/export/starexec/sandbox2/solver/bin/starexec_run_rcdcRelativeAlsoLower /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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


WORST_CASE(Omega(n^1), O(n^2))
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


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

(0) DCpxTrs
(1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms]
(2) CpxRelTRS
(3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 297 ms]
(4) CpxRelTRS
(5) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
(6) CpxWeightedTrs
    (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (8) CpxTypedWeightedTrs
    (9) CompletionProof [UPPER BOUND(ID), 0 ms]
    (10) CpxTypedWeightedCompleteTrs
    (11) NarrowingProof [BOTH BOUNDS(ID, ID), 4365 ms]
    (12) CpxTypedWeightedCompleteTrs
    (13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
    (14) CpxRNTS
    (15) InliningProof [UPPER BOUND(ID), 401 ms]
    (16) CpxRNTS
    (17) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (18) CpxRNTS
    (19) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 1 ms]
    (20) CpxRNTS
    (21) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (22) CpxRNTS
    (23) IntTrsBoundProof [UPPER BOUND(ID), 84 ms]
    (24) CpxRNTS
    (25) IntTrsBoundProof [UPPER BOUND(ID), 43 ms]
    (26) CpxRNTS
    (27) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (28) CpxRNTS
    (29) IntTrsBoundProof [UPPER BOUND(ID), 106 ms]
    (30) CpxRNTS
    (31) IntTrsBoundProof [UPPER BOUND(ID), 2 ms]
    (32) CpxRNTS
    (33) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (34) CpxRNTS
    (35) IntTrsBoundProof [UPPER BOUND(ID), 359 ms]
    (36) CpxRNTS
    (37) IntTrsBoundProof [UPPER BOUND(ID), 136 ms]
    (38) CpxRNTS
    (39) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (40) CpxRNTS
    (41) IntTrsBoundProof [UPPER BOUND(ID), 76 ms]
    (42) CpxRNTS
    (43) IntTrsBoundProof [UPPER BOUND(ID), 11 ms]
    (44) CpxRNTS
    (45) ResultPropagationProof [UPPER BOUND(ID), 1 ms]
    (46) CpxRNTS
    (47) IntTrsBoundProof [UPPER BOUND(ID), 5319 ms]
    (48) CpxRNTS
    (49) IntTrsBoundProof [UPPER BOUND(ID), 2375 ms]
    (50) CpxRNTS
    (51) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (52) CpxRNTS
    (53) IntTrsBoundProof [UPPER BOUND(ID), 128 ms]
    (54) CpxRNTS
    (55) IntTrsBoundProof [UPPER BOUND(ID), 53 ms]
    (56) CpxRNTS
    (57) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (58) CpxRNTS
    (59) IntTrsBoundProof [UPPER BOUND(ID), 940 ms]
    (60) CpxRNTS
    (61) IntTrsBoundProof [UPPER BOUND(ID), 1122 ms]
    (62) CpxRNTS
    (63) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (64) CpxRNTS
    (65) IntTrsBoundProof [UPPER BOUND(ID), 311 ms]
    (66) CpxRNTS
    (67) IntTrsBoundProof [UPPER BOUND(ID), 128 ms]
    (68) CpxRNTS
    (69) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (70) CpxRNTS
    (71) IntTrsBoundProof [UPPER BOUND(ID), 198 ms]
    (72) CpxRNTS
    (73) IntTrsBoundProof [UPPER BOUND(ID), 2 ms]
    (74) CpxRNTS
    (75) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (76) CpxRNTS
    (77) IntTrsBoundProof [UPPER BOUND(ID), 66 ms]
    (78) CpxRNTS
    (79) IntTrsBoundProof [UPPER BOUND(ID), 2 ms]
    (80) CpxRNTS
    (81) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (82) CpxRNTS
    (83) IntTrsBoundProof [UPPER BOUND(ID), 138 ms]
    (84) CpxRNTS
    (85) IntTrsBoundProof [UPPER BOUND(ID), 0 ms]
    (86) CpxRNTS
    (87) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (88) CpxRNTS
    (89) IntTrsBoundProof [UPPER BOUND(ID), 136 ms]
    (90) CpxRNTS
    (91) IntTrsBoundProof [UPPER BOUND(ID), 1 ms]
    (92) CpxRNTS
    (93) FinalProof [FINISHED, 0 ms]
    (94) BOUNDS(1, n^2)
(95) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(96) CpxRelTRS
    (97) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (98) typed CpxTrs
    (99) OrderProof [LOWER BOUND(ID), 0 ms]
    (100) typed CpxTrs
    (101) RewriteLemmaProof [LOWER BOUND(ID), 480 ms]
    (102) BEST
        (103) proven lower bound
            (104) LowerBoundPropagationProof [FINISHED, 0 ms]
            (105) BOUNDS(n^1, INF)
        (106) typed CpxTrs
            (107) RewriteLemmaProof [LOWER BOUND(ID), 103 ms]
            (108) typed CpxTrs
            (109) RewriteLemmaProof [LOWER BOUND(ID), 108 ms]
            (110) BOUNDS(1, INF)


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

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


The TRS R consists of the following rules:

   cond1(true, x, y) -> cond2(gr(y, 0), x, y)
   cond2(true, x, y) -> cond2(gr(y, 0), x, p(y))
   cond2(false, x, y) -> cond1(gr(x, 0), p(x), y)
   gr(0, x) -> false
   gr(s(x), 0) -> true
   gr(s(x), s(y)) -> gr(x, y)
   p(0) -> 0
   p(s(x)) -> x

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

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

   encArg(true) -> true
   encArg(0) -> 0
   encArg(false) -> false
   encArg(s(x_1)) -> s(encArg(x_1))
   encArg(cons_cond1(x_1, x_2, x_3)) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3))
   encArg(cons_cond2(x_1, x_2, x_3)) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3))
   encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2))
   encArg(cons_p(x_1)) -> p(encArg(x_1))
   encode_cond1(x_1, x_2, x_3) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3))
   encode_true -> true
   encode_cond2(x_1, x_2, x_3) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3))
   encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2))
   encode_0 -> 0
   encode_p(x_1) -> p(encArg(x_1))
   encode_false -> false
   encode_s(x_1) -> s(encArg(x_1))


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

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


The TRS R consists of the following rules:

   cond1(true, x, y) -> cond2(gr(y, 0), x, y)
   cond2(true, x, y) -> cond2(gr(y, 0), x, p(y))
   cond2(false, x, y) -> cond1(gr(x, 0), p(x), y)
   gr(0, x) -> false
   gr(s(x), 0) -> true
   gr(s(x), s(y)) -> gr(x, y)
   p(0) -> 0
   p(s(x)) -> x

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

   encArg(true) -> true
   encArg(0) -> 0
   encArg(false) -> false
   encArg(s(x_1)) -> s(encArg(x_1))
   encArg(cons_cond1(x_1, x_2, x_3)) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3))
   encArg(cons_cond2(x_1, x_2, x_3)) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3))
   encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2))
   encArg(cons_p(x_1)) -> p(encArg(x_1))
   encode_cond1(x_1, x_2, x_3) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3))
   encode_true -> true
   encode_cond2(x_1, x_2, x_3) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3))
   encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2))
   encode_0 -> 0
   encode_p(x_1) -> p(encArg(x_1))
   encode_false -> false
   encode_s(x_1) -> s(encArg(x_1))

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

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

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


The TRS R consists of the following rules:

   cond1(true, x, y) -> cond2(gr(y, 0), x, y)
   cond2(true, x, y) -> cond2(gr(y, 0), x, p(y))
   cond2(false, x, y) -> cond1(gr(x, 0), p(x), y)
   gr(0, x) -> false
   gr(s(x), 0) -> true
   gr(s(x), s(y)) -> gr(x, y)
   p(0) -> 0
   p(s(x)) -> x

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

   encArg(true) -> true
   encArg(0) -> 0
   encArg(false) -> false
   encArg(s(x_1)) -> s(encArg(x_1))
   encArg(cons_cond1(x_1, x_2, x_3)) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3))
   encArg(cons_cond2(x_1, x_2, x_3)) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3))
   encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2))
   encArg(cons_p(x_1)) -> p(encArg(x_1))
   encode_cond1(x_1, x_2, x_3) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3))
   encode_true -> true
   encode_cond2(x_1, x_2, x_3) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3))
   encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2))
   encode_0 -> 0
   encode_p(x_1) -> p(encArg(x_1))
   encode_false -> false
   encode_s(x_1) -> s(encArg(x_1))

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

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

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


The TRS R consists of the following rules:

   cond1(true, x, y) -> cond2(gr(y, 0), x, y) [1]
   cond2(true, x, y) -> cond2(gr(y, 0), x, p(y)) [1]
   cond2(false, x, y) -> cond1(gr(x, 0), p(x), y) [1]
   gr(0, x) -> false [1]
   gr(s(x), 0) -> true [1]
   gr(s(x), s(y)) -> gr(x, y) [1]
   p(0) -> 0 [1]
   p(s(x)) -> x [1]
   encArg(true) -> true [0]
   encArg(0) -> 0 [0]
   encArg(false) -> false [0]
   encArg(s(x_1)) -> s(encArg(x_1)) [0]
   encArg(cons_cond1(x_1, x_2, x_3)) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encArg(cons_cond2(x_1, x_2, x_3)) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2)) [0]
   encArg(cons_p(x_1)) -> p(encArg(x_1)) [0]
   encode_cond1(x_1, x_2, x_3) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encode_true -> true [0]
   encode_cond2(x_1, x_2, x_3) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2)) [0]
   encode_0 -> 0 [0]
   encode_p(x_1) -> p(encArg(x_1)) [0]
   encode_false -> false [0]
   encode_s(x_1) -> s(encArg(x_1)) [0]

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

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

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

   cond1(true, x, y) -> cond2(gr(y, 0), x, y) [1]
   cond2(true, x, y) -> cond2(gr(y, 0), x, p(y)) [1]
   cond2(false, x, y) -> cond1(gr(x, 0), p(x), y) [1]
   gr(0, x) -> false [1]
   gr(s(x), 0) -> true [1]
   gr(s(x), s(y)) -> gr(x, y) [1]
   p(0) -> 0 [1]
   p(s(x)) -> x [1]
   encArg(true) -> true [0]
   encArg(0) -> 0 [0]
   encArg(false) -> false [0]
   encArg(s(x_1)) -> s(encArg(x_1)) [0]
   encArg(cons_cond1(x_1, x_2, x_3)) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encArg(cons_cond2(x_1, x_2, x_3)) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2)) [0]
   encArg(cons_p(x_1)) -> p(encArg(x_1)) [0]
   encode_cond1(x_1, x_2, x_3) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encode_true -> true [0]
   encode_cond2(x_1, x_2, x_3) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2)) [0]
   encode_0 -> 0 [0]
   encode_p(x_1) -> p(encArg(x_1)) [0]
   encode_false -> false [0]
   encode_s(x_1) -> s(encArg(x_1)) [0]

The TRS has the following type information:
cond1 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p
true :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p
cond2 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p
gr :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p
0 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p
p :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p
false :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p
s :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p
encArg :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p
cons_cond1 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p
cons_cond2 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p
cons_gr :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p
cons_p :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p
encode_cond1 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p
encode_true :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p
encode_cond2 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p
encode_gr :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p
encode_0 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p
encode_p :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p
encode_false :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p
encode_s :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p

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

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

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

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

(c) The following functions are completely defined:

   gr_2
   p_1
   cond1_3
   cond2_3
   encArg_1
   encode_cond1_3
   encode_true
   encode_cond2_3
   encode_gr_2
   encode_0
   encode_p_1
   encode_false
   encode_s_1

Due to the following rules being added:

   encArg(v0) -> null_encArg [0]
   encode_cond1(v0, v1, v2) -> null_encode_cond1 [0]
   encode_true -> null_encode_true [0]
   encode_cond2(v0, v1, v2) -> null_encode_cond2 [0]
   encode_gr(v0, v1) -> null_encode_gr [0]
   encode_0 -> null_encode_0 [0]
   encode_p(v0) -> null_encode_p [0]
   encode_false -> null_encode_false [0]
   encode_s(v0) -> null_encode_s [0]
   gr(v0, v1) -> null_gr [0]
   p(v0) -> null_p [0]
   cond1(v0, v1, v2) -> null_cond1 [0]
   cond2(v0, v1, v2) -> null_cond2 [0]

And the following fresh constants:    null_encArg, null_encode_cond1, null_encode_true, null_encode_cond2, null_encode_gr, null_encode_0, null_encode_p, null_encode_false, null_encode_s, null_gr, null_p, null_cond1, null_cond2

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

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

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

   cond1(true, x, y) -> cond2(gr(y, 0), x, y) [1]
   cond2(true, x, y) -> cond2(gr(y, 0), x, p(y)) [1]
   cond2(false, x, y) -> cond1(gr(x, 0), p(x), y) [1]
   gr(0, x) -> false [1]
   gr(s(x), 0) -> true [1]
   gr(s(x), s(y)) -> gr(x, y) [1]
   p(0) -> 0 [1]
   p(s(x)) -> x [1]
   encArg(true) -> true [0]
   encArg(0) -> 0 [0]
   encArg(false) -> false [0]
   encArg(s(x_1)) -> s(encArg(x_1)) [0]
   encArg(cons_cond1(x_1, x_2, x_3)) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encArg(cons_cond2(x_1, x_2, x_3)) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2)) [0]
   encArg(cons_p(x_1)) -> p(encArg(x_1)) [0]
   encode_cond1(x_1, x_2, x_3) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encode_true -> true [0]
   encode_cond2(x_1, x_2, x_3) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2)) [0]
   encode_0 -> 0 [0]
   encode_p(x_1) -> p(encArg(x_1)) [0]
   encode_false -> false [0]
   encode_s(x_1) -> s(encArg(x_1)) [0]
   encArg(v0) -> null_encArg [0]
   encode_cond1(v0, v1, v2) -> null_encode_cond1 [0]
   encode_true -> null_encode_true [0]
   encode_cond2(v0, v1, v2) -> null_encode_cond2 [0]
   encode_gr(v0, v1) -> null_encode_gr [0]
   encode_0 -> null_encode_0 [0]
   encode_p(v0) -> null_encode_p [0]
   encode_false -> null_encode_false [0]
   encode_s(v0) -> null_encode_s [0]
   gr(v0, v1) -> null_gr [0]
   p(v0) -> null_p [0]
   cond1(v0, v1, v2) -> null_cond1 [0]
   cond2(v0, v1, v2) -> null_cond2 [0]

The TRS has the following type information:
cond1 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2 -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2 -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2 -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2
true :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2
cond2 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2 -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2 -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2 -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2
gr :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2 -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2 -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2
0 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2
p :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2 -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2
false :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2
s :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2 -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2
encArg :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2 -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2
cons_cond1 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2 -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2 -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2 -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2
cons_cond2 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2 -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2 -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2 -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2
cons_gr :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2 -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2 -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2
cons_p :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2 -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2
encode_cond1 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2 -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2 -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2 -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2
encode_true :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2
encode_cond2 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2 -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2 -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2 -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2
encode_gr :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2 -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2 -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2
encode_0 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2
encode_p :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2 -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2
encode_false :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2
encode_s :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2 -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2
null_encArg :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2
null_encode_cond1 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2
null_encode_true :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2
null_encode_cond2 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2
null_encode_gr :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2
null_encode_0 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2
null_encode_p :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2
null_encode_false :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2
null_encode_s :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2
null_gr :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2
null_p :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2
null_cond1 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2
null_cond2 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2

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

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

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

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

   cond1(true, x, 0) -> cond2(false, x, 0) [2]
   cond1(true, x, s(x')) -> cond2(true, x, s(x')) [2]
   cond1(true, x, y) -> cond2(null_gr, x, y) [1]
   cond2(true, x, 0) -> cond2(false, x, 0) [3]
   cond2(true, x, 0) -> cond2(false, x, null_p) [2]
   cond2(true, x, s(x'')) -> cond2(true, x, x'') [3]
   cond2(true, x, s(x'')) -> cond2(true, x, null_p) [2]
   cond2(true, x, 0) -> cond2(null_gr, x, 0) [2]
   cond2(true, x, s(x1)) -> cond2(null_gr, x, x1) [2]
   cond2(true, x, y) -> cond2(null_gr, x, null_p) [1]
   cond2(false, 0, y) -> cond1(false, 0, y) [3]
   cond2(false, 0, y) -> cond1(false, null_p, y) [2]
   cond2(false, s(x2), y) -> cond1(true, x2, y) [3]
   cond2(false, s(x2), y) -> cond1(true, null_p, y) [2]
   cond2(false, 0, y) -> cond1(null_gr, 0, y) [2]
   cond2(false, s(x3), y) -> cond1(null_gr, x3, y) [2]
   cond2(false, x, y) -> cond1(null_gr, null_p, y) [1]
   gr(0, x) -> false [1]
   gr(s(x), 0) -> true [1]
   gr(s(x), s(y)) -> gr(x, y) [1]
   p(0) -> 0 [1]
   p(s(x)) -> x [1]
   encArg(true) -> true [0]
   encArg(0) -> 0 [0]
   encArg(false) -> false [0]
   encArg(s(x_1)) -> s(encArg(x_1)) [0]
   encArg(cons_cond1(x_1, x_2, x_3)) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encArg(cons_cond2(x_1, x_2, x_3)) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2)) [0]
   encArg(cons_p(true)) -> p(true) [0]
   encArg(cons_p(0)) -> p(0) [0]
   encArg(cons_p(false)) -> p(false) [0]
   encArg(cons_p(s(x_1959))) -> p(s(encArg(x_1959))) [0]
   encArg(cons_p(cons_cond1(x_1960, x_2575, x_3383))) -> p(cond1(encArg(x_1960), encArg(x_2575), encArg(x_3383))) [0]
   encArg(cons_p(cons_cond2(x_1961, x_2576, x_3384))) -> p(cond2(encArg(x_1961), encArg(x_2576), encArg(x_3384))) [0]
   encArg(cons_p(cons_gr(x_1962, x_2577))) -> p(gr(encArg(x_1962), encArg(x_2577))) [0]
   encArg(cons_p(cons_p(x_1963))) -> p(p(encArg(x_1963))) [0]
   encArg(cons_p(x_1)) -> p(null_encArg) [0]
   encode_cond1(x_1, x_2, x_3) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encode_true -> true [0]
   encode_cond2(x_1, x_2, x_3) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2)) [0]
   encode_0 -> 0 [0]
   encode_p(true) -> p(true) [0]
   encode_p(0) -> p(0) [0]
   encode_p(false) -> p(false) [0]
   encode_p(s(x_11924)) -> p(s(encArg(x_11924))) [0]
   encode_p(cons_cond1(x_11925, x_21154, x_3769)) -> p(cond1(encArg(x_11925), encArg(x_21154), encArg(x_3769))) [0]
   encode_p(cons_cond2(x_11926, x_21155, x_3770)) -> p(cond2(encArg(x_11926), encArg(x_21155), encArg(x_3770))) [0]
   encode_p(cons_gr(x_11927, x_21156)) -> p(gr(encArg(x_11927), encArg(x_21156))) [0]
   encode_p(cons_p(x_11928)) -> p(p(encArg(x_11928))) [0]
   encode_p(x_1) -> p(null_encArg) [0]
   encode_false -> false [0]
   encode_s(x_1) -> s(encArg(x_1)) [0]
   encArg(v0) -> null_encArg [0]
   encode_cond1(v0, v1, v2) -> null_encode_cond1 [0]
   encode_true -> null_encode_true [0]
   encode_cond2(v0, v1, v2) -> null_encode_cond2 [0]
   encode_gr(v0, v1) -> null_encode_gr [0]
   encode_0 -> null_encode_0 [0]
   encode_p(v0) -> null_encode_p [0]
   encode_false -> null_encode_false [0]
   encode_s(v0) -> null_encode_s [0]
   gr(v0, v1) -> null_gr [0]
   p(v0) -> null_p [0]
   cond1(v0, v1, v2) -> null_cond1 [0]
   cond2(v0, v1, v2) -> null_cond2 [0]

The TRS has the following type information:
cond1 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2 -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2 -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2 -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2
true :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2
cond2 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2 -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2 -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2 -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2
gr :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2 -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2 -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2
0 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2
p :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2 -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2
false :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2
s :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2 -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2
encArg :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2 -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2
cons_cond1 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2 -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2 -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2 -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2
cons_cond2 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2 -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2 -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2 -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2
cons_gr :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2 -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2 -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2
cons_p :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2 -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2
encode_cond1 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2 -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2 -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2 -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2
encode_true :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2
encode_cond2 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2 -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2 -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2 -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2
encode_gr :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2 -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2 -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2
encode_0 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2
encode_p :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2 -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2
encode_false :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2
encode_s :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2 -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2
null_encArg :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2
null_encode_cond1 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2
null_encode_true :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2
null_encode_cond2 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2
null_encode_gr :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2
null_encode_0 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2
null_encode_p :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2
null_encode_false :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2
null_encode_s :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2
null_gr :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2
null_p :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2
null_cond1 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2
null_cond2 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_gr:null_p:null_cond1:null_cond2

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

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

   true => 2
   0 => 0
   false => 1
   null_encArg => 0
   null_encode_cond1 => 0
   null_encode_true => 0
   null_encode_cond2 => 0
   null_encode_gr => 0
   null_encode_0 => 0
   null_encode_p => 0
   null_encode_false => 0
   null_encode_s => 0
   null_gr => 0
   null_p => 0
   null_cond1 => 0
   null_cond2 => 0

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

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

   cond1(z, z', z'') -{ 2 }-> cond2(2, x, 1 + x') :|: z = 2, z' = x, z'' = 1 + x', x >= 0, x' >= 0
   cond1(z, z', z'') -{ 2 }-> cond2(1, x, 0) :|: z = 2, z'' = 0, z' = x, x >= 0
   cond1(z, z', z'') -{ 1 }-> cond2(0, x, y) :|: z = 2, z' = x, z'' = y, x >= 0, y >= 0
   cond1(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   cond2(z, z', z'') -{ 3 }-> cond2(2, x, x'') :|: z = 2, z' = x, x >= 0, z'' = 1 + x'', x'' >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(2, x, 0) :|: z = 2, z' = x, x >= 0, z'' = 1 + x'', x'' >= 0
   cond2(z, z', z'') -{ 3 }-> cond2(1, x, 0) :|: z = 2, z'' = 0, z' = x, x >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(1, x, 0) :|: z = 2, z'' = 0, z' = x, x >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(0, x, x1) :|: z = 2, x1 >= 0, z' = x, z'' = 1 + x1, x >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(0, x, 0) :|: z = 2, z'' = 0, z' = x, x >= 0
   cond2(z, z', z'') -{ 1 }-> cond2(0, x, 0) :|: z = 2, z' = x, z'' = y, x >= 0, y >= 0
   cond2(z, z', z'') -{ 3 }-> cond1(2, x2, y) :|: z' = 1 + x2, z'' = y, z = 1, y >= 0, x2 >= 0
   cond2(z, z', z'') -{ 2 }-> cond1(2, 0, y) :|: z' = 1 + x2, z'' = y, z = 1, y >= 0, x2 >= 0
   cond2(z, z', z'') -{ 3 }-> cond1(1, 0, y) :|: z'' = y, z = 1, y >= 0, z' = 0
   cond2(z, z', z'') -{ 2 }-> cond1(1, 0, y) :|: z'' = y, z = 1, y >= 0, z' = 0
   cond2(z, z', z'') -{ 2 }-> cond1(0, x3, y) :|: z'' = y, z = 1, z' = 1 + x3, y >= 0, x3 >= 0
   cond2(z, z', z'') -{ 2 }-> cond1(0, 0, y) :|: z'' = y, z = 1, y >= 0, z' = 0
   cond2(z, z', z'') -{ 1 }-> cond1(0, 0, y) :|: z' = x, z'' = y, z = 1, x >= 0, y >= 0
   cond2(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   encArg(z) -{ 0 }-> p(p(encArg(x_1963))) :|: z = 1 + (1 + x_1963), x_1963 >= 0
   encArg(z) -{ 0 }-> p(gr(encArg(x_1962), encArg(x_2577))) :|: x_2577 >= 0, z = 1 + (1 + x_1962 + x_2577), x_1962 >= 0
   encArg(z) -{ 0 }-> p(cond2(encArg(x_1961), encArg(x_2576), encArg(x_3384))) :|: x_3384 >= 0, x_2576 >= 0, z = 1 + (1 + x_1961 + x_2576 + x_3384), x_1961 >= 0
   encArg(z) -{ 0 }-> p(cond1(encArg(x_1960), encArg(x_2575), encArg(x_3383))) :|: x_1960 >= 0, x_2575 >= 0, x_3383 >= 0, z = 1 + (1 + x_1960 + x_2575 + x_3383)
   encArg(z) -{ 0 }-> p(2) :|: z = 1 + 2
   encArg(z) -{ 0 }-> p(1) :|: z = 1 + 1
   encArg(z) -{ 0 }-> p(0) :|: z = 1 + 0
   encArg(z) -{ 0 }-> p(0) :|: z = 1 + x_1, x_1 >= 0
   encArg(z) -{ 0 }-> p(1 + encArg(x_1959)) :|: z = 1 + (1 + x_1959), x_1959 >= 0
   encArg(z) -{ 0 }-> gr(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encArg(z) -{ 0 }-> 1 + encArg(x_1) :|: z = 1 + x_1, x_1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_cond1(z, z', z'') -{ 0 }-> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, x_3 >= 0, x_2 >= 0, z = x_1, z' = x_2, z'' = x_3
   encode_cond1(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   encode_cond2(z, z', z'') -{ 0 }-> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, x_3 >= 0, x_2 >= 0, z = x_1, z' = x_2, z'' = x_3
   encode_cond2(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_gr(z, z') -{ 0 }-> gr(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2
   encode_gr(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   encode_p(z) -{ 0 }-> p(p(encArg(x_11928))) :|: z = 1 + x_11928, x_11928 >= 0
   encode_p(z) -{ 0 }-> p(gr(encArg(x_11927), encArg(x_21156))) :|: z = 1 + x_11927 + x_21156, x_21156 >= 0, x_11927 >= 0
   encode_p(z) -{ 0 }-> p(cond2(encArg(x_11926), encArg(x_21155), encArg(x_3770))) :|: x_11926 >= 0, x_21155 >= 0, z = 1 + x_11926 + x_21155 + x_3770, x_3770 >= 0
   encode_p(z) -{ 0 }-> p(cond1(encArg(x_11925), encArg(x_21154), encArg(x_3769))) :|: z = 1 + x_11925 + x_21154 + x_3769, x_11925 >= 0, x_21154 >= 0, x_3769 >= 0
   encode_p(z) -{ 0 }-> p(2) :|: z = 2
   encode_p(z) -{ 0 }-> p(1) :|: z = 1
   encode_p(z) -{ 0 }-> p(0) :|: z = 0
   encode_p(z) -{ 0 }-> p(0) :|: x_1 >= 0, z = x_1
   encode_p(z) -{ 0 }-> p(1 + encArg(x_11924)) :|: z = 1 + x_11924, x_11924 >= 0
   encode_p(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_s(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_s(z) -{ 0 }-> 1 + encArg(x_1) :|: x_1 >= 0, z = x_1
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   gr(z, z') -{ 1 }-> gr(x, y) :|: z' = 1 + y, x >= 0, y >= 0, z = 1 + x
   gr(z, z') -{ 1 }-> 2 :|: x >= 0, z = 1 + x, z' = 0
   gr(z, z') -{ 1 }-> 1 :|: z' = x, x >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   p(z) -{ 1 }-> x :|: x >= 0, z = 1 + x
   p(z) -{ 1 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0


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

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

   p(z) -{ 1 }-> x :|: x >= 0, z = 1 + x
   p(z) -{ 1 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0

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

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

   cond1(z, z', z'') -{ 2 }-> cond2(2, x, 1 + x') :|: z = 2, z' = x, z'' = 1 + x', x >= 0, x' >= 0
   cond1(z, z', z'') -{ 2 }-> cond2(1, x, 0) :|: z = 2, z'' = 0, z' = x, x >= 0
   cond1(z, z', z'') -{ 1 }-> cond2(0, x, y) :|: z = 2, z' = x, z'' = y, x >= 0, y >= 0
   cond1(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   cond2(z, z', z'') -{ 3 }-> cond2(2, x, x'') :|: z = 2, z' = x, x >= 0, z'' = 1 + x'', x'' >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(2, x, 0) :|: z = 2, z' = x, x >= 0, z'' = 1 + x'', x'' >= 0
   cond2(z, z', z'') -{ 3 }-> cond2(1, x, 0) :|: z = 2, z'' = 0, z' = x, x >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(1, x, 0) :|: z = 2, z'' = 0, z' = x, x >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(0, x, x1) :|: z = 2, x1 >= 0, z' = x, z'' = 1 + x1, x >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(0, x, 0) :|: z = 2, z'' = 0, z' = x, x >= 0
   cond2(z, z', z'') -{ 1 }-> cond2(0, x, 0) :|: z = 2, z' = x, z'' = y, x >= 0, y >= 0
   cond2(z, z', z'') -{ 3 }-> cond1(2, x2, y) :|: z' = 1 + x2, z'' = y, z = 1, y >= 0, x2 >= 0
   cond2(z, z', z'') -{ 2 }-> cond1(2, 0, y) :|: z' = 1 + x2, z'' = y, z = 1, y >= 0, x2 >= 0
   cond2(z, z', z'') -{ 3 }-> cond1(1, 0, y) :|: z'' = y, z = 1, y >= 0, z' = 0
   cond2(z, z', z'') -{ 2 }-> cond1(1, 0, y) :|: z'' = y, z = 1, y >= 0, z' = 0
   cond2(z, z', z'') -{ 2 }-> cond1(0, x3, y) :|: z'' = y, z = 1, z' = 1 + x3, y >= 0, x3 >= 0
   cond2(z, z', z'') -{ 2 }-> cond1(0, 0, y) :|: z'' = y, z = 1, y >= 0, z' = 0
   cond2(z, z', z'') -{ 1 }-> cond1(0, 0, y) :|: z' = x, z'' = y, z = 1, x >= 0, y >= 0
   cond2(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   encArg(z) -{ 1 }-> x :|: z = 1 + 2, x >= 0, 2 = 1 + x
   encArg(z) -{ 1 }-> x :|: z = 1 + 1, x >= 0, 1 = 1 + x
   encArg(z) -{ 0 }-> p(p(encArg(x_1963))) :|: z = 1 + (1 + x_1963), x_1963 >= 0
   encArg(z) -{ 0 }-> p(gr(encArg(x_1962), encArg(x_2577))) :|: x_2577 >= 0, z = 1 + (1 + x_1962 + x_2577), x_1962 >= 0
   encArg(z) -{ 0 }-> p(cond2(encArg(x_1961), encArg(x_2576), encArg(x_3384))) :|: x_3384 >= 0, x_2576 >= 0, z = 1 + (1 + x_1961 + x_2576 + x_3384), x_1961 >= 0
   encArg(z) -{ 0 }-> p(cond1(encArg(x_1960), encArg(x_2575), encArg(x_3383))) :|: x_1960 >= 0, x_2575 >= 0, x_3383 >= 0, z = 1 + (1 + x_1960 + x_2575 + x_3383)
   encArg(z) -{ 0 }-> p(1 + encArg(x_1959)) :|: z = 1 + (1 + x_1959), x_1959 >= 0
   encArg(z) -{ 0 }-> gr(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 2 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 0, 0 = 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 1, v0 >= 0, 1 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + x_1, x_1 >= 0, 0 = 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + x_1, x_1 >= 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 1 + encArg(x_1) :|: z = 1 + x_1, x_1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_cond1(z, z', z'') -{ 0 }-> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, x_3 >= 0, x_2 >= 0, z = x_1, z' = x_2, z'' = x_3
   encode_cond1(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   encode_cond2(z, z', z'') -{ 0 }-> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, x_3 >= 0, x_2 >= 0, z = x_1, z' = x_2, z'' = x_3
   encode_cond2(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_gr(z, z') -{ 0 }-> gr(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2
   encode_gr(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   encode_p(z) -{ 1 }-> x :|: z = 2, x >= 0, 2 = 1 + x
   encode_p(z) -{ 1 }-> x :|: z = 1, x >= 0, 1 = 1 + x
   encode_p(z) -{ 0 }-> p(p(encArg(x_11928))) :|: z = 1 + x_11928, x_11928 >= 0
   encode_p(z) -{ 0 }-> p(gr(encArg(x_11927), encArg(x_21156))) :|: z = 1 + x_11927 + x_21156, x_21156 >= 0, x_11927 >= 0
   encode_p(z) -{ 0 }-> p(cond2(encArg(x_11926), encArg(x_21155), encArg(x_3770))) :|: x_11926 >= 0, x_21155 >= 0, z = 1 + x_11926 + x_21155 + x_3770, x_3770 >= 0
   encode_p(z) -{ 0 }-> p(cond1(encArg(x_11925), encArg(x_21154), encArg(x_3769))) :|: z = 1 + x_11925 + x_21154 + x_3769, x_11925 >= 0, x_21154 >= 0, x_3769 >= 0
   encode_p(z) -{ 0 }-> p(1 + encArg(x_11924)) :|: z = 1 + x_11924, x_11924 >= 0
   encode_p(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_p(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 2 = v0
   encode_p(z) -{ 1 }-> 0 :|: z = 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z = 0, v0 >= 0, 0 = v0
   encode_p(z) -{ 0 }-> 0 :|: z = 1, v0 >= 0, 1 = v0
   encode_p(z) -{ 1 }-> 0 :|: x_1 >= 0, z = x_1, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: x_1 >= 0, z = x_1, v0 >= 0, 0 = v0
   encode_s(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_s(z) -{ 0 }-> 1 + encArg(x_1) :|: x_1 >= 0, z = x_1
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   gr(z, z') -{ 1 }-> gr(x, y) :|: z' = 1 + y, x >= 0, y >= 0, z = 1 + x
   gr(z, z') -{ 1 }-> 2 :|: x >= 0, z = 1 + x, z' = 0
   gr(z, z') -{ 1 }-> 1 :|: z' = x, x >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   p(z) -{ 1 }-> x :|: x >= 0, z = 1 + x
   p(z) -{ 1 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0


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

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

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

   cond1(z, z', z'') -{ 2 }-> cond2(2, z', 1 + (z'' - 1)) :|: z = 2, z' >= 0, z'' - 1 >= 0
   cond1(z, z', z'') -{ 2 }-> cond2(1, z', 0) :|: z = 2, z'' = 0, z' >= 0
   cond1(z, z', z'') -{ 1 }-> cond2(0, z', z'') :|: z = 2, z' >= 0, z'' >= 0
   cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(2, z', 0) :|: z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 3 }-> cond2(2, z', z'' - 1) :|: z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 3 }-> cond2(1, z', 0) :|: z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(1, z', 0) :|: z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(0, z', 0) :|: z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 1 }-> cond2(0, z', 0) :|: z = 2, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(0, z', z'' - 1) :|: z = 2, z'' - 1 >= 0, z' >= 0
   cond2(z, z', z'') -{ 2 }-> cond1(2, 0, z'') :|: z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 3 }-> cond1(2, z' - 1, z'') :|: z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 3 }-> cond1(1, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 2 }-> cond1(1, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 2 }-> cond1(0, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 1 }-> cond1(0, 0, z'') :|: z = 1, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 2 }-> cond1(0, z' - 1, z'') :|: z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encArg(z) -{ 1 }-> x :|: z = 1 + 2, x >= 0, 2 = 1 + x
   encArg(z) -{ 1 }-> x :|: z = 1 + 1, x >= 0, 1 = 1 + x
   encArg(z) -{ 0 }-> p(p(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> p(gr(encArg(x_1962), encArg(x_2577))) :|: x_2577 >= 0, z = 1 + (1 + x_1962 + x_2577), x_1962 >= 0
   encArg(z) -{ 0 }-> p(cond2(encArg(x_1961), encArg(x_2576), encArg(x_3384))) :|: x_3384 >= 0, x_2576 >= 0, z = 1 + (1 + x_1961 + x_2576 + x_3384), x_1961 >= 0
   encArg(z) -{ 0 }-> p(cond1(encArg(x_1960), encArg(x_2575), encArg(x_3383))) :|: x_1960 >= 0, x_2575 >= 0, x_3383 >= 0, z = 1 + (1 + x_1960 + x_2575 + x_3383)
   encArg(z) -{ 0 }-> p(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> gr(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 2 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 0, 0 = 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 1, v0 >= 0, 1 = 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 + encArg(z - 1) :|: z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_cond1(z, z', z'') -{ 0 }-> cond1(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_cond2(z, z', z'') -{ 0 }-> cond2(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_gr(z, z') -{ 0 }-> gr(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_p(z) -{ 1 }-> x :|: z = 2, x >= 0, 2 = 1 + x
   encode_p(z) -{ 1 }-> x :|: z = 1, x >= 0, 1 = 1 + x
   encode_p(z) -{ 0 }-> p(p(encArg(z - 1))) :|: z - 1 >= 0
   encode_p(z) -{ 0 }-> p(gr(encArg(x_11927), encArg(x_21156))) :|: z = 1 + x_11927 + x_21156, x_21156 >= 0, x_11927 >= 0
   encode_p(z) -{ 0 }-> p(cond2(encArg(x_11926), encArg(x_21155), encArg(x_3770))) :|: x_11926 >= 0, x_21155 >= 0, z = 1 + x_11926 + x_21155 + x_3770, x_3770 >= 0
   encode_p(z) -{ 0 }-> p(cond1(encArg(x_11925), encArg(x_21154), encArg(x_3769))) :|: z = 1 + x_11925 + x_21154 + x_3769, x_11925 >= 0, x_21154 >= 0, x_3769 >= 0
   encode_p(z) -{ 0 }-> p(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_p(z) -{ 0 }-> 0 :|: z >= 0
   encode_p(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 2 = v0
   encode_p(z) -{ 1 }-> 0 :|: z = 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z = 0, v0 >= 0, 0 = v0
   encode_p(z) -{ 0 }-> 0 :|: z = 1, v0 >= 0, 1 = v0
   encode_p(z) -{ 1 }-> 0 :|: z >= 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   gr(z, z') -{ 1 }-> gr(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
   gr(z, z') -{ 1 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 1 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 1 }-> z - 1 :|: z - 1 >= 0


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

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

   { encode_0 }
   { encode_false }
   { gr }
   { encode_true }
   { cond2, cond1 }
   { p }
   { encArg }
   { encode_p }
   { encode_gr }
   { encode_cond2 }
   { encode_cond1 }
   { encode_s }

