + 107*x_140 + 32*x_140^2 + 107*x_220 + 32*x_220^2 + 107*x_226 + 32*x_226^2 }-> s203 :|: s197 >= 0, s197 <= x_131, s198 >= 0, s198 <= x_220, s199 >= 0, s199 <= s197, s200 >= 0, s200 <= x_140, s201 >= 0, s201 <= x_226, s202 >= 0, s202 <= s200, s203 >= 0, s203 <= s199, z = 1 + x_131 + x_220, x_226 >= 0, z' = 1 + x_140 + x_226, x_140 >= 0, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ 3 + 4*s204 + 4*s206 + 107*x_131 + 32*x_131^2 + 107*x_220 + 32*x_220^2 }-> s207 :|: s204 >= 0, s204 <= x_131, s205 >= 0, s205 <= x_220, s206 >= 0, s206 <= s204, s207 >= 0, s207 <= s206, z = 1 + x_131 + x_220, z' >= 0, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ -74 + 43*z' + 32*z'^2 }-> s209 :|: s208 >= 0, s208 <= z' - 1, s209 >= 0, s209 <= 0, z >= 0, z' - 1 >= 0
   encode_h(z, z') -{ 2 + 4*s210 + 107*x_142 + 32*x_142^2 + 107*x_227 + 32*x_227^2 }-> s213 :|: s210 >= 0, s210 <= x_142, s211 >= 0, s211 <= x_227, s212 >= 0, s212 <= s210, s213 >= 0, s213 <= 0, z >= 0, z' = 1 + x_142 + x_227, x_142 >= 0, x_227 >= 0
   encode_h(z, z') -{ 3 + 4*s214 + 107*x_143 + 32*x_143^2 + 107*x_228 + 32*x_228^2 }-> s217 :|: s214 >= 0, s214 <= x_143, s215 >= 0, s215 <= x_228, s216 >= 0, s216 <= s214, s217 >= 0, s217 <= 0, z >= 0, z' = 1 + x_143 + x_228, x_143 >= 0, x_228 >= 0
   encode_h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   g(z, z') -{ 1 + 4*z }-> s' :|: s' >= 0, s' <= z, z >= 0, z' >= 0
   h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   h(z, z') -{ -2 + 4*z }-> 1 + s :|: s >= 0, s <= z - 1, z - 1 >= 0, z' >= 0

Function symbols to be analyzed: {encode_f}, {encode_h}, {encode_g}
Previous analysis results are:
  h: runtime: O(n^1) [4*z], size: O(n^1) [z]
  g: runtime: O(n^1) [1 + 4*z], size: O(n^1) [z]
  encArg: runtime: O(n^2) [1 + 107*z + 32*z^2], size: O(n^1) [z]

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

(33) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   encArg(z) -{ 0 }-> s'' :|: s'' >= 0, s'' <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 1 }-> s1 :|: s1 >= 0, s1 <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 5 + 4*s96 + 4*s98 + 4*s99 + 107*x_115 + 32*x_115^2 + 107*x_121 + 32*x_121^2 + 107*x_213 + 32*x_213^2 + 107*x_29 + 32*x_29^2 }-> s102 :|: s96 >= 0, s96 <= x_115, s97 >= 0, s97 <= x_29, s98 >= 0, s98 <= s96, s99 >= 0, s99 <= x_121, s100 >= 0, s100 <= x_213, s101 >= 0, s101 <= s99, s102 >= 0, s102 <= s98, x_213 >= 0, x_115 >= 0, z = 1 + (1 + x_115 + x_29) + (1 + x_121 + x_213), x_29 >= 0, x_121 >= 0
   encArg(z) -{ 6 + 4*s103 + 4*s105 + 4*s106 + 107*x_115 + 32*x_115^2 + 107*x_122 + 32*x_122^2 + 107*x_214 + 32*x_214^2 + 107*x_29 + 32*x_29^2 }-> s109 :|: s103 >= 0, s103 <= x_115, s104 >= 0, s104 <= x_29, s105 >= 0, s105 <= s103, s106 >= 0, s106 <= x_122, s107 >= 0, s107 <= x_214, s108 >= 0, s108 <= s106, s109 >= 0, s109 <= s105, z = 1 + (1 + x_115 + x_29) + (1 + x_122 + x_214), x_115 >= 0, x_214 >= 0, x_122 >= 0, x_29 >= 0
   encArg(z) -{ 3 + 4*s110 + 4*s112 + 107*x_115 + 32*x_115^2 + 107*x_29 + 32*x_29^2 }-> s113 :|: s110 >= 0, s110 <= x_115, s111 >= 0, s111 <= x_29, s112 >= 0, s112 <= s110, s113 >= 0, s113 <= s112, x_115 >= 0, x_2 >= 0, z = 1 + (1 + x_115 + x_29) + x_2, x_29 >= 0
   encArg(z) -{ 5 + 4*s114 + 4*s116 + 107*x_116 + 32*x_116^2 + 107*x_123 + 32*x_123^2 + 107*x_210 + 32*x_210^2 }-> s118 :|: s114 >= 0, s114 <= x_116, s115 >= 0, s115 <= x_210, s116 >= 0, s116 <= s114, s117 >= 0, s117 <= x_123, s118 >= 0, s118 <= s116, x_123 >= 0, z = 1 + (1 + x_116 + x_210) + (1 + x_123), x_116 >= 0, x_210 >= 0
   encArg(z) -{ 7 + 4*s8 + 4*s9 + 107*x_1' + 32*x_1'^2 + 107*x_13 + 32*x_13^2 + 107*x_21 + 32*x_21^2 }-> s12 :|: s8 >= 0, s8 <= x_1', s9 >= 0, s9 <= x_13, s10 >= 0, s10 <= x_21, s11 >= 0, s11 <= s9, s12 >= 0, s12 <= 1 + s8, x_13 >= 0, x_1' >= 0, z = 1 + (1 + x_1') + (1 + x_13 + x_21), x_21 >= 0
   encArg(z) -{ 6 + 4*s119 + 4*s121 + 4*s122 + 107*x_116 + 32*x_116^2 + 107*x_124 + 32*x_124^2 + 107*x_210 + 32*x_210^2 + 107*x_215 + 32*x_215^2 }-> s125 :|: s119 >= 0, s119 <= x_116, s120 >= 0, s120 <= x_210, s121 >= 0, s121 <= s119, s122 >= 0, s122 <= x_124, s123 >= 0, s123 <= x_215, s124 >= 0, s124 <= s122, s125 >= 0, s125 <= s121, x_124 >= 0, x_215 >= 0, x_116 >= 0, z = 1 + (1 + x_116 + x_210) + (1 + x_124 + x_215), x_210 >= 0
   encArg(z) -{ 7 + 4*s126 + 4*s128 + 4*s129 + 107*x_116 + 32*x_116^2 + 107*x_125 + 32*x_125^2 + 107*x_210 + 32*x_210^2 + 107*x_216 + 32*x_216^2 }-> s132 :|: s126 >= 0, s126 <= x_116, s127 >= 0, s127 <= x_210, s128 >= 0, s128 <= s126, s129 >= 0, s129 <= x_125, s130 >= 0, s130 <= x_216, s131 >= 0, s131 <= s129, s132 >= 0, s132 <= s128, x_216 >= 0, z = 1 + (1 + x_116 + x_210) + (1 + x_125 + x_216), x_116 >= 0, x_125 >= 0, x_210 >= 0
   encArg(z) -{ 4 + 4*s133 + 4*s135 + 107*x_116 + 32*x_116^2 + 107*x_210 + 32*x_210^2 }-> s136 :|: s133 >= 0, s133 <= x_116, s134 >= 0, s134 <= x_210, s135 >= 0, s135 <= s133, s136 >= 0, s136 <= s135, x_116 >= 0, x_2 >= 0, z = 1 + (1 + x_116 + x_210) + x_2, x_210 >= 0
   encArg(z) -{ 2 + 107*x_126 + 32*x_126^2 }-> s138 :|: s137 >= 0, s137 <= x_126, s138 >= 0, s138 <= 0, x_1 >= 0, z = 1 + x_1 + (1 + x_126), x_126 >= 0
   encArg(z) -{ 3 + 4*s139 + 107*x_127 + 32*x_127^2 + 107*x_217 + 32*x_217^2 }-> s142 :|: s139 >= 0, s139 <= x_127, s140 >= 0, s140 <= x_217, s141 >= 0, s141 <= s139, s142 >= 0, s142 <= 0, x_1 >= 0, x_127 >= 0, z = 1 + x_1 + (1 + x_127 + x_217), x_217 >= 0
   encArg(z) -{ 4 + 4*s143 + 107*x_128 + 32*x_128^2 + 107*x_218 + 32*x_218^2 }-> s146 :|: s143 >= 0, s143 <= x_128, s144 >= 0, s144 <= x_218, s145 >= 0, s145 <= s143, s146 >= 0, s146 <= 0, x_1 >= 0, x_128 >= 0, z = 1 + x_1 + (1 + x_128 + x_218), x_218 >= 0
   encArg(z) -{ 8 + 4*s13 + 4*s14 + 107*x_1' + 32*x_1'^2 + 107*x_14 + 32*x_14^2 + 107*x_22 + 32*x_22^2 }-> s17 :|: s13 >= 0, s13 <= x_1', s14 >= 0, s14 <= x_14, s15 >= 0, s15 <= x_22, s16 >= 0, s16 <= s14, s17 >= 0, s17 <= 1 + s13, z = 1 + (1 + x_1') + (1 + x_14 + x_22), x_14 >= 0, x_1' >= 0, x_22 >= 0
   encArg(z) -{ 5 + 4*s18 + 107*x_1' + 32*x_1'^2 }-> s19 :|: s18 >= 0, s18 <= x_1', s19 >= 0, s19 <= 1 + s18, x_1' >= 0, x_2 >= 0, z = 1 + (1 + x_1') + x_2
   encArg(z) -{ 3 + 4*s20 + 4*s22 + 107*x_1'' + 32*x_1''^2 + 107*x_15 + 32*x_15^2 + 107*x_2' + 32*x_2'^2 }-> s24 :|: s20 >= 0, s20 <= x_1'', s21 >= 0, s21 <= x_2', s22 >= 0, s22 <= s20, s23 >= 0, s23 <= x_15, s24 >= 0, s24 <= s22, x_15 >= 0, z = 1 + (1 + x_1'' + x_2') + (1 + x_15), x_1'' >= 0, x_2' >= 0
   encArg(z) -{ 4 + 4*s25 + 4*s27 + 4*s28 + 107*x_1'' + 32*x_1''^2 + 107*x_16 + 32*x_16^2 + 107*x_2' + 32*x_2'^2 + 107*x_23 + 32*x_23^2 }-> s31 :|: s25 >= 0, s25 <= x_1'', s26 >= 0, s26 <= x_2', s27 >= 0, s27 <= s25, s28 >= 0, s28 <= x_16, s29 >= 0, s29 <= x_23, s30 >= 0, s30 <= s28, s31 >= 0, s31 <= s27, x_1'' >= 0, x_16 >= 0, x_2' >= 0, x_23 >= 0, z = 1 + (1 + x_1'' + x_2') + (1 + x_16 + x_23)
   encArg(z) -{ 5 + 4*s32 + 4*s34 + 4*s35 + 107*x_1'' + 32*x_1''^2 + 107*x_17 + 32*x_17^2 + 107*x_2' + 32*x_2'^2 + 107*x_24 + 32*x_24^2 }-> s38 :|: s32 >= 0, s32 <= x_1'', s33 >= 0, s33 <= x_2', s34 >= 0, s34 <= s32, s35 >= 0, s35 <= x_17, s36 >= 0, s36 <= x_24, s37 >= 0, s37 <= s35, s38 >= 0, s38 <= s34, x_1'' >= 0, x_2' >= 0, x_17 >= 0, x_24 >= 0, z = 1 + (1 + x_1'' + x_2') + (1 + x_17 + x_24)
   encArg(z) -{ 2 + 4*s39 + 4*s41 + 107*x_1'' + 32*x_1''^2 + 107*x_2' + 32*x_2'^2 }-> s42 :|: s39 >= 0, s39 <= x_1'', s40 >= 0, s40 <= x_2', s41 >= 0, s41 <= s39, s42 >= 0, s42 <= s41, x_1'' >= 0, x_2' >= 0, z = 1 + (1 + x_1'' + x_2') + x_2, x_2 >= 0
   encArg(z) -{ 4 + 4*s43 + 4*s45 + 107*x_11 + 32*x_11^2 + 107*x_18 + 32*x_18^2 + 107*x_2'' + 32*x_2''^2 }-> s47 :|: s43 >= 0, s43 <= x_11, s44 >= 0, s44 <= x_2'', s45 >= 0, s45 <= s43, s46 >= 0, s46 <= x_18, s47 >= 0, s47 <= s45, x_11 >= 0, z = 1 + (1 + x_11 + x_2'') + (1 + x_18), x_2'' >= 0, x_18 >= 0
   encArg(z) -{ 5 + 4*s48 + 4*s50 + 4*s51 + 107*x_11 + 32*x_11^2 + 107*x_19 + 32*x_19^2 + 107*x_2'' + 32*x_2''^2 + 107*x_25 + 32*x_25^2 }-> s54 :|: s48 >= 0, s48 <= x_11, s49 >= 0, s49 <= x_2'', s50 >= 0, s50 <= s48, s51 >= 0, s51 <= x_19, s52 >= 0, s52 <= x_25, s53 >= 0, s53 <= s51, s54 >= 0, s54 <= s50, x_11 >= 0, z = 1 + (1 + x_11 + x_2'') + (1 + x_19 + x_25), x_25 >= 0, x_2'' >= 0, x_19 >= 0
   encArg(z) -{ 6 + 4*s55 + 4*s57 + 4*s58 + 107*x_11 + 32*x_11^2 + 107*x_110 + 32*x_110^2 + 107*x_2'' + 32*x_2''^2 + 107*x_26 + 32*x_26^2 }-> s61 :|: s55 >= 0, s55 <= x_11, s56 >= 0, s56 <= x_2'', s57 >= 0, s57 <= s55, s58 >= 0, s58 <= x_110, s59 >= 0, s59 <= x_26, s60 >= 0, s60 <= s58, s61 >= 0, s61 <= s57, x_11 >= 0, x_26 >= 0, x_2'' >= 0, z = 1 + (1 + x_11 + x_2'') + (1 + x_110 + x_26), x_110 >= 0
   encArg(z) -{ 3 + 4*s62 + 4*s64 + 107*x_11 + 32*x_11^2 + 107*x_2'' + 32*x_2''^2 }-> s65 :|: s62 >= 0, s62 <= x_11, s63 >= 0, s63 <= x_2'', s64 >= 0, s64 <= s62, s65 >= 0, s65 <= s64, x_11 >= 0, x_2'' >= 0, x_2 >= 0, z = 1 + (1 + x_11 + x_2'') + x_2
   encArg(z) -{ 1 + 107*x_111 + 32*x_111^2 }-> s67 :|: s66 >= 0, s66 <= x_111, s67 >= 0, s67 <= 0, x_1 >= 0, z = 1 + x_1 + (1 + x_111), x_111 >= 0
   encArg(z) -{ 6 + 4*s5 + 107*x_1' + 32*x_1'^2 + 107*x_12 + 32*x_12^2 }-> s7 :|: s5 >= 0, s5 <= x_1', s6 >= 0, s6 <= x_12, s7 >= 0, s7 <= 1 + s5, z = 1 + (1 + x_1') + (1 + x_12), x_1' >= 0, x_12 >= 0
   encArg(z) -{ 2 + 4*s68 + 107*x_112 + 32*x_112^2 + 107*x_27 + 32*x_27^2 }-> s71 :|: s68 >= 0, s68 <= x_112, s69 >= 0, s69 <= x_27, s70 >= 0, s70 <= s68, s71 >= 0, s71 <= 0, x_1 >= 0, x_27 >= 0, z = 1 + x_1 + (1 + x_112 + x_27), x_112 >= 0
   encArg(z) -{ 3 + 4*s72 + 107*x_113 + 32*x_113^2 + 107*x_28 + 32*x_28^2 }-> s75 :|: s72 >= 0, s72 <= x_113, s73 >= 0, s73 <= x_28, s74 >= 0, s74 <= s72, s75 >= 0, s75 <= 0, x_1 >= 0, x_113 >= 0, x_28 >= 0, z = 1 + x_1 + (1 + x_113 + x_28)
   encArg(z) -{ 7 + 4*s76 + 107*x_114 + 32*x_114^2 + 107*x_117 + 32*x_117^2 }-> s78 :|: s76 >= 0, s76 <= x_114, s77 >= 0, s77 <= x_117, s78 >= 0, s78 <= 1 + s76, z = 1 + (1 + x_114) + (1 + x_117), x_117 >= 0, x_114 >= 0
   encArg(z) -{ 8 + 4*s79 + 4*s80 + 107*x_114 + 32*x_114^2 + 107*x_118 + 32*x_118^2 + 107*x_211 + 32*x_211^2 }-> s83 :|: s79 >= 0, s79 <= x_114, s80 >= 0, s80 <= x_118, s81 >= 0, s81 <= x_211, s82 >= 0, s82 <= s80, s83 >= 0, s83 <= 1 + s79, z = 1 + (1 + x_114) + (1 + x_118 + x_211), x_114 >= 0, x_118 >= 0, x_211 >= 0
   encArg(z) -{ 9 + 4*s84 + 4*s85 + 107*x_114 + 32*x_114^2 + 107*x_119 + 32*x_119^2 + 107*x_212 + 32*x_212^2 }-> s88 :|: s84 >= 0, s84 <= x_114, s85 >= 0, s85 <= x_119, s86 >= 0, s86 <= x_212, s87 >= 0, s87 <= s85, s88 >= 0, s88 <= 1 + s84, x_212 >= 0, x_114 >= 0, z = 1 + (1 + x_114) + (1 + x_119 + x_212), x_119 >= 0
   encArg(z) -{ 6 + 4*s89 + 107*x_114 + 32*x_114^2 }-> s90 :|: s89 >= 0, s89 <= x_114, s90 >= 0, s90 <= 1 + s89, z = 1 + (1 + x_114) + x_2, x_114 >= 0, x_2 >= 0
   encArg(z) -{ 4 + 4*s91 + 4*s93 + 107*x_115 + 32*x_115^2 + 107*x_120 + 32*x_120^2 + 107*x_29 + 32*x_29^2 }-> s95 :|: s91 >= 0, s91 <= x_115, s92 >= 0, s92 <= x_29, s93 >= 0, s93 <= s91, s94 >= 0, s94 <= x_120, s95 >= 0, s95 <= s93, x_120 >= 0, x_115 >= 0, z = 1 + (1 + x_115 + x_29) + (1 + x_120), x_29 >= 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ -74 + 43*z + 32*z^2 }-> 1 + s4 :|: s4 >= 0, s4 <= z - 1, z - 1 >= 0
   encode_f(z) -{ 0 }-> 0 :|: z >= 0
   encode_f(z) -{ 1 + 107*z + 32*z^2 }-> 1 + s218 :|: s218 >= 0, s218 <= z, z >= 0
   encode_g(z, z') -{ -143 + 4*s219 + 43*z + 32*z^2 + 43*z' + 32*z'^2 }-> s221 :|: s219 >= 0, s219 <= z - 1, s220 >= 0, s220 <= z' - 1, s221 >= 0, s221 <= 1 + s219, z - 1 >= 0, z' - 1 >= 0
   encode_g(z, z') -{ -67 + 4*s222 + 4*s223 + 107*x_148 + 32*x_148^2 + 107*x_231 + 32*x_231^2 + 43*z + 32*z^2 }-> s226 :|: s222 >= 0, s222 <= z - 1, s223 >= 0, s223 <= x_148, s224 >= 0, s224 <= x_231, s225 >= 0, s225 <= s223, s226 >= 0, s226 <= 1 + s222, z' = 1 + x_148 + x_231, z - 1 >= 0, x_231 >= 0, x_148 >= 0
   encode_g(z, z') -{ -66 + 4*s227 + 4*s228 + 107*x_149 + 32*x_149^2 + 107*x_232 + 32*x_232^2 + 43*z + 32*z^2 }-> s231 :|: s227 >= 0, s227 <= z - 1, s228 >= 0, s228 <= x_149, s229 >= 0, s229 <= x_232, s230 >= 0, s230 <= s228, s231 >= 0, s231 <= 1 + s227, x_232 >= 0, z - 1 >= 0, z' = 1 + x_149 + x_232, x_149 >= 0
   encode_g(z, z') -{ -69 + 4*s232 + 43*z + 32*z^2 }-> s233 :|: s232 >= 0, s232 <= z - 1, s233 >= 0, s233 <= 1 + s232, z - 1 >= 0, z' >= 0
   encode_g(z, z') -{ -71 + 4*s234 + 4*s236 + 107*x_145 + 32*x_145^2 + 107*x_229 + 32*x_229^2 + 43*z' + 32*z'^2 }-> s238 :|: s234 >= 0, s234 <= x_145, s235 >= 0, s235 <= x_229, s236 >= 0, s236 <= s234, s237 >= 0, s237 <= z' - 1, s238 >= 0, s238 <= s236, z = 1 + x_145 + x_229, x_145 >= 0, x_229 >= 0, z' - 1 >= 0
   encode_g(z, z') -{ 5 + 4*s239 + 4*s241 + 4*s242 + 107*x_145 + 32*x_145^2 + 107*x_151 + 32*x_151^2 + 107*x_229 + 32*x_229^2 + 107*x_233 + 32*x_233^2 }-> s245 :|: s239 >= 0, s239 <= x_145, s240 >= 0, s240 <= x_229, s241 >= 0, s241 <= s239, s242 >= 0, s242 <= x_151, s243 >= 0, s243 <= x_233, s244 >= 0, s244 <= s242, s245 >= 0, s245 <= s241, x_233 >= 0, z = 1 + x_145 + x_229, x_145 >= 0, x_229 >= 0, z' = 1 + x_151 + x_233, x_151 >= 0
   encode_g(z, z') -{ 6 + 4*s246 + 4*s248 + 4*s249 + 107*x_145 + 32*x_145^2 + 107*x_152 + 32*x_152^2 + 107*x_229 + 32*x_229^2 + 107*x_234 + 32*x_234^2 }-> s252 :|: s246 >= 0, s246 <= x_145, s247 >= 0, s247 <= x_229, s248 >= 0, s248 <= s246, s249 >= 0, s249 <= x_152, s250 >= 0, s250 <= x_234, s251 >= 0, s251 <= s249, s252 >= 0, s252 <= s248, z = 1 + x_145 + x_229, x_234 >= 0, x_145 >= 0, z' = 1 + x_152 + x_234, x_229 >= 0, x_152 >= 0
   encode_g(z, z') -{ 3 + 4*s253 + 4*s255 + 107*x_145 + 32*x_145^2 + 107*x_229 + 32*x_229^2 }-> s256 :|: s253 >= 0, s253 <= x_145, s254 >= 0, s254 <= x_229, s255 >= 0, s255 <= s253, s256 >= 0, s256 <= s255, z = 1 + x_145 + x_229, x_145 >= 0, x_229 >= 0, z' >= 0
   encode_g(z, z') -{ -70 + 4*s257 + 4*s259 + 107*x_146 + 32*x_146^2 + 107*x_230 + 32*x_230^2 + 43*z' + 32*z'^2 }-> s261 :|: s257 >= 0, s257 <= x_146, s258 >= 0, s258 <= x_230, s259 >= 0, s259 <= s257, s260 >= 0, s260 <= z' - 1, s261 >= 0, s261 <= s259, z = 1 + x_146 + x_230, x_146 >= 0, z' - 1 >= 0, x_230 >= 0
   encode_g(z, z') -{ 6 + 4*s262 + 4*s264 + 4*s265 + 107*x_146 + 32*x_146^2 + 107*x_154 + 32*x_154^2 + 107*x_230 + 32*x_230^2 + 107*x_235 + 32*x_235^2 }-> s268 :|: s262 >= 0, s262 <= x_146, s263 >= 0, s263 <= x_230, s264 >= 0, s264 <= s262, s265 >= 0, s265 <= x_154, s266 >= 0, s266 <= x_235, s267 >= 0, s267 <= s265, s268 >= 0, s268 <= s264, z = 1 + x_146 + x_230, x_146 >= 0, x_154 >= 0, z' = 1 + x_154 + x_235, x_235 >= 0, x_230 >= 0
   encode_g(z, z') -{ 7 + 4*s269 + 4*s271 + 4*s272 + 107*x_146 + 32*x_146^2 + 107*x_155 + 32*x_155^2 + 107*x_230 + 32*x_230^2 + 107*x_236 + 32*x_236^2 }-> s275 :|: s269 >= 0, s269 <= x_146, s270 >= 0, s270 <= x_230, s271 >= 0, s271 <= s269, s272 >= 0, s272 <= x_155, s273 >= 0, s273 <= x_236, s274 >= 0, s274 <= s272, s275 >= 0, s275 <= s271, z = 1 + x_146 + x_230, x_146 >= 0, x_155 >= 0, z' = 1 + x_155 + x_236, x_236 >= 0, x_230 >= 0
   encode_g(z, z') -{ 4 + 4*s276 + 4*s278 + 107*x_146 + 32*x_146^2 + 107*x_230 + 32*x_230^2 }-> s279 :|: s276 >= 0, s276 <= x_146, s277 >= 0, s277 <= x_230, s278 >= 0, s278 <= s276, s279 >= 0, s279 <= s278, z = 1 + x_146 + x_230, x_146 >= 0, z' >= 0, x_230 >= 0
   encode_g(z, z') -{ -73 + 43*z' + 32*z'^2 }-> s281 :|: s280 >= 0, s280 <= z' - 1, s281 >= 0, s281 <= 0, z >= 0, z' - 1 >= 0
   encode_g(z, z') -{ 3 + 4*s282 + 107*x_157 + 32*x_157^2 + 107*x_237 + 32*x_237^2 }-> s285 :|: s282 >= 0, s282 <= x_157, s283 >= 0, s283 <= x_237, s284 >= 0, s284 <= s282, s285 >= 0, s285 <= 0, x_237 >= 0, z >= 0, x_157 >= 0, z' = 1 + x_157 + x_237
   encode_g(z, z') -{ 4 + 4*s286 + 107*x_158 + 32*x_158^2 + 107*x_238 + 32*x_238^2 }-> s289 :|: s286 >= 0, s286 <= x_158, s287 >= 0, s287 <= x_238, s288 >= 0, s288 <= s286, s289 >= 0, s289 <= 0, z >= 0, z' = 1 + x_158 + x_238, x_158 >= 0, x_238 >= 0
   encode_g(z, z') -{ 1 }-> s3 :|: s3 >= 0, s3 <= 0, z >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_h(z, z') -{ -144 + 4*s147 + 43*z + 32*z^2 + 43*z' + 32*z'^2 }-> s149 :|: s147 >= 0, s147 <= z - 1, s148 >= 0, s148 <= z' - 1, s149 >= 0, s149 <= 1 + s147, z' - 1 >= 0, z - 1 >= 0
   encode_h(z, z') -{ -68 + 4*s150 + 4*s151 + 107*x_133 + 32*x_133^2 + 107*x_221 + 32*x_221^2 + 43*z + 32*z^2 }-> s154 :|: s150 >= 0, s150 <= z - 1, s151 >= 0, s151 <= x_133, s152 >= 0, s152 <= x_221, s153 >= 0, s153 <= s151, s154 >= 0, s154 <= 1 + s150, z' = 1 + x_133 + x_221, x_221 >= 0, x_133 >= 0, z - 1 >= 0
   encode_h(z, z') -{ -67 + 4*s155 + 4*s156 + 107*x_134 + 32*x_134^2 + 107*x_222 + 32*x_222^2 + 43*z + 32*z^2 }-> s159 :|: s155 >= 0, s155 <= z - 1, s156 >= 0, s156 <= x_134, s157 >= 0, s157 <= x_222, s158 >= 0, s158 <= s156, s159 >= 0, s159 <= 1 + s155, z' = 1 + x_134 + x_222, x_134 >= 0, x_222 >= 0, z - 1 >= 0
   encode_h(z, z') -{ -70 + 4*s160 + 43*z + 32*z^2 }-> s161 :|: s160 >= 0, s160 <= z - 1, s161 >= 0, s161 <= 1 + s160, z' >= 0, z - 1 >= 0
   encode_h(z, z') -{ -72 + 4*s162 + 4*s164 + 107*x_130 + 32*x_130^2 + 107*x_219 + 32*x_219^2 + 43*z' + 32*z'^2 }-> s166 :|: s162 >= 0, s162 <= x_130, s163 >= 0, s163 <= x_219, s164 >= 0, s164 <= s162, s165 >= 0, s165 <= z' - 1, s166 >= 0, s166 <= s164, x_130 >= 0, z = 1 + x_130 + x_219, z' - 1 >= 0, x_219 >= 0
   encode_h(z, z') -{ 4 + 4*s167 + 4*s169 + 4*s170 + 107*x_130 + 32*x_130^2 + 107*x_136 + 32*x_136^2 + 107*x_219 + 32*x_219^2 + 107*x_223 + 32*x_223^2 }-> s173 :|: s167 >= 0, s167 <= x_130, s168 >= 0, s168 <= x_219, s169 >= 0, s169 <= s167, s170 >= 0, s170 <= x_136, s171 >= 0, s171 <= x_223, s172 >= 0, s172 <= s170, s173 >= 0, s173 <= s169, z' = 1 + x_136 + x_223, x_130 >= 0, z = 1 + x_130 + x_219, x_223 >= 0, x_136 >= 0, x_219 >= 0
   encode_h(z, z') -{ 5 + 4*s174 + 4*s176 + 4*s177 + 107*x_130 + 32*x_130^2 + 107*x_137 + 32*x_137^2 + 107*x_219 + 32*x_219^2 + 107*x_224 + 32*x_224^2 }-> s180 :|: s174 >= 0, s174 <= x_130, s175 >= 0, s175 <= x_219, s176 >= 0, s176 <= s174, s177 >= 0, s177 <= x_137, s178 >= 0, s178 <= x_224, s179 >= 0, s179 <= s177, s180 >= 0, s180 <= s176, z' = 1 + x_137 + x_224, x_130 >= 0, z = 1 + x_130 + x_219, x_224 >= 0, x_137 >= 0, x_219 >= 0
   encode_h(z, z') -{ 2 + 4*s181 + 4*s183 + 107*x_130 + 32*x_130^2 + 107*x_219 + 32*x_219^2 }-> s184 :|: s181 >= 0, s181 <= x_130, s182 >= 0, s182 <= x_219, s183 >= 0, s183 <= s181, s184 >= 0, s184 <= s183, x_130 >= 0, z = 1 + x_130 + x_219, z' >= 0, x_219 >= 0
   encode_h(z, z') -{ -71 + 4*s185 + 4*s187 + 107*x_131 + 32*x_131^2 + 107*x_220 + 32*x_220^2 + 43*z' + 32*z'^2 }-> s189 :|: s185 >= 0, s185 <= x_131, s186 >= 0, s186 <= x_220, s187 >= 0, s187 <= s185, s188 >= 0, s188 <= z' - 1, s189 >= 0, s189 <= s187, z' - 1 >= 0, z = 1 + x_131 + x_220, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ 5 + 4*s190 + 4*s192 + 4*s193 + 107*x_131 + 32*x_131^2 + 107*x_139 + 32*x_139^2 + 107*x_220 + 32*x_220^2 + 107*x_225 + 32*x_225^2 }-> s196 :|: s190 >= 0, s190 <= x_131, s191 >= 0, s191 <= x_220, s192 >= 0, s192 <= s190, s193 >= 0, s193 <= x_139, s194 >= 0, s194 <= x_225, s195 >= 0, s195 <= s193, s196 >= 0, s196 <= s192, z = 1 + x_131 + x_220, z' = 1 + x_139 + x_225, x_225 >= 0, x_139 >= 0, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ 0 }-> s2 :|: s2 >= 0, s2 <= 0, z >= 0, z' >= 0
   encode_h(z, z') -{ 6 + 4*s197 + 4*s199 + 4*s200 + 107*x_131 + 32*x_131^2 + 107*x_140 + 32*x_140^2 + 107*x_220 + 32*x_220^2 + 107*x_226 + 32*x_226^2 }-> s203 :|: s197 >= 0, s197 <= x_131, s198 >= 0, s198 <= x_220, s199 >= 0, s199 <= s197, s200 >= 0, s200 <= x_140, s201 >= 0, s201 <= x_226, s202 >= 0, s202 <= s200, s203 >= 0, s203 <= s199, z = 1 + x_131 + x_220, x_226 >= 0, z' = 1 + x_140 + x_226, x_140 >= 0, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ 3 + 4*s204 + 4*s206 + 107*x_131 + 32*x_131^2 + 107*x_220 + 32*x_220^2 }-> s207 :|: s204 >= 0, s204 <= x_131, s205 >= 0, s205 <= x_220, s206 >= 0, s206 <= s204, s207 >= 0, s207 <= s206, z = 1 + x_131 + x_220, z' >= 0, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ -74 + 43*z' + 32*z'^2 }-> s209 :|: s208 >= 0, s208 <= z' - 1, s209 >= 0, s209 <= 0, z >= 0, z' - 1 >= 0
   encode_h(z, z') -{ 2 + 4*s210 + 107*x_142 + 32*x_142^2 + 107*x_227 + 32*x_227^2 }-> s213 :|: s210 >= 0, s210 <= x_142, s211 >= 0, s211 <= x_227, s212 >= 0, s212 <= s210, s213 >= 0, s213 <= 0, z >= 0, z' = 1 + x_142 + x_227, x_142 >= 0, x_227 >= 0
   encode_h(z, z') -{ 3 + 4*s214 + 107*x_143 + 32*x_143^2 + 107*x_228 + 32*x_228^2 }-> s217 :|: s214 >= 0, s214 <= x_143, s215 >= 0, s215 <= x_228, s216 >= 0, s216 <= s214, s217 >= 0, s217 <= 0, z >= 0, z' = 1 + x_143 + x_228, x_143 >= 0, x_228 >= 0
   encode_h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   g(z, z') -{ 1 + 4*z }-> s' :|: s' >= 0, s' <= z, z >= 0, z' >= 0
   h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   h(z, z') -{ -2 + 4*z }-> 1 + s :|: s >= 0, s <= z - 1, z - 1 >= 0, z' >= 0

Function symbols to be analyzed: {encode_f}, {encode_h}, {encode_g}
Previous analysis results are:
  h: runtime: O(n^1) [4*z], size: O(n^1) [z]
  g: runtime: O(n^1) [1 + 4*z], size: O(n^1) [z]
  encArg: runtime: O(n^2) [1 + 107*z + 32*z^2], size: O(n^1) [z]
  encode_f: runtime: ?, size: O(n^1) [1 + z]

