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


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


WORST_CASE(?, O(n^1))
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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(1, n^1).

(0) DCpxTrs
(1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms]
(2) CpxRelTRS
(3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 182 ms]
(4) CpxRelTRS
(5) NonCtorToCtorProof [UPPER BOUND(ID), 0 ms]
(6) CpxRelTRS
(7) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms]
(8) CpxRelTRS
(9) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
(10) CpxWeightedTrs
(11) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(12) CpxWeightedTrs
(13) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
(14) CpxTypedWeightedTrs
(15) CompletionProof [UPPER BOUND(ID), 0 ms]
(16) CpxTypedWeightedCompleteTrs
(17) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
(18) CpxTypedWeightedCompleteTrs
(19) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
(20) CpxRNTS
(21) InliningProof [UPPER BOUND(ID), 1089 ms]
(22) CpxRNTS
(23) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
(24) CpxRNTS
(25) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms]
(26) CpxRNTS
(27) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(28) CpxRNTS
(29) IntTrsBoundProof [UPPER BOUND(ID), 196 ms]
(30) CpxRNTS
(31) IntTrsBoundProof [UPPER BOUND(ID), 45 ms]
(32) CpxRNTS
(33) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(34) CpxRNTS
(35) IntTrsBoundProof [UPPER BOUND(ID), 1422 ms]
(36) CpxRNTS
(37) IntTrsBoundProof [UPPER BOUND(ID), 123 ms]
(38) CpxRNTS
(39) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(40) CpxRNTS
(41) IntTrsBoundProof [UPPER BOUND(ID), 342 ms]
(42) CpxRNTS
(43) IntTrsBoundProof [UPPER BOUND(ID), 65 ms]
(44) CpxRNTS
(45) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(46) CpxRNTS
(47) IntTrsBoundProof [UPPER BOUND(ID), 3344 ms]
(48) CpxRNTS
(49) IntTrsBoundProof [UPPER BOUND(ID), 1286 ms]
(50) CpxRNTS
(51) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(52) CpxRNTS
(53) IntTrsBoundProof [UPPER BOUND(ID), 437 ms]
(54) CpxRNTS
(55) IntTrsBoundProof [UPPER BOUND(ID), 85 ms]
(56) CpxRNTS
(57) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(58) CpxRNTS
(59) IntTrsBoundProof [UPPER BOUND(ID), 1902 ms]
(60) CpxRNTS
(61) IntTrsBoundProof [UPPER BOUND(ID), 683 ms]
(62) CpxRNTS
(63) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(64) CpxRNTS
(65) IntTrsBoundProof [UPPER BOUND(ID), 252 ms]
(66) CpxRNTS
(67) IntTrsBoundProof [UPPER BOUND(ID), 75 ms]
(68) CpxRNTS
(69) FinalProof [FINISHED, 0 ms]
(70) BOUNDS(1, n^1)


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

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


The TRS R consists of the following rules:

   minus(minus(x)) -> x
   minux(+(x, y)) -> +(minus(y), minus(x))
   +(minus(x), +(x, y)) -> y
   +(+(x, y), minus(y)) -> x

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

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

   encArg(cons_minus(x_1)) -> minus(encArg(x_1))
   encArg(cons_minux(x_1)) -> minux(encArg(x_1))
   encArg(cons_+(x_1, x_2)) -> +(encArg(x_1), encArg(x_2))
   encode_minus(x_1) -> minus(encArg(x_1))
   encode_minux(x_1) -> minux(encArg(x_1))
   encode_+(x_1, x_2) -> +(encArg(x_1), encArg(x_2))


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

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


The TRS R consists of the following rules:

   minus(minus(x)) -> x
   minux(+(x, y)) -> +(minus(y), minus(x))
   +(minus(x), +(x, y)) -> y
   +(+(x, y), minus(y)) -> x

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

   encArg(cons_minus(x_1)) -> minus(encArg(x_1))
   encArg(cons_minux(x_1)) -> minux(encArg(x_1))
   encArg(cons_+(x_1, x_2)) -> +(encArg(x_1), encArg(x_2))
   encode_minus(x_1) -> minus(encArg(x_1))
   encode_minux(x_1) -> minux(encArg(x_1))
   encode_+(x_1, x_2) -> +(encArg(x_1), encArg(x_2))

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

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

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


The TRS R consists of the following rules:

   minus(minus(x)) -> x
   minux(+(x, y)) -> +(minus(y), minus(x))
   +(minus(x), +(x, y)) -> y
   +(+(x, y), minus(y)) -> x

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

   encArg(cons_minus(x_1)) -> minus(encArg(x_1))
   encArg(cons_minux(x_1)) -> minux(encArg(x_1))
   encArg(cons_+(x_1, x_2)) -> +(encArg(x_1), encArg(x_2))
   encode_minus(x_1) -> minus(encArg(x_1))
   encode_minux(x_1) -> minux(encArg(x_1))
   encode_+(x_1, x_2) -> +(encArg(x_1), encArg(x_2))

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

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

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


The TRS R consists of the following rules:

   minus(c_minus(x)) -> x
   +(c_+(x, y), c_minus(y)) -> x
   minux(c_+(x, y)) -> +(minus(y), minus(x))
   +(c_minus(x), c_+(x, y)) -> y

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

   encArg(cons_minus(x_1)) -> minus(encArg(x_1))
   encArg(cons_minux(x_1)) -> minux(encArg(x_1))
   encArg(cons_+(x_1, x_2)) -> +(encArg(x_1), encArg(x_2))
   encode_minus(x_1) -> minus(encArg(x_1))
   encode_minux(x_1) -> minux(encArg(x_1))
   encode_+(x_1, x_2) -> +(encArg(x_1), encArg(x_2))
   +(x0, x1) -> c_+(x0, x1)
   minus(x0) -> c_minus(x0)

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

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

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

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


The TRS R consists of the following rules:

   minus(c_minus(x)) -> x
   +(c_+(x, y), c_minus(y)) -> x
   minux(c_+(x, y)) -> +(minus(y), minus(x))
   +(c_minus(x), c_+(x, y)) -> y

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

   encArg(cons_minus(x_1)) -> minus(encArg(x_1))
   encArg(cons_minux(x_1)) -> minux(encArg(x_1))
   encArg(cons_+(x_1, x_2)) -> +(encArg(x_1), encArg(x_2))
   encode_minus(x_1) -> minus(encArg(x_1))
   encode_minux(x_1) -> minux(encArg(x_1))
   encode_+(x_1, x_2) -> +(encArg(x_1), encArg(x_2))
   +(x0, x1) -> c_+(x0, x1)
   minus(x0) -> c_minus(x0)

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

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

(10)
Obligation:
The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1).


The TRS R consists of the following rules:

   minus(c_minus(x)) -> x [1]
   +(c_+(x, y), c_minus(y)) -> x [1]
   minux(c_+(x, y)) -> +(minus(y), minus(x)) [1]
   +(c_minus(x), c_+(x, y)) -> y [1]
   encArg(cons_minus(x_1)) -> minus(encArg(x_1)) [0]
   encArg(cons_minux(x_1)) -> minux(encArg(x_1)) [0]
   encArg(cons_+(x_1, x_2)) -> +(encArg(x_1), encArg(x_2)) [0]
   encode_minus(x_1) -> minus(encArg(x_1)) [0]
   encode_minux(x_1) -> minux(encArg(x_1)) [0]
   encode_+(x_1, x_2) -> +(encArg(x_1), encArg(x_2)) [0]
   +(x0, x1) -> c_+(x0, x1) [0]
   minus(x0) -> c_minus(x0) [0]

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

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

+ => plus

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

(12)
Obligation:
The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1).


The TRS R consists of the following rules:

   minus(c_minus(x)) -> x [1]
   plus(c_+(x, y), c_minus(y)) -> x [1]
   minux(c_+(x, y)) -> plus(minus(y), minus(x)) [1]
   plus(c_minus(x), c_+(x, y)) -> y [1]
   encArg(cons_minus(x_1)) -> minus(encArg(x_1)) [0]
   encArg(cons_minux(x_1)) -> minux(encArg(x_1)) [0]
   encArg(cons_+(x_1, x_2)) -> plus(encArg(x_1), encArg(x_2)) [0]
   encode_minus(x_1) -> minus(encArg(x_1)) [0]
   encode_minux(x_1) -> minux(encArg(x_1)) [0]
   encode_+(x_1, x_2) -> plus(encArg(x_1), encArg(x_2)) [0]
   plus(x0, x1) -> c_+(x0, x1) [0]
   minus(x0) -> c_minus(x0) [0]

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

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

(14)
Obligation:
Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   minus(c_minus(x)) -> x [1]
   plus(c_+(x, y), c_minus(y)) -> x [1]
   minux(c_+(x, y)) -> plus(minus(y), minus(x)) [1]
   plus(c_minus(x), c_+(x, y)) -> y [1]
   encArg(cons_minus(x_1)) -> minus(encArg(x_1)) [0]
   encArg(cons_minux(x_1)) -> minux(encArg(x_1)) [0]
   encArg(cons_+(x_1, x_2)) -> plus(encArg(x_1), encArg(x_2)) [0]
   encode_minus(x_1) -> minus(encArg(x_1)) [0]
   encode_minux(x_1) -> minux(encArg(x_1)) [0]
   encode_+(x_1, x_2) -> plus(encArg(x_1), encArg(x_2)) [0]
   plus(x0, x1) -> c_+(x0, x1) [0]
   minus(x0) -> c_minus(x0) [0]

The TRS has the following type information:
minus :: c_minus:c_+ -> c_minus:c_+
c_minus :: c_minus:c_+ -> c_minus:c_+
plus :: c_minus:c_+ -> c_minus:c_+ -> c_minus:c_+
c_+ :: c_minus:c_+ -> c_minus:c_+ -> c_minus:c_+
minux :: c_minus:c_+ -> c_minus:c_+
encArg :: cons_minus:cons_minux:cons_+ -> c_minus:c_+
cons_minus :: cons_minus:cons_minux:cons_+ -> cons_minus:cons_minux:cons_+
cons_minux :: cons_minus:cons_minux:cons_+ -> cons_minus:cons_minux:cons_+
cons_+ :: cons_minus:cons_minux:cons_+ -> cons_minus:cons_minux:cons_+ -> cons_minus:cons_minux:cons_+
encode_minus :: cons_minus:cons_minux:cons_+ -> c_minus:c_+
encode_minux :: cons_minus:cons_minux:cons_+ -> c_minus:c_+
encode_+ :: cons_minus:cons_minux:cons_+ -> cons_minus:cons_minux:cons_+ -> c_minus:c_+

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

(15) 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:

   minux_1
   encArg_1
   encode_minus_1
   encode_minux_1
   encode_+_2
   plus_2
   minus_1

Due to the following rules being added:

   encArg(v0) -> const [0]
   encode_minus(v0) -> const [0]
   encode_minux(v0) -> const [0]
   encode_+(v0, v1) -> const [0]
   plus(v0, v1) -> const [0]
   minus(v0) -> const [0]
   minux(v0) -> const [0]

And the following fresh constants:    const, const1

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

(16)
Obligation:
Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is:

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

   minus(c_minus(x)) -> x [1]
   plus(c_+(x, y), c_minus(y)) -> x [1]
   minux(c_+(x, y)) -> plus(minus(y), minus(x)) [1]
   plus(c_minus(x), c_+(x, y)) -> y [1]
   encArg(cons_minus(x_1)) -> minus(encArg(x_1)) [0]
   encArg(cons_minux(x_1)) -> minux(encArg(x_1)) [0]
   encArg(cons_+(x_1, x_2)) -> plus(encArg(x_1), encArg(x_2)) [0]
   encode_minus(x_1) -> minus(encArg(x_1)) [0]
   encode_minux(x_1) -> minux(encArg(x_1)) [0]
   encode_+(x_1, x_2) -> plus(encArg(x_1), encArg(x_2)) [0]
   plus(x0, x1) -> c_+(x0, x1) [0]
   minus(x0) -> c_minus(x0) [0]
   encArg(v0) -> const [0]
   encode_minus(v0) -> const [0]
   encode_minux(v0) -> const [0]
   encode_+(v0, v1) -> const [0]
   plus(v0, v1) -> const [0]
   minus(v0) -> const [0]
   minux(v0) -> const [0]

The TRS has the following type information:
minus :: c_minus:c_+:const -> c_minus:c_+:const
c_minus :: c_minus:c_+:const -> c_minus:c_+:const
plus :: c_minus:c_+:const -> c_minus:c_+:const -> c_minus:c_+:const
c_+ :: c_minus:c_+:const -> c_minus:c_+:const -> c_minus:c_+:const
minux :: c_minus:c_+:const -> c_minus:c_+:const
encArg :: cons_minus:cons_minux:cons_+ -> c_minus:c_+:const
cons_minus :: cons_minus:cons_minux:cons_+ -> cons_minus:cons_minux:cons_+
cons_minux :: cons_minus:cons_minux:cons_+ -> cons_minus:cons_minux:cons_+
cons_+ :: cons_minus:cons_minux:cons_+ -> cons_minus:cons_minux:cons_+ -> cons_minus:cons_minux:cons_+
encode_minus :: cons_minus:cons_minux:cons_+ -> c_minus:c_+:const
encode_minux :: cons_minus:cons_minux:cons_+ -> c_minus:c_+:const
encode_+ :: cons_minus:cons_minux:cons_+ -> cons_minus:cons_minux:cons_+ -> c_minus:c_+:const
const :: c_minus:c_+:const
const1 :: cons_minus:cons_minux:cons_+

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

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

(18)
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:

   minus(c_minus(x)) -> x [1]
   plus(c_+(x, y), c_minus(y)) -> x [1]
   minux(c_+(c_minus(x''), c_minus(x'))) -> plus(x', x'') [3]
   minux(c_+(x, c_minus(x'))) -> plus(x', c_minus(x)) [2]
   minux(c_+(x, c_minus(x'))) -> plus(x', const) [2]
   minux(c_+(c_minus(x2), y)) -> plus(c_minus(y), x2) [2]
   minux(c_+(x, y)) -> plus(c_minus(y), c_minus(x)) [1]
   minux(c_+(x, y)) -> plus(c_minus(y), const) [1]
   minux(c_+(c_minus(x3), y)) -> plus(const, x3) [2]
   minux(c_+(x, y)) -> plus(const, c_minus(x)) [1]
   minux(c_+(x, y)) -> plus(const, const) [1]
   plus(c_minus(x), c_+(x, y)) -> y [1]
   encArg(cons_minus(cons_minus(x_1'))) -> minus(minus(encArg(x_1'))) [0]
   encArg(cons_minus(cons_minux(x_1''))) -> minus(minux(encArg(x_1''))) [0]
   encArg(cons_minus(cons_+(x_11, x_2'))) -> minus(plus(encArg(x_11), encArg(x_2'))) [0]
   encArg(cons_minus(x_1)) -> minus(const) [0]
   encArg(cons_minux(cons_minus(x_12))) -> minux(minus(encArg(x_12))) [0]
   encArg(cons_minux(cons_minux(x_13))) -> minux(minux(encArg(x_13))) [0]
   encArg(cons_minux(cons_+(x_14, x_2''))) -> minux(plus(encArg(x_14), encArg(x_2''))) [0]
   encArg(cons_minux(x_1)) -> minux(const) [0]
   encArg(cons_+(cons_minus(x_15), cons_minus(x_18))) -> plus(minus(encArg(x_15)), minus(encArg(x_18))) [0]
   encArg(cons_+(cons_minus(x_15), cons_minux(x_19))) -> plus(minus(encArg(x_15)), minux(encArg(x_19))) [0]
   encArg(cons_+(cons_minus(x_15), cons_+(x_110, x_22))) -> plus(minus(encArg(x_15)), plus(encArg(x_110), encArg(x_22))) [0]
   encArg(cons_+(cons_minus(x_15), x_2)) -> plus(minus(encArg(x_15)), const) [0]
   encArg(cons_+(cons_minux(x_16), cons_minus(x_111))) -> plus(minux(encArg(x_16)), minus(encArg(x_111))) [0]
   encArg(cons_+(cons_minux(x_16), cons_minux(x_112))) -> plus(minux(encArg(x_16)), minux(encArg(x_112))) [0]
   encArg(cons_+(cons_minux(x_16), cons_+(x_113, x_23))) -> plus(minux(encArg(x_16)), plus(encArg(x_113), encArg(x_23))) [0]
   encArg(cons_+(cons_minux(x_16), x_2)) -> plus(minux(encArg(x_16)), const) [0]
   encArg(cons_+(cons_+(x_17, x_21), cons_minus(x_114))) -> plus(plus(encArg(x_17), encArg(x_21)), minus(encArg(x_114))) [0]
   encArg(cons_+(cons_+(x_17, x_21), cons_minux(x_115))) -> plus(plus(encArg(x_17), encArg(x_21)), minux(encArg(x_115))) [0]
   encArg(cons_+(cons_+(x_17, x_21), cons_+(x_116, x_24))) -> plus(plus(encArg(x_17), encArg(x_21)), plus(encArg(x_116), encArg(x_24))) [0]
   encArg(cons_+(cons_+(x_17, x_21), x_2)) -> plus(plus(encArg(x_17), encArg(x_21)), const) [0]
   encArg(cons_+(x_1, cons_minus(x_117))) -> plus(const, minus(encArg(x_117))) [0]
   encArg(cons_+(x_1, cons_minux(x_118))) -> plus(const, minux(encArg(x_118))) [0]
   encArg(cons_+(x_1, cons_+(x_119, x_25))) -> plus(const, plus(encArg(x_119), encArg(x_25))) [0]
   encArg(cons_+(x_1, x_2)) -> plus(const, const) [0]
   encode_minus(cons_minus(x_120)) -> minus(minus(encArg(x_120))) [0]
   encode_minus(cons_minux(x_121)) -> minus(minux(encArg(x_121))) [0]
   encode_minus(cons_+(x_122, x_26)) -> minus(plus(encArg(x_122), encArg(x_26))) [0]
   encode_minus(x_1) -> minus(const) [0]
   encode_minux(cons_minus(x_123)) -> minux(minus(encArg(x_123))) [0]
   encode_minux(cons_minux(x_124)) -> minux(minux(encArg(x_124))) [0]
   encode_minux(cons_+(x_125, x_27)) -> minux(plus(encArg(x_125), encArg(x_27))) [0]
   encode_minux(x_1) -> minux(const) [0]
   encode_+(cons_minus(x_126), cons_minus(x_129)) -> plus(minus(encArg(x_126)), minus(encArg(x_129))) [0]
   encode_+(cons_minus(x_126), cons_minux(x_130)) -> plus(minus(encArg(x_126)), minux(encArg(x_130))) [0]
   encode_+(cons_minus(x_126), cons_+(x_131, x_29)) -> plus(minus(encArg(x_126)), plus(encArg(x_131), encArg(x_29))) [0]
   encode_+(cons_minus(x_126), x_2) -> plus(minus(encArg(x_126)), const) [0]
   encode_+(cons_minux(x_127), cons_minus(x_132)) -> plus(minux(encArg(x_127)), minus(encArg(x_132))) [0]
   encode_+(cons_minux(x_127), cons_minux(x_133)) -> plus(minux(encArg(x_127)), minux(encArg(x_133))) [0]
   encode_+(cons_minux(x_127), cons_+(x_134, x_210)) -> plus(minux(encArg(x_127)), plus(encArg(x_134), encArg(x_210))) [0]
   encode_+(cons_minux(x_127), x_2) -> plus(minux(encArg(x_127)), const) [0]
   encode_+(cons_+(x_128, x_28), cons_minus(x_135)) -> plus(plus(encArg(x_128), encArg(x_28)), minus(encArg(x_135))) [0]
   encode_+(cons_+(x_128, x_28), cons_minux(x_136)) -> plus(plus(encArg(x_128), encArg(x_28)), minux(encArg(x_136))) [0]
   encode_+(cons_+(x_128, x_28), cons_+(x_137, x_211)) -> plus(plus(encArg(x_128), encArg(x_28)), plus(encArg(x_137), encArg(x_211))) [0]
   encode_+(cons_+(x_128, x_28), x_2) -> plus(plus(encArg(x_128), encArg(x_28)), const) [0]
   encode_+(x_1, cons_minus(x_138)) -> plus(const, minus(encArg(x_138))) [0]
   encode_+(x_1, cons_minux(x_139)) -> plus(const, minux(encArg(x_139))) [0]
   encode_+(x_1, cons_+(x_140, x_212)) -> plus(const, plus(encArg(x_140), encArg(x_212))) [0]
   encode_+(x_1, x_2) -> plus(const, const) [0]
   plus(x0, x1) -> c_+(x0, x1) [0]
   minus(x0) -> c_minus(x0) [0]
   encArg(v0) -> const [0]
   encode_minus(v0) -> const [0]
   encode_minux(v0) -> const [0]
   encode_+(v0, v1) -> const [0]
   plus(v0, v1) -> const [0]
   minus(v0) -> const [0]
   minux(v0) -> const [0]

The TRS has the following type information:
minus :: c_minus:c_+:const -> c_minus:c_+:const
c_minus :: c_minus:c_+:const -> c_minus:c_+:const
plus :: c_minus:c_+:const -> c_minus:c_+:const -> c_minus:c_+:const
c_+ :: c_minus:c_+:const -> c_minus:c_+:const -> c_minus:c_+:const
minux :: c_minus:c_+:const -> c_minus:c_+:const
encArg :: cons_minus:cons_minux:cons_+ -> c_minus:c_+:const
cons_minus :: cons_minus:cons_minux:cons_+ -> cons_minus:cons_minux:cons_+
cons_minux :: cons_minus:cons_minux:cons_+ -> cons_minus:cons_minux:cons_+
cons_+ :: cons_minus:cons_minux:cons_+ -> cons_minus:cons_minux:cons_+ -> cons_minus:cons_minux:cons_+
encode_minus :: cons_minus:cons_minux:cons_+ -> c_minus:c_+:const
encode_minux :: cons_minus:cons_minux:cons_+ -> c_minus:c_+:const
encode_+ :: cons_minus:cons_minux:cons_+ -> cons_minus:cons_minux:cons_+ -> c_minus:c_+:const
const :: c_minus:c_+:const
const1 :: cons_minus:cons_minux:cons_+

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

(19) 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
   const1 => 0

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

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

   encArg(z) -{ 0 }-> plus(plus(encArg(x_17), encArg(x_21)), plus(encArg(x_116), encArg(x_24))) :|: x_116 >= 0, x_17 >= 0, z = 1 + (1 + x_17 + x_21) + (1 + x_116 + x_24), x_24 >= 0, x_21 >= 0
   encArg(z) -{ 0 }-> plus(plus(encArg(x_17), encArg(x_21)), minux(encArg(x_115))) :|: z = 1 + (1 + x_17 + x_21) + (1 + x_115), x_115 >= 0, x_17 >= 0, x_21 >= 0
   encArg(z) -{ 0 }-> plus(plus(encArg(x_17), encArg(x_21)), minus(encArg(x_114))) :|: z = 1 + (1 + x_17 + x_21) + (1 + x_114), x_114 >= 0, x_17 >= 0, x_21 >= 0
   encArg(z) -{ 0 }-> plus(plus(encArg(x_17), encArg(x_21)), 0) :|: z = 1 + (1 + x_17 + x_21) + x_2, x_17 >= 0, x_2 >= 0, x_21 >= 0
   encArg(z) -{ 0 }-> plus(minux(encArg(x_16)), plus(encArg(x_113), encArg(x_23))) :|: x_113 >= 0, x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_113 + x_23), x_23 >= 0
   encArg(z) -{ 0 }-> plus(minux(encArg(x_16)), minux(encArg(x_112))) :|: x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_112), x_112 >= 0
   encArg(z) -{ 0 }-> plus(minux(encArg(x_16)), minus(encArg(x_111))) :|: x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_111), x_111 >= 0
   encArg(z) -{ 0 }-> plus(minux(encArg(x_16)), 0) :|: x_16 >= 0, x_2 >= 0, z = 1 + (1 + x_16) + x_2
   encArg(z) -{ 0 }-> plus(minus(encArg(x_15)), plus(encArg(x_110), encArg(x_22))) :|: x_15 >= 0, z = 1 + (1 + x_15) + (1 + x_110 + x_22), x_110 >= 0, x_22 >= 0
   encArg(z) -{ 0 }-> plus(minus(encArg(x_15)), minux(encArg(x_19))) :|: x_15 >= 0, z = 1 + (1 + x_15) + (1 + x_19), x_19 >= 0
   encArg(z) -{ 0 }-> plus(minus(encArg(x_15)), minus(encArg(x_18))) :|: x_15 >= 0, x_18 >= 0, z = 1 + (1 + x_15) + (1 + x_18)
   encArg(z) -{ 0 }-> plus(minus(encArg(x_15)), 0) :|: x_15 >= 0, z = 1 + (1 + x_15) + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> plus(0, plus(encArg(x_119), encArg(x_25))) :|: x_1 >= 0, z = 1 + x_1 + (1 + x_119 + x_25), x_25 >= 0, x_119 >= 0
   encArg(z) -{ 0 }-> plus(0, minux(encArg(x_118))) :|: x_1 >= 0, z = 1 + x_1 + (1 + x_118), x_118 >= 0
   encArg(z) -{ 0 }-> plus(0, minus(encArg(x_117))) :|: x_1 >= 0, x_117 >= 0, z = 1 + x_1 + (1 + x_117)
   encArg(z) -{ 0 }-> plus(0, 0) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> minux(plus(encArg(x_14), encArg(x_2''))) :|: x_14 >= 0, z = 1 + (1 + x_14 + x_2''), x_2'' >= 0
   encArg(z) -{ 0 }-> minux(minux(encArg(x_13))) :|: z = 1 + (1 + x_13), x_13 >= 0
   encArg(z) -{ 0 }-> minux(minus(encArg(x_12))) :|: z = 1 + (1 + x_12), x_12 >= 0
   encArg(z) -{ 0 }-> minux(0) :|: z = 1 + x_1, x_1 >= 0
   encArg(z) -{ 0 }-> minus(plus(encArg(x_11), encArg(x_2'))) :|: x_11 >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2')
   encArg(z) -{ 0 }-> minus(minux(encArg(x_1''))) :|: z = 1 + (1 + x_1''), x_1'' >= 0
   encArg(z) -{ 0 }-> minus(minus(encArg(x_1'))) :|: z = 1 + (1 + x_1'), x_1' >= 0
   encArg(z) -{ 0 }-> minus(0) :|: z = 1 + x_1, x_1 >= 0
   encArg(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_+(z, z') -{ 0 }-> plus(plus(encArg(x_128), encArg(x_28)), plus(encArg(x_137), encArg(x_211))) :|: x_128 >= 0, z = 1 + x_128 + x_28, z' = 1 + x_137 + x_211, x_137 >= 0, x_28 >= 0, x_211 >= 0
   encode_+(z, z') -{ 0 }-> plus(plus(encArg(x_128), encArg(x_28)), minux(encArg(x_136))) :|: x_128 >= 0, z = 1 + x_128 + x_28, x_136 >= 0, z' = 1 + x_136, x_28 >= 0
   encode_+(z, z') -{ 0 }-> plus(plus(encArg(x_128), encArg(x_28)), minus(encArg(x_135))) :|: x_128 >= 0, z = 1 + x_128 + x_28, x_135 >= 0, z' = 1 + x_135, x_28 >= 0
   encode_+(z, z') -{ 0 }-> plus(plus(encArg(x_128), encArg(x_28)), 0) :|: x_128 >= 0, z = 1 + x_128 + x_28, x_2 >= 0, z' = x_2, x_28 >= 0
   encode_+(z, z') -{ 0 }-> plus(minux(encArg(x_127)), plus(encArg(x_134), encArg(x_210))) :|: x_134 >= 0, x_127 >= 0, z = 1 + x_127, z' = 1 + x_134 + x_210, x_210 >= 0
   encode_+(z, z') -{ 0 }-> plus(minux(encArg(x_127)), minux(encArg(x_133))) :|: x_127 >= 0, z = 1 + x_127, z' = 1 + x_133, x_133 >= 0
   encode_+(z, z') -{ 0 }-> plus(minux(encArg(x_127)), minus(encArg(x_132))) :|: x_127 >= 0, z = 1 + x_127, z' = 1 + x_132, x_132 >= 0
   encode_+(z, z') -{ 0 }-> plus(minux(encArg(x_127)), 0) :|: x_127 >= 0, z = 1 + x_127, x_2 >= 0, z' = x_2
   encode_+(z, z') -{ 0 }-> plus(minus(encArg(x_126)), plus(encArg(x_131), encArg(x_29))) :|: z = 1 + x_126, z' = 1 + x_131 + x_29, x_126 >= 0, x_131 >= 0, x_29 >= 0
   encode_+(z, z') -{ 0 }-> plus(minus(encArg(x_126)), minux(encArg(x_130))) :|: x_130 >= 0, z = 1 + x_126, z' = 1 + x_130, x_126 >= 0
   encode_+(z, z') -{ 0 }-> plus(minus(encArg(x_126)), minus(encArg(x_129))) :|: z' = 1 + x_129, z = 1 + x_126, x_126 >= 0, x_129 >= 0
   encode_+(z, z') -{ 0 }-> plus(minus(encArg(x_126)), 0) :|: z = 1 + x_126, x_126 >= 0, x_2 >= 0, z' = x_2
   encode_+(z, z') -{ 0 }-> plus(0, plus(encArg(x_140), encArg(x_212))) :|: x_1 >= 0, x_212 >= 0, z = x_1, x_140 >= 0, z' = 1 + x_140 + x_212
   encode_+(z, z') -{ 0 }-> plus(0, minux(encArg(x_139))) :|: x_1 >= 0, z = x_1, z' = 1 + x_139, x_139 >= 0
   encode_+(z, z') -{ 0 }-> plus(0, minus(encArg(x_138))) :|: x_138 >= 0, x_1 >= 0, z = x_1, z' = 1 + x_138
   encode_+(z, z') -{ 0 }-> plus(0, 0) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2
   encode_+(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   encode_minus(z) -{ 0 }-> minus(plus(encArg(x_122), encArg(x_26))) :|: z = 1 + x_122 + x_26, x_26 >= 0, x_122 >= 0
   encode_minus(z) -{ 0 }-> minus(minux(encArg(x_121))) :|: z = 1 + x_121, x_121 >= 0
   encode_minus(z) -{ 0 }-> minus(minus(encArg(x_120))) :|: x_120 >= 0, z = 1 + x_120
   encode_minus(z) -{ 0 }-> minus(0) :|: x_1 >= 0, z = x_1
   encode_minus(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_minux(z) -{ 0 }-> minux(plus(encArg(x_125), encArg(x_27))) :|: x_125 >= 0, x_27 >= 0, z = 1 + x_125 + x_27
   encode_minux(z) -{ 0 }-> minux(minux(encArg(x_124))) :|: x_124 >= 0, z = 1 + x_124
   encode_minux(z) -{ 0 }-> minux(minus(encArg(x_123))) :|: x_123 >= 0, z = 1 + x_123
   encode_minux(z) -{ 0 }-> minux(0) :|: x_1 >= 0, z = x_1
   encode_minux(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   minus(z) -{ 1 }-> x :|: x >= 0, z = 1 + x
   minus(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   minus(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0
   minux(z) -{ 3 }-> plus(x', x'') :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0
   minux(z) -{ 2 }-> plus(x', 0) :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0
   minux(z) -{ 2 }-> plus(x', 1 + x) :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0
   minux(z) -{ 2 }-> plus(0, x3) :|: z = 1 + (1 + x3) + y, y >= 0, x3 >= 0
   minux(z) -{ 1 }-> plus(0, 0) :|: z = 1 + x + y, x >= 0, y >= 0
   minux(z) -{ 1 }-> plus(0, 1 + x) :|: z = 1 + x + y, x >= 0, y >= 0
   minux(z) -{ 2 }-> plus(1 + y, x2) :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0
   minux(z) -{ 1 }-> plus(1 + y, 0) :|: z = 1 + x + y, x >= 0, y >= 0
   minux(z) -{ 1 }-> plus(1 + y, 1 + x) :|: z = 1 + x + y, x >= 0, y >= 0
   minux(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   plus(z, z') -{ 1 }-> x :|: z' = 1 + y, z = 1 + x + y, x >= 0, y >= 0
   plus(z, z') -{ 1 }-> y :|: z' = 1 + x + y, x >= 0, y >= 0, z = 1 + x
   plus(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   plus(z, z') -{ 0 }-> 1 + x0 + x1 :|: z = x0, x0 >= 0, x1 >= 0, z' = x1


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

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

   minus(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   minus(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0
   minus(z) -{ 1 }-> x :|: x >= 0, z = 1 + x
   plus(z, z') -{ 1 }-> x :|: z' = 1 + y, z = 1 + x + y, x >= 0, y >= 0
   plus(z, z') -{ 1 }-> y :|: z' = 1 + x + y, x >= 0, y >= 0, z = 1 + x
   plus(z, z') -{ 0 }-> 1 + x0 + x1 :|: z = x0, x0 >= 0, x1 >= 0, z' = x1
   plus(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   minux(z) -{ 1 }-> plus(0, 1 + x) :|: z = 1 + x + y, x >= 0, y >= 0
   minux(z) -{ 2 }-> plus(x', 1 + x) :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0
   minux(z) -{ 1 }-> plus(1 + y, 0) :|: z = 1 + x + y, x >= 0, y >= 0
   minux(z) -{ 3 }-> plus(x', x'') :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0
   minux(z) -{ 1 }-> plus(1 + y, 1 + x) :|: z = 1 + x + y, x >= 0, y >= 0
   minux(z) -{ 1 }-> plus(0, 0) :|: z = 1 + x + y, x >= 0, y >= 0
   minux(z) -{ 2 }-> plus(1 + y, x2) :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0
   minux(z) -{ 2 }-> plus(x', 0) :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0
   minux(z) -{ 2 }-> plus(0, x3) :|: z = 1 + (1 + x3) + y, y >= 0, x3 >= 0
   minux(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0

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

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

   encArg(z) -{ 0 }-> plus(plus(encArg(x_17), encArg(x_21)), plus(encArg(x_116), encArg(x_24))) :|: x_116 >= 0, x_17 >= 0, z = 1 + (1 + x_17 + x_21) + (1 + x_116 + x_24), x_24 >= 0, x_21 >= 0
   encArg(z) -{ 0 }-> plus(plus(encArg(x_17), encArg(x_21)), minux(encArg(x_115))) :|: z = 1 + (1 + x_17 + x_21) + (1 + x_115), x_115 >= 0, x_17 >= 0, x_21 >= 0
   encArg(z) -{ 0 }-> plus(plus(encArg(x_17), encArg(x_21)), minus(encArg(x_114))) :|: z = 1 + (1 + x_17 + x_21) + (1 + x_114), x_114 >= 0, x_17 >= 0, x_21 >= 0
   encArg(z) -{ 0 }-> plus(plus(encArg(x_17), encArg(x_21)), 0) :|: z = 1 + (1 + x_17 + x_21) + x_2, x_17 >= 0, x_2 >= 0, x_21 >= 0
   encArg(z) -{ 0 }-> plus(minux(encArg(x_16)), plus(encArg(x_113), encArg(x_23))) :|: x_113 >= 0, x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_113 + x_23), x_23 >= 0
   encArg(z) -{ 0 }-> plus(minux(encArg(x_16)), minux(encArg(x_112))) :|: x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_112), x_112 >= 0
   encArg(z) -{ 0 }-> plus(minux(encArg(x_16)), minus(encArg(x_111))) :|: x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_111), x_111 >= 0
   encArg(z) -{ 0 }-> plus(minux(encArg(x_16)), 0) :|: x_16 >= 0, x_2 >= 0, z = 1 + (1 + x_16) + x_2
   encArg(z) -{ 0 }-> plus(minus(encArg(x_15)), plus(encArg(x_110), encArg(x_22))) :|: x_15 >= 0, z = 1 + (1 + x_15) + (1 + x_110 + x_22), x_110 >= 0, x_22 >= 0
   encArg(z) -{ 0 }-> plus(minus(encArg(x_15)), minux(encArg(x_19))) :|: x_15 >= 0, z = 1 + (1 + x_15) + (1 + x_19), x_19 >= 0
   encArg(z) -{ 0 }-> plus(minus(encArg(x_15)), minus(encArg(x_18))) :|: x_15 >= 0, x_18 >= 0, z = 1 + (1 + x_15) + (1 + x_18)
   encArg(z) -{ 0 }-> plus(minus(encArg(x_15)), 0) :|: x_15 >= 0, z = 1 + (1 + x_15) + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> plus(0, plus(encArg(x_119), encArg(x_25))) :|: x_1 >= 0, z = 1 + x_1 + (1 + x_119 + x_25), x_25 >= 0, x_119 >= 0
   encArg(z) -{ 0 }-> plus(0, minux(encArg(x_118))) :|: x_1 >= 0, z = 1 + x_1 + (1 + x_118), x_118 >= 0
   encArg(z) -{ 0 }-> plus(0, minus(encArg(x_117))) :|: x_1 >= 0, x_117 >= 0, z = 1 + x_1 + (1 + x_117)
   encArg(z) -{ 0 }-> minux(plus(encArg(x_14), encArg(x_2''))) :|: x_14 >= 0, z = 1 + (1 + x_14 + x_2''), x_2'' >= 0
   encArg(z) -{ 0 }-> minux(minux(encArg(x_13))) :|: z = 1 + (1 + x_13), x_13 >= 0
   encArg(z) -{ 0 }-> minux(minus(encArg(x_12))) :|: z = 1 + (1 + x_12), x_12 >= 0
   encArg(z) -{ 0 }-> minus(plus(encArg(x_11), encArg(x_2'))) :|: x_11 >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2')
   encArg(z) -{ 0 }-> minus(minux(encArg(x_1''))) :|: z = 1 + (1 + x_1''), x_1'' >= 0
   encArg(z) -{ 0 }-> minus(minus(encArg(x_1'))) :|: z = 1 + (1 + x_1'), x_1' >= 0
   encArg(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + x_1, x_1 >= 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + x_1, x_1 >= 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 + x1 :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   encode_+(z, z') -{ 0 }-> plus(plus(encArg(x_128), encArg(x_28)), plus(encArg(x_137), encArg(x_211))) :|: x_128 >= 0, z = 1 + x_128 + x_28, z' = 1 + x_137 + x_211, x_137 >= 0, x_28 >= 0, x_211 >= 0
   encode_+(z, z') -{ 0 }-> plus(plus(encArg(x_128), encArg(x_28)), minux(encArg(x_136))) :|: x_128 >= 0, z = 1 + x_128 + x_28, x_136 >= 0, z' = 1 + x_136, x_28 >= 0
   encode_+(z, z') -{ 0 }-> plus(plus(encArg(x_128), encArg(x_28)), minus(encArg(x_135))) :|: x_128 >= 0, z = 1 + x_128 + x_28, x_135 >= 0, z' = 1 + x_135, x_28 >= 0
   encode_+(z, z') -{ 0 }-> plus(plus(encArg(x_128), encArg(x_28)), 0) :|: x_128 >= 0, z = 1 + x_128 + x_28, x_2 >= 0, z' = x_2, x_28 >= 0
   encode_+(z, z') -{ 0 }-> plus(minux(encArg(x_127)), plus(encArg(x_134), encArg(x_210))) :|: x_134 >= 0, x_127 >= 0, z = 1 + x_127, z' = 1 + x_134 + x_210, x_210 >= 0
   encode_+(z, z') -{ 0 }-> plus(minux(encArg(x_127)), minux(encArg(x_133))) :|: x_127 >= 0, z = 1 + x_127, z' = 1 + x_133, x_133 >= 0
   encode_+(z, z') -{ 0 }-> plus(minux(encArg(x_127)), minus(encArg(x_132))) :|: x_127 >= 0, z = 1 + x_127, z' = 1 + x_132, x_132 >= 0
   encode_+(z, z') -{ 0 }-> plus(minux(encArg(x_127)), 0) :|: x_127 >= 0, z = 1 + x_127, x_2 >= 0, z' = x_2
   encode_+(z, z') -{ 0 }-> plus(minus(encArg(x_126)), plus(encArg(x_131), encArg(x_29))) :|: z = 1 + x_126, z' = 1 + x_131 + x_29, x_126 >= 0, x_131 >= 0, x_29 >= 0
   encode_+(z, z') -{ 0 }-> plus(minus(encArg(x_126)), minux(encArg(x_130))) :|: x_130 >= 0, z = 1 + x_126, z' = 1 + x_130, x_126 >= 0
   encode_+(z, z') -{ 0 }-> plus(minus(encArg(x_126)), minus(encArg(x_129))) :|: z' = 1 + x_129, z = 1 + x_126, x_126 >= 0, x_129 >= 0
   encode_+(z, z') -{ 0 }-> plus(minus(encArg(x_126)), 0) :|: z = 1 + x_126, x_126 >= 0, x_2 >= 0, z' = x_2
   encode_+(z, z') -{ 0 }-> plus(0, plus(encArg(x_140), encArg(x_212))) :|: x_1 >= 0, x_212 >= 0, z = x_1, x_140 >= 0, z' = 1 + x_140 + x_212
   encode_+(z, z') -{ 0 }-> plus(0, minux(encArg(x_139))) :|: x_1 >= 0, z = x_1, z' = 1 + x_139, x_139 >= 0
   encode_+(z, z') -{ 0 }-> plus(0, minus(encArg(x_138))) :|: x_138 >= 0, x_1 >= 0, z = x_1, z' = 1 + x_138
   encode_+(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   encode_+(z, z') -{ 0 }-> 0 :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   encode_+(z, z') -{ 0 }-> 1 + x0 + x1 :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   encode_minus(z) -{ 0 }-> minus(plus(encArg(x_122), encArg(x_26))) :|: z = 1 + x_122 + x_26, x_26 >= 0, x_122 >= 0
   encode_minus(z) -{ 0 }-> minus(minux(encArg(x_121))) :|: z = 1 + x_121, x_121 >= 0
   encode_minus(z) -{ 0 }-> minus(minus(encArg(x_120))) :|: x_120 >= 0, z = 1 + x_120
   encode_minus(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_minus(z) -{ 0 }-> 0 :|: x_1 >= 0, z = x_1, v0 >= 0, 0 = v0
   encode_minus(z) -{ 0 }-> 1 + x0 :|: x_1 >= 0, z = x_1, 0 = x0, x0 >= 0
   encode_minux(z) -{ 0 }-> minux(plus(encArg(x_125), encArg(x_27))) :|: x_125 >= 0, x_27 >= 0, z = 1 + x_125 + x_27
   encode_minux(z) -{ 0 }-> minux(minux(encArg(x_124))) :|: x_124 >= 0, z = 1 + x_124
   encode_minux(z) -{ 0 }-> minux(minus(encArg(x_123))) :|: x_123 >= 0, z = 1 + x_123
   encode_minux(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_minux(z) -{ 0 }-> 0 :|: x_1 >= 0, z = x_1, v0 >= 0, 0 = v0
   minus(z) -{ 1 }-> x :|: x >= 0, z = 1 + x
   minus(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   minus(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0
   minux(z) -{ 4 }-> x :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x'' = 1 + y, x' = 1 + x + y, x >= 0, y >= 0
   minux(z) -{ 3 }-> x :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, x2 = 1 + y', 1 + y = 1 + x + y', x >= 0, y' >= 0
   minux(z) -{ 2 }-> x' :|: z = 1 + x + y, x >= 0, y >= 0, 1 + x = 1 + y', 1 + y = 1 + x' + y', x' >= 0, y' >= 0
   minux(z) -{ 3 }-> x'' :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, 1 + x = 1 + y, x' = 1 + x'' + y, x'' >= 0, y >= 0
   minux(z) -{ 4 }-> y :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x'' = 1 + x + y, x >= 0, y >= 0, x' = 1 + x
   minux(z) -{ 3 }-> y :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, 1 + x = 1 + x'' + y, x'' >= 0, y >= 0, x' = 1 + x''
   minux(z) -{ 3 }-> y' :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, x2 = 1 + x + y', x >= 0, y' >= 0, 1 + y = 1 + x
   minux(z) -{ 2 }-> y' :|: z = 1 + x + y, x >= 0, y >= 0, 1 + x = 1 + x' + y', x' >= 0, y' >= 0, 1 + y = 1 + x'
   minux(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   minux(z) -{ 3 }-> 0 :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, v0 >= 0, v1 >= 0, x' = v0, x'' = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, v0 >= 0, v1 >= 0, x' = v0, 1 + x = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, v0 >= 0, v1 >= 0, x' = v0, 0 = v1
   minux(z) -{ 2 }-> 0 :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, x2 = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, 1 + x = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, 0 = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + (1 + x3) + y, y >= 0, x3 >= 0, v0 >= 0, v1 >= 0, 0 = v0, x3 = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 0 = v0, 1 + x = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   minux(z) -{ 3 }-> 1 + x0 + x1 :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x' = x0, x0 >= 0, x1 >= 0, x'' = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, x' = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, x' = x0, x0 >= 0, x1 >= 0, 0 = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, x2 = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, 0 = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + (1 + x3) + y, y >= 0, x3 >= 0, 0 = x0, x0 >= 0, x1 >= 0, x3 = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 0 = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   plus(z, z') -{ 1 }-> x :|: z' = 1 + y, z = 1 + x + y, x >= 0, y >= 0
   plus(z, z') -{ 1 }-> y :|: z' = 1 + x + y, x >= 0, y >= 0, z = 1 + x
   plus(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   plus(z, z') -{ 0 }-> 1 + x0 + x1 :|: z = x0, x0 >= 0, x1 >= 0, z' = x1