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

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

   cond1(z, z', z'') -{ 2 }-> cond2(2, z', 1 + (z'' - 1)) :|: z = 2, z' >= 0, z'' - 1 >= 0
   cond1(z, z', z'') -{ 2 }-> cond2(1, z', 0) :|: z = 2, z'' = 0, z' >= 0
   cond1(z, z', z'') -{ 1 }-> cond2(0, z', z'') :|: z = 2, z' >= 0, z'' >= 0
   cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(2, z', 0) :|: z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 3 }-> cond2(2, z', z'' - 1) :|: z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 3 }-> cond2(1, z', 0) :|: z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(1, z', 0) :|: z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(0, z', 0) :|: z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 1 }-> cond2(0, z', 0) :|: z = 2, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(0, z', z'' - 1) :|: z = 2, z'' - 1 >= 0, z' >= 0
   cond2(z, z', z'') -{ 2 }-> cond1(2, 0, z'') :|: z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 3 }-> cond1(2, z' - 1, z'') :|: z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 3 }-> cond1(1, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 2 }-> cond1(1, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 2 }-> cond1(0, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 1 }-> cond1(0, 0, z'') :|: z = 1, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 2 }-> cond1(0, z' - 1, z'') :|: z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encArg(z) -{ 1 }-> x :|: z = 1 + 2, x >= 0, 2 = 1 + x
   encArg(z) -{ 1 }-> x :|: z = 1 + 1, x >= 0, 1 = 1 + x
   encArg(z) -{ 0 }-> p(p(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> p(gr(encArg(x_1962), encArg(x_2577))) :|: x_2577 >= 0, z = 1 + (1 + x_1962 + x_2577), x_1962 >= 0
   encArg(z) -{ 0 }-> p(cond2(encArg(x_1961), encArg(x_2576), encArg(x_3384))) :|: x_3384 >= 0, x_2576 >= 0, z = 1 + (1 + x_1961 + x_2576 + x_3384), x_1961 >= 0
   encArg(z) -{ 0 }-> p(cond1(encArg(x_1960), encArg(x_2575), encArg(x_3383))) :|: x_1960 >= 0, x_2575 >= 0, x_3383 >= 0, z = 1 + (1 + x_1960 + x_2575 + x_3383)
   encArg(z) -{ 0 }-> p(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> gr(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 2 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 0, 0 = 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 1, v0 >= 0, 1 = 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 + encArg(z - 1) :|: z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_cond1(z, z', z'') -{ 0 }-> cond1(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_cond2(z, z', z'') -{ 0 }-> cond2(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_gr(z, z') -{ 0 }-> gr(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_p(z) -{ 1 }-> x :|: z = 2, x >= 0, 2 = 1 + x
   encode_p(z) -{ 1 }-> x :|: z = 1, x >= 0, 1 = 1 + x
   encode_p(z) -{ 0 }-> p(p(encArg(z - 1))) :|: z - 1 >= 0
   encode_p(z) -{ 0 }-> p(gr(encArg(x_11927), encArg(x_21156))) :|: z = 1 + x_11927 + x_21156, x_21156 >= 0, x_11927 >= 0
   encode_p(z) -{ 0 }-> p(cond2(encArg(x_11926), encArg(x_21155), encArg(x_3770))) :|: x_11926 >= 0, x_21155 >= 0, z = 1 + x_11926 + x_21155 + x_3770, x_3770 >= 0
   encode_p(z) -{ 0 }-> p(cond1(encArg(x_11925), encArg(x_21154), encArg(x_3769))) :|: z = 1 + x_11925 + x_21154 + x_3769, x_11925 >= 0, x_21154 >= 0, x_3769 >= 0
   encode_p(z) -{ 0 }-> p(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_p(z) -{ 0 }-> 0 :|: z >= 0
   encode_p(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 2 = v0
   encode_p(z) -{ 1 }-> 0 :|: z = 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z = 0, v0 >= 0, 0 = v0
   encode_p(z) -{ 0 }-> 0 :|: z = 1, v0 >= 0, 1 = v0
   encode_p(z) -{ 1 }-> 0 :|: z >= 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   gr(z, z') -{ 1 }-> gr(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
   gr(z, z') -{ 1 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 1 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 1 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {encode_0}, {encode_false}, {gr}, {encode_true}, {cond2,cond1}, {p}, {encArg}, {encode_p}, {encode_gr}, {encode_cond2}, {encode_cond1}, {encode_s}

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

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

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

   cond1(z, z', z'') -{ 2 }-> cond2(2, z', 1 + (z'' - 1)) :|: z = 2, z' >= 0, z'' - 1 >= 0
   cond1(z, z', z'') -{ 2 }-> cond2(1, z', 0) :|: z = 2, z'' = 0, z' >= 0
   cond1(z, z', z'') -{ 1 }-> cond2(0, z', z'') :|: z = 2, z' >= 0, z'' >= 0
   cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(2, z', 0) :|: z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 3 }-> cond2(2, z', z'' - 1) :|: z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 3 }-> cond2(1, z', 0) :|: z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(1, z', 0) :|: z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(0, z', 0) :|: z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 1 }-> cond2(0, z', 0) :|: z = 2, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(0, z', z'' - 1) :|: z = 2, z'' - 1 >= 0, z' >= 0
   cond2(z, z', z'') -{ 2 }-> cond1(2, 0, z'') :|: z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 3 }-> cond1(2, z' - 1, z'') :|: z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 3 }-> cond1(1, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 2 }-> cond1(1, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 2 }-> cond1(0, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 1 }-> cond1(0, 0, z'') :|: z = 1, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 2 }-> cond1(0, z' - 1, z'') :|: z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encArg(z) -{ 1 }-> x :|: z = 1 + 2, x >= 0, 2 = 1 + x
   encArg(z) -{ 1 }-> x :|: z = 1 + 1, x >= 0, 1 = 1 + x
   encArg(z) -{ 0 }-> p(p(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> p(gr(encArg(x_1962), encArg(x_2577))) :|: x_2577 >= 0, z = 1 + (1 + x_1962 + x_2577), x_1962 >= 0
   encArg(z) -{ 0 }-> p(cond2(encArg(x_1961), encArg(x_2576), encArg(x_3384))) :|: x_3384 >= 0, x_2576 >= 0, z = 1 + (1 + x_1961 + x_2576 + x_3384), x_1961 >= 0
   encArg(z) -{ 0 }-> p(cond1(encArg(x_1960), encArg(x_2575), encArg(x_3383))) :|: x_1960 >= 0, x_2575 >= 0, x_3383 >= 0, z = 1 + (1 + x_1960 + x_2575 + x_3383)
   encArg(z) -{ 0 }-> p(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> gr(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 2 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 0, 0 = 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 1, v0 >= 0, 1 = 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 + encArg(z - 1) :|: z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_cond1(z, z', z'') -{ 0 }-> cond1(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_cond2(z, z', z'') -{ 0 }-> cond2(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_gr(z, z') -{ 0 }-> gr(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_p(z) -{ 1 }-> x :|: z = 2, x >= 0, 2 = 1 + x
   encode_p(z) -{ 1 }-> x :|: z = 1, x >= 0, 1 = 1 + x
   encode_p(z) -{ 0 }-> p(p(encArg(z - 1))) :|: z - 1 >= 0
   encode_p(z) -{ 0 }-> p(gr(encArg(x_11927), encArg(x_21156))) :|: z = 1 + x_11927 + x_21156, x_21156 >= 0, x_11927 >= 0
   encode_p(z) -{ 0 }-> p(cond2(encArg(x_11926), encArg(x_21155), encArg(x_3770))) :|: x_11926 >= 0, x_21155 >= 0, z = 1 + x_11926 + x_21155 + x_3770, x_3770 >= 0
   encode_p(z) -{ 0 }-> p(cond1(encArg(x_11925), encArg(x_21154), encArg(x_3769))) :|: z = 1 + x_11925 + x_21154 + x_3769, x_11925 >= 0, x_21154 >= 0, x_3769 >= 0
   encode_p(z) -{ 0 }-> p(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_p(z) -{ 0 }-> 0 :|: z >= 0
   encode_p(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 2 = v0
   encode_p(z) -{ 1 }-> 0 :|: z = 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z = 0, v0 >= 0, 0 = v0
   encode_p(z) -{ 0 }-> 0 :|: z = 1, v0 >= 0, 1 = v0
   encode_p(z) -{ 1 }-> 0 :|: z >= 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   gr(z, z') -{ 1 }-> gr(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
   gr(z, z') -{ 1 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 1 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 1 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {encode_0}, {encode_false}, {gr}, {encode_true}, {cond2,cond1}, {p}, {encArg}, {encode_p}, {encode_gr}, {encode_cond2}, {encode_cond1}, {encode_s}

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

(23) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: encode_0
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 0

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

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

   cond1(z, z', z'') -{ 2 }-> cond2(2, z', 1 + (z'' - 1)) :|: z = 2, z' >= 0, z'' - 1 >= 0
   cond1(z, z', z'') -{ 2 }-> cond2(1, z', 0) :|: z = 2, z'' = 0, z' >= 0
   cond1(z, z', z'') -{ 1 }-> cond2(0, z', z'') :|: z = 2, z' >= 0, z'' >= 0
   cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(2, z', 0) :|: z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 3 }-> cond2(2, z', z'' - 1) :|: z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 3 }-> cond2(1, z', 0) :|: z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(1, z', 0) :|: z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(0, z', 0) :|: z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 1 }-> cond2(0, z', 0) :|: z = 2, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(0, z', z'' - 1) :|: z = 2, z'' - 1 >= 0, z' >= 0
   cond2(z, z', z'') -{ 2 }-> cond1(2, 0, z'') :|: z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 3 }-> cond1(2, z' - 1, z'') :|: z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 3 }-> cond1(1, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 2 }-> cond1(1, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 2 }-> cond1(0, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 1 }-> cond1(0, 0, z'') :|: z = 1, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 2 }-> cond1(0, z' - 1, z'') :|: z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encArg(z) -{ 1 }-> x :|: z = 1 + 2, x >= 0, 2 = 1 + x
   encArg(z) -{ 1 }-> x :|: z = 1 + 1, x >= 0, 1 = 1 + x
   encArg(z) -{ 0 }-> p(p(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> p(gr(encArg(x_1962), encArg(x_2577))) :|: x_2577 >= 0, z = 1 + (1 + x_1962 + x_2577), x_1962 >= 0
   encArg(z) -{ 0 }-> p(cond2(encArg(x_1961), encArg(x_2576), encArg(x_3384))) :|: x_3384 >= 0, x_2576 >= 0, z = 1 + (1 + x_1961 + x_2576 + x_3384), x_1961 >= 0
   encArg(z) -{ 0 }-> p(cond1(encArg(x_1960), encArg(x_2575), encArg(x_3383))) :|: x_1960 >= 0, x_2575 >= 0, x_3383 >= 0, z = 1 + (1 + x_1960 + x_2575 + x_3383)
   encArg(z) -{ 0 }-> p(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> gr(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 2 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 0, 0 = 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 1, v0 >= 0, 1 = 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 + encArg(z - 1) :|: z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_cond1(z, z', z'') -{ 0 }-> cond1(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_cond2(z, z', z'') -{ 0 }-> cond2(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_gr(z, z') -{ 0 }-> gr(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_p(z) -{ 1 }-> x :|: z = 2, x >= 0, 2 = 1 + x
   encode_p(z) -{ 1 }-> x :|: z = 1, x >= 0, 1 = 1 + x
   encode_p(z) -{ 0 }-> p(p(encArg(z - 1))) :|: z - 1 >= 0
   encode_p(z) -{ 0 }-> p(gr(encArg(x_11927), encArg(x_21156))) :|: z = 1 + x_11927 + x_21156, x_21156 >= 0, x_11927 >= 0
   encode_p(z) -{ 0 }-> p(cond2(encArg(x_11926), encArg(x_21155), encArg(x_3770))) :|: x_11926 >= 0, x_21155 >= 0, z = 1 + x_11926 + x_21155 + x_3770, x_3770 >= 0
   encode_p(z) -{ 0 }-> p(cond1(encArg(x_11925), encArg(x_21154), encArg(x_3769))) :|: z = 1 + x_11925 + x_21154 + x_3769, x_11925 >= 0, x_21154 >= 0, x_3769 >= 0
   encode_p(z) -{ 0 }-> p(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_p(z) -{ 0 }-> 0 :|: z >= 0
   encode_p(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 2 = v0
   encode_p(z) -{ 1 }-> 0 :|: z = 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z = 0, v0 >= 0, 0 = v0
   encode_p(z) -{ 0 }-> 0 :|: z = 1, v0 >= 0, 1 = v0
   encode_p(z) -{ 1 }-> 0 :|: z >= 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   gr(z, z') -{ 1 }-> gr(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
   gr(z, z') -{ 1 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 1 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 1 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {encode_0}, {encode_false}, {gr}, {encode_true}, {cond2,cond1}, {p}, {encArg}, {encode_p}, {encode_gr}, {encode_cond2}, {encode_cond1}, {encode_s}
Previous analysis results are:
  encode_0: runtime: ?, size: O(1) [0]

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

(25) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: encode_0
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 0

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

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

   cond1(z, z', z'') -{ 2 }-> cond2(2, z', 1 + (z'' - 1)) :|: z = 2, z' >= 0, z'' - 1 >= 0
   cond1(z, z', z'') -{ 2 }-> cond2(1, z', 0) :|: z = 2, z'' = 0, z' >= 0
   cond1(z, z', z'') -{ 1 }-> cond2(0, z', z'') :|: z = 2, z' >= 0, z'' >= 0
   cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(2, z', 0) :|: z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 3 }-> cond2(2, z', z'' - 1) :|: z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 3 }-> cond2(1, z', 0) :|: z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(1, z', 0) :|: z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(0, z', 0) :|: z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 1 }-> cond2(0, z', 0) :|: z = 2, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(0, z', z'' - 1) :|: z = 2, z'' - 1 >= 0, z' >= 0
   cond2(z, z', z'') -{ 2 }-> cond1(2, 0, z'') :|: z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 3 }-> cond1(2, z' - 1, z'') :|: z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 3 }-> cond1(1, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 2 }-> cond1(1, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 2 }-> cond1(0, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 1 }-> cond1(0, 0, z'') :|: z = 1, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 2 }-> cond1(0, z' - 1, z'') :|: z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encArg(z) -{ 1 }-> x :|: z = 1 + 2, x >= 0, 2 = 1 + x
   encArg(z) -{ 1 }-> x :|: z = 1 + 1, x >= 0, 1 = 1 + x
   encArg(z) -{ 0 }-> p(p(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> p(gr(encArg(x_1962), encArg(x_2577))) :|: x_2577 >= 0, z = 1 + (1 + x_1962 + x_2577), x_1962 >= 0
   encArg(z) -{ 0 }-> p(cond2(encArg(x_1961), encArg(x_2576), encArg(x_3384))) :|: x_3384 >= 0, x_2576 >= 0, z = 1 + (1 + x_1961 + x_2576 + x_3384), x_1961 >= 0
   encArg(z) -{ 0 }-> p(cond1(encArg(x_1960), encArg(x_2575), encArg(x_3383))) :|: x_1960 >= 0, x_2575 >= 0, x_3383 >= 0, z = 1 + (1 + x_1960 + x_2575 + x_3383)
   encArg(z) -{ 0 }-> p(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> gr(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 2 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 0, 0 = 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 1, v0 >= 0, 1 = 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 + encArg(z - 1) :|: z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_cond1(z, z', z'') -{ 0 }-> cond1(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_cond2(z, z', z'') -{ 0 }-> cond2(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_gr(z, z') -{ 0 }-> gr(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_p(z) -{ 1 }-> x :|: z = 2, x >= 0, 2 = 1 + x
   encode_p(z) -{ 1 }-> x :|: z = 1, x >= 0, 1 = 1 + x
   encode_p(z) -{ 0 }-> p(p(encArg(z - 1))) :|: z - 1 >= 0
   encode_p(z) -{ 0 }-> p(gr(encArg(x_11927), encArg(x_21156))) :|: z = 1 + x_11927 + x_21156, x_21156 >= 0, x_11927 >= 0
   encode_p(z) -{ 0 }-> p(cond2(encArg(x_11926), encArg(x_21155), encArg(x_3770))) :|: x_11926 >= 0, x_21155 >= 0, z = 1 + x_11926 + x_21155 + x_3770, x_3770 >= 0
   encode_p(z) -{ 0 }-> p(cond1(encArg(x_11925), encArg(x_21154), encArg(x_3769))) :|: z = 1 + x_11925 + x_21154 + x_3769, x_11925 >= 0, x_21154 >= 0, x_3769 >= 0
   encode_p(z) -{ 0 }-> p(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_p(z) -{ 0 }-> 0 :|: z >= 0
   encode_p(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 2 = v0
   encode_p(z) -{ 1 }-> 0 :|: z = 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z = 0, v0 >= 0, 0 = v0
   encode_p(z) -{ 0 }-> 0 :|: z = 1, v0 >= 0, 1 = v0
   encode_p(z) -{ 1 }-> 0 :|: z >= 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   gr(z, z') -{ 1 }-> gr(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
   gr(z, z') -{ 1 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 1 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 1 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {encode_false}, {gr}, {encode_true}, {cond2,cond1}, {p}, {encArg}, {encode_p}, {encode_gr}, {encode_cond2}, {encode_cond1}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [0], size: O(1) [0]

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

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

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

   cond1(z, z', z'') -{ 2 }-> cond2(2, z', 1 + (z'' - 1)) :|: z = 2, z' >= 0, z'' - 1 >= 0
   cond1(z, z', z'') -{ 2 }-> cond2(1, z', 0) :|: z = 2, z'' = 0, z' >= 0
   cond1(z, z', z'') -{ 1 }-> cond2(0, z', z'') :|: z = 2, z' >= 0, z'' >= 0
   cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(2, z', 0) :|: z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 3 }-> cond2(2, z', z'' - 1) :|: z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 3 }-> cond2(1, z', 0) :|: z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(1, z', 0) :|: z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(0, z', 0) :|: z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 1 }-> cond2(0, z', 0) :|: z = 2, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(0, z', z'' - 1) :|: z = 2, z'' - 1 >= 0, z' >= 0
   cond2(z, z', z'') -{ 2 }-> cond1(2, 0, z'') :|: z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 3 }-> cond1(2, z' - 1, z'') :|: z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 3 }-> cond1(1, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 2 }-> cond1(1, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 2 }-> cond1(0, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 1 }-> cond1(0, 0, z'') :|: z = 1, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 2 }-> cond1(0, z' - 1, z'') :|: z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encArg(z) -{ 1 }-> x :|: z = 1 + 2, x >= 0, 2 = 1 + x
   encArg(z) -{ 1 }-> x :|: z = 1 + 1, x >= 0, 1 = 1 + x
   encArg(z) -{ 0 }-> p(p(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> p(gr(encArg(x_1962), encArg(x_2577))) :|: x_2577 >= 0, z = 1 + (1 + x_1962 + x_2577), x_1962 >= 0
   encArg(z) -{ 0 }-> p(cond2(encArg(x_1961), encArg(x_2576), encArg(x_3384))) :|: x_3384 >= 0, x_2576 >= 0, z = 1 + (1 + x_1961 + x_2576 + x_3384), x_1961 >= 0
   encArg(z) -{ 0 }-> p(cond1(encArg(x_1960), encArg(x_2575), encArg(x_3383))) :|: x_1960 >= 0, x_2575 >= 0, x_3383 >= 0, z = 1 + (1 + x_1960 + x_2575 + x_3383)
   encArg(z) -{ 0 }-> p(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> gr(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 2 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 0, 0 = 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 1, v0 >= 0, 1 = 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 + encArg(z - 1) :|: z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_cond1(z, z', z'') -{ 0 }-> cond1(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_cond2(z, z', z'') -{ 0 }-> cond2(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_gr(z, z') -{ 0 }-> gr(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_p(z) -{ 1 }-> x :|: z = 2, x >= 0, 2 = 1 + x
   encode_p(z) -{ 1 }-> x :|: z = 1, x >= 0, 1 = 1 + x
   encode_p(z) -{ 0 }-> p(p(encArg(z - 1))) :|: z - 1 >= 0
   encode_p(z) -{ 0 }-> p(gr(encArg(x_11927), encArg(x_21156))) :|: z = 1 + x_11927 + x_21156, x_21156 >= 0, x_11927 >= 0
   encode_p(z) -{ 0 }-> p(cond2(encArg(x_11926), encArg(x_21155), encArg(x_3770))) :|: x_11926 >= 0, x_21155 >= 0, z = 1 + x_11926 + x_21155 + x_3770, x_3770 >= 0
   encode_p(z) -{ 0 }-> p(cond1(encArg(x_11925), encArg(x_21154), encArg(x_3769))) :|: z = 1 + x_11925 + x_21154 + x_3769, x_11925 >= 0, x_21154 >= 0, x_3769 >= 0
   encode_p(z) -{ 0 }-> p(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_p(z) -{ 0 }-> 0 :|: z >= 0
   encode_p(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 2 = v0
   encode_p(z) -{ 1 }-> 0 :|: z = 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z = 0, v0 >= 0, 0 = v0
   encode_p(z) -{ 0 }-> 0 :|: z = 1, v0 >= 0, 1 = v0
   encode_p(z) -{ 1 }-> 0 :|: z >= 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   gr(z, z') -{ 1 }-> gr(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
   gr(z, z') -{ 1 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 1 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 1 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {encode_false}, {gr}, {encode_true}, {cond2,cond1}, {p}, {encArg}, {encode_p}, {encode_gr}, {encode_cond2}, {encode_cond1}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [0], size: O(1) [0]

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

(29) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: encode_false
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:

   cond1(z, z', z'') -{ 2 }-> cond2(2, z', 1 + (z'' - 1)) :|: z = 2, z' >= 0, z'' - 1 >= 0
   cond1(z, z', z'') -{ 2 }-> cond2(1, z', 0) :|: z = 2, z'' = 0, z' >= 0
   cond1(z, z', z'') -{ 1 }-> cond2(0, z', z'') :|: z = 2, z' >= 0, z'' >= 0
   cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(2, z', 0) :|: z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 3 }-> cond2(2, z', z'' - 1) :|: z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 3 }-> cond2(1, z', 0) :|: z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(1, z', 0) :|: z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(0, z', 0) :|: z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 1 }-> cond2(0, z', 0) :|: z = 2, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(0, z', z'' - 1) :|: z = 2, z'' - 1 >= 0, z' >= 0
   cond2(z, z', z'') -{ 2 }-> cond1(2, 0, z'') :|: z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 3 }-> cond1(2, z' - 1, z'') :|: z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 3 }-> cond1(1, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 2 }-> cond1(1, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 2 }-> cond1(0, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 1 }-> cond1(0, 0, z'') :|: z = 1, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 2 }-> cond1(0, z' - 1, z'') :|: z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encArg(z) -{ 1 }-> x :|: z = 1 + 2, x >= 0, 2 = 1 + x
   encArg(z) -{ 1 }-> x :|: z = 1 + 1, x >= 0, 1 = 1 + x
   encArg(z) -{ 0 }-> p(p(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> p(gr(encArg(x_1962), encArg(x_2577))) :|: x_2577 >= 0, z = 1 + (1 + x_1962 + x_2577), x_1962 >= 0
   encArg(z) -{ 0 }-> p(cond2(encArg(x_1961), encArg(x_2576), encArg(x_3384))) :|: x_3384 >= 0, x_2576 >= 0, z = 1 + (1 + x_1961 + x_2576 + x_3384), x_1961 >= 0
   encArg(z) -{ 0 }-> p(cond1(encArg(x_1960), encArg(x_2575), encArg(x_3383))) :|: x_1960 >= 0, x_2575 >= 0, x_3383 >= 0, z = 1 + (1 + x_1960 + x_2575 + x_3383)
   encArg(z) -{ 0 }-> p(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> gr(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 2 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 0, 0 = 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 1, v0 >= 0, 1 = 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 + encArg(z - 1) :|: z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_cond1(z, z', z'') -{ 0 }-> cond1(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_cond2(z, z', z'') -{ 0 }-> cond2(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_gr(z, z') -{ 0 }-> gr(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_p(z) -{ 1 }-> x :|: z = 2, x >= 0, 2 = 1 + x
   encode_p(z) -{ 1 }-> x :|: z = 1, x >= 0, 1 = 1 + x
   encode_p(z) -{ 0 }-> p(p(encArg(z - 1))) :|: z - 1 >= 0
   encode_p(z) -{ 0 }-> p(gr(encArg(x_11927), encArg(x_21156))) :|: z = 1 + x_11927 + x_21156, x_21156 >= 0, x_11927 >= 0
   encode_p(z) -{ 0 }-> p(cond2(encArg(x_11926), encArg(x_21155), encArg(x_3770))) :|: x_11926 >= 0, x_21155 >= 0, z = 1 + x_11926 + x_21155 + x_3770, x_3770 >= 0
   encode_p(z) -{ 0 }-> p(cond1(encArg(x_11925), encArg(x_21154), encArg(x_3769))) :|: z = 1 + x_11925 + x_21154 + x_3769, x_11925 >= 0, x_21154 >= 0, x_3769 >= 0
   encode_p(z) -{ 0 }-> p(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_p(z) -{ 0 }-> 0 :|: z >= 0
   encode_p(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 2 = v0
   encode_p(z) -{ 1 }-> 0 :|: z = 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z = 0, v0 >= 0, 0 = v0
   encode_p(z) -{ 0 }-> 0 :|: z = 1, v0 >= 0, 1 = v0
   encode_p(z) -{ 1 }-> 0 :|: z >= 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   gr(z, z') -{ 1 }-> gr(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
   gr(z, z') -{ 1 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 1 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 1 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {encode_false}, {gr}, {encode_true}, {cond2,cond1}, {p}, {encArg}, {encode_p}, {encode_gr}, {encode_cond2}, {encode_cond1}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [0], size: O(1) [0]
  encode_false: runtime: ?, size: O(1) [1]

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

(31) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   cond1(z, z', z'') -{ 2 }-> cond2(2, z', 1 + (z'' - 1)) :|: z = 2, z' >= 0, z'' - 1 >= 0
   cond1(z, z', z'') -{ 2 }-> cond2(1, z', 0) :|: z = 2, z'' = 0, z' >= 0
   cond1(z, z', z'') -{ 1 }-> cond2(0, z', z'') :|: z = 2, z' >= 0, z'' >= 0
   cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(2, z', 0) :|: z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 3 }-> cond2(2, z', z'' - 1) :|: z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 3 }-> cond2(1, z', 0) :|: z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(1, z', 0) :|: z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(0, z', 0) :|: z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 1 }-> cond2(0, z', 0) :|: z = 2, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(0, z', z'' - 1) :|: z = 2, z'' - 1 >= 0, z' >= 0
   cond2(z, z', z'') -{ 2 }-> cond1(2, 0, z'') :|: z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 3 }-> cond1(2, z' - 1, z'') :|: z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 3 }-> cond1(1, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 2 }-> cond1(1, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 2 }-> cond1(0, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 1 }-> cond1(0, 0, z'') :|: z = 1, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 2 }-> cond1(0, z' - 1, z'') :|: z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encArg(z) -{ 1 }-> x :|: z = 1 + 2, x >= 0, 2 = 1 + x
   encArg(z) -{ 1 }-> x :|: z = 1 + 1, x >= 0, 1 = 1 + x
   encArg(z) -{ 0 }-> p(p(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> p(gr(encArg(x_1962), encArg(x_2577))) :|: x_2577 >= 0, z = 1 + (1 + x_1962 + x_2577), x_1962 >= 0
   encArg(z) -{ 0 }-> p(cond2(encArg(x_1961), encArg(x_2576), encArg(x_3384))) :|: x_3384 >= 0, x_2576 >= 0, z = 1 + (1 + x_1961 + x_2576 + x_3384), x_1961 >= 0
   encArg(z) -{ 0 }-> p(cond1(encArg(x_1960), encArg(x_2575), encArg(x_3383))) :|: x_1960 >= 0, x_2575 >= 0, x_3383 >= 0, z = 1 + (1 + x_1960 + x_2575 + x_3383)
   encArg(z) -{ 0 }-> p(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> gr(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 2 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 0, 0 = 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 1, v0 >= 0, 1 = 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 + encArg(z - 1) :|: z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_cond1(z, z', z'') -{ 0 }-> cond1(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_cond2(z, z', z'') -{ 0 }-> cond2(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_gr(z, z') -{ 0 }-> gr(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_p(z) -{ 1 }-> x :|: z = 2, x >= 0, 2 = 1 + x
   encode_p(z) -{ 1 }-> x :|: z = 1, x >= 0, 1 = 1 + x
   encode_p(z) -{ 0 }-> p(p(encArg(z - 1))) :|: z - 1 >= 0
   encode_p(z) -{ 0 }-> p(gr(encArg(x_11927), encArg(x_21156))) :|: z = 1 + x_11927 + x_21156, x_21156 >= 0, x_11927 >= 0
   encode_p(z) -{ 0 }-> p(cond2(encArg(x_11926), encArg(x_21155), encArg(x_3770))) :|: x_11926 >= 0, x_21155 >= 0, z = 1 + x_11926 + x_21155 + x_3770, x_3770 >= 0
   encode_p(z) -{ 0 }-> p(cond1(encArg(x_11925), encArg(x_21154), encArg(x_3769))) :|: z = 1 + x_11925 + x_21154 + x_3769, x_11925 >= 0, x_21154 >= 0, x_3769 >= 0
   encode_p(z) -{ 0 }-> p(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_p(z) -{ 0 }-> 0 :|: z >= 0
   encode_p(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 2 = v0
   encode_p(z) -{ 1 }-> 0 :|: z = 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z = 0, v0 >= 0, 0 = v0
   encode_p(z) -{ 0 }-> 0 :|: z = 1, v0 >= 0, 1 = v0
   encode_p(z) -{ 1 }-> 0 :|: z >= 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   gr(z, z') -{ 1 }-> gr(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
   gr(z, z') -{ 1 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 1 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 1 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {gr}, {encode_true}, {cond2,cond1}, {p}, {encArg}, {encode_p}, {encode_gr}, {encode_cond2}, {encode_cond1}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [0], size: O(1) [0]
  encode_false: runtime: O(1) [0], size: O(1) [1]

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

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

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

   cond1(z, z', z'') -{ 2 }-> cond2(2, z', 1 + (z'' - 1)) :|: z = 2, z' >= 0, z'' - 1 >= 0
   cond1(z, z', z'') -{ 2 }-> cond2(1, z', 0) :|: z = 2, z'' = 0, z' >= 0
   cond1(z, z', z'') -{ 1 }-> cond2(0, z', z'') :|: z = 2, z' >= 0, z'' >= 0
   cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(2, z', 0) :|: z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 3 }-> cond2(2, z', z'' - 1) :|: z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 3 }-> cond2(1, z', 0) :|: z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(1, z', 0) :|: z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(0, z', 0) :|: z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 1 }-> cond2(0, z', 0) :|: z = 2, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(0, z', z'' - 1) :|: z = 2, z'' - 1 >= 0, z' >= 0
   cond2(z, z', z'') -{ 2 }-> cond1(2, 0, z'') :|: z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 3 }-> cond1(2, z' - 1, z'') :|: z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 3 }-> cond1(1, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 2 }-> cond1(1, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 2 }-> cond1(0, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 1 }-> cond1(0, 0, z'') :|: z = 1, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 2 }-> cond1(0, z' - 1, z'') :|: z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encArg(z) -{ 1 }-> x :|: z = 1 + 2, x >= 0, 2 = 1 + x
   encArg(z) -{ 1 }-> x :|: z = 1 + 1, x >= 0, 1 = 1 + x
   encArg(z) -{ 0 }-> p(p(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> p(gr(encArg(x_1962), encArg(x_2577))) :|: x_2577 >= 0, z = 1 + (1 + x_1962 + x_2577), x_1962 >= 0
   encArg(z) -{ 0 }-> p(cond2(encArg(x_1961), encArg(x_2576), encArg(x_3384))) :|: x_3384 >= 0, x_2576 >= 0, z = 1 + (1 + x_1961 + x_2576 + x_3384), x_1961 >= 0
   encArg(z) -{ 0 }-> p(cond1(encArg(x_1960), encArg(x_2575), encArg(x_3383))) :|: x_1960 >= 0, x_2575 >= 0, x_3383 >= 0, z = 1 + (1 + x_1960 + x_2575 + x_3383)
   encArg(z) -{ 0 }-> p(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> gr(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 2 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 0, 0 = 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 1, v0 >= 0, 1 = 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 + encArg(z - 1) :|: z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_cond1(z, z', z'') -{ 0 }-> cond1(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_cond2(z, z', z'') -{ 0 }-> cond2(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_gr(z, z') -{ 0 }-> gr(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_p(z) -{ 1 }-> x :|: z = 2, x >= 0, 2 = 1 + x
   encode_p(z) -{ 1 }-> x :|: z = 1, x >= 0, 1 = 1 + x
   encode_p(z) -{ 0 }-> p(p(encArg(z - 1))) :|: z - 1 >= 0
   encode_p(z) -{ 0 }-> p(gr(encArg(x_11927), encArg(x_21156))) :|: z = 1 + x_11927 + x_21156, x_21156 >= 0, x_11927 >= 0
   encode_p(z) -{ 0 }-> p(cond2(encArg(x_11926), encArg(x_21155), encArg(x_3770))) :|: x_11926 >= 0, x_21155 >= 0, z = 1 + x_11926 + x_21155 + x_3770, x_3770 >= 0
   encode_p(z) -{ 0 }-> p(cond1(encArg(x_11925), encArg(x_21154), encArg(x_3769))) :|: z = 1 + x_11925 + x_21154 + x_3769, x_11925 >= 0, x_21154 >= 0, x_3769 >= 0
   encode_p(z) -{ 0 }-> p(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_p(z) -{ 0 }-> 0 :|: z >= 0
   encode_p(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 2 = v0
   encode_p(z) -{ 1 }-> 0 :|: z = 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z = 0, v0 >= 0, 0 = v0
   encode_p(z) -{ 0 }-> 0 :|: z = 1, v0 >= 0, 1 = v0
   encode_p(z) -{ 1 }-> 0 :|: z >= 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   gr(z, z') -{ 1 }-> gr(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
   gr(z, z') -{ 1 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 1 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 1 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {gr}, {encode_true}, {cond2,cond1}, {p}, {encArg}, {encode_p}, {encode_gr}, {encode_cond2}, {encode_cond1}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [0], size: O(1) [0]
  encode_false: runtime: O(1) [0], size: O(1) [1]

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

(35) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   cond1(z, z', z'') -{ 2 }-> cond2(2, z', 1 + (z'' - 1)) :|: z = 2, z' >= 0, z'' - 1 >= 0
   cond1(z, z', z'') -{ 2 }-> cond2(1, z', 0) :|: z = 2, z'' = 0, z' >= 0
   cond1(z, z', z'') -{ 1 }-> cond2(0, z', z'') :|: z = 2, z' >= 0, z'' >= 0
   cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(2, z', 0) :|: z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 3 }-> cond2(2, z', z'' - 1) :|: z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 3 }-> cond2(1, z', 0) :|: z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(1, z', 0) :|: z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(0, z', 0) :|: z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 1 }-> cond2(0, z', 0) :|: z = 2, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(0, z', z'' - 1) :|: z = 2, z'' - 1 >= 0, z' >= 0
   cond2(z, z', z'') -{ 2 }-> cond1(2, 0, z'') :|: z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 3 }-> cond1(2, z' - 1, z'') :|: z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 3 }-> cond1(1, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 2 }-> cond1(1, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 2 }-> cond1(0, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 1 }-> cond1(0, 0, z'') :|: z = 1, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 2 }-> cond1(0, z' - 1, z'') :|: z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encArg(z) -{ 1 }-> x :|: z = 1 + 2, x >= 0, 2 = 1 + x
   encArg(z) -{ 1 }-> x :|: z = 1 + 1, x >= 0, 1 = 1 + x
   encArg(z) -{ 0 }-> p(p(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> p(gr(encArg(x_1962), encArg(x_2577))) :|: x_2577 >= 0, z = 1 + (1 + x_1962 + x_2577), x_1962 >= 0
   encArg(z) -{ 0 }-> p(cond2(encArg(x_1961), encArg(x_2576), encArg(x_3384))) :|: x_3384 >= 0, x_2576 >= 0, z = 1 + (1 + x_1961 + x_2576 + x_3384), x_1961 >= 0
   encArg(z) -{ 0 }-> p(cond1(encArg(x_1960), encArg(x_2575), encArg(x_3383))) :|: x_1960 >= 0, x_2575 >= 0, x_3383 >= 0, z = 1 + (1 + x_1960 + x_2575 + x_3383)
   encArg(z) -{ 0 }-> p(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> gr(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 2 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 0, 0 = 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 1, v0 >= 0, 1 = 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 + encArg(z - 1) :|: z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_cond1(z, z', z'') -{ 0 }-> cond1(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_cond2(z, z', z'') -{ 0 }-> cond2(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_gr(z, z') -{ 0 }-> gr(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_p(z) -{ 1 }-> x :|: z = 2, x >= 0, 2 = 1 + x
   encode_p(z) -{ 1 }-> x :|: z = 1, x >= 0, 1 = 1 + x
   encode_p(z) -{ 0 }-> p(p(encArg(z - 1))) :|: z - 1 >= 0
   encode_p(z) -{ 0 }-> p(gr(encArg(x_11927), encArg(x_21156))) :|: z = 1 + x_11927 + x_21156, x_21156 >= 0, x_11927 >= 0
   encode_p(z) -{ 0 }-> p(cond2(encArg(x_11926), encArg(x_21155), encArg(x_3770))) :|: x_11926 >= 0, x_21155 >= 0, z = 1 + x_11926 + x_21155 + x_3770, x_3770 >= 0
   encode_p(z) -{ 0 }-> p(cond1(encArg(x_11925), encArg(x_21154), encArg(x_3769))) :|: z = 1 + x_11925 + x_21154 + x_3769, x_11925 >= 0, x_21154 >= 0, x_3769 >= 0
   encode_p(z) -{ 0 }-> p(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_p(z) -{ 0 }-> 0 :|: z >= 0
   encode_p(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 2 = v0
   encode_p(z) -{ 1 }-> 0 :|: z = 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z = 0, v0 >= 0, 0 = v0
   encode_p(z) -{ 0 }-> 0 :|: z = 1, v0 >= 0, 1 = v0
   encode_p(z) -{ 1 }-> 0 :|: z >= 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   gr(z, z') -{ 1 }-> gr(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
   gr(z, z') -{ 1 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 1 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 1 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {gr}, {encode_true}, {cond2,cond1}, {p}, {encArg}, {encode_p}, {encode_gr}, {encode_cond2}, {encode_cond1}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [0], size: O(1) [0]
  encode_false: runtime: O(1) [0], size: O(1) [1]
  gr: runtime: ?, size: O(1) [2]