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

(35) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using KoAT for: encode_f
after applying outer abstraction to obtain an ITS,
resulting in: O(n^2) with polynomial bound: 1 + 107*z + 32*z^2

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

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

   encArg(z) -{ 0 }-> s'' :|: s'' >= 0, s'' <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 1 }-> s1 :|: s1 >= 0, s1 <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 5 + 4*s96 + 4*s98 + 4*s99 + 107*x_115 + 32*x_115^2 + 107*x_121 + 32*x_121^2 + 107*x_213 + 32*x_213^2 + 107*x_29 + 32*x_29^2 }-> s102 :|: s96 >= 0, s96 <= x_115, s97 >= 0, s97 <= x_29, s98 >= 0, s98 <= s96, s99 >= 0, s99 <= x_121, s100 >= 0, s100 <= x_213, s101 >= 0, s101 <= s99, s102 >= 0, s102 <= s98, x_213 >= 0, x_115 >= 0, z = 1 + (1 + x_115 + x_29) + (1 + x_121 + x_213), x_29 >= 0, x_121 >= 0
   encArg(z) -{ 6 + 4*s103 + 4*s105 + 4*s106 + 107*x_115 + 32*x_115^2 + 107*x_122 + 32*x_122^2 + 107*x_214 + 32*x_214^2 + 107*x_29 + 32*x_29^2 }-> s109 :|: s103 >= 0, s103 <= x_115, s104 >= 0, s104 <= x_29, s105 >= 0, s105 <= s103, s106 >= 0, s106 <= x_122, s107 >= 0, s107 <= x_214, s108 >= 0, s108 <= s106, s109 >= 0, s109 <= s105, z = 1 + (1 + x_115 + x_29) + (1 + x_122 + x_214), x_115 >= 0, x_214 >= 0, x_122 >= 0, x_29 >= 0
   encArg(z) -{ 3 + 4*s110 + 4*s112 + 107*x_115 + 32*x_115^2 + 107*x_29 + 32*x_29^2 }-> s113 :|: s110 >= 0, s110 <= x_115, s111 >= 0, s111 <= x_29, s112 >= 0, s112 <= s110, s113 >= 0, s113 <= s112, x_115 >= 0, x_2 >= 0, z = 1 + (1 + x_115 + x_29) + x_2, x_29 >= 0
   encArg(z) -{ 5 + 4*s114 + 4*s116 + 107*x_116 + 32*x_116^2 + 107*x_123 + 32*x_123^2 + 107*x_210 + 32*x_210^2 }-> s118 :|: s114 >= 0, s114 <= x_116, s115 >= 0, s115 <= x_210, s116 >= 0, s116 <= s114, s117 >= 0, s117 <= x_123, s118 >= 0, s118 <= s116, x_123 >= 0, z = 1 + (1 + x_116 + x_210) + (1 + x_123), x_116 >= 0, x_210 >= 0
   encArg(z) -{ 7 + 4*s8 + 4*s9 + 107*x_1' + 32*x_1'^2 + 107*x_13 + 32*x_13^2 + 107*x_21 + 32*x_21^2 }-> s12 :|: s8 >= 0, s8 <= x_1', s9 >= 0, s9 <= x_13, s10 >= 0, s10 <= x_21, s11 >= 0, s11 <= s9, s12 >= 0, s12 <= 1 + s8, x_13 >= 0, x_1' >= 0, z = 1 + (1 + x_1') + (1 + x_13 + x_21), x_21 >= 0
   encArg(z) -{ 6 + 4*s119 + 4*s121 + 4*s122 + 107*x_116 + 32*x_116^2 + 107*x_124 + 32*x_124^2 + 107*x_210 + 32*x_210^2 + 107*x_215 + 32*x_215^2 }-> s125 :|: s119 >= 0, s119 <= x_116, s120 >= 0, s120 <= x_210, s121 >= 0, s121 <= s119, s122 >= 0, s122 <= x_124, s123 >= 0, s123 <= x_215, s124 >= 0, s124 <= s122, s125 >= 0, s125 <= s121, x_124 >= 0, x_215 >= 0, x_116 >= 0, z = 1 + (1 + x_116 + x_210) + (1 + x_124 + x_215), x_210 >= 0
   encArg(z) -{ 7 + 4*s126 + 4*s128 + 4*s129 + 107*x_116 + 32*x_116^2 + 107*x_125 + 32*x_125^2 + 107*x_210 + 32*x_210^2 + 107*x_216 + 32*x_216^2 }-> s132 :|: s126 >= 0, s126 <= x_116, s127 >= 0, s127 <= x_210, s128 >= 0, s128 <= s126, s129 >= 0, s129 <= x_125, s130 >= 0, s130 <= x_216, s131 >= 0, s131 <= s129, s132 >= 0, s132 <= s128, x_216 >= 0, z = 1 + (1 + x_116 + x_210) + (1 + x_125 + x_216), x_116 >= 0, x_125 >= 0, x_210 >= 0
   encArg(z) -{ 4 + 4*s133 + 4*s135 + 107*x_116 + 32*x_116^2 + 107*x_210 + 32*x_210^2 }-> s136 :|: s133 >= 0, s133 <= x_116, s134 >= 0, s134 <= x_210, s135 >= 0, s135 <= s133, s136 >= 0, s136 <= s135, x_116 >= 0, x_2 >= 0, z = 1 + (1 + x_116 + x_210) + x_2, x_210 >= 0
   encArg(z) -{ 2 + 107*x_126 + 32*x_126^2 }-> s138 :|: s137 >= 0, s137 <= x_126, s138 >= 0, s138 <= 0, x_1 >= 0, z = 1 + x_1 + (1 + x_126), x_126 >= 0
   encArg(z) -{ 3 + 4*s139 + 107*x_127 + 32*x_127^2 + 107*x_217 + 32*x_217^2 }-> s142 :|: s139 >= 0, s139 <= x_127, s140 >= 0, s140 <= x_217, s141 >= 0, s141 <= s139, s142 >= 0, s142 <= 0, x_1 >= 0, x_127 >= 0, z = 1 + x_1 + (1 + x_127 + x_217), x_217 >= 0
   encArg(z) -{ 4 + 4*s143 + 107*x_128 + 32*x_128^2 + 107*x_218 + 32*x_218^2 }-> s146 :|: s143 >= 0, s143 <= x_128, s144 >= 0, s144 <= x_218, s145 >= 0, s145 <= s143, s146 >= 0, s146 <= 0, x_1 >= 0, x_128 >= 0, z = 1 + x_1 + (1 + x_128 + x_218), x_218 >= 0
   encArg(z) -{ 8 + 4*s13 + 4*s14 + 107*x_1' + 32*x_1'^2 + 107*x_14 + 32*x_14^2 + 107*x_22 + 32*x_22^2 }-> s17 :|: s13 >= 0, s13 <= x_1', s14 >= 0, s14 <= x_14, s15 >= 0, s15 <= x_22, s16 >= 0, s16 <= s14, s17 >= 0, s17 <= 1 + s13, z = 1 + (1 + x_1') + (1 + x_14 + x_22), x_14 >= 0, x_1' >= 0, x_22 >= 0
   encArg(z) -{ 5 + 4*s18 + 107*x_1' + 32*x_1'^2 }-> s19 :|: s18 >= 0, s18 <= x_1', s19 >= 0, s19 <= 1 + s18, x_1' >= 0, x_2 >= 0, z = 1 + (1 + x_1') + x_2
   encArg(z) -{ 3 + 4*s20 + 4*s22 + 107*x_1'' + 32*x_1''^2 + 107*x_15 + 32*x_15^2 + 107*x_2' + 32*x_2'^2 }-> s24 :|: s20 >= 0, s20 <= x_1'', s21 >= 0, s21 <= x_2', s22 >= 0, s22 <= s20, s23 >= 0, s23 <= x_15, s24 >= 0, s24 <= s22, x_15 >= 0, z = 1 + (1 + x_1'' + x_2') + (1 + x_15), x_1'' >= 0, x_2' >= 0
   encArg(z) -{ 4 + 4*s25 + 4*s27 + 4*s28 + 107*x_1'' + 32*x_1''^2 + 107*x_16 + 32*x_16^2 + 107*x_2' + 32*x_2'^2 + 107*x_23 + 32*x_23^2 }-> s31 :|: s25 >= 0, s25 <= x_1'', s26 >= 0, s26 <= x_2', s27 >= 0, s27 <= s25, s28 >= 0, s28 <= x_16, s29 >= 0, s29 <= x_23, s30 >= 0, s30 <= s28, s31 >= 0, s31 <= s27, x_1'' >= 0, x_16 >= 0, x_2' >= 0, x_23 >= 0, z = 1 + (1 + x_1'' + x_2') + (1 + x_16 + x_23)
   encArg(z) -{ 5 + 4*s32 + 4*s34 + 4*s35 + 107*x_1'' + 32*x_1''^2 + 107*x_17 + 32*x_17^2 + 107*x_2' + 32*x_2'^2 + 107*x_24 + 32*x_24^2 }-> s38 :|: s32 >= 0, s32 <= x_1'', s33 >= 0, s33 <= x_2', s34 >= 0, s34 <= s32, s35 >= 0, s35 <= x_17, s36 >= 0, s36 <= x_24, s37 >= 0, s37 <= s35, s38 >= 0, s38 <= s34, x_1'' >= 0, x_2' >= 0, x_17 >= 0, x_24 >= 0, z = 1 + (1 + x_1'' + x_2') + (1 + x_17 + x_24)
   encArg(z) -{ 2 + 4*s39 + 4*s41 + 107*x_1'' + 32*x_1''^2 + 107*x_2' + 32*x_2'^2 }-> s42 :|: s39 >= 0, s39 <= x_1'', s40 >= 0, s40 <= x_2', s41 >= 0, s41 <= s39, s42 >= 0, s42 <= s41, x_1'' >= 0, x_2' >= 0, z = 1 + (1 + x_1'' + x_2') + x_2, x_2 >= 0
   encArg(z) -{ 4 + 4*s43 + 4*s45 + 107*x_11 + 32*x_11^2 + 107*x_18 + 32*x_18^2 + 107*x_2'' + 32*x_2''^2 }-> s47 :|: s43 >= 0, s43 <= x_11, s44 >= 0, s44 <= x_2'', s45 >= 0, s45 <= s43, s46 >= 0, s46 <= x_18, s47 >= 0, s47 <= s45, x_11 >= 0, z = 1 + (1 + x_11 + x_2'') + (1 + x_18), x_2'' >= 0, x_18 >= 0
   encArg(z) -{ 5 + 4*s48 + 4*s50 + 4*s51 + 107*x_11 + 32*x_11^2 + 107*x_19 + 32*x_19^2 + 107*x_2'' + 32*x_2''^2 + 107*x_25 + 32*x_25^2 }-> s54 :|: s48 >= 0, s48 <= x_11, s49 >= 0, s49 <= x_2'', s50 >= 0, s50 <= s48, s51 >= 0, s51 <= x_19, s52 >= 0, s52 <= x_25, s53 >= 0, s53 <= s51, s54 >= 0, s54 <= s50, x_11 >= 0, z = 1 + (1 + x_11 + x_2'') + (1 + x_19 + x_25), x_25 >= 0, x_2'' >= 0, x_19 >= 0
   encArg(z) -{ 6 + 4*s55 + 4*s57 + 4*s58 + 107*x_11 + 32*x_11^2 + 107*x_110 + 32*x_110^2 + 107*x_2'' + 32*x_2''^2 + 107*x_26 + 32*x_26^2 }-> s61 :|: s55 >= 0, s55 <= x_11, s56 >= 0, s56 <= x_2'', s57 >= 0, s57 <= s55, s58 >= 0, s58 <= x_110, s59 >= 0, s59 <= x_26, s60 >= 0, s60 <= s58, s61 >= 0, s61 <= s57, x_11 >= 0, x_26 >= 0, x_2'' >= 0, z = 1 + (1 + x_11 + x_2'') + (1 + x_110 + x_26), x_110 >= 0
   encArg(z) -{ 3 + 4*s62 + 4*s64 + 107*x_11 + 32*x_11^2 + 107*x_2'' + 32*x_2''^2 }-> s65 :|: s62 >= 0, s62 <= x_11, s63 >= 0, s63 <= x_2'', s64 >= 0, s64 <= s62, s65 >= 0, s65 <= s64, x_11 >= 0, x_2'' >= 0, x_2 >= 0, z = 1 + (1 + x_11 + x_2'') + x_2
   encArg(z) -{ 1 + 107*x_111 + 32*x_111^2 }-> s67 :|: s66 >= 0, s66 <= x_111, s67 >= 0, s67 <= 0, x_1 >= 0, z = 1 + x_1 + (1 + x_111), x_111 >= 0
   encArg(z) -{ 6 + 4*s5 + 107*x_1' + 32*x_1'^2 + 107*x_12 + 32*x_12^2 }-> s7 :|: s5 >= 0, s5 <= x_1', s6 >= 0, s6 <= x_12, s7 >= 0, s7 <= 1 + s5, z = 1 + (1 + x_1') + (1 + x_12), x_1' >= 0, x_12 >= 0
   encArg(z) -{ 2 + 4*s68 + 107*x_112 + 32*x_112^2 + 107*x_27 + 32*x_27^2 }-> s71 :|: s68 >= 0, s68 <= x_112, s69 >= 0, s69 <= x_27, s70 >= 0, s70 <= s68, s71 >= 0, s71 <= 0, x_1 >= 0, x_27 >= 0, z = 1 + x_1 + (1 + x_112 + x_27), x_112 >= 0
   encArg(z) -{ 3 + 4*s72 + 107*x_113 + 32*x_113^2 + 107*x_28 + 32*x_28^2 }-> s75 :|: s72 >= 0, s72 <= x_113, s73 >= 0, s73 <= x_28, s74 >= 0, s74 <= s72, s75 >= 0, s75 <= 0, x_1 >= 0, x_113 >= 0, x_28 >= 0, z = 1 + x_1 + (1 + x_113 + x_28)
   encArg(z) -{ 7 + 4*s76 + 107*x_114 + 32*x_114^2 + 107*x_117 + 32*x_117^2 }-> s78 :|: s76 >= 0, s76 <= x_114, s77 >= 0, s77 <= x_117, s78 >= 0, s78 <= 1 + s76, z = 1 + (1 + x_114) + (1 + x_117), x_117 >= 0, x_114 >= 0
   encArg(z) -{ 8 + 4*s79 + 4*s80 + 107*x_114 + 32*x_114^2 + 107*x_118 + 32*x_118^2 + 107*x_211 + 32*x_211^2 }-> s83 :|: s79 >= 0, s79 <= x_114, s80 >= 0, s80 <= x_118, s81 >= 0, s81 <= x_211, s82 >= 0, s82 <= s80, s83 >= 0, s83 <= 1 + s79, z = 1 + (1 + x_114) + (1 + x_118 + x_211), x_114 >= 0, x_118 >= 0, x_211 >= 0
   encArg(z) -{ 9 + 4*s84 + 4*s85 + 107*x_114 + 32*x_114^2 + 107*x_119 + 32*x_119^2 + 107*x_212 + 32*x_212^2 }-> s88 :|: s84 >= 0, s84 <= x_114, s85 >= 0, s85 <= x_119, s86 >= 0, s86 <= x_212, s87 >= 0, s87 <= s85, s88 >= 0, s88 <= 1 + s84, x_212 >= 0, x_114 >= 0, z = 1 + (1 + x_114) + (1 + x_119 + x_212), x_119 >= 0
   encArg(z) -{ 6 + 4*s89 + 107*x_114 + 32*x_114^2 }-> s90 :|: s89 >= 0, s89 <= x_114, s90 >= 0, s90 <= 1 + s89, z = 1 + (1 + x_114) + x_2, x_114 >= 0, x_2 >= 0
   encArg(z) -{ 4 + 4*s91 + 4*s93 + 107*x_115 + 32*x_115^2 + 107*x_120 + 32*x_120^2 + 107*x_29 + 32*x_29^2 }-> s95 :|: s91 >= 0, s91 <= x_115, s92 >= 0, s92 <= x_29, s93 >= 0, s93 <= s91, s94 >= 0, s94 <= x_120, s95 >= 0, s95 <= s93, x_120 >= 0, x_115 >= 0, z = 1 + (1 + x_115 + x_29) + (1 + x_120), x_29 >= 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ -74 + 43*z + 32*z^2 }-> 1 + s4 :|: s4 >= 0, s4 <= z - 1, z - 1 >= 0
   encode_f(z) -{ 0 }-> 0 :|: z >= 0
   encode_f(z) -{ 1 + 107*z + 32*z^2 }-> 1 + s218 :|: s218 >= 0, s218 <= z, z >= 0
   encode_g(z, z') -{ -143 + 4*s219 + 43*z + 32*z^2 + 43*z' + 32*z'^2 }-> s221 :|: s219 >= 0, s219 <= z - 1, s220 >= 0, s220 <= z' - 1, s221 >= 0, s221 <= 1 + s219, z - 1 >= 0, z' - 1 >= 0
   encode_g(z, z') -{ -67 + 4*s222 + 4*s223 + 107*x_148 + 32*x_148^2 + 107*x_231 + 32*x_231^2 + 43*z + 32*z^2 }-> s226 :|: s222 >= 0, s222 <= z - 1, s223 >= 0, s223 <= x_148, s224 >= 0, s224 <= x_231, s225 >= 0, s225 <= s223, s226 >= 0, s226 <= 1 + s222, z' = 1 + x_148 + x_231, z - 1 >= 0, x_231 >= 0, x_148 >= 0
   encode_g(z, z') -{ -66 + 4*s227 + 4*s228 + 107*x_149 + 32*x_149^2 + 107*x_232 + 32*x_232^2 + 43*z + 32*z^2 }-> s231 :|: s227 >= 0, s227 <= z - 1, s228 >= 0, s228 <= x_149, s229 >= 0, s229 <= x_232, s230 >= 0, s230 <= s228, s231 >= 0, s231 <= 1 + s227, x_232 >= 0, z - 1 >= 0, z' = 1 + x_149 + x_232, x_149 >= 0
   encode_g(z, z') -{ -69 + 4*s232 + 43*z + 32*z^2 }-> s233 :|: s232 >= 0, s232 <= z - 1, s233 >= 0, s233 <= 1 + s232, z - 1 >= 0, z' >= 0
   encode_g(z, z') -{ -71 + 4*s234 + 4*s236 + 107*x_145 + 32*x_145^2 + 107*x_229 + 32*x_229^2 + 43*z' + 32*z'^2 }-> s238 :|: s234 >= 0, s234 <= x_145, s235 >= 0, s235 <= x_229, s236 >= 0, s236 <= s234, s237 >= 0, s237 <= z' - 1, s238 >= 0, s238 <= s236, z = 1 + x_145 + x_229, x_145 >= 0, x_229 >= 0, z' - 1 >= 0
   encode_g(z, z') -{ 5 + 4*s239 + 4*s241 + 4*s242 + 107*x_145 + 32*x_145^2 + 107*x_151 + 32*x_151^2 + 107*x_229 + 32*x_229^2 + 107*x_233 + 32*x_233^2 }-> s245 :|: s239 >= 0, s239 <= x_145, s240 >= 0, s240 <= x_229, s241 >= 0, s241 <= s239, s242 >= 0, s242 <= x_151, s243 >= 0, s243 <= x_233, s244 >= 0, s244 <= s242, s245 >= 0, s245 <= s241, x_233 >= 0, z = 1 + x_145 + x_229, x_145 >= 0, x_229 >= 0, z' = 1 + x_151 + x_233, x_151 >= 0
   encode_g(z, z') -{ 6 + 4*s246 + 4*s248 + 4*s249 + 107*x_145 + 32*x_145^2 + 107*x_152 + 32*x_152^2 + 107*x_229 + 32*x_229^2 + 107*x_234 + 32*x_234^2 }-> s252 :|: s246 >= 0, s246 <= x_145, s247 >= 0, s247 <= x_229, s248 >= 0, s248 <= s246, s249 >= 0, s249 <= x_152, s250 >= 0, s250 <= x_234, s251 >= 0, s251 <= s249, s252 >= 0, s252 <= s248, z = 1 + x_145 + x_229, x_234 >= 0, x_145 >= 0, z' = 1 + x_152 + x_234, x_229 >= 0, x_152 >= 0
   encode_g(z, z') -{ 3 + 4*s253 + 4*s255 + 107*x_145 + 32*x_145^2 + 107*x_229 + 32*x_229^2 }-> s256 :|: s253 >= 0, s253 <= x_145, s254 >= 0, s254 <= x_229, s255 >= 0, s255 <= s253, s256 >= 0, s256 <= s255, z = 1 + x_145 + x_229, x_145 >= 0, x_229 >= 0, z' >= 0
   encode_g(z, z') -{ -70 + 4*s257 + 4*s259 + 107*x_146 + 32*x_146^2 + 107*x_230 + 32*x_230^2 + 43*z' + 32*z'^2 }-> s261 :|: s257 >= 0, s257 <= x_146, s258 >= 0, s258 <= x_230, s259 >= 0, s259 <= s257, s260 >= 0, s260 <= z' - 1, s261 >= 0, s261 <= s259, z = 1 + x_146 + x_230, x_146 >= 0, z' - 1 >= 0, x_230 >= 0
   encode_g(z, z') -{ 6 + 4*s262 + 4*s264 + 4*s265 + 107*x_146 + 32*x_146^2 + 107*x_154 + 32*x_154^2 + 107*x_230 + 32*x_230^2 + 107*x_235 + 32*x_235^2 }-> s268 :|: s262 >= 0, s262 <= x_146, s263 >= 0, s263 <= x_230, s264 >= 0, s264 <= s262, s265 >= 0, s265 <= x_154, s266 >= 0, s266 <= x_235, s267 >= 0, s267 <= s265, s268 >= 0, s268 <= s264, z = 1 + x_146 + x_230, x_146 >= 0, x_154 >= 0, z' = 1 + x_154 + x_235, x_235 >= 0, x_230 >= 0
   encode_g(z, z') -{ 7 + 4*s269 + 4*s271 + 4*s272 + 107*x_146 + 32*x_146^2 + 107*x_155 + 32*x_155^2 + 107*x_230 + 32*x_230^2 + 107*x_236 + 32*x_236^2 }-> s275 :|: s269 >= 0, s269 <= x_146, s270 >= 0, s270 <= x_230, s271 >= 0, s271 <= s269, s272 >= 0, s272 <= x_155, s273 >= 0, s273 <= x_236, s274 >= 0, s274 <= s272, s275 >= 0, s275 <= s271, z = 1 + x_146 + x_230, x_146 >= 0, x_155 >= 0, z' = 1 + x_155 + x_236, x_236 >= 0, x_230 >= 0
   encode_g(z, z') -{ 4 + 4*s276 + 4*s278 + 107*x_146 + 32*x_146^2 + 107*x_230 + 32*x_230^2 }-> s279 :|: s276 >= 0, s276 <= x_146, s277 >= 0, s277 <= x_230, s278 >= 0, s278 <= s276, s279 >= 0, s279 <= s278, z = 1 + x_146 + x_230, x_146 >= 0, z' >= 0, x_230 >= 0
   encode_g(z, z') -{ -73 + 43*z' + 32*z'^2 }-> s281 :|: s280 >= 0, s280 <= z' - 1, s281 >= 0, s281 <= 0, z >= 0, z' - 1 >= 0
   encode_g(z, z') -{ 3 + 4*s282 + 107*x_157 + 32*x_157^2 + 107*x_237 + 32*x_237^2 }-> s285 :|: s282 >= 0, s282 <= x_157, s283 >= 0, s283 <= x_237, s284 >= 0, s284 <= s282, s285 >= 0, s285 <= 0, x_237 >= 0, z >= 0, x_157 >= 0, z' = 1 + x_157 + x_237
   encode_g(z, z') -{ 4 + 4*s286 + 107*x_158 + 32*x_158^2 + 107*x_238 + 32*x_238^2 }-> s289 :|: s286 >= 0, s286 <= x_158, s287 >= 0, s287 <= x_238, s288 >= 0, s288 <= s286, s289 >= 0, s289 <= 0, z >= 0, z' = 1 + x_158 + x_238, x_158 >= 0, x_238 >= 0
   encode_g(z, z') -{ 1 }-> s3 :|: s3 >= 0, s3 <= 0, z >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_h(z, z') -{ -144 + 4*s147 + 43*z + 32*z^2 + 43*z' + 32*z'^2 }-> s149 :|: s147 >= 0, s147 <= z - 1, s148 >= 0, s148 <= z' - 1, s149 >= 0, s149 <= 1 + s147, z' - 1 >= 0, z - 1 >= 0
   encode_h(z, z') -{ -68 + 4*s150 + 4*s151 + 107*x_133 + 32*x_133^2 + 107*x_221 + 32*x_221^2 + 43*z + 32*z^2 }-> s154 :|: s150 >= 0, s150 <= z - 1, s151 >= 0, s151 <= x_133, s152 >= 0, s152 <= x_221, s153 >= 0, s153 <= s151, s154 >= 0, s154 <= 1 + s150, z' = 1 + x_133 + x_221, x_221 >= 0, x_133 >= 0, z - 1 >= 0
   encode_h(z, z') -{ -67 + 4*s155 + 4*s156 + 107*x_134 + 32*x_134^2 + 107*x_222 + 32*x_222^2 + 43*z + 32*z^2 }-> s159 :|: s155 >= 0, s155 <= z - 1, s156 >= 0, s156 <= x_134, s157 >= 0, s157 <= x_222, s158 >= 0, s158 <= s156, s159 >= 0, s159 <= 1 + s155, z' = 1 + x_134 + x_222, x_134 >= 0, x_222 >= 0, z - 1 >= 0
   encode_h(z, z') -{ -70 + 4*s160 + 43*z + 32*z^2 }-> s161 :|: s160 >= 0, s160 <= z - 1, s161 >= 0, s161 <= 1 + s160, z' >= 0, z - 1 >= 0
   encode_h(z, z') -{ -72 + 4*s162 + 4*s164 + 107*x_130 + 32*x_130^2 + 107*x_219 + 32*x_219^2 + 43*z' + 32*z'^2 }-> s166 :|: s162 >= 0, s162 <= x_130, s163 >= 0, s163 <= x_219, s164 >= 0, s164 <= s162, s165 >= 0, s165 <= z' - 1, s166 >= 0, s166 <= s164, x_130 >= 0, z = 1 + x_130 + x_219, z' - 1 >= 0, x_219 >= 0
   encode_h(z, z') -{ 4 + 4*s167 + 4*s169 + 4*s170 + 107*x_130 + 32*x_130^2 + 107*x_136 + 32*x_136^2 + 107*x_219 + 32*x_219^2 + 107*x_223 + 32*x_223^2 }-> s173 :|: s167 >= 0, s167 <= x_130, s168 >= 0, s168 <= x_219, s169 >= 0, s169 <= s167, s170 >= 0, s170 <= x_136, s171 >= 0, s171 <= x_223, s172 >= 0, s172 <= s170, s173 >= 0, s173 <= s169, z' = 1 + x_136 + x_223, x_130 >= 0, z = 1 + x_130 + x_219, x_223 >= 0, x_136 >= 0, x_219 >= 0
   encode_h(z, z') -{ 5 + 4*s174 + 4*s176 + 4*s177 + 107*x_130 + 32*x_130^2 + 107*x_137 + 32*x_137^2 + 107*x_219 + 32*x_219^2 + 107*x_224 + 32*x_224^2 }-> s180 :|: s174 >= 0, s174 <= x_130, s175 >= 0, s175 <= x_219, s176 >= 0, s176 <= s174, s177 >= 0, s177 <= x_137, s178 >= 0, s178 <= x_224, s179 >= 0, s179 <= s177, s180 >= 0, s180 <= s176, z' = 1 + x_137 + x_224, x_130 >= 0, z = 1 + x_130 + x_219, x_224 >= 0, x_137 >= 0, x_219 >= 0
   encode_h(z, z') -{ 2 + 4*s181 + 4*s183 + 107*x_130 + 32*x_130^2 + 107*x_219 + 32*x_219^2 }-> s184 :|: s181 >= 0, s181 <= x_130, s182 >= 0, s182 <= x_219, s183 >= 0, s183 <= s181, s184 >= 0, s184 <= s183, x_130 >= 0, z = 1 + x_130 + x_219, z' >= 0, x_219 >= 0
   encode_h(z, z') -{ -71 + 4*s185 + 4*s187 + 107*x_131 + 32*x_131^2 + 107*x_220 + 32*x_220^2 + 43*z' + 32*z'^2 }-> s189 :|: s185 >= 0, s185 <= x_131, s186 >= 0, s186 <= x_220, s187 >= 0, s187 <= s185, s188 >= 0, s188 <= z' - 1, s189 >= 0, s189 <= s187, z' - 1 >= 0, z = 1 + x_131 + x_220, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ 5 + 4*s190 + 4*s192 + 4*s193 + 107*x_131 + 32*x_131^2 + 107*x_139 + 32*x_139^2 + 107*x_220 + 32*x_220^2 + 107*x_225 + 32*x_225^2 }-> s196 :|: s190 >= 0, s190 <= x_131, s191 >= 0, s191 <= x_220, s192 >= 0, s192 <= s190, s193 >= 0, s193 <= x_139, s194 >= 0, s194 <= x_225, s195 >= 0, s195 <= s193, s196 >= 0, s196 <= s192, z = 1 + x_131 + x_220, z' = 1 + x_139 + x_225, x_225 >= 0, x_139 >= 0, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ 0 }-> s2 :|: s2 >= 0, s2 <= 0, z >= 0, z' >= 0
   encode_h(z, z') -{ 6 + 4*s197 + 4*s199 + 4*s200 + 107*x_131 + 32*x_131^2 + 107*x_140 + 32*x_140^2 + 107*x_220 + 32*x_220^2 + 107*x_226 + 32*x_226^2 }-> s203 :|: s197 >= 0, s197 <= x_131, s198 >= 0, s198 <= x_220, s199 >= 0, s199 <= s197, s200 >= 0, s200 <= x_140, s201 >= 0, s201 <= x_226, s202 >= 0, s202 <= s200, s203 >= 0, s203 <= s199, z = 1 + x_131 + x_220, x_226 >= 0, z' = 1 + x_140 + x_226, x_140 >= 0, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ 3 + 4*s204 + 4*s206 + 107*x_131 + 32*x_131^2 + 107*x_220 + 32*x_220^2 }-> s207 :|: s204 >= 0, s204 <= x_131, s205 >= 0, s205 <= x_220, s206 >= 0, s206 <= s204, s207 >= 0, s207 <= s206, z = 1 + x_131 + x_220, z' >= 0, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ -74 + 43*z' + 32*z'^2 }-> s209 :|: s208 >= 0, s208 <= z' - 1, s209 >= 0, s209 <= 0, z >= 0, z' - 1 >= 0
   encode_h(z, z') -{ 2 + 4*s210 + 107*x_142 + 32*x_142^2 + 107*x_227 + 32*x_227^2 }-> s213 :|: s210 >= 0, s210 <= x_142, s211 >= 0, s211 <= x_227, s212 >= 0, s212 <= s210, s213 >= 0, s213 <= 0, z >= 0, z' = 1 + x_142 + x_227, x_142 >= 0, x_227 >= 0
   encode_h(z, z') -{ 3 + 4*s214 + 107*x_143 + 32*x_143^2 + 107*x_228 + 32*x_228^2 }-> s217 :|: s214 >= 0, s214 <= x_143, s215 >= 0, s215 <= x_228, s216 >= 0, s216 <= s214, s217 >= 0, s217 <= 0, z >= 0, z' = 1 + x_143 + x_228, x_143 >= 0, x_228 >= 0
   encode_h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   g(z, z') -{ 1 + 4*z }-> s' :|: s' >= 0, s' <= z, z >= 0, z' >= 0
   h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   h(z, z') -{ -2 + 4*z }-> 1 + s :|: s >= 0, s <= z - 1, z - 1 >= 0, z' >= 0

Function symbols to be analyzed: {encode_h}, {encode_g}
Previous analysis results are:
  h: runtime: O(n^1) [4*z], size: O(n^1) [z]
  g: runtime: O(n^1) [1 + 4*z], size: O(n^1) [z]
  encArg: runtime: O(n^2) [1 + 107*z + 32*z^2], size: O(n^1) [z]
  encode_f: runtime: O(n^2) [1 + 107*z + 32*z^2], size: O(n^1) [1 + z]

