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


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


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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


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

(0) DCpxTrs
(1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms]
(2) CpxRelTRS
(3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 159 ms]
(4) CpxRelTRS
(5) NonCtorToCtorProof [UPPER BOUND(ID), 0 ms]
(6) CpxRelTRS
    (7) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms]
    (8) CpxRelTRS
    (9) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (10) CpxWeightedTrs
    (11) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (12) CpxTypedWeightedTrs
    (13) CompletionProof [UPPER BOUND(ID), 0 ms]
    (14) CpxTypedWeightedCompleteTrs
    (15) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (16) CpxTypedWeightedCompleteTrs
    (17) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
    (18) CpxRNTS
    (19) InliningProof [UPPER BOUND(ID), 1170 ms]
    (20) CpxRNTS
    (21) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (22) CpxRNTS
    (23) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms]
    (24) CpxRNTS
    (25) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (26) CpxRNTS
    (27) IntTrsBoundProof [UPPER BOUND(ID), 525 ms]
    (28) CpxRNTS
    (29) IntTrsBoundProof [UPPER BOUND(ID), 98 ms]
    (30) CpxRNTS
    (31) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (32) CpxRNTS
    (33) IntTrsBoundProof [UPPER BOUND(ID), 181 ms]
    (34) CpxRNTS
    (35) IntTrsBoundProof [UPPER BOUND(ID), 53 ms]
    (36) CpxRNTS
    (37) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (38) CpxRNTS
    (39) IntTrsBoundProof [UPPER BOUND(ID), 42 ms]
    (40) CpxRNTS
    (41) IntTrsBoundProof [UPPER BOUND(ID), 1 ms]
    (42) CpxRNTS
    (43) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (44) CpxRNTS
    (45) IntTrsBoundProof [UPPER BOUND(ID), 2676 ms]
    (46) CpxRNTS
    (47) IntTrsBoundProof [UPPER BOUND(ID), 951 ms]
    (48) CpxRNTS
    (49) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (50) CpxRNTS
    (51) IntTrsBoundProof [UPPER BOUND(ID), 303 ms]
    (52) CpxRNTS
    (53) IntTrsBoundProof [UPPER BOUND(ID), 78 ms]
    (54) CpxRNTS
    (55) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (56) CpxRNTS
    (57) IntTrsBoundProof [UPPER BOUND(ID), 1612 ms]
    (58) CpxRNTS
    (59) IntTrsBoundProof [UPPER BOUND(ID), 641 ms]
    (60) CpxRNTS
    (61) FinalProof [FINISHED, 0 ms]
    (62) BOUNDS(1, n^1)
(63) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(64) CpxRelTRS
    (65) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (66) typed CpxTrs
    (67) OrderProof [LOWER BOUND(ID), 0 ms]
    (68) typed CpxTrs
    (69) RewriteLemmaProof [LOWER BOUND(ID), 247 ms]
    (70) proven lower bound
    (71) LowerBoundPropagationProof [FINISHED, 0 ms]
    (72) BOUNDS(n^1, INF)


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

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


The TRS R consists of the following rules:

   .(1, x) -> x
   .(x, 1) -> x
   .(i(x), x) -> 1
   .(x, i(x)) -> 1
   i(1) -> 1
   i(i(x)) -> x
   .(i(y), .(y, z)) -> z
   .(y, .(i(y), z)) -> z

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

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

   encArg(1) -> 1
   encArg(cons_.(x_1, x_2)) -> .(encArg(x_1), encArg(x_2))
   encArg(cons_i(x_1)) -> i(encArg(x_1))
   encode_.(x_1, x_2) -> .(encArg(x_1), encArg(x_2))
   encode_1 -> 1
   encode_i(x_1) -> i(encArg(x_1))


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

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


The TRS R consists of the following rules:

   .(1, x) -> x
   .(x, 1) -> x
   .(i(x), x) -> 1
   .(x, i(x)) -> 1
   i(1) -> 1
   i(i(x)) -> x
   .(i(y), .(y, z)) -> z
   .(y, .(i(y), z)) -> z

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

   encArg(1) -> 1
   encArg(cons_.(x_1, x_2)) -> .(encArg(x_1), encArg(x_2))
   encArg(cons_i(x_1)) -> i(encArg(x_1))
   encode_.(x_1, x_2) -> .(encArg(x_1), encArg(x_2))
   encode_1 -> 1
   encode_i(x_1) -> i(encArg(x_1))

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

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

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


The TRS R consists of the following rules:

   .(1, x) -> x
   .(x, 1) -> x
   .(i(x), x) -> 1
   .(x, i(x)) -> 1
   i(1) -> 1
   i(i(x)) -> x
   .(i(y), .(y, z)) -> z
   .(y, .(i(y), z)) -> z

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

   encArg(1) -> 1
   encArg(cons_.(x_1, x_2)) -> .(encArg(x_1), encArg(x_2))
   encArg(cons_i(x_1)) -> i(encArg(x_1))
   encode_.(x_1, x_2) -> .(encArg(x_1), encArg(x_2))
   encode_1 -> 1
   encode_i(x_1) -> i(encArg(x_1))

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

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

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


The TRS R consists of the following rules:

   .(1, x) -> x
   .(x, 1) -> x
   i(1) -> 1
   .(c_i(x), x) -> 1
   .(x, c_i(x)) -> 1
   i(c_i(x)) -> x
   .(y, c_.(c_i(y), z)) -> z
   .(c_i(y), c_.(y, z)) -> z

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

   encArg(1) -> 1
   encArg(cons_.(x_1, x_2)) -> .(encArg(x_1), encArg(x_2))
   encArg(cons_i(x_1)) -> i(encArg(x_1))
   encode_.(x_1, x_2) -> .(encArg(x_1), encArg(x_2))
   encode_1 -> 1
   encode_i(x_1) -> i(encArg(x_1))
   i(x0) -> c_i(x0)
   .(x0, x1) -> c_.(x0, x1)

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

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

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

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


The TRS R consists of the following rules:

   .(1, x) -> x
   .(x, 1) -> x
   i(1) -> 1
   .(c_i(x), x) -> 1
   .(x, c_i(x)) -> 1
   i(c_i(x)) -> x
   .(y, c_.(c_i(y), z)) -> z
   .(c_i(y), c_.(y, z)) -> z

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

   encArg(1) -> 1
   encArg(cons_.(x_1, x_2)) -> .(encArg(x_1), encArg(x_2))
   encArg(cons_i(x_1)) -> i(encArg(x_1))
   encode_.(x_1, x_2) -> .(encArg(x_1), encArg(x_2))
   encode_1 -> 1
   encode_i(x_1) -> i(encArg(x_1))
   i(x0) -> c_i(x0)
   .(x0, x1) -> c_.(x0, x1)

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

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

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


The TRS R consists of the following rules:

   .(1, x) -> x [1]
   .(x, 1) -> x [1]
   i(1) -> 1 [1]
   .(c_i(x), x) -> 1 [1]
   .(x, c_i(x)) -> 1 [1]
   i(c_i(x)) -> x [1]
   .(y, c_.(c_i(y), z)) -> z [1]
   .(c_i(y), c_.(y, z)) -> z [1]
   encArg(1) -> 1 [0]
   encArg(cons_.(x_1, x_2)) -> .(encArg(x_1), encArg(x_2)) [0]
   encArg(cons_i(x_1)) -> i(encArg(x_1)) [0]
   encode_.(x_1, x_2) -> .(encArg(x_1), encArg(x_2)) [0]
   encode_1 -> 1 [0]
   encode_i(x_1) -> i(encArg(x_1)) [0]
   i(x0) -> c_i(x0) [0]
   .(x0, x1) -> c_.(x0, x1) [0]

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

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

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

   .(1, x) -> x [1]
   .(x, 1) -> x [1]
   i(1) -> 1 [1]
   .(c_i(x), x) -> 1 [1]
   .(x, c_i(x)) -> 1 [1]
   i(c_i(x)) -> x [1]
   .(y, c_.(c_i(y), z)) -> z [1]
   .(c_i(y), c_.(y, z)) -> z [1]
   encArg(1) -> 1 [0]
   encArg(cons_.(x_1, x_2)) -> .(encArg(x_1), encArg(x_2)) [0]
   encArg(cons_i(x_1)) -> i(encArg(x_1)) [0]
   encode_.(x_1, x_2) -> .(encArg(x_1), encArg(x_2)) [0]
   encode_1 -> 1 [0]
   encode_i(x_1) -> i(encArg(x_1)) [0]
   i(x0) -> c_i(x0) [0]
   .(x0, x1) -> c_.(x0, x1) [0]

The TRS has the following type information:
. :: 1:c_i:c_.:cons_.:cons_i -> 1:c_i:c_.:cons_.:cons_i -> 1:c_i:c_.:cons_.:cons_i
1 :: 1:c_i:c_.:cons_.:cons_i
i :: 1:c_i:c_.:cons_.:cons_i -> 1:c_i:c_.:cons_.:cons_i
c_i :: 1:c_i:c_.:cons_.:cons_i -> 1:c_i:c_.:cons_.:cons_i
c_. :: 1:c_i:c_.:cons_.:cons_i -> 1:c_i:c_.:cons_.:cons_i -> 1:c_i:c_.:cons_.:cons_i
encArg :: 1:c_i:c_.:cons_.:cons_i -> 1:c_i:c_.:cons_.:cons_i
cons_. :: 1:c_i:c_.:cons_.:cons_i -> 1:c_i:c_.:cons_.:cons_i -> 1:c_i:c_.:cons_.:cons_i
cons_i :: 1:c_i:c_.:cons_.:cons_i -> 1:c_i:c_.:cons_.:cons_i
encode_. :: 1:c_i:c_.:cons_.:cons_i -> 1:c_i:c_.:cons_.:cons_i -> 1:c_i:c_.:cons_.:cons_i
encode_1 :: 1:c_i:c_.:cons_.:cons_i
encode_i :: 1:c_i:c_.:cons_.:cons_i -> 1:c_i:c_.:cons_.:cons_i

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

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

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

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

(c) The following functions are completely defined:

   encArg_1
   encode_._2
   encode_1
   encode_i_1
   i_1
   ._2

Due to the following rules being added:

   encArg(v0) -> 1 [0]
   encode_.(v0, v1) -> 1 [0]
   encode_1 -> 1 [0]
   encode_i(v0) -> 1 [0]
   i(v0) -> 1 [0]
   .(v0, v1) -> 1 [0]

And the following fresh constants: none

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

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

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

   .(1, x) -> x [1]
   .(x, 1) -> x [1]
   i(1) -> 1 [1]
   .(c_i(x), x) -> 1 [1]
   .(x, c_i(x)) -> 1 [1]
   i(c_i(x)) -> x [1]
   .(y, c_.(c_i(y), z)) -> z [1]
   .(c_i(y), c_.(y, z)) -> z [1]
   encArg(1) -> 1 [0]
   encArg(cons_.(x_1, x_2)) -> .(encArg(x_1), encArg(x_2)) [0]
   encArg(cons_i(x_1)) -> i(encArg(x_1)) [0]
   encode_.(x_1, x_2) -> .(encArg(x_1), encArg(x_2)) [0]
   encode_1 -> 1 [0]
   encode_i(x_1) -> i(encArg(x_1)) [0]
   i(x0) -> c_i(x0) [0]
   .(x0, x1) -> c_.(x0, x1) [0]
   encArg(v0) -> 1 [0]
   encode_.(v0, v1) -> 1 [0]
   encode_1 -> 1 [0]
   encode_i(v0) -> 1 [0]
   i(v0) -> 1 [0]
   .(v0, v1) -> 1 [0]

The TRS has the following type information:
. :: 1:c_i:c_.:cons_.:cons_i -> 1:c_i:c_.:cons_.:cons_i -> 1:c_i:c_.:cons_.:cons_i
1 :: 1:c_i:c_.:cons_.:cons_i
i :: 1:c_i:c_.:cons_.:cons_i -> 1:c_i:c_.:cons_.:cons_i
c_i :: 1:c_i:c_.:cons_.:cons_i -> 1:c_i:c_.:cons_.:cons_i
c_. :: 1:c_i:c_.:cons_.:cons_i -> 1:c_i:c_.:cons_.:cons_i -> 1:c_i:c_.:cons_.:cons_i
encArg :: 1:c_i:c_.:cons_.:cons_i -> 1:c_i:c_.:cons_.:cons_i
cons_. :: 1:c_i:c_.:cons_.:cons_i -> 1:c_i:c_.:cons_.:cons_i -> 1:c_i:c_.:cons_.:cons_i
cons_i :: 1:c_i:c_.:cons_.:cons_i -> 1:c_i:c_.:cons_.:cons_i
encode_. :: 1:c_i:c_.:cons_.:cons_i -> 1:c_i:c_.:cons_.:cons_i -> 1:c_i:c_.:cons_.:cons_i
encode_1 :: 1:c_i:c_.:cons_.:cons_i
encode_i :: 1:c_i:c_.:cons_.:cons_i -> 1:c_i:c_.:cons_.:cons_i

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

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

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

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

   .(1, x) -> x [1]
   .(x, 1) -> x [1]
   i(1) -> 1 [1]
   .(c_i(x), x) -> 1 [1]
   .(x, c_i(x)) -> 1 [1]
   i(c_i(x)) -> x [1]
   .(y, c_.(c_i(y), z)) -> z [1]
   .(c_i(y), c_.(y, z)) -> z [1]
   encArg(1) -> 1 [0]
   encArg(cons_.(1, 1)) -> .(1, 1) [0]
   encArg(cons_.(1, cons_.(x_11, x_2''))) -> .(1, .(encArg(x_11), encArg(x_2''))) [0]
   encArg(cons_.(1, cons_i(x_12))) -> .(1, i(encArg(x_12))) [0]
   encArg(cons_.(1, x_2)) -> .(1, 1) [0]
   encArg(cons_.(cons_.(x_1', x_2'), 1)) -> .(.(encArg(x_1'), encArg(x_2')), 1) [0]
   encArg(cons_.(cons_.(x_1', x_2'), cons_.(x_13, x_21))) -> .(.(encArg(x_1'), encArg(x_2')), .(encArg(x_13), encArg(x_21))) [0]
   encArg(cons_.(cons_.(x_1', x_2'), cons_i(x_14))) -> .(.(encArg(x_1'), encArg(x_2')), i(encArg(x_14))) [0]
   encArg(cons_.(cons_.(x_1', x_2'), x_2)) -> .(.(encArg(x_1'), encArg(x_2')), 1) [0]
   encArg(cons_.(cons_i(x_1''), 1)) -> .(i(encArg(x_1'')), 1) [0]
   encArg(cons_.(cons_i(x_1''), cons_.(x_15, x_22))) -> .(i(encArg(x_1'')), .(encArg(x_15), encArg(x_22))) [0]
   encArg(cons_.(cons_i(x_1''), cons_i(x_16))) -> .(i(encArg(x_1'')), i(encArg(x_16))) [0]
   encArg(cons_.(cons_i(x_1''), x_2)) -> .(i(encArg(x_1'')), 1) [0]
   encArg(cons_.(x_1, 1)) -> .(1, 1) [0]
   encArg(cons_.(x_1, cons_.(x_17, x_23))) -> .(1, .(encArg(x_17), encArg(x_23))) [0]
   encArg(cons_.(x_1, cons_i(x_18))) -> .(1, i(encArg(x_18))) [0]
   encArg(cons_.(x_1, x_2)) -> .(1, 1) [0]
   encArg(cons_i(1)) -> i(1) [0]
   encArg(cons_i(cons_.(x_19, x_24))) -> i(.(encArg(x_19), encArg(x_24))) [0]
   encArg(cons_i(cons_i(x_110))) -> i(i(encArg(x_110))) [0]
   encArg(cons_i(x_1)) -> i(1) [0]
   encode_.(1, 1) -> .(1, 1) [0]
   encode_.(1, cons_.(x_113, x_26)) -> .(1, .(encArg(x_113), encArg(x_26))) [0]
   encode_.(1, cons_i(x_114)) -> .(1, i(encArg(x_114))) [0]
   encode_.(1, x_2) -> .(1, 1) [0]
   encode_.(cons_.(x_111, x_25), 1) -> .(.(encArg(x_111), encArg(x_25)), 1) [0]
   encode_.(cons_.(x_111, x_25), cons_.(x_115, x_27)) -> .(.(encArg(x_111), encArg(x_25)), .(encArg(x_115), encArg(x_27))) [0]
   encode_.(cons_.(x_111, x_25), cons_i(x_116)) -> .(.(encArg(x_111), encArg(x_25)), i(encArg(x_116))) [0]
   encode_.(cons_.(x_111, x_25), x_2) -> .(.(encArg(x_111), encArg(x_25)), 1) [0]
   encode_.(cons_i(x_112), 1) -> .(i(encArg(x_112)), 1) [0]
   encode_.(cons_i(x_112), cons_.(x_117, x_28)) -> .(i(encArg(x_112)), .(encArg(x_117), encArg(x_28))) [0]
   encode_.(cons_i(x_112), cons_i(x_118)) -> .(i(encArg(x_112)), i(encArg(x_118))) [0]
   encode_.(cons_i(x_112), x_2) -> .(i(encArg(x_112)), 1) [0]
   encode_.(x_1, 1) -> .(1, 1) [0]
   encode_.(x_1, cons_.(x_119, x_29)) -> .(1, .(encArg(x_119), encArg(x_29))) [0]
   encode_.(x_1, cons_i(x_120)) -> .(1, i(encArg(x_120))) [0]
   encode_.(x_1, x_2) -> .(1, 1) [0]
   encode_1 -> 1 [0]
   encode_i(1) -> i(1) [0]
   encode_i(cons_.(x_121, x_210)) -> i(.(encArg(x_121), encArg(x_210))) [0]
   encode_i(cons_i(x_122)) -> i(i(encArg(x_122))) [0]
   encode_i(x_1) -> i(1) [0]
   i(x0) -> c_i(x0) [0]
   .(x0, x1) -> c_.(x0, x1) [0]
   encArg(v0) -> 1 [0]
   encode_.(v0, v1) -> 1 [0]
   encode_1 -> 1 [0]
   encode_i(v0) -> 1 [0]
   i(v0) -> 1 [0]
   .(v0, v1) -> 1 [0]

The TRS has the following type information:
. :: 1:c_i:c_.:cons_.:cons_i -> 1:c_i:c_.:cons_.:cons_i -> 1:c_i:c_.:cons_.:cons_i
1 :: 1:c_i:c_.:cons_.:cons_i
i :: 1:c_i:c_.:cons_.:cons_i -> 1:c_i:c_.:cons_.:cons_i
c_i :: 1:c_i:c_.:cons_.:cons_i -> 1:c_i:c_.:cons_.:cons_i
c_. :: 1:c_i:c_.:cons_.:cons_i -> 1:c_i:c_.:cons_.:cons_i -> 1:c_i:c_.:cons_.:cons_i
encArg :: 1:c_i:c_.:cons_.:cons_i -> 1:c_i:c_.:cons_.:cons_i
cons_. :: 1:c_i:c_.:cons_.:cons_i -> 1:c_i:c_.:cons_.:cons_i -> 1:c_i:c_.:cons_.:cons_i
cons_i :: 1:c_i:c_.:cons_.:cons_i -> 1:c_i:c_.:cons_.:cons_i
encode_. :: 1:c_i:c_.:cons_.:cons_i -> 1:c_i:c_.:cons_.:cons_i -> 1:c_i:c_.:cons_.:cons_i
encode_1 :: 1:c_i:c_.:cons_.:cons_i
encode_i :: 1:c_i:c_.:cons_.:cons_i -> 1:c_i:c_.:cons_.:cons_i

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

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

   1 => 0

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

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

   .(z', z'') -{ 1 }-> x :|: x >= 0, z'' = x, z' = 0
   .(z', z'') -{ 1 }-> x :|: z'' = 0, z' = x, x >= 0
   .(z', z'') -{ 1 }-> z :|: z >= 0, z'' = 1 + (1 + y) + z, y >= 0, z' = y
   .(z', z'') -{ 1 }-> z :|: z' = 1 + y, z >= 0, y >= 0, z'' = 1 + y + z
   .(z', z'') -{ 1 }-> 0 :|: z' = 1 + x, x >= 0, z'' = x
   .(z', z'') -{ 1 }-> 0 :|: z' = x, x >= 0, z'' = 1 + x
   .(z', z'') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z'' = v1, z' = v0
   .(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' = x1, x0 >= 0, x1 >= 0, z' = x0
   encArg(z') -{ 0 }-> i(i(encArg(x_110))) :|: z' = 1 + (1 + x_110), x_110 >= 0
   encArg(z') -{ 0 }-> i(0) :|: z' = 1 + 0
   encArg(z') -{ 0 }-> i(0) :|: x_1 >= 0, z' = 1 + x_1
   encArg(z') -{ 0 }-> i(.(encArg(x_19), encArg(x_24))) :|: z' = 1 + (1 + x_19 + x_24), x_24 >= 0, x_19 >= 0
   encArg(z') -{ 0 }-> 0 :|: z' = 0
   encArg(z') -{ 0 }-> 0 :|: v0 >= 0, z' = v0
   encArg(z') -{ 0 }-> .(i(encArg(x_1'')), i(encArg(x_16))) :|: x_1'' >= 0, x_16 >= 0, z' = 1 + (1 + x_1'') + (1 + x_16)
   encArg(z') -{ 0 }-> .(i(encArg(x_1'')), 0) :|: z' = 1 + (1 + x_1'') + 0, x_1'' >= 0
   encArg(z') -{ 0 }-> .(i(encArg(x_1'')), 0) :|: z' = 1 + (1 + x_1'') + x_2, x_1'' >= 0, x_2 >= 0
   encArg(z') -{ 0 }-> .(i(encArg(x_1'')), .(encArg(x_15), encArg(x_22))) :|: x_15 >= 0, x_1'' >= 0, z' = 1 + (1 + x_1'') + (1 + x_15 + x_22), x_22 >= 0
   encArg(z') -{ 0 }-> .(0, i(encArg(x_12))) :|: z' = 1 + 0 + (1 + x_12), x_12 >= 0
   encArg(z') -{ 0 }-> .(0, i(encArg(x_18))) :|: x_1 >= 0, z' = 1 + x_1 + (1 + x_18), x_18 >= 0
   encArg(z') -{ 0 }-> .(0, 0) :|: z' = 1 + 0 + 0
   encArg(z') -{ 0 }-> .(0, 0) :|: x_2 >= 0, z' = 1 + 0 + x_2
   encArg(z') -{ 0 }-> .(0, 0) :|: x_1 >= 0, z' = 1 + x_1 + 0
   encArg(z') -{ 0 }-> .(0, 0) :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2
   encArg(z') -{ 0 }-> .(0, .(encArg(x_11), encArg(x_2''))) :|: x_11 >= 0, x_2'' >= 0, z' = 1 + 0 + (1 + x_11 + x_2'')
   encArg(z') -{ 0 }-> .(0, .(encArg(x_17), encArg(x_23))) :|: x_1 >= 0, x_17 >= 0, x_23 >= 0, z' = 1 + x_1 + (1 + x_17 + x_23)
   encArg(z') -{ 0 }-> .(.(encArg(x_1'), encArg(x_2')), i(encArg(x_14))) :|: z' = 1 + (1 + x_1' + x_2') + (1 + x_14), x_14 >= 0, x_2' >= 0, x_1' >= 0
   encArg(z') -{ 0 }-> .(.(encArg(x_1'), encArg(x_2')), 0) :|: x_2' >= 0, z' = 1 + (1 + x_1' + x_2') + 0, x_1' >= 0
   encArg(z') -{ 0 }-> .(.(encArg(x_1'), encArg(x_2')), 0) :|: x_2' >= 0, z' = 1 + (1 + x_1' + x_2') + x_2, x_1' >= 0, x_2 >= 0
   encArg(z') -{ 0 }-> .(.(encArg(x_1'), encArg(x_2')), .(encArg(x_13), encArg(x_21))) :|: x_2' >= 0, z' = 1 + (1 + x_1' + x_2') + (1 + x_13 + x_21), x_13 >= 0, x_1' >= 0, x_21 >= 0
   encode_.(z', z'') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z'' = v1, z' = v0
   encode_.(z', z'') -{ 0 }-> .(i(encArg(x_112)), i(encArg(x_118))) :|: z'' = 1 + x_118, z' = 1 + x_112, x_112 >= 0, x_118 >= 0
   encode_.(z', z'') -{ 0 }-> .(i(encArg(x_112)), 0) :|: z'' = 0, z' = 1 + x_112, x_112 >= 0
   encode_.(z', z'') -{ 0 }-> .(i(encArg(x_112)), 0) :|: x_2 >= 0, z' = 1 + x_112, z'' = x_2, x_112 >= 0
   encode_.(z', z'') -{ 0 }-> .(i(encArg(x_112)), .(encArg(x_117), encArg(x_28))) :|: x_117 >= 0, z' = 1 + x_112, z'' = 1 + x_117 + x_28, x_112 >= 0, x_28 >= 0
   encode_.(z', z'') -{ 0 }-> .(0, i(encArg(x_114))) :|: z'' = 1 + x_114, x_114 >= 0, z' = 0
   encode_.(z', z'') -{ 0 }-> .(0, i(encArg(x_120))) :|: x_1 >= 0, x_120 >= 0, z'' = 1 + x_120, z' = x_1
   encode_.(z', z'') -{ 0 }-> .(0, 0) :|: z'' = 0, z' = 0
   encode_.(z', z'') -{ 0 }-> .(0, 0) :|: x_2 >= 0, z'' = x_2, z' = 0
   encode_.(z', z'') -{ 0 }-> .(0, 0) :|: z'' = 0, x_1 >= 0, z' = x_1
   encode_.(z', z'') -{ 0 }-> .(0, 0) :|: x_1 >= 0, z' = x_1, x_2 >= 0, z'' = x_2
   encode_.(z', z'') -{ 0 }-> .(0, .(encArg(x_113), encArg(x_26))) :|: z'' = 1 + x_113 + x_26, x_113 >= 0, x_26 >= 0, z' = 0
   encode_.(z', z'') -{ 0 }-> .(0, .(encArg(x_119), encArg(x_29))) :|: x_1 >= 0, z'' = 1 + x_119 + x_29, z' = x_1, x_119 >= 0, x_29 >= 0
   encode_.(z', z'') -{ 0 }-> .(.(encArg(x_111), encArg(x_25)), i(encArg(x_116))) :|: z'' = 1 + x_116, x_116 >= 0, x_25 >= 0, z' = 1 + x_111 + x_25, x_111 >= 0
   encode_.(z', z'') -{ 0 }-> .(.(encArg(x_111), encArg(x_25)), 0) :|: z'' = 0, x_25 >= 0, z' = 1 + x_111 + x_25, x_111 >= 0
   encode_.(z', z'') -{ 0 }-> .(.(encArg(x_111), encArg(x_25)), 0) :|: x_25 >= 0, z' = 1 + x_111 + x_25, x_2 >= 0, z'' = x_2, x_111 >= 0
   encode_.(z', z'') -{ 0 }-> .(.(encArg(x_111), encArg(x_25)), .(encArg(x_115), encArg(x_27))) :|: z'' = 1 + x_115 + x_27, x_25 >= 0, x_115 >= 0, z' = 1 + x_111 + x_25, x_27 >= 0, x_111 >= 0
   encode_1 -{ 0 }-> 0 :|: 
   encode_i(z') -{ 0 }-> i(i(encArg(x_122))) :|: z' = 1 + x_122, x_122 >= 0
   encode_i(z') -{ 0 }-> i(0) :|: z' = 0
   encode_i(z') -{ 0 }-> i(0) :|: x_1 >= 0, z' = x_1
   encode_i(z') -{ 0 }-> i(.(encArg(x_121), encArg(x_210))) :|: z' = 1 + x_121 + x_210, x_121 >= 0, x_210 >= 0
   encode_i(z') -{ 0 }-> 0 :|: v0 >= 0, z' = v0
   i(z') -{ 1 }-> x :|: z' = 1 + x, x >= 0
   i(z') -{ 1 }-> 0 :|: z' = 0
   i(z') -{ 0 }-> 0 :|: v0 >= 0, z' = v0
   i(z') -{ 0 }-> 1 + x0 :|: x0 >= 0, z' = x0


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

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

   .(z', z'') -{ 1 }-> z :|: z >= 0, z'' = 1 + (1 + y) + z, y >= 0, z' = y
   .(z', z'') -{ 1 }-> z :|: z' = 1 + y, z >= 0, y >= 0, z'' = 1 + y + z
   .(z', z'') -{ 1 }-> 0 :|: z' = 1 + x, x >= 0, z'' = x
   .(z', z'') -{ 1 }-> 0 :|: z' = x, x >= 0, z'' = 1 + x
   .(z', z'') -{ 1 }-> x :|: x >= 0, z'' = x, z' = 0
   .(z', z'') -{ 1 }-> x :|: z'' = 0, z' = x, x >= 0
   .(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' = x1, x0 >= 0, x1 >= 0, z' = x0
   .(z', z'') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z'' = v1, z' = v0
   i(z') -{ 1 }-> x :|: z' = 1 + x, x >= 0
   i(z') -{ 1 }-> 0 :|: z' = 0
   i(z') -{ 0 }-> 1 + x0 :|: x0 >= 0, z' = x0
   i(z') -{ 0 }-> 0 :|: v0 >= 0, z' = v0

