/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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 (full) 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), 172 ms]
(4) CpxRelTRS
(5) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms]
(6) CpxRelTRS
    (7) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (8) CpxWeightedTrs
    (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (10) CpxTypedWeightedTrs
    (11) CompletionProof [UPPER BOUND(ID), 0 ms]
    (12) CpxTypedWeightedCompleteTrs
    (13) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (14) CpxTypedWeightedCompleteTrs
    (15) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
    (16) CpxRNTS
    (17) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (18) CpxRNTS
    (19) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms]
    (20) CpxRNTS
    (21) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (22) CpxRNTS
    (23) IntTrsBoundProof [UPPER BOUND(ID), 579 ms]
    (24) CpxRNTS
    (25) IntTrsBoundProof [UPPER BOUND(ID), 215 ms]
    (26) CpxRNTS
    (27) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (28) CpxRNTS
    (29) IntTrsBoundProof [UPPER BOUND(ID), 2730 ms]
    (30) CpxRNTS
    (31) IntTrsBoundProof [UPPER BOUND(ID), 5092 ms]
    (32) CpxRNTS
    (33) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (34) CpxRNTS
    (35) IntTrsBoundProof [UPPER BOUND(ID), 178 ms]
    (36) CpxRNTS
    (37) IntTrsBoundProof [UPPER BOUND(ID), 0 ms]
    (38) CpxRNTS
    (39) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (40) CpxRNTS
    (41) IntTrsBoundProof [UPPER BOUND(ID), 1204 ms]
    (42) CpxRNTS
    (43) IntTrsBoundProof [UPPER BOUND(ID), 817 ms]
    (44) CpxRNTS
    (45) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (46) CpxRNTS
    (47) IntTrsBoundProof [UPPER BOUND(ID), 1299 ms]
    (48) CpxRNTS
    (49) IntTrsBoundProof [UPPER BOUND(ID), 787 ms]
    (50) CpxRNTS
    (51) FinalProof [FINISHED, 0 ms]
    (52) BOUNDS(1, n^2)
(53) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(54) CpxRelTRS
    (55) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (56) typed CpxTrs
    (57) OrderProof [LOWER BOUND(ID), 0 ms]
    (58) typed CpxTrs
    (59) RewriteLemmaProof [LOWER BOUND(ID), 512 ms]
    (60) BEST
        (61) proven lower bound
            (62) LowerBoundPropagationProof [FINISHED, 0 ms]
            (63) BOUNDS(n^1, INF)
        (64) typed CpxTrs
            (65) RewriteLemmaProof [LOWER BOUND(ID), 132 ms]
            (66) typed CpxTrs
            (67) RewriteLemmaProof [LOWER BOUND(ID), 96 ms]
            (68) typed CpxTrs
            (69) RewriteLemmaProof [LOWER BOUND(ID), 70 ms]
            (70) BOUNDS(1, INF)


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

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


The TRS R consists of the following rules:

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

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

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

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


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

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


The TRS R consists of the following rules:

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

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

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

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

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

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


The TRS R consists of the following rules:

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

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

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

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

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

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

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


The TRS R consists of the following rules:

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

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

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

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

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

(8)
Obligation:
The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2).


The TRS R consists of the following rules:

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

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

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

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

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

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

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

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

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

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

(c) The following functions are completely defined:

   g_2
   f_2
   encArg_1
   encode_f_2
   encode_g_2
   encode_h_1

Due to the following rules being added:

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

And the following fresh constants:    const

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

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

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

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

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

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

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

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

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

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

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

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

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

   const => 0

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

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

   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)), f(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)), 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(f(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(f(encArg(x_115), encArg(x_29)), f(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(f(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(f(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(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, f(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, 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), 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), f(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), 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 }-> f(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 }-> f(g(encArg(x_11), encArg(x_2'')), f(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 }-> f(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 }-> f(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 }-> f(f(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 }-> f(f(encArg(x_1''), encArg(x_2')), f(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 }-> f(f(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 }-> f(f(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 }-> f(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 }-> f(0, f(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 }-> f(0, 0) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> f(0, 1 + encArg(x_111)) :|: x_1 >= 0, z = 1 + x_1 + (1 + x_111), x_111 >= 0
   encArg(z) -{ 0 }-> f(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 }-> f(1 + encArg(x_1'), f(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 }-> f(1 + encArg(x_1'), 0) :|: x_1' >= 0, x_2 >= 0, z = 1 + (1 + x_1') + x_2
   encArg(z) -{ 0 }-> f(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 }-> 0 :|: v0 >= 0, z = v0
   encArg(z) -{ 0 }-> 1 + encArg(x_1) :|: z = 1 + x_1, x_1 >= 0
   encode_f(z, z') -{ 0 }-> f(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_f(z, z') -{ 0 }-> f(g(encArg(x_131), encArg(x_220)), f(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_f(z, z') -{ 0 }-> f(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_f(z, z') -{ 0 }-> f(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_f(z, z') -{ 0 }-> f(f(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_f(z, z') -{ 0 }-> f(f(encArg(x_130), encArg(x_219)), f(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_f(z, z') -{ 0 }-> f(f(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_f(z, z') -{ 0 }-> f(f(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_f(z, z') -{ 0 }-> f(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_f(z, z') -{ 0 }-> f(0, f(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_f(z, z') -{ 0 }-> f(0, 0) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2
   encode_f(z, z') -{ 0 }-> f(0, 1 + encArg(x_141)) :|: x_1 >= 0, z' = 1 + x_141, z = x_1, x_141 >= 0
   encode_f(z, z') -{ 0 }-> f(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_f(z, z') -{ 0 }-> f(1 + encArg(x_129), f(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_f(z, z') -{ 0 }-> f(1 + encArg(x_129), 0) :|: z = 1 + x_129, x_2 >= 0, z' = x_2, x_129 >= 0
   encode_f(z, z') -{ 0 }-> f(1 + encArg(x_129), 1 + encArg(x_132)) :|: z = 1 + x_129, z' = 1 + x_132, x_132 >= 0, x_129 >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   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)), f(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)), 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(f(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(f(encArg(x_145), encArg(x_229)), f(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(f(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(f(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(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, f(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, 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), 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), f(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), 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) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_h(z) -{ 0 }-> 1 + encArg(x_1) :|: x_1 >= 0, z = x_1
   f(z, z') -{ 1 }-> g(x, y) :|: x >= 0, y >= 0, z = x, z' = y
   g(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   g(z, z') -{ 1 }-> 1 + g(x, y) :|: x >= 0, y >= 0, z = 1 + x, z' = y
   g(z, z') -{ 1 }-> 1 + f(x, y) :|: x >= 0, y >= 0, z = 1 + x, z' = y


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

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

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

   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)), f(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)), 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(f(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(f(encArg(x_115), encArg(x_29)), f(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(f(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(f(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(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, f(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, 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), 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), f(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), 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 }-> f(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 }-> f(g(encArg(x_11), encArg(x_2'')), f(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 }-> f(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 }-> f(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 }-> f(f(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 }-> f(f(encArg(x_1''), encArg(x_2')), f(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 }-> f(f(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 }-> f(f(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 }-> f(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 }-> f(0, f(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 }-> f(0, 0) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> f(0, 1 + encArg(x_111)) :|: x_1 >= 0, z = 1 + x_1 + (1 + x_111), x_111 >= 0
   encArg(z) -{ 0 }-> f(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 }-> f(1 + encArg(x_1'), f(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 }-> f(1 + encArg(x_1'), 0) :|: x_1' >= 0, x_2 >= 0, z = 1 + (1 + x_1') + x_2
   encArg(z) -{ 0 }-> f(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 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_f(z, z') -{ 0 }-> f(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_f(z, z') -{ 0 }-> f(g(encArg(x_131), encArg(x_220)), f(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_f(z, z') -{ 0 }-> f(g(encArg(x_131), encArg(x_220)), 0) :|: z = 1 + x_131 + x_220, z' >= 0, x_131 >= 0, x_220 >= 0
   encode_f(z, z') -{ 0 }-> f(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_f(z, z') -{ 0 }-> f(f(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_f(z, z') -{ 0 }-> f(f(encArg(x_130), encArg(x_219)), f(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_f(z, z') -{ 0 }-> f(f(encArg(x_130), encArg(x_219)), 0) :|: x_130 >= 0, z = 1 + x_130 + x_219, z' >= 0, x_219 >= 0
   encode_f(z, z') -{ 0 }-> f(f(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_f(z, z') -{ 0 }-> f(0, g(encArg(x_143), encArg(x_228))) :|: z >= 0, z' = 1 + x_143 + x_228, x_143 >= 0, x_228 >= 0
   encode_f(z, z') -{ 0 }-> f(0, f(encArg(x_142), encArg(x_227))) :|: z >= 0, z' = 1 + x_142 + x_227, x_142 >= 0, x_227 >= 0
   encode_f(z, z') -{ 0 }-> f(0, 0) :|: z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> f(0, 1 + encArg(z' - 1)) :|: z >= 0, z' - 1 >= 0
   encode_f(z, z') -{ 0 }-> f(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_f(z, z') -{ 0 }-> f(1 + encArg(z - 1), f(encArg(x_133), encArg(x_221))) :|: z' = 1 + x_133 + x_221, x_221 >= 0, x_133 >= 0, z - 1 >= 0
   encode_f(z, z') -{ 0 }-> f(1 + encArg(z - 1), 0) :|: z' >= 0, z - 1 >= 0
   encode_f(z, z') -{ 0 }-> f(1 + encArg(z - 1), 1 + encArg(z' - 1)) :|: z' - 1 >= 0, z - 1 >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 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)), f(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)), 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(f(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(f(encArg(x_145), encArg(x_229)), f(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(f(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(f(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(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, f(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, 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), 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), f(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), 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) -{ 0 }-> 0 :|: z >= 0
   encode_h(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   f(z, z') -{ 1 }-> g(z, z') :|: z >= 0, z' >= 0
   g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   g(z, z') -{ 1 }-> 1 + g(z - 1, z') :|: z - 1 >= 0, z' >= 0
   g(z, z') -{ 1 }-> 1 + f(z - 1, z') :|: z - 1 >= 0, z' >= 0


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

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

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

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

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

   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)), f(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)), 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(f(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(f(encArg(x_115), encArg(x_29)), f(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(f(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(f(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(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, f(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, 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), 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), f(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), 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 }-> f(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 }-> f(g(encArg(x_11), encArg(x_2'')), f(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 }-> f(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 }-> f(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 }-> f(f(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 }-> f(f(encArg(x_1''), encArg(x_2')), f(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 }-> f(f(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 }-> f(f(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 }-> f(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 }-> f(0, f(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 }-> f(0, 0) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> f(0, 1 + encArg(x_111)) :|: x_1 >= 0, z = 1 + x_1 + (1 + x_111), x_111 >= 0
   encArg(z) -{ 0 }-> f(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 }-> f(1 + encArg(x_1'), f(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 }-> f(1 + encArg(x_1'), 0) :|: x_1' >= 0, x_2 >= 0, z = 1 + (1 + x_1') + x_2
   encArg(z) -{ 0 }-> f(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 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_f(z, z') -{ 0 }-> f(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_f(z, z') -{ 0 }-> f(g(encArg(x_131), encArg(x_220)), f(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_f(z, z') -{ 0 }-> f(g(encArg(x_131), encArg(x_220)), 0) :|: z = 1 + x_131 + x_220, z' >= 0, x_131 >= 0, x_220 >= 0
   encode_f(z, z') -{ 0 }-> f(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_f(z, z') -{ 0 }-> f(f(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_f(z, z') -{ 0 }-> f(f(encArg(x_130), encArg(x_219)), f(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_f(z, z') -{ 0 }-> f(f(encArg(x_130), encArg(x_219)), 0) :|: x_130 >= 0, z = 1 + x_130 + x_219, z' >= 0, x_219 >= 0
   encode_f(z, z') -{ 0 }-> f(f(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_f(z, z') -{ 0 }-> f(0, g(encArg(x_143), encArg(x_228))) :|: z >= 0, z' = 1 + x_143 + x_228, x_143 >= 0, x_228 >= 0
   encode_f(z, z') -{ 0 }-> f(0, f(encArg(x_142), encArg(x_227))) :|: z >= 0, z' = 1 + x_142 + x_227, x_142 >= 0, x_227 >= 0
   encode_f(z, z') -{ 0 }-> f(0, 0) :|: z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> f(0, 1 + encArg(z' - 1)) :|: z >= 0, z' - 1 >= 0
   encode_f(z, z') -{ 0 }-> f(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_f(z, z') -{ 0 }-> f(1 + encArg(z - 1), f(encArg(x_133), encArg(x_221))) :|: z' = 1 + x_133 + x_221, x_221 >= 0, x_133 >= 0, z - 1 >= 0
   encode_f(z, z') -{ 0 }-> f(1 + encArg(z - 1), 0) :|: z' >= 0, z - 1 >= 0
   encode_f(z, z') -{ 0 }-> f(1 + encArg(z - 1), 1 + encArg(z' - 1)) :|: z' - 1 >= 0, z - 1 >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 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)), f(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)), 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(f(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(f(encArg(x_145), encArg(x_229)), f(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(f(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(f(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(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, f(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, 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), 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), f(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), 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) -{ 0 }-> 0 :|: z >= 0
   encode_h(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   f(z, z') -{ 1 }-> g(z, z') :|: z >= 0, z' >= 0
   g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   g(z, z') -{ 1 }-> 1 + g(z - 1, z') :|: z - 1 >= 0, z' >= 0
   g(z, z') -{ 1 }-> 1 + f(z - 1, z') :|: z - 1 >= 0, z' >= 0

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

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

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

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

   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)), f(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)), 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(f(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(f(encArg(x_115), encArg(x_29)), f(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(f(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(f(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(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, f(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, 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), 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), f(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), 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 }-> f(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 }-> f(g(encArg(x_11), encArg(x_2'')), f(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 }-> f(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 }-> f(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 }-> f(f(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 }-> f(f(encArg(x_1''), encArg(x_2')), f(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 }-> f(f(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 }-> f(f(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 }-> f(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 }-> f(0, f(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 }-> f(0, 0) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> f(0, 1 + encArg(x_111)) :|: x_1 >= 0, z = 1 + x_1 + (1 + x_111), x_111 >= 0
   encArg(z) -{ 0 }-> f(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 }-> f(1 + encArg(x_1'), f(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 }-> f(1 + encArg(x_1'), 0) :|: x_1' >= 0, x_2 >= 0, z = 1 + (1 + x_1') + x_2
   encArg(z) -{ 0 }-> f(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 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_f(z, z') -{ 0 }-> f(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_f(z, z') -{ 0 }-> f(g(encArg(x_131), encArg(x_220)), f(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_f(z, z') -{ 0 }-> f(g(encArg(x_131), encArg(x_220)), 0) :|: z = 1 + x_131 + x_220, z' >= 0, x_131 >= 0, x_220 >= 0
   encode_f(z, z') -{ 0 }-> f(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_f(z, z') -{ 0 }-> f(f(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_f(z, z') -{ 0 }-> f(f(encArg(x_130), encArg(x_219)), f(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_f(z, z') -{ 0 }-> f(f(encArg(x_130), encArg(x_219)), 0) :|: x_130 >= 0, z = 1 + x_130 + x_219, z' >= 0, x_219 >= 0
   encode_f(z, z') -{ 0 }-> f(f(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_f(z, z') -{ 0 }-> f(0, g(encArg(x_143), encArg(x_228))) :|: z >= 0, z' = 1 + x_143 + x_228, x_143 >= 0, x_228 >= 0
   encode_f(z, z') -{ 0 }-> f(0, f(encArg(x_142), encArg(x_227))) :|: z >= 0, z' = 1 + x_142 + x_227, x_142 >= 0, x_227 >= 0
   encode_f(z, z') -{ 0 }-> f(0, 0) :|: z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> f(0, 1 + encArg(z' - 1)) :|: z >= 0, z' - 1 >= 0
   encode_f(z, z') -{ 0 }-> f(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_f(z, z') -{ 0 }-> f(1 + encArg(z - 1), f(encArg(x_133), encArg(x_221))) :|: z' = 1 + x_133 + x_221, x_221 >= 0, x_133 >= 0, z - 1 >= 0
   encode_f(z, z') -{ 0 }-> f(1 + encArg(z - 1), 0) :|: z' >= 0, z - 1 >= 0
   encode_f(z, z') -{ 0 }-> f(1 + encArg(z - 1), 1 + encArg(z' - 1)) :|: z' - 1 >= 0, z - 1 >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 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)), f(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)), 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(f(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(f(encArg(x_145), encArg(x_229)), f(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(f(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(f(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(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, f(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, 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), 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), f(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), 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) -{ 0 }-> 0 :|: z >= 0
   encode_h(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   f(z, z') -{ 1 }-> g(z, z') :|: z >= 0, z' >= 0
   g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   g(z, z') -{ 1 }-> 1 + g(z - 1, z') :|: z - 1 >= 0, z' >= 0
   g(z, z') -{ 1 }-> 1 + f(z - 1, z') :|: z - 1 >= 0, z' >= 0

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

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

(23) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   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)), f(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)), 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(f(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(f(encArg(x_115), encArg(x_29)), f(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(f(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(f(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(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, f(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, 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), 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), f(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), 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 }-> f(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 }-> f(g(encArg(x_11), encArg(x_2'')), f(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 }-> f(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 }-> f(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 }-> f(f(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 }-> f(f(encArg(x_1''), encArg(x_2')), f(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 }-> f(f(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 }-> f(f(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 }-> f(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 }-> f(0, f(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 }-> f(0, 0) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> f(0, 1 + encArg(x_111)) :|: x_1 >= 0, z = 1 + x_1 + (1 + x_111), x_111 >= 0
   encArg(z) -{ 0 }-> f(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 }-> f(1 + encArg(x_1'), f(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 }-> f(1 + encArg(x_1'), 0) :|: x_1' >= 0, x_2 >= 0, z = 1 + (1 + x_1') + x_2
   encArg(z) -{ 0 }-> f(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 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_f(z, z') -{ 0 }-> f(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_f(z, z') -{ 0 }-> f(g(encArg(x_131), encArg(x_220)), f(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_f(z, z') -{ 0 }-> f(g(encArg(x_131), encArg(x_220)), 0) :|: z = 1 + x_131 + x_220, z' >= 0, x_131 >= 0, x_220 >= 0
   encode_f(z, z') -{ 0 }-> f(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_f(z, z') -{ 0 }-> f(f(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_f(z, z') -{ 0 }-> f(f(encArg(x_130), encArg(x_219)), f(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_f(z, z') -{ 0 }-> f(f(encArg(x_130), encArg(x_219)), 0) :|: x_130 >= 0, z = 1 + x_130 + x_219, z' >= 0, x_219 >= 0
   encode_f(z, z') -{ 0 }-> f(f(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_f(z, z') -{ 0 }-> f(0, g(encArg(x_143), encArg(x_228))) :|: z >= 0, z' = 1 + x_143 + x_228, x_143 >= 0, x_228 >= 0
   encode_f(z, z') -{ 0 }-> f(0, f(encArg(x_142), encArg(x_227))) :|: z >= 0, z' = 1 + x_142 + x_227, x_142 >= 0, x_227 >= 0
   encode_f(z, z') -{ 0 }-> f(0, 0) :|: z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> f(0, 1 + encArg(z' - 1)) :|: z >= 0, z' - 1 >= 0
   encode_f(z, z') -{ 0 }-> f(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_f(z, z') -{ 0 }-> f(1 + encArg(z - 1), f(encArg(x_133), encArg(x_221))) :|: z' = 1 + x_133 + x_221, x_221 >= 0, x_133 >= 0, z - 1 >= 0
   encode_f(z, z') -{ 0 }-> f(1 + encArg(z - 1), 0) :|: z' >= 0, z - 1 >= 0
   encode_f(z, z') -{ 0 }-> f(1 + encArg(z - 1), 1 + encArg(z' - 1)) :|: z' - 1 >= 0, z - 1 >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 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)), f(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)), 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(f(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(f(encArg(x_145), encArg(x_229)), f(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(f(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(f(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(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, f(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, 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), 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), f(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), 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) -{ 0 }-> 0 :|: z >= 0
   encode_h(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   f(z, z') -{ 1 }-> g(z, z') :|: z >= 0, z' >= 0
   g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   g(z, z') -{ 1 }-> 1 + g(z - 1, z') :|: z - 1 >= 0, z' >= 0
   g(z, z') -{ 1 }-> 1 + f(z - 1, z') :|: z - 1 >= 0, z' >= 0

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

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

(25) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: f
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 4 + 2*z

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

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

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

   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)), f(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)), 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(f(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(f(encArg(x_115), encArg(x_29)), f(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(f(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(f(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(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, f(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, 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), 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), f(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), 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 }-> f(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 }-> f(g(encArg(x_11), encArg(x_2'')), f(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 }-> f(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 }-> f(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 }-> f(f(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 }-> f(f(encArg(x_1''), encArg(x_2')), f(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 }-> f(f(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 }-> f(f(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 }-> f(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 }-> f(0, f(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 }-> f(0, 0) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> f(0, 1 + encArg(x_111)) :|: x_1 >= 0, z = 1 + x_1 + (1 + x_111), x_111 >= 0
   encArg(z) -{ 0 }-> f(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 }-> f(1 + encArg(x_1'), f(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 }-> f(1 + encArg(x_1'), 0) :|: x_1' >= 0, x_2 >= 0, z = 1 + (1 + x_1') + x_2
   encArg(z) -{ 0 }-> f(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 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_f(z, z') -{ 0 }-> f(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_f(z, z') -{ 0 }-> f(g(encArg(x_131), encArg(x_220)), f(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_f(z, z') -{ 0 }-> f(g(encArg(x_131), encArg(x_220)), 0) :|: z = 1 + x_131 + x_220, z' >= 0, x_131 >= 0, x_220 >= 0
   encode_f(z, z') -{ 0 }-> f(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_f(z, z') -{ 0 }-> f(f(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_f(z, z') -{ 0 }-> f(f(encArg(x_130), encArg(x_219)), f(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_f(z, z') -{ 0 }-> f(f(encArg(x_130), encArg(x_219)), 0) :|: x_130 >= 0, z = 1 + x_130 + x_219, z' >= 0, x_219 >= 0
   encode_f(z, z') -{ 0 }-> f(f(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_f(z, z') -{ 0 }-> f(0, g(encArg(x_143), encArg(x_228))) :|: z >= 0, z' = 1 + x_143 + x_228, x_143 >= 0, x_228 >= 0
   encode_f(z, z') -{ 0 }-> f(0, f(encArg(x_142), encArg(x_227))) :|: z >= 0, z' = 1 + x_142 + x_227, x_142 >= 0, x_227 >= 0
   encode_f(z, z') -{ 0 }-> f(0, 0) :|: z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> f(0, 1 + encArg(z' - 1)) :|: z >= 0, z' - 1 >= 0
   encode_f(z, z') -{ 0 }-> f(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_f(z, z') -{ 0 }-> f(1 + encArg(z - 1), f(encArg(x_133), encArg(x_221))) :|: z' = 1 + x_133 + x_221, x_221 >= 0, x_133 >= 0, z - 1 >= 0
   encode_f(z, z') -{ 0 }-> f(1 + encArg(z - 1), 0) :|: z' >= 0, z - 1 >= 0
   encode_f(z, z') -{ 0 }-> f(1 + encArg(z - 1), 1 + encArg(z' - 1)) :|: z' - 1 >= 0, z - 1 >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 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)), f(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)), 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(f(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(f(encArg(x_145), encArg(x_229)), f(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(f(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(f(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(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, f(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, 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), 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), f(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), 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) -{ 0 }-> 0 :|: z >= 0
   encode_h(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   f(z, z') -{ 1 }-> g(z, z') :|: z >= 0, z' >= 0
   g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   g(z, z') -{ 1 }-> 1 + g(z - 1, z') :|: z - 1 >= 0, z' >= 0
   g(z, z') -{ 1 }-> 1 + f(z - 1, z') :|: z - 1 >= 0, z' >= 0

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

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

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

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

   encArg(z) -{ 4 }-> s1 :|: s1 >= 0, s1 <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 3 }-> s2 :|: s2 >= 0, s2 <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 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)), f(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)), 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(f(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(f(encArg(x_115), encArg(x_29)), f(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(f(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(f(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(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, f(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, 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), 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), f(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), 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 }-> f(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 }-> f(g(encArg(x_11), encArg(x_2'')), f(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 }-> f(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 }-> f(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 }-> f(f(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 }-> f(f(encArg(x_1''), encArg(x_2')), f(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 }-> f(f(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 }-> f(f(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 }-> f(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 }-> f(0, f(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 }-> f(0, 1 + encArg(x_111)) :|: x_1 >= 0, z = 1 + x_1 + (1 + x_111), x_111 >= 0
   encArg(z) -{ 0 }-> f(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 }-> f(1 + encArg(x_1'), f(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 }-> f(1 + encArg(x_1'), 0) :|: x_1' >= 0, x_2 >= 0, z = 1 + (1 + x_1') + x_2
   encArg(z) -{ 0 }-> f(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 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_f(z, z') -{ 4 }-> s3 :|: s3 >= 0, s3 <= 0, z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> f(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_f(z, z') -{ 0 }-> f(g(encArg(x_131), encArg(x_220)), f(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_f(z, z') -{ 0 }-> f(g(encArg(x_131), encArg(x_220)), 0) :|: z = 1 + x_131 + x_220, z' >= 0, x_131 >= 0, x_220 >= 0
   encode_f(z, z') -{ 0 }-> f(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_f(z, z') -{ 0 }-> f(f(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_f(z, z') -{ 0 }-> f(f(encArg(x_130), encArg(x_219)), f(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_f(z, z') -{ 0 }-> f(f(encArg(x_130), encArg(x_219)), 0) :|: x_130 >= 0, z = 1 + x_130 + x_219, z' >= 0, x_219 >= 0
   encode_f(z, z') -{ 0 }-> f(f(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_f(z, z') -{ 0 }-> f(0, g(encArg(x_143), encArg(x_228))) :|: z >= 0, z' = 1 + x_143 + x_228, x_143 >= 0, x_228 >= 0
   encode_f(z, z') -{ 0 }-> f(0, f(encArg(x_142), encArg(x_227))) :|: z >= 0, z' = 1 + x_142 + x_227, x_142 >= 0, x_227 >= 0
   encode_f(z, z') -{ 0 }-> f(0, 1 + encArg(z' - 1)) :|: z >= 0, z' - 1 >= 0
   encode_f(z, z') -{ 0 }-> f(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_f(z, z') -{ 0 }-> f(1 + encArg(z - 1), f(encArg(x_133), encArg(x_221))) :|: z' = 1 + x_133 + x_221, x_221 >= 0, x_133 >= 0, z - 1 >= 0
   encode_f(z, z') -{ 0 }-> f(1 + encArg(z - 1), 0) :|: z' >= 0, z - 1 >= 0
   encode_f(z, z') -{ 0 }-> f(1 + encArg(z - 1), 1 + encArg(z' - 1)) :|: z' - 1 >= 0, z - 1 >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_g(z, z') -{ 3 }-> s4 :|: s4 >= 0, s4 <= 0, z >= 0, z' >= 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)), f(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)), 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(f(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(f(encArg(x_145), encArg(x_229)), f(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(f(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(f(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(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, f(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, 1 + encArg(z' - 1)) :|: z >= 0, z' - 1 >= 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), f(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), 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) -{ 0 }-> 0 :|: z >= 0
   encode_h(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   f(z, z') -{ 4 + 2*z }-> s :|: s >= 0, s <= z, z >= 0, z' >= 0
   g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   g(z, z') -{ 3 + 2*z }-> 1 + s' :|: s' >= 0, s' <= z - 1, z - 1 >= 0, z' >= 0
   g(z, z') -{ 2 + 2*z }-> 1 + s'' :|: s'' >= 0, s'' <= z - 1, z - 1 >= 0, z' >= 0

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

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

(29) 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

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

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

   encArg(z) -{ 4 }-> s1 :|: s1 >= 0, s1 <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 3 }-> s2 :|: s2 >= 0, s2 <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 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)), f(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)), 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(f(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(f(encArg(x_115), encArg(x_29)), f(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(f(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(f(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(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, f(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, 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), 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), f(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), 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 }-> f(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 }-> f(g(encArg(x_11), encArg(x_2'')), f(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 }-> f(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 }-> f(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 }-> f(f(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 }-> f(f(encArg(x_1''), encArg(x_2')), f(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 }-> f(f(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 }-> f(f(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 }-> f(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 }-> f(0, f(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 }-> f(0, 1 + encArg(x_111)) :|: x_1 >= 0, z = 1 + x_1 + (1 + x_111), x_111 >= 0
   encArg(z) -{ 0 }-> f(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 }-> f(1 + encArg(x_1'), f(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 }-> f(1 + encArg(x_1'), 0) :|: x_1' >= 0, x_2 >= 0, z = 1 + (1 + x_1') + x_2
   encArg(z) -{ 0 }-> f(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 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_f(z, z') -{ 4 }-> s3 :|: s3 >= 0, s3 <= 0, z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> f(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_f(z, z') -{ 0 }-> f(g(encArg(x_131), encArg(x_220)), f(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_f(z, z') -{ 0 }-> f(g(encArg(x_131), encArg(x_220)), 0) :|: z = 1 + x_131 + x_220, z' >= 0, x_131 >= 0, x_220 >= 0
   encode_f(z, z') -{ 0 }-> f(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_f(z, z') -{ 0 }-> f(f(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_f(z, z') -{ 0 }-> f(f(encArg(x_130), encArg(x_219)), f(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_f(z, z') -{ 0 }-> f(f(encArg(x_130), encArg(x_219)), 0) :|: x_130 >= 0, z = 1 + x_130 + x_219, z' >= 0, x_219 >= 0
   encode_f(z, z') -{ 0 }-> f(f(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_f(z, z') -{ 0 }-> f(0, g(encArg(x_143), encArg(x_228))) :|: z >= 0, z' = 1 + x_143 + x_228, x_143 >= 0, x_228 >= 0
   encode_f(z, z') -{ 0 }-> f(0, f(encArg(x_142), encArg(x_227))) :|: z >= 0, z' = 1 + x_142 + x_227, x_142 >= 0, x_227 >= 0
   encode_f(z, z') -{ 0 }-> f(0, 1 + encArg(z' - 1)) :|: z >= 0, z' - 1 >= 0
   encode_f(z, z') -{ 0 }-> f(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_f(z, z') -{ 0 }-> f(1 + encArg(z - 1), f(encArg(x_133), encArg(x_221))) :|: z' = 1 + x_133 + x_221, x_221 >= 0, x_133 >= 0, z - 1 >= 0
   encode_f(z, z') -{ 0 }-> f(1 + encArg(z - 1), 0) :|: z' >= 0, z - 1 >= 0
   encode_f(z, z') -{ 0 }-> f(1 + encArg(z - 1), 1 + encArg(z' - 1)) :|: z' - 1 >= 0, z - 1 >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_g(z, z') -{ 3 }-> s4 :|: s4 >= 0, s4 <= 0, z >= 0, z' >= 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)), f(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)), 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(f(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(f(encArg(x_145), encArg(x_229)), f(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(f(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(f(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(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, f(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, 1 + encArg(z' - 1)) :|: z >= 0, z' - 1 >= 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), f(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), 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) -{ 0 }-> 0 :|: z >= 0
   encode_h(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   f(z, z') -{ 4 + 2*z }-> s :|: s >= 0, s <= z, z >= 0, z' >= 0
   g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   g(z, z') -{ 3 + 2*z }-> 1 + s' :|: s' >= 0, s' <= z - 1, z - 1 >= 0, z' >= 0
   g(z, z') -{ 2 + 2*z }-> 1 + s'' :|: s'' >= 0, s'' <= z - 1, z - 1 >= 0, z' >= 0

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

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

(31) 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: 4 + 6*z + 4*z^2

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

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

   encArg(z) -{ 4 }-> s1 :|: s1 >= 0, s1 <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 3 }-> s2 :|: s2 >= 0, s2 <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 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)), f(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)), 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(f(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(f(encArg(x_115), encArg(x_29)), f(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(f(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(f(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(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, f(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, 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), 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), f(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), 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 }-> f(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 }-> f(g(encArg(x_11), encArg(x_2'')), f(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 }-> f(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 }-> f(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 }-> f(f(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 }-> f(f(encArg(x_1''), encArg(x_2')), f(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 }-> f(f(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 }-> f(f(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 }-> f(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 }-> f(0, f(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 }-> f(0, 1 + encArg(x_111)) :|: x_1 >= 0, z = 1 + x_1 + (1 + x_111), x_111 >= 0
   encArg(z) -{ 0 }-> f(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 }-> f(1 + encArg(x_1'), f(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 }-> f(1 + encArg(x_1'), 0) :|: x_1' >= 0, x_2 >= 0, z = 1 + (1 + x_1') + x_2
   encArg(z) -{ 0 }-> f(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 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_f(z, z') -{ 4 }-> s3 :|: s3 >= 0, s3 <= 0, z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> f(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_f(z, z') -{ 0 }-> f(g(encArg(x_131), encArg(x_220)), f(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_f(z, z') -{ 0 }-> f(g(encArg(x_131), encArg(x_220)), 0) :|: z = 1 + x_131 + x_220, z' >= 0, x_131 >= 0, x_220 >= 0
   encode_f(z, z') -{ 0 }-> f(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_f(z, z') -{ 0 }-> f(f(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_f(z, z') -{ 0 }-> f(f(encArg(x_130), encArg(x_219)), f(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_f(z, z') -{ 0 }-> f(f(encArg(x_130), encArg(x_219)), 0) :|: x_130 >= 0, z = 1 + x_130 + x_219, z' >= 0, x_219 >= 0
   encode_f(z, z') -{ 0 }-> f(f(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_f(z, z') -{ 0 }-> f(0, g(encArg(x_143), encArg(x_228))) :|: z >= 0, z' = 1 + x_143 + x_228, x_143 >= 0, x_228 >= 0
   encode_f(z, z') -{ 0 }-> f(0, f(encArg(x_142), encArg(x_227))) :|: z >= 0, z' = 1 + x_142 + x_227, x_142 >= 0, x_227 >= 0
   encode_f(z, z') -{ 0 }-> f(0, 1 + encArg(z' - 1)) :|: z >= 0, z' - 1 >= 0
   encode_f(z, z') -{ 0 }-> f(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_f(z, z') -{ 0 }-> f(1 + encArg(z - 1), f(encArg(x_133), encArg(x_221))) :|: z' = 1 + x_133 + x_221, x_221 >= 0, x_133 >= 0, z - 1 >= 0
   encode_f(z, z') -{ 0 }-> f(1 + encArg(z - 1), 0) :|: z' >= 0, z - 1 >= 0
   encode_f(z, z') -{ 0 }-> f(1 + encArg(z - 1), 1 + encArg(z' - 1)) :|: z' - 1 >= 0, z - 1 >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_g(z, z') -{ 3 }-> s4 :|: s4 >= 0, s4 <= 0, z >= 0, z' >= 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)), f(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)), 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(f(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(f(encArg(x_145), encArg(x_229)), f(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(f(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(f(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(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, f(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, 1 + encArg(z' - 1)) :|: z >= 0, z' - 1 >= 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), f(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), 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) -{ 0 }-> 0 :|: z >= 0
   encode_h(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   f(z, z') -{ 4 + 2*z }-> s :|: s >= 0, s <= z, z >= 0, z' >= 0
   g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   g(z, z') -{ 3 + 2*z }-> 1 + s' :|: s' >= 0, s' <= z - 1, z - 1 >= 0, z' >= 0
   g(z, z') -{ 2 + 2*z }-> 1 + s'' :|: s'' >= 0, s'' <= z - 1, z - 1 >= 0, z' >= 0