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

(37) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   cond1(z, z', z'') -{ 2 }-> cond2(2, z', 1 + (z'' - 1)) :|: z = 2, z' >= 0, z'' - 1 >= 0
   cond1(z, z', z'') -{ 2 }-> cond2(1, z', 0) :|: z = 2, z'' = 0, z' >= 0
   cond1(z, z', z'') -{ 1 }-> cond2(0, z', z'') :|: z = 2, z' >= 0, z'' >= 0
   cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(2, z', 0) :|: z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 3 }-> cond2(2, z', z'' - 1) :|: z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 3 }-> cond2(1, z', 0) :|: z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(1, z', 0) :|: z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(0, z', 0) :|: z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 1 }-> cond2(0, z', 0) :|: z = 2, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(0, z', z'' - 1) :|: z = 2, z'' - 1 >= 0, z' >= 0
   cond2(z, z', z'') -{ 2 }-> cond1(2, 0, z'') :|: z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 3 }-> cond1(2, z' - 1, z'') :|: z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 3 }-> cond1(1, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 2 }-> cond1(1, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 2 }-> cond1(0, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 1 }-> cond1(0, 0, z'') :|: z = 1, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 2 }-> cond1(0, z' - 1, z'') :|: z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encArg(z) -{ 1 }-> x :|: z = 1 + 2, x >= 0, 2 = 1 + x
   encArg(z) -{ 1 }-> x :|: z = 1 + 1, x >= 0, 1 = 1 + x
   encArg(z) -{ 0 }-> p(p(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> p(gr(encArg(x_1962), encArg(x_2577))) :|: x_2577 >= 0, z = 1 + (1 + x_1962 + x_2577), x_1962 >= 0
   encArg(z) -{ 0 }-> p(cond2(encArg(x_1961), encArg(x_2576), encArg(x_3384))) :|: x_3384 >= 0, x_2576 >= 0, z = 1 + (1 + x_1961 + x_2576 + x_3384), x_1961 >= 0
   encArg(z) -{ 0 }-> p(cond1(encArg(x_1960), encArg(x_2575), encArg(x_3383))) :|: x_1960 >= 0, x_2575 >= 0, x_3383 >= 0, z = 1 + (1 + x_1960 + x_2575 + x_3383)
   encArg(z) -{ 0 }-> p(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> gr(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 2 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 0, 0 = 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 1, v0 >= 0, 1 = 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 + encArg(z - 1) :|: z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_cond1(z, z', z'') -{ 0 }-> cond1(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_cond2(z, z', z'') -{ 0 }-> cond2(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_gr(z, z') -{ 0 }-> gr(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_p(z) -{ 1 }-> x :|: z = 2, x >= 0, 2 = 1 + x
   encode_p(z) -{ 1 }-> x :|: z = 1, x >= 0, 1 = 1 + x
   encode_p(z) -{ 0 }-> p(p(encArg(z - 1))) :|: z - 1 >= 0
   encode_p(z) -{ 0 }-> p(gr(encArg(x_11927), encArg(x_21156))) :|: z = 1 + x_11927 + x_21156, x_21156 >= 0, x_11927 >= 0
   encode_p(z) -{ 0 }-> p(cond2(encArg(x_11926), encArg(x_21155), encArg(x_3770))) :|: x_11926 >= 0, x_21155 >= 0, z = 1 + x_11926 + x_21155 + x_3770, x_3770 >= 0
   encode_p(z) -{ 0 }-> p(cond1(encArg(x_11925), encArg(x_21154), encArg(x_3769))) :|: z = 1 + x_11925 + x_21154 + x_3769, x_11925 >= 0, x_21154 >= 0, x_3769 >= 0
   encode_p(z) -{ 0 }-> p(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_p(z) -{ 0 }-> 0 :|: z >= 0
   encode_p(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 2 = v0
   encode_p(z) -{ 1 }-> 0 :|: z = 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z = 0, v0 >= 0, 0 = v0
   encode_p(z) -{ 0 }-> 0 :|: z = 1, v0 >= 0, 1 = v0
   encode_p(z) -{ 1 }-> 0 :|: z >= 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   gr(z, z') -{ 1 }-> gr(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
   gr(z, z') -{ 1 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 1 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 1 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {encode_true}, {cond2,cond1}, {p}, {encArg}, {encode_p}, {encode_gr}, {encode_cond2}, {encode_cond1}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [0], size: O(1) [0]
  encode_false: runtime: O(1) [0], size: O(1) [1]
  gr: runtime: O(n^1) [2 + z'], size: O(1) [2]

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

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

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

   cond1(z, z', z'') -{ 2 }-> cond2(2, z', 1 + (z'' - 1)) :|: z = 2, z' >= 0, z'' - 1 >= 0
   cond1(z, z', z'') -{ 2 }-> cond2(1, z', 0) :|: z = 2, z'' = 0, z' >= 0
   cond1(z, z', z'') -{ 1 }-> cond2(0, z', z'') :|: z = 2, z' >= 0, z'' >= 0
   cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(2, z', 0) :|: z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 3 }-> cond2(2, z', z'' - 1) :|: z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 3 }-> cond2(1, z', 0) :|: z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(1, z', 0) :|: z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(0, z', 0) :|: z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 1 }-> cond2(0, z', 0) :|: z = 2, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(0, z', z'' - 1) :|: z = 2, z'' - 1 >= 0, z' >= 0
   cond2(z, z', z'') -{ 2 }-> cond1(2, 0, z'') :|: z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 3 }-> cond1(2, z' - 1, z'') :|: z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 3 }-> cond1(1, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 2 }-> cond1(1, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 2 }-> cond1(0, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 1 }-> cond1(0, 0, z'') :|: z = 1, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 2 }-> cond1(0, z' - 1, z'') :|: z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encArg(z) -{ 1 }-> x :|: z = 1 + 2, x >= 0, 2 = 1 + x
   encArg(z) -{ 1 }-> x :|: z = 1 + 1, x >= 0, 1 = 1 + x
   encArg(z) -{ 0 }-> p(p(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> p(gr(encArg(x_1962), encArg(x_2577))) :|: x_2577 >= 0, z = 1 + (1 + x_1962 + x_2577), x_1962 >= 0
   encArg(z) -{ 0 }-> p(cond2(encArg(x_1961), encArg(x_2576), encArg(x_3384))) :|: x_3384 >= 0, x_2576 >= 0, z = 1 + (1 + x_1961 + x_2576 + x_3384), x_1961 >= 0
   encArg(z) -{ 0 }-> p(cond1(encArg(x_1960), encArg(x_2575), encArg(x_3383))) :|: x_1960 >= 0, x_2575 >= 0, x_3383 >= 0, z = 1 + (1 + x_1960 + x_2575 + x_3383)
   encArg(z) -{ 0 }-> p(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> gr(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 2 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 0, 0 = 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 1, v0 >= 0, 1 = 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 + encArg(z - 1) :|: z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_cond1(z, z', z'') -{ 0 }-> cond1(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_cond2(z, z', z'') -{ 0 }-> cond2(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_gr(z, z') -{ 0 }-> gr(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_p(z) -{ 1 }-> x :|: z = 2, x >= 0, 2 = 1 + x
   encode_p(z) -{ 1 }-> x :|: z = 1, x >= 0, 1 = 1 + x
   encode_p(z) -{ 0 }-> p(p(encArg(z - 1))) :|: z - 1 >= 0
   encode_p(z) -{ 0 }-> p(gr(encArg(x_11927), encArg(x_21156))) :|: z = 1 + x_11927 + x_21156, x_21156 >= 0, x_11927 >= 0
   encode_p(z) -{ 0 }-> p(cond2(encArg(x_11926), encArg(x_21155), encArg(x_3770))) :|: x_11926 >= 0, x_21155 >= 0, z = 1 + x_11926 + x_21155 + x_3770, x_3770 >= 0
   encode_p(z) -{ 0 }-> p(cond1(encArg(x_11925), encArg(x_21154), encArg(x_3769))) :|: z = 1 + x_11925 + x_21154 + x_3769, x_11925 >= 0, x_21154 >= 0, x_3769 >= 0
   encode_p(z) -{ 0 }-> p(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_p(z) -{ 0 }-> 0 :|: z >= 0
   encode_p(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 2 = v0
   encode_p(z) -{ 1 }-> 0 :|: z = 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z = 0, v0 >= 0, 0 = v0
   encode_p(z) -{ 0 }-> 0 :|: z = 1, v0 >= 0, 1 = v0
   encode_p(z) -{ 1 }-> 0 :|: z >= 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   gr(z, z') -{ 2 + z' }-> s :|: s >= 0, s <= 2, z - 1 >= 0, z' - 1 >= 0
   gr(z, z') -{ 1 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 1 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 1 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {encode_true}, {cond2,cond1}, {p}, {encArg}, {encode_p}, {encode_gr}, {encode_cond2}, {encode_cond1}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [0], size: O(1) [0]
  encode_false: runtime: O(1) [0], size: O(1) [1]
  gr: runtime: O(n^1) [2 + z'], size: O(1) [2]

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

(41) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   cond1(z, z', z'') -{ 2 }-> cond2(2, z', 1 + (z'' - 1)) :|: z = 2, z' >= 0, z'' - 1 >= 0
   cond1(z, z', z'') -{ 2 }-> cond2(1, z', 0) :|: z = 2, z'' = 0, z' >= 0
   cond1(z, z', z'') -{ 1 }-> cond2(0, z', z'') :|: z = 2, z' >= 0, z'' >= 0
   cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(2, z', 0) :|: z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 3 }-> cond2(2, z', z'' - 1) :|: z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 3 }-> cond2(1, z', 0) :|: z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(1, z', 0) :|: z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(0, z', 0) :|: z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 1 }-> cond2(0, z', 0) :|: z = 2, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(0, z', z'' - 1) :|: z = 2, z'' - 1 >= 0, z' >= 0
   cond2(z, z', z'') -{ 2 }-> cond1(2, 0, z'') :|: z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 3 }-> cond1(2, z' - 1, z'') :|: z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 3 }-> cond1(1, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 2 }-> cond1(1, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 2 }-> cond1(0, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 1 }-> cond1(0, 0, z'') :|: z = 1, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 2 }-> cond1(0, z' - 1, z'') :|: z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encArg(z) -{ 1 }-> x :|: z = 1 + 2, x >= 0, 2 = 1 + x
   encArg(z) -{ 1 }-> x :|: z = 1 + 1, x >= 0, 1 = 1 + x
   encArg(z) -{ 0 }-> p(p(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> p(gr(encArg(x_1962), encArg(x_2577))) :|: x_2577 >= 0, z = 1 + (1 + x_1962 + x_2577), x_1962 >= 0
   encArg(z) -{ 0 }-> p(cond2(encArg(x_1961), encArg(x_2576), encArg(x_3384))) :|: x_3384 >= 0, x_2576 >= 0, z = 1 + (1 + x_1961 + x_2576 + x_3384), x_1961 >= 0
   encArg(z) -{ 0 }-> p(cond1(encArg(x_1960), encArg(x_2575), encArg(x_3383))) :|: x_1960 >= 0, x_2575 >= 0, x_3383 >= 0, z = 1 + (1 + x_1960 + x_2575 + x_3383)
   encArg(z) -{ 0 }-> p(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> gr(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 2 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 0, 0 = 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 1, v0 >= 0, 1 = 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 + encArg(z - 1) :|: z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_cond1(z, z', z'') -{ 0 }-> cond1(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_cond2(z, z', z'') -{ 0 }-> cond2(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_gr(z, z') -{ 0 }-> gr(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_p(z) -{ 1 }-> x :|: z = 2, x >= 0, 2 = 1 + x
   encode_p(z) -{ 1 }-> x :|: z = 1, x >= 0, 1 = 1 + x
   encode_p(z) -{ 0 }-> p(p(encArg(z - 1))) :|: z - 1 >= 0
   encode_p(z) -{ 0 }-> p(gr(encArg(x_11927), encArg(x_21156))) :|: z = 1 + x_11927 + x_21156, x_21156 >= 0, x_11927 >= 0
   encode_p(z) -{ 0 }-> p(cond2(encArg(x_11926), encArg(x_21155), encArg(x_3770))) :|: x_11926 >= 0, x_21155 >= 0, z = 1 + x_11926 + x_21155 + x_3770, x_3770 >= 0
   encode_p(z) -{ 0 }-> p(cond1(encArg(x_11925), encArg(x_21154), encArg(x_3769))) :|: z = 1 + x_11925 + x_21154 + x_3769, x_11925 >= 0, x_21154 >= 0, x_3769 >= 0
   encode_p(z) -{ 0 }-> p(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_p(z) -{ 0 }-> 0 :|: z >= 0
   encode_p(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 2 = v0
   encode_p(z) -{ 1 }-> 0 :|: z = 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z = 0, v0 >= 0, 0 = v0
   encode_p(z) -{ 0 }-> 0 :|: z = 1, v0 >= 0, 1 = v0
   encode_p(z) -{ 1 }-> 0 :|: z >= 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   gr(z, z') -{ 2 + z' }-> s :|: s >= 0, s <= 2, z - 1 >= 0, z' - 1 >= 0
   gr(z, z') -{ 1 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 1 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 1 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {encode_true}, {cond2,cond1}, {p}, {encArg}, {encode_p}, {encode_gr}, {encode_cond2}, {encode_cond1}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [0], size: O(1) [0]
  encode_false: runtime: O(1) [0], size: O(1) [1]
  gr: runtime: O(n^1) [2 + z'], size: O(1) [2]
  encode_true: runtime: ?, size: O(1) [2]

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

(43) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   cond1(z, z', z'') -{ 2 }-> cond2(2, z', 1 + (z'' - 1)) :|: z = 2, z' >= 0, z'' - 1 >= 0
   cond1(z, z', z'') -{ 2 }-> cond2(1, z', 0) :|: z = 2, z'' = 0, z' >= 0
   cond1(z, z', z'') -{ 1 }-> cond2(0, z', z'') :|: z = 2, z' >= 0, z'' >= 0
   cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(2, z', 0) :|: z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 3 }-> cond2(2, z', z'' - 1) :|: z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 3 }-> cond2(1, z', 0) :|: z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(1, z', 0) :|: z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(0, z', 0) :|: z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 1 }-> cond2(0, z', 0) :|: z = 2, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(0, z', z'' - 1) :|: z = 2, z'' - 1 >= 0, z' >= 0
   cond2(z, z', z'') -{ 2 }-> cond1(2, 0, z'') :|: z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 3 }-> cond1(2, z' - 1, z'') :|: z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 3 }-> cond1(1, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 2 }-> cond1(1, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 2 }-> cond1(0, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 1 }-> cond1(0, 0, z'') :|: z = 1, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 2 }-> cond1(0, z' - 1, z'') :|: z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encArg(z) -{ 1 }-> x :|: z = 1 + 2, x >= 0, 2 = 1 + x
   encArg(z) -{ 1 }-> x :|: z = 1 + 1, x >= 0, 1 = 1 + x
   encArg(z) -{ 0 }-> p(p(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> p(gr(encArg(x_1962), encArg(x_2577))) :|: x_2577 >= 0, z = 1 + (1 + x_1962 + x_2577), x_1962 >= 0
   encArg(z) -{ 0 }-> p(cond2(encArg(x_1961), encArg(x_2576), encArg(x_3384))) :|: x_3384 >= 0, x_2576 >= 0, z = 1 + (1 + x_1961 + x_2576 + x_3384), x_1961 >= 0
   encArg(z) -{ 0 }-> p(cond1(encArg(x_1960), encArg(x_2575), encArg(x_3383))) :|: x_1960 >= 0, x_2575 >= 0, x_3383 >= 0, z = 1 + (1 + x_1960 + x_2575 + x_3383)
   encArg(z) -{ 0 }-> p(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> gr(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 2 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 0, 0 = 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 1, v0 >= 0, 1 = 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 + encArg(z - 1) :|: z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_cond1(z, z', z'') -{ 0 }-> cond1(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_cond2(z, z', z'') -{ 0 }-> cond2(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_gr(z, z') -{ 0 }-> gr(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_p(z) -{ 1 }-> x :|: z = 2, x >= 0, 2 = 1 + x
   encode_p(z) -{ 1 }-> x :|: z = 1, x >= 0, 1 = 1 + x
   encode_p(z) -{ 0 }-> p(p(encArg(z - 1))) :|: z - 1 >= 0
   encode_p(z) -{ 0 }-> p(gr(encArg(x_11927), encArg(x_21156))) :|: z = 1 + x_11927 + x_21156, x_21156 >= 0, x_11927 >= 0
   encode_p(z) -{ 0 }-> p(cond2(encArg(x_11926), encArg(x_21155), encArg(x_3770))) :|: x_11926 >= 0, x_21155 >= 0, z = 1 + x_11926 + x_21155 + x_3770, x_3770 >= 0
   encode_p(z) -{ 0 }-> p(cond1(encArg(x_11925), encArg(x_21154), encArg(x_3769))) :|: z = 1 + x_11925 + x_21154 + x_3769, x_11925 >= 0, x_21154 >= 0, x_3769 >= 0
   encode_p(z) -{ 0 }-> p(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_p(z) -{ 0 }-> 0 :|: z >= 0
   encode_p(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 2 = v0
   encode_p(z) -{ 1 }-> 0 :|: z = 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z = 0, v0 >= 0, 0 = v0
   encode_p(z) -{ 0 }-> 0 :|: z = 1, v0 >= 0, 1 = v0
   encode_p(z) -{ 1 }-> 0 :|: z >= 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   gr(z, z') -{ 2 + z' }-> s :|: s >= 0, s <= 2, z - 1 >= 0, z' - 1 >= 0
   gr(z, z') -{ 1 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 1 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 1 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {cond2,cond1}, {p}, {encArg}, {encode_p}, {encode_gr}, {encode_cond2}, {encode_cond1}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [0], size: O(1) [0]
  encode_false: runtime: O(1) [0], size: O(1) [1]
  gr: runtime: O(n^1) [2 + z'], size: O(1) [2]
  encode_true: runtime: O(1) [0], size: O(1) [2]

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

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

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

   cond1(z, z', z'') -{ 2 }-> cond2(2, z', 1 + (z'' - 1)) :|: z = 2, z' >= 0, z'' - 1 >= 0
   cond1(z, z', z'') -{ 2 }-> cond2(1, z', 0) :|: z = 2, z'' = 0, z' >= 0
   cond1(z, z', z'') -{ 1 }-> cond2(0, z', z'') :|: z = 2, z' >= 0, z'' >= 0
   cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(2, z', 0) :|: z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 3 }-> cond2(2, z', z'' - 1) :|: z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 3 }-> cond2(1, z', 0) :|: z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(1, z', 0) :|: z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(0, z', 0) :|: z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 1 }-> cond2(0, z', 0) :|: z = 2, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(0, z', z'' - 1) :|: z = 2, z'' - 1 >= 0, z' >= 0
   cond2(z, z', z'') -{ 2 }-> cond1(2, 0, z'') :|: z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 3 }-> cond1(2, z' - 1, z'') :|: z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 3 }-> cond1(1, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 2 }-> cond1(1, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 2 }-> cond1(0, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 1 }-> cond1(0, 0, z'') :|: z = 1, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 2 }-> cond1(0, z' - 1, z'') :|: z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encArg(z) -{ 1 }-> x :|: z = 1 + 2, x >= 0, 2 = 1 + x
   encArg(z) -{ 1 }-> x :|: z = 1 + 1, x >= 0, 1 = 1 + x
   encArg(z) -{ 0 }-> p(p(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> p(gr(encArg(x_1962), encArg(x_2577))) :|: x_2577 >= 0, z = 1 + (1 + x_1962 + x_2577), x_1962 >= 0
   encArg(z) -{ 0 }-> p(cond2(encArg(x_1961), encArg(x_2576), encArg(x_3384))) :|: x_3384 >= 0, x_2576 >= 0, z = 1 + (1 + x_1961 + x_2576 + x_3384), x_1961 >= 0
   encArg(z) -{ 0 }-> p(cond1(encArg(x_1960), encArg(x_2575), encArg(x_3383))) :|: x_1960 >= 0, x_2575 >= 0, x_3383 >= 0, z = 1 + (1 + x_1960 + x_2575 + x_3383)
   encArg(z) -{ 0 }-> p(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> gr(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 2 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 0, 0 = 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 1, v0 >= 0, 1 = 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 + encArg(z - 1) :|: z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_cond1(z, z', z'') -{ 0 }-> cond1(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_cond2(z, z', z'') -{ 0 }-> cond2(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_gr(z, z') -{ 0 }-> gr(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_p(z) -{ 1 }-> x :|: z = 2, x >= 0, 2 = 1 + x
   encode_p(z) -{ 1 }-> x :|: z = 1, x >= 0, 1 = 1 + x
   encode_p(z) -{ 0 }-> p(p(encArg(z - 1))) :|: z - 1 >= 0
   encode_p(z) -{ 0 }-> p(gr(encArg(x_11927), encArg(x_21156))) :|: z = 1 + x_11927 + x_21156, x_21156 >= 0, x_11927 >= 0
   encode_p(z) -{ 0 }-> p(cond2(encArg(x_11926), encArg(x_21155), encArg(x_3770))) :|: x_11926 >= 0, x_21155 >= 0, z = 1 + x_11926 + x_21155 + x_3770, x_3770 >= 0
   encode_p(z) -{ 0 }-> p(cond1(encArg(x_11925), encArg(x_21154), encArg(x_3769))) :|: z = 1 + x_11925 + x_21154 + x_3769, x_11925 >= 0, x_21154 >= 0, x_3769 >= 0
   encode_p(z) -{ 0 }-> p(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_p(z) -{ 0 }-> 0 :|: z >= 0
   encode_p(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 2 = v0
   encode_p(z) -{ 1 }-> 0 :|: z = 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z = 0, v0 >= 0, 0 = v0
   encode_p(z) -{ 0 }-> 0 :|: z = 1, v0 >= 0, 1 = v0
   encode_p(z) -{ 1 }-> 0 :|: z >= 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   gr(z, z') -{ 2 + z' }-> s :|: s >= 0, s <= 2, z - 1 >= 0, z' - 1 >= 0
   gr(z, z') -{ 1 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 1 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 1 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {cond2,cond1}, {p}, {encArg}, {encode_p}, {encode_gr}, {encode_cond2}, {encode_cond1}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [0], size: O(1) [0]
  encode_false: runtime: O(1) [0], size: O(1) [1]
  gr: runtime: O(n^1) [2 + z'], size: O(1) [2]
  encode_true: runtime: O(1) [0], size: O(1) [2]

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

(47) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using KoAT for: cond2
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 0

Computed SIZE bound using CoFloCo for: cond1
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 0

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

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

   cond1(z, z', z'') -{ 2 }-> cond2(2, z', 1 + (z'' - 1)) :|: z = 2, z' >= 0, z'' - 1 >= 0
   cond1(z, z', z'') -{ 2 }-> cond2(1, z', 0) :|: z = 2, z'' = 0, z' >= 0
   cond1(z, z', z'') -{ 1 }-> cond2(0, z', z'') :|: z = 2, z' >= 0, z'' >= 0
   cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(2, z', 0) :|: z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 3 }-> cond2(2, z', z'' - 1) :|: z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 3 }-> cond2(1, z', 0) :|: z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(1, z', 0) :|: z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(0, z', 0) :|: z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 1 }-> cond2(0, z', 0) :|: z = 2, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(0, z', z'' - 1) :|: z = 2, z'' - 1 >= 0, z' >= 0
   cond2(z, z', z'') -{ 2 }-> cond1(2, 0, z'') :|: z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 3 }-> cond1(2, z' - 1, z'') :|: z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 3 }-> cond1(1, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 2 }-> cond1(1, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 2 }-> cond1(0, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 1 }-> cond1(0, 0, z'') :|: z = 1, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 2 }-> cond1(0, z' - 1, z'') :|: z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encArg(z) -{ 1 }-> x :|: z = 1 + 2, x >= 0, 2 = 1 + x
   encArg(z) -{ 1 }-> x :|: z = 1 + 1, x >= 0, 1 = 1 + x
   encArg(z) -{ 0 }-> p(p(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> p(gr(encArg(x_1962), encArg(x_2577))) :|: x_2577 >= 0, z = 1 + (1 + x_1962 + x_2577), x_1962 >= 0
   encArg(z) -{ 0 }-> p(cond2(encArg(x_1961), encArg(x_2576), encArg(x_3384))) :|: x_3384 >= 0, x_2576 >= 0, z = 1 + (1 + x_1961 + x_2576 + x_3384), x_1961 >= 0
   encArg(z) -{ 0 }-> p(cond1(encArg(x_1960), encArg(x_2575), encArg(x_3383))) :|: x_1960 >= 0, x_2575 >= 0, x_3383 >= 0, z = 1 + (1 + x_1960 + x_2575 + x_3383)
   encArg(z) -{ 0 }-> p(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> gr(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 2 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 0, 0 = 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 1, v0 >= 0, 1 = 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 + encArg(z - 1) :|: z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_cond1(z, z', z'') -{ 0 }-> cond1(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_cond2(z, z', z'') -{ 0 }-> cond2(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_gr(z, z') -{ 0 }-> gr(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_p(z) -{ 1 }-> x :|: z = 2, x >= 0, 2 = 1 + x
   encode_p(z) -{ 1 }-> x :|: z = 1, x >= 0, 1 = 1 + x
   encode_p(z) -{ 0 }-> p(p(encArg(z - 1))) :|: z - 1 >= 0
   encode_p(z) -{ 0 }-> p(gr(encArg(x_11927), encArg(x_21156))) :|: z = 1 + x_11927 + x_21156, x_21156 >= 0, x_11927 >= 0
   encode_p(z) -{ 0 }-> p(cond2(encArg(x_11926), encArg(x_21155), encArg(x_3770))) :|: x_11926 >= 0, x_21155 >= 0, z = 1 + x_11926 + x_21155 + x_3770, x_3770 >= 0
   encode_p(z) -{ 0 }-> p(cond1(encArg(x_11925), encArg(x_21154), encArg(x_3769))) :|: z = 1 + x_11925 + x_21154 + x_3769, x_11925 >= 0, x_21154 >= 0, x_3769 >= 0
   encode_p(z) -{ 0 }-> p(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_p(z) -{ 0 }-> 0 :|: z >= 0
   encode_p(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 2 = v0
   encode_p(z) -{ 1 }-> 0 :|: z = 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z = 0, v0 >= 0, 0 = v0
   encode_p(z) -{ 0 }-> 0 :|: z = 1, v0 >= 0, 1 = v0
   encode_p(z) -{ 1 }-> 0 :|: z >= 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   gr(z, z') -{ 2 + z' }-> s :|: s >= 0, s <= 2, z - 1 >= 0, z' - 1 >= 0
   gr(z, z') -{ 1 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 1 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 1 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {cond2,cond1}, {p}, {encArg}, {encode_p}, {encode_gr}, {encode_cond2}, {encode_cond1}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [0], size: O(1) [0]
  encode_false: runtime: O(1) [0], size: O(1) [1]
  gr: runtime: O(n^1) [2 + z'], size: O(1) [2]
  encode_true: runtime: O(1) [0], size: O(1) [2]
  cond2: runtime: ?, size: O(1) [0]
  cond1: runtime: ?, size: O(1) [0]

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

(49) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using KoAT for: cond2
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 35*z + 105*z' + 35*z''

Computed RUNTIME bound using CoFloCo for: cond1
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 72 + 105*z' + 35*z''

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

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

   cond1(z, z', z'') -{ 2 }-> cond2(2, z', 1 + (z'' - 1)) :|: z = 2, z' >= 0, z'' - 1 >= 0
   cond1(z, z', z'') -{ 2 }-> cond2(1, z', 0) :|: z = 2, z'' = 0, z' >= 0
   cond1(z, z', z'') -{ 1 }-> cond2(0, z', z'') :|: z = 2, z' >= 0, z'' >= 0
   cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(2, z', 0) :|: z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 3 }-> cond2(2, z', z'' - 1) :|: z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 3 }-> cond2(1, z', 0) :|: z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(1, z', 0) :|: z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(0, z', 0) :|: z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 1 }-> cond2(0, z', 0) :|: z = 2, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 2 }-> cond2(0, z', z'' - 1) :|: z = 2, z'' - 1 >= 0, z' >= 0
   cond2(z, z', z'') -{ 2 }-> cond1(2, 0, z'') :|: z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 3 }-> cond1(2, z' - 1, z'') :|: z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 3 }-> cond1(1, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 2 }-> cond1(1, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 2 }-> cond1(0, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 1 }-> cond1(0, 0, z'') :|: z = 1, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 2 }-> cond1(0, z' - 1, z'') :|: z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encArg(z) -{ 1 }-> x :|: z = 1 + 2, x >= 0, 2 = 1 + x
   encArg(z) -{ 1 }-> x :|: z = 1 + 1, x >= 0, 1 = 1 + x
   encArg(z) -{ 0 }-> p(p(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> p(gr(encArg(x_1962), encArg(x_2577))) :|: x_2577 >= 0, z = 1 + (1 + x_1962 + x_2577), x_1962 >= 0
   encArg(z) -{ 0 }-> p(cond2(encArg(x_1961), encArg(x_2576), encArg(x_3384))) :|: x_3384 >= 0, x_2576 >= 0, z = 1 + (1 + x_1961 + x_2576 + x_3384), x_1961 >= 0
   encArg(z) -{ 0 }-> p(cond1(encArg(x_1960), encArg(x_2575), encArg(x_3383))) :|: x_1960 >= 0, x_2575 >= 0, x_3383 >= 0, z = 1 + (1 + x_1960 + x_2575 + x_3383)
   encArg(z) -{ 0 }-> p(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> gr(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 2 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 0, 0 = 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 1, v0 >= 0, 1 = 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 + encArg(z - 1) :|: z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_cond1(z, z', z'') -{ 0 }-> cond1(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_cond2(z, z', z'') -{ 0 }-> cond2(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_gr(z, z') -{ 0 }-> gr(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_p(z) -{ 1 }-> x :|: z = 2, x >= 0, 2 = 1 + x
   encode_p(z) -{ 1 }-> x :|: z = 1, x >= 0, 1 = 1 + x
   encode_p(z) -{ 0 }-> p(p(encArg(z - 1))) :|: z - 1 >= 0
   encode_p(z) -{ 0 }-> p(gr(encArg(x_11927), encArg(x_21156))) :|: z = 1 + x_11927 + x_21156, x_21156 >= 0, x_11927 >= 0
   encode_p(z) -{ 0 }-> p(cond2(encArg(x_11926), encArg(x_21155), encArg(x_3770))) :|: x_11926 >= 0, x_21155 >= 0, z = 1 + x_11926 + x_21155 + x_3770, x_3770 >= 0
   encode_p(z) -{ 0 }-> p(cond1(encArg(x_11925), encArg(x_21154), encArg(x_3769))) :|: z = 1 + x_11925 + x_21154 + x_3769, x_11925 >= 0, x_21154 >= 0, x_3769 >= 0
   encode_p(z) -{ 0 }-> p(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_p(z) -{ 0 }-> 0 :|: z >= 0
   encode_p(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 2 = v0
   encode_p(z) -{ 1 }-> 0 :|: z = 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z = 0, v0 >= 0, 0 = v0
   encode_p(z) -{ 0 }-> 0 :|: z = 1, v0 >= 0, 1 = v0
   encode_p(z) -{ 1 }-> 0 :|: z >= 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   gr(z, z') -{ 2 + z' }-> s :|: s >= 0, s <= 2, z - 1 >= 0, z' - 1 >= 0
   gr(z, z') -{ 1 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 1 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 1 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {p}, {encArg}, {encode_p}, {encode_gr}, {encode_cond2}, {encode_cond1}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [0], size: O(1) [0]
  encode_false: runtime: O(1) [0], size: O(1) [1]
  gr: runtime: O(n^1) [2 + z'], size: O(1) [2]
  encode_true: runtime: O(1) [0], size: O(1) [2]
  cond2: runtime: O(n^1) [35*z + 105*z' + 35*z''], size: O(1) [0]
  cond1: runtime: O(n^1) [72 + 105*z' + 35*z''], size: O(1) [0]

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

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

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

   cond1(z, z', z'') -{ 37 + 105*z' }-> s' :|: s' >= 0, s' <= 0, z = 2, z'' = 0, z' >= 0
   cond1(z, z', z'') -{ 72 + 105*z' + 35*z'' }-> s'' :|: s'' >= 0, s'' <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   cond1(z, z', z'') -{ 1 + 105*z' + 35*z'' }-> s1 :|: s1 >= 0, s1 <= 0, z = 2, z' >= 0, z'' >= 0
   cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 74 + 35*z'' }-> s10 :|: s10 >= 0, s10 <= 0, z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ -30 + 105*z' + 35*z'' }-> s11 :|: s11 >= 0, s11 <= 0, z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 74 + 35*z'' }-> s12 :|: s12 >= 0, s12 <= 0, z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 74 + 35*z'' }-> s13 :|: s13 >= 0, s13 <= 0, z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ -31 + 105*z' + 35*z'' }-> s14 :|: s14 >= 0, s14 <= 0, z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 73 + 35*z'' }-> s15 :|: s15 >= 0, s15 <= 0, z = 1, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 38 + 105*z' }-> s2 :|: s2 >= 0, s2 <= 0, z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 37 + 105*z' }-> s3 :|: s3 >= 0, s3 <= 0, z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 38 + 105*z' + 35*z'' }-> s4 :|: s4 >= 0, s4 <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 72 + 105*z' }-> s5 :|: s5 >= 0, s5 <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 2 + 105*z' }-> s6 :|: s6 >= 0, s6 <= 0, z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ -33 + 105*z' + 35*z'' }-> s7 :|: s7 >= 0, s7 <= 0, z = 2, z'' - 1 >= 0, z' >= 0
   cond2(z, z', z'') -{ 1 + 105*z' }-> s8 :|: s8 >= 0, s8 <= 0, z = 2, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 75 + 35*z'' }-> s9 :|: s9 >= 0, s9 <= 0, z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encArg(z) -{ 1 }-> x :|: z = 1 + 2, x >= 0, 2 = 1 + x
   encArg(z) -{ 1 }-> x :|: z = 1 + 1, x >= 0, 1 = 1 + x
   encArg(z) -{ 0 }-> p(p(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> p(gr(encArg(x_1962), encArg(x_2577))) :|: x_2577 >= 0, z = 1 + (1 + x_1962 + x_2577), x_1962 >= 0
   encArg(z) -{ 0 }-> p(cond2(encArg(x_1961), encArg(x_2576), encArg(x_3384))) :|: x_3384 >= 0, x_2576 >= 0, z = 1 + (1 + x_1961 + x_2576 + x_3384), x_1961 >= 0
   encArg(z) -{ 0 }-> p(cond1(encArg(x_1960), encArg(x_2575), encArg(x_3383))) :|: x_1960 >= 0, x_2575 >= 0, x_3383 >= 0, z = 1 + (1 + x_1960 + x_2575 + x_3383)
   encArg(z) -{ 0 }-> p(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> gr(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 2 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 0, 0 = 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 1, v0 >= 0, 1 = 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 + encArg(z - 1) :|: z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_cond1(z, z', z'') -{ 0 }-> cond1(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_cond2(z, z', z'') -{ 0 }-> cond2(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_gr(z, z') -{ 0 }-> gr(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_p(z) -{ 1 }-> x :|: z = 2, x >= 0, 2 = 1 + x
   encode_p(z) -{ 1 }-> x :|: z = 1, x >= 0, 1 = 1 + x
   encode_p(z) -{ 0 }-> p(p(encArg(z - 1))) :|: z - 1 >= 0
   encode_p(z) -{ 0 }-> p(gr(encArg(x_11927), encArg(x_21156))) :|: z = 1 + x_11927 + x_21156, x_21156 >= 0, x_11927 >= 0
   encode_p(z) -{ 0 }-> p(cond2(encArg(x_11926), encArg(x_21155), encArg(x_3770))) :|: x_11926 >= 0, x_21155 >= 0, z = 1 + x_11926 + x_21155 + x_3770, x_3770 >= 0
   encode_p(z) -{ 0 }-> p(cond1(encArg(x_11925), encArg(x_21154), encArg(x_3769))) :|: z = 1 + x_11925 + x_21154 + x_3769, x_11925 >= 0, x_21154 >= 0, x_3769 >= 0
   encode_p(z) -{ 0 }-> p(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_p(z) -{ 0 }-> 0 :|: z >= 0
   encode_p(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 2 = v0
   encode_p(z) -{ 1 }-> 0 :|: z = 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z = 0, v0 >= 0, 0 = v0
   encode_p(z) -{ 0 }-> 0 :|: z = 1, v0 >= 0, 1 = v0
   encode_p(z) -{ 1 }-> 0 :|: z >= 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   gr(z, z') -{ 2 + z' }-> s :|: s >= 0, s <= 2, z - 1 >= 0, z' - 1 >= 0
   gr(z, z') -{ 1 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 1 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 1 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {p}, {encArg}, {encode_p}, {encode_gr}, {encode_cond2}, {encode_cond1}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [0], size: O(1) [0]
  encode_false: runtime: O(1) [0], size: O(1) [1]
  gr: runtime: O(n^1) [2 + z'], size: O(1) [2]
  encode_true: runtime: O(1) [0], size: O(1) [2]
  cond2: runtime: O(n^1) [35*z + 105*z' + 35*z''], size: O(1) [0]
  cond1: runtime: O(n^1) [72 + 105*z' + 35*z''], size: O(1) [0]

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

(53) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   cond1(z, z', z'') -{ 37 + 105*z' }-> s' :|: s' >= 0, s' <= 0, z = 2, z'' = 0, z' >= 0
   cond1(z, z', z'') -{ 72 + 105*z' + 35*z'' }-> s'' :|: s'' >= 0, s'' <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   cond1(z, z', z'') -{ 1 + 105*z' + 35*z'' }-> s1 :|: s1 >= 0, s1 <= 0, z = 2, z' >= 0, z'' >= 0
   cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 74 + 35*z'' }-> s10 :|: s10 >= 0, s10 <= 0, z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ -30 + 105*z' + 35*z'' }-> s11 :|: s11 >= 0, s11 <= 0, z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 74 + 35*z'' }-> s12 :|: s12 >= 0, s12 <= 0, z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 74 + 35*z'' }-> s13 :|: s13 >= 0, s13 <= 0, z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ -31 + 105*z' + 35*z'' }-> s14 :|: s14 >= 0, s14 <= 0, z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 73 + 35*z'' }-> s15 :|: s15 >= 0, s15 <= 0, z = 1, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 38 + 105*z' }-> s2 :|: s2 >= 0, s2 <= 0, z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 37 + 105*z' }-> s3 :|: s3 >= 0, s3 <= 0, z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 38 + 105*z' + 35*z'' }-> s4 :|: s4 >= 0, s4 <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 72 + 105*z' }-> s5 :|: s5 >= 0, s5 <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 2 + 105*z' }-> s6 :|: s6 >= 0, s6 <= 0, z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ -33 + 105*z' + 35*z'' }-> s7 :|: s7 >= 0, s7 <= 0, z = 2, z'' - 1 >= 0, z' >= 0
   cond2(z, z', z'') -{ 1 + 105*z' }-> s8 :|: s8 >= 0, s8 <= 0, z = 2, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 75 + 35*z'' }-> s9 :|: s9 >= 0, s9 <= 0, z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encArg(z) -{ 1 }-> x :|: z = 1 + 2, x >= 0, 2 = 1 + x
   encArg(z) -{ 1 }-> x :|: z = 1 + 1, x >= 0, 1 = 1 + x
   encArg(z) -{ 0 }-> p(p(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> p(gr(encArg(x_1962), encArg(x_2577))) :|: x_2577 >= 0, z = 1 + (1 + x_1962 + x_2577), x_1962 >= 0
   encArg(z) -{ 0 }-> p(cond2(encArg(x_1961), encArg(x_2576), encArg(x_3384))) :|: x_3384 >= 0, x_2576 >= 0, z = 1 + (1 + x_1961 + x_2576 + x_3384), x_1961 >= 0
   encArg(z) -{ 0 }-> p(cond1(encArg(x_1960), encArg(x_2575), encArg(x_3383))) :|: x_1960 >= 0, x_2575 >= 0, x_3383 >= 0, z = 1 + (1 + x_1960 + x_2575 + x_3383)
   encArg(z) -{ 0 }-> p(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> gr(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 2 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 0, 0 = 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 1, v0 >= 0, 1 = 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 + encArg(z - 1) :|: z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_cond1(z, z', z'') -{ 0 }-> cond1(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_cond2(z, z', z'') -{ 0 }-> cond2(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_gr(z, z') -{ 0 }-> gr(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_p(z) -{ 1 }-> x :|: z = 2, x >= 0, 2 = 1 + x
   encode_p(z) -{ 1 }-> x :|: z = 1, x >= 0, 1 = 1 + x
   encode_p(z) -{ 0 }-> p(p(encArg(z - 1))) :|: z - 1 >= 0
   encode_p(z) -{ 0 }-> p(gr(encArg(x_11927), encArg(x_21156))) :|: z = 1 + x_11927 + x_21156, x_21156 >= 0, x_11927 >= 0
   encode_p(z) -{ 0 }-> p(cond2(encArg(x_11926), encArg(x_21155), encArg(x_3770))) :|: x_11926 >= 0, x_21155 >= 0, z = 1 + x_11926 + x_21155 + x_3770, x_3770 >= 0
   encode_p(z) -{ 0 }-> p(cond1(encArg(x_11925), encArg(x_21154), encArg(x_3769))) :|: z = 1 + x_11925 + x_21154 + x_3769, x_11925 >= 0, x_21154 >= 0, x_3769 >= 0
   encode_p(z) -{ 0 }-> p(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_p(z) -{ 0 }-> 0 :|: z >= 0
   encode_p(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 2 = v0
   encode_p(z) -{ 1 }-> 0 :|: z = 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z = 0, v0 >= 0, 0 = v0
   encode_p(z) -{ 0 }-> 0 :|: z = 1, v0 >= 0, 1 = v0
   encode_p(z) -{ 1 }-> 0 :|: z >= 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   gr(z, z') -{ 2 + z' }-> s :|: s >= 0, s <= 2, z - 1 >= 0, z' - 1 >= 0
   gr(z, z') -{ 1 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 1 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 1 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {p}, {encArg}, {encode_p}, {encode_gr}, {encode_cond2}, {encode_cond1}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [0], size: O(1) [0]
  encode_false: runtime: O(1) [0], size: O(1) [1]
  gr: runtime: O(n^1) [2 + z'], size: O(1) [2]
  encode_true: runtime: O(1) [0], size: O(1) [2]
  cond2: runtime: O(n^1) [35*z + 105*z' + 35*z''], size: O(1) [0]
  cond1: runtime: O(n^1) [72 + 105*z' + 35*z''], size: O(1) [0]
  p: runtime: ?, size: O(n^1) [z]