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(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:

   encArg(z) -{ 0 }-> s'' :|: s'' >= 0, s'' <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 1 }-> s1 :|: s1 >= 0, s1 <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 5 + 4*s96 + 4*s98 + 4*s99 + 107*x_115 + 32*x_115^2 + 107*x_121 + 32*x_121^2 + 107*x_213 + 32*x_213^2 + 107*x_29 + 32*x_29^2 }-> s102 :|: s96 >= 0, s96 <= x_115, s97 >= 0, s97 <= x_29, s98 >= 0, s98 <= s96, s99 >= 0, s99 <= x_121, s100 >= 0, s100 <= x_213, s101 >= 0, s101 <= s99, s102 >= 0, s102 <= s98, x_213 >= 0, x_115 >= 0, z = 1 + (1 + x_115 + x_29) + (1 + x_121 + x_213), x_29 >= 0, x_121 >= 0
   encArg(z) -{ 6 + 4*s103 + 4*s105 + 4*s106 + 107*x_115 + 32*x_115^2 + 107*x_122 + 32*x_122^2 + 107*x_214 + 32*x_214^2 + 107*x_29 + 32*x_29^2 }-> s109 :|: s103 >= 0, s103 <= x_115, s104 >= 0, s104 <= x_29, s105 >= 0, s105 <= s103, s106 >= 0, s106 <= x_122, s107 >= 0, s107 <= x_214, s108 >= 0, s108 <= s106, s109 >= 0, s109 <= s105, z = 1 + (1 + x_115 + x_29) + (1 + x_122 + x_214), x_115 >= 0, x_214 >= 0, x_122 >= 0, x_29 >= 0
   encArg(z) -{ 3 + 4*s110 + 4*s112 + 107*x_115 + 32*x_115^2 + 107*x_29 + 32*x_29^2 }-> s113 :|: s110 >= 0, s110 <= x_115, s111 >= 0, s111 <= x_29, s112 >= 0, s112 <= s110, s113 >= 0, s113 <= s112, x_115 >= 0, x_2 >= 0, z = 1 + (1 + x_115 + x_29) + x_2, x_29 >= 0
   encArg(z) -{ 5 + 4*s114 + 4*s116 + 107*x_116 + 32*x_116^2 + 107*x_123 + 32*x_123^2 + 107*x_210 + 32*x_210^2 }-> s118 :|: s114 >= 0, s114 <= x_116, s115 >= 0, s115 <= x_210, s116 >= 0, s116 <= s114, s117 >= 0, s117 <= x_123, s118 >= 0, s118 <= s116, x_123 >= 0, z = 1 + (1 + x_116 + x_210) + (1 + x_123), x_116 >= 0, x_210 >= 0
   encArg(z) -{ 7 + 4*s8 + 4*s9 + 107*x_1' + 32*x_1'^2 + 107*x_13 + 32*x_13^2 + 107*x_21 + 32*x_21^2 }-> s12 :|: s8 >= 0, s8 <= x_1', s9 >= 0, s9 <= x_13, s10 >= 0, s10 <= x_21, s11 >= 0, s11 <= s9, s12 >= 0, s12 <= 1 + s8, x_13 >= 0, x_1' >= 0, z = 1 + (1 + x_1') + (1 + x_13 + x_21), x_21 >= 0
   encArg(z) -{ 6 + 4*s119 + 4*s121 + 4*s122 + 107*x_116 + 32*x_116^2 + 107*x_124 + 32*x_124^2 + 107*x_210 + 32*x_210^2 + 107*x_215 + 32*x_215^2 }-> s125 :|: s119 >= 0, s119 <= x_116, s120 >= 0, s120 <= x_210, s121 >= 0, s121 <= s119, s122 >= 0, s122 <= x_124, s123 >= 0, s123 <= x_215, s124 >= 0, s124 <= s122, s125 >= 0, s125 <= s121, x_124 >= 0, x_215 >= 0, x_116 >= 0, z = 1 + (1 + x_116 + x_210) + (1 + x_124 + x_215), x_210 >= 0
   encArg(z) -{ 7 + 4*s126 + 4*s128 + 4*s129 + 107*x_116 + 32*x_116^2 + 107*x_125 + 32*x_125^2 + 107*x_210 + 32*x_210^2 + 107*x_216 + 32*x_216^2 }-> s132 :|: s126 >= 0, s126 <= x_116, s127 >= 0, s127 <= x_210, s128 >= 0, s128 <= s126, s129 >= 0, s129 <= x_125, s130 >= 0, s130 <= x_216, s131 >= 0, s131 <= s129, s132 >= 0, s132 <= s128, x_216 >= 0, z = 1 + (1 + x_116 + x_210) + (1 + x_125 + x_216), x_116 >= 0, x_125 >= 0, x_210 >= 0
   encArg(z) -{ 4 + 4*s133 + 4*s135 + 107*x_116 + 32*x_116^2 + 107*x_210 + 32*x_210^2 }-> s136 :|: s133 >= 0, s133 <= x_116, s134 >= 0, s134 <= x_210, s135 >= 0, s135 <= s133, s136 >= 0, s136 <= s135, x_116 >= 0, x_2 >= 0, z = 1 + (1 + x_116 + x_210) + x_2, x_210 >= 0
   encArg(z) -{ 2 + 107*x_126 + 32*x_126^2 }-> s138 :|: s137 >= 0, s137 <= x_126, s138 >= 0, s138 <= 0, x_1 >= 0, z = 1 + x_1 + (1 + x_126), x_126 >= 0
   encArg(z) -{ 3 + 4*s139 + 107*x_127 + 32*x_127^2 + 107*x_217 + 32*x_217^2 }-> s142 :|: s139 >= 0, s139 <= x_127, s140 >= 0, s140 <= x_217, s141 >= 0, s141 <= s139, s142 >= 0, s142 <= 0, x_1 >= 0, x_127 >= 0, z = 1 + x_1 + (1 + x_127 + x_217), x_217 >= 0
   encArg(z) -{ 4 + 4*s143 + 107*x_128 + 32*x_128^2 + 107*x_218 + 32*x_218^2 }-> s146 :|: s143 >= 0, s143 <= x_128, s144 >= 0, s144 <= x_218, s145 >= 0, s145 <= s143, s146 >= 0, s146 <= 0, x_1 >= 0, x_128 >= 0, z = 1 + x_1 + (1 + x_128 + x_218), x_218 >= 0
   encArg(z) -{ 8 + 4*s13 + 4*s14 + 107*x_1' + 32*x_1'^2 + 107*x_14 + 32*x_14^2 + 107*x_22 + 32*x_22^2 }-> s17 :|: s13 >= 0, s13 <= x_1', s14 >= 0, s14 <= x_14, s15 >= 0, s15 <= x_22, s16 >= 0, s16 <= s14, s17 >= 0, s17 <= 1 + s13, z = 1 + (1 + x_1') + (1 + x_14 + x_22), x_14 >= 0, x_1' >= 0, x_22 >= 0
   encArg(z) -{ 5 + 4*s18 + 107*x_1' + 32*x_1'^2 }-> s19 :|: s18 >= 0, s18 <= x_1', s19 >= 0, s19 <= 1 + s18, x_1' >= 0, x_2 >= 0, z = 1 + (1 + x_1') + x_2
   encArg(z) -{ 3 + 4*s20 + 4*s22 + 107*x_1'' + 32*x_1''^2 + 107*x_15 + 32*x_15^2 + 107*x_2' + 32*x_2'^2 }-> s24 :|: s20 >= 0, s20 <= x_1'', s21 >= 0, s21 <= x_2', s22 >= 0, s22 <= s20, s23 >= 0, s23 <= x_15, s24 >= 0, s24 <= s22, x_15 >= 0, z = 1 + (1 + x_1'' + x_2') + (1 + x_15), x_1'' >= 0, x_2' >= 0
   encArg(z) -{ 4 + 4*s25 + 4*s27 + 4*s28 + 107*x_1'' + 32*x_1''^2 + 107*x_16 + 32*x_16^2 + 107*x_2' + 32*x_2'^2 + 107*x_23 + 32*x_23^2 }-> s31 :|: s25 >= 0, s25 <= x_1'', s26 >= 0, s26 <= x_2', s27 >= 0, s27 <= s25, s28 >= 0, s28 <= x_16, s29 >= 0, s29 <= x_23, s30 >= 0, s30 <= s28, s31 >= 0, s31 <= s27, x_1'' >= 0, x_16 >= 0, x_2' >= 0, x_23 >= 0, z = 1 + (1 + x_1'' + x_2') + (1 + x_16 + x_23)
   encArg(z) -{ 5 + 4*s32 + 4*s34 + 4*s35 + 107*x_1'' + 32*x_1''^2 + 107*x_17 + 32*x_17^2 + 107*x_2' + 32*x_2'^2 + 107*x_24 + 32*x_24^2 }-> s38 :|: s32 >= 0, s32 <= x_1'', s33 >= 0, s33 <= x_2', s34 >= 0, s34 <= s32, s35 >= 0, s35 <= x_17, s36 >= 0, s36 <= x_24, s37 >= 0, s37 <= s35, s38 >= 0, s38 <= s34, x_1'' >= 0, x_2' >= 0, x_17 >= 0, x_24 >= 0, z = 1 + (1 + x_1'' + x_2') + (1 + x_17 + x_24)
   encArg(z) -{ 2 + 4*s39 + 4*s41 + 107*x_1'' + 32*x_1''^2 + 107*x_2' + 32*x_2'^2 }-> s42 :|: s39 >= 0, s39 <= x_1'', s40 >= 0, s40 <= x_2', s41 >= 0, s41 <= s39, s42 >= 0, s42 <= s41, x_1'' >= 0, x_2' >= 0, z = 1 + (1 + x_1'' + x_2') + x_2, x_2 >= 0
   encArg(z) -{ 4 + 4*s43 + 4*s45 + 107*x_11 + 32*x_11^2 + 107*x_18 + 32*x_18^2 + 107*x_2'' + 32*x_2''^2 }-> s47 :|: s43 >= 0, s43 <= x_11, s44 >= 0, s44 <= x_2'', s45 >= 0, s45 <= s43, s46 >= 0, s46 <= x_18, s47 >= 0, s47 <= s45, x_11 >= 0, z = 1 + (1 + x_11 + x_2'') + (1 + x_18), x_2'' >= 0, x_18 >= 0
   encArg(z) -{ 5 + 4*s48 + 4*s50 + 4*s51 + 107*x_11 + 32*x_11^2 + 107*x_19 + 32*x_19^2 + 107*x_2'' + 32*x_2''^2 + 107*x_25 + 32*x_25^2 }-> s54 :|: s48 >= 0, s48 <= x_11, s49 >= 0, s49 <= x_2'', s50 >= 0, s50 <= s48, s51 >= 0, s51 <= x_19, s52 >= 0, s52 <= x_25, s53 >= 0, s53 <= s51, s54 >= 0, s54 <= s50, x_11 >= 0, z = 1 + (1 + x_11 + x_2'') + (1 + x_19 + x_25), x_25 >= 0, x_2'' >= 0, x_19 >= 0
   encArg(z) -{ 6 + 4*s55 + 4*s57 + 4*s58 + 107*x_11 + 32*x_11^2 + 107*x_110 + 32*x_110^2 + 107*x_2'' + 32*x_2''^2 + 107*x_26 + 32*x_26^2 }-> s61 :|: s55 >= 0, s55 <= x_11, s56 >= 0, s56 <= x_2'', s57 >= 0, s57 <= s55, s58 >= 0, s58 <= x_110, s59 >= 0, s59 <= x_26, s60 >= 0, s60 <= s58, s61 >= 0, s61 <= s57, x_11 >= 0, x_26 >= 0, x_2'' >= 0, z = 1 + (1 + x_11 + x_2'') + (1 + x_110 + x_26), x_110 >= 0
   encArg(z) -{ 3 + 4*s62 + 4*s64 + 107*x_11 + 32*x_11^2 + 107*x_2'' + 32*x_2''^2 }-> s65 :|: s62 >= 0, s62 <= x_11, s63 >= 0, s63 <= x_2'', s64 >= 0, s64 <= s62, s65 >= 0, s65 <= s64, x_11 >= 0, x_2'' >= 0, x_2 >= 0, z = 1 + (1 + x_11 + x_2'') + x_2
   encArg(z) -{ 1 + 107*x_111 + 32*x_111^2 }-> s67 :|: s66 >= 0, s66 <= x_111, s67 >= 0, s67 <= 0, x_1 >= 0, z = 1 + x_1 + (1 + x_111), x_111 >= 0
   encArg(z) -{ 6 + 4*s5 + 107*x_1' + 32*x_1'^2 + 107*x_12 + 32*x_12^2 }-> s7 :|: s5 >= 0, s5 <= x_1', s6 >= 0, s6 <= x_12, s7 >= 0, s7 <= 1 + s5, z = 1 + (1 + x_1') + (1 + x_12), x_1' >= 0, x_12 >= 0
   encArg(z) -{ 2 + 4*s68 + 107*x_112 + 32*x_112^2 + 107*x_27 + 32*x_27^2 }-> s71 :|: s68 >= 0, s68 <= x_112, s69 >= 0, s69 <= x_27, s70 >= 0, s70 <= s68, s71 >= 0, s71 <= 0, x_1 >= 0, x_27 >= 0, z = 1 + x_1 + (1 + x_112 + x_27), x_112 >= 0
   encArg(z) -{ 3 + 4*s72 + 107*x_113 + 32*x_113^2 + 107*x_28 + 32*x_28^2 }-> s75 :|: s72 >= 0, s72 <= x_113, s73 >= 0, s73 <= x_28, s74 >= 0, s74 <= s72, s75 >= 0, s75 <= 0, x_1 >= 0, x_113 >= 0, x_28 >= 0, z = 1 + x_1 + (1 + x_113 + x_28)
   encArg(z) -{ 7 + 4*s76 + 107*x_114 + 32*x_114^2 + 107*x_117 + 32*x_117^2 }-> s78 :|: s76 >= 0, s76 <= x_114, s77 >= 0, s77 <= x_117, s78 >= 0, s78 <= 1 + s76, z = 1 + (1 + x_114) + (1 + x_117), x_117 >= 0, x_114 >= 0
   encArg(z) -{ 8 + 4*s79 + 4*s80 + 107*x_114 + 32*x_114^2 + 107*x_118 + 32*x_118^2 + 107*x_211 + 32*x_211^2 }-> s83 :|: s79 >= 0, s79 <= x_114, s80 >= 0, s80 <= x_118, s81 >= 0, s81 <= x_211, s82 >= 0, s82 <= s80, s83 >= 0, s83 <= 1 + s79, z = 1 + (1 + x_114) + (1 + x_118 + x_211), x_114 >= 0, x_118 >= 0, x_211 >= 0
   encArg(z) -{ 9 + 4*s84 + 4*s85 + 107*x_114 + 32*x_114^2 + 107*x_119 + 32*x_119^2 + 107*x_212 + 32*x_212^2 }-> s88 :|: s84 >= 0, s84 <= x_114, s85 >= 0, s85 <= x_119, s86 >= 0, s86 <= x_212, s87 >= 0, s87 <= s85, s88 >= 0, s88 <= 1 + s84, x_212 >= 0, x_114 >= 0, z = 1 + (1 + x_114) + (1 + x_119 + x_212), x_119 >= 0
   encArg(z) -{ 6 + 4*s89 + 107*x_114 + 32*x_114^2 }-> s90 :|: s89 >= 0, s89 <= x_114, s90 >= 0, s90 <= 1 + s89, z = 1 + (1 + x_114) + x_2, x_114 >= 0, x_2 >= 0
   encArg(z) -{ 4 + 4*s91 + 4*s93 + 107*x_115 + 32*x_115^2 + 107*x_120 + 32*x_120^2 + 107*x_29 + 32*x_29^2 }-> s95 :|: s91 >= 0, s91 <= x_115, s92 >= 0, s92 <= x_29, s93 >= 0, s93 <= s91, s94 >= 0, s94 <= x_120, s95 >= 0, s95 <= s93, x_120 >= 0, x_115 >= 0, z = 1 + (1 + x_115 + x_29) + (1 + x_120), x_29 >= 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ -74 + 43*z + 32*z^2 }-> 1 + s4 :|: s4 >= 0, s4 <= z - 1, z - 1 >= 0
   encode_f(z) -{ 0 }-> 0 :|: z >= 0
   encode_f(z) -{ 1 + 107*z + 32*z^2 }-> 1 + s218 :|: s218 >= 0, s218 <= z, z >= 0
   encode_g(z, z') -{ -143 + 4*s219 + 43*z + 32*z^2 + 43*z' + 32*z'^2 }-> s221 :|: s219 >= 0, s219 <= z - 1, s220 >= 0, s220 <= z' - 1, s221 >= 0, s221 <= 1 + s219, z - 1 >= 0, z' - 1 >= 0
   encode_g(z, z') -{ -67 + 4*s222 + 4*s223 + 107*x_148 + 32*x_148^2 + 107*x_231 + 32*x_231^2 + 43*z + 32*z^2 }-> s226 :|: s222 >= 0, s222 <= z - 1, s223 >= 0, s223 <= x_148, s224 >= 0, s224 <= x_231, s225 >= 0, s225 <= s223, s226 >= 0, s226 <= 1 + s222, z' = 1 + x_148 + x_231, z - 1 >= 0, x_231 >= 0, x_148 >= 0
   encode_g(z, z') -{ -66 + 4*s227 + 4*s228 + 107*x_149 + 32*x_149^2 + 107*x_232 + 32*x_232^2 + 43*z + 32*z^2 }-> s231 :|: s227 >= 0, s227 <= z - 1, s228 >= 0, s228 <= x_149, s229 >= 0, s229 <= x_232, s230 >= 0, s230 <= s228, s231 >= 0, s231 <= 1 + s227, x_232 >= 0, z - 1 >= 0, z' = 1 + x_149 + x_232, x_149 >= 0
   encode_g(z, z') -{ -69 + 4*s232 + 43*z + 32*z^2 }-> s233 :|: s232 >= 0, s232 <= z - 1, s233 >= 0, s233 <= 1 + s232, z - 1 >= 0, z' >= 0
   encode_g(z, z') -{ -71 + 4*s234 + 4*s236 + 107*x_145 + 32*x_145^2 + 107*x_229 + 32*x_229^2 + 43*z' + 32*z'^2 }-> s238 :|: s234 >= 0, s234 <= x_145, s235 >= 0, s235 <= x_229, s236 >= 0, s236 <= s234, s237 >= 0, s237 <= z' - 1, s238 >= 0, s238 <= s236, z = 1 + x_145 + x_229, x_145 >= 0, x_229 >= 0, z' - 1 >= 0
   encode_g(z, z') -{ 5 + 4*s239 + 4*s241 + 4*s242 + 107*x_145 + 32*x_145^2 + 107*x_151 + 32*x_151^2 + 107*x_229 + 32*x_229^2 + 107*x_233 + 32*x_233^2 }-> s245 :|: s239 >= 0, s239 <= x_145, s240 >= 0, s240 <= x_229, s241 >= 0, s241 <= s239, s242 >= 0, s242 <= x_151, s243 >= 0, s243 <= x_233, s244 >= 0, s244 <= s242, s245 >= 0, s245 <= s241, x_233 >= 0, z = 1 + x_145 + x_229, x_145 >= 0, x_229 >= 0, z' = 1 + x_151 + x_233, x_151 >= 0
   encode_g(z, z') -{ 6 + 4*s246 + 4*s248 + 4*s249 + 107*x_145 + 32*x_145^2 + 107*x_152 + 32*x_152^2 + 107*x_229 + 32*x_229^2 + 107*x_234 + 32*x_234^2 }-> s252 :|: s246 >= 0, s246 <= x_145, s247 >= 0, s247 <= x_229, s248 >= 0, s248 <= s246, s249 >= 0, s249 <= x_152, s250 >= 0, s250 <= x_234, s251 >= 0, s251 <= s249, s252 >= 0, s252 <= s248, z = 1 + x_145 + x_229, x_234 >= 0, x_145 >= 0, z' = 1 + x_152 + x_234, x_229 >= 0, x_152 >= 0
   encode_g(z, z') -{ 3 + 4*s253 + 4*s255 + 107*x_145 + 32*x_145^2 + 107*x_229 + 32*x_229^2 }-> s256 :|: s253 >= 0, s253 <= x_145, s254 >= 0, s254 <= x_229, s255 >= 0, s255 <= s253, s256 >= 0, s256 <= s255, z = 1 + x_145 + x_229, x_145 >= 0, x_229 >= 0, z' >= 0
   encode_g(z, z') -{ -70 + 4*s257 + 4*s259 + 107*x_146 + 32*x_146^2 + 107*x_230 + 32*x_230^2 + 43*z' + 32*z'^2 }-> s261 :|: s257 >= 0, s257 <= x_146, s258 >= 0, s258 <= x_230, s259 >= 0, s259 <= s257, s260 >= 0, s260 <= z' - 1, s261 >= 0, s261 <= s259, z = 1 + x_146 + x_230, x_146 >= 0, z' - 1 >= 0, x_230 >= 0
   encode_g(z, z') -{ 6 + 4*s262 + 4*s264 + 4*s265 + 107*x_146 + 32*x_146^2 + 107*x_154 + 32*x_154^2 + 107*x_230 + 32*x_230^2 + 107*x_235 + 32*x_235^2 }-> s268 :|: s262 >= 0, s262 <= x_146, s263 >= 0, s263 <= x_230, s264 >= 0, s264 <= s262, s265 >= 0, s265 <= x_154, s266 >= 0, s266 <= x_235, s267 >= 0, s267 <= s265, s268 >= 0, s268 <= s264, z = 1 + x_146 + x_230, x_146 >= 0, x_154 >= 0, z' = 1 + x_154 + x_235, x_235 >= 0, x_230 >= 0
   encode_g(z, z') -{ 7 + 4*s269 + 4*s271 + 4*s272 + 107*x_146 + 32*x_146^2 + 107*x_155 + 32*x_155^2 + 107*x_230 + 32*x_230^2 + 107*x_236 + 32*x_236^2 }-> s275 :|: s269 >= 0, s269 <= x_146, s270 >= 0, s270 <= x_230, s271 >= 0, s271 <= s269, s272 >= 0, s272 <= x_155, s273 >= 0, s273 <= x_236, s274 >= 0, s274 <= s272, s275 >= 0, s275 <= s271, z = 1 + x_146 + x_230, x_146 >= 0, x_155 >= 0, z' = 1 + x_155 + x_236, x_236 >= 0, x_230 >= 0
   encode_g(z, z') -{ 4 + 4*s276 + 4*s278 + 107*x_146 + 32*x_146^2 + 107*x_230 + 32*x_230^2 }-> s279 :|: s276 >= 0, s276 <= x_146, s277 >= 0, s277 <= x_230, s278 >= 0, s278 <= s276, s279 >= 0, s279 <= s278, z = 1 + x_146 + x_230, x_146 >= 0, z' >= 0, x_230 >= 0
   encode_g(z, z') -{ -73 + 43*z' + 32*z'^2 }-> s281 :|: s280 >= 0, s280 <= z' - 1, s281 >= 0, s281 <= 0, z >= 0, z' - 1 >= 0
   encode_g(z, z') -{ 3 + 4*s282 + 107*x_157 + 32*x_157^2 + 107*x_237 + 32*x_237^2 }-> s285 :|: s282 >= 0, s282 <= x_157, s283 >= 0, s283 <= x_237, s284 >= 0, s284 <= s282, s285 >= 0, s285 <= 0, x_237 >= 0, z >= 0, x_157 >= 0, z' = 1 + x_157 + x_237
   encode_g(z, z') -{ 4 + 4*s286 + 107*x_158 + 32*x_158^2 + 107*x_238 + 32*x_238^2 }-> s289 :|: s286 >= 0, s286 <= x_158, s287 >= 0, s287 <= x_238, s288 >= 0, s288 <= s286, s289 >= 0, s289 <= 0, z >= 0, z' = 1 + x_158 + x_238, x_158 >= 0, x_238 >= 0
   encode_g(z, z') -{ 1 }-> s3 :|: s3 >= 0, s3 <= 0, z >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_h(z, z') -{ -144 + 4*s147 + 43*z + 32*z^2 + 43*z' + 32*z'^2 }-> s149 :|: s147 >= 0, s147 <= z - 1, s148 >= 0, s148 <= z' - 1, s149 >= 0, s149 <= 1 + s147, z' - 1 >= 0, z - 1 >= 0
   encode_h(z, z') -{ -68 + 4*s150 + 4*s151 + 107*x_133 + 32*x_133^2 + 107*x_221 + 32*x_221^2 + 43*z + 32*z^2 }-> s154 :|: s150 >= 0, s150 <= z - 1, s151 >= 0, s151 <= x_133, s152 >= 0, s152 <= x_221, s153 >= 0, s153 <= s151, s154 >= 0, s154 <= 1 + s150, z' = 1 + x_133 + x_221, x_221 >= 0, x_133 >= 0, z - 1 >= 0
   encode_h(z, z') -{ -67 + 4*s155 + 4*s156 + 107*x_134 + 32*x_134^2 + 107*x_222 + 32*x_222^2 + 43*z + 32*z^2 }-> s159 :|: s155 >= 0, s155 <= z - 1, s156 >= 0, s156 <= x_134, s157 >= 0, s157 <= x_222, s158 >= 0, s158 <= s156, s159 >= 0, s159 <= 1 + s155, z' = 1 + x_134 + x_222, x_134 >= 0, x_222 >= 0, z - 1 >= 0
   encode_h(z, z') -{ -70 + 4*s160 + 43*z + 32*z^2 }-> s161 :|: s160 >= 0, s160 <= z - 1, s161 >= 0, s161 <= 1 + s160, z' >= 0, z - 1 >= 0
   encode_h(z, z') -{ -72 + 4*s162 + 4*s164 + 107*x_130 + 32*x_130^2 + 107*x_219 + 32*x_219^2 + 43*z' + 32*z'^2 }-> s166 :|: s162 >= 0, s162 <= x_130, s163 >= 0, s163 <= x_219, s164 >= 0, s164 <= s162, s165 >= 0, s165 <= z' - 1, s166 >= 0, s166 <= s164, x_130 >= 0, z = 1 + x_130 + x_219, z' - 1 >= 0, x_219 >= 0
   encode_h(z, z') -{ 4 + 4*s167 + 4*s169 + 4*s170 + 107*x_130 + 32*x_130^2 + 107*x_136 + 32*x_136^2 + 107*x_219 + 32*x_219^2 + 107*x_223 + 32*x_223^2 }-> s173 :|: s167 >= 0, s167 <= x_130, s168 >= 0, s168 <= x_219, s169 >= 0, s169 <= s167, s170 >= 0, s170 <= x_136, s171 >= 0, s171 <= x_223, s172 >= 0, s172 <= s170, s173 >= 0, s173 <= s169, z' = 1 + x_136 + x_223, x_130 >= 0, z = 1 + x_130 + x_219, x_223 >= 0, x_136 >= 0, x_219 >= 0
   encode_h(z, z') -{ 5 + 4*s174 + 4*s176 + 4*s177 + 107*x_130 + 32*x_130^2 + 107*x_137 + 32*x_137^2 + 107*x_219 + 32*x_219^2 + 107*x_224 + 32*x_224^2 }-> s180 :|: s174 >= 0, s174 <= x_130, s175 >= 0, s175 <= x_219, s176 >= 0, s176 <= s174, s177 >= 0, s177 <= x_137, s178 >= 0, s178 <= x_224, s179 >= 0, s179 <= s177, s180 >= 0, s180 <= s176, z' = 1 + x_137 + x_224, x_130 >= 0, z = 1 + x_130 + x_219, x_224 >= 0, x_137 >= 0, x_219 >= 0
   encode_h(z, z') -{ 2 + 4*s181 + 4*s183 + 107*x_130 + 32*x_130^2 + 107*x_219 + 32*x_219^2 }-> s184 :|: s181 >= 0, s181 <= x_130, s182 >= 0, s182 <= x_219, s183 >= 0, s183 <= s181, s184 >= 0, s184 <= s183, x_130 >= 0, z = 1 + x_130 + x_219, z' >= 0, x_219 >= 0
   encode_h(z, z') -{ -71 + 4*s185 + 4*s187 + 107*x_131 + 32*x_131^2 + 107*x_220 + 32*x_220^2 + 43*z' + 32*z'^2 }-> s189 :|: s185 >= 0, s185 <= x_131, s186 >= 0, s186 <= x_220, s187 >= 0, s187 <= s185, s188 >= 0, s188 <= z' - 1, s189 >= 0, s189 <= s187, z' - 1 >= 0, z = 1 + x_131 + x_220, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ 5 + 4*s190 + 4*s192 + 4*s193 + 107*x_131 + 32*x_131^2 + 107*x_139 + 32*x_139^2 + 107*x_220 + 32*x_220^2 + 107*x_225 + 32*x_225^2 }-> s196 :|: s190 >= 0, s190 <= x_131, s191 >= 0, s191 <= x_220, s192 >= 0, s192 <= s190, s193 >= 0, s193 <= x_139, s194 >= 0, s194 <= x_225, s195 >= 0, s195 <= s193, s196 >= 0, s196 <= s192, z = 1 + x_131 + x_220, z' = 1 + x_139 + x_225, x_225 >= 0, x_139 >= 0, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ 0 }-> s2 :|: s2 >= 0, s2 <= 0, z >= 0, z' >= 0
   encode_h(z, z') -{ 6 + 4*s197 + 4*s199 + 4*s200 + 107*x_131 + 32*x_131^2 + 107*x_140 + 32*x_140^2 + 107*x_220 + 32*x_220^2 + 107*x_226 + 32*x_226^2 }-> s203 :|: s197 >= 0, s197 <= x_131, s198 >= 0, s198 <= x_220, s199 >= 0, s199 <= s197, s200 >= 0, s200 <= x_140, s201 >= 0, s201 <= x_226, s202 >= 0, s202 <= s200, s203 >= 0, s203 <= s199, z = 1 + x_131 + x_220, x_226 >= 0, z' = 1 + x_140 + x_226, x_140 >= 0, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ 3 + 4*s204 + 4*s206 + 107*x_131 + 32*x_131^2 + 107*x_220 + 32*x_220^2 }-> s207 :|: s204 >= 0, s204 <= x_131, s205 >= 0, s205 <= x_220, s206 >= 0, s206 <= s204, s207 >= 0, s207 <= s206, z = 1 + x_131 + x_220, z' >= 0, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ -74 + 43*z' + 32*z'^2 }-> s209 :|: s208 >= 0, s208 <= z' - 1, s209 >= 0, s209 <= 0, z >= 0, z' - 1 >= 0
   encode_h(z, z') -{ 2 + 4*s210 + 107*x_142 + 32*x_142^2 + 107*x_227 + 32*x_227^2 }-> s213 :|: s210 >= 0, s210 <= x_142, s211 >= 0, s211 <= x_227, s212 >= 0, s212 <= s210, s213 >= 0, s213 <= 0, z >= 0, z' = 1 + x_142 + x_227, x_142 >= 0, x_227 >= 0
   encode_h(z, z') -{ 3 + 4*s214 + 107*x_143 + 32*x_143^2 + 107*x_228 + 32*x_228^2 }-> s217 :|: s214 >= 0, s214 <= x_143, s215 >= 0, s215 <= x_228, s216 >= 0, s216 <= s214, s217 >= 0, s217 <= 0, z >= 0, z' = 1 + x_143 + x_228, x_143 >= 0, x_228 >= 0
   encode_h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   g(z, z') -{ 1 + 4*z }-> s' :|: s' >= 0, s' <= z, z >= 0, z' >= 0
   h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   h(z, z') -{ -2 + 4*z }-> 1 + s :|: s >= 0, s <= z - 1, z - 1 >= 0, z' >= 0

Function symbols to be analyzed: {encode_h}, {encode_g}
Previous analysis results are:
  h: runtime: O(n^1) [4*z], size: O(n^1) [z]
  g: runtime: O(n^1) [1 + 4*z], size: O(n^1) [z]
  encArg: runtime: O(n^2) [1 + 107*z + 32*z^2], size: O(n^1) [z]
  encode_f: runtime: O(n^2) [1 + 107*z + 32*z^2], size: O(n^1) [1 + z]