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

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

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

   encArg(z) -{ 4 }-> s1 :|: s1 >= 0, s1 <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 27 + 2*s100 + 2*s97 + 2*s99 + 6*x_115 + 4*x_115^2 + 6*x_121 + 4*x_121^2 + 6*x_213 + 4*x_213^2 + 6*x_29 + 4*x_29^2 }-> s103 :|: s97 >= 0, s97 <= x_115, s98 >= 0, s98 <= x_29, s99 >= 0, s99 <= s97, s100 >= 0, s100 <= x_121, s101 >= 0, s101 <= x_213, s102 >= 0, s102 <= s100, s103 >= 0, s103 <= s99, 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) -{ 26 + 2*s104 + 2*s106 + 2*s107 + 6*x_115 + 4*x_115^2 + 6*x_122 + 4*x_122^2 + 6*x_214 + 4*x_214^2 + 6*x_29 + 4*x_29^2 }-> s110 :|: s104 >= 0, s104 <= x_115, s105 >= 0, s105 <= x_29, s106 >= 0, s106 <= s104, s107 >= 0, s107 <= x_122, s108 >= 0, s108 <= x_214, s109 >= 0, s109 <= s107, s110 >= 0, s110 <= s106, 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) -{ 15 + 2*s111 + 2*s113 + 6*x_115 + 4*x_115^2 + 6*x_29 + 4*x_29^2 }-> s114 :|: s111 >= 0, s111 <= x_115, s112 >= 0, s112 <= x_29, s113 >= 0, s113 <= s111, s114 >= 0, s114 <= s113, x_115 >= 0, x_2 >= 0, z = 1 + (1 + x_115 + x_29) + x_2, x_29 >= 0
   encArg(z) -{ 18 + 2*s115 + 2*s117 + 6*x_116 + 4*x_116^2 + 6*x_123 + 4*x_123^2 + 6*x_210 + 4*x_210^2 }-> s119 :|: s115 >= 0, s115 <= x_116, s116 >= 0, s116 <= x_210, s117 >= 0, s117 <= s115, s118 >= 0, s118 <= x_123, s119 >= 0, s119 <= s117, x_123 >= 0, z = 1 + (1 + x_116 + x_210) + (1 + x_123), x_116 >= 0, x_210 >= 0
   encArg(z) -{ 26 + 2*s120 + 2*s122 + 2*s123 + 6*x_116 + 4*x_116^2 + 6*x_124 + 4*x_124^2 + 6*x_210 + 4*x_210^2 + 6*x_215 + 4*x_215^2 }-> s126 :|: s120 >= 0, s120 <= x_116, s121 >= 0, s121 <= x_210, s122 >= 0, s122 <= s120, s123 >= 0, s123 <= x_124, s124 >= 0, s124 <= x_215, s125 >= 0, s125 <= s123, s126 >= 0, s126 <= s122, 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) -{ 22 + 2*s10 + 2*s9 + 6*x_1' + 4*x_1'^2 + 6*x_13 + 4*x_13^2 + 6*x_21 + 4*x_21^2 }-> s13 :|: s9 >= 0, s9 <= x_1', s10 >= 0, s10 <= x_13, s11 >= 0, s11 <= x_21, s12 >= 0, s12 <= s10, s13 >= 0, s13 <= 1 + s9, x_13 >= 0, x_1' >= 0, z = 1 + (1 + x_1') + (1 + x_13 + x_21), x_21 >= 0
   encArg(z) -{ 25 + 2*s127 + 2*s129 + 2*s130 + 6*x_116 + 4*x_116^2 + 6*x_125 + 4*x_125^2 + 6*x_210 + 4*x_210^2 + 6*x_216 + 4*x_216^2 }-> s133 :|: s127 >= 0, s127 <= x_116, s128 >= 0, s128 <= x_210, s129 >= 0, s129 <= s127, s130 >= 0, s130 <= x_125, s131 >= 0, s131 <= x_216, s132 >= 0, s132 <= s130, s133 >= 0, s133 <= s129, 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) -{ 14 + 2*s134 + 2*s136 + 6*x_116 + 4*x_116^2 + 6*x_210 + 4*x_210^2 }-> s137 :|: s134 >= 0, s134 <= x_116, s135 >= 0, s135 <= x_210, s136 >= 0, s136 <= s134, s137 >= 0, s137 <= s136, x_116 >= 0, x_2 >= 0, z = 1 + (1 + x_116 + x_210) + x_2, x_210 >= 0
   encArg(z) -{ 7 + 6*x_126 + 4*x_126^2 }-> s139 :|: s138 >= 0, s138 <= x_126, s139 >= 0, s139 <= 0, x_1 >= 0, z = 1 + x_1 + (1 + x_126), x_126 >= 0
   encArg(z) -{ 15 + 2*s140 + 6*x_127 + 4*x_127^2 + 6*x_217 + 4*x_217^2 }-> s143 :|: s140 >= 0, s140 <= x_127, s141 >= 0, s141 <= x_217, s142 >= 0, s142 <= s140, s143 >= 0, s143 <= 0, x_1 >= 0, x_127 >= 0, z = 1 + x_1 + (1 + x_127 + x_217), x_217 >= 0
   encArg(z) -{ 14 + 2*s144 + 6*x_128 + 4*x_128^2 + 6*x_218 + 4*x_218^2 }-> s147 :|: s144 >= 0, s144 <= x_128, s145 >= 0, s145 <= x_218, s146 >= 0, s146 <= s144, s147 >= 0, s147 <= 0, x_1 >= 0, x_128 >= 0, z = 1 + x_1 + (1 + x_128 + x_218), x_218 >= 0
   encArg(z) -{ 21 + 2*s14 + 2*s15 + 6*x_1' + 4*x_1'^2 + 6*x_14 + 4*x_14^2 + 6*x_22 + 4*x_22^2 }-> s18 :|: s14 >= 0, s14 <= x_1', s15 >= 0, s15 <= x_14, s16 >= 0, s16 <= x_22, s17 >= 0, s17 <= s15, s18 >= 0, s18 <= 1 + s14, z = 1 + (1 + x_1') + (1 + x_14 + x_22), x_14 >= 0, x_1' >= 0, x_22 >= 0
   encArg(z) -{ 3 }-> s2 :|: s2 >= 0, s2 <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 10 + 2*s19 + 6*x_1' + 4*x_1'^2 }-> s20 :|: s19 >= 0, s19 <= x_1', s20 >= 0, s20 <= 1 + s19, x_1' >= 0, x_2 >= 0, z = 1 + (1 + x_1') + x_2
   encArg(z) -{ 20 + 2*s21 + 2*s23 + 6*x_1'' + 4*x_1''^2 + 6*x_15 + 4*x_15^2 + 6*x_2' + 4*x_2'^2 }-> s25 :|: s21 >= 0, s21 <= x_1'', s22 >= 0, s22 <= x_2', s23 >= 0, s23 <= s21, s24 >= 0, s24 <= x_15, s25 >= 0, s25 <= s23, x_15 >= 0, z = 1 + (1 + x_1'' + x_2') + (1 + x_15), x_1'' >= 0, x_2' >= 0
   encArg(z) -{ 28 + 2*s26 + 2*s28 + 2*s29 + 6*x_1'' + 4*x_1''^2 + 6*x_16 + 4*x_16^2 + 6*x_2' + 4*x_2'^2 + 6*x_23 + 4*x_23^2 }-> s32 :|: s26 >= 0, s26 <= x_1'', s27 >= 0, s27 <= x_2', s28 >= 0, s28 <= s26, s29 >= 0, s29 <= x_16, s30 >= 0, s30 <= x_23, s31 >= 0, s31 <= s29, s32 >= 0, s32 <= s28, 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) -{ 27 + 2*s33 + 2*s35 + 2*s36 + 6*x_1'' + 4*x_1''^2 + 6*x_17 + 4*x_17^2 + 6*x_2' + 4*x_2'^2 + 6*x_24 + 4*x_24^2 }-> s39 :|: s33 >= 0, s33 <= x_1'', s34 >= 0, s34 <= x_2', s35 >= 0, s35 <= s33, s36 >= 0, s36 <= x_17, s37 >= 0, s37 <= x_24, s38 >= 0, s38 <= s36, s39 >= 0, s39 <= s35, 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) -{ 16 + 2*s40 + 2*s42 + 6*x_1'' + 4*x_1''^2 + 6*x_2' + 4*x_2'^2 }-> s43 :|: s40 >= 0, s40 <= x_1'', s41 >= 0, s41 <= x_2', s42 >= 0, s42 <= s40, s43 >= 0, s43 <= s42, x_1'' >= 0, x_2' >= 0, z = 1 + (1 + x_1'' + x_2') + x_2, x_2 >= 0
   encArg(z) -{ 19 + 2*s44 + 2*s46 + 6*x_11 + 4*x_11^2 + 6*x_18 + 4*x_18^2 + 6*x_2'' + 4*x_2''^2 }-> s48 :|: s44 >= 0, s44 <= x_11, s45 >= 0, s45 <= x_2'', s46 >= 0, s46 <= s44, s47 >= 0, s47 <= x_18, s48 >= 0, s48 <= s46, x_11 >= 0, z = 1 + (1 + x_11 + x_2'') + (1 + x_18), x_2'' >= 0, x_18 >= 0
   encArg(z) -{ 27 + 2*s49 + 2*s51 + 2*s52 + 6*x_11 + 4*x_11^2 + 6*x_19 + 4*x_19^2 + 6*x_2'' + 4*x_2''^2 + 6*x_25 + 4*x_25^2 }-> s55 :|: s49 >= 0, s49 <= x_11, s50 >= 0, s50 <= x_2'', s51 >= 0, s51 <= s49, s52 >= 0, s52 <= x_19, s53 >= 0, s53 <= x_25, s54 >= 0, s54 <= s52, s55 >= 0, s55 <= s51, 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) -{ 26 + 2*s56 + 2*s58 + 2*s59 + 6*x_11 + 4*x_11^2 + 6*x_110 + 4*x_110^2 + 6*x_2'' + 4*x_2''^2 + 6*x_26 + 4*x_26^2 }-> s62 :|: s56 >= 0, s56 <= x_11, s57 >= 0, s57 <= x_2'', s58 >= 0, s58 <= s56, s59 >= 0, s59 <= x_110, s60 >= 0, s60 <= x_26, s61 >= 0, s61 <= s59, s62 >= 0, s62 <= s58, 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) -{ 15 + 2*s63 + 2*s65 + 6*x_11 + 4*x_11^2 + 6*x_2'' + 4*x_2''^2 }-> s66 :|: s63 >= 0, s63 <= x_11, s64 >= 0, s64 <= x_2'', s65 >= 0, s65 <= s63, s66 >= 0, s66 <= s65, x_11 >= 0, x_2'' >= 0, x_2 >= 0, z = 1 + (1 + x_11 + x_2'') + x_2
   encArg(z) -{ 8 + 6*x_111 + 4*x_111^2 }-> s68 :|: s67 >= 0, s67 <= x_111, s68 >= 0, s68 <= 0, x_1 >= 0, z = 1 + x_1 + (1 + x_111), x_111 >= 0
   encArg(z) -{ 16 + 2*s69 + 6*x_112 + 4*x_112^2 + 6*x_27 + 4*x_27^2 }-> s72 :|: s69 >= 0, s69 <= x_112, s70 >= 0, s70 <= x_27, s71 >= 0, s71 <= s69, s72 >= 0, s72 <= 0, x_1 >= 0, x_27 >= 0, z = 1 + x_1 + (1 + x_112 + x_27), x_112 >= 0
   encArg(z) -{ 15 + 2*s73 + 6*x_113 + 4*x_113^2 + 6*x_28 + 4*x_28^2 }-> s76 :|: s73 >= 0, s73 <= x_113, s74 >= 0, s74 <= x_28, s75 >= 0, s75 <= s73, s76 >= 0, s76 <= 0, x_1 >= 0, x_113 >= 0, x_28 >= 0, z = 1 + x_1 + (1 + x_113 + x_28)
   encArg(z) -{ 13 + 2*s77 + 6*x_114 + 4*x_114^2 + 6*x_117 + 4*x_117^2 }-> s79 :|: s77 >= 0, s77 <= x_114, s78 >= 0, s78 <= x_117, s79 >= 0, s79 <= 1 + s77, z = 1 + (1 + x_114) + (1 + x_117), x_117 >= 0, x_114 >= 0
   encArg(z) -{ 14 + 2*s6 + 6*x_1' + 4*x_1'^2 + 6*x_12 + 4*x_12^2 }-> s8 :|: s6 >= 0, s6 <= x_1', s7 >= 0, s7 <= x_12, s8 >= 0, s8 <= 1 + s6, z = 1 + (1 + x_1') + (1 + x_12), x_1' >= 0, x_12 >= 0
   encArg(z) -{ 21 + 2*s80 + 2*s81 + 6*x_114 + 4*x_114^2 + 6*x_118 + 4*x_118^2 + 6*x_211 + 4*x_211^2 }-> s84 :|: s80 >= 0, s80 <= x_114, s81 >= 0, s81 <= x_118, s82 >= 0, s82 <= x_211, s83 >= 0, s83 <= s81, s84 >= 0, s84 <= 1 + s80, z = 1 + (1 + x_114) + (1 + x_118 + x_211), x_114 >= 0, x_118 >= 0, x_211 >= 0
   encArg(z) -{ 20 + 2*s85 + 2*s86 + 6*x_114 + 4*x_114^2 + 6*x_119 + 4*x_119^2 + 6*x_212 + 4*x_212^2 }-> s89 :|: s85 >= 0, s85 <= x_114, s86 >= 0, s86 <= x_119, s87 >= 0, s87 <= x_212, s88 >= 0, s88 <= s86, s89 >= 0, s89 <= 1 + s85, x_212 >= 0, x_114 >= 0, z = 1 + (1 + x_114) + (1 + x_119 + x_212), x_119 >= 0
   encArg(z) -{ 9 + 2*s90 + 6*x_114 + 4*x_114^2 }-> s91 :|: s90 >= 0, s90 <= x_114, s91 >= 0, s91 <= 1 + s90, z = 1 + (1 + x_114) + x_2, x_114 >= 0, x_2 >= 0
   encArg(z) -{ 19 + 2*s92 + 2*s94 + 6*x_115 + 4*x_115^2 + 6*x_120 + 4*x_120^2 + 6*x_29 + 4*x_29^2 }-> s96 :|: s92 >= 0, s92 <= x_115, s93 >= 0, s93 <= x_29, s94 >= 0, s94 <= s92, s95 >= 0, s95 <= x_120, s96 >= 0, s96 <= s94, 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) -{ 2 + -2*z + 4*z^2 }-> 1 + s5 :|: s5 >= 0, s5 <= z - 1, z - 1 >= 0
   encode_f(z, z') -{ 10 + 2*s148 + -2*z + 4*z^2 + -2*z' + 4*z'^2 }-> s150 :|: s148 >= 0, s148 <= z - 1, s149 >= 0, s149 <= z' - 1, s150 >= 0, s150 <= 1 + s148, z' - 1 >= 0, z - 1 >= 0
   encode_f(z, z') -{ 20 + 2*s151 + 2*s152 + 6*x_133 + 4*x_133^2 + 6*x_221 + 4*x_221^2 + -2*z + 4*z^2 }-> s155 :|: s151 >= 0, s151 <= z - 1, s152 >= 0, s152 <= x_133, s153 >= 0, s153 <= x_221, s154 >= 0, s154 <= s152, s155 >= 0, s155 <= 1 + s151, z' = 1 + x_133 + x_221, x_221 >= 0, x_133 >= 0, z - 1 >= 0
   encode_f(z, z') -{ 19 + 2*s156 + 2*s157 + 6*x_134 + 4*x_134^2 + 6*x_222 + 4*x_222^2 + -2*z + 4*z^2 }-> s160 :|: s156 >= 0, s156 <= z - 1, s157 >= 0, s157 <= x_134, s158 >= 0, s158 <= x_222, s159 >= 0, s159 <= s157, s160 >= 0, s160 <= 1 + s156, z' = 1 + x_134 + x_222, x_134 >= 0, x_222 >= 0, z - 1 >= 0
   encode_f(z, z') -{ 8 + 2*s161 + -2*z + 4*z^2 }-> s162 :|: s161 >= 0, s161 <= z - 1, s162 >= 0, s162 <= 1 + s161, z' >= 0, z - 1 >= 0
   encode_f(z, z') -{ 18 + 2*s163 + 2*s165 + 6*x_130 + 4*x_130^2 + 6*x_219 + 4*x_219^2 + -2*z' + 4*z'^2 }-> s167 :|: s163 >= 0, s163 <= x_130, s164 >= 0, s164 <= x_219, s165 >= 0, s165 <= s163, s166 >= 0, s166 <= z' - 1, s167 >= 0, s167 <= s165, x_130 >= 0, z = 1 + x_130 + x_219, z' - 1 >= 0, x_219 >= 0
   encode_f(z, z') -{ 28 + 2*s168 + 2*s170 + 2*s171 + 6*x_130 + 4*x_130^2 + 6*x_136 + 4*x_136^2 + 6*x_219 + 4*x_219^2 + 6*x_223 + 4*x_223^2 }-> s174 :|: s168 >= 0, s168 <= x_130, s169 >= 0, s169 <= x_219, s170 >= 0, s170 <= s168, s171 >= 0, s171 <= x_136, s172 >= 0, s172 <= x_223, s173 >= 0, s173 <= s171, s174 >= 0, s174 <= s170, 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_f(z, z') -{ 27 + 2*s175 + 2*s177 + 2*s178 + 6*x_130 + 4*x_130^2 + 6*x_137 + 4*x_137^2 + 6*x_219 + 4*x_219^2 + 6*x_224 + 4*x_224^2 }-> s181 :|: s175 >= 0, s175 <= x_130, s176 >= 0, s176 <= x_219, s177 >= 0, s177 <= s175, s178 >= 0, s178 <= x_137, s179 >= 0, s179 <= x_224, s180 >= 0, s180 <= s178, s181 >= 0, s181 <= s177, 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_f(z, z') -{ 16 + 2*s182 + 2*s184 + 6*x_130 + 4*x_130^2 + 6*x_219 + 4*x_219^2 }-> s185 :|: s182 >= 0, s182 <= x_130, s183 >= 0, s183 <= x_219, s184 >= 0, s184 <= s182, s185 >= 0, s185 <= s184, x_130 >= 0, z = 1 + x_130 + x_219, z' >= 0, x_219 >= 0
   encode_f(z, z') -{ 17 + 2*s186 + 2*s188 + 6*x_131 + 4*x_131^2 + 6*x_220 + 4*x_220^2 + -2*z' + 4*z'^2 }-> s190 :|: s186 >= 0, s186 <= x_131, s187 >= 0, s187 <= x_220, s188 >= 0, s188 <= s186, s189 >= 0, s189 <= z' - 1, s190 >= 0, s190 <= s188, z' - 1 >= 0, z = 1 + x_131 + x_220, x_131 >= 0, x_220 >= 0
   encode_f(z, z') -{ 27 + 2*s191 + 2*s193 + 2*s194 + 6*x_131 + 4*x_131^2 + 6*x_139 + 4*x_139^2 + 6*x_220 + 4*x_220^2 + 6*x_225 + 4*x_225^2 }-> s197 :|: s191 >= 0, s191 <= x_131, s192 >= 0, s192 <= x_220, s193 >= 0, s193 <= s191, s194 >= 0, s194 <= x_139, s195 >= 0, s195 <= x_225, s196 >= 0, s196 <= s194, s197 >= 0, s197 <= s193, 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_f(z, z') -{ 26 + 2*s198 + 2*s200 + 2*s201 + 6*x_131 + 4*x_131^2 + 6*x_140 + 4*x_140^2 + 6*x_220 + 4*x_220^2 + 6*x_226 + 4*x_226^2 }-> s204 :|: s198 >= 0, s198 <= x_131, s199 >= 0, s199 <= x_220, s200 >= 0, s200 <= s198, s201 >= 0, s201 <= x_140, s202 >= 0, s202 <= x_226, s203 >= 0, s203 <= s201, s204 >= 0, s204 <= s200, 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_f(z, z') -{ 15 + 2*s205 + 2*s207 + 6*x_131 + 4*x_131^2 + 6*x_220 + 4*x_220^2 }-> s208 :|: s205 >= 0, s205 <= x_131, s206 >= 0, s206 <= x_220, s207 >= 0, s207 <= s205, s208 >= 0, s208 <= s207, z = 1 + x_131 + x_220, z' >= 0, x_131 >= 0, x_220 >= 0
   encode_f(z, z') -{ 6 + -2*z' + 4*z'^2 }-> s210 :|: s209 >= 0, s209 <= z' - 1, s210 >= 0, s210 <= 0, z >= 0, z' - 1 >= 0
   encode_f(z, z') -{ 16 + 2*s211 + 6*x_142 + 4*x_142^2 + 6*x_227 + 4*x_227^2 }-> s214 :|: s211 >= 0, s211 <= x_142, s212 >= 0, s212 <= x_227, s213 >= 0, s213 <= s211, s214 >= 0, s214 <= 0, z >= 0, z' = 1 + x_142 + x_227, x_142 >= 0, x_227 >= 0
   encode_f(z, z') -{ 15 + 2*s215 + 6*x_143 + 4*x_143^2 + 6*x_228 + 4*x_228^2 }-> s218 :|: s215 >= 0, s215 <= x_143, s216 >= 0, s216 <= x_228, s217 >= 0, s217 <= s215, s218 >= 0, s218 <= 0, z >= 0, z' = 1 + x_143 + x_228, x_143 >= 0, x_228 >= 0
   encode_f(z, z') -{ 4 }-> s3 :|: s3 >= 0, s3 <= 0, z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_g(z, z') -{ 9 + 2*s219 + -2*z + 4*z^2 + -2*z' + 4*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') -{ 19 + 2*s222 + 2*s223 + 6*x_148 + 4*x_148^2 + 6*x_231 + 4*x_231^2 + -2*z + 4*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') -{ 18 + 2*s227 + 2*s228 + 6*x_149 + 4*x_149^2 + 6*x_232 + 4*x_232^2 + -2*z + 4*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') -{ 7 + 2*s232 + -2*z + 4*z^2 }-> s233 :|: s232 >= 0, s232 <= z - 1, s233 >= 0, s233 <= 1 + s232, z - 1 >= 0, z' >= 0
   encode_g(z, z') -{ 17 + 2*s234 + 2*s236 + 6*x_145 + 4*x_145^2 + 6*x_229 + 4*x_229^2 + -2*z' + 4*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') -{ 27 + 2*s239 + 2*s241 + 2*s242 + 6*x_145 + 4*x_145^2 + 6*x_151 + 4*x_151^2 + 6*x_229 + 4*x_229^2 + 6*x_233 + 4*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') -{ 26 + 2*s246 + 2*s248 + 2*s249 + 6*x_145 + 4*x_145^2 + 6*x_152 + 4*x_152^2 + 6*x_229 + 4*x_229^2 + 6*x_234 + 4*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') -{ 15 + 2*s253 + 2*s255 + 6*x_145 + 4*x_145^2 + 6*x_229 + 4*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') -{ 16 + 2*s257 + 2*s259 + 6*x_146 + 4*x_146^2 + 6*x_230 + 4*x_230^2 + -2*z' + 4*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') -{ 26 + 2*s262 + 2*s264 + 2*s265 + 6*x_146 + 4*x_146^2 + 6*x_154 + 4*x_154^2 + 6*x_230 + 4*x_230^2 + 6*x_235 + 4*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') -{ 25 + 2*s269 + 2*s271 + 2*s272 + 6*x_146 + 4*x_146^2 + 6*x_155 + 4*x_155^2 + 6*x_230 + 4*x_230^2 + 6*x_236 + 4*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') -{ 14 + 2*s276 + 2*s278 + 6*x_146 + 4*x_146^2 + 6*x_230 + 4*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') -{ 5 + -2*z' + 4*z'^2 }-> s281 :|: s280 >= 0, s280 <= z' - 1, s281 >= 0, s281 <= 0, z >= 0, z' - 1 >= 0
   encode_g(z, z') -{ 15 + 2*s282 + 6*x_157 + 4*x_157^2 + 6*x_237 + 4*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') -{ 14 + 2*s286 + 6*x_158 + 4*x_158^2 + 6*x_238 + 4*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') -{ 3 }-> s4 :|: s4 >= 0, s4 <= 0, z >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_h(z) -{ 0 }-> 0 :|: z >= 0
   encode_h(z) -{ 4 + 6*z + 4*z^2 }-> 1 + s290 :|: s290 >= 0, s290 <= z, z >= 0
   f(z, z') -{ 4 + 2*z }-> s :|: s >= 0, s <= z, z >= 0, z' >= 0
   g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   g(z, z') -{ 3 + 2*z }-> 1 + s' :|: s' >= 0, s' <= z - 1, z - 1 >= 0, z' >= 0
   g(z, z') -{ 2 + 2*z }-> 1 + s'' :|: s'' >= 0, s'' <= z - 1, z - 1 >= 0, z' >= 0