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

(55) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   cond1(z, z', z'') -{ 37 + 105*z' }-> s' :|: s' >= 0, s' <= 0, z = 2, z'' = 0, z' >= 0
   cond1(z, z', z'') -{ 72 + 105*z' + 35*z'' }-> s'' :|: s'' >= 0, s'' <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   cond1(z, z', z'') -{ 1 + 105*z' + 35*z'' }-> s1 :|: s1 >= 0, s1 <= 0, z = 2, z' >= 0, z'' >= 0
   cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 74 + 35*z'' }-> s10 :|: s10 >= 0, s10 <= 0, z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ -30 + 105*z' + 35*z'' }-> s11 :|: s11 >= 0, s11 <= 0, z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 74 + 35*z'' }-> s12 :|: s12 >= 0, s12 <= 0, z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 74 + 35*z'' }-> s13 :|: s13 >= 0, s13 <= 0, z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ -31 + 105*z' + 35*z'' }-> s14 :|: s14 >= 0, s14 <= 0, z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 73 + 35*z'' }-> s15 :|: s15 >= 0, s15 <= 0, z = 1, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 38 + 105*z' }-> s2 :|: s2 >= 0, s2 <= 0, z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 37 + 105*z' }-> s3 :|: s3 >= 0, s3 <= 0, z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 38 + 105*z' + 35*z'' }-> s4 :|: s4 >= 0, s4 <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 72 + 105*z' }-> s5 :|: s5 >= 0, s5 <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 2 + 105*z' }-> s6 :|: s6 >= 0, s6 <= 0, z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ -33 + 105*z' + 35*z'' }-> s7 :|: s7 >= 0, s7 <= 0, z = 2, z'' - 1 >= 0, z' >= 0
   cond2(z, z', z'') -{ 1 + 105*z' }-> s8 :|: s8 >= 0, s8 <= 0, z = 2, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 75 + 35*z'' }-> s9 :|: s9 >= 0, s9 <= 0, z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encArg(z) -{ 1 }-> x :|: z = 1 + 2, x >= 0, 2 = 1 + x
   encArg(z) -{ 1 }-> x :|: z = 1 + 1, x >= 0, 1 = 1 + x
   encArg(z) -{ 0 }-> p(p(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> p(gr(encArg(x_1962), encArg(x_2577))) :|: x_2577 >= 0, z = 1 + (1 + x_1962 + x_2577), x_1962 >= 0
   encArg(z) -{ 0 }-> p(cond2(encArg(x_1961), encArg(x_2576), encArg(x_3384))) :|: x_3384 >= 0, x_2576 >= 0, z = 1 + (1 + x_1961 + x_2576 + x_3384), x_1961 >= 0
   encArg(z) -{ 0 }-> p(cond1(encArg(x_1960), encArg(x_2575), encArg(x_3383))) :|: x_1960 >= 0, x_2575 >= 0, x_3383 >= 0, z = 1 + (1 + x_1960 + x_2575 + x_3383)
   encArg(z) -{ 0 }-> p(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> gr(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 2 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 0, 0 = 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 1, v0 >= 0, 1 = 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 + encArg(z - 1) :|: z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_cond1(z, z', z'') -{ 0 }-> cond1(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_cond2(z, z', z'') -{ 0 }-> cond2(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_gr(z, z') -{ 0 }-> gr(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_p(z) -{ 1 }-> x :|: z = 2, x >= 0, 2 = 1 + x
   encode_p(z) -{ 1 }-> x :|: z = 1, x >= 0, 1 = 1 + x
   encode_p(z) -{ 0 }-> p(p(encArg(z - 1))) :|: z - 1 >= 0
   encode_p(z) -{ 0 }-> p(gr(encArg(x_11927), encArg(x_21156))) :|: z = 1 + x_11927 + x_21156, x_21156 >= 0, x_11927 >= 0
   encode_p(z) -{ 0 }-> p(cond2(encArg(x_11926), encArg(x_21155), encArg(x_3770))) :|: x_11926 >= 0, x_21155 >= 0, z = 1 + x_11926 + x_21155 + x_3770, x_3770 >= 0
   encode_p(z) -{ 0 }-> p(cond1(encArg(x_11925), encArg(x_21154), encArg(x_3769))) :|: z = 1 + x_11925 + x_21154 + x_3769, x_11925 >= 0, x_21154 >= 0, x_3769 >= 0
   encode_p(z) -{ 0 }-> p(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_p(z) -{ 0 }-> 0 :|: z >= 0
   encode_p(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 2 = v0
   encode_p(z) -{ 1 }-> 0 :|: z = 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z = 0, v0 >= 0, 0 = v0
   encode_p(z) -{ 0 }-> 0 :|: z = 1, v0 >= 0, 1 = v0
   encode_p(z) -{ 1 }-> 0 :|: z >= 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   gr(z, z') -{ 2 + z' }-> s :|: s >= 0, s <= 2, z - 1 >= 0, z' - 1 >= 0
   gr(z, z') -{ 1 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 1 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 1 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {encArg}, {encode_p}, {encode_gr}, {encode_cond2}, {encode_cond1}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [0], size: O(1) [0]
  encode_false: runtime: O(1) [0], size: O(1) [1]
  gr: runtime: O(n^1) [2 + z'], size: O(1) [2]
  encode_true: runtime: O(1) [0], size: O(1) [2]
  cond2: runtime: O(n^1) [35*z + 105*z' + 35*z''], size: O(1) [0]
  cond1: runtime: O(n^1) [72 + 105*z' + 35*z''], size: O(1) [0]
  p: runtime: O(1) [1], size: O(n^1) [z]

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

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

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

   cond1(z, z', z'') -{ 37 + 105*z' }-> s' :|: s' >= 0, s' <= 0, z = 2, z'' = 0, z' >= 0
   cond1(z, z', z'') -{ 72 + 105*z' + 35*z'' }-> s'' :|: s'' >= 0, s'' <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   cond1(z, z', z'') -{ 1 + 105*z' + 35*z'' }-> s1 :|: s1 >= 0, s1 <= 0, z = 2, z' >= 0, z'' >= 0
   cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 74 + 35*z'' }-> s10 :|: s10 >= 0, s10 <= 0, z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ -30 + 105*z' + 35*z'' }-> s11 :|: s11 >= 0, s11 <= 0, z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 74 + 35*z'' }-> s12 :|: s12 >= 0, s12 <= 0, z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 74 + 35*z'' }-> s13 :|: s13 >= 0, s13 <= 0, z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ -31 + 105*z' + 35*z'' }-> s14 :|: s14 >= 0, s14 <= 0, z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 73 + 35*z'' }-> s15 :|: s15 >= 0, s15 <= 0, z = 1, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 38 + 105*z' }-> s2 :|: s2 >= 0, s2 <= 0, z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 37 + 105*z' }-> s3 :|: s3 >= 0, s3 <= 0, z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 38 + 105*z' + 35*z'' }-> s4 :|: s4 >= 0, s4 <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 72 + 105*z' }-> s5 :|: s5 >= 0, s5 <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 2 + 105*z' }-> s6 :|: s6 >= 0, s6 <= 0, z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ -33 + 105*z' + 35*z'' }-> s7 :|: s7 >= 0, s7 <= 0, z = 2, z'' - 1 >= 0, z' >= 0
   cond2(z, z', z'') -{ 1 + 105*z' }-> s8 :|: s8 >= 0, s8 <= 0, z = 2, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 75 + 35*z'' }-> s9 :|: s9 >= 0, s9 <= 0, z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encArg(z) -{ 1 }-> x :|: z = 1 + 2, x >= 0, 2 = 1 + x
   encArg(z) -{ 1 }-> x :|: z = 1 + 1, x >= 0, 1 = 1 + x
   encArg(z) -{ 0 }-> p(p(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> p(gr(encArg(x_1962), encArg(x_2577))) :|: x_2577 >= 0, z = 1 + (1 + x_1962 + x_2577), x_1962 >= 0
   encArg(z) -{ 0 }-> p(cond2(encArg(x_1961), encArg(x_2576), encArg(x_3384))) :|: x_3384 >= 0, x_2576 >= 0, z = 1 + (1 + x_1961 + x_2576 + x_3384), x_1961 >= 0
   encArg(z) -{ 0 }-> p(cond1(encArg(x_1960), encArg(x_2575), encArg(x_3383))) :|: x_1960 >= 0, x_2575 >= 0, x_3383 >= 0, z = 1 + (1 + x_1960 + x_2575 + x_3383)
   encArg(z) -{ 0 }-> p(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> gr(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 2 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 0, 0 = 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 1, v0 >= 0, 1 = 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 + encArg(z - 1) :|: z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_cond1(z, z', z'') -{ 0 }-> cond1(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_cond2(z, z', z'') -{ 0 }-> cond2(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_gr(z, z') -{ 0 }-> gr(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_p(z) -{ 1 }-> x :|: z = 2, x >= 0, 2 = 1 + x
   encode_p(z) -{ 1 }-> x :|: z = 1, x >= 0, 1 = 1 + x
   encode_p(z) -{ 0 }-> p(p(encArg(z - 1))) :|: z - 1 >= 0
   encode_p(z) -{ 0 }-> p(gr(encArg(x_11927), encArg(x_21156))) :|: z = 1 + x_11927 + x_21156, x_21156 >= 0, x_11927 >= 0
   encode_p(z) -{ 0 }-> p(cond2(encArg(x_11926), encArg(x_21155), encArg(x_3770))) :|: x_11926 >= 0, x_21155 >= 0, z = 1 + x_11926 + x_21155 + x_3770, x_3770 >= 0
   encode_p(z) -{ 0 }-> p(cond1(encArg(x_11925), encArg(x_21154), encArg(x_3769))) :|: z = 1 + x_11925 + x_21154 + x_3769, x_11925 >= 0, x_21154 >= 0, x_3769 >= 0
   encode_p(z) -{ 0 }-> p(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_p(z) -{ 0 }-> 0 :|: z >= 0
   encode_p(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 2 = v0
   encode_p(z) -{ 1 }-> 0 :|: z = 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z = 0, v0 >= 0, 0 = v0
   encode_p(z) -{ 0 }-> 0 :|: z = 1, v0 >= 0, 1 = v0
   encode_p(z) -{ 1 }-> 0 :|: z >= 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   gr(z, z') -{ 2 + z' }-> s :|: s >= 0, s <= 2, z - 1 >= 0, z' - 1 >= 0
   gr(z, z') -{ 1 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 1 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 1 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {encArg}, {encode_p}, {encode_gr}, {encode_cond2}, {encode_cond1}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [0], size: O(1) [0]
  encode_false: runtime: O(1) [0], size: O(1) [1]
  gr: runtime: O(n^1) [2 + z'], size: O(1) [2]
  encode_true: runtime: O(1) [0], size: O(1) [2]
  cond2: runtime: O(n^1) [35*z + 105*z' + 35*z''], size: O(1) [0]
  cond1: runtime: O(n^1) [72 + 105*z' + 35*z''], size: O(1) [0]
  p: runtime: O(1) [1], size: O(n^1) [z]

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

(59) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   cond1(z, z', z'') -{ 37 + 105*z' }-> s' :|: s' >= 0, s' <= 0, z = 2, z'' = 0, z' >= 0
   cond1(z, z', z'') -{ 72 + 105*z' + 35*z'' }-> s'' :|: s'' >= 0, s'' <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   cond1(z, z', z'') -{ 1 + 105*z' + 35*z'' }-> s1 :|: s1 >= 0, s1 <= 0, z = 2, z' >= 0, z'' >= 0
   cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 74 + 35*z'' }-> s10 :|: s10 >= 0, s10 <= 0, z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ -30 + 105*z' + 35*z'' }-> s11 :|: s11 >= 0, s11 <= 0, z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 74 + 35*z'' }-> s12 :|: s12 >= 0, s12 <= 0, z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 74 + 35*z'' }-> s13 :|: s13 >= 0, s13 <= 0, z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ -31 + 105*z' + 35*z'' }-> s14 :|: s14 >= 0, s14 <= 0, z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 73 + 35*z'' }-> s15 :|: s15 >= 0, s15 <= 0, z = 1, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 38 + 105*z' }-> s2 :|: s2 >= 0, s2 <= 0, z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 37 + 105*z' }-> s3 :|: s3 >= 0, s3 <= 0, z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 38 + 105*z' + 35*z'' }-> s4 :|: s4 >= 0, s4 <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 72 + 105*z' }-> s5 :|: s5 >= 0, s5 <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 2 + 105*z' }-> s6 :|: s6 >= 0, s6 <= 0, z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ -33 + 105*z' + 35*z'' }-> s7 :|: s7 >= 0, s7 <= 0, z = 2, z'' - 1 >= 0, z' >= 0
   cond2(z, z', z'') -{ 1 + 105*z' }-> s8 :|: s8 >= 0, s8 <= 0, z = 2, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 75 + 35*z'' }-> s9 :|: s9 >= 0, s9 <= 0, z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encArg(z) -{ 1 }-> x :|: z = 1 + 2, x >= 0, 2 = 1 + x
   encArg(z) -{ 1 }-> x :|: z = 1 + 1, x >= 0, 1 = 1 + x
   encArg(z) -{ 0 }-> p(p(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> p(gr(encArg(x_1962), encArg(x_2577))) :|: x_2577 >= 0, z = 1 + (1 + x_1962 + x_2577), x_1962 >= 0
   encArg(z) -{ 0 }-> p(cond2(encArg(x_1961), encArg(x_2576), encArg(x_3384))) :|: x_3384 >= 0, x_2576 >= 0, z = 1 + (1 + x_1961 + x_2576 + x_3384), x_1961 >= 0
   encArg(z) -{ 0 }-> p(cond1(encArg(x_1960), encArg(x_2575), encArg(x_3383))) :|: x_1960 >= 0, x_2575 >= 0, x_3383 >= 0, z = 1 + (1 + x_1960 + x_2575 + x_3383)
   encArg(z) -{ 0 }-> p(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> gr(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 2 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 0, 0 = 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 1, v0 >= 0, 1 = 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 + encArg(z - 1) :|: z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_cond1(z, z', z'') -{ 0 }-> cond1(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_cond2(z, z', z'') -{ 0 }-> cond2(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_gr(z, z') -{ 0 }-> gr(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_p(z) -{ 1 }-> x :|: z = 2, x >= 0, 2 = 1 + x
   encode_p(z) -{ 1 }-> x :|: z = 1, x >= 0, 1 = 1 + x
   encode_p(z) -{ 0 }-> p(p(encArg(z - 1))) :|: z - 1 >= 0
   encode_p(z) -{ 0 }-> p(gr(encArg(x_11927), encArg(x_21156))) :|: z = 1 + x_11927 + x_21156, x_21156 >= 0, x_11927 >= 0
   encode_p(z) -{ 0 }-> p(cond2(encArg(x_11926), encArg(x_21155), encArg(x_3770))) :|: x_11926 >= 0, x_21155 >= 0, z = 1 + x_11926 + x_21155 + x_3770, x_3770 >= 0
   encode_p(z) -{ 0 }-> p(cond1(encArg(x_11925), encArg(x_21154), encArg(x_3769))) :|: z = 1 + x_11925 + x_21154 + x_3769, x_11925 >= 0, x_21154 >= 0, x_3769 >= 0
   encode_p(z) -{ 0 }-> p(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_p(z) -{ 0 }-> 0 :|: z >= 0
   encode_p(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 2 = v0
   encode_p(z) -{ 1 }-> 0 :|: z = 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z = 0, v0 >= 0, 0 = v0
   encode_p(z) -{ 0 }-> 0 :|: z = 1, v0 >= 0, 1 = v0
   encode_p(z) -{ 1 }-> 0 :|: z >= 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   gr(z, z') -{ 2 + z' }-> s :|: s >= 0, s <= 2, z - 1 >= 0, z' - 1 >= 0
   gr(z, z') -{ 1 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 1 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 1 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {encArg}, {encode_p}, {encode_gr}, {encode_cond2}, {encode_cond1}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [0], size: O(1) [0]
  encode_false: runtime: O(1) [0], size: O(1) [1]
  gr: runtime: O(n^1) [2 + z'], size: O(1) [2]
  encode_true: runtime: O(1) [0], size: O(1) [2]
  cond2: runtime: O(n^1) [35*z + 105*z' + 35*z''], size: O(1) [0]
  cond1: runtime: O(n^1) [72 + 105*z' + 35*z''], size: O(1) [0]
  p: runtime: O(1) [1], size: O(n^1) [z]
  encArg: runtime: ?, size: O(n^1) [1 + z]

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

(61) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: encArg
after applying outer abstraction to obtain an ITS,
resulting in: O(n^2) with polynomial bound: 1 + 107*z + 105*z^2

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

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

   cond1(z, z', z'') -{ 37 + 105*z' }-> s' :|: s' >= 0, s' <= 0, z = 2, z'' = 0, z' >= 0
   cond1(z, z', z'') -{ 72 + 105*z' + 35*z'' }-> s'' :|: s'' >= 0, s'' <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   cond1(z, z', z'') -{ 1 + 105*z' + 35*z'' }-> s1 :|: s1 >= 0, s1 <= 0, z = 2, z' >= 0, z'' >= 0
   cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 74 + 35*z'' }-> s10 :|: s10 >= 0, s10 <= 0, z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ -30 + 105*z' + 35*z'' }-> s11 :|: s11 >= 0, s11 <= 0, z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 74 + 35*z'' }-> s12 :|: s12 >= 0, s12 <= 0, z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 74 + 35*z'' }-> s13 :|: s13 >= 0, s13 <= 0, z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ -31 + 105*z' + 35*z'' }-> s14 :|: s14 >= 0, s14 <= 0, z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 73 + 35*z'' }-> s15 :|: s15 >= 0, s15 <= 0, z = 1, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 38 + 105*z' }-> s2 :|: s2 >= 0, s2 <= 0, z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 37 + 105*z' }-> s3 :|: s3 >= 0, s3 <= 0, z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 38 + 105*z' + 35*z'' }-> s4 :|: s4 >= 0, s4 <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 72 + 105*z' }-> s5 :|: s5 >= 0, s5 <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 2 + 105*z' }-> s6 :|: s6 >= 0, s6 <= 0, z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ -33 + 105*z' + 35*z'' }-> s7 :|: s7 >= 0, s7 <= 0, z = 2, z'' - 1 >= 0, z' >= 0
   cond2(z, z', z'') -{ 1 + 105*z' }-> s8 :|: s8 >= 0, s8 <= 0, z = 2, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 75 + 35*z'' }-> s9 :|: s9 >= 0, s9 <= 0, z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encArg(z) -{ 1 }-> x :|: z = 1 + 2, x >= 0, 2 = 1 + x
   encArg(z) -{ 1 }-> x :|: z = 1 + 1, x >= 0, 1 = 1 + x
   encArg(z) -{ 0 }-> p(p(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> p(gr(encArg(x_1962), encArg(x_2577))) :|: x_2577 >= 0, z = 1 + (1 + x_1962 + x_2577), x_1962 >= 0
   encArg(z) -{ 0 }-> p(cond2(encArg(x_1961), encArg(x_2576), encArg(x_3384))) :|: x_3384 >= 0, x_2576 >= 0, z = 1 + (1 + x_1961 + x_2576 + x_3384), x_1961 >= 0
   encArg(z) -{ 0 }-> p(cond1(encArg(x_1960), encArg(x_2575), encArg(x_3383))) :|: x_1960 >= 0, x_2575 >= 0, x_3383 >= 0, z = 1 + (1 + x_1960 + x_2575 + x_3383)
   encArg(z) -{ 0 }-> p(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> gr(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 2 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 0, 0 = 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 1, v0 >= 0, 1 = 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 + encArg(z - 1) :|: z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_cond1(z, z', z'') -{ 0 }-> cond1(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_cond2(z, z', z'') -{ 0 }-> cond2(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_gr(z, z') -{ 0 }-> gr(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_p(z) -{ 1 }-> x :|: z = 2, x >= 0, 2 = 1 + x
   encode_p(z) -{ 1 }-> x :|: z = 1, x >= 0, 1 = 1 + x
   encode_p(z) -{ 0 }-> p(p(encArg(z - 1))) :|: z - 1 >= 0
   encode_p(z) -{ 0 }-> p(gr(encArg(x_11927), encArg(x_21156))) :|: z = 1 + x_11927 + x_21156, x_21156 >= 0, x_11927 >= 0
   encode_p(z) -{ 0 }-> p(cond2(encArg(x_11926), encArg(x_21155), encArg(x_3770))) :|: x_11926 >= 0, x_21155 >= 0, z = 1 + x_11926 + x_21155 + x_3770, x_3770 >= 0
   encode_p(z) -{ 0 }-> p(cond1(encArg(x_11925), encArg(x_21154), encArg(x_3769))) :|: z = 1 + x_11925 + x_21154 + x_3769, x_11925 >= 0, x_21154 >= 0, x_3769 >= 0
   encode_p(z) -{ 0 }-> p(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_p(z) -{ 0 }-> 0 :|: z >= 0
   encode_p(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 2 = v0
   encode_p(z) -{ 1 }-> 0 :|: z = 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z = 0, v0 >= 0, 0 = v0
   encode_p(z) -{ 0 }-> 0 :|: z = 1, v0 >= 0, 1 = v0
   encode_p(z) -{ 1 }-> 0 :|: z >= 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   gr(z, z') -{ 2 + z' }-> s :|: s >= 0, s <= 2, z - 1 >= 0, z' - 1 >= 0
   gr(z, z') -{ 1 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 1 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 1 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {encode_p}, {encode_gr}, {encode_cond2}, {encode_cond1}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [0], size: O(1) [0]
  encode_false: runtime: O(1) [0], size: O(1) [1]
  gr: runtime: O(n^1) [2 + z'], size: O(1) [2]
  encode_true: runtime: O(1) [0], size: O(1) [2]
  cond2: runtime: O(n^1) [35*z + 105*z' + 35*z''], size: O(1) [0]
  cond1: runtime: O(n^1) [72 + 105*z' + 35*z''], size: O(1) [0]
  p: runtime: O(1) [1], size: O(n^1) [z]
  encArg: runtime: O(n^2) [1 + 107*z + 105*z^2], size: O(n^1) [1 + z]

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

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

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

   cond1(z, z', z'') -{ 37 + 105*z' }-> s' :|: s' >= 0, s' <= 0, z = 2, z'' = 0, z' >= 0
   cond1(z, z', z'') -{ 72 + 105*z' + 35*z'' }-> s'' :|: s'' >= 0, s'' <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   cond1(z, z', z'') -{ 1 + 105*z' + 35*z'' }-> s1 :|: s1 >= 0, s1 <= 0, z = 2, z' >= 0, z'' >= 0
   cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 74 + 35*z'' }-> s10 :|: s10 >= 0, s10 <= 0, z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ -30 + 105*z' + 35*z'' }-> s11 :|: s11 >= 0, s11 <= 0, z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 74 + 35*z'' }-> s12 :|: s12 >= 0, s12 <= 0, z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 74 + 35*z'' }-> s13 :|: s13 >= 0, s13 <= 0, z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ -31 + 105*z' + 35*z'' }-> s14 :|: s14 >= 0, s14 <= 0, z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 73 + 35*z'' }-> s15 :|: s15 >= 0, s15 <= 0, z = 1, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 38 + 105*z' }-> s2 :|: s2 >= 0, s2 <= 0, z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 37 + 105*z' }-> s3 :|: s3 >= 0, s3 <= 0, z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 38 + 105*z' + 35*z'' }-> s4 :|: s4 >= 0, s4 <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 72 + 105*z' }-> s5 :|: s5 >= 0, s5 <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 2 + 105*z' }-> s6 :|: s6 >= 0, s6 <= 0, z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ -33 + 105*z' + 35*z'' }-> s7 :|: s7 >= 0, s7 <= 0, z = 2, z'' - 1 >= 0, z' >= 0
   cond2(z, z', z'') -{ 1 + 105*z' }-> s8 :|: s8 >= 0, s8 <= 0, z = 2, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 75 + 35*z'' }-> s9 :|: s9 >= 0, s9 <= 0, z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encArg(z) -{ 75 + 105*s18 + 35*s19 + 107*x_1 + 105*x_1^2 + 107*x_2 + 105*x_2^2 + 107*x_3 + 105*x_3^2 }-> s20 :|: s17 >= 0, s17 <= x_1 + 1, s18 >= 0, s18 <= x_2 + 1, s19 >= 0, s19 <= x_3 + 1, s20 >= 0, s20 <= 0, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 3 + 35*s21 + 105*s22 + 35*s23 + 107*x_1 + 105*x_1^2 + 107*x_2 + 105*x_2^2 + 107*x_3 + 105*x_3^2 }-> s24 :|: s21 >= 0, s21 <= x_1 + 1, s22 >= 0, s22 <= x_2 + 1, s23 >= 0, s23 <= x_3 + 1, s24 >= 0, s24 <= 0, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 4 + s26 + 107*x_1 + 105*x_1^2 + 107*x_2 + 105*x_2^2 }-> s27 :|: s25 >= 0, s25 <= x_1 + 1, s26 >= 0, s26 <= x_2 + 1, s27 >= 0, s27 <= 2, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 208 + -313*z + 105*z^2 }-> s41 :|: s40 >= 0, s40 <= z - 2 + 1, s41 >= 0, s41 <= 1 + s40, z - 2 >= 0
   encArg(z) -{ 76 + 105*s43 + 35*s44 + 107*x_1960 + 105*x_1960^2 + 107*x_2575 + 105*x_2575^2 + 107*x_3383 + 105*x_3383^2 }-> s46 :|: s42 >= 0, s42 <= x_1960 + 1, s43 >= 0, s43 <= x_2575 + 1, s44 >= 0, s44 <= x_3383 + 1, s45 >= 0, s45 <= 0, s46 >= 0, s46 <= s45, x_1960 >= 0, x_2575 >= 0, x_3383 >= 0, z = 1 + (1 + x_1960 + x_2575 + x_3383)
   encArg(z) -{ 4 + 35*s47 + 105*s48 + 35*s49 + 107*x_1961 + 105*x_1961^2 + 107*x_2576 + 105*x_2576^2 + 107*x_3384 + 105*x_3384^2 }-> s51 :|: s47 >= 0, s47 <= x_1961 + 1, s48 >= 0, s48 <= x_2576 + 1, s49 >= 0, s49 <= x_3384 + 1, s50 >= 0, s50 <= 0, s51 >= 0, s51 <= s50, x_3384 >= 0, x_2576 >= 0, z = 1 + (1 + x_1961 + x_2576 + x_3384), x_1961 >= 0
   encArg(z) -{ 5 + s53 + 107*x_1962 + 105*x_1962^2 + 107*x_2577 + 105*x_2577^2 }-> s55 :|: s52 >= 0, s52 <= x_1962 + 1, s53 >= 0, s53 <= x_2577 + 1, s54 >= 0, s54 <= 2, s55 >= 0, s55 <= s54, x_2577 >= 0, z = 1 + (1 + x_1962 + x_2577), x_1962 >= 0
   encArg(z) -{ 209 + -313*z + 105*z^2 }-> s58 :|: s56 >= 0, s56 <= z - 2 + 1, s57 >= 0, s57 <= s56, s58 >= 0, s58 <= s57, z - 2 >= 0
   encArg(z) -{ 1 }-> x :|: z = 1 + 2, x >= 0, 2 = 1 + x
   encArg(z) -{ 1 }-> x :|: z = 1 + 1, x >= 0, 1 = 1 + x
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 2 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 0, 0 = 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 1, v0 >= 0, 1 = v0
   encArg(z) -{ 1 }-> 0 :|: z - 1 >= 0, 0 = 0
   encArg(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z) -{ -1 + -103*z + 105*z^2 }-> 1 + s16 :|: s16 >= 0, s16 <= z - 1 + 1, z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_cond1(z, z', z'') -{ 75 + 105*s29 + 35*s30 + 107*z + 105*z^2 + 107*z' + 105*z'^2 + 107*z'' + 105*z''^2 }-> s31 :|: s28 >= 0, s28 <= z + 1, s29 >= 0, s29 <= z' + 1, s30 >= 0, s30 <= z'' + 1, s31 >= 0, s31 <= 0, z >= 0, z'' >= 0, z' >= 0
   encode_cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_cond2(z, z', z'') -{ 3 + 35*s32 + 105*s33 + 35*s34 + 107*z + 105*z^2 + 107*z' + 105*z'^2 + 107*z'' + 105*z''^2 }-> s35 :|: s32 >= 0, s32 <= z + 1, s33 >= 0, s33 <= z' + 1, s34 >= 0, s34 <= z'' + 1, s35 >= 0, s35 <= 0, z >= 0, z'' >= 0, z' >= 0
   encode_cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_gr(z, z') -{ 4 + s37 + 107*z + 105*z^2 + 107*z' + 105*z'^2 }-> s38 :|: s36 >= 0, s36 <= z + 1, s37 >= 0, s37 <= z' + 1, s38 >= 0, s38 <= 2, z >= 0, z' >= 0
   encode_gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_p(z) -{ -103*z + 105*z^2 }-> s60 :|: s59 >= 0, s59 <= z - 1 + 1, s60 >= 0, s60 <= 1 + s59, z - 1 >= 0
   encode_p(z) -{ 76 + 105*s62 + 35*s63 + 107*x_11925 + 105*x_11925^2 + 107*x_21154 + 105*x_21154^2 + 107*x_3769 + 105*x_3769^2 }-> s65 :|: s61 >= 0, s61 <= x_11925 + 1, s62 >= 0, s62 <= x_21154 + 1, s63 >= 0, s63 <= x_3769 + 1, s64 >= 0, s64 <= 0, s65 >= 0, s65 <= s64, z = 1 + x_11925 + x_21154 + x_3769, x_11925 >= 0, x_21154 >= 0, x_3769 >= 0
   encode_p(z) -{ 4 + 35*s66 + 105*s67 + 35*s68 + 107*x_11926 + 105*x_11926^2 + 107*x_21155 + 105*x_21155^2 + 107*x_3770 + 105*x_3770^2 }-> s70 :|: s66 >= 0, s66 <= x_11926 + 1, s67 >= 0, s67 <= x_21155 + 1, s68 >= 0, s68 <= x_3770 + 1, s69 >= 0, s69 <= 0, s70 >= 0, s70 <= s69, x_11926 >= 0, x_21155 >= 0, z = 1 + x_11926 + x_21155 + x_3770, x_3770 >= 0
   encode_p(z) -{ 5 + s72 + 107*x_11927 + 105*x_11927^2 + 107*x_21156 + 105*x_21156^2 }-> s74 :|: s71 >= 0, s71 <= x_11927 + 1, s72 >= 0, s72 <= x_21156 + 1, s73 >= 0, s73 <= 2, s74 >= 0, s74 <= s73, z = 1 + x_11927 + x_21156, x_21156 >= 0, x_11927 >= 0
   encode_p(z) -{ 1 + -103*z + 105*z^2 }-> s77 :|: s75 >= 0, s75 <= z - 1 + 1, s76 >= 0, s76 <= s75, s77 >= 0, s77 <= s76, z - 1 >= 0
   encode_p(z) -{ 1 }-> x :|: z = 2, x >= 0, 2 = 1 + x
   encode_p(z) -{ 1 }-> x :|: z = 1, x >= 0, 1 = 1 + x
   encode_p(z) -{ 0 }-> 0 :|: z >= 0
   encode_p(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 2 = v0
   encode_p(z) -{ 1 }-> 0 :|: z = 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z = 0, v0 >= 0, 0 = v0
   encode_p(z) -{ 0 }-> 0 :|: z = 1, v0 >= 0, 1 = v0
   encode_p(z) -{ 1 }-> 0 :|: z >= 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 1 + 107*z + 105*z^2 }-> 1 + s39 :|: s39 >= 0, s39 <= z + 1, z >= 0
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   gr(z, z') -{ 2 + z' }-> s :|: s >= 0, s <= 2, z - 1 >= 0, z' - 1 >= 0
   gr(z, z') -{ 1 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 1 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 1 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {encode_p}, {encode_gr}, {encode_cond2}, {encode_cond1}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [0], size: O(1) [0]
  encode_false: runtime: O(1) [0], size: O(1) [1]
  gr: runtime: O(n^1) [2 + z'], size: O(1) [2]
  encode_true: runtime: O(1) [0], size: O(1) [2]
  cond2: runtime: O(n^1) [35*z + 105*z' + 35*z''], size: O(1) [0]
  cond1: runtime: O(n^1) [72 + 105*z' + 35*z''], size: O(1) [0]
  p: runtime: O(1) [1], size: O(n^1) [z]
  encArg: runtime: O(n^2) [1 + 107*z + 105*z^2], size: O(n^1) [1 + z]