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

(39) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   encArg(z) -{ 0 }-> s'' :|: s'' >= 0, s'' <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 1 }-> s1 :|: s1 >= 0, s1 <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 5 + 4*s96 + 4*s98 + 4*s99 + 107*x_115 + 32*x_115^2 + 107*x_121 + 32*x_121^2 + 107*x_213 + 32*x_213^2 + 107*x_29 + 32*x_29^2 }-> s102 :|: s96 >= 0, s96 <= x_115, s97 >= 0, s97 <= x_29, s98 >= 0, s98 <= s96, s99 >= 0, s99 <= x_121, s100 >= 0, s100 <= x_213, s101 >= 0, s101 <= s99, s102 >= 0, s102 <= s98, x_213 >= 0, x_115 >= 0, z = 1 + (1 + x_115 + x_29) + (1 + x_121 + x_213), x_29 >= 0, x_121 >= 0
   encArg(z) -{ 6 + 4*s103 + 4*s105 + 4*s106 + 107*x_115 + 32*x_115^2 + 107*x_122 + 32*x_122^2 + 107*x_214 + 32*x_214^2 + 107*x_29 + 32*x_29^2 }-> s109 :|: s103 >= 0, s103 <= x_115, s104 >= 0, s104 <= x_29, s105 >= 0, s105 <= s103, s106 >= 0, s106 <= x_122, s107 >= 0, s107 <= x_214, s108 >= 0, s108 <= s106, s109 >= 0, s109 <= s105, z = 1 + (1 + x_115 + x_29) + (1 + x_122 + x_214), x_115 >= 0, x_214 >= 0, x_122 >= 0, x_29 >= 0
   encArg(z) -{ 3 + 4*s110 + 4*s112 + 107*x_115 + 32*x_115^2 + 107*x_29 + 32*x_29^2 }-> s113 :|: s110 >= 0, s110 <= x_115, s111 >= 0, s111 <= x_29, s112 >= 0, s112 <= s110, s113 >= 0, s113 <= s112, x_115 >= 0, x_2 >= 0, z = 1 + (1 + x_115 + x_29) + x_2, x_29 >= 0
   encArg(z) -{ 5 + 4*s114 + 4*s116 + 107*x_116 + 32*x_116^2 + 107*x_123 + 32*x_123^2 + 107*x_210 + 32*x_210^2 }-> s118 :|: s114 >= 0, s114 <= x_116, s115 >= 0, s115 <= x_210, s116 >= 0, s116 <= s114, s117 >= 0, s117 <= x_123, s118 >= 0, s118 <= s116, x_123 >= 0, z = 1 + (1 + x_116 + x_210) + (1 + x_123), x_116 >= 0, x_210 >= 0
   encArg(z) -{ 7 + 4*s8 + 4*s9 + 107*x_1' + 32*x_1'^2 + 107*x_13 + 32*x_13^2 + 107*x_21 + 32*x_21^2 }-> s12 :|: s8 >= 0, s8 <= x_1', s9 >= 0, s9 <= x_13, s10 >= 0, s10 <= x_21, s11 >= 0, s11 <= s9, s12 >= 0, s12 <= 1 + s8, x_13 >= 0, x_1' >= 0, z = 1 + (1 + x_1') + (1 + x_13 + x_21), x_21 >= 0
   encArg(z) -{ 6 + 4*s119 + 4*s121 + 4*s122 + 107*x_116 + 32*x_116^2 + 107*x_124 + 32*x_124^2 + 107*x_210 + 32*x_210^2 + 107*x_215 + 32*x_215^2 }-> s125 :|: s119 >= 0, s119 <= x_116, s120 >= 0, s120 <= x_210, s121 >= 0, s121 <= s119, s122 >= 0, s122 <= x_124, s123 >= 0, s123 <= x_215, s124 >= 0, s124 <= s122, s125 >= 0, s125 <= s121, x_124 >= 0, x_215 >= 0, x_116 >= 0, z = 1 + (1 + x_116 + x_210) + (1 + x_124 + x_215), x_210 >= 0
   encArg(z) -{ 7 + 4*s126 + 4*s128 + 4*s129 + 107*x_116 + 32*x_116^2 + 107*x_125 + 32*x_125^2 + 107*x_210 + 32*x_210^2 + 107*x_216 + 32*x_216^2 }-> s132 :|: s126 >= 0, s126 <= x_116, s127 >= 0, s127 <= x_210, s128 >= 0, s128 <= s126, s129 >= 0, s129 <= x_125, s130 >= 0, s130 <= x_216, s131 >= 0, s131 <= s129, s132 >= 0, s132 <= s128, x_216 >= 0, z = 1 + (1 + x_116 + x_210) + (1 + x_125 + x_216), x_116 >= 0, x_125 >= 0, x_210 >= 0
   encArg(z) -{ 4 + 4*s133 + 4*s135 + 107*x_116 + 32*x_116^2 + 107*x_210 + 32*x_210^2 }-> s136 :|: s133 >= 0, s133 <= x_116, s134 >= 0, s134 <= x_210, s135 >= 0, s135 <= s133, s136 >= 0, s136 <= s135, x_116 >= 0, x_2 >= 0, z = 1 + (1 + x_116 + x_210) + x_2, x_210 >= 0
   encArg(z) -{ 2 + 107*x_126 + 32*x_126^2 }-> s138 :|: s137 >= 0, s137 <= x_126, s138 >= 0, s138 <= 0, x_1 >= 0, z = 1 + x_1 + (1 + x_126), x_126 >= 0
   encArg(z) -{ 3 + 4*s139 + 107*x_127 + 32*x_127^2 + 107*x_217 + 32*x_217^2 }-> s142 :|: s139 >= 0, s139 <= x_127, s140 >= 0, s140 <= x_217, s141 >= 0, s141 <= s139, s142 >= 0, s142 <= 0, x_1 >= 0, x_127 >= 0, z = 1 + x_1 + (1 + x_127 + x_217), x_217 >= 0
   encArg(z) -{ 4 + 4*s143 + 107*x_128 + 32*x_128^2 + 107*x_218 + 32*x_218^2 }-> s146 :|: s143 >= 0, s143 <= x_128, s144 >= 0, s144 <= x_218, s145 >= 0, s145 <= s143, s146 >= 0, s146 <= 0, x_1 >= 0, x_128 >= 0, z = 1 + x_1 + (1 + x_128 + x_218), x_218 >= 0
   encArg(z) -{ 8 + 4*s13 + 4*s14 + 107*x_1' + 32*x_1'^2 + 107*x_14 + 32*x_14^2 + 107*x_22 + 32*x_22^2 }-> s17 :|: s13 >= 0, s13 <= x_1', s14 >= 0, s14 <= x_14, s15 >= 0, s15 <= x_22, s16 >= 0, s16 <= s14, s17 >= 0, s17 <= 1 + s13, z = 1 + (1 + x_1') + (1 + x_14 + x_22), x_14 >= 0, x_1' >= 0, x_22 >= 0
   encArg(z) -{ 5 + 4*s18 + 107*x_1' + 32*x_1'^2 }-> s19 :|: s18 >= 0, s18 <= x_1', s19 >= 0, s19 <= 1 + s18, x_1' >= 0, x_2 >= 0, z = 1 + (1 + x_1') + x_2
   encArg(z) -{ 3 + 4*s20 + 4*s22 + 107*x_1'' + 32*x_1''^2 + 107*x_15 + 32*x_15^2 + 107*x_2' + 32*x_2'^2 }-> s24 :|: s20 >= 0, s20 <= x_1'', s21 >= 0, s21 <= x_2', s22 >= 0, s22 <= s20, s23 >= 0, s23 <= x_15, s24 >= 0, s24 <= s22, x_15 >= 0, z = 1 + (1 + x_1'' + x_2') + (1 + x_15), x_1'' >= 0, x_2' >= 0
   encArg(z) -{ 4 + 4*s25 + 4*s27 + 4*s28 + 107*x_1'' + 32*x_1''^2 + 107*x_16 + 32*x_16^2 + 107*x_2' + 32*x_2'^2 + 107*x_23 + 32*x_23^2 }-> s31 :|: s25 >= 0, s25 <= x_1'', s26 >= 0, s26 <= x_2', s27 >= 0, s27 <= s25, s28 >= 0, s28 <= x_16, s29 >= 0, s29 <= x_23, s30 >= 0, s30 <= s28, s31 >= 0, s31 <= s27, x_1'' >= 0, x_16 >= 0, x_2' >= 0, x_23 >= 0, z = 1 + (1 + x_1'' + x_2') + (1 + x_16 + x_23)
   encArg(z) -{ 5 + 4*s32 + 4*s34 + 4*s35 + 107*x_1'' + 32*x_1''^2 + 107*x_17 + 32*x_17^2 + 107*x_2' + 32*x_2'^2 + 107*x_24 + 32*x_24^2 }-> s38 :|: s32 >= 0, s32 <= x_1'', s33 >= 0, s33 <= x_2', s34 >= 0, s34 <= s32, s35 >= 0, s35 <= x_17, s36 >= 0, s36 <= x_24, s37 >= 0, s37 <= s35, s38 >= 0, s38 <= s34, x_1'' >= 0, x_2' >= 0, x_17 >= 0, x_24 >= 0, z = 1 + (1 + x_1'' + x_2') + (1 + x_17 + x_24)
   encArg(z) -{ 2 + 4*s39 + 4*s41 + 107*x_1'' + 32*x_1''^2 + 107*x_2' + 32*x_2'^2 }-> s42 :|: s39 >= 0, s39 <= x_1'', s40 >= 0, s40 <= x_2', s41 >= 0, s41 <= s39, s42 >= 0, s42 <= s41, x_1'' >= 0, x_2' >= 0, z = 1 + (1 + x_1'' + x_2') + x_2, x_2 >= 0
   encArg(z) -{ 4 + 4*s43 + 4*s45 + 107*x_11 + 32*x_11^2 + 107*x_18 + 32*x_18^2 + 107*x_2'' + 32*x_2''^2 }-> s47 :|: s43 >= 0, s43 <= x_11, s44 >= 0, s44 <= x_2'', s45 >= 0, s45 <= s43, s46 >= 0, s46 <= x_18, s47 >= 0, s47 <= s45, x_11 >= 0, z = 1 + (1 + x_11 + x_2'') + (1 + x_18), x_2'' >= 0, x_18 >= 0
   encArg(z) -{ 5 + 4*s48 + 4*s50 + 4*s51 + 107*x_11 + 32*x_11^2 + 107*x_19 + 32*x_19^2 + 107*x_2'' + 32*x_2''^2 + 107*x_25 + 32*x_25^2 }-> s54 :|: s48 >= 0, s48 <= x_11, s49 >= 0, s49 <= x_2'', s50 >= 0, s50 <= s48, s51 >= 0, s51 <= x_19, s52 >= 0, s52 <= x_25, s53 >= 0, s53 <= s51, s54 >= 0, s54 <= s50, x_11 >= 0, z = 1 + (1 + x_11 + x_2'') + (1 + x_19 + x_25), x_25 >= 0, x_2'' >= 0, x_19 >= 0
   encArg(z) -{ 6 + 4*s55 + 4*s57 + 4*s58 + 107*x_11 + 32*x_11^2 + 107*x_110 + 32*x_110^2 + 107*x_2'' + 32*x_2''^2 + 107*x_26 + 32*x_26^2 }-> s61 :|: s55 >= 0, s55 <= x_11, s56 >= 0, s56 <= x_2'', s57 >= 0, s57 <= s55, s58 >= 0, s58 <= x_110, s59 >= 0, s59 <= x_26, s60 >= 0, s60 <= s58, s61 >= 0, s61 <= s57, x_11 >= 0, x_26 >= 0, x_2'' >= 0, z = 1 + (1 + x_11 + x_2'') + (1 + x_110 + x_26), x_110 >= 0
   encArg(z) -{ 3 + 4*s62 + 4*s64 + 107*x_11 + 32*x_11^2 + 107*x_2'' + 32*x_2''^2 }-> s65 :|: s62 >= 0, s62 <= x_11, s63 >= 0, s63 <= x_2'', s64 >= 0, s64 <= s62, s65 >= 0, s65 <= s64, x_11 >= 0, x_2'' >= 0, x_2 >= 0, z = 1 + (1 + x_11 + x_2'') + x_2
   encArg(z) -{ 1 + 107*x_111 + 32*x_111^2 }-> s67 :|: s66 >= 0, s66 <= x_111, s67 >= 0, s67 <= 0, x_1 >= 0, z = 1 + x_1 + (1 + x_111), x_111 >= 0
   encArg(z) -{ 6 + 4*s5 + 107*x_1' + 32*x_1'^2 + 107*x_12 + 32*x_12^2 }-> s7 :|: s5 >= 0, s5 <= x_1', s6 >= 0, s6 <= x_12, s7 >= 0, s7 <= 1 + s5, z = 1 + (1 + x_1') + (1 + x_12), x_1' >= 0, x_12 >= 0
   encArg(z) -{ 2 + 4*s68 + 107*x_112 + 32*x_112^2 + 107*x_27 + 32*x_27^2 }-> s71 :|: s68 >= 0, s68 <= x_112, s69 >= 0, s69 <= x_27, s70 >= 0, s70 <= s68, s71 >= 0, s71 <= 0, x_1 >= 0, x_27 >= 0, z = 1 + x_1 + (1 + x_112 + x_27), x_112 >= 0
   encArg(z) -{ 3 + 4*s72 + 107*x_113 + 32*x_113^2 + 107*x_28 + 32*x_28^2 }-> s75 :|: s72 >= 0, s72 <= x_113, s73 >= 0, s73 <= x_28, s74 >= 0, s74 <= s72, s75 >= 0, s75 <= 0, x_1 >= 0, x_113 >= 0, x_28 >= 0, z = 1 + x_1 + (1 + x_113 + x_28)
   encArg(z) -{ 7 + 4*s76 + 107*x_114 + 32*x_114^2 + 107*x_117 + 32*x_117^2 }-> s78 :|: s76 >= 0, s76 <= x_114, s77 >= 0, s77 <= x_117, s78 >= 0, s78 <= 1 + s76, z = 1 + (1 + x_114) + (1 + x_117), x_117 >= 0, x_114 >= 0
   encArg(z) -{ 8 + 4*s79 + 4*s80 + 107*x_114 + 32*x_114^2 + 107*x_118 + 32*x_118^2 + 107*x_211 + 32*x_211^2 }-> s83 :|: s79 >= 0, s79 <= x_114, s80 >= 0, s80 <= x_118, s81 >= 0, s81 <= x_211, s82 >= 0, s82 <= s80, s83 >= 0, s83 <= 1 + s79, z = 1 + (1 + x_114) + (1 + x_118 + x_211), x_114 >= 0, x_118 >= 0, x_211 >= 0
   encArg(z) -{ 9 + 4*s84 + 4*s85 + 107*x_114 + 32*x_114^2 + 107*x_119 + 32*x_119^2 + 107*x_212 + 32*x_212^2 }-> s88 :|: s84 >= 0, s84 <= x_114, s85 >= 0, s85 <= x_119, s86 >= 0, s86 <= x_212, s87 >= 0, s87 <= s85, s88 >= 0, s88 <= 1 + s84, x_212 >= 0, x_114 >= 0, z = 1 + (1 + x_114) + (1 + x_119 + x_212), x_119 >= 0
   encArg(z) -{ 6 + 4*s89 + 107*x_114 + 32*x_114^2 }-> s90 :|: s89 >= 0, s89 <= x_114, s90 >= 0, s90 <= 1 + s89, z = 1 + (1 + x_114) + x_2, x_114 >= 0, x_2 >= 0
   encArg(z) -{ 4 + 4*s91 + 4*s93 + 107*x_115 + 32*x_115^2 + 107*x_120 + 32*x_120^2 + 107*x_29 + 32*x_29^2 }-> s95 :|: s91 >= 0, s91 <= x_115, s92 >= 0, s92 <= x_29, s93 >= 0, s93 <= s91, s94 >= 0, s94 <= x_120, s95 >= 0, s95 <= s93, x_120 >= 0, x_115 >= 0, z = 1 + (1 + x_115 + x_29) + (1 + x_120), x_29 >= 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ -74 + 43*z + 32*z^2 }-> 1 + s4 :|: s4 >= 0, s4 <= z - 1, z - 1 >= 0
   encode_f(z) -{ 0 }-> 0 :|: z >= 0
   encode_f(z) -{ 1 + 107*z + 32*z^2 }-> 1 + s218 :|: s218 >= 0, s218 <= z, z >= 0
   encode_g(z, z') -{ -143 + 4*s219 + 43*z + 32*z^2 + 43*z' + 32*z'^2 }-> s221 :|: s219 >= 0, s219 <= z - 1, s220 >= 0, s220 <= z' - 1, s221 >= 0, s221 <= 1 + s219, z - 1 >= 0, z' - 1 >= 0
   encode_g(z, z') -{ -67 + 4*s222 + 4*s223 + 107*x_148 + 32*x_148^2 + 107*x_231 + 32*x_231^2 + 43*z + 32*z^2 }-> s226 :|: s222 >= 0, s222 <= z - 1, s223 >= 0, s223 <= x_148, s224 >= 0, s224 <= x_231, s225 >= 0, s225 <= s223, s226 >= 0, s226 <= 1 + s222, z' = 1 + x_148 + x_231, z - 1 >= 0, x_231 >= 0, x_148 >= 0
   encode_g(z, z') -{ -66 + 4*s227 + 4*s228 + 107*x_149 + 32*x_149^2 + 107*x_232 + 32*x_232^2 + 43*z + 32*z^2 }-> s231 :|: s227 >= 0, s227 <= z - 1, s228 >= 0, s228 <= x_149, s229 >= 0, s229 <= x_232, s230 >= 0, s230 <= s228, s231 >= 0, s231 <= 1 + s227, x_232 >= 0, z - 1 >= 0, z' = 1 + x_149 + x_232, x_149 >= 0
   encode_g(z, z') -{ -69 + 4*s232 + 43*z + 32*z^2 }-> s233 :|: s232 >= 0, s232 <= z - 1, s233 >= 0, s233 <= 1 + s232, z - 1 >= 0, z' >= 0
   encode_g(z, z') -{ -71 + 4*s234 + 4*s236 + 107*x_145 + 32*x_145^2 + 107*x_229 + 32*x_229^2 + 43*z' + 32*z'^2 }-> s238 :|: s234 >= 0, s234 <= x_145, s235 >= 0, s235 <= x_229, s236 >= 0, s236 <= s234, s237 >= 0, s237 <= z' - 1, s238 >= 0, s238 <= s236, z = 1 + x_145 + x_229, x_145 >= 0, x_229 >= 0, z' - 1 >= 0
   encode_g(z, z') -{ 5 + 4*s239 + 4*s241 + 4*s242 + 107*x_145 + 32*x_145^2 + 107*x_151 + 32*x_151^2 + 107*x_229 + 32*x_229^2 + 107*x_233 + 32*x_233^2 }-> s245 :|: s239 >= 0, s239 <= x_145, s240 >= 0, s240 <= x_229, s241 >= 0, s241 <= s239, s242 >= 0, s242 <= x_151, s243 >= 0, s243 <= x_233, s244 >= 0, s244 <= s242, s245 >= 0, s245 <= s241, x_233 >= 0, z = 1 + x_145 + x_229, x_145 >= 0, x_229 >= 0, z' = 1 + x_151 + x_233, x_151 >= 0
   encode_g(z, z') -{ 6 + 4*s246 + 4*s248 + 4*s249 + 107*x_145 + 32*x_145^2 + 107*x_152 + 32*x_152^2 + 107*x_229 + 32*x_229^2 + 107*x_234 + 32*x_234^2 }-> s252 :|: s246 >= 0, s246 <= x_145, s247 >= 0, s247 <= x_229, s248 >= 0, s248 <= s246, s249 >= 0, s249 <= x_152, s250 >= 0, s250 <= x_234, s251 >= 0, s251 <= s249, s252 >= 0, s252 <= s248, z = 1 + x_145 + x_229, x_234 >= 0, x_145 >= 0, z' = 1 + x_152 + x_234, x_229 >= 0, x_152 >= 0
   encode_g(z, z') -{ 3 + 4*s253 + 4*s255 + 107*x_145 + 32*x_145^2 + 107*x_229 + 32*x_229^2 }-> s256 :|: s253 >= 0, s253 <= x_145, s254 >= 0, s254 <= x_229, s255 >= 0, s255 <= s253, s256 >= 0, s256 <= s255, z = 1 + x_145 + x_229, x_145 >= 0, x_229 >= 0, z' >= 0
   encode_g(z, z') -{ -70 + 4*s257 + 4*s259 + 107*x_146 + 32*x_146^2 + 107*x_230 + 32*x_230^2 + 43*z' + 32*z'^2 }-> s261 :|: s257 >= 0, s257 <= x_146, s258 >= 0, s258 <= x_230, s259 >= 0, s259 <= s257, s260 >= 0, s260 <= z' - 1, s261 >= 0, s261 <= s259, z = 1 + x_146 + x_230, x_146 >= 0, z' - 1 >= 0, x_230 >= 0
   encode_g(z, z') -{ 6 + 4*s262 + 4*s264 + 4*s265 + 107*x_146 + 32*x_146^2 + 107*x_154 + 32*x_154^2 + 107*x_230 + 32*x_230^2 + 107*x_235 + 32*x_235^2 }-> s268 :|: s262 >= 0, s262 <= x_146, s263 >= 0, s263 <= x_230, s264 >= 0, s264 <= s262, s265 >= 0, s265 <= x_154, s266 >= 0, s266 <= x_235, s267 >= 0, s267 <= s265, s268 >= 0, s268 <= s264, z = 1 + x_146 + x_230, x_146 >= 0, x_154 >= 0, z' = 1 + x_154 + x_235, x_235 >= 0, x_230 >= 0
   encode_g(z, z') -{ 7 + 4*s269 + 4*s271 + 4*s272 + 107*x_146 + 32*x_146^2 + 107*x_155 + 32*x_155^2 + 107*x_230 + 32*x_230^2 + 107*x_236 + 32*x_236^2 }-> s275 :|: s269 >= 0, s269 <= x_146, s270 >= 0, s270 <= x_230, s271 >= 0, s271 <= s269, s272 >= 0, s272 <= x_155, s273 >= 0, s273 <= x_236, s274 >= 0, s274 <= s272, s275 >= 0, s275 <= s271, z = 1 + x_146 + x_230, x_146 >= 0, x_155 >= 0, z' = 1 + x_155 + x_236, x_236 >= 0, x_230 >= 0
   encode_g(z, z') -{ 4 + 4*s276 + 4*s278 + 107*x_146 + 32*x_146^2 + 107*x_230 + 32*x_230^2 }-> s279 :|: s276 >= 0, s276 <= x_146, s277 >= 0, s277 <= x_230, s278 >= 0, s278 <= s276, s279 >= 0, s279 <= s278, z = 1 + x_146 + x_230, x_146 >= 0, z' >= 0, x_230 >= 0
   encode_g(z, z') -{ -73 + 43*z' + 32*z'^2 }-> s281 :|: s280 >= 0, s280 <= z' - 1, s281 >= 0, s281 <= 0, z >= 0, z' - 1 >= 0
   encode_g(z, z') -{ 3 + 4*s282 + 107*x_157 + 32*x_157^2 + 107*x_237 + 32*x_237^2 }-> s285 :|: s282 >= 0, s282 <= x_157, s283 >= 0, s283 <= x_237, s284 >= 0, s284 <= s282, s285 >= 0, s285 <= 0, x_237 >= 0, z >= 0, x_157 >= 0, z' = 1 + x_157 + x_237
   encode_g(z, z') -{ 4 + 4*s286 + 107*x_158 + 32*x_158^2 + 107*x_238 + 32*x_238^2 }-> s289 :|: s286 >= 0, s286 <= x_158, s287 >= 0, s287 <= x_238, s288 >= 0, s288 <= s286, s289 >= 0, s289 <= 0, z >= 0, z' = 1 + x_158 + x_238, x_158 >= 0, x_238 >= 0
   encode_g(z, z') -{ 1 }-> s3 :|: s3 >= 0, s3 <= 0, z >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_h(z, z') -{ -144 + 4*s147 + 43*z + 32*z^2 + 43*z' + 32*z'^2 }-> s149 :|: s147 >= 0, s147 <= z - 1, s148 >= 0, s148 <= z' - 1, s149 >= 0, s149 <= 1 + s147, z' - 1 >= 0, z - 1 >= 0
   encode_h(z, z') -{ -68 + 4*s150 + 4*s151 + 107*x_133 + 32*x_133^2 + 107*x_221 + 32*x_221^2 + 43*z + 32*z^2 }-> s154 :|: s150 >= 0, s150 <= z - 1, s151 >= 0, s151 <= x_133, s152 >= 0, s152 <= x_221, s153 >= 0, s153 <= s151, s154 >= 0, s154 <= 1 + s150, z' = 1 + x_133 + x_221, x_221 >= 0, x_133 >= 0, z - 1 >= 0
   encode_h(z, z') -{ -67 + 4*s155 + 4*s156 + 107*x_134 + 32*x_134^2 + 107*x_222 + 32*x_222^2 + 43*z + 32*z^2 }-> s159 :|: s155 >= 0, s155 <= z - 1, s156 >= 0, s156 <= x_134, s157 >= 0, s157 <= x_222, s158 >= 0, s158 <= s156, s159 >= 0, s159 <= 1 + s155, z' = 1 + x_134 + x_222, x_134 >= 0, x_222 >= 0, z - 1 >= 0
   encode_h(z, z') -{ -70 + 4*s160 + 43*z + 32*z^2 }-> s161 :|: s160 >= 0, s160 <= z - 1, s161 >= 0, s161 <= 1 + s160, z' >= 0, z - 1 >= 0
   encode_h(z, z') -{ -72 + 4*s162 + 4*s164 + 107*x_130 + 32*x_130^2 + 107*x_219 + 32*x_219^2 + 43*z' + 32*z'^2 }-> s166 :|: s162 >= 0, s162 <= x_130, s163 >= 0, s163 <= x_219, s164 >= 0, s164 <= s162, s165 >= 0, s165 <= z' - 1, s166 >= 0, s166 <= s164, x_130 >= 0, z = 1 + x_130 + x_219, z' - 1 >= 0, x_219 >= 0
   encode_h(z, z') -{ 4 + 4*s167 + 4*s169 + 4*s170 + 107*x_130 + 32*x_130^2 + 107*x_136 + 32*x_136^2 + 107*x_219 + 32*x_219^2 + 107*x_223 + 32*x_223^2 }-> s173 :|: s167 >= 0, s167 <= x_130, s168 >= 0, s168 <= x_219, s169 >= 0, s169 <= s167, s170 >= 0, s170 <= x_136, s171 >= 0, s171 <= x_223, s172 >= 0, s172 <= s170, s173 >= 0, s173 <= s169, z' = 1 + x_136 + x_223, x_130 >= 0, z = 1 + x_130 + x_219, x_223 >= 0, x_136 >= 0, x_219 >= 0
   encode_h(z, z') -{ 5 + 4*s174 + 4*s176 + 4*s177 + 107*x_130 + 32*x_130^2 + 107*x_137 + 32*x_137^2 + 107*x_219 + 32*x_219^2 + 107*x_224 + 32*x_224^2 }-> s180 :|: s174 >= 0, s174 <= x_130, s175 >= 0, s175 <= x_219, s176 >= 0, s176 <= s174, s177 >= 0, s177 <= x_137, s178 >= 0, s178 <= x_224, s179 >= 0, s179 <= s177, s180 >= 0, s180 <= s176, z' = 1 + x_137 + x_224, x_130 >= 0, z = 1 + x_130 + x_219, x_224 >= 0, x_137 >= 0, x_219 >= 0
   encode_h(z, z') -{ 2 + 4*s181 + 4*s183 + 107*x_130 + 32*x_130^2 + 107*x_219 + 32*x_219^2 }-> s184 :|: s181 >= 0, s181 <= x_130, s182 >= 0, s182 <= x_219, s183 >= 0, s183 <= s181, s184 >= 0, s184 <= s183, x_130 >= 0, z = 1 + x_130 + x_219, z' >= 0, x_219 >= 0
   encode_h(z, z') -{ -71 + 4*s185 + 4*s187 + 107*x_131 + 32*x_131^2 + 107*x_220 + 32*x_220^2 + 43*z' + 32*z'^2 }-> s189 :|: s185 >= 0, s185 <= x_131, s186 >= 0, s186 <= x_220, s187 >= 0, s187 <= s185, s188 >= 0, s188 <= z' - 1, s189 >= 0, s189 <= s187, z' - 1 >= 0, z = 1 + x_131 + x_220, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ 5 + 4*s190 + 4*s192 + 4*s193 + 107*x_131 + 32*x_131^2 + 107*x_139 + 32*x_139^2 + 107*x_220 + 32*x_220^2 + 107*x_225 + 32*x_225^2 }-> s196 :|: s190 >= 0, s190 <= x_131, s191 >= 0, s191 <= x_220, s192 >= 0, s192 <= s190, s193 >= 0, s193 <= x_139, s194 >= 0, s194 <= x_225, s195 >= 0, s195 <= s193, s196 >= 0, s196 <= s192, z = 1 + x_131 + x_220, z' = 1 + x_139 + x_225, x_225 >= 0, x_139 >= 0, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ 0 }-> s2 :|: s2 >= 0, s2 <= 0, z >= 0, z' >= 0
   encode_h(z, z') -{ 6 + 4*s197 + 4*s199 + 4*s200 + 107*x_131 + 32*x_131^2 + 107*x_140 + 32*x_140^2 + 107*x_220 + 32*x_220^2 + 107*x_226 + 32*x_226^2 }-> s203 :|: s197 >= 0, s197 <= x_131, s198 >= 0, s198 <= x_220, s199 >= 0, s199 <= s197, s200 >= 0, s200 <= x_140, s201 >= 0, s201 <= x_226, s202 >= 0, s202 <= s200, s203 >= 0, s203 <= s199, z = 1 + x_131 + x_220, x_226 >= 0, z' = 1 + x_140 + x_226, x_140 >= 0, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ 3 + 4*s204 + 4*s206 + 107*x_131 + 32*x_131^2 + 107*x_220 + 32*x_220^2 }-> s207 :|: s204 >= 0, s204 <= x_131, s205 >= 0, s205 <= x_220, s206 >= 0, s206 <= s204, s207 >= 0, s207 <= s206, z = 1 + x_131 + x_220, z' >= 0, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ -74 + 43*z' + 32*z'^2 }-> s209 :|: s208 >= 0, s208 <= z' - 1, s209 >= 0, s209 <= 0, z >= 0, z' - 1 >= 0
   encode_h(z, z') -{ 2 + 4*s210 + 107*x_142 + 32*x_142^2 + 107*x_227 + 32*x_227^2 }-> s213 :|: s210 >= 0, s210 <= x_142, s211 >= 0, s211 <= x_227, s212 >= 0, s212 <= s210, s213 >= 0, s213 <= 0, z >= 0, z' = 1 + x_142 + x_227, x_142 >= 0, x_227 >= 0
   encode_h(z, z') -{ 3 + 4*s214 + 107*x_143 + 32*x_143^2 + 107*x_228 + 32*x_228^2 }-> s217 :|: s214 >= 0, s214 <= x_143, s215 >= 0, s215 <= x_228, s216 >= 0, s216 <= s214, s217 >= 0, s217 <= 0, z >= 0, z' = 1 + x_143 + x_228, x_143 >= 0, x_228 >= 0
   encode_h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   g(z, z') -{ 1 + 4*z }-> s' :|: s' >= 0, s' <= z, z >= 0, z' >= 0
   h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   h(z, z') -{ -2 + 4*z }-> 1 + s :|: s >= 0, s <= z - 1, z - 1 >= 0, z' >= 0

Function symbols to be analyzed: {encode_h}, {encode_g}
Previous analysis results are:
  h: runtime: O(n^1) [4*z], size: O(n^1) [z]
  g: runtime: O(n^1) [1 + 4*z], size: O(n^1) [z]
  encArg: runtime: O(n^2) [1 + 107*z + 32*z^2], size: O(n^1) [z]
  encode_f: runtime: O(n^2) [1 + 107*z + 32*z^2], size: O(n^1) [1 + z]
  encode_h: runtime: ?, size: O(n^1) [z]

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

(41) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using KoAT for: encode_h
after applying outer abstraction to obtain an ITS,
resulting in: O(n^2) with polynomial bound: 30 + 1964*z + 640*z^2 + 1916*z' + 640*z'^2

