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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


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

(0) DCpxTrs
(1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms]
(2) CpxRelTRS
(3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 164 ms]
(4) CpxRelTRS
(5) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
(6) CpxWeightedTrs
(7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
(8) CpxTypedWeightedTrs
(9) CompletionProof [UPPER BOUND(ID), 0 ms]
(10) CpxTypedWeightedCompleteTrs
(11) NarrowingProof [BOTH BOUNDS(ID, ID), 570 ms]
(12) CpxTypedWeightedCompleteTrs
(13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
(14) CpxRNTS
(15) InliningProof [UPPER BOUND(ID), 422 ms]
(16) CpxRNTS
(17) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
(18) CpxRNTS
(19) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms]
(20) CpxRNTS
(21) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(22) CpxRNTS
(23) IntTrsBoundProof [UPPER BOUND(ID), 249 ms]
(24) CpxRNTS
(25) IntTrsBoundProof [UPPER BOUND(ID), 46 ms]
(26) CpxRNTS
(27) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(28) CpxRNTS
(29) IntTrsBoundProof [UPPER BOUND(ID), 158 ms]
(30) CpxRNTS
(31) IntTrsBoundProof [UPPER BOUND(ID), 62 ms]
(32) CpxRNTS
(33) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(34) CpxRNTS
(35) IntTrsBoundProof [UPPER BOUND(ID), 229 ms]
(36) CpxRNTS
(37) IntTrsBoundProof [UPPER BOUND(ID), 93 ms]
(38) CpxRNTS
(39) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(40) CpxRNTS
(41) IntTrsBoundProof [UPPER BOUND(ID), 301 ms]
(42) CpxRNTS
(43) IntTrsBoundProof [UPPER BOUND(ID), 63 ms]
(44) CpxRNTS
(45) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(46) CpxRNTS
(47) IntTrsBoundProof [UPPER BOUND(ID), 179 ms]
(48) CpxRNTS
(49) IntTrsBoundProof [UPPER BOUND(ID), 225 ms]
(50) CpxRNTS
(51) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(52) CpxRNTS
(53) IntTrsBoundProof [UPPER BOUND(ID), 137 ms]
(54) CpxRNTS
(55) IntTrsBoundProof [UPPER BOUND(ID), 73 ms]
(56) CpxRNTS
(57) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(58) CpxRNTS
(59) IntTrsBoundProof [UPPER BOUND(ID), 159 ms]
(60) CpxRNTS
(61) IntTrsBoundProof [UPPER BOUND(ID), 86 ms]
(62) CpxRNTS
(63) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(64) CpxRNTS
(65) IntTrsBoundProof [UPPER BOUND(ID), 117 ms]
(66) CpxRNTS
(67) IntTrsBoundProof [UPPER BOUND(ID), 53 ms]
(68) CpxRNTS
(69) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(70) CpxRNTS
(71) IntTrsBoundProof [UPPER BOUND(ID), 126 ms]
(72) CpxRNTS
(73) IntTrsBoundProof [UPPER BOUND(ID), 62 ms]
(74) CpxRNTS
(75) FinalProof [FINISHED, 0 ms]
(76) BOUNDS(1, n^1)


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

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


The TRS R consists of the following rules:

   f(x, y) -> g1(x, x, y)
   f(x, y) -> g1(y, x, x)
   f(x, y) -> g2(x, y, y)
   f(x, y) -> g2(y, y, x)
   g1(x, x, y) -> h(x, y)
   g1(y, x, x) -> h(x, y)
   g2(x, y, y) -> h(x, y)
   g2(y, y, x) -> h(x, y)
   h(x, x) -> x

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

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

   encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2))
   encArg(cons_g1(x_1, x_2, x_3)) -> g1(encArg(x_1), encArg(x_2), encArg(x_3))
   encArg(cons_g2(x_1, x_2, x_3)) -> g2(encArg(x_1), encArg(x_2), encArg(x_3))
   encArg(cons_h(x_1, x_2)) -> h(encArg(x_1), encArg(x_2))
   encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2))
   encode_g1(x_1, x_2, x_3) -> g1(encArg(x_1), encArg(x_2), encArg(x_3))
   encode_g2(x_1, x_2, x_3) -> g2(encArg(x_1), encArg(x_2), encArg(x_3))
   encode_h(x_1, x_2) -> h(encArg(x_1), encArg(x_2))


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

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


The TRS R consists of the following rules:

   f(x, y) -> g1(x, x, y)
   f(x, y) -> g1(y, x, x)
   f(x, y) -> g2(x, y, y)
   f(x, y) -> g2(y, y, x)
   g1(x, x, y) -> h(x, y)
   g1(y, x, x) -> h(x, y)
   g2(x, y, y) -> h(x, y)
   g2(y, y, x) -> h(x, y)
   h(x, x) -> x

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

   encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2))
   encArg(cons_g1(x_1, x_2, x_3)) -> g1(encArg(x_1), encArg(x_2), encArg(x_3))
   encArg(cons_g2(x_1, x_2, x_3)) -> g2(encArg(x_1), encArg(x_2), encArg(x_3))
   encArg(cons_h(x_1, x_2)) -> h(encArg(x_1), encArg(x_2))
   encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2))
   encode_g1(x_1, x_2, x_3) -> g1(encArg(x_1), encArg(x_2), encArg(x_3))
   encode_g2(x_1, x_2, x_3) -> g2(encArg(x_1), encArg(x_2), encArg(x_3))
   encode_h(x_1, x_2) -> h(encArg(x_1), encArg(x_2))

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

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

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


The TRS R consists of the following rules:

   f(x, y) -> g1(x, x, y)
   f(x, y) -> g1(y, x, x)
   f(x, y) -> g2(x, y, y)
   f(x, y) -> g2(y, y, x)
   g1(x, x, y) -> h(x, y)
   g1(y, x, x) -> h(x, y)
   g2(x, y, y) -> h(x, y)
   g2(y, y, x) -> h(x, y)
   h(x, x) -> x

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

   encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2))
   encArg(cons_g1(x_1, x_2, x_3)) -> g1(encArg(x_1), encArg(x_2), encArg(x_3))
   encArg(cons_g2(x_1, x_2, x_3)) -> g2(encArg(x_1), encArg(x_2), encArg(x_3))
   encArg(cons_h(x_1, x_2)) -> h(encArg(x_1), encArg(x_2))
   encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2))
   encode_g1(x_1, x_2, x_3) -> g1(encArg(x_1), encArg(x_2), encArg(x_3))
   encode_g2(x_1, x_2, x_3) -> g2(encArg(x_1), encArg(x_2), encArg(x_3))
   encode_h(x_1, x_2) -> h(encArg(x_1), encArg(x_2))

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

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

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


The TRS R consists of the following rules:

   f(x, y) -> g1(x, x, y) [1]
   f(x, y) -> g1(y, x, x) [1]
   f(x, y) -> g2(x, y, y) [1]
   f(x, y) -> g2(y, y, x) [1]
   g1(x, x, y) -> h(x, y) [1]
   g1(y, x, x) -> h(x, y) [1]
   g2(x, y, y) -> h(x, y) [1]
   g2(y, y, x) -> h(x, y) [1]
   h(x, x) -> x [1]
   encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2)) [0]
   encArg(cons_g1(x_1, x_2, x_3)) -> g1(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encArg(cons_g2(x_1, x_2, x_3)) -> g2(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encArg(cons_h(x_1, x_2)) -> h(encArg(x_1), encArg(x_2)) [0]
   encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2)) [0]
   encode_g1(x_1, x_2, x_3) -> g1(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encode_g2(x_1, x_2, x_3) -> g2(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encode_h(x_1, x_2) -> h(encArg(x_1), encArg(x_2)) [0]

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

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

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

   f(x, y) -> g1(x, x, y) [1]
   f(x, y) -> g1(y, x, x) [1]
   f(x, y) -> g2(x, y, y) [1]
   f(x, y) -> g2(y, y, x) [1]
   g1(x, x, y) -> h(x, y) [1]
   g1(y, x, x) -> h(x, y) [1]
   g2(x, y, y) -> h(x, y) [1]
   g2(y, y, x) -> h(x, y) [1]
   h(x, x) -> x [1]
   encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2)) [0]
   encArg(cons_g1(x_1, x_2, x_3)) -> g1(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encArg(cons_g2(x_1, x_2, x_3)) -> g2(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encArg(cons_h(x_1, x_2)) -> h(encArg(x_1), encArg(x_2)) [0]
   encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2)) [0]
   encode_g1(x_1, x_2, x_3) -> g1(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encode_g2(x_1, x_2, x_3) -> g2(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encode_h(x_1, x_2) -> h(encArg(x_1), encArg(x_2)) [0]

The TRS has the following type information:
f :: f:g1:g2:h:encArg:encode_f:encode_g1:encode_g2:encode_h -> f:g1:g2:h:encArg:encode_f:encode_g1:encode_g2:encode_h -> f:g1:g2:h:encArg:encode_f:encode_g1:encode_g2:encode_h
g1 :: f:g1:g2:h:encArg:encode_f:encode_g1:encode_g2:encode_h -> f:g1:g2:h:encArg:encode_f:encode_g1:encode_g2:encode_h -> f:g1:g2:h:encArg:encode_f:encode_g1:encode_g2:encode_h -> f:g1:g2:h:encArg:encode_f:encode_g1:encode_g2:encode_h
g2 :: f:g1:g2:h:encArg:encode_f:encode_g1:encode_g2:encode_h -> f:g1:g2:h:encArg:encode_f:encode_g1:encode_g2:encode_h -> f:g1:g2:h:encArg:encode_f:encode_g1:encode_g2:encode_h -> f:g1:g2:h:encArg:encode_f:encode_g1:encode_g2:encode_h
h :: f:g1:g2:h:encArg:encode_f:encode_g1:encode_g2:encode_h -> f:g1:g2:h:encArg:encode_f:encode_g1:encode_g2:encode_h -> f:g1:g2:h:encArg:encode_f:encode_g1:encode_g2:encode_h
encArg :: cons_f:cons_g1:cons_g2:cons_h -> f:g1:g2:h:encArg:encode_f:encode_g1:encode_g2:encode_h
cons_f :: cons_f:cons_g1:cons_g2:cons_h -> cons_f:cons_g1:cons_g2:cons_h -> cons_f:cons_g1:cons_g2:cons_h
cons_g1 :: cons_f:cons_g1:cons_g2:cons_h -> cons_f:cons_g1:cons_g2:cons_h -> cons_f:cons_g1:cons_g2:cons_h -> cons_f:cons_g1:cons_g2:cons_h
cons_g2 :: cons_f:cons_g1:cons_g2:cons_h -> cons_f:cons_g1:cons_g2:cons_h -> cons_f:cons_g1:cons_g2:cons_h -> cons_f:cons_g1:cons_g2:cons_h
cons_h :: cons_f:cons_g1:cons_g2:cons_h -> cons_f:cons_g1:cons_g2:cons_h -> cons_f:cons_g1:cons_g2:cons_h
encode_f :: cons_f:cons_g1:cons_g2:cons_h -> cons_f:cons_g1:cons_g2:cons_h -> f:g1:g2:h:encArg:encode_f:encode_g1:encode_g2:encode_h
encode_g1 :: cons_f:cons_g1:cons_g2:cons_h -> cons_f:cons_g1:cons_g2:cons_h -> cons_f:cons_g1:cons_g2:cons_h -> f:g1:g2:h:encArg:encode_f:encode_g1:encode_g2:encode_h
encode_g2 :: cons_f:cons_g1:cons_g2:cons_h -> cons_f:cons_g1:cons_g2:cons_h -> cons_f:cons_g1:cons_g2:cons_h -> f:g1:g2:h:encArg:encode_f:encode_g1:encode_g2:encode_h
encode_h :: cons_f:cons_g1:cons_g2:cons_h -> cons_f:cons_g1:cons_g2:cons_h -> f:g1:g2:h:encArg:encode_f:encode_g1:encode_g2:encode_h

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

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

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

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

(c) The following functions are completely defined:

   g2_3
   h_2
   g1_3
   f_2
   encArg_1
   encode_f_2
   encode_g1_3
   encode_g2_3
   encode_h_2

Due to the following rules being added:

   encArg(v0) -> const [0]
   encode_f(v0, v1) -> const [0]
   encode_g1(v0, v1, v2) -> const [0]
   encode_g2(v0, v1, v2) -> const [0]
   encode_h(v0, v1) -> const [0]
   g2(v0, v1, v2) -> const [0]
   h(v0, v1) -> const [0]
   g1(v0, v1, v2) -> const [0]

And the following fresh constants:    const, const1

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

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

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

   f(x, y) -> g1(x, x, y) [1]
   f(x, y) -> g1(y, x, x) [1]
   f(x, y) -> g2(x, y, y) [1]
   f(x, y) -> g2(y, y, x) [1]
   g1(x, x, y) -> h(x, y) [1]
   g1(y, x, x) -> h(x, y) [1]
   g2(x, y, y) -> h(x, y) [1]
   g2(y, y, x) -> h(x, y) [1]
   h(x, x) -> x [1]
   encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2)) [0]
   encArg(cons_g1(x_1, x_2, x_3)) -> g1(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encArg(cons_g2(x_1, x_2, x_3)) -> g2(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encArg(cons_h(x_1, x_2)) -> h(encArg(x_1), encArg(x_2)) [0]
   encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2)) [0]
   encode_g1(x_1, x_2, x_3) -> g1(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encode_g2(x_1, x_2, x_3) -> g2(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encode_h(x_1, x_2) -> h(encArg(x_1), encArg(x_2)) [0]
   encArg(v0) -> const [0]
   encode_f(v0, v1) -> const [0]
   encode_g1(v0, v1, v2) -> const [0]
   encode_g2(v0, v1, v2) -> const [0]
   encode_h(v0, v1) -> const [0]
   g2(v0, v1, v2) -> const [0]
   h(v0, v1) -> const [0]
   g1(v0, v1, v2) -> const [0]