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

(65) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   cond1(z, z', z'') -{ 37 + 105*z' }-> s' :|: s' >= 0, s' <= 0, z = 2, z'' = 0, z' >= 0
   cond1(z, z', z'') -{ 72 + 105*z' + 35*z'' }-> s'' :|: s'' >= 0, s'' <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   cond1(z, z', z'') -{ 1 + 105*z' + 35*z'' }-> s1 :|: s1 >= 0, s1 <= 0, z = 2, z' >= 0, z'' >= 0
   cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 74 + 35*z'' }-> s10 :|: s10 >= 0, s10 <= 0, z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ -30 + 105*z' + 35*z'' }-> s11 :|: s11 >= 0, s11 <= 0, z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 74 + 35*z'' }-> s12 :|: s12 >= 0, s12 <= 0, z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 74 + 35*z'' }-> s13 :|: s13 >= 0, s13 <= 0, z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ -31 + 105*z' + 35*z'' }-> s14 :|: s14 >= 0, s14 <= 0, z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 73 + 35*z'' }-> s15 :|: s15 >= 0, s15 <= 0, z = 1, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 38 + 105*z' }-> s2 :|: s2 >= 0, s2 <= 0, z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 37 + 105*z' }-> s3 :|: s3 >= 0, s3 <= 0, z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 38 + 105*z' + 35*z'' }-> s4 :|: s4 >= 0, s4 <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 72 + 105*z' }-> s5 :|: s5 >= 0, s5 <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 2 + 105*z' }-> s6 :|: s6 >= 0, s6 <= 0, z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ -33 + 105*z' + 35*z'' }-> s7 :|: s7 >= 0, s7 <= 0, z = 2, z'' - 1 >= 0, z' >= 0
   cond2(z, z', z'') -{ 1 + 105*z' }-> s8 :|: s8 >= 0, s8 <= 0, z = 2, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 75 + 35*z'' }-> s9 :|: s9 >= 0, s9 <= 0, z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encArg(z) -{ 75 + 105*s18 + 35*s19 + 107*x_1 + 105*x_1^2 + 107*x_2 + 105*x_2^2 + 107*x_3 + 105*x_3^2 }-> s20 :|: s17 >= 0, s17 <= x_1 + 1, s18 >= 0, s18 <= x_2 + 1, s19 >= 0, s19 <= x_3 + 1, s20 >= 0, s20 <= 0, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 3 + 35*s21 + 105*s22 + 35*s23 + 107*x_1 + 105*x_1^2 + 107*x_2 + 105*x_2^2 + 107*x_3 + 105*x_3^2 }-> s24 :|: s21 >= 0, s21 <= x_1 + 1, s22 >= 0, s22 <= x_2 + 1, s23 >= 0, s23 <= x_3 + 1, s24 >= 0, s24 <= 0, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 4 + s26 + 107*x_1 + 105*x_1^2 + 107*x_2 + 105*x_2^2 }-> s27 :|: s25 >= 0, s25 <= x_1 + 1, s26 >= 0, s26 <= x_2 + 1, s27 >= 0, s27 <= 2, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 208 + -313*z + 105*z^2 }-> s41 :|: s40 >= 0, s40 <= z - 2 + 1, s41 >= 0, s41 <= 1 + s40, z - 2 >= 0
   encArg(z) -{ 76 + 105*s43 + 35*s44 + 107*x_1960 + 105*x_1960^2 + 107*x_2575 + 105*x_2575^2 + 107*x_3383 + 105*x_3383^2 }-> s46 :|: s42 >= 0, s42 <= x_1960 + 1, s43 >= 0, s43 <= x_2575 + 1, s44 >= 0, s44 <= x_3383 + 1, s45 >= 0, s45 <= 0, s46 >= 0, s46 <= s45, x_1960 >= 0, x_2575 >= 0, x_3383 >= 0, z = 1 + (1 + x_1960 + x_2575 + x_3383)
   encArg(z) -{ 4 + 35*s47 + 105*s48 + 35*s49 + 107*x_1961 + 105*x_1961^2 + 107*x_2576 + 105*x_2576^2 + 107*x_3384 + 105*x_3384^2 }-> s51 :|: s47 >= 0, s47 <= x_1961 + 1, s48 >= 0, s48 <= x_2576 + 1, s49 >= 0, s49 <= x_3384 + 1, s50 >= 0, s50 <= 0, s51 >= 0, s51 <= s50, x_3384 >= 0, x_2576 >= 0, z = 1 + (1 + x_1961 + x_2576 + x_3384), x_1961 >= 0
   encArg(z) -{ 5 + s53 + 107*x_1962 + 105*x_1962^2 + 107*x_2577 + 105*x_2577^2 }-> s55 :|: s52 >= 0, s52 <= x_1962 + 1, s53 >= 0, s53 <= x_2577 + 1, s54 >= 0, s54 <= 2, s55 >= 0, s55 <= s54, x_2577 >= 0, z = 1 + (1 + x_1962 + x_2577), x_1962 >= 0
   encArg(z) -{ 209 + -313*z + 105*z^2 }-> s58 :|: s56 >= 0, s56 <= z - 2 + 1, s57 >= 0, s57 <= s56, s58 >= 0, s58 <= s57, z - 2 >= 0
   encArg(z) -{ 1 }-> x :|: z = 1 + 2, x >= 0, 2 = 1 + x
   encArg(z) -{ 1 }-> x :|: z = 1 + 1, x >= 0, 1 = 1 + x
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 2 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 0, 0 = 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 1, v0 >= 0, 1 = v0
   encArg(z) -{ 1 }-> 0 :|: z - 1 >= 0, 0 = 0
   encArg(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z) -{ -1 + -103*z + 105*z^2 }-> 1 + s16 :|: s16 >= 0, s16 <= z - 1 + 1, z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_cond1(z, z', z'') -{ 75 + 105*s29 + 35*s30 + 107*z + 105*z^2 + 107*z' + 105*z'^2 + 107*z'' + 105*z''^2 }-> s31 :|: s28 >= 0, s28 <= z + 1, s29 >= 0, s29 <= z' + 1, s30 >= 0, s30 <= z'' + 1, s31 >= 0, s31 <= 0, z >= 0, z'' >= 0, z' >= 0
   encode_cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_cond2(z, z', z'') -{ 3 + 35*s32 + 105*s33 + 35*s34 + 107*z + 105*z^2 + 107*z' + 105*z'^2 + 107*z'' + 105*z''^2 }-> s35 :|: s32 >= 0, s32 <= z + 1, s33 >= 0, s33 <= z' + 1, s34 >= 0, s34 <= z'' + 1, s35 >= 0, s35 <= 0, z >= 0, z'' >= 0, z' >= 0
   encode_cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_gr(z, z') -{ 4 + s37 + 107*z + 105*z^2 + 107*z' + 105*z'^2 }-> s38 :|: s36 >= 0, s36 <= z + 1, s37 >= 0, s37 <= z' + 1, s38 >= 0, s38 <= 2, z >= 0, z' >= 0
   encode_gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_p(z) -{ -103*z + 105*z^2 }-> s60 :|: s59 >= 0, s59 <= z - 1 + 1, s60 >= 0, s60 <= 1 + s59, z - 1 >= 0
   encode_p(z) -{ 76 + 105*s62 + 35*s63 + 107*x_11925 + 105*x_11925^2 + 107*x_21154 + 105*x_21154^2 + 107*x_3769 + 105*x_3769^2 }-> s65 :|: s61 >= 0, s61 <= x_11925 + 1, s62 >= 0, s62 <= x_21154 + 1, s63 >= 0, s63 <= x_3769 + 1, s64 >= 0, s64 <= 0, s65 >= 0, s65 <= s64, z = 1 + x_11925 + x_21154 + x_3769, x_11925 >= 0, x_21154 >= 0, x_3769 >= 0
   encode_p(z) -{ 4 + 35*s66 + 105*s67 + 35*s68 + 107*x_11926 + 105*x_11926^2 + 107*x_21155 + 105*x_21155^2 + 107*x_3770 + 105*x_3770^2 }-> s70 :|: s66 >= 0, s66 <= x_11926 + 1, s67 >= 0, s67 <= x_21155 + 1, s68 >= 0, s68 <= x_3770 + 1, s69 >= 0, s69 <= 0, s70 >= 0, s70 <= s69, x_11926 >= 0, x_21155 >= 0, z = 1 + x_11926 + x_21155 + x_3770, x_3770 >= 0
   encode_p(z) -{ 5 + s72 + 107*x_11927 + 105*x_11927^2 + 107*x_21156 + 105*x_21156^2 }-> s74 :|: s71 >= 0, s71 <= x_11927 + 1, s72 >= 0, s72 <= x_21156 + 1, s73 >= 0, s73 <= 2, s74 >= 0, s74 <= s73, z = 1 + x_11927 + x_21156, x_21156 >= 0, x_11927 >= 0
   encode_p(z) -{ 1 + -103*z + 105*z^2 }-> s77 :|: s75 >= 0, s75 <= z - 1 + 1, s76 >= 0, s76 <= s75, s77 >= 0, s77 <= s76, z - 1 >= 0
   encode_p(z) -{ 1 }-> x :|: z = 2, x >= 0, 2 = 1 + x
   encode_p(z) -{ 1 }-> x :|: z = 1, x >= 0, 1 = 1 + x
   encode_p(z) -{ 0 }-> 0 :|: z >= 0
   encode_p(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 2 = v0
   encode_p(z) -{ 1 }-> 0 :|: z = 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z = 0, v0 >= 0, 0 = v0
   encode_p(z) -{ 0 }-> 0 :|: z = 1, v0 >= 0, 1 = v0
   encode_p(z) -{ 1 }-> 0 :|: z >= 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 1 + 107*z + 105*z^2 }-> 1 + s39 :|: s39 >= 0, s39 <= z + 1, z >= 0
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   gr(z, z') -{ 2 + z' }-> s :|: s >= 0, s <= 2, z - 1 >= 0, z' - 1 >= 0
   gr(z, z') -{ 1 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 1 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 1 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {encode_p}, {encode_gr}, {encode_cond2}, {encode_cond1}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [0], size: O(1) [0]
  encode_false: runtime: O(1) [0], size: O(1) [1]
  gr: runtime: O(n^1) [2 + z'], size: O(1) [2]
  encode_true: runtime: O(1) [0], size: O(1) [2]
  cond2: runtime: O(n^1) [35*z + 105*z' + 35*z''], size: O(1) [0]
  cond1: runtime: O(n^1) [72 + 105*z' + 35*z''], size: O(1) [0]
  p: runtime: O(1) [1], size: O(n^1) [z]
  encArg: runtime: O(n^2) [1 + 107*z + 105*z^2], size: O(n^1) [1 + z]
  encode_p: runtime: ?, size: O(n^1) [1 + z]

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

(67) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using KoAT for: encode_p
after applying outer abstraction to obtain an ITS,
resulting in: O(n^2) with polynomial bound: 406 + 1172*z + 1050*z^2

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

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

   cond1(z, z', z'') -{ 37 + 105*z' }-> s' :|: s' >= 0, s' <= 0, z = 2, z'' = 0, z' >= 0
   cond1(z, z', z'') -{ 72 + 105*z' + 35*z'' }-> s'' :|: s'' >= 0, s'' <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   cond1(z, z', z'') -{ 1 + 105*z' + 35*z'' }-> s1 :|: s1 >= 0, s1 <= 0, z = 2, z' >= 0, z'' >= 0
   cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 74 + 35*z'' }-> s10 :|: s10 >= 0, s10 <= 0, z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ -30 + 105*z' + 35*z'' }-> s11 :|: s11 >= 0, s11 <= 0, z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 74 + 35*z'' }-> s12 :|: s12 >= 0, s12 <= 0, z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 74 + 35*z'' }-> s13 :|: s13 >= 0, s13 <= 0, z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ -31 + 105*z' + 35*z'' }-> s14 :|: s14 >= 0, s14 <= 0, z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 73 + 35*z'' }-> s15 :|: s15 >= 0, s15 <= 0, z = 1, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 38 + 105*z' }-> s2 :|: s2 >= 0, s2 <= 0, z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 37 + 105*z' }-> s3 :|: s3 >= 0, s3 <= 0, z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 38 + 105*z' + 35*z'' }-> s4 :|: s4 >= 0, s4 <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 72 + 105*z' }-> s5 :|: s5 >= 0, s5 <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 2 + 105*z' }-> s6 :|: s6 >= 0, s6 <= 0, z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ -33 + 105*z' + 35*z'' }-> s7 :|: s7 >= 0, s7 <= 0, z = 2, z'' - 1 >= 0, z' >= 0
   cond2(z, z', z'') -{ 1 + 105*z' }-> s8 :|: s8 >= 0, s8 <= 0, z = 2, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 75 + 35*z'' }-> s9 :|: s9 >= 0, s9 <= 0, z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encArg(z) -{ 75 + 105*s18 + 35*s19 + 107*x_1 + 105*x_1^2 + 107*x_2 + 105*x_2^2 + 107*x_3 + 105*x_3^2 }-> s20 :|: s17 >= 0, s17 <= x_1 + 1, s18 >= 0, s18 <= x_2 + 1, s19 >= 0, s19 <= x_3 + 1, s20 >= 0, s20 <= 0, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 3 + 35*s21 + 105*s22 + 35*s23 + 107*x_1 + 105*x_1^2 + 107*x_2 + 105*x_2^2 + 107*x_3 + 105*x_3^2 }-> s24 :|: s21 >= 0, s21 <= x_1 + 1, s22 >= 0, s22 <= x_2 + 1, s23 >= 0, s23 <= x_3 + 1, s24 >= 0, s24 <= 0, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 4 + s26 + 107*x_1 + 105*x_1^2 + 107*x_2 + 105*x_2^2 }-> s27 :|: s25 >= 0, s25 <= x_1 + 1, s26 >= 0, s26 <= x_2 + 1, s27 >= 0, s27 <= 2, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 208 + -313*z + 105*z^2 }-> s41 :|: s40 >= 0, s40 <= z - 2 + 1, s41 >= 0, s41 <= 1 + s40, z - 2 >= 0
   encArg(z) -{ 76 + 105*s43 + 35*s44 + 107*x_1960 + 105*x_1960^2 + 107*x_2575 + 105*x_2575^2 + 107*x_3383 + 105*x_3383^2 }-> s46 :|: s42 >= 0, s42 <= x_1960 + 1, s43 >= 0, s43 <= x_2575 + 1, s44 >= 0, s44 <= x_3383 + 1, s45 >= 0, s45 <= 0, s46 >= 0, s46 <= s45, x_1960 >= 0, x_2575 >= 0, x_3383 >= 0, z = 1 + (1 + x_1960 + x_2575 + x_3383)
   encArg(z) -{ 4 + 35*s47 + 105*s48 + 35*s49 + 107*x_1961 + 105*x_1961^2 + 107*x_2576 + 105*x_2576^2 + 107*x_3384 + 105*x_3384^2 }-> s51 :|: s47 >= 0, s47 <= x_1961 + 1, s48 >= 0, s48 <= x_2576 + 1, s49 >= 0, s49 <= x_3384 + 1, s50 >= 0, s50 <= 0, s51 >= 0, s51 <= s50, x_3384 >= 0, x_2576 >= 0, z = 1 + (1 + x_1961 + x_2576 + x_3384), x_1961 >= 0
   encArg(z) -{ 5 + s53 + 107*x_1962 + 105*x_1962^2 + 107*x_2577 + 105*x_2577^2 }-> s55 :|: s52 >= 0, s52 <= x_1962 + 1, s53 >= 0, s53 <= x_2577 + 1, s54 >= 0, s54 <= 2, s55 >= 0, s55 <= s54, x_2577 >= 0, z = 1 + (1 + x_1962 + x_2577), x_1962 >= 0
   encArg(z) -{ 209 + -313*z + 105*z^2 }-> s58 :|: s56 >= 0, s56 <= z - 2 + 1, s57 >= 0, s57 <= s56, s58 >= 0, s58 <= s57, z - 2 >= 0
   encArg(z) -{ 1 }-> x :|: z = 1 + 2, x >= 0, 2 = 1 + x
   encArg(z) -{ 1 }-> x :|: z = 1 + 1, x >= 0, 1 = 1 + x
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 2 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 0, 0 = 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 1, v0 >= 0, 1 = v0
   encArg(z) -{ 1 }-> 0 :|: z - 1 >= 0, 0 = 0
   encArg(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z) -{ -1 + -103*z + 105*z^2 }-> 1 + s16 :|: s16 >= 0, s16 <= z - 1 + 1, z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_cond1(z, z', z'') -{ 75 + 105*s29 + 35*s30 + 107*z + 105*z^2 + 107*z' + 105*z'^2 + 107*z'' + 105*z''^2 }-> s31 :|: s28 >= 0, s28 <= z + 1, s29 >= 0, s29 <= z' + 1, s30 >= 0, s30 <= z'' + 1, s31 >= 0, s31 <= 0, z >= 0, z'' >= 0, z' >= 0
   encode_cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_cond2(z, z', z'') -{ 3 + 35*s32 + 105*s33 + 35*s34 + 107*z + 105*z^2 + 107*z' + 105*z'^2 + 107*z'' + 105*z''^2 }-> s35 :|: s32 >= 0, s32 <= z + 1, s33 >= 0, s33 <= z' + 1, s34 >= 0, s34 <= z'' + 1, s35 >= 0, s35 <= 0, z >= 0, z'' >= 0, z' >= 0
   encode_cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_gr(z, z') -{ 4 + s37 + 107*z + 105*z^2 + 107*z' + 105*z'^2 }-> s38 :|: s36 >= 0, s36 <= z + 1, s37 >= 0, s37 <= z' + 1, s38 >= 0, s38 <= 2, z >= 0, z' >= 0
   encode_gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_p(z) -{ -103*z + 105*z^2 }-> s60 :|: s59 >= 0, s59 <= z - 1 + 1, s60 >= 0, s60 <= 1 + s59, z - 1 >= 0
   encode_p(z) -{ 76 + 105*s62 + 35*s63 + 107*x_11925 + 105*x_11925^2 + 107*x_21154 + 105*x_21154^2 + 107*x_3769 + 105*x_3769^2 }-> s65 :|: s61 >= 0, s61 <= x_11925 + 1, s62 >= 0, s62 <= x_21154 + 1, s63 >= 0, s63 <= x_3769 + 1, s64 >= 0, s64 <= 0, s65 >= 0, s65 <= s64, z = 1 + x_11925 + x_21154 + x_3769, x_11925 >= 0, x_21154 >= 0, x_3769 >= 0
   encode_p(z) -{ 4 + 35*s66 + 105*s67 + 35*s68 + 107*x_11926 + 105*x_11926^2 + 107*x_21155 + 105*x_21155^2 + 107*x_3770 + 105*x_3770^2 }-> s70 :|: s66 >= 0, s66 <= x_11926 + 1, s67 >= 0, s67 <= x_21155 + 1, s68 >= 0, s68 <= x_3770 + 1, s69 >= 0, s69 <= 0, s70 >= 0, s70 <= s69, x_11926 >= 0, x_21155 >= 0, z = 1 + x_11926 + x_21155 + x_3770, x_3770 >= 0
   encode_p(z) -{ 5 + s72 + 107*x_11927 + 105*x_11927^2 + 107*x_21156 + 105*x_21156^2 }-> s74 :|: s71 >= 0, s71 <= x_11927 + 1, s72 >= 0, s72 <= x_21156 + 1, s73 >= 0, s73 <= 2, s74 >= 0, s74 <= s73, z = 1 + x_11927 + x_21156, x_21156 >= 0, x_11927 >= 0
   encode_p(z) -{ 1 + -103*z + 105*z^2 }-> s77 :|: s75 >= 0, s75 <= z - 1 + 1, s76 >= 0, s76 <= s75, s77 >= 0, s77 <= s76, z - 1 >= 0
   encode_p(z) -{ 1 }-> x :|: z = 2, x >= 0, 2 = 1 + x
   encode_p(z) -{ 1 }-> x :|: z = 1, x >= 0, 1 = 1 + x
   encode_p(z) -{ 0 }-> 0 :|: z >= 0
   encode_p(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 2 = v0
   encode_p(z) -{ 1 }-> 0 :|: z = 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z = 0, v0 >= 0, 0 = v0
   encode_p(z) -{ 0 }-> 0 :|: z = 1, v0 >= 0, 1 = v0
   encode_p(z) -{ 1 }-> 0 :|: z >= 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 1 + 107*z + 105*z^2 }-> 1 + s39 :|: s39 >= 0, s39 <= z + 1, z >= 0
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   gr(z, z') -{ 2 + z' }-> s :|: s >= 0, s <= 2, z - 1 >= 0, z' - 1 >= 0
   gr(z, z') -{ 1 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 1 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 1 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {encode_gr}, {encode_cond2}, {encode_cond1}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [0], size: O(1) [0]
  encode_false: runtime: O(1) [0], size: O(1) [1]
  gr: runtime: O(n^1) [2 + z'], size: O(1) [2]
  encode_true: runtime: O(1) [0], size: O(1) [2]
  cond2: runtime: O(n^1) [35*z + 105*z' + 35*z''], size: O(1) [0]
  cond1: runtime: O(n^1) [72 + 105*z' + 35*z''], size: O(1) [0]
  p: runtime: O(1) [1], size: O(n^1) [z]
  encArg: runtime: O(n^2) [1 + 107*z + 105*z^2], size: O(n^1) [1 + z]
  encode_p: runtime: O(n^2) [406 + 1172*z + 1050*z^2], size: O(n^1) [1 + z]

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

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

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

   cond1(z, z', z'') -{ 37 + 105*z' }-> s' :|: s' >= 0, s' <= 0, z = 2, z'' = 0, z' >= 0
   cond1(z, z', z'') -{ 72 + 105*z' + 35*z'' }-> s'' :|: s'' >= 0, s'' <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   cond1(z, z', z'') -{ 1 + 105*z' + 35*z'' }-> s1 :|: s1 >= 0, s1 <= 0, z = 2, z' >= 0, z'' >= 0
   cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 74 + 35*z'' }-> s10 :|: s10 >= 0, s10 <= 0, z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ -30 + 105*z' + 35*z'' }-> s11 :|: s11 >= 0, s11 <= 0, z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 74 + 35*z'' }-> s12 :|: s12 >= 0, s12 <= 0, z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 74 + 35*z'' }-> s13 :|: s13 >= 0, s13 <= 0, z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ -31 + 105*z' + 35*z'' }-> s14 :|: s14 >= 0, s14 <= 0, z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 73 + 35*z'' }-> s15 :|: s15 >= 0, s15 <= 0, z = 1, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 38 + 105*z' }-> s2 :|: s2 >= 0, s2 <= 0, z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 37 + 105*z' }-> s3 :|: s3 >= 0, s3 <= 0, z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 38 + 105*z' + 35*z'' }-> s4 :|: s4 >= 0, s4 <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 72 + 105*z' }-> s5 :|: s5 >= 0, s5 <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 2 + 105*z' }-> s6 :|: s6 >= 0, s6 <= 0, z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ -33 + 105*z' + 35*z'' }-> s7 :|: s7 >= 0, s7 <= 0, z = 2, z'' - 1 >= 0, z' >= 0
   cond2(z, z', z'') -{ 1 + 105*z' }-> s8 :|: s8 >= 0, s8 <= 0, z = 2, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 75 + 35*z'' }-> s9 :|: s9 >= 0, s9 <= 0, z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encArg(z) -{ 75 + 105*s18 + 35*s19 + 107*x_1 + 105*x_1^2 + 107*x_2 + 105*x_2^2 + 107*x_3 + 105*x_3^2 }-> s20 :|: s17 >= 0, s17 <= x_1 + 1, s18 >= 0, s18 <= x_2 + 1, s19 >= 0, s19 <= x_3 + 1, s20 >= 0, s20 <= 0, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 3 + 35*s21 + 105*s22 + 35*s23 + 107*x_1 + 105*x_1^2 + 107*x_2 + 105*x_2^2 + 107*x_3 + 105*x_3^2 }-> s24 :|: s21 >= 0, s21 <= x_1 + 1, s22 >= 0, s22 <= x_2 + 1, s23 >= 0, s23 <= x_3 + 1, s24 >= 0, s24 <= 0, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 4 + s26 + 107*x_1 + 105*x_1^2 + 107*x_2 + 105*x_2^2 }-> s27 :|: s25 >= 0, s25 <= x_1 + 1, s26 >= 0, s26 <= x_2 + 1, s27 >= 0, s27 <= 2, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 208 + -313*z + 105*z^2 }-> s41 :|: s40 >= 0, s40 <= z - 2 + 1, s41 >= 0, s41 <= 1 + s40, z - 2 >= 0
   encArg(z) -{ 76 + 105*s43 + 35*s44 + 107*x_1960 + 105*x_1960^2 + 107*x_2575 + 105*x_2575^2 + 107*x_3383 + 105*x_3383^2 }-> s46 :|: s42 >= 0, s42 <= x_1960 + 1, s43 >= 0, s43 <= x_2575 + 1, s44 >= 0, s44 <= x_3383 + 1, s45 >= 0, s45 <= 0, s46 >= 0, s46 <= s45, x_1960 >= 0, x_2575 >= 0, x_3383 >= 0, z = 1 + (1 + x_1960 + x_2575 + x_3383)
   encArg(z) -{ 4 + 35*s47 + 105*s48 + 35*s49 + 107*x_1961 + 105*x_1961^2 + 107*x_2576 + 105*x_2576^2 + 107*x_3384 + 105*x_3384^2 }-> s51 :|: s47 >= 0, s47 <= x_1961 + 1, s48 >= 0, s48 <= x_2576 + 1, s49 >= 0, s49 <= x_3384 + 1, s50 >= 0, s50 <= 0, s51 >= 0, s51 <= s50, x_3384 >= 0, x_2576 >= 0, z = 1 + (1 + x_1961 + x_2576 + x_3384), x_1961 >= 0
   encArg(z) -{ 5 + s53 + 107*x_1962 + 105*x_1962^2 + 107*x_2577 + 105*x_2577^2 }-> s55 :|: s52 >= 0, s52 <= x_1962 + 1, s53 >= 0, s53 <= x_2577 + 1, s54 >= 0, s54 <= 2, s55 >= 0, s55 <= s54, x_2577 >= 0, z = 1 + (1 + x_1962 + x_2577), x_1962 >= 0
   encArg(z) -{ 209 + -313*z + 105*z^2 }-> s58 :|: s56 >= 0, s56 <= z - 2 + 1, s57 >= 0, s57 <= s56, s58 >= 0, s58 <= s57, z - 2 >= 0
   encArg(z) -{ 1 }-> x :|: z = 1 + 2, x >= 0, 2 = 1 + x
   encArg(z) -{ 1 }-> x :|: z = 1 + 1, x >= 0, 1 = 1 + x
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 2 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 0, 0 = 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 1, v0 >= 0, 1 = v0
   encArg(z) -{ 1 }-> 0 :|: z - 1 >= 0, 0 = 0
   encArg(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z) -{ -1 + -103*z + 105*z^2 }-> 1 + s16 :|: s16 >= 0, s16 <= z - 1 + 1, z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_cond1(z, z', z'') -{ 75 + 105*s29 + 35*s30 + 107*z + 105*z^2 + 107*z' + 105*z'^2 + 107*z'' + 105*z''^2 }-> s31 :|: s28 >= 0, s28 <= z + 1, s29 >= 0, s29 <= z' + 1, s30 >= 0, s30 <= z'' + 1, s31 >= 0, s31 <= 0, z >= 0, z'' >= 0, z' >= 0
   encode_cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_cond2(z, z', z'') -{ 3 + 35*s32 + 105*s33 + 35*s34 + 107*z + 105*z^2 + 107*z' + 105*z'^2 + 107*z'' + 105*z''^2 }-> s35 :|: s32 >= 0, s32 <= z + 1, s33 >= 0, s33 <= z' + 1, s34 >= 0, s34 <= z'' + 1, s35 >= 0, s35 <= 0, z >= 0, z'' >= 0, z' >= 0
   encode_cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_gr(z, z') -{ 4 + s37 + 107*z + 105*z^2 + 107*z' + 105*z'^2 }-> s38 :|: s36 >= 0, s36 <= z + 1, s37 >= 0, s37 <= z' + 1, s38 >= 0, s38 <= 2, z >= 0, z' >= 0
   encode_gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_p(z) -{ -103*z + 105*z^2 }-> s60 :|: s59 >= 0, s59 <= z - 1 + 1, s60 >= 0, s60 <= 1 + s59, z - 1 >= 0
   encode_p(z) -{ 76 + 105*s62 + 35*s63 + 107*x_11925 + 105*x_11925^2 + 107*x_21154 + 105*x_21154^2 + 107*x_3769 + 105*x_3769^2 }-> s65 :|: s61 >= 0, s61 <= x_11925 + 1, s62 >= 0, s62 <= x_21154 + 1, s63 >= 0, s63 <= x_3769 + 1, s64 >= 0, s64 <= 0, s65 >= 0, s65 <= s64, z = 1 + x_11925 + x_21154 + x_3769, x_11925 >= 0, x_21154 >= 0, x_3769 >= 0
   encode_p(z) -{ 4 + 35*s66 + 105*s67 + 35*s68 + 107*x_11926 + 105*x_11926^2 + 107*x_21155 + 105*x_21155^2 + 107*x_3770 + 105*x_3770^2 }-> s70 :|: s66 >= 0, s66 <= x_11926 + 1, s67 >= 0, s67 <= x_21155 + 1, s68 >= 0, s68 <= x_3770 + 1, s69 >= 0, s69 <= 0, s70 >= 0, s70 <= s69, x_11926 >= 0, x_21155 >= 0, z = 1 + x_11926 + x_21155 + x_3770, x_3770 >= 0
   encode_p(z) -{ 5 + s72 + 107*x_11927 + 105*x_11927^2 + 107*x_21156 + 105*x_21156^2 }-> s74 :|: s71 >= 0, s71 <= x_11927 + 1, s72 >= 0, s72 <= x_21156 + 1, s73 >= 0, s73 <= 2, s74 >= 0, s74 <= s73, z = 1 + x_11927 + x_21156, x_21156 >= 0, x_11927 >= 0
   encode_p(z) -{ 1 + -103*z + 105*z^2 }-> s77 :|: s75 >= 0, s75 <= z - 1 + 1, s76 >= 0, s76 <= s75, s77 >= 0, s77 <= s76, z - 1 >= 0
   encode_p(z) -{ 1 }-> x :|: z = 2, x >= 0, 2 = 1 + x
   encode_p(z) -{ 1 }-> x :|: z = 1, x >= 0, 1 = 1 + x
   encode_p(z) -{ 0 }-> 0 :|: z >= 0
   encode_p(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 2 = v0
   encode_p(z) -{ 1 }-> 0 :|: z = 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z = 0, v0 >= 0, 0 = v0
   encode_p(z) -{ 0 }-> 0 :|: z = 1, v0 >= 0, 1 = v0
   encode_p(z) -{ 1 }-> 0 :|: z >= 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 1 + 107*z + 105*z^2 }-> 1 + s39 :|: s39 >= 0, s39 <= z + 1, z >= 0
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   gr(z, z') -{ 2 + z' }-> s :|: s >= 0, s <= 2, z - 1 >= 0, z' - 1 >= 0
   gr(z, z') -{ 1 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 1 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 1 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {encode_gr}, {encode_cond2}, {encode_cond1}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [0], size: O(1) [0]
  encode_false: runtime: O(1) [0], size: O(1) [1]
  gr: runtime: O(n^1) [2 + z'], size: O(1) [2]
  encode_true: runtime: O(1) [0], size: O(1) [2]
  cond2: runtime: O(n^1) [35*z + 105*z' + 35*z''], size: O(1) [0]
  cond1: runtime: O(n^1) [72 + 105*z' + 35*z''], size: O(1) [0]
  p: runtime: O(1) [1], size: O(n^1) [z]
  encArg: runtime: O(n^2) [1 + 107*z + 105*z^2], size: O(n^1) [1 + z]
  encode_p: runtime: O(n^2) [406 + 1172*z + 1050*z^2], size: O(n^1) [1 + z]

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

(71) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   cond1(z, z', z'') -{ 37 + 105*z' }-> s' :|: s' >= 0, s' <= 0, z = 2, z'' = 0, z' >= 0
   cond1(z, z', z'') -{ 72 + 105*z' + 35*z'' }-> s'' :|: s'' >= 0, s'' <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   cond1(z, z', z'') -{ 1 + 105*z' + 35*z'' }-> s1 :|: s1 >= 0, s1 <= 0, z = 2, z' >= 0, z'' >= 0
   cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 74 + 35*z'' }-> s10 :|: s10 >= 0, s10 <= 0, z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ -30 + 105*z' + 35*z'' }-> s11 :|: s11 >= 0, s11 <= 0, z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 74 + 35*z'' }-> s12 :|: s12 >= 0, s12 <= 0, z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 74 + 35*z'' }-> s13 :|: s13 >= 0, s13 <= 0, z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ -31 + 105*z' + 35*z'' }-> s14 :|: s14 >= 0, s14 <= 0, z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 73 + 35*z'' }-> s15 :|: s15 >= 0, s15 <= 0, z = 1, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 38 + 105*z' }-> s2 :|: s2 >= 0, s2 <= 0, z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 37 + 105*z' }-> s3 :|: s3 >= 0, s3 <= 0, z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 38 + 105*z' + 35*z'' }-> s4 :|: s4 >= 0, s4 <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 72 + 105*z' }-> s5 :|: s5 >= 0, s5 <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 2 + 105*z' }-> s6 :|: s6 >= 0, s6 <= 0, z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ -33 + 105*z' + 35*z'' }-> s7 :|: s7 >= 0, s7 <= 0, z = 2, z'' - 1 >= 0, z' >= 0
   cond2(z, z', z'') -{ 1 + 105*z' }-> s8 :|: s8 >= 0, s8 <= 0, z = 2, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 75 + 35*z'' }-> s9 :|: s9 >= 0, s9 <= 0, z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encArg(z) -{ 75 + 105*s18 + 35*s19 + 107*x_1 + 105*x_1^2 + 107*x_2 + 105*x_2^2 + 107*x_3 + 105*x_3^2 }-> s20 :|: s17 >= 0, s17 <= x_1 + 1, s18 >= 0, s18 <= x_2 + 1, s19 >= 0, s19 <= x_3 + 1, s20 >= 0, s20 <= 0, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 3 + 35*s21 + 105*s22 + 35*s23 + 107*x_1 + 105*x_1^2 + 107*x_2 + 105*x_2^2 + 107*x_3 + 105*x_3^2 }-> s24 :|: s21 >= 0, s21 <= x_1 + 1, s22 >= 0, s22 <= x_2 + 1, s23 >= 0, s23 <= x_3 + 1, s24 >= 0, s24 <= 0, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 4 + s26 + 107*x_1 + 105*x_1^2 + 107*x_2 + 105*x_2^2 }-> s27 :|: s25 >= 0, s25 <= x_1 + 1, s26 >= 0, s26 <= x_2 + 1, s27 >= 0, s27 <= 2, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 208 + -313*z + 105*z^2 }-> s41 :|: s40 >= 0, s40 <= z - 2 + 1, s41 >= 0, s41 <= 1 + s40, z - 2 >= 0
   encArg(z) -{ 76 + 105*s43 + 35*s44 + 107*x_1960 + 105*x_1960^2 + 107*x_2575 + 105*x_2575^2 + 107*x_3383 + 105*x_3383^2 }-> s46 :|: s42 >= 0, s42 <= x_1960 + 1, s43 >= 0, s43 <= x_2575 + 1, s44 >= 0, s44 <= x_3383 + 1, s45 >= 0, s45 <= 0, s46 >= 0, s46 <= s45, x_1960 >= 0, x_2575 >= 0, x_3383 >= 0, z = 1 + (1 + x_1960 + x_2575 + x_3383)
   encArg(z) -{ 4 + 35*s47 + 105*s48 + 35*s49 + 107*x_1961 + 105*x_1961^2 + 107*x_2576 + 105*x_2576^2 + 107*x_3384 + 105*x_3384^2 }-> s51 :|: s47 >= 0, s47 <= x_1961 + 1, s48 >= 0, s48 <= x_2576 + 1, s49 >= 0, s49 <= x_3384 + 1, s50 >= 0, s50 <= 0, s51 >= 0, s51 <= s50, x_3384 >= 0, x_2576 >= 0, z = 1 + (1 + x_1961 + x_2576 + x_3384), x_1961 >= 0
   encArg(z) -{ 5 + s53 + 107*x_1962 + 105*x_1962^2 + 107*x_2577 + 105*x_2577^2 }-> s55 :|: s52 >= 0, s52 <= x_1962 + 1, s53 >= 0, s53 <= x_2577 + 1, s54 >= 0, s54 <= 2, s55 >= 0, s55 <= s54, x_2577 >= 0, z = 1 + (1 + x_1962 + x_2577), x_1962 >= 0
   encArg(z) -{ 209 + -313*z + 105*z^2 }-> s58 :|: s56 >= 0, s56 <= z - 2 + 1, s57 >= 0, s57 <= s56, s58 >= 0, s58 <= s57, z - 2 >= 0
   encArg(z) -{ 1 }-> x :|: z = 1 + 2, x >= 0, 2 = 1 + x
   encArg(z) -{ 1 }-> x :|: z = 1 + 1, x >= 0, 1 = 1 + x
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 2 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 0, 0 = 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 1, v0 >= 0, 1 = v0
   encArg(z) -{ 1 }-> 0 :|: z - 1 >= 0, 0 = 0
   encArg(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z) -{ -1 + -103*z + 105*z^2 }-> 1 + s16 :|: s16 >= 0, s16 <= z - 1 + 1, z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_cond1(z, z', z'') -{ 75 + 105*s29 + 35*s30 + 107*z + 105*z^2 + 107*z' + 105*z'^2 + 107*z'' + 105*z''^2 }-> s31 :|: s28 >= 0, s28 <= z + 1, s29 >= 0, s29 <= z' + 1, s30 >= 0, s30 <= z'' + 1, s31 >= 0, s31 <= 0, z >= 0, z'' >= 0, z' >= 0
   encode_cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_cond2(z, z', z'') -{ 3 + 35*s32 + 105*s33 + 35*s34 + 107*z + 105*z^2 + 107*z' + 105*z'^2 + 107*z'' + 105*z''^2 }-> s35 :|: s32 >= 0, s32 <= z + 1, s33 >= 0, s33 <= z' + 1, s34 >= 0, s34 <= z'' + 1, s35 >= 0, s35 <= 0, z >= 0, z'' >= 0, z' >= 0
   encode_cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_gr(z, z') -{ 4 + s37 + 107*z + 105*z^2 + 107*z' + 105*z'^2 }-> s38 :|: s36 >= 0, s36 <= z + 1, s37 >= 0, s37 <= z' + 1, s38 >= 0, s38 <= 2, z >= 0, z' >= 0
   encode_gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_p(z) -{ -103*z + 105*z^2 }-> s60 :|: s59 >= 0, s59 <= z - 1 + 1, s60 >= 0, s60 <= 1 + s59, z - 1 >= 0
   encode_p(z) -{ 76 + 105*s62 + 35*s63 + 107*x_11925 + 105*x_11925^2 + 107*x_21154 + 105*x_21154^2 + 107*x_3769 + 105*x_3769^2 }-> s65 :|: s61 >= 0, s61 <= x_11925 + 1, s62 >= 0, s62 <= x_21154 + 1, s63 >= 0, s63 <= x_3769 + 1, s64 >= 0, s64 <= 0, s65 >= 0, s65 <= s64, z = 1 + x_11925 + x_21154 + x_3769, x_11925 >= 0, x_21154 >= 0, x_3769 >= 0
   encode_p(z) -{ 4 + 35*s66 + 105*s67 + 35*s68 + 107*x_11926 + 105*x_11926^2 + 107*x_21155 + 105*x_21155^2 + 107*x_3770 + 105*x_3770^2 }-> s70 :|: s66 >= 0, s66 <= x_11926 + 1, s67 >= 0, s67 <= x_21155 + 1, s68 >= 0, s68 <= x_3770 + 1, s69 >= 0, s69 <= 0, s70 >= 0, s70 <= s69, x_11926 >= 0, x_21155 >= 0, z = 1 + x_11926 + x_21155 + x_3770, x_3770 >= 0
   encode_p(z) -{ 5 + s72 + 107*x_11927 + 105*x_11927^2 + 107*x_21156 + 105*x_21156^2 }-> s74 :|: s71 >= 0, s71 <= x_11927 + 1, s72 >= 0, s72 <= x_21156 + 1, s73 >= 0, s73 <= 2, s74 >= 0, s74 <= s73, z = 1 + x_11927 + x_21156, x_21156 >= 0, x_11927 >= 0
   encode_p(z) -{ 1 + -103*z + 105*z^2 }-> s77 :|: s75 >= 0, s75 <= z - 1 + 1, s76 >= 0, s76 <= s75, s77 >= 0, s77 <= s76, z - 1 >= 0
   encode_p(z) -{ 1 }-> x :|: z = 2, x >= 0, 2 = 1 + x
   encode_p(z) -{ 1 }-> x :|: z = 1, x >= 0, 1 = 1 + x
   encode_p(z) -{ 0 }-> 0 :|: z >= 0
   encode_p(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 2 = v0
   encode_p(z) -{ 1 }-> 0 :|: z = 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z = 0, v0 >= 0, 0 = v0
   encode_p(z) -{ 0 }-> 0 :|: z = 1, v0 >= 0, 1 = v0
   encode_p(z) -{ 1 }-> 0 :|: z >= 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 1 + 107*z + 105*z^2 }-> 1 + s39 :|: s39 >= 0, s39 <= z + 1, z >= 0
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   gr(z, z') -{ 2 + z' }-> s :|: s >= 0, s <= 2, z - 1 >= 0, z' - 1 >= 0
   gr(z, z') -{ 1 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 1 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 1 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {encode_gr}, {encode_cond2}, {encode_cond1}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [0], size: O(1) [0]
  encode_false: runtime: O(1) [0], size: O(1) [1]
  gr: runtime: O(n^1) [2 + z'], size: O(1) [2]
  encode_true: runtime: O(1) [0], size: O(1) [2]
  cond2: runtime: O(n^1) [35*z + 105*z' + 35*z''], size: O(1) [0]
  cond1: runtime: O(n^1) [72 + 105*z' + 35*z''], size: O(1) [0]
  p: runtime: O(1) [1], size: O(n^1) [z]
  encArg: runtime: O(n^2) [1 + 107*z + 105*z^2], size: O(n^1) [1 + z]
  encode_p: runtime: O(n^2) [406 + 1172*z + 1050*z^2], size: O(n^1) [1 + z]
  encode_gr: runtime: ?, size: O(1) [2]

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

(73) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using KoAT for: encode_gr
after applying outer abstraction to obtain an ITS,
resulting in: O(n^2) with polynomial bound: 5 + 107*z + 105*z^2 + 108*z' + 105*z'^2