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

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

   .(z', z'') -{ 1 }-> x :|: x >= 0, z'' = x, z' = 0
   .(z', z'') -{ 1 }-> x :|: z'' = 0, z' = x, x >= 0
   .(z', z'') -{ 1 }-> z :|: z >= 0, z'' = 1 + (1 + y) + z, y >= 0, z' = y
   .(z', z'') -{ 1 }-> z :|: z' = 1 + y, z >= 0, y >= 0, z'' = 1 + y + z
   .(z', z'') -{ 1 }-> 0 :|: z' = 1 + x, x >= 0, z'' = x
   .(z', z'') -{ 1 }-> 0 :|: z' = x, x >= 0, z'' = 1 + x
   .(z', z'') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z'' = v1, z' = v0
   .(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' = x1, x0 >= 0, x1 >= 0, z' = x0
   encArg(z') -{ 1 }-> x :|: z' = 1 + 0 + 0, x >= 0, 0 = x, 0 = 0
   encArg(z') -{ 1 }-> x :|: x_2 >= 0, z' = 1 + 0 + x_2, x >= 0, 0 = x, 0 = 0
   encArg(z') -{ 1 }-> x :|: x_1 >= 0, z' = 1 + x_1 + 0, x >= 0, 0 = x, 0 = 0
   encArg(z') -{ 1 }-> x :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2, x >= 0, 0 = x, 0 = 0
   encArg(z') -{ 0 }-> i(i(encArg(x_110))) :|: z' = 1 + (1 + x_110), x_110 >= 0
   encArg(z') -{ 0 }-> i(.(encArg(x_19), encArg(x_24))) :|: z' = 1 + (1 + x_19 + x_24), x_24 >= 0, x_19 >= 0
   encArg(z') -{ 0 }-> 0 :|: z' = 0
   encArg(z') -{ 0 }-> 0 :|: v0 >= 0, z' = v0
   encArg(z') -{ 0 }-> 0 :|: z' = 1 + 0 + 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encArg(z') -{ 0 }-> 0 :|: x_2 >= 0, z' = 1 + 0 + x_2, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encArg(z') -{ 0 }-> 0 :|: x_1 >= 0, z' = 1 + x_1 + 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encArg(z') -{ 0 }-> 0 :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encArg(z') -{ 1 }-> 0 :|: z' = 1 + 0, 0 = 0
   encArg(z') -{ 0 }-> 0 :|: z' = 1 + 0, v0 >= 0, 0 = v0
   encArg(z') -{ 1 }-> 0 :|: x_1 >= 0, z' = 1 + x_1, 0 = 0
   encArg(z') -{ 0 }-> 0 :|: x_1 >= 0, z' = 1 + x_1, v0 >= 0, 0 = v0
   encArg(z') -{ 0 }-> .(i(encArg(x_1'')), i(encArg(x_16))) :|: x_1'' >= 0, x_16 >= 0, z' = 1 + (1 + x_1'') + (1 + x_16)
   encArg(z') -{ 0 }-> .(i(encArg(x_1'')), 0) :|: z' = 1 + (1 + x_1'') + 0, x_1'' >= 0
   encArg(z') -{ 0 }-> .(i(encArg(x_1'')), 0) :|: z' = 1 + (1 + x_1'') + x_2, x_1'' >= 0, x_2 >= 0
   encArg(z') -{ 0 }-> .(i(encArg(x_1'')), .(encArg(x_15), encArg(x_22))) :|: x_15 >= 0, x_1'' >= 0, z' = 1 + (1 + x_1'') + (1 + x_15 + x_22), x_22 >= 0
   encArg(z') -{ 0 }-> .(0, i(encArg(x_12))) :|: z' = 1 + 0 + (1 + x_12), x_12 >= 0
   encArg(z') -{ 0 }-> .(0, i(encArg(x_18))) :|: x_1 >= 0, z' = 1 + x_1 + (1 + x_18), x_18 >= 0
   encArg(z') -{ 0 }-> .(0, .(encArg(x_11), encArg(x_2''))) :|: x_11 >= 0, x_2'' >= 0, z' = 1 + 0 + (1 + x_11 + x_2'')
   encArg(z') -{ 0 }-> .(0, .(encArg(x_17), encArg(x_23))) :|: x_1 >= 0, x_17 >= 0, x_23 >= 0, z' = 1 + x_1 + (1 + x_17 + x_23)
   encArg(z') -{ 0 }-> .(.(encArg(x_1'), encArg(x_2')), i(encArg(x_14))) :|: z' = 1 + (1 + x_1' + x_2') + (1 + x_14), x_14 >= 0, x_2' >= 0, x_1' >= 0
   encArg(z') -{ 0 }-> .(.(encArg(x_1'), encArg(x_2')), 0) :|: x_2' >= 0, z' = 1 + (1 + x_1' + x_2') + 0, x_1' >= 0
   encArg(z') -{ 0 }-> .(.(encArg(x_1'), encArg(x_2')), 0) :|: x_2' >= 0, z' = 1 + (1 + x_1' + x_2') + x_2, x_1' >= 0, x_2 >= 0
   encArg(z') -{ 0 }-> .(.(encArg(x_1'), encArg(x_2')), .(encArg(x_13), encArg(x_21))) :|: x_2' >= 0, z' = 1 + (1 + x_1' + x_2') + (1 + x_13 + x_21), x_13 >= 0, x_1' >= 0, x_21 >= 0
   encArg(z') -{ 0 }-> 1 + x0 :|: z' = 1 + 0, x0 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 :|: x_1 >= 0, z' = 1 + x_1, x0 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 + x1 :|: z' = 1 + 0 + 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 + x1 :|: x_2 >= 0, z' = 1 + 0 + x_2, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 + x1 :|: x_1 >= 0, z' = 1 + x_1 + 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 + x1 :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 1 }-> x :|: z'' = 0, z' = 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 1 }-> x :|: x_2 >= 0, z'' = x_2, z' = 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 1 }-> x :|: z'' = 0, x_1 >= 0, z' = x_1, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 1 }-> x :|: x_1 >= 0, z' = x_1, x_2 >= 0, z'' = x_2, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z'' = v1, z' = v0
   encode_.(z', z'') -{ 0 }-> 0 :|: z'' = 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> 0 :|: x_2 >= 0, z'' = x_2, z' = 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> 0 :|: z'' = 0, x_1 >= 0, z' = x_1, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> 0 :|: x_1 >= 0, z' = x_1, x_2 >= 0, z'' = x_2, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> .(i(encArg(x_112)), i(encArg(x_118))) :|: z'' = 1 + x_118, z' = 1 + x_112, x_112 >= 0, x_118 >= 0
   encode_.(z', z'') -{ 0 }-> .(i(encArg(x_112)), 0) :|: z'' = 0, z' = 1 + x_112, x_112 >= 0
   encode_.(z', z'') -{ 0 }-> .(i(encArg(x_112)), 0) :|: x_2 >= 0, z' = 1 + x_112, z'' = x_2, x_112 >= 0
   encode_.(z', z'') -{ 0 }-> .(i(encArg(x_112)), .(encArg(x_117), encArg(x_28))) :|: x_117 >= 0, z' = 1 + x_112, z'' = 1 + x_117 + x_28, x_112 >= 0, x_28 >= 0
   encode_.(z', z'') -{ 0 }-> .(0, i(encArg(x_114))) :|: z'' = 1 + x_114, x_114 >= 0, z' = 0
   encode_.(z', z'') -{ 0 }-> .(0, i(encArg(x_120))) :|: x_1 >= 0, x_120 >= 0, z'' = 1 + x_120, z' = x_1
   encode_.(z', z'') -{ 0 }-> .(0, .(encArg(x_113), encArg(x_26))) :|: z'' = 1 + x_113 + x_26, x_113 >= 0, x_26 >= 0, z' = 0
   encode_.(z', z'') -{ 0 }-> .(0, .(encArg(x_119), encArg(x_29))) :|: x_1 >= 0, z'' = 1 + x_119 + x_29, z' = x_1, x_119 >= 0, x_29 >= 0
   encode_.(z', z'') -{ 0 }-> .(.(encArg(x_111), encArg(x_25)), i(encArg(x_116))) :|: z'' = 1 + x_116, x_116 >= 0, x_25 >= 0, z' = 1 + x_111 + x_25, x_111 >= 0
   encode_.(z', z'') -{ 0 }-> .(.(encArg(x_111), encArg(x_25)), 0) :|: z'' = 0, x_25 >= 0, z' = 1 + x_111 + x_25, x_111 >= 0
   encode_.(z', z'') -{ 0 }-> .(.(encArg(x_111), encArg(x_25)), 0) :|: x_25 >= 0, z' = 1 + x_111 + x_25, x_2 >= 0, z'' = x_2, x_111 >= 0
   encode_.(z', z'') -{ 0 }-> .(.(encArg(x_111), encArg(x_25)), .(encArg(x_115), encArg(x_27))) :|: z'' = 1 + x_115 + x_27, x_25 >= 0, x_115 >= 0, z' = 1 + x_111 + x_25, x_27 >= 0, x_111 >= 0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' = 0, z' = 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: x_2 >= 0, z'' = x_2, z' = 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' = 0, x_1 >= 0, z' = x_1, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: x_1 >= 0, z' = x_1, x_2 >= 0, z'' = x_2, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_1 -{ 0 }-> 0 :|: 
   encode_i(z') -{ 0 }-> i(i(encArg(x_122))) :|: z' = 1 + x_122, x_122 >= 0
   encode_i(z') -{ 0 }-> i(.(encArg(x_121), encArg(x_210))) :|: z' = 1 + x_121 + x_210, x_121 >= 0, x_210 >= 0
   encode_i(z') -{ 0 }-> 0 :|: v0 >= 0, z' = v0
   encode_i(z') -{ 1 }-> 0 :|: z' = 0, 0 = 0
   encode_i(z') -{ 0 }-> 0 :|: z' = 0, v0 >= 0, 0 = v0
   encode_i(z') -{ 1 }-> 0 :|: x_1 >= 0, z' = x_1, 0 = 0
   encode_i(z') -{ 0 }-> 0 :|: x_1 >= 0, z' = x_1, v0 >= 0, 0 = v0
   encode_i(z') -{ 0 }-> 1 + x0 :|: z' = 0, x0 >= 0, 0 = x0
   encode_i(z') -{ 0 }-> 1 + x0 :|: x_1 >= 0, z' = x_1, x0 >= 0, 0 = x0
   i(z') -{ 1 }-> x :|: z' = 1 + x, x >= 0
   i(z') -{ 1 }-> 0 :|: z' = 0
   i(z') -{ 0 }-> 0 :|: v0 >= 0, z' = v0
   i(z') -{ 0 }-> 1 + x0 :|: x0 >= 0, z' = x0


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

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

   .(z', z'') -{ 1 }-> z :|: z >= 0, z'' = 1 + (1 + z') + z, z' >= 0
   .(z', z'') -{ 1 }-> z :|: z >= 0, z' - 1 >= 0, z'' = 1 + (z' - 1) + z
   .(z', z'') -{ 1 }-> z' :|: z'' = 0, z' >= 0
   .(z', z'') -{ 1 }-> z'' :|: z'' >= 0, z' = 0
   .(z', z'') -{ 1 }-> 0 :|: z' - 1 >= 0, z'' = z' - 1
   .(z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' = 1 + z'
   .(z', z'') -{ 0 }-> 0 :|: z' >= 0, z'' >= 0
   .(z', z'') -{ 0 }-> 1 + z' + z'' :|: z' >= 0, z'' >= 0
   encArg(z') -{ 1 }-> x :|: z' = 1 + 0 + 0, x >= 0, 0 = x, 0 = 0
   encArg(z') -{ 1 }-> x :|: z' - 1 >= 0, x >= 0, 0 = x, 0 = 0
   encArg(z') -{ 1 }-> x :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2, x >= 0, 0 = x, 0 = 0
   encArg(z') -{ 0 }-> i(i(encArg(z' - 2))) :|: z' - 2 >= 0
   encArg(z') -{ 0 }-> i(.(encArg(x_19), encArg(x_24))) :|: z' = 1 + (1 + x_19 + x_24), x_24 >= 0, x_19 >= 0
   encArg(z') -{ 0 }-> 0 :|: z' = 0
   encArg(z') -{ 0 }-> 0 :|: z' >= 0
   encArg(z') -{ 0 }-> 0 :|: z' = 1 + 0 + 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encArg(z') -{ 0 }-> 0 :|: z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encArg(z') -{ 0 }-> 0 :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encArg(z') -{ 1 }-> 0 :|: z' = 1 + 0, 0 = 0
   encArg(z') -{ 0 }-> 0 :|: z' = 1 + 0, v0 >= 0, 0 = v0
   encArg(z') -{ 1 }-> 0 :|: z' - 1 >= 0, 0 = 0
   encArg(z') -{ 0 }-> 0 :|: z' - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z') -{ 0 }-> .(i(encArg(x_1'')), i(encArg(x_16))) :|: x_1'' >= 0, x_16 >= 0, z' = 1 + (1 + x_1'') + (1 + x_16)
   encArg(z') -{ 0 }-> .(i(encArg(x_1'')), 0) :|: z' = 1 + (1 + x_1'') + x_2, x_1'' >= 0, x_2 >= 0
   encArg(z') -{ 0 }-> .(i(encArg(x_1'')), .(encArg(x_15), encArg(x_22))) :|: x_15 >= 0, x_1'' >= 0, z' = 1 + (1 + x_1'') + (1 + x_15 + x_22), x_22 >= 0
   encArg(z') -{ 0 }-> .(i(encArg(z' - 2)), 0) :|: z' - 2 >= 0
   encArg(z') -{ 0 }-> .(0, i(encArg(x_18))) :|: x_1 >= 0, z' = 1 + x_1 + (1 + x_18), x_18 >= 0
   encArg(z') -{ 0 }-> .(0, i(encArg(z' - 2))) :|: z' - 2 >= 0
   encArg(z') -{ 0 }-> .(0, .(encArg(x_11), encArg(x_2''))) :|: x_11 >= 0, x_2'' >= 0, z' = 1 + 0 + (1 + x_11 + x_2'')
   encArg(z') -{ 0 }-> .(0, .(encArg(x_17), encArg(x_23))) :|: x_1 >= 0, x_17 >= 0, x_23 >= 0, z' = 1 + x_1 + (1 + x_17 + x_23)
   encArg(z') -{ 0 }-> .(.(encArg(x_1'), encArg(x_2')), i(encArg(x_14))) :|: z' = 1 + (1 + x_1' + x_2') + (1 + x_14), x_14 >= 0, x_2' >= 0, x_1' >= 0
   encArg(z') -{ 0 }-> .(.(encArg(x_1'), encArg(x_2')), 0) :|: x_2' >= 0, z' = 1 + (1 + x_1' + x_2') + 0, x_1' >= 0
   encArg(z') -{ 0 }-> .(.(encArg(x_1'), encArg(x_2')), 0) :|: x_2' >= 0, z' = 1 + (1 + x_1' + x_2') + x_2, x_1' >= 0, x_2 >= 0
   encArg(z') -{ 0 }-> .(.(encArg(x_1'), encArg(x_2')), .(encArg(x_13), encArg(x_21))) :|: x_2' >= 0, z' = 1 + (1 + x_1' + x_2') + (1 + x_13 + x_21), x_13 >= 0, x_1' >= 0, x_21 >= 0
   encArg(z') -{ 0 }-> 1 + x0 :|: z' = 1 + 0, x0 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 :|: z' - 1 >= 0, x0 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 + x1 :|: z' = 1 + 0 + 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 + x1 :|: z' - 1 >= 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 + x1 :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 1 }-> x :|: z'' = 0, z' = 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 1 }-> x :|: z'' >= 0, z' = 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 1 }-> x :|: z'' = 0, z' >= 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 1 }-> x :|: z' >= 0, z'' >= 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 0 }-> 0 :|: z' >= 0, z'' >= 0
   encode_.(z', z'') -{ 0 }-> 0 :|: z'' = 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> 0 :|: z'' >= 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> 0 :|: z'' = 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> 0 :|: z' >= 0, z'' >= 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> .(i(encArg(z' - 1)), i(encArg(z'' - 1))) :|: z' - 1 >= 0, z'' - 1 >= 0
   encode_.(z', z'') -{ 0 }-> .(i(encArg(z' - 1)), 0) :|: z'' = 0, z' - 1 >= 0
   encode_.(z', z'') -{ 0 }-> .(i(encArg(z' - 1)), 0) :|: z'' >= 0, z' - 1 >= 0
   encode_.(z', z'') -{ 0 }-> .(i(encArg(z' - 1)), .(encArg(x_117), encArg(x_28))) :|: x_117 >= 0, z'' = 1 + x_117 + x_28, z' - 1 >= 0, x_28 >= 0
   encode_.(z', z'') -{ 0 }-> .(0, i(encArg(z'' - 1))) :|: z'' - 1 >= 0, z' = 0
   encode_.(z', z'') -{ 0 }-> .(0, i(encArg(z'' - 1))) :|: z' >= 0, z'' - 1 >= 0
   encode_.(z', z'') -{ 0 }-> .(0, .(encArg(x_113), encArg(x_26))) :|: z'' = 1 + x_113 + x_26, x_113 >= 0, x_26 >= 0, z' = 0
   encode_.(z', z'') -{ 0 }-> .(0, .(encArg(x_119), encArg(x_29))) :|: z' >= 0, z'' = 1 + x_119 + x_29, x_119 >= 0, x_29 >= 0
   encode_.(z', z'') -{ 0 }-> .(.(encArg(x_111), encArg(x_25)), i(encArg(z'' - 1))) :|: z'' - 1 >= 0, x_25 >= 0, z' = 1 + x_111 + x_25, x_111 >= 0
   encode_.(z', z'') -{ 0 }-> .(.(encArg(x_111), encArg(x_25)), 0) :|: z'' = 0, x_25 >= 0, z' = 1 + x_111 + x_25, x_111 >= 0
   encode_.(z', z'') -{ 0 }-> .(.(encArg(x_111), encArg(x_25)), 0) :|: x_25 >= 0, z' = 1 + x_111 + x_25, z'' >= 0, x_111 >= 0
   encode_.(z', z'') -{ 0 }-> .(.(encArg(x_111), encArg(x_25)), .(encArg(x_115), encArg(x_27))) :|: z'' = 1 + x_115 + x_27, x_25 >= 0, x_115 >= 0, z' = 1 + x_111 + x_25, x_27 >= 0, x_111 >= 0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' = 0, z' = 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' >= 0, z' = 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' = 0, z' >= 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z' >= 0, z'' >= 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_1 -{ 0 }-> 0 :|: 
   encode_i(z') -{ 0 }-> i(i(encArg(z' - 1))) :|: z' - 1 >= 0
   encode_i(z') -{ 0 }-> i(.(encArg(x_121), encArg(x_210))) :|: z' = 1 + x_121 + x_210, x_121 >= 0, x_210 >= 0
   encode_i(z') -{ 0 }-> 0 :|: z' >= 0
   encode_i(z') -{ 1 }-> 0 :|: z' = 0, 0 = 0
   encode_i(z') -{ 0 }-> 0 :|: z' = 0, v0 >= 0, 0 = v0
   encode_i(z') -{ 1 }-> 0 :|: z' >= 0, 0 = 0
   encode_i(z') -{ 0 }-> 0 :|: z' >= 0, v0 >= 0, 0 = v0
   encode_i(z') -{ 0 }-> 1 + x0 :|: z' = 0, x0 >= 0, 0 = x0
   encode_i(z') -{ 0 }-> 1 + x0 :|: z' >= 0, x0 >= 0, 0 = x0
   i(z') -{ 1 }-> 0 :|: z' = 0
   i(z') -{ 0 }-> 0 :|: z' >= 0
   i(z') -{ 1 }-> z' - 1 :|: z' - 1 >= 0
   i(z') -{ 0 }-> 1 + z' :|: z' >= 0


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

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

   { . }
   { i }
   { encode_1 }
   { encArg }
   { encode_i }
   { encode_. }

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

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

   .(z', z'') -{ 1 }-> z :|: z >= 0, z'' = 1 + (1 + z') + z, z' >= 0
   .(z', z'') -{ 1 }-> z :|: z >= 0, z' - 1 >= 0, z'' = 1 + (z' - 1) + z
   .(z', z'') -{ 1 }-> z' :|: z'' = 0, z' >= 0
   .(z', z'') -{ 1 }-> z'' :|: z'' >= 0, z' = 0
   .(z', z'') -{ 1 }-> 0 :|: z' - 1 >= 0, z'' = z' - 1
   .(z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' = 1 + z'
   .(z', z'') -{ 0 }-> 0 :|: z' >= 0, z'' >= 0
   .(z', z'') -{ 0 }-> 1 + z' + z'' :|: z' >= 0, z'' >= 0
   encArg(z') -{ 1 }-> x :|: z' = 1 + 0 + 0, x >= 0, 0 = x, 0 = 0
   encArg(z') -{ 1 }-> x :|: z' - 1 >= 0, x >= 0, 0 = x, 0 = 0
   encArg(z') -{ 1 }-> x :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2, x >= 0, 0 = x, 0 = 0
   encArg(z') -{ 0 }-> i(i(encArg(z' - 2))) :|: z' - 2 >= 0
   encArg(z') -{ 0 }-> i(.(encArg(x_19), encArg(x_24))) :|: z' = 1 + (1 + x_19 + x_24), x_24 >= 0, x_19 >= 0
   encArg(z') -{ 0 }-> 0 :|: z' = 0
   encArg(z') -{ 0 }-> 0 :|: z' >= 0
   encArg(z') -{ 0 }-> 0 :|: z' = 1 + 0 + 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encArg(z') -{ 0 }-> 0 :|: z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encArg(z') -{ 0 }-> 0 :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encArg(z') -{ 1 }-> 0 :|: z' = 1 + 0, 0 = 0
   encArg(z') -{ 0 }-> 0 :|: z' = 1 + 0, v0 >= 0, 0 = v0
   encArg(z') -{ 1 }-> 0 :|: z' - 1 >= 0, 0 = 0
   encArg(z') -{ 0 }-> 0 :|: z' - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z') -{ 0 }-> .(i(encArg(x_1'')), i(encArg(x_16))) :|: x_1'' >= 0, x_16 >= 0, z' = 1 + (1 + x_1'') + (1 + x_16)
   encArg(z') -{ 0 }-> .(i(encArg(x_1'')), 0) :|: z' = 1 + (1 + x_1'') + x_2, x_1'' >= 0, x_2 >= 0
   encArg(z') -{ 0 }-> .(i(encArg(x_1'')), .(encArg(x_15), encArg(x_22))) :|: x_15 >= 0, x_1'' >= 0, z' = 1 + (1 + x_1'') + (1 + x_15 + x_22), x_22 >= 0
   encArg(z') -{ 0 }-> .(i(encArg(z' - 2)), 0) :|: z' - 2 >= 0
   encArg(z') -{ 0 }-> .(0, i(encArg(x_18))) :|: x_1 >= 0, z' = 1 + x_1 + (1 + x_18), x_18 >= 0
   encArg(z') -{ 0 }-> .(0, i(encArg(z' - 2))) :|: z' - 2 >= 0
   encArg(z') -{ 0 }-> .(0, .(encArg(x_11), encArg(x_2''))) :|: x_11 >= 0, x_2'' >= 0, z' = 1 + 0 + (1 + x_11 + x_2'')
   encArg(z') -{ 0 }-> .(0, .(encArg(x_17), encArg(x_23))) :|: x_1 >= 0, x_17 >= 0, x_23 >= 0, z' = 1 + x_1 + (1 + x_17 + x_23)
   encArg(z') -{ 0 }-> .(.(encArg(x_1'), encArg(x_2')), i(encArg(x_14))) :|: z' = 1 + (1 + x_1' + x_2') + (1 + x_14), x_14 >= 0, x_2' >= 0, x_1' >= 0
   encArg(z') -{ 0 }-> .(.(encArg(x_1'), encArg(x_2')), 0) :|: x_2' >= 0, z' = 1 + (1 + x_1' + x_2') + 0, x_1' >= 0
   encArg(z') -{ 0 }-> .(.(encArg(x_1'), encArg(x_2')), 0) :|: x_2' >= 0, z' = 1 + (1 + x_1' + x_2') + x_2, x_1' >= 0, x_2 >= 0
   encArg(z') -{ 0 }-> .(.(encArg(x_1'), encArg(x_2')), .(encArg(x_13), encArg(x_21))) :|: x_2' >= 0, z' = 1 + (1 + x_1' + x_2') + (1 + x_13 + x_21), x_13 >= 0, x_1' >= 0, x_21 >= 0
   encArg(z') -{ 0 }-> 1 + x0 :|: z' = 1 + 0, x0 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 :|: z' - 1 >= 0, x0 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 + x1 :|: z' = 1 + 0 + 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 + x1 :|: z' - 1 >= 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 + x1 :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 1 }-> x :|: z'' = 0, z' = 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 1 }-> x :|: z'' >= 0, z' = 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 1 }-> x :|: z'' = 0, z' >= 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 1 }-> x :|: z' >= 0, z'' >= 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 0 }-> 0 :|: z' >= 0, z'' >= 0
   encode_.(z', z'') -{ 0 }-> 0 :|: z'' = 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> 0 :|: z'' >= 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> 0 :|: z'' = 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> 0 :|: z' >= 0, z'' >= 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> .(i(encArg(z' - 1)), i(encArg(z'' - 1))) :|: z' - 1 >= 0, z'' - 1 >= 0
   encode_.(z', z'') -{ 0 }-> .(i(encArg(z' - 1)), 0) :|: z'' = 0, z' - 1 >= 0
   encode_.(z', z'') -{ 0 }-> .(i(encArg(z' - 1)), 0) :|: z'' >= 0, z' - 1 >= 0
   encode_.(z', z'') -{ 0 }-> .(i(encArg(z' - 1)), .(encArg(x_117), encArg(x_28))) :|: x_117 >= 0, z'' = 1 + x_117 + x_28, z' - 1 >= 0, x_28 >= 0
   encode_.(z', z'') -{ 0 }-> .(0, i(encArg(z'' - 1))) :|: z'' - 1 >= 0, z' = 0
   encode_.(z', z'') -{ 0 }-> .(0, i(encArg(z'' - 1))) :|: z' >= 0, z'' - 1 >= 0
   encode_.(z', z'') -{ 0 }-> .(0, .(encArg(x_113), encArg(x_26))) :|: z'' = 1 + x_113 + x_26, x_113 >= 0, x_26 >= 0, z' = 0
   encode_.(z', z'') -{ 0 }-> .(0, .(encArg(x_119), encArg(x_29))) :|: z' >= 0, z'' = 1 + x_119 + x_29, x_119 >= 0, x_29 >= 0
   encode_.(z', z'') -{ 0 }-> .(.(encArg(x_111), encArg(x_25)), i(encArg(z'' - 1))) :|: z'' - 1 >= 0, x_25 >= 0, z' = 1 + x_111 + x_25, x_111 >= 0
   encode_.(z', z'') -{ 0 }-> .(.(encArg(x_111), encArg(x_25)), 0) :|: z'' = 0, x_25 >= 0, z' = 1 + x_111 + x_25, x_111 >= 0
   encode_.(z', z'') -{ 0 }-> .(.(encArg(x_111), encArg(x_25)), 0) :|: x_25 >= 0, z' = 1 + x_111 + x_25, z'' >= 0, x_111 >= 0
   encode_.(z', z'') -{ 0 }-> .(.(encArg(x_111), encArg(x_25)), .(encArg(x_115), encArg(x_27))) :|: z'' = 1 + x_115 + x_27, x_25 >= 0, x_115 >= 0, z' = 1 + x_111 + x_25, x_27 >= 0, x_111 >= 0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' = 0, z' = 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' >= 0, z' = 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' = 0, z' >= 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z' >= 0, z'' >= 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_1 -{ 0 }-> 0 :|: 
   encode_i(z') -{ 0 }-> i(i(encArg(z' - 1))) :|: z' - 1 >= 0
   encode_i(z') -{ 0 }-> i(.(encArg(x_121), encArg(x_210))) :|: z' = 1 + x_121 + x_210, x_121 >= 0, x_210 >= 0
   encode_i(z') -{ 0 }-> 0 :|: z' >= 0
   encode_i(z') -{ 1 }-> 0 :|: z' = 0, 0 = 0
   encode_i(z') -{ 0 }-> 0 :|: z' = 0, v0 >= 0, 0 = v0
   encode_i(z') -{ 1 }-> 0 :|: z' >= 0, 0 = 0
   encode_i(z') -{ 0 }-> 0 :|: z' >= 0, v0 >= 0, 0 = v0
   encode_i(z') -{ 0 }-> 1 + x0 :|: z' = 0, x0 >= 0, 0 = x0
   encode_i(z') -{ 0 }-> 1 + x0 :|: z' >= 0, x0 >= 0, 0 = x0
   i(z') -{ 1 }-> 0 :|: z' = 0
   i(z') -{ 0 }-> 0 :|: z' >= 0
   i(z') -{ 1 }-> z' - 1 :|: z' - 1 >= 0
   i(z') -{ 0 }-> 1 + z' :|: z' >= 0

Function symbols to be analyzed: {.}, {i}, {encode_1}, {encArg}, {encode_i}, {encode_.}

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

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

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

   .(z', z'') -{ 1 }-> z :|: z >= 0, z'' = 1 + (1 + z') + z, z' >= 0
   .(z', z'') -{ 1 }-> z :|: z >= 0, z' - 1 >= 0, z'' = 1 + (z' - 1) + z
   .(z', z'') -{ 1 }-> z' :|: z'' = 0, z' >= 0
   .(z', z'') -{ 1 }-> z'' :|: z'' >= 0, z' = 0
   .(z', z'') -{ 1 }-> 0 :|: z' - 1 >= 0, z'' = z' - 1
   .(z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' = 1 + z'
   .(z', z'') -{ 0 }-> 0 :|: z' >= 0, z'' >= 0
   .(z', z'') -{ 0 }-> 1 + z' + z'' :|: z' >= 0, z'' >= 0
   encArg(z') -{ 1 }-> x :|: z' = 1 + 0 + 0, x >= 0, 0 = x, 0 = 0
   encArg(z') -{ 1 }-> x :|: z' - 1 >= 0, x >= 0, 0 = x, 0 = 0
   encArg(z') -{ 1 }-> x :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2, x >= 0, 0 = x, 0 = 0
   encArg(z') -{ 0 }-> i(i(encArg(z' - 2))) :|: z' - 2 >= 0
   encArg(z') -{ 0 }-> i(.(encArg(x_19), encArg(x_24))) :|: z' = 1 + (1 + x_19 + x_24), x_24 >= 0, x_19 >= 0
   encArg(z') -{ 0 }-> 0 :|: z' = 0
   encArg(z') -{ 0 }-> 0 :|: z' >= 0
   encArg(z') -{ 0 }-> 0 :|: z' = 1 + 0 + 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encArg(z') -{ 0 }-> 0 :|: z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encArg(z') -{ 0 }-> 0 :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encArg(z') -{ 1 }-> 0 :|: z' = 1 + 0, 0 = 0
   encArg(z') -{ 0 }-> 0 :|: z' = 1 + 0, v0 >= 0, 0 = v0
   encArg(z') -{ 1 }-> 0 :|: z' - 1 >= 0, 0 = 0
   encArg(z') -{ 0 }-> 0 :|: z' - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z') -{ 0 }-> .(i(encArg(x_1'')), i(encArg(x_16))) :|: x_1'' >= 0, x_16 >= 0, z' = 1 + (1 + x_1'') + (1 + x_16)
   encArg(z') -{ 0 }-> .(i(encArg(x_1'')), 0) :|: z' = 1 + (1 + x_1'') + x_2, x_1'' >= 0, x_2 >= 0
   encArg(z') -{ 0 }-> .(i(encArg(x_1'')), .(encArg(x_15), encArg(x_22))) :|: x_15 >= 0, x_1'' >= 0, z' = 1 + (1 + x_1'') + (1 + x_15 + x_22), x_22 >= 0
   encArg(z') -{ 0 }-> .(i(encArg(z' - 2)), 0) :|: z' - 2 >= 0
   encArg(z') -{ 0 }-> .(0, i(encArg(x_18))) :|: x_1 >= 0, z' = 1 + x_1 + (1 + x_18), x_18 >= 0
   encArg(z') -{ 0 }-> .(0, i(encArg(z' - 2))) :|: z' - 2 >= 0
   encArg(z') -{ 0 }-> .(0, .(encArg(x_11), encArg(x_2''))) :|: x_11 >= 0, x_2'' >= 0, z' = 1 + 0 + (1 + x_11 + x_2'')
   encArg(z') -{ 0 }-> .(0, .(encArg(x_17), encArg(x_23))) :|: x_1 >= 0, x_17 >= 0, x_23 >= 0, z' = 1 + x_1 + (1 + x_17 + x_23)
   encArg(z') -{ 0 }-> .(.(encArg(x_1'), encArg(x_2')), i(encArg(x_14))) :|: z' = 1 + (1 + x_1' + x_2') + (1 + x_14), x_14 >= 0, x_2' >= 0, x_1' >= 0
   encArg(z') -{ 0 }-> .(.(encArg(x_1'), encArg(x_2')), 0) :|: x_2' >= 0, z' = 1 + (1 + x_1' + x_2') + 0, x_1' >= 0
   encArg(z') -{ 0 }-> .(.(encArg(x_1'), encArg(x_2')), 0) :|: x_2' >= 0, z' = 1 + (1 + x_1' + x_2') + x_2, x_1' >= 0, x_2 >= 0
   encArg(z') -{ 0 }-> .(.(encArg(x_1'), encArg(x_2')), .(encArg(x_13), encArg(x_21))) :|: x_2' >= 0, z' = 1 + (1 + x_1' + x_2') + (1 + x_13 + x_21), x_13 >= 0, x_1' >= 0, x_21 >= 0
   encArg(z') -{ 0 }-> 1 + x0 :|: z' = 1 + 0, x0 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 :|: z' - 1 >= 0, x0 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 + x1 :|: z' = 1 + 0 + 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 + x1 :|: z' - 1 >= 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 + x1 :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 1 }-> x :|: z'' = 0, z' = 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 1 }-> x :|: z'' >= 0, z' = 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 1 }-> x :|: z'' = 0, z' >= 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 1 }-> x :|: z' >= 0, z'' >= 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 0 }-> 0 :|: z' >= 0, z'' >= 0
   encode_.(z', z'') -{ 0 }-> 0 :|: z'' = 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> 0 :|: z'' >= 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> 0 :|: z'' = 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> 0 :|: z' >= 0, z'' >= 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> .(i(encArg(z' - 1)), i(encArg(z'' - 1))) :|: z' - 1 >= 0, z'' - 1 >= 0
   encode_.(z', z'') -{ 0 }-> .(i(encArg(z' - 1)), 0) :|: z'' = 0, z' - 1 >= 0
   encode_.(z', z'') -{ 0 }-> .(i(encArg(z' - 1)), 0) :|: z'' >= 0, z' - 1 >= 0
   encode_.(z', z'') -{ 0 }-> .(i(encArg(z' - 1)), .(encArg(x_117), encArg(x_28))) :|: x_117 >= 0, z'' = 1 + x_117 + x_28, z' - 1 >= 0, x_28 >= 0
   encode_.(z', z'') -{ 0 }-> .(0, i(encArg(z'' - 1))) :|: z'' - 1 >= 0, z' = 0
   encode_.(z', z'') -{ 0 }-> .(0, i(encArg(z'' - 1))) :|: z' >= 0, z'' - 1 >= 0
   encode_.(z', z'') -{ 0 }-> .(0, .(encArg(x_113), encArg(x_26))) :|: z'' = 1 + x_113 + x_26, x_113 >= 0, x_26 >= 0, z' = 0
   encode_.(z', z'') -{ 0 }-> .(0, .(encArg(x_119), encArg(x_29))) :|: z' >= 0, z'' = 1 + x_119 + x_29, x_119 >= 0, x_29 >= 0
   encode_.(z', z'') -{ 0 }-> .(.(encArg(x_111), encArg(x_25)), i(encArg(z'' - 1))) :|: z'' - 1 >= 0, x_25 >= 0, z' = 1 + x_111 + x_25, x_111 >= 0
   encode_.(z', z'') -{ 0 }-> .(.(encArg(x_111), encArg(x_25)), 0) :|: z'' = 0, x_25 >= 0, z' = 1 + x_111 + x_25, x_111 >= 0
   encode_.(z', z'') -{ 0 }-> .(.(encArg(x_111), encArg(x_25)), 0) :|: x_25 >= 0, z' = 1 + x_111 + x_25, z'' >= 0, x_111 >= 0
   encode_.(z', z'') -{ 0 }-> .(.(encArg(x_111), encArg(x_25)), .(encArg(x_115), encArg(x_27))) :|: z'' = 1 + x_115 + x_27, x_25 >= 0, x_115 >= 0, z' = 1 + x_111 + x_25, x_27 >= 0, x_111 >= 0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' = 0, z' = 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' >= 0, z' = 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' = 0, z' >= 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z' >= 0, z'' >= 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_1 -{ 0 }-> 0 :|: 
   encode_i(z') -{ 0 }-> i(i(encArg(z' - 1))) :|: z' - 1 >= 0
   encode_i(z') -{ 0 }-> i(.(encArg(x_121), encArg(x_210))) :|: z' = 1 + x_121 + x_210, x_121 >= 0, x_210 >= 0
   encode_i(z') -{ 0 }-> 0 :|: z' >= 0
   encode_i(z') -{ 1 }-> 0 :|: z' = 0, 0 = 0
   encode_i(z') -{ 0 }-> 0 :|: z' = 0, v0 >= 0, 0 = v0
   encode_i(z') -{ 1 }-> 0 :|: z' >= 0, 0 = 0
   encode_i(z') -{ 0 }-> 0 :|: z' >= 0, v0 >= 0, 0 = v0
   encode_i(z') -{ 0 }-> 1 + x0 :|: z' = 0, x0 >= 0, 0 = x0
   encode_i(z') -{ 0 }-> 1 + x0 :|: z' >= 0, x0 >= 0, 0 = x0
   i(z') -{ 1 }-> 0 :|: z' = 0
   i(z') -{ 0 }-> 0 :|: z' >= 0
   i(z') -{ 1 }-> z' - 1 :|: z' - 1 >= 0
   i(z') -{ 0 }-> 1 + z' :|: z' >= 0

Function symbols to be analyzed: {.}, {i}, {encode_1}, {encArg}, {encode_i}, {encode_.}