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

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

(35) 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: 1 + z

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

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

   encArg(z) -{ 4 }-> s1 :|: s1 >= 0, s1 <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 27 + 2*s100 + 2*s97 + 2*s99 + 6*x_115 + 4*x_115^2 + 6*x_121 + 4*x_121^2 + 6*x_213 + 4*x_213^2 + 6*x_29 + 4*x_29^2 }-> s103 :|: s97 >= 0, s97 <= x_115, s98 >= 0, s98 <= x_29, s99 >= 0, s99 <= s97, s100 >= 0, s100 <= x_121, s101 >= 0, s101 <= x_213, s102 >= 0, s102 <= s100, s103 >= 0, s103 <= s99, 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) -{ 26 + 2*s104 + 2*s106 + 2*s107 + 6*x_115 + 4*x_115^2 + 6*x_122 + 4*x_122^2 + 6*x_214 + 4*x_214^2 + 6*x_29 + 4*x_29^2 }-> s110 :|: s104 >= 0, s104 <= x_115, s105 >= 0, s105 <= x_29, s106 >= 0, s106 <= s104, s107 >= 0, s107 <= x_122, s108 >= 0, s108 <= x_214, s109 >= 0, s109 <= s107, s110 >= 0, s110 <= s106, 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) -{ 15 + 2*s111 + 2*s113 + 6*x_115 + 4*x_115^2 + 6*x_29 + 4*x_29^2 }-> s114 :|: s111 >= 0, s111 <= x_115, s112 >= 0, s112 <= x_29, s113 >= 0, s113 <= s111, s114 >= 0, s114 <= s113, x_115 >= 0, x_2 >= 0, z = 1 + (1 + x_115 + x_29) + x_2, x_29 >= 0
   encArg(z) -{ 18 + 2*s115 + 2*s117 + 6*x_116 + 4*x_116^2 + 6*x_123 + 4*x_123^2 + 6*x_210 + 4*x_210^2 }-> s119 :|: s115 >= 0, s115 <= x_116, s116 >= 0, s116 <= x_210, s117 >= 0, s117 <= s115, s118 >= 0, s118 <= x_123, s119 >= 0, s119 <= s117, x_123 >= 0, z = 1 + (1 + x_116 + x_210) + (1 + x_123), x_116 >= 0, x_210 >= 0
   encArg(z) -{ 26 + 2*s120 + 2*s122 + 2*s123 + 6*x_116 + 4*x_116^2 + 6*x_124 + 4*x_124^2 + 6*x_210 + 4*x_210^2 + 6*x_215 + 4*x_215^2 }-> s126 :|: s120 >= 0, s120 <= x_116, s121 >= 0, s121 <= x_210, s122 >= 0, s122 <= s120, s123 >= 0, s123 <= x_124, s124 >= 0, s124 <= x_215, s125 >= 0, s125 <= s123, s126 >= 0, s126 <= s122, 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) -{ 22 + 2*s10 + 2*s9 + 6*x_1' + 4*x_1'^2 + 6*x_13 + 4*x_13^2 + 6*x_21 + 4*x_21^2 }-> s13 :|: s9 >= 0, s9 <= x_1', s10 >= 0, s10 <= x_13, s11 >= 0, s11 <= x_21, s12 >= 0, s12 <= s10, s13 >= 0, s13 <= 1 + s9, x_13 >= 0, x_1' >= 0, z = 1 + (1 + x_1') + (1 + x_13 + x_21), x_21 >= 0
   encArg(z) -{ 25 + 2*s127 + 2*s129 + 2*s130 + 6*x_116 + 4*x_116^2 + 6*x_125 + 4*x_125^2 + 6*x_210 + 4*x_210^2 + 6*x_216 + 4*x_216^2 }-> s133 :|: s127 >= 0, s127 <= x_116, s128 >= 0, s128 <= x_210, s129 >= 0, s129 <= s127, s130 >= 0, s130 <= x_125, s131 >= 0, s131 <= x_216, s132 >= 0, s132 <= s130, s133 >= 0, s133 <= s129, 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) -{ 14 + 2*s134 + 2*s136 + 6*x_116 + 4*x_116^2 + 6*x_210 + 4*x_210^2 }-> s137 :|: s134 >= 0, s134 <= x_116, s135 >= 0, s135 <= x_210, s136 >= 0, s136 <= s134, s137 >= 0, s137 <= s136, x_116 >= 0, x_2 >= 0, z = 1 + (1 + x_116 + x_210) + x_2, x_210 >= 0
   encArg(z) -{ 7 + 6*x_126 + 4*x_126^2 }-> s139 :|: s138 >= 0, s138 <= x_126, s139 >= 0, s139 <= 0, x_1 >= 0, z = 1 + x_1 + (1 + x_126), x_126 >= 0
   encArg(z) -{ 15 + 2*s140 + 6*x_127 + 4*x_127^2 + 6*x_217 + 4*x_217^2 }-> s143 :|: s140 >= 0, s140 <= x_127, s141 >= 0, s141 <= x_217, s142 >= 0, s142 <= s140, s143 >= 0, s143 <= 0, x_1 >= 0, x_127 >= 0, z = 1 + x_1 + (1 + x_127 + x_217), x_217 >= 0
   encArg(z) -{ 14 + 2*s144 + 6*x_128 + 4*x_128^2 + 6*x_218 + 4*x_218^2 }-> s147 :|: s144 >= 0, s144 <= x_128, s145 >= 0, s145 <= x_218, s146 >= 0, s146 <= s144, s147 >= 0, s147 <= 0, x_1 >= 0, x_128 >= 0, z = 1 + x_1 + (1 + x_128 + x_218), x_218 >= 0
   encArg(z) -{ 21 + 2*s14 + 2*s15 + 6*x_1' + 4*x_1'^2 + 6*x_14 + 4*x_14^2 + 6*x_22 + 4*x_22^2 }-> s18 :|: s14 >= 0, s14 <= x_1', s15 >= 0, s15 <= x_14, s16 >= 0, s16 <= x_22, s17 >= 0, s17 <= s15, s18 >= 0, s18 <= 1 + s14, z = 1 + (1 + x_1') + (1 + x_14 + x_22), x_14 >= 0, x_1' >= 0, x_22 >= 0
   encArg(z) -{ 3 }-> s2 :|: s2 >= 0, s2 <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 10 + 2*s19 + 6*x_1' + 4*x_1'^2 }-> s20 :|: s19 >= 0, s19 <= x_1', s20 >= 0, s20 <= 1 + s19, x_1' >= 0, x_2 >= 0, z = 1 + (1 + x_1') + x_2
   encArg(z) -{ 20 + 2*s21 + 2*s23 + 6*x_1'' + 4*x_1''^2 + 6*x_15 + 4*x_15^2 + 6*x_2' + 4*x_2'^2 }-> s25 :|: s21 >= 0, s21 <= x_1'', s22 >= 0, s22 <= x_2', s23 >= 0, s23 <= s21, s24 >= 0, s24 <= x_15, s25 >= 0, s25 <= s23, x_15 >= 0, z = 1 + (1 + x_1'' + x_2') + (1 + x_15), x_1'' >= 0, x_2' >= 0
   encArg(z) -{ 28 + 2*s26 + 2*s28 + 2*s29 + 6*x_1'' + 4*x_1''^2 + 6*x_16 + 4*x_16^2 + 6*x_2' + 4*x_2'^2 + 6*x_23 + 4*x_23^2 }-> s32 :|: s26 >= 0, s26 <= x_1'', s27 >= 0, s27 <= x_2', s28 >= 0, s28 <= s26, s29 >= 0, s29 <= x_16, s30 >= 0, s30 <= x_23, s31 >= 0, s31 <= s29, s32 >= 0, s32 <= s28, 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) -{ 27 + 2*s33 + 2*s35 + 2*s36 + 6*x_1'' + 4*x_1''^2 + 6*x_17 + 4*x_17^2 + 6*x_2' + 4*x_2'^2 + 6*x_24 + 4*x_24^2 }-> s39 :|: s33 >= 0, s33 <= x_1'', s34 >= 0, s34 <= x_2', s35 >= 0, s35 <= s33, s36 >= 0, s36 <= x_17, s37 >= 0, s37 <= x_24, s38 >= 0, s38 <= s36, s39 >= 0, s39 <= s35, 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) -{ 16 + 2*s40 + 2*s42 + 6*x_1'' + 4*x_1''^2 + 6*x_2' + 4*x_2'^2 }-> s43 :|: s40 >= 0, s40 <= x_1'', s41 >= 0, s41 <= x_2', s42 >= 0, s42 <= s40, s43 >= 0, s43 <= s42, x_1'' >= 0, x_2' >= 0, z = 1 + (1 + x_1'' + x_2') + x_2, x_2 >= 0
   encArg(z) -{ 19 + 2*s44 + 2*s46 + 6*x_11 + 4*x_11^2 + 6*x_18 + 4*x_18^2 + 6*x_2'' + 4*x_2''^2 }-> s48 :|: s44 >= 0, s44 <= x_11, s45 >= 0, s45 <= x_2'', s46 >= 0, s46 <= s44, s47 >= 0, s47 <= x_18, s48 >= 0, s48 <= s46, x_11 >= 0, z = 1 + (1 + x_11 + x_2'') + (1 + x_18), x_2'' >= 0, x_18 >= 0
   encArg(z) -{ 27 + 2*s49 + 2*s51 + 2*s52 + 6*x_11 + 4*x_11^2 + 6*x_19 + 4*x_19^2 + 6*x_2'' + 4*x_2''^2 + 6*x_25 + 4*x_25^2 }-> s55 :|: s49 >= 0, s49 <= x_11, s50 >= 0, s50 <= x_2'', s51 >= 0, s51 <= s49, s52 >= 0, s52 <= x_19, s53 >= 0, s53 <= x_25, s54 >= 0, s54 <= s52, s55 >= 0, s55 <= s51, 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) -{ 26 + 2*s56 + 2*s58 + 2*s59 + 6*x_11 + 4*x_11^2 + 6*x_110 + 4*x_110^2 + 6*x_2'' + 4*x_2''^2 + 6*x_26 + 4*x_26^2 }-> s62 :|: s56 >= 0, s56 <= x_11, s57 >= 0, s57 <= x_2'', s58 >= 0, s58 <= s56, s59 >= 0, s59 <= x_110, s60 >= 0, s60 <= x_26, s61 >= 0, s61 <= s59, s62 >= 0, s62 <= s58, 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) -{ 15 + 2*s63 + 2*s65 + 6*x_11 + 4*x_11^2 + 6*x_2'' + 4*x_2''^2 }-> s66 :|: s63 >= 0, s63 <= x_11, s64 >= 0, s64 <= x_2'', s65 >= 0, s65 <= s63, s66 >= 0, s66 <= s65, x_11 >= 0, x_2'' >= 0, x_2 >= 0, z = 1 + (1 + x_11 + x_2'') + x_2
   encArg(z) -{ 8 + 6*x_111 + 4*x_111^2 }-> s68 :|: s67 >= 0, s67 <= x_111, s68 >= 0, s68 <= 0, x_1 >= 0, z = 1 + x_1 + (1 + x_111), x_111 >= 0
   encArg(z) -{ 16 + 2*s69 + 6*x_112 + 4*x_112^2 + 6*x_27 + 4*x_27^2 }-> s72 :|: s69 >= 0, s69 <= x_112, s70 >= 0, s70 <= x_27, s71 >= 0, s71 <= s69, s72 >= 0, s72 <= 0, x_1 >= 0, x_27 >= 0, z = 1 + x_1 + (1 + x_112 + x_27), x_112 >= 0
   encArg(z) -{ 15 + 2*s73 + 6*x_113 + 4*x_113^2 + 6*x_28 + 4*x_28^2 }-> s76 :|: s73 >= 0, s73 <= x_113, s74 >= 0, s74 <= x_28, s75 >= 0, s75 <= s73, s76 >= 0, s76 <= 0, x_1 >= 0, x_113 >= 0, x_28 >= 0, z = 1 + x_1 + (1 + x_113 + x_28)
   encArg(z) -{ 13 + 2*s77 + 6*x_114 + 4*x_114^2 + 6*x_117 + 4*x_117^2 }-> s79 :|: s77 >= 0, s77 <= x_114, s78 >= 0, s78 <= x_117, s79 >= 0, s79 <= 1 + s77, z = 1 + (1 + x_114) + (1 + x_117), x_117 >= 0, x_114 >= 0
   encArg(z) -{ 14 + 2*s6 + 6*x_1' + 4*x_1'^2 + 6*x_12 + 4*x_12^2 }-> s8 :|: s6 >= 0, s6 <= x_1', s7 >= 0, s7 <= x_12, s8 >= 0, s8 <= 1 + s6, z = 1 + (1 + x_1') + (1 + x_12), x_1' >= 0, x_12 >= 0
   encArg(z) -{ 21 + 2*s80 + 2*s81 + 6*x_114 + 4*x_114^2 + 6*x_118 + 4*x_118^2 + 6*x_211 + 4*x_211^2 }-> s84 :|: s80 >= 0, s80 <= x_114, s81 >= 0, s81 <= x_118, s82 >= 0, s82 <= x_211, s83 >= 0, s83 <= s81, s84 >= 0, s84 <= 1 + s80, z = 1 + (1 + x_114) + (1 + x_118 + x_211), x_114 >= 0, x_118 >= 0, x_211 >= 0
   encArg(z) -{ 20 + 2*s85 + 2*s86 + 6*x_114 + 4*x_114^2 + 6*x_119 + 4*x_119^2 + 6*x_212 + 4*x_212^2 }-> s89 :|: s85 >= 0, s85 <= x_114, s86 >= 0, s86 <= x_119, s87 >= 0, s87 <= x_212, s88 >= 0, s88 <= s86, s89 >= 0, s89 <= 1 + s85, x_212 >= 0, x_114 >= 0, z = 1 + (1 + x_114) + (1 + x_119 + x_212), x_119 >= 0
   encArg(z) -{ 9 + 2*s90 + 6*x_114 + 4*x_114^2 }-> s91 :|: s90 >= 0, s90 <= x_114, s91 >= 0, s91 <= 1 + s90, z = 1 + (1 + x_114) + x_2, x_114 >= 0, x_2 >= 0
   encArg(z) -{ 19 + 2*s92 + 2*s94 + 6*x_115 + 4*x_115^2 + 6*x_120 + 4*x_120^2 + 6*x_29 + 4*x_29^2 }-> s96 :|: s92 >= 0, s92 <= x_115, s93 >= 0, s93 <= x_29, s94 >= 0, s94 <= s92, s95 >= 0, s95 <= x_120, s96 >= 0, s96 <= s94, 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) -{ 2 + -2*z + 4*z^2 }-> 1 + s5 :|: s5 >= 0, s5 <= z - 1, z - 1 >= 0
   encode_f(z, z') -{ 10 + 2*s148 + -2*z + 4*z^2 + -2*z' + 4*z'^2 }-> s150 :|: s148 >= 0, s148 <= z - 1, s149 >= 0, s149 <= z' - 1, s150 >= 0, s150 <= 1 + s148, z' - 1 >= 0, z - 1 >= 0
   encode_f(z, z') -{ 20 + 2*s151 + 2*s152 + 6*x_133 + 4*x_133^2 + 6*x_221 + 4*x_221^2 + -2*z + 4*z^2 }-> s155 :|: s151 >= 0, s151 <= z - 1, s152 >= 0, s152 <= x_133, s153 >= 0, s153 <= x_221, s154 >= 0, s154 <= s152, s155 >= 0, s155 <= 1 + s151, z' = 1 + x_133 + x_221, x_221 >= 0, x_133 >= 0, z - 1 >= 0
   encode_f(z, z') -{ 19 + 2*s156 + 2*s157 + 6*x_134 + 4*x_134^2 + 6*x_222 + 4*x_222^2 + -2*z + 4*z^2 }-> s160 :|: s156 >= 0, s156 <= z - 1, s157 >= 0, s157 <= x_134, s158 >= 0, s158 <= x_222, s159 >= 0, s159 <= s157, s160 >= 0, s160 <= 1 + s156, z' = 1 + x_134 + x_222, x_134 >= 0, x_222 >= 0, z - 1 >= 0
   encode_f(z, z') -{ 8 + 2*s161 + -2*z + 4*z^2 }-> s162 :|: s161 >= 0, s161 <= z - 1, s162 >= 0, s162 <= 1 + s161, z' >= 0, z - 1 >= 0
   encode_f(z, z') -{ 18 + 2*s163 + 2*s165 + 6*x_130 + 4*x_130^2 + 6*x_219 + 4*x_219^2 + -2*z' + 4*z'^2 }-> s167 :|: s163 >= 0, s163 <= x_130, s164 >= 0, s164 <= x_219, s165 >= 0, s165 <= s163, s166 >= 0, s166 <= z' - 1, s167 >= 0, s167 <= s165, x_130 >= 0, z = 1 + x_130 + x_219, z' - 1 >= 0, x_219 >= 0
   encode_f(z, z') -{ 28 + 2*s168 + 2*s170 + 2*s171 + 6*x_130 + 4*x_130^2 + 6*x_136 + 4*x_136^2 + 6*x_219 + 4*x_219^2 + 6*x_223 + 4*x_223^2 }-> s174 :|: s168 >= 0, s168 <= x_130, s169 >= 0, s169 <= x_219, s170 >= 0, s170 <= s168, s171 >= 0, s171 <= x_136, s172 >= 0, s172 <= x_223, s173 >= 0, s173 <= s171, s174 >= 0, s174 <= s170, 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_f(z, z') -{ 27 + 2*s175 + 2*s177 + 2*s178 + 6*x_130 + 4*x_130^2 + 6*x_137 + 4*x_137^2 + 6*x_219 + 4*x_219^2 + 6*x_224 + 4*x_224^2 }-> s181 :|: s175 >= 0, s175 <= x_130, s176 >= 0, s176 <= x_219, s177 >= 0, s177 <= s175, s178 >= 0, s178 <= x_137, s179 >= 0, s179 <= x_224, s180 >= 0, s180 <= s178, s181 >= 0, s181 <= s177, 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_f(z, z') -{ 16 + 2*s182 + 2*s184 + 6*x_130 + 4*x_130^2 + 6*x_219 + 4*x_219^2 }-> s185 :|: s182 >= 0, s182 <= x_130, s183 >= 0, s183 <= x_219, s184 >= 0, s184 <= s182, s185 >= 0, s185 <= s184, x_130 >= 0, z = 1 + x_130 + x_219, z' >= 0, x_219 >= 0
   encode_f(z, z') -{ 17 + 2*s186 + 2*s188 + 6*x_131 + 4*x_131^2 + 6*x_220 + 4*x_220^2 + -2*z' + 4*z'^2 }-> s190 :|: s186 >= 0, s186 <= x_131, s187 >= 0, s187 <= x_220, s188 >= 0, s188 <= s186, s189 >= 0, s189 <= z' - 1, s190 >= 0, s190 <= s188, z' - 1 >= 0, z = 1 + x_131 + x_220, x_131 >= 0, x_220 >= 0
   encode_f(z, z') -{ 27 + 2*s191 + 2*s193 + 2*s194 + 6*x_131 + 4*x_131^2 + 6*x_139 + 4*x_139^2 + 6*x_220 + 4*x_220^2 + 6*x_225 + 4*x_225^2 }-> s197 :|: s191 >= 0, s191 <= x_131, s192 >= 0, s192 <= x_220, s193 >= 0, s193 <= s191, s194 >= 0, s194 <= x_139, s195 >= 0, s195 <= x_225, s196 >= 0, s196 <= s194, s197 >= 0, s197 <= s193, 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_f(z, z') -{ 26 + 2*s198 + 2*s200 + 2*s201 + 6*x_131 + 4*x_131^2 + 6*x_140 + 4*x_140^2 + 6*x_220 + 4*x_220^2 + 6*x_226 + 4*x_226^2 }-> s204 :|: s198 >= 0, s198 <= x_131, s199 >= 0, s199 <= x_220, s200 >= 0, s200 <= s198, s201 >= 0, s201 <= x_140, s202 >= 0, s202 <= x_226, s203 >= 0, s203 <= s201, s204 >= 0, s204 <= s200, 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_f(z, z') -{ 15 + 2*s205 + 2*s207 + 6*x_131 + 4*x_131^2 + 6*x_220 + 4*x_220^2 }-> s208 :|: s205 >= 0, s205 <= x_131, s206 >= 0, s206 <= x_220, s207 >= 0, s207 <= s205, s208 >= 0, s208 <= s207, z = 1 + x_131 + x_220, z' >= 0, x_131 >= 0, x_220 >= 0
   encode_f(z, z') -{ 6 + -2*z' + 4*z'^2 }-> s210 :|: s209 >= 0, s209 <= z' - 1, s210 >= 0, s210 <= 0, z >= 0, z' - 1 >= 0
   encode_f(z, z') -{ 16 + 2*s211 + 6*x_142 + 4*x_142^2 + 6*x_227 + 4*x_227^2 }-> s214 :|: s211 >= 0, s211 <= x_142, s212 >= 0, s212 <= x_227, s213 >= 0, s213 <= s211, s214 >= 0, s214 <= 0, z >= 0, z' = 1 + x_142 + x_227, x_142 >= 0, x_227 >= 0
   encode_f(z, z') -{ 15 + 2*s215 + 6*x_143 + 4*x_143^2 + 6*x_228 + 4*x_228^2 }-> s218 :|: s215 >= 0, s215 <= x_143, s216 >= 0, s216 <= x_228, s217 >= 0, s217 <= s215, s218 >= 0, s218 <= 0, z >= 0, z' = 1 + x_143 + x_228, x_143 >= 0, x_228 >= 0
   encode_f(z, z') -{ 4 }-> s3 :|: s3 >= 0, s3 <= 0, z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_g(z, z') -{ 9 + 2*s219 + -2*z + 4*z^2 + -2*z' + 4*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') -{ 19 + 2*s222 + 2*s223 + 6*x_148 + 4*x_148^2 + 6*x_231 + 4*x_231^2 + -2*z + 4*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') -{ 18 + 2*s227 + 2*s228 + 6*x_149 + 4*x_149^2 + 6*x_232 + 4*x_232^2 + -2*z + 4*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') -{ 7 + 2*s232 + -2*z + 4*z^2 }-> s233 :|: s232 >= 0, s232 <= z - 1, s233 >= 0, s233 <= 1 + s232, z - 1 >= 0, z' >= 0
   encode_g(z, z') -{ 17 + 2*s234 + 2*s236 + 6*x_145 + 4*x_145^2 + 6*x_229 + 4*x_229^2 + -2*z' + 4*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') -{ 27 + 2*s239 + 2*s241 + 2*s242 + 6*x_145 + 4*x_145^2 + 6*x_151 + 4*x_151^2 + 6*x_229 + 4*x_229^2 + 6*x_233 + 4*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') -{ 26 + 2*s246 + 2*s248 + 2*s249 + 6*x_145 + 4*x_145^2 + 6*x_152 + 4*x_152^2 + 6*x_229 + 4*x_229^2 + 6*x_234 + 4*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') -{ 15 + 2*s253 + 2*s255 + 6*x_145 + 4*x_145^2 + 6*x_229 + 4*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') -{ 16 + 2*s257 + 2*s259 + 6*x_146 + 4*x_146^2 + 6*x_230 + 4*x_230^2 + -2*z' + 4*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') -{ 26 + 2*s262 + 2*s264 + 2*s265 + 6*x_146 + 4*x_146^2 + 6*x_154 + 4*x_154^2 + 6*x_230 + 4*x_230^2 + 6*x_235 + 4*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') -{ 25 + 2*s269 + 2*s271 + 2*s272 + 6*x_146 + 4*x_146^2 + 6*x_155 + 4*x_155^2 + 6*x_230 + 4*x_230^2 + 6*x_236 + 4*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') -{ 14 + 2*s276 + 2*s278 + 6*x_146 + 4*x_146^2 + 6*x_230 + 4*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') -{ 5 + -2*z' + 4*z'^2 }-> s281 :|: s280 >= 0, s280 <= z' - 1, s281 >= 0, s281 <= 0, z >= 0, z' - 1 >= 0
   encode_g(z, z') -{ 15 + 2*s282 + 6*x_157 + 4*x_157^2 + 6*x_237 + 4*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') -{ 14 + 2*s286 + 6*x_158 + 4*x_158^2 + 6*x_238 + 4*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') -{ 3 }-> s4 :|: s4 >= 0, s4 <= 0, z >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_h(z) -{ 0 }-> 0 :|: z >= 0
   encode_h(z) -{ 4 + 6*z + 4*z^2 }-> 1 + s290 :|: s290 >= 0, s290 <= z, z >= 0
   f(z, z') -{ 4 + 2*z }-> s :|: s >= 0, s <= z, z >= 0, z' >= 0
   g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   g(z, z') -{ 3 + 2*z }-> 1 + s' :|: s' >= 0, s' <= z - 1, z - 1 >= 0, z' >= 0
   g(z, z') -{ 2 + 2*z }-> 1 + s'' :|: s'' >= 0, s'' <= z - 1, z - 1 >= 0, z' >= 0

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

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

(37) 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: 4 + 6*z + 4*z^2

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

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

   encArg(z) -{ 4 }-> s1 :|: s1 >= 0, s1 <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 27 + 2*s100 + 2*s97 + 2*s99 + 6*x_115 + 4*x_115^2 + 6*x_121 + 4*x_121^2 + 6*x_213 + 4*x_213^2 + 6*x_29 + 4*x_29^2 }-> s103 :|: s97 >= 0, s97 <= x_115, s98 >= 0, s98 <= x_29, s99 >= 0, s99 <= s97, s100 >= 0, s100 <= x_121, s101 >= 0, s101 <= x_213, s102 >= 0, s102 <= s100, s103 >= 0, s103 <= s99, 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) -{ 26 + 2*s104 + 2*s106 + 2*s107 + 6*x_115 + 4*x_115^2 + 6*x_122 + 4*x_122^2 + 6*x_214 + 4*x_214^2 + 6*x_29 + 4*x_29^2 }-> s110 :|: s104 >= 0, s104 <= x_115, s105 >= 0, s105 <= x_29, s106 >= 0, s106 <= s104, s107 >= 0, s107 <= x_122, s108 >= 0, s108 <= x_214, s109 >= 0, s109 <= s107, s110 >= 0, s110 <= s106, 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) -{ 15 + 2*s111 + 2*s113 + 6*x_115 + 4*x_115^2 + 6*x_29 + 4*x_29^2 }-> s114 :|: s111 >= 0, s111 <= x_115, s112 >= 0, s112 <= x_29, s113 >= 0, s113 <= s111, s114 >= 0, s114 <= s113, x_115 >= 0, x_2 >= 0, z = 1 + (1 + x_115 + x_29) + x_2, x_29 >= 0
   encArg(z) -{ 18 + 2*s115 + 2*s117 + 6*x_116 + 4*x_116^2 + 6*x_123 + 4*x_123^2 + 6*x_210 + 4*x_210^2 }-> s119 :|: s115 >= 0, s115 <= x_116, s116 >= 0, s116 <= x_210, s117 >= 0, s117 <= s115, s118 >= 0, s118 <= x_123, s119 >= 0, s119 <= s117, x_123 >= 0, z = 1 + (1 + x_116 + x_210) + (1 + x_123), x_116 >= 0, x_210 >= 0
   encArg(z) -{ 26 + 2*s120 + 2*s122 + 2*s123 + 6*x_116 + 4*x_116^2 + 6*x_124 + 4*x_124^2 + 6*x_210 + 4*x_210^2 + 6*x_215 + 4*x_215^2 }-> s126 :|: s120 >= 0, s120 <= x_116, s121 >= 0, s121 <= x_210, s122 >= 0, s122 <= s120, s123 >= 0, s123 <= x_124, s124 >= 0, s124 <= x_215, s125 >= 0, s125 <= s123, s126 >= 0, s126 <= s122, 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) -{ 22 + 2*s10 + 2*s9 + 6*x_1' + 4*x_1'^2 + 6*x_13 + 4*x_13^2 + 6*x_21 + 4*x_21^2 }-> s13 :|: s9 >= 0, s9 <= x_1', s10 >= 0, s10 <= x_13, s11 >= 0, s11 <= x_21, s12 >= 0, s12 <= s10, s13 >= 0, s13 <= 1 + s9, x_13 >= 0, x_1' >= 0, z = 1 + (1 + x_1') + (1 + x_13 + x_21), x_21 >= 0
   encArg(z) -{ 25 + 2*s127 + 2*s129 + 2*s130 + 6*x_116 + 4*x_116^2 + 6*x_125 + 4*x_125^2 + 6*x_210 + 4*x_210^2 + 6*x_216 + 4*x_216^2 }-> s133 :|: s127 >= 0, s127 <= x_116, s128 >= 0, s128 <= x_210, s129 >= 0, s129 <= s127, s130 >= 0, s130 <= x_125, s131 >= 0, s131 <= x_216, s132 >= 0, s132 <= s130, s133 >= 0, s133 <= s129, 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) -{ 14 + 2*s134 + 2*s136 + 6*x_116 + 4*x_116^2 + 6*x_210 + 4*x_210^2 }-> s137 :|: s134 >= 0, s134 <= x_116, s135 >= 0, s135 <= x_210, s136 >= 0, s136 <= s134, s137 >= 0, s137 <= s136, x_116 >= 0, x_2 >= 0, z = 1 + (1 + x_116 + x_210) + x_2, x_210 >= 0
   encArg(z) -{ 7 + 6*x_126 + 4*x_126^2 }-> s139 :|: s138 >= 0, s138 <= x_126, s139 >= 0, s139 <= 0, x_1 >= 0, z = 1 + x_1 + (1 + x_126), x_126 >= 0
   encArg(z) -{ 15 + 2*s140 + 6*x_127 + 4*x_127^2 + 6*x_217 + 4*x_217^2 }-> s143 :|: s140 >= 0, s140 <= x_127, s141 >= 0, s141 <= x_217, s142 >= 0, s142 <= s140, s143 >= 0, s143 <= 0, x_1 >= 0, x_127 >= 0, z = 1 + x_1 + (1 + x_127 + x_217), x_217 >= 0
   encArg(z) -{ 14 + 2*s144 + 6*x_128 + 4*x_128^2 + 6*x_218 + 4*x_218^2 }-> s147 :|: s144 >= 0, s144 <= x_128, s145 >= 0, s145 <= x_218, s146 >= 0, s146 <= s144, s147 >= 0, s147 <= 0, x_1 >= 0, x_128 >= 0, z = 1 + x_1 + (1 + x_128 + x_218), x_218 >= 0
   encArg(z) -{ 21 + 2*s14 + 2*s15 + 6*x_1' + 4*x_1'^2 + 6*x_14 + 4*x_14^2 + 6*x_22 + 4*x_22^2 }-> s18 :|: s14 >= 0, s14 <= x_1', s15 >= 0, s15 <= x_14, s16 >= 0, s16 <= x_22, s17 >= 0, s17 <= s15, s18 >= 0, s18 <= 1 + s14, z = 1 + (1 + x_1') + (1 + x_14 + x_22), x_14 >= 0, x_1' >= 0, x_22 >= 0
   encArg(z) -{ 3 }-> s2 :|: s2 >= 0, s2 <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 10 + 2*s19 + 6*x_1' + 4*x_1'^2 }-> s20 :|: s19 >= 0, s19 <= x_1', s20 >= 0, s20 <= 1 + s19, x_1' >= 0, x_2 >= 0, z = 1 + (1 + x_1') + x_2
   encArg(z) -{ 20 + 2*s21 + 2*s23 + 6*x_1'' + 4*x_1''^2 + 6*x_15 + 4*x_15^2 + 6*x_2' + 4*x_2'^2 }-> s25 :|: s21 >= 0, s21 <= x_1'', s22 >= 0, s22 <= x_2', s23 >= 0, s23 <= s21, s24 >= 0, s24 <= x_15, s25 >= 0, s25 <= s23, x_15 >= 0, z = 1 + (1 + x_1'' + x_2') + (1 + x_15), x_1'' >= 0, x_2' >= 0
   encArg(z) -{ 28 + 2*s26 + 2*s28 + 2*s29 + 6*x_1'' + 4*x_1''^2 + 6*x_16 + 4*x_16^2 + 6*x_2' + 4*x_2'^2 + 6*x_23 + 4*x_23^2 }-> s32 :|: s26 >= 0, s26 <= x_1'', s27 >= 0, s27 <= x_2', s28 >= 0, s28 <= s26, s29 >= 0, s29 <= x_16, s30 >= 0, s30 <= x_23, s31 >= 0, s31 <= s29, s32 >= 0, s32 <= s28, 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) -{ 27 + 2*s33 + 2*s35 + 2*s36 + 6*x_1'' + 4*x_1''^2 + 6*x_17 + 4*x_17^2 + 6*x_2' + 4*x_2'^2 + 6*x_24 + 4*x_24^2 }-> s39 :|: s33 >= 0, s33 <= x_1'', s34 >= 0, s34 <= x_2', s35 >= 0, s35 <= s33, s36 >= 0, s36 <= x_17, s37 >= 0, s37 <= x_24, s38 >= 0, s38 <= s36, s39 >= 0, s39 <= s35, 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) -{ 16 + 2*s40 + 2*s42 + 6*x_1'' + 4*x_1''^2 + 6*x_2' + 4*x_2'^2 }-> s43 :|: s40 >= 0, s40 <= x_1'', s41 >= 0, s41 <= x_2', s42 >= 0, s42 <= s40, s43 >= 0, s43 <= s42, x_1'' >= 0, x_2' >= 0, z = 1 + (1 + x_1'' + x_2') + x_2, x_2 >= 0
   encArg(z) -{ 19 + 2*s44 + 2*s46 + 6*x_11 + 4*x_11^2 + 6*x_18 + 4*x_18^2 + 6*x_2'' + 4*x_2''^2 }-> s48 :|: s44 >= 0, s44 <= x_11, s45 >= 0, s45 <= x_2'', s46 >= 0, s46 <= s44, s47 >= 0, s47 <= x_18, s48 >= 0, s48 <= s46, x_11 >= 0, z = 1 + (1 + x_11 + x_2'') + (1 + x_18), x_2'' >= 0, x_18 >= 0
   encArg(z) -{ 27 + 2*s49 + 2*s51 + 2*s52 + 6*x_11 + 4*x_11^2 + 6*x_19 + 4*x_19^2 + 6*x_2'' + 4*x_2''^2 + 6*x_25 + 4*x_25^2 }-> s55 :|: s49 >= 0, s49 <= x_11, s50 >= 0, s50 <= x_2'', s51 >= 0, s51 <= s49, s52 >= 0, s52 <= x_19, s53 >= 0, s53 <= x_25, s54 >= 0, s54 <= s52, s55 >= 0, s55 <= s51, 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) -{ 26 + 2*s56 + 2*s58 + 2*s59 + 6*x_11 + 4*x_11^2 + 6*x_110 + 4*x_110^2 + 6*x_2'' + 4*x_2''^2 + 6*x_26 + 4*x_26^2 }-> s62 :|: s56 >= 0, s56 <= x_11, s57 >= 0, s57 <= x_2'', s58 >= 0, s58 <= s56, s59 >= 0, s59 <= x_110, s60 >= 0, s60 <= x_26, s61 >= 0, s61 <= s59, s62 >= 0, s62 <= s58, 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) -{ 15 + 2*s63 + 2*s65 + 6*x_11 + 4*x_11^2 + 6*x_2'' + 4*x_2''^2 }-> s66 :|: s63 >= 0, s63 <= x_11, s64 >= 0, s64 <= x_2'', s65 >= 0, s65 <= s63, s66 >= 0, s66 <= s65, x_11 >= 0, x_2'' >= 0, x_2 >= 0, z = 1 + (1 + x_11 + x_2'') + x_2
   encArg(z) -{ 8 + 6*x_111 + 4*x_111^2 }-> s68 :|: s67 >= 0, s67 <= x_111, s68 >= 0, s68 <= 0, x_1 >= 0, z = 1 + x_1 + (1 + x_111), x_111 >= 0
   encArg(z) -{ 16 + 2*s69 + 6*x_112 + 4*x_112^2 + 6*x_27 + 4*x_27^2 }-> s72 :|: s69 >= 0, s69 <= x_112, s70 >= 0, s70 <= x_27, s71 >= 0, s71 <= s69, s72 >= 0, s72 <= 0, x_1 >= 0, x_27 >= 0, z = 1 + x_1 + (1 + x_112 + x_27), x_112 >= 0
   encArg(z) -{ 15 + 2*s73 + 6*x_113 + 4*x_113^2 + 6*x_28 + 4*x_28^2 }-> s76 :|: s73 >= 0, s73 <= x_113, s74 >= 0, s74 <= x_28, s75 >= 0, s75 <= s73, s76 >= 0, s76 <= 0, x_1 >= 0, x_113 >= 0, x_28 >= 0, z = 1 + x_1 + (1 + x_113 + x_28)
   encArg(z) -{ 13 + 2*s77 + 6*x_114 + 4*x_114^2 + 6*x_117 + 4*x_117^2 }-> s79 :|: s77 >= 0, s77 <= x_114, s78 >= 0, s78 <= x_117, s79 >= 0, s79 <= 1 + s77, z = 1 + (1 + x_114) + (1 + x_117), x_117 >= 0, x_114 >= 0
   encArg(z) -{ 14 + 2*s6 + 6*x_1' + 4*x_1'^2 + 6*x_12 + 4*x_12^2 }-> s8 :|: s6 >= 0, s6 <= x_1', s7 >= 0, s7 <= x_12, s8 >= 0, s8 <= 1 + s6, z = 1 + (1 + x_1') + (1 + x_12), x_1' >= 0, x_12 >= 0
   encArg(z) -{ 21 + 2*s80 + 2*s81 + 6*x_114 + 4*x_114^2 + 6*x_118 + 4*x_118^2 + 6*x_211 + 4*x_211^2 }-> s84 :|: s80 >= 0, s80 <= x_114, s81 >= 0, s81 <= x_118, s82 >= 0, s82 <= x_211, s83 >= 0, s83 <= s81, s84 >= 0, s84 <= 1 + s80, z = 1 + (1 + x_114) + (1 + x_118 + x_211), x_114 >= 0, x_118 >= 0, x_211 >= 0
   encArg(z) -{ 20 + 2*s85 + 2*s86 + 6*x_114 + 4*x_114^2 + 6*x_119 + 4*x_119^2 + 6*x_212 + 4*x_212^2 }-> s89 :|: s85 >= 0, s85 <= x_114, s86 >= 0, s86 <= x_119, s87 >= 0, s87 <= x_212, s88 >= 0, s88 <= s86, s89 >= 0, s89 <= 1 + s85, x_212 >= 0, x_114 >= 0, z = 1 + (1 + x_114) + (1 + x_119 + x_212), x_119 >= 0
   encArg(z) -{ 9 + 2*s90 + 6*x_114 + 4*x_114^2 }-> s91 :|: s90 >= 0, s90 <= x_114, s91 >= 0, s91 <= 1 + s90, z = 1 + (1 + x_114) + x_2, x_114 >= 0, x_2 >= 0
   encArg(z) -{ 19 + 2*s92 + 2*s94 + 6*x_115 + 4*x_115^2 + 6*x_120 + 4*x_120^2 + 6*x_29 + 4*x_29^2 }-> s96 :|: s92 >= 0, s92 <= x_115, s93 >= 0, s93 <= x_29, s94 >= 0, s94 <= s92, s95 >= 0, s95 <= x_120, s96 >= 0, s96 <= s94, 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) -{ 2 + -2*z + 4*z^2 }-> 1 + s5 :|: s5 >= 0, s5 <= z - 1, z - 1 >= 0
   encode_f(z, z') -{ 10 + 2*s148 + -2*z + 4*z^2 + -2*z' + 4*z'^2 }-> s150 :|: s148 >= 0, s148 <= z - 1, s149 >= 0, s149 <= z' - 1, s150 >= 0, s150 <= 1 + s148, z' - 1 >= 0, z - 1 >= 0
   encode_f(z, z') -{ 20 + 2*s151 + 2*s152 + 6*x_133 + 4*x_133^2 + 6*x_221 + 4*x_221^2 + -2*z + 4*z^2 }-> s155 :|: s151 >= 0, s151 <= z - 1, s152 >= 0, s152 <= x_133, s153 >= 0, s153 <= x_221, s154 >= 0, s154 <= s152, s155 >= 0, s155 <= 1 + s151, z' = 1 + x_133 + x_221, x_221 >= 0, x_133 >= 0, z - 1 >= 0
   encode_f(z, z') -{ 19 + 2*s156 + 2*s157 + 6*x_134 + 4*x_134^2 + 6*x_222 + 4*x_222^2 + -2*z + 4*z^2 }-> s160 :|: s156 >= 0, s156 <= z - 1, s157 >= 0, s157 <= x_134, s158 >= 0, s158 <= x_222, s159 >= 0, s159 <= s157, s160 >= 0, s160 <= 1 + s156, z' = 1 + x_134 + x_222, x_134 >= 0, x_222 >= 0, z - 1 >= 0
   encode_f(z, z') -{ 8 + 2*s161 + -2*z + 4*z^2 }-> s162 :|: s161 >= 0, s161 <= z - 1, s162 >= 0, s162 <= 1 + s161, z' >= 0, z - 1 >= 0
   encode_f(z, z') -{ 18 + 2*s163 + 2*s165 + 6*x_130 + 4*x_130^2 + 6*x_219 + 4*x_219^2 + -2*z' + 4*z'^2 }-> s167 :|: s163 >= 0, s163 <= x_130, s164 >= 0, s164 <= x_219, s165 >= 0, s165 <= s163, s166 >= 0, s166 <= z' - 1, s167 >= 0, s167 <= s165, x_130 >= 0, z = 1 + x_130 + x_219, z' - 1 >= 0, x_219 >= 0
   encode_f(z, z') -{ 28 + 2*s168 + 2*s170 + 2*s171 + 6*x_130 + 4*x_130^2 + 6*x_136 + 4*x_136^2 + 6*x_219 + 4*x_219^2 + 6*x_223 + 4*x_223^2 }-> s174 :|: s168 >= 0, s168 <= x_130, s169 >= 0, s169 <= x_219, s170 >= 0, s170 <= s168, s171 >= 0, s171 <= x_136, s172 >= 0, s172 <= x_223, s173 >= 0, s173 <= s171, s174 >= 0, s174 <= s170, 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_f(z, z') -{ 27 + 2*s175 + 2*s177 + 2*s178 + 6*x_130 + 4*x_130^2 + 6*x_137 + 4*x_137^2 + 6*x_219 + 4*x_219^2 + 6*x_224 + 4*x_224^2 }-> s181 :|: s175 >= 0, s175 <= x_130, s176 >= 0, s176 <= x_219, s177 >= 0, s177 <= s175, s178 >= 0, s178 <= x_137, s179 >= 0, s179 <= x_224, s180 >= 0, s180 <= s178, s181 >= 0, s181 <= s177, 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_f(z, z') -{ 16 + 2*s182 + 2*s184 + 6*x_130 + 4*x_130^2 + 6*x_219 + 4*x_219^2 }-> s185 :|: s182 >= 0, s182 <= x_130, s183 >= 0, s183 <= x_219, s184 >= 0, s184 <= s182, s185 >= 0, s185 <= s184, x_130 >= 0, z = 1 + x_130 + x_219, z' >= 0, x_219 >= 0
   encode_f(z, z') -{ 17 + 2*s186 + 2*s188 + 6*x_131 + 4*x_131^2 + 6*x_220 + 4*x_220^2 + -2*z' + 4*z'^2 }-> s190 :|: s186 >= 0, s186 <= x_131, s187 >= 0, s187 <= x_220, s188 >= 0, s188 <= s186, s189 >= 0, s189 <= z' - 1, s190 >= 0, s190 <= s188, z' - 1 >= 0, z = 1 + x_131 + x_220, x_131 >= 0, x_220 >= 0
   encode_f(z, z') -{ 27 + 2*s191 + 2*s193 + 2*s194 + 6*x_131 + 4*x_131^2 + 6*x_139 + 4*x_139^2 + 6*x_220 + 4*x_220^2 + 6*x_225 + 4*x_225^2 }-> s197 :|: s191 >= 0, s191 <= x_131, s192 >= 0, s192 <= x_220, s193 >= 0, s193 <= s191, s194 >= 0, s194 <= x_139, s195 >= 0, s195 <= x_225, s196 >= 0, s196 <= s194, s197 >= 0, s197 <= s193, 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_f(z, z') -{ 26 + 2*s198 + 2*s200 + 2*s201 + 6*x_131 + 4*x_131^2 + 6*x_140 + 4*x_140^2 + 6*x_220 + 4*x_220^2 + 6*x_226 + 4*x_226^2 }-> s204 :|: s198 >= 0, s198 <= x_131, s199 >= 0, s199 <= x_220, s200 >= 0, s200 <= s198, s201 >= 0, s201 <= x_140, s202 >= 0, s202 <= x_226, s203 >= 0, s203 <= s201, s204 >= 0, s204 <= s200, 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_f(z, z') -{ 15 + 2*s205 + 2*s207 + 6*x_131 + 4*x_131^2 + 6*x_220 + 4*x_220^2 }-> s208 :|: s205 >= 0, s205 <= x_131, s206 >= 0, s206 <= x_220, s207 >= 0, s207 <= s205, s208 >= 0, s208 <= s207, z = 1 + x_131 + x_220, z' >= 0, x_131 >= 0, x_220 >= 0
   encode_f(z, z') -{ 6 + -2*z' + 4*z'^2 }-> s210 :|: s209 >= 0, s209 <= z' - 1, s210 >= 0, s210 <= 0, z >= 0, z' - 1 >= 0
   encode_f(z, z') -{ 16 + 2*s211 + 6*x_142 + 4*x_142^2 + 6*x_227 + 4*x_227^2 }-> s214 :|: s211 >= 0, s211 <= x_142, s212 >= 0, s212 <= x_227, s213 >= 0, s213 <= s211, s214 >= 0, s214 <= 0, z >= 0, z' = 1 + x_142 + x_227, x_142 >= 0, x_227 >= 0
   encode_f(z, z') -{ 15 + 2*s215 + 6*x_143 + 4*x_143^2 + 6*x_228 + 4*x_228^2 }-> s218 :|: s215 >= 0, s215 <= x_143, s216 >= 0, s216 <= x_228, s217 >= 0, s217 <= s215, s218 >= 0, s218 <= 0, z >= 0, z' = 1 + x_143 + x_228, x_143 >= 0, x_228 >= 0
   encode_f(z, z') -{ 4 }-> s3 :|: s3 >= 0, s3 <= 0, z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_g(z, z') -{ 9 + 2*s219 + -2*z + 4*z^2 + -2*z' + 4*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') -{ 19 + 2*s222 + 2*s223 + 6*x_148 + 4*x_148^2 + 6*x_231 + 4*x_231^2 + -2*z + 4*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') -{ 18 + 2*s227 + 2*s228 + 6*x_149 + 4*x_149^2 + 6*x_232 + 4*x_232^2 + -2*z + 4*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') -{ 7 + 2*s232 + -2*z + 4*z^2 }-> s233 :|: s232 >= 0, s232 <= z - 1, s233 >= 0, s233 <= 1 + s232, z - 1 >= 0, z' >= 0
   encode_g(z, z') -{ 17 + 2*s234 + 2*s236 + 6*x_145 + 4*x_145^2 + 6*x_229 + 4*x_229^2 + -2*z' + 4*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') -{ 27 + 2*s239 + 2*s241 + 2*s242 + 6*x_145 + 4*x_145^2 + 6*x_151 + 4*x_151^2 + 6*x_229 + 4*x_229^2 + 6*x_233 + 4*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') -{ 26 + 2*s246 + 2*s248 + 2*s249 + 6*x_145 + 4*x_145^2 + 6*x_152 + 4*x_152^2 + 6*x_229 + 4*x_229^2 + 6*x_234 + 4*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') -{ 15 + 2*s253 + 2*s255 + 6*x_145 + 4*x_145^2 + 6*x_229 + 4*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') -{ 16 + 2*s257 + 2*s259 + 6*x_146 + 4*x_146^2 + 6*x_230 + 4*x_230^2 + -2*z' + 4*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') -{ 26 + 2*s262 + 2*s264 + 2*s265 + 6*x_146 + 4*x_146^2 + 6*x_154 + 4*x_154^2 + 6*x_230 + 4*x_230^2 + 6*x_235 + 4*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') -{ 25 + 2*s269 + 2*s271 + 2*s272 + 6*x_146 + 4*x_146^2 + 6*x_155 + 4*x_155^2 + 6*x_230 + 4*x_230^2 + 6*x_236 + 4*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') -{ 14 + 2*s276 + 2*s278 + 6*x_146 + 4*x_146^2 + 6*x_230 + 4*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') -{ 5 + -2*z' + 4*z'^2 }-> s281 :|: s280 >= 0, s280 <= z' - 1, s281 >= 0, s281 <= 0, z >= 0, z' - 1 >= 0
   encode_g(z, z') -{ 15 + 2*s282 + 6*x_157 + 4*x_157^2 + 6*x_237 + 4*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') -{ 14 + 2*s286 + 6*x_158 + 4*x_158^2 + 6*x_238 + 4*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') -{ 3 }-> s4 :|: s4 >= 0, s4 <= 0, z >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_h(z) -{ 0 }-> 0 :|: z >= 0
   encode_h(z) -{ 4 + 6*z + 4*z^2 }-> 1 + s290 :|: s290 >= 0, s290 <= z, z >= 0
   f(z, z') -{ 4 + 2*z }-> s :|: s >= 0, s <= z, z >= 0, z' >= 0
   g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   g(z, z') -{ 3 + 2*z }-> 1 + s' :|: s' >= 0, s' <= z - 1, z - 1 >= 0, z' >= 0
   g(z, z') -{ 2 + 2*z }-> 1 + s'' :|: s'' >= 0, s'' <= z - 1, z - 1 >= 0, z' >= 0