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

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

   cond1(z, z', z'') -{ 37 + 105*z' }-> s' :|: s' >= 0, s' <= 0, z = 2, z'' = 0, z' >= 0
   cond1(z, z', z'') -{ 72 + 105*z' + 35*z'' }-> s'' :|: s'' >= 0, s'' <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   cond1(z, z', z'') -{ 1 + 105*z' + 35*z'' }-> s1 :|: s1 >= 0, s1 <= 0, z = 2, z' >= 0, z'' >= 0
   cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 74 + 35*z'' }-> s10 :|: s10 >= 0, s10 <= 0, z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ -30 + 105*z' + 35*z'' }-> s11 :|: s11 >= 0, s11 <= 0, z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 74 + 35*z'' }-> s12 :|: s12 >= 0, s12 <= 0, z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 74 + 35*z'' }-> s13 :|: s13 >= 0, s13 <= 0, z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ -31 + 105*z' + 35*z'' }-> s14 :|: s14 >= 0, s14 <= 0, z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 73 + 35*z'' }-> s15 :|: s15 >= 0, s15 <= 0, z = 1, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 38 + 105*z' }-> s2 :|: s2 >= 0, s2 <= 0, z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 37 + 105*z' }-> s3 :|: s3 >= 0, s3 <= 0, z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 38 + 105*z' + 35*z'' }-> s4 :|: s4 >= 0, s4 <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 72 + 105*z' }-> s5 :|: s5 >= 0, s5 <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 2 + 105*z' }-> s6 :|: s6 >= 0, s6 <= 0, z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ -33 + 105*z' + 35*z'' }-> s7 :|: s7 >= 0, s7 <= 0, z = 2, z'' - 1 >= 0, z' >= 0
   cond2(z, z', z'') -{ 1 + 105*z' }-> s8 :|: s8 >= 0, s8 <= 0, z = 2, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 75 + 35*z'' }-> s9 :|: s9 >= 0, s9 <= 0, z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encArg(z) -{ 75 + 105*s18 + 35*s19 + 107*x_1 + 105*x_1^2 + 107*x_2 + 105*x_2^2 + 107*x_3 + 105*x_3^2 }-> s20 :|: s17 >= 0, s17 <= x_1 + 1, s18 >= 0, s18 <= x_2 + 1, s19 >= 0, s19 <= x_3 + 1, s20 >= 0, s20 <= 0, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 3 + 35*s21 + 105*s22 + 35*s23 + 107*x_1 + 105*x_1^2 + 107*x_2 + 105*x_2^2 + 107*x_3 + 105*x_3^2 }-> s24 :|: s21 >= 0, s21 <= x_1 + 1, s22 >= 0, s22 <= x_2 + 1, s23 >= 0, s23 <= x_3 + 1, s24 >= 0, s24 <= 0, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 4 + s26 + 107*x_1 + 105*x_1^2 + 107*x_2 + 105*x_2^2 }-> s27 :|: s25 >= 0, s25 <= x_1 + 1, s26 >= 0, s26 <= x_2 + 1, s27 >= 0, s27 <= 2, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 208 + -313*z + 105*z^2 }-> s41 :|: s40 >= 0, s40 <= z - 2 + 1, s41 >= 0, s41 <= 1 + s40, z - 2 >= 0
   encArg(z) -{ 76 + 105*s43 + 35*s44 + 107*x_1960 + 105*x_1960^2 + 107*x_2575 + 105*x_2575^2 + 107*x_3383 + 105*x_3383^2 }-> s46 :|: s42 >= 0, s42 <= x_1960 + 1, s43 >= 0, s43 <= x_2575 + 1, s44 >= 0, s44 <= x_3383 + 1, s45 >= 0, s45 <= 0, s46 >= 0, s46 <= s45, x_1960 >= 0, x_2575 >= 0, x_3383 >= 0, z = 1 + (1 + x_1960 + x_2575 + x_3383)
   encArg(z) -{ 4 + 35*s47 + 105*s48 + 35*s49 + 107*x_1961 + 105*x_1961^2 + 107*x_2576 + 105*x_2576^2 + 107*x_3384 + 105*x_3384^2 }-> s51 :|: s47 >= 0, s47 <= x_1961 + 1, s48 >= 0, s48 <= x_2576 + 1, s49 >= 0, s49 <= x_3384 + 1, s50 >= 0, s50 <= 0, s51 >= 0, s51 <= s50, x_3384 >= 0, x_2576 >= 0, z = 1 + (1 + x_1961 + x_2576 + x_3384), x_1961 >= 0
   encArg(z) -{ 5 + s53 + 107*x_1962 + 105*x_1962^2 + 107*x_2577 + 105*x_2577^2 }-> s55 :|: s52 >= 0, s52 <= x_1962 + 1, s53 >= 0, s53 <= x_2577 + 1, s54 >= 0, s54 <= 2, s55 >= 0, s55 <= s54, x_2577 >= 0, z = 1 + (1 + x_1962 + x_2577), x_1962 >= 0
   encArg(z) -{ 209 + -313*z + 105*z^2 }-> s58 :|: s56 >= 0, s56 <= z - 2 + 1, s57 >= 0, s57 <= s56, s58 >= 0, s58 <= s57, z - 2 >= 0
   encArg(z) -{ 1 }-> x :|: z = 1 + 2, x >= 0, 2 = 1 + x
   encArg(z) -{ 1 }-> x :|: z = 1 + 1, x >= 0, 1 = 1 + x
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 2 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 0, 0 = 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 1, v0 >= 0, 1 = v0
   encArg(z) -{ 1 }-> 0 :|: z - 1 >= 0, 0 = 0
   encArg(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z) -{ -1 + -103*z + 105*z^2 }-> 1 + s16 :|: s16 >= 0, s16 <= z - 1 + 1, z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_cond1(z, z', z'') -{ 75 + 105*s29 + 35*s30 + 107*z + 105*z^2 + 107*z' + 105*z'^2 + 107*z'' + 105*z''^2 }-> s31 :|: s28 >= 0, s28 <= z + 1, s29 >= 0, s29 <= z' + 1, s30 >= 0, s30 <= z'' + 1, s31 >= 0, s31 <= 0, z >= 0, z'' >= 0, z' >= 0
   encode_cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_cond2(z, z', z'') -{ 3 + 35*s32 + 105*s33 + 35*s34 + 107*z + 105*z^2 + 107*z' + 105*z'^2 + 107*z'' + 105*z''^2 }-> s35 :|: s32 >= 0, s32 <= z + 1, s33 >= 0, s33 <= z' + 1, s34 >= 0, s34 <= z'' + 1, s35 >= 0, s35 <= 0, z >= 0, z'' >= 0, z' >= 0
   encode_cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_gr(z, z') -{ 4 + s37 + 107*z + 105*z^2 + 107*z' + 105*z'^2 }-> s38 :|: s36 >= 0, s36 <= z + 1, s37 >= 0, s37 <= z' + 1, s38 >= 0, s38 <= 2, z >= 0, z' >= 0
   encode_gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_p(z) -{ -103*z + 105*z^2 }-> s60 :|: s59 >= 0, s59 <= z - 1 + 1, s60 >= 0, s60 <= 1 + s59, z - 1 >= 0
   encode_p(z) -{ 76 + 105*s62 + 35*s63 + 107*x_11925 + 105*x_11925^2 + 107*x_21154 + 105*x_21154^2 + 107*x_3769 + 105*x_3769^2 }-> s65 :|: s61 >= 0, s61 <= x_11925 + 1, s62 >= 0, s62 <= x_21154 + 1, s63 >= 0, s63 <= x_3769 + 1, s64 >= 0, s64 <= 0, s65 >= 0, s65 <= s64, z = 1 + x_11925 + x_21154 + x_3769, x_11925 >= 0, x_21154 >= 0, x_3769 >= 0
   encode_p(z) -{ 4 + 35*s66 + 105*s67 + 35*s68 + 107*x_11926 + 105*x_11926^2 + 107*x_21155 + 105*x_21155^2 + 107*x_3770 + 105*x_3770^2 }-> s70 :|: s66 >= 0, s66 <= x_11926 + 1, s67 >= 0, s67 <= x_21155 + 1, s68 >= 0, s68 <= x_3770 + 1, s69 >= 0, s69 <= 0, s70 >= 0, s70 <= s69, x_11926 >= 0, x_21155 >= 0, z = 1 + x_11926 + x_21155 + x_3770, x_3770 >= 0
   encode_p(z) -{ 5 + s72 + 107*x_11927 + 105*x_11927^2 + 107*x_21156 + 105*x_21156^2 }-> s74 :|: s71 >= 0, s71 <= x_11927 + 1, s72 >= 0, s72 <= x_21156 + 1, s73 >= 0, s73 <= 2, s74 >= 0, s74 <= s73, z = 1 + x_11927 + x_21156, x_21156 >= 0, x_11927 >= 0
   encode_p(z) -{ 1 + -103*z + 105*z^2 }-> s77 :|: s75 >= 0, s75 <= z - 1 + 1, s76 >= 0, s76 <= s75, s77 >= 0, s77 <= s76, z - 1 >= 0
   encode_p(z) -{ 1 }-> x :|: z = 2, x >= 0, 2 = 1 + x
   encode_p(z) -{ 1 }-> x :|: z = 1, x >= 0, 1 = 1 + x
   encode_p(z) -{ 0 }-> 0 :|: z >= 0
   encode_p(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 2 = v0
   encode_p(z) -{ 1 }-> 0 :|: z = 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z = 0, v0 >= 0, 0 = v0
   encode_p(z) -{ 0 }-> 0 :|: z = 1, v0 >= 0, 1 = v0
   encode_p(z) -{ 1 }-> 0 :|: z >= 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 1 + 107*z + 105*z^2 }-> 1 + s39 :|: s39 >= 0, s39 <= z + 1, z >= 0
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   gr(z, z') -{ 2 + z' }-> s :|: s >= 0, s <= 2, z - 1 >= 0, z' - 1 >= 0
   gr(z, z') -{ 1 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 1 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 1 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {encode_cond2}, {encode_cond1}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [0], size: O(1) [0]
  encode_false: runtime: O(1) [0], size: O(1) [1]
  gr: runtime: O(n^1) [2 + z'], size: O(1) [2]
  encode_true: runtime: O(1) [0], size: O(1) [2]
  cond2: runtime: O(n^1) [35*z + 105*z' + 35*z''], size: O(1) [0]
  cond1: runtime: O(n^1) [72 + 105*z' + 35*z''], size: O(1) [0]
  p: runtime: O(1) [1], size: O(n^1) [z]
  encArg: runtime: O(n^2) [1 + 107*z + 105*z^2], size: O(n^1) [1 + z]
  encode_p: runtime: O(n^2) [406 + 1172*z + 1050*z^2], size: O(n^1) [1 + z]
  encode_gr: runtime: O(n^2) [5 + 107*z + 105*z^2 + 108*z' + 105*z'^2], size: O(1) [2]

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

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

(76)
Obligation:
Complexity RNTS consisting of the following rules:

   cond1(z, z', z'') -{ 37 + 105*z' }-> s' :|: s' >= 0, s' <= 0, z = 2, z'' = 0, z' >= 0
   cond1(z, z', z'') -{ 72 + 105*z' + 35*z'' }-> s'' :|: s'' >= 0, s'' <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   cond1(z, z', z'') -{ 1 + 105*z' + 35*z'' }-> s1 :|: s1 >= 0, s1 <= 0, z = 2, z' >= 0, z'' >= 0
   cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 74 + 35*z'' }-> s10 :|: s10 >= 0, s10 <= 0, z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ -30 + 105*z' + 35*z'' }-> s11 :|: s11 >= 0, s11 <= 0, z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 74 + 35*z'' }-> s12 :|: s12 >= 0, s12 <= 0, z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 74 + 35*z'' }-> s13 :|: s13 >= 0, s13 <= 0, z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ -31 + 105*z' + 35*z'' }-> s14 :|: s14 >= 0, s14 <= 0, z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 73 + 35*z'' }-> s15 :|: s15 >= 0, s15 <= 0, z = 1, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 38 + 105*z' }-> s2 :|: s2 >= 0, s2 <= 0, z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 37 + 105*z' }-> s3 :|: s3 >= 0, s3 <= 0, z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 38 + 105*z' + 35*z'' }-> s4 :|: s4 >= 0, s4 <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 72 + 105*z' }-> s5 :|: s5 >= 0, s5 <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 2 + 105*z' }-> s6 :|: s6 >= 0, s6 <= 0, z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ -33 + 105*z' + 35*z'' }-> s7 :|: s7 >= 0, s7 <= 0, z = 2, z'' - 1 >= 0, z' >= 0
   cond2(z, z', z'') -{ 1 + 105*z' }-> s8 :|: s8 >= 0, s8 <= 0, z = 2, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 75 + 35*z'' }-> s9 :|: s9 >= 0, s9 <= 0, z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encArg(z) -{ 75 + 105*s18 + 35*s19 + 107*x_1 + 105*x_1^2 + 107*x_2 + 105*x_2^2 + 107*x_3 + 105*x_3^2 }-> s20 :|: s17 >= 0, s17 <= x_1 + 1, s18 >= 0, s18 <= x_2 + 1, s19 >= 0, s19 <= x_3 + 1, s20 >= 0, s20 <= 0, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 3 + 35*s21 + 105*s22 + 35*s23 + 107*x_1 + 105*x_1^2 + 107*x_2 + 105*x_2^2 + 107*x_3 + 105*x_3^2 }-> s24 :|: s21 >= 0, s21 <= x_1 + 1, s22 >= 0, s22 <= x_2 + 1, s23 >= 0, s23 <= x_3 + 1, s24 >= 0, s24 <= 0, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 4 + s26 + 107*x_1 + 105*x_1^2 + 107*x_2 + 105*x_2^2 }-> s27 :|: s25 >= 0, s25 <= x_1 + 1, s26 >= 0, s26 <= x_2 + 1, s27 >= 0, s27 <= 2, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 208 + -313*z + 105*z^2 }-> s41 :|: s40 >= 0, s40 <= z - 2 + 1, s41 >= 0, s41 <= 1 + s40, z - 2 >= 0
   encArg(z) -{ 76 + 105*s43 + 35*s44 + 107*x_1960 + 105*x_1960^2 + 107*x_2575 + 105*x_2575^2 + 107*x_3383 + 105*x_3383^2 }-> s46 :|: s42 >= 0, s42 <= x_1960 + 1, s43 >= 0, s43 <= x_2575 + 1, s44 >= 0, s44 <= x_3383 + 1, s45 >= 0, s45 <= 0, s46 >= 0, s46 <= s45, x_1960 >= 0, x_2575 >= 0, x_3383 >= 0, z = 1 + (1 + x_1960 + x_2575 + x_3383)
   encArg(z) -{ 4 + 35*s47 + 105*s48 + 35*s49 + 107*x_1961 + 105*x_1961^2 + 107*x_2576 + 105*x_2576^2 + 107*x_3384 + 105*x_3384^2 }-> s51 :|: s47 >= 0, s47 <= x_1961 + 1, s48 >= 0, s48 <= x_2576 + 1, s49 >= 0, s49 <= x_3384 + 1, s50 >= 0, s50 <= 0, s51 >= 0, s51 <= s50, x_3384 >= 0, x_2576 >= 0, z = 1 + (1 + x_1961 + x_2576 + x_3384), x_1961 >= 0
   encArg(z) -{ 5 + s53 + 107*x_1962 + 105*x_1962^2 + 107*x_2577 + 105*x_2577^2 }-> s55 :|: s52 >= 0, s52 <= x_1962 + 1, s53 >= 0, s53 <= x_2577 + 1, s54 >= 0, s54 <= 2, s55 >= 0, s55 <= s54, x_2577 >= 0, z = 1 + (1 + x_1962 + x_2577), x_1962 >= 0
   encArg(z) -{ 209 + -313*z + 105*z^2 }-> s58 :|: s56 >= 0, s56 <= z - 2 + 1, s57 >= 0, s57 <= s56, s58 >= 0, s58 <= s57, z - 2 >= 0
   encArg(z) -{ 1 }-> x :|: z = 1 + 2, x >= 0, 2 = 1 + x
   encArg(z) -{ 1 }-> x :|: z = 1 + 1, x >= 0, 1 = 1 + x
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 2 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 0, 0 = 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 1, v0 >= 0, 1 = v0
   encArg(z) -{ 1 }-> 0 :|: z - 1 >= 0, 0 = 0
   encArg(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z) -{ -1 + -103*z + 105*z^2 }-> 1 + s16 :|: s16 >= 0, s16 <= z - 1 + 1, z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_cond1(z, z', z'') -{ 75 + 105*s29 + 35*s30 + 107*z + 105*z^2 + 107*z' + 105*z'^2 + 107*z'' + 105*z''^2 }-> s31 :|: s28 >= 0, s28 <= z + 1, s29 >= 0, s29 <= z' + 1, s30 >= 0, s30 <= z'' + 1, s31 >= 0, s31 <= 0, z >= 0, z'' >= 0, z' >= 0
   encode_cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_cond2(z, z', z'') -{ 3 + 35*s32 + 105*s33 + 35*s34 + 107*z + 105*z^2 + 107*z' + 105*z'^2 + 107*z'' + 105*z''^2 }-> s35 :|: s32 >= 0, s32 <= z + 1, s33 >= 0, s33 <= z' + 1, s34 >= 0, s34 <= z'' + 1, s35 >= 0, s35 <= 0, z >= 0, z'' >= 0, z' >= 0
   encode_cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_gr(z, z') -{ 4 + s37 + 107*z + 105*z^2 + 107*z' + 105*z'^2 }-> s38 :|: s36 >= 0, s36 <= z + 1, s37 >= 0, s37 <= z' + 1, s38 >= 0, s38 <= 2, z >= 0, z' >= 0
   encode_gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_p(z) -{ -103*z + 105*z^2 }-> s60 :|: s59 >= 0, s59 <= z - 1 + 1, s60 >= 0, s60 <= 1 + s59, z - 1 >= 0
   encode_p(z) -{ 76 + 105*s62 + 35*s63 + 107*x_11925 + 105*x_11925^2 + 107*x_21154 + 105*x_21154^2 + 107*x_3769 + 105*x_3769^2 }-> s65 :|: s61 >= 0, s61 <= x_11925 + 1, s62 >= 0, s62 <= x_21154 + 1, s63 >= 0, s63 <= x_3769 + 1, s64 >= 0, s64 <= 0, s65 >= 0, s65 <= s64, z = 1 + x_11925 + x_21154 + x_3769, x_11925 >= 0, x_21154 >= 0, x_3769 >= 0
   encode_p(z) -{ 4 + 35*s66 + 105*s67 + 35*s68 + 107*x_11926 + 105*x_11926^2 + 107*x_21155 + 105*x_21155^2 + 107*x_3770 + 105*x_3770^2 }-> s70 :|: s66 >= 0, s66 <= x_11926 + 1, s67 >= 0, s67 <= x_21155 + 1, s68 >= 0, s68 <= x_3770 + 1, s69 >= 0, s69 <= 0, s70 >= 0, s70 <= s69, x_11926 >= 0, x_21155 >= 0, z = 1 + x_11926 + x_21155 + x_3770, x_3770 >= 0
   encode_p(z) -{ 5 + s72 + 107*x_11927 + 105*x_11927^2 + 107*x_21156 + 105*x_21156^2 }-> s74 :|: s71 >= 0, s71 <= x_11927 + 1, s72 >= 0, s72 <= x_21156 + 1, s73 >= 0, s73 <= 2, s74 >= 0, s74 <= s73, z = 1 + x_11927 + x_21156, x_21156 >= 0, x_11927 >= 0
   encode_p(z) -{ 1 + -103*z + 105*z^2 }-> s77 :|: s75 >= 0, s75 <= z - 1 + 1, s76 >= 0, s76 <= s75, s77 >= 0, s77 <= s76, z - 1 >= 0
   encode_p(z) -{ 1 }-> x :|: z = 2, x >= 0, 2 = 1 + x
   encode_p(z) -{ 1 }-> x :|: z = 1, x >= 0, 1 = 1 + x
   encode_p(z) -{ 0 }-> 0 :|: z >= 0
   encode_p(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 2 = v0
   encode_p(z) -{ 1 }-> 0 :|: z = 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z = 0, v0 >= 0, 0 = v0
   encode_p(z) -{ 0 }-> 0 :|: z = 1, v0 >= 0, 1 = v0
   encode_p(z) -{ 1 }-> 0 :|: z >= 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 1 + 107*z + 105*z^2 }-> 1 + s39 :|: s39 >= 0, s39 <= z + 1, z >= 0
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   gr(z, z') -{ 2 + z' }-> s :|: s >= 0, s <= 2, z - 1 >= 0, z' - 1 >= 0
   gr(z, z') -{ 1 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 1 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 1 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {encode_cond2}, {encode_cond1}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [0], size: O(1) [0]
  encode_false: runtime: O(1) [0], size: O(1) [1]
  gr: runtime: O(n^1) [2 + z'], size: O(1) [2]
  encode_true: runtime: O(1) [0], size: O(1) [2]
  cond2: runtime: O(n^1) [35*z + 105*z' + 35*z''], size: O(1) [0]
  cond1: runtime: O(n^1) [72 + 105*z' + 35*z''], size: O(1) [0]
  p: runtime: O(1) [1], size: O(n^1) [z]
  encArg: runtime: O(n^2) [1 + 107*z + 105*z^2], size: O(n^1) [1 + z]
  encode_p: runtime: O(n^2) [406 + 1172*z + 1050*z^2], size: O(n^1) [1 + z]
  encode_gr: runtime: O(n^2) [5 + 107*z + 105*z^2 + 108*z' + 105*z'^2], size: O(1) [2]

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

(77) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: encode_cond2
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 0

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

(78)
Obligation:
Complexity RNTS consisting of the following rules:

   cond1(z, z', z'') -{ 37 + 105*z' }-> s' :|: s' >= 0, s' <= 0, z = 2, z'' = 0, z' >= 0
   cond1(z, z', z'') -{ 72 + 105*z' + 35*z'' }-> s'' :|: s'' >= 0, s'' <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   cond1(z, z', z'') -{ 1 + 105*z' + 35*z'' }-> s1 :|: s1 >= 0, s1 <= 0, z = 2, z' >= 0, z'' >= 0
   cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 74 + 35*z'' }-> s10 :|: s10 >= 0, s10 <= 0, z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ -30 + 105*z' + 35*z'' }-> s11 :|: s11 >= 0, s11 <= 0, z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 74 + 35*z'' }-> s12 :|: s12 >= 0, s12 <= 0, z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 74 + 35*z'' }-> s13 :|: s13 >= 0, s13 <= 0, z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ -31 + 105*z' + 35*z'' }-> s14 :|: s14 >= 0, s14 <= 0, z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 73 + 35*z'' }-> s15 :|: s15 >= 0, s15 <= 0, z = 1, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 38 + 105*z' }-> s2 :|: s2 >= 0, s2 <= 0, z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 37 + 105*z' }-> s3 :|: s3 >= 0, s3 <= 0, z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 38 + 105*z' + 35*z'' }-> s4 :|: s4 >= 0, s4 <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 72 + 105*z' }-> s5 :|: s5 >= 0, s5 <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 2 + 105*z' }-> s6 :|: s6 >= 0, s6 <= 0, z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ -33 + 105*z' + 35*z'' }-> s7 :|: s7 >= 0, s7 <= 0, z = 2, z'' - 1 >= 0, z' >= 0
   cond2(z, z', z'') -{ 1 + 105*z' }-> s8 :|: s8 >= 0, s8 <= 0, z = 2, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 75 + 35*z'' }-> s9 :|: s9 >= 0, s9 <= 0, z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encArg(z) -{ 75 + 105*s18 + 35*s19 + 107*x_1 + 105*x_1^2 + 107*x_2 + 105*x_2^2 + 107*x_3 + 105*x_3^2 }-> s20 :|: s17 >= 0, s17 <= x_1 + 1, s18 >= 0, s18 <= x_2 + 1, s19 >= 0, s19 <= x_3 + 1, s20 >= 0, s20 <= 0, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 3 + 35*s21 + 105*s22 + 35*s23 + 107*x_1 + 105*x_1^2 + 107*x_2 + 105*x_2^2 + 107*x_3 + 105*x_3^2 }-> s24 :|: s21 >= 0, s21 <= x_1 + 1, s22 >= 0, s22 <= x_2 + 1, s23 >= 0, s23 <= x_3 + 1, s24 >= 0, s24 <= 0, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 4 + s26 + 107*x_1 + 105*x_1^2 + 107*x_2 + 105*x_2^2 }-> s27 :|: s25 >= 0, s25 <= x_1 + 1, s26 >= 0, s26 <= x_2 + 1, s27 >= 0, s27 <= 2, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 208 + -313*z + 105*z^2 }-> s41 :|: s40 >= 0, s40 <= z - 2 + 1, s41 >= 0, s41 <= 1 + s40, z - 2 >= 0
   encArg(z) -{ 76 + 105*s43 + 35*s44 + 107*x_1960 + 105*x_1960^2 + 107*x_2575 + 105*x_2575^2 + 107*x_3383 + 105*x_3383^2 }-> s46 :|: s42 >= 0, s42 <= x_1960 + 1, s43 >= 0, s43 <= x_2575 + 1, s44 >= 0, s44 <= x_3383 + 1, s45 >= 0, s45 <= 0, s46 >= 0, s46 <= s45, x_1960 >= 0, x_2575 >= 0, x_3383 >= 0, z = 1 + (1 + x_1960 + x_2575 + x_3383)
   encArg(z) -{ 4 + 35*s47 + 105*s48 + 35*s49 + 107*x_1961 + 105*x_1961^2 + 107*x_2576 + 105*x_2576^2 + 107*x_3384 + 105*x_3384^2 }-> s51 :|: s47 >= 0, s47 <= x_1961 + 1, s48 >= 0, s48 <= x_2576 + 1, s49 >= 0, s49 <= x_3384 + 1, s50 >= 0, s50 <= 0, s51 >= 0, s51 <= s50, x_3384 >= 0, x_2576 >= 0, z = 1 + (1 + x_1961 + x_2576 + x_3384), x_1961 >= 0
   encArg(z) -{ 5 + s53 + 107*x_1962 + 105*x_1962^2 + 107*x_2577 + 105*x_2577^2 }-> s55 :|: s52 >= 0, s52 <= x_1962 + 1, s53 >= 0, s53 <= x_2577 + 1, s54 >= 0, s54 <= 2, s55 >= 0, s55 <= s54, x_2577 >= 0, z = 1 + (1 + x_1962 + x_2577), x_1962 >= 0
   encArg(z) -{ 209 + -313*z + 105*z^2 }-> s58 :|: s56 >= 0, s56 <= z - 2 + 1, s57 >= 0, s57 <= s56, s58 >= 0, s58 <= s57, z - 2 >= 0
   encArg(z) -{ 1 }-> x :|: z = 1 + 2, x >= 0, 2 = 1 + x
   encArg(z) -{ 1 }-> x :|: z = 1 + 1, x >= 0, 1 = 1 + x
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 2 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 0, 0 = 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 1, v0 >= 0, 1 = v0
   encArg(z) -{ 1 }-> 0 :|: z - 1 >= 0, 0 = 0
   encArg(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z) -{ -1 + -103*z + 105*z^2 }-> 1 + s16 :|: s16 >= 0, s16 <= z - 1 + 1, z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_cond1(z, z', z'') -{ 75 + 105*s29 + 35*s30 + 107*z + 105*z^2 + 107*z' + 105*z'^2 + 107*z'' + 105*z''^2 }-> s31 :|: s28 >= 0, s28 <= z + 1, s29 >= 0, s29 <= z' + 1, s30 >= 0, s30 <= z'' + 1, s31 >= 0, s31 <= 0, z >= 0, z'' >= 0, z' >= 0
   encode_cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_cond2(z, z', z'') -{ 3 + 35*s32 + 105*s33 + 35*s34 + 107*z + 105*z^2 + 107*z' + 105*z'^2 + 107*z'' + 105*z''^2 }-> s35 :|: s32 >= 0, s32 <= z + 1, s33 >= 0, s33 <= z' + 1, s34 >= 0, s34 <= z'' + 1, s35 >= 0, s35 <= 0, z >= 0, z'' >= 0, z' >= 0
   encode_cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_gr(z, z') -{ 4 + s37 + 107*z + 105*z^2 + 107*z' + 105*z'^2 }-> s38 :|: s36 >= 0, s36 <= z + 1, s37 >= 0, s37 <= z' + 1, s38 >= 0, s38 <= 2, z >= 0, z' >= 0
   encode_gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_p(z) -{ -103*z + 105*z^2 }-> s60 :|: s59 >= 0, s59 <= z - 1 + 1, s60 >= 0, s60 <= 1 + s59, z - 1 >= 0
   encode_p(z) -{ 76 + 105*s62 + 35*s63 + 107*x_11925 + 105*x_11925^2 + 107*x_21154 + 105*x_21154^2 + 107*x_3769 + 105*x_3769^2 }-> s65 :|: s61 >= 0, s61 <= x_11925 + 1, s62 >= 0, s62 <= x_21154 + 1, s63 >= 0, s63 <= x_3769 + 1, s64 >= 0, s64 <= 0, s65 >= 0, s65 <= s64, z = 1 + x_11925 + x_21154 + x_3769, x_11925 >= 0, x_21154 >= 0, x_3769 >= 0
   encode_p(z) -{ 4 + 35*s66 + 105*s67 + 35*s68 + 107*x_11926 + 105*x_11926^2 + 107*x_21155 + 105*x_21155^2 + 107*x_3770 + 105*x_3770^2 }-> s70 :|: s66 >= 0, s66 <= x_11926 + 1, s67 >= 0, s67 <= x_21155 + 1, s68 >= 0, s68 <= x_3770 + 1, s69 >= 0, s69 <= 0, s70 >= 0, s70 <= s69, x_11926 >= 0, x_21155 >= 0, z = 1 + x_11926 + x_21155 + x_3770, x_3770 >= 0
   encode_p(z) -{ 5 + s72 + 107*x_11927 + 105*x_11927^2 + 107*x_21156 + 105*x_21156^2 }-> s74 :|: s71 >= 0, s71 <= x_11927 + 1, s72 >= 0, s72 <= x_21156 + 1, s73 >= 0, s73 <= 2, s74 >= 0, s74 <= s73, z = 1 + x_11927 + x_21156, x_21156 >= 0, x_11927 >= 0
   encode_p(z) -{ 1 + -103*z + 105*z^2 }-> s77 :|: s75 >= 0, s75 <= z - 1 + 1, s76 >= 0, s76 <= s75, s77 >= 0, s77 <= s76, z - 1 >= 0
   encode_p(z) -{ 1 }-> x :|: z = 2, x >= 0, 2 = 1 + x
   encode_p(z) -{ 1 }-> x :|: z = 1, x >= 0, 1 = 1 + x
   encode_p(z) -{ 0 }-> 0 :|: z >= 0
   encode_p(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 2 = v0
   encode_p(z) -{ 1 }-> 0 :|: z = 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z = 0, v0 >= 0, 0 = v0
   encode_p(z) -{ 0 }-> 0 :|: z = 1, v0 >= 0, 1 = v0
   encode_p(z) -{ 1 }-> 0 :|: z >= 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 1 + 107*z + 105*z^2 }-> 1 + s39 :|: s39 >= 0, s39 <= z + 1, z >= 0
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   gr(z, z') -{ 2 + z' }-> s :|: s >= 0, s <= 2, z - 1 >= 0, z' - 1 >= 0
   gr(z, z') -{ 1 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 1 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 1 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {encode_cond2}, {encode_cond1}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [0], size: O(1) [0]
  encode_false: runtime: O(1) [0], size: O(1) [1]
  gr: runtime: O(n^1) [2 + z'], size: O(1) [2]
  encode_true: runtime: O(1) [0], size: O(1) [2]
  cond2: runtime: O(n^1) [35*z + 105*z' + 35*z''], size: O(1) [0]
  cond1: runtime: O(n^1) [72 + 105*z' + 35*z''], size: O(1) [0]
  p: runtime: O(1) [1], size: O(n^1) [z]
  encArg: runtime: O(n^2) [1 + 107*z + 105*z^2], size: O(n^1) [1 + z]
  encode_p: runtime: O(n^2) [406 + 1172*z + 1050*z^2], size: O(n^1) [1 + z]
  encode_gr: runtime: O(n^2) [5 + 107*z + 105*z^2 + 108*z' + 105*z'^2], size: O(1) [2]
  encode_cond2: runtime: ?, size: O(1) [0]

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

(79) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using KoAT for: encode_cond2
after applying outer abstraction to obtain an ITS,
resulting in: O(n^2) with polynomial bound: 178 + 142*z + 105*z^2 + 212*z' + 105*z'^2 + 142*z'' + 105*z''^2

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

(80)
Obligation:
Complexity RNTS consisting of the following rules:

   cond1(z, z', z'') -{ 37 + 105*z' }-> s' :|: s' >= 0, s' <= 0, z = 2, z'' = 0, z' >= 0
   cond1(z, z', z'') -{ 72 + 105*z' + 35*z'' }-> s'' :|: s'' >= 0, s'' <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   cond1(z, z', z'') -{ 1 + 105*z' + 35*z'' }-> s1 :|: s1 >= 0, s1 <= 0, z = 2, z' >= 0, z'' >= 0
   cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 74 + 35*z'' }-> s10 :|: s10 >= 0, s10 <= 0, z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ -30 + 105*z' + 35*z'' }-> s11 :|: s11 >= 0, s11 <= 0, z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 74 + 35*z'' }-> s12 :|: s12 >= 0, s12 <= 0, z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 74 + 35*z'' }-> s13 :|: s13 >= 0, s13 <= 0, z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ -31 + 105*z' + 35*z'' }-> s14 :|: s14 >= 0, s14 <= 0, z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 73 + 35*z'' }-> s15 :|: s15 >= 0, s15 <= 0, z = 1, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 38 + 105*z' }-> s2 :|: s2 >= 0, s2 <= 0, z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 37 + 105*z' }-> s3 :|: s3 >= 0, s3 <= 0, z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 38 + 105*z' + 35*z'' }-> s4 :|: s4 >= 0, s4 <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 72 + 105*z' }-> s5 :|: s5 >= 0, s5 <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 2 + 105*z' }-> s6 :|: s6 >= 0, s6 <= 0, z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ -33 + 105*z' + 35*z'' }-> s7 :|: s7 >= 0, s7 <= 0, z = 2, z'' - 1 >= 0, z' >= 0
   cond2(z, z', z'') -{ 1 + 105*z' }-> s8 :|: s8 >= 0, s8 <= 0, z = 2, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 75 + 35*z'' }-> s9 :|: s9 >= 0, s9 <= 0, z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encArg(z) -{ 75 + 105*s18 + 35*s19 + 107*x_1 + 105*x_1^2 + 107*x_2 + 105*x_2^2 + 107*x_3 + 105*x_3^2 }-> s20 :|: s17 >= 0, s17 <= x_1 + 1, s18 >= 0, s18 <= x_2 + 1, s19 >= 0, s19 <= x_3 + 1, s20 >= 0, s20 <= 0, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 3 + 35*s21 + 105*s22 + 35*s23 + 107*x_1 + 105*x_1^2 + 107*x_2 + 105*x_2^2 + 107*x_3 + 105*x_3^2 }-> s24 :|: s21 >= 0, s21 <= x_1 + 1, s22 >= 0, s22 <= x_2 + 1, s23 >= 0, s23 <= x_3 + 1, s24 >= 0, s24 <= 0, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 4 + s26 + 107*x_1 + 105*x_1^2 + 107*x_2 + 105*x_2^2 }-> s27 :|: s25 >= 0, s25 <= x_1 + 1, s26 >= 0, s26 <= x_2 + 1, s27 >= 0, s27 <= 2, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 208 + -313*z + 105*z^2 }-> s41 :|: s40 >= 0, s40 <= z - 2 + 1, s41 >= 0, s41 <= 1 + s40, z - 2 >= 0
   encArg(z) -{ 76 + 105*s43 + 35*s44 + 107*x_1960 + 105*x_1960^2 + 107*x_2575 + 105*x_2575^2 + 107*x_3383 + 105*x_3383^2 }-> s46 :|: s42 >= 0, s42 <= x_1960 + 1, s43 >= 0, s43 <= x_2575 + 1, s44 >= 0, s44 <= x_3383 + 1, s45 >= 0, s45 <= 0, s46 >= 0, s46 <= s45, x_1960 >= 0, x_2575 >= 0, x_3383 >= 0, z = 1 + (1 + x_1960 + x_2575 + x_3383)
   encArg(z) -{ 4 + 35*s47 + 105*s48 + 35*s49 + 107*x_1961 + 105*x_1961^2 + 107*x_2576 + 105*x_2576^2 + 107*x_3384 + 105*x_3384^2 }-> s51 :|: s47 >= 0, s47 <= x_1961 + 1, s48 >= 0, s48 <= x_2576 + 1, s49 >= 0, s49 <= x_3384 + 1, s50 >= 0, s50 <= 0, s51 >= 0, s51 <= s50, x_3384 >= 0, x_2576 >= 0, z = 1 + (1 + x_1961 + x_2576 + x_3384), x_1961 >= 0
   encArg(z) -{ 5 + s53 + 107*x_1962 + 105*x_1962^2 + 107*x_2577 + 105*x_2577^2 }-> s55 :|: s52 >= 0, s52 <= x_1962 + 1, s53 >= 0, s53 <= x_2577 + 1, s54 >= 0, s54 <= 2, s55 >= 0, s55 <= s54, x_2577 >= 0, z = 1 + (1 + x_1962 + x_2577), x_1962 >= 0
   encArg(z) -{ 209 + -313*z + 105*z^2 }-> s58 :|: s56 >= 0, s56 <= z - 2 + 1, s57 >= 0, s57 <= s56, s58 >= 0, s58 <= s57, z - 2 >= 0
   encArg(z) -{ 1 }-> x :|: z = 1 + 2, x >= 0, 2 = 1 + x
   encArg(z) -{ 1 }-> x :|: z = 1 + 1, x >= 0, 1 = 1 + x
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 2 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 0, 0 = 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 1, v0 >= 0, 1 = v0
   encArg(z) -{ 1 }-> 0 :|: z - 1 >= 0, 0 = 0
   encArg(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z) -{ -1 + -103*z + 105*z^2 }-> 1 + s16 :|: s16 >= 0, s16 <= z - 1 + 1, z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_cond1(z, z', z'') -{ 75 + 105*s29 + 35*s30 + 107*z + 105*z^2 + 107*z' + 105*z'^2 + 107*z'' + 105*z''^2 }-> s31 :|: s28 >= 0, s28 <= z + 1, s29 >= 0, s29 <= z' + 1, s30 >= 0, s30 <= z'' + 1, s31 >= 0, s31 <= 0, z >= 0, z'' >= 0, z' >= 0
   encode_cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_cond2(z, z', z'') -{ 3 + 35*s32 + 105*s33 + 35*s34 + 107*z + 105*z^2 + 107*z' + 105*z'^2 + 107*z'' + 105*z''^2 }-> s35 :|: s32 >= 0, s32 <= z + 1, s33 >= 0, s33 <= z' + 1, s34 >= 0, s34 <= z'' + 1, s35 >= 0, s35 <= 0, z >= 0, z'' >= 0, z' >= 0
   encode_cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_gr(z, z') -{ 4 + s37 + 107*z + 105*z^2 + 107*z' + 105*z'^2 }-> s38 :|: s36 >= 0, s36 <= z + 1, s37 >= 0, s37 <= z' + 1, s38 >= 0, s38 <= 2, z >= 0, z' >= 0
   encode_gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_p(z) -{ -103*z + 105*z^2 }-> s60 :|: s59 >= 0, s59 <= z - 1 + 1, s60 >= 0, s60 <= 1 + s59, z - 1 >= 0
   encode_p(z) -{ 76 + 105*s62 + 35*s63 + 107*x_11925 + 105*x_11925^2 + 107*x_21154 + 105*x_21154^2 + 107*x_3769 + 105*x_3769^2 }-> s65 :|: s61 >= 0, s61 <= x_11925 + 1, s62 >= 0, s62 <= x_21154 + 1, s63 >= 0, s63 <= x_3769 + 1, s64 >= 0, s64 <= 0, s65 >= 0, s65 <= s64, z = 1 + x_11925 + x_21154 + x_3769, x_11925 >= 0, x_21154 >= 0, x_3769 >= 0
   encode_p(z) -{ 4 + 35*s66 + 105*s67 + 35*s68 + 107*x_11926 + 105*x_11926^2 + 107*x_21155 + 105*x_21155^2 + 107*x_3770 + 105*x_3770^2 }-> s70 :|: s66 >= 0, s66 <= x_11926 + 1, s67 >= 0, s67 <= x_21155 + 1, s68 >= 0, s68 <= x_3770 + 1, s69 >= 0, s69 <= 0, s70 >= 0, s70 <= s69, x_11926 >= 0, x_21155 >= 0, z = 1 + x_11926 + x_21155 + x_3770, x_3770 >= 0
   encode_p(z) -{ 5 + s72 + 107*x_11927 + 105*x_11927^2 + 107*x_21156 + 105*x_21156^2 }-> s74 :|: s71 >= 0, s71 <= x_11927 + 1, s72 >= 0, s72 <= x_21156 + 1, s73 >= 0, s73 <= 2, s74 >= 0, s74 <= s73, z = 1 + x_11927 + x_21156, x_21156 >= 0, x_11927 >= 0
   encode_p(z) -{ 1 + -103*z + 105*z^2 }-> s77 :|: s75 >= 0, s75 <= z - 1 + 1, s76 >= 0, s76 <= s75, s77 >= 0, s77 <= s76, z - 1 >= 0
   encode_p(z) -{ 1 }-> x :|: z = 2, x >= 0, 2 = 1 + x
   encode_p(z) -{ 1 }-> x :|: z = 1, x >= 0, 1 = 1 + x
   encode_p(z) -{ 0 }-> 0 :|: z >= 0
   encode_p(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 2 = v0
   encode_p(z) -{ 1 }-> 0 :|: z = 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z = 0, v0 >= 0, 0 = v0
   encode_p(z) -{ 0 }-> 0 :|: z = 1, v0 >= 0, 1 = v0
   encode_p(z) -{ 1 }-> 0 :|: z >= 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 1 + 107*z + 105*z^2 }-> 1 + s39 :|: s39 >= 0, s39 <= z + 1, z >= 0
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   gr(z, z') -{ 2 + z' }-> s :|: s >= 0, s <= 2, z - 1 >= 0, z' - 1 >= 0
   gr(z, z') -{ 1 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 1 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 1 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {encode_cond1}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [0], size: O(1) [0]
  encode_false: runtime: O(1) [0], size: O(1) [1]
  gr: runtime: O(n^1) [2 + z'], size: O(1) [2]
  encode_true: runtime: O(1) [0], size: O(1) [2]
  cond2: runtime: O(n^1) [35*z + 105*z' + 35*z''], size: O(1) [0]
  cond1: runtime: O(n^1) [72 + 105*z' + 35*z''], size: O(1) [0]
  p: runtime: O(1) [1], size: O(n^1) [z]
  encArg: runtime: O(n^2) [1 + 107*z + 105*z^2], size: O(n^1) [1 + z]
  encode_p: runtime: O(n^2) [406 + 1172*z + 1050*z^2], size: O(n^1) [1 + z]
  encode_gr: runtime: O(n^2) [5 + 107*z + 105*z^2 + 108*z' + 105*z'^2], size: O(1) [2]
  encode_cond2: runtime: O(n^2) [178 + 142*z + 105*z^2 + 212*z' + 105*z'^2 + 142*z'' + 105*z''^2], size: O(1) [0]