The TRS has the following type information:
f :: const -> const -> const
g1 :: const -> const -> const -> const
g2 :: const -> const -> const -> const
h :: const -> const -> const
encArg :: cons_f:cons_g1:cons_g2:cons_h -> const
cons_f :: cons_f:cons_g1:cons_g2:cons_h -> cons_f:cons_g1:cons_g2:cons_h -> cons_f:cons_g1:cons_g2:cons_h
cons_g1 :: cons_f:cons_g1:cons_g2:cons_h -> cons_f:cons_g1:cons_g2:cons_h -> cons_f:cons_g1:cons_g2:cons_h -> cons_f:cons_g1:cons_g2:cons_h
cons_g2 :: cons_f:cons_g1:cons_g2:cons_h -> cons_f:cons_g1:cons_g2:cons_h -> cons_f:cons_g1:cons_g2:cons_h -> cons_f:cons_g1:cons_g2:cons_h
cons_h :: cons_f:cons_g1:cons_g2:cons_h -> cons_f:cons_g1:cons_g2:cons_h -> cons_f:cons_g1:cons_g2:cons_h
encode_f :: cons_f:cons_g1:cons_g2:cons_h -> cons_f:cons_g1:cons_g2:cons_h -> const
encode_g1 :: cons_f:cons_g1:cons_g2:cons_h -> cons_f:cons_g1:cons_g2:cons_h -> cons_f:cons_g1:cons_g2:cons_h -> const
encode_g2 :: cons_f:cons_g1:cons_g2:cons_h -> cons_f:cons_g1:cons_g2:cons_h -> cons_f:cons_g1:cons_g2:cons_h -> const
encode_h :: cons_f:cons_g1:cons_g2:cons_h -> cons_f:cons_g1:cons_g2:cons_h -> const
const :: const
const1 :: cons_f:cons_g1:cons_g2:cons_h

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

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

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

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

   f(x, y) -> g1(x, x, y) [1]
   f(x, y) -> g1(y, x, x) [1]
   f(x, y) -> g2(x, y, y) [1]
   f(x, y) -> g2(y, y, x) [1]
   g1(x, x, y) -> h(x, y) [1]
   g1(y, x, x) -> h(x, y) [1]
   g2(x, y, y) -> h(x, y) [1]
   g2(y, y, x) -> h(x, y) [1]
   h(x, x) -> x [1]
   encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2)) [0]
   encArg(cons_g1(x_1, x_2, x_3)) -> g1(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encArg(cons_g2(x_1, x_2, x_3)) -> g2(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encArg(cons_h(x_1, x_2)) -> h(encArg(x_1), encArg(x_2)) [0]
   encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2)) [0]
   encode_g1(x_1, x_2, x_3) -> g1(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encode_g2(x_1, x_2, x_3) -> g2(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encode_h(x_1, x_2) -> h(encArg(x_1), encArg(x_2)) [0]
   encArg(v0) -> const [0]
   encode_f(v0, v1) -> const [0]
   encode_g1(v0, v1, v2) -> const [0]
   encode_g2(v0, v1, v2) -> const [0]
   encode_h(v0, v1) -> const [0]
   g2(v0, v1, v2) -> const [0]
   h(v0, v1) -> const [0]
   g1(v0, v1, v2) -> const [0]

The TRS has the following type information:
f :: const -> const -> const
g1 :: const -> const -> const -> const
g2 :: const -> const -> const -> const
h :: const -> const -> const
encArg :: cons_f:cons_g1:cons_g2:cons_h -> const
cons_f :: cons_f:cons_g1:cons_g2:cons_h -> cons_f:cons_g1:cons_g2:cons_h -> cons_f:cons_g1:cons_g2:cons_h
cons_g1 :: cons_f:cons_g1:cons_g2:cons_h -> cons_f:cons_g1:cons_g2:cons_h -> cons_f:cons_g1:cons_g2:cons_h -> cons_f:cons_g1:cons_g2:cons_h
cons_g2 :: cons_f:cons_g1:cons_g2:cons_h -> cons_f:cons_g1:cons_g2:cons_h -> cons_f:cons_g1:cons_g2:cons_h -> cons_f:cons_g1:cons_g2:cons_h
cons_h :: cons_f:cons_g1:cons_g2:cons_h -> cons_f:cons_g1:cons_g2:cons_h -> cons_f:cons_g1:cons_g2:cons_h
encode_f :: cons_f:cons_g1:cons_g2:cons_h -> cons_f:cons_g1:cons_g2:cons_h -> const
encode_g1 :: cons_f:cons_g1:cons_g2:cons_h -> cons_f:cons_g1:cons_g2:cons_h -> cons_f:cons_g1:cons_g2:cons_h -> const
encode_g2 :: cons_f:cons_g1:cons_g2:cons_h -> cons_f:cons_g1:cons_g2:cons_h -> cons_f:cons_g1:cons_g2:cons_h -> const
encode_h :: cons_f:cons_g1:cons_g2:cons_h -> cons_f:cons_g1:cons_g2:cons_h -> const
const :: const
const1 :: cons_f:cons_g1:cons_g2:cons_h

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

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

   const => 0
   const1 => 0

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

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

   encArg(z) -{ 0 }-> h(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> g2(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> g1(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_f(z, z') -{ 0 }-> f(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2
   encode_f(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   encode_g1(z, z', z'') -{ 0 }-> g1(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, x_3 >= 0, x_2 >= 0, z = x_1, z' = x_2, z'' = x_3
   encode_g1(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   encode_g2(z, z', z'') -{ 0 }-> g2(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, x_3 >= 0, x_2 >= 0, z = x_1, z' = x_2, z'' = x_3
   encode_g2(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   encode_h(z, z') -{ 0 }-> h(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2
   encode_h(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   f(z, z') -{ 1 }-> g2(x, y, y) :|: x >= 0, y >= 0, z = x, z' = y
   f(z, z') -{ 1 }-> g2(y, y, x) :|: x >= 0, y >= 0, z = x, z' = y
   f(z, z') -{ 1 }-> g1(x, x, y) :|: x >= 0, y >= 0, z = x, z' = y
   f(z, z') -{ 1 }-> g1(y, x, x) :|: x >= 0, y >= 0, z = x, z' = y
   g1(z, z', z'') -{ 1 }-> h(x, y) :|: z' = x, z'' = y, x >= 0, y >= 0, z = x
   g1(z, z', z'') -{ 1 }-> h(x, y) :|: z' = x, y >= 0, x >= 0, z'' = x, z = y
   g1(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   g2(z, z', z'') -{ 1 }-> h(x, y) :|: z'' = y, x >= 0, y >= 0, z = x, z' = y
   g2(z, z', z'') -{ 1 }-> h(x, y) :|: y >= 0, x >= 0, z'' = x, z' = y, z = y
   g2(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   h(z, z') -{ 1 }-> x :|: z' = x, x >= 0, z = x
   h(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1


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

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

   h(z, z') -{ 1 }-> x :|: z' = x, x >= 0, z = x
   h(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   g1(z, z', z'') -{ 1 }-> h(x, y) :|: z' = x, z'' = y, x >= 0, y >= 0, z = x
   g1(z, z', z'') -{ 1 }-> h(x, y) :|: z' = x, y >= 0, x >= 0, z'' = x, z = y
   g1(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   g2(z, z', z'') -{ 1 }-> h(x, y) :|: z'' = y, x >= 0, y >= 0, z = x, z' = y
   g2(z, z', z'') -{ 1 }-> h(x, y) :|: y >= 0, x >= 0, z'' = x, z' = y, z = y
   g2(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0

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

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

   encArg(z) -{ 0 }-> h(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> g2(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> g1(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_f(z, z') -{ 0 }-> f(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2
   encode_f(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   encode_g1(z, z', z'') -{ 0 }-> g1(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, x_3 >= 0, x_2 >= 0, z = x_1, z' = x_2, z'' = x_3
   encode_g1(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   encode_g2(z, z', z'') -{ 0 }-> g2(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, x_3 >= 0, x_2 >= 0, z = x_1, z' = x_2, z'' = x_3
   encode_g2(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   encode_h(z, z') -{ 0 }-> h(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2
   encode_h(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   f(z, z') -{ 2 }-> h(x', y') :|: x >= 0, y >= 0, z = x, z' = y, x = x', y = y', x' >= 0, y' >= 0
   f(z, z') -{ 2 }-> h(x', y') :|: x >= 0, y >= 0, z = x, z' = y, x = x', y' >= 0, x' >= 0, y = x', x = y'
   f(z, z') -{ 2 }-> h(x', y') :|: x >= 0, y >= 0, z = x, z' = y, y' >= 0, x' >= 0, y = x', y = y', x = y'
   f(z, z') -{ 1 }-> 0 :|: x >= 0, y >= 0, z = x, z' = y, v0 >= 0, y = v2, v1 >= 0, x = v0, x = v1, v2 >= 0
   f(z, z') -{ 1 }-> 0 :|: x >= 0, y >= 0, z = x, z' = y, v0 >= 0, x = v2, v1 >= 0, y = v0, x = v1, v2 >= 0
   f(z, z') -{ 1 }-> 0 :|: x >= 0, y >= 0, z = x, z' = y, v0 >= 0, y = v2, v1 >= 0, x = v0, y = v1, v2 >= 0
   f(z, z') -{ 1 }-> 0 :|: x >= 0, y >= 0, z = x, z' = y, v0 >= 0, x = v2, v1 >= 0, y = v0, y = v1, v2 >= 0
   g1(z, z', z'') -{ 2 }-> x' :|: z' = x, z'' = y, x >= 0, y >= 0, z = x, y = x', x' >= 0, x = x'
   g1(z, z', z'') -{ 2 }-> x' :|: z' = x, y >= 0, x >= 0, z'' = x, z = y, y = x', x' >= 0, x = x'
   g1(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   g1(z, z', z'') -{ 1 }-> 0 :|: z' = x, z'' = y, x >= 0, y >= 0, z = x, v0 >= 0, v1 >= 0, x = v0, y = v1
   g1(z, z', z'') -{ 1 }-> 0 :|: z' = x, y >= 0, x >= 0, z'' = x, z = y, v0 >= 0, v1 >= 0, x = v0, y = v1
   g2(z, z', z'') -{ 2 }-> x' :|: z'' = y, x >= 0, y >= 0, z = x, z' = y, y = x', x' >= 0, x = x'
   g2(z, z', z'') -{ 2 }-> x' :|: y >= 0, x >= 0, z'' = x, z' = y, z = y, y = x', x' >= 0, x = x'
   g2(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   g2(z, z', z'') -{ 1 }-> 0 :|: z'' = y, x >= 0, y >= 0, z = x, z' = y, v0 >= 0, v1 >= 0, x = v0, y = v1
   g2(z, z', z'') -{ 1 }-> 0 :|: y >= 0, x >= 0, z'' = x, z' = y, z = y, v0 >= 0, v1 >= 0, x = v0, y = v1
   h(z, z') -{ 1 }-> x :|: z' = x, x >= 0, z = x
   h(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1


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

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

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

   encArg(z) -{ 0 }-> h(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> g2(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> g1(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encode_f(z, z') -{ 0 }-> f(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_g1(z, z', z'') -{ 0 }-> g1(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_g1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g2(z, z', z'') -{ 0 }-> g2(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_g2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_h(z, z') -{ 0 }-> h(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   f(z, z') -{ 2 }-> h(z, z) :|: z >= 0, z' >= 0, z' = z
   f(z, z') -{ 2 }-> h(z, z') :|: z >= 0, z' >= 0
   f(z, z') -{ 2 }-> h(z', z') :|: z >= 0, z' >= 0, z = z'
   f(z, z') -{ 1 }-> 0 :|: z >= 0, z' >= 0
   g1(z, z', z'') -{ 2 }-> z :|: z >= 0, z' >= 0, z'' = z', z' = z
   g1(z, z', z'') -{ 2 }-> z'' :|: z' >= 0, z'' >= 0, z = z', z' = z''
   g1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g1(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' >= 0, z = z'
   g1(z, z', z'') -{ 1 }-> 0 :|: z >= 0, z' >= 0, z'' = z'
   g2(z, z', z'') -{ 2 }-> z' :|: z' >= 0, z'' >= 0, z = z', z'' = z'
   g2(z, z', z'') -{ 2 }-> z'' :|: z >= 0, z'' >= 0, z' = z'', z = z''
   g2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g2(z, z', z'') -{ 1 }-> 0 :|: z >= 0, z'' >= 0, z' = z''
   g2(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' >= 0, z = z'
   h(z, z') -{ 1 }-> z' :|: z' >= 0, z = z'
   h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0


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

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

   { g2 }
   { h }
   { g1 }
   { f }
   { encArg }
   { encode_g2 }
   { encode_g1 }
   { encode_h }
   { encode_f }