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

(27) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   .(z', z'') -{ 1 }-> z :|: z >= 0, z'' = 1 + (1 + z') + z, z' >= 0
   .(z', z'') -{ 1 }-> z :|: z >= 0, z' - 1 >= 0, z'' = 1 + (z' - 1) + z
   .(z', z'') -{ 1 }-> z' :|: z'' = 0, z' >= 0
   .(z', z'') -{ 1 }-> z'' :|: z'' >= 0, z' = 0
   .(z', z'') -{ 1 }-> 0 :|: z' - 1 >= 0, z'' = z' - 1
   .(z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' = 1 + z'
   .(z', z'') -{ 0 }-> 0 :|: z' >= 0, z'' >= 0
   .(z', z'') -{ 0 }-> 1 + z' + z'' :|: z' >= 0, z'' >= 0
   encArg(z') -{ 1 }-> x :|: z' = 1 + 0 + 0, x >= 0, 0 = x, 0 = 0
   encArg(z') -{ 1 }-> x :|: z' - 1 >= 0, x >= 0, 0 = x, 0 = 0
   encArg(z') -{ 1 }-> x :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2, x >= 0, 0 = x, 0 = 0
   encArg(z') -{ 0 }-> i(i(encArg(z' - 2))) :|: z' - 2 >= 0
   encArg(z') -{ 0 }-> i(.(encArg(x_19), encArg(x_24))) :|: z' = 1 + (1 + x_19 + x_24), x_24 >= 0, x_19 >= 0
   encArg(z') -{ 0 }-> 0 :|: z' = 0
   encArg(z') -{ 0 }-> 0 :|: z' >= 0
   encArg(z') -{ 0 }-> 0 :|: z' = 1 + 0 + 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encArg(z') -{ 0 }-> 0 :|: z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encArg(z') -{ 0 }-> 0 :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encArg(z') -{ 1 }-> 0 :|: z' = 1 + 0, 0 = 0
   encArg(z') -{ 0 }-> 0 :|: z' = 1 + 0, v0 >= 0, 0 = v0
   encArg(z') -{ 1 }-> 0 :|: z' - 1 >= 0, 0 = 0
   encArg(z') -{ 0 }-> 0 :|: z' - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z') -{ 0 }-> .(i(encArg(x_1'')), i(encArg(x_16))) :|: x_1'' >= 0, x_16 >= 0, z' = 1 + (1 + x_1'') + (1 + x_16)
   encArg(z') -{ 0 }-> .(i(encArg(x_1'')), 0) :|: z' = 1 + (1 + x_1'') + x_2, x_1'' >= 0, x_2 >= 0
   encArg(z') -{ 0 }-> .(i(encArg(x_1'')), .(encArg(x_15), encArg(x_22))) :|: x_15 >= 0, x_1'' >= 0, z' = 1 + (1 + x_1'') + (1 + x_15 + x_22), x_22 >= 0
   encArg(z') -{ 0 }-> .(i(encArg(z' - 2)), 0) :|: z' - 2 >= 0
   encArg(z') -{ 0 }-> .(0, i(encArg(x_18))) :|: x_1 >= 0, z' = 1 + x_1 + (1 + x_18), x_18 >= 0
   encArg(z') -{ 0 }-> .(0, i(encArg(z' - 2))) :|: z' - 2 >= 0
   encArg(z') -{ 0 }-> .(0, .(encArg(x_11), encArg(x_2''))) :|: x_11 >= 0, x_2'' >= 0, z' = 1 + 0 + (1 + x_11 + x_2'')
   encArg(z') -{ 0 }-> .(0, .(encArg(x_17), encArg(x_23))) :|: x_1 >= 0, x_17 >= 0, x_23 >= 0, z' = 1 + x_1 + (1 + x_17 + x_23)
   encArg(z') -{ 0 }-> .(.(encArg(x_1'), encArg(x_2')), i(encArg(x_14))) :|: z' = 1 + (1 + x_1' + x_2') + (1 + x_14), x_14 >= 0, x_2' >= 0, x_1' >= 0
   encArg(z') -{ 0 }-> .(.(encArg(x_1'), encArg(x_2')), 0) :|: x_2' >= 0, z' = 1 + (1 + x_1' + x_2') + 0, x_1' >= 0
   encArg(z') -{ 0 }-> .(.(encArg(x_1'), encArg(x_2')), 0) :|: x_2' >= 0, z' = 1 + (1 + x_1' + x_2') + x_2, x_1' >= 0, x_2 >= 0
   encArg(z') -{ 0 }-> .(.(encArg(x_1'), encArg(x_2')), .(encArg(x_13), encArg(x_21))) :|: x_2' >= 0, z' = 1 + (1 + x_1' + x_2') + (1 + x_13 + x_21), x_13 >= 0, x_1' >= 0, x_21 >= 0
   encArg(z') -{ 0 }-> 1 + x0 :|: z' = 1 + 0, x0 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 :|: z' - 1 >= 0, x0 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 + x1 :|: z' = 1 + 0 + 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 + x1 :|: z' - 1 >= 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 + x1 :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 1 }-> x :|: z'' = 0, z' = 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 1 }-> x :|: z'' >= 0, z' = 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 1 }-> x :|: z'' = 0, z' >= 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 1 }-> x :|: z' >= 0, z'' >= 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 0 }-> 0 :|: z' >= 0, z'' >= 0
   encode_.(z', z'') -{ 0 }-> 0 :|: z'' = 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> 0 :|: z'' >= 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> 0 :|: z'' = 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> 0 :|: z' >= 0, z'' >= 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> .(i(encArg(z' - 1)), i(encArg(z'' - 1))) :|: z' - 1 >= 0, z'' - 1 >= 0
   encode_.(z', z'') -{ 0 }-> .(i(encArg(z' - 1)), 0) :|: z'' = 0, z' - 1 >= 0
   encode_.(z', z'') -{ 0 }-> .(i(encArg(z' - 1)), 0) :|: z'' >= 0, z' - 1 >= 0
   encode_.(z', z'') -{ 0 }-> .(i(encArg(z' - 1)), .(encArg(x_117), encArg(x_28))) :|: x_117 >= 0, z'' = 1 + x_117 + x_28, z' - 1 >= 0, x_28 >= 0
   encode_.(z', z'') -{ 0 }-> .(0, i(encArg(z'' - 1))) :|: z'' - 1 >= 0, z' = 0
   encode_.(z', z'') -{ 0 }-> .(0, i(encArg(z'' - 1))) :|: z' >= 0, z'' - 1 >= 0
   encode_.(z', z'') -{ 0 }-> .(0, .(encArg(x_113), encArg(x_26))) :|: z'' = 1 + x_113 + x_26, x_113 >= 0, x_26 >= 0, z' = 0
   encode_.(z', z'') -{ 0 }-> .(0, .(encArg(x_119), encArg(x_29))) :|: z' >= 0, z'' = 1 + x_119 + x_29, x_119 >= 0, x_29 >= 0
   encode_.(z', z'') -{ 0 }-> .(.(encArg(x_111), encArg(x_25)), i(encArg(z'' - 1))) :|: z'' - 1 >= 0, x_25 >= 0, z' = 1 + x_111 + x_25, x_111 >= 0
   encode_.(z', z'') -{ 0 }-> .(.(encArg(x_111), encArg(x_25)), 0) :|: z'' = 0, x_25 >= 0, z' = 1 + x_111 + x_25, x_111 >= 0
   encode_.(z', z'') -{ 0 }-> .(.(encArg(x_111), encArg(x_25)), 0) :|: x_25 >= 0, z' = 1 + x_111 + x_25, z'' >= 0, x_111 >= 0
   encode_.(z', z'') -{ 0 }-> .(.(encArg(x_111), encArg(x_25)), .(encArg(x_115), encArg(x_27))) :|: z'' = 1 + x_115 + x_27, x_25 >= 0, x_115 >= 0, z' = 1 + x_111 + x_25, x_27 >= 0, x_111 >= 0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' = 0, z' = 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' >= 0, z' = 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' = 0, z' >= 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z' >= 0, z'' >= 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_1 -{ 0 }-> 0 :|: 
   encode_i(z') -{ 0 }-> i(i(encArg(z' - 1))) :|: z' - 1 >= 0
   encode_i(z') -{ 0 }-> i(.(encArg(x_121), encArg(x_210))) :|: z' = 1 + x_121 + x_210, x_121 >= 0, x_210 >= 0
   encode_i(z') -{ 0 }-> 0 :|: z' >= 0
   encode_i(z') -{ 1 }-> 0 :|: z' = 0, 0 = 0
   encode_i(z') -{ 0 }-> 0 :|: z' = 0, v0 >= 0, 0 = v0
   encode_i(z') -{ 1 }-> 0 :|: z' >= 0, 0 = 0
   encode_i(z') -{ 0 }-> 0 :|: z' >= 0, v0 >= 0, 0 = v0
   encode_i(z') -{ 0 }-> 1 + x0 :|: z' = 0, x0 >= 0, 0 = x0
   encode_i(z') -{ 0 }-> 1 + x0 :|: z' >= 0, x0 >= 0, 0 = x0
   i(z') -{ 1 }-> 0 :|: z' = 0
   i(z') -{ 0 }-> 0 :|: z' >= 0
   i(z') -{ 1 }-> z' - 1 :|: z' - 1 >= 0
   i(z') -{ 0 }-> 1 + z' :|: z' >= 0

Function symbols to be analyzed: {.}, {i}, {encode_1}, {encArg}, {encode_i}, {encode_.}
Previous analysis results are:
  .: runtime: ?, size: O(n^1) [1 + z' + z'']

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

(29) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   .(z', z'') -{ 1 }-> z :|: z >= 0, z'' = 1 + (1 + z') + z, z' >= 0
   .(z', z'') -{ 1 }-> z :|: z >= 0, z' - 1 >= 0, z'' = 1 + (z' - 1) + z
   .(z', z'') -{ 1 }-> z' :|: z'' = 0, z' >= 0
   .(z', z'') -{ 1 }-> z'' :|: z'' >= 0, z' = 0
   .(z', z'') -{ 1 }-> 0 :|: z' - 1 >= 0, z'' = z' - 1
   .(z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' = 1 + z'
   .(z', z'') -{ 0 }-> 0 :|: z' >= 0, z'' >= 0
   .(z', z'') -{ 0 }-> 1 + z' + z'' :|: z' >= 0, z'' >= 0
   encArg(z') -{ 1 }-> x :|: z' = 1 + 0 + 0, x >= 0, 0 = x, 0 = 0
   encArg(z') -{ 1 }-> x :|: z' - 1 >= 0, x >= 0, 0 = x, 0 = 0
   encArg(z') -{ 1 }-> x :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2, x >= 0, 0 = x, 0 = 0
   encArg(z') -{ 0 }-> i(i(encArg(z' - 2))) :|: z' - 2 >= 0
   encArg(z') -{ 0 }-> i(.(encArg(x_19), encArg(x_24))) :|: z' = 1 + (1 + x_19 + x_24), x_24 >= 0, x_19 >= 0
   encArg(z') -{ 0 }-> 0 :|: z' = 0
   encArg(z') -{ 0 }-> 0 :|: z' >= 0
   encArg(z') -{ 0 }-> 0 :|: z' = 1 + 0 + 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encArg(z') -{ 0 }-> 0 :|: z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encArg(z') -{ 0 }-> 0 :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encArg(z') -{ 1 }-> 0 :|: z' = 1 + 0, 0 = 0
   encArg(z') -{ 0 }-> 0 :|: z' = 1 + 0, v0 >= 0, 0 = v0
   encArg(z') -{ 1 }-> 0 :|: z' - 1 >= 0, 0 = 0
   encArg(z') -{ 0 }-> 0 :|: z' - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z') -{ 0 }-> .(i(encArg(x_1'')), i(encArg(x_16))) :|: x_1'' >= 0, x_16 >= 0, z' = 1 + (1 + x_1'') + (1 + x_16)
   encArg(z') -{ 0 }-> .(i(encArg(x_1'')), 0) :|: z' = 1 + (1 + x_1'') + x_2, x_1'' >= 0, x_2 >= 0
   encArg(z') -{ 0 }-> .(i(encArg(x_1'')), .(encArg(x_15), encArg(x_22))) :|: x_15 >= 0, x_1'' >= 0, z' = 1 + (1 + x_1'') + (1 + x_15 + x_22), x_22 >= 0
   encArg(z') -{ 0 }-> .(i(encArg(z' - 2)), 0) :|: z' - 2 >= 0
   encArg(z') -{ 0 }-> .(0, i(encArg(x_18))) :|: x_1 >= 0, z' = 1 + x_1 + (1 + x_18), x_18 >= 0
   encArg(z') -{ 0 }-> .(0, i(encArg(z' - 2))) :|: z' - 2 >= 0
   encArg(z') -{ 0 }-> .(0, .(encArg(x_11), encArg(x_2''))) :|: x_11 >= 0, x_2'' >= 0, z' = 1 + 0 + (1 + x_11 + x_2'')
   encArg(z') -{ 0 }-> .(0, .(encArg(x_17), encArg(x_23))) :|: x_1 >= 0, x_17 >= 0, x_23 >= 0, z' = 1 + x_1 + (1 + x_17 + x_23)
   encArg(z') -{ 0 }-> .(.(encArg(x_1'), encArg(x_2')), i(encArg(x_14))) :|: z' = 1 + (1 + x_1' + x_2') + (1 + x_14), x_14 >= 0, x_2' >= 0, x_1' >= 0
   encArg(z') -{ 0 }-> .(.(encArg(x_1'), encArg(x_2')), 0) :|: x_2' >= 0, z' = 1 + (1 + x_1' + x_2') + 0, x_1' >= 0
   encArg(z') -{ 0 }-> .(.(encArg(x_1'), encArg(x_2')), 0) :|: x_2' >= 0, z' = 1 + (1 + x_1' + x_2') + x_2, x_1' >= 0, x_2 >= 0
   encArg(z') -{ 0 }-> .(.(encArg(x_1'), encArg(x_2')), .(encArg(x_13), encArg(x_21))) :|: x_2' >= 0, z' = 1 + (1 + x_1' + x_2') + (1 + x_13 + x_21), x_13 >= 0, x_1' >= 0, x_21 >= 0
   encArg(z') -{ 0 }-> 1 + x0 :|: z' = 1 + 0, x0 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 :|: z' - 1 >= 0, x0 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 + x1 :|: z' = 1 + 0 + 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 + x1 :|: z' - 1 >= 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 + x1 :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 1 }-> x :|: z'' = 0, z' = 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 1 }-> x :|: z'' >= 0, z' = 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 1 }-> x :|: z'' = 0, z' >= 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 1 }-> x :|: z' >= 0, z'' >= 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 0 }-> 0 :|: z' >= 0, z'' >= 0
   encode_.(z', z'') -{ 0 }-> 0 :|: z'' = 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> 0 :|: z'' >= 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> 0 :|: z'' = 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> 0 :|: z' >= 0, z'' >= 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> .(i(encArg(z' - 1)), i(encArg(z'' - 1))) :|: z' - 1 >= 0, z'' - 1 >= 0
   encode_.(z', z'') -{ 0 }-> .(i(encArg(z' - 1)), 0) :|: z'' = 0, z' - 1 >= 0
   encode_.(z', z'') -{ 0 }-> .(i(encArg(z' - 1)), 0) :|: z'' >= 0, z' - 1 >= 0
   encode_.(z', z'') -{ 0 }-> .(i(encArg(z' - 1)), .(encArg(x_117), encArg(x_28))) :|: x_117 >= 0, z'' = 1 + x_117 + x_28, z' - 1 >= 0, x_28 >= 0
   encode_.(z', z'') -{ 0 }-> .(0, i(encArg(z'' - 1))) :|: z'' - 1 >= 0, z' = 0
   encode_.(z', z'') -{ 0 }-> .(0, i(encArg(z'' - 1))) :|: z' >= 0, z'' - 1 >= 0
   encode_.(z', z'') -{ 0 }-> .(0, .(encArg(x_113), encArg(x_26))) :|: z'' = 1 + x_113 + x_26, x_113 >= 0, x_26 >= 0, z' = 0
   encode_.(z', z'') -{ 0 }-> .(0, .(encArg(x_119), encArg(x_29))) :|: z' >= 0, z'' = 1 + x_119 + x_29, x_119 >= 0, x_29 >= 0
   encode_.(z', z'') -{ 0 }-> .(.(encArg(x_111), encArg(x_25)), i(encArg(z'' - 1))) :|: z'' - 1 >= 0, x_25 >= 0, z' = 1 + x_111 + x_25, x_111 >= 0
   encode_.(z', z'') -{ 0 }-> .(.(encArg(x_111), encArg(x_25)), 0) :|: z'' = 0, x_25 >= 0, z' = 1 + x_111 + x_25, x_111 >= 0
   encode_.(z', z'') -{ 0 }-> .(.(encArg(x_111), encArg(x_25)), 0) :|: x_25 >= 0, z' = 1 + x_111 + x_25, z'' >= 0, x_111 >= 0
   encode_.(z', z'') -{ 0 }-> .(.(encArg(x_111), encArg(x_25)), .(encArg(x_115), encArg(x_27))) :|: z'' = 1 + x_115 + x_27, x_25 >= 0, x_115 >= 0, z' = 1 + x_111 + x_25, x_27 >= 0, x_111 >= 0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' = 0, z' = 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' >= 0, z' = 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' = 0, z' >= 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z' >= 0, z'' >= 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_1 -{ 0 }-> 0 :|: 
   encode_i(z') -{ 0 }-> i(i(encArg(z' - 1))) :|: z' - 1 >= 0
   encode_i(z') -{ 0 }-> i(.(encArg(x_121), encArg(x_210))) :|: z' = 1 + x_121 + x_210, x_121 >= 0, x_210 >= 0
   encode_i(z') -{ 0 }-> 0 :|: z' >= 0
   encode_i(z') -{ 1 }-> 0 :|: z' = 0, 0 = 0
   encode_i(z') -{ 0 }-> 0 :|: z' = 0, v0 >= 0, 0 = v0
   encode_i(z') -{ 1 }-> 0 :|: z' >= 0, 0 = 0
   encode_i(z') -{ 0 }-> 0 :|: z' >= 0, v0 >= 0, 0 = v0
   encode_i(z') -{ 0 }-> 1 + x0 :|: z' = 0, x0 >= 0, 0 = x0
   encode_i(z') -{ 0 }-> 1 + x0 :|: z' >= 0, x0 >= 0, 0 = x0
   i(z') -{ 1 }-> 0 :|: z' = 0
   i(z') -{ 0 }-> 0 :|: z' >= 0
   i(z') -{ 1 }-> z' - 1 :|: z' - 1 >= 0
   i(z') -{ 0 }-> 1 + z' :|: z' >= 0

Function symbols to be analyzed: {i}, {encode_1}, {encArg}, {encode_i}, {encode_.}
Previous analysis results are:
  .: runtime: O(1) [1], size: O(n^1) [1 + z' + z'']

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

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

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

   .(z', z'') -{ 1 }-> z :|: z >= 0, z'' = 1 + (1 + z') + z, z' >= 0
   .(z', z'') -{ 1 }-> z :|: z >= 0, z' - 1 >= 0, z'' = 1 + (z' - 1) + z
   .(z', z'') -{ 1 }-> z' :|: z'' = 0, z' >= 0
   .(z', z'') -{ 1 }-> z'' :|: z'' >= 0, z' = 0
   .(z', z'') -{ 1 }-> 0 :|: z' - 1 >= 0, z'' = z' - 1
   .(z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' = 1 + z'
   .(z', z'') -{ 0 }-> 0 :|: z' >= 0, z'' >= 0
   .(z', z'') -{ 0 }-> 1 + z' + z'' :|: z' >= 0, z'' >= 0
   encArg(z') -{ 1 }-> x :|: z' = 1 + 0 + 0, x >= 0, 0 = x, 0 = 0
   encArg(z') -{ 1 }-> x :|: z' - 1 >= 0, x >= 0, 0 = x, 0 = 0
   encArg(z') -{ 1 }-> x :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2, x >= 0, 0 = x, 0 = 0
   encArg(z') -{ 0 }-> i(i(encArg(z' - 2))) :|: z' - 2 >= 0
   encArg(z') -{ 0 }-> i(.(encArg(x_19), encArg(x_24))) :|: z' = 1 + (1 + x_19 + x_24), x_24 >= 0, x_19 >= 0
   encArg(z') -{ 0 }-> 0 :|: z' = 0
   encArg(z') -{ 0 }-> 0 :|: z' >= 0
   encArg(z') -{ 0 }-> 0 :|: z' = 1 + 0 + 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encArg(z') -{ 0 }-> 0 :|: z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encArg(z') -{ 0 }-> 0 :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encArg(z') -{ 1 }-> 0 :|: z' = 1 + 0, 0 = 0
   encArg(z') -{ 0 }-> 0 :|: z' = 1 + 0, v0 >= 0, 0 = v0
   encArg(z') -{ 1 }-> 0 :|: z' - 1 >= 0, 0 = 0
   encArg(z') -{ 0 }-> 0 :|: z' - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z') -{ 0 }-> .(i(encArg(x_1'')), i(encArg(x_16))) :|: x_1'' >= 0, x_16 >= 0, z' = 1 + (1 + x_1'') + (1 + x_16)
   encArg(z') -{ 0 }-> .(i(encArg(x_1'')), 0) :|: z' = 1 + (1 + x_1'') + x_2, x_1'' >= 0, x_2 >= 0
   encArg(z') -{ 0 }-> .(i(encArg(x_1'')), .(encArg(x_15), encArg(x_22))) :|: x_15 >= 0, x_1'' >= 0, z' = 1 + (1 + x_1'') + (1 + x_15 + x_22), x_22 >= 0
   encArg(z') -{ 0 }-> .(i(encArg(z' - 2)), 0) :|: z' - 2 >= 0
   encArg(z') -{ 0 }-> .(0, i(encArg(x_18))) :|: x_1 >= 0, z' = 1 + x_1 + (1 + x_18), x_18 >= 0
   encArg(z') -{ 0 }-> .(0, i(encArg(z' - 2))) :|: z' - 2 >= 0
   encArg(z') -{ 0 }-> .(0, .(encArg(x_11), encArg(x_2''))) :|: x_11 >= 0, x_2'' >= 0, z' = 1 + 0 + (1 + x_11 + x_2'')
   encArg(z') -{ 0 }-> .(0, .(encArg(x_17), encArg(x_23))) :|: x_1 >= 0, x_17 >= 0, x_23 >= 0, z' = 1 + x_1 + (1 + x_17 + x_23)
   encArg(z') -{ 0 }-> .(.(encArg(x_1'), encArg(x_2')), i(encArg(x_14))) :|: z' = 1 + (1 + x_1' + x_2') + (1 + x_14), x_14 >= 0, x_2' >= 0, x_1' >= 0
   encArg(z') -{ 0 }-> .(.(encArg(x_1'), encArg(x_2')), 0) :|: x_2' >= 0, z' = 1 + (1 + x_1' + x_2') + 0, x_1' >= 0
   encArg(z') -{ 0 }-> .(.(encArg(x_1'), encArg(x_2')), 0) :|: x_2' >= 0, z' = 1 + (1 + x_1' + x_2') + x_2, x_1' >= 0, x_2 >= 0
   encArg(z') -{ 0 }-> .(.(encArg(x_1'), encArg(x_2')), .(encArg(x_13), encArg(x_21))) :|: x_2' >= 0, z' = 1 + (1 + x_1' + x_2') + (1 + x_13 + x_21), x_13 >= 0, x_1' >= 0, x_21 >= 0
   encArg(z') -{ 0 }-> 1 + x0 :|: z' = 1 + 0, x0 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 :|: z' - 1 >= 0, x0 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 + x1 :|: z' = 1 + 0 + 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 + x1 :|: z' - 1 >= 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 + x1 :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 1 }-> x :|: z'' = 0, z' = 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 1 }-> x :|: z'' >= 0, z' = 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 1 }-> x :|: z'' = 0, z' >= 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 1 }-> x :|: z' >= 0, z'' >= 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 0 }-> 0 :|: z' >= 0, z'' >= 0
   encode_.(z', z'') -{ 0 }-> 0 :|: z'' = 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> 0 :|: z'' >= 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> 0 :|: z'' = 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> 0 :|: z' >= 0, z'' >= 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> .(i(encArg(z' - 1)), i(encArg(z'' - 1))) :|: z' - 1 >= 0, z'' - 1 >= 0
   encode_.(z', z'') -{ 0 }-> .(i(encArg(z' - 1)), 0) :|: z'' = 0, z' - 1 >= 0
   encode_.(z', z'') -{ 0 }-> .(i(encArg(z' - 1)), 0) :|: z'' >= 0, z' - 1 >= 0
   encode_.(z', z'') -{ 0 }-> .(i(encArg(z' - 1)), .(encArg(x_117), encArg(x_28))) :|: x_117 >= 0, z'' = 1 + x_117 + x_28, z' - 1 >= 0, x_28 >= 0
   encode_.(z', z'') -{ 0 }-> .(0, i(encArg(z'' - 1))) :|: z'' - 1 >= 0, z' = 0
   encode_.(z', z'') -{ 0 }-> .(0, i(encArg(z'' - 1))) :|: z' >= 0, z'' - 1 >= 0
   encode_.(z', z'') -{ 0 }-> .(0, .(encArg(x_113), encArg(x_26))) :|: z'' = 1 + x_113 + x_26, x_113 >= 0, x_26 >= 0, z' = 0
   encode_.(z', z'') -{ 0 }-> .(0, .(encArg(x_119), encArg(x_29))) :|: z' >= 0, z'' = 1 + x_119 + x_29, x_119 >= 0, x_29 >= 0
   encode_.(z', z'') -{ 0 }-> .(.(encArg(x_111), encArg(x_25)), i(encArg(z'' - 1))) :|: z'' - 1 >= 0, x_25 >= 0, z' = 1 + x_111 + x_25, x_111 >= 0
   encode_.(z', z'') -{ 0 }-> .(.(encArg(x_111), encArg(x_25)), 0) :|: z'' = 0, x_25 >= 0, z' = 1 + x_111 + x_25, x_111 >= 0
   encode_.(z', z'') -{ 0 }-> .(.(encArg(x_111), encArg(x_25)), 0) :|: x_25 >= 0, z' = 1 + x_111 + x_25, z'' >= 0, x_111 >= 0
   encode_.(z', z'') -{ 0 }-> .(.(encArg(x_111), encArg(x_25)), .(encArg(x_115), encArg(x_27))) :|: z'' = 1 + x_115 + x_27, x_25 >= 0, x_115 >= 0, z' = 1 + x_111 + x_25, x_27 >= 0, x_111 >= 0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' = 0, z' = 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' >= 0, z' = 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' = 0, z' >= 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z' >= 0, z'' >= 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_1 -{ 0 }-> 0 :|: 
   encode_i(z') -{ 0 }-> i(i(encArg(z' - 1))) :|: z' - 1 >= 0
   encode_i(z') -{ 0 }-> i(.(encArg(x_121), encArg(x_210))) :|: z' = 1 + x_121 + x_210, x_121 >= 0, x_210 >= 0
   encode_i(z') -{ 0 }-> 0 :|: z' >= 0
   encode_i(z') -{ 1 }-> 0 :|: z' = 0, 0 = 0
   encode_i(z') -{ 0 }-> 0 :|: z' = 0, v0 >= 0, 0 = v0
   encode_i(z') -{ 1 }-> 0 :|: z' >= 0, 0 = 0
   encode_i(z') -{ 0 }-> 0 :|: z' >= 0, v0 >= 0, 0 = v0
   encode_i(z') -{ 0 }-> 1 + x0 :|: z' = 0, x0 >= 0, 0 = x0
   encode_i(z') -{ 0 }-> 1 + x0 :|: z' >= 0, x0 >= 0, 0 = x0
   i(z') -{ 1 }-> 0 :|: z' = 0
   i(z') -{ 0 }-> 0 :|: z' >= 0
   i(z') -{ 1 }-> z' - 1 :|: z' - 1 >= 0
   i(z') -{ 0 }-> 1 + z' :|: z' >= 0

Function symbols to be analyzed: {i}, {encode_1}, {encArg}, {encode_i}, {encode_.}
Previous analysis results are:
  .: runtime: O(1) [1], size: O(n^1) [1 + z' + z'']

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

(33) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   .(z', z'') -{ 1 }-> z :|: z >= 0, z'' = 1 + (1 + z') + z, z' >= 0
   .(z', z'') -{ 1 }-> z :|: z >= 0, z' - 1 >= 0, z'' = 1 + (z' - 1) + z
   .(z', z'') -{ 1 }-> z' :|: z'' = 0, z' >= 0
   .(z', z'') -{ 1 }-> z'' :|: z'' >= 0, z' = 0
   .(z', z'') -{ 1 }-> 0 :|: z' - 1 >= 0, z'' = z' - 1
   .(z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' = 1 + z'
   .(z', z'') -{ 0 }-> 0 :|: z' >= 0, z'' >= 0
   .(z', z'') -{ 0 }-> 1 + z' + z'' :|: z' >= 0, z'' >= 0
   encArg(z') -{ 1 }-> x :|: z' = 1 + 0 + 0, x >= 0, 0 = x, 0 = 0
   encArg(z') -{ 1 }-> x :|: z' - 1 >= 0, x >= 0, 0 = x, 0 = 0
   encArg(z') -{ 1 }-> x :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2, x >= 0, 0 = x, 0 = 0
   encArg(z') -{ 0 }-> i(i(encArg(z' - 2))) :|: z' - 2 >= 0
   encArg(z') -{ 0 }-> i(.(encArg(x_19), encArg(x_24))) :|: z' = 1 + (1 + x_19 + x_24), x_24 >= 0, x_19 >= 0
   encArg(z') -{ 0 }-> 0 :|: z' = 0
   encArg(z') -{ 0 }-> 0 :|: z' >= 0
   encArg(z') -{ 0 }-> 0 :|: z' = 1 + 0 + 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encArg(z') -{ 0 }-> 0 :|: z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encArg(z') -{ 0 }-> 0 :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encArg(z') -{ 1 }-> 0 :|: z' = 1 + 0, 0 = 0
   encArg(z') -{ 0 }-> 0 :|: z' = 1 + 0, v0 >= 0, 0 = v0
   encArg(z') -{ 1 }-> 0 :|: z' - 1 >= 0, 0 = 0
   encArg(z') -{ 0 }-> 0 :|: z' - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z') -{ 0 }-> .(i(encArg(x_1'')), i(encArg(x_16))) :|: x_1'' >= 0, x_16 >= 0, z' = 1 + (1 + x_1'') + (1 + x_16)
   encArg(z') -{ 0 }-> .(i(encArg(x_1'')), 0) :|: z' = 1 + (1 + x_1'') + x_2, x_1'' >= 0, x_2 >= 0
   encArg(z') -{ 0 }-> .(i(encArg(x_1'')), .(encArg(x_15), encArg(x_22))) :|: x_15 >= 0, x_1'' >= 0, z' = 1 + (1 + x_1'') + (1 + x_15 + x_22), x_22 >= 0
   encArg(z') -{ 0 }-> .(i(encArg(z' - 2)), 0) :|: z' - 2 >= 0
   encArg(z') -{ 0 }-> .(0, i(encArg(x_18))) :|: x_1 >= 0, z' = 1 + x_1 + (1 + x_18), x_18 >= 0
   encArg(z') -{ 0 }-> .(0, i(encArg(z' - 2))) :|: z' - 2 >= 0
   encArg(z') -{ 0 }-> .(0, .(encArg(x_11), encArg(x_2''))) :|: x_11 >= 0, x_2'' >= 0, z' = 1 + 0 + (1 + x_11 + x_2'')
   encArg(z') -{ 0 }-> .(0, .(encArg(x_17), encArg(x_23))) :|: x_1 >= 0, x_17 >= 0, x_23 >= 0, z' = 1 + x_1 + (1 + x_17 + x_23)
   encArg(z') -{ 0 }-> .(.(encArg(x_1'), encArg(x_2')), i(encArg(x_14))) :|: z' = 1 + (1 + x_1' + x_2') + (1 + x_14), x_14 >= 0, x_2' >= 0, x_1' >= 0
   encArg(z') -{ 0 }-> .(.(encArg(x_1'), encArg(x_2')), 0) :|: x_2' >= 0, z' = 1 + (1 + x_1' + x_2') + 0, x_1' >= 0
   encArg(z') -{ 0 }-> .(.(encArg(x_1'), encArg(x_2')), 0) :|: x_2' >= 0, z' = 1 + (1 + x_1' + x_2') + x_2, x_1' >= 0, x_2 >= 0
   encArg(z') -{ 0 }-> .(.(encArg(x_1'), encArg(x_2')), .(encArg(x_13), encArg(x_21))) :|: x_2' >= 0, z' = 1 + (1 + x_1' + x_2') + (1 + x_13 + x_21), x_13 >= 0, x_1' >= 0, x_21 >= 0
   encArg(z') -{ 0 }-> 1 + x0 :|: z' = 1 + 0, x0 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 :|: z' - 1 >= 0, x0 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 + x1 :|: z' = 1 + 0 + 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 + x1 :|: z' - 1 >= 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 + x1 :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 1 }-> x :|: z'' = 0, z' = 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 1 }-> x :|: z'' >= 0, z' = 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 1 }-> x :|: z'' = 0, z' >= 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 1 }-> x :|: z' >= 0, z'' >= 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 0 }-> 0 :|: z' >= 0, z'' >= 0
   encode_.(z', z'') -{ 0 }-> 0 :|: z'' = 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> 0 :|: z'' >= 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> 0 :|: z'' = 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> 0 :|: z' >= 0, z'' >= 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> .(i(encArg(z' - 1)), i(encArg(z'' - 1))) :|: z' - 1 >= 0, z'' - 1 >= 0
   encode_.(z', z'') -{ 0 }-> .(i(encArg(z' - 1)), 0) :|: z'' = 0, z' - 1 >= 0
   encode_.(z', z'') -{ 0 }-> .(i(encArg(z' - 1)), 0) :|: z'' >= 0, z' - 1 >= 0
   encode_.(z', z'') -{ 0 }-> .(i(encArg(z' - 1)), .(encArg(x_117), encArg(x_28))) :|: x_117 >= 0, z'' = 1 + x_117 + x_28, z' - 1 >= 0, x_28 >= 0
   encode_.(z', z'') -{ 0 }-> .(0, i(encArg(z'' - 1))) :|: z'' - 1 >= 0, z' = 0
   encode_.(z', z'') -{ 0 }-> .(0, i(encArg(z'' - 1))) :|: z' >= 0, z'' - 1 >= 0
   encode_.(z', z'') -{ 0 }-> .(0, .(encArg(x_113), encArg(x_26))) :|: z'' = 1 + x_113 + x_26, x_113 >= 0, x_26 >= 0, z' = 0
   encode_.(z', z'') -{ 0 }-> .(0, .(encArg(x_119), encArg(x_29))) :|: z' >= 0, z'' = 1 + x_119 + x_29, x_119 >= 0, x_29 >= 0
   encode_.(z', z'') -{ 0 }-> .(.(encArg(x_111), encArg(x_25)), i(encArg(z'' - 1))) :|: z'' - 1 >= 0, x_25 >= 0, z' = 1 + x_111 + x_25, x_111 >= 0
   encode_.(z', z'') -{ 0 }-> .(.(encArg(x_111), encArg(x_25)), 0) :|: z'' = 0, x_25 >= 0, z' = 1 + x_111 + x_25, x_111 >= 0
   encode_.(z', z'') -{ 0 }-> .(.(encArg(x_111), encArg(x_25)), 0) :|: x_25 >= 0, z' = 1 + x_111 + x_25, z'' >= 0, x_111 >= 0
   encode_.(z', z'') -{ 0 }-> .(.(encArg(x_111), encArg(x_25)), .(encArg(x_115), encArg(x_27))) :|: z'' = 1 + x_115 + x_27, x_25 >= 0, x_115 >= 0, z' = 1 + x_111 + x_25, x_27 >= 0, x_111 >= 0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' = 0, z' = 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' >= 0, z' = 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' = 0, z' >= 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z' >= 0, z'' >= 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_1 -{ 0 }-> 0 :|: 
   encode_i(z') -{ 0 }-> i(i(encArg(z' - 1))) :|: z' - 1 >= 0
   encode_i(z') -{ 0 }-> i(.(encArg(x_121), encArg(x_210))) :|: z' = 1 + x_121 + x_210, x_121 >= 0, x_210 >= 0
   encode_i(z') -{ 0 }-> 0 :|: z' >= 0
   encode_i(z') -{ 1 }-> 0 :|: z' = 0, 0 = 0
   encode_i(z') -{ 0 }-> 0 :|: z' = 0, v0 >= 0, 0 = v0
   encode_i(z') -{ 1 }-> 0 :|: z' >= 0, 0 = 0
   encode_i(z') -{ 0 }-> 0 :|: z' >= 0, v0 >= 0, 0 = v0
   encode_i(z') -{ 0 }-> 1 + x0 :|: z' = 0, x0 >= 0, 0 = x0
   encode_i(z') -{ 0 }-> 1 + x0 :|: z' >= 0, x0 >= 0, 0 = x0
   i(z') -{ 1 }-> 0 :|: z' = 0
   i(z') -{ 0 }-> 0 :|: z' >= 0
   i(z') -{ 1 }-> z' - 1 :|: z' - 1 >= 0
   i(z') -{ 0 }-> 1 + z' :|: z' >= 0