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

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

   encArg(z) -{ 0 }-> s'' :|: s'' >= 0, s'' <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 1 }-> s1 :|: s1 >= 0, s1 <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 5 + 4*s96 + 4*s98 + 4*s99 + 107*x_115 + 32*x_115^2 + 107*x_121 + 32*x_121^2 + 107*x_213 + 32*x_213^2 + 107*x_29 + 32*x_29^2 }-> s102 :|: s96 >= 0, s96 <= x_115, s97 >= 0, s97 <= x_29, s98 >= 0, s98 <= s96, s99 >= 0, s99 <= x_121, s100 >= 0, s100 <= x_213, s101 >= 0, s101 <= s99, s102 >= 0, s102 <= s98, x_213 >= 0, x_115 >= 0, z = 1 + (1 + x_115 + x_29) + (1 + x_121 + x_213), x_29 >= 0, x_121 >= 0
   encArg(z) -{ 6 + 4*s103 + 4*s105 + 4*s106 + 107*x_115 + 32*x_115^2 + 107*x_122 + 32*x_122^2 + 107*x_214 + 32*x_214^2 + 107*x_29 + 32*x_29^2 }-> s109 :|: s103 >= 0, s103 <= x_115, s104 >= 0, s104 <= x_29, s105 >= 0, s105 <= s103, s106 >= 0, s106 <= x_122, s107 >= 0, s107 <= x_214, s108 >= 0, s108 <= s106, s109 >= 0, s109 <= s105, z = 1 + (1 + x_115 + x_29) + (1 + x_122 + x_214), x_115 >= 0, x_214 >= 0, x_122 >= 0, x_29 >= 0
   encArg(z) -{ 3 + 4*s110 + 4*s112 + 107*x_115 + 32*x_115^2 + 107*x_29 + 32*x_29^2 }-> s113 :|: s110 >= 0, s110 <= x_115, s111 >= 0, s111 <= x_29, s112 >= 0, s112 <= s110, s113 >= 0, s113 <= s112, x_115 >= 0, x_2 >= 0, z = 1 + (1 + x_115 + x_29) + x_2, x_29 >= 0
   encArg(z) -{ 5 + 4*s114 + 4*s116 + 107*x_116 + 32*x_116^2 + 107*x_123 + 32*x_123^2 + 107*x_210 + 32*x_210^2 }-> s118 :|: s114 >= 0, s114 <= x_116, s115 >= 0, s115 <= x_210, s116 >= 0, s116 <= s114, s117 >= 0, s117 <= x_123, s118 >= 0, s118 <= s116, x_123 >= 0, z = 1 + (1 + x_116 + x_210) + (1 + x_123), x_116 >= 0, x_210 >= 0
   encArg(z) -{ 7 + 4*s8 + 4*s9 + 107*x_1' + 32*x_1'^2 + 107*x_13 + 32*x_13^2 + 107*x_21 + 32*x_21^2 }-> s12 :|: s8 >= 0, s8 <= x_1', s9 >= 0, s9 <= x_13, s10 >= 0, s10 <= x_21, s11 >= 0, s11 <= s9, s12 >= 0, s12 <= 1 + s8, x_13 >= 0, x_1' >= 0, z = 1 + (1 + x_1') + (1 + x_13 + x_21), x_21 >= 0
   encArg(z) -{ 6 + 4*s119 + 4*s121 + 4*s122 + 107*x_116 + 32*x_116^2 + 107*x_124 + 32*x_124^2 + 107*x_210 + 32*x_210^2 + 107*x_215 + 32*x_215^2 }-> s125 :|: s119 >= 0, s119 <= x_116, s120 >= 0, s120 <= x_210, s121 >= 0, s121 <= s119, s122 >= 0, s122 <= x_124, s123 >= 0, s123 <= x_215, s124 >= 0, s124 <= s122, s125 >= 0, s125 <= s121, x_124 >= 0, x_215 >= 0, x_116 >= 0, z = 1 + (1 + x_116 + x_210) + (1 + x_124 + x_215), x_210 >= 0
   encArg(z) -{ 7 + 4*s126 + 4*s128 + 4*s129 + 107*x_116 + 32*x_116^2 + 107*x_125 + 32*x_125^2 + 107*x_210 + 32*x_210^2 + 107*x_216 + 32*x_216^2 }-> s132 :|: s126 >= 0, s126 <= x_116, s127 >= 0, s127 <= x_210, s128 >= 0, s128 <= s126, s129 >= 0, s129 <= x_125, s130 >= 0, s130 <= x_216, s131 >= 0, s131 <= s129, s132 >= 0, s132 <= s128, x_216 >= 0, z = 1 + (1 + x_116 + x_210) + (1 + x_125 + x_216), x_116 >= 0, x_125 >= 0, x_210 >= 0
   encArg(z) -{ 4 + 4*s133 + 4*s135 + 107*x_116 + 32*x_116^2 + 107*x_210 + 32*x_210^2 }-> s136 :|: s133 >= 0, s133 <= x_116, s134 >= 0, s134 <= x_210, s135 >= 0, s135 <= s133, s136 >= 0, s136 <= s135, x_116 >= 0, x_2 >= 0, z = 1 + (1 + x_116 + x_210) + x_2, x_210 >= 0
   encArg(z) -{ 2 + 107*x_126 + 32*x_126^2 }-> s138 :|: s137 >= 0, s137 <= x_126, s138 >= 0, s138 <= 0, x_1 >= 0, z = 1 + x_1 + (1 + x_126), x_126 >= 0
   encArg(z) -{ 3 + 4*s139 + 107*x_127 + 32*x_127^2 + 107*x_217 + 32*x_217^2 }-> s142 :|: s139 >= 0, s139 <= x_127, s140 >= 0, s140 <= x_217, s141 >= 0, s141 <= s139, s142 >= 0, s142 <= 0, x_1 >= 0, x_127 >= 0, z = 1 + x_1 + (1 + x_127 + x_217), x_217 >= 0
   encArg(z) -{ 4 + 4*s143 + 107*x_128 + 32*x_128^2 + 107*x_218 + 32*x_218^2 }-> s146 :|: s143 >= 0, s143 <= x_128, s144 >= 0, s144 <= x_218, s145 >= 0, s145 <= s143, s146 >= 0, s146 <= 0, x_1 >= 0, x_128 >= 0, z = 1 + x_1 + (1 + x_128 + x_218), x_218 >= 0
   encArg(z) -{ 8 + 4*s13 + 4*s14 + 107*x_1' + 32*x_1'^2 + 107*x_14 + 32*x_14^2 + 107*x_22 + 32*x_22^2 }-> s17 :|: s13 >= 0, s13 <= x_1', s14 >= 0, s14 <= x_14, s15 >= 0, s15 <= x_22, s16 >= 0, s16 <= s14, s17 >= 0, s17 <= 1 + s13, z = 1 + (1 + x_1') + (1 + x_14 + x_22), x_14 >= 0, x_1' >= 0, x_22 >= 0
   encArg(z) -{ 5 + 4*s18 + 107*x_1' + 32*x_1'^2 }-> s19 :|: s18 >= 0, s18 <= x_1', s19 >= 0, s19 <= 1 + s18, x_1' >= 0, x_2 >= 0, z = 1 + (1 + x_1') + x_2
   encArg(z) -{ 3 + 4*s20 + 4*s22 + 107*x_1'' + 32*x_1''^2 + 107*x_15 + 32*x_15^2 + 107*x_2' + 32*x_2'^2 }-> s24 :|: s20 >= 0, s20 <= x_1'', s21 >= 0, s21 <= x_2', s22 >= 0, s22 <= s20, s23 >= 0, s23 <= x_15, s24 >= 0, s24 <= s22, x_15 >= 0, z = 1 + (1 + x_1'' + x_2') + (1 + x_15), x_1'' >= 0, x_2' >= 0
   encArg(z) -{ 4 + 4*s25 + 4*s27 + 4*s28 + 107*x_1'' + 32*x_1''^2 + 107*x_16 + 32*x_16^2 + 107*x_2' + 32*x_2'^2 + 107*x_23 + 32*x_23^2 }-> s31 :|: s25 >= 0, s25 <= x_1'', s26 >= 0, s26 <= x_2', s27 >= 0, s27 <= s25, s28 >= 0, s28 <= x_16, s29 >= 0, s29 <= x_23, s30 >= 0, s30 <= s28, s31 >= 0, s31 <= s27, x_1'' >= 0, x_16 >= 0, x_2' >= 0, x_23 >= 0, z = 1 + (1 + x_1'' + x_2') + (1 + x_16 + x_23)
   encArg(z) -{ 5 + 4*s32 + 4*s34 + 4*s35 + 107*x_1'' + 32*x_1''^2 + 107*x_17 + 32*x_17^2 + 107*x_2' + 32*x_2'^2 + 107*x_24 + 32*x_24^2 }-> s38 :|: s32 >= 0, s32 <= x_1'', s33 >= 0, s33 <= x_2', s34 >= 0, s34 <= s32, s35 >= 0, s35 <= x_17, s36 >= 0, s36 <= x_24, s37 >= 0, s37 <= s35, s38 >= 0, s38 <= s34, x_1'' >= 0, x_2' >= 0, x_17 >= 0, x_24 >= 0, z = 1 + (1 + x_1'' + x_2') + (1 + x_17 + x_24)
   encArg(z) -{ 2 + 4*s39 + 4*s41 + 107*x_1'' + 32*x_1''^2 + 107*x_2' + 32*x_2'^2 }-> s42 :|: s39 >= 0, s39 <= x_1'', s40 >= 0, s40 <= x_2', s41 >= 0, s41 <= s39, s42 >= 0, s42 <= s41, x_1'' >= 0, x_2' >= 0, z = 1 + (1 + x_1'' + x_2') + x_2, x_2 >= 0
   encArg(z) -{ 4 + 4*s43 + 4*s45 + 107*x_11 + 32*x_11^2 + 107*x_18 + 32*x_18^2 + 107*x_2'' + 32*x_2''^2 }-> s47 :|: s43 >= 0, s43 <= x_11, s44 >= 0, s44 <= x_2'', s45 >= 0, s45 <= s43, s46 >= 0, s46 <= x_18, s47 >= 0, s47 <= s45, x_11 >= 0, z = 1 + (1 + x_11 + x_2'') + (1 + x_18), x_2'' >= 0, x_18 >= 0
   encArg(z) -{ 5 + 4*s48 + 4*s50 + 4*s51 + 107*x_11 + 32*x_11^2 + 107*x_19 + 32*x_19^2 + 107*x_2'' + 32*x_2''^2 + 107*x_25 + 32*x_25^2 }-> s54 :|: s48 >= 0, s48 <= x_11, s49 >= 0, s49 <= x_2'', s50 >= 0, s50 <= s48, s51 >= 0, s51 <= x_19, s52 >= 0, s52 <= x_25, s53 >= 0, s53 <= s51, s54 >= 0, s54 <= s50, x_11 >= 0, z = 1 + (1 + x_11 + x_2'') + (1 + x_19 + x_25), x_25 >= 0, x_2'' >= 0, x_19 >= 0
   encArg(z) -{ 6 + 4*s55 + 4*s57 + 4*s58 + 107*x_11 + 32*x_11^2 + 107*x_110 + 32*x_110^2 + 107*x_2'' + 32*x_2''^2 + 107*x_26 + 32*x_26^2 }-> s61 :|: s55 >= 0, s55 <= x_11, s56 >= 0, s56 <= x_2'', s57 >= 0, s57 <= s55, s58 >= 0, s58 <= x_110, s59 >= 0, s59 <= x_26, s60 >= 0, s60 <= s58, s61 >= 0, s61 <= s57, x_11 >= 0, x_26 >= 0, x_2'' >= 0, z = 1 + (1 + x_11 + x_2'') + (1 + x_110 + x_26), x_110 >= 0
   encArg(z) -{ 3 + 4*s62 + 4*s64 + 107*x_11 + 32*x_11^2 + 107*x_2'' + 32*x_2''^2 }-> s65 :|: s62 >= 0, s62 <= x_11, s63 >= 0, s63 <= x_2'', s64 >= 0, s64 <= s62, s65 >= 0, s65 <= s64, x_11 >= 0, x_2'' >= 0, x_2 >= 0, z = 1 + (1 + x_11 + x_2'') + x_2
   encArg(z) -{ 1 + 107*x_111 + 32*x_111^2 }-> s67 :|: s66 >= 0, s66 <= x_111, s67 >= 0, s67 <= 0, x_1 >= 0, z = 1 + x_1 + (1 + x_111), x_111 >= 0
   encArg(z) -{ 6 + 4*s5 + 107*x_1' + 32*x_1'^2 + 107*x_12 + 32*x_12^2 }-> s7 :|: s5 >= 0, s5 <= x_1', s6 >= 0, s6 <= x_12, s7 >= 0, s7 <= 1 + s5, z = 1 + (1 + x_1') + (1 + x_12), x_1' >= 0, x_12 >= 0
   encArg(z) -{ 2 + 4*s68 + 107*x_112 + 32*x_112^2 + 107*x_27 + 32*x_27^2 }-> s71 :|: s68 >= 0, s68 <= x_112, s69 >= 0, s69 <= x_27, s70 >= 0, s70 <= s68, s71 >= 0, s71 <= 0, x_1 >= 0, x_27 >= 0, z = 1 + x_1 + (1 + x_112 + x_27), x_112 >= 0
   encArg(z) -{ 3 + 4*s72 + 107*x_113 + 32*x_113^2 + 107*x_28 + 32*x_28^2 }-> s75 :|: s72 >= 0, s72 <= x_113, s73 >= 0, s73 <= x_28, s74 >= 0, s74 <= s72, s75 >= 0, s75 <= 0, x_1 >= 0, x_113 >= 0, x_28 >= 0, z = 1 + x_1 + (1 + x_113 + x_28)
   encArg(z) -{ 7 + 4*s76 + 107*x_114 + 32*x_114^2 + 107*x_117 + 32*x_117^2 }-> s78 :|: s76 >= 0, s76 <= x_114, s77 >= 0, s77 <= x_117, s78 >= 0, s78 <= 1 + s76, z = 1 + (1 + x_114) + (1 + x_117), x_117 >= 0, x_114 >= 0
   encArg(z) -{ 8 + 4*s79 + 4*s80 + 107*x_114 + 32*x_114^2 + 107*x_118 + 32*x_118^2 + 107*x_211 + 32*x_211^2 }-> s83 :|: s79 >= 0, s79 <= x_114, s80 >= 0, s80 <= x_118, s81 >= 0, s81 <= x_211, s82 >= 0, s82 <= s80, s83 >= 0, s83 <= 1 + s79, z = 1 + (1 + x_114) + (1 + x_118 + x_211), x_114 >= 0, x_118 >= 0, x_211 >= 0
   encArg(z) -{ 9 + 4*s84 + 4*s85 + 107*x_114 + 32*x_114^2 + 107*x_119 + 32*x_119^2 + 107*x_212 + 32*x_212^2 }-> s88 :|: s84 >= 0, s84 <= x_114, s85 >= 0, s85 <= x_119, s86 >= 0, s86 <= x_212, s87 >= 0, s87 <= s85, s88 >= 0, s88 <= 1 + s84, x_212 >= 0, x_114 >= 0, z = 1 + (1 + x_114) + (1 + x_119 + x_212), x_119 >= 0
   encArg(z) -{ 6 + 4*s89 + 107*x_114 + 32*x_114^2 }-> s90 :|: s89 >= 0, s89 <= x_114, s90 >= 0, s90 <= 1 + s89, z = 1 + (1 + x_114) + x_2, x_114 >= 0, x_2 >= 0
   encArg(z) -{ 4 + 4*s91 + 4*s93 + 107*x_115 + 32*x_115^2 + 107*x_120 + 32*x_120^2 + 107*x_29 + 32*x_29^2 }-> s95 :|: s91 >= 0, s91 <= x_115, s92 >= 0, s92 <= x_29, s93 >= 0, s93 <= s91, s94 >= 0, s94 <= x_120, s95 >= 0, s95 <= s93, x_120 >= 0, x_115 >= 0, z = 1 + (1 + x_115 + x_29) + (1 + x_120), x_29 >= 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ -74 + 43*z + 32*z^2 }-> 1 + s4 :|: s4 >= 0, s4 <= z - 1, z - 1 >= 0
   encode_f(z) -{ 0 }-> 0 :|: z >= 0
   encode_f(z) -{ 1 + 107*z + 32*z^2 }-> 1 + s218 :|: s218 >= 0, s218 <= z, z >= 0
   encode_g(z, z') -{ -143 + 4*s219 + 43*z + 32*z^2 + 43*z' + 32*z'^2 }-> s221 :|: s219 >= 0, s219 <= z - 1, s220 >= 0, s220 <= z' - 1, s221 >= 0, s221 <= 1 + s219, z - 1 >= 0, z' - 1 >= 0
   encode_g(z, z') -{ -67 + 4*s222 + 4*s223 + 107*x_148 + 32*x_148^2 + 107*x_231 + 32*x_231^2 + 43*z + 32*z^2 }-> s226 :|: s222 >= 0, s222 <= z - 1, s223 >= 0, s223 <= x_148, s224 >= 0, s224 <= x_231, s225 >= 0, s225 <= s223, s226 >= 0, s226 <= 1 + s222, z' = 1 + x_148 + x_231, z - 1 >= 0, x_231 >= 0, x_148 >= 0
   encode_g(z, z') -{ -66 + 4*s227 + 4*s228 + 107*x_149 + 32*x_149^2 + 107*x_232 + 32*x_232^2 + 43*z + 32*z^2 }-> s231 :|: s227 >= 0, s227 <= z - 1, s228 >= 0, s228 <= x_149, s229 >= 0, s229 <= x_232, s230 >= 0, s230 <= s228, s231 >= 0, s231 <= 1 + s227, x_232 >= 0, z - 1 >= 0, z' = 1 + x_149 + x_232, x_149 >= 0
   encode_g(z, z') -{ -69 + 4*s232 + 43*z + 32*z^2 }-> s233 :|: s232 >= 0, s232 <= z - 1, s233 >= 0, s233 <= 1 + s232, z - 1 >= 0, z' >= 0
   encode_g(z, z') -{ -71 + 4*s234 + 4*s236 + 107*x_145 + 32*x_145^2 + 107*x_229 + 32*x_229^2 + 43*z' + 32*z'^2 }-> s238 :|: s234 >= 0, s234 <= x_145, s235 >= 0, s235 <= x_229, s236 >= 0, s236 <= s234, s237 >= 0, s237 <= z' - 1, s238 >= 0, s238 <= s236, z = 1 + x_145 + x_229, x_145 >= 0, x_229 >= 0, z' - 1 >= 0
   encode_g(z, z') -{ 5 + 4*s239 + 4*s241 + 4*s242 + 107*x_145 + 32*x_145^2 + 107*x_151 + 32*x_151^2 + 107*x_229 + 32*x_229^2 + 107*x_233 + 32*x_233^2 }-> s245 :|: s239 >= 0, s239 <= x_145, s240 >= 0, s240 <= x_229, s241 >= 0, s241 <= s239, s242 >= 0, s242 <= x_151, s243 >= 0, s243 <= x_233, s244 >= 0, s244 <= s242, s245 >= 0, s245 <= s241, x_233 >= 0, z = 1 + x_145 + x_229, x_145 >= 0, x_229 >= 0, z' = 1 + x_151 + x_233, x_151 >= 0
   encode_g(z, z') -{ 6 + 4*s246 + 4*s248 + 4*s249 + 107*x_145 + 32*x_145^2 + 107*x_152 + 32*x_152^2 + 107*x_229 + 32*x_229^2 + 107*x_234 + 32*x_234^2 }-> s252 :|: s246 >= 0, s246 <= x_145, s247 >= 0, s247 <= x_229, s248 >= 0, s248 <= s246, s249 >= 0, s249 <= x_152, s250 >= 0, s250 <= x_234, s251 >= 0, s251 <= s249, s252 >= 0, s252 <= s248, z = 1 + x_145 + x_229, x_234 >= 0, x_145 >= 0, z' = 1 + x_152 + x_234, x_229 >= 0, x_152 >= 0
   encode_g(z, z') -{ 3 + 4*s253 + 4*s255 + 107*x_145 + 32*x_145^2 + 107*x_229 + 32*x_229^2 }-> s256 :|: s253 >= 0, s253 <= x_145, s254 >= 0, s254 <= x_229, s255 >= 0, s255 <= s253, s256 >= 0, s256 <= s255, z = 1 + x_145 + x_229, x_145 >= 0, x_229 >= 0, z' >= 0
   encode_g(z, z') -{ -70 + 4*s257 + 4*s259 + 107*x_146 + 32*x_146^2 + 107*x_230 + 32*x_230^2 + 43*z' + 32*z'^2 }-> s261 :|: s257 >= 0, s257 <= x_146, s258 >= 0, s258 <= x_230, s259 >= 0, s259 <= s257, s260 >= 0, s260 <= z' - 1, s261 >= 0, s261 <= s259, z = 1 + x_146 + x_230, x_146 >= 0, z' - 1 >= 0, x_230 >= 0
   encode_g(z, z') -{ 6 + 4*s262 + 4*s264 + 4*s265 + 107*x_146 + 32*x_146^2 + 107*x_154 + 32*x_154^2 + 107*x_230 + 32*x_230^2 + 107*x_235 + 32*x_235^2 }-> s268 :|: s262 >= 0, s262 <= x_146, s263 >= 0, s263 <= x_230, s264 >= 0, s264 <= s262, s265 >= 0, s265 <= x_154, s266 >= 0, s266 <= x_235, s267 >= 0, s267 <= s265, s268 >= 0, s268 <= s264, z = 1 + x_146 + x_230, x_146 >= 0, x_154 >= 0, z' = 1 + x_154 + x_235, x_235 >= 0, x_230 >= 0
   encode_g(z, z') -{ 7 + 4*s269 + 4*s271 + 4*s272 + 107*x_146 + 32*x_146^2 + 107*x_155 + 32*x_155^2 + 107*x_230 + 32*x_230^2 + 107*x_236 + 32*x_236^2 }-> s275 :|: s269 >= 0, s269 <= x_146, s270 >= 0, s270 <= x_230, s271 >= 0, s271 <= s269, s272 >= 0, s272 <= x_155, s273 >= 0, s273 <= x_236, s274 >= 0, s274 <= s272, s275 >= 0, s275 <= s271, z = 1 + x_146 + x_230, x_146 >= 0, x_155 >= 0, z' = 1 + x_155 + x_236, x_236 >= 0, x_230 >= 0
   encode_g(z, z') -{ 4 + 4*s276 + 4*s278 + 107*x_146 + 32*x_146^2 + 107*x_230 + 32*x_230^2 }-> s279 :|: s276 >= 0, s276 <= x_146, s277 >= 0, s277 <= x_230, s278 >= 0, s278 <= s276, s279 >= 0, s279 <= s278, z = 1 + x_146 + x_230, x_146 >= 0, z' >= 0, x_230 >= 0
   encode_g(z, z') -{ -73 + 43*z' + 32*z'^2 }-> s281 :|: s280 >= 0, s280 <= z' - 1, s281 >= 0, s281 <= 0, z >= 0, z' - 1 >= 0
   encode_g(z, z') -{ 3 + 4*s282 + 107*x_157 + 32*x_157^2 + 107*x_237 + 32*x_237^2 }-> s285 :|: s282 >= 0, s282 <= x_157, s283 >= 0, s283 <= x_237, s284 >= 0, s284 <= s282, s285 >= 0, s285 <= 0, x_237 >= 0, z >= 0, x_157 >= 0, z' = 1 + x_157 + x_237
   encode_g(z, z') -{ 4 + 4*s286 + 107*x_158 + 32*x_158^2 + 107*x_238 + 32*x_238^2 }-> s289 :|: s286 >= 0, s286 <= x_158, s287 >= 0, s287 <= x_238, s288 >= 0, s288 <= s286, s289 >= 0, s289 <= 0, z >= 0, z' = 1 + x_158 + x_238, x_158 >= 0, x_238 >= 0
   encode_g(z, z') -{ 1 }-> s3 :|: s3 >= 0, s3 <= 0, z >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_h(z, z') -{ -144 + 4*s147 + 43*z + 32*z^2 + 43*z' + 32*z'^2 }-> s149 :|: s147 >= 0, s147 <= z - 1, s148 >= 0, s148 <= z' - 1, s149 >= 0, s149 <= 1 + s147, z' - 1 >= 0, z - 1 >= 0
   encode_h(z, z') -{ -68 + 4*s150 + 4*s151 + 107*x_133 + 32*x_133^2 + 107*x_221 + 32*x_221^2 + 43*z + 32*z^2 }-> s154 :|: s150 >= 0, s150 <= z - 1, s151 >= 0, s151 <= x_133, s152 >= 0, s152 <= x_221, s153 >= 0, s153 <= s151, s154 >= 0, s154 <= 1 + s150, z' = 1 + x_133 + x_221, x_221 >= 0, x_133 >= 0, z - 1 >= 0
   encode_h(z, z') -{ -67 + 4*s155 + 4*s156 + 107*x_134 + 32*x_134^2 + 107*x_222 + 32*x_222^2 + 43*z + 32*z^2 }-> s159 :|: s155 >= 0, s155 <= z - 1, s156 >= 0, s156 <= x_134, s157 >= 0, s157 <= x_222, s158 >= 0, s158 <= s156, s159 >= 0, s159 <= 1 + s155, z' = 1 + x_134 + x_222, x_134 >= 0, x_222 >= 0, z - 1 >= 0
   encode_h(z, z') -{ -70 + 4*s160 + 43*z + 32*z^2 }-> s161 :|: s160 >= 0, s160 <= z - 1, s161 >= 0, s161 <= 1 + s160, z' >= 0, z - 1 >= 0
   encode_h(z, z') -{ -72 + 4*s162 + 4*s164 + 107*x_130 + 32*x_130^2 + 107*x_219 + 32*x_219^2 + 43*z' + 32*z'^2 }-> s166 :|: s162 >= 0, s162 <= x_130, s163 >= 0, s163 <= x_219, s164 >= 0, s164 <= s162, s165 >= 0, s165 <= z' - 1, s166 >= 0, s166 <= s164, x_130 >= 0, z = 1 + x_130 + x_219, z' - 1 >= 0, x_219 >= 0
   encode_h(z, z') -{ 4 + 4*s167 + 4*s169 + 4*s170 + 107*x_130 + 32*x_130^2 + 107*x_136 + 32*x_136^2 + 107*x_219 + 32*x_219^2 + 107*x_223 + 32*x_223^2 }-> s173 :|: s167 >= 0, s167 <= x_130, s168 >= 0, s168 <= x_219, s169 >= 0, s169 <= s167, s170 >= 0, s170 <= x_136, s171 >= 0, s171 <= x_223, s172 >= 0, s172 <= s170, s173 >= 0, s173 <= s169, z' = 1 + x_136 + x_223, x_130 >= 0, z = 1 + x_130 + x_219, x_223 >= 0, x_136 >= 0, x_219 >= 0
   encode_h(z, z') -{ 5 + 4*s174 + 4*s176 + 4*s177 + 107*x_130 + 32*x_130^2 + 107*x_137 + 32*x_137^2 + 107*x_219 + 32*x_219^2 + 107*x_224 + 32*x_224^2 }-> s180 :|: s174 >= 0, s174 <= x_130, s175 >= 0, s175 <= x_219, s176 >= 0, s176 <= s174, s177 >= 0, s177 <= x_137, s178 >= 0, s178 <= x_224, s179 >= 0, s179 <= s177, s180 >= 0, s180 <= s176, z' = 1 + x_137 + x_224, x_130 >= 0, z = 1 + x_130 + x_219, x_224 >= 0, x_137 >= 0, x_219 >= 0
   encode_h(z, z') -{ 2 + 4*s181 + 4*s183 + 107*x_130 + 32*x_130^2 + 107*x_219 + 32*x_219^2 }-> s184 :|: s181 >= 0, s181 <= x_130, s182 >= 0, s182 <= x_219, s183 >= 0, s183 <= s181, s184 >= 0, s184 <= s183, x_130 >= 0, z = 1 + x_130 + x_219, z' >= 0, x_219 >= 0
   encode_h(z, z') -{ -71 + 4*s185 + 4*s187 + 107*x_131 + 32*x_131^2 + 107*x_220 + 32*x_220^2 + 43*z' + 32*z'^2 }-> s189 :|: s185 >= 0, s185 <= x_131, s186 >= 0, s186 <= x_220, s187 >= 0, s187 <= s185, s188 >= 0, s188 <= z' - 1, s189 >= 0, s189 <= s187, z' - 1 >= 0, z = 1 + x_131 + x_220, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ 5 + 4*s190 + 4*s192 + 4*s193 + 107*x_131 + 32*x_131^2 + 107*x_139 + 32*x_139^2 + 107*x_220 + 32*x_220^2 + 107*x_225 + 32*x_225^2 }-> s196 :|: s190 >= 0, s190 <= x_131, s191 >= 0, s191 <= x_220, s192 >= 0, s192 <= s190, s193 >= 0, s193 <= x_139, s194 >= 0, s194 <= x_225, s195 >= 0, s195 <= s193, s196 >= 0, s196 <= s192, z = 1 + x_131 + x_220, z' = 1 + x_139 + x_225, x_225 >= 0, x_139 >= 0, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ 0 }-> s2 :|: s2 >= 0, s2 <= 0, z >= 0, z' >= 0
   encode_h(z, z') -{ 6 + 4*s197 + 4*s199 + 4*s200 + 107*x_131 + 32*x_131^2 + 107*x_140 + 32*x_140^2 + 107*x_220 + 32*x_220^2 + 107*x_226 + 32*x_226^2 }-> s203 :|: s197 >= 0, s197 <= x_131, s198 >= 0, s198 <= x_220, s199 >= 0, s199 <= s197, s200 >= 0, s200 <= x_140, s201 >= 0, s201 <= x_226, s202 >= 0, s202 <= s200, s203 >= 0, s203 <= s199, z = 1 + x_131 + x_220, x_226 >= 0, z' = 1 + x_140 + x_226, x_140 >= 0, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ 3 + 4*s204 + 4*s206 + 107*x_131 + 32*x_131^2 + 107*x_220 + 32*x_220^2 }-> s207 :|: s204 >= 0, s204 <= x_131, s205 >= 0, s205 <= x_220, s206 >= 0, s206 <= s204, s207 >= 0, s207 <= s206, z = 1 + x_131 + x_220, z' >= 0, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ -74 + 43*z' + 32*z'^2 }-> s209 :|: s208 >= 0, s208 <= z' - 1, s209 >= 0, s209 <= 0, z >= 0, z' - 1 >= 0
   encode_h(z, z') -{ 2 + 4*s210 + 107*x_142 + 32*x_142^2 + 107*x_227 + 32*x_227^2 }-> s213 :|: s210 >= 0, s210 <= x_142, s211 >= 0, s211 <= x_227, s212 >= 0, s212 <= s210, s213 >= 0, s213 <= 0, z >= 0, z' = 1 + x_142 + x_227, x_142 >= 0, x_227 >= 0
   encode_h(z, z') -{ 3 + 4*s214 + 107*x_143 + 32*x_143^2 + 107*x_228 + 32*x_228^2 }-> s217 :|: s214 >= 0, s214 <= x_143, s215 >= 0, s215 <= x_228, s216 >= 0, s216 <= s214, s217 >= 0, s217 <= 0, z >= 0, z' = 1 + x_143 + x_228, x_143 >= 0, x_228 >= 0
   encode_h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   g(z, z') -{ 1 + 4*z }-> s' :|: s' >= 0, s' <= z, z >= 0, z' >= 0
   h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   h(z, z') -{ -2 + 4*z }-> 1 + s :|: s >= 0, s <= z - 1, z - 1 >= 0, z' >= 0

Function symbols to be analyzed: {encode_g}
Previous analysis results are:
  h: runtime: O(n^1) [4*z], size: O(n^1) [z]
  g: runtime: O(n^1) [1 + 4*z], size: O(n^1) [z]
  encArg: runtime: O(n^2) [1 + 107*z + 32*z^2], size: O(n^1) [z]
  encode_f: runtime: O(n^2) [1 + 107*z + 32*z^2], size: O(n^1) [1 + z]
  encode_h: runtime: O(n^2) [30 + 1964*z + 640*z^2 + 1916*z' + 640*z'^2], size: O(n^1) [z]

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(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:

   encArg(z) -{ 0 }-> s'' :|: s'' >= 0, s'' <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 1 }-> s1 :|: s1 >= 0, s1 <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 5 + 4*s96 + 4*s98 + 4*s99 + 107*x_115 + 32*x_115^2 + 107*x_121 + 32*x_121^2 + 107*x_213 + 32*x_213^2 + 107*x_29 + 32*x_29^2 }-> s102 :|: s96 >= 0, s96 <= x_115, s97 >= 0, s97 <= x_29, s98 >= 0, s98 <= s96, s99 >= 0, s99 <= x_121, s100 >= 0, s100 <= x_213, s101 >= 0, s101 <= s99, s102 >= 0, s102 <= s98, x_213 >= 0, x_115 >= 0, z = 1 + (1 + x_115 + x_29) + (1 + x_121 + x_213), x_29 >= 0, x_121 >= 0
   encArg(z) -{ 6 + 4*s103 + 4*s105 + 4*s106 + 107*x_115 + 32*x_115^2 + 107*x_122 + 32*x_122^2 + 107*x_214 + 32*x_214^2 + 107*x_29 + 32*x_29^2 }-> s109 :|: s103 >= 0, s103 <= x_115, s104 >= 0, s104 <= x_29, s105 >= 0, s105 <= s103, s106 >= 0, s106 <= x_122, s107 >= 0, s107 <= x_214, s108 >= 0, s108 <= s106, s109 >= 0, s109 <= s105, z = 1 + (1 + x_115 + x_29) + (1 + x_122 + x_214), x_115 >= 0, x_214 >= 0, x_122 >= 0, x_29 >= 0
   encArg(z) -{ 3 + 4*s110 + 4*s112 + 107*x_115 + 32*x_115^2 + 107*x_29 + 32*x_29^2 }-> s113 :|: s110 >= 0, s110 <= x_115, s111 >= 0, s111 <= x_29, s112 >= 0, s112 <= s110, s113 >= 0, s113 <= s112, x_115 >= 0, x_2 >= 0, z = 1 + (1 + x_115 + x_29) + x_2, x_29 >= 0
   encArg(z) -{ 5 + 4*s114 + 4*s116 + 107*x_116 + 32*x_116^2 + 107*x_123 + 32*x_123^2 + 107*x_210 + 32*x_210^2 }-> s118 :|: s114 >= 0, s114 <= x_116, s115 >= 0, s115 <= x_210, s116 >= 0, s116 <= s114, s117 >= 0, s117 <= x_123, s118 >= 0, s118 <= s116, x_123 >= 0, z = 1 + (1 + x_116 + x_210) + (1 + x_123), x_116 >= 0, x_210 >= 0
   encArg(z) -{ 7 + 4*s8 + 4*s9 + 107*x_1' + 32*x_1'^2 + 107*x_13 + 32*x_13^2 + 107*x_21 + 32*x_21^2 }-> s12 :|: s8 >= 0, s8 <= x_1', s9 >= 0, s9 <= x_13, s10 >= 0, s10 <= x_21, s11 >= 0, s11 <= s9, s12 >= 0, s12 <= 1 + s8, x_13 >= 0, x_1' >= 0, z = 1 + (1 + x_1') + (1 + x_13 + x_21), x_21 >= 0
   encArg(z) -{ 6 + 4*s119 + 4*s121 + 4*s122 + 107*x_116 + 32*x_116^2 + 107*x_124 + 32*x_124^2 + 107*x_210 + 32*x_210^2 + 107*x_215 + 32*x_215^2 }-> s125 :|: s119 >= 0, s119 <= x_116, s120 >= 0, s120 <= x_210, s121 >= 0, s121 <= s119, s122 >= 0, s122 <= x_124, s123 >= 0, s123 <= x_215, s124 >= 0, s124 <= s122, s125 >= 0, s125 <= s121, x_124 >= 0, x_215 >= 0, x_116 >= 0, z = 1 + (1 + x_116 + x_210) + (1 + x_124 + x_215), x_210 >= 0
   encArg(z) -{ 7 + 4*s126 + 4*s128 + 4*s129 + 107*x_116 + 32*x_116^2 + 107*x_125 + 32*x_125^2 + 107*x_210 + 32*x_210^2 + 107*x_216 + 32*x_216^2 }-> s132 :|: s126 >= 0, s126 <= x_116, s127 >= 0, s127 <= x_210, s128 >= 0, s128 <= s126, s129 >= 0, s129 <= x_125, s130 >= 0, s130 <= x_216, s131 >= 0, s131 <= s129, s132 >= 0, s132 <= s128, x_216 >= 0, z = 1 + (1 + x_116 + x_210) + (1 + x_125 + x_216), x_116 >= 0, x_125 >= 0, x_210 >= 0
   encArg(z) -{ 4 + 4*s133 + 4*s135 + 107*x_116 + 32*x_116^2 + 107*x_210 + 32*x_210^2 }-> s136 :|: s133 >= 0, s133 <= x_116, s134 >= 0, s134 <= x_210, s135 >= 0, s135 <= s133, s136 >= 0, s136 <= s135, x_116 >= 0, x_2 >= 0, z = 1 + (1 + x_116 + x_210) + x_2, x_210 >= 0
   encArg(z) -{ 2 + 107*x_126 + 32*x_126^2 }-> s138 :|: s137 >= 0, s137 <= x_126, s138 >= 0, s138 <= 0, x_1 >= 0, z = 1 + x_1 + (1 + x_126), x_126 >= 0
   encArg(z) -{ 3 + 4*s139 + 107*x_127 + 32*x_127^2 + 107*x_217 + 32*x_217^2 }-> s142 :|: s139 >= 0, s139 <= x_127, s140 >= 0, s140 <= x_217, s141 >= 0, s141 <= s139, s142 >= 0, s142 <= 0, x_1 >= 0, x_127 >= 0, z = 1 + x_1 + (1 + x_127 + x_217), x_217 >= 0
   encArg(z) -{ 4 + 4*s143 + 107*x_128 + 32*x_128^2 + 107*x_218 + 32*x_218^2 }-> s146 :|: s143 >= 0, s143 <= x_128, s144 >= 0, s144 <= x_218, s145 >= 0, s145 <= s143, s146 >= 0, s146 <= 0, x_1 >= 0, x_128 >= 0, z = 1 + x_1 + (1 + x_128 + x_218), x_218 >= 0
   encArg(z) -{ 8 + 4*s13 + 4*s14 + 107*x_1' + 32*x_1'^2 + 107*x_14 + 32*x_14^2 + 107*x_22 + 32*x_22^2 }-> s17 :|: s13 >= 0, s13 <= x_1', s14 >= 0, s14 <= x_14, s15 >= 0, s15 <= x_22, s16 >= 0, s16 <= s14, s17 >= 0, s17 <= 1 + s13, z = 1 + (1 + x_1') + (1 + x_14 + x_22), x_14 >= 0, x_1' >= 0, x_22 >= 0
   encArg(z) -{ 5 + 4*s18 + 107*x_1' + 32*x_1'^2 }-> s19 :|: s18 >= 0, s18 <= x_1', s19 >= 0, s19 <= 1 + s18, x_1' >= 0, x_2 >= 0, z = 1 + (1 + x_1') + x_2
   encArg(z) -{ 3 + 4*s20 + 4*s22 + 107*x_1'' + 32*x_1''^2 + 107*x_15 + 32*x_15^2 + 107*x_2' + 32*x_2'^2 }-> s24 :|: s20 >= 0, s20 <= x_1'', s21 >= 0, s21 <= x_2', s22 >= 0, s22 <= s20, s23 >= 0, s23 <= x_15, s24 >= 0, s24 <= s22, x_15 >= 0, z = 1 + (1 + x_1'' + x_2') + (1 + x_15), x_1'' >= 0, x_2' >= 0
   encArg(z) -{ 4 + 4*s25 + 4*s27 + 4*s28 + 107*x_1'' + 32*x_1''^2 + 107*x_16 + 32*x_16^2 + 107*x_2' + 32*x_2'^2 + 107*x_23 + 32*x_23^2 }-> s31 :|: s25 >= 0, s25 <= x_1'', s26 >= 0, s26 <= x_2', s27 >= 0, s27 <= s25, s28 >= 0, s28 <= x_16, s29 >= 0, s29 <= x_23, s30 >= 0, s30 <= s28, s31 >= 0, s31 <= s27, x_1'' >= 0, x_16 >= 0, x_2' >= 0, x_23 >= 0, z = 1 + (1 + x_1'' + x_2') + (1 + x_16 + x_23)
   encArg(z) -{ 5 + 4*s32 + 4*s34 + 4*s35 + 107*x_1'' + 32*x_1''^2 + 107*x_17 + 32*x_17^2 + 107*x_2' + 32*x_2'^2 + 107*x_24 + 32*x_24^2 }-> s38 :|: s32 >= 0, s32 <= x_1'', s33 >= 0, s33 <= x_2', s34 >= 0, s34 <= s32, s35 >= 0, s35 <= x_17, s36 >= 0, s36 <= x_24, s37 >= 0, s37 <= s35, s38 >= 0, s38 <= s34, x_1'' >= 0, x_2' >= 0, x_17 >= 0, x_24 >= 0, z = 1 + (1 + x_1'' + x_2') + (1 + x_17 + x_24)
   encArg(z) -{ 2 + 4*s39 + 4*s41 + 107*x_1'' + 32*x_1''^2 + 107*x_2' + 32*x_2'^2 }-> s42 :|: s39 >= 0, s39 <= x_1'', s40 >= 0, s40 <= x_2', s41 >= 0, s41 <= s39, s42 >= 0, s42 <= s41, x_1'' >= 0, x_2' >= 0, z = 1 + (1 + x_1'' + x_2') + x_2, x_2 >= 0
   encArg(z) -{ 4 + 4*s43 + 4*s45 + 107*x_11 + 32*x_11^2 + 107*x_18 + 32*x_18^2 + 107*x_2'' + 32*x_2''^2 }-> s47 :|: s43 >= 0, s43 <= x_11, s44 >= 0, s44 <= x_2'', s45 >= 0, s45 <= s43, s46 >= 0, s46 <= x_18, s47 >= 0, s47 <= s45, x_11 >= 0, z = 1 + (1 + x_11 + x_2'') + (1 + x_18), x_2'' >= 0, x_18 >= 0
   encArg(z) -{ 5 + 4*s48 + 4*s50 + 4*s51 + 107*x_11 + 32*x_11^2 + 107*x_19 + 32*x_19^2 + 107*x_2'' + 32*x_2''^2 + 107*x_25 + 32*x_25^2 }-> s54 :|: s48 >= 0, s48 <= x_11, s49 >= 0, s49 <= x_2'', s50 >= 0, s50 <= s48, s51 >= 0, s51 <= x_19, s52 >= 0, s52 <= x_25, s53 >= 0, s53 <= s51, s54 >= 0, s54 <= s50, x_11 >= 0, z = 1 + (1 + x_11 + x_2'') + (1 + x_19 + x_25), x_25 >= 0, x_2'' >= 0, x_19 >= 0
   encArg(z) -{ 6 + 4*s55 + 4*s57 + 4*s58 + 107*x_11 + 32*x_11^2 + 107*x_110 + 32*x_110^2 + 107*x_2'' + 32*x_2''^2 + 107*x_26 + 32*x_26^2 }-> s61 :|: s55 >= 0, s55 <= x_11, s56 >= 0, s56 <= x_2'', s57 >= 0, s57 <= s55, s58 >= 0, s58 <= x_110, s59 >= 0, s59 <= x_26, s60 >= 0, s60 <= s58, s61 >= 0, s61 <= s57, x_11 >= 0, x_26 >= 0, x_2'' >= 0, z = 1 + (1 + x_11 + x_2'') + (1 + x_110 + x_26), x_110 >= 0
   encArg(z) -{ 3 + 4*s62 + 4*s64 + 107*x_11 + 32*x_11^2 + 107*x_2'' + 32*x_2''^2 }-> s65 :|: s62 >= 0, s62 <= x_11, s63 >= 0, s63 <= x_2'', s64 >= 0, s64 <= s62, s65 >= 0, s65 <= s64, x_11 >= 0, x_2'' >= 0, x_2 >= 0, z = 1 + (1 + x_11 + x_2'') + x_2
   encArg(z) -{ 1 + 107*x_111 + 32*x_111^2 }-> s67 :|: s66 >= 0, s66 <= x_111, s67 >= 0, s67 <= 0, x_1 >= 0, z = 1 + x_1 + (1 + x_111), x_111 >= 0
   encArg(z) -{ 6 + 4*s5 + 107*x_1' + 32*x_1'^2 + 107*x_12 + 32*x_12^2 }-> s7 :|: s5 >= 0, s5 <= x_1', s6 >= 0, s6 <= x_12, s7 >= 0, s7 <= 1 + s5, z = 1 + (1 + x_1') + (1 + x_12), x_1' >= 0, x_12 >= 0
   encArg(z) -{ 2 + 4*s68 + 107*x_112 + 32*x_112^2 + 107*x_27 + 32*x_27^2 }-> s71 :|: s68 >= 0, s68 <= x_112, s69 >= 0, s69 <= x_27, s70 >= 0, s70 <= s68, s71 >= 0, s71 <= 0, x_1 >= 0, x_27 >= 0, z = 1 + x_1 + (1 + x_112 + x_27), x_112 >= 0
   encArg(z) -{ 3 + 4*s72 + 107*x_113 + 32*x_113^2 + 107*x_28 + 32*x_28^2 }-> s75 :|: s72 >= 0, s72 <= x_113, s73 >= 0, s73 <= x_28, s74 >= 0, s74 <= s72, s75 >= 0, s75 <= 0, x_1 >= 0, x_113 >= 0, x_28 >= 0, z = 1 + x_1 + (1 + x_113 + x_28)
   encArg(z) -{ 7 + 4*s76 + 107*x_114 + 32*x_114^2 + 107*x_117 + 32*x_117^2 }-> s78 :|: s76 >= 0, s76 <= x_114, s77 >= 0, s77 <= x_117, s78 >= 0, s78 <= 1 + s76, z = 1 + (1 + x_114) + (1 + x_117), x_117 >= 0, x_114 >= 0
   encArg(z) -{ 8 + 4*s79 + 4*s80 + 107*x_114 + 32*x_114^2 + 107*x_118 + 32*x_118^2 + 107*x_211 + 32*x_211^2 }-> s83 :|: s79 >= 0, s79 <= x_114, s80 >= 0, s80 <= x_118, s81 >= 0, s81 <= x_211, s82 >= 0, s82 <= s80, s83 >= 0, s83 <= 1 + s79, z = 1 + (1 + x_114) + (1 + x_118 + x_211), x_114 >= 0, x_118 >= 0, x_211 >= 0
   encArg(z) -{ 9 + 4*s84 + 4*s85 + 107*x_114 + 32*x_114^2 + 107*x_119 + 32*x_119^2 + 107*x_212 + 32*x_212^2 }-> s88 :|: s84 >= 0, s84 <= x_114, s85 >= 0, s85 <= x_119, s86 >= 0, s86 <= x_212, s87 >= 0, s87 <= s85, s88 >= 0, s88 <= 1 + s84, x_212 >= 0, x_114 >= 0, z = 1 + (1 + x_114) + (1 + x_119 + x_212), x_119 >= 0
   encArg(z) -{ 6 + 4*s89 + 107*x_114 + 32*x_114^2 }-> s90 :|: s89 >= 0, s89 <= x_114, s90 >= 0, s90 <= 1 + s89, z = 1 + (1 + x_114) + x_2, x_114 >= 0, x_2 >= 0
   encArg(z) -{ 4 + 4*s91 + 4*s93 + 107*x_115 + 32*x_115^2 + 107*x_120 + 32*x_120^2 + 107*x_29 + 32*x_29^2 }-> s95 :|: s91 >= 0, s91 <= x_115, s92 >= 0, s92 <= x_29, s93 >= 0, s93 <= s91, s94 >= 0, s94 <= x_120, s95 >= 0, s95 <= s93, x_120 >= 0, x_115 >= 0, z = 1 + (1 + x_115 + x_29) + (1 + x_120), x_29 >= 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ -74 + 43*z + 32*z^2 }-> 1 + s4 :|: s4 >= 0, s4 <= z - 1, z - 1 >= 0
   encode_f(z) -{ 0 }-> 0 :|: z >= 0
   encode_f(z) -{ 1 + 107*z + 32*z^2 }-> 1 + s218 :|: s218 >= 0, s218 <= z, z >= 0
   encode_g(z, z') -{ -143 + 4*s219 + 43*z + 32*z^2 + 43*z' + 32*z'^2 }-> s221 :|: s219 >= 0, s219 <= z - 1, s220 >= 0, s220 <= z' - 1, s221 >= 0, s221 <= 1 + s219, z - 1 >= 0, z' - 1 >= 0
   encode_g(z, z') -{ -67 + 4*s222 + 4*s223 + 107*x_148 + 32*x_148^2 + 107*x_231 + 32*x_231^2 + 43*z + 32*z^2 }-> s226 :|: s222 >= 0, s222 <= z - 1, s223 >= 0, s223 <= x_148, s224 >= 0, s224 <= x_231, s225 >= 0, s225 <= s223, s226 >= 0, s226 <= 1 + s222, z' = 1 + x_148 + x_231, z - 1 >= 0, x_231 >= 0, x_148 >= 0
   encode_g(z, z') -{ -66 + 4*s227 + 4*s228 + 107*x_149 + 32*x_149^2 + 107*x_232 + 32*x_232^2 + 43*z + 32*z^2 }-> s231 :|: s227 >= 0, s227 <= z - 1, s228 >= 0, s228 <= x_149, s229 >= 0, s229 <= x_232, s230 >= 0, s230 <= s228, s231 >= 0, s231 <= 1 + s227, x_232 >= 0, z - 1 >= 0, z' = 1 + x_149 + x_232, x_149 >= 0
   encode_g(z, z') -{ -69 + 4*s232 + 43*z + 32*z^2 }-> s233 :|: s232 >= 0, s232 <= z - 1, s233 >= 0, s233 <= 1 + s232, z - 1 >= 0, z' >= 0
   encode_g(z, z') -{ -71 + 4*s234 + 4*s236 + 107*x_145 + 32*x_145^2 + 107*x_229 + 32*x_229^2 + 43*z' + 32*z'^2 }-> s238 :|: s234 >= 0, s234 <= x_145, s235 >= 0, s235 <= x_229, s236 >= 0, s236 <= s234, s237 >= 0, s237 <= z' - 1, s238 >= 0, s238 <= s236, z = 1 + x_145 + x_229, x_145 >= 0, x_229 >= 0, z' - 1 >= 0
   encode_g(z, z') -{ 5 + 4*s239 + 4*s241 + 4*s242 + 107*x_145 + 32*x_145^2 + 107*x_151 + 32*x_151^2 + 107*x_229 + 32*x_229^2 + 107*x_233 + 32*x_233^2 }-> s245 :|: s239 >= 0, s239 <= x_145, s240 >= 0, s240 <= x_229, s241 >= 0, s241 <= s239, s242 >= 0, s242 <= x_151, s243 >= 0, s243 <= x_233, s244 >= 0, s244 <= s242, s245 >= 0, s245 <= s241, x_233 >= 0, z = 1 + x_145 + x_229, x_145 >= 0, x_229 >= 0, z' = 1 + x_151 + x_233, x_151 >= 0
   encode_g(z, z') -{ 6 + 4*s246 + 4*s248 + 4*s249 + 107*x_145 + 32*x_145^2 + 107*x_152 + 32*x_152^2 + 107*x_229 + 32*x_229^2 + 107*x_234 + 32*x_234^2 }-> s252 :|: s246 >= 0, s246 <= x_145, s247 >= 0, s247 <= x_229, s248 >= 0, s248 <= s246, s249 >= 0, s249 <= x_152, s250 >= 0, s250 <= x_234, s251 >= 0, s251 <= s249, s252 >= 0, s252 <= s248, z = 1 + x_145 + x_229, x_234 >= 0, x_145 >= 0, z' = 1 + x_152 + x_234, x_229 >= 0, x_152 >= 0
   encode_g(z, z') -{ 3 + 4*s253 + 4*s255 + 107*x_145 + 32*x_145^2 + 107*x_229 + 32*x_229^2 }-> s256 :|: s253 >= 0, s253 <= x_145, s254 >= 0, s254 <= x_229, s255 >= 0, s255 <= s253, s256 >= 0, s256 <= s255, z = 1 + x_145 + x_229, x_145 >= 0, x_229 >= 0, z' >= 0
   encode_g(z, z') -{ -70 + 4*s257 + 4*s259 + 107*x_146 + 32*x_146^2 + 107*x_230 + 32*x_230^2 + 43*z' + 32*z'^2 }-> s261 :|: s257 >= 0, s257 <= x_146, s258 >= 0, s258 <= x_230, s259 >= 0, s259 <= s257, s260 >= 0, s260 <= z' - 1, s261 >= 0, s261 <= s259, z = 1 + x_146 + x_230, x_146 >= 0, z' - 1 >= 0, x_230 >= 0
   encode_g(z, z') -{ 6 + 4*s262 + 4*s264 + 4*s265 + 107*x_146 + 32*x_146^2 + 107*x_154 + 32*x_154^2 + 107*x_230 + 32*x_230^2 + 107*x_235 + 32*x_235^2 }-> s268 :|: s262 >= 0, s262 <= x_146, s263 >= 0, s263 <= x_230, s264 >= 0, s264 <= s262, s265 >= 0, s265 <= x_154, s266 >= 0, s266 <= x_235, s267 >= 0, s267 <= s265, s268 >= 0, s268 <= s264, z = 1 + x_146 + x_230, x_146 >= 0, x_154 >= 0, z' = 1 + x_154 + x_235, x_235 >= 0, x_230 >= 0
   encode_g(z, z') -{ 7 + 4*s269 + 4*s271 + 4*s272 + 107*x_146 + 32*x_146^2 + 107*x_155 + 32*x_155^2 + 107*x_230 + 32*x_230^2 + 107*x_236 + 32*x_236^2 }-> s275 :|: s269 >= 0, s269 <= x_146, s270 >= 0, s270 <= x_230, s271 >= 0, s271 <= s269, s272 >= 0, s272 <= x_155, s273 >= 0, s273 <= x_236, s274 >= 0, s274 <= s272, s275 >= 0, s275 <= s271, z = 1 + x_146 + x_230, x_146 >= 0, x_155 >= 0, z' = 1 + x_155 + x_236, x_236 >= 0, x_230 >= 0
   encode_g(z, z') -{ 4 + 4*s276 + 4*s278 + 107*x_146 + 32*x_146^2 + 107*x_230 + 32*x_230^2 }-> s279 :|: s276 >= 0, s276 <= x_146, s277 >= 0, s277 <= x_230, s278 >= 0, s278 <= s276, s279 >= 0, s279 <= s278, z = 1 + x_146 + x_230, x_146 >= 0, z' >= 0, x_230 >= 0
   encode_g(z, z') -{ -73 + 43*z' + 32*z'^2 }-> s281 :|: s280 >= 0, s280 <= z' - 1, s281 >= 0, s281 <= 0, z >= 0, z' - 1 >= 0
   encode_g(z, z') -{ 3 + 4*s282 + 107*x_157 + 32*x_157^2 + 107*x_237 + 32*x_237^2 }-> s285 :|: s282 >= 0, s282 <= x_157, s283 >= 0, s283 <= x_237, s284 >= 0, s284 <= s282, s285 >= 0, s285 <= 0, x_237 >= 0, z >= 0, x_157 >= 0, z' = 1 + x_157 + x_237
   encode_g(z, z') -{ 4 + 4*s286 + 107*x_158 + 32*x_158^2 + 107*x_238 + 32*x_238^2 }-> s289 :|: s286 >= 0, s286 <= x_158, s287 >= 0, s287 <= x_238, s288 >= 0, s288 <= s286, s289 >= 0, s289 <= 0, z >= 0, z' = 1 + x_158 + x_238, x_158 >= 0, x_238 >= 0
   encode_g(z, z') -{ 1 }-> s3 :|: s3 >= 0, s3 <= 0, z >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_h(z, z') -{ -144 + 4*s147 + 43*z + 32*z^2 + 43*z' + 32*z'^2 }-> s149 :|: s147 >= 0, s147 <= z - 1, s148 >= 0, s148 <= z' - 1, s149 >= 0, s149 <= 1 + s147, z' - 1 >= 0, z - 1 >= 0
   encode_h(z, z') -{ -68 + 4*s150 + 4*s151 + 107*x_133 + 32*x_133^2 + 107*x_221 + 32*x_221^2 + 43*z + 32*z^2 }-> s154 :|: s150 >= 0, s150 <= z - 1, s151 >= 0, s151 <= x_133, s152 >= 0, s152 <= x_221, s153 >= 0, s153 <= s151, s154 >= 0, s154 <= 1 + s150, z' = 1 + x_133 + x_221, x_221 >= 0, x_133 >= 0, z - 1 >= 0
   encode_h(z, z') -{ -67 + 4*s155 + 4*s156 + 107*x_134 + 32*x_134^2 + 107*x_222 + 32*x_222^2 + 43*z + 32*z^2 }-> s159 :|: s155 >= 0, s155 <= z - 1, s156 >= 0, s156 <= x_134, s157 >= 0, s157 <= x_222, s158 >= 0, s158 <= s156, s159 >= 0, s159 <= 1 + s155, z' = 1 + x_134 + x_222, x_134 >= 0, x_222 >= 0, z - 1 >= 0
   encode_h(z, z') -{ -70 + 4*s160 + 43*z + 32*z^2 }-> s161 :|: s160 >= 0, s160 <= z - 1, s161 >= 0, s161 <= 1 + s160, z' >= 0, z - 1 >= 0
   encode_h(z, z') -{ -72 + 4*s162 + 4*s164 + 107*x_130 + 32*x_130^2 + 107*x_219 + 32*x_219^2 + 43*z' + 32*z'^2 }-> s166 :|: s162 >= 0, s162 <= x_130, s163 >= 0, s163 <= x_219, s164 >= 0, s164 <= s162, s165 >= 0, s165 <= z' - 1, s166 >= 0, s166 <= s164, x_130 >= 0, z = 1 + x_130 + x_219, z' - 1 >= 0, x_219 >= 0
   encode_h(z, z') -{ 4 + 4*s167 + 4*s169 + 4*s170 + 107*x_130 + 32*x_130^2 + 107*x_136 + 32*x_136^2 + 107*x_219 + 32*x_219^2 + 107*x_223 + 32*x_223^2 }-> s173 :|: s167 >= 0, s167 <= x_130, s168 >= 0, s168 <= x_219, s169 >= 0, s169 <= s167, s170 >= 0, s170 <= x_136, s171 >= 0, s171 <= x_223, s172 >= 0, s172 <= s170, s173 >= 0, s173 <= s169, z' = 1 + x_136 + x_223, x_130 >= 0, z = 1 + x_130 + x_219, x_223 >= 0, x_136 >= 0, x_219 >= 0
   encode_h(z, z') -{ 5 + 4*s174 + 4*s176 + 4*s177 + 107*x_130 + 32*x_130^2 + 107*x_137 + 32*x_137^2 + 107*x_219 + 32*x_219^2 + 107*x_224 + 32*x_224^2 }-> s180 :|: s174 >= 0, s174 <= x_130, s175 >= 0, s175 <= x_219, s176 >= 0, s176 <= s174, s177 >= 0, s177 <= x_137, s178 >= 0, s178 <= x_224, s179 >= 0, s179 <= s177, s180 >= 0, s180 <= s176, z' = 1 + x_137 + x_224, x_130 >= 0, z = 1 + x_130 + x_219, x_224 >= 0, x_137 >= 0, x_219 >= 0
   encode_h(z, z') -{ 2 + 4*s181 + 4*s183 + 107*x_130 + 32*x_130^2 + 107*x_219 + 32*x_219^2 }-> s184 :|: s181 >= 0, s181 <= x_130, s182 >= 0, s182 <= x_219, s183 >= 0, s183 <= s181, s184 >= 0, s184 <= s183, x_130 >= 0, z = 1 + x_130 + x_219, z' >= 0, x_219 >= 0
   encode_h(z, z') -{ -71 + 4*s185 + 4*s187 + 107*x_131 + 32*x_131^2 + 107*x_220 + 32*x_220^2 + 43*z' + 32*z'^2 }-> s189 :|: s185 >= 0, s185 <= x_131, s186 >= 0, s186 <= x_220, s187 >= 0, s187 <= s185, s188 >= 0, s188 <= z' - 1, s189 >= 0, s189 <= s187, z' - 1 >= 0, z = 1 + x_131 + x_220, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ 5 + 4*s190 + 4*s192 + 4*s193 + 107*x_131 + 32*x_131^2 + 107*x_139 + 32*x_139^2 + 107*x_220 + 32*x_220^2 + 107*x_225 + 32*x_225^2 }-> s196 :|: s190 >= 0, s190 <= x_131, s191 >= 0, s191 <= x_220, s192 >= 0, s192 <= s190, s193 >= 0, s193 <= x_139, s194 >= 0, s194 <= x_225, s195 >= 0, s195 <= s193, s196 >= 0, s196 <= s192, z = 1 + x_131 + x_220, z' = 1 + x_139 + x_225, x_225 >= 0, x_139 >= 0, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ 0 }-> s2 :|: s2 >= 0, s2 <= 0, z >= 0, z' >= 0
   encode_h(z, z') -{ 6 + 4*s197 + 4*s199 + 4*s200 + 107*x_131 + 32*x_131^2 + 107*x_140 + 32*x_140^2 + 107*x_220 + 32*x_220^2 + 107*x_226 + 32*x_226^2 }-> s203 :|: s197 >= 0, s197 <= x_131, s198 >= 0, s198 <= x_220, s199 >= 0, s199 <= s197, s200 >= 0, s200 <= x_140, s201 >= 0, s201 <= x_226, s202 >= 0, s202 <= s200, s203 >= 0, s203 <= s199, z = 1 + x_131 + x_220, x_226 >= 0, z' = 1 + x_140 + x_226, x_140 >= 0, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ 3 + 4*s204 + 4*s206 + 107*x_131 + 32*x_131^2 + 107*x_220 + 32*x_220^2 }-> s207 :|: s204 >= 0, s204 <= x_131, s205 >= 0, s205 <= x_220, s206 >= 0, s206 <= s204, s207 >= 0, s207 <= s206, z = 1 + x_131 + x_220, z' >= 0, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ -74 + 43*z' + 32*z'^2 }-> s209 :|: s208 >= 0, s208 <= z' - 1, s209 >= 0, s209 <= 0, z >= 0, z' - 1 >= 0
   encode_h(z, z') -{ 2 + 4*s210 + 107*x_142 + 32*x_142^2 + 107*x_227 + 32*x_227^2 }-> s213 :|: s210 >= 0, s210 <= x_142, s211 >= 0, s211 <= x_227, s212 >= 0, s212 <= s210, s213 >= 0, s213 <= 0, z >= 0, z' = 1 + x_142 + x_227, x_142 >= 0, x_227 >= 0
   encode_h(z, z') -{ 3 + 4*s214 + 107*x_143 + 32*x_143^2 + 107*x_228 + 32*x_228^2 }-> s217 :|: s214 >= 0, s214 <= x_143, s215 >= 0, s215 <= x_228, s216 >= 0, s216 <= s214, s217 >= 0, s217 <= 0, z >= 0, z' = 1 + x_143 + x_228, x_143 >= 0, x_228 >= 0
   encode_h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   g(z, z') -{ 1 + 4*z }-> s' :|: s' >= 0, s' <= z, z >= 0, z' >= 0
   h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   h(z, z') -{ -2 + 4*z }-> 1 + s :|: s >= 0, s <= z - 1, z - 1 >= 0, z' >= 0

Function symbols to be analyzed: {encode_g}
Previous analysis results are:
  h: runtime: O(n^1) [4*z], size: O(n^1) [z]
  g: runtime: O(n^1) [1 + 4*z], size: O(n^1) [z]
  encArg: runtime: O(n^2) [1 + 107*z + 32*z^2], size: O(n^1) [z]
  encode_f: runtime: O(n^2) [1 + 107*z + 32*z^2], size: O(n^1) [1 + z]
  encode_h: runtime: O(n^2) [30 + 1964*z + 640*z^2 + 1916*z' + 640*z'^2], size: O(n^1) [z]