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

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

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

   encArg(z) -{ 0 }-> plus(plus(encArg(x_17), encArg(x_21)), plus(encArg(x_116), encArg(x_24))) :|: x_116 >= 0, x_17 >= 0, z = 1 + (1 + x_17 + x_21) + (1 + x_116 + x_24), x_24 >= 0, x_21 >= 0
   encArg(z) -{ 0 }-> plus(plus(encArg(x_17), encArg(x_21)), minux(encArg(x_115))) :|: z = 1 + (1 + x_17 + x_21) + (1 + x_115), x_115 >= 0, x_17 >= 0, x_21 >= 0
   encArg(z) -{ 0 }-> plus(plus(encArg(x_17), encArg(x_21)), minus(encArg(x_114))) :|: z = 1 + (1 + x_17 + x_21) + (1 + x_114), x_114 >= 0, x_17 >= 0, x_21 >= 0
   encArg(z) -{ 0 }-> plus(plus(encArg(x_17), encArg(x_21)), 0) :|: z = 1 + (1 + x_17 + x_21) + x_2, x_17 >= 0, x_2 >= 0, x_21 >= 0
   encArg(z) -{ 0 }-> plus(minux(encArg(x_16)), plus(encArg(x_113), encArg(x_23))) :|: x_113 >= 0, x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_113 + x_23), x_23 >= 0
   encArg(z) -{ 0 }-> plus(minux(encArg(x_16)), minux(encArg(x_112))) :|: x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_112), x_112 >= 0
   encArg(z) -{ 0 }-> plus(minux(encArg(x_16)), minus(encArg(x_111))) :|: x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_111), x_111 >= 0
   encArg(z) -{ 0 }-> plus(minux(encArg(x_16)), 0) :|: x_16 >= 0, x_2 >= 0, z = 1 + (1 + x_16) + x_2
   encArg(z) -{ 0 }-> plus(minus(encArg(x_15)), plus(encArg(x_110), encArg(x_22))) :|: x_15 >= 0, z = 1 + (1 + x_15) + (1 + x_110 + x_22), x_110 >= 0, x_22 >= 0
   encArg(z) -{ 0 }-> plus(minus(encArg(x_15)), minux(encArg(x_19))) :|: x_15 >= 0, z = 1 + (1 + x_15) + (1 + x_19), x_19 >= 0
   encArg(z) -{ 0 }-> plus(minus(encArg(x_15)), minus(encArg(x_18))) :|: x_15 >= 0, x_18 >= 0, z = 1 + (1 + x_15) + (1 + x_18)
   encArg(z) -{ 0 }-> plus(minus(encArg(x_15)), 0) :|: x_15 >= 0, z = 1 + (1 + x_15) + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> plus(0, plus(encArg(x_119), encArg(x_25))) :|: x_1 >= 0, z = 1 + x_1 + (1 + x_119 + x_25), x_25 >= 0, x_119 >= 0
   encArg(z) -{ 0 }-> plus(0, minux(encArg(x_118))) :|: x_1 >= 0, z = 1 + x_1 + (1 + x_118), x_118 >= 0
   encArg(z) -{ 0 }-> plus(0, minus(encArg(x_117))) :|: x_1 >= 0, x_117 >= 0, z = 1 + x_1 + (1 + x_117)
   encArg(z) -{ 0 }-> minux(plus(encArg(x_14), encArg(x_2''))) :|: x_14 >= 0, z = 1 + (1 + x_14 + x_2''), x_2'' >= 0
   encArg(z) -{ 0 }-> minux(minux(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> minux(minus(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> minus(plus(encArg(x_11), encArg(x_2'))) :|: x_11 >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2')
   encArg(z) -{ 0 }-> minus(minux(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> minus(minus(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   encArg(z) -{ 0 }-> 1 + x0 :|: z - 1 >= 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 + x1 :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   encode_+(z, z') -{ 0 }-> plus(plus(encArg(x_128), encArg(x_28)), plus(encArg(x_137), encArg(x_211))) :|: x_128 >= 0, z = 1 + x_128 + x_28, z' = 1 + x_137 + x_211, x_137 >= 0, x_28 >= 0, x_211 >= 0
   encode_+(z, z') -{ 0 }-> plus(plus(encArg(x_128), encArg(x_28)), minux(encArg(z' - 1))) :|: x_128 >= 0, z = 1 + x_128 + x_28, z' - 1 >= 0, x_28 >= 0
   encode_+(z, z') -{ 0 }-> plus(plus(encArg(x_128), encArg(x_28)), minus(encArg(z' - 1))) :|: x_128 >= 0, z = 1 + x_128 + x_28, z' - 1 >= 0, x_28 >= 0
   encode_+(z, z') -{ 0 }-> plus(plus(encArg(x_128), encArg(x_28)), 0) :|: x_128 >= 0, z = 1 + x_128 + x_28, z' >= 0, x_28 >= 0
   encode_+(z, z') -{ 0 }-> plus(minux(encArg(z - 1)), plus(encArg(x_134), encArg(x_210))) :|: x_134 >= 0, z - 1 >= 0, z' = 1 + x_134 + x_210, x_210 >= 0
   encode_+(z, z') -{ 0 }-> plus(minux(encArg(z - 1)), minux(encArg(z' - 1))) :|: z - 1 >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 0 }-> plus(minux(encArg(z - 1)), minus(encArg(z' - 1))) :|: z - 1 >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 0 }-> plus(minux(encArg(z - 1)), 0) :|: z - 1 >= 0, z' >= 0
   encode_+(z, z') -{ 0 }-> plus(minus(encArg(z - 1)), plus(encArg(x_131), encArg(x_29))) :|: z' = 1 + x_131 + x_29, z - 1 >= 0, x_131 >= 0, x_29 >= 0
   encode_+(z, z') -{ 0 }-> plus(minus(encArg(z - 1)), minux(encArg(z' - 1))) :|: z' - 1 >= 0, z - 1 >= 0
   encode_+(z, z') -{ 0 }-> plus(minus(encArg(z - 1)), minus(encArg(z' - 1))) :|: z - 1 >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 0 }-> plus(minus(encArg(z - 1)), 0) :|: z - 1 >= 0, z' >= 0
   encode_+(z, z') -{ 0 }-> plus(0, plus(encArg(x_140), encArg(x_212))) :|: z >= 0, x_212 >= 0, x_140 >= 0, z' = 1 + x_140 + x_212
   encode_+(z, z') -{ 0 }-> plus(0, minux(encArg(z' - 1))) :|: z >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 0 }-> plus(0, minus(encArg(z' - 1))) :|: z' - 1 >= 0, z >= 0
   encode_+(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_+(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   encode_+(z, z') -{ 0 }-> 1 + x0 + x1 :|: z >= 0, z' >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   encode_minus(z) -{ 0 }-> minus(plus(encArg(x_122), encArg(x_26))) :|: z = 1 + x_122 + x_26, x_26 >= 0, x_122 >= 0
   encode_minus(z) -{ 0 }-> minus(minux(encArg(z - 1))) :|: z - 1 >= 0
   encode_minus(z) -{ 0 }-> minus(minus(encArg(z - 1))) :|: z - 1 >= 0
   encode_minus(z) -{ 0 }-> 0 :|: z >= 0
   encode_minus(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_minus(z) -{ 0 }-> 1 + x0 :|: z >= 0, 0 = x0, x0 >= 0
   encode_minux(z) -{ 0 }-> minux(plus(encArg(x_125), encArg(x_27))) :|: x_125 >= 0, x_27 >= 0, z = 1 + x_125 + x_27
   encode_minux(z) -{ 0 }-> minux(minux(encArg(z - 1))) :|: z - 1 >= 0
   encode_minux(z) -{ 0 }-> minux(minus(encArg(z - 1))) :|: z - 1 >= 0
   encode_minux(z) -{ 0 }-> 0 :|: z >= 0
   encode_minux(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   minus(z) -{ 0 }-> 0 :|: z >= 0
   minus(z) -{ 1 }-> z - 1 :|: z - 1 >= 0
   minus(z) -{ 0 }-> 1 + z :|: z >= 0
   minux(z) -{ 4 }-> x :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x'' = 1 + y, x' = 1 + x + y, x >= 0, y >= 0
   minux(z) -{ 3 }-> x :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, x2 = 1 + y', 1 + y = 1 + x + y', x >= 0, y' >= 0
   minux(z) -{ 2 }-> x' :|: z = 1 + x + y, x >= 0, y >= 0, 1 + x = 1 + y', 1 + y = 1 + x' + y', x' >= 0, y' >= 0
   minux(z) -{ 3 }-> x'' :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, 1 + x = 1 + y, x' = 1 + x'' + y, x'' >= 0, y >= 0
   minux(z) -{ 4 }-> y :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x'' = 1 + x + y, x >= 0, y >= 0, x' = 1 + x
   minux(z) -{ 3 }-> y :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, 1 + x = 1 + x'' + y, x'' >= 0, y >= 0, x' = 1 + x''
   minux(z) -{ 3 }-> y' :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, x2 = 1 + x + y', x >= 0, y' >= 0, 1 + y = 1 + x
   minux(z) -{ 2 }-> y' :|: z = 1 + x + y, x >= 0, y >= 0, 1 + x = 1 + x' + y', x' >= 0, y' >= 0, 1 + y = 1 + x'
   minux(z) -{ 0 }-> 0 :|: z >= 0
   minux(z) -{ 3 }-> 0 :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, v0 >= 0, v1 >= 0, x' = v0, x'' = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, v0 >= 0, v1 >= 0, x' = v0, 1 + x = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, v0 >= 0, v1 >= 0, x' = v0, 0 = v1
   minux(z) -{ 2 }-> 0 :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, x2 = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, 1 + x = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, 0 = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + (1 + x3) + y, y >= 0, x3 >= 0, v0 >= 0, v1 >= 0, 0 = v0, x3 = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 0 = v0, 1 + x = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   minux(z) -{ 3 }-> 1 + x0 + x1 :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x' = x0, x0 >= 0, x1 >= 0, x'' = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, x' = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, x' = x0, x0 >= 0, x1 >= 0, 0 = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, x2 = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, 0 = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + (1 + x3) + y, y >= 0, x3 >= 0, 0 = x0, x0 >= 0, x1 >= 0, x3 = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 0 = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   plus(z, z') -{ 1 }-> x :|: z = 1 + x + (z' - 1), x >= 0, z' - 1 >= 0
   plus(z, z') -{ 1 }-> y :|: z' = 1 + (z - 1) + y, z - 1 >= 0, y >= 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 0 }-> 1 + z + z' :|: z >= 0, z' >= 0


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

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

   { minus }
   { minux }
   { plus }
   { encArg }
   { encode_minus }
   { encode_+ }
   { encode_minux }

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

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

   encArg(z) -{ 0 }-> plus(plus(encArg(x_17), encArg(x_21)), plus(encArg(x_116), encArg(x_24))) :|: x_116 >= 0, x_17 >= 0, z = 1 + (1 + x_17 + x_21) + (1 + x_116 + x_24), x_24 >= 0, x_21 >= 0
   encArg(z) -{ 0 }-> plus(plus(encArg(x_17), encArg(x_21)), minux(encArg(x_115))) :|: z = 1 + (1 + x_17 + x_21) + (1 + x_115), x_115 >= 0, x_17 >= 0, x_21 >= 0
   encArg(z) -{ 0 }-> plus(plus(encArg(x_17), encArg(x_21)), minus(encArg(x_114))) :|: z = 1 + (1 + x_17 + x_21) + (1 + x_114), x_114 >= 0, x_17 >= 0, x_21 >= 0
   encArg(z) -{ 0 }-> plus(plus(encArg(x_17), encArg(x_21)), 0) :|: z = 1 + (1 + x_17 + x_21) + x_2, x_17 >= 0, x_2 >= 0, x_21 >= 0
   encArg(z) -{ 0 }-> plus(minux(encArg(x_16)), plus(encArg(x_113), encArg(x_23))) :|: x_113 >= 0, x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_113 + x_23), x_23 >= 0
   encArg(z) -{ 0 }-> plus(minux(encArg(x_16)), minux(encArg(x_112))) :|: x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_112), x_112 >= 0
   encArg(z) -{ 0 }-> plus(minux(encArg(x_16)), minus(encArg(x_111))) :|: x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_111), x_111 >= 0
   encArg(z) -{ 0 }-> plus(minux(encArg(x_16)), 0) :|: x_16 >= 0, x_2 >= 0, z = 1 + (1 + x_16) + x_2
   encArg(z) -{ 0 }-> plus(minus(encArg(x_15)), plus(encArg(x_110), encArg(x_22))) :|: x_15 >= 0, z = 1 + (1 + x_15) + (1 + x_110 + x_22), x_110 >= 0, x_22 >= 0
   encArg(z) -{ 0 }-> plus(minus(encArg(x_15)), minux(encArg(x_19))) :|: x_15 >= 0, z = 1 + (1 + x_15) + (1 + x_19), x_19 >= 0
   encArg(z) -{ 0 }-> plus(minus(encArg(x_15)), minus(encArg(x_18))) :|: x_15 >= 0, x_18 >= 0, z = 1 + (1 + x_15) + (1 + x_18)
   encArg(z) -{ 0 }-> plus(minus(encArg(x_15)), 0) :|: x_15 >= 0, z = 1 + (1 + x_15) + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> plus(0, plus(encArg(x_119), encArg(x_25))) :|: x_1 >= 0, z = 1 + x_1 + (1 + x_119 + x_25), x_25 >= 0, x_119 >= 0
   encArg(z) -{ 0 }-> plus(0, minux(encArg(x_118))) :|: x_1 >= 0, z = 1 + x_1 + (1 + x_118), x_118 >= 0
   encArg(z) -{ 0 }-> plus(0, minus(encArg(x_117))) :|: x_1 >= 0, x_117 >= 0, z = 1 + x_1 + (1 + x_117)
   encArg(z) -{ 0 }-> minux(plus(encArg(x_14), encArg(x_2''))) :|: x_14 >= 0, z = 1 + (1 + x_14 + x_2''), x_2'' >= 0
   encArg(z) -{ 0 }-> minux(minux(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> minux(minus(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> minus(plus(encArg(x_11), encArg(x_2'))) :|: x_11 >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2')
   encArg(z) -{ 0 }-> minus(minux(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> minus(minus(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   encArg(z) -{ 0 }-> 1 + x0 :|: z - 1 >= 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 + x1 :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   encode_+(z, z') -{ 0 }-> plus(plus(encArg(x_128), encArg(x_28)), plus(encArg(x_137), encArg(x_211))) :|: x_128 >= 0, z = 1 + x_128 + x_28, z' = 1 + x_137 + x_211, x_137 >= 0, x_28 >= 0, x_211 >= 0
   encode_+(z, z') -{ 0 }-> plus(plus(encArg(x_128), encArg(x_28)), minux(encArg(z' - 1))) :|: x_128 >= 0, z = 1 + x_128 + x_28, z' - 1 >= 0, x_28 >= 0
   encode_+(z, z') -{ 0 }-> plus(plus(encArg(x_128), encArg(x_28)), minus(encArg(z' - 1))) :|: x_128 >= 0, z = 1 + x_128 + x_28, z' - 1 >= 0, x_28 >= 0
   encode_+(z, z') -{ 0 }-> plus(plus(encArg(x_128), encArg(x_28)), 0) :|: x_128 >= 0, z = 1 + x_128 + x_28, z' >= 0, x_28 >= 0
   encode_+(z, z') -{ 0 }-> plus(minux(encArg(z - 1)), plus(encArg(x_134), encArg(x_210))) :|: x_134 >= 0, z - 1 >= 0, z' = 1 + x_134 + x_210, x_210 >= 0
   encode_+(z, z') -{ 0 }-> plus(minux(encArg(z - 1)), minux(encArg(z' - 1))) :|: z - 1 >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 0 }-> plus(minux(encArg(z - 1)), minus(encArg(z' - 1))) :|: z - 1 >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 0 }-> plus(minux(encArg(z - 1)), 0) :|: z - 1 >= 0, z' >= 0
   encode_+(z, z') -{ 0 }-> plus(minus(encArg(z - 1)), plus(encArg(x_131), encArg(x_29))) :|: z' = 1 + x_131 + x_29, z - 1 >= 0, x_131 >= 0, x_29 >= 0
   encode_+(z, z') -{ 0 }-> plus(minus(encArg(z - 1)), minux(encArg(z' - 1))) :|: z' - 1 >= 0, z - 1 >= 0
   encode_+(z, z') -{ 0 }-> plus(minus(encArg(z - 1)), minus(encArg(z' - 1))) :|: z - 1 >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 0 }-> plus(minus(encArg(z - 1)), 0) :|: z - 1 >= 0, z' >= 0
   encode_+(z, z') -{ 0 }-> plus(0, plus(encArg(x_140), encArg(x_212))) :|: z >= 0, x_212 >= 0, x_140 >= 0, z' = 1 + x_140 + x_212
   encode_+(z, z') -{ 0 }-> plus(0, minux(encArg(z' - 1))) :|: z >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 0 }-> plus(0, minus(encArg(z' - 1))) :|: z' - 1 >= 0, z >= 0
   encode_+(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_+(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   encode_+(z, z') -{ 0 }-> 1 + x0 + x1 :|: z >= 0, z' >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   encode_minus(z) -{ 0 }-> minus(plus(encArg(x_122), encArg(x_26))) :|: z = 1 + x_122 + x_26, x_26 >= 0, x_122 >= 0
   encode_minus(z) -{ 0 }-> minus(minux(encArg(z - 1))) :|: z - 1 >= 0
   encode_minus(z) -{ 0 }-> minus(minus(encArg(z - 1))) :|: z - 1 >= 0
   encode_minus(z) -{ 0 }-> 0 :|: z >= 0
   encode_minus(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_minus(z) -{ 0 }-> 1 + x0 :|: z >= 0, 0 = x0, x0 >= 0
   encode_minux(z) -{ 0 }-> minux(plus(encArg(x_125), encArg(x_27))) :|: x_125 >= 0, x_27 >= 0, z = 1 + x_125 + x_27
   encode_minux(z) -{ 0 }-> minux(minux(encArg(z - 1))) :|: z - 1 >= 0
   encode_minux(z) -{ 0 }-> minux(minus(encArg(z - 1))) :|: z - 1 >= 0
   encode_minux(z) -{ 0 }-> 0 :|: z >= 0
   encode_minux(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   minus(z) -{ 0 }-> 0 :|: z >= 0
   minus(z) -{ 1 }-> z - 1 :|: z - 1 >= 0
   minus(z) -{ 0 }-> 1 + z :|: z >= 0
   minux(z) -{ 4 }-> x :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x'' = 1 + y, x' = 1 + x + y, x >= 0, y >= 0
   minux(z) -{ 3 }-> x :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, x2 = 1 + y', 1 + y = 1 + x + y', x >= 0, y' >= 0
   minux(z) -{ 2 }-> x' :|: z = 1 + x + y, x >= 0, y >= 0, 1 + x = 1 + y', 1 + y = 1 + x' + y', x' >= 0, y' >= 0
   minux(z) -{ 3 }-> x'' :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, 1 + x = 1 + y, x' = 1 + x'' + y, x'' >= 0, y >= 0
   minux(z) -{ 4 }-> y :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x'' = 1 + x + y, x >= 0, y >= 0, x' = 1 + x
   minux(z) -{ 3 }-> y :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, 1 + x = 1 + x'' + y, x'' >= 0, y >= 0, x' = 1 + x''
   minux(z) -{ 3 }-> y' :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, x2 = 1 + x + y', x >= 0, y' >= 0, 1 + y = 1 + x
   minux(z) -{ 2 }-> y' :|: z = 1 + x + y, x >= 0, y >= 0, 1 + x = 1 + x' + y', x' >= 0, y' >= 0, 1 + y = 1 + x'
   minux(z) -{ 0 }-> 0 :|: z >= 0
   minux(z) -{ 3 }-> 0 :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, v0 >= 0, v1 >= 0, x' = v0, x'' = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, v0 >= 0, v1 >= 0, x' = v0, 1 + x = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, v0 >= 0, v1 >= 0, x' = v0, 0 = v1
   minux(z) -{ 2 }-> 0 :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, x2 = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, 1 + x = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, 0 = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + (1 + x3) + y, y >= 0, x3 >= 0, v0 >= 0, v1 >= 0, 0 = v0, x3 = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 0 = v0, 1 + x = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   minux(z) -{ 3 }-> 1 + x0 + x1 :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x' = x0, x0 >= 0, x1 >= 0, x'' = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, x' = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, x' = x0, x0 >= 0, x1 >= 0, 0 = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, x2 = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, 0 = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + (1 + x3) + y, y >= 0, x3 >= 0, 0 = x0, x0 >= 0, x1 >= 0, x3 = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 0 = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   plus(z, z') -{ 1 }-> x :|: z = 1 + x + (z' - 1), x >= 0, z' - 1 >= 0
   plus(z, z') -{ 1 }-> y :|: z' = 1 + (z - 1) + y, z - 1 >= 0, y >= 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 0 }-> 1 + z + z' :|: z >= 0, z' >= 0

Function symbols to be analyzed: {minus}, {minux}, {plus}, {encArg}, {encode_minus}, {encode_+}, {encode_minux}

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(27) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
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(28)
Obligation:
Complexity RNTS consisting of the following rules:

   encArg(z) -{ 0 }-> plus(plus(encArg(x_17), encArg(x_21)), plus(encArg(x_116), encArg(x_24))) :|: x_116 >= 0, x_17 >= 0, z = 1 + (1 + x_17 + x_21) + (1 + x_116 + x_24), x_24 >= 0, x_21 >= 0
   encArg(z) -{ 0 }-> plus(plus(encArg(x_17), encArg(x_21)), minux(encArg(x_115))) :|: z = 1 + (1 + x_17 + x_21) + (1 + x_115), x_115 >= 0, x_17 >= 0, x_21 >= 0
   encArg(z) -{ 0 }-> plus(plus(encArg(x_17), encArg(x_21)), minus(encArg(x_114))) :|: z = 1 + (1 + x_17 + x_21) + (1 + x_114), x_114 >= 0, x_17 >= 0, x_21 >= 0
   encArg(z) -{ 0 }-> plus(plus(encArg(x_17), encArg(x_21)), 0) :|: z = 1 + (1 + x_17 + x_21) + x_2, x_17 >= 0, x_2 >= 0, x_21 >= 0
   encArg(z) -{ 0 }-> plus(minux(encArg(x_16)), plus(encArg(x_113), encArg(x_23))) :|: x_113 >= 0, x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_113 + x_23), x_23 >= 0
   encArg(z) -{ 0 }-> plus(minux(encArg(x_16)), minux(encArg(x_112))) :|: x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_112), x_112 >= 0
   encArg(z) -{ 0 }-> plus(minux(encArg(x_16)), minus(encArg(x_111))) :|: x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_111), x_111 >= 0
   encArg(z) -{ 0 }-> plus(minux(encArg(x_16)), 0) :|: x_16 >= 0, x_2 >= 0, z = 1 + (1 + x_16) + x_2
   encArg(z) -{ 0 }-> plus(minus(encArg(x_15)), plus(encArg(x_110), encArg(x_22))) :|: x_15 >= 0, z = 1 + (1 + x_15) + (1 + x_110 + x_22), x_110 >= 0, x_22 >= 0
   encArg(z) -{ 0 }-> plus(minus(encArg(x_15)), minux(encArg(x_19))) :|: x_15 >= 0, z = 1 + (1 + x_15) + (1 + x_19), x_19 >= 0
   encArg(z) -{ 0 }-> plus(minus(encArg(x_15)), minus(encArg(x_18))) :|: x_15 >= 0, x_18 >= 0, z = 1 + (1 + x_15) + (1 + x_18)
   encArg(z) -{ 0 }-> plus(minus(encArg(x_15)), 0) :|: x_15 >= 0, z = 1 + (1 + x_15) + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> plus(0, plus(encArg(x_119), encArg(x_25))) :|: x_1 >= 0, z = 1 + x_1 + (1 + x_119 + x_25), x_25 >= 0, x_119 >= 0
   encArg(z) -{ 0 }-> plus(0, minux(encArg(x_118))) :|: x_1 >= 0, z = 1 + x_1 + (1 + x_118), x_118 >= 0
   encArg(z) -{ 0 }-> plus(0, minus(encArg(x_117))) :|: x_1 >= 0, x_117 >= 0, z = 1 + x_1 + (1 + x_117)
   encArg(z) -{ 0 }-> minux(plus(encArg(x_14), encArg(x_2''))) :|: x_14 >= 0, z = 1 + (1 + x_14 + x_2''), x_2'' >= 0
   encArg(z) -{ 0 }-> minux(minux(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> minux(minus(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> minus(plus(encArg(x_11), encArg(x_2'))) :|: x_11 >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2')
   encArg(z) -{ 0 }-> minus(minux(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> minus(minus(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   encArg(z) -{ 0 }-> 1 + x0 :|: z - 1 >= 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 + x1 :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   encode_+(z, z') -{ 0 }-> plus(plus(encArg(x_128), encArg(x_28)), plus(encArg(x_137), encArg(x_211))) :|: x_128 >= 0, z = 1 + x_128 + x_28, z' = 1 + x_137 + x_211, x_137 >= 0, x_28 >= 0, x_211 >= 0
   encode_+(z, z') -{ 0 }-> plus(plus(encArg(x_128), encArg(x_28)), minux(encArg(z' - 1))) :|: x_128 >= 0, z = 1 + x_128 + x_28, z' - 1 >= 0, x_28 >= 0
   encode_+(z, z') -{ 0 }-> plus(plus(encArg(x_128), encArg(x_28)), minus(encArg(z' - 1))) :|: x_128 >= 0, z = 1 + x_128 + x_28, z' - 1 >= 0, x_28 >= 0
   encode_+(z, z') -{ 0 }-> plus(plus(encArg(x_128), encArg(x_28)), 0) :|: x_128 >= 0, z = 1 + x_128 + x_28, z' >= 0, x_28 >= 0
   encode_+(z, z') -{ 0 }-> plus(minux(encArg(z - 1)), plus(encArg(x_134), encArg(x_210))) :|: x_134 >= 0, z - 1 >= 0, z' = 1 + x_134 + x_210, x_210 >= 0
   encode_+(z, z') -{ 0 }-> plus(minux(encArg(z - 1)), minux(encArg(z' - 1))) :|: z - 1 >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 0 }-> plus(minux(encArg(z - 1)), minus(encArg(z' - 1))) :|: z - 1 >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 0 }-> plus(minux(encArg(z - 1)), 0) :|: z - 1 >= 0, z' >= 0
   encode_+(z, z') -{ 0 }-> plus(minus(encArg(z - 1)), plus(encArg(x_131), encArg(x_29))) :|: z' = 1 + x_131 + x_29, z - 1 >= 0, x_131 >= 0, x_29 >= 0
   encode_+(z, z') -{ 0 }-> plus(minus(encArg(z - 1)), minux(encArg(z' - 1))) :|: z' - 1 >= 0, z - 1 >= 0
   encode_+(z, z') -{ 0 }-> plus(minus(encArg(z - 1)), minus(encArg(z' - 1))) :|: z - 1 >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 0 }-> plus(minus(encArg(z - 1)), 0) :|: z - 1 >= 0, z' >= 0
   encode_+(z, z') -{ 0 }-> plus(0, plus(encArg(x_140), encArg(x_212))) :|: z >= 0, x_212 >= 0, x_140 >= 0, z' = 1 + x_140 + x_212
   encode_+(z, z') -{ 0 }-> plus(0, minux(encArg(z' - 1))) :|: z >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 0 }-> plus(0, minus(encArg(z' - 1))) :|: z' - 1 >= 0, z >= 0
   encode_+(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_+(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   encode_+(z, z') -{ 0 }-> 1 + x0 + x1 :|: z >= 0, z' >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   encode_minus(z) -{ 0 }-> minus(plus(encArg(x_122), encArg(x_26))) :|: z = 1 + x_122 + x_26, x_26 >= 0, x_122 >= 0
   encode_minus(z) -{ 0 }-> minus(minux(encArg(z - 1))) :|: z - 1 >= 0
   encode_minus(z) -{ 0 }-> minus(minus(encArg(z - 1))) :|: z - 1 >= 0
   encode_minus(z) -{ 0 }-> 0 :|: z >= 0
   encode_minus(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_minus(z) -{ 0 }-> 1 + x0 :|: z >= 0, 0 = x0, x0 >= 0
   encode_minux(z) -{ 0 }-> minux(plus(encArg(x_125), encArg(x_27))) :|: x_125 >= 0, x_27 >= 0, z = 1 + x_125 + x_27
   encode_minux(z) -{ 0 }-> minux(minux(encArg(z - 1))) :|: z - 1 >= 0
   encode_minux(z) -{ 0 }-> minux(minus(encArg(z - 1))) :|: z - 1 >= 0
   encode_minux(z) -{ 0 }-> 0 :|: z >= 0
   encode_minux(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   minus(z) -{ 0 }-> 0 :|: z >= 0
   minus(z) -{ 1 }-> z - 1 :|: z - 1 >= 0
   minus(z) -{ 0 }-> 1 + z :|: z >= 0
   minux(z) -{ 4 }-> x :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x'' = 1 + y, x' = 1 + x + y, x >= 0, y >= 0
   minux(z) -{ 3 }-> x :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, x2 = 1 + y', 1 + y = 1 + x + y', x >= 0, y' >= 0
   minux(z) -{ 2 }-> x' :|: z = 1 + x + y, x >= 0, y >= 0, 1 + x = 1 + y', 1 + y = 1 + x' + y', x' >= 0, y' >= 0
   minux(z) -{ 3 }-> x'' :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, 1 + x = 1 + y, x' = 1 + x'' + y, x'' >= 0, y >= 0
   minux(z) -{ 4 }-> y :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x'' = 1 + x + y, x >= 0, y >= 0, x' = 1 + x
   minux(z) -{ 3 }-> y :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, 1 + x = 1 + x'' + y, x'' >= 0, y >= 0, x' = 1 + x''
   minux(z) -{ 3 }-> y' :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, x2 = 1 + x + y', x >= 0, y' >= 0, 1 + y = 1 + x
   minux(z) -{ 2 }-> y' :|: z = 1 + x + y, x >= 0, y >= 0, 1 + x = 1 + x' + y', x' >= 0, y' >= 0, 1 + y = 1 + x'
   minux(z) -{ 0 }-> 0 :|: z >= 0
   minux(z) -{ 3 }-> 0 :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, v0 >= 0, v1 >= 0, x' = v0, x'' = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, v0 >= 0, v1 >= 0, x' = v0, 1 + x = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, v0 >= 0, v1 >= 0, x' = v0, 0 = v1
   minux(z) -{ 2 }-> 0 :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, x2 = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, 1 + x = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, 0 = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + (1 + x3) + y, y >= 0, x3 >= 0, v0 >= 0, v1 >= 0, 0 = v0, x3 = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 0 = v0, 1 + x = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   minux(z) -{ 3 }-> 1 + x0 + x1 :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x' = x0, x0 >= 0, x1 >= 0, x'' = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, x' = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, x' = x0, x0 >= 0, x1 >= 0, 0 = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, x2 = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, 0 = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + (1 + x3) + y, y >= 0, x3 >= 0, 0 = x0, x0 >= 0, x1 >= 0, x3 = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 0 = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   plus(z, z') -{ 1 }-> x :|: z = 1 + x + (z' - 1), x >= 0, z' - 1 >= 0
   plus(z, z') -{ 1 }-> y :|: z' = 1 + (z - 1) + y, z - 1 >= 0, y >= 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 0 }-> 1 + z + z' :|: z >= 0, z' >= 0

Function symbols to be analyzed: {minus}, {minux}, {plus}, {encArg}, {encode_minus}, {encode_+}, {encode_minux}

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

(29) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   encArg(z) -{ 0 }-> plus(plus(encArg(x_17), encArg(x_21)), plus(encArg(x_116), encArg(x_24))) :|: x_116 >= 0, x_17 >= 0, z = 1 + (1 + x_17 + x_21) + (1 + x_116 + x_24), x_24 >= 0, x_21 >= 0
   encArg(z) -{ 0 }-> plus(plus(encArg(x_17), encArg(x_21)), minux(encArg(x_115))) :|: z = 1 + (1 + x_17 + x_21) + (1 + x_115), x_115 >= 0, x_17 >= 0, x_21 >= 0
   encArg(z) -{ 0 }-> plus(plus(encArg(x_17), encArg(x_21)), minus(encArg(x_114))) :|: z = 1 + (1 + x_17 + x_21) + (1 + x_114), x_114 >= 0, x_17 >= 0, x_21 >= 0
   encArg(z) -{ 0 }-> plus(plus(encArg(x_17), encArg(x_21)), 0) :|: z = 1 + (1 + x_17 + x_21) + x_2, x_17 >= 0, x_2 >= 0, x_21 >= 0
   encArg(z) -{ 0 }-> plus(minux(encArg(x_16)), plus(encArg(x_113), encArg(x_23))) :|: x_113 >= 0, x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_113 + x_23), x_23 >= 0
   encArg(z) -{ 0 }-> plus(minux(encArg(x_16)), minux(encArg(x_112))) :|: x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_112), x_112 >= 0
   encArg(z) -{ 0 }-> plus(minux(encArg(x_16)), minus(encArg(x_111))) :|: x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_111), x_111 >= 0
   encArg(z) -{ 0 }-> plus(minux(encArg(x_16)), 0) :|: x_16 >= 0, x_2 >= 0, z = 1 + (1 + x_16) + x_2
   encArg(z) -{ 0 }-> plus(minus(encArg(x_15)), plus(encArg(x_110), encArg(x_22))) :|: x_15 >= 0, z = 1 + (1 + x_15) + (1 + x_110 + x_22), x_110 >= 0, x_22 >= 0
   encArg(z) -{ 0 }-> plus(minus(encArg(x_15)), minux(encArg(x_19))) :|: x_15 >= 0, z = 1 + (1 + x_15) + (1 + x_19), x_19 >= 0
   encArg(z) -{ 0 }-> plus(minus(encArg(x_15)), minus(encArg(x_18))) :|: x_15 >= 0, x_18 >= 0, z = 1 + (1 + x_15) + (1 + x_18)
   encArg(z) -{ 0 }-> plus(minus(encArg(x_15)), 0) :|: x_15 >= 0, z = 1 + (1 + x_15) + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> plus(0, plus(encArg(x_119), encArg(x_25))) :|: x_1 >= 0, z = 1 + x_1 + (1 + x_119 + x_25), x_25 >= 0, x_119 >= 0
   encArg(z) -{ 0 }-> plus(0, minux(encArg(x_118))) :|: x_1 >= 0, z = 1 + x_1 + (1 + x_118), x_118 >= 0
   encArg(z) -{ 0 }-> plus(0, minus(encArg(x_117))) :|: x_1 >= 0, x_117 >= 0, z = 1 + x_1 + (1 + x_117)
   encArg(z) -{ 0 }-> minux(plus(encArg(x_14), encArg(x_2''))) :|: x_14 >= 0, z = 1 + (1 + x_14 + x_2''), x_2'' >= 0
   encArg(z) -{ 0 }-> minux(minux(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> minux(minus(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> minus(plus(encArg(x_11), encArg(x_2'))) :|: x_11 >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2')
   encArg(z) -{ 0 }-> minus(minux(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> minus(minus(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   encArg(z) -{ 0 }-> 1 + x0 :|: z - 1 >= 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 + x1 :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   encode_+(z, z') -{ 0 }-> plus(plus(encArg(x_128), encArg(x_28)), plus(encArg(x_137), encArg(x_211))) :|: x_128 >= 0, z = 1 + x_128 + x_28, z' = 1 + x_137 + x_211, x_137 >= 0, x_28 >= 0, x_211 >= 0
   encode_+(z, z') -{ 0 }-> plus(plus(encArg(x_128), encArg(x_28)), minux(encArg(z' - 1))) :|: x_128 >= 0, z = 1 + x_128 + x_28, z' - 1 >= 0, x_28 >= 0
   encode_+(z, z') -{ 0 }-> plus(plus(encArg(x_128), encArg(x_28)), minus(encArg(z' - 1))) :|: x_128 >= 0, z = 1 + x_128 + x_28, z' - 1 >= 0, x_28 >= 0
   encode_+(z, z') -{ 0 }-> plus(plus(encArg(x_128), encArg(x_28)), 0) :|: x_128 >= 0, z = 1 + x_128 + x_28, z' >= 0, x_28 >= 0
   encode_+(z, z') -{ 0 }-> plus(minux(encArg(z - 1)), plus(encArg(x_134), encArg(x_210))) :|: x_134 >= 0, z - 1 >= 0, z' = 1 + x_134 + x_210, x_210 >= 0
   encode_+(z, z') -{ 0 }-> plus(minux(encArg(z - 1)), minux(encArg(z' - 1))) :|: z - 1 >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 0 }-> plus(minux(encArg(z - 1)), minus(encArg(z' - 1))) :|: z - 1 >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 0 }-> plus(minux(encArg(z - 1)), 0) :|: z - 1 >= 0, z' >= 0
   encode_+(z, z') -{ 0 }-> plus(minus(encArg(z - 1)), plus(encArg(x_131), encArg(x_29))) :|: z' = 1 + x_131 + x_29, z - 1 >= 0, x_131 >= 0, x_29 >= 0
   encode_+(z, z') -{ 0 }-> plus(minus(encArg(z - 1)), minux(encArg(z' - 1))) :|: z' - 1 >= 0, z - 1 >= 0
   encode_+(z, z') -{ 0 }-> plus(minus(encArg(z - 1)), minus(encArg(z' - 1))) :|: z - 1 >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 0 }-> plus(minus(encArg(z - 1)), 0) :|: z - 1 >= 0, z' >= 0
   encode_+(z, z') -{ 0 }-> plus(0, plus(encArg(x_140), encArg(x_212))) :|: z >= 0, x_212 >= 0, x_140 >= 0, z' = 1 + x_140 + x_212
   encode_+(z, z') -{ 0 }-> plus(0, minux(encArg(z' - 1))) :|: z >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 0 }-> plus(0, minus(encArg(z' - 1))) :|: z' - 1 >= 0, z >= 0
   encode_+(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_+(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   encode_+(z, z') -{ 0 }-> 1 + x0 + x1 :|: z >= 0, z' >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   encode_minus(z) -{ 0 }-> minus(plus(encArg(x_122), encArg(x_26))) :|: z = 1 + x_122 + x_26, x_26 >= 0, x_122 >= 0
   encode_minus(z) -{ 0 }-> minus(minux(encArg(z - 1))) :|: z - 1 >= 0
   encode_minus(z) -{ 0 }-> minus(minus(encArg(z - 1))) :|: z - 1 >= 0
   encode_minus(z) -{ 0 }-> 0 :|: z >= 0
   encode_minus(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_minus(z) -{ 0 }-> 1 + x0 :|: z >= 0, 0 = x0, x0 >= 0
   encode_minux(z) -{ 0 }-> minux(plus(encArg(x_125), encArg(x_27))) :|: x_125 >= 0, x_27 >= 0, z = 1 + x_125 + x_27
   encode_minux(z) -{ 0 }-> minux(minux(encArg(z - 1))) :|: z - 1 >= 0
   encode_minux(z) -{ 0 }-> minux(minus(encArg(z - 1))) :|: z - 1 >= 0
   encode_minux(z) -{ 0 }-> 0 :|: z >= 0
   encode_minux(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   minus(z) -{ 0 }-> 0 :|: z >= 0
   minus(z) -{ 1 }-> z - 1 :|: z - 1 >= 0
   minus(z) -{ 0 }-> 1 + z :|: z >= 0
   minux(z) -{ 4 }-> x :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x'' = 1 + y, x' = 1 + x + y, x >= 0, y >= 0
   minux(z) -{ 3 }-> x :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, x2 = 1 + y', 1 + y = 1 + x + y', x >= 0, y' >= 0
   minux(z) -{ 2 }-> x' :|: z = 1 + x + y, x >= 0, y >= 0, 1 + x = 1 + y', 1 + y = 1 + x' + y', x' >= 0, y' >= 0
   minux(z) -{ 3 }-> x'' :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, 1 + x = 1 + y, x' = 1 + x'' + y, x'' >= 0, y >= 0
   minux(z) -{ 4 }-> y :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x'' = 1 + x + y, x >= 0, y >= 0, x' = 1 + x
   minux(z) -{ 3 }-> y :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, 1 + x = 1 + x'' + y, x'' >= 0, y >= 0, x' = 1 + x''
   minux(z) -{ 3 }-> y' :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, x2 = 1 + x + y', x >= 0, y' >= 0, 1 + y = 1 + x
   minux(z) -{ 2 }-> y' :|: z = 1 + x + y, x >= 0, y >= 0, 1 + x = 1 + x' + y', x' >= 0, y' >= 0, 1 + y = 1 + x'
   minux(z) -{ 0 }-> 0 :|: z >= 0
   minux(z) -{ 3 }-> 0 :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, v0 >= 0, v1 >= 0, x' = v0, x'' = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, v0 >= 0, v1 >= 0, x' = v0, 1 + x = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, v0 >= 0, v1 >= 0, x' = v0, 0 = v1
   minux(z) -{ 2 }-> 0 :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, x2 = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, 1 + x = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, 0 = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + (1 + x3) + y, y >= 0, x3 >= 0, v0 >= 0, v1 >= 0, 0 = v0, x3 = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 0 = v0, 1 + x = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   minux(z) -{ 3 }-> 1 + x0 + x1 :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x' = x0, x0 >= 0, x1 >= 0, x'' = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, x' = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, x' = x0, x0 >= 0, x1 >= 0, 0 = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, x2 = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, 0 = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + (1 + x3) + y, y >= 0, x3 >= 0, 0 = x0, x0 >= 0, x1 >= 0, x3 = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 0 = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   plus(z, z') -{ 1 }-> x :|: z = 1 + x + (z' - 1), x >= 0, z' - 1 >= 0
   plus(z, z') -{ 1 }-> y :|: z' = 1 + (z - 1) + y, z - 1 >= 0, y >= 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 0 }-> 1 + z + z' :|: z >= 0, z' >= 0

Function symbols to be analyzed: {minus}, {minux}, {plus}, {encArg}, {encode_minus}, {encode_+}, {encode_minux}
Previous analysis results are:
  minus: runtime: ?, size: O(n^1) [1 + z]

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

(31) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   encArg(z) -{ 0 }-> plus(plus(encArg(x_17), encArg(x_21)), plus(encArg(x_116), encArg(x_24))) :|: x_116 >= 0, x_17 >= 0, z = 1 + (1 + x_17 + x_21) + (1 + x_116 + x_24), x_24 >= 0, x_21 >= 0
   encArg(z) -{ 0 }-> plus(plus(encArg(x_17), encArg(x_21)), minux(encArg(x_115))) :|: z = 1 + (1 + x_17 + x_21) + (1 + x_115), x_115 >= 0, x_17 >= 0, x_21 >= 0
   encArg(z) -{ 0 }-> plus(plus(encArg(x_17), encArg(x_21)), minus(encArg(x_114))) :|: z = 1 + (1 + x_17 + x_21) + (1 + x_114), x_114 >= 0, x_17 >= 0, x_21 >= 0
   encArg(z) -{ 0 }-> plus(plus(encArg(x_17), encArg(x_21)), 0) :|: z = 1 + (1 + x_17 + x_21) + x_2, x_17 >= 0, x_2 >= 0, x_21 >= 0
   encArg(z) -{ 0 }-> plus(minux(encArg(x_16)), plus(encArg(x_113), encArg(x_23))) :|: x_113 >= 0, x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_113 + x_23), x_23 >= 0
   encArg(z) -{ 0 }-> plus(minux(encArg(x_16)), minux(encArg(x_112))) :|: x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_112), x_112 >= 0
   encArg(z) -{ 0 }-> plus(minux(encArg(x_16)), minus(encArg(x_111))) :|: x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_111), x_111 >= 0
   encArg(z) -{ 0 }-> plus(minux(encArg(x_16)), 0) :|: x_16 >= 0, x_2 >= 0, z = 1 + (1 + x_16) + x_2
   encArg(z) -{ 0 }-> plus(minus(encArg(x_15)), plus(encArg(x_110), encArg(x_22))) :|: x_15 >= 0, z = 1 + (1 + x_15) + (1 + x_110 + x_22), x_110 >= 0, x_22 >= 0
   encArg(z) -{ 0 }-> plus(minus(encArg(x_15)), minux(encArg(x_19))) :|: x_15 >= 0, z = 1 + (1 + x_15) + (1 + x_19), x_19 >= 0
   encArg(z) -{ 0 }-> plus(minus(encArg(x_15)), minus(encArg(x_18))) :|: x_15 >= 0, x_18 >= 0, z = 1 + (1 + x_15) + (1 + x_18)
   encArg(z) -{ 0 }-> plus(minus(encArg(x_15)), 0) :|: x_15 >= 0, z = 1 + (1 + x_15) + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> plus(0, plus(encArg(x_119), encArg(x_25))) :|: x_1 >= 0, z = 1 + x_1 + (1 + x_119 + x_25), x_25 >= 0, x_119 >= 0
   encArg(z) -{ 0 }-> plus(0, minux(encArg(x_118))) :|: x_1 >= 0, z = 1 + x_1 + (1 + x_118), x_118 >= 0
   encArg(z) -{ 0 }-> plus(0, minus(encArg(x_117))) :|: x_1 >= 0, x_117 >= 0, z = 1 + x_1 + (1 + x_117)
   encArg(z) -{ 0 }-> minux(plus(encArg(x_14), encArg(x_2''))) :|: x_14 >= 0, z = 1 + (1 + x_14 + x_2''), x_2'' >= 0
   encArg(z) -{ 0 }-> minux(minux(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> minux(minus(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> minus(plus(encArg(x_11), encArg(x_2'))) :|: x_11 >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2')
   encArg(z) -{ 0 }-> minus(minux(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> minus(minus(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   encArg(z) -{ 0 }-> 1 + x0 :|: z - 1 >= 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 + x1 :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   encode_+(z, z') -{ 0 }-> plus(plus(encArg(x_128), encArg(x_28)), plus(encArg(x_137), encArg(x_211))) :|: x_128 >= 0, z = 1 + x_128 + x_28, z' = 1 + x_137 + x_211, x_137 >= 0, x_28 >= 0, x_211 >= 0
   encode_+(z, z') -{ 0 }-> plus(plus(encArg(x_128), encArg(x_28)), minux(encArg(z' - 1))) :|: x_128 >= 0, z = 1 + x_128 + x_28, z' - 1 >= 0, x_28 >= 0
   encode_+(z, z') -{ 0 }-> plus(plus(encArg(x_128), encArg(x_28)), minus(encArg(z' - 1))) :|: x_128 >= 0, z = 1 + x_128 + x_28, z' - 1 >= 0, x_28 >= 0
   encode_+(z, z') -{ 0 }-> plus(plus(encArg(x_128), encArg(x_28)), 0) :|: x_128 >= 0, z = 1 + x_128 + x_28, z' >= 0, x_28 >= 0
   encode_+(z, z') -{ 0 }-> plus(minux(encArg(z - 1)), plus(encArg(x_134), encArg(x_210))) :|: x_134 >= 0, z - 1 >= 0, z' = 1 + x_134 + x_210, x_210 >= 0
   encode_+(z, z') -{ 0 }-> plus(minux(encArg(z - 1)), minux(encArg(z' - 1))) :|: z - 1 >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 0 }-> plus(minux(encArg(z - 1)), minus(encArg(z' - 1))) :|: z - 1 >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 0 }-> plus(minux(encArg(z - 1)), 0) :|: z - 1 >= 0, z' >= 0
   encode_+(z, z') -{ 0 }-> plus(minus(encArg(z - 1)), plus(encArg(x_131), encArg(x_29))) :|: z' = 1 + x_131 + x_29, z - 1 >= 0, x_131 >= 0, x_29 >= 0
   encode_+(z, z') -{ 0 }-> plus(minus(encArg(z - 1)), minux(encArg(z' - 1))) :|: z' - 1 >= 0, z - 1 >= 0
   encode_+(z, z') -{ 0 }-> plus(minus(encArg(z - 1)), minus(encArg(z' - 1))) :|: z - 1 >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 0 }-> plus(minus(encArg(z - 1)), 0) :|: z - 1 >= 0, z' >= 0
   encode_+(z, z') -{ 0 }-> plus(0, plus(encArg(x_140), encArg(x_212))) :|: z >= 0, x_212 >= 0, x_140 >= 0, z' = 1 + x_140 + x_212
   encode_+(z, z') -{ 0 }-> plus(0, minux(encArg(z' - 1))) :|: z >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 0 }-> plus(0, minus(encArg(z' - 1))) :|: z' - 1 >= 0, z >= 0
   encode_+(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_+(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   encode_+(z, z') -{ 0 }-> 1 + x0 + x1 :|: z >= 0, z' >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   encode_minus(z) -{ 0 }-> minus(plus(encArg(x_122), encArg(x_26))) :|: z = 1 + x_122 + x_26, x_26 >= 0, x_122 >= 0
   encode_minus(z) -{ 0 }-> minus(minux(encArg(z - 1))) :|: z - 1 >= 0
   encode_minus(z) -{ 0 }-> minus(minus(encArg(z - 1))) :|: z - 1 >= 0
   encode_minus(z) -{ 0 }-> 0 :|: z >= 0
   encode_minus(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_minus(z) -{ 0 }-> 1 + x0 :|: z >= 0, 0 = x0, x0 >= 0
   encode_minux(z) -{ 0 }-> minux(plus(encArg(x_125), encArg(x_27))) :|: x_125 >= 0, x_27 >= 0, z = 1 + x_125 + x_27
   encode_minux(z) -{ 0 }-> minux(minux(encArg(z - 1))) :|: z - 1 >= 0
   encode_minux(z) -{ 0 }-> minux(minus(encArg(z - 1))) :|: z - 1 >= 0
   encode_minux(z) -{ 0 }-> 0 :|: z >= 0
   encode_minux(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   minus(z) -{ 0 }-> 0 :|: z >= 0
   minus(z) -{ 1 }-> z - 1 :|: z - 1 >= 0
   minus(z) -{ 0 }-> 1 + z :|: z >= 0
   minux(z) -{ 4 }-> x :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x'' = 1 + y, x' = 1 + x + y, x >= 0, y >= 0
   minux(z) -{ 3 }-> x :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, x2 = 1 + y', 1 + y = 1 + x + y', x >= 0, y' >= 0
   minux(z) -{ 2 }-> x' :|: z = 1 + x + y, x >= 0, y >= 0, 1 + x = 1 + y', 1 + y = 1 + x' + y', x' >= 0, y' >= 0
   minux(z) -{ 3 }-> x'' :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, 1 + x = 1 + y, x' = 1 + x'' + y, x'' >= 0, y >= 0
   minux(z) -{ 4 }-> y :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x'' = 1 + x + y, x >= 0, y >= 0, x' = 1 + x
   minux(z) -{ 3 }-> y :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, 1 + x = 1 + x'' + y, x'' >= 0, y >= 0, x' = 1 + x''
   minux(z) -{ 3 }-> y' :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, x2 = 1 + x + y', x >= 0, y' >= 0, 1 + y = 1 + x
   minux(z) -{ 2 }-> y' :|: z = 1 + x + y, x >= 0, y >= 0, 1 + x = 1 + x' + y', x' >= 0, y' >= 0, 1 + y = 1 + x'
   minux(z) -{ 0 }-> 0 :|: z >= 0
   minux(z) -{ 3 }-> 0 :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, v0 >= 0, v1 >= 0, x' = v0, x'' = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, v0 >= 0, v1 >= 0, x' = v0, 1 + x = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, v0 >= 0, v1 >= 0, x' = v0, 0 = v1
   minux(z) -{ 2 }-> 0 :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, x2 = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, 1 + x = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, 0 = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + (1 + x3) + y, y >= 0, x3 >= 0, v0 >= 0, v1 >= 0, 0 = v0, x3 = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 0 = v0, 1 + x = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   minux(z) -{ 3 }-> 1 + x0 + x1 :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x' = x0, x0 >= 0, x1 >= 0, x'' = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, x' = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, x' = x0, x0 >= 0, x1 >= 0, 0 = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, x2 = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, 0 = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + (1 + x3) + y, y >= 0, x3 >= 0, 0 = x0, x0 >= 0, x1 >= 0, x3 = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 0 = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   plus(z, z') -{ 1 }-> x :|: z = 1 + x + (z' - 1), x >= 0, z' - 1 >= 0
   plus(z, z') -{ 1 }-> y :|: z' = 1 + (z - 1) + y, z - 1 >= 0, y >= 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 0 }-> 1 + z + z' :|: z >= 0, z' >= 0