Function symbols to be analyzed: {i}, {encode_1}, {encArg}, {encode_i}, {encode_.}
Previous analysis results are:
  .: runtime: O(1) [1], size: O(n^1) [1 + z' + z'']
  i: runtime: ?, size: O(n^1) [1 + z']

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

(35) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   .(z', z'') -{ 1 }-> z :|: z >= 0, z'' = 1 + (1 + z') + z, z' >= 0
   .(z', z'') -{ 1 }-> z :|: z >= 0, z' - 1 >= 0, z'' = 1 + (z' - 1) + z
   .(z', z'') -{ 1 }-> z' :|: z'' = 0, z' >= 0
   .(z', z'') -{ 1 }-> z'' :|: z'' >= 0, z' = 0
   .(z', z'') -{ 1 }-> 0 :|: z' - 1 >= 0, z'' = z' - 1
   .(z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' = 1 + z'
   .(z', z'') -{ 0 }-> 0 :|: z' >= 0, z'' >= 0
   .(z', z'') -{ 0 }-> 1 + z' + z'' :|: z' >= 0, z'' >= 0
   encArg(z') -{ 1 }-> x :|: z' = 1 + 0 + 0, x >= 0, 0 = x, 0 = 0
   encArg(z') -{ 1 }-> x :|: z' - 1 >= 0, x >= 0, 0 = x, 0 = 0
   encArg(z') -{ 1 }-> x :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2, x >= 0, 0 = x, 0 = 0
   encArg(z') -{ 0 }-> i(i(encArg(z' - 2))) :|: z' - 2 >= 0
   encArg(z') -{ 0 }-> i(.(encArg(x_19), encArg(x_24))) :|: z' = 1 + (1 + x_19 + x_24), x_24 >= 0, x_19 >= 0
   encArg(z') -{ 0 }-> 0 :|: z' = 0
   encArg(z') -{ 0 }-> 0 :|: z' >= 0
   encArg(z') -{ 0 }-> 0 :|: z' = 1 + 0 + 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encArg(z') -{ 0 }-> 0 :|: z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encArg(z') -{ 0 }-> 0 :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encArg(z') -{ 1 }-> 0 :|: z' = 1 + 0, 0 = 0
   encArg(z') -{ 0 }-> 0 :|: z' = 1 + 0, v0 >= 0, 0 = v0
   encArg(z') -{ 1 }-> 0 :|: z' - 1 >= 0, 0 = 0
   encArg(z') -{ 0 }-> 0 :|: z' - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z') -{ 0 }-> .(i(encArg(x_1'')), i(encArg(x_16))) :|: x_1'' >= 0, x_16 >= 0, z' = 1 + (1 + x_1'') + (1 + x_16)
   encArg(z') -{ 0 }-> .(i(encArg(x_1'')), 0) :|: z' = 1 + (1 + x_1'') + x_2, x_1'' >= 0, x_2 >= 0
   encArg(z') -{ 0 }-> .(i(encArg(x_1'')), .(encArg(x_15), encArg(x_22))) :|: x_15 >= 0, x_1'' >= 0, z' = 1 + (1 + x_1'') + (1 + x_15 + x_22), x_22 >= 0
   encArg(z') -{ 0 }-> .(i(encArg(z' - 2)), 0) :|: z' - 2 >= 0
   encArg(z') -{ 0 }-> .(0, i(encArg(x_18))) :|: x_1 >= 0, z' = 1 + x_1 + (1 + x_18), x_18 >= 0
   encArg(z') -{ 0 }-> .(0, i(encArg(z' - 2))) :|: z' - 2 >= 0
   encArg(z') -{ 0 }-> .(0, .(encArg(x_11), encArg(x_2''))) :|: x_11 >= 0, x_2'' >= 0, z' = 1 + 0 + (1 + x_11 + x_2'')
   encArg(z') -{ 0 }-> .(0, .(encArg(x_17), encArg(x_23))) :|: x_1 >= 0, x_17 >= 0, x_23 >= 0, z' = 1 + x_1 + (1 + x_17 + x_23)
   encArg(z') -{ 0 }-> .(.(encArg(x_1'), encArg(x_2')), i(encArg(x_14))) :|: z' = 1 + (1 + x_1' + x_2') + (1 + x_14), x_14 >= 0, x_2' >= 0, x_1' >= 0
   encArg(z') -{ 0 }-> .(.(encArg(x_1'), encArg(x_2')), 0) :|: x_2' >= 0, z' = 1 + (1 + x_1' + x_2') + 0, x_1' >= 0
   encArg(z') -{ 0 }-> .(.(encArg(x_1'), encArg(x_2')), 0) :|: x_2' >= 0, z' = 1 + (1 + x_1' + x_2') + x_2, x_1' >= 0, x_2 >= 0
   encArg(z') -{ 0 }-> .(.(encArg(x_1'), encArg(x_2')), .(encArg(x_13), encArg(x_21))) :|: x_2' >= 0, z' = 1 + (1 + x_1' + x_2') + (1 + x_13 + x_21), x_13 >= 0, x_1' >= 0, x_21 >= 0
   encArg(z') -{ 0 }-> 1 + x0 :|: z' = 1 + 0, x0 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 :|: z' - 1 >= 0, x0 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 + x1 :|: z' = 1 + 0 + 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 + x1 :|: z' - 1 >= 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 + x1 :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 1 }-> x :|: z'' = 0, z' = 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 1 }-> x :|: z'' >= 0, z' = 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 1 }-> x :|: z'' = 0, z' >= 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 1 }-> x :|: z' >= 0, z'' >= 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 0 }-> 0 :|: z' >= 0, z'' >= 0
   encode_.(z', z'') -{ 0 }-> 0 :|: z'' = 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> 0 :|: z'' >= 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> 0 :|: z'' = 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> 0 :|: z' >= 0, z'' >= 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> .(i(encArg(z' - 1)), i(encArg(z'' - 1))) :|: z' - 1 >= 0, z'' - 1 >= 0
   encode_.(z', z'') -{ 0 }-> .(i(encArg(z' - 1)), 0) :|: z'' = 0, z' - 1 >= 0
   encode_.(z', z'') -{ 0 }-> .(i(encArg(z' - 1)), 0) :|: z'' >= 0, z' - 1 >= 0
   encode_.(z', z'') -{ 0 }-> .(i(encArg(z' - 1)), .(encArg(x_117), encArg(x_28))) :|: x_117 >= 0, z'' = 1 + x_117 + x_28, z' - 1 >= 0, x_28 >= 0
   encode_.(z', z'') -{ 0 }-> .(0, i(encArg(z'' - 1))) :|: z'' - 1 >= 0, z' = 0
   encode_.(z', z'') -{ 0 }-> .(0, i(encArg(z'' - 1))) :|: z' >= 0, z'' - 1 >= 0
   encode_.(z', z'') -{ 0 }-> .(0, .(encArg(x_113), encArg(x_26))) :|: z'' = 1 + x_113 + x_26, x_113 >= 0, x_26 >= 0, z' = 0
   encode_.(z', z'') -{ 0 }-> .(0, .(encArg(x_119), encArg(x_29))) :|: z' >= 0, z'' = 1 + x_119 + x_29, x_119 >= 0, x_29 >= 0
   encode_.(z', z'') -{ 0 }-> .(.(encArg(x_111), encArg(x_25)), i(encArg(z'' - 1))) :|: z'' - 1 >= 0, x_25 >= 0, z' = 1 + x_111 + x_25, x_111 >= 0
   encode_.(z', z'') -{ 0 }-> .(.(encArg(x_111), encArg(x_25)), 0) :|: z'' = 0, x_25 >= 0, z' = 1 + x_111 + x_25, x_111 >= 0
   encode_.(z', z'') -{ 0 }-> .(.(encArg(x_111), encArg(x_25)), 0) :|: x_25 >= 0, z' = 1 + x_111 + x_25, z'' >= 0, x_111 >= 0
   encode_.(z', z'') -{ 0 }-> .(.(encArg(x_111), encArg(x_25)), .(encArg(x_115), encArg(x_27))) :|: z'' = 1 + x_115 + x_27, x_25 >= 0, x_115 >= 0, z' = 1 + x_111 + x_25, x_27 >= 0, x_111 >= 0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' = 0, z' = 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' >= 0, z' = 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' = 0, z' >= 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z' >= 0, z'' >= 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_1 -{ 0 }-> 0 :|: 
   encode_i(z') -{ 0 }-> i(i(encArg(z' - 1))) :|: z' - 1 >= 0
   encode_i(z') -{ 0 }-> i(.(encArg(x_121), encArg(x_210))) :|: z' = 1 + x_121 + x_210, x_121 >= 0, x_210 >= 0
   encode_i(z') -{ 0 }-> 0 :|: z' >= 0
   encode_i(z') -{ 1 }-> 0 :|: z' = 0, 0 = 0
   encode_i(z') -{ 0 }-> 0 :|: z' = 0, v0 >= 0, 0 = v0
   encode_i(z') -{ 1 }-> 0 :|: z' >= 0, 0 = 0
   encode_i(z') -{ 0 }-> 0 :|: z' >= 0, v0 >= 0, 0 = v0
   encode_i(z') -{ 0 }-> 1 + x0 :|: z' = 0, x0 >= 0, 0 = x0
   encode_i(z') -{ 0 }-> 1 + x0 :|: z' >= 0, x0 >= 0, 0 = x0
   i(z') -{ 1 }-> 0 :|: z' = 0
   i(z') -{ 0 }-> 0 :|: z' >= 0
   i(z') -{ 1 }-> z' - 1 :|: z' - 1 >= 0
   i(z') -{ 0 }-> 1 + z' :|: z' >= 0

Function symbols to be analyzed: {encode_1}, {encArg}, {encode_i}, {encode_.}
Previous analysis results are:
  .: runtime: O(1) [1], size: O(n^1) [1 + z' + z'']
  i: runtime: O(1) [1], size: O(n^1) [1 + z']

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

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

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

   .(z', z'') -{ 1 }-> z :|: z >= 0, z'' = 1 + (1 + z') + z, z' >= 0
   .(z', z'') -{ 1 }-> z :|: z >= 0, z' - 1 >= 0, z'' = 1 + (z' - 1) + z
   .(z', z'') -{ 1 }-> z' :|: z'' = 0, z' >= 0
   .(z', z'') -{ 1 }-> z'' :|: z'' >= 0, z' = 0
   .(z', z'') -{ 1 }-> 0 :|: z' - 1 >= 0, z'' = z' - 1
   .(z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' = 1 + z'
   .(z', z'') -{ 0 }-> 0 :|: z' >= 0, z'' >= 0
   .(z', z'') -{ 0 }-> 1 + z' + z'' :|: z' >= 0, z'' >= 0
   encArg(z') -{ 1 }-> x :|: z' = 1 + 0 + 0, x >= 0, 0 = x, 0 = 0
   encArg(z') -{ 1 }-> x :|: z' - 1 >= 0, x >= 0, 0 = x, 0 = 0
   encArg(z') -{ 1 }-> x :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2, x >= 0, 0 = x, 0 = 0
   encArg(z') -{ 0 }-> i(i(encArg(z' - 2))) :|: z' - 2 >= 0
   encArg(z') -{ 0 }-> i(.(encArg(x_19), encArg(x_24))) :|: z' = 1 + (1 + x_19 + x_24), x_24 >= 0, x_19 >= 0
   encArg(z') -{ 0 }-> 0 :|: z' = 0
   encArg(z') -{ 0 }-> 0 :|: z' >= 0
   encArg(z') -{ 0 }-> 0 :|: z' = 1 + 0 + 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encArg(z') -{ 0 }-> 0 :|: z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encArg(z') -{ 0 }-> 0 :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encArg(z') -{ 1 }-> 0 :|: z' = 1 + 0, 0 = 0
   encArg(z') -{ 0 }-> 0 :|: z' = 1 + 0, v0 >= 0, 0 = v0
   encArg(z') -{ 1 }-> 0 :|: z' - 1 >= 0, 0 = 0
   encArg(z') -{ 0 }-> 0 :|: z' - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z') -{ 0 }-> .(i(encArg(x_1'')), i(encArg(x_16))) :|: x_1'' >= 0, x_16 >= 0, z' = 1 + (1 + x_1'') + (1 + x_16)
   encArg(z') -{ 0 }-> .(i(encArg(x_1'')), 0) :|: z' = 1 + (1 + x_1'') + x_2, x_1'' >= 0, x_2 >= 0
   encArg(z') -{ 0 }-> .(i(encArg(x_1'')), .(encArg(x_15), encArg(x_22))) :|: x_15 >= 0, x_1'' >= 0, z' = 1 + (1 + x_1'') + (1 + x_15 + x_22), x_22 >= 0
   encArg(z') -{ 0 }-> .(i(encArg(z' - 2)), 0) :|: z' - 2 >= 0
   encArg(z') -{ 0 }-> .(0, i(encArg(x_18))) :|: x_1 >= 0, z' = 1 + x_1 + (1 + x_18), x_18 >= 0
   encArg(z') -{ 0 }-> .(0, i(encArg(z' - 2))) :|: z' - 2 >= 0
   encArg(z') -{ 0 }-> .(0, .(encArg(x_11), encArg(x_2''))) :|: x_11 >= 0, x_2'' >= 0, z' = 1 + 0 + (1 + x_11 + x_2'')
   encArg(z') -{ 0 }-> .(0, .(encArg(x_17), encArg(x_23))) :|: x_1 >= 0, x_17 >= 0, x_23 >= 0, z' = 1 + x_1 + (1 + x_17 + x_23)
   encArg(z') -{ 0 }-> .(.(encArg(x_1'), encArg(x_2')), i(encArg(x_14))) :|: z' = 1 + (1 + x_1' + x_2') + (1 + x_14), x_14 >= 0, x_2' >= 0, x_1' >= 0
   encArg(z') -{ 0 }-> .(.(encArg(x_1'), encArg(x_2')), 0) :|: x_2' >= 0, z' = 1 + (1 + x_1' + x_2') + 0, x_1' >= 0
   encArg(z') -{ 0 }-> .(.(encArg(x_1'), encArg(x_2')), 0) :|: x_2' >= 0, z' = 1 + (1 + x_1' + x_2') + x_2, x_1' >= 0, x_2 >= 0
   encArg(z') -{ 0 }-> .(.(encArg(x_1'), encArg(x_2')), .(encArg(x_13), encArg(x_21))) :|: x_2' >= 0, z' = 1 + (1 + x_1' + x_2') + (1 + x_13 + x_21), x_13 >= 0, x_1' >= 0, x_21 >= 0
   encArg(z') -{ 0 }-> 1 + x0 :|: z' = 1 + 0, x0 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 :|: z' - 1 >= 0, x0 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 + x1 :|: z' = 1 + 0 + 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 + x1 :|: z' - 1 >= 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 + x1 :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 1 }-> x :|: z'' = 0, z' = 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 1 }-> x :|: z'' >= 0, z' = 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 1 }-> x :|: z'' = 0, z' >= 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 1 }-> x :|: z' >= 0, z'' >= 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 0 }-> 0 :|: z' >= 0, z'' >= 0
   encode_.(z', z'') -{ 0 }-> 0 :|: z'' = 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> 0 :|: z'' >= 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> 0 :|: z'' = 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> 0 :|: z' >= 0, z'' >= 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> .(i(encArg(z' - 1)), i(encArg(z'' - 1))) :|: z' - 1 >= 0, z'' - 1 >= 0
   encode_.(z', z'') -{ 0 }-> .(i(encArg(z' - 1)), 0) :|: z'' = 0, z' - 1 >= 0
   encode_.(z', z'') -{ 0 }-> .(i(encArg(z' - 1)), 0) :|: z'' >= 0, z' - 1 >= 0
   encode_.(z', z'') -{ 0 }-> .(i(encArg(z' - 1)), .(encArg(x_117), encArg(x_28))) :|: x_117 >= 0, z'' = 1 + x_117 + x_28, z' - 1 >= 0, x_28 >= 0
   encode_.(z', z'') -{ 0 }-> .(0, i(encArg(z'' - 1))) :|: z'' - 1 >= 0, z' = 0
   encode_.(z', z'') -{ 0 }-> .(0, i(encArg(z'' - 1))) :|: z' >= 0, z'' - 1 >= 0
   encode_.(z', z'') -{ 0 }-> .(0, .(encArg(x_113), encArg(x_26))) :|: z'' = 1 + x_113 + x_26, x_113 >= 0, x_26 >= 0, z' = 0
   encode_.(z', z'') -{ 0 }-> .(0, .(encArg(x_119), encArg(x_29))) :|: z' >= 0, z'' = 1 + x_119 + x_29, x_119 >= 0, x_29 >= 0
   encode_.(z', z'') -{ 0 }-> .(.(encArg(x_111), encArg(x_25)), i(encArg(z'' - 1))) :|: z'' - 1 >= 0, x_25 >= 0, z' = 1 + x_111 + x_25, x_111 >= 0
   encode_.(z', z'') -{ 0 }-> .(.(encArg(x_111), encArg(x_25)), 0) :|: z'' = 0, x_25 >= 0, z' = 1 + x_111 + x_25, x_111 >= 0
   encode_.(z', z'') -{ 0 }-> .(.(encArg(x_111), encArg(x_25)), 0) :|: x_25 >= 0, z' = 1 + x_111 + x_25, z'' >= 0, x_111 >= 0
   encode_.(z', z'') -{ 0 }-> .(.(encArg(x_111), encArg(x_25)), .(encArg(x_115), encArg(x_27))) :|: z'' = 1 + x_115 + x_27, x_25 >= 0, x_115 >= 0, z' = 1 + x_111 + x_25, x_27 >= 0, x_111 >= 0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' = 0, z' = 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' >= 0, z' = 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' = 0, z' >= 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z' >= 0, z'' >= 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_1 -{ 0 }-> 0 :|: 
   encode_i(z') -{ 0 }-> i(i(encArg(z' - 1))) :|: z' - 1 >= 0
   encode_i(z') -{ 0 }-> i(.(encArg(x_121), encArg(x_210))) :|: z' = 1 + x_121 + x_210, x_121 >= 0, x_210 >= 0
   encode_i(z') -{ 0 }-> 0 :|: z' >= 0
   encode_i(z') -{ 1 }-> 0 :|: z' = 0, 0 = 0
   encode_i(z') -{ 0 }-> 0 :|: z' = 0, v0 >= 0, 0 = v0
   encode_i(z') -{ 1 }-> 0 :|: z' >= 0, 0 = 0
   encode_i(z') -{ 0 }-> 0 :|: z' >= 0, v0 >= 0, 0 = v0
   encode_i(z') -{ 0 }-> 1 + x0 :|: z' = 0, x0 >= 0, 0 = x0
   encode_i(z') -{ 0 }-> 1 + x0 :|: z' >= 0, x0 >= 0, 0 = x0
   i(z') -{ 1 }-> 0 :|: z' = 0
   i(z') -{ 0 }-> 0 :|: z' >= 0
   i(z') -{ 1 }-> z' - 1 :|: z' - 1 >= 0
   i(z') -{ 0 }-> 1 + z' :|: z' >= 0

Function symbols to be analyzed: {encode_1}, {encArg}, {encode_i}, {encode_.}
Previous analysis results are:
  .: runtime: O(1) [1], size: O(n^1) [1 + z' + z'']
  i: runtime: O(1) [1], size: O(n^1) [1 + z']

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

(39) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   .(z', z'') -{ 1 }-> z :|: z >= 0, z'' = 1 + (1 + z') + z, z' >= 0
   .(z', z'') -{ 1 }-> z :|: z >= 0, z' - 1 >= 0, z'' = 1 + (z' - 1) + z
   .(z', z'') -{ 1 }-> z' :|: z'' = 0, z' >= 0
   .(z', z'') -{ 1 }-> z'' :|: z'' >= 0, z' = 0
   .(z', z'') -{ 1 }-> 0 :|: z' - 1 >= 0, z'' = z' - 1
   .(z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' = 1 + z'
   .(z', z'') -{ 0 }-> 0 :|: z' >= 0, z'' >= 0
   .(z', z'') -{ 0 }-> 1 + z' + z'' :|: z' >= 0, z'' >= 0
   encArg(z') -{ 1 }-> x :|: z' = 1 + 0 + 0, x >= 0, 0 = x, 0 = 0
   encArg(z') -{ 1 }-> x :|: z' - 1 >= 0, x >= 0, 0 = x, 0 = 0
   encArg(z') -{ 1 }-> x :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2, x >= 0, 0 = x, 0 = 0
   encArg(z') -{ 0 }-> i(i(encArg(z' - 2))) :|: z' - 2 >= 0
   encArg(z') -{ 0 }-> i(.(encArg(x_19), encArg(x_24))) :|: z' = 1 + (1 + x_19 + x_24), x_24 >= 0, x_19 >= 0
   encArg(z') -{ 0 }-> 0 :|: z' = 0
   encArg(z') -{ 0 }-> 0 :|: z' >= 0
   encArg(z') -{ 0 }-> 0 :|: z' = 1 + 0 + 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encArg(z') -{ 0 }-> 0 :|: z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encArg(z') -{ 0 }-> 0 :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encArg(z') -{ 1 }-> 0 :|: z' = 1 + 0, 0 = 0
   encArg(z') -{ 0 }-> 0 :|: z' = 1 + 0, v0 >= 0, 0 = v0
   encArg(z') -{ 1 }-> 0 :|: z' - 1 >= 0, 0 = 0
   encArg(z') -{ 0 }-> 0 :|: z' - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z') -{ 0 }-> .(i(encArg(x_1'')), i(encArg(x_16))) :|: x_1'' >= 0, x_16 >= 0, z' = 1 + (1 + x_1'') + (1 + x_16)
   encArg(z') -{ 0 }-> .(i(encArg(x_1'')), 0) :|: z' = 1 + (1 + x_1'') + x_2, x_1'' >= 0, x_2 >= 0
   encArg(z') -{ 0 }-> .(i(encArg(x_1'')), .(encArg(x_15), encArg(x_22))) :|: x_15 >= 0, x_1'' >= 0, z' = 1 + (1 + x_1'') + (1 + x_15 + x_22), x_22 >= 0
   encArg(z') -{ 0 }-> .(i(encArg(z' - 2)), 0) :|: z' - 2 >= 0
   encArg(z') -{ 0 }-> .(0, i(encArg(x_18))) :|: x_1 >= 0, z' = 1 + x_1 + (1 + x_18), x_18 >= 0
   encArg(z') -{ 0 }-> .(0, i(encArg(z' - 2))) :|: z' - 2 >= 0
   encArg(z') -{ 0 }-> .(0, .(encArg(x_11), encArg(x_2''))) :|: x_11 >= 0, x_2'' >= 0, z' = 1 + 0 + (1 + x_11 + x_2'')
   encArg(z') -{ 0 }-> .(0, .(encArg(x_17), encArg(x_23))) :|: x_1 >= 0, x_17 >= 0, x_23 >= 0, z' = 1 + x_1 + (1 + x_17 + x_23)
   encArg(z') -{ 0 }-> .(.(encArg(x_1'), encArg(x_2')), i(encArg(x_14))) :|: z' = 1 + (1 + x_1' + x_2') + (1 + x_14), x_14 >= 0, x_2' >= 0, x_1' >= 0
   encArg(z') -{ 0 }-> .(.(encArg(x_1'), encArg(x_2')), 0) :|: x_2' >= 0, z' = 1 + (1 + x_1' + x_2') + 0, x_1' >= 0
   encArg(z') -{ 0 }-> .(.(encArg(x_1'), encArg(x_2')), 0) :|: x_2' >= 0, z' = 1 + (1 + x_1' + x_2') + x_2, x_1' >= 0, x_2 >= 0
   encArg(z') -{ 0 }-> .(.(encArg(x_1'), encArg(x_2')), .(encArg(x_13), encArg(x_21))) :|: x_2' >= 0, z' = 1 + (1 + x_1' + x_2') + (1 + x_13 + x_21), x_13 >= 0, x_1' >= 0, x_21 >= 0
   encArg(z') -{ 0 }-> 1 + x0 :|: z' = 1 + 0, x0 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 :|: z' - 1 >= 0, x0 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 + x1 :|: z' = 1 + 0 + 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 + x1 :|: z' - 1 >= 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 + x1 :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 1 }-> x :|: z'' = 0, z' = 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 1 }-> x :|: z'' >= 0, z' = 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 1 }-> x :|: z'' = 0, z' >= 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 1 }-> x :|: z' >= 0, z'' >= 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 0 }-> 0 :|: z' >= 0, z'' >= 0
   encode_.(z', z'') -{ 0 }-> 0 :|: z'' = 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> 0 :|: z'' >= 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> 0 :|: z'' = 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> 0 :|: z' >= 0, z'' >= 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> .(i(encArg(z' - 1)), i(encArg(z'' - 1))) :|: z' - 1 >= 0, z'' - 1 >= 0
   encode_.(z', z'') -{ 0 }-> .(i(encArg(z' - 1)), 0) :|: z'' = 0, z' - 1 >= 0
   encode_.(z', z'') -{ 0 }-> .(i(encArg(z' - 1)), 0) :|: z'' >= 0, z' - 1 >= 0
   encode_.(z', z'') -{ 0 }-> .(i(encArg(z' - 1)), .(encArg(x_117), encArg(x_28))) :|: x_117 >= 0, z'' = 1 + x_117 + x_28, z' - 1 >= 0, x_28 >= 0
   encode_.(z', z'') -{ 0 }-> .(0, i(encArg(z'' - 1))) :|: z'' - 1 >= 0, z' = 0
   encode_.(z', z'') -{ 0 }-> .(0, i(encArg(z'' - 1))) :|: z' >= 0, z'' - 1 >= 0
   encode_.(z', z'') -{ 0 }-> .(0, .(encArg(x_113), encArg(x_26))) :|: z'' = 1 + x_113 + x_26, x_113 >= 0, x_26 >= 0, z' = 0
   encode_.(z', z'') -{ 0 }-> .(0, .(encArg(x_119), encArg(x_29))) :|: z' >= 0, z'' = 1 + x_119 + x_29, x_119 >= 0, x_29 >= 0
   encode_.(z', z'') -{ 0 }-> .(.(encArg(x_111), encArg(x_25)), i(encArg(z'' - 1))) :|: z'' - 1 >= 0, x_25 >= 0, z' = 1 + x_111 + x_25, x_111 >= 0
   encode_.(z', z'') -{ 0 }-> .(.(encArg(x_111), encArg(x_25)), 0) :|: z'' = 0, x_25 >= 0, z' = 1 + x_111 + x_25, x_111 >= 0
   encode_.(z', z'') -{ 0 }-> .(.(encArg(x_111), encArg(x_25)), 0) :|: x_25 >= 0, z' = 1 + x_111 + x_25, z'' >= 0, x_111 >= 0
   encode_.(z', z'') -{ 0 }-> .(.(encArg(x_111), encArg(x_25)), .(encArg(x_115), encArg(x_27))) :|: z'' = 1 + x_115 + x_27, x_25 >= 0, x_115 >= 0, z' = 1 + x_111 + x_25, x_27 >= 0, x_111 >= 0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' = 0, z' = 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' >= 0, z' = 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' = 0, z' >= 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z' >= 0, z'' >= 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_1 -{ 0 }-> 0 :|: 
   encode_i(z') -{ 0 }-> i(i(encArg(z' - 1))) :|: z' - 1 >= 0
   encode_i(z') -{ 0 }-> i(.(encArg(x_121), encArg(x_210))) :|: z' = 1 + x_121 + x_210, x_121 >= 0, x_210 >= 0
   encode_i(z') -{ 0 }-> 0 :|: z' >= 0
   encode_i(z') -{ 1 }-> 0 :|: z' = 0, 0 = 0
   encode_i(z') -{ 0 }-> 0 :|: z' = 0, v0 >= 0, 0 = v0
   encode_i(z') -{ 1 }-> 0 :|: z' >= 0, 0 = 0
   encode_i(z') -{ 0 }-> 0 :|: z' >= 0, v0 >= 0, 0 = v0
   encode_i(z') -{ 0 }-> 1 + x0 :|: z' = 0, x0 >= 0, 0 = x0
   encode_i(z') -{ 0 }-> 1 + x0 :|: z' >= 0, x0 >= 0, 0 = x0
   i(z') -{ 1 }-> 0 :|: z' = 0
   i(z') -{ 0 }-> 0 :|: z' >= 0
   i(z') -{ 1 }-> z' - 1 :|: z' - 1 >= 0
   i(z') -{ 0 }-> 1 + z' :|: z' >= 0

Function symbols to be analyzed: {encode_1}, {encArg}, {encode_i}, {encode_.}
Previous analysis results are:
  .: runtime: O(1) [1], size: O(n^1) [1 + z' + z'']
  i: runtime: O(1) [1], size: O(n^1) [1 + z']
  encode_1: runtime: ?, size: O(1) [0]