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

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

   encArg(z) -{ 0 }-> h(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> g2(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> g1(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encode_f(z, z') -{ 0 }-> f(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_g1(z, z', z'') -{ 0 }-> g1(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_g1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g2(z, z', z'') -{ 0 }-> g2(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_g2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_h(z, z') -{ 0 }-> h(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   f(z, z') -{ 2 }-> h(z, z) :|: z >= 0, z' >= 0, z' = z
   f(z, z') -{ 2 }-> h(z, z') :|: z >= 0, z' >= 0
   f(z, z') -{ 2 }-> h(z', z') :|: z >= 0, z' >= 0, z = z'
   f(z, z') -{ 1 }-> 0 :|: z >= 0, z' >= 0
   g1(z, z', z'') -{ 2 }-> z :|: z >= 0, z' >= 0, z'' = z', z' = z
   g1(z, z', z'') -{ 2 }-> z'' :|: z' >= 0, z'' >= 0, z = z', z' = z''
   g1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g1(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' >= 0, z = z'
   g1(z, z', z'') -{ 1 }-> 0 :|: z >= 0, z' >= 0, z'' = z'
   g2(z, z', z'') -{ 2 }-> z' :|: z' >= 0, z'' >= 0, z = z', z'' = z'
   g2(z, z', z'') -{ 2 }-> z'' :|: z >= 0, z'' >= 0, z' = z'', z = z''
   g2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g2(z, z', z'') -{ 1 }-> 0 :|: z >= 0, z'' >= 0, z' = z''
   g2(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' >= 0, z = z'
   h(z, z') -{ 1 }-> z' :|: z' >= 0, z = z'
   h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0

Function symbols to be analyzed: {g2}, {h}, {g1}, {f}, {encArg}, {encode_g2}, {encode_g1}, {encode_h}, {encode_f}

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

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

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

   encArg(z) -{ 0 }-> h(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> g2(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> g1(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encode_f(z, z') -{ 0 }-> f(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_g1(z, z', z'') -{ 0 }-> g1(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_g1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g2(z, z', z'') -{ 0 }-> g2(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_g2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_h(z, z') -{ 0 }-> h(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   f(z, z') -{ 2 }-> h(z, z) :|: z >= 0, z' >= 0, z' = z
   f(z, z') -{ 2 }-> h(z, z') :|: z >= 0, z' >= 0
   f(z, z') -{ 2 }-> h(z', z') :|: z >= 0, z' >= 0, z = z'
   f(z, z') -{ 1 }-> 0 :|: z >= 0, z' >= 0
   g1(z, z', z'') -{ 2 }-> z :|: z >= 0, z' >= 0, z'' = z', z' = z
   g1(z, z', z'') -{ 2 }-> z'' :|: z' >= 0, z'' >= 0, z = z', z' = z''
   g1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g1(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' >= 0, z = z'
   g1(z, z', z'') -{ 1 }-> 0 :|: z >= 0, z' >= 0, z'' = z'
   g2(z, z', z'') -{ 2 }-> z' :|: z' >= 0, z'' >= 0, z = z', z'' = z'
   g2(z, z', z'') -{ 2 }-> z'' :|: z >= 0, z'' >= 0, z' = z'', z = z''
   g2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g2(z, z', z'') -{ 1 }-> 0 :|: z >= 0, z'' >= 0, z' = z''
   g2(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' >= 0, z = z'
   h(z, z') -{ 1 }-> z' :|: z' >= 0, z = z'
   h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0

Function symbols to be analyzed: {g2}, {h}, {g1}, {f}, {encArg}, {encode_g2}, {encode_g1}, {encode_h}, {encode_f}

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

(23) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: g2
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: z''

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

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

   encArg(z) -{ 0 }-> h(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> g2(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> g1(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encode_f(z, z') -{ 0 }-> f(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_g1(z, z', z'') -{ 0 }-> g1(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_g1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g2(z, z', z'') -{ 0 }-> g2(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_g2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_h(z, z') -{ 0 }-> h(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   f(z, z') -{ 2 }-> h(z, z) :|: z >= 0, z' >= 0, z' = z
   f(z, z') -{ 2 }-> h(z, z') :|: z >= 0, z' >= 0
   f(z, z') -{ 2 }-> h(z', z') :|: z >= 0, z' >= 0, z = z'
   f(z, z') -{ 1 }-> 0 :|: z >= 0, z' >= 0
   g1(z, z', z'') -{ 2 }-> z :|: z >= 0, z' >= 0, z'' = z', z' = z
   g1(z, z', z'') -{ 2 }-> z'' :|: z' >= 0, z'' >= 0, z = z', z' = z''
   g1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g1(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' >= 0, z = z'
   g1(z, z', z'') -{ 1 }-> 0 :|: z >= 0, z' >= 0, z'' = z'
   g2(z, z', z'') -{ 2 }-> z' :|: z' >= 0, z'' >= 0, z = z', z'' = z'
   g2(z, z', z'') -{ 2 }-> z'' :|: z >= 0, z'' >= 0, z' = z'', z = z''
   g2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g2(z, z', z'') -{ 1 }-> 0 :|: z >= 0, z'' >= 0, z' = z''
   g2(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' >= 0, z = z'
   h(z, z') -{ 1 }-> z' :|: z' >= 0, z = z'
   h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0

Function symbols to be analyzed: {g2}, {h}, {g1}, {f}, {encArg}, {encode_g2}, {encode_g1}, {encode_h}, {encode_f}
Previous analysis results are:
  g2: runtime: ?, size: O(n^1) [z'']

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

(25) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: g2
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 2

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

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

   encArg(z) -{ 0 }-> h(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> g2(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> g1(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encode_f(z, z') -{ 0 }-> f(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_g1(z, z', z'') -{ 0 }-> g1(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_g1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g2(z, z', z'') -{ 0 }-> g2(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_g2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_h(z, z') -{ 0 }-> h(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   f(z, z') -{ 2 }-> h(z, z) :|: z >= 0, z' >= 0, z' = z
   f(z, z') -{ 2 }-> h(z, z') :|: z >= 0, z' >= 0
   f(z, z') -{ 2 }-> h(z', z') :|: z >= 0, z' >= 0, z = z'
   f(z, z') -{ 1 }-> 0 :|: z >= 0, z' >= 0
   g1(z, z', z'') -{ 2 }-> z :|: z >= 0, z' >= 0, z'' = z', z' = z
   g1(z, z', z'') -{ 2 }-> z'' :|: z' >= 0, z'' >= 0, z = z', z' = z''
   g1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g1(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' >= 0, z = z'
   g1(z, z', z'') -{ 1 }-> 0 :|: z >= 0, z' >= 0, z'' = z'
   g2(z, z', z'') -{ 2 }-> z' :|: z' >= 0, z'' >= 0, z = z', z'' = z'
   g2(z, z', z'') -{ 2 }-> z'' :|: z >= 0, z'' >= 0, z' = z'', z = z''
   g2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g2(z, z', z'') -{ 1 }-> 0 :|: z >= 0, z'' >= 0, z' = z''
   g2(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' >= 0, z = z'
   h(z, z') -{ 1 }-> z' :|: z' >= 0, z = z'
   h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0

Function symbols to be analyzed: {h}, {g1}, {f}, {encArg}, {encode_g2}, {encode_g1}, {encode_h}, {encode_f}
Previous analysis results are:
  g2: runtime: O(1) [2], size: O(n^1) [z'']

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

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

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

   encArg(z) -{ 0 }-> h(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> g2(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> g1(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encode_f(z, z') -{ 0 }-> f(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_g1(z, z', z'') -{ 0 }-> g1(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_g1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g2(z, z', z'') -{ 0 }-> g2(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_g2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_h(z, z') -{ 0 }-> h(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   f(z, z') -{ 2 }-> h(z, z) :|: z >= 0, z' >= 0, z' = z
   f(z, z') -{ 2 }-> h(z, z') :|: z >= 0, z' >= 0
   f(z, z') -{ 2 }-> h(z', z') :|: z >= 0, z' >= 0, z = z'
   f(z, z') -{ 1 }-> 0 :|: z >= 0, z' >= 0
   g1(z, z', z'') -{ 2 }-> z :|: z >= 0, z' >= 0, z'' = z', z' = z
   g1(z, z', z'') -{ 2 }-> z'' :|: z' >= 0, z'' >= 0, z = z', z' = z''
   g1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g1(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' >= 0, z = z'
   g1(z, z', z'') -{ 1 }-> 0 :|: z >= 0, z' >= 0, z'' = z'
   g2(z, z', z'') -{ 2 }-> z' :|: z' >= 0, z'' >= 0, z = z', z'' = z'
   g2(z, z', z'') -{ 2 }-> z'' :|: z >= 0, z'' >= 0, z' = z'', z = z''
   g2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g2(z, z', z'') -{ 1 }-> 0 :|: z >= 0, z'' >= 0, z' = z''
   g2(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' >= 0, z = z'
   h(z, z') -{ 1 }-> z' :|: z' >= 0, z = z'
   h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0

Function symbols to be analyzed: {h}, {g1}, {f}, {encArg}, {encode_g2}, {encode_g1}, {encode_h}, {encode_f}
Previous analysis results are:
  g2: runtime: O(1) [2], size: O(n^1) [z'']

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

(29) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   encArg(z) -{ 0 }-> h(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> g2(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> g1(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encode_f(z, z') -{ 0 }-> f(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_g1(z, z', z'') -{ 0 }-> g1(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_g1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g2(z, z', z'') -{ 0 }-> g2(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_g2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_h(z, z') -{ 0 }-> h(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   f(z, z') -{ 2 }-> h(z, z) :|: z >= 0, z' >= 0, z' = z
   f(z, z') -{ 2 }-> h(z, z') :|: z >= 0, z' >= 0
   f(z, z') -{ 2 }-> h(z', z') :|: z >= 0, z' >= 0, z = z'
   f(z, z') -{ 1 }-> 0 :|: z >= 0, z' >= 0
   g1(z, z', z'') -{ 2 }-> z :|: z >= 0, z' >= 0, z'' = z', z' = z
   g1(z, z', z'') -{ 2 }-> z'' :|: z' >= 0, z'' >= 0, z = z', z' = z''
   g1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g1(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' >= 0, z = z'
   g1(z, z', z'') -{ 1 }-> 0 :|: z >= 0, z' >= 0, z'' = z'
   g2(z, z', z'') -{ 2 }-> z' :|: z' >= 0, z'' >= 0, z = z', z'' = z'
   g2(z, z', z'') -{ 2 }-> z'' :|: z >= 0, z'' >= 0, z' = z'', z = z''
   g2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g2(z, z', z'') -{ 1 }-> 0 :|: z >= 0, z'' >= 0, z' = z''
   g2(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' >= 0, z = z'
   h(z, z') -{ 1 }-> z' :|: z' >= 0, z = z'
   h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0

Function symbols to be analyzed: {h}, {g1}, {f}, {encArg}, {encode_g2}, {encode_g1}, {encode_h}, {encode_f}
Previous analysis results are:
  g2: runtime: O(1) [2], size: O(n^1) [z'']
  h: runtime: ?, size: O(n^1) [z']

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

(31) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: h
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 }-> h(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> g2(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> g1(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encode_f(z, z') -{ 0 }-> f(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_g1(z, z', z'') -{ 0 }-> g1(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_g1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g2(z, z', z'') -{ 0 }-> g2(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_g2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_h(z, z') -{ 0 }-> h(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   f(z, z') -{ 2 }-> h(z, z) :|: z >= 0, z' >= 0, z' = z
   f(z, z') -{ 2 }-> h(z, z') :|: z >= 0, z' >= 0
   f(z, z') -{ 2 }-> h(z', z') :|: z >= 0, z' >= 0, z = z'
   f(z, z') -{ 1 }-> 0 :|: z >= 0, z' >= 0
   g1(z, z', z'') -{ 2 }-> z :|: z >= 0, z' >= 0, z'' = z', z' = z
   g1(z, z', z'') -{ 2 }-> z'' :|: z' >= 0, z'' >= 0, z = z', z' = z''
   g1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g1(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' >= 0, z = z'
   g1(z, z', z'') -{ 1 }-> 0 :|: z >= 0, z' >= 0, z'' = z'
   g2(z, z', z'') -{ 2 }-> z' :|: z' >= 0, z'' >= 0, z = z', z'' = z'
   g2(z, z', z'') -{ 2 }-> z'' :|: z >= 0, z'' >= 0, z' = z'', z = z''
   g2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g2(z, z', z'') -{ 1 }-> 0 :|: z >= 0, z'' >= 0, z' = z''
   g2(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' >= 0, z = z'
   h(z, z') -{ 1 }-> z' :|: z' >= 0, z = z'
   h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0

Function symbols to be analyzed: {g1}, {f}, {encArg}, {encode_g2}, {encode_g1}, {encode_h}, {encode_f}
Previous analysis results are:
  g2: runtime: O(1) [2], size: O(n^1) [z'']
  h: runtime: O(1) [1], size: O(n^1) [z']