Function symbols to be analyzed: {minux}, {plus}, {encArg}, {encode_minus}, {encode_+}, {encode_minux}
Previous analysis results are:
  minus: runtime: O(1) [1], size: O(n^1) [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) -{ 0 }-> plus(plus(encArg(x_17), encArg(x_21)), plus(encArg(x_116), encArg(x_24))) :|: x_116 >= 0, x_17 >= 0, z = 1 + (1 + x_17 + x_21) + (1 + x_116 + x_24), x_24 >= 0, x_21 >= 0
   encArg(z) -{ 0 }-> plus(plus(encArg(x_17), encArg(x_21)), minux(encArg(x_115))) :|: z = 1 + (1 + x_17 + x_21) + (1 + x_115), x_115 >= 0, x_17 >= 0, x_21 >= 0
   encArg(z) -{ 0 }-> plus(plus(encArg(x_17), encArg(x_21)), minus(encArg(x_114))) :|: z = 1 + (1 + x_17 + x_21) + (1 + x_114), x_114 >= 0, x_17 >= 0, x_21 >= 0
   encArg(z) -{ 0 }-> plus(plus(encArg(x_17), encArg(x_21)), 0) :|: z = 1 + (1 + x_17 + x_21) + x_2, x_17 >= 0, x_2 >= 0, x_21 >= 0
   encArg(z) -{ 0 }-> plus(minux(encArg(x_16)), plus(encArg(x_113), encArg(x_23))) :|: x_113 >= 0, x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_113 + x_23), x_23 >= 0
   encArg(z) -{ 0 }-> plus(minux(encArg(x_16)), minux(encArg(x_112))) :|: x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_112), x_112 >= 0
   encArg(z) -{ 0 }-> plus(minux(encArg(x_16)), minus(encArg(x_111))) :|: x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_111), x_111 >= 0
   encArg(z) -{ 0 }-> plus(minux(encArg(x_16)), 0) :|: x_16 >= 0, x_2 >= 0, z = 1 + (1 + x_16) + x_2
   encArg(z) -{ 0 }-> plus(minus(encArg(x_15)), plus(encArg(x_110), encArg(x_22))) :|: x_15 >= 0, z = 1 + (1 + x_15) + (1 + x_110 + x_22), x_110 >= 0, x_22 >= 0
   encArg(z) -{ 0 }-> plus(minus(encArg(x_15)), minux(encArg(x_19))) :|: x_15 >= 0, z = 1 + (1 + x_15) + (1 + x_19), x_19 >= 0
   encArg(z) -{ 0 }-> plus(minus(encArg(x_15)), minus(encArg(x_18))) :|: x_15 >= 0, x_18 >= 0, z = 1 + (1 + x_15) + (1 + x_18)
   encArg(z) -{ 0 }-> plus(minus(encArg(x_15)), 0) :|: x_15 >= 0, z = 1 + (1 + x_15) + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> plus(0, plus(encArg(x_119), encArg(x_25))) :|: x_1 >= 0, z = 1 + x_1 + (1 + x_119 + x_25), x_25 >= 0, x_119 >= 0
   encArg(z) -{ 0 }-> plus(0, minux(encArg(x_118))) :|: x_1 >= 0, z = 1 + x_1 + (1 + x_118), x_118 >= 0
   encArg(z) -{ 0 }-> plus(0, minus(encArg(x_117))) :|: x_1 >= 0, x_117 >= 0, z = 1 + x_1 + (1 + x_117)
   encArg(z) -{ 0 }-> minux(plus(encArg(x_14), encArg(x_2''))) :|: x_14 >= 0, z = 1 + (1 + x_14 + x_2''), x_2'' >= 0
   encArg(z) -{ 0 }-> minux(minux(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> minux(minus(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> minus(plus(encArg(x_11), encArg(x_2'))) :|: x_11 >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2')
   encArg(z) -{ 0 }-> minus(minux(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> minus(minus(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   encArg(z) -{ 0 }-> 1 + x0 :|: z - 1 >= 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 + x1 :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   encode_+(z, z') -{ 0 }-> plus(plus(encArg(x_128), encArg(x_28)), plus(encArg(x_137), encArg(x_211))) :|: x_128 >= 0, z = 1 + x_128 + x_28, z' = 1 + x_137 + x_211, x_137 >= 0, x_28 >= 0, x_211 >= 0
   encode_+(z, z') -{ 0 }-> plus(plus(encArg(x_128), encArg(x_28)), minux(encArg(z' - 1))) :|: x_128 >= 0, z = 1 + x_128 + x_28, z' - 1 >= 0, x_28 >= 0
   encode_+(z, z') -{ 0 }-> plus(plus(encArg(x_128), encArg(x_28)), minus(encArg(z' - 1))) :|: x_128 >= 0, z = 1 + x_128 + x_28, z' - 1 >= 0, x_28 >= 0
   encode_+(z, z') -{ 0 }-> plus(plus(encArg(x_128), encArg(x_28)), 0) :|: x_128 >= 0, z = 1 + x_128 + x_28, z' >= 0, x_28 >= 0
   encode_+(z, z') -{ 0 }-> plus(minux(encArg(z - 1)), plus(encArg(x_134), encArg(x_210))) :|: x_134 >= 0, z - 1 >= 0, z' = 1 + x_134 + x_210, x_210 >= 0
   encode_+(z, z') -{ 0 }-> plus(minux(encArg(z - 1)), minux(encArg(z' - 1))) :|: z - 1 >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 0 }-> plus(minux(encArg(z - 1)), minus(encArg(z' - 1))) :|: z - 1 >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 0 }-> plus(minux(encArg(z - 1)), 0) :|: z - 1 >= 0, z' >= 0
   encode_+(z, z') -{ 0 }-> plus(minus(encArg(z - 1)), plus(encArg(x_131), encArg(x_29))) :|: z' = 1 + x_131 + x_29, z - 1 >= 0, x_131 >= 0, x_29 >= 0
   encode_+(z, z') -{ 0 }-> plus(minus(encArg(z - 1)), minux(encArg(z' - 1))) :|: z' - 1 >= 0, z - 1 >= 0
   encode_+(z, z') -{ 0 }-> plus(minus(encArg(z - 1)), minus(encArg(z' - 1))) :|: z - 1 >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 0 }-> plus(minus(encArg(z - 1)), 0) :|: z - 1 >= 0, z' >= 0
   encode_+(z, z') -{ 0 }-> plus(0, plus(encArg(x_140), encArg(x_212))) :|: z >= 0, x_212 >= 0, x_140 >= 0, z' = 1 + x_140 + x_212
   encode_+(z, z') -{ 0 }-> plus(0, minux(encArg(z' - 1))) :|: z >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 0 }-> plus(0, minus(encArg(z' - 1))) :|: z' - 1 >= 0, z >= 0
   encode_+(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_+(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   encode_+(z, z') -{ 0 }-> 1 + x0 + x1 :|: z >= 0, z' >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   encode_minus(z) -{ 0 }-> minus(plus(encArg(x_122), encArg(x_26))) :|: z = 1 + x_122 + x_26, x_26 >= 0, x_122 >= 0
   encode_minus(z) -{ 0 }-> minus(minux(encArg(z - 1))) :|: z - 1 >= 0
   encode_minus(z) -{ 0 }-> minus(minus(encArg(z - 1))) :|: z - 1 >= 0
   encode_minus(z) -{ 0 }-> 0 :|: z >= 0
   encode_minus(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_minus(z) -{ 0 }-> 1 + x0 :|: z >= 0, 0 = x0, x0 >= 0
   encode_minux(z) -{ 0 }-> minux(plus(encArg(x_125), encArg(x_27))) :|: x_125 >= 0, x_27 >= 0, z = 1 + x_125 + x_27
   encode_minux(z) -{ 0 }-> minux(minux(encArg(z - 1))) :|: z - 1 >= 0
   encode_minux(z) -{ 0 }-> minux(minus(encArg(z - 1))) :|: z - 1 >= 0
   encode_minux(z) -{ 0 }-> 0 :|: z >= 0
   encode_minux(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   minus(z) -{ 0 }-> 0 :|: z >= 0
   minus(z) -{ 1 }-> z - 1 :|: z - 1 >= 0
   minus(z) -{ 0 }-> 1 + z :|: z >= 0
   minux(z) -{ 4 }-> x :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x'' = 1 + y, x' = 1 + x + y, x >= 0, y >= 0
   minux(z) -{ 3 }-> x :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, x2 = 1 + y', 1 + y = 1 + x + y', x >= 0, y' >= 0
   minux(z) -{ 2 }-> x' :|: z = 1 + x + y, x >= 0, y >= 0, 1 + x = 1 + y', 1 + y = 1 + x' + y', x' >= 0, y' >= 0
   minux(z) -{ 3 }-> x'' :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, 1 + x = 1 + y, x' = 1 + x'' + y, x'' >= 0, y >= 0
   minux(z) -{ 4 }-> y :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x'' = 1 + x + y, x >= 0, y >= 0, x' = 1 + x
   minux(z) -{ 3 }-> y :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, 1 + x = 1 + x'' + y, x'' >= 0, y >= 0, x' = 1 + x''
   minux(z) -{ 3 }-> y' :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, x2 = 1 + x + y', x >= 0, y' >= 0, 1 + y = 1 + x
   minux(z) -{ 2 }-> y' :|: z = 1 + x + y, x >= 0, y >= 0, 1 + x = 1 + x' + y', x' >= 0, y' >= 0, 1 + y = 1 + x'
   minux(z) -{ 0 }-> 0 :|: z >= 0
   minux(z) -{ 3 }-> 0 :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, v0 >= 0, v1 >= 0, x' = v0, x'' = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, v0 >= 0, v1 >= 0, x' = v0, 1 + x = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, v0 >= 0, v1 >= 0, x' = v0, 0 = v1
   minux(z) -{ 2 }-> 0 :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, x2 = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, 1 + x = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, 0 = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + (1 + x3) + y, y >= 0, x3 >= 0, v0 >= 0, v1 >= 0, 0 = v0, x3 = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 0 = v0, 1 + x = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   minux(z) -{ 3 }-> 1 + x0 + x1 :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x' = x0, x0 >= 0, x1 >= 0, x'' = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, x' = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, x' = x0, x0 >= 0, x1 >= 0, 0 = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, x2 = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, 0 = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + (1 + x3) + y, y >= 0, x3 >= 0, 0 = x0, x0 >= 0, x1 >= 0, x3 = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 0 = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   plus(z, z') -{ 1 }-> x :|: z = 1 + x + (z' - 1), x >= 0, z' - 1 >= 0
   plus(z, z') -{ 1 }-> y :|: z' = 1 + (z - 1) + y, z - 1 >= 0, y >= 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 0 }-> 1 + z + z' :|: z >= 0, z' >= 0

Function symbols to be analyzed: {minux}, {plus}, {encArg}, {encode_minus}, {encode_+}, {encode_minux}
Previous analysis results are:
  minus: runtime: O(1) [1], size: O(n^1) [1 + z]

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(35) IntTrsBoundProof (UPPER BOUND(ID))

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

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

   encArg(z) -{ 0 }-> plus(plus(encArg(x_17), encArg(x_21)), plus(encArg(x_116), encArg(x_24))) :|: x_116 >= 0, x_17 >= 0, z = 1 + (1 + x_17 + x_21) + (1 + x_116 + x_24), x_24 >= 0, x_21 >= 0
   encArg(z) -{ 0 }-> plus(plus(encArg(x_17), encArg(x_21)), minux(encArg(x_115))) :|: z = 1 + (1 + x_17 + x_21) + (1 + x_115), x_115 >= 0, x_17 >= 0, x_21 >= 0
   encArg(z) -{ 0 }-> plus(plus(encArg(x_17), encArg(x_21)), minus(encArg(x_114))) :|: z = 1 + (1 + x_17 + x_21) + (1 + x_114), x_114 >= 0, x_17 >= 0, x_21 >= 0
   encArg(z) -{ 0 }-> plus(plus(encArg(x_17), encArg(x_21)), 0) :|: z = 1 + (1 + x_17 + x_21) + x_2, x_17 >= 0, x_2 >= 0, x_21 >= 0
   encArg(z) -{ 0 }-> plus(minux(encArg(x_16)), plus(encArg(x_113), encArg(x_23))) :|: x_113 >= 0, x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_113 + x_23), x_23 >= 0
   encArg(z) -{ 0 }-> plus(minux(encArg(x_16)), minux(encArg(x_112))) :|: x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_112), x_112 >= 0
   encArg(z) -{ 0 }-> plus(minux(encArg(x_16)), minus(encArg(x_111))) :|: x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_111), x_111 >= 0
   encArg(z) -{ 0 }-> plus(minux(encArg(x_16)), 0) :|: x_16 >= 0, x_2 >= 0, z = 1 + (1 + x_16) + x_2
   encArg(z) -{ 0 }-> plus(minus(encArg(x_15)), plus(encArg(x_110), encArg(x_22))) :|: x_15 >= 0, z = 1 + (1 + x_15) + (1 + x_110 + x_22), x_110 >= 0, x_22 >= 0
   encArg(z) -{ 0 }-> plus(minus(encArg(x_15)), minux(encArg(x_19))) :|: x_15 >= 0, z = 1 + (1 + x_15) + (1 + x_19), x_19 >= 0
   encArg(z) -{ 0 }-> plus(minus(encArg(x_15)), minus(encArg(x_18))) :|: x_15 >= 0, x_18 >= 0, z = 1 + (1 + x_15) + (1 + x_18)
   encArg(z) -{ 0 }-> plus(minus(encArg(x_15)), 0) :|: x_15 >= 0, z = 1 + (1 + x_15) + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> plus(0, plus(encArg(x_119), encArg(x_25))) :|: x_1 >= 0, z = 1 + x_1 + (1 + x_119 + x_25), x_25 >= 0, x_119 >= 0
   encArg(z) -{ 0 }-> plus(0, minux(encArg(x_118))) :|: x_1 >= 0, z = 1 + x_1 + (1 + x_118), x_118 >= 0
   encArg(z) -{ 0 }-> plus(0, minus(encArg(x_117))) :|: x_1 >= 0, x_117 >= 0, z = 1 + x_1 + (1 + x_117)
   encArg(z) -{ 0 }-> minux(plus(encArg(x_14), encArg(x_2''))) :|: x_14 >= 0, z = 1 + (1 + x_14 + x_2''), x_2'' >= 0
   encArg(z) -{ 0 }-> minux(minux(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> minux(minus(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> minus(plus(encArg(x_11), encArg(x_2'))) :|: x_11 >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2')
   encArg(z) -{ 0 }-> minus(minux(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> minus(minus(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   encArg(z) -{ 0 }-> 1 + x0 :|: z - 1 >= 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 + x1 :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   encode_+(z, z') -{ 0 }-> plus(plus(encArg(x_128), encArg(x_28)), plus(encArg(x_137), encArg(x_211))) :|: x_128 >= 0, z = 1 + x_128 + x_28, z' = 1 + x_137 + x_211, x_137 >= 0, x_28 >= 0, x_211 >= 0
   encode_+(z, z') -{ 0 }-> plus(plus(encArg(x_128), encArg(x_28)), minux(encArg(z' - 1))) :|: x_128 >= 0, z = 1 + x_128 + x_28, z' - 1 >= 0, x_28 >= 0
   encode_+(z, z') -{ 0 }-> plus(plus(encArg(x_128), encArg(x_28)), minus(encArg(z' - 1))) :|: x_128 >= 0, z = 1 + x_128 + x_28, z' - 1 >= 0, x_28 >= 0
   encode_+(z, z') -{ 0 }-> plus(plus(encArg(x_128), encArg(x_28)), 0) :|: x_128 >= 0, z = 1 + x_128 + x_28, z' >= 0, x_28 >= 0
   encode_+(z, z') -{ 0 }-> plus(minux(encArg(z - 1)), plus(encArg(x_134), encArg(x_210))) :|: x_134 >= 0, z - 1 >= 0, z' = 1 + x_134 + x_210, x_210 >= 0
   encode_+(z, z') -{ 0 }-> plus(minux(encArg(z - 1)), minux(encArg(z' - 1))) :|: z - 1 >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 0 }-> plus(minux(encArg(z - 1)), minus(encArg(z' - 1))) :|: z - 1 >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 0 }-> plus(minux(encArg(z - 1)), 0) :|: z - 1 >= 0, z' >= 0
   encode_+(z, z') -{ 0 }-> plus(minus(encArg(z - 1)), plus(encArg(x_131), encArg(x_29))) :|: z' = 1 + x_131 + x_29, z - 1 >= 0, x_131 >= 0, x_29 >= 0
   encode_+(z, z') -{ 0 }-> plus(minus(encArg(z - 1)), minux(encArg(z' - 1))) :|: z' - 1 >= 0, z - 1 >= 0
   encode_+(z, z') -{ 0 }-> plus(minus(encArg(z - 1)), minus(encArg(z' - 1))) :|: z - 1 >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 0 }-> plus(minus(encArg(z - 1)), 0) :|: z - 1 >= 0, z' >= 0
   encode_+(z, z') -{ 0 }-> plus(0, plus(encArg(x_140), encArg(x_212))) :|: z >= 0, x_212 >= 0, x_140 >= 0, z' = 1 + x_140 + x_212
   encode_+(z, z') -{ 0 }-> plus(0, minux(encArg(z' - 1))) :|: z >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 0 }-> plus(0, minus(encArg(z' - 1))) :|: z' - 1 >= 0, z >= 0
   encode_+(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_+(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   encode_+(z, z') -{ 0 }-> 1 + x0 + x1 :|: z >= 0, z' >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   encode_minus(z) -{ 0 }-> minus(plus(encArg(x_122), encArg(x_26))) :|: z = 1 + x_122 + x_26, x_26 >= 0, x_122 >= 0
   encode_minus(z) -{ 0 }-> minus(minux(encArg(z - 1))) :|: z - 1 >= 0
   encode_minus(z) -{ 0 }-> minus(minus(encArg(z - 1))) :|: z - 1 >= 0
   encode_minus(z) -{ 0 }-> 0 :|: z >= 0
   encode_minus(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_minus(z) -{ 0 }-> 1 + x0 :|: z >= 0, 0 = x0, x0 >= 0
   encode_minux(z) -{ 0 }-> minux(plus(encArg(x_125), encArg(x_27))) :|: x_125 >= 0, x_27 >= 0, z = 1 + x_125 + x_27
   encode_minux(z) -{ 0 }-> minux(minux(encArg(z - 1))) :|: z - 1 >= 0
   encode_minux(z) -{ 0 }-> minux(minus(encArg(z - 1))) :|: z - 1 >= 0
   encode_minux(z) -{ 0 }-> 0 :|: z >= 0
   encode_minux(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   minus(z) -{ 0 }-> 0 :|: z >= 0
   minus(z) -{ 1 }-> z - 1 :|: z - 1 >= 0
   minus(z) -{ 0 }-> 1 + z :|: z >= 0
   minux(z) -{ 4 }-> x :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x'' = 1 + y, x' = 1 + x + y, x >= 0, y >= 0
   minux(z) -{ 3 }-> x :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, x2 = 1 + y', 1 + y = 1 + x + y', x >= 0, y' >= 0
   minux(z) -{ 2 }-> x' :|: z = 1 + x + y, x >= 0, y >= 0, 1 + x = 1 + y', 1 + y = 1 + x' + y', x' >= 0, y' >= 0
   minux(z) -{ 3 }-> x'' :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, 1 + x = 1 + y, x' = 1 + x'' + y, x'' >= 0, y >= 0
   minux(z) -{ 4 }-> y :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x'' = 1 + x + y, x >= 0, y >= 0, x' = 1 + x
   minux(z) -{ 3 }-> y :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, 1 + x = 1 + x'' + y, x'' >= 0, y >= 0, x' = 1 + x''
   minux(z) -{ 3 }-> y' :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, x2 = 1 + x + y', x >= 0, y' >= 0, 1 + y = 1 + x
   minux(z) -{ 2 }-> y' :|: z = 1 + x + y, x >= 0, y >= 0, 1 + x = 1 + x' + y', x' >= 0, y' >= 0, 1 + y = 1 + x'
   minux(z) -{ 0 }-> 0 :|: z >= 0
   minux(z) -{ 3 }-> 0 :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, v0 >= 0, v1 >= 0, x' = v0, x'' = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, v0 >= 0, v1 >= 0, x' = v0, 1 + x = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, v0 >= 0, v1 >= 0, x' = v0, 0 = v1
   minux(z) -{ 2 }-> 0 :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, x2 = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, 1 + x = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, 0 = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + (1 + x3) + y, y >= 0, x3 >= 0, v0 >= 0, v1 >= 0, 0 = v0, x3 = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 0 = v0, 1 + x = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   minux(z) -{ 3 }-> 1 + x0 + x1 :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x' = x0, x0 >= 0, x1 >= 0, x'' = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, x' = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, x' = x0, x0 >= 0, x1 >= 0, 0 = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, x2 = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, 0 = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + (1 + x3) + y, y >= 0, x3 >= 0, 0 = x0, x0 >= 0, x1 >= 0, x3 = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 0 = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   plus(z, z') -{ 1 }-> x :|: z = 1 + x + (z' - 1), x >= 0, z' - 1 >= 0
   plus(z, z') -{ 1 }-> y :|: z' = 1 + (z - 1) + y, z - 1 >= 0, y >= 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 0 }-> 1 + z + z' :|: z >= 0, z' >= 0

Function symbols to be analyzed: {minux}, {plus}, {encArg}, {encode_minus}, {encode_+}, {encode_minux}
Previous analysis results are:
  minus: runtime: O(1) [1], size: O(n^1) [1 + z]
  minux: runtime: ?, size: O(n^1) [2 + z]

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(37) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: minux
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 4

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

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

   encArg(z) -{ 0 }-> plus(plus(encArg(x_17), encArg(x_21)), plus(encArg(x_116), encArg(x_24))) :|: x_116 >= 0, x_17 >= 0, z = 1 + (1 + x_17 + x_21) + (1 + x_116 + x_24), x_24 >= 0, x_21 >= 0
   encArg(z) -{ 0 }-> plus(plus(encArg(x_17), encArg(x_21)), minux(encArg(x_115))) :|: z = 1 + (1 + x_17 + x_21) + (1 + x_115), x_115 >= 0, x_17 >= 0, x_21 >= 0
   encArg(z) -{ 0 }-> plus(plus(encArg(x_17), encArg(x_21)), minus(encArg(x_114))) :|: z = 1 + (1 + x_17 + x_21) + (1 + x_114), x_114 >= 0, x_17 >= 0, x_21 >= 0
   encArg(z) -{ 0 }-> plus(plus(encArg(x_17), encArg(x_21)), 0) :|: z = 1 + (1 + x_17 + x_21) + x_2, x_17 >= 0, x_2 >= 0, x_21 >= 0
   encArg(z) -{ 0 }-> plus(minux(encArg(x_16)), plus(encArg(x_113), encArg(x_23))) :|: x_113 >= 0, x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_113 + x_23), x_23 >= 0
   encArg(z) -{ 0 }-> plus(minux(encArg(x_16)), minux(encArg(x_112))) :|: x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_112), x_112 >= 0
   encArg(z) -{ 0 }-> plus(minux(encArg(x_16)), minus(encArg(x_111))) :|: x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_111), x_111 >= 0
   encArg(z) -{ 0 }-> plus(minux(encArg(x_16)), 0) :|: x_16 >= 0, x_2 >= 0, z = 1 + (1 + x_16) + x_2
   encArg(z) -{ 0 }-> plus(minus(encArg(x_15)), plus(encArg(x_110), encArg(x_22))) :|: x_15 >= 0, z = 1 + (1 + x_15) + (1 + x_110 + x_22), x_110 >= 0, x_22 >= 0
   encArg(z) -{ 0 }-> plus(minus(encArg(x_15)), minux(encArg(x_19))) :|: x_15 >= 0, z = 1 + (1 + x_15) + (1 + x_19), x_19 >= 0
   encArg(z) -{ 0 }-> plus(minus(encArg(x_15)), minus(encArg(x_18))) :|: x_15 >= 0, x_18 >= 0, z = 1 + (1 + x_15) + (1 + x_18)
   encArg(z) -{ 0 }-> plus(minus(encArg(x_15)), 0) :|: x_15 >= 0, z = 1 + (1 + x_15) + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> plus(0, plus(encArg(x_119), encArg(x_25))) :|: x_1 >= 0, z = 1 + x_1 + (1 + x_119 + x_25), x_25 >= 0, x_119 >= 0
   encArg(z) -{ 0 }-> plus(0, minux(encArg(x_118))) :|: x_1 >= 0, z = 1 + x_1 + (1 + x_118), x_118 >= 0
   encArg(z) -{ 0 }-> plus(0, minus(encArg(x_117))) :|: x_1 >= 0, x_117 >= 0, z = 1 + x_1 + (1 + x_117)
   encArg(z) -{ 0 }-> minux(plus(encArg(x_14), encArg(x_2''))) :|: x_14 >= 0, z = 1 + (1 + x_14 + x_2''), x_2'' >= 0
   encArg(z) -{ 0 }-> minux(minux(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> minux(minus(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> minus(plus(encArg(x_11), encArg(x_2'))) :|: x_11 >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2')
   encArg(z) -{ 0 }-> minus(minux(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> minus(minus(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   encArg(z) -{ 0 }-> 1 + x0 :|: z - 1 >= 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 + x1 :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   encode_+(z, z') -{ 0 }-> plus(plus(encArg(x_128), encArg(x_28)), plus(encArg(x_137), encArg(x_211))) :|: x_128 >= 0, z = 1 + x_128 + x_28, z' = 1 + x_137 + x_211, x_137 >= 0, x_28 >= 0, x_211 >= 0
   encode_+(z, z') -{ 0 }-> plus(plus(encArg(x_128), encArg(x_28)), minux(encArg(z' - 1))) :|: x_128 >= 0, z = 1 + x_128 + x_28, z' - 1 >= 0, x_28 >= 0
   encode_+(z, z') -{ 0 }-> plus(plus(encArg(x_128), encArg(x_28)), minus(encArg(z' - 1))) :|: x_128 >= 0, z = 1 + x_128 + x_28, z' - 1 >= 0, x_28 >= 0
   encode_+(z, z') -{ 0 }-> plus(plus(encArg(x_128), encArg(x_28)), 0) :|: x_128 >= 0, z = 1 + x_128 + x_28, z' >= 0, x_28 >= 0
   encode_+(z, z') -{ 0 }-> plus(minux(encArg(z - 1)), plus(encArg(x_134), encArg(x_210))) :|: x_134 >= 0, z - 1 >= 0, z' = 1 + x_134 + x_210, x_210 >= 0
   encode_+(z, z') -{ 0 }-> plus(minux(encArg(z - 1)), minux(encArg(z' - 1))) :|: z - 1 >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 0 }-> plus(minux(encArg(z - 1)), minus(encArg(z' - 1))) :|: z - 1 >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 0 }-> plus(minux(encArg(z - 1)), 0) :|: z - 1 >= 0, z' >= 0
   encode_+(z, z') -{ 0 }-> plus(minus(encArg(z - 1)), plus(encArg(x_131), encArg(x_29))) :|: z' = 1 + x_131 + x_29, z - 1 >= 0, x_131 >= 0, x_29 >= 0
   encode_+(z, z') -{ 0 }-> plus(minus(encArg(z - 1)), minux(encArg(z' - 1))) :|: z' - 1 >= 0, z - 1 >= 0
   encode_+(z, z') -{ 0 }-> plus(minus(encArg(z - 1)), minus(encArg(z' - 1))) :|: z - 1 >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 0 }-> plus(minus(encArg(z - 1)), 0) :|: z - 1 >= 0, z' >= 0
   encode_+(z, z') -{ 0 }-> plus(0, plus(encArg(x_140), encArg(x_212))) :|: z >= 0, x_212 >= 0, x_140 >= 0, z' = 1 + x_140 + x_212
   encode_+(z, z') -{ 0 }-> plus(0, minux(encArg(z' - 1))) :|: z >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 0 }-> plus(0, minus(encArg(z' - 1))) :|: z' - 1 >= 0, z >= 0
   encode_+(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_+(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   encode_+(z, z') -{ 0 }-> 1 + x0 + x1 :|: z >= 0, z' >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   encode_minus(z) -{ 0 }-> minus(plus(encArg(x_122), encArg(x_26))) :|: z = 1 + x_122 + x_26, x_26 >= 0, x_122 >= 0
   encode_minus(z) -{ 0 }-> minus(minux(encArg(z - 1))) :|: z - 1 >= 0
   encode_minus(z) -{ 0 }-> minus(minus(encArg(z - 1))) :|: z - 1 >= 0
   encode_minus(z) -{ 0 }-> 0 :|: z >= 0
   encode_minus(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_minus(z) -{ 0 }-> 1 + x0 :|: z >= 0, 0 = x0, x0 >= 0
   encode_minux(z) -{ 0 }-> minux(plus(encArg(x_125), encArg(x_27))) :|: x_125 >= 0, x_27 >= 0, z = 1 + x_125 + x_27
   encode_minux(z) -{ 0 }-> minux(minux(encArg(z - 1))) :|: z - 1 >= 0
   encode_minux(z) -{ 0 }-> minux(minus(encArg(z - 1))) :|: z - 1 >= 0
   encode_minux(z) -{ 0 }-> 0 :|: z >= 0
   encode_minux(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   minus(z) -{ 0 }-> 0 :|: z >= 0
   minus(z) -{ 1 }-> z - 1 :|: z - 1 >= 0
   minus(z) -{ 0 }-> 1 + z :|: z >= 0
   minux(z) -{ 4 }-> x :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x'' = 1 + y, x' = 1 + x + y, x >= 0, y >= 0
   minux(z) -{ 3 }-> x :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, x2 = 1 + y', 1 + y = 1 + x + y', x >= 0, y' >= 0
   minux(z) -{ 2 }-> x' :|: z = 1 + x + y, x >= 0, y >= 0, 1 + x = 1 + y', 1 + y = 1 + x' + y', x' >= 0, y' >= 0
   minux(z) -{ 3 }-> x'' :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, 1 + x = 1 + y, x' = 1 + x'' + y, x'' >= 0, y >= 0
   minux(z) -{ 4 }-> y :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x'' = 1 + x + y, x >= 0, y >= 0, x' = 1 + x
   minux(z) -{ 3 }-> y :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, 1 + x = 1 + x'' + y, x'' >= 0, y >= 0, x' = 1 + x''
   minux(z) -{ 3 }-> y' :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, x2 = 1 + x + y', x >= 0, y' >= 0, 1 + y = 1 + x
   minux(z) -{ 2 }-> y' :|: z = 1 + x + y, x >= 0, y >= 0, 1 + x = 1 + x' + y', x' >= 0, y' >= 0, 1 + y = 1 + x'
   minux(z) -{ 0 }-> 0 :|: z >= 0
   minux(z) -{ 3 }-> 0 :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, v0 >= 0, v1 >= 0, x' = v0, x'' = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, v0 >= 0, v1 >= 0, x' = v0, 1 + x = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, v0 >= 0, v1 >= 0, x' = v0, 0 = v1
   minux(z) -{ 2 }-> 0 :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, x2 = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, 1 + x = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, 0 = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + (1 + x3) + y, y >= 0, x3 >= 0, v0 >= 0, v1 >= 0, 0 = v0, x3 = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 0 = v0, 1 + x = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   minux(z) -{ 3 }-> 1 + x0 + x1 :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x' = x0, x0 >= 0, x1 >= 0, x'' = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, x' = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, x' = x0, x0 >= 0, x1 >= 0, 0 = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, x2 = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, 0 = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + (1 + x3) + y, y >= 0, x3 >= 0, 0 = x0, x0 >= 0, x1 >= 0, x3 = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 0 = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   plus(z, z') -{ 1 }-> x :|: z = 1 + x + (z' - 1), x >= 0, z' - 1 >= 0
   plus(z, z') -{ 1 }-> y :|: z' = 1 + (z - 1) + y, z - 1 >= 0, y >= 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 0 }-> 1 + z + z' :|: z >= 0, z' >= 0

Function symbols to be analyzed: {plus}, {encArg}, {encode_minus}, {encode_+}, {encode_minux}
Previous analysis results are:
  minus: runtime: O(1) [1], size: O(n^1) [1 + z]
  minux: runtime: O(1) [4], size: O(n^1) [2 + z]

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

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

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

   encArg(z) -{ 0 }-> plus(plus(encArg(x_17), encArg(x_21)), plus(encArg(x_116), encArg(x_24))) :|: x_116 >= 0, x_17 >= 0, z = 1 + (1 + x_17 + x_21) + (1 + x_116 + x_24), x_24 >= 0, x_21 >= 0
   encArg(z) -{ 0 }-> plus(plus(encArg(x_17), encArg(x_21)), minux(encArg(x_115))) :|: z = 1 + (1 + x_17 + x_21) + (1 + x_115), x_115 >= 0, x_17 >= 0, x_21 >= 0
   encArg(z) -{ 0 }-> plus(plus(encArg(x_17), encArg(x_21)), minus(encArg(x_114))) :|: z = 1 + (1 + x_17 + x_21) + (1 + x_114), x_114 >= 0, x_17 >= 0, x_21 >= 0
   encArg(z) -{ 0 }-> plus(plus(encArg(x_17), encArg(x_21)), 0) :|: z = 1 + (1 + x_17 + x_21) + x_2, x_17 >= 0, x_2 >= 0, x_21 >= 0
   encArg(z) -{ 0 }-> plus(minux(encArg(x_16)), plus(encArg(x_113), encArg(x_23))) :|: x_113 >= 0, x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_113 + x_23), x_23 >= 0
   encArg(z) -{ 0 }-> plus(minux(encArg(x_16)), minux(encArg(x_112))) :|: x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_112), x_112 >= 0
   encArg(z) -{ 0 }-> plus(minux(encArg(x_16)), minus(encArg(x_111))) :|: x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_111), x_111 >= 0
   encArg(z) -{ 0 }-> plus(minux(encArg(x_16)), 0) :|: x_16 >= 0, x_2 >= 0, z = 1 + (1 + x_16) + x_2
   encArg(z) -{ 0 }-> plus(minus(encArg(x_15)), plus(encArg(x_110), encArg(x_22))) :|: x_15 >= 0, z = 1 + (1 + x_15) + (1 + x_110 + x_22), x_110 >= 0, x_22 >= 0
   encArg(z) -{ 0 }-> plus(minus(encArg(x_15)), minux(encArg(x_19))) :|: x_15 >= 0, z = 1 + (1 + x_15) + (1 + x_19), x_19 >= 0
   encArg(z) -{ 0 }-> plus(minus(encArg(x_15)), minus(encArg(x_18))) :|: x_15 >= 0, x_18 >= 0, z = 1 + (1 + x_15) + (1 + x_18)
   encArg(z) -{ 0 }-> plus(minus(encArg(x_15)), 0) :|: x_15 >= 0, z = 1 + (1 + x_15) + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> plus(0, plus(encArg(x_119), encArg(x_25))) :|: x_1 >= 0, z = 1 + x_1 + (1 + x_119 + x_25), x_25 >= 0, x_119 >= 0
   encArg(z) -{ 0 }-> plus(0, minux(encArg(x_118))) :|: x_1 >= 0, z = 1 + x_1 + (1 + x_118), x_118 >= 0
   encArg(z) -{ 0 }-> plus(0, minus(encArg(x_117))) :|: x_1 >= 0, x_117 >= 0, z = 1 + x_1 + (1 + x_117)
   encArg(z) -{ 0 }-> minux(plus(encArg(x_14), encArg(x_2''))) :|: x_14 >= 0, z = 1 + (1 + x_14 + x_2''), x_2'' >= 0
   encArg(z) -{ 0 }-> minux(minux(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> minux(minus(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> minus(plus(encArg(x_11), encArg(x_2'))) :|: x_11 >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2')
   encArg(z) -{ 0 }-> minus(minux(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> minus(minus(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   encArg(z) -{ 0 }-> 1 + x0 :|: z - 1 >= 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 + x1 :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   encode_+(z, z') -{ 0 }-> plus(plus(encArg(x_128), encArg(x_28)), plus(encArg(x_137), encArg(x_211))) :|: x_128 >= 0, z = 1 + x_128 + x_28, z' = 1 + x_137 + x_211, x_137 >= 0, x_28 >= 0, x_211 >= 0
   encode_+(z, z') -{ 0 }-> plus(plus(encArg(x_128), encArg(x_28)), minux(encArg(z' - 1))) :|: x_128 >= 0, z = 1 + x_128 + x_28, z' - 1 >= 0, x_28 >= 0
   encode_+(z, z') -{ 0 }-> plus(plus(encArg(x_128), encArg(x_28)), minus(encArg(z' - 1))) :|: x_128 >= 0, z = 1 + x_128 + x_28, z' - 1 >= 0, x_28 >= 0
   encode_+(z, z') -{ 0 }-> plus(plus(encArg(x_128), encArg(x_28)), 0) :|: x_128 >= 0, z = 1 + x_128 + x_28, z' >= 0, x_28 >= 0
   encode_+(z, z') -{ 0 }-> plus(minux(encArg(z - 1)), plus(encArg(x_134), encArg(x_210))) :|: x_134 >= 0, z - 1 >= 0, z' = 1 + x_134 + x_210, x_210 >= 0
   encode_+(z, z') -{ 0 }-> plus(minux(encArg(z - 1)), minux(encArg(z' - 1))) :|: z - 1 >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 0 }-> plus(minux(encArg(z - 1)), minus(encArg(z' - 1))) :|: z - 1 >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 0 }-> plus(minux(encArg(z - 1)), 0) :|: z - 1 >= 0, z' >= 0
   encode_+(z, z') -{ 0 }-> plus(minus(encArg(z - 1)), plus(encArg(x_131), encArg(x_29))) :|: z' = 1 + x_131 + x_29, z - 1 >= 0, x_131 >= 0, x_29 >= 0
   encode_+(z, z') -{ 0 }-> plus(minus(encArg(z - 1)), minux(encArg(z' - 1))) :|: z' - 1 >= 0, z - 1 >= 0
   encode_+(z, z') -{ 0 }-> plus(minus(encArg(z - 1)), minus(encArg(z' - 1))) :|: z - 1 >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 0 }-> plus(minus(encArg(z - 1)), 0) :|: z - 1 >= 0, z' >= 0
   encode_+(z, z') -{ 0 }-> plus(0, plus(encArg(x_140), encArg(x_212))) :|: z >= 0, x_212 >= 0, x_140 >= 0, z' = 1 + x_140 + x_212
   encode_+(z, z') -{ 0 }-> plus(0, minux(encArg(z' - 1))) :|: z >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 0 }-> plus(0, minus(encArg(z' - 1))) :|: z' - 1 >= 0, z >= 0
   encode_+(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_+(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   encode_+(z, z') -{ 0 }-> 1 + x0 + x1 :|: z >= 0, z' >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   encode_minus(z) -{ 0 }-> minus(plus(encArg(x_122), encArg(x_26))) :|: z = 1 + x_122 + x_26, x_26 >= 0, x_122 >= 0
   encode_minus(z) -{ 0 }-> minus(minux(encArg(z - 1))) :|: z - 1 >= 0
   encode_minus(z) -{ 0 }-> minus(minus(encArg(z - 1))) :|: z - 1 >= 0
   encode_minus(z) -{ 0 }-> 0 :|: z >= 0
   encode_minus(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_minus(z) -{ 0 }-> 1 + x0 :|: z >= 0, 0 = x0, x0 >= 0
   encode_minux(z) -{ 0 }-> minux(plus(encArg(x_125), encArg(x_27))) :|: x_125 >= 0, x_27 >= 0, z = 1 + x_125 + x_27
   encode_minux(z) -{ 0 }-> minux(minux(encArg(z - 1))) :|: z - 1 >= 0
   encode_minux(z) -{ 0 }-> minux(minus(encArg(z - 1))) :|: z - 1 >= 0
   encode_minux(z) -{ 0 }-> 0 :|: z >= 0
   encode_minux(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   minus(z) -{ 0 }-> 0 :|: z >= 0
   minus(z) -{ 1 }-> z - 1 :|: z - 1 >= 0
   minus(z) -{ 0 }-> 1 + z :|: z >= 0
   minux(z) -{ 4 }-> x :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x'' = 1 + y, x' = 1 + x + y, x >= 0, y >= 0
   minux(z) -{ 3 }-> x :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, x2 = 1 + y', 1 + y = 1 + x + y', x >= 0, y' >= 0
   minux(z) -{ 2 }-> x' :|: z = 1 + x + y, x >= 0, y >= 0, 1 + x = 1 + y', 1 + y = 1 + x' + y', x' >= 0, y' >= 0
   minux(z) -{ 3 }-> x'' :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, 1 + x = 1 + y, x' = 1 + x'' + y, x'' >= 0, y >= 0
   minux(z) -{ 4 }-> y :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x'' = 1 + x + y, x >= 0, y >= 0, x' = 1 + x
   minux(z) -{ 3 }-> y :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, 1 + x = 1 + x'' + y, x'' >= 0, y >= 0, x' = 1 + x''
   minux(z) -{ 3 }-> y' :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, x2 = 1 + x + y', x >= 0, y' >= 0, 1 + y = 1 + x
   minux(z) -{ 2 }-> y' :|: z = 1 + x + y, x >= 0, y >= 0, 1 + x = 1 + x' + y', x' >= 0, y' >= 0, 1 + y = 1 + x'
   minux(z) -{ 0 }-> 0 :|: z >= 0
   minux(z) -{ 3 }-> 0 :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, v0 >= 0, v1 >= 0, x' = v0, x'' = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, v0 >= 0, v1 >= 0, x' = v0, 1 + x = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, v0 >= 0, v1 >= 0, x' = v0, 0 = v1
   minux(z) -{ 2 }-> 0 :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, x2 = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, 1 + x = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, 0 = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + (1 + x3) + y, y >= 0, x3 >= 0, v0 >= 0, v1 >= 0, 0 = v0, x3 = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 0 = v0, 1 + x = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   minux(z) -{ 3 }-> 1 + x0 + x1 :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x' = x0, x0 >= 0, x1 >= 0, x'' = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, x' = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, x' = x0, x0 >= 0, x1 >= 0, 0 = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, x2 = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, 0 = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + (1 + x3) + y, y >= 0, x3 >= 0, 0 = x0, x0 >= 0, x1 >= 0, x3 = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 0 = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   plus(z, z') -{ 1 }-> x :|: z = 1 + x + (z' - 1), x >= 0, z' - 1 >= 0
   plus(z, z') -{ 1 }-> y :|: z' = 1 + (z - 1) + y, z - 1 >= 0, y >= 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 0 }-> 1 + z + z' :|: z >= 0, z' >= 0

Function symbols to be analyzed: {plus}, {encArg}, {encode_minus}, {encode_+}, {encode_minux}
Previous analysis results are:
  minus: runtime: O(1) [1], size: O(n^1) [1 + z]
  minux: runtime: O(1) [4], size: O(n^1) [2 + z]