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

(41) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   .(z', z'') -{ 1 }-> z :|: z >= 0, z'' = 1 + (1 + z') + z, z' >= 0
   .(z', z'') -{ 1 }-> z :|: z >= 0, z' - 1 >= 0, z'' = 1 + (z' - 1) + z
   .(z', z'') -{ 1 }-> z' :|: z'' = 0, z' >= 0
   .(z', z'') -{ 1 }-> z'' :|: z'' >= 0, z' = 0
   .(z', z'') -{ 1 }-> 0 :|: z' - 1 >= 0, z'' = z' - 1
   .(z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' = 1 + z'
   .(z', z'') -{ 0 }-> 0 :|: z' >= 0, z'' >= 0
   .(z', z'') -{ 0 }-> 1 + z' + z'' :|: z' >= 0, z'' >= 0
   encArg(z') -{ 1 }-> x :|: z' = 1 + 0 + 0, x >= 0, 0 = x, 0 = 0
   encArg(z') -{ 1 }-> x :|: z' - 1 >= 0, x >= 0, 0 = x, 0 = 0
   encArg(z') -{ 1 }-> x :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2, x >= 0, 0 = x, 0 = 0
   encArg(z') -{ 0 }-> i(i(encArg(z' - 2))) :|: z' - 2 >= 0
   encArg(z') -{ 0 }-> i(.(encArg(x_19), encArg(x_24))) :|: z' = 1 + (1 + x_19 + x_24), x_24 >= 0, x_19 >= 0
   encArg(z') -{ 0 }-> 0 :|: z' = 0
   encArg(z') -{ 0 }-> 0 :|: z' >= 0
   encArg(z') -{ 0 }-> 0 :|: z' = 1 + 0 + 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encArg(z') -{ 0 }-> 0 :|: z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encArg(z') -{ 0 }-> 0 :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encArg(z') -{ 1 }-> 0 :|: z' = 1 + 0, 0 = 0
   encArg(z') -{ 0 }-> 0 :|: z' = 1 + 0, v0 >= 0, 0 = v0
   encArg(z') -{ 1 }-> 0 :|: z' - 1 >= 0, 0 = 0
   encArg(z') -{ 0 }-> 0 :|: z' - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z') -{ 0 }-> .(i(encArg(x_1'')), i(encArg(x_16))) :|: x_1'' >= 0, x_16 >= 0, z' = 1 + (1 + x_1'') + (1 + x_16)
   encArg(z') -{ 0 }-> .(i(encArg(x_1'')), 0) :|: z' = 1 + (1 + x_1'') + x_2, x_1'' >= 0, x_2 >= 0
   encArg(z') -{ 0 }-> .(i(encArg(x_1'')), .(encArg(x_15), encArg(x_22))) :|: x_15 >= 0, x_1'' >= 0, z' = 1 + (1 + x_1'') + (1 + x_15 + x_22), x_22 >= 0
   encArg(z') -{ 0 }-> .(i(encArg(z' - 2)), 0) :|: z' - 2 >= 0
   encArg(z') -{ 0 }-> .(0, i(encArg(x_18))) :|: x_1 >= 0, z' = 1 + x_1 + (1 + x_18), x_18 >= 0
   encArg(z') -{ 0 }-> .(0, i(encArg(z' - 2))) :|: z' - 2 >= 0
   encArg(z') -{ 0 }-> .(0, .(encArg(x_11), encArg(x_2''))) :|: x_11 >= 0, x_2'' >= 0, z' = 1 + 0 + (1 + x_11 + x_2'')
   encArg(z') -{ 0 }-> .(0, .(encArg(x_17), encArg(x_23))) :|: x_1 >= 0, x_17 >= 0, x_23 >= 0, z' = 1 + x_1 + (1 + x_17 + x_23)
   encArg(z') -{ 0 }-> .(.(encArg(x_1'), encArg(x_2')), i(encArg(x_14))) :|: z' = 1 + (1 + x_1' + x_2') + (1 + x_14), x_14 >= 0, x_2' >= 0, x_1' >= 0
   encArg(z') -{ 0 }-> .(.(encArg(x_1'), encArg(x_2')), 0) :|: x_2' >= 0, z' = 1 + (1 + x_1' + x_2') + 0, x_1' >= 0
   encArg(z') -{ 0 }-> .(.(encArg(x_1'), encArg(x_2')), 0) :|: x_2' >= 0, z' = 1 + (1 + x_1' + x_2') + x_2, x_1' >= 0, x_2 >= 0
   encArg(z') -{ 0 }-> .(.(encArg(x_1'), encArg(x_2')), .(encArg(x_13), encArg(x_21))) :|: x_2' >= 0, z' = 1 + (1 + x_1' + x_2') + (1 + x_13 + x_21), x_13 >= 0, x_1' >= 0, x_21 >= 0
   encArg(z') -{ 0 }-> 1 + x0 :|: z' = 1 + 0, x0 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 :|: z' - 1 >= 0, x0 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 + x1 :|: z' = 1 + 0 + 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 + x1 :|: z' - 1 >= 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 + x1 :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 1 }-> x :|: z'' = 0, z' = 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 1 }-> x :|: z'' >= 0, z' = 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 1 }-> x :|: z'' = 0, z' >= 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 1 }-> x :|: z' >= 0, z'' >= 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 0 }-> 0 :|: z' >= 0, z'' >= 0
   encode_.(z', z'') -{ 0 }-> 0 :|: z'' = 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> 0 :|: z'' >= 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> 0 :|: z'' = 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> 0 :|: z' >= 0, z'' >= 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> .(i(encArg(z' - 1)), i(encArg(z'' - 1))) :|: z' - 1 >= 0, z'' - 1 >= 0
   encode_.(z', z'') -{ 0 }-> .(i(encArg(z' - 1)), 0) :|: z'' = 0, z' - 1 >= 0
   encode_.(z', z'') -{ 0 }-> .(i(encArg(z' - 1)), 0) :|: z'' >= 0, z' - 1 >= 0
   encode_.(z', z'') -{ 0 }-> .(i(encArg(z' - 1)), .(encArg(x_117), encArg(x_28))) :|: x_117 >= 0, z'' = 1 + x_117 + x_28, z' - 1 >= 0, x_28 >= 0
   encode_.(z', z'') -{ 0 }-> .(0, i(encArg(z'' - 1))) :|: z'' - 1 >= 0, z' = 0
   encode_.(z', z'') -{ 0 }-> .(0, i(encArg(z'' - 1))) :|: z' >= 0, z'' - 1 >= 0
   encode_.(z', z'') -{ 0 }-> .(0, .(encArg(x_113), encArg(x_26))) :|: z'' = 1 + x_113 + x_26, x_113 >= 0, x_26 >= 0, z' = 0
   encode_.(z', z'') -{ 0 }-> .(0, .(encArg(x_119), encArg(x_29))) :|: z' >= 0, z'' = 1 + x_119 + x_29, x_119 >= 0, x_29 >= 0
   encode_.(z', z'') -{ 0 }-> .(.(encArg(x_111), encArg(x_25)), i(encArg(z'' - 1))) :|: z'' - 1 >= 0, x_25 >= 0, z' = 1 + x_111 + x_25, x_111 >= 0
   encode_.(z', z'') -{ 0 }-> .(.(encArg(x_111), encArg(x_25)), 0) :|: z'' = 0, x_25 >= 0, z' = 1 + x_111 + x_25, x_111 >= 0
   encode_.(z', z'') -{ 0 }-> .(.(encArg(x_111), encArg(x_25)), 0) :|: x_25 >= 0, z' = 1 + x_111 + x_25, z'' >= 0, x_111 >= 0
   encode_.(z', z'') -{ 0 }-> .(.(encArg(x_111), encArg(x_25)), .(encArg(x_115), encArg(x_27))) :|: z'' = 1 + x_115 + x_27, x_25 >= 0, x_115 >= 0, z' = 1 + x_111 + x_25, x_27 >= 0, x_111 >= 0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' = 0, z' = 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' >= 0, z' = 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' = 0, z' >= 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z' >= 0, z'' >= 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_1 -{ 0 }-> 0 :|: 
   encode_i(z') -{ 0 }-> i(i(encArg(z' - 1))) :|: z' - 1 >= 0
   encode_i(z') -{ 0 }-> i(.(encArg(x_121), encArg(x_210))) :|: z' = 1 + x_121 + x_210, x_121 >= 0, x_210 >= 0
   encode_i(z') -{ 0 }-> 0 :|: z' >= 0
   encode_i(z') -{ 1 }-> 0 :|: z' = 0, 0 = 0
   encode_i(z') -{ 0 }-> 0 :|: z' = 0, v0 >= 0, 0 = v0
   encode_i(z') -{ 1 }-> 0 :|: z' >= 0, 0 = 0
   encode_i(z') -{ 0 }-> 0 :|: z' >= 0, v0 >= 0, 0 = v0
   encode_i(z') -{ 0 }-> 1 + x0 :|: z' = 0, x0 >= 0, 0 = x0
   encode_i(z') -{ 0 }-> 1 + x0 :|: z' >= 0, x0 >= 0, 0 = x0
   i(z') -{ 1 }-> 0 :|: z' = 0
   i(z') -{ 0 }-> 0 :|: z' >= 0
   i(z') -{ 1 }-> z' - 1 :|: z' - 1 >= 0
   i(z') -{ 0 }-> 1 + z' :|: z' >= 0

Function symbols to be analyzed: {encArg}, {encode_i}, {encode_.}
Previous analysis results are:
  .: runtime: O(1) [1], size: O(n^1) [1 + z' + z'']
  i: runtime: O(1) [1], size: O(n^1) [1 + z']
  encode_1: runtime: O(1) [0], size: O(1) [0]

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

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

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

   .(z', z'') -{ 1 }-> z :|: z >= 0, z'' = 1 + (1 + z') + z, z' >= 0
   .(z', z'') -{ 1 }-> z :|: z >= 0, z' - 1 >= 0, z'' = 1 + (z' - 1) + z
   .(z', z'') -{ 1 }-> z' :|: z'' = 0, z' >= 0
   .(z', z'') -{ 1 }-> z'' :|: z'' >= 0, z' = 0
   .(z', z'') -{ 1 }-> 0 :|: z' - 1 >= 0, z'' = z' - 1
   .(z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' = 1 + z'
   .(z', z'') -{ 0 }-> 0 :|: z' >= 0, z'' >= 0
   .(z', z'') -{ 0 }-> 1 + z' + z'' :|: z' >= 0, z'' >= 0
   encArg(z') -{ 1 }-> x :|: z' = 1 + 0 + 0, x >= 0, 0 = x, 0 = 0
   encArg(z') -{ 1 }-> x :|: z' - 1 >= 0, x >= 0, 0 = x, 0 = 0
   encArg(z') -{ 1 }-> x :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2, x >= 0, 0 = x, 0 = 0
   encArg(z') -{ 0 }-> i(i(encArg(z' - 2))) :|: z' - 2 >= 0
   encArg(z') -{ 0 }-> i(.(encArg(x_19), encArg(x_24))) :|: z' = 1 + (1 + x_19 + x_24), x_24 >= 0, x_19 >= 0
   encArg(z') -{ 0 }-> 0 :|: z' = 0
   encArg(z') -{ 0 }-> 0 :|: z' >= 0
   encArg(z') -{ 0 }-> 0 :|: z' = 1 + 0 + 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encArg(z') -{ 0 }-> 0 :|: z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encArg(z') -{ 0 }-> 0 :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encArg(z') -{ 1 }-> 0 :|: z' = 1 + 0, 0 = 0
   encArg(z') -{ 0 }-> 0 :|: z' = 1 + 0, v0 >= 0, 0 = v0
   encArg(z') -{ 1 }-> 0 :|: z' - 1 >= 0, 0 = 0
   encArg(z') -{ 0 }-> 0 :|: z' - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z') -{ 0 }-> .(i(encArg(x_1'')), i(encArg(x_16))) :|: x_1'' >= 0, x_16 >= 0, z' = 1 + (1 + x_1'') + (1 + x_16)
   encArg(z') -{ 0 }-> .(i(encArg(x_1'')), 0) :|: z' = 1 + (1 + x_1'') + x_2, x_1'' >= 0, x_2 >= 0
   encArg(z') -{ 0 }-> .(i(encArg(x_1'')), .(encArg(x_15), encArg(x_22))) :|: x_15 >= 0, x_1'' >= 0, z' = 1 + (1 + x_1'') + (1 + x_15 + x_22), x_22 >= 0
   encArg(z') -{ 0 }-> .(i(encArg(z' - 2)), 0) :|: z' - 2 >= 0
   encArg(z') -{ 0 }-> .(0, i(encArg(x_18))) :|: x_1 >= 0, z' = 1 + x_1 + (1 + x_18), x_18 >= 0
   encArg(z') -{ 0 }-> .(0, i(encArg(z' - 2))) :|: z' - 2 >= 0
   encArg(z') -{ 0 }-> .(0, .(encArg(x_11), encArg(x_2''))) :|: x_11 >= 0, x_2'' >= 0, z' = 1 + 0 + (1 + x_11 + x_2'')
   encArg(z') -{ 0 }-> .(0, .(encArg(x_17), encArg(x_23))) :|: x_1 >= 0, x_17 >= 0, x_23 >= 0, z' = 1 + x_1 + (1 + x_17 + x_23)
   encArg(z') -{ 0 }-> .(.(encArg(x_1'), encArg(x_2')), i(encArg(x_14))) :|: z' = 1 + (1 + x_1' + x_2') + (1 + x_14), x_14 >= 0, x_2' >= 0, x_1' >= 0
   encArg(z') -{ 0 }-> .(.(encArg(x_1'), encArg(x_2')), 0) :|: x_2' >= 0, z' = 1 + (1 + x_1' + x_2') + 0, x_1' >= 0
   encArg(z') -{ 0 }-> .(.(encArg(x_1'), encArg(x_2')), 0) :|: x_2' >= 0, z' = 1 + (1 + x_1' + x_2') + x_2, x_1' >= 0, x_2 >= 0
   encArg(z') -{ 0 }-> .(.(encArg(x_1'), encArg(x_2')), .(encArg(x_13), encArg(x_21))) :|: x_2' >= 0, z' = 1 + (1 + x_1' + x_2') + (1 + x_13 + x_21), x_13 >= 0, x_1' >= 0, x_21 >= 0
   encArg(z') -{ 0 }-> 1 + x0 :|: z' = 1 + 0, x0 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 :|: z' - 1 >= 0, x0 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 + x1 :|: z' = 1 + 0 + 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 + x1 :|: z' - 1 >= 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 + x1 :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 1 }-> x :|: z'' = 0, z' = 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 1 }-> x :|: z'' >= 0, z' = 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 1 }-> x :|: z'' = 0, z' >= 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 1 }-> x :|: z' >= 0, z'' >= 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 0 }-> 0 :|: z' >= 0, z'' >= 0
   encode_.(z', z'') -{ 0 }-> 0 :|: z'' = 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> 0 :|: z'' >= 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> 0 :|: z'' = 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> 0 :|: z' >= 0, z'' >= 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> .(i(encArg(z' - 1)), i(encArg(z'' - 1))) :|: z' - 1 >= 0, z'' - 1 >= 0
   encode_.(z', z'') -{ 0 }-> .(i(encArg(z' - 1)), 0) :|: z'' = 0, z' - 1 >= 0
   encode_.(z', z'') -{ 0 }-> .(i(encArg(z' - 1)), 0) :|: z'' >= 0, z' - 1 >= 0
   encode_.(z', z'') -{ 0 }-> .(i(encArg(z' - 1)), .(encArg(x_117), encArg(x_28))) :|: x_117 >= 0, z'' = 1 + x_117 + x_28, z' - 1 >= 0, x_28 >= 0
   encode_.(z', z'') -{ 0 }-> .(0, i(encArg(z'' - 1))) :|: z'' - 1 >= 0, z' = 0
   encode_.(z', z'') -{ 0 }-> .(0, i(encArg(z'' - 1))) :|: z' >= 0, z'' - 1 >= 0
   encode_.(z', z'') -{ 0 }-> .(0, .(encArg(x_113), encArg(x_26))) :|: z'' = 1 + x_113 + x_26, x_113 >= 0, x_26 >= 0, z' = 0
   encode_.(z', z'') -{ 0 }-> .(0, .(encArg(x_119), encArg(x_29))) :|: z' >= 0, z'' = 1 + x_119 + x_29, x_119 >= 0, x_29 >= 0
   encode_.(z', z'') -{ 0 }-> .(.(encArg(x_111), encArg(x_25)), i(encArg(z'' - 1))) :|: z'' - 1 >= 0, x_25 >= 0, z' = 1 + x_111 + x_25, x_111 >= 0
   encode_.(z', z'') -{ 0 }-> .(.(encArg(x_111), encArg(x_25)), 0) :|: z'' = 0, x_25 >= 0, z' = 1 + x_111 + x_25, x_111 >= 0
   encode_.(z', z'') -{ 0 }-> .(.(encArg(x_111), encArg(x_25)), 0) :|: x_25 >= 0, z' = 1 + x_111 + x_25, z'' >= 0, x_111 >= 0
   encode_.(z', z'') -{ 0 }-> .(.(encArg(x_111), encArg(x_25)), .(encArg(x_115), encArg(x_27))) :|: z'' = 1 + x_115 + x_27, x_25 >= 0, x_115 >= 0, z' = 1 + x_111 + x_25, x_27 >= 0, x_111 >= 0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' = 0, z' = 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' >= 0, z' = 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' = 0, z' >= 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z' >= 0, z'' >= 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_1 -{ 0 }-> 0 :|: 
   encode_i(z') -{ 0 }-> i(i(encArg(z' - 1))) :|: z' - 1 >= 0
   encode_i(z') -{ 0 }-> i(.(encArg(x_121), encArg(x_210))) :|: z' = 1 + x_121 + x_210, x_121 >= 0, x_210 >= 0
   encode_i(z') -{ 0 }-> 0 :|: z' >= 0
   encode_i(z') -{ 1 }-> 0 :|: z' = 0, 0 = 0
   encode_i(z') -{ 0 }-> 0 :|: z' = 0, v0 >= 0, 0 = v0
   encode_i(z') -{ 1 }-> 0 :|: z' >= 0, 0 = 0
   encode_i(z') -{ 0 }-> 0 :|: z' >= 0, v0 >= 0, 0 = v0
   encode_i(z') -{ 0 }-> 1 + x0 :|: z' = 0, x0 >= 0, 0 = x0
   encode_i(z') -{ 0 }-> 1 + x0 :|: z' >= 0, x0 >= 0, 0 = x0
   i(z') -{ 1 }-> 0 :|: z' = 0
   i(z') -{ 0 }-> 0 :|: z' >= 0
   i(z') -{ 1 }-> z' - 1 :|: z' - 1 >= 0
   i(z') -{ 0 }-> 1 + z' :|: z' >= 0

Function symbols to be analyzed: {encArg}, {encode_i}, {encode_.}
Previous analysis results are:
  .: runtime: O(1) [1], size: O(n^1) [1 + z' + z'']
  i: runtime: O(1) [1], size: O(n^1) [1 + z']
  encode_1: runtime: O(1) [0], size: O(1) [0]

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

(45) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   .(z', z'') -{ 1 }-> z :|: z >= 0, z'' = 1 + (1 + z') + z, z' >= 0
   .(z', z'') -{ 1 }-> z :|: z >= 0, z' - 1 >= 0, z'' = 1 + (z' - 1) + z
   .(z', z'') -{ 1 }-> z' :|: z'' = 0, z' >= 0
   .(z', z'') -{ 1 }-> z'' :|: z'' >= 0, z' = 0
   .(z', z'') -{ 1 }-> 0 :|: z' - 1 >= 0, z'' = z' - 1
   .(z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' = 1 + z'
   .(z', z'') -{ 0 }-> 0 :|: z' >= 0, z'' >= 0
   .(z', z'') -{ 0 }-> 1 + z' + z'' :|: z' >= 0, z'' >= 0
   encArg(z') -{ 1 }-> x :|: z' = 1 + 0 + 0, x >= 0, 0 = x, 0 = 0
   encArg(z') -{ 1 }-> x :|: z' - 1 >= 0, x >= 0, 0 = x, 0 = 0
   encArg(z') -{ 1 }-> x :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2, x >= 0, 0 = x, 0 = 0
   encArg(z') -{ 0 }-> i(i(encArg(z' - 2))) :|: z' - 2 >= 0
   encArg(z') -{ 0 }-> i(.(encArg(x_19), encArg(x_24))) :|: z' = 1 + (1 + x_19 + x_24), x_24 >= 0, x_19 >= 0
   encArg(z') -{ 0 }-> 0 :|: z' = 0
   encArg(z') -{ 0 }-> 0 :|: z' >= 0
   encArg(z') -{ 0 }-> 0 :|: z' = 1 + 0 + 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encArg(z') -{ 0 }-> 0 :|: z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encArg(z') -{ 0 }-> 0 :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encArg(z') -{ 1 }-> 0 :|: z' = 1 + 0, 0 = 0
   encArg(z') -{ 0 }-> 0 :|: z' = 1 + 0, v0 >= 0, 0 = v0
   encArg(z') -{ 1 }-> 0 :|: z' - 1 >= 0, 0 = 0
   encArg(z') -{ 0 }-> 0 :|: z' - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z') -{ 0 }-> .(i(encArg(x_1'')), i(encArg(x_16))) :|: x_1'' >= 0, x_16 >= 0, z' = 1 + (1 + x_1'') + (1 + x_16)
   encArg(z') -{ 0 }-> .(i(encArg(x_1'')), 0) :|: z' = 1 + (1 + x_1'') + x_2, x_1'' >= 0, x_2 >= 0
   encArg(z') -{ 0 }-> .(i(encArg(x_1'')), .(encArg(x_15), encArg(x_22))) :|: x_15 >= 0, x_1'' >= 0, z' = 1 + (1 + x_1'') + (1 + x_15 + x_22), x_22 >= 0
   encArg(z') -{ 0 }-> .(i(encArg(z' - 2)), 0) :|: z' - 2 >= 0
   encArg(z') -{ 0 }-> .(0, i(encArg(x_18))) :|: x_1 >= 0, z' = 1 + x_1 + (1 + x_18), x_18 >= 0
   encArg(z') -{ 0 }-> .(0, i(encArg(z' - 2))) :|: z' - 2 >= 0
   encArg(z') -{ 0 }-> .(0, .(encArg(x_11), encArg(x_2''))) :|: x_11 >= 0, x_2'' >= 0, z' = 1 + 0 + (1 + x_11 + x_2'')
   encArg(z') -{ 0 }-> .(0, .(encArg(x_17), encArg(x_23))) :|: x_1 >= 0, x_17 >= 0, x_23 >= 0, z' = 1 + x_1 + (1 + x_17 + x_23)
   encArg(z') -{ 0 }-> .(.(encArg(x_1'), encArg(x_2')), i(encArg(x_14))) :|: z' = 1 + (1 + x_1' + x_2') + (1 + x_14), x_14 >= 0, x_2' >= 0, x_1' >= 0
   encArg(z') -{ 0 }-> .(.(encArg(x_1'), encArg(x_2')), 0) :|: x_2' >= 0, z' = 1 + (1 + x_1' + x_2') + 0, x_1' >= 0
   encArg(z') -{ 0 }-> .(.(encArg(x_1'), encArg(x_2')), 0) :|: x_2' >= 0, z' = 1 + (1 + x_1' + x_2') + x_2, x_1' >= 0, x_2 >= 0
   encArg(z') -{ 0 }-> .(.(encArg(x_1'), encArg(x_2')), .(encArg(x_13), encArg(x_21))) :|: x_2' >= 0, z' = 1 + (1 + x_1' + x_2') + (1 + x_13 + x_21), x_13 >= 0, x_1' >= 0, x_21 >= 0
   encArg(z') -{ 0 }-> 1 + x0 :|: z' = 1 + 0, x0 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 :|: z' - 1 >= 0, x0 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 + x1 :|: z' = 1 + 0 + 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 + x1 :|: z' - 1 >= 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 + x1 :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 1 }-> x :|: z'' = 0, z' = 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 1 }-> x :|: z'' >= 0, z' = 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 1 }-> x :|: z'' = 0, z' >= 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 1 }-> x :|: z' >= 0, z'' >= 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 0 }-> 0 :|: z' >= 0, z'' >= 0
   encode_.(z', z'') -{ 0 }-> 0 :|: z'' = 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> 0 :|: z'' >= 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> 0 :|: z'' = 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> 0 :|: z' >= 0, z'' >= 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> .(i(encArg(z' - 1)), i(encArg(z'' - 1))) :|: z' - 1 >= 0, z'' - 1 >= 0
   encode_.(z', z'') -{ 0 }-> .(i(encArg(z' - 1)), 0) :|: z'' = 0, z' - 1 >= 0
   encode_.(z', z'') -{ 0 }-> .(i(encArg(z' - 1)), 0) :|: z'' >= 0, z' - 1 >= 0
   encode_.(z', z'') -{ 0 }-> .(i(encArg(z' - 1)), .(encArg(x_117), encArg(x_28))) :|: x_117 >= 0, z'' = 1 + x_117 + x_28, z' - 1 >= 0, x_28 >= 0
   encode_.(z', z'') -{ 0 }-> .(0, i(encArg(z'' - 1))) :|: z'' - 1 >= 0, z' = 0
   encode_.(z', z'') -{ 0 }-> .(0, i(encArg(z'' - 1))) :|: z' >= 0, z'' - 1 >= 0
   encode_.(z', z'') -{ 0 }-> .(0, .(encArg(x_113), encArg(x_26))) :|: z'' = 1 + x_113 + x_26, x_113 >= 0, x_26 >= 0, z' = 0
   encode_.(z', z'') -{ 0 }-> .(0, .(encArg(x_119), encArg(x_29))) :|: z' >= 0, z'' = 1 + x_119 + x_29, x_119 >= 0, x_29 >= 0
   encode_.(z', z'') -{ 0 }-> .(.(encArg(x_111), encArg(x_25)), i(encArg(z'' - 1))) :|: z'' - 1 >= 0, x_25 >= 0, z' = 1 + x_111 + x_25, x_111 >= 0
   encode_.(z', z'') -{ 0 }-> .(.(encArg(x_111), encArg(x_25)), 0) :|: z'' = 0, x_25 >= 0, z' = 1 + x_111 + x_25, x_111 >= 0
   encode_.(z', z'') -{ 0 }-> .(.(encArg(x_111), encArg(x_25)), 0) :|: x_25 >= 0, z' = 1 + x_111 + x_25, z'' >= 0, x_111 >= 0
   encode_.(z', z'') -{ 0 }-> .(.(encArg(x_111), encArg(x_25)), .(encArg(x_115), encArg(x_27))) :|: z'' = 1 + x_115 + x_27, x_25 >= 0, x_115 >= 0, z' = 1 + x_111 + x_25, x_27 >= 0, x_111 >= 0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' = 0, z' = 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' >= 0, z' = 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' = 0, z' >= 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z' >= 0, z'' >= 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_1 -{ 0 }-> 0 :|: 
   encode_i(z') -{ 0 }-> i(i(encArg(z' - 1))) :|: z' - 1 >= 0
   encode_i(z') -{ 0 }-> i(.(encArg(x_121), encArg(x_210))) :|: z' = 1 + x_121 + x_210, x_121 >= 0, x_210 >= 0
   encode_i(z') -{ 0 }-> 0 :|: z' >= 0
   encode_i(z') -{ 1 }-> 0 :|: z' = 0, 0 = 0
   encode_i(z') -{ 0 }-> 0 :|: z' = 0, v0 >= 0, 0 = v0
   encode_i(z') -{ 1 }-> 0 :|: z' >= 0, 0 = 0
   encode_i(z') -{ 0 }-> 0 :|: z' >= 0, v0 >= 0, 0 = v0
   encode_i(z') -{ 0 }-> 1 + x0 :|: z' = 0, x0 >= 0, 0 = x0
   encode_i(z') -{ 0 }-> 1 + x0 :|: z' >= 0, x0 >= 0, 0 = x0
   i(z') -{ 1 }-> 0 :|: z' = 0
   i(z') -{ 0 }-> 0 :|: z' >= 0
   i(z') -{ 1 }-> z' - 1 :|: z' - 1 >= 0
   i(z') -{ 0 }-> 1 + z' :|: z' >= 0

Function symbols to be analyzed: {encArg}, {encode_i}, {encode_.}
Previous analysis results are:
  .: runtime: O(1) [1], size: O(n^1) [1 + z' + z'']
  i: runtime: O(1) [1], size: O(n^1) [1 + z']
  encode_1: runtime: O(1) [0], size: O(1) [0]
  encArg: runtime: ?, size: O(n^1) [1 + z']

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

(47) 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: 4 + 5*z'

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

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

   .(z', z'') -{ 1 }-> z :|: z >= 0, z'' = 1 + (1 + z') + z, z' >= 0
   .(z', z'') -{ 1 }-> z :|: z >= 0, z' - 1 >= 0, z'' = 1 + (z' - 1) + z
   .(z', z'') -{ 1 }-> z' :|: z'' = 0, z' >= 0
   .(z', z'') -{ 1 }-> z'' :|: z'' >= 0, z' = 0
   .(z', z'') -{ 1 }-> 0 :|: z' - 1 >= 0, z'' = z' - 1
   .(z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' = 1 + z'
   .(z', z'') -{ 0 }-> 0 :|: z' >= 0, z'' >= 0
   .(z', z'') -{ 0 }-> 1 + z' + z'' :|: z' >= 0, z'' >= 0
   encArg(z') -{ 1 }-> x :|: z' = 1 + 0 + 0, x >= 0, 0 = x, 0 = 0
   encArg(z') -{ 1 }-> x :|: z' - 1 >= 0, x >= 0, 0 = x, 0 = 0
   encArg(z') -{ 1 }-> x :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2, x >= 0, 0 = x, 0 = 0
   encArg(z') -{ 0 }-> i(i(encArg(z' - 2))) :|: z' - 2 >= 0
   encArg(z') -{ 0 }-> i(.(encArg(x_19), encArg(x_24))) :|: z' = 1 + (1 + x_19 + x_24), x_24 >= 0, x_19 >= 0
   encArg(z') -{ 0 }-> 0 :|: z' = 0
   encArg(z') -{ 0 }-> 0 :|: z' >= 0
   encArg(z') -{ 0 }-> 0 :|: z' = 1 + 0 + 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encArg(z') -{ 0 }-> 0 :|: z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encArg(z') -{ 0 }-> 0 :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encArg(z') -{ 1 }-> 0 :|: z' = 1 + 0, 0 = 0
   encArg(z') -{ 0 }-> 0 :|: z' = 1 + 0, v0 >= 0, 0 = v0
   encArg(z') -{ 1 }-> 0 :|: z' - 1 >= 0, 0 = 0
   encArg(z') -{ 0 }-> 0 :|: z' - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z') -{ 0 }-> .(i(encArg(x_1'')), i(encArg(x_16))) :|: x_1'' >= 0, x_16 >= 0, z' = 1 + (1 + x_1'') + (1 + x_16)
   encArg(z') -{ 0 }-> .(i(encArg(x_1'')), 0) :|: z' = 1 + (1 + x_1'') + x_2, x_1'' >= 0, x_2 >= 0
   encArg(z') -{ 0 }-> .(i(encArg(x_1'')), .(encArg(x_15), encArg(x_22))) :|: x_15 >= 0, x_1'' >= 0, z' = 1 + (1 + x_1'') + (1 + x_15 + x_22), x_22 >= 0
   encArg(z') -{ 0 }-> .(i(encArg(z' - 2)), 0) :|: z' - 2 >= 0
   encArg(z') -{ 0 }-> .(0, i(encArg(x_18))) :|: x_1 >= 0, z' = 1 + x_1 + (1 + x_18), x_18 >= 0
   encArg(z') -{ 0 }-> .(0, i(encArg(z' - 2))) :|: z' - 2 >= 0
   encArg(z') -{ 0 }-> .(0, .(encArg(x_11), encArg(x_2''))) :|: x_11 >= 0, x_2'' >= 0, z' = 1 + 0 + (1 + x_11 + x_2'')
   encArg(z') -{ 0 }-> .(0, .(encArg(x_17), encArg(x_23))) :|: x_1 >= 0, x_17 >= 0, x_23 >= 0, z' = 1 + x_1 + (1 + x_17 + x_23)
   encArg(z') -{ 0 }-> .(.(encArg(x_1'), encArg(x_2')), i(encArg(x_14))) :|: z' = 1 + (1 + x_1' + x_2') + (1 + x_14), x_14 >= 0, x_2' >= 0, x_1' >= 0
   encArg(z') -{ 0 }-> .(.(encArg(x_1'), encArg(x_2')), 0) :|: x_2' >= 0, z' = 1 + (1 + x_1' + x_2') + 0, x_1' >= 0
   encArg(z') -{ 0 }-> .(.(encArg(x_1'), encArg(x_2')), 0) :|: x_2' >= 0, z' = 1 + (1 + x_1' + x_2') + x_2, x_1' >= 0, x_2 >= 0
   encArg(z') -{ 0 }-> .(.(encArg(x_1'), encArg(x_2')), .(encArg(x_13), encArg(x_21))) :|: x_2' >= 0, z' = 1 + (1 + x_1' + x_2') + (1 + x_13 + x_21), x_13 >= 0, x_1' >= 0, x_21 >= 0
   encArg(z') -{ 0 }-> 1 + x0 :|: z' = 1 + 0, x0 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 :|: z' - 1 >= 0, x0 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 + x1 :|: z' = 1 + 0 + 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 + x1 :|: z' - 1 >= 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 + x1 :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 1 }-> x :|: z'' = 0, z' = 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 1 }-> x :|: z'' >= 0, z' = 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 1 }-> x :|: z'' = 0, z' >= 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 1 }-> x :|: z' >= 0, z'' >= 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 0 }-> 0 :|: z' >= 0, z'' >= 0
   encode_.(z', z'') -{ 0 }-> 0 :|: z'' = 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> 0 :|: z'' >= 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> 0 :|: z'' = 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> 0 :|: z' >= 0, z'' >= 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> .(i(encArg(z' - 1)), i(encArg(z'' - 1))) :|: z' - 1 >= 0, z'' - 1 >= 0
   encode_.(z', z'') -{ 0 }-> .(i(encArg(z' - 1)), 0) :|: z'' = 0, z' - 1 >= 0
   encode_.(z', z'') -{ 0 }-> .(i(encArg(z' - 1)), 0) :|: z'' >= 0, z' - 1 >= 0
   encode_.(z', z'') -{ 0 }-> .(i(encArg(z' - 1)), .(encArg(x_117), encArg(x_28))) :|: x_117 >= 0, z'' = 1 + x_117 + x_28, z' - 1 >= 0, x_28 >= 0
   encode_.(z', z'') -{ 0 }-> .(0, i(encArg(z'' - 1))) :|: z'' - 1 >= 0, z' = 0
   encode_.(z', z'') -{ 0 }-> .(0, i(encArg(z'' - 1))) :|: z' >= 0, z'' - 1 >= 0
   encode_.(z', z'') -{ 0 }-> .(0, .(encArg(x_113), encArg(x_26))) :|: z'' = 1 + x_113 + x_26, x_113 >= 0, x_26 >= 0, z' = 0
   encode_.(z', z'') -{ 0 }-> .(0, .(encArg(x_119), encArg(x_29))) :|: z' >= 0, z'' = 1 + x_119 + x_29, x_119 >= 0, x_29 >= 0
   encode_.(z', z'') -{ 0 }-> .(.(encArg(x_111), encArg(x_25)), i(encArg(z'' - 1))) :|: z'' - 1 >= 0, x_25 >= 0, z' = 1 + x_111 + x_25, x_111 >= 0
   encode_.(z', z'') -{ 0 }-> .(.(encArg(x_111), encArg(x_25)), 0) :|: z'' = 0, x_25 >= 0, z' = 1 + x_111 + x_25, x_111 >= 0
   encode_.(z', z'') -{ 0 }-> .(.(encArg(x_111), encArg(x_25)), 0) :|: x_25 >= 0, z' = 1 + x_111 + x_25, z'' >= 0, x_111 >= 0
   encode_.(z', z'') -{ 0 }-> .(.(encArg(x_111), encArg(x_25)), .(encArg(x_115), encArg(x_27))) :|: z'' = 1 + x_115 + x_27, x_25 >= 0, x_115 >= 0, z' = 1 + x_111 + x_25, x_27 >= 0, x_111 >= 0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' = 0, z' = 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' >= 0, z' = 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' = 0, z' >= 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z' >= 0, z'' >= 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_1 -{ 0 }-> 0 :|: 
   encode_i(z') -{ 0 }-> i(i(encArg(z' - 1))) :|: z' - 1 >= 0
   encode_i(z') -{ 0 }-> i(.(encArg(x_121), encArg(x_210))) :|: z' = 1 + x_121 + x_210, x_121 >= 0, x_210 >= 0
   encode_i(z') -{ 0 }-> 0 :|: z' >= 0
   encode_i(z') -{ 1 }-> 0 :|: z' = 0, 0 = 0
   encode_i(z') -{ 0 }-> 0 :|: z' = 0, v0 >= 0, 0 = v0
   encode_i(z') -{ 1 }-> 0 :|: z' >= 0, 0 = 0
   encode_i(z') -{ 0 }-> 0 :|: z' >= 0, v0 >= 0, 0 = v0
   encode_i(z') -{ 0 }-> 1 + x0 :|: z' = 0, x0 >= 0, 0 = x0
   encode_i(z') -{ 0 }-> 1 + x0 :|: z' >= 0, x0 >= 0, 0 = x0
   i(z') -{ 1 }-> 0 :|: z' = 0
   i(z') -{ 0 }-> 0 :|: z' >= 0
   i(z') -{ 1 }-> z' - 1 :|: z' - 1 >= 0
   i(z') -{ 0 }-> 1 + z' :|: z' >= 0