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

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

(82)
Obligation:
Complexity RNTS consisting of the following rules:

   cond1(z, z', z'') -{ 37 + 105*z' }-> s' :|: s' >= 0, s' <= 0, z = 2, z'' = 0, z' >= 0
   cond1(z, z', z'') -{ 72 + 105*z' + 35*z'' }-> s'' :|: s'' >= 0, s'' <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   cond1(z, z', z'') -{ 1 + 105*z' + 35*z'' }-> s1 :|: s1 >= 0, s1 <= 0, z = 2, z' >= 0, z'' >= 0
   cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 74 + 35*z'' }-> s10 :|: s10 >= 0, s10 <= 0, z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ -30 + 105*z' + 35*z'' }-> s11 :|: s11 >= 0, s11 <= 0, z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 74 + 35*z'' }-> s12 :|: s12 >= 0, s12 <= 0, z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 74 + 35*z'' }-> s13 :|: s13 >= 0, s13 <= 0, z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ -31 + 105*z' + 35*z'' }-> s14 :|: s14 >= 0, s14 <= 0, z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 73 + 35*z'' }-> s15 :|: s15 >= 0, s15 <= 0, z = 1, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 38 + 105*z' }-> s2 :|: s2 >= 0, s2 <= 0, z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 37 + 105*z' }-> s3 :|: s3 >= 0, s3 <= 0, z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 38 + 105*z' + 35*z'' }-> s4 :|: s4 >= 0, s4 <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 72 + 105*z' }-> s5 :|: s5 >= 0, s5 <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 2 + 105*z' }-> s6 :|: s6 >= 0, s6 <= 0, z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ -33 + 105*z' + 35*z'' }-> s7 :|: s7 >= 0, s7 <= 0, z = 2, z'' - 1 >= 0, z' >= 0
   cond2(z, z', z'') -{ 1 + 105*z' }-> s8 :|: s8 >= 0, s8 <= 0, z = 2, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 75 + 35*z'' }-> s9 :|: s9 >= 0, s9 <= 0, z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encArg(z) -{ 75 + 105*s18 + 35*s19 + 107*x_1 + 105*x_1^2 + 107*x_2 + 105*x_2^2 + 107*x_3 + 105*x_3^2 }-> s20 :|: s17 >= 0, s17 <= x_1 + 1, s18 >= 0, s18 <= x_2 + 1, s19 >= 0, s19 <= x_3 + 1, s20 >= 0, s20 <= 0, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 3 + 35*s21 + 105*s22 + 35*s23 + 107*x_1 + 105*x_1^2 + 107*x_2 + 105*x_2^2 + 107*x_3 + 105*x_3^2 }-> s24 :|: s21 >= 0, s21 <= x_1 + 1, s22 >= 0, s22 <= x_2 + 1, s23 >= 0, s23 <= x_3 + 1, s24 >= 0, s24 <= 0, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 4 + s26 + 107*x_1 + 105*x_1^2 + 107*x_2 + 105*x_2^2 }-> s27 :|: s25 >= 0, s25 <= x_1 + 1, s26 >= 0, s26 <= x_2 + 1, s27 >= 0, s27 <= 2, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 208 + -313*z + 105*z^2 }-> s41 :|: s40 >= 0, s40 <= z - 2 + 1, s41 >= 0, s41 <= 1 + s40, z - 2 >= 0
   encArg(z) -{ 76 + 105*s43 + 35*s44 + 107*x_1960 + 105*x_1960^2 + 107*x_2575 + 105*x_2575^2 + 107*x_3383 + 105*x_3383^2 }-> s46 :|: s42 >= 0, s42 <= x_1960 + 1, s43 >= 0, s43 <= x_2575 + 1, s44 >= 0, s44 <= x_3383 + 1, s45 >= 0, s45 <= 0, s46 >= 0, s46 <= s45, x_1960 >= 0, x_2575 >= 0, x_3383 >= 0, z = 1 + (1 + x_1960 + x_2575 + x_3383)
   encArg(z) -{ 4 + 35*s47 + 105*s48 + 35*s49 + 107*x_1961 + 105*x_1961^2 + 107*x_2576 + 105*x_2576^2 + 107*x_3384 + 105*x_3384^2 }-> s51 :|: s47 >= 0, s47 <= x_1961 + 1, s48 >= 0, s48 <= x_2576 + 1, s49 >= 0, s49 <= x_3384 + 1, s50 >= 0, s50 <= 0, s51 >= 0, s51 <= s50, x_3384 >= 0, x_2576 >= 0, z = 1 + (1 + x_1961 + x_2576 + x_3384), x_1961 >= 0
   encArg(z) -{ 5 + s53 + 107*x_1962 + 105*x_1962^2 + 107*x_2577 + 105*x_2577^2 }-> s55 :|: s52 >= 0, s52 <= x_1962 + 1, s53 >= 0, s53 <= x_2577 + 1, s54 >= 0, s54 <= 2, s55 >= 0, s55 <= s54, x_2577 >= 0, z = 1 + (1 + x_1962 + x_2577), x_1962 >= 0
   encArg(z) -{ 209 + -313*z + 105*z^2 }-> s58 :|: s56 >= 0, s56 <= z - 2 + 1, s57 >= 0, s57 <= s56, s58 >= 0, s58 <= s57, z - 2 >= 0
   encArg(z) -{ 1 }-> x :|: z = 1 + 2, x >= 0, 2 = 1 + x
   encArg(z) -{ 1 }-> x :|: z = 1 + 1, x >= 0, 1 = 1 + x
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 2 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 0, 0 = 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 1, v0 >= 0, 1 = v0
   encArg(z) -{ 1 }-> 0 :|: z - 1 >= 0, 0 = 0
   encArg(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z) -{ -1 + -103*z + 105*z^2 }-> 1 + s16 :|: s16 >= 0, s16 <= z - 1 + 1, z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_cond1(z, z', z'') -{ 75 + 105*s29 + 35*s30 + 107*z + 105*z^2 + 107*z' + 105*z'^2 + 107*z'' + 105*z''^2 }-> s31 :|: s28 >= 0, s28 <= z + 1, s29 >= 0, s29 <= z' + 1, s30 >= 0, s30 <= z'' + 1, s31 >= 0, s31 <= 0, z >= 0, z'' >= 0, z' >= 0
   encode_cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_cond2(z, z', z'') -{ 3 + 35*s32 + 105*s33 + 35*s34 + 107*z + 105*z^2 + 107*z' + 105*z'^2 + 107*z'' + 105*z''^2 }-> s35 :|: s32 >= 0, s32 <= z + 1, s33 >= 0, s33 <= z' + 1, s34 >= 0, s34 <= z'' + 1, s35 >= 0, s35 <= 0, z >= 0, z'' >= 0, z' >= 0
   encode_cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_gr(z, z') -{ 4 + s37 + 107*z + 105*z^2 + 107*z' + 105*z'^2 }-> s38 :|: s36 >= 0, s36 <= z + 1, s37 >= 0, s37 <= z' + 1, s38 >= 0, s38 <= 2, z >= 0, z' >= 0
   encode_gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_p(z) -{ -103*z + 105*z^2 }-> s60 :|: s59 >= 0, s59 <= z - 1 + 1, s60 >= 0, s60 <= 1 + s59, z - 1 >= 0
   encode_p(z) -{ 76 + 105*s62 + 35*s63 + 107*x_11925 + 105*x_11925^2 + 107*x_21154 + 105*x_21154^2 + 107*x_3769 + 105*x_3769^2 }-> s65 :|: s61 >= 0, s61 <= x_11925 + 1, s62 >= 0, s62 <= x_21154 + 1, s63 >= 0, s63 <= x_3769 + 1, s64 >= 0, s64 <= 0, s65 >= 0, s65 <= s64, z = 1 + x_11925 + x_21154 + x_3769, x_11925 >= 0, x_21154 >= 0, x_3769 >= 0
   encode_p(z) -{ 4 + 35*s66 + 105*s67 + 35*s68 + 107*x_11926 + 105*x_11926^2 + 107*x_21155 + 105*x_21155^2 + 107*x_3770 + 105*x_3770^2 }-> s70 :|: s66 >= 0, s66 <= x_11926 + 1, s67 >= 0, s67 <= x_21155 + 1, s68 >= 0, s68 <= x_3770 + 1, s69 >= 0, s69 <= 0, s70 >= 0, s70 <= s69, x_11926 >= 0, x_21155 >= 0, z = 1 + x_11926 + x_21155 + x_3770, x_3770 >= 0
   encode_p(z) -{ 5 + s72 + 107*x_11927 + 105*x_11927^2 + 107*x_21156 + 105*x_21156^2 }-> s74 :|: s71 >= 0, s71 <= x_11927 + 1, s72 >= 0, s72 <= x_21156 + 1, s73 >= 0, s73 <= 2, s74 >= 0, s74 <= s73, z = 1 + x_11927 + x_21156, x_21156 >= 0, x_11927 >= 0
   encode_p(z) -{ 1 + -103*z + 105*z^2 }-> s77 :|: s75 >= 0, s75 <= z - 1 + 1, s76 >= 0, s76 <= s75, s77 >= 0, s77 <= s76, z - 1 >= 0
   encode_p(z) -{ 1 }-> x :|: z = 2, x >= 0, 2 = 1 + x
   encode_p(z) -{ 1 }-> x :|: z = 1, x >= 0, 1 = 1 + x
   encode_p(z) -{ 0 }-> 0 :|: z >= 0
   encode_p(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 2 = v0
   encode_p(z) -{ 1 }-> 0 :|: z = 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z = 0, v0 >= 0, 0 = v0
   encode_p(z) -{ 0 }-> 0 :|: z = 1, v0 >= 0, 1 = v0
   encode_p(z) -{ 1 }-> 0 :|: z >= 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 1 + 107*z + 105*z^2 }-> 1 + s39 :|: s39 >= 0, s39 <= z + 1, z >= 0
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   gr(z, z') -{ 2 + z' }-> s :|: s >= 0, s <= 2, z - 1 >= 0, z' - 1 >= 0
   gr(z, z') -{ 1 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 1 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 1 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {encode_cond1}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [0], size: O(1) [0]
  encode_false: runtime: O(1) [0], size: O(1) [1]
  gr: runtime: O(n^1) [2 + z'], size: O(1) [2]
  encode_true: runtime: O(1) [0], size: O(1) [2]
  cond2: runtime: O(n^1) [35*z + 105*z' + 35*z''], size: O(1) [0]
  cond1: runtime: O(n^1) [72 + 105*z' + 35*z''], size: O(1) [0]
  p: runtime: O(1) [1], size: O(n^1) [z]
  encArg: runtime: O(n^2) [1 + 107*z + 105*z^2], size: O(n^1) [1 + z]
  encode_p: runtime: O(n^2) [406 + 1172*z + 1050*z^2], size: O(n^1) [1 + z]
  encode_gr: runtime: O(n^2) [5 + 107*z + 105*z^2 + 108*z' + 105*z'^2], size: O(1) [2]
  encode_cond2: runtime: O(n^2) [178 + 142*z + 105*z^2 + 212*z' + 105*z'^2 + 142*z'' + 105*z''^2], size: O(1) [0]

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

(83) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: encode_cond1
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 0

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

(84)
Obligation:
Complexity RNTS consisting of the following rules:

   cond1(z, z', z'') -{ 37 + 105*z' }-> s' :|: s' >= 0, s' <= 0, z = 2, z'' = 0, z' >= 0
   cond1(z, z', z'') -{ 72 + 105*z' + 35*z'' }-> s'' :|: s'' >= 0, s'' <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   cond1(z, z', z'') -{ 1 + 105*z' + 35*z'' }-> s1 :|: s1 >= 0, s1 <= 0, z = 2, z' >= 0, z'' >= 0
   cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 74 + 35*z'' }-> s10 :|: s10 >= 0, s10 <= 0, z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ -30 + 105*z' + 35*z'' }-> s11 :|: s11 >= 0, s11 <= 0, z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 74 + 35*z'' }-> s12 :|: s12 >= 0, s12 <= 0, z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 74 + 35*z'' }-> s13 :|: s13 >= 0, s13 <= 0, z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ -31 + 105*z' + 35*z'' }-> s14 :|: s14 >= 0, s14 <= 0, z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 73 + 35*z'' }-> s15 :|: s15 >= 0, s15 <= 0, z = 1, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 38 + 105*z' }-> s2 :|: s2 >= 0, s2 <= 0, z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 37 + 105*z' }-> s3 :|: s3 >= 0, s3 <= 0, z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 38 + 105*z' + 35*z'' }-> s4 :|: s4 >= 0, s4 <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 72 + 105*z' }-> s5 :|: s5 >= 0, s5 <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 2 + 105*z' }-> s6 :|: s6 >= 0, s6 <= 0, z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ -33 + 105*z' + 35*z'' }-> s7 :|: s7 >= 0, s7 <= 0, z = 2, z'' - 1 >= 0, z' >= 0
   cond2(z, z', z'') -{ 1 + 105*z' }-> s8 :|: s8 >= 0, s8 <= 0, z = 2, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 75 + 35*z'' }-> s9 :|: s9 >= 0, s9 <= 0, z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encArg(z) -{ 75 + 105*s18 + 35*s19 + 107*x_1 + 105*x_1^2 + 107*x_2 + 105*x_2^2 + 107*x_3 + 105*x_3^2 }-> s20 :|: s17 >= 0, s17 <= x_1 + 1, s18 >= 0, s18 <= x_2 + 1, s19 >= 0, s19 <= x_3 + 1, s20 >= 0, s20 <= 0, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 3 + 35*s21 + 105*s22 + 35*s23 + 107*x_1 + 105*x_1^2 + 107*x_2 + 105*x_2^2 + 107*x_3 + 105*x_3^2 }-> s24 :|: s21 >= 0, s21 <= x_1 + 1, s22 >= 0, s22 <= x_2 + 1, s23 >= 0, s23 <= x_3 + 1, s24 >= 0, s24 <= 0, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 4 + s26 + 107*x_1 + 105*x_1^2 + 107*x_2 + 105*x_2^2 }-> s27 :|: s25 >= 0, s25 <= x_1 + 1, s26 >= 0, s26 <= x_2 + 1, s27 >= 0, s27 <= 2, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 208 + -313*z + 105*z^2 }-> s41 :|: s40 >= 0, s40 <= z - 2 + 1, s41 >= 0, s41 <= 1 + s40, z - 2 >= 0
   encArg(z) -{ 76 + 105*s43 + 35*s44 + 107*x_1960 + 105*x_1960^2 + 107*x_2575 + 105*x_2575^2 + 107*x_3383 + 105*x_3383^2 }-> s46 :|: s42 >= 0, s42 <= x_1960 + 1, s43 >= 0, s43 <= x_2575 + 1, s44 >= 0, s44 <= x_3383 + 1, s45 >= 0, s45 <= 0, s46 >= 0, s46 <= s45, x_1960 >= 0, x_2575 >= 0, x_3383 >= 0, z = 1 + (1 + x_1960 + x_2575 + x_3383)
   encArg(z) -{ 4 + 35*s47 + 105*s48 + 35*s49 + 107*x_1961 + 105*x_1961^2 + 107*x_2576 + 105*x_2576^2 + 107*x_3384 + 105*x_3384^2 }-> s51 :|: s47 >= 0, s47 <= x_1961 + 1, s48 >= 0, s48 <= x_2576 + 1, s49 >= 0, s49 <= x_3384 + 1, s50 >= 0, s50 <= 0, s51 >= 0, s51 <= s50, x_3384 >= 0, x_2576 >= 0, z = 1 + (1 + x_1961 + x_2576 + x_3384), x_1961 >= 0
   encArg(z) -{ 5 + s53 + 107*x_1962 + 105*x_1962^2 + 107*x_2577 + 105*x_2577^2 }-> s55 :|: s52 >= 0, s52 <= x_1962 + 1, s53 >= 0, s53 <= x_2577 + 1, s54 >= 0, s54 <= 2, s55 >= 0, s55 <= s54, x_2577 >= 0, z = 1 + (1 + x_1962 + x_2577), x_1962 >= 0
   encArg(z) -{ 209 + -313*z + 105*z^2 }-> s58 :|: s56 >= 0, s56 <= z - 2 + 1, s57 >= 0, s57 <= s56, s58 >= 0, s58 <= s57, z - 2 >= 0
   encArg(z) -{ 1 }-> x :|: z = 1 + 2, x >= 0, 2 = 1 + x
   encArg(z) -{ 1 }-> x :|: z = 1 + 1, x >= 0, 1 = 1 + x
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 2 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 0, 0 = 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 1, v0 >= 0, 1 = v0
   encArg(z) -{ 1 }-> 0 :|: z - 1 >= 0, 0 = 0
   encArg(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z) -{ -1 + -103*z + 105*z^2 }-> 1 + s16 :|: s16 >= 0, s16 <= z - 1 + 1, z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_cond1(z, z', z'') -{ 75 + 105*s29 + 35*s30 + 107*z + 105*z^2 + 107*z' + 105*z'^2 + 107*z'' + 105*z''^2 }-> s31 :|: s28 >= 0, s28 <= z + 1, s29 >= 0, s29 <= z' + 1, s30 >= 0, s30 <= z'' + 1, s31 >= 0, s31 <= 0, z >= 0, z'' >= 0, z' >= 0
   encode_cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_cond2(z, z', z'') -{ 3 + 35*s32 + 105*s33 + 35*s34 + 107*z + 105*z^2 + 107*z' + 105*z'^2 + 107*z'' + 105*z''^2 }-> s35 :|: s32 >= 0, s32 <= z + 1, s33 >= 0, s33 <= z' + 1, s34 >= 0, s34 <= z'' + 1, s35 >= 0, s35 <= 0, z >= 0, z'' >= 0, z' >= 0
   encode_cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_gr(z, z') -{ 4 + s37 + 107*z + 105*z^2 + 107*z' + 105*z'^2 }-> s38 :|: s36 >= 0, s36 <= z + 1, s37 >= 0, s37 <= z' + 1, s38 >= 0, s38 <= 2, z >= 0, z' >= 0
   encode_gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_p(z) -{ -103*z + 105*z^2 }-> s60 :|: s59 >= 0, s59 <= z - 1 + 1, s60 >= 0, s60 <= 1 + s59, z - 1 >= 0
   encode_p(z) -{ 76 + 105*s62 + 35*s63 + 107*x_11925 + 105*x_11925^2 + 107*x_21154 + 105*x_21154^2 + 107*x_3769 + 105*x_3769^2 }-> s65 :|: s61 >= 0, s61 <= x_11925 + 1, s62 >= 0, s62 <= x_21154 + 1, s63 >= 0, s63 <= x_3769 + 1, s64 >= 0, s64 <= 0, s65 >= 0, s65 <= s64, z = 1 + x_11925 + x_21154 + x_3769, x_11925 >= 0, x_21154 >= 0, x_3769 >= 0
   encode_p(z) -{ 4 + 35*s66 + 105*s67 + 35*s68 + 107*x_11926 + 105*x_11926^2 + 107*x_21155 + 105*x_21155^2 + 107*x_3770 + 105*x_3770^2 }-> s70 :|: s66 >= 0, s66 <= x_11926 + 1, s67 >= 0, s67 <= x_21155 + 1, s68 >= 0, s68 <= x_3770 + 1, s69 >= 0, s69 <= 0, s70 >= 0, s70 <= s69, x_11926 >= 0, x_21155 >= 0, z = 1 + x_11926 + x_21155 + x_3770, x_3770 >= 0
   encode_p(z) -{ 5 + s72 + 107*x_11927 + 105*x_11927^2 + 107*x_21156 + 105*x_21156^2 }-> s74 :|: s71 >= 0, s71 <= x_11927 + 1, s72 >= 0, s72 <= x_21156 + 1, s73 >= 0, s73 <= 2, s74 >= 0, s74 <= s73, z = 1 + x_11927 + x_21156, x_21156 >= 0, x_11927 >= 0
   encode_p(z) -{ 1 + -103*z + 105*z^2 }-> s77 :|: s75 >= 0, s75 <= z - 1 + 1, s76 >= 0, s76 <= s75, s77 >= 0, s77 <= s76, z - 1 >= 0
   encode_p(z) -{ 1 }-> x :|: z = 2, x >= 0, 2 = 1 + x
   encode_p(z) -{ 1 }-> x :|: z = 1, x >= 0, 1 = 1 + x
   encode_p(z) -{ 0 }-> 0 :|: z >= 0
   encode_p(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 2 = v0
   encode_p(z) -{ 1 }-> 0 :|: z = 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z = 0, v0 >= 0, 0 = v0
   encode_p(z) -{ 0 }-> 0 :|: z = 1, v0 >= 0, 1 = v0
   encode_p(z) -{ 1 }-> 0 :|: z >= 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 1 + 107*z + 105*z^2 }-> 1 + s39 :|: s39 >= 0, s39 <= z + 1, z >= 0
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   gr(z, z') -{ 2 + z' }-> s :|: s >= 0, s <= 2, z - 1 >= 0, z' - 1 >= 0
   gr(z, z') -{ 1 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 1 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 1 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {encode_cond1}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [0], size: O(1) [0]
  encode_false: runtime: O(1) [0], size: O(1) [1]
  gr: runtime: O(n^1) [2 + z'], size: O(1) [2]
  encode_true: runtime: O(1) [0], size: O(1) [2]
  cond2: runtime: O(n^1) [35*z + 105*z' + 35*z''], size: O(1) [0]
  cond1: runtime: O(n^1) [72 + 105*z' + 35*z''], size: O(1) [0]
  p: runtime: O(1) [1], size: O(n^1) [z]
  encArg: runtime: O(n^2) [1 + 107*z + 105*z^2], size: O(n^1) [1 + z]
  encode_p: runtime: O(n^2) [406 + 1172*z + 1050*z^2], size: O(n^1) [1 + z]
  encode_gr: runtime: O(n^2) [5 + 107*z + 105*z^2 + 108*z' + 105*z'^2], size: O(1) [2]
  encode_cond2: runtime: O(n^2) [178 + 142*z + 105*z^2 + 212*z' + 105*z'^2 + 142*z'' + 105*z''^2], size: O(1) [0]
  encode_cond1: runtime: ?, size: O(1) [0]

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

(85) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using KoAT for: encode_cond1
after applying outer abstraction to obtain an ITS,
resulting in: O(n^2) with polynomial bound: 215 + 107*z + 105*z^2 + 212*z' + 105*z'^2 + 142*z'' + 105*z''^2

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

(86)
Obligation:
Complexity RNTS consisting of the following rules:

   cond1(z, z', z'') -{ 37 + 105*z' }-> s' :|: s' >= 0, s' <= 0, z = 2, z'' = 0, z' >= 0
   cond1(z, z', z'') -{ 72 + 105*z' + 35*z'' }-> s'' :|: s'' >= 0, s'' <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   cond1(z, z', z'') -{ 1 + 105*z' + 35*z'' }-> s1 :|: s1 >= 0, s1 <= 0, z = 2, z' >= 0, z'' >= 0
   cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 74 + 35*z'' }-> s10 :|: s10 >= 0, s10 <= 0, z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ -30 + 105*z' + 35*z'' }-> s11 :|: s11 >= 0, s11 <= 0, z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 74 + 35*z'' }-> s12 :|: s12 >= 0, s12 <= 0, z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 74 + 35*z'' }-> s13 :|: s13 >= 0, s13 <= 0, z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ -31 + 105*z' + 35*z'' }-> s14 :|: s14 >= 0, s14 <= 0, z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 73 + 35*z'' }-> s15 :|: s15 >= 0, s15 <= 0, z = 1, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 38 + 105*z' }-> s2 :|: s2 >= 0, s2 <= 0, z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 37 + 105*z' }-> s3 :|: s3 >= 0, s3 <= 0, z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 38 + 105*z' + 35*z'' }-> s4 :|: s4 >= 0, s4 <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 72 + 105*z' }-> s5 :|: s5 >= 0, s5 <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 2 + 105*z' }-> s6 :|: s6 >= 0, s6 <= 0, z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ -33 + 105*z' + 35*z'' }-> s7 :|: s7 >= 0, s7 <= 0, z = 2, z'' - 1 >= 0, z' >= 0
   cond2(z, z', z'') -{ 1 + 105*z' }-> s8 :|: s8 >= 0, s8 <= 0, z = 2, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 75 + 35*z'' }-> s9 :|: s9 >= 0, s9 <= 0, z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encArg(z) -{ 75 + 105*s18 + 35*s19 + 107*x_1 + 105*x_1^2 + 107*x_2 + 105*x_2^2 + 107*x_3 + 105*x_3^2 }-> s20 :|: s17 >= 0, s17 <= x_1 + 1, s18 >= 0, s18 <= x_2 + 1, s19 >= 0, s19 <= x_3 + 1, s20 >= 0, s20 <= 0, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 3 + 35*s21 + 105*s22 + 35*s23 + 107*x_1 + 105*x_1^2 + 107*x_2 + 105*x_2^2 + 107*x_3 + 105*x_3^2 }-> s24 :|: s21 >= 0, s21 <= x_1 + 1, s22 >= 0, s22 <= x_2 + 1, s23 >= 0, s23 <= x_3 + 1, s24 >= 0, s24 <= 0, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 4 + s26 + 107*x_1 + 105*x_1^2 + 107*x_2 + 105*x_2^2 }-> s27 :|: s25 >= 0, s25 <= x_1 + 1, s26 >= 0, s26 <= x_2 + 1, s27 >= 0, s27 <= 2, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 208 + -313*z + 105*z^2 }-> s41 :|: s40 >= 0, s40 <= z - 2 + 1, s41 >= 0, s41 <= 1 + s40, z - 2 >= 0
   encArg(z) -{ 76 + 105*s43 + 35*s44 + 107*x_1960 + 105*x_1960^2 + 107*x_2575 + 105*x_2575^2 + 107*x_3383 + 105*x_3383^2 }-> s46 :|: s42 >= 0, s42 <= x_1960 + 1, s43 >= 0, s43 <= x_2575 + 1, s44 >= 0, s44 <= x_3383 + 1, s45 >= 0, s45 <= 0, s46 >= 0, s46 <= s45, x_1960 >= 0, x_2575 >= 0, x_3383 >= 0, z = 1 + (1 + x_1960 + x_2575 + x_3383)
   encArg(z) -{ 4 + 35*s47 + 105*s48 + 35*s49 + 107*x_1961 + 105*x_1961^2 + 107*x_2576 + 105*x_2576^2 + 107*x_3384 + 105*x_3384^2 }-> s51 :|: s47 >= 0, s47 <= x_1961 + 1, s48 >= 0, s48 <= x_2576 + 1, s49 >= 0, s49 <= x_3384 + 1, s50 >= 0, s50 <= 0, s51 >= 0, s51 <= s50, x_3384 >= 0, x_2576 >= 0, z = 1 + (1 + x_1961 + x_2576 + x_3384), x_1961 >= 0
   encArg(z) -{ 5 + s53 + 107*x_1962 + 105*x_1962^2 + 107*x_2577 + 105*x_2577^2 }-> s55 :|: s52 >= 0, s52 <= x_1962 + 1, s53 >= 0, s53 <= x_2577 + 1, s54 >= 0, s54 <= 2, s55 >= 0, s55 <= s54, x_2577 >= 0, z = 1 + (1 + x_1962 + x_2577), x_1962 >= 0
   encArg(z) -{ 209 + -313*z + 105*z^2 }-> s58 :|: s56 >= 0, s56 <= z - 2 + 1, s57 >= 0, s57 <= s56, s58 >= 0, s58 <= s57, z - 2 >= 0
   encArg(z) -{ 1 }-> x :|: z = 1 + 2, x >= 0, 2 = 1 + x
   encArg(z) -{ 1 }-> x :|: z = 1 + 1, x >= 0, 1 = 1 + x
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 2 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 0, 0 = 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 1, v0 >= 0, 1 = v0
   encArg(z) -{ 1 }-> 0 :|: z - 1 >= 0, 0 = 0
   encArg(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z) -{ -1 + -103*z + 105*z^2 }-> 1 + s16 :|: s16 >= 0, s16 <= z - 1 + 1, z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_cond1(z, z', z'') -{ 75 + 105*s29 + 35*s30 + 107*z + 105*z^2 + 107*z' + 105*z'^2 + 107*z'' + 105*z''^2 }-> s31 :|: s28 >= 0, s28 <= z + 1, s29 >= 0, s29 <= z' + 1, s30 >= 0, s30 <= z'' + 1, s31 >= 0, s31 <= 0, z >= 0, z'' >= 0, z' >= 0
   encode_cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_cond2(z, z', z'') -{ 3 + 35*s32 + 105*s33 + 35*s34 + 107*z + 105*z^2 + 107*z' + 105*z'^2 + 107*z'' + 105*z''^2 }-> s35 :|: s32 >= 0, s32 <= z + 1, s33 >= 0, s33 <= z' + 1, s34 >= 0, s34 <= z'' + 1, s35 >= 0, s35 <= 0, z >= 0, z'' >= 0, z' >= 0
   encode_cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_gr(z, z') -{ 4 + s37 + 107*z + 105*z^2 + 107*z' + 105*z'^2 }-> s38 :|: s36 >= 0, s36 <= z + 1, s37 >= 0, s37 <= z' + 1, s38 >= 0, s38 <= 2, z >= 0, z' >= 0
   encode_gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_p(z) -{ -103*z + 105*z^2 }-> s60 :|: s59 >= 0, s59 <= z - 1 + 1, s60 >= 0, s60 <= 1 + s59, z - 1 >= 0
   encode_p(z) -{ 76 + 105*s62 + 35*s63 + 107*x_11925 + 105*x_11925^2 + 107*x_21154 + 105*x_21154^2 + 107*x_3769 + 105*x_3769^2 }-> s65 :|: s61 >= 0, s61 <= x_11925 + 1, s62 >= 0, s62 <= x_21154 + 1, s63 >= 0, s63 <= x_3769 + 1, s64 >= 0, s64 <= 0, s65 >= 0, s65 <= s64, z = 1 + x_11925 + x_21154 + x_3769, x_11925 >= 0, x_21154 >= 0, x_3769 >= 0
   encode_p(z) -{ 4 + 35*s66 + 105*s67 + 35*s68 + 107*x_11926 + 105*x_11926^2 + 107*x_21155 + 105*x_21155^2 + 107*x_3770 + 105*x_3770^2 }-> s70 :|: s66 >= 0, s66 <= x_11926 + 1, s67 >= 0, s67 <= x_21155 + 1, s68 >= 0, s68 <= x_3770 + 1, s69 >= 0, s69 <= 0, s70 >= 0, s70 <= s69, x_11926 >= 0, x_21155 >= 0, z = 1 + x_11926 + x_21155 + x_3770, x_3770 >= 0
   encode_p(z) -{ 5 + s72 + 107*x_11927 + 105*x_11927^2 + 107*x_21156 + 105*x_21156^2 }-> s74 :|: s71 >= 0, s71 <= x_11927 + 1, s72 >= 0, s72 <= x_21156 + 1, s73 >= 0, s73 <= 2, s74 >= 0, s74 <= s73, z = 1 + x_11927 + x_21156, x_21156 >= 0, x_11927 >= 0
   encode_p(z) -{ 1 + -103*z + 105*z^2 }-> s77 :|: s75 >= 0, s75 <= z - 1 + 1, s76 >= 0, s76 <= s75, s77 >= 0, s77 <= s76, z - 1 >= 0
   encode_p(z) -{ 1 }-> x :|: z = 2, x >= 0, 2 = 1 + x
   encode_p(z) -{ 1 }-> x :|: z = 1, x >= 0, 1 = 1 + x
   encode_p(z) -{ 0 }-> 0 :|: z >= 0
   encode_p(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 2 = v0
   encode_p(z) -{ 1 }-> 0 :|: z = 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z = 0, v0 >= 0, 0 = v0
   encode_p(z) -{ 0 }-> 0 :|: z = 1, v0 >= 0, 1 = v0
   encode_p(z) -{ 1 }-> 0 :|: z >= 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 1 + 107*z + 105*z^2 }-> 1 + s39 :|: s39 >= 0, s39 <= z + 1, z >= 0
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   gr(z, z') -{ 2 + z' }-> s :|: s >= 0, s <= 2, z - 1 >= 0, z' - 1 >= 0
   gr(z, z') -{ 1 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 1 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 1 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [0], size: O(1) [0]
  encode_false: runtime: O(1) [0], size: O(1) [1]
  gr: runtime: O(n^1) [2 + z'], size: O(1) [2]
  encode_true: runtime: O(1) [0], size: O(1) [2]
  cond2: runtime: O(n^1) [35*z + 105*z' + 35*z''], size: O(1) [0]
  cond1: runtime: O(n^1) [72 + 105*z' + 35*z''], size: O(1) [0]
  p: runtime: O(1) [1], size: O(n^1) [z]
  encArg: runtime: O(n^2) [1 + 107*z + 105*z^2], size: O(n^1) [1 + z]
  encode_p: runtime: O(n^2) [406 + 1172*z + 1050*z^2], size: O(n^1) [1 + z]
  encode_gr: runtime: O(n^2) [5 + 107*z + 105*z^2 + 108*z' + 105*z'^2], size: O(1) [2]
  encode_cond2: runtime: O(n^2) [178 + 142*z + 105*z^2 + 212*z' + 105*z'^2 + 142*z'' + 105*z''^2], size: O(1) [0]
  encode_cond1: runtime: O(n^2) [215 + 107*z + 105*z^2 + 212*z' + 105*z'^2 + 142*z'' + 105*z''^2], size: O(1) [0]