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

(41) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   encArg(z) -{ 0 }-> plus(plus(encArg(x_17), encArg(x_21)), plus(encArg(x_116), encArg(x_24))) :|: x_116 >= 0, x_17 >= 0, z = 1 + (1 + x_17 + x_21) + (1 + x_116 + x_24), x_24 >= 0, x_21 >= 0
   encArg(z) -{ 0 }-> plus(plus(encArg(x_17), encArg(x_21)), minux(encArg(x_115))) :|: z = 1 + (1 + x_17 + x_21) + (1 + x_115), x_115 >= 0, x_17 >= 0, x_21 >= 0
   encArg(z) -{ 0 }-> plus(plus(encArg(x_17), encArg(x_21)), minus(encArg(x_114))) :|: z = 1 + (1 + x_17 + x_21) + (1 + x_114), x_114 >= 0, x_17 >= 0, x_21 >= 0
   encArg(z) -{ 0 }-> plus(plus(encArg(x_17), encArg(x_21)), 0) :|: z = 1 + (1 + x_17 + x_21) + x_2, x_17 >= 0, x_2 >= 0, x_21 >= 0
   encArg(z) -{ 0 }-> plus(minux(encArg(x_16)), plus(encArg(x_113), encArg(x_23))) :|: x_113 >= 0, x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_113 + x_23), x_23 >= 0
   encArg(z) -{ 0 }-> plus(minux(encArg(x_16)), minux(encArg(x_112))) :|: x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_112), x_112 >= 0
   encArg(z) -{ 0 }-> plus(minux(encArg(x_16)), minus(encArg(x_111))) :|: x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_111), x_111 >= 0
   encArg(z) -{ 0 }-> plus(minux(encArg(x_16)), 0) :|: x_16 >= 0, x_2 >= 0, z = 1 + (1 + x_16) + x_2
   encArg(z) -{ 0 }-> plus(minus(encArg(x_15)), plus(encArg(x_110), encArg(x_22))) :|: x_15 >= 0, z = 1 + (1 + x_15) + (1 + x_110 + x_22), x_110 >= 0, x_22 >= 0
   encArg(z) -{ 0 }-> plus(minus(encArg(x_15)), minux(encArg(x_19))) :|: x_15 >= 0, z = 1 + (1 + x_15) + (1 + x_19), x_19 >= 0
   encArg(z) -{ 0 }-> plus(minus(encArg(x_15)), minus(encArg(x_18))) :|: x_15 >= 0, x_18 >= 0, z = 1 + (1 + x_15) + (1 + x_18)
   encArg(z) -{ 0 }-> plus(minus(encArg(x_15)), 0) :|: x_15 >= 0, z = 1 + (1 + x_15) + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> plus(0, plus(encArg(x_119), encArg(x_25))) :|: x_1 >= 0, z = 1 + x_1 + (1 + x_119 + x_25), x_25 >= 0, x_119 >= 0
   encArg(z) -{ 0 }-> plus(0, minux(encArg(x_118))) :|: x_1 >= 0, z = 1 + x_1 + (1 + x_118), x_118 >= 0
   encArg(z) -{ 0 }-> plus(0, minus(encArg(x_117))) :|: x_1 >= 0, x_117 >= 0, z = 1 + x_1 + (1 + x_117)
   encArg(z) -{ 0 }-> minux(plus(encArg(x_14), encArg(x_2''))) :|: x_14 >= 0, z = 1 + (1 + x_14 + x_2''), x_2'' >= 0
   encArg(z) -{ 0 }-> minux(minux(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> minux(minus(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> minus(plus(encArg(x_11), encArg(x_2'))) :|: x_11 >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2')
   encArg(z) -{ 0 }-> minus(minux(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> minus(minus(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   encArg(z) -{ 0 }-> 1 + x0 :|: z - 1 >= 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 + x1 :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   encode_+(z, z') -{ 0 }-> plus(plus(encArg(x_128), encArg(x_28)), plus(encArg(x_137), encArg(x_211))) :|: x_128 >= 0, z = 1 + x_128 + x_28, z' = 1 + x_137 + x_211, x_137 >= 0, x_28 >= 0, x_211 >= 0
   encode_+(z, z') -{ 0 }-> plus(plus(encArg(x_128), encArg(x_28)), minux(encArg(z' - 1))) :|: x_128 >= 0, z = 1 + x_128 + x_28, z' - 1 >= 0, x_28 >= 0
   encode_+(z, z') -{ 0 }-> plus(plus(encArg(x_128), encArg(x_28)), minus(encArg(z' - 1))) :|: x_128 >= 0, z = 1 + x_128 + x_28, z' - 1 >= 0, x_28 >= 0
   encode_+(z, z') -{ 0 }-> plus(plus(encArg(x_128), encArg(x_28)), 0) :|: x_128 >= 0, z = 1 + x_128 + x_28, z' >= 0, x_28 >= 0
   encode_+(z, z') -{ 0 }-> plus(minux(encArg(z - 1)), plus(encArg(x_134), encArg(x_210))) :|: x_134 >= 0, z - 1 >= 0, z' = 1 + x_134 + x_210, x_210 >= 0
   encode_+(z, z') -{ 0 }-> plus(minux(encArg(z - 1)), minux(encArg(z' - 1))) :|: z - 1 >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 0 }-> plus(minux(encArg(z - 1)), minus(encArg(z' - 1))) :|: z - 1 >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 0 }-> plus(minux(encArg(z - 1)), 0) :|: z - 1 >= 0, z' >= 0
   encode_+(z, z') -{ 0 }-> plus(minus(encArg(z - 1)), plus(encArg(x_131), encArg(x_29))) :|: z' = 1 + x_131 + x_29, z - 1 >= 0, x_131 >= 0, x_29 >= 0
   encode_+(z, z') -{ 0 }-> plus(minus(encArg(z - 1)), minux(encArg(z' - 1))) :|: z' - 1 >= 0, z - 1 >= 0
   encode_+(z, z') -{ 0 }-> plus(minus(encArg(z - 1)), minus(encArg(z' - 1))) :|: z - 1 >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 0 }-> plus(minus(encArg(z - 1)), 0) :|: z - 1 >= 0, z' >= 0
   encode_+(z, z') -{ 0 }-> plus(0, plus(encArg(x_140), encArg(x_212))) :|: z >= 0, x_212 >= 0, x_140 >= 0, z' = 1 + x_140 + x_212
   encode_+(z, z') -{ 0 }-> plus(0, minux(encArg(z' - 1))) :|: z >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 0 }-> plus(0, minus(encArg(z' - 1))) :|: z' - 1 >= 0, z >= 0
   encode_+(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_+(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   encode_+(z, z') -{ 0 }-> 1 + x0 + x1 :|: z >= 0, z' >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   encode_minus(z) -{ 0 }-> minus(plus(encArg(x_122), encArg(x_26))) :|: z = 1 + x_122 + x_26, x_26 >= 0, x_122 >= 0
   encode_minus(z) -{ 0 }-> minus(minux(encArg(z - 1))) :|: z - 1 >= 0
   encode_minus(z) -{ 0 }-> minus(minus(encArg(z - 1))) :|: z - 1 >= 0
   encode_minus(z) -{ 0 }-> 0 :|: z >= 0
   encode_minus(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_minus(z) -{ 0 }-> 1 + x0 :|: z >= 0, 0 = x0, x0 >= 0
   encode_minux(z) -{ 0 }-> minux(plus(encArg(x_125), encArg(x_27))) :|: x_125 >= 0, x_27 >= 0, z = 1 + x_125 + x_27
   encode_minux(z) -{ 0 }-> minux(minux(encArg(z - 1))) :|: z - 1 >= 0
   encode_minux(z) -{ 0 }-> minux(minus(encArg(z - 1))) :|: z - 1 >= 0
   encode_minux(z) -{ 0 }-> 0 :|: z >= 0
   encode_minux(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   minus(z) -{ 0 }-> 0 :|: z >= 0
   minus(z) -{ 1 }-> z - 1 :|: z - 1 >= 0
   minus(z) -{ 0 }-> 1 + z :|: z >= 0
   minux(z) -{ 4 }-> x :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x'' = 1 + y, x' = 1 + x + y, x >= 0, y >= 0
   minux(z) -{ 3 }-> x :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, x2 = 1 + y', 1 + y = 1 + x + y', x >= 0, y' >= 0
   minux(z) -{ 2 }-> x' :|: z = 1 + x + y, x >= 0, y >= 0, 1 + x = 1 + y', 1 + y = 1 + x' + y', x' >= 0, y' >= 0
   minux(z) -{ 3 }-> x'' :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, 1 + x = 1 + y, x' = 1 + x'' + y, x'' >= 0, y >= 0
   minux(z) -{ 4 }-> y :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x'' = 1 + x + y, x >= 0, y >= 0, x' = 1 + x
   minux(z) -{ 3 }-> y :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, 1 + x = 1 + x'' + y, x'' >= 0, y >= 0, x' = 1 + x''
   minux(z) -{ 3 }-> y' :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, x2 = 1 + x + y', x >= 0, y' >= 0, 1 + y = 1 + x
   minux(z) -{ 2 }-> y' :|: z = 1 + x + y, x >= 0, y >= 0, 1 + x = 1 + x' + y', x' >= 0, y' >= 0, 1 + y = 1 + x'
   minux(z) -{ 0 }-> 0 :|: z >= 0
   minux(z) -{ 3 }-> 0 :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, v0 >= 0, v1 >= 0, x' = v0, x'' = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, v0 >= 0, v1 >= 0, x' = v0, 1 + x = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, v0 >= 0, v1 >= 0, x' = v0, 0 = v1
   minux(z) -{ 2 }-> 0 :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, x2 = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, 1 + x = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, 0 = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + (1 + x3) + y, y >= 0, x3 >= 0, v0 >= 0, v1 >= 0, 0 = v0, x3 = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 0 = v0, 1 + x = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   minux(z) -{ 3 }-> 1 + x0 + x1 :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x' = x0, x0 >= 0, x1 >= 0, x'' = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, x' = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, x' = x0, x0 >= 0, x1 >= 0, 0 = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, x2 = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, 0 = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + (1 + x3) + y, y >= 0, x3 >= 0, 0 = x0, x0 >= 0, x1 >= 0, x3 = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 0 = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   plus(z, z') -{ 1 }-> x :|: z = 1 + x + (z' - 1), x >= 0, z' - 1 >= 0
   plus(z, z') -{ 1 }-> y :|: z' = 1 + (z - 1) + y, z - 1 >= 0, y >= 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 0 }-> 1 + z + z' :|: z >= 0, z' >= 0

Function symbols to be analyzed: {plus}, {encArg}, {encode_minus}, {encode_+}, {encode_minux}
Previous analysis results are:
  minus: runtime: O(1) [1], size: O(n^1) [1 + z]
  minux: runtime: O(1) [4], size: O(n^1) [2 + z]
  plus: runtime: ?, size: O(n^1) [1 + z + z']

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

(43) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   encArg(z) -{ 0 }-> plus(plus(encArg(x_17), encArg(x_21)), plus(encArg(x_116), encArg(x_24))) :|: x_116 >= 0, x_17 >= 0, z = 1 + (1 + x_17 + x_21) + (1 + x_116 + x_24), x_24 >= 0, x_21 >= 0
   encArg(z) -{ 0 }-> plus(plus(encArg(x_17), encArg(x_21)), minux(encArg(x_115))) :|: z = 1 + (1 + x_17 + x_21) + (1 + x_115), x_115 >= 0, x_17 >= 0, x_21 >= 0
   encArg(z) -{ 0 }-> plus(plus(encArg(x_17), encArg(x_21)), minus(encArg(x_114))) :|: z = 1 + (1 + x_17 + x_21) + (1 + x_114), x_114 >= 0, x_17 >= 0, x_21 >= 0
   encArg(z) -{ 0 }-> plus(plus(encArg(x_17), encArg(x_21)), 0) :|: z = 1 + (1 + x_17 + x_21) + x_2, x_17 >= 0, x_2 >= 0, x_21 >= 0
   encArg(z) -{ 0 }-> plus(minux(encArg(x_16)), plus(encArg(x_113), encArg(x_23))) :|: x_113 >= 0, x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_113 + x_23), x_23 >= 0
   encArg(z) -{ 0 }-> plus(minux(encArg(x_16)), minux(encArg(x_112))) :|: x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_112), x_112 >= 0
   encArg(z) -{ 0 }-> plus(minux(encArg(x_16)), minus(encArg(x_111))) :|: x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_111), x_111 >= 0
   encArg(z) -{ 0 }-> plus(minux(encArg(x_16)), 0) :|: x_16 >= 0, x_2 >= 0, z = 1 + (1 + x_16) + x_2
   encArg(z) -{ 0 }-> plus(minus(encArg(x_15)), plus(encArg(x_110), encArg(x_22))) :|: x_15 >= 0, z = 1 + (1 + x_15) + (1 + x_110 + x_22), x_110 >= 0, x_22 >= 0
   encArg(z) -{ 0 }-> plus(minus(encArg(x_15)), minux(encArg(x_19))) :|: x_15 >= 0, z = 1 + (1 + x_15) + (1 + x_19), x_19 >= 0
   encArg(z) -{ 0 }-> plus(minus(encArg(x_15)), minus(encArg(x_18))) :|: x_15 >= 0, x_18 >= 0, z = 1 + (1 + x_15) + (1 + x_18)
   encArg(z) -{ 0 }-> plus(minus(encArg(x_15)), 0) :|: x_15 >= 0, z = 1 + (1 + x_15) + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> plus(0, plus(encArg(x_119), encArg(x_25))) :|: x_1 >= 0, z = 1 + x_1 + (1 + x_119 + x_25), x_25 >= 0, x_119 >= 0
   encArg(z) -{ 0 }-> plus(0, minux(encArg(x_118))) :|: x_1 >= 0, z = 1 + x_1 + (1 + x_118), x_118 >= 0
   encArg(z) -{ 0 }-> plus(0, minus(encArg(x_117))) :|: x_1 >= 0, x_117 >= 0, z = 1 + x_1 + (1 + x_117)
   encArg(z) -{ 0 }-> minux(plus(encArg(x_14), encArg(x_2''))) :|: x_14 >= 0, z = 1 + (1 + x_14 + x_2''), x_2'' >= 0
   encArg(z) -{ 0 }-> minux(minux(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> minux(minus(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> minus(plus(encArg(x_11), encArg(x_2'))) :|: x_11 >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2')
   encArg(z) -{ 0 }-> minus(minux(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> minus(minus(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   encArg(z) -{ 0 }-> 1 + x0 :|: z - 1 >= 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 + x1 :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   encode_+(z, z') -{ 0 }-> plus(plus(encArg(x_128), encArg(x_28)), plus(encArg(x_137), encArg(x_211))) :|: x_128 >= 0, z = 1 + x_128 + x_28, z' = 1 + x_137 + x_211, x_137 >= 0, x_28 >= 0, x_211 >= 0
   encode_+(z, z') -{ 0 }-> plus(plus(encArg(x_128), encArg(x_28)), minux(encArg(z' - 1))) :|: x_128 >= 0, z = 1 + x_128 + x_28, z' - 1 >= 0, x_28 >= 0
   encode_+(z, z') -{ 0 }-> plus(plus(encArg(x_128), encArg(x_28)), minus(encArg(z' - 1))) :|: x_128 >= 0, z = 1 + x_128 + x_28, z' - 1 >= 0, x_28 >= 0
   encode_+(z, z') -{ 0 }-> plus(plus(encArg(x_128), encArg(x_28)), 0) :|: x_128 >= 0, z = 1 + x_128 + x_28, z' >= 0, x_28 >= 0
   encode_+(z, z') -{ 0 }-> plus(minux(encArg(z - 1)), plus(encArg(x_134), encArg(x_210))) :|: x_134 >= 0, z - 1 >= 0, z' = 1 + x_134 + x_210, x_210 >= 0
   encode_+(z, z') -{ 0 }-> plus(minux(encArg(z - 1)), minux(encArg(z' - 1))) :|: z - 1 >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 0 }-> plus(minux(encArg(z - 1)), minus(encArg(z' - 1))) :|: z - 1 >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 0 }-> plus(minux(encArg(z - 1)), 0) :|: z - 1 >= 0, z' >= 0
   encode_+(z, z') -{ 0 }-> plus(minus(encArg(z - 1)), plus(encArg(x_131), encArg(x_29))) :|: z' = 1 + x_131 + x_29, z - 1 >= 0, x_131 >= 0, x_29 >= 0
   encode_+(z, z') -{ 0 }-> plus(minus(encArg(z - 1)), minux(encArg(z' - 1))) :|: z' - 1 >= 0, z - 1 >= 0
   encode_+(z, z') -{ 0 }-> plus(minus(encArg(z - 1)), minus(encArg(z' - 1))) :|: z - 1 >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 0 }-> plus(minus(encArg(z - 1)), 0) :|: z - 1 >= 0, z' >= 0
   encode_+(z, z') -{ 0 }-> plus(0, plus(encArg(x_140), encArg(x_212))) :|: z >= 0, x_212 >= 0, x_140 >= 0, z' = 1 + x_140 + x_212
   encode_+(z, z') -{ 0 }-> plus(0, minux(encArg(z' - 1))) :|: z >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 0 }-> plus(0, minus(encArg(z' - 1))) :|: z' - 1 >= 0, z >= 0
   encode_+(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_+(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   encode_+(z, z') -{ 0 }-> 1 + x0 + x1 :|: z >= 0, z' >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   encode_minus(z) -{ 0 }-> minus(plus(encArg(x_122), encArg(x_26))) :|: z = 1 + x_122 + x_26, x_26 >= 0, x_122 >= 0
   encode_minus(z) -{ 0 }-> minus(minux(encArg(z - 1))) :|: z - 1 >= 0
   encode_minus(z) -{ 0 }-> minus(minus(encArg(z - 1))) :|: z - 1 >= 0
   encode_minus(z) -{ 0 }-> 0 :|: z >= 0
   encode_minus(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_minus(z) -{ 0 }-> 1 + x0 :|: z >= 0, 0 = x0, x0 >= 0
   encode_minux(z) -{ 0 }-> minux(plus(encArg(x_125), encArg(x_27))) :|: x_125 >= 0, x_27 >= 0, z = 1 + x_125 + x_27
   encode_minux(z) -{ 0 }-> minux(minux(encArg(z - 1))) :|: z - 1 >= 0
   encode_minux(z) -{ 0 }-> minux(minus(encArg(z - 1))) :|: z - 1 >= 0
   encode_minux(z) -{ 0 }-> 0 :|: z >= 0
   encode_minux(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   minus(z) -{ 0 }-> 0 :|: z >= 0
   minus(z) -{ 1 }-> z - 1 :|: z - 1 >= 0
   minus(z) -{ 0 }-> 1 + z :|: z >= 0
   minux(z) -{ 4 }-> x :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x'' = 1 + y, x' = 1 + x + y, x >= 0, y >= 0
   minux(z) -{ 3 }-> x :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, x2 = 1 + y', 1 + y = 1 + x + y', x >= 0, y' >= 0
   minux(z) -{ 2 }-> x' :|: z = 1 + x + y, x >= 0, y >= 0, 1 + x = 1 + y', 1 + y = 1 + x' + y', x' >= 0, y' >= 0
   minux(z) -{ 3 }-> x'' :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, 1 + x = 1 + y, x' = 1 + x'' + y, x'' >= 0, y >= 0
   minux(z) -{ 4 }-> y :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x'' = 1 + x + y, x >= 0, y >= 0, x' = 1 + x
   minux(z) -{ 3 }-> y :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, 1 + x = 1 + x'' + y, x'' >= 0, y >= 0, x' = 1 + x''
   minux(z) -{ 3 }-> y' :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, x2 = 1 + x + y', x >= 0, y' >= 0, 1 + y = 1 + x
   minux(z) -{ 2 }-> y' :|: z = 1 + x + y, x >= 0, y >= 0, 1 + x = 1 + x' + y', x' >= 0, y' >= 0, 1 + y = 1 + x'
   minux(z) -{ 0 }-> 0 :|: z >= 0
   minux(z) -{ 3 }-> 0 :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, v0 >= 0, v1 >= 0, x' = v0, x'' = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, v0 >= 0, v1 >= 0, x' = v0, 1 + x = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, v0 >= 0, v1 >= 0, x' = v0, 0 = v1
   minux(z) -{ 2 }-> 0 :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, x2 = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, 1 + x = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, 0 = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + (1 + x3) + y, y >= 0, x3 >= 0, v0 >= 0, v1 >= 0, 0 = v0, x3 = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 0 = v0, 1 + x = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   minux(z) -{ 3 }-> 1 + x0 + x1 :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x' = x0, x0 >= 0, x1 >= 0, x'' = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, x' = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, x' = x0, x0 >= 0, x1 >= 0, 0 = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, x2 = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, 0 = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + (1 + x3) + y, y >= 0, x3 >= 0, 0 = x0, x0 >= 0, x1 >= 0, x3 = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 0 = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   plus(z, z') -{ 1 }-> x :|: z = 1 + x + (z' - 1), x >= 0, z' - 1 >= 0
   plus(z, z') -{ 1 }-> y :|: z' = 1 + (z - 1) + y, z - 1 >= 0, y >= 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 0 }-> 1 + z + z' :|: z >= 0, z' >= 0

Function symbols to be analyzed: {encArg}, {encode_minus}, {encode_+}, {encode_minux}
Previous analysis results are:
  minus: runtime: O(1) [1], size: O(n^1) [1 + z]
  minux: runtime: O(1) [4], size: O(n^1) [2 + z]
  plus: runtime: O(1) [1], size: O(n^1) [1 + z + z']

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

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

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

   encArg(z) -{ 0 }-> plus(plus(encArg(x_17), encArg(x_21)), plus(encArg(x_116), encArg(x_24))) :|: x_116 >= 0, x_17 >= 0, z = 1 + (1 + x_17 + x_21) + (1 + x_116 + x_24), x_24 >= 0, x_21 >= 0
   encArg(z) -{ 0 }-> plus(plus(encArg(x_17), encArg(x_21)), minux(encArg(x_115))) :|: z = 1 + (1 + x_17 + x_21) + (1 + x_115), x_115 >= 0, x_17 >= 0, x_21 >= 0
   encArg(z) -{ 0 }-> plus(plus(encArg(x_17), encArg(x_21)), minus(encArg(x_114))) :|: z = 1 + (1 + x_17 + x_21) + (1 + x_114), x_114 >= 0, x_17 >= 0, x_21 >= 0
   encArg(z) -{ 0 }-> plus(plus(encArg(x_17), encArg(x_21)), 0) :|: z = 1 + (1 + x_17 + x_21) + x_2, x_17 >= 0, x_2 >= 0, x_21 >= 0
   encArg(z) -{ 0 }-> plus(minux(encArg(x_16)), plus(encArg(x_113), encArg(x_23))) :|: x_113 >= 0, x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_113 + x_23), x_23 >= 0
   encArg(z) -{ 0 }-> plus(minux(encArg(x_16)), minux(encArg(x_112))) :|: x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_112), x_112 >= 0
   encArg(z) -{ 0 }-> plus(minux(encArg(x_16)), minus(encArg(x_111))) :|: x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_111), x_111 >= 0
   encArg(z) -{ 0 }-> plus(minux(encArg(x_16)), 0) :|: x_16 >= 0, x_2 >= 0, z = 1 + (1 + x_16) + x_2
   encArg(z) -{ 0 }-> plus(minus(encArg(x_15)), plus(encArg(x_110), encArg(x_22))) :|: x_15 >= 0, z = 1 + (1 + x_15) + (1 + x_110 + x_22), x_110 >= 0, x_22 >= 0
   encArg(z) -{ 0 }-> plus(minus(encArg(x_15)), minux(encArg(x_19))) :|: x_15 >= 0, z = 1 + (1 + x_15) + (1 + x_19), x_19 >= 0
   encArg(z) -{ 0 }-> plus(minus(encArg(x_15)), minus(encArg(x_18))) :|: x_15 >= 0, x_18 >= 0, z = 1 + (1 + x_15) + (1 + x_18)
   encArg(z) -{ 0 }-> plus(minus(encArg(x_15)), 0) :|: x_15 >= 0, z = 1 + (1 + x_15) + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> plus(0, plus(encArg(x_119), encArg(x_25))) :|: x_1 >= 0, z = 1 + x_1 + (1 + x_119 + x_25), x_25 >= 0, x_119 >= 0
   encArg(z) -{ 0 }-> plus(0, minux(encArg(x_118))) :|: x_1 >= 0, z = 1 + x_1 + (1 + x_118), x_118 >= 0
   encArg(z) -{ 0 }-> plus(0, minus(encArg(x_117))) :|: x_1 >= 0, x_117 >= 0, z = 1 + x_1 + (1 + x_117)
   encArg(z) -{ 0 }-> minux(plus(encArg(x_14), encArg(x_2''))) :|: x_14 >= 0, z = 1 + (1 + x_14 + x_2''), x_2'' >= 0
   encArg(z) -{ 0 }-> minux(minux(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> minux(minus(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> minus(plus(encArg(x_11), encArg(x_2'))) :|: x_11 >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2')
   encArg(z) -{ 0 }-> minus(minux(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> minus(minus(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   encArg(z) -{ 0 }-> 1 + x0 :|: z - 1 >= 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 + x1 :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   encode_+(z, z') -{ 0 }-> plus(plus(encArg(x_128), encArg(x_28)), plus(encArg(x_137), encArg(x_211))) :|: x_128 >= 0, z = 1 + x_128 + x_28, z' = 1 + x_137 + x_211, x_137 >= 0, x_28 >= 0, x_211 >= 0
   encode_+(z, z') -{ 0 }-> plus(plus(encArg(x_128), encArg(x_28)), minux(encArg(z' - 1))) :|: x_128 >= 0, z = 1 + x_128 + x_28, z' - 1 >= 0, x_28 >= 0
   encode_+(z, z') -{ 0 }-> plus(plus(encArg(x_128), encArg(x_28)), minus(encArg(z' - 1))) :|: x_128 >= 0, z = 1 + x_128 + x_28, z' - 1 >= 0, x_28 >= 0
   encode_+(z, z') -{ 0 }-> plus(plus(encArg(x_128), encArg(x_28)), 0) :|: x_128 >= 0, z = 1 + x_128 + x_28, z' >= 0, x_28 >= 0
   encode_+(z, z') -{ 0 }-> plus(minux(encArg(z - 1)), plus(encArg(x_134), encArg(x_210))) :|: x_134 >= 0, z - 1 >= 0, z' = 1 + x_134 + x_210, x_210 >= 0
   encode_+(z, z') -{ 0 }-> plus(minux(encArg(z - 1)), minux(encArg(z' - 1))) :|: z - 1 >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 0 }-> plus(minux(encArg(z - 1)), minus(encArg(z' - 1))) :|: z - 1 >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 0 }-> plus(minux(encArg(z - 1)), 0) :|: z - 1 >= 0, z' >= 0
   encode_+(z, z') -{ 0 }-> plus(minus(encArg(z - 1)), plus(encArg(x_131), encArg(x_29))) :|: z' = 1 + x_131 + x_29, z - 1 >= 0, x_131 >= 0, x_29 >= 0
   encode_+(z, z') -{ 0 }-> plus(minus(encArg(z - 1)), minux(encArg(z' - 1))) :|: z' - 1 >= 0, z - 1 >= 0
   encode_+(z, z') -{ 0 }-> plus(minus(encArg(z - 1)), minus(encArg(z' - 1))) :|: z - 1 >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 0 }-> plus(minus(encArg(z - 1)), 0) :|: z - 1 >= 0, z' >= 0
   encode_+(z, z') -{ 0 }-> plus(0, plus(encArg(x_140), encArg(x_212))) :|: z >= 0, x_212 >= 0, x_140 >= 0, z' = 1 + x_140 + x_212
   encode_+(z, z') -{ 0 }-> plus(0, minux(encArg(z' - 1))) :|: z >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 0 }-> plus(0, minus(encArg(z' - 1))) :|: z' - 1 >= 0, z >= 0
   encode_+(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_+(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   encode_+(z, z') -{ 0 }-> 1 + x0 + x1 :|: z >= 0, z' >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   encode_minus(z) -{ 0 }-> minus(plus(encArg(x_122), encArg(x_26))) :|: z = 1 + x_122 + x_26, x_26 >= 0, x_122 >= 0
   encode_minus(z) -{ 0 }-> minus(minux(encArg(z - 1))) :|: z - 1 >= 0
   encode_minus(z) -{ 0 }-> minus(minus(encArg(z - 1))) :|: z - 1 >= 0
   encode_minus(z) -{ 0 }-> 0 :|: z >= 0
   encode_minus(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_minus(z) -{ 0 }-> 1 + x0 :|: z >= 0, 0 = x0, x0 >= 0
   encode_minux(z) -{ 0 }-> minux(plus(encArg(x_125), encArg(x_27))) :|: x_125 >= 0, x_27 >= 0, z = 1 + x_125 + x_27
   encode_minux(z) -{ 0 }-> minux(minux(encArg(z - 1))) :|: z - 1 >= 0
   encode_minux(z) -{ 0 }-> minux(minus(encArg(z - 1))) :|: z - 1 >= 0
   encode_minux(z) -{ 0 }-> 0 :|: z >= 0
   encode_minux(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   minus(z) -{ 0 }-> 0 :|: z >= 0
   minus(z) -{ 1 }-> z - 1 :|: z - 1 >= 0
   minus(z) -{ 0 }-> 1 + z :|: z >= 0
   minux(z) -{ 4 }-> x :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x'' = 1 + y, x' = 1 + x + y, x >= 0, y >= 0
   minux(z) -{ 3 }-> x :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, x2 = 1 + y', 1 + y = 1 + x + y', x >= 0, y' >= 0
   minux(z) -{ 2 }-> x' :|: z = 1 + x + y, x >= 0, y >= 0, 1 + x = 1 + y', 1 + y = 1 + x' + y', x' >= 0, y' >= 0
   minux(z) -{ 3 }-> x'' :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, 1 + x = 1 + y, x' = 1 + x'' + y, x'' >= 0, y >= 0
   minux(z) -{ 4 }-> y :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x'' = 1 + x + y, x >= 0, y >= 0, x' = 1 + x
   minux(z) -{ 3 }-> y :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, 1 + x = 1 + x'' + y, x'' >= 0, y >= 0, x' = 1 + x''
   minux(z) -{ 3 }-> y' :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, x2 = 1 + x + y', x >= 0, y' >= 0, 1 + y = 1 + x
   minux(z) -{ 2 }-> y' :|: z = 1 + x + y, x >= 0, y >= 0, 1 + x = 1 + x' + y', x' >= 0, y' >= 0, 1 + y = 1 + x'
   minux(z) -{ 0 }-> 0 :|: z >= 0
   minux(z) -{ 3 }-> 0 :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, v0 >= 0, v1 >= 0, x' = v0, x'' = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, v0 >= 0, v1 >= 0, x' = v0, 1 + x = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, v0 >= 0, v1 >= 0, x' = v0, 0 = v1
   minux(z) -{ 2 }-> 0 :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, x2 = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, 1 + x = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, 0 = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + (1 + x3) + y, y >= 0, x3 >= 0, v0 >= 0, v1 >= 0, 0 = v0, x3 = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 0 = v0, 1 + x = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   minux(z) -{ 3 }-> 1 + x0 + x1 :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x' = x0, x0 >= 0, x1 >= 0, x'' = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, x' = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, x' = x0, x0 >= 0, x1 >= 0, 0 = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, x2 = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, 0 = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + (1 + x3) + y, y >= 0, x3 >= 0, 0 = x0, x0 >= 0, x1 >= 0, x3 = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 0 = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   plus(z, z') -{ 1 }-> x :|: z = 1 + x + (z' - 1), x >= 0, z' - 1 >= 0
   plus(z, z') -{ 1 }-> y :|: z' = 1 + (z - 1) + y, z - 1 >= 0, y >= 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 0 }-> 1 + z + z' :|: z >= 0, z' >= 0

Function symbols to be analyzed: {encArg}, {encode_minus}, {encode_+}, {encode_minux}
Previous analysis results are:
  minus: runtime: O(1) [1], size: O(n^1) [1 + z]
  minux: runtime: O(1) [4], size: O(n^1) [2 + z]
  plus: runtime: O(1) [1], size: O(n^1) [1 + z + z']

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

(47) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: encArg
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 6 + 10*z

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

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

   encArg(z) -{ 0 }-> plus(plus(encArg(x_17), encArg(x_21)), plus(encArg(x_116), encArg(x_24))) :|: x_116 >= 0, x_17 >= 0, z = 1 + (1 + x_17 + x_21) + (1 + x_116 + x_24), x_24 >= 0, x_21 >= 0
   encArg(z) -{ 0 }-> plus(plus(encArg(x_17), encArg(x_21)), minux(encArg(x_115))) :|: z = 1 + (1 + x_17 + x_21) + (1 + x_115), x_115 >= 0, x_17 >= 0, x_21 >= 0
   encArg(z) -{ 0 }-> plus(plus(encArg(x_17), encArg(x_21)), minus(encArg(x_114))) :|: z = 1 + (1 + x_17 + x_21) + (1 + x_114), x_114 >= 0, x_17 >= 0, x_21 >= 0
   encArg(z) -{ 0 }-> plus(plus(encArg(x_17), encArg(x_21)), 0) :|: z = 1 + (1 + x_17 + x_21) + x_2, x_17 >= 0, x_2 >= 0, x_21 >= 0
   encArg(z) -{ 0 }-> plus(minux(encArg(x_16)), plus(encArg(x_113), encArg(x_23))) :|: x_113 >= 0, x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_113 + x_23), x_23 >= 0
   encArg(z) -{ 0 }-> plus(minux(encArg(x_16)), minux(encArg(x_112))) :|: x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_112), x_112 >= 0
   encArg(z) -{ 0 }-> plus(minux(encArg(x_16)), minus(encArg(x_111))) :|: x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_111), x_111 >= 0
   encArg(z) -{ 0 }-> plus(minux(encArg(x_16)), 0) :|: x_16 >= 0, x_2 >= 0, z = 1 + (1 + x_16) + x_2
   encArg(z) -{ 0 }-> plus(minus(encArg(x_15)), plus(encArg(x_110), encArg(x_22))) :|: x_15 >= 0, z = 1 + (1 + x_15) + (1 + x_110 + x_22), x_110 >= 0, x_22 >= 0
   encArg(z) -{ 0 }-> plus(minus(encArg(x_15)), minux(encArg(x_19))) :|: x_15 >= 0, z = 1 + (1 + x_15) + (1 + x_19), x_19 >= 0
   encArg(z) -{ 0 }-> plus(minus(encArg(x_15)), minus(encArg(x_18))) :|: x_15 >= 0, x_18 >= 0, z = 1 + (1 + x_15) + (1 + x_18)
   encArg(z) -{ 0 }-> plus(minus(encArg(x_15)), 0) :|: x_15 >= 0, z = 1 + (1 + x_15) + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> plus(0, plus(encArg(x_119), encArg(x_25))) :|: x_1 >= 0, z = 1 + x_1 + (1 + x_119 + x_25), x_25 >= 0, x_119 >= 0
   encArg(z) -{ 0 }-> plus(0, minux(encArg(x_118))) :|: x_1 >= 0, z = 1 + x_1 + (1 + x_118), x_118 >= 0
   encArg(z) -{ 0 }-> plus(0, minus(encArg(x_117))) :|: x_1 >= 0, x_117 >= 0, z = 1 + x_1 + (1 + x_117)
   encArg(z) -{ 0 }-> minux(plus(encArg(x_14), encArg(x_2''))) :|: x_14 >= 0, z = 1 + (1 + x_14 + x_2''), x_2'' >= 0
   encArg(z) -{ 0 }-> minux(minux(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> minux(minus(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> minus(plus(encArg(x_11), encArg(x_2'))) :|: x_11 >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2')
   encArg(z) -{ 0 }-> minus(minux(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> minus(minus(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   encArg(z) -{ 0 }-> 1 + x0 :|: z - 1 >= 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 + x1 :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   encode_+(z, z') -{ 0 }-> plus(plus(encArg(x_128), encArg(x_28)), plus(encArg(x_137), encArg(x_211))) :|: x_128 >= 0, z = 1 + x_128 + x_28, z' = 1 + x_137 + x_211, x_137 >= 0, x_28 >= 0, x_211 >= 0
   encode_+(z, z') -{ 0 }-> plus(plus(encArg(x_128), encArg(x_28)), minux(encArg(z' - 1))) :|: x_128 >= 0, z = 1 + x_128 + x_28, z' - 1 >= 0, x_28 >= 0
   encode_+(z, z') -{ 0 }-> plus(plus(encArg(x_128), encArg(x_28)), minus(encArg(z' - 1))) :|: x_128 >= 0, z = 1 + x_128 + x_28, z' - 1 >= 0, x_28 >= 0
   encode_+(z, z') -{ 0 }-> plus(plus(encArg(x_128), encArg(x_28)), 0) :|: x_128 >= 0, z = 1 + x_128 + x_28, z' >= 0, x_28 >= 0
   encode_+(z, z') -{ 0 }-> plus(minux(encArg(z - 1)), plus(encArg(x_134), encArg(x_210))) :|: x_134 >= 0, z - 1 >= 0, z' = 1 + x_134 + x_210, x_210 >= 0
   encode_+(z, z') -{ 0 }-> plus(minux(encArg(z - 1)), minux(encArg(z' - 1))) :|: z - 1 >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 0 }-> plus(minux(encArg(z - 1)), minus(encArg(z' - 1))) :|: z - 1 >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 0 }-> plus(minux(encArg(z - 1)), 0) :|: z - 1 >= 0, z' >= 0
   encode_+(z, z') -{ 0 }-> plus(minus(encArg(z - 1)), plus(encArg(x_131), encArg(x_29))) :|: z' = 1 + x_131 + x_29, z - 1 >= 0, x_131 >= 0, x_29 >= 0
   encode_+(z, z') -{ 0 }-> plus(minus(encArg(z - 1)), minux(encArg(z' - 1))) :|: z' - 1 >= 0, z - 1 >= 0
   encode_+(z, z') -{ 0 }-> plus(minus(encArg(z - 1)), minus(encArg(z' - 1))) :|: z - 1 >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 0 }-> plus(minus(encArg(z - 1)), 0) :|: z - 1 >= 0, z' >= 0
   encode_+(z, z') -{ 0 }-> plus(0, plus(encArg(x_140), encArg(x_212))) :|: z >= 0, x_212 >= 0, x_140 >= 0, z' = 1 + x_140 + x_212
   encode_+(z, z') -{ 0 }-> plus(0, minux(encArg(z' - 1))) :|: z >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 0 }-> plus(0, minus(encArg(z' - 1))) :|: z' - 1 >= 0, z >= 0
   encode_+(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_+(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   encode_+(z, z') -{ 0 }-> 1 + x0 + x1 :|: z >= 0, z' >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   encode_minus(z) -{ 0 }-> minus(plus(encArg(x_122), encArg(x_26))) :|: z = 1 + x_122 + x_26, x_26 >= 0, x_122 >= 0
   encode_minus(z) -{ 0 }-> minus(minux(encArg(z - 1))) :|: z - 1 >= 0
   encode_minus(z) -{ 0 }-> minus(minus(encArg(z - 1))) :|: z - 1 >= 0
   encode_minus(z) -{ 0 }-> 0 :|: z >= 0
   encode_minus(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_minus(z) -{ 0 }-> 1 + x0 :|: z >= 0, 0 = x0, x0 >= 0
   encode_minux(z) -{ 0 }-> minux(plus(encArg(x_125), encArg(x_27))) :|: x_125 >= 0, x_27 >= 0, z = 1 + x_125 + x_27
   encode_minux(z) -{ 0 }-> minux(minux(encArg(z - 1))) :|: z - 1 >= 0
   encode_minux(z) -{ 0 }-> minux(minus(encArg(z - 1))) :|: z - 1 >= 0
   encode_minux(z) -{ 0 }-> 0 :|: z >= 0
   encode_minux(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   minus(z) -{ 0 }-> 0 :|: z >= 0
   minus(z) -{ 1 }-> z - 1 :|: z - 1 >= 0
   minus(z) -{ 0 }-> 1 + z :|: z >= 0
   minux(z) -{ 4 }-> x :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x'' = 1 + y, x' = 1 + x + y, x >= 0, y >= 0
   minux(z) -{ 3 }-> x :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, x2 = 1 + y', 1 + y = 1 + x + y', x >= 0, y' >= 0
   minux(z) -{ 2 }-> x' :|: z = 1 + x + y, x >= 0, y >= 0, 1 + x = 1 + y', 1 + y = 1 + x' + y', x' >= 0, y' >= 0
   minux(z) -{ 3 }-> x'' :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, 1 + x = 1 + y, x' = 1 + x'' + y, x'' >= 0, y >= 0
   minux(z) -{ 4 }-> y :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x'' = 1 + x + y, x >= 0, y >= 0, x' = 1 + x
   minux(z) -{ 3 }-> y :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, 1 + x = 1 + x'' + y, x'' >= 0, y >= 0, x' = 1 + x''
   minux(z) -{ 3 }-> y' :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, x2 = 1 + x + y', x >= 0, y' >= 0, 1 + y = 1 + x
   minux(z) -{ 2 }-> y' :|: z = 1 + x + y, x >= 0, y >= 0, 1 + x = 1 + x' + y', x' >= 0, y' >= 0, 1 + y = 1 + x'
   minux(z) -{ 0 }-> 0 :|: z >= 0
   minux(z) -{ 3 }-> 0 :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, v0 >= 0, v1 >= 0, x' = v0, x'' = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, v0 >= 0, v1 >= 0, x' = v0, 1 + x = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, v0 >= 0, v1 >= 0, x' = v0, 0 = v1
   minux(z) -{ 2 }-> 0 :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, x2 = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, 1 + x = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, 0 = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + (1 + x3) + y, y >= 0, x3 >= 0, v0 >= 0, v1 >= 0, 0 = v0, x3 = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 0 = v0, 1 + x = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   minux(z) -{ 3 }-> 1 + x0 + x1 :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x' = x0, x0 >= 0, x1 >= 0, x'' = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, x' = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, x' = x0, x0 >= 0, x1 >= 0, 0 = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, x2 = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, 0 = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + (1 + x3) + y, y >= 0, x3 >= 0, 0 = x0, x0 >= 0, x1 >= 0, x3 = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 0 = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   plus(z, z') -{ 1 }-> x :|: z = 1 + x + (z' - 1), x >= 0, z' - 1 >= 0
   plus(z, z') -{ 1 }-> y :|: z' = 1 + (z - 1) + y, z - 1 >= 0, y >= 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 0 }-> 1 + z + z' :|: z >= 0, z' >= 0

Function symbols to be analyzed: {encArg}, {encode_minus}, {encode_+}, {encode_minux}
Previous analysis results are:
  minus: runtime: O(1) [1], size: O(n^1) [1 + z]
  minux: runtime: O(1) [4], size: O(n^1) [2 + z]
  plus: runtime: O(1) [1], size: O(n^1) [1 + z + z']
  encArg: runtime: ?, size: O(n^1) [6 + 10*z]

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

(49) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: encArg
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 9 + 11*z

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

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

   encArg(z) -{ 0 }-> plus(plus(encArg(x_17), encArg(x_21)), plus(encArg(x_116), encArg(x_24))) :|: x_116 >= 0, x_17 >= 0, z = 1 + (1 + x_17 + x_21) + (1 + x_116 + x_24), x_24 >= 0, x_21 >= 0
   encArg(z) -{ 0 }-> plus(plus(encArg(x_17), encArg(x_21)), minux(encArg(x_115))) :|: z = 1 + (1 + x_17 + x_21) + (1 + x_115), x_115 >= 0, x_17 >= 0, x_21 >= 0
   encArg(z) -{ 0 }-> plus(plus(encArg(x_17), encArg(x_21)), minus(encArg(x_114))) :|: z = 1 + (1 + x_17 + x_21) + (1 + x_114), x_114 >= 0, x_17 >= 0, x_21 >= 0
   encArg(z) -{ 0 }-> plus(plus(encArg(x_17), encArg(x_21)), 0) :|: z = 1 + (1 + x_17 + x_21) + x_2, x_17 >= 0, x_2 >= 0, x_21 >= 0
   encArg(z) -{ 0 }-> plus(minux(encArg(x_16)), plus(encArg(x_113), encArg(x_23))) :|: x_113 >= 0, x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_113 + x_23), x_23 >= 0
   encArg(z) -{ 0 }-> plus(minux(encArg(x_16)), minux(encArg(x_112))) :|: x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_112), x_112 >= 0
   encArg(z) -{ 0 }-> plus(minux(encArg(x_16)), minus(encArg(x_111))) :|: x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_111), x_111 >= 0
   encArg(z) -{ 0 }-> plus(minux(encArg(x_16)), 0) :|: x_16 >= 0, x_2 >= 0, z = 1 + (1 + x_16) + x_2
   encArg(z) -{ 0 }-> plus(minus(encArg(x_15)), plus(encArg(x_110), encArg(x_22))) :|: x_15 >= 0, z = 1 + (1 + x_15) + (1 + x_110 + x_22), x_110 >= 0, x_22 >= 0
   encArg(z) -{ 0 }-> plus(minus(encArg(x_15)), minux(encArg(x_19))) :|: x_15 >= 0, z = 1 + (1 + x_15) + (1 + x_19), x_19 >= 0
   encArg(z) -{ 0 }-> plus(minus(encArg(x_15)), minus(encArg(x_18))) :|: x_15 >= 0, x_18 >= 0, z = 1 + (1 + x_15) + (1 + x_18)
   encArg(z) -{ 0 }-> plus(minus(encArg(x_15)), 0) :|: x_15 >= 0, z = 1 + (1 + x_15) + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> plus(0, plus(encArg(x_119), encArg(x_25))) :|: x_1 >= 0, z = 1 + x_1 + (1 + x_119 + x_25), x_25 >= 0, x_119 >= 0
   encArg(z) -{ 0 }-> plus(0, minux(encArg(x_118))) :|: x_1 >= 0, z = 1 + x_1 + (1 + x_118), x_118 >= 0
   encArg(z) -{ 0 }-> plus(0, minus(encArg(x_117))) :|: x_1 >= 0, x_117 >= 0, z = 1 + x_1 + (1 + x_117)
   encArg(z) -{ 0 }-> minux(plus(encArg(x_14), encArg(x_2''))) :|: x_14 >= 0, z = 1 + (1 + x_14 + x_2''), x_2'' >= 0
   encArg(z) -{ 0 }-> minux(minux(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> minux(minus(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> minus(plus(encArg(x_11), encArg(x_2'))) :|: x_11 >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2')
   encArg(z) -{ 0 }-> minus(minux(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> minus(minus(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   encArg(z) -{ 0 }-> 1 + x0 :|: z - 1 >= 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 + x1 :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   encode_+(z, z') -{ 0 }-> plus(plus(encArg(x_128), encArg(x_28)), plus(encArg(x_137), encArg(x_211))) :|: x_128 >= 0, z = 1 + x_128 + x_28, z' = 1 + x_137 + x_211, x_137 >= 0, x_28 >= 0, x_211 >= 0
   encode_+(z, z') -{ 0 }-> plus(plus(encArg(x_128), encArg(x_28)), minux(encArg(z' - 1))) :|: x_128 >= 0, z = 1 + x_128 + x_28, z' - 1 >= 0, x_28 >= 0
   encode_+(z, z') -{ 0 }-> plus(plus(encArg(x_128), encArg(x_28)), minus(encArg(z' - 1))) :|: x_128 >= 0, z = 1 + x_128 + x_28, z' - 1 >= 0, x_28 >= 0
   encode_+(z, z') -{ 0 }-> plus(plus(encArg(x_128), encArg(x_28)), 0) :|: x_128 >= 0, z = 1 + x_128 + x_28, z' >= 0, x_28 >= 0
   encode_+(z, z') -{ 0 }-> plus(minux(encArg(z - 1)), plus(encArg(x_134), encArg(x_210))) :|: x_134 >= 0, z - 1 >= 0, z' = 1 + x_134 + x_210, x_210 >= 0
   encode_+(z, z') -{ 0 }-> plus(minux(encArg(z - 1)), minux(encArg(z' - 1))) :|: z - 1 >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 0 }-> plus(minux(encArg(z - 1)), minus(encArg(z' - 1))) :|: z - 1 >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 0 }-> plus(minux(encArg(z - 1)), 0) :|: z - 1 >= 0, z' >= 0
   encode_+(z, z') -{ 0 }-> plus(minus(encArg(z - 1)), plus(encArg(x_131), encArg(x_29))) :|: z' = 1 + x_131 + x_29, z - 1 >= 0, x_131 >= 0, x_29 >= 0
   encode_+(z, z') -{ 0 }-> plus(minus(encArg(z - 1)), minux(encArg(z' - 1))) :|: z' - 1 >= 0, z - 1 >= 0
   encode_+(z, z') -{ 0 }-> plus(minus(encArg(z - 1)), minus(encArg(z' - 1))) :|: z - 1 >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 0 }-> plus(minus(encArg(z - 1)), 0) :|: z - 1 >= 0, z' >= 0
   encode_+(z, z') -{ 0 }-> plus(0, plus(encArg(x_140), encArg(x_212))) :|: z >= 0, x_212 >= 0, x_140 >= 0, z' = 1 + x_140 + x_212
   encode_+(z, z') -{ 0 }-> plus(0, minux(encArg(z' - 1))) :|: z >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 0 }-> plus(0, minus(encArg(z' - 1))) :|: z' - 1 >= 0, z >= 0
   encode_+(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_+(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   encode_+(z, z') -{ 0 }-> 1 + x0 + x1 :|: z >= 0, z' >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   encode_minus(z) -{ 0 }-> minus(plus(encArg(x_122), encArg(x_26))) :|: z = 1 + x_122 + x_26, x_26 >= 0, x_122 >= 0
   encode_minus(z) -{ 0 }-> minus(minux(encArg(z - 1))) :|: z - 1 >= 0
   encode_minus(z) -{ 0 }-> minus(minus(encArg(z - 1))) :|: z - 1 >= 0
   encode_minus(z) -{ 0 }-> 0 :|: z >= 0
   encode_minus(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_minus(z) -{ 0 }-> 1 + x0 :|: z >= 0, 0 = x0, x0 >= 0
   encode_minux(z) -{ 0 }-> minux(plus(encArg(x_125), encArg(x_27))) :|: x_125 >= 0, x_27 >= 0, z = 1 + x_125 + x_27
   encode_minux(z) -{ 0 }-> minux(minux(encArg(z - 1))) :|: z - 1 >= 0
   encode_minux(z) -{ 0 }-> minux(minus(encArg(z - 1))) :|: z - 1 >= 0
   encode_minux(z) -{ 0 }-> 0 :|: z >= 0
   encode_minux(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   minus(z) -{ 0 }-> 0 :|: z >= 0
   minus(z) -{ 1 }-> z - 1 :|: z - 1 >= 0
   minus(z) -{ 0 }-> 1 + z :|: z >= 0
   minux(z) -{ 4 }-> x :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x'' = 1 + y, x' = 1 + x + y, x >= 0, y >= 0
   minux(z) -{ 3 }-> x :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, x2 = 1 + y', 1 + y = 1 + x + y', x >= 0, y' >= 0
   minux(z) -{ 2 }-> x' :|: z = 1 + x + y, x >= 0, y >= 0, 1 + x = 1 + y', 1 + y = 1 + x' + y', x' >= 0, y' >= 0
   minux(z) -{ 3 }-> x'' :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, 1 + x = 1 + y, x' = 1 + x'' + y, x'' >= 0, y >= 0
   minux(z) -{ 4 }-> y :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x'' = 1 + x + y, x >= 0, y >= 0, x' = 1 + x
   minux(z) -{ 3 }-> y :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, 1 + x = 1 + x'' + y, x'' >= 0, y >= 0, x' = 1 + x''
   minux(z) -{ 3 }-> y' :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, x2 = 1 + x + y', x >= 0, y' >= 0, 1 + y = 1 + x
   minux(z) -{ 2 }-> y' :|: z = 1 + x + y, x >= 0, y >= 0, 1 + x = 1 + x' + y', x' >= 0, y' >= 0, 1 + y = 1 + x'
   minux(z) -{ 0 }-> 0 :|: z >= 0
   minux(z) -{ 3 }-> 0 :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, v0 >= 0, v1 >= 0, x' = v0, x'' = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, v0 >= 0, v1 >= 0, x' = v0, 1 + x = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, v0 >= 0, v1 >= 0, x' = v0, 0 = v1
   minux(z) -{ 2 }-> 0 :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, x2 = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, 1 + x = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, 0 = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + (1 + x3) + y, y >= 0, x3 >= 0, v0 >= 0, v1 >= 0, 0 = v0, x3 = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 0 = v0, 1 + x = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   minux(z) -{ 3 }-> 1 + x0 + x1 :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x' = x0, x0 >= 0, x1 >= 0, x'' = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, x' = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, x' = x0, x0 >= 0, x1 >= 0, 0 = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, x2 = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, 0 = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + (1 + x3) + y, y >= 0, x3 >= 0, 0 = x0, x0 >= 0, x1 >= 0, x3 = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 0 = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   plus(z, z') -{ 1 }-> x :|: z = 1 + x + (z' - 1), x >= 0, z' - 1 >= 0
   plus(z, z') -{ 1 }-> y :|: z' = 1 + (z - 1) + y, z - 1 >= 0, y >= 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 0 }-> 1 + z + z' :|: z >= 0, z' >= 0