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

(45) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   encArg(z) -{ 0 }-> s'' :|: s'' >= 0, s'' <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 1 }-> s1 :|: s1 >= 0, s1 <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 5 + 4*s96 + 4*s98 + 4*s99 + 107*x_115 + 32*x_115^2 + 107*x_121 + 32*x_121^2 + 107*x_213 + 32*x_213^2 + 107*x_29 + 32*x_29^2 }-> s102 :|: s96 >= 0, s96 <= x_115, s97 >= 0, s97 <= x_29, s98 >= 0, s98 <= s96, s99 >= 0, s99 <= x_121, s100 >= 0, s100 <= x_213, s101 >= 0, s101 <= s99, s102 >= 0, s102 <= s98, x_213 >= 0, x_115 >= 0, z = 1 + (1 + x_115 + x_29) + (1 + x_121 + x_213), x_29 >= 0, x_121 >= 0
   encArg(z) -{ 6 + 4*s103 + 4*s105 + 4*s106 + 107*x_115 + 32*x_115^2 + 107*x_122 + 32*x_122^2 + 107*x_214 + 32*x_214^2 + 107*x_29 + 32*x_29^2 }-> s109 :|: s103 >= 0, s103 <= x_115, s104 >= 0, s104 <= x_29, s105 >= 0, s105 <= s103, s106 >= 0, s106 <= x_122, s107 >= 0, s107 <= x_214, s108 >= 0, s108 <= s106, s109 >= 0, s109 <= s105, z = 1 + (1 + x_115 + x_29) + (1 + x_122 + x_214), x_115 >= 0, x_214 >= 0, x_122 >= 0, x_29 >= 0
   encArg(z) -{ 3 + 4*s110 + 4*s112 + 107*x_115 + 32*x_115^2 + 107*x_29 + 32*x_29^2 }-> s113 :|: s110 >= 0, s110 <= x_115, s111 >= 0, s111 <= x_29, s112 >= 0, s112 <= s110, s113 >= 0, s113 <= s112, x_115 >= 0, x_2 >= 0, z = 1 + (1 + x_115 + x_29) + x_2, x_29 >= 0
   encArg(z) -{ 5 + 4*s114 + 4*s116 + 107*x_116 + 32*x_116^2 + 107*x_123 + 32*x_123^2 + 107*x_210 + 32*x_210^2 }-> s118 :|: s114 >= 0, s114 <= x_116, s115 >= 0, s115 <= x_210, s116 >= 0, s116 <= s114, s117 >= 0, s117 <= x_123, s118 >= 0, s118 <= s116, x_123 >= 0, z = 1 + (1 + x_116 + x_210) + (1 + x_123), x_116 >= 0, x_210 >= 0
   encArg(z) -{ 7 + 4*s8 + 4*s9 + 107*x_1' + 32*x_1'^2 + 107*x_13 + 32*x_13^2 + 107*x_21 + 32*x_21^2 }-> s12 :|: s8 >= 0, s8 <= x_1', s9 >= 0, s9 <= x_13, s10 >= 0, s10 <= x_21, s11 >= 0, s11 <= s9, s12 >= 0, s12 <= 1 + s8, x_13 >= 0, x_1' >= 0, z = 1 + (1 + x_1') + (1 + x_13 + x_21), x_21 >= 0
   encArg(z) -{ 6 + 4*s119 + 4*s121 + 4*s122 + 107*x_116 + 32*x_116^2 + 107*x_124 + 32*x_124^2 + 107*x_210 + 32*x_210^2 + 107*x_215 + 32*x_215^2 }-> s125 :|: s119 >= 0, s119 <= x_116, s120 >= 0, s120 <= x_210, s121 >= 0, s121 <= s119, s122 >= 0, s122 <= x_124, s123 >= 0, s123 <= x_215, s124 >= 0, s124 <= s122, s125 >= 0, s125 <= s121, x_124 >= 0, x_215 >= 0, x_116 >= 0, z = 1 + (1 + x_116 + x_210) + (1 + x_124 + x_215), x_210 >= 0
   encArg(z) -{ 7 + 4*s126 + 4*s128 + 4*s129 + 107*x_116 + 32*x_116^2 + 107*x_125 + 32*x_125^2 + 107*x_210 + 32*x_210^2 + 107*x_216 + 32*x_216^2 }-> s132 :|: s126 >= 0, s126 <= x_116, s127 >= 0, s127 <= x_210, s128 >= 0, s128 <= s126, s129 >= 0, s129 <= x_125, s130 >= 0, s130 <= x_216, s131 >= 0, s131 <= s129, s132 >= 0, s132 <= s128, x_216 >= 0, z = 1 + (1 + x_116 + x_210) + (1 + x_125 + x_216), x_116 >= 0, x_125 >= 0, x_210 >= 0
   encArg(z) -{ 4 + 4*s133 + 4*s135 + 107*x_116 + 32*x_116^2 + 107*x_210 + 32*x_210^2 }-> s136 :|: s133 >= 0, s133 <= x_116, s134 >= 0, s134 <= x_210, s135 >= 0, s135 <= s133, s136 >= 0, s136 <= s135, x_116 >= 0, x_2 >= 0, z = 1 + (1 + x_116 + x_210) + x_2, x_210 >= 0
   encArg(z) -{ 2 + 107*x_126 + 32*x_126^2 }-> s138 :|: s137 >= 0, s137 <= x_126, s138 >= 0, s138 <= 0, x_1 >= 0, z = 1 + x_1 + (1 + x_126), x_126 >= 0
   encArg(z) -{ 3 + 4*s139 + 107*x_127 + 32*x_127^2 + 107*x_217 + 32*x_217^2 }-> s142 :|: s139 >= 0, s139 <= x_127, s140 >= 0, s140 <= x_217, s141 >= 0, s141 <= s139, s142 >= 0, s142 <= 0, x_1 >= 0, x_127 >= 0, z = 1 + x_1 + (1 + x_127 + x_217), x_217 >= 0
   encArg(z) -{ 4 + 4*s143 + 107*x_128 + 32*x_128^2 + 107*x_218 + 32*x_218^2 }-> s146 :|: s143 >= 0, s143 <= x_128, s144 >= 0, s144 <= x_218, s145 >= 0, s145 <= s143, s146 >= 0, s146 <= 0, x_1 >= 0, x_128 >= 0, z = 1 + x_1 + (1 + x_128 + x_218), x_218 >= 0
   encArg(z) -{ 8 + 4*s13 + 4*s14 + 107*x_1' + 32*x_1'^2 + 107*x_14 + 32*x_14^2 + 107*x_22 + 32*x_22^2 }-> s17 :|: s13 >= 0, s13 <= x_1', s14 >= 0, s14 <= x_14, s15 >= 0, s15 <= x_22, s16 >= 0, s16 <= s14, s17 >= 0, s17 <= 1 + s13, z = 1 + (1 + x_1') + (1 + x_14 + x_22), x_14 >= 0, x_1' >= 0, x_22 >= 0
   encArg(z) -{ 5 + 4*s18 + 107*x_1' + 32*x_1'^2 }-> s19 :|: s18 >= 0, s18 <= x_1', s19 >= 0, s19 <= 1 + s18, x_1' >= 0, x_2 >= 0, z = 1 + (1 + x_1') + x_2
   encArg(z) -{ 3 + 4*s20 + 4*s22 + 107*x_1'' + 32*x_1''^2 + 107*x_15 + 32*x_15^2 + 107*x_2' + 32*x_2'^2 }-> s24 :|: s20 >= 0, s20 <= x_1'', s21 >= 0, s21 <= x_2', s22 >= 0, s22 <= s20, s23 >= 0, s23 <= x_15, s24 >= 0, s24 <= s22, x_15 >= 0, z = 1 + (1 + x_1'' + x_2') + (1 + x_15), x_1'' >= 0, x_2' >= 0
   encArg(z) -{ 4 + 4*s25 + 4*s27 + 4*s28 + 107*x_1'' + 32*x_1''^2 + 107*x_16 + 32*x_16^2 + 107*x_2' + 32*x_2'^2 + 107*x_23 + 32*x_23^2 }-> s31 :|: s25 >= 0, s25 <= x_1'', s26 >= 0, s26 <= x_2', s27 >= 0, s27 <= s25, s28 >= 0, s28 <= x_16, s29 >= 0, s29 <= x_23, s30 >= 0, s30 <= s28, s31 >= 0, s31 <= s27, x_1'' >= 0, x_16 >= 0, x_2' >= 0, x_23 >= 0, z = 1 + (1 + x_1'' + x_2') + (1 + x_16 + x_23)
   encArg(z) -{ 5 + 4*s32 + 4*s34 + 4*s35 + 107*x_1'' + 32*x_1''^2 + 107*x_17 + 32*x_17^2 + 107*x_2' + 32*x_2'^2 + 107*x_24 + 32*x_24^2 }-> s38 :|: s32 >= 0, s32 <= x_1'', s33 >= 0, s33 <= x_2', s34 >= 0, s34 <= s32, s35 >= 0, s35 <= x_17, s36 >= 0, s36 <= x_24, s37 >= 0, s37 <= s35, s38 >= 0, s38 <= s34, x_1'' >= 0, x_2' >= 0, x_17 >= 0, x_24 >= 0, z = 1 + (1 + x_1'' + x_2') + (1 + x_17 + x_24)
   encArg(z) -{ 2 + 4*s39 + 4*s41 + 107*x_1'' + 32*x_1''^2 + 107*x_2' + 32*x_2'^2 }-> s42 :|: s39 >= 0, s39 <= x_1'', s40 >= 0, s40 <= x_2', s41 >= 0, s41 <= s39, s42 >= 0, s42 <= s41, x_1'' >= 0, x_2' >= 0, z = 1 + (1 + x_1'' + x_2') + x_2, x_2 >= 0
   encArg(z) -{ 4 + 4*s43 + 4*s45 + 107*x_11 + 32*x_11^2 + 107*x_18 + 32*x_18^2 + 107*x_2'' + 32*x_2''^2 }-> s47 :|: s43 >= 0, s43 <= x_11, s44 >= 0, s44 <= x_2'', s45 >= 0, s45 <= s43, s46 >= 0, s46 <= x_18, s47 >= 0, s47 <= s45, x_11 >= 0, z = 1 + (1 + x_11 + x_2'') + (1 + x_18), x_2'' >= 0, x_18 >= 0
   encArg(z) -{ 5 + 4*s48 + 4*s50 + 4*s51 + 107*x_11 + 32*x_11^2 + 107*x_19 + 32*x_19^2 + 107*x_2'' + 32*x_2''^2 + 107*x_25 + 32*x_25^2 }-> s54 :|: s48 >= 0, s48 <= x_11, s49 >= 0, s49 <= x_2'', s50 >= 0, s50 <= s48, s51 >= 0, s51 <= x_19, s52 >= 0, s52 <= x_25, s53 >= 0, s53 <= s51, s54 >= 0, s54 <= s50, x_11 >= 0, z = 1 + (1 + x_11 + x_2'') + (1 + x_19 + x_25), x_25 >= 0, x_2'' >= 0, x_19 >= 0
   encArg(z) -{ 6 + 4*s55 + 4*s57 + 4*s58 + 107*x_11 + 32*x_11^2 + 107*x_110 + 32*x_110^2 + 107*x_2'' + 32*x_2''^2 + 107*x_26 + 32*x_26^2 }-> s61 :|: s55 >= 0, s55 <= x_11, s56 >= 0, s56 <= x_2'', s57 >= 0, s57 <= s55, s58 >= 0, s58 <= x_110, s59 >= 0, s59 <= x_26, s60 >= 0, s60 <= s58, s61 >= 0, s61 <= s57, x_11 >= 0, x_26 >= 0, x_2'' >= 0, z = 1 + (1 + x_11 + x_2'') + (1 + x_110 + x_26), x_110 >= 0
   encArg(z) -{ 3 + 4*s62 + 4*s64 + 107*x_11 + 32*x_11^2 + 107*x_2'' + 32*x_2''^2 }-> s65 :|: s62 >= 0, s62 <= x_11, s63 >= 0, s63 <= x_2'', s64 >= 0, s64 <= s62, s65 >= 0, s65 <= s64, x_11 >= 0, x_2'' >= 0, x_2 >= 0, z = 1 + (1 + x_11 + x_2'') + x_2
   encArg(z) -{ 1 + 107*x_111 + 32*x_111^2 }-> s67 :|: s66 >= 0, s66 <= x_111, s67 >= 0, s67 <= 0, x_1 >= 0, z = 1 + x_1 + (1 + x_111), x_111 >= 0
   encArg(z) -{ 6 + 4*s5 + 107*x_1' + 32*x_1'^2 + 107*x_12 + 32*x_12^2 }-> s7 :|: s5 >= 0, s5 <= x_1', s6 >= 0, s6 <= x_12, s7 >= 0, s7 <= 1 + s5, z = 1 + (1 + x_1') + (1 + x_12), x_1' >= 0, x_12 >= 0
   encArg(z) -{ 2 + 4*s68 + 107*x_112 + 32*x_112^2 + 107*x_27 + 32*x_27^2 }-> s71 :|: s68 >= 0, s68 <= x_112, s69 >= 0, s69 <= x_27, s70 >= 0, s70 <= s68, s71 >= 0, s71 <= 0, x_1 >= 0, x_27 >= 0, z = 1 + x_1 + (1 + x_112 + x_27), x_112 >= 0
   encArg(z) -{ 3 + 4*s72 + 107*x_113 + 32*x_113^2 + 107*x_28 + 32*x_28^2 }-> s75 :|: s72 >= 0, s72 <= x_113, s73 >= 0, s73 <= x_28, s74 >= 0, s74 <= s72, s75 >= 0, s75 <= 0, x_1 >= 0, x_113 >= 0, x_28 >= 0, z = 1 + x_1 + (1 + x_113 + x_28)
   encArg(z) -{ 7 + 4*s76 + 107*x_114 + 32*x_114^2 + 107*x_117 + 32*x_117^2 }-> s78 :|: s76 >= 0, s76 <= x_114, s77 >= 0, s77 <= x_117, s78 >= 0, s78 <= 1 + s76, z = 1 + (1 + x_114) + (1 + x_117), x_117 >= 0, x_114 >= 0
   encArg(z) -{ 8 + 4*s79 + 4*s80 + 107*x_114 + 32*x_114^2 + 107*x_118 + 32*x_118^2 + 107*x_211 + 32*x_211^2 }-> s83 :|: s79 >= 0, s79 <= x_114, s80 >= 0, s80 <= x_118, s81 >= 0, s81 <= x_211, s82 >= 0, s82 <= s80, s83 >= 0, s83 <= 1 + s79, z = 1 + (1 + x_114) + (1 + x_118 + x_211), x_114 >= 0, x_118 >= 0, x_211 >= 0
   encArg(z) -{ 9 + 4*s84 + 4*s85 + 107*x_114 + 32*x_114^2 + 107*x_119 + 32*x_119^2 + 107*x_212 + 32*x_212^2 }-> s88 :|: s84 >= 0, s84 <= x_114, s85 >= 0, s85 <= x_119, s86 >= 0, s86 <= x_212, s87 >= 0, s87 <= s85, s88 >= 0, s88 <= 1 + s84, x_212 >= 0, x_114 >= 0, z = 1 + (1 + x_114) + (1 + x_119 + x_212), x_119 >= 0
   encArg(z) -{ 6 + 4*s89 + 107*x_114 + 32*x_114^2 }-> s90 :|: s89 >= 0, s89 <= x_114, s90 >= 0, s90 <= 1 + s89, z = 1 + (1 + x_114) + x_2, x_114 >= 0, x_2 >= 0
   encArg(z) -{ 4 + 4*s91 + 4*s93 + 107*x_115 + 32*x_115^2 + 107*x_120 + 32*x_120^2 + 107*x_29 + 32*x_29^2 }-> s95 :|: s91 >= 0, s91 <= x_115, s92 >= 0, s92 <= x_29, s93 >= 0, s93 <= s91, s94 >= 0, s94 <= x_120, s95 >= 0, s95 <= s93, x_120 >= 0, x_115 >= 0, z = 1 + (1 + x_115 + x_29) + (1 + x_120), x_29 >= 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ -74 + 43*z + 32*z^2 }-> 1 + s4 :|: s4 >= 0, s4 <= z - 1, z - 1 >= 0
   encode_f(z) -{ 0 }-> 0 :|: z >= 0
   encode_f(z) -{ 1 + 107*z + 32*z^2 }-> 1 + s218 :|: s218 >= 0, s218 <= z, z >= 0
   encode_g(z, z') -{ -143 + 4*s219 + 43*z + 32*z^2 + 43*z' + 32*z'^2 }-> s221 :|: s219 >= 0, s219 <= z - 1, s220 >= 0, s220 <= z' - 1, s221 >= 0, s221 <= 1 + s219, z - 1 >= 0, z' - 1 >= 0
   encode_g(z, z') -{ -67 + 4*s222 + 4*s223 + 107*x_148 + 32*x_148^2 + 107*x_231 + 32*x_231^2 + 43*z + 32*z^2 }-> s226 :|: s222 >= 0, s222 <= z - 1, s223 >= 0, s223 <= x_148, s224 >= 0, s224 <= x_231, s225 >= 0, s225 <= s223, s226 >= 0, s226 <= 1 + s222, z' = 1 + x_148 + x_231, z - 1 >= 0, x_231 >= 0, x_148 >= 0
   encode_g(z, z') -{ -66 + 4*s227 + 4*s228 + 107*x_149 + 32*x_149^2 + 107*x_232 + 32*x_232^2 + 43*z + 32*z^2 }-> s231 :|: s227 >= 0, s227 <= z - 1, s228 >= 0, s228 <= x_149, s229 >= 0, s229 <= x_232, s230 >= 0, s230 <= s228, s231 >= 0, s231 <= 1 + s227, x_232 >= 0, z - 1 >= 0, z' = 1 + x_149 + x_232, x_149 >= 0
   encode_g(z, z') -{ -69 + 4*s232 + 43*z + 32*z^2 }-> s233 :|: s232 >= 0, s232 <= z - 1, s233 >= 0, s233 <= 1 + s232, z - 1 >= 0, z' >= 0
   encode_g(z, z') -{ -71 + 4*s234 + 4*s236 + 107*x_145 + 32*x_145^2 + 107*x_229 + 32*x_229^2 + 43*z' + 32*z'^2 }-> s238 :|: s234 >= 0, s234 <= x_145, s235 >= 0, s235 <= x_229, s236 >= 0, s236 <= s234, s237 >= 0, s237 <= z' - 1, s238 >= 0, s238 <= s236, z = 1 + x_145 + x_229, x_145 >= 0, x_229 >= 0, z' - 1 >= 0
   encode_g(z, z') -{ 5 + 4*s239 + 4*s241 + 4*s242 + 107*x_145 + 32*x_145^2 + 107*x_151 + 32*x_151^2 + 107*x_229 + 32*x_229^2 + 107*x_233 + 32*x_233^2 }-> s245 :|: s239 >= 0, s239 <= x_145, s240 >= 0, s240 <= x_229, s241 >= 0, s241 <= s239, s242 >= 0, s242 <= x_151, s243 >= 0, s243 <= x_233, s244 >= 0, s244 <= s242, s245 >= 0, s245 <= s241, x_233 >= 0, z = 1 + x_145 + x_229, x_145 >= 0, x_229 >= 0, z' = 1 + x_151 + x_233, x_151 >= 0
   encode_g(z, z') -{ 6 + 4*s246 + 4*s248 + 4*s249 + 107*x_145 + 32*x_145^2 + 107*x_152 + 32*x_152^2 + 107*x_229 + 32*x_229^2 + 107*x_234 + 32*x_234^2 }-> s252 :|: s246 >= 0, s246 <= x_145, s247 >= 0, s247 <= x_229, s248 >= 0, s248 <= s246, s249 >= 0, s249 <= x_152, s250 >= 0, s250 <= x_234, s251 >= 0, s251 <= s249, s252 >= 0, s252 <= s248, z = 1 + x_145 + x_229, x_234 >= 0, x_145 >= 0, z' = 1 + x_152 + x_234, x_229 >= 0, x_152 >= 0
   encode_g(z, z') -{ 3 + 4*s253 + 4*s255 + 107*x_145 + 32*x_145^2 + 107*x_229 + 32*x_229^2 }-> s256 :|: s253 >= 0, s253 <= x_145, s254 >= 0, s254 <= x_229, s255 >= 0, s255 <= s253, s256 >= 0, s256 <= s255, z = 1 + x_145 + x_229, x_145 >= 0, x_229 >= 0, z' >= 0
   encode_g(z, z') -{ -70 + 4*s257 + 4*s259 + 107*x_146 + 32*x_146^2 + 107*x_230 + 32*x_230^2 + 43*z' + 32*z'^2 }-> s261 :|: s257 >= 0, s257 <= x_146, s258 >= 0, s258 <= x_230, s259 >= 0, s259 <= s257, s260 >= 0, s260 <= z' - 1, s261 >= 0, s261 <= s259, z = 1 + x_146 + x_230, x_146 >= 0, z' - 1 >= 0, x_230 >= 0
   encode_g(z, z') -{ 6 + 4*s262 + 4*s264 + 4*s265 + 107*x_146 + 32*x_146^2 + 107*x_154 + 32*x_154^2 + 107*x_230 + 32*x_230^2 + 107*x_235 + 32*x_235^2 }-> s268 :|: s262 >= 0, s262 <= x_146, s263 >= 0, s263 <= x_230, s264 >= 0, s264 <= s262, s265 >= 0, s265 <= x_154, s266 >= 0, s266 <= x_235, s267 >= 0, s267 <= s265, s268 >= 0, s268 <= s264, z = 1 + x_146 + x_230, x_146 >= 0, x_154 >= 0, z' = 1 + x_154 + x_235, x_235 >= 0, x_230 >= 0
   encode_g(z, z') -{ 7 + 4*s269 + 4*s271 + 4*s272 + 107*x_146 + 32*x_146^2 + 107*x_155 + 32*x_155^2 + 107*x_230 + 32*x_230^2 + 107*x_236 + 32*x_236^2 }-> s275 :|: s269 >= 0, s269 <= x_146, s270 >= 0, s270 <= x_230, s271 >= 0, s271 <= s269, s272 >= 0, s272 <= x_155, s273 >= 0, s273 <= x_236, s274 >= 0, s274 <= s272, s275 >= 0, s275 <= s271, z = 1 + x_146 + x_230, x_146 >= 0, x_155 >= 0, z' = 1 + x_155 + x_236, x_236 >= 0, x_230 >= 0
   encode_g(z, z') -{ 4 + 4*s276 + 4*s278 + 107*x_146 + 32*x_146^2 + 107*x_230 + 32*x_230^2 }-> s279 :|: s276 >= 0, s276 <= x_146, s277 >= 0, s277 <= x_230, s278 >= 0, s278 <= s276, s279 >= 0, s279 <= s278, z = 1 + x_146 + x_230, x_146 >= 0, z' >= 0, x_230 >= 0
   encode_g(z, z') -{ -73 + 43*z' + 32*z'^2 }-> s281 :|: s280 >= 0, s280 <= z' - 1, s281 >= 0, s281 <= 0, z >= 0, z' - 1 >= 0
   encode_g(z, z') -{ 3 + 4*s282 + 107*x_157 + 32*x_157^2 + 107*x_237 + 32*x_237^2 }-> s285 :|: s282 >= 0, s282 <= x_157, s283 >= 0, s283 <= x_237, s284 >= 0, s284 <= s282, s285 >= 0, s285 <= 0, x_237 >= 0, z >= 0, x_157 >= 0, z' = 1 + x_157 + x_237
   encode_g(z, z') -{ 4 + 4*s286 + 107*x_158 + 32*x_158^2 + 107*x_238 + 32*x_238^2 }-> s289 :|: s286 >= 0, s286 <= x_158, s287 >= 0, s287 <= x_238, s288 >= 0, s288 <= s286, s289 >= 0, s289 <= 0, z >= 0, z' = 1 + x_158 + x_238, x_158 >= 0, x_238 >= 0
   encode_g(z, z') -{ 1 }-> s3 :|: s3 >= 0, s3 <= 0, z >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_h(z, z') -{ -144 + 4*s147 + 43*z + 32*z^2 + 43*z' + 32*z'^2 }-> s149 :|: s147 >= 0, s147 <= z - 1, s148 >= 0, s148 <= z' - 1, s149 >= 0, s149 <= 1 + s147, z' - 1 >= 0, z - 1 >= 0
   encode_h(z, z') -{ -68 + 4*s150 + 4*s151 + 107*x_133 + 32*x_133^2 + 107*x_221 + 32*x_221^2 + 43*z + 32*z^2 }-> s154 :|: s150 >= 0, s150 <= z - 1, s151 >= 0, s151 <= x_133, s152 >= 0, s152 <= x_221, s153 >= 0, s153 <= s151, s154 >= 0, s154 <= 1 + s150, z' = 1 + x_133 + x_221, x_221 >= 0, x_133 >= 0, z - 1 >= 0
   encode_h(z, z') -{ -67 + 4*s155 + 4*s156 + 107*x_134 + 32*x_134^2 + 107*x_222 + 32*x_222^2 + 43*z + 32*z^2 }-> s159 :|: s155 >= 0, s155 <= z - 1, s156 >= 0, s156 <= x_134, s157 >= 0, s157 <= x_222, s158 >= 0, s158 <= s156, s159 >= 0, s159 <= 1 + s155, z' = 1 + x_134 + x_222, x_134 >= 0, x_222 >= 0, z - 1 >= 0
   encode_h(z, z') -{ -70 + 4*s160 + 43*z + 32*z^2 }-> s161 :|: s160 >= 0, s160 <= z - 1, s161 >= 0, s161 <= 1 + s160, z' >= 0, z - 1 >= 0
   encode_h(z, z') -{ -72 + 4*s162 + 4*s164 + 107*x_130 + 32*x_130^2 + 107*x_219 + 32*x_219^2 + 43*z' + 32*z'^2 }-> s166 :|: s162 >= 0, s162 <= x_130, s163 >= 0, s163 <= x_219, s164 >= 0, s164 <= s162, s165 >= 0, s165 <= z' - 1, s166 >= 0, s166 <= s164, x_130 >= 0, z = 1 + x_130 + x_219, z' - 1 >= 0, x_219 >= 0
   encode_h(z, z') -{ 4 + 4*s167 + 4*s169 + 4*s170 + 107*x_130 + 32*x_130^2 + 107*x_136 + 32*x_136^2 + 107*x_219 + 32*x_219^2 + 107*x_223 + 32*x_223^2 }-> s173 :|: s167 >= 0, s167 <= x_130, s168 >= 0, s168 <= x_219, s169 >= 0, s169 <= s167, s170 >= 0, s170 <= x_136, s171 >= 0, s171 <= x_223, s172 >= 0, s172 <= s170, s173 >= 0, s173 <= s169, z' = 1 + x_136 + x_223, x_130 >= 0, z = 1 + x_130 + x_219, x_223 >= 0, x_136 >= 0, x_219 >= 0
   encode_h(z, z') -{ 5 + 4*s174 + 4*s176 + 4*s177 + 107*x_130 + 32*x_130^2 + 107*x_137 + 32*x_137^2 + 107*x_219 + 32*x_219^2 + 107*x_224 + 32*x_224^2 }-> s180 :|: s174 >= 0, s174 <= x_130, s175 >= 0, s175 <= x_219, s176 >= 0, s176 <= s174, s177 >= 0, s177 <= x_137, s178 >= 0, s178 <= x_224, s179 >= 0, s179 <= s177, s180 >= 0, s180 <= s176, z' = 1 + x_137 + x_224, x_130 >= 0, z = 1 + x_130 + x_219, x_224 >= 0, x_137 >= 0, x_219 >= 0
   encode_h(z, z') -{ 2 + 4*s181 + 4*s183 + 107*x_130 + 32*x_130^2 + 107*x_219 + 32*x_219^2 }-> s184 :|: s181 >= 0, s181 <= x_130, s182 >= 0, s182 <= x_219, s183 >= 0, s183 <= s181, s184 >= 0, s184 <= s183, x_130 >= 0, z = 1 + x_130 + x_219, z' >= 0, x_219 >= 0
   encode_h(z, z') -{ -71 + 4*s185 + 4*s187 + 107*x_131 + 32*x_131^2 + 107*x_220 + 32*x_220^2 + 43*z' + 32*z'^2 }-> s189 :|: s185 >= 0, s185 <= x_131, s186 >= 0, s186 <= x_220, s187 >= 0, s187 <= s185, s188 >= 0, s188 <= z' - 1, s189 >= 0, s189 <= s187, z' - 1 >= 0, z = 1 + x_131 + x_220, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ 5 + 4*s190 + 4*s192 + 4*s193 + 107*x_131 + 32*x_131^2 + 107*x_139 + 32*x_139^2 + 107*x_220 + 32*x_220^2 + 107*x_225 + 32*x_225^2 }-> s196 :|: s190 >= 0, s190 <= x_131, s191 >= 0, s191 <= x_220, s192 >= 0, s192 <= s190, s193 >= 0, s193 <= x_139, s194 >= 0, s194 <= x_225, s195 >= 0, s195 <= s193, s196 >= 0, s196 <= s192, z = 1 + x_131 + x_220, z' = 1 + x_139 + x_225, x_225 >= 0, x_139 >= 0, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ 0 }-> s2 :|: s2 >= 0, s2 <= 0, z >= 0, z' >= 0
   encode_h(z, z') -{ 6 + 4*s197 + 4*s199 + 4*s200 + 107*x_131 + 32*x_131^2 + 107*x_140 + 32*x_140^2 + 107*x_220 + 32*x_220^2 + 107*x_226 + 32*x_226^2 }-> s203 :|: s197 >= 0, s197 <= x_131, s198 >= 0, s198 <= x_220, s199 >= 0, s199 <= s197, s200 >= 0, s200 <= x_140, s201 >= 0, s201 <= x_226, s202 >= 0, s202 <= s200, s203 >= 0, s203 <= s199, z = 1 + x_131 + x_220, x_226 >= 0, z' = 1 + x_140 + x_226, x_140 >= 0, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ 3 + 4*s204 + 4*s206 + 107*x_131 + 32*x_131^2 + 107*x_220 + 32*x_220^2 }-> s207 :|: s204 >= 0, s204 <= x_131, s205 >= 0, s205 <= x_220, s206 >= 0, s206 <= s204, s207 >= 0, s207 <= s206, z = 1 + x_131 + x_220, z' >= 0, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ -74 + 43*z' + 32*z'^2 }-> s209 :|: s208 >= 0, s208 <= z' - 1, s209 >= 0, s209 <= 0, z >= 0, z' - 1 >= 0
   encode_h(z, z') -{ 2 + 4*s210 + 107*x_142 + 32*x_142^2 + 107*x_227 + 32*x_227^2 }-> s213 :|: s210 >= 0, s210 <= x_142, s211 >= 0, s211 <= x_227, s212 >= 0, s212 <= s210, s213 >= 0, s213 <= 0, z >= 0, z' = 1 + x_142 + x_227, x_142 >= 0, x_227 >= 0
   encode_h(z, z') -{ 3 + 4*s214 + 107*x_143 + 32*x_143^2 + 107*x_228 + 32*x_228^2 }-> s217 :|: s214 >= 0, s214 <= x_143, s215 >= 0, s215 <= x_228, s216 >= 0, s216 <= s214, s217 >= 0, s217 <= 0, z >= 0, z' = 1 + x_143 + x_228, x_143 >= 0, x_228 >= 0
   encode_h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   g(z, z') -{ 1 + 4*z }-> s' :|: s' >= 0, s' <= z, z >= 0, z' >= 0
   h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   h(z, z') -{ -2 + 4*z }-> 1 + s :|: s >= 0, s <= z - 1, z - 1 >= 0, z' >= 0

Function symbols to be analyzed: {encode_g}
Previous analysis results are:
  h: runtime: O(n^1) [4*z], size: O(n^1) [z]
  g: runtime: O(n^1) [1 + 4*z], size: O(n^1) [z]
  encArg: runtime: O(n^2) [1 + 107*z + 32*z^2], size: O(n^1) [z]
  encode_f: runtime: O(n^2) [1 + 107*z + 32*z^2], size: O(n^1) [1 + z]
  encode_h: runtime: O(n^2) [30 + 1964*z + 640*z^2 + 1916*z' + 640*z'^2], size: O(n^1) [z]
  encode_g: runtime: ?, size: O(n^1) [z]

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

(47) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using KoAT for: encode_g
after applying outer abstraction to obtain an ITS,
resulting in: O(n^2) with polynomial bound: 39 + 1964*z + 640*z^2 + 1916*z' + 640*z'^2