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

(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 }-> h(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> g2(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> g1(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encode_f(z, z') -{ 0 }-> f(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_g1(z, z', z'') -{ 0 }-> g1(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_g1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g2(z, z', z'') -{ 0 }-> g2(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_g2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_h(z, z') -{ 0 }-> h(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   f(z, z') -{ 3 }-> s :|: s >= 0, s <= z', z >= 0, z' >= 0
   f(z, z') -{ 3 }-> s' :|: s' >= 0, s' <= z, z >= 0, z' >= 0, z' = z
   f(z, z') -{ 3 }-> s'' :|: s'' >= 0, s'' <= z', z >= 0, z' >= 0, z = z'
   f(z, z') -{ 1 }-> 0 :|: z >= 0, z' >= 0
   g1(z, z', z'') -{ 2 }-> z :|: z >= 0, z' >= 0, z'' = z', z' = z
   g1(z, z', z'') -{ 2 }-> z'' :|: z' >= 0, z'' >= 0, z = z', z' = z''
   g1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g1(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' >= 0, z = z'
   g1(z, z', z'') -{ 1 }-> 0 :|: z >= 0, z' >= 0, z'' = z'
   g2(z, z', z'') -{ 2 }-> z' :|: z' >= 0, z'' >= 0, z = z', z'' = z'
   g2(z, z', z'') -{ 2 }-> z'' :|: z >= 0, z'' >= 0, z' = z'', z = z''
   g2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g2(z, z', z'') -{ 1 }-> 0 :|: z >= 0, z'' >= 0, z' = z''
   g2(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' >= 0, z = z'
   h(z, z') -{ 1 }-> z' :|: z' >= 0, z = z'
   h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0

Function symbols to be analyzed: {g1}, {f}, {encArg}, {encode_g2}, {encode_g1}, {encode_h}, {encode_f}
Previous analysis results are:
  g2: runtime: O(1) [2], size: O(n^1) [z'']
  h: runtime: O(1) [1], size: O(n^1) [z']

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

(35) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: g1
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: z''

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

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

   encArg(z) -{ 0 }-> h(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> g2(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> g1(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encode_f(z, z') -{ 0 }-> f(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_g1(z, z', z'') -{ 0 }-> g1(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_g1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g2(z, z', z'') -{ 0 }-> g2(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_g2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_h(z, z') -{ 0 }-> h(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   f(z, z') -{ 3 }-> s :|: s >= 0, s <= z', z >= 0, z' >= 0
   f(z, z') -{ 3 }-> s' :|: s' >= 0, s' <= z, z >= 0, z' >= 0, z' = z
   f(z, z') -{ 3 }-> s'' :|: s'' >= 0, s'' <= z', z >= 0, z' >= 0, z = z'
   f(z, z') -{ 1 }-> 0 :|: z >= 0, z' >= 0
   g1(z, z', z'') -{ 2 }-> z :|: z >= 0, z' >= 0, z'' = z', z' = z
   g1(z, z', z'') -{ 2 }-> z'' :|: z' >= 0, z'' >= 0, z = z', z' = z''
   g1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g1(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' >= 0, z = z'
   g1(z, z', z'') -{ 1 }-> 0 :|: z >= 0, z' >= 0, z'' = z'
   g2(z, z', z'') -{ 2 }-> z' :|: z' >= 0, z'' >= 0, z = z', z'' = z'
   g2(z, z', z'') -{ 2 }-> z'' :|: z >= 0, z'' >= 0, z' = z'', z = z''
   g2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g2(z, z', z'') -{ 1 }-> 0 :|: z >= 0, z'' >= 0, z' = z''
   g2(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' >= 0, z = z'
   h(z, z') -{ 1 }-> z' :|: z' >= 0, z = z'
   h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0

Function symbols to be analyzed: {g1}, {f}, {encArg}, {encode_g2}, {encode_g1}, {encode_h}, {encode_f}
Previous analysis results are:
  g2: runtime: O(1) [2], size: O(n^1) [z'']
  h: runtime: O(1) [1], size: O(n^1) [z']
  g1: runtime: ?, size: O(n^1) [z'']

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

(37) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: g1
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 2

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

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

   encArg(z) -{ 0 }-> h(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> g2(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> g1(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encode_f(z, z') -{ 0 }-> f(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_g1(z, z', z'') -{ 0 }-> g1(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_g1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g2(z, z', z'') -{ 0 }-> g2(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_g2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_h(z, z') -{ 0 }-> h(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   f(z, z') -{ 3 }-> s :|: s >= 0, s <= z', z >= 0, z' >= 0
   f(z, z') -{ 3 }-> s' :|: s' >= 0, s' <= z, z >= 0, z' >= 0, z' = z
   f(z, z') -{ 3 }-> s'' :|: s'' >= 0, s'' <= z', z >= 0, z' >= 0, z = z'
   f(z, z') -{ 1 }-> 0 :|: z >= 0, z' >= 0
   g1(z, z', z'') -{ 2 }-> z :|: z >= 0, z' >= 0, z'' = z', z' = z
   g1(z, z', z'') -{ 2 }-> z'' :|: z' >= 0, z'' >= 0, z = z', z' = z''
   g1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g1(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' >= 0, z = z'
   g1(z, z', z'') -{ 1 }-> 0 :|: z >= 0, z' >= 0, z'' = z'
   g2(z, z', z'') -{ 2 }-> z' :|: z' >= 0, z'' >= 0, z = z', z'' = z'
   g2(z, z', z'') -{ 2 }-> z'' :|: z >= 0, z'' >= 0, z' = z'', z = z''
   g2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g2(z, z', z'') -{ 1 }-> 0 :|: z >= 0, z'' >= 0, z' = z''
   g2(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' >= 0, z = z'
   h(z, z') -{ 1 }-> z' :|: z' >= 0, z = z'
   h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0

Function symbols to be analyzed: {f}, {encArg}, {encode_g2}, {encode_g1}, {encode_h}, {encode_f}
Previous analysis results are:
  g2: runtime: O(1) [2], size: O(n^1) [z'']
  h: runtime: O(1) [1], size: O(n^1) [z']
  g1: runtime: O(1) [2], size: O(n^1) [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 }-> h(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> g2(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> g1(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encode_f(z, z') -{ 0 }-> f(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_g1(z, z', z'') -{ 0 }-> g1(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_g1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g2(z, z', z'') -{ 0 }-> g2(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_g2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_h(z, z') -{ 0 }-> h(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   f(z, z') -{ 3 }-> s :|: s >= 0, s <= z', z >= 0, z' >= 0
   f(z, z') -{ 3 }-> s' :|: s' >= 0, s' <= z, z >= 0, z' >= 0, z' = z
   f(z, z') -{ 3 }-> s'' :|: s'' >= 0, s'' <= z', z >= 0, z' >= 0, z = z'
   f(z, z') -{ 1 }-> 0 :|: z >= 0, z' >= 0
   g1(z, z', z'') -{ 2 }-> z :|: z >= 0, z' >= 0, z'' = z', z' = z
   g1(z, z', z'') -{ 2 }-> z'' :|: z' >= 0, z'' >= 0, z = z', z' = z''
   g1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g1(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' >= 0, z = z'
   g1(z, z', z'') -{ 1 }-> 0 :|: z >= 0, z' >= 0, z'' = z'
   g2(z, z', z'') -{ 2 }-> z' :|: z' >= 0, z'' >= 0, z = z', z'' = z'
   g2(z, z', z'') -{ 2 }-> z'' :|: z >= 0, z'' >= 0, z' = z'', z = z''
   g2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g2(z, z', z'') -{ 1 }-> 0 :|: z >= 0, z'' >= 0, z' = z''
   g2(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' >= 0, z = z'
   h(z, z') -{ 1 }-> z' :|: z' >= 0, z = z'
   h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0

Function symbols to be analyzed: {f}, {encArg}, {encode_g2}, {encode_g1}, {encode_h}, {encode_f}
Previous analysis results are:
  g2: runtime: O(1) [2], size: O(n^1) [z'']
  h: runtime: O(1) [1], size: O(n^1) [z']
  g1: runtime: O(1) [2], size: O(n^1) [z'']

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

(41) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   encArg(z) -{ 0 }-> h(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> g2(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> g1(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encode_f(z, z') -{ 0 }-> f(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_g1(z, z', z'') -{ 0 }-> g1(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_g1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g2(z, z', z'') -{ 0 }-> g2(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_g2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_h(z, z') -{ 0 }-> h(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   f(z, z') -{ 3 }-> s :|: s >= 0, s <= z', z >= 0, z' >= 0
   f(z, z') -{ 3 }-> s' :|: s' >= 0, s' <= z, z >= 0, z' >= 0, z' = z
   f(z, z') -{ 3 }-> s'' :|: s'' >= 0, s'' <= z', z >= 0, z' >= 0, z = z'
   f(z, z') -{ 1 }-> 0 :|: z >= 0, z' >= 0
   g1(z, z', z'') -{ 2 }-> z :|: z >= 0, z' >= 0, z'' = z', z' = z
   g1(z, z', z'') -{ 2 }-> z'' :|: z' >= 0, z'' >= 0, z = z', z' = z''
   g1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g1(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' >= 0, z = z'
   g1(z, z', z'') -{ 1 }-> 0 :|: z >= 0, z' >= 0, z'' = z'
   g2(z, z', z'') -{ 2 }-> z' :|: z' >= 0, z'' >= 0, z = z', z'' = z'
   g2(z, z', z'') -{ 2 }-> z'' :|: z >= 0, z'' >= 0, z' = z'', z = z''
   g2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g2(z, z', z'') -{ 1 }-> 0 :|: z >= 0, z'' >= 0, z' = z''
   g2(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' >= 0, z = z'
   h(z, z') -{ 1 }-> z' :|: z' >= 0, z = z'
   h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0

Function symbols to be analyzed: {f}, {encArg}, {encode_g2}, {encode_g1}, {encode_h}, {encode_f}
Previous analysis results are:
  g2: runtime: O(1) [2], size: O(n^1) [z'']
  h: runtime: O(1) [1], size: O(n^1) [z']
  g1: runtime: O(1) [2], size: O(n^1) [z'']
  f: runtime: ?, size: O(n^1) [z']

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

(43) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   encArg(z) -{ 0 }-> h(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> g2(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> g1(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encode_f(z, z') -{ 0 }-> f(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_g1(z, z', z'') -{ 0 }-> g1(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_g1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g2(z, z', z'') -{ 0 }-> g2(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_g2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_h(z, z') -{ 0 }-> h(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   f(z, z') -{ 3 }-> s :|: s >= 0, s <= z', z >= 0, z' >= 0
   f(z, z') -{ 3 }-> s' :|: s' >= 0, s' <= z, z >= 0, z' >= 0, z' = z
   f(z, z') -{ 3 }-> s'' :|: s'' >= 0, s'' <= z', z >= 0, z' >= 0, z = z'
   f(z, z') -{ 1 }-> 0 :|: z >= 0, z' >= 0
   g1(z, z', z'') -{ 2 }-> z :|: z >= 0, z' >= 0, z'' = z', z' = z
   g1(z, z', z'') -{ 2 }-> z'' :|: z' >= 0, z'' >= 0, z = z', z' = z''
   g1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g1(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' >= 0, z = z'
   g1(z, z', z'') -{ 1 }-> 0 :|: z >= 0, z' >= 0, z'' = z'
   g2(z, z', z'') -{ 2 }-> z' :|: z' >= 0, z'' >= 0, z = z', z'' = z'
   g2(z, z', z'') -{ 2 }-> z'' :|: z >= 0, z'' >= 0, z' = z'', z = z''
   g2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g2(z, z', z'') -{ 1 }-> 0 :|: z >= 0, z'' >= 0, z' = z''
   g2(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' >= 0, z = z'
   h(z, z') -{ 1 }-> z' :|: z' >= 0, z = z'
   h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0

Function symbols to be analyzed: {encArg}, {encode_g2}, {encode_g1}, {encode_h}, {encode_f}
Previous analysis results are:
  g2: runtime: O(1) [2], size: O(n^1) [z'']
  h: runtime: O(1) [1], size: O(n^1) [z']
  g1: runtime: O(1) [2], size: O(n^1) [z'']
  f: runtime: O(1) [3], size: O(n^1) [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 }-> h(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> g2(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> g1(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encode_f(z, z') -{ 0 }-> f(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_g1(z, z', z'') -{ 0 }-> g1(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_g1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g2(z, z', z'') -{ 0 }-> g2(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_g2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_h(z, z') -{ 0 }-> h(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   f(z, z') -{ 3 }-> s :|: s >= 0, s <= z', z >= 0, z' >= 0
   f(z, z') -{ 3 }-> s' :|: s' >= 0, s' <= z, z >= 0, z' >= 0, z' = z
   f(z, z') -{ 3 }-> s'' :|: s'' >= 0, s'' <= z', z >= 0, z' >= 0, z = z'
   f(z, z') -{ 1 }-> 0 :|: z >= 0, z' >= 0
   g1(z, z', z'') -{ 2 }-> z :|: z >= 0, z' >= 0, z'' = z', z' = z
   g1(z, z', z'') -{ 2 }-> z'' :|: z' >= 0, z'' >= 0, z = z', z' = z''
   g1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g1(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' >= 0, z = z'
   g1(z, z', z'') -{ 1 }-> 0 :|: z >= 0, z' >= 0, z'' = z'
   g2(z, z', z'') -{ 2 }-> z' :|: z' >= 0, z'' >= 0, z = z', z'' = z'
   g2(z, z', z'') -{ 2 }-> z'' :|: z >= 0, z'' >= 0, z' = z'', z = z''
   g2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g2(z, z', z'') -{ 1 }-> 0 :|: z >= 0, z'' >= 0, z' = z''
   g2(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' >= 0, z = z'
   h(z, z') -{ 1 }-> z' :|: z' >= 0, z = z'
   h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0