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

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(39) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
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(40)
Obligation:
Complexity RNTS consisting of the following rules:

   encArg(z) -{ 4 }-> s1 :|: s1 >= 0, s1 <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 27 + 2*s100 + 2*s97 + 2*s99 + 6*x_115 + 4*x_115^2 + 6*x_121 + 4*x_121^2 + 6*x_213 + 4*x_213^2 + 6*x_29 + 4*x_29^2 }-> s103 :|: s97 >= 0, s97 <= x_115, s98 >= 0, s98 <= x_29, s99 >= 0, s99 <= s97, s100 >= 0, s100 <= x_121, s101 >= 0, s101 <= x_213, s102 >= 0, s102 <= s100, s103 >= 0, s103 <= s99, 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) -{ 26 + 2*s104 + 2*s106 + 2*s107 + 6*x_115 + 4*x_115^2 + 6*x_122 + 4*x_122^2 + 6*x_214 + 4*x_214^2 + 6*x_29 + 4*x_29^2 }-> s110 :|: s104 >= 0, s104 <= x_115, s105 >= 0, s105 <= x_29, s106 >= 0, s106 <= s104, s107 >= 0, s107 <= x_122, s108 >= 0, s108 <= x_214, s109 >= 0, s109 <= s107, s110 >= 0, s110 <= s106, 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) -{ 15 + 2*s111 + 2*s113 + 6*x_115 + 4*x_115^2 + 6*x_29 + 4*x_29^2 }-> s114 :|: s111 >= 0, s111 <= x_115, s112 >= 0, s112 <= x_29, s113 >= 0, s113 <= s111, s114 >= 0, s114 <= s113, x_115 >= 0, x_2 >= 0, z = 1 + (1 + x_115 + x_29) + x_2, x_29 >= 0
   encArg(z) -{ 18 + 2*s115 + 2*s117 + 6*x_116 + 4*x_116^2 + 6*x_123 + 4*x_123^2 + 6*x_210 + 4*x_210^2 }-> s119 :|: s115 >= 0, s115 <= x_116, s116 >= 0, s116 <= x_210, s117 >= 0, s117 <= s115, s118 >= 0, s118 <= x_123, s119 >= 0, s119 <= s117, x_123 >= 0, z = 1 + (1 + x_116 + x_210) + (1 + x_123), x_116 >= 0, x_210 >= 0
   encArg(z) -{ 26 + 2*s120 + 2*s122 + 2*s123 + 6*x_116 + 4*x_116^2 + 6*x_124 + 4*x_124^2 + 6*x_210 + 4*x_210^2 + 6*x_215 + 4*x_215^2 }-> s126 :|: s120 >= 0, s120 <= x_116, s121 >= 0, s121 <= x_210, s122 >= 0, s122 <= s120, s123 >= 0, s123 <= x_124, s124 >= 0, s124 <= x_215, s125 >= 0, s125 <= s123, s126 >= 0, s126 <= s122, 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) -{ 22 + 2*s10 + 2*s9 + 6*x_1' + 4*x_1'^2 + 6*x_13 + 4*x_13^2 + 6*x_21 + 4*x_21^2 }-> s13 :|: s9 >= 0, s9 <= x_1', s10 >= 0, s10 <= x_13, s11 >= 0, s11 <= x_21, s12 >= 0, s12 <= s10, s13 >= 0, s13 <= 1 + s9, x_13 >= 0, x_1' >= 0, z = 1 + (1 + x_1') + (1 + x_13 + x_21), x_21 >= 0
   encArg(z) -{ 25 + 2*s127 + 2*s129 + 2*s130 + 6*x_116 + 4*x_116^2 + 6*x_125 + 4*x_125^2 + 6*x_210 + 4*x_210^2 + 6*x_216 + 4*x_216^2 }-> s133 :|: s127 >= 0, s127 <= x_116, s128 >= 0, s128 <= x_210, s129 >= 0, s129 <= s127, s130 >= 0, s130 <= x_125, s131 >= 0, s131 <= x_216, s132 >= 0, s132 <= s130, s133 >= 0, s133 <= s129, 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) -{ 14 + 2*s134 + 2*s136 + 6*x_116 + 4*x_116^2 + 6*x_210 + 4*x_210^2 }-> s137 :|: s134 >= 0, s134 <= x_116, s135 >= 0, s135 <= x_210, s136 >= 0, s136 <= s134, s137 >= 0, s137 <= s136, x_116 >= 0, x_2 >= 0, z = 1 + (1 + x_116 + x_210) + x_2, x_210 >= 0
   encArg(z) -{ 7 + 6*x_126 + 4*x_126^2 }-> s139 :|: s138 >= 0, s138 <= x_126, s139 >= 0, s139 <= 0, x_1 >= 0, z = 1 + x_1 + (1 + x_126), x_126 >= 0
   encArg(z) -{ 15 + 2*s140 + 6*x_127 + 4*x_127^2 + 6*x_217 + 4*x_217^2 }-> s143 :|: s140 >= 0, s140 <= x_127, s141 >= 0, s141 <= x_217, s142 >= 0, s142 <= s140, s143 >= 0, s143 <= 0, x_1 >= 0, x_127 >= 0, z = 1 + x_1 + (1 + x_127 + x_217), x_217 >= 0
   encArg(z) -{ 14 + 2*s144 + 6*x_128 + 4*x_128^2 + 6*x_218 + 4*x_218^2 }-> s147 :|: s144 >= 0, s144 <= x_128, s145 >= 0, s145 <= x_218, s146 >= 0, s146 <= s144, s147 >= 0, s147 <= 0, x_1 >= 0, x_128 >= 0, z = 1 + x_1 + (1 + x_128 + x_218), x_218 >= 0
   encArg(z) -{ 21 + 2*s14 + 2*s15 + 6*x_1' + 4*x_1'^2 + 6*x_14 + 4*x_14^2 + 6*x_22 + 4*x_22^2 }-> s18 :|: s14 >= 0, s14 <= x_1', s15 >= 0, s15 <= x_14, s16 >= 0, s16 <= x_22, s17 >= 0, s17 <= s15, s18 >= 0, s18 <= 1 + s14, z = 1 + (1 + x_1') + (1 + x_14 + x_22), x_14 >= 0, x_1' >= 0, x_22 >= 0
   encArg(z) -{ 3 }-> s2 :|: s2 >= 0, s2 <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 10 + 2*s19 + 6*x_1' + 4*x_1'^2 }-> s20 :|: s19 >= 0, s19 <= x_1', s20 >= 0, s20 <= 1 + s19, x_1' >= 0, x_2 >= 0, z = 1 + (1 + x_1') + x_2
   encArg(z) -{ 20 + 2*s21 + 2*s23 + 6*x_1'' + 4*x_1''^2 + 6*x_15 + 4*x_15^2 + 6*x_2' + 4*x_2'^2 }-> s25 :|: s21 >= 0, s21 <= x_1'', s22 >= 0, s22 <= x_2', s23 >= 0, s23 <= s21, s24 >= 0, s24 <= x_15, s25 >= 0, s25 <= s23, x_15 >= 0, z = 1 + (1 + x_1'' + x_2') + (1 + x_15), x_1'' >= 0, x_2' >= 0
   encArg(z) -{ 28 + 2*s26 + 2*s28 + 2*s29 + 6*x_1'' + 4*x_1''^2 + 6*x_16 + 4*x_16^2 + 6*x_2' + 4*x_2'^2 + 6*x_23 + 4*x_23^2 }-> s32 :|: s26 >= 0, s26 <= x_1'', s27 >= 0, s27 <= x_2', s28 >= 0, s28 <= s26, s29 >= 0, s29 <= x_16, s30 >= 0, s30 <= x_23, s31 >= 0, s31 <= s29, s32 >= 0, s32 <= s28, 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) -{ 27 + 2*s33 + 2*s35 + 2*s36 + 6*x_1'' + 4*x_1''^2 + 6*x_17 + 4*x_17^2 + 6*x_2' + 4*x_2'^2 + 6*x_24 + 4*x_24^2 }-> s39 :|: s33 >= 0, s33 <= x_1'', s34 >= 0, s34 <= x_2', s35 >= 0, s35 <= s33, s36 >= 0, s36 <= x_17, s37 >= 0, s37 <= x_24, s38 >= 0, s38 <= s36, s39 >= 0, s39 <= s35, 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) -{ 16 + 2*s40 + 2*s42 + 6*x_1'' + 4*x_1''^2 + 6*x_2' + 4*x_2'^2 }-> s43 :|: s40 >= 0, s40 <= x_1'', s41 >= 0, s41 <= x_2', s42 >= 0, s42 <= s40, s43 >= 0, s43 <= s42, x_1'' >= 0, x_2' >= 0, z = 1 + (1 + x_1'' + x_2') + x_2, x_2 >= 0
   encArg(z) -{ 19 + 2*s44 + 2*s46 + 6*x_11 + 4*x_11^2 + 6*x_18 + 4*x_18^2 + 6*x_2'' + 4*x_2''^2 }-> s48 :|: s44 >= 0, s44 <= x_11, s45 >= 0, s45 <= x_2'', s46 >= 0, s46 <= s44, s47 >= 0, s47 <= x_18, s48 >= 0, s48 <= s46, x_11 >= 0, z = 1 + (1 + x_11 + x_2'') + (1 + x_18), x_2'' >= 0, x_18 >= 0
   encArg(z) -{ 27 + 2*s49 + 2*s51 + 2*s52 + 6*x_11 + 4*x_11^2 + 6*x_19 + 4*x_19^2 + 6*x_2'' + 4*x_2''^2 + 6*x_25 + 4*x_25^2 }-> s55 :|: s49 >= 0, s49 <= x_11, s50 >= 0, s50 <= x_2'', s51 >= 0, s51 <= s49, s52 >= 0, s52 <= x_19, s53 >= 0, s53 <= x_25, s54 >= 0, s54 <= s52, s55 >= 0, s55 <= s51, 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) -{ 26 + 2*s56 + 2*s58 + 2*s59 + 6*x_11 + 4*x_11^2 + 6*x_110 + 4*x_110^2 + 6*x_2'' + 4*x_2''^2 + 6*x_26 + 4*x_26^2 }-> s62 :|: s56 >= 0, s56 <= x_11, s57 >= 0, s57 <= x_2'', s58 >= 0, s58 <= s56, s59 >= 0, s59 <= x_110, s60 >= 0, s60 <= x_26, s61 >= 0, s61 <= s59, s62 >= 0, s62 <= s58, 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) -{ 15 + 2*s63 + 2*s65 + 6*x_11 + 4*x_11^2 + 6*x_2'' + 4*x_2''^2 }-> s66 :|: s63 >= 0, s63 <= x_11, s64 >= 0, s64 <= x_2'', s65 >= 0, s65 <= s63, s66 >= 0, s66 <= s65, x_11 >= 0, x_2'' >= 0, x_2 >= 0, z = 1 + (1 + x_11 + x_2'') + x_2
   encArg(z) -{ 8 + 6*x_111 + 4*x_111^2 }-> s68 :|: s67 >= 0, s67 <= x_111, s68 >= 0, s68 <= 0, x_1 >= 0, z = 1 + x_1 + (1 + x_111), x_111 >= 0
   encArg(z) -{ 16 + 2*s69 + 6*x_112 + 4*x_112^2 + 6*x_27 + 4*x_27^2 }-> s72 :|: s69 >= 0, s69 <= x_112, s70 >= 0, s70 <= x_27, s71 >= 0, s71 <= s69, s72 >= 0, s72 <= 0, x_1 >= 0, x_27 >= 0, z = 1 + x_1 + (1 + x_112 + x_27), x_112 >= 0
   encArg(z) -{ 15 + 2*s73 + 6*x_113 + 4*x_113^2 + 6*x_28 + 4*x_28^2 }-> s76 :|: s73 >= 0, s73 <= x_113, s74 >= 0, s74 <= x_28, s75 >= 0, s75 <= s73, s76 >= 0, s76 <= 0, x_1 >= 0, x_113 >= 0, x_28 >= 0, z = 1 + x_1 + (1 + x_113 + x_28)
   encArg(z) -{ 13 + 2*s77 + 6*x_114 + 4*x_114^2 + 6*x_117 + 4*x_117^2 }-> s79 :|: s77 >= 0, s77 <= x_114, s78 >= 0, s78 <= x_117, s79 >= 0, s79 <= 1 + s77, z = 1 + (1 + x_114) + (1 + x_117), x_117 >= 0, x_114 >= 0
   encArg(z) -{ 14 + 2*s6 + 6*x_1' + 4*x_1'^2 + 6*x_12 + 4*x_12^2 }-> s8 :|: s6 >= 0, s6 <= x_1', s7 >= 0, s7 <= x_12, s8 >= 0, s8 <= 1 + s6, z = 1 + (1 + x_1') + (1 + x_12), x_1' >= 0, x_12 >= 0
   encArg(z) -{ 21 + 2*s80 + 2*s81 + 6*x_114 + 4*x_114^2 + 6*x_118 + 4*x_118^2 + 6*x_211 + 4*x_211^2 }-> s84 :|: s80 >= 0, s80 <= x_114, s81 >= 0, s81 <= x_118, s82 >= 0, s82 <= x_211, s83 >= 0, s83 <= s81, s84 >= 0, s84 <= 1 + s80, z = 1 + (1 + x_114) + (1 + x_118 + x_211), x_114 >= 0, x_118 >= 0, x_211 >= 0
   encArg(z) -{ 20 + 2*s85 + 2*s86 + 6*x_114 + 4*x_114^2 + 6*x_119 + 4*x_119^2 + 6*x_212 + 4*x_212^2 }-> s89 :|: s85 >= 0, s85 <= x_114, s86 >= 0, s86 <= x_119, s87 >= 0, s87 <= x_212, s88 >= 0, s88 <= s86, s89 >= 0, s89 <= 1 + s85, x_212 >= 0, x_114 >= 0, z = 1 + (1 + x_114) + (1 + x_119 + x_212), x_119 >= 0
   encArg(z) -{ 9 + 2*s90 + 6*x_114 + 4*x_114^2 }-> s91 :|: s90 >= 0, s90 <= x_114, s91 >= 0, s91 <= 1 + s90, z = 1 + (1 + x_114) + x_2, x_114 >= 0, x_2 >= 0
   encArg(z) -{ 19 + 2*s92 + 2*s94 + 6*x_115 + 4*x_115^2 + 6*x_120 + 4*x_120^2 + 6*x_29 + 4*x_29^2 }-> s96 :|: s92 >= 0, s92 <= x_115, s93 >= 0, s93 <= x_29, s94 >= 0, s94 <= s92, s95 >= 0, s95 <= x_120, s96 >= 0, s96 <= s94, 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) -{ 2 + -2*z + 4*z^2 }-> 1 + s5 :|: s5 >= 0, s5 <= z - 1, z - 1 >= 0
   encode_f(z, z') -{ 10 + 2*s148 + -2*z + 4*z^2 + -2*z' + 4*z'^2 }-> s150 :|: s148 >= 0, s148 <= z - 1, s149 >= 0, s149 <= z' - 1, s150 >= 0, s150 <= 1 + s148, z' - 1 >= 0, z - 1 >= 0
   encode_f(z, z') -{ 20 + 2*s151 + 2*s152 + 6*x_133 + 4*x_133^2 + 6*x_221 + 4*x_221^2 + -2*z + 4*z^2 }-> s155 :|: s151 >= 0, s151 <= z - 1, s152 >= 0, s152 <= x_133, s153 >= 0, s153 <= x_221, s154 >= 0, s154 <= s152, s155 >= 0, s155 <= 1 + s151, z' = 1 + x_133 + x_221, x_221 >= 0, x_133 >= 0, z - 1 >= 0
   encode_f(z, z') -{ 19 + 2*s156 + 2*s157 + 6*x_134 + 4*x_134^2 + 6*x_222 + 4*x_222^2 + -2*z + 4*z^2 }-> s160 :|: s156 >= 0, s156 <= z - 1, s157 >= 0, s157 <= x_134, s158 >= 0, s158 <= x_222, s159 >= 0, s159 <= s157, s160 >= 0, s160 <= 1 + s156, z' = 1 + x_134 + x_222, x_134 >= 0, x_222 >= 0, z - 1 >= 0
   encode_f(z, z') -{ 8 + 2*s161 + -2*z + 4*z^2 }-> s162 :|: s161 >= 0, s161 <= z - 1, s162 >= 0, s162 <= 1 + s161, z' >= 0, z - 1 >= 0
   encode_f(z, z') -{ 18 + 2*s163 + 2*s165 + 6*x_130 + 4*x_130^2 + 6*x_219 + 4*x_219^2 + -2*z' + 4*z'^2 }-> s167 :|: s163 >= 0, s163 <= x_130, s164 >= 0, s164 <= x_219, s165 >= 0, s165 <= s163, s166 >= 0, s166 <= z' - 1, s167 >= 0, s167 <= s165, x_130 >= 0, z = 1 + x_130 + x_219, z' - 1 >= 0, x_219 >= 0
   encode_f(z, z') -{ 28 + 2*s168 + 2*s170 + 2*s171 + 6*x_130 + 4*x_130^2 + 6*x_136 + 4*x_136^2 + 6*x_219 + 4*x_219^2 + 6*x_223 + 4*x_223^2 }-> s174 :|: s168 >= 0, s168 <= x_130, s169 >= 0, s169 <= x_219, s170 >= 0, s170 <= s168, s171 >= 0, s171 <= x_136, s172 >= 0, s172 <= x_223, s173 >= 0, s173 <= s171, s174 >= 0, s174 <= s170, 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_f(z, z') -{ 27 + 2*s175 + 2*s177 + 2*s178 + 6*x_130 + 4*x_130^2 + 6*x_137 + 4*x_137^2 + 6*x_219 + 4*x_219^2 + 6*x_224 + 4*x_224^2 }-> s181 :|: s175 >= 0, s175 <= x_130, s176 >= 0, s176 <= x_219, s177 >= 0, s177 <= s175, s178 >= 0, s178 <= x_137, s179 >= 0, s179 <= x_224, s180 >= 0, s180 <= s178, s181 >= 0, s181 <= s177, 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_f(z, z') -{ 16 + 2*s182 + 2*s184 + 6*x_130 + 4*x_130^2 + 6*x_219 + 4*x_219^2 }-> s185 :|: s182 >= 0, s182 <= x_130, s183 >= 0, s183 <= x_219, s184 >= 0, s184 <= s182, s185 >= 0, s185 <= s184, x_130 >= 0, z = 1 + x_130 + x_219, z' >= 0, x_219 >= 0
   encode_f(z, z') -{ 17 + 2*s186 + 2*s188 + 6*x_131 + 4*x_131^2 + 6*x_220 + 4*x_220^2 + -2*z' + 4*z'^2 }-> s190 :|: s186 >= 0, s186 <= x_131, s187 >= 0, s187 <= x_220, s188 >= 0, s188 <= s186, s189 >= 0, s189 <= z' - 1, s190 >= 0, s190 <= s188, z' - 1 >= 0, z = 1 + x_131 + x_220, x_131 >= 0, x_220 >= 0
   encode_f(z, z') -{ 27 + 2*s191 + 2*s193 + 2*s194 + 6*x_131 + 4*x_131^2 + 6*x_139 + 4*x_139^2 + 6*x_220 + 4*x_220^2 + 6*x_225 + 4*x_225^2 }-> s197 :|: s191 >= 0, s191 <= x_131, s192 >= 0, s192 <= x_220, s193 >= 0, s193 <= s191, s194 >= 0, s194 <= x_139, s195 >= 0, s195 <= x_225, s196 >= 0, s196 <= s194, s197 >= 0, s197 <= s193, 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_f(z, z') -{ 26 + 2*s198 + 2*s200 + 2*s201 + 6*x_131 + 4*x_131^2 + 6*x_140 + 4*x_140^2 + 6*x_220 + 4*x_220^2 + 6*x_226 + 4*x_226^2 }-> s204 :|: s198 >= 0, s198 <= x_131, s199 >= 0, s199 <= x_220, s200 >= 0, s200 <= s198, s201 >= 0, s201 <= x_140, s202 >= 0, s202 <= x_226, s203 >= 0, s203 <= s201, s204 >= 0, s204 <= s200, 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_f(z, z') -{ 15 + 2*s205 + 2*s207 + 6*x_131 + 4*x_131^2 + 6*x_220 + 4*x_220^2 }-> s208 :|: s205 >= 0, s205 <= x_131, s206 >= 0, s206 <= x_220, s207 >= 0, s207 <= s205, s208 >= 0, s208 <= s207, z = 1 + x_131 + x_220, z' >= 0, x_131 >= 0, x_220 >= 0
   encode_f(z, z') -{ 6 + -2*z' + 4*z'^2 }-> s210 :|: s209 >= 0, s209 <= z' - 1, s210 >= 0, s210 <= 0, z >= 0, z' - 1 >= 0
   encode_f(z, z') -{ 16 + 2*s211 + 6*x_142 + 4*x_142^2 + 6*x_227 + 4*x_227^2 }-> s214 :|: s211 >= 0, s211 <= x_142, s212 >= 0, s212 <= x_227, s213 >= 0, s213 <= s211, s214 >= 0, s214 <= 0, z >= 0, z' = 1 + x_142 + x_227, x_142 >= 0, x_227 >= 0
   encode_f(z, z') -{ 15 + 2*s215 + 6*x_143 + 4*x_143^2 + 6*x_228 + 4*x_228^2 }-> s218 :|: s215 >= 0, s215 <= x_143, s216 >= 0, s216 <= x_228, s217 >= 0, s217 <= s215, s218 >= 0, s218 <= 0, z >= 0, z' = 1 + x_143 + x_228, x_143 >= 0, x_228 >= 0
   encode_f(z, z') -{ 4 }-> s3 :|: s3 >= 0, s3 <= 0, z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_g(z, z') -{ 9 + 2*s219 + -2*z + 4*z^2 + -2*z' + 4*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') -{ 19 + 2*s222 + 2*s223 + 6*x_148 + 4*x_148^2 + 6*x_231 + 4*x_231^2 + -2*z + 4*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') -{ 18 + 2*s227 + 2*s228 + 6*x_149 + 4*x_149^2 + 6*x_232 + 4*x_232^2 + -2*z + 4*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') -{ 7 + 2*s232 + -2*z + 4*z^2 }-> s233 :|: s232 >= 0, s232 <= z - 1, s233 >= 0, s233 <= 1 + s232, z - 1 >= 0, z' >= 0
   encode_g(z, z') -{ 17 + 2*s234 + 2*s236 + 6*x_145 + 4*x_145^2 + 6*x_229 + 4*x_229^2 + -2*z' + 4*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') -{ 27 + 2*s239 + 2*s241 + 2*s242 + 6*x_145 + 4*x_145^2 + 6*x_151 + 4*x_151^2 + 6*x_229 + 4*x_229^2 + 6*x_233 + 4*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') -{ 26 + 2*s246 + 2*s248 + 2*s249 + 6*x_145 + 4*x_145^2 + 6*x_152 + 4*x_152^2 + 6*x_229 + 4*x_229^2 + 6*x_234 + 4*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') -{ 15 + 2*s253 + 2*s255 + 6*x_145 + 4*x_145^2 + 6*x_229 + 4*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') -{ 16 + 2*s257 + 2*s259 + 6*x_146 + 4*x_146^2 + 6*x_230 + 4*x_230^2 + -2*z' + 4*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') -{ 26 + 2*s262 + 2*s264 + 2*s265 + 6*x_146 + 4*x_146^2 + 6*x_154 + 4*x_154^2 + 6*x_230 + 4*x_230^2 + 6*x_235 + 4*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') -{ 25 + 2*s269 + 2*s271 + 2*s272 + 6*x_146 + 4*x_146^2 + 6*x_155 + 4*x_155^2 + 6*x_230 + 4*x_230^2 + 6*x_236 + 4*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') -{ 14 + 2*s276 + 2*s278 + 6*x_146 + 4*x_146^2 + 6*x_230 + 4*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') -{ 5 + -2*z' + 4*z'^2 }-> s281 :|: s280 >= 0, s280 <= z' - 1, s281 >= 0, s281 <= 0, z >= 0, z' - 1 >= 0
   encode_g(z, z') -{ 15 + 2*s282 + 6*x_157 + 4*x_157^2 + 6*x_237 + 4*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') -{ 14 + 2*s286 + 6*x_158 + 4*x_158^2 + 6*x_238 + 4*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') -{ 3 }-> s4 :|: s4 >= 0, s4 <= 0, z >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_h(z) -{ 0 }-> 0 :|: z >= 0
   encode_h(z) -{ 4 + 6*z + 4*z^2 }-> 1 + s290 :|: s290 >= 0, s290 <= z, z >= 0
   f(z, z') -{ 4 + 2*z }-> s :|: s >= 0, s <= z, z >= 0, z' >= 0
   g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   g(z, z') -{ 3 + 2*z }-> 1 + s' :|: s' >= 0, s' <= z - 1, z - 1 >= 0, z' >= 0
   g(z, z') -{ 2 + 2*z }-> 1 + s'' :|: s'' >= 0, s'' <= z - 1, z - 1 >= 0, z' >= 0