Function symbols to be analyzed: {encode_i}, {encode_.}
Previous analysis results are:
  .: runtime: O(1) [1], size: O(n^1) [1 + z' + z'']
  i: runtime: O(1) [1], size: O(n^1) [1 + z']
  encode_1: runtime: O(1) [0], size: O(1) [0]
  encArg: runtime: O(n^1) [4 + 5*z'], size: O(n^1) [1 + z']

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

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

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

   .(z', z'') -{ 1 }-> z :|: z >= 0, z'' = 1 + (1 + z') + z, z' >= 0
   .(z', z'') -{ 1 }-> z :|: z >= 0, z' - 1 >= 0, z'' = 1 + (z' - 1) + z
   .(z', z'') -{ 1 }-> z' :|: z'' = 0, z' >= 0
   .(z', z'') -{ 1 }-> z'' :|: z'' >= 0, z' = 0
   .(z', z'') -{ 1 }-> 0 :|: z' - 1 >= 0, z'' = z' - 1
   .(z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' = 1 + z'
   .(z', z'') -{ 0 }-> 0 :|: z' >= 0, z'' >= 0
   .(z', z'') -{ 0 }-> 1 + z' + z'' :|: z' >= 0, z'' >= 0
   encArg(z') -{ 10 + 5*x_11 + 5*x_2'' }-> s1 :|: s >= 0, s <= x_11 + 1, s' >= 0, s' <= x_2'' + 1, s'' >= 0, s'' <= s + s' + 1, s1 >= 0, s1 <= 0 + s'' + 1, x_11 >= 0, x_2'' >= 0, z' = 1 + 0 + (1 + x_11 + x_2'')
   encArg(z') -{ 19 + 5*x_1' + 5*x_13 + 5*x_2' + 5*x_21 }-> s12 :|: s6 >= 0, s6 <= x_1' + 1, s7 >= 0, s7 <= x_2' + 1, s8 >= 0, s8 <= s6 + s7 + 1, s9 >= 0, s9 <= x_13 + 1, s10 >= 0, s10 <= x_21 + 1, s11 >= 0, s11 <= s9 + s10 + 1, s12 >= 0, s12 <= s8 + s11 + 1, x_2' >= 0, z' = 1 + (1 + x_1' + x_2') + (1 + x_13 + x_21), x_13 >= 0, x_1' >= 0, x_21 >= 0
   encArg(z') -{ 10 + 5*x_1' + 5*x_2' }-> s16 :|: s13 >= 0, s13 <= x_1' + 1, s14 >= 0, s14 <= x_2' + 1, s15 >= 0, s15 <= s13 + s14 + 1, s16 >= 0, s16 <= s15 + 0 + 1, x_2' >= 0, z' = 1 + (1 + x_1' + x_2') + x_2, x_1' >= 0, x_2 >= 0
   encArg(z') -{ 10 + 5*x_17 + 5*x_23 }-> s20 :|: s17 >= 0, s17 <= x_17 + 1, s18 >= 0, s18 <= x_23 + 1, s19 >= 0, s19 <= s17 + s18 + 1, s20 >= 0, s20 <= 0 + s19 + 1, x_1 >= 0, x_17 >= 0, x_23 >= 0, z' = 1 + x_1 + (1 + x_17 + x_23)
   encArg(z') -{ 15 + 5*x_1' + 5*x_14 + 5*x_2' }-> s49 :|: s44 >= 0, s44 <= x_1' + 1, s45 >= 0, s45 <= x_2' + 1, s46 >= 0, s46 <= s44 + s45 + 1, s47 >= 0, s47 <= x_14 + 1, s48 >= 0, s48 <= s47 + 1, s49 >= 0, s49 <= s46 + s48 + 1, z' = 1 + (1 + x_1' + x_2') + (1 + x_14), x_14 >= 0, x_2' >= 0, x_1' >= 0
   encArg(z') -{ 10 + 5*x_1' + 5*x_2' }-> s5 :|: s2 >= 0, s2 <= x_1' + 1, s3 >= 0, s3 <= x_2' + 1, s4 >= 0, s4 <= s2 + s3 + 1, s5 >= 0, s5 <= s4 + 0 + 1, x_2' >= 0, z' = 1 + (1 + x_1' + x_2') + 0, x_1' >= 0
   encArg(z') -{ 15 + 5*x_1'' + 5*x_15 + 5*x_22 }-> s55 :|: s50 >= 0, s50 <= x_1'' + 1, s51 >= 0, s51 <= s50 + 1, s52 >= 0, s52 <= x_15 + 1, s53 >= 0, s53 <= x_22 + 1, s54 >= 0, s54 <= s52 + s53 + 1, s55 >= 0, s55 <= s51 + s54 + 1, x_15 >= 0, x_1'' >= 0, z' = 1 + (1 + x_1'') + (1 + x_15 + x_22), x_22 >= 0
   encArg(z') -{ -4 + 5*z' }-> s58 :|: s56 >= 0, s56 <= z' - 2 + 1, s57 >= 0, s57 <= s56 + 1, s58 >= 0, s58 <= s57 + 1, z' - 2 >= 0
   encArg(z') -{ -4 + 5*z' }-> s76 :|: s74 >= 0, s74 <= z' - 2 + 1, s75 >= 0, s75 <= s74 + 1, s76 >= 0, s76 <= 0 + s75 + 1, z' - 2 >= 0
   encArg(z') -{ -4 + 5*z' }-> s79 :|: s77 >= 0, s77 <= z' - 2 + 1, s78 >= 0, s78 <= s77 + 1, s79 >= 0, s79 <= s78 + 0 + 1, z' - 2 >= 0
   encArg(z') -{ 11 + 5*x_1'' + 5*x_16 }-> s84 :|: s80 >= 0, s80 <= x_1'' + 1, s81 >= 0, s81 <= s80 + 1, s82 >= 0, s82 <= x_16 + 1, s83 >= 0, s83 <= s82 + 1, s84 >= 0, s84 <= s81 + s83 + 1, x_1'' >= 0, x_16 >= 0, z' = 1 + (1 + x_1'') + (1 + x_16)
   encArg(z') -{ 6 + 5*x_1'' }-> s87 :|: s85 >= 0, s85 <= x_1'' + 1, s86 >= 0, s86 <= s85 + 1, s87 >= 0, s87 <= s86 + 0 + 1, z' = 1 + (1 + x_1'') + x_2, x_1'' >= 0, x_2 >= 0
   encArg(z') -{ 6 + 5*x_18 }-> s90 :|: s88 >= 0, s88 <= x_18 + 1, s89 >= 0, s89 <= s88 + 1, s90 >= 0, s90 <= 0 + s89 + 1, x_1 >= 0, z' = 1 + x_1 + (1 + x_18), x_18 >= 0
   encArg(z') -{ 10 + 5*x_19 + 5*x_24 }-> s94 :|: s91 >= 0, s91 <= x_19 + 1, s92 >= 0, s92 <= x_24 + 1, s93 >= 0, s93 <= s91 + s92 + 1, s94 >= 0, s94 <= s93 + 1, z' = 1 + (1 + x_19 + x_24), x_24 >= 0, x_19 >= 0
   encArg(z') -{ 1 }-> x :|: z' = 1 + 0 + 0, x >= 0, 0 = x, 0 = 0
   encArg(z') -{ 1 }-> x :|: z' - 1 >= 0, x >= 0, 0 = x, 0 = 0
   encArg(z') -{ 1 }-> x :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2, x >= 0, 0 = x, 0 = 0
   encArg(z') -{ 0 }-> 0 :|: z' = 0
   encArg(z') -{ 0 }-> 0 :|: z' >= 0
   encArg(z') -{ 0 }-> 0 :|: z' = 1 + 0 + 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encArg(z') -{ 0 }-> 0 :|: z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encArg(z') -{ 0 }-> 0 :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encArg(z') -{ 1 }-> 0 :|: z' = 1 + 0, 0 = 0
   encArg(z') -{ 0 }-> 0 :|: z' = 1 + 0, v0 >= 0, 0 = v0
   encArg(z') -{ 1 }-> 0 :|: z' - 1 >= 0, 0 = 0
   encArg(z') -{ 0 }-> 0 :|: z' - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z') -{ 0 }-> 1 + x0 :|: z' = 1 + 0, x0 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 :|: z' - 1 >= 0, x0 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 + x1 :|: z' = 1 + 0 + 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 + x1 :|: z' - 1 >= 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 + x1 :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 1 + 5*z' }-> s100 :|: s98 >= 0, s98 <= z' - 1 + 1, s99 >= 0, s99 <= s98 + 1, s100 >= 0, s100 <= s99 + 0 + 1, z'' = 0, z' - 1 >= 0
   encode_.(z', z'') -{ 1 + 5*z' + 5*z'' }-> s105 :|: s101 >= 0, s101 <= z' - 1 + 1, s102 >= 0, s102 <= s101 + 1, s103 >= 0, s103 <= z'' - 1 + 1, s104 >= 0, s104 <= s103 + 1, s105 >= 0, s105 <= s102 + s104 + 1, z' - 1 >= 0, z'' - 1 >= 0
   encode_.(z', z'') -{ 1 + 5*z' }-> s108 :|: s106 >= 0, s106 <= z' - 1 + 1, s107 >= 0, s107 <= s106 + 1, s108 >= 0, s108 <= s107 + 0 + 1, z'' >= 0, z' - 1 >= 0
   encode_.(z', z'') -{ 1 + 5*z'' }-> s111 :|: s109 >= 0, s109 <= z'' - 1 + 1, s110 >= 0, s110 <= s109 + 1, s111 >= 0, s111 <= 0 + s110 + 1, z' >= 0, z'' - 1 >= 0
   encode_.(z', z'') -{ 10 + 5*x_113 + 5*x_26 }-> s24 :|: s21 >= 0, s21 <= x_113 + 1, s22 >= 0, s22 <= x_26 + 1, s23 >= 0, s23 <= s21 + s22 + 1, s24 >= 0, s24 <= 0 + s23 + 1, z'' = 1 + x_113 + x_26, x_113 >= 0, x_26 >= 0, z' = 0
   encode_.(z', z'') -{ 10 + 5*x_111 + 5*x_25 }-> s28 :|: s25 >= 0, s25 <= x_111 + 1, s26 >= 0, s26 <= x_25 + 1, s27 >= 0, s27 <= s25 + s26 + 1, s28 >= 0, s28 <= s27 + 0 + 1, z'' = 0, x_25 >= 0, z' = 1 + x_111 + x_25, x_111 >= 0
   encode_.(z', z'') -{ 19 + 5*x_111 + 5*x_115 + 5*x_25 + 5*x_27 }-> s35 :|: s29 >= 0, s29 <= x_111 + 1, s30 >= 0, s30 <= x_25 + 1, s31 >= 0, s31 <= s29 + s30 + 1, s32 >= 0, s32 <= x_115 + 1, s33 >= 0, s33 <= x_27 + 1, s34 >= 0, s34 <= s32 + s33 + 1, s35 >= 0, s35 <= s31 + s34 + 1, z'' = 1 + x_115 + x_27, x_25 >= 0, x_115 >= 0, z' = 1 + x_111 + x_25, x_27 >= 0, x_111 >= 0
   encode_.(z', z'') -{ 10 + 5*x_111 + 5*x_25 }-> s39 :|: s36 >= 0, s36 <= x_111 + 1, s37 >= 0, s37 <= x_25 + 1, s38 >= 0, s38 <= s36 + s37 + 1, s39 >= 0, s39 <= s38 + 0 + 1, x_25 >= 0, z' = 1 + x_111 + x_25, z'' >= 0, x_111 >= 0
   encode_.(z', z'') -{ 10 + 5*x_119 + 5*x_29 }-> s43 :|: s40 >= 0, s40 <= x_119 + 1, s41 >= 0, s41 <= x_29 + 1, s42 >= 0, s42 <= s40 + s41 + 1, s43 >= 0, s43 <= 0 + s42 + 1, z' >= 0, z'' = 1 + x_119 + x_29, x_119 >= 0, x_29 >= 0
   encode_.(z', z'') -{ 10 + 5*x_111 + 5*x_25 + 5*z'' }-> s64 :|: s59 >= 0, s59 <= x_111 + 1, s60 >= 0, s60 <= x_25 + 1, s61 >= 0, s61 <= s59 + s60 + 1, s62 >= 0, s62 <= z'' - 1 + 1, s63 >= 0, s63 <= s62 + 1, s64 >= 0, s64 <= s61 + s63 + 1, z'' - 1 >= 0, x_25 >= 0, z' = 1 + x_111 + x_25, x_111 >= 0
   encode_.(z', z'') -{ 10 + 5*x_117 + 5*x_28 + 5*z' }-> s70 :|: s65 >= 0, s65 <= z' - 1 + 1, s66 >= 0, s66 <= s65 + 1, s67 >= 0, s67 <= x_117 + 1, s68 >= 0, s68 <= x_28 + 1, s69 >= 0, s69 <= s67 + s68 + 1, s70 >= 0, s70 <= s66 + s69 + 1, x_117 >= 0, z'' = 1 + x_117 + x_28, z' - 1 >= 0, x_28 >= 0
   encode_.(z', z'') -{ 1 + 5*z'' }-> s97 :|: s95 >= 0, s95 <= z'' - 1 + 1, s96 >= 0, s96 <= s95 + 1, s97 >= 0, s97 <= 0 + s96 + 1, z'' - 1 >= 0, z' = 0
   encode_.(z', z'') -{ 1 }-> x :|: z'' = 0, z' = 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 1 }-> x :|: z'' >= 0, z' = 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 1 }-> x :|: z'' = 0, z' >= 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 1 }-> x :|: z' >= 0, z'' >= 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 0 }-> 0 :|: z' >= 0, z'' >= 0
   encode_.(z', z'') -{ 0 }-> 0 :|: z'' = 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> 0 :|: z'' >= 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> 0 :|: z'' = 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> 0 :|: z' >= 0, z'' >= 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' = 0, z' = 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' >= 0, z' = 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' = 0, z' >= 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z' >= 0, z'' >= 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_1 -{ 0 }-> 0 :|: 
   encode_i(z') -{ 10 + 5*x_121 + 5*x_210 }-> s115 :|: s112 >= 0, s112 <= x_121 + 1, s113 >= 0, s113 <= x_210 + 1, s114 >= 0, s114 <= s112 + s113 + 1, s115 >= 0, s115 <= s114 + 1, z' = 1 + x_121 + x_210, x_121 >= 0, x_210 >= 0
   encode_i(z') -{ 1 + 5*z' }-> s73 :|: s71 >= 0, s71 <= z' - 1 + 1, s72 >= 0, s72 <= s71 + 1, s73 >= 0, s73 <= s72 + 1, z' - 1 >= 0
   encode_i(z') -{ 0 }-> 0 :|: z' >= 0
   encode_i(z') -{ 1 }-> 0 :|: z' = 0, 0 = 0
   encode_i(z') -{ 0 }-> 0 :|: z' = 0, v0 >= 0, 0 = v0
   encode_i(z') -{ 1 }-> 0 :|: z' >= 0, 0 = 0
   encode_i(z') -{ 0 }-> 0 :|: z' >= 0, v0 >= 0, 0 = v0
   encode_i(z') -{ 0 }-> 1 + x0 :|: z' = 0, x0 >= 0, 0 = x0
   encode_i(z') -{ 0 }-> 1 + x0 :|: z' >= 0, x0 >= 0, 0 = x0
   i(z') -{ 1 }-> 0 :|: z' = 0
   i(z') -{ 0 }-> 0 :|: z' >= 0
   i(z') -{ 1 }-> z' - 1 :|: z' - 1 >= 0
   i(z') -{ 0 }-> 1 + z' :|: z' >= 0

Function symbols to be analyzed: {encode_i}, {encode_.}
Previous analysis results are:
  .: runtime: O(1) [1], size: O(n^1) [1 + z' + z'']
  i: runtime: O(1) [1], size: O(n^1) [1 + z']
  encode_1: runtime: O(1) [0], size: O(1) [0]
  encArg: runtime: O(n^1) [4 + 5*z'], size: O(n^1) [1 + z']

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

(51) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   .(z', z'') -{ 1 }-> z :|: z >= 0, z'' = 1 + (1 + z') + z, z' >= 0
   .(z', z'') -{ 1 }-> z :|: z >= 0, z' - 1 >= 0, z'' = 1 + (z' - 1) + z
   .(z', z'') -{ 1 }-> z' :|: z'' = 0, z' >= 0
   .(z', z'') -{ 1 }-> z'' :|: z'' >= 0, z' = 0
   .(z', z'') -{ 1 }-> 0 :|: z' - 1 >= 0, z'' = z' - 1
   .(z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' = 1 + z'
   .(z', z'') -{ 0 }-> 0 :|: z' >= 0, z'' >= 0
   .(z', z'') -{ 0 }-> 1 + z' + z'' :|: z' >= 0, z'' >= 0
   encArg(z') -{ 10 + 5*x_11 + 5*x_2'' }-> s1 :|: s >= 0, s <= x_11 + 1, s' >= 0, s' <= x_2'' + 1, s'' >= 0, s'' <= s + s' + 1, s1 >= 0, s1 <= 0 + s'' + 1, x_11 >= 0, x_2'' >= 0, z' = 1 + 0 + (1 + x_11 + x_2'')
   encArg(z') -{ 19 + 5*x_1' + 5*x_13 + 5*x_2' + 5*x_21 }-> s12 :|: s6 >= 0, s6 <= x_1' + 1, s7 >= 0, s7 <= x_2' + 1, s8 >= 0, s8 <= s6 + s7 + 1, s9 >= 0, s9 <= x_13 + 1, s10 >= 0, s10 <= x_21 + 1, s11 >= 0, s11 <= s9 + s10 + 1, s12 >= 0, s12 <= s8 + s11 + 1, x_2' >= 0, z' = 1 + (1 + x_1' + x_2') + (1 + x_13 + x_21), x_13 >= 0, x_1' >= 0, x_21 >= 0
   encArg(z') -{ 10 + 5*x_1' + 5*x_2' }-> s16 :|: s13 >= 0, s13 <= x_1' + 1, s14 >= 0, s14 <= x_2' + 1, s15 >= 0, s15 <= s13 + s14 + 1, s16 >= 0, s16 <= s15 + 0 + 1, x_2' >= 0, z' = 1 + (1 + x_1' + x_2') + x_2, x_1' >= 0, x_2 >= 0
   encArg(z') -{ 10 + 5*x_17 + 5*x_23 }-> s20 :|: s17 >= 0, s17 <= x_17 + 1, s18 >= 0, s18 <= x_23 + 1, s19 >= 0, s19 <= s17 + s18 + 1, s20 >= 0, s20 <= 0 + s19 + 1, x_1 >= 0, x_17 >= 0, x_23 >= 0, z' = 1 + x_1 + (1 + x_17 + x_23)
   encArg(z') -{ 15 + 5*x_1' + 5*x_14 + 5*x_2' }-> s49 :|: s44 >= 0, s44 <= x_1' + 1, s45 >= 0, s45 <= x_2' + 1, s46 >= 0, s46 <= s44 + s45 + 1, s47 >= 0, s47 <= x_14 + 1, s48 >= 0, s48 <= s47 + 1, s49 >= 0, s49 <= s46 + s48 + 1, z' = 1 + (1 + x_1' + x_2') + (1 + x_14), x_14 >= 0, x_2' >= 0, x_1' >= 0
   encArg(z') -{ 10 + 5*x_1' + 5*x_2' }-> s5 :|: s2 >= 0, s2 <= x_1' + 1, s3 >= 0, s3 <= x_2' + 1, s4 >= 0, s4 <= s2 + s3 + 1, s5 >= 0, s5 <= s4 + 0 + 1, x_2' >= 0, z' = 1 + (1 + x_1' + x_2') + 0, x_1' >= 0
   encArg(z') -{ 15 + 5*x_1'' + 5*x_15 + 5*x_22 }-> s55 :|: s50 >= 0, s50 <= x_1'' + 1, s51 >= 0, s51 <= s50 + 1, s52 >= 0, s52 <= x_15 + 1, s53 >= 0, s53 <= x_22 + 1, s54 >= 0, s54 <= s52 + s53 + 1, s55 >= 0, s55 <= s51 + s54 + 1, x_15 >= 0, x_1'' >= 0, z' = 1 + (1 + x_1'') + (1 + x_15 + x_22), x_22 >= 0
   encArg(z') -{ -4 + 5*z' }-> s58 :|: s56 >= 0, s56 <= z' - 2 + 1, s57 >= 0, s57 <= s56 + 1, s58 >= 0, s58 <= s57 + 1, z' - 2 >= 0
   encArg(z') -{ -4 + 5*z' }-> s76 :|: s74 >= 0, s74 <= z' - 2 + 1, s75 >= 0, s75 <= s74 + 1, s76 >= 0, s76 <= 0 + s75 + 1, z' - 2 >= 0
   encArg(z') -{ -4 + 5*z' }-> s79 :|: s77 >= 0, s77 <= z' - 2 + 1, s78 >= 0, s78 <= s77 + 1, s79 >= 0, s79 <= s78 + 0 + 1, z' - 2 >= 0
   encArg(z') -{ 11 + 5*x_1'' + 5*x_16 }-> s84 :|: s80 >= 0, s80 <= x_1'' + 1, s81 >= 0, s81 <= s80 + 1, s82 >= 0, s82 <= x_16 + 1, s83 >= 0, s83 <= s82 + 1, s84 >= 0, s84 <= s81 + s83 + 1, x_1'' >= 0, x_16 >= 0, z' = 1 + (1 + x_1'') + (1 + x_16)
   encArg(z') -{ 6 + 5*x_1'' }-> s87 :|: s85 >= 0, s85 <= x_1'' + 1, s86 >= 0, s86 <= s85 + 1, s87 >= 0, s87 <= s86 + 0 + 1, z' = 1 + (1 + x_1'') + x_2, x_1'' >= 0, x_2 >= 0
   encArg(z') -{ 6 + 5*x_18 }-> s90 :|: s88 >= 0, s88 <= x_18 + 1, s89 >= 0, s89 <= s88 + 1, s90 >= 0, s90 <= 0 + s89 + 1, x_1 >= 0, z' = 1 + x_1 + (1 + x_18), x_18 >= 0
   encArg(z') -{ 10 + 5*x_19 + 5*x_24 }-> s94 :|: s91 >= 0, s91 <= x_19 + 1, s92 >= 0, s92 <= x_24 + 1, s93 >= 0, s93 <= s91 + s92 + 1, s94 >= 0, s94 <= s93 + 1, z' = 1 + (1 + x_19 + x_24), x_24 >= 0, x_19 >= 0
   encArg(z') -{ 1 }-> x :|: z' = 1 + 0 + 0, x >= 0, 0 = x, 0 = 0
   encArg(z') -{ 1 }-> x :|: z' - 1 >= 0, x >= 0, 0 = x, 0 = 0
   encArg(z') -{ 1 }-> x :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2, x >= 0, 0 = x, 0 = 0
   encArg(z') -{ 0 }-> 0 :|: z' = 0
   encArg(z') -{ 0 }-> 0 :|: z' >= 0
   encArg(z') -{ 0 }-> 0 :|: z' = 1 + 0 + 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encArg(z') -{ 0 }-> 0 :|: z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encArg(z') -{ 0 }-> 0 :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encArg(z') -{ 1 }-> 0 :|: z' = 1 + 0, 0 = 0
   encArg(z') -{ 0 }-> 0 :|: z' = 1 + 0, v0 >= 0, 0 = v0
   encArg(z') -{ 1 }-> 0 :|: z' - 1 >= 0, 0 = 0
   encArg(z') -{ 0 }-> 0 :|: z' - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z') -{ 0 }-> 1 + x0 :|: z' = 1 + 0, x0 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 :|: z' - 1 >= 0, x0 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 + x1 :|: z' = 1 + 0 + 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 + x1 :|: z' - 1 >= 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 + x1 :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 1 + 5*z' }-> s100 :|: s98 >= 0, s98 <= z' - 1 + 1, s99 >= 0, s99 <= s98 + 1, s100 >= 0, s100 <= s99 + 0 + 1, z'' = 0, z' - 1 >= 0
   encode_.(z', z'') -{ 1 + 5*z' + 5*z'' }-> s105 :|: s101 >= 0, s101 <= z' - 1 + 1, s102 >= 0, s102 <= s101 + 1, s103 >= 0, s103 <= z'' - 1 + 1, s104 >= 0, s104 <= s103 + 1, s105 >= 0, s105 <= s102 + s104 + 1, z' - 1 >= 0, z'' - 1 >= 0
   encode_.(z', z'') -{ 1 + 5*z' }-> s108 :|: s106 >= 0, s106 <= z' - 1 + 1, s107 >= 0, s107 <= s106 + 1, s108 >= 0, s108 <= s107 + 0 + 1, z'' >= 0, z' - 1 >= 0
   encode_.(z', z'') -{ 1 + 5*z'' }-> s111 :|: s109 >= 0, s109 <= z'' - 1 + 1, s110 >= 0, s110 <= s109 + 1, s111 >= 0, s111 <= 0 + s110 + 1, z' >= 0, z'' - 1 >= 0
   encode_.(z', z'') -{ 10 + 5*x_113 + 5*x_26 }-> s24 :|: s21 >= 0, s21 <= x_113 + 1, s22 >= 0, s22 <= x_26 + 1, s23 >= 0, s23 <= s21 + s22 + 1, s24 >= 0, s24 <= 0 + s23 + 1, z'' = 1 + x_113 + x_26, x_113 >= 0, x_26 >= 0, z' = 0
   encode_.(z', z'') -{ 10 + 5*x_111 + 5*x_25 }-> s28 :|: s25 >= 0, s25 <= x_111 + 1, s26 >= 0, s26 <= x_25 + 1, s27 >= 0, s27 <= s25 + s26 + 1, s28 >= 0, s28 <= s27 + 0 + 1, z'' = 0, x_25 >= 0, z' = 1 + x_111 + x_25, x_111 >= 0
   encode_.(z', z'') -{ 19 + 5*x_111 + 5*x_115 + 5*x_25 + 5*x_27 }-> s35 :|: s29 >= 0, s29 <= x_111 + 1, s30 >= 0, s30 <= x_25 + 1, s31 >= 0, s31 <= s29 + s30 + 1, s32 >= 0, s32 <= x_115 + 1, s33 >= 0, s33 <= x_27 + 1, s34 >= 0, s34 <= s32 + s33 + 1, s35 >= 0, s35 <= s31 + s34 + 1, z'' = 1 + x_115 + x_27, x_25 >= 0, x_115 >= 0, z' = 1 + x_111 + x_25, x_27 >= 0, x_111 >= 0
   encode_.(z', z'') -{ 10 + 5*x_111 + 5*x_25 }-> s39 :|: s36 >= 0, s36 <= x_111 + 1, s37 >= 0, s37 <= x_25 + 1, s38 >= 0, s38 <= s36 + s37 + 1, s39 >= 0, s39 <= s38 + 0 + 1, x_25 >= 0, z' = 1 + x_111 + x_25, z'' >= 0, x_111 >= 0
   encode_.(z', z'') -{ 10 + 5*x_119 + 5*x_29 }-> s43 :|: s40 >= 0, s40 <= x_119 + 1, s41 >= 0, s41 <= x_29 + 1, s42 >= 0, s42 <= s40 + s41 + 1, s43 >= 0, s43 <= 0 + s42 + 1, z' >= 0, z'' = 1 + x_119 + x_29, x_119 >= 0, x_29 >= 0
   encode_.(z', z'') -{ 10 + 5*x_111 + 5*x_25 + 5*z'' }-> s64 :|: s59 >= 0, s59 <= x_111 + 1, s60 >= 0, s60 <= x_25 + 1, s61 >= 0, s61 <= s59 + s60 + 1, s62 >= 0, s62 <= z'' - 1 + 1, s63 >= 0, s63 <= s62 + 1, s64 >= 0, s64 <= s61 + s63 + 1, z'' - 1 >= 0, x_25 >= 0, z' = 1 + x_111 + x_25, x_111 >= 0
   encode_.(z', z'') -{ 10 + 5*x_117 + 5*x_28 + 5*z' }-> s70 :|: s65 >= 0, s65 <= z' - 1 + 1, s66 >= 0, s66 <= s65 + 1, s67 >= 0, s67 <= x_117 + 1, s68 >= 0, s68 <= x_28 + 1, s69 >= 0, s69 <= s67 + s68 + 1, s70 >= 0, s70 <= s66 + s69 + 1, x_117 >= 0, z'' = 1 + x_117 + x_28, z' - 1 >= 0, x_28 >= 0
   encode_.(z', z'') -{ 1 + 5*z'' }-> s97 :|: s95 >= 0, s95 <= z'' - 1 + 1, s96 >= 0, s96 <= s95 + 1, s97 >= 0, s97 <= 0 + s96 + 1, z'' - 1 >= 0, z' = 0
   encode_.(z', z'') -{ 1 }-> x :|: z'' = 0, z' = 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 1 }-> x :|: z'' >= 0, z' = 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 1 }-> x :|: z'' = 0, z' >= 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 1 }-> x :|: z' >= 0, z'' >= 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 0 }-> 0 :|: z' >= 0, z'' >= 0
   encode_.(z', z'') -{ 0 }-> 0 :|: z'' = 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> 0 :|: z'' >= 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> 0 :|: z'' = 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> 0 :|: z' >= 0, z'' >= 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' = 0, z' = 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' >= 0, z' = 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' = 0, z' >= 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z' >= 0, z'' >= 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_1 -{ 0 }-> 0 :|: 
   encode_i(z') -{ 10 + 5*x_121 + 5*x_210 }-> s115 :|: s112 >= 0, s112 <= x_121 + 1, s113 >= 0, s113 <= x_210 + 1, s114 >= 0, s114 <= s112 + s113 + 1, s115 >= 0, s115 <= s114 + 1, z' = 1 + x_121 + x_210, x_121 >= 0, x_210 >= 0
   encode_i(z') -{ 1 + 5*z' }-> s73 :|: s71 >= 0, s71 <= z' - 1 + 1, s72 >= 0, s72 <= s71 + 1, s73 >= 0, s73 <= s72 + 1, z' - 1 >= 0
   encode_i(z') -{ 0 }-> 0 :|: z' >= 0
   encode_i(z') -{ 1 }-> 0 :|: z' = 0, 0 = 0
   encode_i(z') -{ 0 }-> 0 :|: z' = 0, v0 >= 0, 0 = v0
   encode_i(z') -{ 1 }-> 0 :|: z' >= 0, 0 = 0
   encode_i(z') -{ 0 }-> 0 :|: z' >= 0, v0 >= 0, 0 = v0
   encode_i(z') -{ 0 }-> 1 + x0 :|: z' = 0, x0 >= 0, 0 = x0
   encode_i(z') -{ 0 }-> 1 + x0 :|: z' >= 0, x0 >= 0, 0 = x0
   i(z') -{ 1 }-> 0 :|: z' = 0
   i(z') -{ 0 }-> 0 :|: z' >= 0
   i(z') -{ 1 }-> z' - 1 :|: z' - 1 >= 0
   i(z') -{ 0 }-> 1 + z' :|: z' >= 0

Function symbols to be analyzed: {encode_i}, {encode_.}
Previous analysis results are:
  .: runtime: O(1) [1], size: O(n^1) [1 + z' + z'']
  i: runtime: O(1) [1], size: O(n^1) [1 + z']
  encode_1: runtime: O(1) [0], size: O(1) [0]
  encArg: runtime: O(n^1) [4 + 5*z'], size: O(n^1) [1 + z']
  encode_i: runtime: ?, size: O(n^1) [3 + z']

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

(53) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: encode_i
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 5 + 5*z'