Function symbols to be analyzed: {encArg}, {encode_g2}, {encode_g1}, {encode_h}, {encode_f}
Previous analysis results are:
  g2: runtime: O(1) [2], size: O(n^1) [z'']
  h: runtime: O(1) [1], size: O(n^1) [z']
  g1: runtime: O(1) [2], size: O(n^1) [z'']
  f: runtime: O(1) [3], size: O(n^1) [z']

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

(47) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   encArg(z) -{ 0 }-> h(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> g2(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> g1(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encode_f(z, z') -{ 0 }-> f(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_g1(z, z', z'') -{ 0 }-> g1(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_g1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g2(z, z', z'') -{ 0 }-> g2(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_g2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_h(z, z') -{ 0 }-> h(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   f(z, z') -{ 3 }-> s :|: s >= 0, s <= z', z >= 0, z' >= 0
   f(z, z') -{ 3 }-> s' :|: s' >= 0, s' <= z, z >= 0, z' >= 0, z' = z
   f(z, z') -{ 3 }-> s'' :|: s'' >= 0, s'' <= z', z >= 0, z' >= 0, z = z'
   f(z, z') -{ 1 }-> 0 :|: z >= 0, z' >= 0
   g1(z, z', z'') -{ 2 }-> z :|: z >= 0, z' >= 0, z'' = z', z' = z
   g1(z, z', z'') -{ 2 }-> z'' :|: z' >= 0, z'' >= 0, z = z', z' = z''
   g1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g1(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' >= 0, z = z'
   g1(z, z', z'') -{ 1 }-> 0 :|: z >= 0, z' >= 0, z'' = z'
   g2(z, z', z'') -{ 2 }-> z' :|: z' >= 0, z'' >= 0, z = z', z'' = z'
   g2(z, z', z'') -{ 2 }-> z'' :|: z >= 0, z'' >= 0, z' = z'', z = z''
   g2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g2(z, z', z'') -{ 1 }-> 0 :|: z >= 0, z'' >= 0, z' = z''
   g2(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' >= 0, z = z'
   h(z, z') -{ 1 }-> z' :|: z' >= 0, z = z'
   h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0

Function symbols to be analyzed: {encArg}, {encode_g2}, {encode_g1}, {encode_h}, {encode_f}
Previous analysis results are:
  g2: runtime: O(1) [2], size: O(n^1) [z'']
  h: runtime: O(1) [1], size: O(n^1) [z']
  g1: runtime: O(1) [2], size: O(n^1) [z'']
  f: runtime: O(1) [3], size: O(n^1) [z']
  encArg: runtime: ?, size: O(1) [0]

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

(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: 3*z

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

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

   encArg(z) -{ 0 }-> h(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> g2(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> g1(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encode_f(z, z') -{ 0 }-> f(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_g1(z, z', z'') -{ 0 }-> g1(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_g1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g2(z, z', z'') -{ 0 }-> g2(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_g2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_h(z, z') -{ 0 }-> h(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   f(z, z') -{ 3 }-> s :|: s >= 0, s <= z', z >= 0, z' >= 0
   f(z, z') -{ 3 }-> s' :|: s' >= 0, s' <= z, z >= 0, z' >= 0, z' = z
   f(z, z') -{ 3 }-> s'' :|: s'' >= 0, s'' <= z', z >= 0, z' >= 0, z = z'
   f(z, z') -{ 1 }-> 0 :|: z >= 0, z' >= 0
   g1(z, z', z'') -{ 2 }-> z :|: z >= 0, z' >= 0, z'' = z', z' = z
   g1(z, z', z'') -{ 2 }-> z'' :|: z' >= 0, z'' >= 0, z = z', z' = z''
   g1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g1(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' >= 0, z = z'
   g1(z, z', z'') -{ 1 }-> 0 :|: z >= 0, z' >= 0, z'' = z'
   g2(z, z', z'') -{ 2 }-> z' :|: z' >= 0, z'' >= 0, z = z', z'' = z'
   g2(z, z', z'') -{ 2 }-> z'' :|: z >= 0, z'' >= 0, z' = z'', z = z''
   g2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g2(z, z', z'') -{ 1 }-> 0 :|: z >= 0, z'' >= 0, z' = z''
   g2(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' >= 0, z = z'
   h(z, z') -{ 1 }-> z' :|: z' >= 0, z = z'
   h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0

Function symbols to be analyzed: {encode_g2}, {encode_g1}, {encode_h}, {encode_f}
Previous analysis results are:
  g2: runtime: O(1) [2], size: O(n^1) [z'']
  h: runtime: O(1) [1], size: O(n^1) [z']
  g1: runtime: O(1) [2], size: O(n^1) [z'']
  f: runtime: O(1) [3], size: O(n^1) [z']
  encArg: runtime: O(n^1) [3*z], size: O(1) [0]

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

(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) -{ 2 + 3*x_1 + 3*x_2 + 3*x_3 }-> s16 :|: s13 >= 0, s13 <= 0, s14 >= 0, s14 <= 0, s15 >= 0, s15 <= 0, s16 >= 0, s16 <= s15, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 2 + 3*x_1 + 3*x_2 + 3*x_3 }-> s24 :|: s21 >= 0, s21 <= 0, s22 >= 0, s22 <= 0, s23 >= 0, s23 <= 0, s24 >= 0, s24 <= s23, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 3 + 3*x_1 + 3*x_2 }-> s3 :|: s1 >= 0, s1 <= 0, s2 >= 0, s2 <= 0, s3 >= 0, s3 <= s2, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 1 + 3*x_1 + 3*x_2 }-> s9 :|: s7 >= 0, s7 <= 0, s8 >= 0, s8 <= 0, s9 >= 0, s9 <= s8, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encode_f(z, z') -{ 3 + 3*z + 3*z' }-> s6 :|: s4 >= 0, s4 <= 0, s5 >= 0, s5 <= 0, s6 >= 0, s6 <= s5, z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_g1(z, z', z'') -{ 2 + 3*z + 3*z' + 3*z'' }-> s20 :|: s17 >= 0, s17 <= 0, s18 >= 0, s18 <= 0, s19 >= 0, s19 <= 0, s20 >= 0, s20 <= s19, z >= 0, z'' >= 0, z' >= 0
   encode_g1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g2(z, z', z'') -{ 2 + 3*z + 3*z' + 3*z'' }-> s28 :|: s25 >= 0, s25 <= 0, s26 >= 0, s26 <= 0, s27 >= 0, s27 <= 0, s28 >= 0, s28 <= s27, z >= 0, z'' >= 0, z' >= 0
   encode_g2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_h(z, z') -{ 1 + 3*z + 3*z' }-> s12 :|: s10 >= 0, s10 <= 0, s11 >= 0, s11 <= 0, s12 >= 0, s12 <= s11, z >= 0, z' >= 0
   encode_h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   f(z, z') -{ 3 }-> s :|: s >= 0, s <= z', z >= 0, z' >= 0
   f(z, z') -{ 3 }-> s' :|: s' >= 0, s' <= z, z >= 0, z' >= 0, z' = z
   f(z, z') -{ 3 }-> s'' :|: s'' >= 0, s'' <= z', z >= 0, z' >= 0, z = z'
   f(z, z') -{ 1 }-> 0 :|: z >= 0, z' >= 0
   g1(z, z', z'') -{ 2 }-> z :|: z >= 0, z' >= 0, z'' = z', z' = z
   g1(z, z', z'') -{ 2 }-> z'' :|: z' >= 0, z'' >= 0, z = z', z' = z''
   g1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g1(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' >= 0, z = z'
   g1(z, z', z'') -{ 1 }-> 0 :|: z >= 0, z' >= 0, z'' = z'
   g2(z, z', z'') -{ 2 }-> z' :|: z' >= 0, z'' >= 0, z = z', z'' = z'
   g2(z, z', z'') -{ 2 }-> z'' :|: z >= 0, z'' >= 0, z' = z'', z = z''
   g2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g2(z, z', z'') -{ 1 }-> 0 :|: z >= 0, z'' >= 0, z' = z''
   g2(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' >= 0, z = z'
   h(z, z') -{ 1 }-> z' :|: z' >= 0, z = z'
   h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0

Function symbols to be analyzed: {encode_g2}, {encode_g1}, {encode_h}, {encode_f}
Previous analysis results are:
  g2: runtime: O(1) [2], size: O(n^1) [z'']
  h: runtime: O(1) [1], size: O(n^1) [z']
  g1: runtime: O(1) [2], size: O(n^1) [z'']
  f: runtime: O(1) [3], size: O(n^1) [z']
  encArg: runtime: O(n^1) [3*z], size: O(1) [0]

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

(53) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: encode_g2
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 0

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

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

   encArg(z) -{ 2 + 3*x_1 + 3*x_2 + 3*x_3 }-> s16 :|: s13 >= 0, s13 <= 0, s14 >= 0, s14 <= 0, s15 >= 0, s15 <= 0, s16 >= 0, s16 <= s15, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 2 + 3*x_1 + 3*x_2 + 3*x_3 }-> s24 :|: s21 >= 0, s21 <= 0, s22 >= 0, s22 <= 0, s23 >= 0, s23 <= 0, s24 >= 0, s24 <= s23, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 3 + 3*x_1 + 3*x_2 }-> s3 :|: s1 >= 0, s1 <= 0, s2 >= 0, s2 <= 0, s3 >= 0, s3 <= s2, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 1 + 3*x_1 + 3*x_2 }-> s9 :|: s7 >= 0, s7 <= 0, s8 >= 0, s8 <= 0, s9 >= 0, s9 <= s8, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encode_f(z, z') -{ 3 + 3*z + 3*z' }-> s6 :|: s4 >= 0, s4 <= 0, s5 >= 0, s5 <= 0, s6 >= 0, s6 <= s5, z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_g1(z, z', z'') -{ 2 + 3*z + 3*z' + 3*z'' }-> s20 :|: s17 >= 0, s17 <= 0, s18 >= 0, s18 <= 0, s19 >= 0, s19 <= 0, s20 >= 0, s20 <= s19, z >= 0, z'' >= 0, z' >= 0
   encode_g1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g2(z, z', z'') -{ 2 + 3*z + 3*z' + 3*z'' }-> s28 :|: s25 >= 0, s25 <= 0, s26 >= 0, s26 <= 0, s27 >= 0, s27 <= 0, s28 >= 0, s28 <= s27, z >= 0, z'' >= 0, z' >= 0
   encode_g2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_h(z, z') -{ 1 + 3*z + 3*z' }-> s12 :|: s10 >= 0, s10 <= 0, s11 >= 0, s11 <= 0, s12 >= 0, s12 <= s11, z >= 0, z' >= 0
   encode_h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   f(z, z') -{ 3 }-> s :|: s >= 0, s <= z', z >= 0, z' >= 0
   f(z, z') -{ 3 }-> s' :|: s' >= 0, s' <= z, z >= 0, z' >= 0, z' = z
   f(z, z') -{ 3 }-> s'' :|: s'' >= 0, s'' <= z', z >= 0, z' >= 0, z = z'
   f(z, z') -{ 1 }-> 0 :|: z >= 0, z' >= 0
   g1(z, z', z'') -{ 2 }-> z :|: z >= 0, z' >= 0, z'' = z', z' = z
   g1(z, z', z'') -{ 2 }-> z'' :|: z' >= 0, z'' >= 0, z = z', z' = z''
   g1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g1(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' >= 0, z = z'
   g1(z, z', z'') -{ 1 }-> 0 :|: z >= 0, z' >= 0, z'' = z'
   g2(z, z', z'') -{ 2 }-> z' :|: z' >= 0, z'' >= 0, z = z', z'' = z'
   g2(z, z', z'') -{ 2 }-> z'' :|: z >= 0, z'' >= 0, z' = z'', z = z''
   g2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g2(z, z', z'') -{ 1 }-> 0 :|: z >= 0, z'' >= 0, z' = z''
   g2(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' >= 0, z = z'
   h(z, z') -{ 1 }-> z' :|: z' >= 0, z = z'
   h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0

Function symbols to be analyzed: {encode_g2}, {encode_g1}, {encode_h}, {encode_f}
Previous analysis results are:
  g2: runtime: O(1) [2], size: O(n^1) [z'']
  h: runtime: O(1) [1], size: O(n^1) [z']
  g1: runtime: O(1) [2], size: O(n^1) [z'']
  f: runtime: O(1) [3], size: O(n^1) [z']
  encArg: runtime: O(n^1) [3*z], size: O(1) [0]
  encode_g2: runtime: ?, size: O(1) [0]

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

(55) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: encode_g2
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 2 + 3*z + 3*z' + 3*z''