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

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

   encArg(z) -{ 0 }-> s'' :|: s'' >= 0, s'' <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 1 }-> s1 :|: s1 >= 0, s1 <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 5 + 4*s96 + 4*s98 + 4*s99 + 107*x_115 + 32*x_115^2 + 107*x_121 + 32*x_121^2 + 107*x_213 + 32*x_213^2 + 107*x_29 + 32*x_29^2 }-> s102 :|: s96 >= 0, s96 <= x_115, s97 >= 0, s97 <= x_29, s98 >= 0, s98 <= s96, s99 >= 0, s99 <= x_121, s100 >= 0, s100 <= x_213, s101 >= 0, s101 <= s99, s102 >= 0, s102 <= s98, x_213 >= 0, x_115 >= 0, z = 1 + (1 + x_115 + x_29) + (1 + x_121 + x_213), x_29 >= 0, x_121 >= 0
   encArg(z) -{ 6 + 4*s103 + 4*s105 + 4*s106 + 107*x_115 + 32*x_115^2 + 107*x_122 + 32*x_122^2 + 107*x_214 + 32*x_214^2 + 107*x_29 + 32*x_29^2 }-> s109 :|: s103 >= 0, s103 <= x_115, s104 >= 0, s104 <= x_29, s105 >= 0, s105 <= s103, s106 >= 0, s106 <= x_122, s107 >= 0, s107 <= x_214, s108 >= 0, s108 <= s106, s109 >= 0, s109 <= s105, z = 1 + (1 + x_115 + x_29) + (1 + x_122 + x_214), x_115 >= 0, x_214 >= 0, x_122 >= 0, x_29 >= 0
   encArg(z) -{ 3 + 4*s110 + 4*s112 + 107*x_115 + 32*x_115^2 + 107*x_29 + 32*x_29^2 }-> s113 :|: s110 >= 0, s110 <= x_115, s111 >= 0, s111 <= x_29, s112 >= 0, s112 <= s110, s113 >= 0, s113 <= s112, x_115 >= 0, x_2 >= 0, z = 1 + (1 + x_115 + x_29) + x_2, x_29 >= 0
   encArg(z) -{ 5 + 4*s114 + 4*s116 + 107*x_116 + 32*x_116^2 + 107*x_123 + 32*x_123^2 + 107*x_210 + 32*x_210^2 }-> s118 :|: s114 >= 0, s114 <= x_116, s115 >= 0, s115 <= x_210, s116 >= 0, s116 <= s114, s117 >= 0, s117 <= x_123, s118 >= 0, s118 <= s116, x_123 >= 0, z = 1 + (1 + x_116 + x_210) + (1 + x_123), x_116 >= 0, x_210 >= 0
   encArg(z) -{ 7 + 4*s8 + 4*s9 + 107*x_1' + 32*x_1'^2 + 107*x_13 + 32*x_13^2 + 107*x_21 + 32*x_21^2 }-> s12 :|: s8 >= 0, s8 <= x_1', s9 >= 0, s9 <= x_13, s10 >= 0, s10 <= x_21, s11 >= 0, s11 <= s9, s12 >= 0, s12 <= 1 + s8, x_13 >= 0, x_1' >= 0, z = 1 + (1 + x_1') + (1 + x_13 + x_21), x_21 >= 0
   encArg(z) -{ 6 + 4*s119 + 4*s121 + 4*s122 + 107*x_116 + 32*x_116^2 + 107*x_124 + 32*x_124^2 + 107*x_210 + 32*x_210^2 + 107*x_215 + 32*x_215^2 }-> s125 :|: s119 >= 0, s119 <= x_116, s120 >= 0, s120 <= x_210, s121 >= 0, s121 <= s119, s122 >= 0, s122 <= x_124, s123 >= 0, s123 <= x_215, s124 >= 0, s124 <= s122, s125 >= 0, s125 <= s121, x_124 >= 0, x_215 >= 0, x_116 >= 0, z = 1 + (1 + x_116 + x_210) + (1 + x_124 + x_215), x_210 >= 0
   encArg(z) -{ 7 + 4*s126 + 4*s128 + 4*s129 + 107*x_116 + 32*x_116^2 + 107*x_125 + 32*x_125^2 + 107*x_210 + 32*x_210^2 + 107*x_216 + 32*x_216^2 }-> s132 :|: s126 >= 0, s126 <= x_116, s127 >= 0, s127 <= x_210, s128 >= 0, s128 <= s126, s129 >= 0, s129 <= x_125, s130 >= 0, s130 <= x_216, s131 >= 0, s131 <= s129, s132 >= 0, s132 <= s128, x_216 >= 0, z = 1 + (1 + x_116 + x_210) + (1 + x_125 + x_216), x_116 >= 0, x_125 >= 0, x_210 >= 0
   encArg(z) -{ 4 + 4*s133 + 4*s135 + 107*x_116 + 32*x_116^2 + 107*x_210 + 32*x_210^2 }-> s136 :|: s133 >= 0, s133 <= x_116, s134 >= 0, s134 <= x_210, s135 >= 0, s135 <= s133, s136 >= 0, s136 <= s135, x_116 >= 0, x_2 >= 0, z = 1 + (1 + x_116 + x_210) + x_2, x_210 >= 0
   encArg(z) -{ 2 + 107*x_126 + 32*x_126^2 }-> s138 :|: s137 >= 0, s137 <= x_126, s138 >= 0, s138 <= 0, x_1 >= 0, z = 1 + x_1 + (1 + x_126), x_126 >= 0
   encArg(z) -{ 3 + 4*s139 + 107*x_127 + 32*x_127^2 + 107*x_217 + 32*x_217^2 }-> s142 :|: s139 >= 0, s139 <= x_127, s140 >= 0, s140 <= x_217, s141 >= 0, s141 <= s139, s142 >= 0, s142 <= 0, x_1 >= 0, x_127 >= 0, z = 1 + x_1 + (1 + x_127 + x_217), x_217 >= 0
   encArg(z) -{ 4 + 4*s143 + 107*x_128 + 32*x_128^2 + 107*x_218 + 32*x_218^2 }-> s146 :|: s143 >= 0, s143 <= x_128, s144 >= 0, s144 <= x_218, s145 >= 0, s145 <= s143, s146 >= 0, s146 <= 0, x_1 >= 0, x_128 >= 0, z = 1 + x_1 + (1 + x_128 + x_218), x_218 >= 0
   encArg(z) -{ 8 + 4*s13 + 4*s14 + 107*x_1' + 32*x_1'^2 + 107*x_14 + 32*x_14^2 + 107*x_22 + 32*x_22^2 }-> s17 :|: s13 >= 0, s13 <= x_1', s14 >= 0, s14 <= x_14, s15 >= 0, s15 <= x_22, s16 >= 0, s16 <= s14, s17 >= 0, s17 <= 1 + s13, z = 1 + (1 + x_1') + (1 + x_14 + x_22), x_14 >= 0, x_1' >= 0, x_22 >= 0
   encArg(z) -{ 5 + 4*s18 + 107*x_1' + 32*x_1'^2 }-> s19 :|: s18 >= 0, s18 <= x_1', s19 >= 0, s19 <= 1 + s18, x_1' >= 0, x_2 >= 0, z = 1 + (1 + x_1') + x_2
   encArg(z) -{ 3 + 4*s20 + 4*s22 + 107*x_1'' + 32*x_1''^2 + 107*x_15 + 32*x_15^2 + 107*x_2' + 32*x_2'^2 }-> s24 :|: s20 >= 0, s20 <= x_1'', s21 >= 0, s21 <= x_2', s22 >= 0, s22 <= s20, s23 >= 0, s23 <= x_15, s24 >= 0, s24 <= s22, x_15 >= 0, z = 1 + (1 + x_1'' + x_2') + (1 + x_15), x_1'' >= 0, x_2' >= 0
   encArg(z) -{ 4 + 4*s25 + 4*s27 + 4*s28 + 107*x_1'' + 32*x_1''^2 + 107*x_16 + 32*x_16^2 + 107*x_2' + 32*x_2'^2 + 107*x_23 + 32*x_23^2 }-> s31 :|: s25 >= 0, s25 <= x_1'', s26 >= 0, s26 <= x_2', s27 >= 0, s27 <= s25, s28 >= 0, s28 <= x_16, s29 >= 0, s29 <= x_23, s30 >= 0, s30 <= s28, s31 >= 0, s31 <= s27, x_1'' >= 0, x_16 >= 0, x_2' >= 0, x_23 >= 0, z = 1 + (1 + x_1'' + x_2') + (1 + x_16 + x_23)
   encArg(z) -{ 5 + 4*s32 + 4*s34 + 4*s35 + 107*x_1'' + 32*x_1''^2 + 107*x_17 + 32*x_17^2 + 107*x_2' + 32*x_2'^2 + 107*x_24 + 32*x_24^2 }-> s38 :|: s32 >= 0, s32 <= x_1'', s33 >= 0, s33 <= x_2', s34 >= 0, s34 <= s32, s35 >= 0, s35 <= x_17, s36 >= 0, s36 <= x_24, s37 >= 0, s37 <= s35, s38 >= 0, s38 <= s34, x_1'' >= 0, x_2' >= 0, x_17 >= 0, x_24 >= 0, z = 1 + (1 + x_1'' + x_2') + (1 + x_17 + x_24)
   encArg(z) -{ 2 + 4*s39 + 4*s41 + 107*x_1'' + 32*x_1''^2 + 107*x_2' + 32*x_2'^2 }-> s42 :|: s39 >= 0, s39 <= x_1'', s40 >= 0, s40 <= x_2', s41 >= 0, s41 <= s39, s42 >= 0, s42 <= s41, x_1'' >= 0, x_2' >= 0, z = 1 + (1 + x_1'' + x_2') + x_2, x_2 >= 0
   encArg(z) -{ 4 + 4*s43 + 4*s45 + 107*x_11 + 32*x_11^2 + 107*x_18 + 32*x_18^2 + 107*x_2'' + 32*x_2''^2 }-> s47 :|: s43 >= 0, s43 <= x_11, s44 >= 0, s44 <= x_2'', s45 >= 0, s45 <= s43, s46 >= 0, s46 <= x_18, s47 >= 0, s47 <= s45, x_11 >= 0, z = 1 + (1 + x_11 + x_2'') + (1 + x_18), x_2'' >= 0, x_18 >= 0
   encArg(z) -{ 5 + 4*s48 + 4*s50 + 4*s51 + 107*x_11 + 32*x_11^2 + 107*x_19 + 32*x_19^2 + 107*x_2'' + 32*x_2''^2 + 107*x_25 + 32*x_25^2 }-> s54 :|: s48 >= 0, s48 <= x_11, s49 >= 0, s49 <= x_2'', s50 >= 0, s50 <= s48, s51 >= 0, s51 <= x_19, s52 >= 0, s52 <= x_25, s53 >= 0, s53 <= s51, s54 >= 0, s54 <= s50, x_11 >= 0, z = 1 + (1 + x_11 + x_2'') + (1 + x_19 + x_25), x_25 >= 0, x_2'' >= 0, x_19 >= 0
   encArg(z) -{ 6 + 4*s55 + 4*s57 + 4*s58 + 107*x_11 + 32*x_11^2 + 107*x_110 + 32*x_110^2 + 107*x_2'' + 32*x_2''^2 + 107*x_26 + 32*x_26^2 }-> s61 :|: s55 >= 0, s55 <= x_11, s56 >= 0, s56 <= x_2'', s57 >= 0, s57 <= s55, s58 >= 0, s58 <= x_110, s59 >= 0, s59 <= x_26, s60 >= 0, s60 <= s58, s61 >= 0, s61 <= s57, x_11 >= 0, x_26 >= 0, x_2'' >= 0, z = 1 + (1 + x_11 + x_2'') + (1 + x_110 + x_26), x_110 >= 0
   encArg(z) -{ 3 + 4*s62 + 4*s64 + 107*x_11 + 32*x_11^2 + 107*x_2'' + 32*x_2''^2 }-> s65 :|: s62 >= 0, s62 <= x_11, s63 >= 0, s63 <= x_2'', s64 >= 0, s64 <= s62, s65 >= 0, s65 <= s64, x_11 >= 0, x_2'' >= 0, x_2 >= 0, z = 1 + (1 + x_11 + x_2'') + x_2
   encArg(z) -{ 1 + 107*x_111 + 32*x_111^2 }-> s67 :|: s66 >= 0, s66 <= x_111, s67 >= 0, s67 <= 0, x_1 >= 0, z = 1 + x_1 + (1 + x_111), x_111 >= 0
   encArg(z) -{ 6 + 4*s5 + 107*x_1' + 32*x_1'^2 + 107*x_12 + 32*x_12^2 }-> s7 :|: s5 >= 0, s5 <= x_1', s6 >= 0, s6 <= x_12, s7 >= 0, s7 <= 1 + s5, z = 1 + (1 + x_1') + (1 + x_12), x_1' >= 0, x_12 >= 0
   encArg(z) -{ 2 + 4*s68 + 107*x_112 + 32*x_112^2 + 107*x_27 + 32*x_27^2 }-> s71 :|: s68 >= 0, s68 <= x_112, s69 >= 0, s69 <= x_27, s70 >= 0, s70 <= s68, s71 >= 0, s71 <= 0, x_1 >= 0, x_27 >= 0, z = 1 + x_1 + (1 + x_112 + x_27), x_112 >= 0
   encArg(z) -{ 3 + 4*s72 + 107*x_113 + 32*x_113^2 + 107*x_28 + 32*x_28^2 }-> s75 :|: s72 >= 0, s72 <= x_113, s73 >= 0, s73 <= x_28, s74 >= 0, s74 <= s72, s75 >= 0, s75 <= 0, x_1 >= 0, x_113 >= 0, x_28 >= 0, z = 1 + x_1 + (1 + x_113 + x_28)
   encArg(z) -{ 7 + 4*s76 + 107*x_114 + 32*x_114^2 + 107*x_117 + 32*x_117^2 }-> s78 :|: s76 >= 0, s76 <= x_114, s77 >= 0, s77 <= x_117, s78 >= 0, s78 <= 1 + s76, z = 1 + (1 + x_114) + (1 + x_117), x_117 >= 0, x_114 >= 0
   encArg(z) -{ 8 + 4*s79 + 4*s80 + 107*x_114 + 32*x_114^2 + 107*x_118 + 32*x_118^2 + 107*x_211 + 32*x_211^2 }-> s83 :|: s79 >= 0, s79 <= x_114, s80 >= 0, s80 <= x_118, s81 >= 0, s81 <= x_211, s82 >= 0, s82 <= s80, s83 >= 0, s83 <= 1 + s79, z = 1 + (1 + x_114) + (1 + x_118 + x_211), x_114 >= 0, x_118 >= 0, x_211 >= 0
   encArg(z) -{ 9 + 4*s84 + 4*s85 + 107*x_114 + 32*x_114^2 + 107*x_119 + 32*x_119^2 + 107*x_212 + 32*x_212^2 }-> s88 :|: s84 >= 0, s84 <= x_114, s85 >= 0, s85 <= x_119, s86 >= 0, s86 <= x_212, s87 >= 0, s87 <= s85, s88 >= 0, s88 <= 1 + s84, x_212 >= 0, x_114 >= 0, z = 1 + (1 + x_114) + (1 + x_119 + x_212), x_119 >= 0
   encArg(z) -{ 6 + 4*s89 + 107*x_114 + 32*x_114^2 }-> s90 :|: s89 >= 0, s89 <= x_114, s90 >= 0, s90 <= 1 + s89, z = 1 + (1 + x_114) + x_2, x_114 >= 0, x_2 >= 0
   encArg(z) -{ 4 + 4*s91 + 4*s93 + 107*x_115 + 32*x_115^2 + 107*x_120 + 32*x_120^2 + 107*x_29 + 32*x_29^2 }-> s95 :|: s91 >= 0, s91 <= x_115, s92 >= 0, s92 <= x_29, s93 >= 0, s93 <= s91, s94 >= 0, s94 <= x_120, s95 >= 0, s95 <= s93, x_120 >= 0, x_115 >= 0, z = 1 + (1 + x_115 + x_29) + (1 + x_120), x_29 >= 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ -74 + 43*z + 32*z^2 }-> 1 + s4 :|: s4 >= 0, s4 <= z - 1, z - 1 >= 0
   encode_f(z) -{ 0 }-> 0 :|: z >= 0
   encode_f(z) -{ 1 + 107*z + 32*z^2 }-> 1 + s218 :|: s218 >= 0, s218 <= z, z >= 0
   encode_g(z, z') -{ -143 + 4*s219 + 43*z + 32*z^2 + 43*z' + 32*z'^2 }-> s221 :|: s219 >= 0, s219 <= z - 1, s220 >= 0, s220 <= z' - 1, s221 >= 0, s221 <= 1 + s219, z - 1 >= 0, z' - 1 >= 0
   encode_g(z, z') -{ -67 + 4*s222 + 4*s223 + 107*x_148 + 32*x_148^2 + 107*x_231 + 32*x_231^2 + 43*z + 32*z^2 }-> s226 :|: s222 >= 0, s222 <= z - 1, s223 >= 0, s223 <= x_148, s224 >= 0, s224 <= x_231, s225 >= 0, s225 <= s223, s226 >= 0, s226 <= 1 + s222, z' = 1 + x_148 + x_231, z - 1 >= 0, x_231 >= 0, x_148 >= 0
   encode_g(z, z') -{ -66 + 4*s227 + 4*s228 + 107*x_149 + 32*x_149^2 + 107*x_232 + 32*x_232^2 + 43*z + 32*z^2 }-> s231 :|: s227 >= 0, s227 <= z - 1, s228 >= 0, s228 <= x_149, s229 >= 0, s229 <= x_232, s230 >= 0, s230 <= s228, s231 >= 0, s231 <= 1 + s227, x_232 >= 0, z - 1 >= 0, z' = 1 + x_149 + x_232, x_149 >= 0
   encode_g(z, z') -{ -69 + 4*s232 + 43*z + 32*z^2 }-> s233 :|: s232 >= 0, s232 <= z - 1, s233 >= 0, s233 <= 1 + s232, z - 1 >= 0, z' >= 0
   encode_g(z, z') -{ -71 + 4*s234 + 4*s236 + 107*x_145 + 32*x_145^2 + 107*x_229 + 32*x_229^2 + 43*z' + 32*z'^2 }-> s238 :|: s234 >= 0, s234 <= x_145, s235 >= 0, s235 <= x_229, s236 >= 0, s236 <= s234, s237 >= 0, s237 <= z' - 1, s238 >= 0, s238 <= s236, z = 1 + x_145 + x_229, x_145 >= 0, x_229 >= 0, z' - 1 >= 0
   encode_g(z, z') -{ 5 + 4*s239 + 4*s241 + 4*s242 + 107*x_145 + 32*x_145^2 + 107*x_151 + 32*x_151^2 + 107*x_229 + 32*x_229^2 + 107*x_233 + 32*x_233^2 }-> s245 :|: s239 >= 0, s239 <= x_145, s240 >= 0, s240 <= x_229, s241 >= 0, s241 <= s239, s242 >= 0, s242 <= x_151, s243 >= 0, s243 <= x_233, s244 >= 0, s244 <= s242, s245 >= 0, s245 <= s241, x_233 >= 0, z = 1 + x_145 + x_229, x_145 >= 0, x_229 >= 0, z' = 1 + x_151 + x_233, x_151 >= 0
   encode_g(z, z') -{ 6 + 4*s246 + 4*s248 + 4*s249 + 107*x_145 + 32*x_145^2 + 107*x_152 + 32*x_152^2 + 107*x_229 + 32*x_229^2 + 107*x_234 + 32*x_234^2 }-> s252 :|: s246 >= 0, s246 <= x_145, s247 >= 0, s247 <= x_229, s248 >= 0, s248 <= s246, s249 >= 0, s249 <= x_152, s250 >= 0, s250 <= x_234, s251 >= 0, s251 <= s249, s252 >= 0, s252 <= s248, z = 1 + x_145 + x_229, x_234 >= 0, x_145 >= 0, z' = 1 + x_152 + x_234, x_229 >= 0, x_152 >= 0
   encode_g(z, z') -{ 3 + 4*s253 + 4*s255 + 107*x_145 + 32*x_145^2 + 107*x_229 + 32*x_229^2 }-> s256 :|: s253 >= 0, s253 <= x_145, s254 >= 0, s254 <= x_229, s255 >= 0, s255 <= s253, s256 >= 0, s256 <= s255, z = 1 + x_145 + x_229, x_145 >= 0, x_229 >= 0, z' >= 0
   encode_g(z, z') -{ -70 + 4*s257 + 4*s259 + 107*x_146 + 32*x_146^2 + 107*x_230 + 32*x_230^2 + 43*z' + 32*z'^2 }-> s261 :|: s257 >= 0, s257 <= x_146, s258 >= 0, s258 <= x_230, s259 >= 0, s259 <= s257, s260 >= 0, s260 <= z' - 1, s261 >= 0, s261 <= s259, z = 1 + x_146 + x_230, x_146 >= 0, z' - 1 >= 0, x_230 >= 0
   encode_g(z, z') -{ 6 + 4*s262 + 4*s264 + 4*s265 + 107*x_146 + 32*x_146^2 + 107*x_154 + 32*x_154^2 + 107*x_230 + 32*x_230^2 + 107*x_235 + 32*x_235^2 }-> s268 :|: s262 >= 0, s262 <= x_146, s263 >= 0, s263 <= x_230, s264 >= 0, s264 <= s262, s265 >= 0, s265 <= x_154, s266 >= 0, s266 <= x_235, s267 >= 0, s267 <= s265, s268 >= 0, s268 <= s264, z = 1 + x_146 + x_230, x_146 >= 0, x_154 >= 0, z' = 1 + x_154 + x_235, x_235 >= 0, x_230 >= 0
   encode_g(z, z') -{ 7 + 4*s269 + 4*s271 + 4*s272 + 107*x_146 + 32*x_146^2 + 107*x_155 + 32*x_155^2 + 107*x_230 + 32*x_230^2 + 107*x_236 + 32*x_236^2 }-> s275 :|: s269 >= 0, s269 <= x_146, s270 >= 0, s270 <= x_230, s271 >= 0, s271 <= s269, s272 >= 0, s272 <= x_155, s273 >= 0, s273 <= x_236, s274 >= 0, s274 <= s272, s275 >= 0, s275 <= s271, z = 1 + x_146 + x_230, x_146 >= 0, x_155 >= 0, z' = 1 + x_155 + x_236, x_236 >= 0, x_230 >= 0
   encode_g(z, z') -{ 4 + 4*s276 + 4*s278 + 107*x_146 + 32*x_146^2 + 107*x_230 + 32*x_230^2 }-> s279 :|: s276 >= 0, s276 <= x_146, s277 >= 0, s277 <= x_230, s278 >= 0, s278 <= s276, s279 >= 0, s279 <= s278, z = 1 + x_146 + x_230, x_146 >= 0, z' >= 0, x_230 >= 0
   encode_g(z, z') -{ -73 + 43*z' + 32*z'^2 }-> s281 :|: s280 >= 0, s280 <= z' - 1, s281 >= 0, s281 <= 0, z >= 0, z' - 1 >= 0
   encode_g(z, z') -{ 3 + 4*s282 + 107*x_157 + 32*x_157^2 + 107*x_237 + 32*x_237^2 }-> s285 :|: s282 >= 0, s282 <= x_157, s283 >= 0, s283 <= x_237, s284 >= 0, s284 <= s282, s285 >= 0, s285 <= 0, x_237 >= 0, z >= 0, x_157 >= 0, z' = 1 + x_157 + x_237
   encode_g(z, z') -{ 4 + 4*s286 + 107*x_158 + 32*x_158^2 + 107*x_238 + 32*x_238^2 }-> s289 :|: s286 >= 0, s286 <= x_158, s287 >= 0, s287 <= x_238, s288 >= 0, s288 <= s286, s289 >= 0, s289 <= 0, z >= 0, z' = 1 + x_158 + x_238, x_158 >= 0, x_238 >= 0
   encode_g(z, z') -{ 1 }-> s3 :|: s3 >= 0, s3 <= 0, z >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_h(z, z') -{ -144 + 4*s147 + 43*z + 32*z^2 + 43*z' + 32*z'^2 }-> s149 :|: s147 >= 0, s147 <= z - 1, s148 >= 0, s148 <= z' - 1, s149 >= 0, s149 <= 1 + s147, z' - 1 >= 0, z - 1 >= 0
   encode_h(z, z') -{ -68 + 4*s150 + 4*s151 + 107*x_133 + 32*x_133^2 + 107*x_221 + 32*x_221^2 + 43*z + 32*z^2 }-> s154 :|: s150 >= 0, s150 <= z - 1, s151 >= 0, s151 <= x_133, s152 >= 0, s152 <= x_221, s153 >= 0, s153 <= s151, s154 >= 0, s154 <= 1 + s150, z' = 1 + x_133 + x_221, x_221 >= 0, x_133 >= 0, z - 1 >= 0
   encode_h(z, z') -{ -67 + 4*s155 + 4*s156 + 107*x_134 + 32*x_134^2 + 107*x_222 + 32*x_222^2 + 43*z + 32*z^2 }-> s159 :|: s155 >= 0, s155 <= z - 1, s156 >= 0, s156 <= x_134, s157 >= 0, s157 <= x_222, s158 >= 0, s158 <= s156, s159 >= 0, s159 <= 1 + s155, z' = 1 + x_134 + x_222, x_134 >= 0, x_222 >= 0, z - 1 >= 0
   encode_h(z, z') -{ -70 + 4*s160 + 43*z + 32*z^2 }-> s161 :|: s160 >= 0, s160 <= z - 1, s161 >= 0, s161 <= 1 + s160, z' >= 0, z - 1 >= 0
   encode_h(z, z') -{ -72 + 4*s162 + 4*s164 + 107*x_130 + 32*x_130^2 + 107*x_219 + 32*x_219^2 + 43*z' + 32*z'^2 }-> s166 :|: s162 >= 0, s162 <= x_130, s163 >= 0, s163 <= x_219, s164 >= 0, s164 <= s162, s165 >= 0, s165 <= z' - 1, s166 >= 0, s166 <= s164, x_130 >= 0, z = 1 + x_130 + x_219, z' - 1 >= 0, x_219 >= 0
   encode_h(z, z') -{ 4 + 4*s167 + 4*s169 + 4*s170 + 107*x_130 + 32*x_130^2 + 107*x_136 + 32*x_136^2 + 107*x_219 + 32*x_219^2 + 107*x_223 + 32*x_223^2 }-> s173 :|: s167 >= 0, s167 <= x_130, s168 >= 0, s168 <= x_219, s169 >= 0, s169 <= s167, s170 >= 0, s170 <= x_136, s171 >= 0, s171 <= x_223, s172 >= 0, s172 <= s170, s173 >= 0, s173 <= s169, z' = 1 + x_136 + x_223, x_130 >= 0, z = 1 + x_130 + x_219, x_223 >= 0, x_136 >= 0, x_219 >= 0
   encode_h(z, z') -{ 5 + 4*s174 + 4*s176 + 4*s177 + 107*x_130 + 32*x_130^2 + 107*x_137 + 32*x_137^2 + 107*x_219 + 32*x_219^2 + 107*x_224 + 32*x_224^2 }-> s180 :|: s174 >= 0, s174 <= x_130, s175 >= 0, s175 <= x_219, s176 >= 0, s176 <= s174, s177 >= 0, s177 <= x_137, s178 >= 0, s178 <= x_224, s179 >= 0, s179 <= s177, s180 >= 0, s180 <= s176, z' = 1 + x_137 + x_224, x_130 >= 0, z = 1 + x_130 + x_219, x_224 >= 0, x_137 >= 0, x_219 >= 0
   encode_h(z, z') -{ 2 + 4*s181 + 4*s183 + 107*x_130 + 32*x_130^2 + 107*x_219 + 32*x_219^2 }-> s184 :|: s181 >= 0, s181 <= x_130, s182 >= 0, s182 <= x_219, s183 >= 0, s183 <= s181, s184 >= 0, s184 <= s183, x_130 >= 0, z = 1 + x_130 + x_219, z' >= 0, x_219 >= 0
   encode_h(z, z') -{ -71 + 4*s185 + 4*s187 + 107*x_131 + 32*x_131^2 + 107*x_220 + 32*x_220^2 + 43*z' + 32*z'^2 }-> s189 :|: s185 >= 0, s185 <= x_131, s186 >= 0, s186 <= x_220, s187 >= 0, s187 <= s185, s188 >= 0, s188 <= z' - 1, s189 >= 0, s189 <= s187, z' - 1 >= 0, z = 1 + x_131 + x_220, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ 5 + 4*s190 + 4*s192 + 4*s193 + 107*x_131 + 32*x_131^2 + 107*x_139 + 32*x_139^2 + 107*x_220 + 32*x_220^2 + 107*x_225 + 32*x_225^2 }-> s196 :|: s190 >= 0, s190 <= x_131, s191 >= 0, s191 <= x_220, s192 >= 0, s192 <= s190, s193 >= 0, s193 <= x_139, s194 >= 0, s194 <= x_225, s195 >= 0, s195 <= s193, s196 >= 0, s196 <= s192, z = 1 + x_131 + x_220, z' = 1 + x_139 + x_225, x_225 >= 0, x_139 >= 0, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ 0 }-> s2 :|: s2 >= 0, s2 <= 0, z >= 0, z' >= 0
   encode_h(z, z') -{ 6 + 4*s197 + 4*s199 + 4*s200 + 107*x_131 + 32*x_131^2 + 107*x_140 + 32*x_140^2 + 107*x_220 + 32*x_220^2 + 107*x_226 + 32*x_226^2 }-> s203 :|: s197 >= 0, s197 <= x_131, s198 >= 0, s198 <= x_220, s199 >= 0, s199 <= s197, s200 >= 0, s200 <= x_140, s201 >= 0, s201 <= x_226, s202 >= 0, s202 <= s200, s203 >= 0, s203 <= s199, z = 1 + x_131 + x_220, x_226 >= 0, z' = 1 + x_140 + x_226, x_140 >= 0, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ 3 + 4*s204 + 4*s206 + 107*x_131 + 32*x_131^2 + 107*x_220 + 32*x_220^2 }-> s207 :|: s204 >= 0, s204 <= x_131, s205 >= 0, s205 <= x_220, s206 >= 0, s206 <= s204, s207 >= 0, s207 <= s206, z = 1 + x_131 + x_220, z' >= 0, x_131 >= 0, x_220 >= 0
   encode_h(z, z') -{ -74 + 43*z' + 32*z'^2 }-> s209 :|: s208 >= 0, s208 <= z' - 1, s209 >= 0, s209 <= 0, z >= 0, z' - 1 >= 0
   encode_h(z, z') -{ 2 + 4*s210 + 107*x_142 + 32*x_142^2 + 107*x_227 + 32*x_227^2 }-> s213 :|: s210 >= 0, s210 <= x_142, s211 >= 0, s211 <= x_227, s212 >= 0, s212 <= s210, s213 >= 0, s213 <= 0, z >= 0, z' = 1 + x_142 + x_227, x_142 >= 0, x_227 >= 0
   encode_h(z, z') -{ 3 + 4*s214 + 107*x_143 + 32*x_143^2 + 107*x_228 + 32*x_228^2 }-> s217 :|: s214 >= 0, s214 <= x_143, s215 >= 0, s215 <= x_228, s216 >= 0, s216 <= s214, s217 >= 0, s217 <= 0, z >= 0, z' = 1 + x_143 + x_228, x_143 >= 0, x_228 >= 0
   encode_h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   g(z, z') -{ 1 + 4*z }-> s' :|: s' >= 0, s' <= z, z >= 0, z' >= 0
   h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   h(z, z') -{ -2 + 4*z }-> 1 + s :|: s >= 0, s <= z - 1, z - 1 >= 0, z' >= 0

Function symbols to be analyzed: 
Previous analysis results are:
  h: runtime: O(n^1) [4*z], size: O(n^1) [z]
  g: runtime: O(n^1) [1 + 4*z], size: O(n^1) [z]
  encArg: runtime: O(n^2) [1 + 107*z + 32*z^2], size: O(n^1) [z]
  encode_f: runtime: O(n^2) [1 + 107*z + 32*z^2], size: O(n^1) [1 + z]
  encode_h: runtime: O(n^2) [30 + 1964*z + 640*z^2 + 1916*z' + 640*z'^2], size: O(n^1) [z]
  encode_g: runtime: O(n^2) [39 + 1964*z + 640*z^2 + 1916*z' + 640*z'^2], size: O(n^1) [z]

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

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

(50)
BOUNDS(1, n^2)

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

(52)
Obligation:
The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF).


The TRS R consists of the following rules:

   h(f(x), y) -> f(g(x, y))
   g(x, y) -> h(x, y)

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

   encArg(f(x_1)) -> f(encArg(x_1))
   encArg(cons_h(x_1, x_2)) -> h(encArg(x_1), encArg(x_2))
   encArg(cons_g(x_1, x_2)) -> g(encArg(x_1), encArg(x_2))
   encode_h(x_1, x_2) -> h(encArg(x_1), encArg(x_2))
   encode_f(x_1) -> f(encArg(x_1))
   encode_g(x_1, x_2) -> g(encArg(x_1), encArg(x_2))

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

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

(54)
Obligation:
Innermost TRS:
Rules:
h(f(x), y) -> f(g(x, y))
g(x, y) -> h(x, y)
encArg(f(x_1)) -> f(encArg(x_1))
encArg(cons_h(x_1, x_2)) -> h(encArg(x_1), encArg(x_2))
encArg(cons_g(x_1, x_2)) -> g(encArg(x_1), encArg(x_2))
encode_h(x_1, x_2) -> h(encArg(x_1), encArg(x_2))
encode_f(x_1) -> f(encArg(x_1))
encode_g(x_1, x_2) -> g(encArg(x_1), encArg(x_2))

Types:
h :: f:cons_h:cons_g -> f:cons_h:cons_g -> f:cons_h:cons_g
f :: f:cons_h:cons_g -> f:cons_h:cons_g
g :: f:cons_h:cons_g -> f:cons_h:cons_g -> f:cons_h:cons_g
encArg :: f:cons_h:cons_g -> f:cons_h:cons_g
cons_h :: f:cons_h:cons_g -> f:cons_h:cons_g -> f:cons_h:cons_g
cons_g :: f:cons_h:cons_g -> f:cons_h:cons_g -> f:cons_h:cons_g
encode_h :: f:cons_h:cons_g -> f:cons_h:cons_g -> f:cons_h:cons_g
encode_f :: f:cons_h:cons_g -> f:cons_h:cons_g
encode_g :: f:cons_h:cons_g -> f:cons_h:cons_g -> f:cons_h:cons_g
hole_f:cons_h:cons_g1_0 :: f:cons_h:cons_g
gen_f:cons_h:cons_g2_0 :: Nat -> f:cons_h:cons_g

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

(55) OrderProof (LOWER BOUND(ID))
Heuristically decided to analyse the following defined symbols:
h, g, encArg

They will be analysed ascendingly in the following order:
h = g
h < encArg
g < encArg

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

(56)
Obligation:
Innermost TRS:
Rules:
h(f(x), y) -> f(g(x, y))
g(x, y) -> h(x, y)
encArg(f(x_1)) -> f(encArg(x_1))
encArg(cons_h(x_1, x_2)) -> h(encArg(x_1), encArg(x_2))
encArg(cons_g(x_1, x_2)) -> g(encArg(x_1), encArg(x_2))
encode_h(x_1, x_2) -> h(encArg(x_1), encArg(x_2))
encode_f(x_1) -> f(encArg(x_1))
encode_g(x_1, x_2) -> g(encArg(x_1), encArg(x_2))

Types:
h :: f:cons_h:cons_g -> f:cons_h:cons_g -> f:cons_h:cons_g
f :: f:cons_h:cons_g -> f:cons_h:cons_g
g :: f:cons_h:cons_g -> f:cons_h:cons_g -> f:cons_h:cons_g
encArg :: f:cons_h:cons_g -> f:cons_h:cons_g
cons_h :: f:cons_h:cons_g -> f:cons_h:cons_g -> f:cons_h:cons_g
cons_g :: f:cons_h:cons_g -> f:cons_h:cons_g -> f:cons_h:cons_g
encode_h :: f:cons_h:cons_g -> f:cons_h:cons_g -> f:cons_h:cons_g
encode_f :: f:cons_h:cons_g -> f:cons_h:cons_g
encode_g :: f:cons_h:cons_g -> f:cons_h:cons_g -> f:cons_h:cons_g
hole_f:cons_h:cons_g1_0 :: f:cons_h:cons_g
gen_f:cons_h:cons_g2_0 :: Nat -> f:cons_h:cons_g


Generator Equations:
gen_f:cons_h:cons_g2_0(0) <=> hole_f:cons_h:cons_g1_0
gen_f:cons_h:cons_g2_0(+(x, 1)) <=> f(gen_f:cons_h:cons_g2_0(x))


The following defined symbols remain to be analysed:
g, h, encArg

They will be analysed ascendingly in the following order:
h = g
h < encArg
g < encArg

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

(57) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
g(gen_f:cons_h:cons_g2_0(n4_0), gen_f:cons_h:cons_g2_0(b)) -> *3_0, rt in Omega(n4_0)

Induction Base:
g(gen_f:cons_h:cons_g2_0(0), gen_f:cons_h:cons_g2_0(b))

Induction Step:
g(gen_f:cons_h:cons_g2_0(+(n4_0, 1)), gen_f:cons_h:cons_g2_0(b)) ->_R^Omega(1)
h(gen_f:cons_h:cons_g2_0(+(n4_0, 1)), gen_f:cons_h:cons_g2_0(b)) ->_R^Omega(1)
f(g(gen_f:cons_h:cons_g2_0(n4_0), gen_f:cons_h:cons_g2_0(b))) ->_IH
f(*3_0)

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

(58)
Complex Obligation (BEST)

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

(59)
Obligation:
Proved the lower bound n^1 for the following obligation:

Innermost TRS:
Rules:
h(f(x), y) -> f(g(x, y))
g(x, y) -> h(x, y)
encArg(f(x_1)) -> f(encArg(x_1))
encArg(cons_h(x_1, x_2)) -> h(encArg(x_1), encArg(x_2))
encArg(cons_g(x_1, x_2)) -> g(encArg(x_1), encArg(x_2))
encode_h(x_1, x_2) -> h(encArg(x_1), encArg(x_2))
encode_f(x_1) -> f(encArg(x_1))
encode_g(x_1, x_2) -> g(encArg(x_1), encArg(x_2))

Types:
h :: f:cons_h:cons_g -> f:cons_h:cons_g -> f:cons_h:cons_g
f :: f:cons_h:cons_g -> f:cons_h:cons_g
g :: f:cons_h:cons_g -> f:cons_h:cons_g -> f:cons_h:cons_g
encArg :: f:cons_h:cons_g -> f:cons_h:cons_g
cons_h :: f:cons_h:cons_g -> f:cons_h:cons_g -> f:cons_h:cons_g
cons_g :: f:cons_h:cons_g -> f:cons_h:cons_g -> f:cons_h:cons_g
encode_h :: f:cons_h:cons_g -> f:cons_h:cons_g -> f:cons_h:cons_g
encode_f :: f:cons_h:cons_g -> f:cons_h:cons_g
encode_g :: f:cons_h:cons_g -> f:cons_h:cons_g -> f:cons_h:cons_g
hole_f:cons_h:cons_g1_0 :: f:cons_h:cons_g
gen_f:cons_h:cons_g2_0 :: Nat -> f:cons_h:cons_g


Generator Equations:
gen_f:cons_h:cons_g2_0(0) <=> hole_f:cons_h:cons_g1_0
gen_f:cons_h:cons_g2_0(+(x, 1)) <=> f(gen_f:cons_h:cons_g2_0(x))


The following defined symbols remain to be analysed:
g, h, encArg

They will be analysed ascendingly in the following order:
h = g
h < encArg
g < encArg

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

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

(61)
BOUNDS(n^1, INF)

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

(62)
Obligation:
Innermost TRS:
Rules:
h(f(x), y) -> f(g(x, y))
g(x, y) -> h(x, y)
encArg(f(x_1)) -> f(encArg(x_1))
encArg(cons_h(x_1, x_2)) -> h(encArg(x_1), encArg(x_2))
encArg(cons_g(x_1, x_2)) -> g(encArg(x_1), encArg(x_2))
encode_h(x_1, x_2) -> h(encArg(x_1), encArg(x_2))
encode_f(x_1) -> f(encArg(x_1))
encode_g(x_1, x_2) -> g(encArg(x_1), encArg(x_2))

Types:
h :: f:cons_h:cons_g -> f:cons_h:cons_g -> f:cons_h:cons_g
f :: f:cons_h:cons_g -> f:cons_h:cons_g
g :: f:cons_h:cons_g -> f:cons_h:cons_g -> f:cons_h:cons_g
encArg :: f:cons_h:cons_g -> f:cons_h:cons_g
cons_h :: f:cons_h:cons_g -> f:cons_h:cons_g -> f:cons_h:cons_g
cons_g :: f:cons_h:cons_g -> f:cons_h:cons_g -> f:cons_h:cons_g
encode_h :: f:cons_h:cons_g -> f:cons_h:cons_g -> f:cons_h:cons_g
encode_f :: f:cons_h:cons_g -> f:cons_h:cons_g
encode_g :: f:cons_h:cons_g -> f:cons_h:cons_g -> f:cons_h:cons_g
hole_f:cons_h:cons_g1_0 :: f:cons_h:cons_g
gen_f:cons_h:cons_g2_0 :: Nat -> f:cons_h:cons_g


Lemmas:
g(gen_f:cons_h:cons_g2_0(n4_0), gen_f:cons_h:cons_g2_0(b)) -> *3_0, rt in Omega(n4_0)


Generator Equations:
gen_f:cons_h:cons_g2_0(0) <=> hole_f:cons_h:cons_g1_0
gen_f:cons_h:cons_g2_0(+(x, 1)) <=> f(gen_f:cons_h:cons_g2_0(x))


The following defined symbols remain to be analysed:
h, encArg

They will be analysed ascendingly in the following order:
h = g
h < encArg
g < encArg

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

(63) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
h(gen_f:cons_h:cons_g2_0(+(1, n385_0)), gen_f:cons_h:cons_g2_0(b)) -> *3_0, rt in Omega(n385_0)

Induction Base:
h(gen_f:cons_h:cons_g2_0(+(1, 0)), gen_f:cons_h:cons_g2_0(b))

Induction Step:
h(gen_f:cons_h:cons_g2_0(+(1, +(n385_0, 1))), gen_f:cons_h:cons_g2_0(b)) ->_R^Omega(1)
f(g(gen_f:cons_h:cons_g2_0(+(1, n385_0)), gen_f:cons_h:cons_g2_0(b))) ->_R^Omega(1)
f(h(gen_f:cons_h:cons_g2_0(+(1, n385_0)), gen_f:cons_h:cons_g2_0(b))) ->_IH
f(*3_0)

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

(64)
Obligation:
Innermost TRS:
Rules:
h(f(x), y) -> f(g(x, y))
g(x, y) -> h(x, y)
encArg(f(x_1)) -> f(encArg(x_1))
encArg(cons_h(x_1, x_2)) -> h(encArg(x_1), encArg(x_2))
encArg(cons_g(x_1, x_2)) -> g(encArg(x_1), encArg(x_2))
encode_h(x_1, x_2) -> h(encArg(x_1), encArg(x_2))
encode_f(x_1) -> f(encArg(x_1))
encode_g(x_1, x_2) -> g(encArg(x_1), encArg(x_2))

Types:
h :: f:cons_h:cons_g -> f:cons_h:cons_g -> f:cons_h:cons_g
f :: f:cons_h:cons_g -> f:cons_h:cons_g
g :: f:cons_h:cons_g -> f:cons_h:cons_g -> f:cons_h:cons_g
encArg :: f:cons_h:cons_g -> f:cons_h:cons_g
cons_h :: f:cons_h:cons_g -> f:cons_h:cons_g -> f:cons_h:cons_g
cons_g :: f:cons_h:cons_g -> f:cons_h:cons_g -> f:cons_h:cons_g
encode_h :: f:cons_h:cons_g -> f:cons_h:cons_g -> f:cons_h:cons_g
encode_f :: f:cons_h:cons_g -> f:cons_h:cons_g
encode_g :: f:cons_h:cons_g -> f:cons_h:cons_g -> f:cons_h:cons_g
hole_f:cons_h:cons_g1_0 :: f:cons_h:cons_g
gen_f:cons_h:cons_g2_0 :: Nat -> f:cons_h:cons_g


Lemmas:
g(gen_f:cons_h:cons_g2_0(n4_0), gen_f:cons_h:cons_g2_0(b)) -> *3_0, rt in Omega(n4_0)
h(gen_f:cons_h:cons_g2_0(+(1, n385_0)), gen_f:cons_h:cons_g2_0(b)) -> *3_0, rt in Omega(n385_0)


Generator Equations:
gen_f:cons_h:cons_g2_0(0) <=> hole_f:cons_h:cons_g1_0
gen_f:cons_h:cons_g2_0(+(x, 1)) <=> f(gen_f:cons_h:cons_g2_0(x))


The following defined symbols remain to be analysed:
g, encArg

They will be analysed ascendingly in the following order:
h = g
h < encArg
g < encArg

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

(65) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
g(gen_f:cons_h:cons_g2_0(n1152_0), gen_f:cons_h:cons_g2_0(b)) -> *3_0, rt in Omega(n1152_0)

Induction Base:
g(gen_f:cons_h:cons_g2_0(0), gen_f:cons_h:cons_g2_0(b))

Induction Step:
g(gen_f:cons_h:cons_g2_0(+(n1152_0, 1)), gen_f:cons_h:cons_g2_0(b)) ->_R^Omega(1)
h(gen_f:cons_h:cons_g2_0(+(n1152_0, 1)), gen_f:cons_h:cons_g2_0(b)) ->_R^Omega(1)
f(g(gen_f:cons_h:cons_g2_0(n1152_0), gen_f:cons_h:cons_g2_0(b))) ->_IH
f(*3_0)

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

(66)
Obligation:
Innermost TRS:
Rules:
h(f(x), y) -> f(g(x, y))
g(x, y) -> h(x, y)
encArg(f(x_1)) -> f(encArg(x_1))
encArg(cons_h(x_1, x_2)) -> h(encArg(x_1), encArg(x_2))
encArg(cons_g(x_1, x_2)) -> g(encArg(x_1), encArg(x_2))
encode_h(x_1, x_2) -> h(encArg(x_1), encArg(x_2))
encode_f(x_1) -> f(encArg(x_1))
encode_g(x_1, x_2) -> g(encArg(x_1), encArg(x_2))

Types:
h :: f:cons_h:cons_g -> f:cons_h:cons_g -> f:cons_h:cons_g
f :: f:cons_h:cons_g -> f:cons_h:cons_g
g :: f:cons_h:cons_g -> f:cons_h:cons_g -> f:cons_h:cons_g
encArg :: f:cons_h:cons_g -> f:cons_h:cons_g
cons_h :: f:cons_h:cons_g -> f:cons_h:cons_g -> f:cons_h:cons_g
cons_g :: f:cons_h:cons_g -> f:cons_h:cons_g -> f:cons_h:cons_g
encode_h :: f:cons_h:cons_g -> f:cons_h:cons_g -> f:cons_h:cons_g
encode_f :: f:cons_h:cons_g -> f:cons_h:cons_g
encode_g :: f:cons_h:cons_g -> f:cons_h:cons_g -> f:cons_h:cons_g
hole_f:cons_h:cons_g1_0 :: f:cons_h:cons_g
gen_f:cons_h:cons_g2_0 :: Nat -> f:cons_h:cons_g


Lemmas:
g(gen_f:cons_h:cons_g2_0(n1152_0), gen_f:cons_h:cons_g2_0(b)) -> *3_0, rt in Omega(n1152_0)
h(gen_f:cons_h:cons_g2_0(+(1, n385_0)), gen_f:cons_h:cons_g2_0(b)) -> *3_0, rt in Omega(n385_0)


Generator Equations:
gen_f:cons_h:cons_g2_0(0) <=> hole_f:cons_h:cons_g1_0
gen_f:cons_h:cons_g2_0(+(x, 1)) <=> f(gen_f:cons_h:cons_g2_0(x))


The following defined symbols remain to be analysed:
encArg
----------------------------------------

(67) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
encArg(gen_f:cons_h:cons_g2_0(+(1, n2149_0))) -> *3_0, rt in Omega(0)

Induction Base:
encArg(gen_f:cons_h:cons_g2_0(+(1, 0)))

Induction Step:
encArg(gen_f:cons_h:cons_g2_0(+(1, +(n2149_0, 1)))) ->_R^Omega(0)
f(encArg(gen_f:cons_h:cons_g2_0(+(1, n2149_0)))) ->_IH
f(*3_0)

We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0).
----------------------------------------

(68)
BOUNDS(1, INF)