Function symbols to be analyzed: {encode_minus}, {encode_+}, {encode_minux}
Previous analysis results are:
  minus: runtime: O(1) [1], size: O(n^1) [1 + z]
  minux: runtime: O(1) [4], size: O(n^1) [2 + z]
  plus: runtime: O(1) [1], size: O(n^1) [1 + z + z']
  encArg: runtime: O(n^1) [9 + 11*z], size: O(n^1) [6 + 10*z]

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

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

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

   encArg(z) -{ -5 + 11*z }-> s'' :|: s >= 0, s <= 6 + 10 * (z - 2), s' >= 0, s' <= s + 2, s'' >= 0, s'' <= s' + 2, z - 2 >= 0
   encArg(z) -{ -8 + 11*z }-> s106 :|: s104 >= 0, s104 <= 6 + 10 * (z - 2), s105 >= 0, s105 <= s104 + 2, s106 >= 0, s106 <= s105 + 1, z - 2 >= 0
   encArg(z) -{ -8 + 11*z }-> s109 :|: s107 >= 0, s107 <= 6 + 10 * (z - 2), s108 >= 0, s108 <= s107 + 1, s109 >= 0, s109 <= s108 + 2, z - 2 >= 0
   encArg(z) -{ 23 + 11*x_14 + 11*x_2'' }-> s119 :|: s116 >= 0, s116 <= 6 + 10 * x_14, s117 >= 0, s117 <= 6 + 10 * x_2'', s118 >= 0, s118 <= s116 + s117 + 1, s119 >= 0, s119 <= s118 + 2, x_14 >= 0, z = 1 + (1 + x_14 + x_2''), x_2'' >= 0
   encArg(z) -{ 33 + 11*x_113 + 11*x_16 + 11*x_23 }-> s125 :|: s120 >= 0, s120 <= 6 + 10 * x_16, s121 >= 0, s121 <= s120 + 2, s122 >= 0, s122 <= 6 + 10 * x_113, s123 >= 0, s123 <= 6 + 10 * x_23, s124 >= 0, s124 <= s122 + s123 + 1, s125 >= 0, s125 <= s121 + s124 + 1, x_113 >= 0, x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_113 + x_23), x_23 >= 0
   encArg(z) -{ 14 + 11*x_16 }-> s128 :|: s126 >= 0, s126 <= 6 + 10 * x_16, s127 >= 0, s127 <= s126 + 2, s128 >= 0, s128 <= s127 + 0 + 1, x_16 >= 0, x_2 >= 0, z = 1 + (1 + x_16) + x_2
   encArg(z) -{ 33 + 11*x_115 + 11*x_17 + 11*x_21 }-> s134 :|: s129 >= 0, s129 <= 6 + 10 * x_17, s130 >= 0, s130 <= 6 + 10 * x_21, s131 >= 0, s131 <= s129 + s130 + 1, s132 >= 0, s132 <= 6 + 10 * x_115, s133 >= 0, s133 <= s132 + 2, s134 >= 0, s134 <= s131 + s133 + 1, z = 1 + (1 + x_17 + x_21) + (1 + x_115), x_115 >= 0, x_17 >= 0, x_21 >= 0
   encArg(z) -{ 14 + 11*x_118 }-> s137 :|: s135 >= 0, s135 <= 6 + 10 * x_118, s136 >= 0, s136 <= s135 + 2, s137 >= 0, s137 <= 0 + s136 + 1, x_1 >= 0, z = 1 + x_1 + (1 + x_118), x_118 >= 0
   encArg(z) -{ 24 + 11*x_15 + 11*x_19 }-> s164 :|: s160 >= 0, s160 <= 6 + 10 * x_15, s161 >= 0, s161 <= s160 + 1, s162 >= 0, s162 <= 6 + 10 * x_19, s163 >= 0, s163 <= s162 + 2, s164 >= 0, s164 <= s161 + s163 + 1, x_15 >= 0, z = 1 + (1 + x_15) + (1 + x_19), x_19 >= 0
   encArg(z) -{ 24 + 11*x_111 + 11*x_16 }-> s169 :|: s165 >= 0, s165 <= 6 + 10 * x_16, s166 >= 0, s166 <= s165 + 2, s167 >= 0, s167 <= 6 + 10 * x_111, s168 >= 0, s168 <= s167 + 1, s169 >= 0, s169 <= s166 + s168 + 1, x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_111), x_111 >= 0
   encArg(z) -{ -11 + 11*z }-> s20 :|: s18 >= 0, s18 <= 6 + 10 * (z - 2), s19 >= 0, s19 <= s18 + 1, s20 >= 0, s20 <= s19 + 1, z - 2 >= 0
   encArg(z) -{ 27 + 11*x_112 + 11*x_16 }-> s28 :|: s24 >= 0, s24 <= 6 + 10 * x_16, s25 >= 0, s25 <= s24 + 2, s26 >= 0, s26 <= 6 + 10 * x_112, s27 >= 0, s27 <= s26 + 2, s28 >= 0, s28 <= s25 + s27 + 1, x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_112), x_112 >= 0
   encArg(z) -{ 20 + 11*x_17 + 11*x_21 }-> s32 :|: s29 >= 0, s29 <= 6 + 10 * x_17, s30 >= 0, s30 <= 6 + 10 * x_21, s31 >= 0, s31 <= s29 + s30 + 1, s32 >= 0, s32 <= s31 + 0 + 1, z = 1 + (1 + x_17 + x_21) + x_2, x_17 >= 0, x_2 >= 0, x_21 >= 0
   encArg(z) -{ 20 + 11*x_119 + 11*x_25 }-> s36 :|: s33 >= 0, s33 <= 6 + 10 * x_119, s34 >= 0, s34 <= 6 + 10 * x_25, s35 >= 0, s35 <= s33 + s34 + 1, s36 >= 0, s36 <= 0 + s35 + 1, x_1 >= 0, z = 1 + x_1 + (1 + x_119 + x_25), x_25 >= 0, x_119 >= 0
   encArg(z) -{ 20 + 11*x_11 + 11*x_2' }-> s53 :|: s50 >= 0, s50 <= 6 + 10 * x_11, s51 >= 0, s51 <= 6 + 10 * x_2', s52 >= 0, s52 <= s50 + s51 + 1, s53 >= 0, s53 <= s52 + 1, x_11 >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2')
   encArg(z) -{ 21 + 11*x_15 + 11*x_18 }-> s58 :|: s54 >= 0, s54 <= 6 + 10 * x_15, s55 >= 0, s55 <= s54 + 1, s56 >= 0, s56 <= 6 + 10 * x_18, s57 >= 0, s57 <= s56 + 1, s58 >= 0, s58 <= s55 + s57 + 1, x_15 >= 0, x_18 >= 0, z = 1 + (1 + x_15) + (1 + x_18)
   encArg(z) -{ 30 + 11*x_110 + 11*x_15 + 11*x_22 }-> s64 :|: s59 >= 0, s59 <= 6 + 10 * x_15, s60 >= 0, s60 <= s59 + 1, s61 >= 0, s61 <= 6 + 10 * x_110, s62 >= 0, s62 <= 6 + 10 * x_22, s63 >= 0, s63 <= s61 + s62 + 1, s64 >= 0, s64 <= s60 + s63 + 1, x_15 >= 0, z = 1 + (1 + x_15) + (1 + x_110 + x_22), x_110 >= 0, x_22 >= 0
   encArg(z) -{ 11 + 11*x_15 }-> s67 :|: s65 >= 0, s65 <= 6 + 10 * x_15, s66 >= 0, s66 <= s65 + 1, s67 >= 0, s67 <= s66 + 0 + 1, x_15 >= 0, z = 1 + (1 + x_15) + x_2, x_2 >= 0
   encArg(z) -{ 39 + 11*x_116 + 11*x_17 + 11*x_21 + 11*x_24 }-> s7 :|: s1 >= 0, s1 <= 6 + 10 * x_17, s2 >= 0, s2 <= 6 + 10 * x_21, s3 >= 0, s3 <= s1 + s2 + 1, s4 >= 0, s4 <= 6 + 10 * x_116, s5 >= 0, s5 <= 6 + 10 * x_24, s6 >= 0, s6 <= s4 + s5 + 1, s7 >= 0, s7 <= s3 + s6 + 1, x_116 >= 0, x_17 >= 0, z = 1 + (1 + x_17 + x_21) + (1 + x_116 + x_24), x_24 >= 0, x_21 >= 0
   encArg(z) -{ 30 + 11*x_114 + 11*x_17 + 11*x_21 }-> s73 :|: s68 >= 0, s68 <= 6 + 10 * x_17, s69 >= 0, s69 <= 6 + 10 * x_21, s70 >= 0, s70 <= s68 + s69 + 1, s71 >= 0, s71 <= 6 + 10 * x_114, s72 >= 0, s72 <= s71 + 1, s73 >= 0, s73 <= s70 + s72 + 1, z = 1 + (1 + x_17 + x_21) + (1 + x_114), x_114 >= 0, x_17 >= 0, x_21 >= 0
   encArg(z) -{ 11 + 11*x_117 }-> s76 :|: s74 >= 0, s74 <= 6 + 10 * x_117, s75 >= 0, s75 <= s74 + 1, s76 >= 0, s76 <= 0 + s75 + 1, x_1 >= 0, x_117 >= 0, z = 1 + x_1 + (1 + x_117)
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   encArg(z) -{ 0 }-> 1 + x0 :|: z - 1 >= 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 + x1 :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   encode_+(z, z') -{ 19 + 11*x_128 + 11*x_28 + 11*z' }-> s100 :|: s95 >= 0, s95 <= 6 + 10 * x_128, s96 >= 0, s96 <= 6 + 10 * x_28, s97 >= 0, s97 <= s95 + s96 + 1, s98 >= 0, s98 <= 6 + 10 * (z' - 1), s99 >= 0, s99 <= s98 + 1, s100 >= 0, s100 <= s97 + s99 + 1, x_128 >= 0, z = 1 + x_128 + x_28, z' - 1 >= 0, x_28 >= 0
   encode_+(z, z') -{ 11*z' }-> s103 :|: s101 >= 0, s101 <= 6 + 10 * (z' - 1), s102 >= 0, s102 <= s101 + 1, s103 >= 0, s103 <= 0 + s102 + 1, z' - 1 >= 0, z >= 0
   encode_+(z, z') -{ 22 + 11*x_134 + 11*x_210 + 11*z }-> s147 :|: s142 >= 0, s142 <= 6 + 10 * (z - 1), s143 >= 0, s143 <= s142 + 2, s144 >= 0, s144 <= 6 + 10 * x_134, s145 >= 0, s145 <= 6 + 10 * x_210, s146 >= 0, s146 <= s144 + s145 + 1, s147 >= 0, s147 <= s143 + s146 + 1, x_134 >= 0, z - 1 >= 0, z' = 1 + x_134 + x_210, x_210 >= 0
   encode_+(z, z') -{ 3 + 11*z }-> s150 :|: s148 >= 0, s148 <= 6 + 10 * (z - 1), s149 >= 0, s149 <= s148 + 2, s150 >= 0, s150 <= s149 + 0 + 1, z - 1 >= 0, z' >= 0
   encode_+(z, z') -{ 22 + 11*x_128 + 11*x_28 + 11*z' }-> s156 :|: s151 >= 0, s151 <= 6 + 10 * x_128, s152 >= 0, s152 <= 6 + 10 * x_28, s153 >= 0, s153 <= s151 + s152 + 1, s154 >= 0, s154 <= 6 + 10 * (z' - 1), s155 >= 0, s155 <= s154 + 2, s156 >= 0, s156 <= s153 + s155 + 1, x_128 >= 0, z = 1 + x_128 + x_28, z' - 1 >= 0, x_28 >= 0
   encode_+(z, z') -{ 3 + 11*z' }-> s159 :|: s157 >= 0, s157 <= 6 + 10 * (z' - 1), s158 >= 0, s158 <= s157 + 2, s159 >= 0, s159 <= 0 + s158 + 1, z >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 39 + 11*x_128 + 11*x_137 + 11*x_211 + 11*x_28 }-> s17 :|: s11 >= 0, s11 <= 6 + 10 * x_128, s12 >= 0, s12 <= 6 + 10 * x_28, s13 >= 0, s13 <= s11 + s12 + 1, s14 >= 0, s14 <= 6 + 10 * x_137, s15 >= 0, s15 <= 6 + 10 * x_211, s16 >= 0, s16 <= s14 + s15 + 1, s17 >= 0, s17 <= s13 + s16 + 1, x_128 >= 0, z = 1 + x_128 + x_28, z' = 1 + x_137 + x_211, x_137 >= 0, x_28 >= 0, x_211 >= 0
   encode_+(z, z') -{ 2 + 11*z + 11*z' }-> s174 :|: s170 >= 0, s170 <= 6 + 10 * (z - 1), s171 >= 0, s171 <= s170 + 1, s172 >= 0, s172 <= 6 + 10 * (z' - 1), s173 >= 0, s173 <= s172 + 2, s174 >= 0, s174 <= s171 + s173 + 1, z' - 1 >= 0, z - 1 >= 0
   encode_+(z, z') -{ 2 + 11*z + 11*z' }-> s179 :|: s175 >= 0, s175 <= 6 + 10 * (z - 1), s176 >= 0, s176 <= s175 + 2, s177 >= 0, s177 <= 6 + 10 * (z' - 1), s178 >= 0, s178 <= s177 + 1, s179 >= 0, s179 <= s176 + s178 + 1, z - 1 >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 5 + 11*z + 11*z' }-> s41 :|: s37 >= 0, s37 <= 6 + 10 * (z - 1), s38 >= 0, s38 <= s37 + 2, s39 >= 0, s39 <= 6 + 10 * (z' - 1), s40 >= 0, s40 <= s39 + 2, s41 >= 0, s41 <= s38 + s40 + 1, z - 1 >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 20 + 11*x_128 + 11*x_28 }-> s45 :|: s42 >= 0, s42 <= 6 + 10 * x_128, s43 >= 0, s43 <= 6 + 10 * x_28, s44 >= 0, s44 <= s42 + s43 + 1, s45 >= 0, s45 <= s44 + 0 + 1, x_128 >= 0, z = 1 + x_128 + x_28, z' >= 0, x_28 >= 0
   encode_+(z, z') -{ 20 + 11*x_140 + 11*x_212 }-> s49 :|: s46 >= 0, s46 <= 6 + 10 * x_140, s47 >= 0, s47 <= 6 + 10 * x_212, s48 >= 0, s48 <= s46 + s47 + 1, s49 >= 0, s49 <= 0 + s48 + 1, z >= 0, x_212 >= 0, x_140 >= 0, z' = 1 + x_140 + x_212
   encode_+(z, z') -{ -1 + 11*z + 11*z' }-> s85 :|: s81 >= 0, s81 <= 6 + 10 * (z - 1), s82 >= 0, s82 <= s81 + 1, s83 >= 0, s83 <= 6 + 10 * (z' - 1), s84 >= 0, s84 <= s83 + 1, s85 >= 0, s85 <= s82 + s84 + 1, z - 1 >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 19 + 11*x_131 + 11*x_29 + 11*z }-> s91 :|: s86 >= 0, s86 <= 6 + 10 * (z - 1), s87 >= 0, s87 <= s86 + 1, s88 >= 0, s88 <= 6 + 10 * x_131, s89 >= 0, s89 <= 6 + 10 * x_29, s90 >= 0, s90 <= s88 + s89 + 1, s91 >= 0, s91 <= s87 + s90 + 1, z' = 1 + x_131 + x_29, z - 1 >= 0, x_131 >= 0, x_29 >= 0
   encode_+(z, z') -{ 11*z }-> s94 :|: s92 >= 0, s92 <= 6 + 10 * (z - 1), s93 >= 0, s93 <= s92 + 1, s94 >= 0, s94 <= s93 + 0 + 1, z - 1 >= 0, z' >= 0
   encode_+(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_+(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   encode_+(z, z') -{ 0 }-> 1 + x0 + x1 :|: z >= 0, z' >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   encode_minus(z) -{ 3 + 11*z }-> s112 :|: s110 >= 0, s110 <= 6 + 10 * (z - 1), s111 >= 0, s111 <= s110 + 2, s112 >= 0, s112 <= s111 + 1, z - 1 >= 0
   encode_minus(z) -{ 11*z }-> s23 :|: s21 >= 0, s21 <= 6 + 10 * (z - 1), s22 >= 0, s22 <= s21 + 1, s23 >= 0, s23 <= s22 + 1, z - 1 >= 0
   encode_minus(z) -{ 20 + 11*x_122 + 11*x_26 }-> s80 :|: s77 >= 0, s77 <= 6 + 10 * x_122, s78 >= 0, s78 <= 6 + 10 * x_26, s79 >= 0, s79 <= s77 + s78 + 1, s80 >= 0, s80 <= s79 + 1, z = 1 + x_122 + x_26, x_26 >= 0, x_122 >= 0
   encode_minus(z) -{ 0 }-> 0 :|: z >= 0
   encode_minus(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_minus(z) -{ 0 }-> 1 + x0 :|: z >= 0, 0 = x0, x0 >= 0
   encode_minux(z) -{ 6 + 11*z }-> s10 :|: s8 >= 0, s8 <= 6 + 10 * (z - 1), s9 >= 0, s9 <= s8 + 2, s10 >= 0, s10 <= s9 + 2, z - 1 >= 0
   encode_minux(z) -{ 3 + 11*z }-> s115 :|: s113 >= 0, s113 <= 6 + 10 * (z - 1), s114 >= 0, s114 <= s113 + 1, s115 >= 0, s115 <= s114 + 2, z - 1 >= 0
   encode_minux(z) -{ 23 + 11*x_125 + 11*x_27 }-> s141 :|: s138 >= 0, s138 <= 6 + 10 * x_125, s139 >= 0, s139 <= 6 + 10 * x_27, s140 >= 0, s140 <= s138 + s139 + 1, s141 >= 0, s141 <= s140 + 2, x_125 >= 0, x_27 >= 0, z = 1 + x_125 + x_27
   encode_minux(z) -{ 0 }-> 0 :|: z >= 0
   encode_minux(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   minus(z) -{ 0 }-> 0 :|: z >= 0
   minus(z) -{ 1 }-> z - 1 :|: z - 1 >= 0
   minus(z) -{ 0 }-> 1 + z :|: z >= 0
   minux(z) -{ 4 }-> x :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x'' = 1 + y, x' = 1 + x + y, x >= 0, y >= 0
   minux(z) -{ 3 }-> x :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, x2 = 1 + y', 1 + y = 1 + x + y', x >= 0, y' >= 0
   minux(z) -{ 2 }-> x' :|: z = 1 + x + y, x >= 0, y >= 0, 1 + x = 1 + y', 1 + y = 1 + x' + y', x' >= 0, y' >= 0
   minux(z) -{ 3 }-> x'' :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, 1 + x = 1 + y, x' = 1 + x'' + y, x'' >= 0, y >= 0
   minux(z) -{ 4 }-> y :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x'' = 1 + x + y, x >= 0, y >= 0, x' = 1 + x
   minux(z) -{ 3 }-> y :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, 1 + x = 1 + x'' + y, x'' >= 0, y >= 0, x' = 1 + x''
   minux(z) -{ 3 }-> y' :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, x2 = 1 + x + y', x >= 0, y' >= 0, 1 + y = 1 + x
   minux(z) -{ 2 }-> y' :|: z = 1 + x + y, x >= 0, y >= 0, 1 + x = 1 + x' + y', x' >= 0, y' >= 0, 1 + y = 1 + x'
   minux(z) -{ 0 }-> 0 :|: z >= 0
   minux(z) -{ 3 }-> 0 :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, v0 >= 0, v1 >= 0, x' = v0, x'' = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, v0 >= 0, v1 >= 0, x' = v0, 1 + x = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, v0 >= 0, v1 >= 0, x' = v0, 0 = v1
   minux(z) -{ 2 }-> 0 :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, x2 = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, 1 + x = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, 0 = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + (1 + x3) + y, y >= 0, x3 >= 0, v0 >= 0, v1 >= 0, 0 = v0, x3 = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 0 = v0, 1 + x = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   minux(z) -{ 3 }-> 1 + x0 + x1 :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x' = x0, x0 >= 0, x1 >= 0, x'' = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, x' = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, x' = x0, x0 >= 0, x1 >= 0, 0 = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, x2 = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, 0 = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + (1 + x3) + y, y >= 0, x3 >= 0, 0 = x0, x0 >= 0, x1 >= 0, x3 = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 0 = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   plus(z, z') -{ 1 }-> x :|: z = 1 + x + (z' - 1), x >= 0, z' - 1 >= 0
   plus(z, z') -{ 1 }-> y :|: z' = 1 + (z - 1) + y, z - 1 >= 0, y >= 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 0 }-> 1 + z + z' :|: z >= 0, z' >= 0

Function symbols to be analyzed: {encode_minus}, {encode_+}, {encode_minux}
Previous analysis results are:
  minus: runtime: O(1) [1], size: O(n^1) [1 + z]
  minux: runtime: O(1) [4], size: O(n^1) [2 + z]
  plus: runtime: O(1) [1], size: O(n^1) [1 + z + z']
  encArg: runtime: O(n^1) [9 + 11*z], size: O(n^1) [6 + 10*z]

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

(53) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: encode_minus
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 4 + 10*z

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

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

   encArg(z) -{ -5 + 11*z }-> s'' :|: s >= 0, s <= 6 + 10 * (z - 2), s' >= 0, s' <= s + 2, s'' >= 0, s'' <= s' + 2, z - 2 >= 0
   encArg(z) -{ -8 + 11*z }-> s106 :|: s104 >= 0, s104 <= 6 + 10 * (z - 2), s105 >= 0, s105 <= s104 + 2, s106 >= 0, s106 <= s105 + 1, z - 2 >= 0
   encArg(z) -{ -8 + 11*z }-> s109 :|: s107 >= 0, s107 <= 6 + 10 * (z - 2), s108 >= 0, s108 <= s107 + 1, s109 >= 0, s109 <= s108 + 2, z - 2 >= 0
   encArg(z) -{ 23 + 11*x_14 + 11*x_2'' }-> s119 :|: s116 >= 0, s116 <= 6 + 10 * x_14, s117 >= 0, s117 <= 6 + 10 * x_2'', s118 >= 0, s118 <= s116 + s117 + 1, s119 >= 0, s119 <= s118 + 2, x_14 >= 0, z = 1 + (1 + x_14 + x_2''), x_2'' >= 0
   encArg(z) -{ 33 + 11*x_113 + 11*x_16 + 11*x_23 }-> s125 :|: s120 >= 0, s120 <= 6 + 10 * x_16, s121 >= 0, s121 <= s120 + 2, s122 >= 0, s122 <= 6 + 10 * x_113, s123 >= 0, s123 <= 6 + 10 * x_23, s124 >= 0, s124 <= s122 + s123 + 1, s125 >= 0, s125 <= s121 + s124 + 1, x_113 >= 0, x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_113 + x_23), x_23 >= 0
   encArg(z) -{ 14 + 11*x_16 }-> s128 :|: s126 >= 0, s126 <= 6 + 10 * x_16, s127 >= 0, s127 <= s126 + 2, s128 >= 0, s128 <= s127 + 0 + 1, x_16 >= 0, x_2 >= 0, z = 1 + (1 + x_16) + x_2
   encArg(z) -{ 33 + 11*x_115 + 11*x_17 + 11*x_21 }-> s134 :|: s129 >= 0, s129 <= 6 + 10 * x_17, s130 >= 0, s130 <= 6 + 10 * x_21, s131 >= 0, s131 <= s129 + s130 + 1, s132 >= 0, s132 <= 6 + 10 * x_115, s133 >= 0, s133 <= s132 + 2, s134 >= 0, s134 <= s131 + s133 + 1, z = 1 + (1 + x_17 + x_21) + (1 + x_115), x_115 >= 0, x_17 >= 0, x_21 >= 0
   encArg(z) -{ 14 + 11*x_118 }-> s137 :|: s135 >= 0, s135 <= 6 + 10 * x_118, s136 >= 0, s136 <= s135 + 2, s137 >= 0, s137 <= 0 + s136 + 1, x_1 >= 0, z = 1 + x_1 + (1 + x_118), x_118 >= 0
   encArg(z) -{ 24 + 11*x_15 + 11*x_19 }-> s164 :|: s160 >= 0, s160 <= 6 + 10 * x_15, s161 >= 0, s161 <= s160 + 1, s162 >= 0, s162 <= 6 + 10 * x_19, s163 >= 0, s163 <= s162 + 2, s164 >= 0, s164 <= s161 + s163 + 1, x_15 >= 0, z = 1 + (1 + x_15) + (1 + x_19), x_19 >= 0
   encArg(z) -{ 24 + 11*x_111 + 11*x_16 }-> s169 :|: s165 >= 0, s165 <= 6 + 10 * x_16, s166 >= 0, s166 <= s165 + 2, s167 >= 0, s167 <= 6 + 10 * x_111, s168 >= 0, s168 <= s167 + 1, s169 >= 0, s169 <= s166 + s168 + 1, x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_111), x_111 >= 0
   encArg(z) -{ -11 + 11*z }-> s20 :|: s18 >= 0, s18 <= 6 + 10 * (z - 2), s19 >= 0, s19 <= s18 + 1, s20 >= 0, s20 <= s19 + 1, z - 2 >= 0
   encArg(z) -{ 27 + 11*x_112 + 11*x_16 }-> s28 :|: s24 >= 0, s24 <= 6 + 10 * x_16, s25 >= 0, s25 <= s24 + 2, s26 >= 0, s26 <= 6 + 10 * x_112, s27 >= 0, s27 <= s26 + 2, s28 >= 0, s28 <= s25 + s27 + 1, x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_112), x_112 >= 0
   encArg(z) -{ 20 + 11*x_17 + 11*x_21 }-> s32 :|: s29 >= 0, s29 <= 6 + 10 * x_17, s30 >= 0, s30 <= 6 + 10 * x_21, s31 >= 0, s31 <= s29 + s30 + 1, s32 >= 0, s32 <= s31 + 0 + 1, z = 1 + (1 + x_17 + x_21) + x_2, x_17 >= 0, x_2 >= 0, x_21 >= 0
   encArg(z) -{ 20 + 11*x_119 + 11*x_25 }-> s36 :|: s33 >= 0, s33 <= 6 + 10 * x_119, s34 >= 0, s34 <= 6 + 10 * x_25, s35 >= 0, s35 <= s33 + s34 + 1, s36 >= 0, s36 <= 0 + s35 + 1, x_1 >= 0, z = 1 + x_1 + (1 + x_119 + x_25), x_25 >= 0, x_119 >= 0
   encArg(z) -{ 20 + 11*x_11 + 11*x_2' }-> s53 :|: s50 >= 0, s50 <= 6 + 10 * x_11, s51 >= 0, s51 <= 6 + 10 * x_2', s52 >= 0, s52 <= s50 + s51 + 1, s53 >= 0, s53 <= s52 + 1, x_11 >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2')
   encArg(z) -{ 21 + 11*x_15 + 11*x_18 }-> s58 :|: s54 >= 0, s54 <= 6 + 10 * x_15, s55 >= 0, s55 <= s54 + 1, s56 >= 0, s56 <= 6 + 10 * x_18, s57 >= 0, s57 <= s56 + 1, s58 >= 0, s58 <= s55 + s57 + 1, x_15 >= 0, x_18 >= 0, z = 1 + (1 + x_15) + (1 + x_18)
   encArg(z) -{ 30 + 11*x_110 + 11*x_15 + 11*x_22 }-> s64 :|: s59 >= 0, s59 <= 6 + 10 * x_15, s60 >= 0, s60 <= s59 + 1, s61 >= 0, s61 <= 6 + 10 * x_110, s62 >= 0, s62 <= 6 + 10 * x_22, s63 >= 0, s63 <= s61 + s62 + 1, s64 >= 0, s64 <= s60 + s63 + 1, x_15 >= 0, z = 1 + (1 + x_15) + (1 + x_110 + x_22), x_110 >= 0, x_22 >= 0
   encArg(z) -{ 11 + 11*x_15 }-> s67 :|: s65 >= 0, s65 <= 6 + 10 * x_15, s66 >= 0, s66 <= s65 + 1, s67 >= 0, s67 <= s66 + 0 + 1, x_15 >= 0, z = 1 + (1 + x_15) + x_2, x_2 >= 0
   encArg(z) -{ 39 + 11*x_116 + 11*x_17 + 11*x_21 + 11*x_24 }-> s7 :|: s1 >= 0, s1 <= 6 + 10 * x_17, s2 >= 0, s2 <= 6 + 10 * x_21, s3 >= 0, s3 <= s1 + s2 + 1, s4 >= 0, s4 <= 6 + 10 * x_116, s5 >= 0, s5 <= 6 + 10 * x_24, s6 >= 0, s6 <= s4 + s5 + 1, s7 >= 0, s7 <= s3 + s6 + 1, x_116 >= 0, x_17 >= 0, z = 1 + (1 + x_17 + x_21) + (1 + x_116 + x_24), x_24 >= 0, x_21 >= 0
   encArg(z) -{ 30 + 11*x_114 + 11*x_17 + 11*x_21 }-> s73 :|: s68 >= 0, s68 <= 6 + 10 * x_17, s69 >= 0, s69 <= 6 + 10 * x_21, s70 >= 0, s70 <= s68 + s69 + 1, s71 >= 0, s71 <= 6 + 10 * x_114, s72 >= 0, s72 <= s71 + 1, s73 >= 0, s73 <= s70 + s72 + 1, z = 1 + (1 + x_17 + x_21) + (1 + x_114), x_114 >= 0, x_17 >= 0, x_21 >= 0
   encArg(z) -{ 11 + 11*x_117 }-> s76 :|: s74 >= 0, s74 <= 6 + 10 * x_117, s75 >= 0, s75 <= s74 + 1, s76 >= 0, s76 <= 0 + s75 + 1, x_1 >= 0, x_117 >= 0, z = 1 + x_1 + (1 + x_117)
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   encArg(z) -{ 0 }-> 1 + x0 :|: z - 1 >= 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 + x1 :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   encode_+(z, z') -{ 19 + 11*x_128 + 11*x_28 + 11*z' }-> s100 :|: s95 >= 0, s95 <= 6 + 10 * x_128, s96 >= 0, s96 <= 6 + 10 * x_28, s97 >= 0, s97 <= s95 + s96 + 1, s98 >= 0, s98 <= 6 + 10 * (z' - 1), s99 >= 0, s99 <= s98 + 1, s100 >= 0, s100 <= s97 + s99 + 1, x_128 >= 0, z = 1 + x_128 + x_28, z' - 1 >= 0, x_28 >= 0
   encode_+(z, z') -{ 11*z' }-> s103 :|: s101 >= 0, s101 <= 6 + 10 * (z' - 1), s102 >= 0, s102 <= s101 + 1, s103 >= 0, s103 <= 0 + s102 + 1, z' - 1 >= 0, z >= 0
   encode_+(z, z') -{ 22 + 11*x_134 + 11*x_210 + 11*z }-> s147 :|: s142 >= 0, s142 <= 6 + 10 * (z - 1), s143 >= 0, s143 <= s142 + 2, s144 >= 0, s144 <= 6 + 10 * x_134, s145 >= 0, s145 <= 6 + 10 * x_210, s146 >= 0, s146 <= s144 + s145 + 1, s147 >= 0, s147 <= s143 + s146 + 1, x_134 >= 0, z - 1 >= 0, z' = 1 + x_134 + x_210, x_210 >= 0
   encode_+(z, z') -{ 3 + 11*z }-> s150 :|: s148 >= 0, s148 <= 6 + 10 * (z - 1), s149 >= 0, s149 <= s148 + 2, s150 >= 0, s150 <= s149 + 0 + 1, z - 1 >= 0, z' >= 0
   encode_+(z, z') -{ 22 + 11*x_128 + 11*x_28 + 11*z' }-> s156 :|: s151 >= 0, s151 <= 6 + 10 * x_128, s152 >= 0, s152 <= 6 + 10 * x_28, s153 >= 0, s153 <= s151 + s152 + 1, s154 >= 0, s154 <= 6 + 10 * (z' - 1), s155 >= 0, s155 <= s154 + 2, s156 >= 0, s156 <= s153 + s155 + 1, x_128 >= 0, z = 1 + x_128 + x_28, z' - 1 >= 0, x_28 >= 0
   encode_+(z, z') -{ 3 + 11*z' }-> s159 :|: s157 >= 0, s157 <= 6 + 10 * (z' - 1), s158 >= 0, s158 <= s157 + 2, s159 >= 0, s159 <= 0 + s158 + 1, z >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 39 + 11*x_128 + 11*x_137 + 11*x_211 + 11*x_28 }-> s17 :|: s11 >= 0, s11 <= 6 + 10 * x_128, s12 >= 0, s12 <= 6 + 10 * x_28, s13 >= 0, s13 <= s11 + s12 + 1, s14 >= 0, s14 <= 6 + 10 * x_137, s15 >= 0, s15 <= 6 + 10 * x_211, s16 >= 0, s16 <= s14 + s15 + 1, s17 >= 0, s17 <= s13 + s16 + 1, x_128 >= 0, z = 1 + x_128 + x_28, z' = 1 + x_137 + x_211, x_137 >= 0, x_28 >= 0, x_211 >= 0
   encode_+(z, z') -{ 2 + 11*z + 11*z' }-> s174 :|: s170 >= 0, s170 <= 6 + 10 * (z - 1), s171 >= 0, s171 <= s170 + 1, s172 >= 0, s172 <= 6 + 10 * (z' - 1), s173 >= 0, s173 <= s172 + 2, s174 >= 0, s174 <= s171 + s173 + 1, z' - 1 >= 0, z - 1 >= 0
   encode_+(z, z') -{ 2 + 11*z + 11*z' }-> s179 :|: s175 >= 0, s175 <= 6 + 10 * (z - 1), s176 >= 0, s176 <= s175 + 2, s177 >= 0, s177 <= 6 + 10 * (z' - 1), s178 >= 0, s178 <= s177 + 1, s179 >= 0, s179 <= s176 + s178 + 1, z - 1 >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 5 + 11*z + 11*z' }-> s41 :|: s37 >= 0, s37 <= 6 + 10 * (z - 1), s38 >= 0, s38 <= s37 + 2, s39 >= 0, s39 <= 6 + 10 * (z' - 1), s40 >= 0, s40 <= s39 + 2, s41 >= 0, s41 <= s38 + s40 + 1, z - 1 >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 20 + 11*x_128 + 11*x_28 }-> s45 :|: s42 >= 0, s42 <= 6 + 10 * x_128, s43 >= 0, s43 <= 6 + 10 * x_28, s44 >= 0, s44 <= s42 + s43 + 1, s45 >= 0, s45 <= s44 + 0 + 1, x_128 >= 0, z = 1 + x_128 + x_28, z' >= 0, x_28 >= 0
   encode_+(z, z') -{ 20 + 11*x_140 + 11*x_212 }-> s49 :|: s46 >= 0, s46 <= 6 + 10 * x_140, s47 >= 0, s47 <= 6 + 10 * x_212, s48 >= 0, s48 <= s46 + s47 + 1, s49 >= 0, s49 <= 0 + s48 + 1, z >= 0, x_212 >= 0, x_140 >= 0, z' = 1 + x_140 + x_212
   encode_+(z, z') -{ -1 + 11*z + 11*z' }-> s85 :|: s81 >= 0, s81 <= 6 + 10 * (z - 1), s82 >= 0, s82 <= s81 + 1, s83 >= 0, s83 <= 6 + 10 * (z' - 1), s84 >= 0, s84 <= s83 + 1, s85 >= 0, s85 <= s82 + s84 + 1, z - 1 >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 19 + 11*x_131 + 11*x_29 + 11*z }-> s91 :|: s86 >= 0, s86 <= 6 + 10 * (z - 1), s87 >= 0, s87 <= s86 + 1, s88 >= 0, s88 <= 6 + 10 * x_131, s89 >= 0, s89 <= 6 + 10 * x_29, s90 >= 0, s90 <= s88 + s89 + 1, s91 >= 0, s91 <= s87 + s90 + 1, z' = 1 + x_131 + x_29, z - 1 >= 0, x_131 >= 0, x_29 >= 0
   encode_+(z, z') -{ 11*z }-> s94 :|: s92 >= 0, s92 <= 6 + 10 * (z - 1), s93 >= 0, s93 <= s92 + 1, s94 >= 0, s94 <= s93 + 0 + 1, z - 1 >= 0, z' >= 0
   encode_+(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_+(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   encode_+(z, z') -{ 0 }-> 1 + x0 + x1 :|: z >= 0, z' >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   encode_minus(z) -{ 3 + 11*z }-> s112 :|: s110 >= 0, s110 <= 6 + 10 * (z - 1), s111 >= 0, s111 <= s110 + 2, s112 >= 0, s112 <= s111 + 1, z - 1 >= 0
   encode_minus(z) -{ 11*z }-> s23 :|: s21 >= 0, s21 <= 6 + 10 * (z - 1), s22 >= 0, s22 <= s21 + 1, s23 >= 0, s23 <= s22 + 1, z - 1 >= 0
   encode_minus(z) -{ 20 + 11*x_122 + 11*x_26 }-> s80 :|: s77 >= 0, s77 <= 6 + 10 * x_122, s78 >= 0, s78 <= 6 + 10 * x_26, s79 >= 0, s79 <= s77 + s78 + 1, s80 >= 0, s80 <= s79 + 1, z = 1 + x_122 + x_26, x_26 >= 0, x_122 >= 0
   encode_minus(z) -{ 0 }-> 0 :|: z >= 0
   encode_minus(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_minus(z) -{ 0 }-> 1 + x0 :|: z >= 0, 0 = x0, x0 >= 0
   encode_minux(z) -{ 6 + 11*z }-> s10 :|: s8 >= 0, s8 <= 6 + 10 * (z - 1), s9 >= 0, s9 <= s8 + 2, s10 >= 0, s10 <= s9 + 2, z - 1 >= 0
   encode_minux(z) -{ 3 + 11*z }-> s115 :|: s113 >= 0, s113 <= 6 + 10 * (z - 1), s114 >= 0, s114 <= s113 + 1, s115 >= 0, s115 <= s114 + 2, z - 1 >= 0
   encode_minux(z) -{ 23 + 11*x_125 + 11*x_27 }-> s141 :|: s138 >= 0, s138 <= 6 + 10 * x_125, s139 >= 0, s139 <= 6 + 10 * x_27, s140 >= 0, s140 <= s138 + s139 + 1, s141 >= 0, s141 <= s140 + 2, x_125 >= 0, x_27 >= 0, z = 1 + x_125 + x_27
   encode_minux(z) -{ 0 }-> 0 :|: z >= 0
   encode_minux(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   minus(z) -{ 0 }-> 0 :|: z >= 0
   minus(z) -{ 1 }-> z - 1 :|: z - 1 >= 0
   minus(z) -{ 0 }-> 1 + z :|: z >= 0
   minux(z) -{ 4 }-> x :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x'' = 1 + y, x' = 1 + x + y, x >= 0, y >= 0
   minux(z) -{ 3 }-> x :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, x2 = 1 + y', 1 + y = 1 + x + y', x >= 0, y' >= 0
   minux(z) -{ 2 }-> x' :|: z = 1 + x + y, x >= 0, y >= 0, 1 + x = 1 + y', 1 + y = 1 + x' + y', x' >= 0, y' >= 0
   minux(z) -{ 3 }-> x'' :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, 1 + x = 1 + y, x' = 1 + x'' + y, x'' >= 0, y >= 0
   minux(z) -{ 4 }-> y :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x'' = 1 + x + y, x >= 0, y >= 0, x' = 1 + x
   minux(z) -{ 3 }-> y :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, 1 + x = 1 + x'' + y, x'' >= 0, y >= 0, x' = 1 + x''
   minux(z) -{ 3 }-> y' :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, x2 = 1 + x + y', x >= 0, y' >= 0, 1 + y = 1 + x
   minux(z) -{ 2 }-> y' :|: z = 1 + x + y, x >= 0, y >= 0, 1 + x = 1 + x' + y', x' >= 0, y' >= 0, 1 + y = 1 + x'
   minux(z) -{ 0 }-> 0 :|: z >= 0
   minux(z) -{ 3 }-> 0 :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, v0 >= 0, v1 >= 0, x' = v0, x'' = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, v0 >= 0, v1 >= 0, x' = v0, 1 + x = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, v0 >= 0, v1 >= 0, x' = v0, 0 = v1
   minux(z) -{ 2 }-> 0 :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, x2 = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, 1 + x = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, 0 = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + (1 + x3) + y, y >= 0, x3 >= 0, v0 >= 0, v1 >= 0, 0 = v0, x3 = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 0 = v0, 1 + x = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   minux(z) -{ 3 }-> 1 + x0 + x1 :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x' = x0, x0 >= 0, x1 >= 0, x'' = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, x' = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, x' = x0, x0 >= 0, x1 >= 0, 0 = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, x2 = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, 0 = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + (1 + x3) + y, y >= 0, x3 >= 0, 0 = x0, x0 >= 0, x1 >= 0, x3 = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 0 = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   plus(z, z') -{ 1 }-> x :|: z = 1 + x + (z' - 1), x >= 0, z' - 1 >= 0
   plus(z, z') -{ 1 }-> y :|: z' = 1 + (z - 1) + y, z - 1 >= 0, y >= 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 0 }-> 1 + z + z' :|: z >= 0, z' >= 0

Function symbols to be analyzed: {encode_minus}, {encode_+}, {encode_minux}
Previous analysis results are:
  minus: runtime: O(1) [1], size: O(n^1) [1 + z]
  minux: runtime: O(1) [4], size: O(n^1) [2 + z]
  plus: runtime: O(1) [1], size: O(n^1) [1 + z + z']
  encArg: runtime: O(n^1) [9 + 11*z], size: O(n^1) [6 + 10*z]
  encode_minus: runtime: ?, size: O(n^1) [4 + 10*z]

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

(55) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: encode_minus
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 9 + 11*z