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

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

   encArg(z) -{ 2 + 3*x_1 + 3*x_2 + 3*x_3 }-> s16 :|: s13 >= 0, s13 <= 0, s14 >= 0, s14 <= 0, s15 >= 0, s15 <= 0, s16 >= 0, s16 <= s15, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 2 + 3*x_1 + 3*x_2 + 3*x_3 }-> s24 :|: s21 >= 0, s21 <= 0, s22 >= 0, s22 <= 0, s23 >= 0, s23 <= 0, s24 >= 0, s24 <= s23, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 3 + 3*x_1 + 3*x_2 }-> s3 :|: s1 >= 0, s1 <= 0, s2 >= 0, s2 <= 0, s3 >= 0, s3 <= s2, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 1 + 3*x_1 + 3*x_2 }-> s9 :|: s7 >= 0, s7 <= 0, s8 >= 0, s8 <= 0, s9 >= 0, s9 <= s8, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encode_f(z, z') -{ 3 + 3*z + 3*z' }-> s6 :|: s4 >= 0, s4 <= 0, s5 >= 0, s5 <= 0, s6 >= 0, s6 <= s5, z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_g1(z, z', z'') -{ 2 + 3*z + 3*z' + 3*z'' }-> s20 :|: s17 >= 0, s17 <= 0, s18 >= 0, s18 <= 0, s19 >= 0, s19 <= 0, s20 >= 0, s20 <= s19, z >= 0, z'' >= 0, z' >= 0
   encode_g1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g2(z, z', z'') -{ 2 + 3*z + 3*z' + 3*z'' }-> s28 :|: s25 >= 0, s25 <= 0, s26 >= 0, s26 <= 0, s27 >= 0, s27 <= 0, s28 >= 0, s28 <= s27, z >= 0, z'' >= 0, z' >= 0
   encode_g2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_h(z, z') -{ 1 + 3*z + 3*z' }-> s12 :|: s10 >= 0, s10 <= 0, s11 >= 0, s11 <= 0, s12 >= 0, s12 <= s11, z >= 0, z' >= 0
   encode_h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   f(z, z') -{ 3 }-> s :|: s >= 0, s <= z', z >= 0, z' >= 0
   f(z, z') -{ 3 }-> s' :|: s' >= 0, s' <= z, z >= 0, z' >= 0, z' = z
   f(z, z') -{ 3 }-> s'' :|: s'' >= 0, s'' <= z', z >= 0, z' >= 0, z = z'
   f(z, z') -{ 1 }-> 0 :|: z >= 0, z' >= 0
   g1(z, z', z'') -{ 2 }-> z :|: z >= 0, z' >= 0, z'' = z', z' = z
   g1(z, z', z'') -{ 2 }-> z'' :|: z' >= 0, z'' >= 0, z = z', z' = z''
   g1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g1(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' >= 0, z = z'
   g1(z, z', z'') -{ 1 }-> 0 :|: z >= 0, z' >= 0, z'' = z'
   g2(z, z', z'') -{ 2 }-> z' :|: z' >= 0, z'' >= 0, z = z', z'' = z'
   g2(z, z', z'') -{ 2 }-> z'' :|: z >= 0, z'' >= 0, z' = z'', z = z''
   g2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g2(z, z', z'') -{ 1 }-> 0 :|: z >= 0, z'' >= 0, z' = z''
   g2(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' >= 0, z = z'
   h(z, z') -{ 1 }-> z' :|: z' >= 0, z = z'
   h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0

Function symbols to be analyzed: {encode_g1}, {encode_h}, {encode_f}
Previous analysis results are:
  g2: runtime: O(1) [2], size: O(n^1) [z'']
  h: runtime: O(1) [1], size: O(n^1) [z']
  g1: runtime: O(1) [2], size: O(n^1) [z'']
  f: runtime: O(1) [3], size: O(n^1) [z']
  encArg: runtime: O(n^1) [3*z], size: O(1) [0]
  encode_g2: runtime: O(n^1) [2 + 3*z + 3*z' + 3*z''], size: O(1) [0]

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

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

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

   encArg(z) -{ 2 + 3*x_1 + 3*x_2 + 3*x_3 }-> s16 :|: s13 >= 0, s13 <= 0, s14 >= 0, s14 <= 0, s15 >= 0, s15 <= 0, s16 >= 0, s16 <= s15, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 2 + 3*x_1 + 3*x_2 + 3*x_3 }-> s24 :|: s21 >= 0, s21 <= 0, s22 >= 0, s22 <= 0, s23 >= 0, s23 <= 0, s24 >= 0, s24 <= s23, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 3 + 3*x_1 + 3*x_2 }-> s3 :|: s1 >= 0, s1 <= 0, s2 >= 0, s2 <= 0, s3 >= 0, s3 <= s2, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 1 + 3*x_1 + 3*x_2 }-> s9 :|: s7 >= 0, s7 <= 0, s8 >= 0, s8 <= 0, s9 >= 0, s9 <= s8, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encode_f(z, z') -{ 3 + 3*z + 3*z' }-> s6 :|: s4 >= 0, s4 <= 0, s5 >= 0, s5 <= 0, s6 >= 0, s6 <= s5, z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_g1(z, z', z'') -{ 2 + 3*z + 3*z' + 3*z'' }-> s20 :|: s17 >= 0, s17 <= 0, s18 >= 0, s18 <= 0, s19 >= 0, s19 <= 0, s20 >= 0, s20 <= s19, z >= 0, z'' >= 0, z' >= 0
   encode_g1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g2(z, z', z'') -{ 2 + 3*z + 3*z' + 3*z'' }-> s28 :|: s25 >= 0, s25 <= 0, s26 >= 0, s26 <= 0, s27 >= 0, s27 <= 0, s28 >= 0, s28 <= s27, z >= 0, z'' >= 0, z' >= 0
   encode_g2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_h(z, z') -{ 1 + 3*z + 3*z' }-> s12 :|: s10 >= 0, s10 <= 0, s11 >= 0, s11 <= 0, s12 >= 0, s12 <= s11, z >= 0, z' >= 0
   encode_h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   f(z, z') -{ 3 }-> s :|: s >= 0, s <= z', z >= 0, z' >= 0
   f(z, z') -{ 3 }-> s' :|: s' >= 0, s' <= z, z >= 0, z' >= 0, z' = z
   f(z, z') -{ 3 }-> s'' :|: s'' >= 0, s'' <= z', z >= 0, z' >= 0, z = z'
   f(z, z') -{ 1 }-> 0 :|: z >= 0, z' >= 0
   g1(z, z', z'') -{ 2 }-> z :|: z >= 0, z' >= 0, z'' = z', z' = z
   g1(z, z', z'') -{ 2 }-> z'' :|: z' >= 0, z'' >= 0, z = z', z' = z''
   g1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g1(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' >= 0, z = z'
   g1(z, z', z'') -{ 1 }-> 0 :|: z >= 0, z' >= 0, z'' = z'
   g2(z, z', z'') -{ 2 }-> z' :|: z' >= 0, z'' >= 0, z = z', z'' = z'
   g2(z, z', z'') -{ 2 }-> z'' :|: z >= 0, z'' >= 0, z' = z'', z = z''
   g2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g2(z, z', z'') -{ 1 }-> 0 :|: z >= 0, z'' >= 0, z' = z''
   g2(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' >= 0, z = z'
   h(z, z') -{ 1 }-> z' :|: z' >= 0, z = z'
   h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0

Function symbols to be analyzed: {encode_g1}, {encode_h}, {encode_f}
Previous analysis results are:
  g2: runtime: O(1) [2], size: O(n^1) [z'']
  h: runtime: O(1) [1], size: O(n^1) [z']
  g1: runtime: O(1) [2], size: O(n^1) [z'']
  f: runtime: O(1) [3], size: O(n^1) [z']
  encArg: runtime: O(n^1) [3*z], size: O(1) [0]
  encode_g2: runtime: O(n^1) [2 + 3*z + 3*z' + 3*z''], size: O(1) [0]

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

(59) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: encode_g1
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 0

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

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

   encArg(z) -{ 2 + 3*x_1 + 3*x_2 + 3*x_3 }-> s16 :|: s13 >= 0, s13 <= 0, s14 >= 0, s14 <= 0, s15 >= 0, s15 <= 0, s16 >= 0, s16 <= s15, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 2 + 3*x_1 + 3*x_2 + 3*x_3 }-> s24 :|: s21 >= 0, s21 <= 0, s22 >= 0, s22 <= 0, s23 >= 0, s23 <= 0, s24 >= 0, s24 <= s23, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 3 + 3*x_1 + 3*x_2 }-> s3 :|: s1 >= 0, s1 <= 0, s2 >= 0, s2 <= 0, s3 >= 0, s3 <= s2, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 1 + 3*x_1 + 3*x_2 }-> s9 :|: s7 >= 0, s7 <= 0, s8 >= 0, s8 <= 0, s9 >= 0, s9 <= s8, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encode_f(z, z') -{ 3 + 3*z + 3*z' }-> s6 :|: s4 >= 0, s4 <= 0, s5 >= 0, s5 <= 0, s6 >= 0, s6 <= s5, z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_g1(z, z', z'') -{ 2 + 3*z + 3*z' + 3*z'' }-> s20 :|: s17 >= 0, s17 <= 0, s18 >= 0, s18 <= 0, s19 >= 0, s19 <= 0, s20 >= 0, s20 <= s19, z >= 0, z'' >= 0, z' >= 0
   encode_g1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g2(z, z', z'') -{ 2 + 3*z + 3*z' + 3*z'' }-> s28 :|: s25 >= 0, s25 <= 0, s26 >= 0, s26 <= 0, s27 >= 0, s27 <= 0, s28 >= 0, s28 <= s27, z >= 0, z'' >= 0, z' >= 0
   encode_g2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_h(z, z') -{ 1 + 3*z + 3*z' }-> s12 :|: s10 >= 0, s10 <= 0, s11 >= 0, s11 <= 0, s12 >= 0, s12 <= s11, z >= 0, z' >= 0
   encode_h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   f(z, z') -{ 3 }-> s :|: s >= 0, s <= z', z >= 0, z' >= 0
   f(z, z') -{ 3 }-> s' :|: s' >= 0, s' <= z, z >= 0, z' >= 0, z' = z
   f(z, z') -{ 3 }-> s'' :|: s'' >= 0, s'' <= z', z >= 0, z' >= 0, z = z'
   f(z, z') -{ 1 }-> 0 :|: z >= 0, z' >= 0
   g1(z, z', z'') -{ 2 }-> z :|: z >= 0, z' >= 0, z'' = z', z' = z
   g1(z, z', z'') -{ 2 }-> z'' :|: z' >= 0, z'' >= 0, z = z', z' = z''
   g1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g1(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' >= 0, z = z'
   g1(z, z', z'') -{ 1 }-> 0 :|: z >= 0, z' >= 0, z'' = z'
   g2(z, z', z'') -{ 2 }-> z' :|: z' >= 0, z'' >= 0, z = z', z'' = z'
   g2(z, z', z'') -{ 2 }-> z'' :|: z >= 0, z'' >= 0, z' = z'', z = z''
   g2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g2(z, z', z'') -{ 1 }-> 0 :|: z >= 0, z'' >= 0, z' = z''
   g2(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' >= 0, z = z'
   h(z, z') -{ 1 }-> z' :|: z' >= 0, z = z'
   h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0

Function symbols to be analyzed: {encode_g1}, {encode_h}, {encode_f}
Previous analysis results are:
  g2: runtime: O(1) [2], size: O(n^1) [z'']
  h: runtime: O(1) [1], size: O(n^1) [z']
  g1: runtime: O(1) [2], size: O(n^1) [z'']
  f: runtime: O(1) [3], size: O(n^1) [z']
  encArg: runtime: O(n^1) [3*z], size: O(1) [0]
  encode_g2: runtime: O(n^1) [2 + 3*z + 3*z' + 3*z''], size: O(1) [0]
  encode_g1: runtime: ?, size: O(1) [0]

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

(61) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: encode_g1
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 2 + 3*z + 3*z' + 3*z''

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

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

   encArg(z) -{ 2 + 3*x_1 + 3*x_2 + 3*x_3 }-> s16 :|: s13 >= 0, s13 <= 0, s14 >= 0, s14 <= 0, s15 >= 0, s15 <= 0, s16 >= 0, s16 <= s15, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 2 + 3*x_1 + 3*x_2 + 3*x_3 }-> s24 :|: s21 >= 0, s21 <= 0, s22 >= 0, s22 <= 0, s23 >= 0, s23 <= 0, s24 >= 0, s24 <= s23, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 3 + 3*x_1 + 3*x_2 }-> s3 :|: s1 >= 0, s1 <= 0, s2 >= 0, s2 <= 0, s3 >= 0, s3 <= s2, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 1 + 3*x_1 + 3*x_2 }-> s9 :|: s7 >= 0, s7 <= 0, s8 >= 0, s8 <= 0, s9 >= 0, s9 <= s8, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encode_f(z, z') -{ 3 + 3*z + 3*z' }-> s6 :|: s4 >= 0, s4 <= 0, s5 >= 0, s5 <= 0, s6 >= 0, s6 <= s5, z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_g1(z, z', z'') -{ 2 + 3*z + 3*z' + 3*z'' }-> s20 :|: s17 >= 0, s17 <= 0, s18 >= 0, s18 <= 0, s19 >= 0, s19 <= 0, s20 >= 0, s20 <= s19, z >= 0, z'' >= 0, z' >= 0
   encode_g1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g2(z, z', z'') -{ 2 + 3*z + 3*z' + 3*z'' }-> s28 :|: s25 >= 0, s25 <= 0, s26 >= 0, s26 <= 0, s27 >= 0, s27 <= 0, s28 >= 0, s28 <= s27, z >= 0, z'' >= 0, z' >= 0
   encode_g2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_h(z, z') -{ 1 + 3*z + 3*z' }-> s12 :|: s10 >= 0, s10 <= 0, s11 >= 0, s11 <= 0, s12 >= 0, s12 <= s11, z >= 0, z' >= 0
   encode_h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   f(z, z') -{ 3 }-> s :|: s >= 0, s <= z', z >= 0, z' >= 0
   f(z, z') -{ 3 }-> s' :|: s' >= 0, s' <= z, z >= 0, z' >= 0, z' = z
   f(z, z') -{ 3 }-> s'' :|: s'' >= 0, s'' <= z', z >= 0, z' >= 0, z = z'
   f(z, z') -{ 1 }-> 0 :|: z >= 0, z' >= 0
   g1(z, z', z'') -{ 2 }-> z :|: z >= 0, z' >= 0, z'' = z', z' = z
   g1(z, z', z'') -{ 2 }-> z'' :|: z' >= 0, z'' >= 0, z = z', z' = z''
   g1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g1(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' >= 0, z = z'
   g1(z, z', z'') -{ 1 }-> 0 :|: z >= 0, z' >= 0, z'' = z'
   g2(z, z', z'') -{ 2 }-> z' :|: z' >= 0, z'' >= 0, z = z', z'' = z'
   g2(z, z', z'') -{ 2 }-> z'' :|: z >= 0, z'' >= 0, z' = z'', z = z''
   g2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g2(z, z', z'') -{ 1 }-> 0 :|: z >= 0, z'' >= 0, z' = z''
   g2(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' >= 0, z = z'
   h(z, z') -{ 1 }-> z' :|: z' >= 0, z = z'
   h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0