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

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

(41) 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: z

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

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

   encArg(z) -{ 4 }-> s1 :|: s1 >= 0, s1 <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 27 + 2*s100 + 2*s97 + 2*s99 + 6*x_115 + 4*x_115^2 + 6*x_121 + 4*x_121^2 + 6*x_213 + 4*x_213^2 + 6*x_29 + 4*x_29^2 }-> s103 :|: s97 >= 0, s97 <= x_115, s98 >= 0, s98 <= x_29, s99 >= 0, s99 <= s97, s100 >= 0, s100 <= x_121, s101 >= 0, s101 <= x_213, s102 >= 0, s102 <= s100, s103 >= 0, s103 <= s99, 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) -{ 26 + 2*s104 + 2*s106 + 2*s107 + 6*x_115 + 4*x_115^2 + 6*x_122 + 4*x_122^2 + 6*x_214 + 4*x_214^2 + 6*x_29 + 4*x_29^2 }-> s110 :|: s104 >= 0, s104 <= x_115, s105 >= 0, s105 <= x_29, s106 >= 0, s106 <= s104, s107 >= 0, s107 <= x_122, s108 >= 0, s108 <= x_214, s109 >= 0, s109 <= s107, s110 >= 0, s110 <= s106, 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) -{ 15 + 2*s111 + 2*s113 + 6*x_115 + 4*x_115^2 + 6*x_29 + 4*x_29^2 }-> s114 :|: s111 >= 0, s111 <= x_115, s112 >= 0, s112 <= x_29, s113 >= 0, s113 <= s111, s114 >= 0, s114 <= s113, x_115 >= 0, x_2 >= 0, z = 1 + (1 + x_115 + x_29) + x_2, x_29 >= 0
   encArg(z) -{ 18 + 2*s115 + 2*s117 + 6*x_116 + 4*x_116^2 + 6*x_123 + 4*x_123^2 + 6*x_210 + 4*x_210^2 }-> s119 :|: s115 >= 0, s115 <= x_116, s116 >= 0, s116 <= x_210, s117 >= 0, s117 <= s115, s118 >= 0, s118 <= x_123, s119 >= 0, s119 <= s117, x_123 >= 0, z = 1 + (1 + x_116 + x_210) + (1 + x_123), x_116 >= 0, x_210 >= 0
   encArg(z) -{ 26 + 2*s120 + 2*s122 + 2*s123 + 6*x_116 + 4*x_116^2 + 6*x_124 + 4*x_124^2 + 6*x_210 + 4*x_210^2 + 6*x_215 + 4*x_215^2 }-> s126 :|: s120 >= 0, s120 <= x_116, s121 >= 0, s121 <= x_210, s122 >= 0, s122 <= s120, s123 >= 0, s123 <= x_124, s124 >= 0, s124 <= x_215, s125 >= 0, s125 <= s123, s126 >= 0, s126 <= s122, 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) -{ 22 + 2*s10 + 2*s9 + 6*x_1' + 4*x_1'^2 + 6*x_13 + 4*x_13^2 + 6*x_21 + 4*x_21^2 }-> s13 :|: s9 >= 0, s9 <= x_1', s10 >= 0, s10 <= x_13, s11 >= 0, s11 <= x_21, s12 >= 0, s12 <= s10, s13 >= 0, s13 <= 1 + s9, x_13 >= 0, x_1' >= 0, z = 1 + (1 + x_1') + (1 + x_13 + x_21), x_21 >= 0
   encArg(z) -{ 25 + 2*s127 + 2*s129 + 2*s130 + 6*x_116 + 4*x_116^2 + 6*x_125 + 4*x_125^2 + 6*x_210 + 4*x_210^2 + 6*x_216 + 4*x_216^2 }-> s133 :|: s127 >= 0, s127 <= x_116, s128 >= 0, s128 <= x_210, s129 >= 0, s129 <= s127, s130 >= 0, s130 <= x_125, s131 >= 0, s131 <= x_216, s132 >= 0, s132 <= s130, s133 >= 0, s133 <= s129, 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) -{ 14 + 2*s134 + 2*s136 + 6*x_116 + 4*x_116^2 + 6*x_210 + 4*x_210^2 }-> s137 :|: s134 >= 0, s134 <= x_116, s135 >= 0, s135 <= x_210, s136 >= 0, s136 <= s134, s137 >= 0, s137 <= s136, x_116 >= 0, x_2 >= 0, z = 1 + (1 + x_116 + x_210) + x_2, x_210 >= 0
   encArg(z) -{ 7 + 6*x_126 + 4*x_126^2 }-> s139 :|: s138 >= 0, s138 <= x_126, s139 >= 0, s139 <= 0, x_1 >= 0, z = 1 + x_1 + (1 + x_126), x_126 >= 0
   encArg(z) -{ 15 + 2*s140 + 6*x_127 + 4*x_127^2 + 6*x_217 + 4*x_217^2 }-> s143 :|: s140 >= 0, s140 <= x_127, s141 >= 0, s141 <= x_217, s142 >= 0, s142 <= s140, s143 >= 0, s143 <= 0, x_1 >= 0, x_127 >= 0, z = 1 + x_1 + (1 + x_127 + x_217), x_217 >= 0
   encArg(z) -{ 14 + 2*s144 + 6*x_128 + 4*x_128^2 + 6*x_218 + 4*x_218^2 }-> s147 :|: s144 >= 0, s144 <= x_128, s145 >= 0, s145 <= x_218, s146 >= 0, s146 <= s144, s147 >= 0, s147 <= 0, x_1 >= 0, x_128 >= 0, z = 1 + x_1 + (1 + x_128 + x_218), x_218 >= 0
   encArg(z) -{ 21 + 2*s14 + 2*s15 + 6*x_1' + 4*x_1'^2 + 6*x_14 + 4*x_14^2 + 6*x_22 + 4*x_22^2 }-> s18 :|: s14 >= 0, s14 <= x_1', s15 >= 0, s15 <= x_14, s16 >= 0, s16 <= x_22, s17 >= 0, s17 <= s15, s18 >= 0, s18 <= 1 + s14, z = 1 + (1 + x_1') + (1 + x_14 + x_22), x_14 >= 0, x_1' >= 0, x_22 >= 0
   encArg(z) -{ 3 }-> s2 :|: s2 >= 0, s2 <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 10 + 2*s19 + 6*x_1' + 4*x_1'^2 }-> s20 :|: s19 >= 0, s19 <= x_1', s20 >= 0, s20 <= 1 + s19, x_1' >= 0, x_2 >= 0, z = 1 + (1 + x_1') + x_2
   encArg(z) -{ 20 + 2*s21 + 2*s23 + 6*x_1'' + 4*x_1''^2 + 6*x_15 + 4*x_15^2 + 6*x_2' + 4*x_2'^2 }-> s25 :|: s21 >= 0, s21 <= x_1'', s22 >= 0, s22 <= x_2', s23 >= 0, s23 <= s21, s24 >= 0, s24 <= x_15, s25 >= 0, s25 <= s23, x_15 >= 0, z = 1 + (1 + x_1'' + x_2') + (1 + x_15), x_1'' >= 0, x_2' >= 0
   encArg(z) -{ 28 + 2*s26 + 2*s28 + 2*s29 + 6*x_1'' + 4*x_1''^2 + 6*x_16 + 4*x_16^2 + 6*x_2' + 4*x_2'^2 + 6*x_23 + 4*x_23^2 }-> s32 :|: s26 >= 0, s26 <= x_1'', s27 >= 0, s27 <= x_2', s28 >= 0, s28 <= s26, s29 >= 0, s29 <= x_16, s30 >= 0, s30 <= x_23, s31 >= 0, s31 <= s29, s32 >= 0, s32 <= s28, 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) -{ 27 + 2*s33 + 2*s35 + 2*s36 + 6*x_1'' + 4*x_1''^2 + 6*x_17 + 4*x_17^2 + 6*x_2' + 4*x_2'^2 + 6*x_24 + 4*x_24^2 }-> s39 :|: s33 >= 0, s33 <= x_1'', s34 >= 0, s34 <= x_2', s35 >= 0, s35 <= s33, s36 >= 0, s36 <= x_17, s37 >= 0, s37 <= x_24, s38 >= 0, s38 <= s36, s39 >= 0, s39 <= s35, 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) -{ 16 + 2*s40 + 2*s42 + 6*x_1'' + 4*x_1''^2 + 6*x_2' + 4*x_2'^2 }-> s43 :|: s40 >= 0, s40 <= x_1'', s41 >= 0, s41 <= x_2', s42 >= 0, s42 <= s40, s43 >= 0, s43 <= s42, x_1'' >= 0, x_2' >= 0, z = 1 + (1 + x_1'' + x_2') + x_2, x_2 >= 0
   encArg(z) -{ 19 + 2*s44 + 2*s46 + 6*x_11 + 4*x_11^2 + 6*x_18 + 4*x_18^2 + 6*x_2'' + 4*x_2''^2 }-> s48 :|: s44 >= 0, s44 <= x_11, s45 >= 0, s45 <= x_2'', s46 >= 0, s46 <= s44, s47 >= 0, s47 <= x_18, s48 >= 0, s48 <= s46, x_11 >= 0, z = 1 + (1 + x_11 + x_2'') + (1 + x_18), x_2'' >= 0, x_18 >= 0
   encArg(z) -{ 27 + 2*s49 + 2*s51 + 2*s52 + 6*x_11 + 4*x_11^2 + 6*x_19 + 4*x_19^2 + 6*x_2'' + 4*x_2''^2 + 6*x_25 + 4*x_25^2 }-> s55 :|: s49 >= 0, s49 <= x_11, s50 >= 0, s50 <= x_2'', s51 >= 0, s51 <= s49, s52 >= 0, s52 <= x_19, s53 >= 0, s53 <= x_25, s54 >= 0, s54 <= s52, s55 >= 0, s55 <= s51, 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) -{ 26 + 2*s56 + 2*s58 + 2*s59 + 6*x_11 + 4*x_11^2 + 6*x_110 + 4*x_110^2 + 6*x_2'' + 4*x_2''^2 + 6*x_26 + 4*x_26^2 }-> s62 :|: s56 >= 0, s56 <= x_11, s57 >= 0, s57 <= x_2'', s58 >= 0, s58 <= s56, s59 >= 0, s59 <= x_110, s60 >= 0, s60 <= x_26, s61 >= 0, s61 <= s59, s62 >= 0, s62 <= s58, 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) -{ 15 + 2*s63 + 2*s65 + 6*x_11 + 4*x_11^2 + 6*x_2'' + 4*x_2''^2 }-> s66 :|: s63 >= 0, s63 <= x_11, s64 >= 0, s64 <= x_2'', s65 >= 0, s65 <= s63, s66 >= 0, s66 <= s65, x_11 >= 0, x_2'' >= 0, x_2 >= 0, z = 1 + (1 + x_11 + x_2'') + x_2
   encArg(z) -{ 8 + 6*x_111 + 4*x_111^2 }-> s68 :|: s67 >= 0, s67 <= x_111, s68 >= 0, s68 <= 0, x_1 >= 0, z = 1 + x_1 + (1 + x_111), x_111 >= 0
   encArg(z) -{ 16 + 2*s69 + 6*x_112 + 4*x_112^2 + 6*x_27 + 4*x_27^2 }-> s72 :|: s69 >= 0, s69 <= x_112, s70 >= 0, s70 <= x_27, s71 >= 0, s71 <= s69, s72 >= 0, s72 <= 0, x_1 >= 0, x_27 >= 0, z = 1 + x_1 + (1 + x_112 + x_27), x_112 >= 0
   encArg(z) -{ 15 + 2*s73 + 6*x_113 + 4*x_113^2 + 6*x_28 + 4*x_28^2 }-> s76 :|: s73 >= 0, s73 <= x_113, s74 >= 0, s74 <= x_28, s75 >= 0, s75 <= s73, s76 >= 0, s76 <= 0, x_1 >= 0, x_113 >= 0, x_28 >= 0, z = 1 + x_1 + (1 + x_113 + x_28)
   encArg(z) -{ 13 + 2*s77 + 6*x_114 + 4*x_114^2 + 6*x_117 + 4*x_117^2 }-> s79 :|: s77 >= 0, s77 <= x_114, s78 >= 0, s78 <= x_117, s79 >= 0, s79 <= 1 + s77, z = 1 + (1 + x_114) + (1 + x_117), x_117 >= 0, x_114 >= 0
   encArg(z) -{ 14 + 2*s6 + 6*x_1' + 4*x_1'^2 + 6*x_12 + 4*x_12^2 }-> s8 :|: s6 >= 0, s6 <= x_1', s7 >= 0, s7 <= x_12, s8 >= 0, s8 <= 1 + s6, z = 1 + (1 + x_1') + (1 + x_12), x_1' >= 0, x_12 >= 0
   encArg(z) -{ 21 + 2*s80 + 2*s81 + 6*x_114 + 4*x_114^2 + 6*x_118 + 4*x_118^2 + 6*x_211 + 4*x_211^2 }-> s84 :|: s80 >= 0, s80 <= x_114, s81 >= 0, s81 <= x_118, s82 >= 0, s82 <= x_211, s83 >= 0, s83 <= s81, s84 >= 0, s84 <= 1 + s80, z = 1 + (1 + x_114) + (1 + x_118 + x_211), x_114 >= 0, x_118 >= 0, x_211 >= 0
   encArg(z) -{ 20 + 2*s85 + 2*s86 + 6*x_114 + 4*x_114^2 + 6*x_119 + 4*x_119^2 + 6*x_212 + 4*x_212^2 }-> s89 :|: s85 >= 0, s85 <= x_114, s86 >= 0, s86 <= x_119, s87 >= 0, s87 <= x_212, s88 >= 0, s88 <= s86, s89 >= 0, s89 <= 1 + s85, x_212 >= 0, x_114 >= 0, z = 1 + (1 + x_114) + (1 + x_119 + x_212), x_119 >= 0
   encArg(z) -{ 9 + 2*s90 + 6*x_114 + 4*x_114^2 }-> s91 :|: s90 >= 0, s90 <= x_114, s91 >= 0, s91 <= 1 + s90, z = 1 + (1 + x_114) + x_2, x_114 >= 0, x_2 >= 0
   encArg(z) -{ 19 + 2*s92 + 2*s94 + 6*x_115 + 4*x_115^2 + 6*x_120 + 4*x_120^2 + 6*x_29 + 4*x_29^2 }-> s96 :|: s92 >= 0, s92 <= x_115, s93 >= 0, s93 <= x_29, s94 >= 0, s94 <= s92, s95 >= 0, s95 <= x_120, s96 >= 0, s96 <= s94, 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) -{ 2 + -2*z + 4*z^2 }-> 1 + s5 :|: s5 >= 0, s5 <= z - 1, z - 1 >= 0
   encode_f(z, z') -{ 10 + 2*s148 + -2*z + 4*z^2 + -2*z' + 4*z'^2 }-> s150 :|: s148 >= 0, s148 <= z - 1, s149 >= 0, s149 <= z' - 1, s150 >= 0, s150 <= 1 + s148, z' - 1 >= 0, z - 1 >= 0
   encode_f(z, z') -{ 20 + 2*s151 + 2*s152 + 6*x_133 + 4*x_133^2 + 6*x_221 + 4*x_221^2 + -2*z + 4*z^2 }-> s155 :|: s151 >= 0, s151 <= z - 1, s152 >= 0, s152 <= x_133, s153 >= 0, s153 <= x_221, s154 >= 0, s154 <= s152, s155 >= 0, s155 <= 1 + s151, z' = 1 + x_133 + x_221, x_221 >= 0, x_133 >= 0, z - 1 >= 0
   encode_f(z, z') -{ 19 + 2*s156 + 2*s157 + 6*x_134 + 4*x_134^2 + 6*x_222 + 4*x_222^2 + -2*z + 4*z^2 }-> s160 :|: s156 >= 0, s156 <= z - 1, s157 >= 0, s157 <= x_134, s158 >= 0, s158 <= x_222, s159 >= 0, s159 <= s157, s160 >= 0, s160 <= 1 + s156, z' = 1 + x_134 + x_222, x_134 >= 0, x_222 >= 0, z - 1 >= 0
   encode_f(z, z') -{ 8 + 2*s161 + -2*z + 4*z^2 }-> s162 :|: s161 >= 0, s161 <= z - 1, s162 >= 0, s162 <= 1 + s161, z' >= 0, z - 1 >= 0
   encode_f(z, z') -{ 18 + 2*s163 + 2*s165 + 6*x_130 + 4*x_130^2 + 6*x_219 + 4*x_219^2 + -2*z' + 4*z'^2 }-> s167 :|: s163 >= 0, s163 <= x_130, s164 >= 0, s164 <= x_219, s165 >= 0, s165 <= s163, s166 >= 0, s166 <= z' - 1, s167 >= 0, s167 <= s165, x_130 >= 0, z = 1 + x_130 + x_219, z' - 1 >= 0, x_219 >= 0
   encode_f(z, z') -{ 28 + 2*s168 + 2*s170 + 2*s171 + 6*x_130 + 4*x_130^2 + 6*x_136 + 4*x_136^2 + 6*x_219 + 4*x_219^2 + 6*x_223 + 4*x_223^2 }-> s174 :|: s168 >= 0, s168 <= x_130, s169 >= 0, s169 <= x_219, s170 >= 0, s170 <= s168, s171 >= 0, s171 <= x_136, s172 >= 0, s172 <= x_223, s173 >= 0, s173 <= s171, s174 >= 0, s174 <= s170, 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_f(z, z') -{ 27 + 2*s175 + 2*s177 + 2*s178 + 6*x_130 + 4*x_130^2 + 6*x_137 + 4*x_137^2 + 6*x_219 + 4*x_219^2 + 6*x_224 + 4*x_224^2 }-> s181 :|: s175 >= 0, s175 <= x_130, s176 >= 0, s176 <= x_219, s177 >= 0, s177 <= s175, s178 >= 0, s178 <= x_137, s179 >= 0, s179 <= x_224, s180 >= 0, s180 <= s178, s181 >= 0, s181 <= s177, 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_f(z, z') -{ 16 + 2*s182 + 2*s184 + 6*x_130 + 4*x_130^2 + 6*x_219 + 4*x_219^2 }-> s185 :|: s182 >= 0, s182 <= x_130, s183 >= 0, s183 <= x_219, s184 >= 0, s184 <= s182, s185 >= 0, s185 <= s184, x_130 >= 0, z = 1 + x_130 + x_219, z' >= 0, x_219 >= 0
   encode_f(z, z') -{ 17 + 2*s186 + 2*s188 + 6*x_131 + 4*x_131^2 + 6*x_220 + 4*x_220^2 + -2*z' + 4*z'^2 }-> s190 :|: s186 >= 0, s186 <= x_131, s187 >= 0, s187 <= x_220, s188 >= 0, s188 <= s186, s189 >= 0, s189 <= z' - 1, s190 >= 0, s190 <= s188, z' - 1 >= 0, z = 1 + x_131 + x_220, x_131 >= 0, x_220 >= 0
   encode_f(z, z') -{ 27 + 2*s191 + 2*s193 + 2*s194 + 6*x_131 + 4*x_131^2 + 6*x_139 + 4*x_139^2 + 6*x_220 + 4*x_220^2 + 6*x_225 + 4*x_225^2 }-> s197 :|: s191 >= 0, s191 <= x_131, s192 >= 0, s192 <= x_220, s193 >= 0, s193 <= s191, s194 >= 0, s194 <= x_139, s195 >= 0, s195 <= x_225, s196 >= 0, s196 <= s194, s197 >= 0, s197 <= s193, 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_f(z, z') -{ 26 + 2*s198 + 2*s200 + 2*s201 + 6*x_131 + 4*x_131^2 + 6*x_140 + 4*x_140^2 + 6*x_220 + 4*x_220^2 + 6*x_226 + 4*x_226^2 }-> s204 :|: s198 >= 0, s198 <= x_131, s199 >= 0, s199 <= x_220, s200 >= 0, s200 <= s198, s201 >= 0, s201 <= x_140, s202 >= 0, s202 <= x_226, s203 >= 0, s203 <= s201, s204 >= 0, s204 <= s200, 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_f(z, z') -{ 15 + 2*s205 + 2*s207 + 6*x_131 + 4*x_131^2 + 6*x_220 + 4*x_220^2 }-> s208 :|: s205 >= 0, s205 <= x_131, s206 >= 0, s206 <= x_220, s207 >= 0, s207 <= s205, s208 >= 0, s208 <= s207, z = 1 + x_131 + x_220, z' >= 0, x_131 >= 0, x_220 >= 0
   encode_f(z, z') -{ 6 + -2*z' + 4*z'^2 }-> s210 :|: s209 >= 0, s209 <= z' - 1, s210 >= 0, s210 <= 0, z >= 0, z' - 1 >= 0
   encode_f(z, z') -{ 16 + 2*s211 + 6*x_142 + 4*x_142^2 + 6*x_227 + 4*x_227^2 }-> s214 :|: s211 >= 0, s211 <= x_142, s212 >= 0, s212 <= x_227, s213 >= 0, s213 <= s211, s214 >= 0, s214 <= 0, z >= 0, z' = 1 + x_142 + x_227, x_142 >= 0, x_227 >= 0
   encode_f(z, z') -{ 15 + 2*s215 + 6*x_143 + 4*x_143^2 + 6*x_228 + 4*x_228^2 }-> s218 :|: s215 >= 0, s215 <= x_143, s216 >= 0, s216 <= x_228, s217 >= 0, s217 <= s215, s218 >= 0, s218 <= 0, z >= 0, z' = 1 + x_143 + x_228, x_143 >= 0, x_228 >= 0
   encode_f(z, z') -{ 4 }-> s3 :|: s3 >= 0, s3 <= 0, z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_g(z, z') -{ 9 + 2*s219 + -2*z + 4*z^2 + -2*z' + 4*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') -{ 19 + 2*s222 + 2*s223 + 6*x_148 + 4*x_148^2 + 6*x_231 + 4*x_231^2 + -2*z + 4*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') -{ 18 + 2*s227 + 2*s228 + 6*x_149 + 4*x_149^2 + 6*x_232 + 4*x_232^2 + -2*z + 4*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') -{ 7 + 2*s232 + -2*z + 4*z^2 }-> s233 :|: s232 >= 0, s232 <= z - 1, s233 >= 0, s233 <= 1 + s232, z - 1 >= 0, z' >= 0
   encode_g(z, z') -{ 17 + 2*s234 + 2*s236 + 6*x_145 + 4*x_145^2 + 6*x_229 + 4*x_229^2 + -2*z' + 4*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') -{ 27 + 2*s239 + 2*s241 + 2*s242 + 6*x_145 + 4*x_145^2 + 6*x_151 + 4*x_151^2 + 6*x_229 + 4*x_229^2 + 6*x_233 + 4*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') -{ 26 + 2*s246 + 2*s248 + 2*s249 + 6*x_145 + 4*x_145^2 + 6*x_152 + 4*x_152^2 + 6*x_229 + 4*x_229^2 + 6*x_234 + 4*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') -{ 15 + 2*s253 + 2*s255 + 6*x_145 + 4*x_145^2 + 6*x_229 + 4*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') -{ 16 + 2*s257 + 2*s259 + 6*x_146 + 4*x_146^2 + 6*x_230 + 4*x_230^2 + -2*z' + 4*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') -{ 26 + 2*s262 + 2*s264 + 2*s265 + 6*x_146 + 4*x_146^2 + 6*x_154 + 4*x_154^2 + 6*x_230 + 4*x_230^2 + 6*x_235 + 4*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') -{ 25 + 2*s269 + 2*s271 + 2*s272 + 6*x_146 + 4*x_146^2 + 6*x_155 + 4*x_155^2 + 6*x_230 + 4*x_230^2 + 6*x_236 + 4*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') -{ 14 + 2*s276 + 2*s278 + 6*x_146 + 4*x_146^2 + 6*x_230 + 4*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') -{ 5 + -2*z' + 4*z'^2 }-> s281 :|: s280 >= 0, s280 <= z' - 1, s281 >= 0, s281 <= 0, z >= 0, z' - 1 >= 0
   encode_g(z, z') -{ 15 + 2*s282 + 6*x_157 + 4*x_157^2 + 6*x_237 + 4*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') -{ 14 + 2*s286 + 6*x_158 + 4*x_158^2 + 6*x_238 + 4*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') -{ 3 }-> s4 :|: s4 >= 0, s4 <= 0, z >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_h(z) -{ 0 }-> 0 :|: z >= 0
   encode_h(z) -{ 4 + 6*z + 4*z^2 }-> 1 + s290 :|: s290 >= 0, s290 <= z, z >= 0
   f(z, z') -{ 4 + 2*z }-> s :|: s >= 0, s <= z, z >= 0, z' >= 0
   g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   g(z, z') -{ 3 + 2*z }-> 1 + s' :|: s' >= 0, s' <= z - 1, z - 1 >= 0, z' >= 0
   g(z, z') -{ 2 + 2*z }-> 1 + s'' :|: s'' >= 0, s'' <= z - 1, z - 1 >= 0, z' >= 0

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

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

(43) 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: 272 + 128*z + 80*z^2 + 112*z' + 80*z'^2