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

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

   encArg(z) -{ -5 + 11*z }-> s'' :|: s >= 0, s <= 6 + 10 * (z - 2), s' >= 0, s' <= s + 2, s'' >= 0, s'' <= s' + 2, z - 2 >= 0
   encArg(z) -{ -8 + 11*z }-> s106 :|: s104 >= 0, s104 <= 6 + 10 * (z - 2), s105 >= 0, s105 <= s104 + 2, s106 >= 0, s106 <= s105 + 1, z - 2 >= 0
   encArg(z) -{ -8 + 11*z }-> s109 :|: s107 >= 0, s107 <= 6 + 10 * (z - 2), s108 >= 0, s108 <= s107 + 1, s109 >= 0, s109 <= s108 + 2, z - 2 >= 0
   encArg(z) -{ 23 + 11*x_14 + 11*x_2'' }-> s119 :|: s116 >= 0, s116 <= 6 + 10 * x_14, s117 >= 0, s117 <= 6 + 10 * x_2'', s118 >= 0, s118 <= s116 + s117 + 1, s119 >= 0, s119 <= s118 + 2, x_14 >= 0, z = 1 + (1 + x_14 + x_2''), x_2'' >= 0
   encArg(z) -{ 33 + 11*x_113 + 11*x_16 + 11*x_23 }-> s125 :|: s120 >= 0, s120 <= 6 + 10 * x_16, s121 >= 0, s121 <= s120 + 2, s122 >= 0, s122 <= 6 + 10 * x_113, s123 >= 0, s123 <= 6 + 10 * x_23, s124 >= 0, s124 <= s122 + s123 + 1, s125 >= 0, s125 <= s121 + s124 + 1, x_113 >= 0, x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_113 + x_23), x_23 >= 0
   encArg(z) -{ 14 + 11*x_16 }-> s128 :|: s126 >= 0, s126 <= 6 + 10 * x_16, s127 >= 0, s127 <= s126 + 2, s128 >= 0, s128 <= s127 + 0 + 1, x_16 >= 0, x_2 >= 0, z = 1 + (1 + x_16) + x_2
   encArg(z) -{ 33 + 11*x_115 + 11*x_17 + 11*x_21 }-> s134 :|: s129 >= 0, s129 <= 6 + 10 * x_17, s130 >= 0, s130 <= 6 + 10 * x_21, s131 >= 0, s131 <= s129 + s130 + 1, s132 >= 0, s132 <= 6 + 10 * x_115, s133 >= 0, s133 <= s132 + 2, s134 >= 0, s134 <= s131 + s133 + 1, z = 1 + (1 + x_17 + x_21) + (1 + x_115), x_115 >= 0, x_17 >= 0, x_21 >= 0
   encArg(z) -{ 14 + 11*x_118 }-> s137 :|: s135 >= 0, s135 <= 6 + 10 * x_118, s136 >= 0, s136 <= s135 + 2, s137 >= 0, s137 <= 0 + s136 + 1, x_1 >= 0, z = 1 + x_1 + (1 + x_118), x_118 >= 0
   encArg(z) -{ 24 + 11*x_15 + 11*x_19 }-> s164 :|: s160 >= 0, s160 <= 6 + 10 * x_15, s161 >= 0, s161 <= s160 + 1, s162 >= 0, s162 <= 6 + 10 * x_19, s163 >= 0, s163 <= s162 + 2, s164 >= 0, s164 <= s161 + s163 + 1, x_15 >= 0, z = 1 + (1 + x_15) + (1 + x_19), x_19 >= 0
   encArg(z) -{ 24 + 11*x_111 + 11*x_16 }-> s169 :|: s165 >= 0, s165 <= 6 + 10 * x_16, s166 >= 0, s166 <= s165 + 2, s167 >= 0, s167 <= 6 + 10 * x_111, s168 >= 0, s168 <= s167 + 1, s169 >= 0, s169 <= s166 + s168 + 1, x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_111), x_111 >= 0
   encArg(z) -{ -11 + 11*z }-> s20 :|: s18 >= 0, s18 <= 6 + 10 * (z - 2), s19 >= 0, s19 <= s18 + 1, s20 >= 0, s20 <= s19 + 1, z - 2 >= 0
   encArg(z) -{ 27 + 11*x_112 + 11*x_16 }-> s28 :|: s24 >= 0, s24 <= 6 + 10 * x_16, s25 >= 0, s25 <= s24 + 2, s26 >= 0, s26 <= 6 + 10 * x_112, s27 >= 0, s27 <= s26 + 2, s28 >= 0, s28 <= s25 + s27 + 1, x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_112), x_112 >= 0
   encArg(z) -{ 20 + 11*x_17 + 11*x_21 }-> s32 :|: s29 >= 0, s29 <= 6 + 10 * x_17, s30 >= 0, s30 <= 6 + 10 * x_21, s31 >= 0, s31 <= s29 + s30 + 1, s32 >= 0, s32 <= s31 + 0 + 1, z = 1 + (1 + x_17 + x_21) + x_2, x_17 >= 0, x_2 >= 0, x_21 >= 0
   encArg(z) -{ 20 + 11*x_119 + 11*x_25 }-> s36 :|: s33 >= 0, s33 <= 6 + 10 * x_119, s34 >= 0, s34 <= 6 + 10 * x_25, s35 >= 0, s35 <= s33 + s34 + 1, s36 >= 0, s36 <= 0 + s35 + 1, x_1 >= 0, z = 1 + x_1 + (1 + x_119 + x_25), x_25 >= 0, x_119 >= 0
   encArg(z) -{ 20 + 11*x_11 + 11*x_2' }-> s53 :|: s50 >= 0, s50 <= 6 + 10 * x_11, s51 >= 0, s51 <= 6 + 10 * x_2', s52 >= 0, s52 <= s50 + s51 + 1, s53 >= 0, s53 <= s52 + 1, x_11 >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2')
   encArg(z) -{ 21 + 11*x_15 + 11*x_18 }-> s58 :|: s54 >= 0, s54 <= 6 + 10 * x_15, s55 >= 0, s55 <= s54 + 1, s56 >= 0, s56 <= 6 + 10 * x_18, s57 >= 0, s57 <= s56 + 1, s58 >= 0, s58 <= s55 + s57 + 1, x_15 >= 0, x_18 >= 0, z = 1 + (1 + x_15) + (1 + x_18)
   encArg(z) -{ 30 + 11*x_110 + 11*x_15 + 11*x_22 }-> s64 :|: s59 >= 0, s59 <= 6 + 10 * x_15, s60 >= 0, s60 <= s59 + 1, s61 >= 0, s61 <= 6 + 10 * x_110, s62 >= 0, s62 <= 6 + 10 * x_22, s63 >= 0, s63 <= s61 + s62 + 1, s64 >= 0, s64 <= s60 + s63 + 1, x_15 >= 0, z = 1 + (1 + x_15) + (1 + x_110 + x_22), x_110 >= 0, x_22 >= 0
   encArg(z) -{ 11 + 11*x_15 }-> s67 :|: s65 >= 0, s65 <= 6 + 10 * x_15, s66 >= 0, s66 <= s65 + 1, s67 >= 0, s67 <= s66 + 0 + 1, x_15 >= 0, z = 1 + (1 + x_15) + x_2, x_2 >= 0
   encArg(z) -{ 39 + 11*x_116 + 11*x_17 + 11*x_21 + 11*x_24 }-> s7 :|: s1 >= 0, s1 <= 6 + 10 * x_17, s2 >= 0, s2 <= 6 + 10 * x_21, s3 >= 0, s3 <= s1 + s2 + 1, s4 >= 0, s4 <= 6 + 10 * x_116, s5 >= 0, s5 <= 6 + 10 * x_24, s6 >= 0, s6 <= s4 + s5 + 1, s7 >= 0, s7 <= s3 + s6 + 1, x_116 >= 0, x_17 >= 0, z = 1 + (1 + x_17 + x_21) + (1 + x_116 + x_24), x_24 >= 0, x_21 >= 0
   encArg(z) -{ 30 + 11*x_114 + 11*x_17 + 11*x_21 }-> s73 :|: s68 >= 0, s68 <= 6 + 10 * x_17, s69 >= 0, s69 <= 6 + 10 * x_21, s70 >= 0, s70 <= s68 + s69 + 1, s71 >= 0, s71 <= 6 + 10 * x_114, s72 >= 0, s72 <= s71 + 1, s73 >= 0, s73 <= s70 + s72 + 1, z = 1 + (1 + x_17 + x_21) + (1 + x_114), x_114 >= 0, x_17 >= 0, x_21 >= 0
   encArg(z) -{ 11 + 11*x_117 }-> s76 :|: s74 >= 0, s74 <= 6 + 10 * x_117, s75 >= 0, s75 <= s74 + 1, s76 >= 0, s76 <= 0 + s75 + 1, x_1 >= 0, x_117 >= 0, z = 1 + x_1 + (1 + x_117)
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   encArg(z) -{ 0 }-> 1 + x0 :|: z - 1 >= 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 + x1 :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   encode_+(z, z') -{ 19 + 11*x_128 + 11*x_28 + 11*z' }-> s100 :|: s95 >= 0, s95 <= 6 + 10 * x_128, s96 >= 0, s96 <= 6 + 10 * x_28, s97 >= 0, s97 <= s95 + s96 + 1, s98 >= 0, s98 <= 6 + 10 * (z' - 1), s99 >= 0, s99 <= s98 + 1, s100 >= 0, s100 <= s97 + s99 + 1, x_128 >= 0, z = 1 + x_128 + x_28, z' - 1 >= 0, x_28 >= 0
   encode_+(z, z') -{ 11*z' }-> s103 :|: s101 >= 0, s101 <= 6 + 10 * (z' - 1), s102 >= 0, s102 <= s101 + 1, s103 >= 0, s103 <= 0 + s102 + 1, z' - 1 >= 0, z >= 0
   encode_+(z, z') -{ 22 + 11*x_134 + 11*x_210 + 11*z }-> s147 :|: s142 >= 0, s142 <= 6 + 10 * (z - 1), s143 >= 0, s143 <= s142 + 2, s144 >= 0, s144 <= 6 + 10 * x_134, s145 >= 0, s145 <= 6 + 10 * x_210, s146 >= 0, s146 <= s144 + s145 + 1, s147 >= 0, s147 <= s143 + s146 + 1, x_134 >= 0, z - 1 >= 0, z' = 1 + x_134 + x_210, x_210 >= 0
   encode_+(z, z') -{ 3 + 11*z }-> s150 :|: s148 >= 0, s148 <= 6 + 10 * (z - 1), s149 >= 0, s149 <= s148 + 2, s150 >= 0, s150 <= s149 + 0 + 1, z - 1 >= 0, z' >= 0
   encode_+(z, z') -{ 22 + 11*x_128 + 11*x_28 + 11*z' }-> s156 :|: s151 >= 0, s151 <= 6 + 10 * x_128, s152 >= 0, s152 <= 6 + 10 * x_28, s153 >= 0, s153 <= s151 + s152 + 1, s154 >= 0, s154 <= 6 + 10 * (z' - 1), s155 >= 0, s155 <= s154 + 2, s156 >= 0, s156 <= s153 + s155 + 1, x_128 >= 0, z = 1 + x_128 + x_28, z' - 1 >= 0, x_28 >= 0
   encode_+(z, z') -{ 3 + 11*z' }-> s159 :|: s157 >= 0, s157 <= 6 + 10 * (z' - 1), s158 >= 0, s158 <= s157 + 2, s159 >= 0, s159 <= 0 + s158 + 1, z >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 39 + 11*x_128 + 11*x_137 + 11*x_211 + 11*x_28 }-> s17 :|: s11 >= 0, s11 <= 6 + 10 * x_128, s12 >= 0, s12 <= 6 + 10 * x_28, s13 >= 0, s13 <= s11 + s12 + 1, s14 >= 0, s14 <= 6 + 10 * x_137, s15 >= 0, s15 <= 6 + 10 * x_211, s16 >= 0, s16 <= s14 + s15 + 1, s17 >= 0, s17 <= s13 + s16 + 1, x_128 >= 0, z = 1 + x_128 + x_28, z' = 1 + x_137 + x_211, x_137 >= 0, x_28 >= 0, x_211 >= 0
   encode_+(z, z') -{ 2 + 11*z + 11*z' }-> s174 :|: s170 >= 0, s170 <= 6 + 10 * (z - 1), s171 >= 0, s171 <= s170 + 1, s172 >= 0, s172 <= 6 + 10 * (z' - 1), s173 >= 0, s173 <= s172 + 2, s174 >= 0, s174 <= s171 + s173 + 1, z' - 1 >= 0, z - 1 >= 0
   encode_+(z, z') -{ 2 + 11*z + 11*z' }-> s179 :|: s175 >= 0, s175 <= 6 + 10 * (z - 1), s176 >= 0, s176 <= s175 + 2, s177 >= 0, s177 <= 6 + 10 * (z' - 1), s178 >= 0, s178 <= s177 + 1, s179 >= 0, s179 <= s176 + s178 + 1, z - 1 >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 5 + 11*z + 11*z' }-> s41 :|: s37 >= 0, s37 <= 6 + 10 * (z - 1), s38 >= 0, s38 <= s37 + 2, s39 >= 0, s39 <= 6 + 10 * (z' - 1), s40 >= 0, s40 <= s39 + 2, s41 >= 0, s41 <= s38 + s40 + 1, z - 1 >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 20 + 11*x_128 + 11*x_28 }-> s45 :|: s42 >= 0, s42 <= 6 + 10 * x_128, s43 >= 0, s43 <= 6 + 10 * x_28, s44 >= 0, s44 <= s42 + s43 + 1, s45 >= 0, s45 <= s44 + 0 + 1, x_128 >= 0, z = 1 + x_128 + x_28, z' >= 0, x_28 >= 0
   encode_+(z, z') -{ 20 + 11*x_140 + 11*x_212 }-> s49 :|: s46 >= 0, s46 <= 6 + 10 * x_140, s47 >= 0, s47 <= 6 + 10 * x_212, s48 >= 0, s48 <= s46 + s47 + 1, s49 >= 0, s49 <= 0 + s48 + 1, z >= 0, x_212 >= 0, x_140 >= 0, z' = 1 + x_140 + x_212
   encode_+(z, z') -{ -1 + 11*z + 11*z' }-> s85 :|: s81 >= 0, s81 <= 6 + 10 * (z - 1), s82 >= 0, s82 <= s81 + 1, s83 >= 0, s83 <= 6 + 10 * (z' - 1), s84 >= 0, s84 <= s83 + 1, s85 >= 0, s85 <= s82 + s84 + 1, z - 1 >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 19 + 11*x_131 + 11*x_29 + 11*z }-> s91 :|: s86 >= 0, s86 <= 6 + 10 * (z - 1), s87 >= 0, s87 <= s86 + 1, s88 >= 0, s88 <= 6 + 10 * x_131, s89 >= 0, s89 <= 6 + 10 * x_29, s90 >= 0, s90 <= s88 + s89 + 1, s91 >= 0, s91 <= s87 + s90 + 1, z' = 1 + x_131 + x_29, z - 1 >= 0, x_131 >= 0, x_29 >= 0
   encode_+(z, z') -{ 11*z }-> s94 :|: s92 >= 0, s92 <= 6 + 10 * (z - 1), s93 >= 0, s93 <= s92 + 1, s94 >= 0, s94 <= s93 + 0 + 1, z - 1 >= 0, z' >= 0
   encode_+(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_+(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   encode_+(z, z') -{ 0 }-> 1 + x0 + x1 :|: z >= 0, z' >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   encode_minus(z) -{ 3 + 11*z }-> s112 :|: s110 >= 0, s110 <= 6 + 10 * (z - 1), s111 >= 0, s111 <= s110 + 2, s112 >= 0, s112 <= s111 + 1, z - 1 >= 0
   encode_minus(z) -{ 11*z }-> s23 :|: s21 >= 0, s21 <= 6 + 10 * (z - 1), s22 >= 0, s22 <= s21 + 1, s23 >= 0, s23 <= s22 + 1, z - 1 >= 0
   encode_minus(z) -{ 20 + 11*x_122 + 11*x_26 }-> s80 :|: s77 >= 0, s77 <= 6 + 10 * x_122, s78 >= 0, s78 <= 6 + 10 * x_26, s79 >= 0, s79 <= s77 + s78 + 1, s80 >= 0, s80 <= s79 + 1, z = 1 + x_122 + x_26, x_26 >= 0, x_122 >= 0
   encode_minus(z) -{ 0 }-> 0 :|: z >= 0
   encode_minus(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_minus(z) -{ 0 }-> 1 + x0 :|: z >= 0, 0 = x0, x0 >= 0
   encode_minux(z) -{ 6 + 11*z }-> s10 :|: s8 >= 0, s8 <= 6 + 10 * (z - 1), s9 >= 0, s9 <= s8 + 2, s10 >= 0, s10 <= s9 + 2, z - 1 >= 0
   encode_minux(z) -{ 3 + 11*z }-> s115 :|: s113 >= 0, s113 <= 6 + 10 * (z - 1), s114 >= 0, s114 <= s113 + 1, s115 >= 0, s115 <= s114 + 2, z - 1 >= 0
   encode_minux(z) -{ 23 + 11*x_125 + 11*x_27 }-> s141 :|: s138 >= 0, s138 <= 6 + 10 * x_125, s139 >= 0, s139 <= 6 + 10 * x_27, s140 >= 0, s140 <= s138 + s139 + 1, s141 >= 0, s141 <= s140 + 2, x_125 >= 0, x_27 >= 0, z = 1 + x_125 + x_27
   encode_minux(z) -{ 0 }-> 0 :|: z >= 0
   encode_minux(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   minus(z) -{ 0 }-> 0 :|: z >= 0
   minus(z) -{ 1 }-> z - 1 :|: z - 1 >= 0
   minus(z) -{ 0 }-> 1 + z :|: z >= 0
   minux(z) -{ 4 }-> x :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x'' = 1 + y, x' = 1 + x + y, x >= 0, y >= 0
   minux(z) -{ 3 }-> x :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, x2 = 1 + y', 1 + y = 1 + x + y', x >= 0, y' >= 0
   minux(z) -{ 2 }-> x' :|: z = 1 + x + y, x >= 0, y >= 0, 1 + x = 1 + y', 1 + y = 1 + x' + y', x' >= 0, y' >= 0
   minux(z) -{ 3 }-> x'' :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, 1 + x = 1 + y, x' = 1 + x'' + y, x'' >= 0, y >= 0
   minux(z) -{ 4 }-> y :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x'' = 1 + x + y, x >= 0, y >= 0, x' = 1 + x
   minux(z) -{ 3 }-> y :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, 1 + x = 1 + x'' + y, x'' >= 0, y >= 0, x' = 1 + x''
   minux(z) -{ 3 }-> y' :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, x2 = 1 + x + y', x >= 0, y' >= 0, 1 + y = 1 + x
   minux(z) -{ 2 }-> y' :|: z = 1 + x + y, x >= 0, y >= 0, 1 + x = 1 + x' + y', x' >= 0, y' >= 0, 1 + y = 1 + x'
   minux(z) -{ 0 }-> 0 :|: z >= 0
   minux(z) -{ 3 }-> 0 :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, v0 >= 0, v1 >= 0, x' = v0, x'' = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, v0 >= 0, v1 >= 0, x' = v0, 1 + x = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, v0 >= 0, v1 >= 0, x' = v0, 0 = v1
   minux(z) -{ 2 }-> 0 :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, x2 = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, 1 + x = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, 0 = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + (1 + x3) + y, y >= 0, x3 >= 0, v0 >= 0, v1 >= 0, 0 = v0, x3 = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 0 = v0, 1 + x = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   minux(z) -{ 3 }-> 1 + x0 + x1 :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x' = x0, x0 >= 0, x1 >= 0, x'' = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, x' = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, x' = x0, x0 >= 0, x1 >= 0, 0 = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, x2 = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, 0 = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + (1 + x3) + y, y >= 0, x3 >= 0, 0 = x0, x0 >= 0, x1 >= 0, x3 = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 0 = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   plus(z, z') -{ 1 }-> x :|: z = 1 + x + (z' - 1), x >= 0, z' - 1 >= 0
   plus(z, z') -{ 1 }-> y :|: z' = 1 + (z - 1) + y, z - 1 >= 0, y >= 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 0 }-> 1 + z + z' :|: z >= 0, z' >= 0

Function symbols to be analyzed: {encode_+}, {encode_minux}
Previous analysis results are:
  minus: runtime: O(1) [1], size: O(n^1) [1 + z]
  minux: runtime: O(1) [4], size: O(n^1) [2 + z]
  plus: runtime: O(1) [1], size: O(n^1) [1 + z + z']
  encArg: runtime: O(n^1) [9 + 11*z], size: O(n^1) [6 + 10*z]
  encode_minus: runtime: O(n^1) [9 + 11*z], size: O(n^1) [4 + 10*z]

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(57) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
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(58)
Obligation:
Complexity RNTS consisting of the following rules:

   encArg(z) -{ -5 + 11*z }-> s'' :|: s >= 0, s <= 6 + 10 * (z - 2), s' >= 0, s' <= s + 2, s'' >= 0, s'' <= s' + 2, z - 2 >= 0
   encArg(z) -{ -8 + 11*z }-> s106 :|: s104 >= 0, s104 <= 6 + 10 * (z - 2), s105 >= 0, s105 <= s104 + 2, s106 >= 0, s106 <= s105 + 1, z - 2 >= 0
   encArg(z) -{ -8 + 11*z }-> s109 :|: s107 >= 0, s107 <= 6 + 10 * (z - 2), s108 >= 0, s108 <= s107 + 1, s109 >= 0, s109 <= s108 + 2, z - 2 >= 0
   encArg(z) -{ 23 + 11*x_14 + 11*x_2'' }-> s119 :|: s116 >= 0, s116 <= 6 + 10 * x_14, s117 >= 0, s117 <= 6 + 10 * x_2'', s118 >= 0, s118 <= s116 + s117 + 1, s119 >= 0, s119 <= s118 + 2, x_14 >= 0, z = 1 + (1 + x_14 + x_2''), x_2'' >= 0
   encArg(z) -{ 33 + 11*x_113 + 11*x_16 + 11*x_23 }-> s125 :|: s120 >= 0, s120 <= 6 + 10 * x_16, s121 >= 0, s121 <= s120 + 2, s122 >= 0, s122 <= 6 + 10 * x_113, s123 >= 0, s123 <= 6 + 10 * x_23, s124 >= 0, s124 <= s122 + s123 + 1, s125 >= 0, s125 <= s121 + s124 + 1, x_113 >= 0, x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_113 + x_23), x_23 >= 0
   encArg(z) -{ 14 + 11*x_16 }-> s128 :|: s126 >= 0, s126 <= 6 + 10 * x_16, s127 >= 0, s127 <= s126 + 2, s128 >= 0, s128 <= s127 + 0 + 1, x_16 >= 0, x_2 >= 0, z = 1 + (1 + x_16) + x_2
   encArg(z) -{ 33 + 11*x_115 + 11*x_17 + 11*x_21 }-> s134 :|: s129 >= 0, s129 <= 6 + 10 * x_17, s130 >= 0, s130 <= 6 + 10 * x_21, s131 >= 0, s131 <= s129 + s130 + 1, s132 >= 0, s132 <= 6 + 10 * x_115, s133 >= 0, s133 <= s132 + 2, s134 >= 0, s134 <= s131 + s133 + 1, z = 1 + (1 + x_17 + x_21) + (1 + x_115), x_115 >= 0, x_17 >= 0, x_21 >= 0
   encArg(z) -{ 14 + 11*x_118 }-> s137 :|: s135 >= 0, s135 <= 6 + 10 * x_118, s136 >= 0, s136 <= s135 + 2, s137 >= 0, s137 <= 0 + s136 + 1, x_1 >= 0, z = 1 + x_1 + (1 + x_118), x_118 >= 0
   encArg(z) -{ 24 + 11*x_15 + 11*x_19 }-> s164 :|: s160 >= 0, s160 <= 6 + 10 * x_15, s161 >= 0, s161 <= s160 + 1, s162 >= 0, s162 <= 6 + 10 * x_19, s163 >= 0, s163 <= s162 + 2, s164 >= 0, s164 <= s161 + s163 + 1, x_15 >= 0, z = 1 + (1 + x_15) + (1 + x_19), x_19 >= 0
   encArg(z) -{ 24 + 11*x_111 + 11*x_16 }-> s169 :|: s165 >= 0, s165 <= 6 + 10 * x_16, s166 >= 0, s166 <= s165 + 2, s167 >= 0, s167 <= 6 + 10 * x_111, s168 >= 0, s168 <= s167 + 1, s169 >= 0, s169 <= s166 + s168 + 1, x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_111), x_111 >= 0
   encArg(z) -{ -11 + 11*z }-> s20 :|: s18 >= 0, s18 <= 6 + 10 * (z - 2), s19 >= 0, s19 <= s18 + 1, s20 >= 0, s20 <= s19 + 1, z - 2 >= 0
   encArg(z) -{ 27 + 11*x_112 + 11*x_16 }-> s28 :|: s24 >= 0, s24 <= 6 + 10 * x_16, s25 >= 0, s25 <= s24 + 2, s26 >= 0, s26 <= 6 + 10 * x_112, s27 >= 0, s27 <= s26 + 2, s28 >= 0, s28 <= s25 + s27 + 1, x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_112), x_112 >= 0
   encArg(z) -{ 20 + 11*x_17 + 11*x_21 }-> s32 :|: s29 >= 0, s29 <= 6 + 10 * x_17, s30 >= 0, s30 <= 6 + 10 * x_21, s31 >= 0, s31 <= s29 + s30 + 1, s32 >= 0, s32 <= s31 + 0 + 1, z = 1 + (1 + x_17 + x_21) + x_2, x_17 >= 0, x_2 >= 0, x_21 >= 0
   encArg(z) -{ 20 + 11*x_119 + 11*x_25 }-> s36 :|: s33 >= 0, s33 <= 6 + 10 * x_119, s34 >= 0, s34 <= 6 + 10 * x_25, s35 >= 0, s35 <= s33 + s34 + 1, s36 >= 0, s36 <= 0 + s35 + 1, x_1 >= 0, z = 1 + x_1 + (1 + x_119 + x_25), x_25 >= 0, x_119 >= 0
   encArg(z) -{ 20 + 11*x_11 + 11*x_2' }-> s53 :|: s50 >= 0, s50 <= 6 + 10 * x_11, s51 >= 0, s51 <= 6 + 10 * x_2', s52 >= 0, s52 <= s50 + s51 + 1, s53 >= 0, s53 <= s52 + 1, x_11 >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2')
   encArg(z) -{ 21 + 11*x_15 + 11*x_18 }-> s58 :|: s54 >= 0, s54 <= 6 + 10 * x_15, s55 >= 0, s55 <= s54 + 1, s56 >= 0, s56 <= 6 + 10 * x_18, s57 >= 0, s57 <= s56 + 1, s58 >= 0, s58 <= s55 + s57 + 1, x_15 >= 0, x_18 >= 0, z = 1 + (1 + x_15) + (1 + x_18)
   encArg(z) -{ 30 + 11*x_110 + 11*x_15 + 11*x_22 }-> s64 :|: s59 >= 0, s59 <= 6 + 10 * x_15, s60 >= 0, s60 <= s59 + 1, s61 >= 0, s61 <= 6 + 10 * x_110, s62 >= 0, s62 <= 6 + 10 * x_22, s63 >= 0, s63 <= s61 + s62 + 1, s64 >= 0, s64 <= s60 + s63 + 1, x_15 >= 0, z = 1 + (1 + x_15) + (1 + x_110 + x_22), x_110 >= 0, x_22 >= 0
   encArg(z) -{ 11 + 11*x_15 }-> s67 :|: s65 >= 0, s65 <= 6 + 10 * x_15, s66 >= 0, s66 <= s65 + 1, s67 >= 0, s67 <= s66 + 0 + 1, x_15 >= 0, z = 1 + (1 + x_15) + x_2, x_2 >= 0
   encArg(z) -{ 39 + 11*x_116 + 11*x_17 + 11*x_21 + 11*x_24 }-> s7 :|: s1 >= 0, s1 <= 6 + 10 * x_17, s2 >= 0, s2 <= 6 + 10 * x_21, s3 >= 0, s3 <= s1 + s2 + 1, s4 >= 0, s4 <= 6 + 10 * x_116, s5 >= 0, s5 <= 6 + 10 * x_24, s6 >= 0, s6 <= s4 + s5 + 1, s7 >= 0, s7 <= s3 + s6 + 1, x_116 >= 0, x_17 >= 0, z = 1 + (1 + x_17 + x_21) + (1 + x_116 + x_24), x_24 >= 0, x_21 >= 0
   encArg(z) -{ 30 + 11*x_114 + 11*x_17 + 11*x_21 }-> s73 :|: s68 >= 0, s68 <= 6 + 10 * x_17, s69 >= 0, s69 <= 6 + 10 * x_21, s70 >= 0, s70 <= s68 + s69 + 1, s71 >= 0, s71 <= 6 + 10 * x_114, s72 >= 0, s72 <= s71 + 1, s73 >= 0, s73 <= s70 + s72 + 1, z = 1 + (1 + x_17 + x_21) + (1 + x_114), x_114 >= 0, x_17 >= 0, x_21 >= 0
   encArg(z) -{ 11 + 11*x_117 }-> s76 :|: s74 >= 0, s74 <= 6 + 10 * x_117, s75 >= 0, s75 <= s74 + 1, s76 >= 0, s76 <= 0 + s75 + 1, x_1 >= 0, x_117 >= 0, z = 1 + x_1 + (1 + x_117)
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   encArg(z) -{ 0 }-> 1 + x0 :|: z - 1 >= 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 + x1 :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   encode_+(z, z') -{ 19 + 11*x_128 + 11*x_28 + 11*z' }-> s100 :|: s95 >= 0, s95 <= 6 + 10 * x_128, s96 >= 0, s96 <= 6 + 10 * x_28, s97 >= 0, s97 <= s95 + s96 + 1, s98 >= 0, s98 <= 6 + 10 * (z' - 1), s99 >= 0, s99 <= s98 + 1, s100 >= 0, s100 <= s97 + s99 + 1, x_128 >= 0, z = 1 + x_128 + x_28, z' - 1 >= 0, x_28 >= 0
   encode_+(z, z') -{ 11*z' }-> s103 :|: s101 >= 0, s101 <= 6 + 10 * (z' - 1), s102 >= 0, s102 <= s101 + 1, s103 >= 0, s103 <= 0 + s102 + 1, z' - 1 >= 0, z >= 0
   encode_+(z, z') -{ 22 + 11*x_134 + 11*x_210 + 11*z }-> s147 :|: s142 >= 0, s142 <= 6 + 10 * (z - 1), s143 >= 0, s143 <= s142 + 2, s144 >= 0, s144 <= 6 + 10 * x_134, s145 >= 0, s145 <= 6 + 10 * x_210, s146 >= 0, s146 <= s144 + s145 + 1, s147 >= 0, s147 <= s143 + s146 + 1, x_134 >= 0, z - 1 >= 0, z' = 1 + x_134 + x_210, x_210 >= 0
   encode_+(z, z') -{ 3 + 11*z }-> s150 :|: s148 >= 0, s148 <= 6 + 10 * (z - 1), s149 >= 0, s149 <= s148 + 2, s150 >= 0, s150 <= s149 + 0 + 1, z - 1 >= 0, z' >= 0
   encode_+(z, z') -{ 22 + 11*x_128 + 11*x_28 + 11*z' }-> s156 :|: s151 >= 0, s151 <= 6 + 10 * x_128, s152 >= 0, s152 <= 6 + 10 * x_28, s153 >= 0, s153 <= s151 + s152 + 1, s154 >= 0, s154 <= 6 + 10 * (z' - 1), s155 >= 0, s155 <= s154 + 2, s156 >= 0, s156 <= s153 + s155 + 1, x_128 >= 0, z = 1 + x_128 + x_28, z' - 1 >= 0, x_28 >= 0
   encode_+(z, z') -{ 3 + 11*z' }-> s159 :|: s157 >= 0, s157 <= 6 + 10 * (z' - 1), s158 >= 0, s158 <= s157 + 2, s159 >= 0, s159 <= 0 + s158 + 1, z >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 39 + 11*x_128 + 11*x_137 + 11*x_211 + 11*x_28 }-> s17 :|: s11 >= 0, s11 <= 6 + 10 * x_128, s12 >= 0, s12 <= 6 + 10 * x_28, s13 >= 0, s13 <= s11 + s12 + 1, s14 >= 0, s14 <= 6 + 10 * x_137, s15 >= 0, s15 <= 6 + 10 * x_211, s16 >= 0, s16 <= s14 + s15 + 1, s17 >= 0, s17 <= s13 + s16 + 1, x_128 >= 0, z = 1 + x_128 + x_28, z' = 1 + x_137 + x_211, x_137 >= 0, x_28 >= 0, x_211 >= 0
   encode_+(z, z') -{ 2 + 11*z + 11*z' }-> s174 :|: s170 >= 0, s170 <= 6 + 10 * (z - 1), s171 >= 0, s171 <= s170 + 1, s172 >= 0, s172 <= 6 + 10 * (z' - 1), s173 >= 0, s173 <= s172 + 2, s174 >= 0, s174 <= s171 + s173 + 1, z' - 1 >= 0, z - 1 >= 0
   encode_+(z, z') -{ 2 + 11*z + 11*z' }-> s179 :|: s175 >= 0, s175 <= 6 + 10 * (z - 1), s176 >= 0, s176 <= s175 + 2, s177 >= 0, s177 <= 6 + 10 * (z' - 1), s178 >= 0, s178 <= s177 + 1, s179 >= 0, s179 <= s176 + s178 + 1, z - 1 >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 5 + 11*z + 11*z' }-> s41 :|: s37 >= 0, s37 <= 6 + 10 * (z - 1), s38 >= 0, s38 <= s37 + 2, s39 >= 0, s39 <= 6 + 10 * (z' - 1), s40 >= 0, s40 <= s39 + 2, s41 >= 0, s41 <= s38 + s40 + 1, z - 1 >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 20 + 11*x_128 + 11*x_28 }-> s45 :|: s42 >= 0, s42 <= 6 + 10 * x_128, s43 >= 0, s43 <= 6 + 10 * x_28, s44 >= 0, s44 <= s42 + s43 + 1, s45 >= 0, s45 <= s44 + 0 + 1, x_128 >= 0, z = 1 + x_128 + x_28, z' >= 0, x_28 >= 0
   encode_+(z, z') -{ 20 + 11*x_140 + 11*x_212 }-> s49 :|: s46 >= 0, s46 <= 6 + 10 * x_140, s47 >= 0, s47 <= 6 + 10 * x_212, s48 >= 0, s48 <= s46 + s47 + 1, s49 >= 0, s49 <= 0 + s48 + 1, z >= 0, x_212 >= 0, x_140 >= 0, z' = 1 + x_140 + x_212
   encode_+(z, z') -{ -1 + 11*z + 11*z' }-> s85 :|: s81 >= 0, s81 <= 6 + 10 * (z - 1), s82 >= 0, s82 <= s81 + 1, s83 >= 0, s83 <= 6 + 10 * (z' - 1), s84 >= 0, s84 <= s83 + 1, s85 >= 0, s85 <= s82 + s84 + 1, z - 1 >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 19 + 11*x_131 + 11*x_29 + 11*z }-> s91 :|: s86 >= 0, s86 <= 6 + 10 * (z - 1), s87 >= 0, s87 <= s86 + 1, s88 >= 0, s88 <= 6 + 10 * x_131, s89 >= 0, s89 <= 6 + 10 * x_29, s90 >= 0, s90 <= s88 + s89 + 1, s91 >= 0, s91 <= s87 + s90 + 1, z' = 1 + x_131 + x_29, z - 1 >= 0, x_131 >= 0, x_29 >= 0
   encode_+(z, z') -{ 11*z }-> s94 :|: s92 >= 0, s92 <= 6 + 10 * (z - 1), s93 >= 0, s93 <= s92 + 1, s94 >= 0, s94 <= s93 + 0 + 1, z - 1 >= 0, z' >= 0
   encode_+(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_+(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   encode_+(z, z') -{ 0 }-> 1 + x0 + x1 :|: z >= 0, z' >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   encode_minus(z) -{ 3 + 11*z }-> s112 :|: s110 >= 0, s110 <= 6 + 10 * (z - 1), s111 >= 0, s111 <= s110 + 2, s112 >= 0, s112 <= s111 + 1, z - 1 >= 0
   encode_minus(z) -{ 11*z }-> s23 :|: s21 >= 0, s21 <= 6 + 10 * (z - 1), s22 >= 0, s22 <= s21 + 1, s23 >= 0, s23 <= s22 + 1, z - 1 >= 0
   encode_minus(z) -{ 20 + 11*x_122 + 11*x_26 }-> s80 :|: s77 >= 0, s77 <= 6 + 10 * x_122, s78 >= 0, s78 <= 6 + 10 * x_26, s79 >= 0, s79 <= s77 + s78 + 1, s80 >= 0, s80 <= s79 + 1, z = 1 + x_122 + x_26, x_26 >= 0, x_122 >= 0
   encode_minus(z) -{ 0 }-> 0 :|: z >= 0
   encode_minus(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_minus(z) -{ 0 }-> 1 + x0 :|: z >= 0, 0 = x0, x0 >= 0
   encode_minux(z) -{ 6 + 11*z }-> s10 :|: s8 >= 0, s8 <= 6 + 10 * (z - 1), s9 >= 0, s9 <= s8 + 2, s10 >= 0, s10 <= s9 + 2, z - 1 >= 0
   encode_minux(z) -{ 3 + 11*z }-> s115 :|: s113 >= 0, s113 <= 6 + 10 * (z - 1), s114 >= 0, s114 <= s113 + 1, s115 >= 0, s115 <= s114 + 2, z - 1 >= 0
   encode_minux(z) -{ 23 + 11*x_125 + 11*x_27 }-> s141 :|: s138 >= 0, s138 <= 6 + 10 * x_125, s139 >= 0, s139 <= 6 + 10 * x_27, s140 >= 0, s140 <= s138 + s139 + 1, s141 >= 0, s141 <= s140 + 2, x_125 >= 0, x_27 >= 0, z = 1 + x_125 + x_27
   encode_minux(z) -{ 0 }-> 0 :|: z >= 0
   encode_minux(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   minus(z) -{ 0 }-> 0 :|: z >= 0
   minus(z) -{ 1 }-> z - 1 :|: z - 1 >= 0
   minus(z) -{ 0 }-> 1 + z :|: z >= 0
   minux(z) -{ 4 }-> x :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x'' = 1 + y, x' = 1 + x + y, x >= 0, y >= 0
   minux(z) -{ 3 }-> x :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, x2 = 1 + y', 1 + y = 1 + x + y', x >= 0, y' >= 0
   minux(z) -{ 2 }-> x' :|: z = 1 + x + y, x >= 0, y >= 0, 1 + x = 1 + y', 1 + y = 1 + x' + y', x' >= 0, y' >= 0
   minux(z) -{ 3 }-> x'' :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, 1 + x = 1 + y, x' = 1 + x'' + y, x'' >= 0, y >= 0
   minux(z) -{ 4 }-> y :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x'' = 1 + x + y, x >= 0, y >= 0, x' = 1 + x
   minux(z) -{ 3 }-> y :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, 1 + x = 1 + x'' + y, x'' >= 0, y >= 0, x' = 1 + x''
   minux(z) -{ 3 }-> y' :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, x2 = 1 + x + y', x >= 0, y' >= 0, 1 + y = 1 + x
   minux(z) -{ 2 }-> y' :|: z = 1 + x + y, x >= 0, y >= 0, 1 + x = 1 + x' + y', x' >= 0, y' >= 0, 1 + y = 1 + x'
   minux(z) -{ 0 }-> 0 :|: z >= 0
   minux(z) -{ 3 }-> 0 :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, v0 >= 0, v1 >= 0, x' = v0, x'' = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, v0 >= 0, v1 >= 0, x' = v0, 1 + x = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, v0 >= 0, v1 >= 0, x' = v0, 0 = v1
   minux(z) -{ 2 }-> 0 :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, x2 = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, 1 + x = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, 0 = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + (1 + x3) + y, y >= 0, x3 >= 0, v0 >= 0, v1 >= 0, 0 = v0, x3 = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 0 = v0, 1 + x = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   minux(z) -{ 3 }-> 1 + x0 + x1 :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x' = x0, x0 >= 0, x1 >= 0, x'' = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, x' = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, x' = x0, x0 >= 0, x1 >= 0, 0 = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, x2 = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, 0 = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + (1 + x3) + y, y >= 0, x3 >= 0, 0 = x0, x0 >= 0, x1 >= 0, x3 = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 0 = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   plus(z, z') -{ 1 }-> x :|: z = 1 + x + (z' - 1), x >= 0, z' - 1 >= 0
   plus(z, z') -{ 1 }-> y :|: z' = 1 + (z - 1) + y, z - 1 >= 0, y >= 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 0 }-> 1 + z + z' :|: z >= 0, z' >= 0

Function symbols to be analyzed: {encode_+}, {encode_minux}
Previous analysis results are:
  minus: runtime: O(1) [1], size: O(n^1) [1 + z]
  minux: runtime: O(1) [4], size: O(n^1) [2 + z]
  plus: runtime: O(1) [1], size: O(n^1) [1 + z + z']
  encArg: runtime: O(n^1) [9 + 11*z], size: O(n^1) [6 + 10*z]
  encode_minus: runtime: O(n^1) [9 + 11*z], size: O(n^1) [4 + 10*z]

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

(59) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: encode_+
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 7 + 10*z + 10*z'