Function symbols to be analyzed: {encode_h}, {encode_f}
Previous analysis results are:
  g2: runtime: O(1) [2], size: O(n^1) [z'']
  h: runtime: O(1) [1], size: O(n^1) [z']
  g1: runtime: O(1) [2], size: O(n^1) [z'']
  f: runtime: O(1) [3], size: O(n^1) [z']
  encArg: runtime: O(n^1) [3*z], size: O(1) [0]
  encode_g2: runtime: O(n^1) [2 + 3*z + 3*z' + 3*z''], size: O(1) [0]
  encode_g1: runtime: O(n^1) [2 + 3*z + 3*z' + 3*z''], size: O(1) [0]

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

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

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

   encArg(z) -{ 2 + 3*x_1 + 3*x_2 + 3*x_3 }-> s16 :|: s13 >= 0, s13 <= 0, s14 >= 0, s14 <= 0, s15 >= 0, s15 <= 0, s16 >= 0, s16 <= s15, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 2 + 3*x_1 + 3*x_2 + 3*x_3 }-> s24 :|: s21 >= 0, s21 <= 0, s22 >= 0, s22 <= 0, s23 >= 0, s23 <= 0, s24 >= 0, s24 <= s23, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 3 + 3*x_1 + 3*x_2 }-> s3 :|: s1 >= 0, s1 <= 0, s2 >= 0, s2 <= 0, s3 >= 0, s3 <= s2, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 1 + 3*x_1 + 3*x_2 }-> s9 :|: s7 >= 0, s7 <= 0, s8 >= 0, s8 <= 0, s9 >= 0, s9 <= s8, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encode_f(z, z') -{ 3 + 3*z + 3*z' }-> s6 :|: s4 >= 0, s4 <= 0, s5 >= 0, s5 <= 0, s6 >= 0, s6 <= s5, z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_g1(z, z', z'') -{ 2 + 3*z + 3*z' + 3*z'' }-> s20 :|: s17 >= 0, s17 <= 0, s18 >= 0, s18 <= 0, s19 >= 0, s19 <= 0, s20 >= 0, s20 <= s19, z >= 0, z'' >= 0, z' >= 0
   encode_g1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g2(z, z', z'') -{ 2 + 3*z + 3*z' + 3*z'' }-> s28 :|: s25 >= 0, s25 <= 0, s26 >= 0, s26 <= 0, s27 >= 0, s27 <= 0, s28 >= 0, s28 <= s27, z >= 0, z'' >= 0, z' >= 0
   encode_g2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_h(z, z') -{ 1 + 3*z + 3*z' }-> s12 :|: s10 >= 0, s10 <= 0, s11 >= 0, s11 <= 0, s12 >= 0, s12 <= s11, z >= 0, z' >= 0
   encode_h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   f(z, z') -{ 3 }-> s :|: s >= 0, s <= z', z >= 0, z' >= 0
   f(z, z') -{ 3 }-> s' :|: s' >= 0, s' <= z, z >= 0, z' >= 0, z' = z
   f(z, z') -{ 3 }-> s'' :|: s'' >= 0, s'' <= z', z >= 0, z' >= 0, z = z'
   f(z, z') -{ 1 }-> 0 :|: z >= 0, z' >= 0
   g1(z, z', z'') -{ 2 }-> z :|: z >= 0, z' >= 0, z'' = z', z' = z
   g1(z, z', z'') -{ 2 }-> z'' :|: z' >= 0, z'' >= 0, z = z', z' = z''
   g1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g1(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' >= 0, z = z'
   g1(z, z', z'') -{ 1 }-> 0 :|: z >= 0, z' >= 0, z'' = z'
   g2(z, z', z'') -{ 2 }-> z' :|: z' >= 0, z'' >= 0, z = z', z'' = z'
   g2(z, z', z'') -{ 2 }-> z'' :|: z >= 0, z'' >= 0, z' = z'', z = z''
   g2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g2(z, z', z'') -{ 1 }-> 0 :|: z >= 0, z'' >= 0, z' = z''
   g2(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' >= 0, z = z'
   h(z, z') -{ 1 }-> z' :|: z' >= 0, z = z'
   h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0

Function symbols to be analyzed: {encode_h}, {encode_f}
Previous analysis results are:
  g2: runtime: O(1) [2], size: O(n^1) [z'']
  h: runtime: O(1) [1], size: O(n^1) [z']
  g1: runtime: O(1) [2], size: O(n^1) [z'']
  f: runtime: O(1) [3], size: O(n^1) [z']
  encArg: runtime: O(n^1) [3*z], size: O(1) [0]
  encode_g2: runtime: O(n^1) [2 + 3*z + 3*z' + 3*z''], size: O(1) [0]
  encode_g1: runtime: O(n^1) [2 + 3*z + 3*z' + 3*z''], size: O(1) [0]

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

(65) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   encArg(z) -{ 2 + 3*x_1 + 3*x_2 + 3*x_3 }-> s16 :|: s13 >= 0, s13 <= 0, s14 >= 0, s14 <= 0, s15 >= 0, s15 <= 0, s16 >= 0, s16 <= s15, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 2 + 3*x_1 + 3*x_2 + 3*x_3 }-> s24 :|: s21 >= 0, s21 <= 0, s22 >= 0, s22 <= 0, s23 >= 0, s23 <= 0, s24 >= 0, s24 <= s23, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 3 + 3*x_1 + 3*x_2 }-> s3 :|: s1 >= 0, s1 <= 0, s2 >= 0, s2 <= 0, s3 >= 0, s3 <= s2, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 1 + 3*x_1 + 3*x_2 }-> s9 :|: s7 >= 0, s7 <= 0, s8 >= 0, s8 <= 0, s9 >= 0, s9 <= s8, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encode_f(z, z') -{ 3 + 3*z + 3*z' }-> s6 :|: s4 >= 0, s4 <= 0, s5 >= 0, s5 <= 0, s6 >= 0, s6 <= s5, z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_g1(z, z', z'') -{ 2 + 3*z + 3*z' + 3*z'' }-> s20 :|: s17 >= 0, s17 <= 0, s18 >= 0, s18 <= 0, s19 >= 0, s19 <= 0, s20 >= 0, s20 <= s19, z >= 0, z'' >= 0, z' >= 0
   encode_g1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g2(z, z', z'') -{ 2 + 3*z + 3*z' + 3*z'' }-> s28 :|: s25 >= 0, s25 <= 0, s26 >= 0, s26 <= 0, s27 >= 0, s27 <= 0, s28 >= 0, s28 <= s27, z >= 0, z'' >= 0, z' >= 0
   encode_g2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_h(z, z') -{ 1 + 3*z + 3*z' }-> s12 :|: s10 >= 0, s10 <= 0, s11 >= 0, s11 <= 0, s12 >= 0, s12 <= s11, z >= 0, z' >= 0
   encode_h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   f(z, z') -{ 3 }-> s :|: s >= 0, s <= z', z >= 0, z' >= 0
   f(z, z') -{ 3 }-> s' :|: s' >= 0, s' <= z, z >= 0, z' >= 0, z' = z
   f(z, z') -{ 3 }-> s'' :|: s'' >= 0, s'' <= z', z >= 0, z' >= 0, z = z'
   f(z, z') -{ 1 }-> 0 :|: z >= 0, z' >= 0
   g1(z, z', z'') -{ 2 }-> z :|: z >= 0, z' >= 0, z'' = z', z' = z
   g1(z, z', z'') -{ 2 }-> z'' :|: z' >= 0, z'' >= 0, z = z', z' = z''
   g1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g1(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' >= 0, z = z'
   g1(z, z', z'') -{ 1 }-> 0 :|: z >= 0, z' >= 0, z'' = z'
   g2(z, z', z'') -{ 2 }-> z' :|: z' >= 0, z'' >= 0, z = z', z'' = z'
   g2(z, z', z'') -{ 2 }-> z'' :|: z >= 0, z'' >= 0, z' = z'', z = z''
   g2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g2(z, z', z'') -{ 1 }-> 0 :|: z >= 0, z'' >= 0, z' = z''
   g2(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' >= 0, z = z'
   h(z, z') -{ 1 }-> z' :|: z' >= 0, z = z'
   h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0

Function symbols to be analyzed: {encode_h}, {encode_f}
Previous analysis results are:
  g2: runtime: O(1) [2], size: O(n^1) [z'']
  h: runtime: O(1) [1], size: O(n^1) [z']
  g1: runtime: O(1) [2], size: O(n^1) [z'']
  f: runtime: O(1) [3], size: O(n^1) [z']
  encArg: runtime: O(n^1) [3*z], size: O(1) [0]
  encode_g2: runtime: O(n^1) [2 + 3*z + 3*z' + 3*z''], size: O(1) [0]
  encode_g1: runtime: O(n^1) [2 + 3*z + 3*z' + 3*z''], size: O(1) [0]
  encode_h: runtime: ?, size: O(1) [0]

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

(67) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   encArg(z) -{ 2 + 3*x_1 + 3*x_2 + 3*x_3 }-> s16 :|: s13 >= 0, s13 <= 0, s14 >= 0, s14 <= 0, s15 >= 0, s15 <= 0, s16 >= 0, s16 <= s15, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 2 + 3*x_1 + 3*x_2 + 3*x_3 }-> s24 :|: s21 >= 0, s21 <= 0, s22 >= 0, s22 <= 0, s23 >= 0, s23 <= 0, s24 >= 0, s24 <= s23, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 3 + 3*x_1 + 3*x_2 }-> s3 :|: s1 >= 0, s1 <= 0, s2 >= 0, s2 <= 0, s3 >= 0, s3 <= s2, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 1 + 3*x_1 + 3*x_2 }-> s9 :|: s7 >= 0, s7 <= 0, s8 >= 0, s8 <= 0, s9 >= 0, s9 <= s8, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encode_f(z, z') -{ 3 + 3*z + 3*z' }-> s6 :|: s4 >= 0, s4 <= 0, s5 >= 0, s5 <= 0, s6 >= 0, s6 <= s5, z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_g1(z, z', z'') -{ 2 + 3*z + 3*z' + 3*z'' }-> s20 :|: s17 >= 0, s17 <= 0, s18 >= 0, s18 <= 0, s19 >= 0, s19 <= 0, s20 >= 0, s20 <= s19, z >= 0, z'' >= 0, z' >= 0
   encode_g1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g2(z, z', z'') -{ 2 + 3*z + 3*z' + 3*z'' }-> s28 :|: s25 >= 0, s25 <= 0, s26 >= 0, s26 <= 0, s27 >= 0, s27 <= 0, s28 >= 0, s28 <= s27, z >= 0, z'' >= 0, z' >= 0
   encode_g2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_h(z, z') -{ 1 + 3*z + 3*z' }-> s12 :|: s10 >= 0, s10 <= 0, s11 >= 0, s11 <= 0, s12 >= 0, s12 <= s11, z >= 0, z' >= 0
   encode_h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   f(z, z') -{ 3 }-> s :|: s >= 0, s <= z', z >= 0, z' >= 0
   f(z, z') -{ 3 }-> s' :|: s' >= 0, s' <= z, z >= 0, z' >= 0, z' = z
   f(z, z') -{ 3 }-> s'' :|: s'' >= 0, s'' <= z', z >= 0, z' >= 0, z = z'
   f(z, z') -{ 1 }-> 0 :|: z >= 0, z' >= 0
   g1(z, z', z'') -{ 2 }-> z :|: z >= 0, z' >= 0, z'' = z', z' = z
   g1(z, z', z'') -{ 2 }-> z'' :|: z' >= 0, z'' >= 0, z = z', z' = z''
   g1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g1(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' >= 0, z = z'
   g1(z, z', z'') -{ 1 }-> 0 :|: z >= 0, z' >= 0, z'' = z'
   g2(z, z', z'') -{ 2 }-> z' :|: z' >= 0, z'' >= 0, z = z', z'' = z'
   g2(z, z', z'') -{ 2 }-> z'' :|: z >= 0, z'' >= 0, z' = z'', z = z''
   g2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g2(z, z', z'') -{ 1 }-> 0 :|: z >= 0, z'' >= 0, z' = z''
   g2(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' >= 0, z = z'
   h(z, z') -{ 1 }-> z' :|: z' >= 0, z = z'
   h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0