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

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

   encArg(z) -{ 4 }-> s1 :|: s1 >= 0, s1 <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 27 + 2*s100 + 2*s97 + 2*s99 + 6*x_115 + 4*x_115^2 + 6*x_121 + 4*x_121^2 + 6*x_213 + 4*x_213^2 + 6*x_29 + 4*x_29^2 }-> s103 :|: s97 >= 0, s97 <= x_115, s98 >= 0, s98 <= x_29, s99 >= 0, s99 <= s97, s100 >= 0, s100 <= x_121, s101 >= 0, s101 <= x_213, s102 >= 0, s102 <= s100, s103 >= 0, s103 <= s99, 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) -{ 26 + 2*s104 + 2*s106 + 2*s107 + 6*x_115 + 4*x_115^2 + 6*x_122 + 4*x_122^2 + 6*x_214 + 4*x_214^2 + 6*x_29 + 4*x_29^2 }-> s110 :|: s104 >= 0, s104 <= x_115, s105 >= 0, s105 <= x_29, s106 >= 0, s106 <= s104, s107 >= 0, s107 <= x_122, s108 >= 0, s108 <= x_214, s109 >= 0, s109 <= s107, s110 >= 0, s110 <= s106, 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) -{ 15 + 2*s111 + 2*s113 + 6*x_115 + 4*x_115^2 + 6*x_29 + 4*x_29^2 }-> s114 :|: s111 >= 0, s111 <= x_115, s112 >= 0, s112 <= x_29, s113 >= 0, s113 <= s111, s114 >= 0, s114 <= s113, x_115 >= 0, x_2 >= 0, z = 1 + (1 + x_115 + x_29) + x_2, x_29 >= 0
   encArg(z) -{ 18 + 2*s115 + 2*s117 + 6*x_116 + 4*x_116^2 + 6*x_123 + 4*x_123^2 + 6*x_210 + 4*x_210^2 }-> s119 :|: s115 >= 0, s115 <= x_116, s116 >= 0, s116 <= x_210, s117 >= 0, s117 <= s115, s118 >= 0, s118 <= x_123, s119 >= 0, s119 <= s117, x_123 >= 0, z = 1 + (1 + x_116 + x_210) + (1 + x_123), x_116 >= 0, x_210 >= 0
   encArg(z) -{ 26 + 2*s120 + 2*s122 + 2*s123 + 6*x_116 + 4*x_116^2 + 6*x_124 + 4*x_124^2 + 6*x_210 + 4*x_210^2 + 6*x_215 + 4*x_215^2 }-> s126 :|: s120 >= 0, s120 <= x_116, s121 >= 0, s121 <= x_210, s122 >= 0, s122 <= s120, s123 >= 0, s123 <= x_124, s124 >= 0, s124 <= x_215, s125 >= 0, s125 <= s123, s126 >= 0, s126 <= s122, 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) -{ 22 + 2*s10 + 2*s9 + 6*x_1' + 4*x_1'^2 + 6*x_13 + 4*x_13^2 + 6*x_21 + 4*x_21^2 }-> s13 :|: s9 >= 0, s9 <= x_1', s10 >= 0, s10 <= x_13, s11 >= 0, s11 <= x_21, s12 >= 0, s12 <= s10, s13 >= 0, s13 <= 1 + s9, x_13 >= 0, x_1' >= 0, z = 1 + (1 + x_1') + (1 + x_13 + x_21), x_21 >= 0
   encArg(z) -{ 25 + 2*s127 + 2*s129 + 2*s130 + 6*x_116 + 4*x_116^2 + 6*x_125 + 4*x_125^2 + 6*x_210 + 4*x_210^2 + 6*x_216 + 4*x_216^2 }-> s133 :|: s127 >= 0, s127 <= x_116, s128 >= 0, s128 <= x_210, s129 >= 0, s129 <= s127, s130 >= 0, s130 <= x_125, s131 >= 0, s131 <= x_216, s132 >= 0, s132 <= s130, s133 >= 0, s133 <= s129, 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) -{ 14 + 2*s134 + 2*s136 + 6*x_116 + 4*x_116^2 + 6*x_210 + 4*x_210^2 }-> s137 :|: s134 >= 0, s134 <= x_116, s135 >= 0, s135 <= x_210, s136 >= 0, s136 <= s134, s137 >= 0, s137 <= s136, x_116 >= 0, x_2 >= 0, z = 1 + (1 + x_116 + x_210) + x_2, x_210 >= 0
   encArg(z) -{ 7 + 6*x_126 + 4*x_126^2 }-> s139 :|: s138 >= 0, s138 <= x_126, s139 >= 0, s139 <= 0, x_1 >= 0, z = 1 + x_1 + (1 + x_126), x_126 >= 0
   encArg(z) -{ 15 + 2*s140 + 6*x_127 + 4*x_127^2 + 6*x_217 + 4*x_217^2 }-> s143 :|: s140 >= 0, s140 <= x_127, s141 >= 0, s141 <= x_217, s142 >= 0, s142 <= s140, s143 >= 0, s143 <= 0, x_1 >= 0, x_127 >= 0, z = 1 + x_1 + (1 + x_127 + x_217), x_217 >= 0
   encArg(z) -{ 14 + 2*s144 + 6*x_128 + 4*x_128^2 + 6*x_218 + 4*x_218^2 }-> s147 :|: s144 >= 0, s144 <= x_128, s145 >= 0, s145 <= x_218, s146 >= 0, s146 <= s144, s147 >= 0, s147 <= 0, x_1 >= 0, x_128 >= 0, z = 1 + x_1 + (1 + x_128 + x_218), x_218 >= 0
   encArg(z) -{ 21 + 2*s14 + 2*s15 + 6*x_1' + 4*x_1'^2 + 6*x_14 + 4*x_14^2 + 6*x_22 + 4*x_22^2 }-> s18 :|: s14 >= 0, s14 <= x_1', s15 >= 0, s15 <= x_14, s16 >= 0, s16 <= x_22, s17 >= 0, s17 <= s15, s18 >= 0, s18 <= 1 + s14, z = 1 + (1 + x_1') + (1 + x_14 + x_22), x_14 >= 0, x_1' >= 0, x_22 >= 0
   encArg(z) -{ 3 }-> s2 :|: s2 >= 0, s2 <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 10 + 2*s19 + 6*x_1' + 4*x_1'^2 }-> s20 :|: s19 >= 0, s19 <= x_1', s20 >= 0, s20 <= 1 + s19, x_1' >= 0, x_2 >= 0, z = 1 + (1 + x_1') + x_2
   encArg(z) -{ 20 + 2*s21 + 2*s23 + 6*x_1'' + 4*x_1''^2 + 6*x_15 + 4*x_15^2 + 6*x_2' + 4*x_2'^2 }-> s25 :|: s21 >= 0, s21 <= x_1'', s22 >= 0, s22 <= x_2', s23 >= 0, s23 <= s21, s24 >= 0, s24 <= x_15, s25 >= 0, s25 <= s23, x_15 >= 0, z = 1 + (1 + x_1'' + x_2') + (1 + x_15), x_1'' >= 0, x_2' >= 0
   encArg(z) -{ 28 + 2*s26 + 2*s28 + 2*s29 + 6*x_1'' + 4*x_1''^2 + 6*x_16 + 4*x_16^2 + 6*x_2' + 4*x_2'^2 + 6*x_23 + 4*x_23^2 }-> s32 :|: s26 >= 0, s26 <= x_1'', s27 >= 0, s27 <= x_2', s28 >= 0, s28 <= s26, s29 >= 0, s29 <= x_16, s30 >= 0, s30 <= x_23, s31 >= 0, s31 <= s29, s32 >= 0, s32 <= s28, 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) -{ 27 + 2*s33 + 2*s35 + 2*s36 + 6*x_1'' + 4*x_1''^2 + 6*x_17 + 4*x_17^2 + 6*x_2' + 4*x_2'^2 + 6*x_24 + 4*x_24^2 }-> s39 :|: s33 >= 0, s33 <= x_1'', s34 >= 0, s34 <= x_2', s35 >= 0, s35 <= s33, s36 >= 0, s36 <= x_17, s37 >= 0, s37 <= x_24, s38 >= 0, s38 <= s36, s39 >= 0, s39 <= s35, 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) -{ 16 + 2*s40 + 2*s42 + 6*x_1'' + 4*x_1''^2 + 6*x_2' + 4*x_2'^2 }-> s43 :|: s40 >= 0, s40 <= x_1'', s41 >= 0, s41 <= x_2', s42 >= 0, s42 <= s40, s43 >= 0, s43 <= s42, x_1'' >= 0, x_2' >= 0, z = 1 + (1 + x_1'' + x_2') + x_2, x_2 >= 0
   encArg(z) -{ 19 + 2*s44 + 2*s46 + 6*x_11 + 4*x_11^2 + 6*x_18 + 4*x_18^2 + 6*x_2'' + 4*x_2''^2 }-> s48 :|: s44 >= 0, s44 <= x_11, s45 >= 0, s45 <= x_2'', s46 >= 0, s46 <= s44, s47 >= 0, s47 <= x_18, s48 >= 0, s48 <= s46, x_11 >= 0, z = 1 + (1 + x_11 + x_2'') + (1 + x_18), x_2'' >= 0, x_18 >= 0
   encArg(z) -{ 27 + 2*s49 + 2*s51 + 2*s52 + 6*x_11 + 4*x_11^2 + 6*x_19 + 4*x_19^2 + 6*x_2'' + 4*x_2''^2 + 6*x_25 + 4*x_25^2 }-> s55 :|: s49 >= 0, s49 <= x_11, s50 >= 0, s50 <= x_2'', s51 >= 0, s51 <= s49, s52 >= 0, s52 <= x_19, s53 >= 0, s53 <= x_25, s54 >= 0, s54 <= s52, s55 >= 0, s55 <= s51, 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) -{ 26 + 2*s56 + 2*s58 + 2*s59 + 6*x_11 + 4*x_11^2 + 6*x_110 + 4*x_110^2 + 6*x_2'' + 4*x_2''^2 + 6*x_26 + 4*x_26^2 }-> s62 :|: s56 >= 0, s56 <= x_11, s57 >= 0, s57 <= x_2'', s58 >= 0, s58 <= s56, s59 >= 0, s59 <= x_110, s60 >= 0, s60 <= x_26, s61 >= 0, s61 <= s59, s62 >= 0, s62 <= s58, 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) -{ 15 + 2*s63 + 2*s65 + 6*x_11 + 4*x_11^2 + 6*x_2'' + 4*x_2''^2 }-> s66 :|: s63 >= 0, s63 <= x_11, s64 >= 0, s64 <= x_2'', s65 >= 0, s65 <= s63, s66 >= 0, s66 <= s65, x_11 >= 0, x_2'' >= 0, x_2 >= 0, z = 1 + (1 + x_11 + x_2'') + x_2
   encArg(z) -{ 8 + 6*x_111 + 4*x_111^2 }-> s68 :|: s67 >= 0, s67 <= x_111, s68 >= 0, s68 <= 0, x_1 >= 0, z = 1 + x_1 + (1 + x_111), x_111 >= 0
   encArg(z) -{ 16 + 2*s69 + 6*x_112 + 4*x_112^2 + 6*x_27 + 4*x_27^2 }-> s72 :|: s69 >= 0, s69 <= x_112, s70 >= 0, s70 <= x_27, s71 >= 0, s71 <= s69, s72 >= 0, s72 <= 0, x_1 >= 0, x_27 >= 0, z = 1 + x_1 + (1 + x_112 + x_27), x_112 >= 0
   encArg(z) -{ 15 + 2*s73 + 6*x_113 + 4*x_113^2 + 6*x_28 + 4*x_28^2 }-> s76 :|: s73 >= 0, s73 <= x_113, s74 >= 0, s74 <= x_28, s75 >= 0, s75 <= s73, s76 >= 0, s76 <= 0, x_1 >= 0, x_113 >= 0, x_28 >= 0, z = 1 + x_1 + (1 + x_113 + x_28)
   encArg(z) -{ 13 + 2*s77 + 6*x_114 + 4*x_114^2 + 6*x_117 + 4*x_117^2 }-> s79 :|: s77 >= 0, s77 <= x_114, s78 >= 0, s78 <= x_117, s79 >= 0, s79 <= 1 + s77, z = 1 + (1 + x_114) + (1 + x_117), x_117 >= 0, x_114 >= 0
   encArg(z) -{ 14 + 2*s6 + 6*x_1' + 4*x_1'^2 + 6*x_12 + 4*x_12^2 }-> s8 :|: s6 >= 0, s6 <= x_1', s7 >= 0, s7 <= x_12, s8 >= 0, s8 <= 1 + s6, z = 1 + (1 + x_1') + (1 + x_12), x_1' >= 0, x_12 >= 0
   encArg(z) -{ 21 + 2*s80 + 2*s81 + 6*x_114 + 4*x_114^2 + 6*x_118 + 4*x_118^2 + 6*x_211 + 4*x_211^2 }-> s84 :|: s80 >= 0, s80 <= x_114, s81 >= 0, s81 <= x_118, s82 >= 0, s82 <= x_211, s83 >= 0, s83 <= s81, s84 >= 0, s84 <= 1 + s80, z = 1 + (1 + x_114) + (1 + x_118 + x_211), x_114 >= 0, x_118 >= 0, x_211 >= 0
   encArg(z) -{ 20 + 2*s85 + 2*s86 + 6*x_114 + 4*x_114^2 + 6*x_119 + 4*x_119^2 + 6*x_212 + 4*x_212^2 }-> s89 :|: s85 >= 0, s85 <= x_114, s86 >= 0, s86 <= x_119, s87 >= 0, s87 <= x_212, s88 >= 0, s88 <= s86, s89 >= 0, s89 <= 1 + s85, x_212 >= 0, x_114 >= 0, z = 1 + (1 + x_114) + (1 + x_119 + x_212), x_119 >= 0
   encArg(z) -{ 9 + 2*s90 + 6*x_114 + 4*x_114^2 }-> s91 :|: s90 >= 0, s90 <= x_114, s91 >= 0, s91 <= 1 + s90, z = 1 + (1 + x_114) + x_2, x_114 >= 0, x_2 >= 0
   encArg(z) -{ 19 + 2*s92 + 2*s94 + 6*x_115 + 4*x_115^2 + 6*x_120 + 4*x_120^2 + 6*x_29 + 4*x_29^2 }-> s96 :|: s92 >= 0, s92 <= x_115, s93 >= 0, s93 <= x_29, s94 >= 0, s94 <= s92, s95 >= 0, s95 <= x_120, s96 >= 0, s96 <= s94, 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) -{ 2 + -2*z + 4*z^2 }-> 1 + s5 :|: s5 >= 0, s5 <= z - 1, z - 1 >= 0
   encode_f(z, z') -{ 10 + 2*s148 + -2*z + 4*z^2 + -2*z' + 4*z'^2 }-> s150 :|: s148 >= 0, s148 <= z - 1, s149 >= 0, s149 <= z' - 1, s150 >= 0, s150 <= 1 + s148, z' - 1 >= 0, z - 1 >= 0
   encode_f(z, z') -{ 20 + 2*s151 + 2*s152 + 6*x_133 + 4*x_133^2 + 6*x_221 + 4*x_221^2 + -2*z + 4*z^2 }-> s155 :|: s151 >= 0, s151 <= z - 1, s152 >= 0, s152 <= x_133, s153 >= 0, s153 <= x_221, s154 >= 0, s154 <= s152, s155 >= 0, s155 <= 1 + s151, z' = 1 + x_133 + x_221, x_221 >= 0, x_133 >= 0, z - 1 >= 0
   encode_f(z, z') -{ 19 + 2*s156 + 2*s157 + 6*x_134 + 4*x_134^2 + 6*x_222 + 4*x_222^2 + -2*z + 4*z^2 }-> s160 :|: s156 >= 0, s156 <= z - 1, s157 >= 0, s157 <= x_134, s158 >= 0, s158 <= x_222, s159 >= 0, s159 <= s157, s160 >= 0, s160 <= 1 + s156, z' = 1 + x_134 + x_222, x_134 >= 0, x_222 >= 0, z - 1 >= 0
   encode_f(z, z') -{ 8 + 2*s161 + -2*z + 4*z^2 }-> s162 :|: s161 >= 0, s161 <= z - 1, s162 >= 0, s162 <= 1 + s161, z' >= 0, z - 1 >= 0
   encode_f(z, z') -{ 18 + 2*s163 + 2*s165 + 6*x_130 + 4*x_130^2 + 6*x_219 + 4*x_219^2 + -2*z' + 4*z'^2 }-> s167 :|: s163 >= 0, s163 <= x_130, s164 >= 0, s164 <= x_219, s165 >= 0, s165 <= s163, s166 >= 0, s166 <= z' - 1, s167 >= 0, s167 <= s165, x_130 >= 0, z = 1 + x_130 + x_219, z' - 1 >= 0, x_219 >= 0
   encode_f(z, z') -{ 28 + 2*s168 + 2*s170 + 2*s171 + 6*x_130 + 4*x_130^2 + 6*x_136 + 4*x_136^2 + 6*x_219 + 4*x_219^2 + 6*x_223 + 4*x_223^2 }-> s174 :|: s168 >= 0, s168 <= x_130, s169 >= 0, s169 <= x_219, s170 >= 0, s170 <= s168, s171 >= 0, s171 <= x_136, s172 >= 0, s172 <= x_223, s173 >= 0, s173 <= s171, s174 >= 0, s174 <= s170, 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_f(z, z') -{ 27 + 2*s175 + 2*s177 + 2*s178 + 6*x_130 + 4*x_130^2 + 6*x_137 + 4*x_137^2 + 6*x_219 + 4*x_219^2 + 6*x_224 + 4*x_224^2 }-> s181 :|: s175 >= 0, s175 <= x_130, s176 >= 0, s176 <= x_219, s177 >= 0, s177 <= s175, s178 >= 0, s178 <= x_137, s179 >= 0, s179 <= x_224, s180 >= 0, s180 <= s178, s181 >= 0, s181 <= s177, 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_f(z, z') -{ 16 + 2*s182 + 2*s184 + 6*x_130 + 4*x_130^2 + 6*x_219 + 4*x_219^2 }-> s185 :|: s182 >= 0, s182 <= x_130, s183 >= 0, s183 <= x_219, s184 >= 0, s184 <= s182, s185 >= 0, s185 <= s184, x_130 >= 0, z = 1 + x_130 + x_219, z' >= 0, x_219 >= 0
   encode_f(z, z') -{ 17 + 2*s186 + 2*s188 + 6*x_131 + 4*x_131^2 + 6*x_220 + 4*x_220^2 + -2*z' + 4*z'^2 }-> s190 :|: s186 >= 0, s186 <= x_131, s187 >= 0, s187 <= x_220, s188 >= 0, s188 <= s186, s189 >= 0, s189 <= z' - 1, s190 >= 0, s190 <= s188, z' - 1 >= 0, z = 1 + x_131 + x_220, x_131 >= 0, x_220 >= 0
   encode_f(z, z') -{ 27 + 2*s191 + 2*s193 + 2*s194 + 6*x_131 + 4*x_131^2 + 6*x_139 + 4*x_139^2 + 6*x_220 + 4*x_220^2 + 6*x_225 + 4*x_225^2 }-> s197 :|: s191 >= 0, s191 <= x_131, s192 >= 0, s192 <= x_220, s193 >= 0, s193 <= s191, s194 >= 0, s194 <= x_139, s195 >= 0, s195 <= x_225, s196 >= 0, s196 <= s194, s197 >= 0, s197 <= s193, 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_f(z, z') -{ 26 + 2*s198 + 2*s200 + 2*s201 + 6*x_131 + 4*x_131^2 + 6*x_140 + 4*x_140^2 + 6*x_220 + 4*x_220^2 + 6*x_226 + 4*x_226^2 }-> s204 :|: s198 >= 0, s198 <= x_131, s199 >= 0, s199 <= x_220, s200 >= 0, s200 <= s198, s201 >= 0, s201 <= x_140, s202 >= 0, s202 <= x_226, s203 >= 0, s203 <= s201, s204 >= 0, s204 <= s200, 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_f(z, z') -{ 15 + 2*s205 + 2*s207 + 6*x_131 + 4*x_131^2 + 6*x_220 + 4*x_220^2 }-> s208 :|: s205 >= 0, s205 <= x_131, s206 >= 0, s206 <= x_220, s207 >= 0, s207 <= s205, s208 >= 0, s208 <= s207, z = 1 + x_131 + x_220, z' >= 0, x_131 >= 0, x_220 >= 0
   encode_f(z, z') -{ 6 + -2*z' + 4*z'^2 }-> s210 :|: s209 >= 0, s209 <= z' - 1, s210 >= 0, s210 <= 0, z >= 0, z' - 1 >= 0
   encode_f(z, z') -{ 16 + 2*s211 + 6*x_142 + 4*x_142^2 + 6*x_227 + 4*x_227^2 }-> s214 :|: s211 >= 0, s211 <= x_142, s212 >= 0, s212 <= x_227, s213 >= 0, s213 <= s211, s214 >= 0, s214 <= 0, z >= 0, z' = 1 + x_142 + x_227, x_142 >= 0, x_227 >= 0
   encode_f(z, z') -{ 15 + 2*s215 + 6*x_143 + 4*x_143^2 + 6*x_228 + 4*x_228^2 }-> s218 :|: s215 >= 0, s215 <= x_143, s216 >= 0, s216 <= x_228, s217 >= 0, s217 <= s215, s218 >= 0, s218 <= 0, z >= 0, z' = 1 + x_143 + x_228, x_143 >= 0, x_228 >= 0
   encode_f(z, z') -{ 4 }-> s3 :|: s3 >= 0, s3 <= 0, z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_g(z, z') -{ 9 + 2*s219 + -2*z + 4*z^2 + -2*z' + 4*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') -{ 19 + 2*s222 + 2*s223 + 6*x_148 + 4*x_148^2 + 6*x_231 + 4*x_231^2 + -2*z + 4*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') -{ 18 + 2*s227 + 2*s228 + 6*x_149 + 4*x_149^2 + 6*x_232 + 4*x_232^2 + -2*z + 4*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') -{ 7 + 2*s232 + -2*z + 4*z^2 }-> s233 :|: s232 >= 0, s232 <= z - 1, s233 >= 0, s233 <= 1 + s232, z - 1 >= 0, z' >= 0
   encode_g(z, z') -{ 17 + 2*s234 + 2*s236 + 6*x_145 + 4*x_145^2 + 6*x_229 + 4*x_229^2 + -2*z' + 4*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') -{ 27 + 2*s239 + 2*s241 + 2*s242 + 6*x_145 + 4*x_145^2 + 6*x_151 + 4*x_151^2 + 6*x_229 + 4*x_229^2 + 6*x_233 + 4*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') -{ 26 + 2*s246 + 2*s248 + 2*s249 + 6*x_145 + 4*x_145^2 + 6*x_152 + 4*x_152^2 + 6*x_229 + 4*x_229^2 + 6*x_234 + 4*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') -{ 15 + 2*s253 + 2*s255 + 6*x_145 + 4*x_145^2 + 6*x_229 + 4*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') -{ 16 + 2*s257 + 2*s259 + 6*x_146 + 4*x_146^2 + 6*x_230 + 4*x_230^2 + -2*z' + 4*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') -{ 26 + 2*s262 + 2*s264 + 2*s265 + 6*x_146 + 4*x_146^2 + 6*x_154 + 4*x_154^2 + 6*x_230 + 4*x_230^2 + 6*x_235 + 4*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') -{ 25 + 2*s269 + 2*s271 + 2*s272 + 6*x_146 + 4*x_146^2 + 6*x_155 + 4*x_155^2 + 6*x_230 + 4*x_230^2 + 6*x_236 + 4*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') -{ 14 + 2*s276 + 2*s278 + 6*x_146 + 4*x_146^2 + 6*x_230 + 4*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') -{ 5 + -2*z' + 4*z'^2 }-> s281 :|: s280 >= 0, s280 <= z' - 1, s281 >= 0, s281 <= 0, z >= 0, z' - 1 >= 0
   encode_g(z, z') -{ 15 + 2*s282 + 6*x_157 + 4*x_157^2 + 6*x_237 + 4*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') -{ 14 + 2*s286 + 6*x_158 + 4*x_158^2 + 6*x_238 + 4*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') -{ 3 }-> s4 :|: s4 >= 0, s4 <= 0, z >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_h(z) -{ 0 }-> 0 :|: z >= 0
   encode_h(z) -{ 4 + 6*z + 4*z^2 }-> 1 + s290 :|: s290 >= 0, s290 <= z, z >= 0
   f(z, z') -{ 4 + 2*z }-> s :|: s >= 0, s <= z, z >= 0, z' >= 0
   g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   g(z, z') -{ 3 + 2*z }-> 1 + s' :|: s' >= 0, s' <= z - 1, z - 1 >= 0, z' >= 0
   g(z, z') -{ 2 + 2*z }-> 1 + s'' :|: s'' >= 0, s'' <= z - 1, z - 1 >= 0, z' >= 0

Function symbols to be analyzed: {encode_g}
Previous analysis results are:
  f: runtime: O(n^1) [4 + 2*z], size: O(n^1) [z]
  g: runtime: O(n^1) [3 + 2*z], size: O(n^1) [z]
  encArg: runtime: O(n^2) [4 + 6*z + 4*z^2], size: O(n^1) [z]
  encode_h: runtime: O(n^2) [4 + 6*z + 4*z^2], size: O(n^1) [1 + z]
  encode_f: runtime: O(n^2) [272 + 128*z + 80*z^2 + 112*z' + 80*z'^2], size: O(n^1) [z]

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

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

   encArg(z) -{ 4 }-> s1 :|: s1 >= 0, s1 <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 27 + 2*s100 + 2*s97 + 2*s99 + 6*x_115 + 4*x_115^2 + 6*x_121 + 4*x_121^2 + 6*x_213 + 4*x_213^2 + 6*x_29 + 4*x_29^2 }-> s103 :|: s97 >= 0, s97 <= x_115, s98 >= 0, s98 <= x_29, s99 >= 0, s99 <= s97, s100 >= 0, s100 <= x_121, s101 >= 0, s101 <= x_213, s102 >= 0, s102 <= s100, s103 >= 0, s103 <= s99, 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) -{ 26 + 2*s104 + 2*s106 + 2*s107 + 6*x_115 + 4*x_115^2 + 6*x_122 + 4*x_122^2 + 6*x_214 + 4*x_214^2 + 6*x_29 + 4*x_29^2 }-> s110 :|: s104 >= 0, s104 <= x_115, s105 >= 0, s105 <= x_29, s106 >= 0, s106 <= s104, s107 >= 0, s107 <= x_122, s108 >= 0, s108 <= x_214, s109 >= 0, s109 <= s107, s110 >= 0, s110 <= s106, 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) -{ 15 + 2*s111 + 2*s113 + 6*x_115 + 4*x_115^2 + 6*x_29 + 4*x_29^2 }-> s114 :|: s111 >= 0, s111 <= x_115, s112 >= 0, s112 <= x_29, s113 >= 0, s113 <= s111, s114 >= 0, s114 <= s113, x_115 >= 0, x_2 >= 0, z = 1 + (1 + x_115 + x_29) + x_2, x_29 >= 0
   encArg(z) -{ 18 + 2*s115 + 2*s117 + 6*x_116 + 4*x_116^2 + 6*x_123 + 4*x_123^2 + 6*x_210 + 4*x_210^2 }-> s119 :|: s115 >= 0, s115 <= x_116, s116 >= 0, s116 <= x_210, s117 >= 0, s117 <= s115, s118 >= 0, s118 <= x_123, s119 >= 0, s119 <= s117, x_123 >= 0, z = 1 + (1 + x_116 + x_210) + (1 + x_123), x_116 >= 0, x_210 >= 0
   encArg(z) -{ 26 + 2*s120 + 2*s122 + 2*s123 + 6*x_116 + 4*x_116^2 + 6*x_124 + 4*x_124^2 + 6*x_210 + 4*x_210^2 + 6*x_215 + 4*x_215^2 }-> s126 :|: s120 >= 0, s120 <= x_116, s121 >= 0, s121 <= x_210, s122 >= 0, s122 <= s120, s123 >= 0, s123 <= x_124, s124 >= 0, s124 <= x_215, s125 >= 0, s125 <= s123, s126 >= 0, s126 <= s122, 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) -{ 22 + 2*s10 + 2*s9 + 6*x_1' + 4*x_1'^2 + 6*x_13 + 4*x_13^2 + 6*x_21 + 4*x_21^2 }-> s13 :|: s9 >= 0, s9 <= x_1', s10 >= 0, s10 <= x_13, s11 >= 0, s11 <= x_21, s12 >= 0, s12 <= s10, s13 >= 0, s13 <= 1 + s9, x_13 >= 0, x_1' >= 0, z = 1 + (1 + x_1') + (1 + x_13 + x_21), x_21 >= 0
   encArg(z) -{ 25 + 2*s127 + 2*s129 + 2*s130 + 6*x_116 + 4*x_116^2 + 6*x_125 + 4*x_125^2 + 6*x_210 + 4*x_210^2 + 6*x_216 + 4*x_216^2 }-> s133 :|: s127 >= 0, s127 <= x_116, s128 >= 0, s128 <= x_210, s129 >= 0, s129 <= s127, s130 >= 0, s130 <= x_125, s131 >= 0, s131 <= x_216, s132 >= 0, s132 <= s130, s133 >= 0, s133 <= s129, 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) -{ 14 + 2*s134 + 2*s136 + 6*x_116 + 4*x_116^2 + 6*x_210 + 4*x_210^2 }-> s137 :|: s134 >= 0, s134 <= x_116, s135 >= 0, s135 <= x_210, s136 >= 0, s136 <= s134, s137 >= 0, s137 <= s136, x_116 >= 0, x_2 >= 0, z = 1 + (1 + x_116 + x_210) + x_2, x_210 >= 0
   encArg(z) -{ 7 + 6*x_126 + 4*x_126^2 }-> s139 :|: s138 >= 0, s138 <= x_126, s139 >= 0, s139 <= 0, x_1 >= 0, z = 1 + x_1 + (1 + x_126), x_126 >= 0
   encArg(z) -{ 15 + 2*s140 + 6*x_127 + 4*x_127^2 + 6*x_217 + 4*x_217^2 }-> s143 :|: s140 >= 0, s140 <= x_127, s141 >= 0, s141 <= x_217, s142 >= 0, s142 <= s140, s143 >= 0, s143 <= 0, x_1 >= 0, x_127 >= 0, z = 1 + x_1 + (1 + x_127 + x_217), x_217 >= 0
   encArg(z) -{ 14 + 2*s144 + 6*x_128 + 4*x_128^2 + 6*x_218 + 4*x_218^2 }-> s147 :|: s144 >= 0, s144 <= x_128, s145 >= 0, s145 <= x_218, s146 >= 0, s146 <= s144, s147 >= 0, s147 <= 0, x_1 >= 0, x_128 >= 0, z = 1 + x_1 + (1 + x_128 + x_218), x_218 >= 0
   encArg(z) -{ 21 + 2*s14 + 2*s15 + 6*x_1' + 4*x_1'^2 + 6*x_14 + 4*x_14^2 + 6*x_22 + 4*x_22^2 }-> s18 :|: s14 >= 0, s14 <= x_1', s15 >= 0, s15 <= x_14, s16 >= 0, s16 <= x_22, s17 >= 0, s17 <= s15, s18 >= 0, s18 <= 1 + s14, z = 1 + (1 + x_1') + (1 + x_14 + x_22), x_14 >= 0, x_1' >= 0, x_22 >= 0
   encArg(z) -{ 3 }-> s2 :|: s2 >= 0, s2 <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 10 + 2*s19 + 6*x_1' + 4*x_1'^2 }-> s20 :|: s19 >= 0, s19 <= x_1', s20 >= 0, s20 <= 1 + s19, x_1' >= 0, x_2 >= 0, z = 1 + (1 + x_1') + x_2
   encArg(z) -{ 20 + 2*s21 + 2*s23 + 6*x_1'' + 4*x_1''^2 + 6*x_15 + 4*x_15^2 + 6*x_2' + 4*x_2'^2 }-> s25 :|: s21 >= 0, s21 <= x_1'', s22 >= 0, s22 <= x_2', s23 >= 0, s23 <= s21, s24 >= 0, s24 <= x_15, s25 >= 0, s25 <= s23, x_15 >= 0, z = 1 + (1 + x_1'' + x_2') + (1 + x_15), x_1'' >= 0, x_2' >= 0
   encArg(z) -{ 28 + 2*s26 + 2*s28 + 2*s29 + 6*x_1'' + 4*x_1''^2 + 6*x_16 + 4*x_16^2 + 6*x_2' + 4*x_2'^2 + 6*x_23 + 4*x_23^2 }-> s32 :|: s26 >= 0, s26 <= x_1'', s27 >= 0, s27 <= x_2', s28 >= 0, s28 <= s26, s29 >= 0, s29 <= x_16, s30 >= 0, s30 <= x_23, s31 >= 0, s31 <= s29, s32 >= 0, s32 <= s28, 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) -{ 27 + 2*s33 + 2*s35 + 2*s36 + 6*x_1'' + 4*x_1''^2 + 6*x_17 + 4*x_17^2 + 6*x_2' + 4*x_2'^2 + 6*x_24 + 4*x_24^2 }-> s39 :|: s33 >= 0, s33 <= x_1'', s34 >= 0, s34 <= x_2', s35 >= 0, s35 <= s33, s36 >= 0, s36 <= x_17, s37 >= 0, s37 <= x_24, s38 >= 0, s38 <= s36, s39 >= 0, s39 <= s35, 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) -{ 16 + 2*s40 + 2*s42 + 6*x_1'' + 4*x_1''^2 + 6*x_2' + 4*x_2'^2 }-> s43 :|: s40 >= 0, s40 <= x_1'', s41 >= 0, s41 <= x_2', s42 >= 0, s42 <= s40, s43 >= 0, s43 <= s42, x_1'' >= 0, x_2' >= 0, z = 1 + (1 + x_1'' + x_2') + x_2, x_2 >= 0
   encArg(z) -{ 19 + 2*s44 + 2*s46 + 6*x_11 + 4*x_11^2 + 6*x_18 + 4*x_18^2 + 6*x_2'' + 4*x_2''^2 }-> s48 :|: s44 >= 0, s44 <= x_11, s45 >= 0, s45 <= x_2'', s46 >= 0, s46 <= s44, s47 >= 0, s47 <= x_18, s48 >= 0, s48 <= s46, x_11 >= 0, z = 1 + (1 + x_11 + x_2'') + (1 + x_18), x_2'' >= 0, x_18 >= 0
   encArg(z) -{ 27 + 2*s49 + 2*s51 + 2*s52 + 6*x_11 + 4*x_11^2 + 6*x_19 + 4*x_19^2 + 6*x_2'' + 4*x_2''^2 + 6*x_25 + 4*x_25^2 }-> s55 :|: s49 >= 0, s49 <= x_11, s50 >= 0, s50 <= x_2'', s51 >= 0, s51 <= s49, s52 >= 0, s52 <= x_19, s53 >= 0, s53 <= x_25, s54 >= 0, s54 <= s52, s55 >= 0, s55 <= s51, 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) -{ 26 + 2*s56 + 2*s58 + 2*s59 + 6*x_11 + 4*x_11^2 + 6*x_110 + 4*x_110^2 + 6*x_2'' + 4*x_2''^2 + 6*x_26 + 4*x_26^2 }-> s62 :|: s56 >= 0, s56 <= x_11, s57 >= 0, s57 <= x_2'', s58 >= 0, s58 <= s56, s59 >= 0, s59 <= x_110, s60 >= 0, s60 <= x_26, s61 >= 0, s61 <= s59, s62 >= 0, s62 <= s58, 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) -{ 15 + 2*s63 + 2*s65 + 6*x_11 + 4*x_11^2 + 6*x_2'' + 4*x_2''^2 }-> s66 :|: s63 >= 0, s63 <= x_11, s64 >= 0, s64 <= x_2'', s65 >= 0, s65 <= s63, s66 >= 0, s66 <= s65, x_11 >= 0, x_2'' >= 0, x_2 >= 0, z = 1 + (1 + x_11 + x_2'') + x_2
   encArg(z) -{ 8 + 6*x_111 + 4*x_111^2 }-> s68 :|: s67 >= 0, s67 <= x_111, s68 >= 0, s68 <= 0, x_1 >= 0, z = 1 + x_1 + (1 + x_111), x_111 >= 0
   encArg(z) -{ 16 + 2*s69 + 6*x_112 + 4*x_112^2 + 6*x_27 + 4*x_27^2 }-> s72 :|: s69 >= 0, s69 <= x_112, s70 >= 0, s70 <= x_27, s71 >= 0, s71 <= s69, s72 >= 0, s72 <= 0, x_1 >= 0, x_27 >= 0, z = 1 + x_1 + (1 + x_112 + x_27), x_112 >= 0
   encArg(z) -{ 15 + 2*s73 + 6*x_113 + 4*x_113^2 + 6*x_28 + 4*x_28^2 }-> s76 :|: s73 >= 0, s73 <= x_113, s74 >= 0, s74 <= x_28, s75 >= 0, s75 <= s73, s76 >= 0, s76 <= 0, x_1 >= 0, x_113 >= 0, x_28 >= 0, z = 1 + x_1 + (1 + x_113 + x_28)
   encArg(z) -{ 13 + 2*s77 + 6*x_114 + 4*x_114^2 + 6*x_117 + 4*x_117^2 }-> s79 :|: s77 >= 0, s77 <= x_114, s78 >= 0, s78 <= x_117, s79 >= 0, s79 <= 1 + s77, z = 1 + (1 + x_114) + (1 + x_117), x_117 >= 0, x_114 >= 0
   encArg(z) -{ 14 + 2*s6 + 6*x_1' + 4*x_1'^2 + 6*x_12 + 4*x_12^2 }-> s8 :|: s6 >= 0, s6 <= x_1', s7 >= 0, s7 <= x_12, s8 >= 0, s8 <= 1 + s6, z = 1 + (1 + x_1') + (1 + x_12), x_1' >= 0, x_12 >= 0
   encArg(z) -{ 21 + 2*s80 + 2*s81 + 6*x_114 + 4*x_114^2 + 6*x_118 + 4*x_118^2 + 6*x_211 + 4*x_211^2 }-> s84 :|: s80 >= 0, s80 <= x_114, s81 >= 0, s81 <= x_118, s82 >= 0, s82 <= x_211, s83 >= 0, s83 <= s81, s84 >= 0, s84 <= 1 + s80, z = 1 + (1 + x_114) + (1 + x_118 + x_211), x_114 >= 0, x_118 >= 0, x_211 >= 0
   encArg(z) -{ 20 + 2*s85 + 2*s86 + 6*x_114 + 4*x_114^2 + 6*x_119 + 4*x_119^2 + 6*x_212 + 4*x_212^2 }-> s89 :|: s85 >= 0, s85 <= x_114, s86 >= 0, s86 <= x_119, s87 >= 0, s87 <= x_212, s88 >= 0, s88 <= s86, s89 >= 0, s89 <= 1 + s85, x_212 >= 0, x_114 >= 0, z = 1 + (1 + x_114) + (1 + x_119 + x_212), x_119 >= 0
   encArg(z) -{ 9 + 2*s90 + 6*x_114 + 4*x_114^2 }-> s91 :|: s90 >= 0, s90 <= x_114, s91 >= 0, s91 <= 1 + s90, z = 1 + (1 + x_114) + x_2, x_114 >= 0, x_2 >= 0
   encArg(z) -{ 19 + 2*s92 + 2*s94 + 6*x_115 + 4*x_115^2 + 6*x_120 + 4*x_120^2 + 6*x_29 + 4*x_29^2 }-> s96 :|: s92 >= 0, s92 <= x_115, s93 >= 0, s93 <= x_29, s94 >= 0, s94 <= s92, s95 >= 0, s95 <= x_120, s96 >= 0, s96 <= s94, 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) -{ 2 + -2*z + 4*z^2 }-> 1 + s5 :|: s5 >= 0, s5 <= z - 1, z - 1 >= 0
   encode_f(z, z') -{ 10 + 2*s148 + -2*z + 4*z^2 + -2*z' + 4*z'^2 }-> s150 :|: s148 >= 0, s148 <= z - 1, s149 >= 0, s149 <= z' - 1, s150 >= 0, s150 <= 1 + s148, z' - 1 >= 0, z - 1 >= 0
   encode_f(z, z') -{ 20 + 2*s151 + 2*s152 + 6*x_133 + 4*x_133^2 + 6*x_221 + 4*x_221^2 + -2*z + 4*z^2 }-> s155 :|: s151 >= 0, s151 <= z - 1, s152 >= 0, s152 <= x_133, s153 >= 0, s153 <= x_221, s154 >= 0, s154 <= s152, s155 >= 0, s155 <= 1 + s151, z' = 1 + x_133 + x_221, x_221 >= 0, x_133 >= 0, z - 1 >= 0
   encode_f(z, z') -{ 19 + 2*s156 + 2*s157 + 6*x_134 + 4*x_134^2 + 6*x_222 + 4*x_222^2 + -2*z + 4*z^2 }-> s160 :|: s156 >= 0, s156 <= z - 1, s157 >= 0, s157 <= x_134, s158 >= 0, s158 <= x_222, s159 >= 0, s159 <= s157, s160 >= 0, s160 <= 1 + s156, z' = 1 + x_134 + x_222, x_134 >= 0, x_222 >= 0, z - 1 >= 0
   encode_f(z, z') -{ 8 + 2*s161 + -2*z + 4*z^2 }-> s162 :|: s161 >= 0, s161 <= z - 1, s162 >= 0, s162 <= 1 + s161, z' >= 0, z - 1 >= 0
   encode_f(z, z') -{ 18 + 2*s163 + 2*s165 + 6*x_130 + 4*x_130^2 + 6*x_219 + 4*x_219^2 + -2*z' + 4*z'^2 }-> s167 :|: s163 >= 0, s163 <= x_130, s164 >= 0, s164 <= x_219, s165 >= 0, s165 <= s163, s166 >= 0, s166 <= z' - 1, s167 >= 0, s167 <= s165, x_130 >= 0, z = 1 + x_130 + x_219, z' - 1 >= 0, x_219 >= 0
   encode_f(z, z') -{ 28 + 2*s168 + 2*s170 + 2*s171 + 6*x_130 + 4*x_130^2 + 6*x_136 + 4*x_136^2 + 6*x_219 + 4*x_219^2 + 6*x_223 + 4*x_223^2 }-> s174 :|: s168 >= 0, s168 <= x_130, s169 >= 0, s169 <= x_219, s170 >= 0, s170 <= s168, s171 >= 0, s171 <= x_136, s172 >= 0, s172 <= x_223, s173 >= 0, s173 <= s171, s174 >= 0, s174 <= s170, 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_f(z, z') -{ 27 + 2*s175 + 2*s177 + 2*s178 + 6*x_130 + 4*x_130^2 + 6*x_137 + 4*x_137^2 + 6*x_219 + 4*x_219^2 + 6*x_224 + 4*x_224^2 }-> s181 :|: s175 >= 0, s175 <= x_130, s176 >= 0, s176 <= x_219, s177 >= 0, s177 <= s175, s178 >= 0, s178 <= x_137, s179 >= 0, s179 <= x_224, s180 >= 0, s180 <= s178, s181 >= 0, s181 <= s177, 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_f(z, z') -{ 16 + 2*s182 + 2*s184 + 6*x_130 + 4*x_130^2 + 6*x_219 + 4*x_219^2 }-> s185 :|: s182 >= 0, s182 <= x_130, s183 >= 0, s183 <= x_219, s184 >= 0, s184 <= s182, s185 >= 0, s185 <= s184, x_130 >= 0, z = 1 + x_130 + x_219, z' >= 0, x_219 >= 0
   encode_f(z, z') -{ 17 + 2*s186 + 2*s188 + 6*x_131 + 4*x_131^2 + 6*x_220 + 4*x_220^2 + -2*z' + 4*z'^2 }-> s190 :|: s186 >= 0, s186 <= x_131, s187 >= 0, s187 <= x_220, s188 >= 0, s188 <= s186, s189 >= 0, s189 <= z' - 1, s190 >= 0, s190 <= s188, z' - 1 >= 0, z = 1 + x_131 + x_220, x_131 >= 0, x_220 >= 0
   encode_f(z, z') -{ 27 + 2*s191 + 2*s193 + 2*s194 + 6*x_131 + 4*x_131^2 + 6*x_139 + 4*x_139^2 + 6*x_220 + 4*x_220^2 + 6*x_225 + 4*x_225^2 }-> s197 :|: s191 >= 0, s191 <= x_131, s192 >= 0, s192 <= x_220, s193 >= 0, s193 <= s191, s194 >= 0, s194 <= x_139, s195 >= 0, s195 <= x_225, s196 >= 0, s196 <= s194, s197 >= 0, s197 <= s193, 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_f(z, z') -{ 26 + 2*s198 + 2*s200 + 2*s201 + 6*x_131 + 4*x_131^2 + 6*x_140 + 4*x_140^2 + 6*x_220 + 4*x_220^2 + 6*x_226 + 4*x_226^2 }-> s204 :|: s198 >= 0, s198 <= x_131, s199 >= 0, s199 <= x_220, s200 >= 0, s200 <= s198, s201 >= 0, s201 <= x_140, s202 >= 0, s202 <= x_226, s203 >= 0, s203 <= s201, s204 >= 0, s204 <= s200, 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_f(z, z') -{ 15 + 2*s205 + 2*s207 + 6*x_131 + 4*x_131^2 + 6*x_220 + 4*x_220^2 }-> s208 :|: s205 >= 0, s205 <= x_131, s206 >= 0, s206 <= x_220, s207 >= 0, s207 <= s205, s208 >= 0, s208 <= s207, z = 1 + x_131 + x_220, z' >= 0, x_131 >= 0, x_220 >= 0
   encode_f(z, z') -{ 6 + -2*z' + 4*z'^2 }-> s210 :|: s209 >= 0, s209 <= z' - 1, s210 >= 0, s210 <= 0, z >= 0, z' - 1 >= 0
   encode_f(z, z') -{ 16 + 2*s211 + 6*x_142 + 4*x_142^2 + 6*x_227 + 4*x_227^2 }-> s214 :|: s211 >= 0, s211 <= x_142, s212 >= 0, s212 <= x_227, s213 >= 0, s213 <= s211, s214 >= 0, s214 <= 0, z >= 0, z' = 1 + x_142 + x_227, x_142 >= 0, x_227 >= 0
   encode_f(z, z') -{ 15 + 2*s215 + 6*x_143 + 4*x_143^2 + 6*x_228 + 4*x_228^2 }-> s218 :|: s215 >= 0, s215 <= x_143, s216 >= 0, s216 <= x_228, s217 >= 0, s217 <= s215, s218 >= 0, s218 <= 0, z >= 0, z' = 1 + x_143 + x_228, x_143 >= 0, x_228 >= 0
   encode_f(z, z') -{ 4 }-> s3 :|: s3 >= 0, s3 <= 0, z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_g(z, z') -{ 9 + 2*s219 + -2*z + 4*z^2 + -2*z' + 4*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') -{ 19 + 2*s222 + 2*s223 + 6*x_148 + 4*x_148^2 + 6*x_231 + 4*x_231^2 + -2*z + 4*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') -{ 18 + 2*s227 + 2*s228 + 6*x_149 + 4*x_149^2 + 6*x_232 + 4*x_232^2 + -2*z + 4*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') -{ 7 + 2*s232 + -2*z + 4*z^2 }-> s233 :|: s232 >= 0, s232 <= z - 1, s233 >= 0, s233 <= 1 + s232, z - 1 >= 0, z' >= 0
   encode_g(z, z') -{ 17 + 2*s234 + 2*s236 + 6*x_145 + 4*x_145^2 + 6*x_229 + 4*x_229^2 + -2*z' + 4*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') -{ 27 + 2*s239 + 2*s241 + 2*s242 + 6*x_145 + 4*x_145^2 + 6*x_151 + 4*x_151^2 + 6*x_229 + 4*x_229^2 + 6*x_233 + 4*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') -{ 26 + 2*s246 + 2*s248 + 2*s249 + 6*x_145 + 4*x_145^2 + 6*x_152 + 4*x_152^2 + 6*x_229 + 4*x_229^2 + 6*x_234 + 4*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') -{ 15 + 2*s253 + 2*s255 + 6*x_145 + 4*x_145^2 + 6*x_229 + 4*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') -{ 16 + 2*s257 + 2*s259 + 6*x_146 + 4*x_146^2 + 6*x_230 + 4*x_230^2 + -2*z' + 4*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') -{ 26 + 2*s262 + 2*s264 + 2*s265 + 6*x_146 + 4*x_146^2 + 6*x_154 + 4*x_154^2 + 6*x_230 + 4*x_230^2 + 6*x_235 + 4*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') -{ 25 + 2*s269 + 2*s271 + 2*s272 + 6*x_146 + 4*x_146^2 + 6*x_155 + 4*x_155^2 + 6*x_230 + 4*x_230^2 + 6*x_236 + 4*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') -{ 14 + 2*s276 + 2*s278 + 6*x_146 + 4*x_146^2 + 6*x_230 + 4*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') -{ 5 + -2*z' + 4*z'^2 }-> s281 :|: s280 >= 0, s280 <= z' - 1, s281 >= 0, s281 <= 0, z >= 0, z' - 1 >= 0
   encode_g(z, z') -{ 15 + 2*s282 + 6*x_157 + 4*x_157^2 + 6*x_237 + 4*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') -{ 14 + 2*s286 + 6*x_158 + 4*x_158^2 + 6*x_238 + 4*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') -{ 3 }-> s4 :|: s4 >= 0, s4 <= 0, z >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_h(z) -{ 0 }-> 0 :|: z >= 0
   encode_h(z) -{ 4 + 6*z + 4*z^2 }-> 1 + s290 :|: s290 >= 0, s290 <= z, z >= 0
   f(z, z') -{ 4 + 2*z }-> s :|: s >= 0, s <= z, z >= 0, z' >= 0
   g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   g(z, z') -{ 3 + 2*z }-> 1 + s' :|: s' >= 0, s' <= z - 1, z - 1 >= 0, z' >= 0
   g(z, z') -{ 2 + 2*z }-> 1 + s'' :|: s'' >= 0, s'' <= z - 1, z - 1 >= 0, z' >= 0