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

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

   .(z', z'') -{ 1 }-> z :|: z >= 0, z'' = 1 + (1 + z') + z, z' >= 0
   .(z', z'') -{ 1 }-> z :|: z >= 0, z' - 1 >= 0, z'' = 1 + (z' - 1) + z
   .(z', z'') -{ 1 }-> z' :|: z'' = 0, z' >= 0
   .(z', z'') -{ 1 }-> z'' :|: z'' >= 0, z' = 0
   .(z', z'') -{ 1 }-> 0 :|: z' - 1 >= 0, z'' = z' - 1
   .(z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' = 1 + z'
   .(z', z'') -{ 0 }-> 0 :|: z' >= 0, z'' >= 0
   .(z', z'') -{ 0 }-> 1 + z' + z'' :|: z' >= 0, z'' >= 0
   encArg(z') -{ 10 + 5*x_11 + 5*x_2'' }-> s1 :|: s >= 0, s <= x_11 + 1, s' >= 0, s' <= x_2'' + 1, s'' >= 0, s'' <= s + s' + 1, s1 >= 0, s1 <= 0 + s'' + 1, x_11 >= 0, x_2'' >= 0, z' = 1 + 0 + (1 + x_11 + x_2'')
   encArg(z') -{ 19 + 5*x_1' + 5*x_13 + 5*x_2' + 5*x_21 }-> s12 :|: s6 >= 0, s6 <= x_1' + 1, s7 >= 0, s7 <= x_2' + 1, s8 >= 0, s8 <= s6 + s7 + 1, s9 >= 0, s9 <= x_13 + 1, s10 >= 0, s10 <= x_21 + 1, s11 >= 0, s11 <= s9 + s10 + 1, s12 >= 0, s12 <= s8 + s11 + 1, x_2' >= 0, z' = 1 + (1 + x_1' + x_2') + (1 + x_13 + x_21), x_13 >= 0, x_1' >= 0, x_21 >= 0
   encArg(z') -{ 10 + 5*x_1' + 5*x_2' }-> s16 :|: s13 >= 0, s13 <= x_1' + 1, s14 >= 0, s14 <= x_2' + 1, s15 >= 0, s15 <= s13 + s14 + 1, s16 >= 0, s16 <= s15 + 0 + 1, x_2' >= 0, z' = 1 + (1 + x_1' + x_2') + x_2, x_1' >= 0, x_2 >= 0
   encArg(z') -{ 10 + 5*x_17 + 5*x_23 }-> s20 :|: s17 >= 0, s17 <= x_17 + 1, s18 >= 0, s18 <= x_23 + 1, s19 >= 0, s19 <= s17 + s18 + 1, s20 >= 0, s20 <= 0 + s19 + 1, x_1 >= 0, x_17 >= 0, x_23 >= 0, z' = 1 + x_1 + (1 + x_17 + x_23)
   encArg(z') -{ 15 + 5*x_1' + 5*x_14 + 5*x_2' }-> s49 :|: s44 >= 0, s44 <= x_1' + 1, s45 >= 0, s45 <= x_2' + 1, s46 >= 0, s46 <= s44 + s45 + 1, s47 >= 0, s47 <= x_14 + 1, s48 >= 0, s48 <= s47 + 1, s49 >= 0, s49 <= s46 + s48 + 1, z' = 1 + (1 + x_1' + x_2') + (1 + x_14), x_14 >= 0, x_2' >= 0, x_1' >= 0
   encArg(z') -{ 10 + 5*x_1' + 5*x_2' }-> s5 :|: s2 >= 0, s2 <= x_1' + 1, s3 >= 0, s3 <= x_2' + 1, s4 >= 0, s4 <= s2 + s3 + 1, s5 >= 0, s5 <= s4 + 0 + 1, x_2' >= 0, z' = 1 + (1 + x_1' + x_2') + 0, x_1' >= 0
   encArg(z') -{ 15 + 5*x_1'' + 5*x_15 + 5*x_22 }-> s55 :|: s50 >= 0, s50 <= x_1'' + 1, s51 >= 0, s51 <= s50 + 1, s52 >= 0, s52 <= x_15 + 1, s53 >= 0, s53 <= x_22 + 1, s54 >= 0, s54 <= s52 + s53 + 1, s55 >= 0, s55 <= s51 + s54 + 1, x_15 >= 0, x_1'' >= 0, z' = 1 + (1 + x_1'') + (1 + x_15 + x_22), x_22 >= 0
   encArg(z') -{ -4 + 5*z' }-> s58 :|: s56 >= 0, s56 <= z' - 2 + 1, s57 >= 0, s57 <= s56 + 1, s58 >= 0, s58 <= s57 + 1, z' - 2 >= 0
   encArg(z') -{ -4 + 5*z' }-> s76 :|: s74 >= 0, s74 <= z' - 2 + 1, s75 >= 0, s75 <= s74 + 1, s76 >= 0, s76 <= 0 + s75 + 1, z' - 2 >= 0
   encArg(z') -{ -4 + 5*z' }-> s79 :|: s77 >= 0, s77 <= z' - 2 + 1, s78 >= 0, s78 <= s77 + 1, s79 >= 0, s79 <= s78 + 0 + 1, z' - 2 >= 0
   encArg(z') -{ 11 + 5*x_1'' + 5*x_16 }-> s84 :|: s80 >= 0, s80 <= x_1'' + 1, s81 >= 0, s81 <= s80 + 1, s82 >= 0, s82 <= x_16 + 1, s83 >= 0, s83 <= s82 + 1, s84 >= 0, s84 <= s81 + s83 + 1, x_1'' >= 0, x_16 >= 0, z' = 1 + (1 + x_1'') + (1 + x_16)
   encArg(z') -{ 6 + 5*x_1'' }-> s87 :|: s85 >= 0, s85 <= x_1'' + 1, s86 >= 0, s86 <= s85 + 1, s87 >= 0, s87 <= s86 + 0 + 1, z' = 1 + (1 + x_1'') + x_2, x_1'' >= 0, x_2 >= 0
   encArg(z') -{ 6 + 5*x_18 }-> s90 :|: s88 >= 0, s88 <= x_18 + 1, s89 >= 0, s89 <= s88 + 1, s90 >= 0, s90 <= 0 + s89 + 1, x_1 >= 0, z' = 1 + x_1 + (1 + x_18), x_18 >= 0
   encArg(z') -{ 10 + 5*x_19 + 5*x_24 }-> s94 :|: s91 >= 0, s91 <= x_19 + 1, s92 >= 0, s92 <= x_24 + 1, s93 >= 0, s93 <= s91 + s92 + 1, s94 >= 0, s94 <= s93 + 1, z' = 1 + (1 + x_19 + x_24), x_24 >= 0, x_19 >= 0
   encArg(z') -{ 1 }-> x :|: z' = 1 + 0 + 0, x >= 0, 0 = x, 0 = 0
   encArg(z') -{ 1 }-> x :|: z' - 1 >= 0, x >= 0, 0 = x, 0 = 0
   encArg(z') -{ 1 }-> x :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2, x >= 0, 0 = x, 0 = 0
   encArg(z') -{ 0 }-> 0 :|: z' = 0
   encArg(z') -{ 0 }-> 0 :|: z' >= 0
   encArg(z') -{ 0 }-> 0 :|: z' = 1 + 0 + 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encArg(z') -{ 0 }-> 0 :|: z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encArg(z') -{ 0 }-> 0 :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encArg(z') -{ 1 }-> 0 :|: z' = 1 + 0, 0 = 0
   encArg(z') -{ 0 }-> 0 :|: z' = 1 + 0, v0 >= 0, 0 = v0
   encArg(z') -{ 1 }-> 0 :|: z' - 1 >= 0, 0 = 0
   encArg(z') -{ 0 }-> 0 :|: z' - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z') -{ 0 }-> 1 + x0 :|: z' = 1 + 0, x0 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 :|: z' - 1 >= 0, x0 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 + x1 :|: z' = 1 + 0 + 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 + x1 :|: z' - 1 >= 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 + x1 :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 1 + 5*z' }-> s100 :|: s98 >= 0, s98 <= z' - 1 + 1, s99 >= 0, s99 <= s98 + 1, s100 >= 0, s100 <= s99 + 0 + 1, z'' = 0, z' - 1 >= 0
   encode_.(z', z'') -{ 1 + 5*z' + 5*z'' }-> s105 :|: s101 >= 0, s101 <= z' - 1 + 1, s102 >= 0, s102 <= s101 + 1, s103 >= 0, s103 <= z'' - 1 + 1, s104 >= 0, s104 <= s103 + 1, s105 >= 0, s105 <= s102 + s104 + 1, z' - 1 >= 0, z'' - 1 >= 0
   encode_.(z', z'') -{ 1 + 5*z' }-> s108 :|: s106 >= 0, s106 <= z' - 1 + 1, s107 >= 0, s107 <= s106 + 1, s108 >= 0, s108 <= s107 + 0 + 1, z'' >= 0, z' - 1 >= 0
   encode_.(z', z'') -{ 1 + 5*z'' }-> s111 :|: s109 >= 0, s109 <= z'' - 1 + 1, s110 >= 0, s110 <= s109 + 1, s111 >= 0, s111 <= 0 + s110 + 1, z' >= 0, z'' - 1 >= 0
   encode_.(z', z'') -{ 10 + 5*x_113 + 5*x_26 }-> s24 :|: s21 >= 0, s21 <= x_113 + 1, s22 >= 0, s22 <= x_26 + 1, s23 >= 0, s23 <= s21 + s22 + 1, s24 >= 0, s24 <= 0 + s23 + 1, z'' = 1 + x_113 + x_26, x_113 >= 0, x_26 >= 0, z' = 0
   encode_.(z', z'') -{ 10 + 5*x_111 + 5*x_25 }-> s28 :|: s25 >= 0, s25 <= x_111 + 1, s26 >= 0, s26 <= x_25 + 1, s27 >= 0, s27 <= s25 + s26 + 1, s28 >= 0, s28 <= s27 + 0 + 1, z'' = 0, x_25 >= 0, z' = 1 + x_111 + x_25, x_111 >= 0
   encode_.(z', z'') -{ 19 + 5*x_111 + 5*x_115 + 5*x_25 + 5*x_27 }-> s35 :|: s29 >= 0, s29 <= x_111 + 1, s30 >= 0, s30 <= x_25 + 1, s31 >= 0, s31 <= s29 + s30 + 1, s32 >= 0, s32 <= x_115 + 1, s33 >= 0, s33 <= x_27 + 1, s34 >= 0, s34 <= s32 + s33 + 1, s35 >= 0, s35 <= s31 + s34 + 1, z'' = 1 + x_115 + x_27, x_25 >= 0, x_115 >= 0, z' = 1 + x_111 + x_25, x_27 >= 0, x_111 >= 0
   encode_.(z', z'') -{ 10 + 5*x_111 + 5*x_25 }-> s39 :|: s36 >= 0, s36 <= x_111 + 1, s37 >= 0, s37 <= x_25 + 1, s38 >= 0, s38 <= s36 + s37 + 1, s39 >= 0, s39 <= s38 + 0 + 1, x_25 >= 0, z' = 1 + x_111 + x_25, z'' >= 0, x_111 >= 0
   encode_.(z', z'') -{ 10 + 5*x_119 + 5*x_29 }-> s43 :|: s40 >= 0, s40 <= x_119 + 1, s41 >= 0, s41 <= x_29 + 1, s42 >= 0, s42 <= s40 + s41 + 1, s43 >= 0, s43 <= 0 + s42 + 1, z' >= 0, z'' = 1 + x_119 + x_29, x_119 >= 0, x_29 >= 0
   encode_.(z', z'') -{ 10 + 5*x_111 + 5*x_25 + 5*z'' }-> s64 :|: s59 >= 0, s59 <= x_111 + 1, s60 >= 0, s60 <= x_25 + 1, s61 >= 0, s61 <= s59 + s60 + 1, s62 >= 0, s62 <= z'' - 1 + 1, s63 >= 0, s63 <= s62 + 1, s64 >= 0, s64 <= s61 + s63 + 1, z'' - 1 >= 0, x_25 >= 0, z' = 1 + x_111 + x_25, x_111 >= 0
   encode_.(z', z'') -{ 10 + 5*x_117 + 5*x_28 + 5*z' }-> s70 :|: s65 >= 0, s65 <= z' - 1 + 1, s66 >= 0, s66 <= s65 + 1, s67 >= 0, s67 <= x_117 + 1, s68 >= 0, s68 <= x_28 + 1, s69 >= 0, s69 <= s67 + s68 + 1, s70 >= 0, s70 <= s66 + s69 + 1, x_117 >= 0, z'' = 1 + x_117 + x_28, z' - 1 >= 0, x_28 >= 0
   encode_.(z', z'') -{ 1 + 5*z'' }-> s97 :|: s95 >= 0, s95 <= z'' - 1 + 1, s96 >= 0, s96 <= s95 + 1, s97 >= 0, s97 <= 0 + s96 + 1, z'' - 1 >= 0, z' = 0
   encode_.(z', z'') -{ 1 }-> x :|: z'' = 0, z' = 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 1 }-> x :|: z'' >= 0, z' = 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 1 }-> x :|: z'' = 0, z' >= 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 1 }-> x :|: z' >= 0, z'' >= 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 0 }-> 0 :|: z' >= 0, z'' >= 0
   encode_.(z', z'') -{ 0 }-> 0 :|: z'' = 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> 0 :|: z'' >= 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> 0 :|: z'' = 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> 0 :|: z' >= 0, z'' >= 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' = 0, z' = 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' >= 0, z' = 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' = 0, z' >= 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z' >= 0, z'' >= 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_1 -{ 0 }-> 0 :|: 
   encode_i(z') -{ 10 + 5*x_121 + 5*x_210 }-> s115 :|: s112 >= 0, s112 <= x_121 + 1, s113 >= 0, s113 <= x_210 + 1, s114 >= 0, s114 <= s112 + s113 + 1, s115 >= 0, s115 <= s114 + 1, z' = 1 + x_121 + x_210, x_121 >= 0, x_210 >= 0
   encode_i(z') -{ 1 + 5*z' }-> s73 :|: s71 >= 0, s71 <= z' - 1 + 1, s72 >= 0, s72 <= s71 + 1, s73 >= 0, s73 <= s72 + 1, z' - 1 >= 0
   encode_i(z') -{ 0 }-> 0 :|: z' >= 0
   encode_i(z') -{ 1 }-> 0 :|: z' = 0, 0 = 0
   encode_i(z') -{ 0 }-> 0 :|: z' = 0, v0 >= 0, 0 = v0
   encode_i(z') -{ 1 }-> 0 :|: z' >= 0, 0 = 0
   encode_i(z') -{ 0 }-> 0 :|: z' >= 0, v0 >= 0, 0 = v0
   encode_i(z') -{ 0 }-> 1 + x0 :|: z' = 0, x0 >= 0, 0 = x0
   encode_i(z') -{ 0 }-> 1 + x0 :|: z' >= 0, x0 >= 0, 0 = x0
   i(z') -{ 1 }-> 0 :|: z' = 0
   i(z') -{ 0 }-> 0 :|: z' >= 0
   i(z') -{ 1 }-> z' - 1 :|: z' - 1 >= 0
   i(z') -{ 0 }-> 1 + z' :|: z' >= 0

Function symbols to be analyzed: {encode_.}
Previous analysis results are:
  .: runtime: O(1) [1], size: O(n^1) [1 + z' + z'']
  i: runtime: O(1) [1], size: O(n^1) [1 + z']
  encode_1: runtime: O(1) [0], size: O(1) [0]
  encArg: runtime: O(n^1) [4 + 5*z'], size: O(n^1) [1 + z']
  encode_i: runtime: O(n^1) [5 + 5*z'], size: O(n^1) [3 + z']

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

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

   .(z', z'') -{ 1 }-> z :|: z >= 0, z'' = 1 + (1 + z') + z, z' >= 0
   .(z', z'') -{ 1 }-> z :|: z >= 0, z' - 1 >= 0, z'' = 1 + (z' - 1) + z
   .(z', z'') -{ 1 }-> z' :|: z'' = 0, z' >= 0
   .(z', z'') -{ 1 }-> z'' :|: z'' >= 0, z' = 0
   .(z', z'') -{ 1 }-> 0 :|: z' - 1 >= 0, z'' = z' - 1
   .(z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' = 1 + z'
   .(z', z'') -{ 0 }-> 0 :|: z' >= 0, z'' >= 0
   .(z', z'') -{ 0 }-> 1 + z' + z'' :|: z' >= 0, z'' >= 0
   encArg(z') -{ 10 + 5*x_11 + 5*x_2'' }-> s1 :|: s >= 0, s <= x_11 + 1, s' >= 0, s' <= x_2'' + 1, s'' >= 0, s'' <= s + s' + 1, s1 >= 0, s1 <= 0 + s'' + 1, x_11 >= 0, x_2'' >= 0, z' = 1 + 0 + (1 + x_11 + x_2'')
   encArg(z') -{ 19 + 5*x_1' + 5*x_13 + 5*x_2' + 5*x_21 }-> s12 :|: s6 >= 0, s6 <= x_1' + 1, s7 >= 0, s7 <= x_2' + 1, s8 >= 0, s8 <= s6 + s7 + 1, s9 >= 0, s9 <= x_13 + 1, s10 >= 0, s10 <= x_21 + 1, s11 >= 0, s11 <= s9 + s10 + 1, s12 >= 0, s12 <= s8 + s11 + 1, x_2' >= 0, z' = 1 + (1 + x_1' + x_2') + (1 + x_13 + x_21), x_13 >= 0, x_1' >= 0, x_21 >= 0
   encArg(z') -{ 10 + 5*x_1' + 5*x_2' }-> s16 :|: s13 >= 0, s13 <= x_1' + 1, s14 >= 0, s14 <= x_2' + 1, s15 >= 0, s15 <= s13 + s14 + 1, s16 >= 0, s16 <= s15 + 0 + 1, x_2' >= 0, z' = 1 + (1 + x_1' + x_2') + x_2, x_1' >= 0, x_2 >= 0
   encArg(z') -{ 10 + 5*x_17 + 5*x_23 }-> s20 :|: s17 >= 0, s17 <= x_17 + 1, s18 >= 0, s18 <= x_23 + 1, s19 >= 0, s19 <= s17 + s18 + 1, s20 >= 0, s20 <= 0 + s19 + 1, x_1 >= 0, x_17 >= 0, x_23 >= 0, z' = 1 + x_1 + (1 + x_17 + x_23)
   encArg(z') -{ 15 + 5*x_1' + 5*x_14 + 5*x_2' }-> s49 :|: s44 >= 0, s44 <= x_1' + 1, s45 >= 0, s45 <= x_2' + 1, s46 >= 0, s46 <= s44 + s45 + 1, s47 >= 0, s47 <= x_14 + 1, s48 >= 0, s48 <= s47 + 1, s49 >= 0, s49 <= s46 + s48 + 1, z' = 1 + (1 + x_1' + x_2') + (1 + x_14), x_14 >= 0, x_2' >= 0, x_1' >= 0
   encArg(z') -{ 10 + 5*x_1' + 5*x_2' }-> s5 :|: s2 >= 0, s2 <= x_1' + 1, s3 >= 0, s3 <= x_2' + 1, s4 >= 0, s4 <= s2 + s3 + 1, s5 >= 0, s5 <= s4 + 0 + 1, x_2' >= 0, z' = 1 + (1 + x_1' + x_2') + 0, x_1' >= 0
   encArg(z') -{ 15 + 5*x_1'' + 5*x_15 + 5*x_22 }-> s55 :|: s50 >= 0, s50 <= x_1'' + 1, s51 >= 0, s51 <= s50 + 1, s52 >= 0, s52 <= x_15 + 1, s53 >= 0, s53 <= x_22 + 1, s54 >= 0, s54 <= s52 + s53 + 1, s55 >= 0, s55 <= s51 + s54 + 1, x_15 >= 0, x_1'' >= 0, z' = 1 + (1 + x_1'') + (1 + x_15 + x_22), x_22 >= 0
   encArg(z') -{ -4 + 5*z' }-> s58 :|: s56 >= 0, s56 <= z' - 2 + 1, s57 >= 0, s57 <= s56 + 1, s58 >= 0, s58 <= s57 + 1, z' - 2 >= 0
   encArg(z') -{ -4 + 5*z' }-> s76 :|: s74 >= 0, s74 <= z' - 2 + 1, s75 >= 0, s75 <= s74 + 1, s76 >= 0, s76 <= 0 + s75 + 1, z' - 2 >= 0
   encArg(z') -{ -4 + 5*z' }-> s79 :|: s77 >= 0, s77 <= z' - 2 + 1, s78 >= 0, s78 <= s77 + 1, s79 >= 0, s79 <= s78 + 0 + 1, z' - 2 >= 0
   encArg(z') -{ 11 + 5*x_1'' + 5*x_16 }-> s84 :|: s80 >= 0, s80 <= x_1'' + 1, s81 >= 0, s81 <= s80 + 1, s82 >= 0, s82 <= x_16 + 1, s83 >= 0, s83 <= s82 + 1, s84 >= 0, s84 <= s81 + s83 + 1, x_1'' >= 0, x_16 >= 0, z' = 1 + (1 + x_1'') + (1 + x_16)
   encArg(z') -{ 6 + 5*x_1'' }-> s87 :|: s85 >= 0, s85 <= x_1'' + 1, s86 >= 0, s86 <= s85 + 1, s87 >= 0, s87 <= s86 + 0 + 1, z' = 1 + (1 + x_1'') + x_2, x_1'' >= 0, x_2 >= 0
   encArg(z') -{ 6 + 5*x_18 }-> s90 :|: s88 >= 0, s88 <= x_18 + 1, s89 >= 0, s89 <= s88 + 1, s90 >= 0, s90 <= 0 + s89 + 1, x_1 >= 0, z' = 1 + x_1 + (1 + x_18), x_18 >= 0
   encArg(z') -{ 10 + 5*x_19 + 5*x_24 }-> s94 :|: s91 >= 0, s91 <= x_19 + 1, s92 >= 0, s92 <= x_24 + 1, s93 >= 0, s93 <= s91 + s92 + 1, s94 >= 0, s94 <= s93 + 1, z' = 1 + (1 + x_19 + x_24), x_24 >= 0, x_19 >= 0
   encArg(z') -{ 1 }-> x :|: z' = 1 + 0 + 0, x >= 0, 0 = x, 0 = 0
   encArg(z') -{ 1 }-> x :|: z' - 1 >= 0, x >= 0, 0 = x, 0 = 0
   encArg(z') -{ 1 }-> x :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2, x >= 0, 0 = x, 0 = 0
   encArg(z') -{ 0 }-> 0 :|: z' = 0
   encArg(z') -{ 0 }-> 0 :|: z' >= 0
   encArg(z') -{ 0 }-> 0 :|: z' = 1 + 0 + 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encArg(z') -{ 0 }-> 0 :|: z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encArg(z') -{ 0 }-> 0 :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encArg(z') -{ 1 }-> 0 :|: z' = 1 + 0, 0 = 0
   encArg(z') -{ 0 }-> 0 :|: z' = 1 + 0, v0 >= 0, 0 = v0
   encArg(z') -{ 1 }-> 0 :|: z' - 1 >= 0, 0 = 0
   encArg(z') -{ 0 }-> 0 :|: z' - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z') -{ 0 }-> 1 + x0 :|: z' = 1 + 0, x0 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 :|: z' - 1 >= 0, x0 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 + x1 :|: z' = 1 + 0 + 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 + x1 :|: z' - 1 >= 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 + x1 :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 1 + 5*z' }-> s100 :|: s98 >= 0, s98 <= z' - 1 + 1, s99 >= 0, s99 <= s98 + 1, s100 >= 0, s100 <= s99 + 0 + 1, z'' = 0, z' - 1 >= 0
   encode_.(z', z'') -{ 1 + 5*z' + 5*z'' }-> s105 :|: s101 >= 0, s101 <= z' - 1 + 1, s102 >= 0, s102 <= s101 + 1, s103 >= 0, s103 <= z'' - 1 + 1, s104 >= 0, s104 <= s103 + 1, s105 >= 0, s105 <= s102 + s104 + 1, z' - 1 >= 0, z'' - 1 >= 0
   encode_.(z', z'') -{ 1 + 5*z' }-> s108 :|: s106 >= 0, s106 <= z' - 1 + 1, s107 >= 0, s107 <= s106 + 1, s108 >= 0, s108 <= s107 + 0 + 1, z'' >= 0, z' - 1 >= 0
   encode_.(z', z'') -{ 1 + 5*z'' }-> s111 :|: s109 >= 0, s109 <= z'' - 1 + 1, s110 >= 0, s110 <= s109 + 1, s111 >= 0, s111 <= 0 + s110 + 1, z' >= 0, z'' - 1 >= 0
   encode_.(z', z'') -{ 10 + 5*x_113 + 5*x_26 }-> s24 :|: s21 >= 0, s21 <= x_113 + 1, s22 >= 0, s22 <= x_26 + 1, s23 >= 0, s23 <= s21 + s22 + 1, s24 >= 0, s24 <= 0 + s23 + 1, z'' = 1 + x_113 + x_26, x_113 >= 0, x_26 >= 0, z' = 0
   encode_.(z', z'') -{ 10 + 5*x_111 + 5*x_25 }-> s28 :|: s25 >= 0, s25 <= x_111 + 1, s26 >= 0, s26 <= x_25 + 1, s27 >= 0, s27 <= s25 + s26 + 1, s28 >= 0, s28 <= s27 + 0 + 1, z'' = 0, x_25 >= 0, z' = 1 + x_111 + x_25, x_111 >= 0
   encode_.(z', z'') -{ 19 + 5*x_111 + 5*x_115 + 5*x_25 + 5*x_27 }-> s35 :|: s29 >= 0, s29 <= x_111 + 1, s30 >= 0, s30 <= x_25 + 1, s31 >= 0, s31 <= s29 + s30 + 1, s32 >= 0, s32 <= x_115 + 1, s33 >= 0, s33 <= x_27 + 1, s34 >= 0, s34 <= s32 + s33 + 1, s35 >= 0, s35 <= s31 + s34 + 1, z'' = 1 + x_115 + x_27, x_25 >= 0, x_115 >= 0, z' = 1 + x_111 + x_25, x_27 >= 0, x_111 >= 0
   encode_.(z', z'') -{ 10 + 5*x_111 + 5*x_25 }-> s39 :|: s36 >= 0, s36 <= x_111 + 1, s37 >= 0, s37 <= x_25 + 1, s38 >= 0, s38 <= s36 + s37 + 1, s39 >= 0, s39 <= s38 + 0 + 1, x_25 >= 0, z' = 1 + x_111 + x_25, z'' >= 0, x_111 >= 0
   encode_.(z', z'') -{ 10 + 5*x_119 + 5*x_29 }-> s43 :|: s40 >= 0, s40 <= x_119 + 1, s41 >= 0, s41 <= x_29 + 1, s42 >= 0, s42 <= s40 + s41 + 1, s43 >= 0, s43 <= 0 + s42 + 1, z' >= 0, z'' = 1 + x_119 + x_29, x_119 >= 0, x_29 >= 0
   encode_.(z', z'') -{ 10 + 5*x_111 + 5*x_25 + 5*z'' }-> s64 :|: s59 >= 0, s59 <= x_111 + 1, s60 >= 0, s60 <= x_25 + 1, s61 >= 0, s61 <= s59 + s60 + 1, s62 >= 0, s62 <= z'' - 1 + 1, s63 >= 0, s63 <= s62 + 1, s64 >= 0, s64 <= s61 + s63 + 1, z'' - 1 >= 0, x_25 >= 0, z' = 1 + x_111 + x_25, x_111 >= 0
   encode_.(z', z'') -{ 10 + 5*x_117 + 5*x_28 + 5*z' }-> s70 :|: s65 >= 0, s65 <= z' - 1 + 1, s66 >= 0, s66 <= s65 + 1, s67 >= 0, s67 <= x_117 + 1, s68 >= 0, s68 <= x_28 + 1, s69 >= 0, s69 <= s67 + s68 + 1, s70 >= 0, s70 <= s66 + s69 + 1, x_117 >= 0, z'' = 1 + x_117 + x_28, z' - 1 >= 0, x_28 >= 0
   encode_.(z', z'') -{ 1 + 5*z'' }-> s97 :|: s95 >= 0, s95 <= z'' - 1 + 1, s96 >= 0, s96 <= s95 + 1, s97 >= 0, s97 <= 0 + s96 + 1, z'' - 1 >= 0, z' = 0
   encode_.(z', z'') -{ 1 }-> x :|: z'' = 0, z' = 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 1 }-> x :|: z'' >= 0, z' = 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 1 }-> x :|: z'' = 0, z' >= 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 1 }-> x :|: z' >= 0, z'' >= 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 0 }-> 0 :|: z' >= 0, z'' >= 0
   encode_.(z', z'') -{ 0 }-> 0 :|: z'' = 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> 0 :|: z'' >= 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> 0 :|: z'' = 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> 0 :|: z' >= 0, z'' >= 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' = 0, z' = 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' >= 0, z' = 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' = 0, z' >= 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z' >= 0, z'' >= 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_1 -{ 0 }-> 0 :|: 
   encode_i(z') -{ 10 + 5*x_121 + 5*x_210 }-> s115 :|: s112 >= 0, s112 <= x_121 + 1, s113 >= 0, s113 <= x_210 + 1, s114 >= 0, s114 <= s112 + s113 + 1, s115 >= 0, s115 <= s114 + 1, z' = 1 + x_121 + x_210, x_121 >= 0, x_210 >= 0
   encode_i(z') -{ 1 + 5*z' }-> s73 :|: s71 >= 0, s71 <= z' - 1 + 1, s72 >= 0, s72 <= s71 + 1, s73 >= 0, s73 <= s72 + 1, z' - 1 >= 0
   encode_i(z') -{ 0 }-> 0 :|: z' >= 0
   encode_i(z') -{ 1 }-> 0 :|: z' = 0, 0 = 0
   encode_i(z') -{ 0 }-> 0 :|: z' = 0, v0 >= 0, 0 = v0
   encode_i(z') -{ 1 }-> 0 :|: z' >= 0, 0 = 0
   encode_i(z') -{ 0 }-> 0 :|: z' >= 0, v0 >= 0, 0 = v0
   encode_i(z') -{ 0 }-> 1 + x0 :|: z' = 0, x0 >= 0, 0 = x0
   encode_i(z') -{ 0 }-> 1 + x0 :|: z' >= 0, x0 >= 0, 0 = x0
   i(z') -{ 1 }-> 0 :|: z' = 0
   i(z') -{ 0 }-> 0 :|: z' >= 0
   i(z') -{ 1 }-> z' - 1 :|: z' - 1 >= 0
   i(z') -{ 0 }-> 1 + z' :|: z' >= 0

Function symbols to be analyzed: {encode_.}
Previous analysis results are:
  .: runtime: O(1) [1], size: O(n^1) [1 + z' + z'']
  i: runtime: O(1) [1], size: O(n^1) [1 + z']
  encode_1: runtime: O(1) [0], size: O(1) [0]
  encArg: runtime: O(n^1) [4 + 5*z'], size: O(n^1) [1 + z']
  encode_i: runtime: O(n^1) [5 + 5*z'], size: O(n^1) [3 + z']

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

(57) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: encode_.
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 5 + z' + z''