Function symbols to be analyzed: {encode_f}
Previous analysis results are:
  g2: runtime: O(1) [2], size: O(n^1) [z'']
  h: runtime: O(1) [1], size: O(n^1) [z']
  g1: runtime: O(1) [2], size: O(n^1) [z'']
  f: runtime: O(1) [3], size: O(n^1) [z']
  encArg: runtime: O(n^1) [3*z], size: O(1) [0]
  encode_g2: runtime: O(n^1) [2 + 3*z + 3*z' + 3*z''], size: O(1) [0]
  encode_g1: runtime: O(n^1) [2 + 3*z + 3*z' + 3*z''], size: O(1) [0]
  encode_h: runtime: O(n^1) [1 + 3*z + 3*z'], size: O(1) [0]

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

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

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

   encArg(z) -{ 2 + 3*x_1 + 3*x_2 + 3*x_3 }-> s16 :|: s13 >= 0, s13 <= 0, s14 >= 0, s14 <= 0, s15 >= 0, s15 <= 0, s16 >= 0, s16 <= s15, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 2 + 3*x_1 + 3*x_2 + 3*x_3 }-> s24 :|: s21 >= 0, s21 <= 0, s22 >= 0, s22 <= 0, s23 >= 0, s23 <= 0, s24 >= 0, s24 <= s23, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 3 + 3*x_1 + 3*x_2 }-> s3 :|: s1 >= 0, s1 <= 0, s2 >= 0, s2 <= 0, s3 >= 0, s3 <= s2, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 1 + 3*x_1 + 3*x_2 }-> s9 :|: s7 >= 0, s7 <= 0, s8 >= 0, s8 <= 0, s9 >= 0, s9 <= s8, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encode_f(z, z') -{ 3 + 3*z + 3*z' }-> s6 :|: s4 >= 0, s4 <= 0, s5 >= 0, s5 <= 0, s6 >= 0, s6 <= s5, z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_g1(z, z', z'') -{ 2 + 3*z + 3*z' + 3*z'' }-> s20 :|: s17 >= 0, s17 <= 0, s18 >= 0, s18 <= 0, s19 >= 0, s19 <= 0, s20 >= 0, s20 <= s19, z >= 0, z'' >= 0, z' >= 0
   encode_g1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g2(z, z', z'') -{ 2 + 3*z + 3*z' + 3*z'' }-> s28 :|: s25 >= 0, s25 <= 0, s26 >= 0, s26 <= 0, s27 >= 0, s27 <= 0, s28 >= 0, s28 <= s27, z >= 0, z'' >= 0, z' >= 0
   encode_g2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_h(z, z') -{ 1 + 3*z + 3*z' }-> s12 :|: s10 >= 0, s10 <= 0, s11 >= 0, s11 <= 0, s12 >= 0, s12 <= s11, z >= 0, z' >= 0
   encode_h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   f(z, z') -{ 3 }-> s :|: s >= 0, s <= z', z >= 0, z' >= 0
   f(z, z') -{ 3 }-> s' :|: s' >= 0, s' <= z, z >= 0, z' >= 0, z' = z
   f(z, z') -{ 3 }-> s'' :|: s'' >= 0, s'' <= z', z >= 0, z' >= 0, z = z'
   f(z, z') -{ 1 }-> 0 :|: z >= 0, z' >= 0
   g1(z, z', z'') -{ 2 }-> z :|: z >= 0, z' >= 0, z'' = z', z' = z
   g1(z, z', z'') -{ 2 }-> z'' :|: z' >= 0, z'' >= 0, z = z', z' = z''
   g1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g1(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' >= 0, z = z'
   g1(z, z', z'') -{ 1 }-> 0 :|: z >= 0, z' >= 0, z'' = z'
   g2(z, z', z'') -{ 2 }-> z' :|: z' >= 0, z'' >= 0, z = z', z'' = z'
   g2(z, z', z'') -{ 2 }-> z'' :|: z >= 0, z'' >= 0, z' = z'', z = z''
   g2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g2(z, z', z'') -{ 1 }-> 0 :|: z >= 0, z'' >= 0, z' = z''
   g2(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' >= 0, z = z'
   h(z, z') -{ 1 }-> z' :|: z' >= 0, z = z'
   h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0

Function symbols to be analyzed: {encode_f}
Previous analysis results are:
  g2: runtime: O(1) [2], size: O(n^1) [z'']
  h: runtime: O(1) [1], size: O(n^1) [z']
  g1: runtime: O(1) [2], size: O(n^1) [z'']
  f: runtime: O(1) [3], size: O(n^1) [z']
  encArg: runtime: O(n^1) [3*z], size: O(1) [0]
  encode_g2: runtime: O(n^1) [2 + 3*z + 3*z' + 3*z''], size: O(1) [0]
  encode_g1: runtime: O(n^1) [2 + 3*z + 3*z' + 3*z''], size: O(1) [0]
  encode_h: runtime: O(n^1) [1 + 3*z + 3*z'], size: O(1) [0]

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

(71) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   encArg(z) -{ 2 + 3*x_1 + 3*x_2 + 3*x_3 }-> s16 :|: s13 >= 0, s13 <= 0, s14 >= 0, s14 <= 0, s15 >= 0, s15 <= 0, s16 >= 0, s16 <= s15, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 2 + 3*x_1 + 3*x_2 + 3*x_3 }-> s24 :|: s21 >= 0, s21 <= 0, s22 >= 0, s22 <= 0, s23 >= 0, s23 <= 0, s24 >= 0, s24 <= s23, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 3 + 3*x_1 + 3*x_2 }-> s3 :|: s1 >= 0, s1 <= 0, s2 >= 0, s2 <= 0, s3 >= 0, s3 <= s2, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 1 + 3*x_1 + 3*x_2 }-> s9 :|: s7 >= 0, s7 <= 0, s8 >= 0, s8 <= 0, s9 >= 0, s9 <= s8, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encode_f(z, z') -{ 3 + 3*z + 3*z' }-> s6 :|: s4 >= 0, s4 <= 0, s5 >= 0, s5 <= 0, s6 >= 0, s6 <= s5, z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_g1(z, z', z'') -{ 2 + 3*z + 3*z' + 3*z'' }-> s20 :|: s17 >= 0, s17 <= 0, s18 >= 0, s18 <= 0, s19 >= 0, s19 <= 0, s20 >= 0, s20 <= s19, z >= 0, z'' >= 0, z' >= 0
   encode_g1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g2(z, z', z'') -{ 2 + 3*z + 3*z' + 3*z'' }-> s28 :|: s25 >= 0, s25 <= 0, s26 >= 0, s26 <= 0, s27 >= 0, s27 <= 0, s28 >= 0, s28 <= s27, z >= 0, z'' >= 0, z' >= 0
   encode_g2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_h(z, z') -{ 1 + 3*z + 3*z' }-> s12 :|: s10 >= 0, s10 <= 0, s11 >= 0, s11 <= 0, s12 >= 0, s12 <= s11, z >= 0, z' >= 0
   encode_h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   f(z, z') -{ 3 }-> s :|: s >= 0, s <= z', z >= 0, z' >= 0
   f(z, z') -{ 3 }-> s' :|: s' >= 0, s' <= z, z >= 0, z' >= 0, z' = z
   f(z, z') -{ 3 }-> s'' :|: s'' >= 0, s'' <= z', z >= 0, z' >= 0, z = z'
   f(z, z') -{ 1 }-> 0 :|: z >= 0, z' >= 0
   g1(z, z', z'') -{ 2 }-> z :|: z >= 0, z' >= 0, z'' = z', z' = z
   g1(z, z', z'') -{ 2 }-> z'' :|: z' >= 0, z'' >= 0, z = z', z' = z''
   g1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g1(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' >= 0, z = z'
   g1(z, z', z'') -{ 1 }-> 0 :|: z >= 0, z' >= 0, z'' = z'
   g2(z, z', z'') -{ 2 }-> z' :|: z' >= 0, z'' >= 0, z = z', z'' = z'
   g2(z, z', z'') -{ 2 }-> z'' :|: z >= 0, z'' >= 0, z' = z'', z = z''
   g2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g2(z, z', z'') -{ 1 }-> 0 :|: z >= 0, z'' >= 0, z' = z''
   g2(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' >= 0, z = z'
   h(z, z') -{ 1 }-> z' :|: z' >= 0, z = z'
   h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0

Function symbols to be analyzed: {encode_f}
Previous analysis results are:
  g2: runtime: O(1) [2], size: O(n^1) [z'']
  h: runtime: O(1) [1], size: O(n^1) [z']
  g1: runtime: O(1) [2], size: O(n^1) [z'']
  f: runtime: O(1) [3], size: O(n^1) [z']
  encArg: runtime: O(n^1) [3*z], size: O(1) [0]
  encode_g2: runtime: O(n^1) [2 + 3*z + 3*z' + 3*z''], size: O(1) [0]
  encode_g1: runtime: O(n^1) [2 + 3*z + 3*z' + 3*z''], size: O(1) [0]
  encode_h: runtime: O(n^1) [1 + 3*z + 3*z'], size: O(1) [0]
  encode_f: runtime: ?, size: O(1) [0]

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

(73) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   encArg(z) -{ 2 + 3*x_1 + 3*x_2 + 3*x_3 }-> s16 :|: s13 >= 0, s13 <= 0, s14 >= 0, s14 <= 0, s15 >= 0, s15 <= 0, s16 >= 0, s16 <= s15, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 2 + 3*x_1 + 3*x_2 + 3*x_3 }-> s24 :|: s21 >= 0, s21 <= 0, s22 >= 0, s22 <= 0, s23 >= 0, s23 <= 0, s24 >= 0, s24 <= s23, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 3 + 3*x_1 + 3*x_2 }-> s3 :|: s1 >= 0, s1 <= 0, s2 >= 0, s2 <= 0, s3 >= 0, s3 <= s2, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 1 + 3*x_1 + 3*x_2 }-> s9 :|: s7 >= 0, s7 <= 0, s8 >= 0, s8 <= 0, s9 >= 0, s9 <= s8, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encode_f(z, z') -{ 3 + 3*z + 3*z' }-> s6 :|: s4 >= 0, s4 <= 0, s5 >= 0, s5 <= 0, s6 >= 0, s6 <= s5, z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_g1(z, z', z'') -{ 2 + 3*z + 3*z' + 3*z'' }-> s20 :|: s17 >= 0, s17 <= 0, s18 >= 0, s18 <= 0, s19 >= 0, s19 <= 0, s20 >= 0, s20 <= s19, z >= 0, z'' >= 0, z' >= 0
   encode_g1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g2(z, z', z'') -{ 2 + 3*z + 3*z' + 3*z'' }-> s28 :|: s25 >= 0, s25 <= 0, s26 >= 0, s26 <= 0, s27 >= 0, s27 <= 0, s28 >= 0, s28 <= s27, z >= 0, z'' >= 0, z' >= 0
   encode_g2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_h(z, z') -{ 1 + 3*z + 3*z' }-> s12 :|: s10 >= 0, s10 <= 0, s11 >= 0, s11 <= 0, s12 >= 0, s12 <= s11, z >= 0, z' >= 0
   encode_h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   f(z, z') -{ 3 }-> s :|: s >= 0, s <= z', z >= 0, z' >= 0
   f(z, z') -{ 3 }-> s' :|: s' >= 0, s' <= z, z >= 0, z' >= 0, z' = z
   f(z, z') -{ 3 }-> s'' :|: s'' >= 0, s'' <= z', z >= 0, z' >= 0, z = z'
   f(z, z') -{ 1 }-> 0 :|: z >= 0, z' >= 0
   g1(z, z', z'') -{ 2 }-> z :|: z >= 0, z' >= 0, z'' = z', z' = z
   g1(z, z', z'') -{ 2 }-> z'' :|: z' >= 0, z'' >= 0, z = z', z' = z''
   g1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g1(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' >= 0, z = z'
   g1(z, z', z'') -{ 1 }-> 0 :|: z >= 0, z' >= 0, z'' = z'
   g2(z, z', z'') -{ 2 }-> z' :|: z' >= 0, z'' >= 0, z = z', z'' = z'
   g2(z, z', z'') -{ 2 }-> z'' :|: z >= 0, z'' >= 0, z' = z'', z = z''
   g2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g2(z, z', z'') -{ 1 }-> 0 :|: z >= 0, z'' >= 0, z' = z''
   g2(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' >= 0, z = z'
   h(z, z') -{ 1 }-> z' :|: z' >= 0, z = z'
   h(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0

Function symbols to be analyzed: 
Previous analysis results are:
  g2: runtime: O(1) [2], size: O(n^1) [z'']
  h: runtime: O(1) [1], size: O(n^1) [z']
  g1: runtime: O(1) [2], size: O(n^1) [z'']
  f: runtime: O(1) [3], size: O(n^1) [z']
  encArg: runtime: O(n^1) [3*z], size: O(1) [0]
  encode_g2: runtime: O(n^1) [2 + 3*z + 3*z' + 3*z''], size: O(1) [0]
  encode_g1: runtime: O(n^1) [2 + 3*z + 3*z' + 3*z''], size: O(1) [0]
  encode_h: runtime: O(n^1) [1 + 3*z + 3*z'], size: O(1) [0]
  encode_f: runtime: O(n^1) [3 + 3*z + 3*z'], size: O(1) [0]

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

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

(76)
BOUNDS(1, n^1)