Function symbols to be analyzed: {encode_g}
Previous analysis results are:
  f: runtime: O(n^1) [4 + 2*z], size: O(n^1) [z]
  g: runtime: O(n^1) [3 + 2*z], size: O(n^1) [z]
  encArg: runtime: O(n^2) [4 + 6*z + 4*z^2], size: O(n^1) [z]
  encode_h: runtime: O(n^2) [4 + 6*z + 4*z^2], size: O(n^1) [1 + z]
  encode_f: runtime: O(n^2) [272 + 128*z + 80*z^2 + 112*z' + 80*z'^2], size: O(n^1) [z]

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

(47) 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

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

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

   encArg(z) -{ 4 }-> s1 :|: s1 >= 0, s1 <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 27 + 2*s100 + 2*s97 + 2*s99 + 6*x_115 + 4*x_115^2 + 6*x_121 + 4*x_121^2 + 6*x_213 + 4*x_213^2 + 6*x_29 + 4*x_29^2 }-> s103 :|: s97 >= 0, s97 <= x_115, s98 >= 0, s98 <= x_29, s99 >= 0, s99 <= s97, s100 >= 0, s100 <= x_121, s101 >= 0, s101 <= x_213, s102 >= 0, s102 <= s100, s103 >= 0, s103 <= s99, 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) -{ 26 + 2*s104 + 2*s106 + 2*s107 + 6*x_115 + 4*x_115^2 + 6*x_122 + 4*x_122^2 + 6*x_214 + 4*x_214^2 + 6*x_29 + 4*x_29^2 }-> s110 :|: s104 >= 0, s104 <= x_115, s105 >= 0, s105 <= x_29, s106 >= 0, s106 <= s104, s107 >= 0, s107 <= x_122, s108 >= 0, s108 <= x_214, s109 >= 0, s109 <= s107, s110 >= 0, s110 <= s106, 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) -{ 15 + 2*s111 + 2*s113 + 6*x_115 + 4*x_115^2 + 6*x_29 + 4*x_29^2 }-> s114 :|: s111 >= 0, s111 <= x_115, s112 >= 0, s112 <= x_29, s113 >= 0, s113 <= s111, s114 >= 0, s114 <= s113, x_115 >= 0, x_2 >= 0, z = 1 + (1 + x_115 + x_29) + x_2, x_29 >= 0
   encArg(z) -{ 18 + 2*s115 + 2*s117 + 6*x_116 + 4*x_116^2 + 6*x_123 + 4*x_123^2 + 6*x_210 + 4*x_210^2 }-> s119 :|: s115 >= 0, s115 <= x_116, s116 >= 0, s116 <= x_210, s117 >= 0, s117 <= s115, s118 >= 0, s118 <= x_123, s119 >= 0, s119 <= s117, x_123 >= 0, z = 1 + (1 + x_116 + x_210) + (1 + x_123), x_116 >= 0, x_210 >= 0
   encArg(z) -{ 26 + 2*s120 + 2*s122 + 2*s123 + 6*x_116 + 4*x_116^2 + 6*x_124 + 4*x_124^2 + 6*x_210 + 4*x_210^2 + 6*x_215 + 4*x_215^2 }-> s126 :|: s120 >= 0, s120 <= x_116, s121 >= 0, s121 <= x_210, s122 >= 0, s122 <= s120, s123 >= 0, s123 <= x_124, s124 >= 0, s124 <= x_215, s125 >= 0, s125 <= s123, s126 >= 0, s126 <= s122, 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) -{ 22 + 2*s10 + 2*s9 + 6*x_1' + 4*x_1'^2 + 6*x_13 + 4*x_13^2 + 6*x_21 + 4*x_21^2 }-> s13 :|: s9 >= 0, s9 <= x_1', s10 >= 0, s10 <= x_13, s11 >= 0, s11 <= x_21, s12 >= 0, s12 <= s10, s13 >= 0, s13 <= 1 + s9, x_13 >= 0, x_1' >= 0, z = 1 + (1 + x_1') + (1 + x_13 + x_21), x_21 >= 0
   encArg(z) -{ 25 + 2*s127 + 2*s129 + 2*s130 + 6*x_116 + 4*x_116^2 + 6*x_125 + 4*x_125^2 + 6*x_210 + 4*x_210^2 + 6*x_216 + 4*x_216^2 }-> s133 :|: s127 >= 0, s127 <= x_116, s128 >= 0, s128 <= x_210, s129 >= 0, s129 <= s127, s130 >= 0, s130 <= x_125, s131 >= 0, s131 <= x_216, s132 >= 0, s132 <= s130, s133 >= 0, s133 <= s129, 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) -{ 14 + 2*s134 + 2*s136 + 6*x_116 + 4*x_116^2 + 6*x_210 + 4*x_210^2 }-> s137 :|: s134 >= 0, s134 <= x_116, s135 >= 0, s135 <= x_210, s136 >= 0, s136 <= s134, s137 >= 0, s137 <= s136, x_116 >= 0, x_2 >= 0, z = 1 + (1 + x_116 + x_210) + x_2, x_210 >= 0
   encArg(z) -{ 7 + 6*x_126 + 4*x_126^2 }-> s139 :|: s138 >= 0, s138 <= x_126, s139 >= 0, s139 <= 0, x_1 >= 0, z = 1 + x_1 + (1 + x_126), x_126 >= 0
   encArg(z) -{ 15 + 2*s140 + 6*x_127 + 4*x_127^2 + 6*x_217 + 4*x_217^2 }-> s143 :|: s140 >= 0, s140 <= x_127, s141 >= 0, s141 <= x_217, s142 >= 0, s142 <= s140, s143 >= 0, s143 <= 0, x_1 >= 0, x_127 >= 0, z = 1 + x_1 + (1 + x_127 + x_217), x_217 >= 0
   encArg(z) -{ 14 + 2*s144 + 6*x_128 + 4*x_128^2 + 6*x_218 + 4*x_218^2 }-> s147 :|: s144 >= 0, s144 <= x_128, s145 >= 0, s145 <= x_218, s146 >= 0, s146 <= s144, s147 >= 0, s147 <= 0, x_1 >= 0, x_128 >= 0, z = 1 + x_1 + (1 + x_128 + x_218), x_218 >= 0
   encArg(z) -{ 21 + 2*s14 + 2*s15 + 6*x_1' + 4*x_1'^2 + 6*x_14 + 4*x_14^2 + 6*x_22 + 4*x_22^2 }-> s18 :|: s14 >= 0, s14 <= x_1', s15 >= 0, s15 <= x_14, s16 >= 0, s16 <= x_22, s17 >= 0, s17 <= s15, s18 >= 0, s18 <= 1 + s14, z = 1 + (1 + x_1') + (1 + x_14 + x_22), x_14 >= 0, x_1' >= 0, x_22 >= 0
   encArg(z) -{ 3 }-> s2 :|: s2 >= 0, s2 <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 10 + 2*s19 + 6*x_1' + 4*x_1'^2 }-> s20 :|: s19 >= 0, s19 <= x_1', s20 >= 0, s20 <= 1 + s19, x_1' >= 0, x_2 >= 0, z = 1 + (1 + x_1') + x_2
   encArg(z) -{ 20 + 2*s21 + 2*s23 + 6*x_1'' + 4*x_1''^2 + 6*x_15 + 4*x_15^2 + 6*x_2' + 4*x_2'^2 }-> s25 :|: s21 >= 0, s21 <= x_1'', s22 >= 0, s22 <= x_2', s23 >= 0, s23 <= s21, s24 >= 0, s24 <= x_15, s25 >= 0, s25 <= s23, x_15 >= 0, z = 1 + (1 + x_1'' + x_2') + (1 + x_15), x_1'' >= 0, x_2' >= 0
   encArg(z) -{ 28 + 2*s26 + 2*s28 + 2*s29 + 6*x_1'' + 4*x_1''^2 + 6*x_16 + 4*x_16^2 + 6*x_2' + 4*x_2'^2 + 6*x_23 + 4*x_23^2 }-> s32 :|: s26 >= 0, s26 <= x_1'', s27 >= 0, s27 <= x_2', s28 >= 0, s28 <= s26, s29 >= 0, s29 <= x_16, s30 >= 0, s30 <= x_23, s31 >= 0, s31 <= s29, s32 >= 0, s32 <= s28, 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) -{ 27 + 2*s33 + 2*s35 + 2*s36 + 6*x_1'' + 4*x_1''^2 + 6*x_17 + 4*x_17^2 + 6*x_2' + 4*x_2'^2 + 6*x_24 + 4*x_24^2 }-> s39 :|: s33 >= 0, s33 <= x_1'', s34 >= 0, s34 <= x_2', s35 >= 0, s35 <= s33, s36 >= 0, s36 <= x_17, s37 >= 0, s37 <= x_24, s38 >= 0, s38 <= s36, s39 >= 0, s39 <= s35, 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) -{ 16 + 2*s40 + 2*s42 + 6*x_1'' + 4*x_1''^2 + 6*x_2' + 4*x_2'^2 }-> s43 :|: s40 >= 0, s40 <= x_1'', s41 >= 0, s41 <= x_2', s42 >= 0, s42 <= s40, s43 >= 0, s43 <= s42, x_1'' >= 0, x_2' >= 0, z = 1 + (1 + x_1'' + x_2') + x_2, x_2 >= 0
   encArg(z) -{ 19 + 2*s44 + 2*s46 + 6*x_11 + 4*x_11^2 + 6*x_18 + 4*x_18^2 + 6*x_2'' + 4*x_2''^2 }-> s48 :|: s44 >= 0, s44 <= x_11, s45 >= 0, s45 <= x_2'', s46 >= 0, s46 <= s44, s47 >= 0, s47 <= x_18, s48 >= 0, s48 <= s46, x_11 >= 0, z = 1 + (1 + x_11 + x_2'') + (1 + x_18), x_2'' >= 0, x_18 >= 0
   encArg(z) -{ 27 + 2*s49 + 2*s51 + 2*s52 + 6*x_11 + 4*x_11^2 + 6*x_19 + 4*x_19^2 + 6*x_2'' + 4*x_2''^2 + 6*x_25 + 4*x_25^2 }-> s55 :|: s49 >= 0, s49 <= x_11, s50 >= 0, s50 <= x_2'', s51 >= 0, s51 <= s49, s52 >= 0, s52 <= x_19, s53 >= 0, s53 <= x_25, s54 >= 0, s54 <= s52, s55 >= 0, s55 <= s51, 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) -{ 26 + 2*s56 + 2*s58 + 2*s59 + 6*x_11 + 4*x_11^2 + 6*x_110 + 4*x_110^2 + 6*x_2'' + 4*x_2''^2 + 6*x_26 + 4*x_26^2 }-> s62 :|: s56 >= 0, s56 <= x_11, s57 >= 0, s57 <= x_2'', s58 >= 0, s58 <= s56, s59 >= 0, s59 <= x_110, s60 >= 0, s60 <= x_26, s61 >= 0, s61 <= s59, s62 >= 0, s62 <= s58, 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) -{ 15 + 2*s63 + 2*s65 + 6*x_11 + 4*x_11^2 + 6*x_2'' + 4*x_2''^2 }-> s66 :|: s63 >= 0, s63 <= x_11, s64 >= 0, s64 <= x_2'', s65 >= 0, s65 <= s63, s66 >= 0, s66 <= s65, x_11 >= 0, x_2'' >= 0, x_2 >= 0, z = 1 + (1 + x_11 + x_2'') + x_2
   encArg(z) -{ 8 + 6*x_111 + 4*x_111^2 }-> s68 :|: s67 >= 0, s67 <= x_111, s68 >= 0, s68 <= 0, x_1 >= 0, z = 1 + x_1 + (1 + x_111), x_111 >= 0
   encArg(z) -{ 16 + 2*s69 + 6*x_112 + 4*x_112^2 + 6*x_27 + 4*x_27^2 }-> s72 :|: s69 >= 0, s69 <= x_112, s70 >= 0, s70 <= x_27, s71 >= 0, s71 <= s69, s72 >= 0, s72 <= 0, x_1 >= 0, x_27 >= 0, z = 1 + x_1 + (1 + x_112 + x_27), x_112 >= 0
   encArg(z) -{ 15 + 2*s73 + 6*x_113 + 4*x_113^2 + 6*x_28 + 4*x_28^2 }-> s76 :|: s73 >= 0, s73 <= x_113, s74 >= 0, s74 <= x_28, s75 >= 0, s75 <= s73, s76 >= 0, s76 <= 0, x_1 >= 0, x_113 >= 0, x_28 >= 0, z = 1 + x_1 + (1 + x_113 + x_28)
   encArg(z) -{ 13 + 2*s77 + 6*x_114 + 4*x_114^2 + 6*x_117 + 4*x_117^2 }-> s79 :|: s77 >= 0, s77 <= x_114, s78 >= 0, s78 <= x_117, s79 >= 0, s79 <= 1 + s77, z = 1 + (1 + x_114) + (1 + x_117), x_117 >= 0, x_114 >= 0
   encArg(z) -{ 14 + 2*s6 + 6*x_1' + 4*x_1'^2 + 6*x_12 + 4*x_12^2 }-> s8 :|: s6 >= 0, s6 <= x_1', s7 >= 0, s7 <= x_12, s8 >= 0, s8 <= 1 + s6, z = 1 + (1 + x_1') + (1 + x_12), x_1' >= 0, x_12 >= 0
   encArg(z) -{ 21 + 2*s80 + 2*s81 + 6*x_114 + 4*x_114^2 + 6*x_118 + 4*x_118^2 + 6*x_211 + 4*x_211^2 }-> s84 :|: s80 >= 0, s80 <= x_114, s81 >= 0, s81 <= x_118, s82 >= 0, s82 <= x_211, s83 >= 0, s83 <= s81, s84 >= 0, s84 <= 1 + s80, z = 1 + (1 + x_114) + (1 + x_118 + x_211), x_114 >= 0, x_118 >= 0, x_211 >= 0
   encArg(z) -{ 20 + 2*s85 + 2*s86 + 6*x_114 + 4*x_114^2 + 6*x_119 + 4*x_119^2 + 6*x_212 + 4*x_212^2 }-> s89 :|: s85 >= 0, s85 <= x_114, s86 >= 0, s86 <= x_119, s87 >= 0, s87 <= x_212, s88 >= 0, s88 <= s86, s89 >= 0, s89 <= 1 + s85, x_212 >= 0, x_114 >= 0, z = 1 + (1 + x_114) + (1 + x_119 + x_212), x_119 >= 0
   encArg(z) -{ 9 + 2*s90 + 6*x_114 + 4*x_114^2 }-> s91 :|: s90 >= 0, s90 <= x_114, s91 >= 0, s91 <= 1 + s90, z = 1 + (1 + x_114) + x_2, x_114 >= 0, x_2 >= 0
   encArg(z) -{ 19 + 2*s92 + 2*s94 + 6*x_115 + 4*x_115^2 + 6*x_120 + 4*x_120^2 + 6*x_29 + 4*x_29^2 }-> s96 :|: s92 >= 0, s92 <= x_115, s93 >= 0, s93 <= x_29, s94 >= 0, s94 <= s92, s95 >= 0, s95 <= x_120, s96 >= 0, s96 <= s94, 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) -{ 2 + -2*z + 4*z^2 }-> 1 + s5 :|: s5 >= 0, s5 <= z - 1, z - 1 >= 0
   encode_f(z, z') -{ 10 + 2*s148 + -2*z + 4*z^2 + -2*z' + 4*z'^2 }-> s150 :|: s148 >= 0, s148 <= z - 1, s149 >= 0, s149 <= z' - 1, s150 >= 0, s150 <= 1 + s148, z' - 1 >= 0, z - 1 >= 0
   encode_f(z, z') -{ 20 + 2*s151 + 2*s152 + 6*x_133 + 4*x_133^2 + 6*x_221 + 4*x_221^2 + -2*z + 4*z^2 }-> s155 :|: s151 >= 0, s151 <= z - 1, s152 >= 0, s152 <= x_133, s153 >= 0, s153 <= x_221, s154 >= 0, s154 <= s152, s155 >= 0, s155 <= 1 + s151, z' = 1 + x_133 + x_221, x_221 >= 0, x_133 >= 0, z - 1 >= 0
   encode_f(z, z') -{ 19 + 2*s156 + 2*s157 + 6*x_134 + 4*x_134^2 + 6*x_222 + 4*x_222^2 + -2*z + 4*z^2 }-> s160 :|: s156 >= 0, s156 <= z - 1, s157 >= 0, s157 <= x_134, s158 >= 0, s158 <= x_222, s159 >= 0, s159 <= s157, s160 >= 0, s160 <= 1 + s156, z' = 1 + x_134 + x_222, x_134 >= 0, x_222 >= 0, z - 1 >= 0
   encode_f(z, z') -{ 8 + 2*s161 + -2*z + 4*z^2 }-> s162 :|: s161 >= 0, s161 <= z - 1, s162 >= 0, s162 <= 1 + s161, z' >= 0, z - 1 >= 0
   encode_f(z, z') -{ 18 + 2*s163 + 2*s165 + 6*x_130 + 4*x_130^2 + 6*x_219 + 4*x_219^2 + -2*z' + 4*z'^2 }-> s167 :|: s163 >= 0, s163 <= x_130, s164 >= 0, s164 <= x_219, s165 >= 0, s165 <= s163, s166 >= 0, s166 <= z' - 1, s167 >= 0, s167 <= s165, x_130 >= 0, z = 1 + x_130 + x_219, z' - 1 >= 0, x_219 >= 0
   encode_f(z, z') -{ 28 + 2*s168 + 2*s170 + 2*s171 + 6*x_130 + 4*x_130^2 + 6*x_136 + 4*x_136^2 + 6*x_219 + 4*x_219^2 + 6*x_223 + 4*x_223^2 }-> s174 :|: s168 >= 0, s168 <= x_130, s169 >= 0, s169 <= x_219, s170 >= 0, s170 <= s168, s171 >= 0, s171 <= x_136, s172 >= 0, s172 <= x_223, s173 >= 0, s173 <= s171, s174 >= 0, s174 <= s170, 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_f(z, z') -{ 27 + 2*s175 + 2*s177 + 2*s178 + 6*x_130 + 4*x_130^2 + 6*x_137 + 4*x_137^2 + 6*x_219 + 4*x_219^2 + 6*x_224 + 4*x_224^2 }-> s181 :|: s175 >= 0, s175 <= x_130, s176 >= 0, s176 <= x_219, s177 >= 0, s177 <= s175, s178 >= 0, s178 <= x_137, s179 >= 0, s179 <= x_224, s180 >= 0, s180 <= s178, s181 >= 0, s181 <= s177, 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_f(z, z') -{ 16 + 2*s182 + 2*s184 + 6*x_130 + 4*x_130^2 + 6*x_219 + 4*x_219^2 }-> s185 :|: s182 >= 0, s182 <= x_130, s183 >= 0, s183 <= x_219, s184 >= 0, s184 <= s182, s185 >= 0, s185 <= s184, x_130 >= 0, z = 1 + x_130 + x_219, z' >= 0, x_219 >= 0
   encode_f(z, z') -{ 17 + 2*s186 + 2*s188 + 6*x_131 + 4*x_131^2 + 6*x_220 + 4*x_220^2 + -2*z' + 4*z'^2 }-> s190 :|: s186 >= 0, s186 <= x_131, s187 >= 0, s187 <= x_220, s188 >= 0, s188 <= s186, s189 >= 0, s189 <= z' - 1, s190 >= 0, s190 <= s188, z' - 1 >= 0, z = 1 + x_131 + x_220, x_131 >= 0, x_220 >= 0
   encode_f(z, z') -{ 27 + 2*s191 + 2*s193 + 2*s194 + 6*x_131 + 4*x_131^2 + 6*x_139 + 4*x_139^2 + 6*x_220 + 4*x_220^2 + 6*x_225 + 4*x_225^2 }-> s197 :|: s191 >= 0, s191 <= x_131, s192 >= 0, s192 <= x_220, s193 >= 0, s193 <= s191, s194 >= 0, s194 <= x_139, s195 >= 0, s195 <= x_225, s196 >= 0, s196 <= s194, s197 >= 0, s197 <= s193, 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_f(z, z') -{ 26 + 2*s198 + 2*s200 + 2*s201 + 6*x_131 + 4*x_131^2 + 6*x_140 + 4*x_140^2 + 6*x_220 + 4*x_220^2 + 6*x_226 + 4*x_226^2 }-> s204 :|: s198 >= 0, s198 <= x_131, s199 >= 0, s199 <= x_220, s200 >= 0, s200 <= s198, s201 >= 0, s201 <= x_140, s202 >= 0, s202 <= x_226, s203 >= 0, s203 <= s201, s204 >= 0, s204 <= s200, 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_f(z, z') -{ 15 + 2*s205 + 2*s207 + 6*x_131 + 4*x_131^2 + 6*x_220 + 4*x_220^2 }-> s208 :|: s205 >= 0, s205 <= x_131, s206 >= 0, s206 <= x_220, s207 >= 0, s207 <= s205, s208 >= 0, s208 <= s207, z = 1 + x_131 + x_220, z' >= 0, x_131 >= 0, x_220 >= 0
   encode_f(z, z') -{ 6 + -2*z' + 4*z'^2 }-> s210 :|: s209 >= 0, s209 <= z' - 1, s210 >= 0, s210 <= 0, z >= 0, z' - 1 >= 0
   encode_f(z, z') -{ 16 + 2*s211 + 6*x_142 + 4*x_142^2 + 6*x_227 + 4*x_227^2 }-> s214 :|: s211 >= 0, s211 <= x_142, s212 >= 0, s212 <= x_227, s213 >= 0, s213 <= s211, s214 >= 0, s214 <= 0, z >= 0, z' = 1 + x_142 + x_227, x_142 >= 0, x_227 >= 0
   encode_f(z, z') -{ 15 + 2*s215 + 6*x_143 + 4*x_143^2 + 6*x_228 + 4*x_228^2 }-> s218 :|: s215 >= 0, s215 <= x_143, s216 >= 0, s216 <= x_228, s217 >= 0, s217 <= s215, s218 >= 0, s218 <= 0, z >= 0, z' = 1 + x_143 + x_228, x_143 >= 0, x_228 >= 0
   encode_f(z, z') -{ 4 }-> s3 :|: s3 >= 0, s3 <= 0, z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_g(z, z') -{ 9 + 2*s219 + -2*z + 4*z^2 + -2*z' + 4*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') -{ 19 + 2*s222 + 2*s223 + 6*x_148 + 4*x_148^2 + 6*x_231 + 4*x_231^2 + -2*z + 4*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') -{ 18 + 2*s227 + 2*s228 + 6*x_149 + 4*x_149^2 + 6*x_232 + 4*x_232^2 + -2*z + 4*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') -{ 7 + 2*s232 + -2*z + 4*z^2 }-> s233 :|: s232 >= 0, s232 <= z - 1, s233 >= 0, s233 <= 1 + s232, z - 1 >= 0, z' >= 0
   encode_g(z, z') -{ 17 + 2*s234 + 2*s236 + 6*x_145 + 4*x_145^2 + 6*x_229 + 4*x_229^2 + -2*z' + 4*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') -{ 27 + 2*s239 + 2*s241 + 2*s242 + 6*x_145 + 4*x_145^2 + 6*x_151 + 4*x_151^2 + 6*x_229 + 4*x_229^2 + 6*x_233 + 4*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') -{ 26 + 2*s246 + 2*s248 + 2*s249 + 6*x_145 + 4*x_145^2 + 6*x_152 + 4*x_152^2 + 6*x_229 + 4*x_229^2 + 6*x_234 + 4*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') -{ 15 + 2*s253 + 2*s255 + 6*x_145 + 4*x_145^2 + 6*x_229 + 4*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') -{ 16 + 2*s257 + 2*s259 + 6*x_146 + 4*x_146^2 + 6*x_230 + 4*x_230^2 + -2*z' + 4*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') -{ 26 + 2*s262 + 2*s264 + 2*s265 + 6*x_146 + 4*x_146^2 + 6*x_154 + 4*x_154^2 + 6*x_230 + 4*x_230^2 + 6*x_235 + 4*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') -{ 25 + 2*s269 + 2*s271 + 2*s272 + 6*x_146 + 4*x_146^2 + 6*x_155 + 4*x_155^2 + 6*x_230 + 4*x_230^2 + 6*x_236 + 4*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') -{ 14 + 2*s276 + 2*s278 + 6*x_146 + 4*x_146^2 + 6*x_230 + 4*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') -{ 5 + -2*z' + 4*z'^2 }-> s281 :|: s280 >= 0, s280 <= z' - 1, s281 >= 0, s281 <= 0, z >= 0, z' - 1 >= 0
   encode_g(z, z') -{ 15 + 2*s282 + 6*x_157 + 4*x_157^2 + 6*x_237 + 4*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') -{ 14 + 2*s286 + 6*x_158 + 4*x_158^2 + 6*x_238 + 4*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') -{ 3 }-> s4 :|: s4 >= 0, s4 <= 0, z >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_h(z) -{ 0 }-> 0 :|: z >= 0
   encode_h(z) -{ 4 + 6*z + 4*z^2 }-> 1 + s290 :|: s290 >= 0, s290 <= z, z >= 0
   f(z, z') -{ 4 + 2*z }-> s :|: s >= 0, s <= z, z >= 0, z' >= 0
   g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   g(z, z') -{ 3 + 2*z }-> 1 + s' :|: s' >= 0, s' <= z - 1, z - 1 >= 0, z' >= 0
   g(z, z') -{ 2 + 2*z }-> 1 + s'' :|: s'' >= 0, s'' <= z - 1, z - 1 >= 0, z' >= 0

Function symbols to be analyzed: {encode_g}
Previous analysis results are:
  f: runtime: O(n^1) [4 + 2*z], size: O(n^1) [z]
  g: runtime: O(n^1) [3 + 2*z], size: O(n^1) [z]
  encArg: runtime: O(n^2) [4 + 6*z + 4*z^2], size: O(n^1) [z]
  encode_h: runtime: O(n^2) [4 + 6*z + 4*z^2], size: O(n^1) [1 + z]
  encode_f: runtime: O(n^2) [272 + 128*z + 80*z^2 + 112*z' + 80*z'^2], size: O(n^1) [z]
  encode_g: runtime: ?, size: O(n^1) [z]

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

(49) 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: 256 + 128*z + 80*z^2 + 112*z' + 80*z'^2