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

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

   encArg(z) -{ -5 + 11*z }-> s'' :|: s >= 0, s <= 6 + 10 * (z - 2), s' >= 0, s' <= s + 2, s'' >= 0, s'' <= s' + 2, z - 2 >= 0
   encArg(z) -{ -8 + 11*z }-> s106 :|: s104 >= 0, s104 <= 6 + 10 * (z - 2), s105 >= 0, s105 <= s104 + 2, s106 >= 0, s106 <= s105 + 1, z - 2 >= 0
   encArg(z) -{ -8 + 11*z }-> s109 :|: s107 >= 0, s107 <= 6 + 10 * (z - 2), s108 >= 0, s108 <= s107 + 1, s109 >= 0, s109 <= s108 + 2, z - 2 >= 0
   encArg(z) -{ 23 + 11*x_14 + 11*x_2'' }-> s119 :|: s116 >= 0, s116 <= 6 + 10 * x_14, s117 >= 0, s117 <= 6 + 10 * x_2'', s118 >= 0, s118 <= s116 + s117 + 1, s119 >= 0, s119 <= s118 + 2, x_14 >= 0, z = 1 + (1 + x_14 + x_2''), x_2'' >= 0
   encArg(z) -{ 33 + 11*x_113 + 11*x_16 + 11*x_23 }-> s125 :|: s120 >= 0, s120 <= 6 + 10 * x_16, s121 >= 0, s121 <= s120 + 2, s122 >= 0, s122 <= 6 + 10 * x_113, s123 >= 0, s123 <= 6 + 10 * x_23, s124 >= 0, s124 <= s122 + s123 + 1, s125 >= 0, s125 <= s121 + s124 + 1, x_113 >= 0, x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_113 + x_23), x_23 >= 0
   encArg(z) -{ 14 + 11*x_16 }-> s128 :|: s126 >= 0, s126 <= 6 + 10 * x_16, s127 >= 0, s127 <= s126 + 2, s128 >= 0, s128 <= s127 + 0 + 1, x_16 >= 0, x_2 >= 0, z = 1 + (1 + x_16) + x_2
   encArg(z) -{ 33 + 11*x_115 + 11*x_17 + 11*x_21 }-> s134 :|: s129 >= 0, s129 <= 6 + 10 * x_17, s130 >= 0, s130 <= 6 + 10 * x_21, s131 >= 0, s131 <= s129 + s130 + 1, s132 >= 0, s132 <= 6 + 10 * x_115, s133 >= 0, s133 <= s132 + 2, s134 >= 0, s134 <= s131 + s133 + 1, z = 1 + (1 + x_17 + x_21) + (1 + x_115), x_115 >= 0, x_17 >= 0, x_21 >= 0
   encArg(z) -{ 14 + 11*x_118 }-> s137 :|: s135 >= 0, s135 <= 6 + 10 * x_118, s136 >= 0, s136 <= s135 + 2, s137 >= 0, s137 <= 0 + s136 + 1, x_1 >= 0, z = 1 + x_1 + (1 + x_118), x_118 >= 0
   encArg(z) -{ 24 + 11*x_15 + 11*x_19 }-> s164 :|: s160 >= 0, s160 <= 6 + 10 * x_15, s161 >= 0, s161 <= s160 + 1, s162 >= 0, s162 <= 6 + 10 * x_19, s163 >= 0, s163 <= s162 + 2, s164 >= 0, s164 <= s161 + s163 + 1, x_15 >= 0, z = 1 + (1 + x_15) + (1 + x_19), x_19 >= 0
   encArg(z) -{ 24 + 11*x_111 + 11*x_16 }-> s169 :|: s165 >= 0, s165 <= 6 + 10 * x_16, s166 >= 0, s166 <= s165 + 2, s167 >= 0, s167 <= 6 + 10 * x_111, s168 >= 0, s168 <= s167 + 1, s169 >= 0, s169 <= s166 + s168 + 1, x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_111), x_111 >= 0
   encArg(z) -{ -11 + 11*z }-> s20 :|: s18 >= 0, s18 <= 6 + 10 * (z - 2), s19 >= 0, s19 <= s18 + 1, s20 >= 0, s20 <= s19 + 1, z - 2 >= 0
   encArg(z) -{ 27 + 11*x_112 + 11*x_16 }-> s28 :|: s24 >= 0, s24 <= 6 + 10 * x_16, s25 >= 0, s25 <= s24 + 2, s26 >= 0, s26 <= 6 + 10 * x_112, s27 >= 0, s27 <= s26 + 2, s28 >= 0, s28 <= s25 + s27 + 1, x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_112), x_112 >= 0
   encArg(z) -{ 20 + 11*x_17 + 11*x_21 }-> s32 :|: s29 >= 0, s29 <= 6 + 10 * x_17, s30 >= 0, s30 <= 6 + 10 * x_21, s31 >= 0, s31 <= s29 + s30 + 1, s32 >= 0, s32 <= s31 + 0 + 1, z = 1 + (1 + x_17 + x_21) + x_2, x_17 >= 0, x_2 >= 0, x_21 >= 0
   encArg(z) -{ 20 + 11*x_119 + 11*x_25 }-> s36 :|: s33 >= 0, s33 <= 6 + 10 * x_119, s34 >= 0, s34 <= 6 + 10 * x_25, s35 >= 0, s35 <= s33 + s34 + 1, s36 >= 0, s36 <= 0 + s35 + 1, x_1 >= 0, z = 1 + x_1 + (1 + x_119 + x_25), x_25 >= 0, x_119 >= 0
   encArg(z) -{ 20 + 11*x_11 + 11*x_2' }-> s53 :|: s50 >= 0, s50 <= 6 + 10 * x_11, s51 >= 0, s51 <= 6 + 10 * x_2', s52 >= 0, s52 <= s50 + s51 + 1, s53 >= 0, s53 <= s52 + 1, x_11 >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2')
   encArg(z) -{ 21 + 11*x_15 + 11*x_18 }-> s58 :|: s54 >= 0, s54 <= 6 + 10 * x_15, s55 >= 0, s55 <= s54 + 1, s56 >= 0, s56 <= 6 + 10 * x_18, s57 >= 0, s57 <= s56 + 1, s58 >= 0, s58 <= s55 + s57 + 1, x_15 >= 0, x_18 >= 0, z = 1 + (1 + x_15) + (1 + x_18)
   encArg(z) -{ 30 + 11*x_110 + 11*x_15 + 11*x_22 }-> s64 :|: s59 >= 0, s59 <= 6 + 10 * x_15, s60 >= 0, s60 <= s59 + 1, s61 >= 0, s61 <= 6 + 10 * x_110, s62 >= 0, s62 <= 6 + 10 * x_22, s63 >= 0, s63 <= s61 + s62 + 1, s64 >= 0, s64 <= s60 + s63 + 1, x_15 >= 0, z = 1 + (1 + x_15) + (1 + x_110 + x_22), x_110 >= 0, x_22 >= 0
   encArg(z) -{ 11 + 11*x_15 }-> s67 :|: s65 >= 0, s65 <= 6 + 10 * x_15, s66 >= 0, s66 <= s65 + 1, s67 >= 0, s67 <= s66 + 0 + 1, x_15 >= 0, z = 1 + (1 + x_15) + x_2, x_2 >= 0
   encArg(z) -{ 39 + 11*x_116 + 11*x_17 + 11*x_21 + 11*x_24 }-> s7 :|: s1 >= 0, s1 <= 6 + 10 * x_17, s2 >= 0, s2 <= 6 + 10 * x_21, s3 >= 0, s3 <= s1 + s2 + 1, s4 >= 0, s4 <= 6 + 10 * x_116, s5 >= 0, s5 <= 6 + 10 * x_24, s6 >= 0, s6 <= s4 + s5 + 1, s7 >= 0, s7 <= s3 + s6 + 1, x_116 >= 0, x_17 >= 0, z = 1 + (1 + x_17 + x_21) + (1 + x_116 + x_24), x_24 >= 0, x_21 >= 0
   encArg(z) -{ 30 + 11*x_114 + 11*x_17 + 11*x_21 }-> s73 :|: s68 >= 0, s68 <= 6 + 10 * x_17, s69 >= 0, s69 <= 6 + 10 * x_21, s70 >= 0, s70 <= s68 + s69 + 1, s71 >= 0, s71 <= 6 + 10 * x_114, s72 >= 0, s72 <= s71 + 1, s73 >= 0, s73 <= s70 + s72 + 1, z = 1 + (1 + x_17 + x_21) + (1 + x_114), x_114 >= 0, x_17 >= 0, x_21 >= 0
   encArg(z) -{ 11 + 11*x_117 }-> s76 :|: s74 >= 0, s74 <= 6 + 10 * x_117, s75 >= 0, s75 <= s74 + 1, s76 >= 0, s76 <= 0 + s75 + 1, x_1 >= 0, x_117 >= 0, z = 1 + x_1 + (1 + x_117)
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   encArg(z) -{ 0 }-> 1 + x0 :|: z - 1 >= 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 + x1 :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   encode_+(z, z') -{ 19 + 11*x_128 + 11*x_28 + 11*z' }-> s100 :|: s95 >= 0, s95 <= 6 + 10 * x_128, s96 >= 0, s96 <= 6 + 10 * x_28, s97 >= 0, s97 <= s95 + s96 + 1, s98 >= 0, s98 <= 6 + 10 * (z' - 1), s99 >= 0, s99 <= s98 + 1, s100 >= 0, s100 <= s97 + s99 + 1, x_128 >= 0, z = 1 + x_128 + x_28, z' - 1 >= 0, x_28 >= 0
   encode_+(z, z') -{ 11*z' }-> s103 :|: s101 >= 0, s101 <= 6 + 10 * (z' - 1), s102 >= 0, s102 <= s101 + 1, s103 >= 0, s103 <= 0 + s102 + 1, z' - 1 >= 0, z >= 0
   encode_+(z, z') -{ 22 + 11*x_134 + 11*x_210 + 11*z }-> s147 :|: s142 >= 0, s142 <= 6 + 10 * (z - 1), s143 >= 0, s143 <= s142 + 2, s144 >= 0, s144 <= 6 + 10 * x_134, s145 >= 0, s145 <= 6 + 10 * x_210, s146 >= 0, s146 <= s144 + s145 + 1, s147 >= 0, s147 <= s143 + s146 + 1, x_134 >= 0, z - 1 >= 0, z' = 1 + x_134 + x_210, x_210 >= 0
   encode_+(z, z') -{ 3 + 11*z }-> s150 :|: s148 >= 0, s148 <= 6 + 10 * (z - 1), s149 >= 0, s149 <= s148 + 2, s150 >= 0, s150 <= s149 + 0 + 1, z - 1 >= 0, z' >= 0
   encode_+(z, z') -{ 22 + 11*x_128 + 11*x_28 + 11*z' }-> s156 :|: s151 >= 0, s151 <= 6 + 10 * x_128, s152 >= 0, s152 <= 6 + 10 * x_28, s153 >= 0, s153 <= s151 + s152 + 1, s154 >= 0, s154 <= 6 + 10 * (z' - 1), s155 >= 0, s155 <= s154 + 2, s156 >= 0, s156 <= s153 + s155 + 1, x_128 >= 0, z = 1 + x_128 + x_28, z' - 1 >= 0, x_28 >= 0
   encode_+(z, z') -{ 3 + 11*z' }-> s159 :|: s157 >= 0, s157 <= 6 + 10 * (z' - 1), s158 >= 0, s158 <= s157 + 2, s159 >= 0, s159 <= 0 + s158 + 1, z >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 39 + 11*x_128 + 11*x_137 + 11*x_211 + 11*x_28 }-> s17 :|: s11 >= 0, s11 <= 6 + 10 * x_128, s12 >= 0, s12 <= 6 + 10 * x_28, s13 >= 0, s13 <= s11 + s12 + 1, s14 >= 0, s14 <= 6 + 10 * x_137, s15 >= 0, s15 <= 6 + 10 * x_211, s16 >= 0, s16 <= s14 + s15 + 1, s17 >= 0, s17 <= s13 + s16 + 1, x_128 >= 0, z = 1 + x_128 + x_28, z' = 1 + x_137 + x_211, x_137 >= 0, x_28 >= 0, x_211 >= 0
   encode_+(z, z') -{ 2 + 11*z + 11*z' }-> s174 :|: s170 >= 0, s170 <= 6 + 10 * (z - 1), s171 >= 0, s171 <= s170 + 1, s172 >= 0, s172 <= 6 + 10 * (z' - 1), s173 >= 0, s173 <= s172 + 2, s174 >= 0, s174 <= s171 + s173 + 1, z' - 1 >= 0, z - 1 >= 0
   encode_+(z, z') -{ 2 + 11*z + 11*z' }-> s179 :|: s175 >= 0, s175 <= 6 + 10 * (z - 1), s176 >= 0, s176 <= s175 + 2, s177 >= 0, s177 <= 6 + 10 * (z' - 1), s178 >= 0, s178 <= s177 + 1, s179 >= 0, s179 <= s176 + s178 + 1, z - 1 >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 5 + 11*z + 11*z' }-> s41 :|: s37 >= 0, s37 <= 6 + 10 * (z - 1), s38 >= 0, s38 <= s37 + 2, s39 >= 0, s39 <= 6 + 10 * (z' - 1), s40 >= 0, s40 <= s39 + 2, s41 >= 0, s41 <= s38 + s40 + 1, z - 1 >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 20 + 11*x_128 + 11*x_28 }-> s45 :|: s42 >= 0, s42 <= 6 + 10 * x_128, s43 >= 0, s43 <= 6 + 10 * x_28, s44 >= 0, s44 <= s42 + s43 + 1, s45 >= 0, s45 <= s44 + 0 + 1, x_128 >= 0, z = 1 + x_128 + x_28, z' >= 0, x_28 >= 0
   encode_+(z, z') -{ 20 + 11*x_140 + 11*x_212 }-> s49 :|: s46 >= 0, s46 <= 6 + 10 * x_140, s47 >= 0, s47 <= 6 + 10 * x_212, s48 >= 0, s48 <= s46 + s47 + 1, s49 >= 0, s49 <= 0 + s48 + 1, z >= 0, x_212 >= 0, x_140 >= 0, z' = 1 + x_140 + x_212
   encode_+(z, z') -{ -1 + 11*z + 11*z' }-> s85 :|: s81 >= 0, s81 <= 6 + 10 * (z - 1), s82 >= 0, s82 <= s81 + 1, s83 >= 0, s83 <= 6 + 10 * (z' - 1), s84 >= 0, s84 <= s83 + 1, s85 >= 0, s85 <= s82 + s84 + 1, z - 1 >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 19 + 11*x_131 + 11*x_29 + 11*z }-> s91 :|: s86 >= 0, s86 <= 6 + 10 * (z - 1), s87 >= 0, s87 <= s86 + 1, s88 >= 0, s88 <= 6 + 10 * x_131, s89 >= 0, s89 <= 6 + 10 * x_29, s90 >= 0, s90 <= s88 + s89 + 1, s91 >= 0, s91 <= s87 + s90 + 1, z' = 1 + x_131 + x_29, z - 1 >= 0, x_131 >= 0, x_29 >= 0
   encode_+(z, z') -{ 11*z }-> s94 :|: s92 >= 0, s92 <= 6 + 10 * (z - 1), s93 >= 0, s93 <= s92 + 1, s94 >= 0, s94 <= s93 + 0 + 1, z - 1 >= 0, z' >= 0
   encode_+(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_+(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   encode_+(z, z') -{ 0 }-> 1 + x0 + x1 :|: z >= 0, z' >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   encode_minus(z) -{ 3 + 11*z }-> s112 :|: s110 >= 0, s110 <= 6 + 10 * (z - 1), s111 >= 0, s111 <= s110 + 2, s112 >= 0, s112 <= s111 + 1, z - 1 >= 0
   encode_minus(z) -{ 11*z }-> s23 :|: s21 >= 0, s21 <= 6 + 10 * (z - 1), s22 >= 0, s22 <= s21 + 1, s23 >= 0, s23 <= s22 + 1, z - 1 >= 0
   encode_minus(z) -{ 20 + 11*x_122 + 11*x_26 }-> s80 :|: s77 >= 0, s77 <= 6 + 10 * x_122, s78 >= 0, s78 <= 6 + 10 * x_26, s79 >= 0, s79 <= s77 + s78 + 1, s80 >= 0, s80 <= s79 + 1, z = 1 + x_122 + x_26, x_26 >= 0, x_122 >= 0
   encode_minus(z) -{ 0 }-> 0 :|: z >= 0
   encode_minus(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_minus(z) -{ 0 }-> 1 + x0 :|: z >= 0, 0 = x0, x0 >= 0
   encode_minux(z) -{ 6 + 11*z }-> s10 :|: s8 >= 0, s8 <= 6 + 10 * (z - 1), s9 >= 0, s9 <= s8 + 2, s10 >= 0, s10 <= s9 + 2, z - 1 >= 0
   encode_minux(z) -{ 3 + 11*z }-> s115 :|: s113 >= 0, s113 <= 6 + 10 * (z - 1), s114 >= 0, s114 <= s113 + 1, s115 >= 0, s115 <= s114 + 2, z - 1 >= 0
   encode_minux(z) -{ 23 + 11*x_125 + 11*x_27 }-> s141 :|: s138 >= 0, s138 <= 6 + 10 * x_125, s139 >= 0, s139 <= 6 + 10 * x_27, s140 >= 0, s140 <= s138 + s139 + 1, s141 >= 0, s141 <= s140 + 2, x_125 >= 0, x_27 >= 0, z = 1 + x_125 + x_27
   encode_minux(z) -{ 0 }-> 0 :|: z >= 0
   encode_minux(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   minus(z) -{ 0 }-> 0 :|: z >= 0
   minus(z) -{ 1 }-> z - 1 :|: z - 1 >= 0
   minus(z) -{ 0 }-> 1 + z :|: z >= 0
   minux(z) -{ 4 }-> x :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x'' = 1 + y, x' = 1 + x + y, x >= 0, y >= 0
   minux(z) -{ 3 }-> x :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, x2 = 1 + y', 1 + y = 1 + x + y', x >= 0, y' >= 0
   minux(z) -{ 2 }-> x' :|: z = 1 + x + y, x >= 0, y >= 0, 1 + x = 1 + y', 1 + y = 1 + x' + y', x' >= 0, y' >= 0
   minux(z) -{ 3 }-> x'' :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, 1 + x = 1 + y, x' = 1 + x'' + y, x'' >= 0, y >= 0
   minux(z) -{ 4 }-> y :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x'' = 1 + x + y, x >= 0, y >= 0, x' = 1 + x
   minux(z) -{ 3 }-> y :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, 1 + x = 1 + x'' + y, x'' >= 0, y >= 0, x' = 1 + x''
   minux(z) -{ 3 }-> y' :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, x2 = 1 + x + y', x >= 0, y' >= 0, 1 + y = 1 + x
   minux(z) -{ 2 }-> y' :|: z = 1 + x + y, x >= 0, y >= 0, 1 + x = 1 + x' + y', x' >= 0, y' >= 0, 1 + y = 1 + x'
   minux(z) -{ 0 }-> 0 :|: z >= 0
   minux(z) -{ 3 }-> 0 :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, v0 >= 0, v1 >= 0, x' = v0, x'' = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, v0 >= 0, v1 >= 0, x' = v0, 1 + x = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, v0 >= 0, v1 >= 0, x' = v0, 0 = v1
   minux(z) -{ 2 }-> 0 :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, x2 = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, 1 + x = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, 0 = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + (1 + x3) + y, y >= 0, x3 >= 0, v0 >= 0, v1 >= 0, 0 = v0, x3 = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 0 = v0, 1 + x = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   minux(z) -{ 3 }-> 1 + x0 + x1 :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x' = x0, x0 >= 0, x1 >= 0, x'' = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, x' = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, x' = x0, x0 >= 0, x1 >= 0, 0 = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, x2 = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, 0 = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + (1 + x3) + y, y >= 0, x3 >= 0, 0 = x0, x0 >= 0, x1 >= 0, x3 = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 0 = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   plus(z, z') -{ 1 }-> x :|: z = 1 + x + (z' - 1), x >= 0, z' - 1 >= 0
   plus(z, z') -{ 1 }-> y :|: z' = 1 + (z - 1) + y, z - 1 >= 0, y >= 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 0 }-> 1 + z + z' :|: z >= 0, z' >= 0

Function symbols to be analyzed: {encode_+}, {encode_minux}
Previous analysis results are:
  minus: runtime: O(1) [1], size: O(n^1) [1 + z]
  minux: runtime: O(1) [4], size: O(n^1) [2 + z]
  plus: runtime: O(1) [1], size: O(n^1) [1 + z + z']
  encArg: runtime: O(n^1) [9 + 11*z], size: O(n^1) [6 + 10*z]
  encode_minus: runtime: O(n^1) [9 + 11*z], size: O(n^1) [4 + 10*z]
  encode_+: runtime: ?, size: O(n^1) [7 + 10*z + 10*z']

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

(61) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: encode_+
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 17 + 11*z + 11*z'

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

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

   encArg(z) -{ -5 + 11*z }-> s'' :|: s >= 0, s <= 6 + 10 * (z - 2), s' >= 0, s' <= s + 2, s'' >= 0, s'' <= s' + 2, z - 2 >= 0
   encArg(z) -{ -8 + 11*z }-> s106 :|: s104 >= 0, s104 <= 6 + 10 * (z - 2), s105 >= 0, s105 <= s104 + 2, s106 >= 0, s106 <= s105 + 1, z - 2 >= 0
   encArg(z) -{ -8 + 11*z }-> s109 :|: s107 >= 0, s107 <= 6 + 10 * (z - 2), s108 >= 0, s108 <= s107 + 1, s109 >= 0, s109 <= s108 + 2, z - 2 >= 0
   encArg(z) -{ 23 + 11*x_14 + 11*x_2'' }-> s119 :|: s116 >= 0, s116 <= 6 + 10 * x_14, s117 >= 0, s117 <= 6 + 10 * x_2'', s118 >= 0, s118 <= s116 + s117 + 1, s119 >= 0, s119 <= s118 + 2, x_14 >= 0, z = 1 + (1 + x_14 + x_2''), x_2'' >= 0
   encArg(z) -{ 33 + 11*x_113 + 11*x_16 + 11*x_23 }-> s125 :|: s120 >= 0, s120 <= 6 + 10 * x_16, s121 >= 0, s121 <= s120 + 2, s122 >= 0, s122 <= 6 + 10 * x_113, s123 >= 0, s123 <= 6 + 10 * x_23, s124 >= 0, s124 <= s122 + s123 + 1, s125 >= 0, s125 <= s121 + s124 + 1, x_113 >= 0, x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_113 + x_23), x_23 >= 0
   encArg(z) -{ 14 + 11*x_16 }-> s128 :|: s126 >= 0, s126 <= 6 + 10 * x_16, s127 >= 0, s127 <= s126 + 2, s128 >= 0, s128 <= s127 + 0 + 1, x_16 >= 0, x_2 >= 0, z = 1 + (1 + x_16) + x_2
   encArg(z) -{ 33 + 11*x_115 + 11*x_17 + 11*x_21 }-> s134 :|: s129 >= 0, s129 <= 6 + 10 * x_17, s130 >= 0, s130 <= 6 + 10 * x_21, s131 >= 0, s131 <= s129 + s130 + 1, s132 >= 0, s132 <= 6 + 10 * x_115, s133 >= 0, s133 <= s132 + 2, s134 >= 0, s134 <= s131 + s133 + 1, z = 1 + (1 + x_17 + x_21) + (1 + x_115), x_115 >= 0, x_17 >= 0, x_21 >= 0
   encArg(z) -{ 14 + 11*x_118 }-> s137 :|: s135 >= 0, s135 <= 6 + 10 * x_118, s136 >= 0, s136 <= s135 + 2, s137 >= 0, s137 <= 0 + s136 + 1, x_1 >= 0, z = 1 + x_1 + (1 + x_118), x_118 >= 0
   encArg(z) -{ 24 + 11*x_15 + 11*x_19 }-> s164 :|: s160 >= 0, s160 <= 6 + 10 * x_15, s161 >= 0, s161 <= s160 + 1, s162 >= 0, s162 <= 6 + 10 * x_19, s163 >= 0, s163 <= s162 + 2, s164 >= 0, s164 <= s161 + s163 + 1, x_15 >= 0, z = 1 + (1 + x_15) + (1 + x_19), x_19 >= 0
   encArg(z) -{ 24 + 11*x_111 + 11*x_16 }-> s169 :|: s165 >= 0, s165 <= 6 + 10 * x_16, s166 >= 0, s166 <= s165 + 2, s167 >= 0, s167 <= 6 + 10 * x_111, s168 >= 0, s168 <= s167 + 1, s169 >= 0, s169 <= s166 + s168 + 1, x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_111), x_111 >= 0
   encArg(z) -{ -11 + 11*z }-> s20 :|: s18 >= 0, s18 <= 6 + 10 * (z - 2), s19 >= 0, s19 <= s18 + 1, s20 >= 0, s20 <= s19 + 1, z - 2 >= 0
   encArg(z) -{ 27 + 11*x_112 + 11*x_16 }-> s28 :|: s24 >= 0, s24 <= 6 + 10 * x_16, s25 >= 0, s25 <= s24 + 2, s26 >= 0, s26 <= 6 + 10 * x_112, s27 >= 0, s27 <= s26 + 2, s28 >= 0, s28 <= s25 + s27 + 1, x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_112), x_112 >= 0
   encArg(z) -{ 20 + 11*x_17 + 11*x_21 }-> s32 :|: s29 >= 0, s29 <= 6 + 10 * x_17, s30 >= 0, s30 <= 6 + 10 * x_21, s31 >= 0, s31 <= s29 + s30 + 1, s32 >= 0, s32 <= s31 + 0 + 1, z = 1 + (1 + x_17 + x_21) + x_2, x_17 >= 0, x_2 >= 0, x_21 >= 0
   encArg(z) -{ 20 + 11*x_119 + 11*x_25 }-> s36 :|: s33 >= 0, s33 <= 6 + 10 * x_119, s34 >= 0, s34 <= 6 + 10 * x_25, s35 >= 0, s35 <= s33 + s34 + 1, s36 >= 0, s36 <= 0 + s35 + 1, x_1 >= 0, z = 1 + x_1 + (1 + x_119 + x_25), x_25 >= 0, x_119 >= 0
   encArg(z) -{ 20 + 11*x_11 + 11*x_2' }-> s53 :|: s50 >= 0, s50 <= 6 + 10 * x_11, s51 >= 0, s51 <= 6 + 10 * x_2', s52 >= 0, s52 <= s50 + s51 + 1, s53 >= 0, s53 <= s52 + 1, x_11 >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2')
   encArg(z) -{ 21 + 11*x_15 + 11*x_18 }-> s58 :|: s54 >= 0, s54 <= 6 + 10 * x_15, s55 >= 0, s55 <= s54 + 1, s56 >= 0, s56 <= 6 + 10 * x_18, s57 >= 0, s57 <= s56 + 1, s58 >= 0, s58 <= s55 + s57 + 1, x_15 >= 0, x_18 >= 0, z = 1 + (1 + x_15) + (1 + x_18)
   encArg(z) -{ 30 + 11*x_110 + 11*x_15 + 11*x_22 }-> s64 :|: s59 >= 0, s59 <= 6 + 10 * x_15, s60 >= 0, s60 <= s59 + 1, s61 >= 0, s61 <= 6 + 10 * x_110, s62 >= 0, s62 <= 6 + 10 * x_22, s63 >= 0, s63 <= s61 + s62 + 1, s64 >= 0, s64 <= s60 + s63 + 1, x_15 >= 0, z = 1 + (1 + x_15) + (1 + x_110 + x_22), x_110 >= 0, x_22 >= 0
   encArg(z) -{ 11 + 11*x_15 }-> s67 :|: s65 >= 0, s65 <= 6 + 10 * x_15, s66 >= 0, s66 <= s65 + 1, s67 >= 0, s67 <= s66 + 0 + 1, x_15 >= 0, z = 1 + (1 + x_15) + x_2, x_2 >= 0
   encArg(z) -{ 39 + 11*x_116 + 11*x_17 + 11*x_21 + 11*x_24 }-> s7 :|: s1 >= 0, s1 <= 6 + 10 * x_17, s2 >= 0, s2 <= 6 + 10 * x_21, s3 >= 0, s3 <= s1 + s2 + 1, s4 >= 0, s4 <= 6 + 10 * x_116, s5 >= 0, s5 <= 6 + 10 * x_24, s6 >= 0, s6 <= s4 + s5 + 1, s7 >= 0, s7 <= s3 + s6 + 1, x_116 >= 0, x_17 >= 0, z = 1 + (1 + x_17 + x_21) + (1 + x_116 + x_24), x_24 >= 0, x_21 >= 0
   encArg(z) -{ 30 + 11*x_114 + 11*x_17 + 11*x_21 }-> s73 :|: s68 >= 0, s68 <= 6 + 10 * x_17, s69 >= 0, s69 <= 6 + 10 * x_21, s70 >= 0, s70 <= s68 + s69 + 1, s71 >= 0, s71 <= 6 + 10 * x_114, s72 >= 0, s72 <= s71 + 1, s73 >= 0, s73 <= s70 + s72 + 1, z = 1 + (1 + x_17 + x_21) + (1 + x_114), x_114 >= 0, x_17 >= 0, x_21 >= 0
   encArg(z) -{ 11 + 11*x_117 }-> s76 :|: s74 >= 0, s74 <= 6 + 10 * x_117, s75 >= 0, s75 <= s74 + 1, s76 >= 0, s76 <= 0 + s75 + 1, x_1 >= 0, x_117 >= 0, z = 1 + x_1 + (1 + x_117)
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   encArg(z) -{ 0 }-> 1 + x0 :|: z - 1 >= 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 + x1 :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   encode_+(z, z') -{ 19 + 11*x_128 + 11*x_28 + 11*z' }-> s100 :|: s95 >= 0, s95 <= 6 + 10 * x_128, s96 >= 0, s96 <= 6 + 10 * x_28, s97 >= 0, s97 <= s95 + s96 + 1, s98 >= 0, s98 <= 6 + 10 * (z' - 1), s99 >= 0, s99 <= s98 + 1, s100 >= 0, s100 <= s97 + s99 + 1, x_128 >= 0, z = 1 + x_128 + x_28, z' - 1 >= 0, x_28 >= 0
   encode_+(z, z') -{ 11*z' }-> s103 :|: s101 >= 0, s101 <= 6 + 10 * (z' - 1), s102 >= 0, s102 <= s101 + 1, s103 >= 0, s103 <= 0 + s102 + 1, z' - 1 >= 0, z >= 0
   encode_+(z, z') -{ 22 + 11*x_134 + 11*x_210 + 11*z }-> s147 :|: s142 >= 0, s142 <= 6 + 10 * (z - 1), s143 >= 0, s143 <= s142 + 2, s144 >= 0, s144 <= 6 + 10 * x_134, s145 >= 0, s145 <= 6 + 10 * x_210, s146 >= 0, s146 <= s144 + s145 + 1, s147 >= 0, s147 <= s143 + s146 + 1, x_134 >= 0, z - 1 >= 0, z' = 1 + x_134 + x_210, x_210 >= 0
   encode_+(z, z') -{ 3 + 11*z }-> s150 :|: s148 >= 0, s148 <= 6 + 10 * (z - 1), s149 >= 0, s149 <= s148 + 2, s150 >= 0, s150 <= s149 + 0 + 1, z - 1 >= 0, z' >= 0
   encode_+(z, z') -{ 22 + 11*x_128 + 11*x_28 + 11*z' }-> s156 :|: s151 >= 0, s151 <= 6 + 10 * x_128, s152 >= 0, s152 <= 6 + 10 * x_28, s153 >= 0, s153 <= s151 + s152 + 1, s154 >= 0, s154 <= 6 + 10 * (z' - 1), s155 >= 0, s155 <= s154 + 2, s156 >= 0, s156 <= s153 + s155 + 1, x_128 >= 0, z = 1 + x_128 + x_28, z' - 1 >= 0, x_28 >= 0
   encode_+(z, z') -{ 3 + 11*z' }-> s159 :|: s157 >= 0, s157 <= 6 + 10 * (z' - 1), s158 >= 0, s158 <= s157 + 2, s159 >= 0, s159 <= 0 + s158 + 1, z >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 39 + 11*x_128 + 11*x_137 + 11*x_211 + 11*x_28 }-> s17 :|: s11 >= 0, s11 <= 6 + 10 * x_128, s12 >= 0, s12 <= 6 + 10 * x_28, s13 >= 0, s13 <= s11 + s12 + 1, s14 >= 0, s14 <= 6 + 10 * x_137, s15 >= 0, s15 <= 6 + 10 * x_211, s16 >= 0, s16 <= s14 + s15 + 1, s17 >= 0, s17 <= s13 + s16 + 1, x_128 >= 0, z = 1 + x_128 + x_28, z' = 1 + x_137 + x_211, x_137 >= 0, x_28 >= 0, x_211 >= 0
   encode_+(z, z') -{ 2 + 11*z + 11*z' }-> s174 :|: s170 >= 0, s170 <= 6 + 10 * (z - 1), s171 >= 0, s171 <= s170 + 1, s172 >= 0, s172 <= 6 + 10 * (z' - 1), s173 >= 0, s173 <= s172 + 2, s174 >= 0, s174 <= s171 + s173 + 1, z' - 1 >= 0, z - 1 >= 0
   encode_+(z, z') -{ 2 + 11*z + 11*z' }-> s179 :|: s175 >= 0, s175 <= 6 + 10 * (z - 1), s176 >= 0, s176 <= s175 + 2, s177 >= 0, s177 <= 6 + 10 * (z' - 1), s178 >= 0, s178 <= s177 + 1, s179 >= 0, s179 <= s176 + s178 + 1, z - 1 >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 5 + 11*z + 11*z' }-> s41 :|: s37 >= 0, s37 <= 6 + 10 * (z - 1), s38 >= 0, s38 <= s37 + 2, s39 >= 0, s39 <= 6 + 10 * (z' - 1), s40 >= 0, s40 <= s39 + 2, s41 >= 0, s41 <= s38 + s40 + 1, z - 1 >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 20 + 11*x_128 + 11*x_28 }-> s45 :|: s42 >= 0, s42 <= 6 + 10 * x_128, s43 >= 0, s43 <= 6 + 10 * x_28, s44 >= 0, s44 <= s42 + s43 + 1, s45 >= 0, s45 <= s44 + 0 + 1, x_128 >= 0, z = 1 + x_128 + x_28, z' >= 0, x_28 >= 0
   encode_+(z, z') -{ 20 + 11*x_140 + 11*x_212 }-> s49 :|: s46 >= 0, s46 <= 6 + 10 * x_140, s47 >= 0, s47 <= 6 + 10 * x_212, s48 >= 0, s48 <= s46 + s47 + 1, s49 >= 0, s49 <= 0 + s48 + 1, z >= 0, x_212 >= 0, x_140 >= 0, z' = 1 + x_140 + x_212
   encode_+(z, z') -{ -1 + 11*z + 11*z' }-> s85 :|: s81 >= 0, s81 <= 6 + 10 * (z - 1), s82 >= 0, s82 <= s81 + 1, s83 >= 0, s83 <= 6 + 10 * (z' - 1), s84 >= 0, s84 <= s83 + 1, s85 >= 0, s85 <= s82 + s84 + 1, z - 1 >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 19 + 11*x_131 + 11*x_29 + 11*z }-> s91 :|: s86 >= 0, s86 <= 6 + 10 * (z - 1), s87 >= 0, s87 <= s86 + 1, s88 >= 0, s88 <= 6 + 10 * x_131, s89 >= 0, s89 <= 6 + 10 * x_29, s90 >= 0, s90 <= s88 + s89 + 1, s91 >= 0, s91 <= s87 + s90 + 1, z' = 1 + x_131 + x_29, z - 1 >= 0, x_131 >= 0, x_29 >= 0
   encode_+(z, z') -{ 11*z }-> s94 :|: s92 >= 0, s92 <= 6 + 10 * (z - 1), s93 >= 0, s93 <= s92 + 1, s94 >= 0, s94 <= s93 + 0 + 1, z - 1 >= 0, z' >= 0
   encode_+(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_+(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   encode_+(z, z') -{ 0 }-> 1 + x0 + x1 :|: z >= 0, z' >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   encode_minus(z) -{ 3 + 11*z }-> s112 :|: s110 >= 0, s110 <= 6 + 10 * (z - 1), s111 >= 0, s111 <= s110 + 2, s112 >= 0, s112 <= s111 + 1, z - 1 >= 0
   encode_minus(z) -{ 11*z }-> s23 :|: s21 >= 0, s21 <= 6 + 10 * (z - 1), s22 >= 0, s22 <= s21 + 1, s23 >= 0, s23 <= s22 + 1, z - 1 >= 0
   encode_minus(z) -{ 20 + 11*x_122 + 11*x_26 }-> s80 :|: s77 >= 0, s77 <= 6 + 10 * x_122, s78 >= 0, s78 <= 6 + 10 * x_26, s79 >= 0, s79 <= s77 + s78 + 1, s80 >= 0, s80 <= s79 + 1, z = 1 + x_122 + x_26, x_26 >= 0, x_122 >= 0
   encode_minus(z) -{ 0 }-> 0 :|: z >= 0
   encode_minus(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_minus(z) -{ 0 }-> 1 + x0 :|: z >= 0, 0 = x0, x0 >= 0
   encode_minux(z) -{ 6 + 11*z }-> s10 :|: s8 >= 0, s8 <= 6 + 10 * (z - 1), s9 >= 0, s9 <= s8 + 2, s10 >= 0, s10 <= s9 + 2, z - 1 >= 0
   encode_minux(z) -{ 3 + 11*z }-> s115 :|: s113 >= 0, s113 <= 6 + 10 * (z - 1), s114 >= 0, s114 <= s113 + 1, s115 >= 0, s115 <= s114 + 2, z - 1 >= 0
   encode_minux(z) -{ 23 + 11*x_125 + 11*x_27 }-> s141 :|: s138 >= 0, s138 <= 6 + 10 * x_125, s139 >= 0, s139 <= 6 + 10 * x_27, s140 >= 0, s140 <= s138 + s139 + 1, s141 >= 0, s141 <= s140 + 2, x_125 >= 0, x_27 >= 0, z = 1 + x_125 + x_27
   encode_minux(z) -{ 0 }-> 0 :|: z >= 0
   encode_minux(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   minus(z) -{ 0 }-> 0 :|: z >= 0
   minus(z) -{ 1 }-> z - 1 :|: z - 1 >= 0
   minus(z) -{ 0 }-> 1 + z :|: z >= 0
   minux(z) -{ 4 }-> x :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x'' = 1 + y, x' = 1 + x + y, x >= 0, y >= 0
   minux(z) -{ 3 }-> x :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, x2 = 1 + y', 1 + y = 1 + x + y', x >= 0, y' >= 0
   minux(z) -{ 2 }-> x' :|: z = 1 + x + y, x >= 0, y >= 0, 1 + x = 1 + y', 1 + y = 1 + x' + y', x' >= 0, y' >= 0
   minux(z) -{ 3 }-> x'' :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, 1 + x = 1 + y, x' = 1 + x'' + y, x'' >= 0, y >= 0
   minux(z) -{ 4 }-> y :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x'' = 1 + x + y, x >= 0, y >= 0, x' = 1 + x
   minux(z) -{ 3 }-> y :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, 1 + x = 1 + x'' + y, x'' >= 0, y >= 0, x' = 1 + x''
   minux(z) -{ 3 }-> y' :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, x2 = 1 + x + y', x >= 0, y' >= 0, 1 + y = 1 + x
   minux(z) -{ 2 }-> y' :|: z = 1 + x + y, x >= 0, y >= 0, 1 + x = 1 + x' + y', x' >= 0, y' >= 0, 1 + y = 1 + x'
   minux(z) -{ 0 }-> 0 :|: z >= 0
   minux(z) -{ 3 }-> 0 :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, v0 >= 0, v1 >= 0, x' = v0, x'' = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, v0 >= 0, v1 >= 0, x' = v0, 1 + x = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, v0 >= 0, v1 >= 0, x' = v0, 0 = v1
   minux(z) -{ 2 }-> 0 :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, x2 = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, 1 + x = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, 0 = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + (1 + x3) + y, y >= 0, x3 >= 0, v0 >= 0, v1 >= 0, 0 = v0, x3 = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 0 = v0, 1 + x = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   minux(z) -{ 3 }-> 1 + x0 + x1 :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x' = x0, x0 >= 0, x1 >= 0, x'' = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, x' = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, x' = x0, x0 >= 0, x1 >= 0, 0 = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, x2 = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, 0 = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + (1 + x3) + y, y >= 0, x3 >= 0, 0 = x0, x0 >= 0, x1 >= 0, x3 = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 0 = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   plus(z, z') -{ 1 }-> x :|: z = 1 + x + (z' - 1), x >= 0, z' - 1 >= 0
   plus(z, z') -{ 1 }-> y :|: z' = 1 + (z - 1) + y, z - 1 >= 0, y >= 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 0 }-> 1 + z + z' :|: z >= 0, z' >= 0

Function symbols to be analyzed: {encode_minux}
Previous analysis results are:
  minus: runtime: O(1) [1], size: O(n^1) [1 + z]
  minux: runtime: O(1) [4], size: O(n^1) [2 + z]
  plus: runtime: O(1) [1], size: O(n^1) [1 + z + z']
  encArg: runtime: O(n^1) [9 + 11*z], size: O(n^1) [6 + 10*z]
  encode_minus: runtime: O(n^1) [9 + 11*z], size: O(n^1) [4 + 10*z]
  encode_+: runtime: O(n^1) [17 + 11*z + 11*z'], size: O(n^1) [7 + 10*z + 10*z']

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(63) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
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(64)
Obligation:
Complexity RNTS consisting of the following rules:

   encArg(z) -{ -5 + 11*z }-> s'' :|: s >= 0, s <= 6 + 10 * (z - 2), s' >= 0, s' <= s + 2, s'' >= 0, s'' <= s' + 2, z - 2 >= 0
   encArg(z) -{ -8 + 11*z }-> s106 :|: s104 >= 0, s104 <= 6 + 10 * (z - 2), s105 >= 0, s105 <= s104 + 2, s106 >= 0, s106 <= s105 + 1, z - 2 >= 0
   encArg(z) -{ -8 + 11*z }-> s109 :|: s107 >= 0, s107 <= 6 + 10 * (z - 2), s108 >= 0, s108 <= s107 + 1, s109 >= 0, s109 <= s108 + 2, z - 2 >= 0
   encArg(z) -{ 23 + 11*x_14 + 11*x_2'' }-> s119 :|: s116 >= 0, s116 <= 6 + 10 * x_14, s117 >= 0, s117 <= 6 + 10 * x_2'', s118 >= 0, s118 <= s116 + s117 + 1, s119 >= 0, s119 <= s118 + 2, x_14 >= 0, z = 1 + (1 + x_14 + x_2''), x_2'' >= 0
   encArg(z) -{ 33 + 11*x_113 + 11*x_16 + 11*x_23 }-> s125 :|: s120 >= 0, s120 <= 6 + 10 * x_16, s121 >= 0, s121 <= s120 + 2, s122 >= 0, s122 <= 6 + 10 * x_113, s123 >= 0, s123 <= 6 + 10 * x_23, s124 >= 0, s124 <= s122 + s123 + 1, s125 >= 0, s125 <= s121 + s124 + 1, x_113 >= 0, x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_113 + x_23), x_23 >= 0
   encArg(z) -{ 14 + 11*x_16 }-> s128 :|: s126 >= 0, s126 <= 6 + 10 * x_16, s127 >= 0, s127 <= s126 + 2, s128 >= 0, s128 <= s127 + 0 + 1, x_16 >= 0, x_2 >= 0, z = 1 + (1 + x_16) + x_2
   encArg(z) -{ 33 + 11*x_115 + 11*x_17 + 11*x_21 }-> s134 :|: s129 >= 0, s129 <= 6 + 10 * x_17, s130 >= 0, s130 <= 6 + 10 * x_21, s131 >= 0, s131 <= s129 + s130 + 1, s132 >= 0, s132 <= 6 + 10 * x_115, s133 >= 0, s133 <= s132 + 2, s134 >= 0, s134 <= s131 + s133 + 1, z = 1 + (1 + x_17 + x_21) + (1 + x_115), x_115 >= 0, x_17 >= 0, x_21 >= 0
   encArg(z) -{ 14 + 11*x_118 }-> s137 :|: s135 >= 0, s135 <= 6 + 10 * x_118, s136 >= 0, s136 <= s135 + 2, s137 >= 0, s137 <= 0 + s136 + 1, x_1 >= 0, z = 1 + x_1 + (1 + x_118), x_118 >= 0
   encArg(z) -{ 24 + 11*x_15 + 11*x_19 }-> s164 :|: s160 >= 0, s160 <= 6 + 10 * x_15, s161 >= 0, s161 <= s160 + 1, s162 >= 0, s162 <= 6 + 10 * x_19, s163 >= 0, s163 <= s162 + 2, s164 >= 0, s164 <= s161 + s163 + 1, x_15 >= 0, z = 1 + (1 + x_15) + (1 + x_19), x_19 >= 0
   encArg(z) -{ 24 + 11*x_111 + 11*x_16 }-> s169 :|: s165 >= 0, s165 <= 6 + 10 * x_16, s166 >= 0, s166 <= s165 + 2, s167 >= 0, s167 <= 6 + 10 * x_111, s168 >= 0, s168 <= s167 + 1, s169 >= 0, s169 <= s166 + s168 + 1, x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_111), x_111 >= 0
   encArg(z) -{ -11 + 11*z }-> s20 :|: s18 >= 0, s18 <= 6 + 10 * (z - 2), s19 >= 0, s19 <= s18 + 1, s20 >= 0, s20 <= s19 + 1, z - 2 >= 0
   encArg(z) -{ 27 + 11*x_112 + 11*x_16 }-> s28 :|: s24 >= 0, s24 <= 6 + 10 * x_16, s25 >= 0, s25 <= s24 + 2, s26 >= 0, s26 <= 6 + 10 * x_112, s27 >= 0, s27 <= s26 + 2, s28 >= 0, s28 <= s25 + s27 + 1, x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_112), x_112 >= 0
   encArg(z) -{ 20 + 11*x_17 + 11*x_21 }-> s32 :|: s29 >= 0, s29 <= 6 + 10 * x_17, s30 >= 0, s30 <= 6 + 10 * x_21, s31 >= 0, s31 <= s29 + s30 + 1, s32 >= 0, s32 <= s31 + 0 + 1, z = 1 + (1 + x_17 + x_21) + x_2, x_17 >= 0, x_2 >= 0, x_21 >= 0
   encArg(z) -{ 20 + 11*x_119 + 11*x_25 }-> s36 :|: s33 >= 0, s33 <= 6 + 10 * x_119, s34 >= 0, s34 <= 6 + 10 * x_25, s35 >= 0, s35 <= s33 + s34 + 1, s36 >= 0, s36 <= 0 + s35 + 1, x_1 >= 0, z = 1 + x_1 + (1 + x_119 + x_25), x_25 >= 0, x_119 >= 0
   encArg(z) -{ 20 + 11*x_11 + 11*x_2' }-> s53 :|: s50 >= 0, s50 <= 6 + 10 * x_11, s51 >= 0, s51 <= 6 + 10 * x_2', s52 >= 0, s52 <= s50 + s51 + 1, s53 >= 0, s53 <= s52 + 1, x_11 >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2')
   encArg(z) -{ 21 + 11*x_15 + 11*x_18 }-> s58 :|: s54 >= 0, s54 <= 6 + 10 * x_15, s55 >= 0, s55 <= s54 + 1, s56 >= 0, s56 <= 6 + 10 * x_18, s57 >= 0, s57 <= s56 + 1, s58 >= 0, s58 <= s55 + s57 + 1, x_15 >= 0, x_18 >= 0, z = 1 + (1 + x_15) + (1 + x_18)
   encArg(z) -{ 30 + 11*x_110 + 11*x_15 + 11*x_22 }-> s64 :|: s59 >= 0, s59 <= 6 + 10 * x_15, s60 >= 0, s60 <= s59 + 1, s61 >= 0, s61 <= 6 + 10 * x_110, s62 >= 0, s62 <= 6 + 10 * x_22, s63 >= 0, s63 <= s61 + s62 + 1, s64 >= 0, s64 <= s60 + s63 + 1, x_15 >= 0, z = 1 + (1 + x_15) + (1 + x_110 + x_22), x_110 >= 0, x_22 >= 0
   encArg(z) -{ 11 + 11*x_15 }-> s67 :|: s65 >= 0, s65 <= 6 + 10 * x_15, s66 >= 0, s66 <= s65 + 1, s67 >= 0, s67 <= s66 + 0 + 1, x_15 >= 0, z = 1 + (1 + x_15) + x_2, x_2 >= 0
   encArg(z) -{ 39 + 11*x_116 + 11*x_17 + 11*x_21 + 11*x_24 }-> s7 :|: s1 >= 0, s1 <= 6 + 10 * x_17, s2 >= 0, s2 <= 6 + 10 * x_21, s3 >= 0, s3 <= s1 + s2 + 1, s4 >= 0, s4 <= 6 + 10 * x_116, s5 >= 0, s5 <= 6 + 10 * x_24, s6 >= 0, s6 <= s4 + s5 + 1, s7 >= 0, s7 <= s3 + s6 + 1, x_116 >= 0, x_17 >= 0, z = 1 + (1 + x_17 + x_21) + (1 + x_116 + x_24), x_24 >= 0, x_21 >= 0
   encArg(z) -{ 30 + 11*x_114 + 11*x_17 + 11*x_21 }-> s73 :|: s68 >= 0, s68 <= 6 + 10 * x_17, s69 >= 0, s69 <= 6 + 10 * x_21, s70 >= 0, s70 <= s68 + s69 + 1, s71 >= 0, s71 <= 6 + 10 * x_114, s72 >= 0, s72 <= s71 + 1, s73 >= 0, s73 <= s70 + s72 + 1, z = 1 + (1 + x_17 + x_21) + (1 + x_114), x_114 >= 0, x_17 >= 0, x_21 >= 0
   encArg(z) -{ 11 + 11*x_117 }-> s76 :|: s74 >= 0, s74 <= 6 + 10 * x_117, s75 >= 0, s75 <= s74 + 1, s76 >= 0, s76 <= 0 + s75 + 1, x_1 >= 0, x_117 >= 0, z = 1 + x_1 + (1 + x_117)
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   encArg(z) -{ 0 }-> 1 + x0 :|: z - 1 >= 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 + x1 :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   encode_+(z, z') -{ 19 + 11*x_128 + 11*x_28 + 11*z' }-> s100 :|: s95 >= 0, s95 <= 6 + 10 * x_128, s96 >= 0, s96 <= 6 + 10 * x_28, s97 >= 0, s97 <= s95 + s96 + 1, s98 >= 0, s98 <= 6 + 10 * (z' - 1), s99 >= 0, s99 <= s98 + 1, s100 >= 0, s100 <= s97 + s99 + 1, x_128 >= 0, z = 1 + x_128 + x_28, z' - 1 >= 0, x_28 >= 0
   encode_+(z, z') -{ 11*z' }-> s103 :|: s101 >= 0, s101 <= 6 + 10 * (z' - 1), s102 >= 0, s102 <= s101 + 1, s103 >= 0, s103 <= 0 + s102 + 1, z' - 1 >= 0, z >= 0
   encode_+(z, z') -{ 22 + 11*x_134 + 11*x_210 + 11*z }-> s147 :|: s142 >= 0, s142 <= 6 + 10 * (z - 1), s143 >= 0, s143 <= s142 + 2, s144 >= 0, s144 <= 6 + 10 * x_134, s145 >= 0, s145 <= 6 + 10 * x_210, s146 >= 0, s146 <= s144 + s145 + 1, s147 >= 0, s147 <= s143 + s146 + 1, x_134 >= 0, z - 1 >= 0, z' = 1 + x_134 + x_210, x_210 >= 0
   encode_+(z, z') -{ 3 + 11*z }-> s150 :|: s148 >= 0, s148 <= 6 + 10 * (z - 1), s149 >= 0, s149 <= s148 + 2, s150 >= 0, s150 <= s149 + 0 + 1, z - 1 >= 0, z' >= 0
   encode_+(z, z') -{ 22 + 11*x_128 + 11*x_28 + 11*z' }-> s156 :|: s151 >= 0, s151 <= 6 + 10 * x_128, s152 >= 0, s152 <= 6 + 10 * x_28, s153 >= 0, s153 <= s151 + s152 + 1, s154 >= 0, s154 <= 6 + 10 * (z' - 1), s155 >= 0, s155 <= s154 + 2, s156 >= 0, s156 <= s153 + s155 + 1, x_128 >= 0, z = 1 + x_128 + x_28, z' - 1 >= 0, x_28 >= 0
   encode_+(z, z') -{ 3 + 11*z' }-> s159 :|: s157 >= 0, s157 <= 6 + 10 * (z' - 1), s158 >= 0, s158 <= s157 + 2, s159 >= 0, s159 <= 0 + s158 + 1, z >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 39 + 11*x_128 + 11*x_137 + 11*x_211 + 11*x_28 }-> s17 :|: s11 >= 0, s11 <= 6 + 10 * x_128, s12 >= 0, s12 <= 6 + 10 * x_28, s13 >= 0, s13 <= s11 + s12 + 1, s14 >= 0, s14 <= 6 + 10 * x_137, s15 >= 0, s15 <= 6 + 10 * x_211, s16 >= 0, s16 <= s14 + s15 + 1, s17 >= 0, s17 <= s13 + s16 + 1, x_128 >= 0, z = 1 + x_128 + x_28, z' = 1 + x_137 + x_211, x_137 >= 0, x_28 >= 0, x_211 >= 0
   encode_+(z, z') -{ 2 + 11*z + 11*z' }-> s174 :|: s170 >= 0, s170 <= 6 + 10 * (z - 1), s171 >= 0, s171 <= s170 + 1, s172 >= 0, s172 <= 6 + 10 * (z' - 1), s173 >= 0, s173 <= s172 + 2, s174 >= 0, s174 <= s171 + s173 + 1, z' - 1 >= 0, z - 1 >= 0
   encode_+(z, z') -{ 2 + 11*z + 11*z' }-> s179 :|: s175 >= 0, s175 <= 6 + 10 * (z - 1), s176 >= 0, s176 <= s175 + 2, s177 >= 0, s177 <= 6 + 10 * (z' - 1), s178 >= 0, s178 <= s177 + 1, s179 >= 0, s179 <= s176 + s178 + 1, z - 1 >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 5 + 11*z + 11*z' }-> s41 :|: s37 >= 0, s37 <= 6 + 10 * (z - 1), s38 >= 0, s38 <= s37 + 2, s39 >= 0, s39 <= 6 + 10 * (z' - 1), s40 >= 0, s40 <= s39 + 2, s41 >= 0, s41 <= s38 + s40 + 1, z - 1 >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 20 + 11*x_128 + 11*x_28 }-> s45 :|: s42 >= 0, s42 <= 6 + 10 * x_128, s43 >= 0, s43 <= 6 + 10 * x_28, s44 >= 0, s44 <= s42 + s43 + 1, s45 >= 0, s45 <= s44 + 0 + 1, x_128 >= 0, z = 1 + x_128 + x_28, z' >= 0, x_28 >= 0
   encode_+(z, z') -{ 20 + 11*x_140 + 11*x_212 }-> s49 :|: s46 >= 0, s46 <= 6 + 10 * x_140, s47 >= 0, s47 <= 6 + 10 * x_212, s48 >= 0, s48 <= s46 + s47 + 1, s49 >= 0, s49 <= 0 + s48 + 1, z >= 0, x_212 >= 0, x_140 >= 0, z' = 1 + x_140 + x_212
   encode_+(z, z') -{ -1 + 11*z + 11*z' }-> s85 :|: s81 >= 0, s81 <= 6 + 10 * (z - 1), s82 >= 0, s82 <= s81 + 1, s83 >= 0, s83 <= 6 + 10 * (z' - 1), s84 >= 0, s84 <= s83 + 1, s85 >= 0, s85 <= s82 + s84 + 1, z - 1 >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 19 + 11*x_131 + 11*x_29 + 11*z }-> s91 :|: s86 >= 0, s86 <= 6 + 10 * (z - 1), s87 >= 0, s87 <= s86 + 1, s88 >= 0, s88 <= 6 + 10 * x_131, s89 >= 0, s89 <= 6 + 10 * x_29, s90 >= 0, s90 <= s88 + s89 + 1, s91 >= 0, s91 <= s87 + s90 + 1, z' = 1 + x_131 + x_29, z - 1 >= 0, x_131 >= 0, x_29 >= 0
   encode_+(z, z') -{ 11*z }-> s94 :|: s92 >= 0, s92 <= 6 + 10 * (z - 1), s93 >= 0, s93 <= s92 + 1, s94 >= 0, s94 <= s93 + 0 + 1, z - 1 >= 0, z' >= 0
   encode_+(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_+(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   encode_+(z, z') -{ 0 }-> 1 + x0 + x1 :|: z >= 0, z' >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   encode_minus(z) -{ 3 + 11*z }-> s112 :|: s110 >= 0, s110 <= 6 + 10 * (z - 1), s111 >= 0, s111 <= s110 + 2, s112 >= 0, s112 <= s111 + 1, z - 1 >= 0
   encode_minus(z) -{ 11*z }-> s23 :|: s21 >= 0, s21 <= 6 + 10 * (z - 1), s22 >= 0, s22 <= s21 + 1, s23 >= 0, s23 <= s22 + 1, z - 1 >= 0
   encode_minus(z) -{ 20 + 11*x_122 + 11*x_26 }-> s80 :|: s77 >= 0, s77 <= 6 + 10 * x_122, s78 >= 0, s78 <= 6 + 10 * x_26, s79 >= 0, s79 <= s77 + s78 + 1, s80 >= 0, s80 <= s79 + 1, z = 1 + x_122 + x_26, x_26 >= 0, x_122 >= 0
   encode_minus(z) -{ 0 }-> 0 :|: z >= 0
   encode_minus(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_minus(z) -{ 0 }-> 1 + x0 :|: z >= 0, 0 = x0, x0 >= 0
   encode_minux(z) -{ 6 + 11*z }-> s10 :|: s8 >= 0, s8 <= 6 + 10 * (z - 1), s9 >= 0, s9 <= s8 + 2, s10 >= 0, s10 <= s9 + 2, z - 1 >= 0
   encode_minux(z) -{ 3 + 11*z }-> s115 :|: s113 >= 0, s113 <= 6 + 10 * (z - 1), s114 >= 0, s114 <= s113 + 1, s115 >= 0, s115 <= s114 + 2, z - 1 >= 0
   encode_minux(z) -{ 23 + 11*x_125 + 11*x_27 }-> s141 :|: s138 >= 0, s138 <= 6 + 10 * x_125, s139 >= 0, s139 <= 6 + 10 * x_27, s140 >= 0, s140 <= s138 + s139 + 1, s141 >= 0, s141 <= s140 + 2, x_125 >= 0, x_27 >= 0, z = 1 + x_125 + x_27
   encode_minux(z) -{ 0 }-> 0 :|: z >= 0
   encode_minux(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   minus(z) -{ 0 }-> 0 :|: z >= 0
   minus(z) -{ 1 }-> z - 1 :|: z - 1 >= 0
   minus(z) -{ 0 }-> 1 + z :|: z >= 0
   minux(z) -{ 4 }-> x :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x'' = 1 + y, x' = 1 + x + y, x >= 0, y >= 0
   minux(z) -{ 3 }-> x :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, x2 = 1 + y', 1 + y = 1 + x + y', x >= 0, y' >= 0
   minux(z) -{ 2 }-> x' :|: z = 1 + x + y, x >= 0, y >= 0, 1 + x = 1 + y', 1 + y = 1 + x' + y', x' >= 0, y' >= 0
   minux(z) -{ 3 }-> x'' :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, 1 + x = 1 + y, x' = 1 + x'' + y, x'' >= 0, y >= 0
   minux(z) -{ 4 }-> y :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x'' = 1 + x + y, x >= 0, y >= 0, x' = 1 + x
   minux(z) -{ 3 }-> y :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, 1 + x = 1 + x'' + y, x'' >= 0, y >= 0, x' = 1 + x''
   minux(z) -{ 3 }-> y' :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, x2 = 1 + x + y', x >= 0, y' >= 0, 1 + y = 1 + x
   minux(z) -{ 2 }-> y' :|: z = 1 + x + y, x >= 0, y >= 0, 1 + x = 1 + x' + y', x' >= 0, y' >= 0, 1 + y = 1 + x'
   minux(z) -{ 0 }-> 0 :|: z >= 0
   minux(z) -{ 3 }-> 0 :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, v0 >= 0, v1 >= 0, x' = v0, x'' = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, v0 >= 0, v1 >= 0, x' = v0, 1 + x = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, v0 >= 0, v1 >= 0, x' = v0, 0 = v1
   minux(z) -{ 2 }-> 0 :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, x2 = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, 1 + x = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, 0 = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + (1 + x3) + y, y >= 0, x3 >= 0, v0 >= 0, v1 >= 0, 0 = v0, x3 = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 0 = v0, 1 + x = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   minux(z) -{ 3 }-> 1 + x0 + x1 :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x' = x0, x0 >= 0, x1 >= 0, x'' = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, x' = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, x' = x0, x0 >= 0, x1 >= 0, 0 = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, x2 = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, 0 = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + (1 + x3) + y, y >= 0, x3 >= 0, 0 = x0, x0 >= 0, x1 >= 0, x3 = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 0 = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   plus(z, z') -{ 1 }-> x :|: z = 1 + x + (z' - 1), x >= 0, z' - 1 >= 0
   plus(z, z') -{ 1 }-> y :|: z' = 1 + (z - 1) + y, z - 1 >= 0, y >= 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 0 }-> 1 + z + z' :|: z >= 0, z' >= 0