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

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

   .(z', z'') -{ 1 }-> z :|: z >= 0, z'' = 1 + (1 + z') + z, z' >= 0
   .(z', z'') -{ 1 }-> z :|: z >= 0, z' - 1 >= 0, z'' = 1 + (z' - 1) + z
   .(z', z'') -{ 1 }-> z' :|: z'' = 0, z' >= 0
   .(z', z'') -{ 1 }-> z'' :|: z'' >= 0, z' = 0
   .(z', z'') -{ 1 }-> 0 :|: z' - 1 >= 0, z'' = z' - 1
   .(z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' = 1 + z'
   .(z', z'') -{ 0 }-> 0 :|: z' >= 0, z'' >= 0
   .(z', z'') -{ 0 }-> 1 + z' + z'' :|: z' >= 0, z'' >= 0
   encArg(z') -{ 10 + 5*x_11 + 5*x_2'' }-> s1 :|: s >= 0, s <= x_11 + 1, s' >= 0, s' <= x_2'' + 1, s'' >= 0, s'' <= s + s' + 1, s1 >= 0, s1 <= 0 + s'' + 1, x_11 >= 0, x_2'' >= 0, z' = 1 + 0 + (1 + x_11 + x_2'')
   encArg(z') -{ 19 + 5*x_1' + 5*x_13 + 5*x_2' + 5*x_21 }-> s12 :|: s6 >= 0, s6 <= x_1' + 1, s7 >= 0, s7 <= x_2' + 1, s8 >= 0, s8 <= s6 + s7 + 1, s9 >= 0, s9 <= x_13 + 1, s10 >= 0, s10 <= x_21 + 1, s11 >= 0, s11 <= s9 + s10 + 1, s12 >= 0, s12 <= s8 + s11 + 1, x_2' >= 0, z' = 1 + (1 + x_1' + x_2') + (1 + x_13 + x_21), x_13 >= 0, x_1' >= 0, x_21 >= 0
   encArg(z') -{ 10 + 5*x_1' + 5*x_2' }-> s16 :|: s13 >= 0, s13 <= x_1' + 1, s14 >= 0, s14 <= x_2' + 1, s15 >= 0, s15 <= s13 + s14 + 1, s16 >= 0, s16 <= s15 + 0 + 1, x_2' >= 0, z' = 1 + (1 + x_1' + x_2') + x_2, x_1' >= 0, x_2 >= 0
   encArg(z') -{ 10 + 5*x_17 + 5*x_23 }-> s20 :|: s17 >= 0, s17 <= x_17 + 1, s18 >= 0, s18 <= x_23 + 1, s19 >= 0, s19 <= s17 + s18 + 1, s20 >= 0, s20 <= 0 + s19 + 1, x_1 >= 0, x_17 >= 0, x_23 >= 0, z' = 1 + x_1 + (1 + x_17 + x_23)
   encArg(z') -{ 15 + 5*x_1' + 5*x_14 + 5*x_2' }-> s49 :|: s44 >= 0, s44 <= x_1' + 1, s45 >= 0, s45 <= x_2' + 1, s46 >= 0, s46 <= s44 + s45 + 1, s47 >= 0, s47 <= x_14 + 1, s48 >= 0, s48 <= s47 + 1, s49 >= 0, s49 <= s46 + s48 + 1, z' = 1 + (1 + x_1' + x_2') + (1 + x_14), x_14 >= 0, x_2' >= 0, x_1' >= 0
   encArg(z') -{ 10 + 5*x_1' + 5*x_2' }-> s5 :|: s2 >= 0, s2 <= x_1' + 1, s3 >= 0, s3 <= x_2' + 1, s4 >= 0, s4 <= s2 + s3 + 1, s5 >= 0, s5 <= s4 + 0 + 1, x_2' >= 0, z' = 1 + (1 + x_1' + x_2') + 0, x_1' >= 0
   encArg(z') -{ 15 + 5*x_1'' + 5*x_15 + 5*x_22 }-> s55 :|: s50 >= 0, s50 <= x_1'' + 1, s51 >= 0, s51 <= s50 + 1, s52 >= 0, s52 <= x_15 + 1, s53 >= 0, s53 <= x_22 + 1, s54 >= 0, s54 <= s52 + s53 + 1, s55 >= 0, s55 <= s51 + s54 + 1, x_15 >= 0, x_1'' >= 0, z' = 1 + (1 + x_1'') + (1 + x_15 + x_22), x_22 >= 0
   encArg(z') -{ -4 + 5*z' }-> s58 :|: s56 >= 0, s56 <= z' - 2 + 1, s57 >= 0, s57 <= s56 + 1, s58 >= 0, s58 <= s57 + 1, z' - 2 >= 0
   encArg(z') -{ -4 + 5*z' }-> s76 :|: s74 >= 0, s74 <= z' - 2 + 1, s75 >= 0, s75 <= s74 + 1, s76 >= 0, s76 <= 0 + s75 + 1, z' - 2 >= 0
   encArg(z') -{ -4 + 5*z' }-> s79 :|: s77 >= 0, s77 <= z' - 2 + 1, s78 >= 0, s78 <= s77 + 1, s79 >= 0, s79 <= s78 + 0 + 1, z' - 2 >= 0
   encArg(z') -{ 11 + 5*x_1'' + 5*x_16 }-> s84 :|: s80 >= 0, s80 <= x_1'' + 1, s81 >= 0, s81 <= s80 + 1, s82 >= 0, s82 <= x_16 + 1, s83 >= 0, s83 <= s82 + 1, s84 >= 0, s84 <= s81 + s83 + 1, x_1'' >= 0, x_16 >= 0, z' = 1 + (1 + x_1'') + (1 + x_16)
   encArg(z') -{ 6 + 5*x_1'' }-> s87 :|: s85 >= 0, s85 <= x_1'' + 1, s86 >= 0, s86 <= s85 + 1, s87 >= 0, s87 <= s86 + 0 + 1, z' = 1 + (1 + x_1'') + x_2, x_1'' >= 0, x_2 >= 0
   encArg(z') -{ 6 + 5*x_18 }-> s90 :|: s88 >= 0, s88 <= x_18 + 1, s89 >= 0, s89 <= s88 + 1, s90 >= 0, s90 <= 0 + s89 + 1, x_1 >= 0, z' = 1 + x_1 + (1 + x_18), x_18 >= 0
   encArg(z') -{ 10 + 5*x_19 + 5*x_24 }-> s94 :|: s91 >= 0, s91 <= x_19 + 1, s92 >= 0, s92 <= x_24 + 1, s93 >= 0, s93 <= s91 + s92 + 1, s94 >= 0, s94 <= s93 + 1, z' = 1 + (1 + x_19 + x_24), x_24 >= 0, x_19 >= 0
   encArg(z') -{ 1 }-> x :|: z' = 1 + 0 + 0, x >= 0, 0 = x, 0 = 0
   encArg(z') -{ 1 }-> x :|: z' - 1 >= 0, x >= 0, 0 = x, 0 = 0
   encArg(z') -{ 1 }-> x :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2, x >= 0, 0 = x, 0 = 0
   encArg(z') -{ 0 }-> 0 :|: z' = 0
   encArg(z') -{ 0 }-> 0 :|: z' >= 0
   encArg(z') -{ 0 }-> 0 :|: z' = 1 + 0 + 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encArg(z') -{ 0 }-> 0 :|: z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encArg(z') -{ 0 }-> 0 :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encArg(z') -{ 1 }-> 0 :|: z' = 1 + 0, 0 = 0
   encArg(z') -{ 0 }-> 0 :|: z' = 1 + 0, v0 >= 0, 0 = v0
   encArg(z') -{ 1 }-> 0 :|: z' - 1 >= 0, 0 = 0
   encArg(z') -{ 0 }-> 0 :|: z' - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z') -{ 0 }-> 1 + x0 :|: z' = 1 + 0, x0 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 :|: z' - 1 >= 0, x0 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 + x1 :|: z' = 1 + 0 + 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 + x1 :|: z' - 1 >= 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 + x1 :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 1 + 5*z' }-> s100 :|: s98 >= 0, s98 <= z' - 1 + 1, s99 >= 0, s99 <= s98 + 1, s100 >= 0, s100 <= s99 + 0 + 1, z'' = 0, z' - 1 >= 0
   encode_.(z', z'') -{ 1 + 5*z' + 5*z'' }-> s105 :|: s101 >= 0, s101 <= z' - 1 + 1, s102 >= 0, s102 <= s101 + 1, s103 >= 0, s103 <= z'' - 1 + 1, s104 >= 0, s104 <= s103 + 1, s105 >= 0, s105 <= s102 + s104 + 1, z' - 1 >= 0, z'' - 1 >= 0
   encode_.(z', z'') -{ 1 + 5*z' }-> s108 :|: s106 >= 0, s106 <= z' - 1 + 1, s107 >= 0, s107 <= s106 + 1, s108 >= 0, s108 <= s107 + 0 + 1, z'' >= 0, z' - 1 >= 0
   encode_.(z', z'') -{ 1 + 5*z'' }-> s111 :|: s109 >= 0, s109 <= z'' - 1 + 1, s110 >= 0, s110 <= s109 + 1, s111 >= 0, s111 <= 0 + s110 + 1, z' >= 0, z'' - 1 >= 0
   encode_.(z', z'') -{ 10 + 5*x_113 + 5*x_26 }-> s24 :|: s21 >= 0, s21 <= x_113 + 1, s22 >= 0, s22 <= x_26 + 1, s23 >= 0, s23 <= s21 + s22 + 1, s24 >= 0, s24 <= 0 + s23 + 1, z'' = 1 + x_113 + x_26, x_113 >= 0, x_26 >= 0, z' = 0
   encode_.(z', z'') -{ 10 + 5*x_111 + 5*x_25 }-> s28 :|: s25 >= 0, s25 <= x_111 + 1, s26 >= 0, s26 <= x_25 + 1, s27 >= 0, s27 <= s25 + s26 + 1, s28 >= 0, s28 <= s27 + 0 + 1, z'' = 0, x_25 >= 0, z' = 1 + x_111 + x_25, x_111 >= 0
   encode_.(z', z'') -{ 19 + 5*x_111 + 5*x_115 + 5*x_25 + 5*x_27 }-> s35 :|: s29 >= 0, s29 <= x_111 + 1, s30 >= 0, s30 <= x_25 + 1, s31 >= 0, s31 <= s29 + s30 + 1, s32 >= 0, s32 <= x_115 + 1, s33 >= 0, s33 <= x_27 + 1, s34 >= 0, s34 <= s32 + s33 + 1, s35 >= 0, s35 <= s31 + s34 + 1, z'' = 1 + x_115 + x_27, x_25 >= 0, x_115 >= 0, z' = 1 + x_111 + x_25, x_27 >= 0, x_111 >= 0
   encode_.(z', z'') -{ 10 + 5*x_111 + 5*x_25 }-> s39 :|: s36 >= 0, s36 <= x_111 + 1, s37 >= 0, s37 <= x_25 + 1, s38 >= 0, s38 <= s36 + s37 + 1, s39 >= 0, s39 <= s38 + 0 + 1, x_25 >= 0, z' = 1 + x_111 + x_25, z'' >= 0, x_111 >= 0
   encode_.(z', z'') -{ 10 + 5*x_119 + 5*x_29 }-> s43 :|: s40 >= 0, s40 <= x_119 + 1, s41 >= 0, s41 <= x_29 + 1, s42 >= 0, s42 <= s40 + s41 + 1, s43 >= 0, s43 <= 0 + s42 + 1, z' >= 0, z'' = 1 + x_119 + x_29, x_119 >= 0, x_29 >= 0
   encode_.(z', z'') -{ 10 + 5*x_111 + 5*x_25 + 5*z'' }-> s64 :|: s59 >= 0, s59 <= x_111 + 1, s60 >= 0, s60 <= x_25 + 1, s61 >= 0, s61 <= s59 + s60 + 1, s62 >= 0, s62 <= z'' - 1 + 1, s63 >= 0, s63 <= s62 + 1, s64 >= 0, s64 <= s61 + s63 + 1, z'' - 1 >= 0, x_25 >= 0, z' = 1 + x_111 + x_25, x_111 >= 0
   encode_.(z', z'') -{ 10 + 5*x_117 + 5*x_28 + 5*z' }-> s70 :|: s65 >= 0, s65 <= z' - 1 + 1, s66 >= 0, s66 <= s65 + 1, s67 >= 0, s67 <= x_117 + 1, s68 >= 0, s68 <= x_28 + 1, s69 >= 0, s69 <= s67 + s68 + 1, s70 >= 0, s70 <= s66 + s69 + 1, x_117 >= 0, z'' = 1 + x_117 + x_28, z' - 1 >= 0, x_28 >= 0
   encode_.(z', z'') -{ 1 + 5*z'' }-> s97 :|: s95 >= 0, s95 <= z'' - 1 + 1, s96 >= 0, s96 <= s95 + 1, s97 >= 0, s97 <= 0 + s96 + 1, z'' - 1 >= 0, z' = 0
   encode_.(z', z'') -{ 1 }-> x :|: z'' = 0, z' = 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 1 }-> x :|: z'' >= 0, z' = 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 1 }-> x :|: z'' = 0, z' >= 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 1 }-> x :|: z' >= 0, z'' >= 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 0 }-> 0 :|: z' >= 0, z'' >= 0
   encode_.(z', z'') -{ 0 }-> 0 :|: z'' = 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> 0 :|: z'' >= 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> 0 :|: z'' = 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> 0 :|: z' >= 0, z'' >= 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' = 0, z' = 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' >= 0, z' = 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' = 0, z' >= 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z' >= 0, z'' >= 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_1 -{ 0 }-> 0 :|: 
   encode_i(z') -{ 10 + 5*x_121 + 5*x_210 }-> s115 :|: s112 >= 0, s112 <= x_121 + 1, s113 >= 0, s113 <= x_210 + 1, s114 >= 0, s114 <= s112 + s113 + 1, s115 >= 0, s115 <= s114 + 1, z' = 1 + x_121 + x_210, x_121 >= 0, x_210 >= 0
   encode_i(z') -{ 1 + 5*z' }-> s73 :|: s71 >= 0, s71 <= z' - 1 + 1, s72 >= 0, s72 <= s71 + 1, s73 >= 0, s73 <= s72 + 1, z' - 1 >= 0
   encode_i(z') -{ 0 }-> 0 :|: z' >= 0
   encode_i(z') -{ 1 }-> 0 :|: z' = 0, 0 = 0
   encode_i(z') -{ 0 }-> 0 :|: z' = 0, v0 >= 0, 0 = v0
   encode_i(z') -{ 1 }-> 0 :|: z' >= 0, 0 = 0
   encode_i(z') -{ 0 }-> 0 :|: z' >= 0, v0 >= 0, 0 = v0
   encode_i(z') -{ 0 }-> 1 + x0 :|: z' = 0, x0 >= 0, 0 = x0
   encode_i(z') -{ 0 }-> 1 + x0 :|: z' >= 0, x0 >= 0, 0 = x0
   i(z') -{ 1 }-> 0 :|: z' = 0
   i(z') -{ 0 }-> 0 :|: z' >= 0
   i(z') -{ 1 }-> z' - 1 :|: z' - 1 >= 0
   i(z') -{ 0 }-> 1 + z' :|: z' >= 0

Function symbols to be analyzed: {encode_.}
Previous analysis results are:
  .: runtime: O(1) [1], size: O(n^1) [1 + z' + z'']
  i: runtime: O(1) [1], size: O(n^1) [1 + z']
  encode_1: runtime: O(1) [0], size: O(1) [0]
  encArg: runtime: O(n^1) [4 + 5*z'], size: O(n^1) [1 + z']
  encode_i: runtime: O(n^1) [5 + 5*z'], size: O(n^1) [3 + z']
  encode_.: runtime: ?, size: O(n^1) [5 + z' + z'']

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

(59) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: encode_.
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 9 + 5*z' + 5*z''

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

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

   .(z', z'') -{ 1 }-> z :|: z >= 0, z'' = 1 + (1 + z') + z, z' >= 0
   .(z', z'') -{ 1 }-> z :|: z >= 0, z' - 1 >= 0, z'' = 1 + (z' - 1) + z
   .(z', z'') -{ 1 }-> z' :|: z'' = 0, z' >= 0
   .(z', z'') -{ 1 }-> z'' :|: z'' >= 0, z' = 0
   .(z', z'') -{ 1 }-> 0 :|: z' - 1 >= 0, z'' = z' - 1
   .(z', z'') -{ 1 }-> 0 :|: z' >= 0, z'' = 1 + z'
   .(z', z'') -{ 0 }-> 0 :|: z' >= 0, z'' >= 0
   .(z', z'') -{ 0 }-> 1 + z' + z'' :|: z' >= 0, z'' >= 0
   encArg(z') -{ 10 + 5*x_11 + 5*x_2'' }-> s1 :|: s >= 0, s <= x_11 + 1, s' >= 0, s' <= x_2'' + 1, s'' >= 0, s'' <= s + s' + 1, s1 >= 0, s1 <= 0 + s'' + 1, x_11 >= 0, x_2'' >= 0, z' = 1 + 0 + (1 + x_11 + x_2'')
   encArg(z') -{ 19 + 5*x_1' + 5*x_13 + 5*x_2' + 5*x_21 }-> s12 :|: s6 >= 0, s6 <= x_1' + 1, s7 >= 0, s7 <= x_2' + 1, s8 >= 0, s8 <= s6 + s7 + 1, s9 >= 0, s9 <= x_13 + 1, s10 >= 0, s10 <= x_21 + 1, s11 >= 0, s11 <= s9 + s10 + 1, s12 >= 0, s12 <= s8 + s11 + 1, x_2' >= 0, z' = 1 + (1 + x_1' + x_2') + (1 + x_13 + x_21), x_13 >= 0, x_1' >= 0, x_21 >= 0
   encArg(z') -{ 10 + 5*x_1' + 5*x_2' }-> s16 :|: s13 >= 0, s13 <= x_1' + 1, s14 >= 0, s14 <= x_2' + 1, s15 >= 0, s15 <= s13 + s14 + 1, s16 >= 0, s16 <= s15 + 0 + 1, x_2' >= 0, z' = 1 + (1 + x_1' + x_2') + x_2, x_1' >= 0, x_2 >= 0
   encArg(z') -{ 10 + 5*x_17 + 5*x_23 }-> s20 :|: s17 >= 0, s17 <= x_17 + 1, s18 >= 0, s18 <= x_23 + 1, s19 >= 0, s19 <= s17 + s18 + 1, s20 >= 0, s20 <= 0 + s19 + 1, x_1 >= 0, x_17 >= 0, x_23 >= 0, z' = 1 + x_1 + (1 + x_17 + x_23)
   encArg(z') -{ 15 + 5*x_1' + 5*x_14 + 5*x_2' }-> s49 :|: s44 >= 0, s44 <= x_1' + 1, s45 >= 0, s45 <= x_2' + 1, s46 >= 0, s46 <= s44 + s45 + 1, s47 >= 0, s47 <= x_14 + 1, s48 >= 0, s48 <= s47 + 1, s49 >= 0, s49 <= s46 + s48 + 1, z' = 1 + (1 + x_1' + x_2') + (1 + x_14), x_14 >= 0, x_2' >= 0, x_1' >= 0
   encArg(z') -{ 10 + 5*x_1' + 5*x_2' }-> s5 :|: s2 >= 0, s2 <= x_1' + 1, s3 >= 0, s3 <= x_2' + 1, s4 >= 0, s4 <= s2 + s3 + 1, s5 >= 0, s5 <= s4 + 0 + 1, x_2' >= 0, z' = 1 + (1 + x_1' + x_2') + 0, x_1' >= 0
   encArg(z') -{ 15 + 5*x_1'' + 5*x_15 + 5*x_22 }-> s55 :|: s50 >= 0, s50 <= x_1'' + 1, s51 >= 0, s51 <= s50 + 1, s52 >= 0, s52 <= x_15 + 1, s53 >= 0, s53 <= x_22 + 1, s54 >= 0, s54 <= s52 + s53 + 1, s55 >= 0, s55 <= s51 + s54 + 1, x_15 >= 0, x_1'' >= 0, z' = 1 + (1 + x_1'') + (1 + x_15 + x_22), x_22 >= 0
   encArg(z') -{ -4 + 5*z' }-> s58 :|: s56 >= 0, s56 <= z' - 2 + 1, s57 >= 0, s57 <= s56 + 1, s58 >= 0, s58 <= s57 + 1, z' - 2 >= 0
   encArg(z') -{ -4 + 5*z' }-> s76 :|: s74 >= 0, s74 <= z' - 2 + 1, s75 >= 0, s75 <= s74 + 1, s76 >= 0, s76 <= 0 + s75 + 1, z' - 2 >= 0
   encArg(z') -{ -4 + 5*z' }-> s79 :|: s77 >= 0, s77 <= z' - 2 + 1, s78 >= 0, s78 <= s77 + 1, s79 >= 0, s79 <= s78 + 0 + 1, z' - 2 >= 0
   encArg(z') -{ 11 + 5*x_1'' + 5*x_16 }-> s84 :|: s80 >= 0, s80 <= x_1'' + 1, s81 >= 0, s81 <= s80 + 1, s82 >= 0, s82 <= x_16 + 1, s83 >= 0, s83 <= s82 + 1, s84 >= 0, s84 <= s81 + s83 + 1, x_1'' >= 0, x_16 >= 0, z' = 1 + (1 + x_1'') + (1 + x_16)
   encArg(z') -{ 6 + 5*x_1'' }-> s87 :|: s85 >= 0, s85 <= x_1'' + 1, s86 >= 0, s86 <= s85 + 1, s87 >= 0, s87 <= s86 + 0 + 1, z' = 1 + (1 + x_1'') + x_2, x_1'' >= 0, x_2 >= 0
   encArg(z') -{ 6 + 5*x_18 }-> s90 :|: s88 >= 0, s88 <= x_18 + 1, s89 >= 0, s89 <= s88 + 1, s90 >= 0, s90 <= 0 + s89 + 1, x_1 >= 0, z' = 1 + x_1 + (1 + x_18), x_18 >= 0
   encArg(z') -{ 10 + 5*x_19 + 5*x_24 }-> s94 :|: s91 >= 0, s91 <= x_19 + 1, s92 >= 0, s92 <= x_24 + 1, s93 >= 0, s93 <= s91 + s92 + 1, s94 >= 0, s94 <= s93 + 1, z' = 1 + (1 + x_19 + x_24), x_24 >= 0, x_19 >= 0
   encArg(z') -{ 1 }-> x :|: z' = 1 + 0 + 0, x >= 0, 0 = x, 0 = 0
   encArg(z') -{ 1 }-> x :|: z' - 1 >= 0, x >= 0, 0 = x, 0 = 0
   encArg(z') -{ 1 }-> x :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2, x >= 0, 0 = x, 0 = 0
   encArg(z') -{ 0 }-> 0 :|: z' = 0
   encArg(z') -{ 0 }-> 0 :|: z' >= 0
   encArg(z') -{ 0 }-> 0 :|: z' = 1 + 0 + 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encArg(z') -{ 0 }-> 0 :|: z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encArg(z') -{ 0 }-> 0 :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encArg(z') -{ 1 }-> 0 :|: z' = 1 + 0, 0 = 0
   encArg(z') -{ 0 }-> 0 :|: z' = 1 + 0, v0 >= 0, 0 = v0
   encArg(z') -{ 1 }-> 0 :|: z' - 1 >= 0, 0 = 0
   encArg(z') -{ 0 }-> 0 :|: z' - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z') -{ 0 }-> 1 + x0 :|: z' = 1 + 0, x0 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 :|: z' - 1 >= 0, x0 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 + x1 :|: z' = 1 + 0 + 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 + x1 :|: z' - 1 >= 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encArg(z') -{ 0 }-> 1 + x0 + x1 :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 1 + 5*z' }-> s100 :|: s98 >= 0, s98 <= z' - 1 + 1, s99 >= 0, s99 <= s98 + 1, s100 >= 0, s100 <= s99 + 0 + 1, z'' = 0, z' - 1 >= 0
   encode_.(z', z'') -{ 1 + 5*z' + 5*z'' }-> s105 :|: s101 >= 0, s101 <= z' - 1 + 1, s102 >= 0, s102 <= s101 + 1, s103 >= 0, s103 <= z'' - 1 + 1, s104 >= 0, s104 <= s103 + 1, s105 >= 0, s105 <= s102 + s104 + 1, z' - 1 >= 0, z'' - 1 >= 0
   encode_.(z', z'') -{ 1 + 5*z' }-> s108 :|: s106 >= 0, s106 <= z' - 1 + 1, s107 >= 0, s107 <= s106 + 1, s108 >= 0, s108 <= s107 + 0 + 1, z'' >= 0, z' - 1 >= 0
   encode_.(z', z'') -{ 1 + 5*z'' }-> s111 :|: s109 >= 0, s109 <= z'' - 1 + 1, s110 >= 0, s110 <= s109 + 1, s111 >= 0, s111 <= 0 + s110 + 1, z' >= 0, z'' - 1 >= 0
   encode_.(z', z'') -{ 10 + 5*x_113 + 5*x_26 }-> s24 :|: s21 >= 0, s21 <= x_113 + 1, s22 >= 0, s22 <= x_26 + 1, s23 >= 0, s23 <= s21 + s22 + 1, s24 >= 0, s24 <= 0 + s23 + 1, z'' = 1 + x_113 + x_26, x_113 >= 0, x_26 >= 0, z' = 0
   encode_.(z', z'') -{ 10 + 5*x_111 + 5*x_25 }-> s28 :|: s25 >= 0, s25 <= x_111 + 1, s26 >= 0, s26 <= x_25 + 1, s27 >= 0, s27 <= s25 + s26 + 1, s28 >= 0, s28 <= s27 + 0 + 1, z'' = 0, x_25 >= 0, z' = 1 + x_111 + x_25, x_111 >= 0
   encode_.(z', z'') -{ 19 + 5*x_111 + 5*x_115 + 5*x_25 + 5*x_27 }-> s35 :|: s29 >= 0, s29 <= x_111 + 1, s30 >= 0, s30 <= x_25 + 1, s31 >= 0, s31 <= s29 + s30 + 1, s32 >= 0, s32 <= x_115 + 1, s33 >= 0, s33 <= x_27 + 1, s34 >= 0, s34 <= s32 + s33 + 1, s35 >= 0, s35 <= s31 + s34 + 1, z'' = 1 + x_115 + x_27, x_25 >= 0, x_115 >= 0, z' = 1 + x_111 + x_25, x_27 >= 0, x_111 >= 0
   encode_.(z', z'') -{ 10 + 5*x_111 + 5*x_25 }-> s39 :|: s36 >= 0, s36 <= x_111 + 1, s37 >= 0, s37 <= x_25 + 1, s38 >= 0, s38 <= s36 + s37 + 1, s39 >= 0, s39 <= s38 + 0 + 1, x_25 >= 0, z' = 1 + x_111 + x_25, z'' >= 0, x_111 >= 0
   encode_.(z', z'') -{ 10 + 5*x_119 + 5*x_29 }-> s43 :|: s40 >= 0, s40 <= x_119 + 1, s41 >= 0, s41 <= x_29 + 1, s42 >= 0, s42 <= s40 + s41 + 1, s43 >= 0, s43 <= 0 + s42 + 1, z' >= 0, z'' = 1 + x_119 + x_29, x_119 >= 0, x_29 >= 0
   encode_.(z', z'') -{ 10 + 5*x_111 + 5*x_25 + 5*z'' }-> s64 :|: s59 >= 0, s59 <= x_111 + 1, s60 >= 0, s60 <= x_25 + 1, s61 >= 0, s61 <= s59 + s60 + 1, s62 >= 0, s62 <= z'' - 1 + 1, s63 >= 0, s63 <= s62 + 1, s64 >= 0, s64 <= s61 + s63 + 1, z'' - 1 >= 0, x_25 >= 0, z' = 1 + x_111 + x_25, x_111 >= 0
   encode_.(z', z'') -{ 10 + 5*x_117 + 5*x_28 + 5*z' }-> s70 :|: s65 >= 0, s65 <= z' - 1 + 1, s66 >= 0, s66 <= s65 + 1, s67 >= 0, s67 <= x_117 + 1, s68 >= 0, s68 <= x_28 + 1, s69 >= 0, s69 <= s67 + s68 + 1, s70 >= 0, s70 <= s66 + s69 + 1, x_117 >= 0, z'' = 1 + x_117 + x_28, z' - 1 >= 0, x_28 >= 0
   encode_.(z', z'') -{ 1 + 5*z'' }-> s97 :|: s95 >= 0, s95 <= z'' - 1 + 1, s96 >= 0, s96 <= s95 + 1, s97 >= 0, s97 <= 0 + s96 + 1, z'' - 1 >= 0, z' = 0
   encode_.(z', z'') -{ 1 }-> x :|: z'' = 0, z' = 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 1 }-> x :|: z'' >= 0, z' = 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 1 }-> x :|: z'' = 0, z' >= 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 1 }-> x :|: z' >= 0, z'' >= 0, x >= 0, 0 = x, 0 = 0
   encode_.(z', z'') -{ 0 }-> 0 :|: z' >= 0, z'' >= 0
   encode_.(z', z'') -{ 0 }-> 0 :|: z'' = 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> 0 :|: z'' >= 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> 0 :|: z'' = 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> 0 :|: z' >= 0, z'' >= 0, v0 >= 0, v1 >= 0, 0 = v1, 0 = v0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' = 0, z' = 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' >= 0, z' = 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' = 0, z' >= 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_.(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z' >= 0, z'' >= 0, 0 = x1, x0 >= 0, x1 >= 0, 0 = x0
   encode_1 -{ 0 }-> 0 :|: 
   encode_i(z') -{ 10 + 5*x_121 + 5*x_210 }-> s115 :|: s112 >= 0, s112 <= x_121 + 1, s113 >= 0, s113 <= x_210 + 1, s114 >= 0, s114 <= s112 + s113 + 1, s115 >= 0, s115 <= s114 + 1, z' = 1 + x_121 + x_210, x_121 >= 0, x_210 >= 0
   encode_i(z') -{ 1 + 5*z' }-> s73 :|: s71 >= 0, s71 <= z' - 1 + 1, s72 >= 0, s72 <= s71 + 1, s73 >= 0, s73 <= s72 + 1, z' - 1 >= 0
   encode_i(z') -{ 0 }-> 0 :|: z' >= 0
   encode_i(z') -{ 1 }-> 0 :|: z' = 0, 0 = 0
   encode_i(z') -{ 0 }-> 0 :|: z' = 0, v0 >= 0, 0 = v0
   encode_i(z') -{ 1 }-> 0 :|: z' >= 0, 0 = 0
   encode_i(z') -{ 0 }-> 0 :|: z' >= 0, v0 >= 0, 0 = v0
   encode_i(z') -{ 0 }-> 1 + x0 :|: z' = 0, x0 >= 0, 0 = x0
   encode_i(z') -{ 0 }-> 1 + x0 :|: z' >= 0, x0 >= 0, 0 = x0
   i(z') -{ 1 }-> 0 :|: z' = 0
   i(z') -{ 0 }-> 0 :|: z' >= 0
   i(z') -{ 1 }-> z' - 1 :|: z' - 1 >= 0
   i(z') -{ 0 }-> 1 + z' :|: z' >= 0

Function symbols to be analyzed: 
Previous analysis results are:
  .: runtime: O(1) [1], size: O(n^1) [1 + z' + z'']
  i: runtime: O(1) [1], size: O(n^1) [1 + z']
  encode_1: runtime: O(1) [0], size: O(1) [0]
  encArg: runtime: O(n^1) [4 + 5*z'], size: O(n^1) [1 + z']
  encode_i: runtime: O(n^1) [5 + 5*z'], size: O(n^1) [3 + z']
  encode_.: runtime: O(n^1) [9 + 5*z' + 5*z''], size: O(n^1) [5 + z' + z'']

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

(62)
BOUNDS(1, n^1)

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

(64)
Obligation:
The Runtime Complexity (full) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF).


The TRS R consists of the following rules:

   .(1', x) -> x
   .(x, 1') -> x
   .(i(x), x) -> 1'
   .(x, i(x)) -> 1'
   i(1') -> 1'
   i(i(x)) -> x
   .(i(y), .(y, z)) -> z
   .(y, .(i(y), z)) -> z

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

   encArg(1') -> 1'
   encArg(cons_.(x_1, x_2)) -> .(encArg(x_1), encArg(x_2))
   encArg(cons_i(x_1)) -> i(encArg(x_1))
   encode_.(x_1, x_2) -> .(encArg(x_1), encArg(x_2))
   encode_1 -> 1'
   encode_i(x_1) -> i(encArg(x_1))

Rewrite Strategy: FULL
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(65) TypeInferenceProof (BOTH BOUNDS(ID, ID))
Infered types.
----------------------------------------

(66)
Obligation:
TRS:
Rules:
.(1', x) -> x
.(x, 1') -> x
.(i(x), x) -> 1'
.(x, i(x)) -> 1'
i(1') -> 1'
i(i(x)) -> x
.(i(y), .(y, z)) -> z
.(y, .(i(y), z)) -> z
encArg(1') -> 1'
encArg(cons_.(x_1, x_2)) -> .(encArg(x_1), encArg(x_2))
encArg(cons_i(x_1)) -> i(encArg(x_1))
encode_.(x_1, x_2) -> .(encArg(x_1), encArg(x_2))
encode_1 -> 1'
encode_i(x_1) -> i(encArg(x_1))

Types:
. :: 1':cons_.:cons_i -> 1':cons_.:cons_i -> 1':cons_.:cons_i
1' :: 1':cons_.:cons_i
i :: 1':cons_.:cons_i -> 1':cons_.:cons_i
encArg :: 1':cons_.:cons_i -> 1':cons_.:cons_i
cons_. :: 1':cons_.:cons_i -> 1':cons_.:cons_i -> 1':cons_.:cons_i
cons_i :: 1':cons_.:cons_i -> 1':cons_.:cons_i
encode_. :: 1':cons_.:cons_i -> 1':cons_.:cons_i -> 1':cons_.:cons_i
encode_1 :: 1':cons_.:cons_i
encode_i :: 1':cons_.:cons_i -> 1':cons_.:cons_i
hole_1':cons_.:cons_i1_0 :: 1':cons_.:cons_i
gen_1':cons_.:cons_i2_0 :: Nat -> 1':cons_.:cons_i

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(67) OrderProof (LOWER BOUND(ID))
Heuristically decided to analyse the following defined symbols:
encArg
----------------------------------------

(68)
Obligation:
TRS:
Rules:
.(1', x) -> x
.(x, 1') -> x
.(i(x), x) -> 1'
.(x, i(x)) -> 1'
i(1') -> 1'
i(i(x)) -> x
.(i(y), .(y, z)) -> z
.(y, .(i(y), z)) -> z
encArg(1') -> 1'
encArg(cons_.(x_1, x_2)) -> .(encArg(x_1), encArg(x_2))
encArg(cons_i(x_1)) -> i(encArg(x_1))
encode_.(x_1, x_2) -> .(encArg(x_1), encArg(x_2))
encode_1 -> 1'
encode_i(x_1) -> i(encArg(x_1))

Types:
. :: 1':cons_.:cons_i -> 1':cons_.:cons_i -> 1':cons_.:cons_i
1' :: 1':cons_.:cons_i
i :: 1':cons_.:cons_i -> 1':cons_.:cons_i
encArg :: 1':cons_.:cons_i -> 1':cons_.:cons_i
cons_. :: 1':cons_.:cons_i -> 1':cons_.:cons_i -> 1':cons_.:cons_i
cons_i :: 1':cons_.:cons_i -> 1':cons_.:cons_i
encode_. :: 1':cons_.:cons_i -> 1':cons_.:cons_i -> 1':cons_.:cons_i
encode_1 :: 1':cons_.:cons_i
encode_i :: 1':cons_.:cons_i -> 1':cons_.:cons_i
hole_1':cons_.:cons_i1_0 :: 1':cons_.:cons_i
gen_1':cons_.:cons_i2_0 :: Nat -> 1':cons_.:cons_i


Generator Equations:
gen_1':cons_.:cons_i2_0(0) <=> 1'
gen_1':cons_.:cons_i2_0(+(x, 1)) <=> cons_.(1', gen_1':cons_.:cons_i2_0(x))


The following defined symbols remain to be analysed:
encArg
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(69) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
encArg(gen_1':cons_.:cons_i2_0(n4_0)) -> gen_1':cons_.:cons_i2_0(0), rt in Omega(n4_0)

Induction Base:
encArg(gen_1':cons_.:cons_i2_0(0)) ->_R^Omega(0)
1'

Induction Step:
encArg(gen_1':cons_.:cons_i2_0(+(n4_0, 1))) ->_R^Omega(0)
.(encArg(1'), encArg(gen_1':cons_.:cons_i2_0(n4_0))) ->_R^Omega(0)
.(1', encArg(gen_1':cons_.:cons_i2_0(n4_0))) ->_IH
.(1', gen_1':cons_.:cons_i2_0(0)) ->_R^Omega(1)
gen_1':cons_.:cons_i2_0(0)

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

(70)
Obligation:
Proved the lower bound n^1 for the following obligation:

TRS:
Rules:
.(1', x) -> x
.(x, 1') -> x
.(i(x), x) -> 1'
.(x, i(x)) -> 1'
i(1') -> 1'
i(i(x)) -> x
.(i(y), .(y, z)) -> z
.(y, .(i(y), z)) -> z
encArg(1') -> 1'
encArg(cons_.(x_1, x_2)) -> .(encArg(x_1), encArg(x_2))
encArg(cons_i(x_1)) -> i(encArg(x_1))
encode_.(x_1, x_2) -> .(encArg(x_1), encArg(x_2))
encode_1 -> 1'
encode_i(x_1) -> i(encArg(x_1))

Types:
. :: 1':cons_.:cons_i -> 1':cons_.:cons_i -> 1':cons_.:cons_i
1' :: 1':cons_.:cons_i
i :: 1':cons_.:cons_i -> 1':cons_.:cons_i
encArg :: 1':cons_.:cons_i -> 1':cons_.:cons_i
cons_. :: 1':cons_.:cons_i -> 1':cons_.:cons_i -> 1':cons_.:cons_i
cons_i :: 1':cons_.:cons_i -> 1':cons_.:cons_i
encode_. :: 1':cons_.:cons_i -> 1':cons_.:cons_i -> 1':cons_.:cons_i
encode_1 :: 1':cons_.:cons_i
encode_i :: 1':cons_.:cons_i -> 1':cons_.:cons_i
hole_1':cons_.:cons_i1_0 :: 1':cons_.:cons_i
gen_1':cons_.:cons_i2_0 :: Nat -> 1':cons_.:cons_i


Generator Equations:
gen_1':cons_.:cons_i2_0(0) <=> 1'
gen_1':cons_.:cons_i2_0(+(x, 1)) <=> cons_.(1', gen_1':cons_.:cons_i2_0(x))


The following defined symbols remain to be analysed:
encArg
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(71) LowerBoundPropagationProof (FINISHED)
Propagated lower bound.
----------------------------------------

(72)
BOUNDS(n^1, INF)