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

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

   encArg(z) -{ 4 }-> s1 :|: s1 >= 0, s1 <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 27 + 2*s100 + 2*s97 + 2*s99 + 6*x_115 + 4*x_115^2 + 6*x_121 + 4*x_121^2 + 6*x_213 + 4*x_213^2 + 6*x_29 + 4*x_29^2 }-> s103 :|: s97 >= 0, s97 <= x_115, s98 >= 0, s98 <= x_29, s99 >= 0, s99 <= s97, s100 >= 0, s100 <= x_121, s101 >= 0, s101 <= x_213, s102 >= 0, s102 <= s100, s103 >= 0, s103 <= s99, 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) -{ 26 + 2*s104 + 2*s106 + 2*s107 + 6*x_115 + 4*x_115^2 + 6*x_122 + 4*x_122^2 + 6*x_214 + 4*x_214^2 + 6*x_29 + 4*x_29^2 }-> s110 :|: s104 >= 0, s104 <= x_115, s105 >= 0, s105 <= x_29, s106 >= 0, s106 <= s104, s107 >= 0, s107 <= x_122, s108 >= 0, s108 <= x_214, s109 >= 0, s109 <= s107, s110 >= 0, s110 <= s106, 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) -{ 15 + 2*s111 + 2*s113 + 6*x_115 + 4*x_115^2 + 6*x_29 + 4*x_29^2 }-> s114 :|: s111 >= 0, s111 <= x_115, s112 >= 0, s112 <= x_29, s113 >= 0, s113 <= s111, s114 >= 0, s114 <= s113, x_115 >= 0, x_2 >= 0, z = 1 + (1 + x_115 + x_29) + x_2, x_29 >= 0
   encArg(z) -{ 18 + 2*s115 + 2*s117 + 6*x_116 + 4*x_116^2 + 6*x_123 + 4*x_123^2 + 6*x_210 + 4*x_210^2 }-> s119 :|: s115 >= 0, s115 <= x_116, s116 >= 0, s116 <= x_210, s117 >= 0, s117 <= s115, s118 >= 0, s118 <= x_123, s119 >= 0, s119 <= s117, x_123 >= 0, z = 1 + (1 + x_116 + x_210) + (1 + x_123), x_116 >= 0, x_210 >= 0
   encArg(z) -{ 26 + 2*s120 + 2*s122 + 2*s123 + 6*x_116 + 4*x_116^2 + 6*x_124 + 4*x_124^2 + 6*x_210 + 4*x_210^2 + 6*x_215 + 4*x_215^2 }-> s126 :|: s120 >= 0, s120 <= x_116, s121 >= 0, s121 <= x_210, s122 >= 0, s122 <= s120, s123 >= 0, s123 <= x_124, s124 >= 0, s124 <= x_215, s125 >= 0, s125 <= s123, s126 >= 0, s126 <= s122, 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) -{ 22 + 2*s10 + 2*s9 + 6*x_1' + 4*x_1'^2 + 6*x_13 + 4*x_13^2 + 6*x_21 + 4*x_21^2 }-> s13 :|: s9 >= 0, s9 <= x_1', s10 >= 0, s10 <= x_13, s11 >= 0, s11 <= x_21, s12 >= 0, s12 <= s10, s13 >= 0, s13 <= 1 + s9, x_13 >= 0, x_1' >= 0, z = 1 + (1 + x_1') + (1 + x_13 + x_21), x_21 >= 0
   encArg(z) -{ 25 + 2*s127 + 2*s129 + 2*s130 + 6*x_116 + 4*x_116^2 + 6*x_125 + 4*x_125^2 + 6*x_210 + 4*x_210^2 + 6*x_216 + 4*x_216^2 }-> s133 :|: s127 >= 0, s127 <= x_116, s128 >= 0, s128 <= x_210, s129 >= 0, s129 <= s127, s130 >= 0, s130 <= x_125, s131 >= 0, s131 <= x_216, s132 >= 0, s132 <= s130, s133 >= 0, s133 <= s129, 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) -{ 14 + 2*s134 + 2*s136 + 6*x_116 + 4*x_116^2 + 6*x_210 + 4*x_210^2 }-> s137 :|: s134 >= 0, s134 <= x_116, s135 >= 0, s135 <= x_210, s136 >= 0, s136 <= s134, s137 >= 0, s137 <= s136, x_116 >= 0, x_2 >= 0, z = 1 + (1 + x_116 + x_210) + x_2, x_210 >= 0
   encArg(z) -{ 7 + 6*x_126 + 4*x_126^2 }-> s139 :|: s138 >= 0, s138 <= x_126, s139 >= 0, s139 <= 0, x_1 >= 0, z = 1 + x_1 + (1 + x_126), x_126 >= 0
   encArg(z) -{ 15 + 2*s140 + 6*x_127 + 4*x_127^2 + 6*x_217 + 4*x_217^2 }-> s143 :|: s140 >= 0, s140 <= x_127, s141 >= 0, s141 <= x_217, s142 >= 0, s142 <= s140, s143 >= 0, s143 <= 0, x_1 >= 0, x_127 >= 0, z = 1 + x_1 + (1 + x_127 + x_217), x_217 >= 0
   encArg(z) -{ 14 + 2*s144 + 6*x_128 + 4*x_128^2 + 6*x_218 + 4*x_218^2 }-> s147 :|: s144 >= 0, s144 <= x_128, s145 >= 0, s145 <= x_218, s146 >= 0, s146 <= s144, s147 >= 0, s147 <= 0, x_1 >= 0, x_128 >= 0, z = 1 + x_1 + (1 + x_128 + x_218), x_218 >= 0
   encArg(z) -{ 21 + 2*s14 + 2*s15 + 6*x_1' + 4*x_1'^2 + 6*x_14 + 4*x_14^2 + 6*x_22 + 4*x_22^2 }-> s18 :|: s14 >= 0, s14 <= x_1', s15 >= 0, s15 <= x_14, s16 >= 0, s16 <= x_22, s17 >= 0, s17 <= s15, s18 >= 0, s18 <= 1 + s14, z = 1 + (1 + x_1') + (1 + x_14 + x_22), x_14 >= 0, x_1' >= 0, x_22 >= 0
   encArg(z) -{ 3 }-> s2 :|: s2 >= 0, s2 <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 10 + 2*s19 + 6*x_1' + 4*x_1'^2 }-> s20 :|: s19 >= 0, s19 <= x_1', s20 >= 0, s20 <= 1 + s19, x_1' >= 0, x_2 >= 0, z = 1 + (1 + x_1') + x_2
   encArg(z) -{ 20 + 2*s21 + 2*s23 + 6*x_1'' + 4*x_1''^2 + 6*x_15 + 4*x_15^2 + 6*x_2' + 4*x_2'^2 }-> s25 :|: s21 >= 0, s21 <= x_1'', s22 >= 0, s22 <= x_2', s23 >= 0, s23 <= s21, s24 >= 0, s24 <= x_15, s25 >= 0, s25 <= s23, x_15 >= 0, z = 1 + (1 + x_1'' + x_2') + (1 + x_15), x_1'' >= 0, x_2' >= 0
   encArg(z) -{ 28 + 2*s26 + 2*s28 + 2*s29 + 6*x_1'' + 4*x_1''^2 + 6*x_16 + 4*x_16^2 + 6*x_2' + 4*x_2'^2 + 6*x_23 + 4*x_23^2 }-> s32 :|: s26 >= 0, s26 <= x_1'', s27 >= 0, s27 <= x_2', s28 >= 0, s28 <= s26, s29 >= 0, s29 <= x_16, s30 >= 0, s30 <= x_23, s31 >= 0, s31 <= s29, s32 >= 0, s32 <= s28, 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) -{ 27 + 2*s33 + 2*s35 + 2*s36 + 6*x_1'' + 4*x_1''^2 + 6*x_17 + 4*x_17^2 + 6*x_2' + 4*x_2'^2 + 6*x_24 + 4*x_24^2 }-> s39 :|: s33 >= 0, s33 <= x_1'', s34 >= 0, s34 <= x_2', s35 >= 0, s35 <= s33, s36 >= 0, s36 <= x_17, s37 >= 0, s37 <= x_24, s38 >= 0, s38 <= s36, s39 >= 0, s39 <= s35, 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) -{ 16 + 2*s40 + 2*s42 + 6*x_1'' + 4*x_1''^2 + 6*x_2' + 4*x_2'^2 }-> s43 :|: s40 >= 0, s40 <= x_1'', s41 >= 0, s41 <= x_2', s42 >= 0, s42 <= s40, s43 >= 0, s43 <= s42, x_1'' >= 0, x_2' >= 0, z = 1 + (1 + x_1'' + x_2') + x_2, x_2 >= 0
   encArg(z) -{ 19 + 2*s44 + 2*s46 + 6*x_11 + 4*x_11^2 + 6*x_18 + 4*x_18^2 + 6*x_2'' + 4*x_2''^2 }-> s48 :|: s44 >= 0, s44 <= x_11, s45 >= 0, s45 <= x_2'', s46 >= 0, s46 <= s44, s47 >= 0, s47 <= x_18, s48 >= 0, s48 <= s46, x_11 >= 0, z = 1 + (1 + x_11 + x_2'') + (1 + x_18), x_2'' >= 0, x_18 >= 0
   encArg(z) -{ 27 + 2*s49 + 2*s51 + 2*s52 + 6*x_11 + 4*x_11^2 + 6*x_19 + 4*x_19^2 + 6*x_2'' + 4*x_2''^2 + 6*x_25 + 4*x_25^2 }-> s55 :|: s49 >= 0, s49 <= x_11, s50 >= 0, s50 <= x_2'', s51 >= 0, s51 <= s49, s52 >= 0, s52 <= x_19, s53 >= 0, s53 <= x_25, s54 >= 0, s54 <= s52, s55 >= 0, s55 <= s51, 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) -{ 26 + 2*s56 + 2*s58 + 2*s59 + 6*x_11 + 4*x_11^2 + 6*x_110 + 4*x_110^2 + 6*x_2'' + 4*x_2''^2 + 6*x_26 + 4*x_26^2 }-> s62 :|: s56 >= 0, s56 <= x_11, s57 >= 0, s57 <= x_2'', s58 >= 0, s58 <= s56, s59 >= 0, s59 <= x_110, s60 >= 0, s60 <= x_26, s61 >= 0, s61 <= s59, s62 >= 0, s62 <= s58, 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) -{ 15 + 2*s63 + 2*s65 + 6*x_11 + 4*x_11^2 + 6*x_2'' + 4*x_2''^2 }-> s66 :|: s63 >= 0, s63 <= x_11, s64 >= 0, s64 <= x_2'', s65 >= 0, s65 <= s63, s66 >= 0, s66 <= s65, x_11 >= 0, x_2'' >= 0, x_2 >= 0, z = 1 + (1 + x_11 + x_2'') + x_2
   encArg(z) -{ 8 + 6*x_111 + 4*x_111^2 }-> s68 :|: s67 >= 0, s67 <= x_111, s68 >= 0, s68 <= 0, x_1 >= 0, z = 1 + x_1 + (1 + x_111), x_111 >= 0
   encArg(z) -{ 16 + 2*s69 + 6*x_112 + 4*x_112^2 + 6*x_27 + 4*x_27^2 }-> s72 :|: s69 >= 0, s69 <= x_112, s70 >= 0, s70 <= x_27, s71 >= 0, s71 <= s69, s72 >= 0, s72 <= 0, x_1 >= 0, x_27 >= 0, z = 1 + x_1 + (1 + x_112 + x_27), x_112 >= 0
   encArg(z) -{ 15 + 2*s73 + 6*x_113 + 4*x_113^2 + 6*x_28 + 4*x_28^2 }-> s76 :|: s73 >= 0, s73 <= x_113, s74 >= 0, s74 <= x_28, s75 >= 0, s75 <= s73, s76 >= 0, s76 <= 0, x_1 >= 0, x_113 >= 0, x_28 >= 0, z = 1 + x_1 + (1 + x_113 + x_28)
   encArg(z) -{ 13 + 2*s77 + 6*x_114 + 4*x_114^2 + 6*x_117 + 4*x_117^2 }-> s79 :|: s77 >= 0, s77 <= x_114, s78 >= 0, s78 <= x_117, s79 >= 0, s79 <= 1 + s77, z = 1 + (1 + x_114) + (1 + x_117), x_117 >= 0, x_114 >= 0
   encArg(z) -{ 14 + 2*s6 + 6*x_1' + 4*x_1'^2 + 6*x_12 + 4*x_12^2 }-> s8 :|: s6 >= 0, s6 <= x_1', s7 >= 0, s7 <= x_12, s8 >= 0, s8 <= 1 + s6, z = 1 + (1 + x_1') + (1 + x_12), x_1' >= 0, x_12 >= 0
   encArg(z) -{ 21 + 2*s80 + 2*s81 + 6*x_114 + 4*x_114^2 + 6*x_118 + 4*x_118^2 + 6*x_211 + 4*x_211^2 }-> s84 :|: s80 >= 0, s80 <= x_114, s81 >= 0, s81 <= x_118, s82 >= 0, s82 <= x_211, s83 >= 0, s83 <= s81, s84 >= 0, s84 <= 1 + s80, z = 1 + (1 + x_114) + (1 + x_118 + x_211), x_114 >= 0, x_118 >= 0, x_211 >= 0
   encArg(z) -{ 20 + 2*s85 + 2*s86 + 6*x_114 + 4*x_114^2 + 6*x_119 + 4*x_119^2 + 6*x_212 + 4*x_212^2 }-> s89 :|: s85 >= 0, s85 <= x_114, s86 >= 0, s86 <= x_119, s87 >= 0, s87 <= x_212, s88 >= 0, s88 <= s86, s89 >= 0, s89 <= 1 + s85, x_212 >= 0, x_114 >= 0, z = 1 + (1 + x_114) + (1 + x_119 + x_212), x_119 >= 0
   encArg(z) -{ 9 + 2*s90 + 6*x_114 + 4*x_114^2 }-> s91 :|: s90 >= 0, s90 <= x_114, s91 >= 0, s91 <= 1 + s90, z = 1 + (1 + x_114) + x_2, x_114 >= 0, x_2 >= 0
   encArg(z) -{ 19 + 2*s92 + 2*s94 + 6*x_115 + 4*x_115^2 + 6*x_120 + 4*x_120^2 + 6*x_29 + 4*x_29^2 }-> s96 :|: s92 >= 0, s92 <= x_115, s93 >= 0, s93 <= x_29, s94 >= 0, s94 <= s92, s95 >= 0, s95 <= x_120, s96 >= 0, s96 <= s94, 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) -{ 2 + -2*z + 4*z^2 }-> 1 + s5 :|: s5 >= 0, s5 <= z - 1, z - 1 >= 0
   encode_f(z, z') -{ 10 + 2*s148 + -2*z + 4*z^2 + -2*z' + 4*z'^2 }-> s150 :|: s148 >= 0, s148 <= z - 1, s149 >= 0, s149 <= z' - 1, s150 >= 0, s150 <= 1 + s148, z' - 1 >= 0, z - 1 >= 0
   encode_f(z, z') -{ 20 + 2*s151 + 2*s152 + 6*x_133 + 4*x_133^2 + 6*x_221 + 4*x_221^2 + -2*z + 4*z^2 }-> s155 :|: s151 >= 0, s151 <= z - 1, s152 >= 0, s152 <= x_133, s153 >= 0, s153 <= x_221, s154 >= 0, s154 <= s152, s155 >= 0, s155 <= 1 + s151, z' = 1 + x_133 + x_221, x_221 >= 0, x_133 >= 0, z - 1 >= 0
   encode_f(z, z') -{ 19 + 2*s156 + 2*s157 + 6*x_134 + 4*x_134^2 + 6*x_222 + 4*x_222^2 + -2*z + 4*z^2 }-> s160 :|: s156 >= 0, s156 <= z - 1, s157 >= 0, s157 <= x_134, s158 >= 0, s158 <= x_222, s159 >= 0, s159 <= s157, s160 >= 0, s160 <= 1 + s156, z' = 1 + x_134 + x_222, x_134 >= 0, x_222 >= 0, z - 1 >= 0
   encode_f(z, z') -{ 8 + 2*s161 + -2*z + 4*z^2 }-> s162 :|: s161 >= 0, s161 <= z - 1, s162 >= 0, s162 <= 1 + s161, z' >= 0, z - 1 >= 0
   encode_f(z, z') -{ 18 + 2*s163 + 2*s165 + 6*x_130 + 4*x_130^2 + 6*x_219 + 4*x_219^2 + -2*z' + 4*z'^2 }-> s167 :|: s163 >= 0, s163 <= x_130, s164 >= 0, s164 <= x_219, s165 >= 0, s165 <= s163, s166 >= 0, s166 <= z' - 1, s167 >= 0, s167 <= s165, x_130 >= 0, z = 1 + x_130 + x_219, z' - 1 >= 0, x_219 >= 0
   encode_f(z, z') -{ 28 + 2*s168 + 2*s170 + 2*s171 + 6*x_130 + 4*x_130^2 + 6*x_136 + 4*x_136^2 + 6*x_219 + 4*x_219^2 + 6*x_223 + 4*x_223^2 }-> s174 :|: s168 >= 0, s168 <= x_130, s169 >= 0, s169 <= x_219, s170 >= 0, s170 <= s168, s171 >= 0, s171 <= x_136, s172 >= 0, s172 <= x_223, s173 >= 0, s173 <= s171, s174 >= 0, s174 <= s170, 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_f(z, z') -{ 27 + 2*s175 + 2*s177 + 2*s178 + 6*x_130 + 4*x_130^2 + 6*x_137 + 4*x_137^2 + 6*x_219 + 4*x_219^2 + 6*x_224 + 4*x_224^2 }-> s181 :|: s175 >= 0, s175 <= x_130, s176 >= 0, s176 <= x_219, s177 >= 0, s177 <= s175, s178 >= 0, s178 <= x_137, s179 >= 0, s179 <= x_224, s180 >= 0, s180 <= s178, s181 >= 0, s181 <= s177, 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_f(z, z') -{ 16 + 2*s182 + 2*s184 + 6*x_130 + 4*x_130^2 + 6*x_219 + 4*x_219^2 }-> s185 :|: s182 >= 0, s182 <= x_130, s183 >= 0, s183 <= x_219, s184 >= 0, s184 <= s182, s185 >= 0, s185 <= s184, x_130 >= 0, z = 1 + x_130 + x_219, z' >= 0, x_219 >= 0
   encode_f(z, z') -{ 17 + 2*s186 + 2*s188 + 6*x_131 + 4*x_131^2 + 6*x_220 + 4*x_220^2 + -2*z' + 4*z'^2 }-> s190 :|: s186 >= 0, s186 <= x_131, s187 >= 0, s187 <= x_220, s188 >= 0, s188 <= s186, s189 >= 0, s189 <= z' - 1, s190 >= 0, s190 <= s188, z' - 1 >= 0, z = 1 + x_131 + x_220, x_131 >= 0, x_220 >= 0
   encode_f(z, z') -{ 27 + 2*s191 + 2*s193 + 2*s194 + 6*x_131 + 4*x_131^2 + 6*x_139 + 4*x_139^2 + 6*x_220 + 4*x_220^2 + 6*x_225 + 4*x_225^2 }-> s197 :|: s191 >= 0, s191 <= x_131, s192 >= 0, s192 <= x_220, s193 >= 0, s193 <= s191, s194 >= 0, s194 <= x_139, s195 >= 0, s195 <= x_225, s196 >= 0, s196 <= s194, s197 >= 0, s197 <= s193, 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_f(z, z') -{ 26 + 2*s198 + 2*s200 + 2*s201 + 6*x_131 + 4*x_131^2 + 6*x_140 + 4*x_140^2 + 6*x_220 + 4*x_220^2 + 6*x_226 + 4*x_226^2 }-> s204 :|: s198 >= 0, s198 <= x_131, s199 >= 0, s199 <= x_220, s200 >= 0, s200 <= s198, s201 >= 0, s201 <= x_140, s202 >= 0, s202 <= x_226, s203 >= 0, s203 <= s201, s204 >= 0, s204 <= s200, 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_f(z, z') -{ 15 + 2*s205 + 2*s207 + 6*x_131 + 4*x_131^2 + 6*x_220 + 4*x_220^2 }-> s208 :|: s205 >= 0, s205 <= x_131, s206 >= 0, s206 <= x_220, s207 >= 0, s207 <= s205, s208 >= 0, s208 <= s207, z = 1 + x_131 + x_220, z' >= 0, x_131 >= 0, x_220 >= 0
   encode_f(z, z') -{ 6 + -2*z' + 4*z'^2 }-> s210 :|: s209 >= 0, s209 <= z' - 1, s210 >= 0, s210 <= 0, z >= 0, z' - 1 >= 0
   encode_f(z, z') -{ 16 + 2*s211 + 6*x_142 + 4*x_142^2 + 6*x_227 + 4*x_227^2 }-> s214 :|: s211 >= 0, s211 <= x_142, s212 >= 0, s212 <= x_227, s213 >= 0, s213 <= s211, s214 >= 0, s214 <= 0, z >= 0, z' = 1 + x_142 + x_227, x_142 >= 0, x_227 >= 0
   encode_f(z, z') -{ 15 + 2*s215 + 6*x_143 + 4*x_143^2 + 6*x_228 + 4*x_228^2 }-> s218 :|: s215 >= 0, s215 <= x_143, s216 >= 0, s216 <= x_228, s217 >= 0, s217 <= s215, s218 >= 0, s218 <= 0, z >= 0, z' = 1 + x_143 + x_228, x_143 >= 0, x_228 >= 0
   encode_f(z, z') -{ 4 }-> s3 :|: s3 >= 0, s3 <= 0, z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_g(z, z') -{ 9 + 2*s219 + -2*z + 4*z^2 + -2*z' + 4*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') -{ 19 + 2*s222 + 2*s223 + 6*x_148 + 4*x_148^2 + 6*x_231 + 4*x_231^2 + -2*z + 4*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') -{ 18 + 2*s227 + 2*s228 + 6*x_149 + 4*x_149^2 + 6*x_232 + 4*x_232^2 + -2*z + 4*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') -{ 7 + 2*s232 + -2*z + 4*z^2 }-> s233 :|: s232 >= 0, s232 <= z - 1, s233 >= 0, s233 <= 1 + s232, z - 1 >= 0, z' >= 0
   encode_g(z, z') -{ 17 + 2*s234 + 2*s236 + 6*x_145 + 4*x_145^2 + 6*x_229 + 4*x_229^2 + -2*z' + 4*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') -{ 27 + 2*s239 + 2*s241 + 2*s242 + 6*x_145 + 4*x_145^2 + 6*x_151 + 4*x_151^2 + 6*x_229 + 4*x_229^2 + 6*x_233 + 4*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') -{ 26 + 2*s246 + 2*s248 + 2*s249 + 6*x_145 + 4*x_145^2 + 6*x_152 + 4*x_152^2 + 6*x_229 + 4*x_229^2 + 6*x_234 + 4*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') -{ 15 + 2*s253 + 2*s255 + 6*x_145 + 4*x_145^2 + 6*x_229 + 4*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') -{ 16 + 2*s257 + 2*s259 + 6*x_146 + 4*x_146^2 + 6*x_230 + 4*x_230^2 + -2*z' + 4*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') -{ 26 + 2*s262 + 2*s264 + 2*s265 + 6*x_146 + 4*x_146^2 + 6*x_154 + 4*x_154^2 + 6*x_230 + 4*x_230^2 + 6*x_235 + 4*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') -{ 25 + 2*s269 + 2*s271 + 2*s272 + 6*x_146 + 4*x_146^2 + 6*x_155 + 4*x_155^2 + 6*x_230 + 4*x_230^2 + 6*x_236 + 4*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') -{ 14 + 2*s276 + 2*s278 + 6*x_146 + 4*x_146^2 + 6*x_230 + 4*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') -{ 5 + -2*z' + 4*z'^2 }-> s281 :|: s280 >= 0, s280 <= z' - 1, s281 >= 0, s281 <= 0, z >= 0, z' - 1 >= 0
   encode_g(z, z') -{ 15 + 2*s282 + 6*x_157 + 4*x_157^2 + 6*x_237 + 4*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') -{ 14 + 2*s286 + 6*x_158 + 4*x_158^2 + 6*x_238 + 4*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') -{ 3 }-> s4 :|: s4 >= 0, s4 <= 0, z >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_h(z) -{ 0 }-> 0 :|: z >= 0
   encode_h(z) -{ 4 + 6*z + 4*z^2 }-> 1 + s290 :|: s290 >= 0, s290 <= z, z >= 0
   f(z, z') -{ 4 + 2*z }-> s :|: s >= 0, s <= z, z >= 0, z' >= 0
   g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   g(z, z') -{ 3 + 2*z }-> 1 + s' :|: s' >= 0, s' <= z - 1, z - 1 >= 0, z' >= 0
   g(z, z') -{ 2 + 2*z }-> 1 + s'' :|: s'' >= 0, s'' <= z - 1, z - 1 >= 0, z' >= 0

Function symbols to be analyzed: 
Previous analysis results are:
  f: runtime: O(n^1) [4 + 2*z], size: O(n^1) [z]
  g: runtime: O(n^1) [3 + 2*z], size: O(n^1) [z]
  encArg: runtime: O(n^2) [4 + 6*z + 4*z^2], size: O(n^1) [z]
  encode_h: runtime: O(n^2) [4 + 6*z + 4*z^2], size: O(n^1) [1 + z]
  encode_f: runtime: O(n^2) [272 + 128*z + 80*z^2 + 112*z' + 80*z'^2], size: O(n^1) [z]
  encode_g: runtime: O(n^2) [256 + 128*z + 80*z^2 + 112*z' + 80*z'^2], size: O(n^1) [z]

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

(52)
BOUNDS(1, n^2)

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

(54)
Obligation:
The Runtime Complexity (full) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF).


The TRS R consists of the following rules:

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

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

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

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

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

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

Types:
f :: h:cons_f:cons_g -> h:cons_f:cons_g -> h:cons_f:cons_g
g :: h:cons_f:cons_g -> h:cons_f:cons_g -> h:cons_f:cons_g
h :: h:cons_f:cons_g -> h:cons_f:cons_g
encArg :: h:cons_f:cons_g -> h:cons_f:cons_g
cons_f :: h:cons_f:cons_g -> h:cons_f:cons_g -> h:cons_f:cons_g
cons_g :: h:cons_f:cons_g -> h:cons_f:cons_g -> h:cons_f:cons_g
encode_f :: h:cons_f:cons_g -> h:cons_f:cons_g -> h:cons_f:cons_g
encode_g :: h:cons_f:cons_g -> h:cons_f:cons_g -> h:cons_f:cons_g
encode_h :: h:cons_f:cons_g -> h:cons_f:cons_g
hole_h:cons_f:cons_g1_0 :: h:cons_f:cons_g
gen_h:cons_f:cons_g2_0 :: Nat -> h:cons_f:cons_g

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

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

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

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

(58)
Obligation:
TRS:
Rules:
f(x, y) -> g(x, y)
g(h(x), y) -> h(f(x, y))
g(h(x), y) -> h(g(x, y))
encArg(h(x_1)) -> h(encArg(x_1))
encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2))
encArg(cons_g(x_1, x_2)) -> g(encArg(x_1), encArg(x_2))
encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2))
encode_g(x_1, x_2) -> g(encArg(x_1), encArg(x_2))
encode_h(x_1) -> h(encArg(x_1))

Types:
f :: h:cons_f:cons_g -> h:cons_f:cons_g -> h:cons_f:cons_g
g :: h:cons_f:cons_g -> h:cons_f:cons_g -> h:cons_f:cons_g
h :: h:cons_f:cons_g -> h:cons_f:cons_g
encArg :: h:cons_f:cons_g -> h:cons_f:cons_g
cons_f :: h:cons_f:cons_g -> h:cons_f:cons_g -> h:cons_f:cons_g
cons_g :: h:cons_f:cons_g -> h:cons_f:cons_g -> h:cons_f:cons_g
encode_f :: h:cons_f:cons_g -> h:cons_f:cons_g -> h:cons_f:cons_g
encode_g :: h:cons_f:cons_g -> h:cons_f:cons_g -> h:cons_f:cons_g
encode_h :: h:cons_f:cons_g -> h:cons_f:cons_g
hole_h:cons_f:cons_g1_0 :: h:cons_f:cons_g
gen_h:cons_f:cons_g2_0 :: Nat -> h:cons_f:cons_g


Generator Equations:
gen_h:cons_f:cons_g2_0(0) <=> hole_h:cons_f:cons_g1_0
gen_h:cons_f:cons_g2_0(+(x, 1)) <=> h(gen_h:cons_f:cons_g2_0(x))


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

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

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

(59) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
g(gen_h:cons_f:cons_g2_0(+(1, n4_0)), gen_h:cons_f:cons_g2_0(b)) -> *3_0, rt in Omega(n4_0)

Induction Base:
g(gen_h:cons_f:cons_g2_0(+(1, 0)), gen_h:cons_f:cons_g2_0(b))

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

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

(60)
Complex Obligation (BEST)

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

(61)
Obligation:
Proved the lower bound n^1 for the following obligation:

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

Types:
f :: h:cons_f:cons_g -> h:cons_f:cons_g -> h:cons_f:cons_g
g :: h:cons_f:cons_g -> h:cons_f:cons_g -> h:cons_f:cons_g
h :: h:cons_f:cons_g -> h:cons_f:cons_g
encArg :: h:cons_f:cons_g -> h:cons_f:cons_g
cons_f :: h:cons_f:cons_g -> h:cons_f:cons_g -> h:cons_f:cons_g
cons_g :: h:cons_f:cons_g -> h:cons_f:cons_g -> h:cons_f:cons_g
encode_f :: h:cons_f:cons_g -> h:cons_f:cons_g -> h:cons_f:cons_g
encode_g :: h:cons_f:cons_g -> h:cons_f:cons_g -> h:cons_f:cons_g
encode_h :: h:cons_f:cons_g -> h:cons_f:cons_g
hole_h:cons_f:cons_g1_0 :: h:cons_f:cons_g
gen_h:cons_f:cons_g2_0 :: Nat -> h:cons_f:cons_g


Generator Equations:
gen_h:cons_f:cons_g2_0(0) <=> hole_h:cons_f:cons_g1_0
gen_h:cons_f:cons_g2_0(+(x, 1)) <=> h(gen_h:cons_f:cons_g2_0(x))


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

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

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

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

(63)
BOUNDS(n^1, INF)

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

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

Types:
f :: h:cons_f:cons_g -> h:cons_f:cons_g -> h:cons_f:cons_g
g :: h:cons_f:cons_g -> h:cons_f:cons_g -> h:cons_f:cons_g
h :: h:cons_f:cons_g -> h:cons_f:cons_g
encArg :: h:cons_f:cons_g -> h:cons_f:cons_g
cons_f :: h:cons_f:cons_g -> h:cons_f:cons_g -> h:cons_f:cons_g
cons_g :: h:cons_f:cons_g -> h:cons_f:cons_g -> h:cons_f:cons_g
encode_f :: h:cons_f:cons_g -> h:cons_f:cons_g -> h:cons_f:cons_g
encode_g :: h:cons_f:cons_g -> h:cons_f:cons_g -> h:cons_f:cons_g
encode_h :: h:cons_f:cons_g -> h:cons_f:cons_g
hole_h:cons_f:cons_g1_0 :: h:cons_f:cons_g
gen_h:cons_f:cons_g2_0 :: Nat -> h:cons_f:cons_g


Lemmas:
g(gen_h:cons_f:cons_g2_0(+(1, n4_0)), gen_h:cons_f:cons_g2_0(b)) -> *3_0, rt in Omega(n4_0)


Generator Equations:
gen_h:cons_f:cons_g2_0(0) <=> hole_h:cons_f:cons_g1_0
gen_h:cons_f:cons_g2_0(+(x, 1)) <=> h(gen_h:cons_f:cons_g2_0(x))


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

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

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

(65) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
f(gen_h:cons_f:cons_g2_0(n721_0), gen_h:cons_f:cons_g2_0(b)) -> *3_0, rt in Omega(n721_0)

Induction Base:
f(gen_h:cons_f:cons_g2_0(0), gen_h:cons_f:cons_g2_0(b))

Induction Step:
f(gen_h:cons_f:cons_g2_0(+(n721_0, 1)), gen_h:cons_f:cons_g2_0(b)) ->_R^Omega(1)
g(gen_h:cons_f:cons_g2_0(+(n721_0, 1)), gen_h:cons_f:cons_g2_0(b)) ->_R^Omega(1)
h(f(gen_h:cons_f:cons_g2_0(n721_0), gen_h:cons_f:cons_g2_0(b))) ->_IH
h(*3_0)

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

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

Types:
f :: h:cons_f:cons_g -> h:cons_f:cons_g -> h:cons_f:cons_g
g :: h:cons_f:cons_g -> h:cons_f:cons_g -> h:cons_f:cons_g
h :: h:cons_f:cons_g -> h:cons_f:cons_g
encArg :: h:cons_f:cons_g -> h:cons_f:cons_g
cons_f :: h:cons_f:cons_g -> h:cons_f:cons_g -> h:cons_f:cons_g
cons_g :: h:cons_f:cons_g -> h:cons_f:cons_g -> h:cons_f:cons_g
encode_f :: h:cons_f:cons_g -> h:cons_f:cons_g -> h:cons_f:cons_g
encode_g :: h:cons_f:cons_g -> h:cons_f:cons_g -> h:cons_f:cons_g
encode_h :: h:cons_f:cons_g -> h:cons_f:cons_g
hole_h:cons_f:cons_g1_0 :: h:cons_f:cons_g
gen_h:cons_f:cons_g2_0 :: Nat -> h:cons_f:cons_g


Lemmas:
g(gen_h:cons_f:cons_g2_0(+(1, n4_0)), gen_h:cons_f:cons_g2_0(b)) -> *3_0, rt in Omega(n4_0)
f(gen_h:cons_f:cons_g2_0(n721_0), gen_h:cons_f:cons_g2_0(b)) -> *3_0, rt in Omega(n721_0)


Generator Equations:
gen_h:cons_f:cons_g2_0(0) <=> hole_h:cons_f:cons_g1_0
gen_h:cons_f:cons_g2_0(+(x, 1)) <=> h(gen_h:cons_f:cons_g2_0(x))


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

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

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

(67) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
g(gen_h:cons_f:cons_g2_0(+(1, n1469_0)), gen_h:cons_f:cons_g2_0(b)) -> *3_0, rt in Omega(n1469_0)

Induction Base:
g(gen_h:cons_f:cons_g2_0(+(1, 0)), gen_h:cons_f:cons_g2_0(b))

Induction Step:
g(gen_h:cons_f:cons_g2_0(+(1, +(n1469_0, 1))), gen_h:cons_f:cons_g2_0(b)) ->_R^Omega(1)
h(g(gen_h:cons_f:cons_g2_0(+(1, n1469_0)), gen_h:cons_f:cons_g2_0(b))) ->_IH
h(*3_0)

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

(68)
Obligation:
TRS:
Rules:
f(x, y) -> g(x, y)
g(h(x), y) -> h(f(x, y))
g(h(x), y) -> h(g(x, y))
encArg(h(x_1)) -> h(encArg(x_1))
encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2))
encArg(cons_g(x_1, x_2)) -> g(encArg(x_1), encArg(x_2))
encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2))
encode_g(x_1, x_2) -> g(encArg(x_1), encArg(x_2))
encode_h(x_1) -> h(encArg(x_1))

Types:
f :: h:cons_f:cons_g -> h:cons_f:cons_g -> h:cons_f:cons_g
g :: h:cons_f:cons_g -> h:cons_f:cons_g -> h:cons_f:cons_g
h :: h:cons_f:cons_g -> h:cons_f:cons_g
encArg :: h:cons_f:cons_g -> h:cons_f:cons_g
cons_f :: h:cons_f:cons_g -> h:cons_f:cons_g -> h:cons_f:cons_g
cons_g :: h:cons_f:cons_g -> h:cons_f:cons_g -> h:cons_f:cons_g
encode_f :: h:cons_f:cons_g -> h:cons_f:cons_g -> h:cons_f:cons_g
encode_g :: h:cons_f:cons_g -> h:cons_f:cons_g -> h:cons_f:cons_g
encode_h :: h:cons_f:cons_g -> h:cons_f:cons_g
hole_h:cons_f:cons_g1_0 :: h:cons_f:cons_g
gen_h:cons_f:cons_g2_0 :: Nat -> h:cons_f:cons_g


Lemmas:
g(gen_h:cons_f:cons_g2_0(+(1, n1469_0)), gen_h:cons_f:cons_g2_0(b)) -> *3_0, rt in Omega(n1469_0)
f(gen_h:cons_f:cons_g2_0(n721_0), gen_h:cons_f:cons_g2_0(b)) -> *3_0, rt in Omega(n721_0)


Generator Equations:
gen_h:cons_f:cons_g2_0(0) <=> hole_h:cons_f:cons_g1_0
gen_h:cons_f:cons_g2_0(+(x, 1)) <=> h(gen_h:cons_f:cons_g2_0(x))


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

(69) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
encArg(gen_h:cons_f:cons_g2_0(+(1, n2858_0))) -> *3_0, rt in Omega(0)

Induction Base:
encArg(gen_h:cons_f:cons_g2_0(+(1, 0)))

Induction Step:
encArg(gen_h:cons_f:cons_g2_0(+(1, +(n2858_0, 1)))) ->_R^Omega(0)
h(encArg(gen_h:cons_f:cons_g2_0(+(1, n2858_0)))) ->_IH
h(*3_0)

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

(70)
BOUNDS(1, INF)