Function symbols to be analyzed: {encode_minux}
Previous analysis results are:
  minus: runtime: O(1) [1], size: O(n^1) [1 + z]
  minux: runtime: O(1) [4], size: O(n^1) [2 + z]
  plus: runtime: O(1) [1], size: O(n^1) [1 + z + z']
  encArg: runtime: O(n^1) [9 + 11*z], size: O(n^1) [6 + 10*z]
  encode_minus: runtime: O(n^1) [9 + 11*z], size: O(n^1) [4 + 10*z]
  encode_+: runtime: O(n^1) [17 + 11*z + 11*z'], size: O(n^1) [7 + 10*z + 10*z']

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

(65) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using KoAT for: encode_minux
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 35*z

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

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

   encArg(z) -{ -5 + 11*z }-> s'' :|: s >= 0, s <= 6 + 10 * (z - 2), s' >= 0, s' <= s + 2, s'' >= 0, s'' <= s' + 2, z - 2 >= 0
   encArg(z) -{ -8 + 11*z }-> s106 :|: s104 >= 0, s104 <= 6 + 10 * (z - 2), s105 >= 0, s105 <= s104 + 2, s106 >= 0, s106 <= s105 + 1, z - 2 >= 0
   encArg(z) -{ -8 + 11*z }-> s109 :|: s107 >= 0, s107 <= 6 + 10 * (z - 2), s108 >= 0, s108 <= s107 + 1, s109 >= 0, s109 <= s108 + 2, z - 2 >= 0
   encArg(z) -{ 23 + 11*x_14 + 11*x_2'' }-> s119 :|: s116 >= 0, s116 <= 6 + 10 * x_14, s117 >= 0, s117 <= 6 + 10 * x_2'', s118 >= 0, s118 <= s116 + s117 + 1, s119 >= 0, s119 <= s118 + 2, x_14 >= 0, z = 1 + (1 + x_14 + x_2''), x_2'' >= 0
   encArg(z) -{ 33 + 11*x_113 + 11*x_16 + 11*x_23 }-> s125 :|: s120 >= 0, s120 <= 6 + 10 * x_16, s121 >= 0, s121 <= s120 + 2, s122 >= 0, s122 <= 6 + 10 * x_113, s123 >= 0, s123 <= 6 + 10 * x_23, s124 >= 0, s124 <= s122 + s123 + 1, s125 >= 0, s125 <= s121 + s124 + 1, x_113 >= 0, x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_113 + x_23), x_23 >= 0
   encArg(z) -{ 14 + 11*x_16 }-> s128 :|: s126 >= 0, s126 <= 6 + 10 * x_16, s127 >= 0, s127 <= s126 + 2, s128 >= 0, s128 <= s127 + 0 + 1, x_16 >= 0, x_2 >= 0, z = 1 + (1 + x_16) + x_2
   encArg(z) -{ 33 + 11*x_115 + 11*x_17 + 11*x_21 }-> s134 :|: s129 >= 0, s129 <= 6 + 10 * x_17, s130 >= 0, s130 <= 6 + 10 * x_21, s131 >= 0, s131 <= s129 + s130 + 1, s132 >= 0, s132 <= 6 + 10 * x_115, s133 >= 0, s133 <= s132 + 2, s134 >= 0, s134 <= s131 + s133 + 1, z = 1 + (1 + x_17 + x_21) + (1 + x_115), x_115 >= 0, x_17 >= 0, x_21 >= 0
   encArg(z) -{ 14 + 11*x_118 }-> s137 :|: s135 >= 0, s135 <= 6 + 10 * x_118, s136 >= 0, s136 <= s135 + 2, s137 >= 0, s137 <= 0 + s136 + 1, x_1 >= 0, z = 1 + x_1 + (1 + x_118), x_118 >= 0
   encArg(z) -{ 24 + 11*x_15 + 11*x_19 }-> s164 :|: s160 >= 0, s160 <= 6 + 10 * x_15, s161 >= 0, s161 <= s160 + 1, s162 >= 0, s162 <= 6 + 10 * x_19, s163 >= 0, s163 <= s162 + 2, s164 >= 0, s164 <= s161 + s163 + 1, x_15 >= 0, z = 1 + (1 + x_15) + (1 + x_19), x_19 >= 0
   encArg(z) -{ 24 + 11*x_111 + 11*x_16 }-> s169 :|: s165 >= 0, s165 <= 6 + 10 * x_16, s166 >= 0, s166 <= s165 + 2, s167 >= 0, s167 <= 6 + 10 * x_111, s168 >= 0, s168 <= s167 + 1, s169 >= 0, s169 <= s166 + s168 + 1, x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_111), x_111 >= 0
   encArg(z) -{ -11 + 11*z }-> s20 :|: s18 >= 0, s18 <= 6 + 10 * (z - 2), s19 >= 0, s19 <= s18 + 1, s20 >= 0, s20 <= s19 + 1, z - 2 >= 0
   encArg(z) -{ 27 + 11*x_112 + 11*x_16 }-> s28 :|: s24 >= 0, s24 <= 6 + 10 * x_16, s25 >= 0, s25 <= s24 + 2, s26 >= 0, s26 <= 6 + 10 * x_112, s27 >= 0, s27 <= s26 + 2, s28 >= 0, s28 <= s25 + s27 + 1, x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_112), x_112 >= 0
   encArg(z) -{ 20 + 11*x_17 + 11*x_21 }-> s32 :|: s29 >= 0, s29 <= 6 + 10 * x_17, s30 >= 0, s30 <= 6 + 10 * x_21, s31 >= 0, s31 <= s29 + s30 + 1, s32 >= 0, s32 <= s31 + 0 + 1, z = 1 + (1 + x_17 + x_21) + x_2, x_17 >= 0, x_2 >= 0, x_21 >= 0
   encArg(z) -{ 20 + 11*x_119 + 11*x_25 }-> s36 :|: s33 >= 0, s33 <= 6 + 10 * x_119, s34 >= 0, s34 <= 6 + 10 * x_25, s35 >= 0, s35 <= s33 + s34 + 1, s36 >= 0, s36 <= 0 + s35 + 1, x_1 >= 0, z = 1 + x_1 + (1 + x_119 + x_25), x_25 >= 0, x_119 >= 0
   encArg(z) -{ 20 + 11*x_11 + 11*x_2' }-> s53 :|: s50 >= 0, s50 <= 6 + 10 * x_11, s51 >= 0, s51 <= 6 + 10 * x_2', s52 >= 0, s52 <= s50 + s51 + 1, s53 >= 0, s53 <= s52 + 1, x_11 >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2')
   encArg(z) -{ 21 + 11*x_15 + 11*x_18 }-> s58 :|: s54 >= 0, s54 <= 6 + 10 * x_15, s55 >= 0, s55 <= s54 + 1, s56 >= 0, s56 <= 6 + 10 * x_18, s57 >= 0, s57 <= s56 + 1, s58 >= 0, s58 <= s55 + s57 + 1, x_15 >= 0, x_18 >= 0, z = 1 + (1 + x_15) + (1 + x_18)
   encArg(z) -{ 30 + 11*x_110 + 11*x_15 + 11*x_22 }-> s64 :|: s59 >= 0, s59 <= 6 + 10 * x_15, s60 >= 0, s60 <= s59 + 1, s61 >= 0, s61 <= 6 + 10 * x_110, s62 >= 0, s62 <= 6 + 10 * x_22, s63 >= 0, s63 <= s61 + s62 + 1, s64 >= 0, s64 <= s60 + s63 + 1, x_15 >= 0, z = 1 + (1 + x_15) + (1 + x_110 + x_22), x_110 >= 0, x_22 >= 0
   encArg(z) -{ 11 + 11*x_15 }-> s67 :|: s65 >= 0, s65 <= 6 + 10 * x_15, s66 >= 0, s66 <= s65 + 1, s67 >= 0, s67 <= s66 + 0 + 1, x_15 >= 0, z = 1 + (1 + x_15) + x_2, x_2 >= 0
   encArg(z) -{ 39 + 11*x_116 + 11*x_17 + 11*x_21 + 11*x_24 }-> s7 :|: s1 >= 0, s1 <= 6 + 10 * x_17, s2 >= 0, s2 <= 6 + 10 * x_21, s3 >= 0, s3 <= s1 + s2 + 1, s4 >= 0, s4 <= 6 + 10 * x_116, s5 >= 0, s5 <= 6 + 10 * x_24, s6 >= 0, s6 <= s4 + s5 + 1, s7 >= 0, s7 <= s3 + s6 + 1, x_116 >= 0, x_17 >= 0, z = 1 + (1 + x_17 + x_21) + (1 + x_116 + x_24), x_24 >= 0, x_21 >= 0
   encArg(z) -{ 30 + 11*x_114 + 11*x_17 + 11*x_21 }-> s73 :|: s68 >= 0, s68 <= 6 + 10 * x_17, s69 >= 0, s69 <= 6 + 10 * x_21, s70 >= 0, s70 <= s68 + s69 + 1, s71 >= 0, s71 <= 6 + 10 * x_114, s72 >= 0, s72 <= s71 + 1, s73 >= 0, s73 <= s70 + s72 + 1, z = 1 + (1 + x_17 + x_21) + (1 + x_114), x_114 >= 0, x_17 >= 0, x_21 >= 0
   encArg(z) -{ 11 + 11*x_117 }-> s76 :|: s74 >= 0, s74 <= 6 + 10 * x_117, s75 >= 0, s75 <= s74 + 1, s76 >= 0, s76 <= 0 + s75 + 1, x_1 >= 0, x_117 >= 0, z = 1 + x_1 + (1 + x_117)
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   encArg(z) -{ 0 }-> 1 + x0 :|: z - 1 >= 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 + x1 :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   encode_+(z, z') -{ 19 + 11*x_128 + 11*x_28 + 11*z' }-> s100 :|: s95 >= 0, s95 <= 6 + 10 * x_128, s96 >= 0, s96 <= 6 + 10 * x_28, s97 >= 0, s97 <= s95 + s96 + 1, s98 >= 0, s98 <= 6 + 10 * (z' - 1), s99 >= 0, s99 <= s98 + 1, s100 >= 0, s100 <= s97 + s99 + 1, x_128 >= 0, z = 1 + x_128 + x_28, z' - 1 >= 0, x_28 >= 0
   encode_+(z, z') -{ 11*z' }-> s103 :|: s101 >= 0, s101 <= 6 + 10 * (z' - 1), s102 >= 0, s102 <= s101 + 1, s103 >= 0, s103 <= 0 + s102 + 1, z' - 1 >= 0, z >= 0
   encode_+(z, z') -{ 22 + 11*x_134 + 11*x_210 + 11*z }-> s147 :|: s142 >= 0, s142 <= 6 + 10 * (z - 1), s143 >= 0, s143 <= s142 + 2, s144 >= 0, s144 <= 6 + 10 * x_134, s145 >= 0, s145 <= 6 + 10 * x_210, s146 >= 0, s146 <= s144 + s145 + 1, s147 >= 0, s147 <= s143 + s146 + 1, x_134 >= 0, z - 1 >= 0, z' = 1 + x_134 + x_210, x_210 >= 0
   encode_+(z, z') -{ 3 + 11*z }-> s150 :|: s148 >= 0, s148 <= 6 + 10 * (z - 1), s149 >= 0, s149 <= s148 + 2, s150 >= 0, s150 <= s149 + 0 + 1, z - 1 >= 0, z' >= 0
   encode_+(z, z') -{ 22 + 11*x_128 + 11*x_28 + 11*z' }-> s156 :|: s151 >= 0, s151 <= 6 + 10 * x_128, s152 >= 0, s152 <= 6 + 10 * x_28, s153 >= 0, s153 <= s151 + s152 + 1, s154 >= 0, s154 <= 6 + 10 * (z' - 1), s155 >= 0, s155 <= s154 + 2, s156 >= 0, s156 <= s153 + s155 + 1, x_128 >= 0, z = 1 + x_128 + x_28, z' - 1 >= 0, x_28 >= 0
   encode_+(z, z') -{ 3 + 11*z' }-> s159 :|: s157 >= 0, s157 <= 6 + 10 * (z' - 1), s158 >= 0, s158 <= s157 + 2, s159 >= 0, s159 <= 0 + s158 + 1, z >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 39 + 11*x_128 + 11*x_137 + 11*x_211 + 11*x_28 }-> s17 :|: s11 >= 0, s11 <= 6 + 10 * x_128, s12 >= 0, s12 <= 6 + 10 * x_28, s13 >= 0, s13 <= s11 + s12 + 1, s14 >= 0, s14 <= 6 + 10 * x_137, s15 >= 0, s15 <= 6 + 10 * x_211, s16 >= 0, s16 <= s14 + s15 + 1, s17 >= 0, s17 <= s13 + s16 + 1, x_128 >= 0, z = 1 + x_128 + x_28, z' = 1 + x_137 + x_211, x_137 >= 0, x_28 >= 0, x_211 >= 0
   encode_+(z, z') -{ 2 + 11*z + 11*z' }-> s174 :|: s170 >= 0, s170 <= 6 + 10 * (z - 1), s171 >= 0, s171 <= s170 + 1, s172 >= 0, s172 <= 6 + 10 * (z' - 1), s173 >= 0, s173 <= s172 + 2, s174 >= 0, s174 <= s171 + s173 + 1, z' - 1 >= 0, z - 1 >= 0
   encode_+(z, z') -{ 2 + 11*z + 11*z' }-> s179 :|: s175 >= 0, s175 <= 6 + 10 * (z - 1), s176 >= 0, s176 <= s175 + 2, s177 >= 0, s177 <= 6 + 10 * (z' - 1), s178 >= 0, s178 <= s177 + 1, s179 >= 0, s179 <= s176 + s178 + 1, z - 1 >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 5 + 11*z + 11*z' }-> s41 :|: s37 >= 0, s37 <= 6 + 10 * (z - 1), s38 >= 0, s38 <= s37 + 2, s39 >= 0, s39 <= 6 + 10 * (z' - 1), s40 >= 0, s40 <= s39 + 2, s41 >= 0, s41 <= s38 + s40 + 1, z - 1 >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 20 + 11*x_128 + 11*x_28 }-> s45 :|: s42 >= 0, s42 <= 6 + 10 * x_128, s43 >= 0, s43 <= 6 + 10 * x_28, s44 >= 0, s44 <= s42 + s43 + 1, s45 >= 0, s45 <= s44 + 0 + 1, x_128 >= 0, z = 1 + x_128 + x_28, z' >= 0, x_28 >= 0
   encode_+(z, z') -{ 20 + 11*x_140 + 11*x_212 }-> s49 :|: s46 >= 0, s46 <= 6 + 10 * x_140, s47 >= 0, s47 <= 6 + 10 * x_212, s48 >= 0, s48 <= s46 + s47 + 1, s49 >= 0, s49 <= 0 + s48 + 1, z >= 0, x_212 >= 0, x_140 >= 0, z' = 1 + x_140 + x_212
   encode_+(z, z') -{ -1 + 11*z + 11*z' }-> s85 :|: s81 >= 0, s81 <= 6 + 10 * (z - 1), s82 >= 0, s82 <= s81 + 1, s83 >= 0, s83 <= 6 + 10 * (z' - 1), s84 >= 0, s84 <= s83 + 1, s85 >= 0, s85 <= s82 + s84 + 1, z - 1 >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 19 + 11*x_131 + 11*x_29 + 11*z }-> s91 :|: s86 >= 0, s86 <= 6 + 10 * (z - 1), s87 >= 0, s87 <= s86 + 1, s88 >= 0, s88 <= 6 + 10 * x_131, s89 >= 0, s89 <= 6 + 10 * x_29, s90 >= 0, s90 <= s88 + s89 + 1, s91 >= 0, s91 <= s87 + s90 + 1, z' = 1 + x_131 + x_29, z - 1 >= 0, x_131 >= 0, x_29 >= 0
   encode_+(z, z') -{ 11*z }-> s94 :|: s92 >= 0, s92 <= 6 + 10 * (z - 1), s93 >= 0, s93 <= s92 + 1, s94 >= 0, s94 <= s93 + 0 + 1, z - 1 >= 0, z' >= 0
   encode_+(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_+(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   encode_+(z, z') -{ 0 }-> 1 + x0 + x1 :|: z >= 0, z' >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   encode_minus(z) -{ 3 + 11*z }-> s112 :|: s110 >= 0, s110 <= 6 + 10 * (z - 1), s111 >= 0, s111 <= s110 + 2, s112 >= 0, s112 <= s111 + 1, z - 1 >= 0
   encode_minus(z) -{ 11*z }-> s23 :|: s21 >= 0, s21 <= 6 + 10 * (z - 1), s22 >= 0, s22 <= s21 + 1, s23 >= 0, s23 <= s22 + 1, z - 1 >= 0
   encode_minus(z) -{ 20 + 11*x_122 + 11*x_26 }-> s80 :|: s77 >= 0, s77 <= 6 + 10 * x_122, s78 >= 0, s78 <= 6 + 10 * x_26, s79 >= 0, s79 <= s77 + s78 + 1, s80 >= 0, s80 <= s79 + 1, z = 1 + x_122 + x_26, x_26 >= 0, x_122 >= 0
   encode_minus(z) -{ 0 }-> 0 :|: z >= 0
   encode_minus(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_minus(z) -{ 0 }-> 1 + x0 :|: z >= 0, 0 = x0, x0 >= 0
   encode_minux(z) -{ 6 + 11*z }-> s10 :|: s8 >= 0, s8 <= 6 + 10 * (z - 1), s9 >= 0, s9 <= s8 + 2, s10 >= 0, s10 <= s9 + 2, z - 1 >= 0
   encode_minux(z) -{ 3 + 11*z }-> s115 :|: s113 >= 0, s113 <= 6 + 10 * (z - 1), s114 >= 0, s114 <= s113 + 1, s115 >= 0, s115 <= s114 + 2, z - 1 >= 0
   encode_minux(z) -{ 23 + 11*x_125 + 11*x_27 }-> s141 :|: s138 >= 0, s138 <= 6 + 10 * x_125, s139 >= 0, s139 <= 6 + 10 * x_27, s140 >= 0, s140 <= s138 + s139 + 1, s141 >= 0, s141 <= s140 + 2, x_125 >= 0, x_27 >= 0, z = 1 + x_125 + x_27
   encode_minux(z) -{ 0 }-> 0 :|: z >= 0
   encode_minux(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   minus(z) -{ 0 }-> 0 :|: z >= 0
   minus(z) -{ 1 }-> z - 1 :|: z - 1 >= 0
   minus(z) -{ 0 }-> 1 + z :|: z >= 0
   minux(z) -{ 4 }-> x :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x'' = 1 + y, x' = 1 + x + y, x >= 0, y >= 0
   minux(z) -{ 3 }-> x :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, x2 = 1 + y', 1 + y = 1 + x + y', x >= 0, y' >= 0
   minux(z) -{ 2 }-> x' :|: z = 1 + x + y, x >= 0, y >= 0, 1 + x = 1 + y', 1 + y = 1 + x' + y', x' >= 0, y' >= 0
   minux(z) -{ 3 }-> x'' :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, 1 + x = 1 + y, x' = 1 + x'' + y, x'' >= 0, y >= 0
   minux(z) -{ 4 }-> y :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x'' = 1 + x + y, x >= 0, y >= 0, x' = 1 + x
   minux(z) -{ 3 }-> y :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, 1 + x = 1 + x'' + y, x'' >= 0, y >= 0, x' = 1 + x''
   minux(z) -{ 3 }-> y' :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, x2 = 1 + x + y', x >= 0, y' >= 0, 1 + y = 1 + x
   minux(z) -{ 2 }-> y' :|: z = 1 + x + y, x >= 0, y >= 0, 1 + x = 1 + x' + y', x' >= 0, y' >= 0, 1 + y = 1 + x'
   minux(z) -{ 0 }-> 0 :|: z >= 0
   minux(z) -{ 3 }-> 0 :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, v0 >= 0, v1 >= 0, x' = v0, x'' = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, v0 >= 0, v1 >= 0, x' = v0, 1 + x = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, v0 >= 0, v1 >= 0, x' = v0, 0 = v1
   minux(z) -{ 2 }-> 0 :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, x2 = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, 1 + x = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, 0 = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + (1 + x3) + y, y >= 0, x3 >= 0, v0 >= 0, v1 >= 0, 0 = v0, x3 = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 0 = v0, 1 + x = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   minux(z) -{ 3 }-> 1 + x0 + x1 :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x' = x0, x0 >= 0, x1 >= 0, x'' = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, x' = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, x' = x0, x0 >= 0, x1 >= 0, 0 = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, x2 = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, 0 = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + (1 + x3) + y, y >= 0, x3 >= 0, 0 = x0, x0 >= 0, x1 >= 0, x3 = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 0 = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   plus(z, z') -{ 1 }-> x :|: z = 1 + x + (z' - 1), x >= 0, z' - 1 >= 0
   plus(z, z') -{ 1 }-> y :|: z' = 1 + (z - 1) + y, z - 1 >= 0, y >= 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 0 }-> 1 + z + z' :|: z >= 0, z' >= 0

Function symbols to be analyzed: {encode_minux}
Previous analysis results are:
  minus: runtime: O(1) [1], size: O(n^1) [1 + z]
  minux: runtime: O(1) [4], size: O(n^1) [2 + z]
  plus: runtime: O(1) [1], size: O(n^1) [1 + z + z']
  encArg: runtime: O(n^1) [9 + 11*z], size: O(n^1) [6 + 10*z]
  encode_minus: runtime: O(n^1) [9 + 11*z], size: O(n^1) [4 + 10*z]
  encode_+: runtime: O(n^1) [17 + 11*z + 11*z'], size: O(n^1) [7 + 10*z + 10*z']
  encode_minux: runtime: ?, size: O(n^1) [35*z]

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

(67) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: encode_minux
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 12 + 11*z

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

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

   encArg(z) -{ -5 + 11*z }-> s'' :|: s >= 0, s <= 6 + 10 * (z - 2), s' >= 0, s' <= s + 2, s'' >= 0, s'' <= s' + 2, z - 2 >= 0
   encArg(z) -{ -8 + 11*z }-> s106 :|: s104 >= 0, s104 <= 6 + 10 * (z - 2), s105 >= 0, s105 <= s104 + 2, s106 >= 0, s106 <= s105 + 1, z - 2 >= 0
   encArg(z) -{ -8 + 11*z }-> s109 :|: s107 >= 0, s107 <= 6 + 10 * (z - 2), s108 >= 0, s108 <= s107 + 1, s109 >= 0, s109 <= s108 + 2, z - 2 >= 0
   encArg(z) -{ 23 + 11*x_14 + 11*x_2'' }-> s119 :|: s116 >= 0, s116 <= 6 + 10 * x_14, s117 >= 0, s117 <= 6 + 10 * x_2'', s118 >= 0, s118 <= s116 + s117 + 1, s119 >= 0, s119 <= s118 + 2, x_14 >= 0, z = 1 + (1 + x_14 + x_2''), x_2'' >= 0
   encArg(z) -{ 33 + 11*x_113 + 11*x_16 + 11*x_23 }-> s125 :|: s120 >= 0, s120 <= 6 + 10 * x_16, s121 >= 0, s121 <= s120 + 2, s122 >= 0, s122 <= 6 + 10 * x_113, s123 >= 0, s123 <= 6 + 10 * x_23, s124 >= 0, s124 <= s122 + s123 + 1, s125 >= 0, s125 <= s121 + s124 + 1, x_113 >= 0, x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_113 + x_23), x_23 >= 0
   encArg(z) -{ 14 + 11*x_16 }-> s128 :|: s126 >= 0, s126 <= 6 + 10 * x_16, s127 >= 0, s127 <= s126 + 2, s128 >= 0, s128 <= s127 + 0 + 1, x_16 >= 0, x_2 >= 0, z = 1 + (1 + x_16) + x_2
   encArg(z) -{ 33 + 11*x_115 + 11*x_17 + 11*x_21 }-> s134 :|: s129 >= 0, s129 <= 6 + 10 * x_17, s130 >= 0, s130 <= 6 + 10 * x_21, s131 >= 0, s131 <= s129 + s130 + 1, s132 >= 0, s132 <= 6 + 10 * x_115, s133 >= 0, s133 <= s132 + 2, s134 >= 0, s134 <= s131 + s133 + 1, z = 1 + (1 + x_17 + x_21) + (1 + x_115), x_115 >= 0, x_17 >= 0, x_21 >= 0
   encArg(z) -{ 14 + 11*x_118 }-> s137 :|: s135 >= 0, s135 <= 6 + 10 * x_118, s136 >= 0, s136 <= s135 + 2, s137 >= 0, s137 <= 0 + s136 + 1, x_1 >= 0, z = 1 + x_1 + (1 + x_118), x_118 >= 0
   encArg(z) -{ 24 + 11*x_15 + 11*x_19 }-> s164 :|: s160 >= 0, s160 <= 6 + 10 * x_15, s161 >= 0, s161 <= s160 + 1, s162 >= 0, s162 <= 6 + 10 * x_19, s163 >= 0, s163 <= s162 + 2, s164 >= 0, s164 <= s161 + s163 + 1, x_15 >= 0, z = 1 + (1 + x_15) + (1 + x_19), x_19 >= 0
   encArg(z) -{ 24 + 11*x_111 + 11*x_16 }-> s169 :|: s165 >= 0, s165 <= 6 + 10 * x_16, s166 >= 0, s166 <= s165 + 2, s167 >= 0, s167 <= 6 + 10 * x_111, s168 >= 0, s168 <= s167 + 1, s169 >= 0, s169 <= s166 + s168 + 1, x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_111), x_111 >= 0
   encArg(z) -{ -11 + 11*z }-> s20 :|: s18 >= 0, s18 <= 6 + 10 * (z - 2), s19 >= 0, s19 <= s18 + 1, s20 >= 0, s20 <= s19 + 1, z - 2 >= 0
   encArg(z) -{ 27 + 11*x_112 + 11*x_16 }-> s28 :|: s24 >= 0, s24 <= 6 + 10 * x_16, s25 >= 0, s25 <= s24 + 2, s26 >= 0, s26 <= 6 + 10 * x_112, s27 >= 0, s27 <= s26 + 2, s28 >= 0, s28 <= s25 + s27 + 1, x_16 >= 0, z = 1 + (1 + x_16) + (1 + x_112), x_112 >= 0
   encArg(z) -{ 20 + 11*x_17 + 11*x_21 }-> s32 :|: s29 >= 0, s29 <= 6 + 10 * x_17, s30 >= 0, s30 <= 6 + 10 * x_21, s31 >= 0, s31 <= s29 + s30 + 1, s32 >= 0, s32 <= s31 + 0 + 1, z = 1 + (1 + x_17 + x_21) + x_2, x_17 >= 0, x_2 >= 0, x_21 >= 0
   encArg(z) -{ 20 + 11*x_119 + 11*x_25 }-> s36 :|: s33 >= 0, s33 <= 6 + 10 * x_119, s34 >= 0, s34 <= 6 + 10 * x_25, s35 >= 0, s35 <= s33 + s34 + 1, s36 >= 0, s36 <= 0 + s35 + 1, x_1 >= 0, z = 1 + x_1 + (1 + x_119 + x_25), x_25 >= 0, x_119 >= 0
   encArg(z) -{ 20 + 11*x_11 + 11*x_2' }-> s53 :|: s50 >= 0, s50 <= 6 + 10 * x_11, s51 >= 0, s51 <= 6 + 10 * x_2', s52 >= 0, s52 <= s50 + s51 + 1, s53 >= 0, s53 <= s52 + 1, x_11 >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2')
   encArg(z) -{ 21 + 11*x_15 + 11*x_18 }-> s58 :|: s54 >= 0, s54 <= 6 + 10 * x_15, s55 >= 0, s55 <= s54 + 1, s56 >= 0, s56 <= 6 + 10 * x_18, s57 >= 0, s57 <= s56 + 1, s58 >= 0, s58 <= s55 + s57 + 1, x_15 >= 0, x_18 >= 0, z = 1 + (1 + x_15) + (1 + x_18)
   encArg(z) -{ 30 + 11*x_110 + 11*x_15 + 11*x_22 }-> s64 :|: s59 >= 0, s59 <= 6 + 10 * x_15, s60 >= 0, s60 <= s59 + 1, s61 >= 0, s61 <= 6 + 10 * x_110, s62 >= 0, s62 <= 6 + 10 * x_22, s63 >= 0, s63 <= s61 + s62 + 1, s64 >= 0, s64 <= s60 + s63 + 1, x_15 >= 0, z = 1 + (1 + x_15) + (1 + x_110 + x_22), x_110 >= 0, x_22 >= 0
   encArg(z) -{ 11 + 11*x_15 }-> s67 :|: s65 >= 0, s65 <= 6 + 10 * x_15, s66 >= 0, s66 <= s65 + 1, s67 >= 0, s67 <= s66 + 0 + 1, x_15 >= 0, z = 1 + (1 + x_15) + x_2, x_2 >= 0
   encArg(z) -{ 39 + 11*x_116 + 11*x_17 + 11*x_21 + 11*x_24 }-> s7 :|: s1 >= 0, s1 <= 6 + 10 * x_17, s2 >= 0, s2 <= 6 + 10 * x_21, s3 >= 0, s3 <= s1 + s2 + 1, s4 >= 0, s4 <= 6 + 10 * x_116, s5 >= 0, s5 <= 6 + 10 * x_24, s6 >= 0, s6 <= s4 + s5 + 1, s7 >= 0, s7 <= s3 + s6 + 1, x_116 >= 0, x_17 >= 0, z = 1 + (1 + x_17 + x_21) + (1 + x_116 + x_24), x_24 >= 0, x_21 >= 0
   encArg(z) -{ 30 + 11*x_114 + 11*x_17 + 11*x_21 }-> s73 :|: s68 >= 0, s68 <= 6 + 10 * x_17, s69 >= 0, s69 <= 6 + 10 * x_21, s70 >= 0, s70 <= s68 + s69 + 1, s71 >= 0, s71 <= 6 + 10 * x_114, s72 >= 0, s72 <= s71 + 1, s73 >= 0, s73 <= s70 + s72 + 1, z = 1 + (1 + x_17 + x_21) + (1 + x_114), x_114 >= 0, x_17 >= 0, x_21 >= 0
   encArg(z) -{ 11 + 11*x_117 }-> s76 :|: s74 >= 0, s74 <= 6 + 10 * x_117, s75 >= 0, s75 <= s74 + 1, s76 >= 0, s76 <= 0 + s75 + 1, x_1 >= 0, x_117 >= 0, z = 1 + x_1 + (1 + x_117)
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   encArg(z) -{ 0 }-> 1 + x0 :|: z - 1 >= 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 + x1 :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   encode_+(z, z') -{ 19 + 11*x_128 + 11*x_28 + 11*z' }-> s100 :|: s95 >= 0, s95 <= 6 + 10 * x_128, s96 >= 0, s96 <= 6 + 10 * x_28, s97 >= 0, s97 <= s95 + s96 + 1, s98 >= 0, s98 <= 6 + 10 * (z' - 1), s99 >= 0, s99 <= s98 + 1, s100 >= 0, s100 <= s97 + s99 + 1, x_128 >= 0, z = 1 + x_128 + x_28, z' - 1 >= 0, x_28 >= 0
   encode_+(z, z') -{ 11*z' }-> s103 :|: s101 >= 0, s101 <= 6 + 10 * (z' - 1), s102 >= 0, s102 <= s101 + 1, s103 >= 0, s103 <= 0 + s102 + 1, z' - 1 >= 0, z >= 0
   encode_+(z, z') -{ 22 + 11*x_134 + 11*x_210 + 11*z }-> s147 :|: s142 >= 0, s142 <= 6 + 10 * (z - 1), s143 >= 0, s143 <= s142 + 2, s144 >= 0, s144 <= 6 + 10 * x_134, s145 >= 0, s145 <= 6 + 10 * x_210, s146 >= 0, s146 <= s144 + s145 + 1, s147 >= 0, s147 <= s143 + s146 + 1, x_134 >= 0, z - 1 >= 0, z' = 1 + x_134 + x_210, x_210 >= 0
   encode_+(z, z') -{ 3 + 11*z }-> s150 :|: s148 >= 0, s148 <= 6 + 10 * (z - 1), s149 >= 0, s149 <= s148 + 2, s150 >= 0, s150 <= s149 + 0 + 1, z - 1 >= 0, z' >= 0
   encode_+(z, z') -{ 22 + 11*x_128 + 11*x_28 + 11*z' }-> s156 :|: s151 >= 0, s151 <= 6 + 10 * x_128, s152 >= 0, s152 <= 6 + 10 * x_28, s153 >= 0, s153 <= s151 + s152 + 1, s154 >= 0, s154 <= 6 + 10 * (z' - 1), s155 >= 0, s155 <= s154 + 2, s156 >= 0, s156 <= s153 + s155 + 1, x_128 >= 0, z = 1 + x_128 + x_28, z' - 1 >= 0, x_28 >= 0
   encode_+(z, z') -{ 3 + 11*z' }-> s159 :|: s157 >= 0, s157 <= 6 + 10 * (z' - 1), s158 >= 0, s158 <= s157 + 2, s159 >= 0, s159 <= 0 + s158 + 1, z >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 39 + 11*x_128 + 11*x_137 + 11*x_211 + 11*x_28 }-> s17 :|: s11 >= 0, s11 <= 6 + 10 * x_128, s12 >= 0, s12 <= 6 + 10 * x_28, s13 >= 0, s13 <= s11 + s12 + 1, s14 >= 0, s14 <= 6 + 10 * x_137, s15 >= 0, s15 <= 6 + 10 * x_211, s16 >= 0, s16 <= s14 + s15 + 1, s17 >= 0, s17 <= s13 + s16 + 1, x_128 >= 0, z = 1 + x_128 + x_28, z' = 1 + x_137 + x_211, x_137 >= 0, x_28 >= 0, x_211 >= 0
   encode_+(z, z') -{ 2 + 11*z + 11*z' }-> s174 :|: s170 >= 0, s170 <= 6 + 10 * (z - 1), s171 >= 0, s171 <= s170 + 1, s172 >= 0, s172 <= 6 + 10 * (z' - 1), s173 >= 0, s173 <= s172 + 2, s174 >= 0, s174 <= s171 + s173 + 1, z' - 1 >= 0, z - 1 >= 0
   encode_+(z, z') -{ 2 + 11*z + 11*z' }-> s179 :|: s175 >= 0, s175 <= 6 + 10 * (z - 1), s176 >= 0, s176 <= s175 + 2, s177 >= 0, s177 <= 6 + 10 * (z' - 1), s178 >= 0, s178 <= s177 + 1, s179 >= 0, s179 <= s176 + s178 + 1, z - 1 >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 5 + 11*z + 11*z' }-> s41 :|: s37 >= 0, s37 <= 6 + 10 * (z - 1), s38 >= 0, s38 <= s37 + 2, s39 >= 0, s39 <= 6 + 10 * (z' - 1), s40 >= 0, s40 <= s39 + 2, s41 >= 0, s41 <= s38 + s40 + 1, z - 1 >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 20 + 11*x_128 + 11*x_28 }-> s45 :|: s42 >= 0, s42 <= 6 + 10 * x_128, s43 >= 0, s43 <= 6 + 10 * x_28, s44 >= 0, s44 <= s42 + s43 + 1, s45 >= 0, s45 <= s44 + 0 + 1, x_128 >= 0, z = 1 + x_128 + x_28, z' >= 0, x_28 >= 0
   encode_+(z, z') -{ 20 + 11*x_140 + 11*x_212 }-> s49 :|: s46 >= 0, s46 <= 6 + 10 * x_140, s47 >= 0, s47 <= 6 + 10 * x_212, s48 >= 0, s48 <= s46 + s47 + 1, s49 >= 0, s49 <= 0 + s48 + 1, z >= 0, x_212 >= 0, x_140 >= 0, z' = 1 + x_140 + x_212
   encode_+(z, z') -{ -1 + 11*z + 11*z' }-> s85 :|: s81 >= 0, s81 <= 6 + 10 * (z - 1), s82 >= 0, s82 <= s81 + 1, s83 >= 0, s83 <= 6 + 10 * (z' - 1), s84 >= 0, s84 <= s83 + 1, s85 >= 0, s85 <= s82 + s84 + 1, z - 1 >= 0, z' - 1 >= 0
   encode_+(z, z') -{ 19 + 11*x_131 + 11*x_29 + 11*z }-> s91 :|: s86 >= 0, s86 <= 6 + 10 * (z - 1), s87 >= 0, s87 <= s86 + 1, s88 >= 0, s88 <= 6 + 10 * x_131, s89 >= 0, s89 <= 6 + 10 * x_29, s90 >= 0, s90 <= s88 + s89 + 1, s91 >= 0, s91 <= s87 + s90 + 1, z' = 1 + x_131 + x_29, z - 1 >= 0, x_131 >= 0, x_29 >= 0
   encode_+(z, z') -{ 11*z }-> s94 :|: s92 >= 0, s92 <= 6 + 10 * (z - 1), s93 >= 0, s93 <= s92 + 1, s94 >= 0, s94 <= s93 + 0 + 1, z - 1 >= 0, z' >= 0
   encode_+(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_+(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   encode_+(z, z') -{ 0 }-> 1 + x0 + x1 :|: z >= 0, z' >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   encode_minus(z) -{ 3 + 11*z }-> s112 :|: s110 >= 0, s110 <= 6 + 10 * (z - 1), s111 >= 0, s111 <= s110 + 2, s112 >= 0, s112 <= s111 + 1, z - 1 >= 0
   encode_minus(z) -{ 11*z }-> s23 :|: s21 >= 0, s21 <= 6 + 10 * (z - 1), s22 >= 0, s22 <= s21 + 1, s23 >= 0, s23 <= s22 + 1, z - 1 >= 0
   encode_minus(z) -{ 20 + 11*x_122 + 11*x_26 }-> s80 :|: s77 >= 0, s77 <= 6 + 10 * x_122, s78 >= 0, s78 <= 6 + 10 * x_26, s79 >= 0, s79 <= s77 + s78 + 1, s80 >= 0, s80 <= s79 + 1, z = 1 + x_122 + x_26, x_26 >= 0, x_122 >= 0
   encode_minus(z) -{ 0 }-> 0 :|: z >= 0
   encode_minus(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_minus(z) -{ 0 }-> 1 + x0 :|: z >= 0, 0 = x0, x0 >= 0
   encode_minux(z) -{ 6 + 11*z }-> s10 :|: s8 >= 0, s8 <= 6 + 10 * (z - 1), s9 >= 0, s9 <= s8 + 2, s10 >= 0, s10 <= s9 + 2, z - 1 >= 0
   encode_minux(z) -{ 3 + 11*z }-> s115 :|: s113 >= 0, s113 <= 6 + 10 * (z - 1), s114 >= 0, s114 <= s113 + 1, s115 >= 0, s115 <= s114 + 2, z - 1 >= 0
   encode_minux(z) -{ 23 + 11*x_125 + 11*x_27 }-> s141 :|: s138 >= 0, s138 <= 6 + 10 * x_125, s139 >= 0, s139 <= 6 + 10 * x_27, s140 >= 0, s140 <= s138 + s139 + 1, s141 >= 0, s141 <= s140 + 2, x_125 >= 0, x_27 >= 0, z = 1 + x_125 + x_27
   encode_minux(z) -{ 0 }-> 0 :|: z >= 0
   encode_minux(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   minus(z) -{ 0 }-> 0 :|: z >= 0
   minus(z) -{ 1 }-> z - 1 :|: z - 1 >= 0
   minus(z) -{ 0 }-> 1 + z :|: z >= 0
   minux(z) -{ 4 }-> x :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x'' = 1 + y, x' = 1 + x + y, x >= 0, y >= 0
   minux(z) -{ 3 }-> x :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, x2 = 1 + y', 1 + y = 1 + x + y', x >= 0, y' >= 0
   minux(z) -{ 2 }-> x' :|: z = 1 + x + y, x >= 0, y >= 0, 1 + x = 1 + y', 1 + y = 1 + x' + y', x' >= 0, y' >= 0
   minux(z) -{ 3 }-> x'' :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, 1 + x = 1 + y, x' = 1 + x'' + y, x'' >= 0, y >= 0
   minux(z) -{ 4 }-> y :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x'' = 1 + x + y, x >= 0, y >= 0, x' = 1 + x
   minux(z) -{ 3 }-> y :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, 1 + x = 1 + x'' + y, x'' >= 0, y >= 0, x' = 1 + x''
   minux(z) -{ 3 }-> y' :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, x2 = 1 + x + y', x >= 0, y' >= 0, 1 + y = 1 + x
   minux(z) -{ 2 }-> y' :|: z = 1 + x + y, x >= 0, y >= 0, 1 + x = 1 + x' + y', x' >= 0, y' >= 0, 1 + y = 1 + x'
   minux(z) -{ 0 }-> 0 :|: z >= 0
   minux(z) -{ 3 }-> 0 :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, v0 >= 0, v1 >= 0, x' = v0, x'' = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, v0 >= 0, v1 >= 0, x' = v0, 1 + x = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, v0 >= 0, v1 >= 0, x' = v0, 0 = v1
   minux(z) -{ 2 }-> 0 :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, x2 = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, 1 + x = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 1 + y = v0, 0 = v1
   minux(z) -{ 2 }-> 0 :|: z = 1 + (1 + x3) + y, y >= 0, x3 >= 0, v0 >= 0, v1 >= 0, 0 = v0, x3 = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 0 = v0, 1 + x = v1
   minux(z) -{ 1 }-> 0 :|: z = 1 + x + y, x >= 0, y >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   minux(z) -{ 3 }-> 1 + x0 + x1 :|: z = 1 + (1 + x'') + (1 + x'), x' >= 0, x'' >= 0, x' = x0, x0 >= 0, x1 >= 0, x'' = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, x' = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + x + (1 + x'), x >= 0, x' >= 0, x' = x0, x0 >= 0, x1 >= 0, 0 = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: y >= 0, z = 1 + (1 + x2) + y, x2 >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, x2 = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 1 + y = x0, x0 >= 0, x1 >= 0, 0 = x1
   minux(z) -{ 2 }-> 1 + x0 + x1 :|: z = 1 + (1 + x3) + y, y >= 0, x3 >= 0, 0 = x0, x0 >= 0, x1 >= 0, x3 = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 0 = x0, x0 >= 0, x1 >= 0, 1 + x = x1
   minux(z) -{ 1 }-> 1 + x0 + x1 :|: z = 1 + x + y, x >= 0, y >= 0, 0 = x0, x0 >= 0, x1 >= 0, 0 = x1
   plus(z, z') -{ 1 }-> x :|: z = 1 + x + (z' - 1), x >= 0, z' - 1 >= 0
   plus(z, z') -{ 1 }-> y :|: z' = 1 + (z - 1) + y, z - 1 >= 0, y >= 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 0 }-> 1 + z + z' :|: z >= 0, z' >= 0

Function symbols to be analyzed: 
Previous analysis results are:
  minus: runtime: O(1) [1], size: O(n^1) [1 + z]
  minux: runtime: O(1) [4], size: O(n^1) [2 + z]
  plus: runtime: O(1) [1], size: O(n^1) [1 + z + z']
  encArg: runtime: O(n^1) [9 + 11*z], size: O(n^1) [6 + 10*z]
  encode_minus: runtime: O(n^1) [9 + 11*z], size: O(n^1) [4 + 10*z]
  encode_+: runtime: O(n^1) [17 + 11*z + 11*z'], size: O(n^1) [7 + 10*z + 10*z']
  encode_minux: runtime: O(n^1) [12 + 11*z], size: O(n^1) [35*z]

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(69) FinalProof (FINISHED)
Computed overall runtime complexity
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(70)
BOUNDS(1, n^1)