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

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

(88)
Obligation:
Complexity RNTS consisting of the following rules:

   cond1(z, z', z'') -{ 37 + 105*z' }-> s' :|: s' >= 0, s' <= 0, z = 2, z'' = 0, z' >= 0
   cond1(z, z', z'') -{ 72 + 105*z' + 35*z'' }-> s'' :|: s'' >= 0, s'' <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   cond1(z, z', z'') -{ 1 + 105*z' + 35*z'' }-> s1 :|: s1 >= 0, s1 <= 0, z = 2, z' >= 0, z'' >= 0
   cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 74 + 35*z'' }-> s10 :|: s10 >= 0, s10 <= 0, z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ -30 + 105*z' + 35*z'' }-> s11 :|: s11 >= 0, s11 <= 0, z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 74 + 35*z'' }-> s12 :|: s12 >= 0, s12 <= 0, z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 74 + 35*z'' }-> s13 :|: s13 >= 0, s13 <= 0, z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ -31 + 105*z' + 35*z'' }-> s14 :|: s14 >= 0, s14 <= 0, z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 73 + 35*z'' }-> s15 :|: s15 >= 0, s15 <= 0, z = 1, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 38 + 105*z' }-> s2 :|: s2 >= 0, s2 <= 0, z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 37 + 105*z' }-> s3 :|: s3 >= 0, s3 <= 0, z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 38 + 105*z' + 35*z'' }-> s4 :|: s4 >= 0, s4 <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 72 + 105*z' }-> s5 :|: s5 >= 0, s5 <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 2 + 105*z' }-> s6 :|: s6 >= 0, s6 <= 0, z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ -33 + 105*z' + 35*z'' }-> s7 :|: s7 >= 0, s7 <= 0, z = 2, z'' - 1 >= 0, z' >= 0
   cond2(z, z', z'') -{ 1 + 105*z' }-> s8 :|: s8 >= 0, s8 <= 0, z = 2, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 75 + 35*z'' }-> s9 :|: s9 >= 0, s9 <= 0, z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encArg(z) -{ 75 + 105*s18 + 35*s19 + 107*x_1 + 105*x_1^2 + 107*x_2 + 105*x_2^2 + 107*x_3 + 105*x_3^2 }-> s20 :|: s17 >= 0, s17 <= x_1 + 1, s18 >= 0, s18 <= x_2 + 1, s19 >= 0, s19 <= x_3 + 1, s20 >= 0, s20 <= 0, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 3 + 35*s21 + 105*s22 + 35*s23 + 107*x_1 + 105*x_1^2 + 107*x_2 + 105*x_2^2 + 107*x_3 + 105*x_3^2 }-> s24 :|: s21 >= 0, s21 <= x_1 + 1, s22 >= 0, s22 <= x_2 + 1, s23 >= 0, s23 <= x_3 + 1, s24 >= 0, s24 <= 0, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 4 + s26 + 107*x_1 + 105*x_1^2 + 107*x_2 + 105*x_2^2 }-> s27 :|: s25 >= 0, s25 <= x_1 + 1, s26 >= 0, s26 <= x_2 + 1, s27 >= 0, s27 <= 2, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 208 + -313*z + 105*z^2 }-> s41 :|: s40 >= 0, s40 <= z - 2 + 1, s41 >= 0, s41 <= 1 + s40, z - 2 >= 0
   encArg(z) -{ 76 + 105*s43 + 35*s44 + 107*x_1960 + 105*x_1960^2 + 107*x_2575 + 105*x_2575^2 + 107*x_3383 + 105*x_3383^2 }-> s46 :|: s42 >= 0, s42 <= x_1960 + 1, s43 >= 0, s43 <= x_2575 + 1, s44 >= 0, s44 <= x_3383 + 1, s45 >= 0, s45 <= 0, s46 >= 0, s46 <= s45, x_1960 >= 0, x_2575 >= 0, x_3383 >= 0, z = 1 + (1 + x_1960 + x_2575 + x_3383)
   encArg(z) -{ 4 + 35*s47 + 105*s48 + 35*s49 + 107*x_1961 + 105*x_1961^2 + 107*x_2576 + 105*x_2576^2 + 107*x_3384 + 105*x_3384^2 }-> s51 :|: s47 >= 0, s47 <= x_1961 + 1, s48 >= 0, s48 <= x_2576 + 1, s49 >= 0, s49 <= x_3384 + 1, s50 >= 0, s50 <= 0, s51 >= 0, s51 <= s50, x_3384 >= 0, x_2576 >= 0, z = 1 + (1 + x_1961 + x_2576 + x_3384), x_1961 >= 0
   encArg(z) -{ 5 + s53 + 107*x_1962 + 105*x_1962^2 + 107*x_2577 + 105*x_2577^2 }-> s55 :|: s52 >= 0, s52 <= x_1962 + 1, s53 >= 0, s53 <= x_2577 + 1, s54 >= 0, s54 <= 2, s55 >= 0, s55 <= s54, x_2577 >= 0, z = 1 + (1 + x_1962 + x_2577), x_1962 >= 0
   encArg(z) -{ 209 + -313*z + 105*z^2 }-> s58 :|: s56 >= 0, s56 <= z - 2 + 1, s57 >= 0, s57 <= s56, s58 >= 0, s58 <= s57, z - 2 >= 0
   encArg(z) -{ 1 }-> x :|: z = 1 + 2, x >= 0, 2 = 1 + x
   encArg(z) -{ 1 }-> x :|: z = 1 + 1, x >= 0, 1 = 1 + x
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 2 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 0, 0 = 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 1, v0 >= 0, 1 = v0
   encArg(z) -{ 1 }-> 0 :|: z - 1 >= 0, 0 = 0
   encArg(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z) -{ -1 + -103*z + 105*z^2 }-> 1 + s16 :|: s16 >= 0, s16 <= z - 1 + 1, z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_cond1(z, z', z'') -{ 75 + 105*s29 + 35*s30 + 107*z + 105*z^2 + 107*z' + 105*z'^2 + 107*z'' + 105*z''^2 }-> s31 :|: s28 >= 0, s28 <= z + 1, s29 >= 0, s29 <= z' + 1, s30 >= 0, s30 <= z'' + 1, s31 >= 0, s31 <= 0, z >= 0, z'' >= 0, z' >= 0
   encode_cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_cond2(z, z', z'') -{ 3 + 35*s32 + 105*s33 + 35*s34 + 107*z + 105*z^2 + 107*z' + 105*z'^2 + 107*z'' + 105*z''^2 }-> s35 :|: s32 >= 0, s32 <= z + 1, s33 >= 0, s33 <= z' + 1, s34 >= 0, s34 <= z'' + 1, s35 >= 0, s35 <= 0, z >= 0, z'' >= 0, z' >= 0
   encode_cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_gr(z, z') -{ 4 + s37 + 107*z + 105*z^2 + 107*z' + 105*z'^2 }-> s38 :|: s36 >= 0, s36 <= z + 1, s37 >= 0, s37 <= z' + 1, s38 >= 0, s38 <= 2, z >= 0, z' >= 0
   encode_gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_p(z) -{ -103*z + 105*z^2 }-> s60 :|: s59 >= 0, s59 <= z - 1 + 1, s60 >= 0, s60 <= 1 + s59, z - 1 >= 0
   encode_p(z) -{ 76 + 105*s62 + 35*s63 + 107*x_11925 + 105*x_11925^2 + 107*x_21154 + 105*x_21154^2 + 107*x_3769 + 105*x_3769^2 }-> s65 :|: s61 >= 0, s61 <= x_11925 + 1, s62 >= 0, s62 <= x_21154 + 1, s63 >= 0, s63 <= x_3769 + 1, s64 >= 0, s64 <= 0, s65 >= 0, s65 <= s64, z = 1 + x_11925 + x_21154 + x_3769, x_11925 >= 0, x_21154 >= 0, x_3769 >= 0
   encode_p(z) -{ 4 + 35*s66 + 105*s67 + 35*s68 + 107*x_11926 + 105*x_11926^2 + 107*x_21155 + 105*x_21155^2 + 107*x_3770 + 105*x_3770^2 }-> s70 :|: s66 >= 0, s66 <= x_11926 + 1, s67 >= 0, s67 <= x_21155 + 1, s68 >= 0, s68 <= x_3770 + 1, s69 >= 0, s69 <= 0, s70 >= 0, s70 <= s69, x_11926 >= 0, x_21155 >= 0, z = 1 + x_11926 + x_21155 + x_3770, x_3770 >= 0
   encode_p(z) -{ 5 + s72 + 107*x_11927 + 105*x_11927^2 + 107*x_21156 + 105*x_21156^2 }-> s74 :|: s71 >= 0, s71 <= x_11927 + 1, s72 >= 0, s72 <= x_21156 + 1, s73 >= 0, s73 <= 2, s74 >= 0, s74 <= s73, z = 1 + x_11927 + x_21156, x_21156 >= 0, x_11927 >= 0
   encode_p(z) -{ 1 + -103*z + 105*z^2 }-> s77 :|: s75 >= 0, s75 <= z - 1 + 1, s76 >= 0, s76 <= s75, s77 >= 0, s77 <= s76, z - 1 >= 0
   encode_p(z) -{ 1 }-> x :|: z = 2, x >= 0, 2 = 1 + x
   encode_p(z) -{ 1 }-> x :|: z = 1, x >= 0, 1 = 1 + x
   encode_p(z) -{ 0 }-> 0 :|: z >= 0
   encode_p(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 2 = v0
   encode_p(z) -{ 1 }-> 0 :|: z = 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z = 0, v0 >= 0, 0 = v0
   encode_p(z) -{ 0 }-> 0 :|: z = 1, v0 >= 0, 1 = v0
   encode_p(z) -{ 1 }-> 0 :|: z >= 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 1 + 107*z + 105*z^2 }-> 1 + s39 :|: s39 >= 0, s39 <= z + 1, z >= 0
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   gr(z, z') -{ 2 + z' }-> s :|: s >= 0, s <= 2, z - 1 >= 0, z' - 1 >= 0
   gr(z, z') -{ 1 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 1 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 1 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [0], size: O(1) [0]
  encode_false: runtime: O(1) [0], size: O(1) [1]
  gr: runtime: O(n^1) [2 + z'], size: O(1) [2]
  encode_true: runtime: O(1) [0], size: O(1) [2]
  cond2: runtime: O(n^1) [35*z + 105*z' + 35*z''], size: O(1) [0]
  cond1: runtime: O(n^1) [72 + 105*z' + 35*z''], size: O(1) [0]
  p: runtime: O(1) [1], size: O(n^1) [z]
  encArg: runtime: O(n^2) [1 + 107*z + 105*z^2], size: O(n^1) [1 + z]
  encode_p: runtime: O(n^2) [406 + 1172*z + 1050*z^2], size: O(n^1) [1 + z]
  encode_gr: runtime: O(n^2) [5 + 107*z + 105*z^2 + 108*z' + 105*z'^2], size: O(1) [2]
  encode_cond2: runtime: O(n^2) [178 + 142*z + 105*z^2 + 212*z' + 105*z'^2 + 142*z'' + 105*z''^2], size: O(1) [0]
  encode_cond1: runtime: O(n^2) [215 + 107*z + 105*z^2 + 212*z' + 105*z'^2 + 142*z'' + 105*z''^2], size: O(1) [0]

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

(89) IntTrsBoundProof (UPPER BOUND(ID))

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

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

(90)
Obligation:
Complexity RNTS consisting of the following rules:

   cond1(z, z', z'') -{ 37 + 105*z' }-> s' :|: s' >= 0, s' <= 0, z = 2, z'' = 0, z' >= 0
   cond1(z, z', z'') -{ 72 + 105*z' + 35*z'' }-> s'' :|: s'' >= 0, s'' <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   cond1(z, z', z'') -{ 1 + 105*z' + 35*z'' }-> s1 :|: s1 >= 0, s1 <= 0, z = 2, z' >= 0, z'' >= 0
   cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 74 + 35*z'' }-> s10 :|: s10 >= 0, s10 <= 0, z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ -30 + 105*z' + 35*z'' }-> s11 :|: s11 >= 0, s11 <= 0, z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 74 + 35*z'' }-> s12 :|: s12 >= 0, s12 <= 0, z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 74 + 35*z'' }-> s13 :|: s13 >= 0, s13 <= 0, z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ -31 + 105*z' + 35*z'' }-> s14 :|: s14 >= 0, s14 <= 0, z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 73 + 35*z'' }-> s15 :|: s15 >= 0, s15 <= 0, z = 1, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 38 + 105*z' }-> s2 :|: s2 >= 0, s2 <= 0, z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 37 + 105*z' }-> s3 :|: s3 >= 0, s3 <= 0, z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 38 + 105*z' + 35*z'' }-> s4 :|: s4 >= 0, s4 <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 72 + 105*z' }-> s5 :|: s5 >= 0, s5 <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 2 + 105*z' }-> s6 :|: s6 >= 0, s6 <= 0, z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ -33 + 105*z' + 35*z'' }-> s7 :|: s7 >= 0, s7 <= 0, z = 2, z'' - 1 >= 0, z' >= 0
   cond2(z, z', z'') -{ 1 + 105*z' }-> s8 :|: s8 >= 0, s8 <= 0, z = 2, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 75 + 35*z'' }-> s9 :|: s9 >= 0, s9 <= 0, z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encArg(z) -{ 75 + 105*s18 + 35*s19 + 107*x_1 + 105*x_1^2 + 107*x_2 + 105*x_2^2 + 107*x_3 + 105*x_3^2 }-> s20 :|: s17 >= 0, s17 <= x_1 + 1, s18 >= 0, s18 <= x_2 + 1, s19 >= 0, s19 <= x_3 + 1, s20 >= 0, s20 <= 0, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 3 + 35*s21 + 105*s22 + 35*s23 + 107*x_1 + 105*x_1^2 + 107*x_2 + 105*x_2^2 + 107*x_3 + 105*x_3^2 }-> s24 :|: s21 >= 0, s21 <= x_1 + 1, s22 >= 0, s22 <= x_2 + 1, s23 >= 0, s23 <= x_3 + 1, s24 >= 0, s24 <= 0, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 4 + s26 + 107*x_1 + 105*x_1^2 + 107*x_2 + 105*x_2^2 }-> s27 :|: s25 >= 0, s25 <= x_1 + 1, s26 >= 0, s26 <= x_2 + 1, s27 >= 0, s27 <= 2, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 208 + -313*z + 105*z^2 }-> s41 :|: s40 >= 0, s40 <= z - 2 + 1, s41 >= 0, s41 <= 1 + s40, z - 2 >= 0
   encArg(z) -{ 76 + 105*s43 + 35*s44 + 107*x_1960 + 105*x_1960^2 + 107*x_2575 + 105*x_2575^2 + 107*x_3383 + 105*x_3383^2 }-> s46 :|: s42 >= 0, s42 <= x_1960 + 1, s43 >= 0, s43 <= x_2575 + 1, s44 >= 0, s44 <= x_3383 + 1, s45 >= 0, s45 <= 0, s46 >= 0, s46 <= s45, x_1960 >= 0, x_2575 >= 0, x_3383 >= 0, z = 1 + (1 + x_1960 + x_2575 + x_3383)
   encArg(z) -{ 4 + 35*s47 + 105*s48 + 35*s49 + 107*x_1961 + 105*x_1961^2 + 107*x_2576 + 105*x_2576^2 + 107*x_3384 + 105*x_3384^2 }-> s51 :|: s47 >= 0, s47 <= x_1961 + 1, s48 >= 0, s48 <= x_2576 + 1, s49 >= 0, s49 <= x_3384 + 1, s50 >= 0, s50 <= 0, s51 >= 0, s51 <= s50, x_3384 >= 0, x_2576 >= 0, z = 1 + (1 + x_1961 + x_2576 + x_3384), x_1961 >= 0
   encArg(z) -{ 5 + s53 + 107*x_1962 + 105*x_1962^2 + 107*x_2577 + 105*x_2577^2 }-> s55 :|: s52 >= 0, s52 <= x_1962 + 1, s53 >= 0, s53 <= x_2577 + 1, s54 >= 0, s54 <= 2, s55 >= 0, s55 <= s54, x_2577 >= 0, z = 1 + (1 + x_1962 + x_2577), x_1962 >= 0
   encArg(z) -{ 209 + -313*z + 105*z^2 }-> s58 :|: s56 >= 0, s56 <= z - 2 + 1, s57 >= 0, s57 <= s56, s58 >= 0, s58 <= s57, z - 2 >= 0
   encArg(z) -{ 1 }-> x :|: z = 1 + 2, x >= 0, 2 = 1 + x
   encArg(z) -{ 1 }-> x :|: z = 1 + 1, x >= 0, 1 = 1 + x
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 2 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 0, 0 = 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 1, v0 >= 0, 1 = v0
   encArg(z) -{ 1 }-> 0 :|: z - 1 >= 0, 0 = 0
   encArg(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z) -{ -1 + -103*z + 105*z^2 }-> 1 + s16 :|: s16 >= 0, s16 <= z - 1 + 1, z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_cond1(z, z', z'') -{ 75 + 105*s29 + 35*s30 + 107*z + 105*z^2 + 107*z' + 105*z'^2 + 107*z'' + 105*z''^2 }-> s31 :|: s28 >= 0, s28 <= z + 1, s29 >= 0, s29 <= z' + 1, s30 >= 0, s30 <= z'' + 1, s31 >= 0, s31 <= 0, z >= 0, z'' >= 0, z' >= 0
   encode_cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_cond2(z, z', z'') -{ 3 + 35*s32 + 105*s33 + 35*s34 + 107*z + 105*z^2 + 107*z' + 105*z'^2 + 107*z'' + 105*z''^2 }-> s35 :|: s32 >= 0, s32 <= z + 1, s33 >= 0, s33 <= z' + 1, s34 >= 0, s34 <= z'' + 1, s35 >= 0, s35 <= 0, z >= 0, z'' >= 0, z' >= 0
   encode_cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_gr(z, z') -{ 4 + s37 + 107*z + 105*z^2 + 107*z' + 105*z'^2 }-> s38 :|: s36 >= 0, s36 <= z + 1, s37 >= 0, s37 <= z' + 1, s38 >= 0, s38 <= 2, z >= 0, z' >= 0
   encode_gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_p(z) -{ -103*z + 105*z^2 }-> s60 :|: s59 >= 0, s59 <= z - 1 + 1, s60 >= 0, s60 <= 1 + s59, z - 1 >= 0
   encode_p(z) -{ 76 + 105*s62 + 35*s63 + 107*x_11925 + 105*x_11925^2 + 107*x_21154 + 105*x_21154^2 + 107*x_3769 + 105*x_3769^2 }-> s65 :|: s61 >= 0, s61 <= x_11925 + 1, s62 >= 0, s62 <= x_21154 + 1, s63 >= 0, s63 <= x_3769 + 1, s64 >= 0, s64 <= 0, s65 >= 0, s65 <= s64, z = 1 + x_11925 + x_21154 + x_3769, x_11925 >= 0, x_21154 >= 0, x_3769 >= 0
   encode_p(z) -{ 4 + 35*s66 + 105*s67 + 35*s68 + 107*x_11926 + 105*x_11926^2 + 107*x_21155 + 105*x_21155^2 + 107*x_3770 + 105*x_3770^2 }-> s70 :|: s66 >= 0, s66 <= x_11926 + 1, s67 >= 0, s67 <= x_21155 + 1, s68 >= 0, s68 <= x_3770 + 1, s69 >= 0, s69 <= 0, s70 >= 0, s70 <= s69, x_11926 >= 0, x_21155 >= 0, z = 1 + x_11926 + x_21155 + x_3770, x_3770 >= 0
   encode_p(z) -{ 5 + s72 + 107*x_11927 + 105*x_11927^2 + 107*x_21156 + 105*x_21156^2 }-> s74 :|: s71 >= 0, s71 <= x_11927 + 1, s72 >= 0, s72 <= x_21156 + 1, s73 >= 0, s73 <= 2, s74 >= 0, s74 <= s73, z = 1 + x_11927 + x_21156, x_21156 >= 0, x_11927 >= 0
   encode_p(z) -{ 1 + -103*z + 105*z^2 }-> s77 :|: s75 >= 0, s75 <= z - 1 + 1, s76 >= 0, s76 <= s75, s77 >= 0, s77 <= s76, z - 1 >= 0
   encode_p(z) -{ 1 }-> x :|: z = 2, x >= 0, 2 = 1 + x
   encode_p(z) -{ 1 }-> x :|: z = 1, x >= 0, 1 = 1 + x
   encode_p(z) -{ 0 }-> 0 :|: z >= 0
   encode_p(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 2 = v0
   encode_p(z) -{ 1 }-> 0 :|: z = 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z = 0, v0 >= 0, 0 = v0
   encode_p(z) -{ 0 }-> 0 :|: z = 1, v0 >= 0, 1 = v0
   encode_p(z) -{ 1 }-> 0 :|: z >= 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 1 + 107*z + 105*z^2 }-> 1 + s39 :|: s39 >= 0, s39 <= z + 1, z >= 0
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   gr(z, z') -{ 2 + z' }-> s :|: s >= 0, s <= 2, z - 1 >= 0, z' - 1 >= 0
   gr(z, z') -{ 1 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 1 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 1 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [0], size: O(1) [0]
  encode_false: runtime: O(1) [0], size: O(1) [1]
  gr: runtime: O(n^1) [2 + z'], size: O(1) [2]
  encode_true: runtime: O(1) [0], size: O(1) [2]
  cond2: runtime: O(n^1) [35*z + 105*z' + 35*z''], size: O(1) [0]
  cond1: runtime: O(n^1) [72 + 105*z' + 35*z''], size: O(1) [0]
  p: runtime: O(1) [1], size: O(n^1) [z]
  encArg: runtime: O(n^2) [1 + 107*z + 105*z^2], size: O(n^1) [1 + z]
  encode_p: runtime: O(n^2) [406 + 1172*z + 1050*z^2], size: O(n^1) [1 + z]
  encode_gr: runtime: O(n^2) [5 + 107*z + 105*z^2 + 108*z' + 105*z'^2], size: O(1) [2]
  encode_cond2: runtime: O(n^2) [178 + 142*z + 105*z^2 + 212*z' + 105*z'^2 + 142*z'' + 105*z''^2], size: O(1) [0]
  encode_cond1: runtime: O(n^2) [215 + 107*z + 105*z^2 + 212*z' + 105*z'^2 + 142*z'' + 105*z''^2], size: O(1) [0]
  encode_s: runtime: ?, size: O(n^1) [2 + z]

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

(91) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using KoAT for: encode_s
after applying outer abstraction to obtain an ITS,
resulting in: O(n^2) with polynomial bound: 1 + 107*z + 105*z^2

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

(92)
Obligation:
Complexity RNTS consisting of the following rules:

   cond1(z, z', z'') -{ 37 + 105*z' }-> s' :|: s' >= 0, s' <= 0, z = 2, z'' = 0, z' >= 0
   cond1(z, z', z'') -{ 72 + 105*z' + 35*z'' }-> s'' :|: s'' >= 0, s'' <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   cond1(z, z', z'') -{ 1 + 105*z' + 35*z'' }-> s1 :|: s1 >= 0, s1 <= 0, z = 2, z' >= 0, z'' >= 0
   cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 74 + 35*z'' }-> s10 :|: s10 >= 0, s10 <= 0, z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ -30 + 105*z' + 35*z'' }-> s11 :|: s11 >= 0, s11 <= 0, z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 74 + 35*z'' }-> s12 :|: s12 >= 0, s12 <= 0, z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 74 + 35*z'' }-> s13 :|: s13 >= 0, s13 <= 0, z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ -31 + 105*z' + 35*z'' }-> s14 :|: s14 >= 0, s14 <= 0, z = 1, z'' >= 0, z' - 1 >= 0
   cond2(z, z', z'') -{ 73 + 35*z'' }-> s15 :|: s15 >= 0, s15 <= 0, z = 1, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 38 + 105*z' }-> s2 :|: s2 >= 0, s2 <= 0, z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 37 + 105*z' }-> s3 :|: s3 >= 0, s3 <= 0, z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ 38 + 105*z' + 35*z'' }-> s4 :|: s4 >= 0, s4 <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 72 + 105*z' }-> s5 :|: s5 >= 0, s5 <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'') -{ 2 + 105*z' }-> s6 :|: s6 >= 0, s6 <= 0, z = 2, z'' = 0, z' >= 0
   cond2(z, z', z'') -{ -33 + 105*z' + 35*z'' }-> s7 :|: s7 >= 0, s7 <= 0, z = 2, z'' - 1 >= 0, z' >= 0
   cond2(z, z', z'') -{ 1 + 105*z' }-> s8 :|: s8 >= 0, s8 <= 0, z = 2, z' >= 0, z'' >= 0
   cond2(z, z', z'') -{ 75 + 35*z'' }-> s9 :|: s9 >= 0, s9 <= 0, z = 1, z'' >= 0, z' = 0
   cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encArg(z) -{ 75 + 105*s18 + 35*s19 + 107*x_1 + 105*x_1^2 + 107*x_2 + 105*x_2^2 + 107*x_3 + 105*x_3^2 }-> s20 :|: s17 >= 0, s17 <= x_1 + 1, s18 >= 0, s18 <= x_2 + 1, s19 >= 0, s19 <= x_3 + 1, s20 >= 0, s20 <= 0, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 3 + 35*s21 + 105*s22 + 35*s23 + 107*x_1 + 105*x_1^2 + 107*x_2 + 105*x_2^2 + 107*x_3 + 105*x_3^2 }-> s24 :|: s21 >= 0, s21 <= x_1 + 1, s22 >= 0, s22 <= x_2 + 1, s23 >= 0, s23 <= x_3 + 1, s24 >= 0, s24 <= 0, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 4 + s26 + 107*x_1 + 105*x_1^2 + 107*x_2 + 105*x_2^2 }-> s27 :|: s25 >= 0, s25 <= x_1 + 1, s26 >= 0, s26 <= x_2 + 1, s27 >= 0, s27 <= 2, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 208 + -313*z + 105*z^2 }-> s41 :|: s40 >= 0, s40 <= z - 2 + 1, s41 >= 0, s41 <= 1 + s40, z - 2 >= 0
   encArg(z) -{ 76 + 105*s43 + 35*s44 + 107*x_1960 + 105*x_1960^2 + 107*x_2575 + 105*x_2575^2 + 107*x_3383 + 105*x_3383^2 }-> s46 :|: s42 >= 0, s42 <= x_1960 + 1, s43 >= 0, s43 <= x_2575 + 1, s44 >= 0, s44 <= x_3383 + 1, s45 >= 0, s45 <= 0, s46 >= 0, s46 <= s45, x_1960 >= 0, x_2575 >= 0, x_3383 >= 0, z = 1 + (1 + x_1960 + x_2575 + x_3383)
   encArg(z) -{ 4 + 35*s47 + 105*s48 + 35*s49 + 107*x_1961 + 105*x_1961^2 + 107*x_2576 + 105*x_2576^2 + 107*x_3384 + 105*x_3384^2 }-> s51 :|: s47 >= 0, s47 <= x_1961 + 1, s48 >= 0, s48 <= x_2576 + 1, s49 >= 0, s49 <= x_3384 + 1, s50 >= 0, s50 <= 0, s51 >= 0, s51 <= s50, x_3384 >= 0, x_2576 >= 0, z = 1 + (1 + x_1961 + x_2576 + x_3384), x_1961 >= 0
   encArg(z) -{ 5 + s53 + 107*x_1962 + 105*x_1962^2 + 107*x_2577 + 105*x_2577^2 }-> s55 :|: s52 >= 0, s52 <= x_1962 + 1, s53 >= 0, s53 <= x_2577 + 1, s54 >= 0, s54 <= 2, s55 >= 0, s55 <= s54, x_2577 >= 0, z = 1 + (1 + x_1962 + x_2577), x_1962 >= 0
   encArg(z) -{ 209 + -313*z + 105*z^2 }-> s58 :|: s56 >= 0, s56 <= z - 2 + 1, s57 >= 0, s57 <= s56, s58 >= 0, s58 <= s57, z - 2 >= 0
   encArg(z) -{ 1 }-> x :|: z = 1 + 2, x >= 0, 2 = 1 + x
   encArg(z) -{ 1 }-> x :|: z = 1 + 1, x >= 0, 1 = 1 + x
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 2 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 0, 0 = 0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 1, v0 >= 0, 1 = v0
   encArg(z) -{ 1 }-> 0 :|: z - 1 >= 0, 0 = 0
   encArg(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z) -{ -1 + -103*z + 105*z^2 }-> 1 + s16 :|: s16 >= 0, s16 <= z - 1 + 1, z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_cond1(z, z', z'') -{ 75 + 105*s29 + 35*s30 + 107*z + 105*z^2 + 107*z' + 105*z'^2 + 107*z'' + 105*z''^2 }-> s31 :|: s28 >= 0, s28 <= z + 1, s29 >= 0, s29 <= z' + 1, s30 >= 0, s30 <= z'' + 1, s31 >= 0, s31 <= 0, z >= 0, z'' >= 0, z' >= 0
   encode_cond1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_cond2(z, z', z'') -{ 3 + 35*s32 + 105*s33 + 35*s34 + 107*z + 105*z^2 + 107*z' + 105*z'^2 + 107*z'' + 105*z''^2 }-> s35 :|: s32 >= 0, s32 <= z + 1, s33 >= 0, s33 <= z' + 1, s34 >= 0, s34 <= z'' + 1, s35 >= 0, s35 <= 0, z >= 0, z'' >= 0, z' >= 0
   encode_cond2(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_gr(z, z') -{ 4 + s37 + 107*z + 105*z^2 + 107*z' + 105*z'^2 }-> s38 :|: s36 >= 0, s36 <= z + 1, s37 >= 0, s37 <= z' + 1, s38 >= 0, s38 <= 2, z >= 0, z' >= 0
   encode_gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_p(z) -{ -103*z + 105*z^2 }-> s60 :|: s59 >= 0, s59 <= z - 1 + 1, s60 >= 0, s60 <= 1 + s59, z - 1 >= 0
   encode_p(z) -{ 76 + 105*s62 + 35*s63 + 107*x_11925 + 105*x_11925^2 + 107*x_21154 + 105*x_21154^2 + 107*x_3769 + 105*x_3769^2 }-> s65 :|: s61 >= 0, s61 <= x_11925 + 1, s62 >= 0, s62 <= x_21154 + 1, s63 >= 0, s63 <= x_3769 + 1, s64 >= 0, s64 <= 0, s65 >= 0, s65 <= s64, z = 1 + x_11925 + x_21154 + x_3769, x_11925 >= 0, x_21154 >= 0, x_3769 >= 0
   encode_p(z) -{ 4 + 35*s66 + 105*s67 + 35*s68 + 107*x_11926 + 105*x_11926^2 + 107*x_21155 + 105*x_21155^2 + 107*x_3770 + 105*x_3770^2 }-> s70 :|: s66 >= 0, s66 <= x_11926 + 1, s67 >= 0, s67 <= x_21155 + 1, s68 >= 0, s68 <= x_3770 + 1, s69 >= 0, s69 <= 0, s70 >= 0, s70 <= s69, x_11926 >= 0, x_21155 >= 0, z = 1 + x_11926 + x_21155 + x_3770, x_3770 >= 0
   encode_p(z) -{ 5 + s72 + 107*x_11927 + 105*x_11927^2 + 107*x_21156 + 105*x_21156^2 }-> s74 :|: s71 >= 0, s71 <= x_11927 + 1, s72 >= 0, s72 <= x_21156 + 1, s73 >= 0, s73 <= 2, s74 >= 0, s74 <= s73, z = 1 + x_11927 + x_21156, x_21156 >= 0, x_11927 >= 0
   encode_p(z) -{ 1 + -103*z + 105*z^2 }-> s77 :|: s75 >= 0, s75 <= z - 1 + 1, s76 >= 0, s76 <= s75, s77 >= 0, s77 <= s76, z - 1 >= 0
   encode_p(z) -{ 1 }-> x :|: z = 2, x >= 0, 2 = 1 + x
   encode_p(z) -{ 1 }-> x :|: z = 1, x >= 0, 1 = 1 + x
   encode_p(z) -{ 0 }-> 0 :|: z >= 0
   encode_p(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 2 = v0
   encode_p(z) -{ 1 }-> 0 :|: z = 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z = 0, v0 >= 0, 0 = v0
   encode_p(z) -{ 0 }-> 0 :|: z = 1, v0 >= 0, 1 = v0
   encode_p(z) -{ 1 }-> 0 :|: z >= 0, 0 = 0
   encode_p(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 1 + 107*z + 105*z^2 }-> 1 + s39 :|: s39 >= 0, s39 <= z + 1, z >= 0
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   gr(z, z') -{ 2 + z' }-> s :|: s >= 0, s <= 2, z - 1 >= 0, z' - 1 >= 0
   gr(z, z') -{ 1 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 1 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 1 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: 
Previous analysis results are:
  encode_0: runtime: O(1) [0], size: O(1) [0]
  encode_false: runtime: O(1) [0], size: O(1) [1]
  gr: runtime: O(n^1) [2 + z'], size: O(1) [2]
  encode_true: runtime: O(1) [0], size: O(1) [2]
  cond2: runtime: O(n^1) [35*z + 105*z' + 35*z''], size: O(1) [0]
  cond1: runtime: O(n^1) [72 + 105*z' + 35*z''], size: O(1) [0]
  p: runtime: O(1) [1], size: O(n^1) [z]
  encArg: runtime: O(n^2) [1 + 107*z + 105*z^2], size: O(n^1) [1 + z]
  encode_p: runtime: O(n^2) [406 + 1172*z + 1050*z^2], size: O(n^1) [1 + z]
  encode_gr: runtime: O(n^2) [5 + 107*z + 105*z^2 + 108*z' + 105*z'^2], size: O(1) [2]
  encode_cond2: runtime: O(n^2) [178 + 142*z + 105*z^2 + 212*z' + 105*z'^2 + 142*z'' + 105*z''^2], size: O(1) [0]
  encode_cond1: runtime: O(n^2) [215 + 107*z + 105*z^2 + 212*z' + 105*z'^2 + 142*z'' + 105*z''^2], size: O(1) [0]
  encode_s: runtime: O(n^2) [1 + 107*z + 105*z^2], size: O(n^1) [2 + z]

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

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

(94)
BOUNDS(1, n^2)

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

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

(96)
Obligation:
The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF).


The TRS R consists of the following rules:

   cond1(true, x, y) -> cond2(gr(y, 0'), x, y)
   cond2(true, x, y) -> cond2(gr(y, 0'), x, p(y))
   cond2(false, x, y) -> cond1(gr(x, 0'), p(x), y)
   gr(0', x) -> false
   gr(s(x), 0') -> true
   gr(s(x), s(y)) -> gr(x, y)
   p(0') -> 0'
   p(s(x)) -> x

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

   encArg(true) -> true
   encArg(0') -> 0'
   encArg(false) -> false
   encArg(s(x_1)) -> s(encArg(x_1))
   encArg(cons_cond1(x_1, x_2, x_3)) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3))
   encArg(cons_cond2(x_1, x_2, x_3)) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3))
   encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2))
   encArg(cons_p(x_1)) -> p(encArg(x_1))
   encode_cond1(x_1, x_2, x_3) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3))
   encode_true -> true
   encode_cond2(x_1, x_2, x_3) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3))
   encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2))
   encode_0 -> 0'
   encode_p(x_1) -> p(encArg(x_1))
   encode_false -> false
   encode_s(x_1) -> s(encArg(x_1))

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

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

(98)
Obligation:
Innermost TRS:
Rules:
cond1(true, x, y) -> cond2(gr(y, 0'), x, y)
cond2(true, x, y) -> cond2(gr(y, 0'), x, p(y))
cond2(false, x, y) -> cond1(gr(x, 0'), p(x), y)
gr(0', x) -> false
gr(s(x), 0') -> true
gr(s(x), s(y)) -> gr(x, y)
p(0') -> 0'
p(s(x)) -> x
encArg(true) -> true
encArg(0') -> 0'
encArg(false) -> false
encArg(s(x_1)) -> s(encArg(x_1))
encArg(cons_cond1(x_1, x_2, x_3)) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3))
encArg(cons_cond2(x_1, x_2, x_3)) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3))
encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2))
encArg(cons_p(x_1)) -> p(encArg(x_1))
encode_cond1(x_1, x_2, x_3) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3))
encode_true -> true
encode_cond2(x_1, x_2, x_3) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3))
encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2))
encode_0 -> 0'
encode_p(x_1) -> p(encArg(x_1))
encode_false -> false
encode_s(x_1) -> s(encArg(x_1))

Types:
cond1 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
true :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
cond2 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
gr :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
0' :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
p :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
false :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
s :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
encArg :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
cons_cond1 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
cons_cond2 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
cons_gr :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
cons_p :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
encode_cond1 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
encode_true :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
encode_cond2 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
encode_gr :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
encode_0 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
encode_p :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
encode_false :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
encode_s :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
hole_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p1_4 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4 :: Nat -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p

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

(99) OrderProof (LOWER BOUND(ID))
Heuristically decided to analyse the following defined symbols:
cond1, cond2, gr, encArg

They will be analysed ascendingly in the following order:
cond1 = cond2
gr < cond1
cond1 < encArg
gr < cond2
cond2 < encArg
gr < encArg

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

(100)
Obligation:
Innermost TRS:
Rules:
cond1(true, x, y) -> cond2(gr(y, 0'), x, y)
cond2(true, x, y) -> cond2(gr(y, 0'), x, p(y))
cond2(false, x, y) -> cond1(gr(x, 0'), p(x), y)
gr(0', x) -> false
gr(s(x), 0') -> true
gr(s(x), s(y)) -> gr(x, y)
p(0') -> 0'
p(s(x)) -> x
encArg(true) -> true
encArg(0') -> 0'
encArg(false) -> false
encArg(s(x_1)) -> s(encArg(x_1))
encArg(cons_cond1(x_1, x_2, x_3)) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3))
encArg(cons_cond2(x_1, x_2, x_3)) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3))
encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2))
encArg(cons_p(x_1)) -> p(encArg(x_1))
encode_cond1(x_1, x_2, x_3) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3))
encode_true -> true
encode_cond2(x_1, x_2, x_3) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3))
encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2))
encode_0 -> 0'
encode_p(x_1) -> p(encArg(x_1))
encode_false -> false
encode_s(x_1) -> s(encArg(x_1))

Types:
cond1 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
true :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
cond2 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
gr :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
0' :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
p :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
false :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
s :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
encArg :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
cons_cond1 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
cons_cond2 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
cons_gr :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
cons_p :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
encode_cond1 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
encode_true :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
encode_cond2 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
encode_gr :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
encode_0 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
encode_p :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
encode_false :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
encode_s :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
hole_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p1_4 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4 :: Nat -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p


Generator Equations:
gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(0) <=> true
gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(+(x, 1)) <=> s(gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(x))


The following defined symbols remain to be analysed:
gr, cond1, cond2, encArg

They will be analysed ascendingly in the following order:
cond1 = cond2
gr < cond1
cond1 < encArg
gr < cond2
cond2 < encArg
gr < encArg

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

(101) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
gr(gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(+(1, n4_4)), gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(+(1, n4_4))) -> *3_4, rt in Omega(n4_4)

Induction Base:
gr(gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(+(1, 0)), gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(+(1, 0)))

Induction Step:
gr(gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(+(1, +(n4_4, 1))), gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(+(1, +(n4_4, 1)))) ->_R^Omega(1)
gr(gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(+(1, n4_4)), gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(+(1, n4_4))) ->_IH
*3_4

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

(102)
Complex Obligation (BEST)

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

(103)
Obligation:
Proved the lower bound n^1 for the following obligation:

Innermost TRS:
Rules:
cond1(true, x, y) -> cond2(gr(y, 0'), x, y)
cond2(true, x, y) -> cond2(gr(y, 0'), x, p(y))
cond2(false, x, y) -> cond1(gr(x, 0'), p(x), y)
gr(0', x) -> false
gr(s(x), 0') -> true
gr(s(x), s(y)) -> gr(x, y)
p(0') -> 0'
p(s(x)) -> x
encArg(true) -> true
encArg(0') -> 0'
encArg(false) -> false
encArg(s(x_1)) -> s(encArg(x_1))
encArg(cons_cond1(x_1, x_2, x_3)) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3))
encArg(cons_cond2(x_1, x_2, x_3)) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3))
encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2))
encArg(cons_p(x_1)) -> p(encArg(x_1))
encode_cond1(x_1, x_2, x_3) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3))
encode_true -> true
encode_cond2(x_1, x_2, x_3) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3))
encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2))
encode_0 -> 0'
encode_p(x_1) -> p(encArg(x_1))
encode_false -> false
encode_s(x_1) -> s(encArg(x_1))

Types:
cond1 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
true :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
cond2 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
gr :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
0' :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
p :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
false :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
s :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
encArg :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
cons_cond1 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
cons_cond2 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
cons_gr :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
cons_p :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
encode_cond1 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
encode_true :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
encode_cond2 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
encode_gr :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
encode_0 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
encode_p :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
encode_false :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
encode_s :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
hole_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p1_4 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4 :: Nat -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p


Generator Equations:
gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(0) <=> true
gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(+(x, 1)) <=> s(gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(x))


The following defined symbols remain to be analysed:
gr, cond1, cond2, encArg

They will be analysed ascendingly in the following order:
cond1 = cond2
gr < cond1
cond1 < encArg
gr < cond2
cond2 < encArg
gr < encArg

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

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

(105)
BOUNDS(n^1, INF)

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

(106)
Obligation:
Innermost TRS:
Rules:
cond1(true, x, y) -> cond2(gr(y, 0'), x, y)
cond2(true, x, y) -> cond2(gr(y, 0'), x, p(y))
cond2(false, x, y) -> cond1(gr(x, 0'), p(x), y)
gr(0', x) -> false
gr(s(x), 0') -> true
gr(s(x), s(y)) -> gr(x, y)
p(0') -> 0'
p(s(x)) -> x
encArg(true) -> true
encArg(0') -> 0'
encArg(false) -> false
encArg(s(x_1)) -> s(encArg(x_1))
encArg(cons_cond1(x_1, x_2, x_3)) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3))
encArg(cons_cond2(x_1, x_2, x_3)) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3))
encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2))
encArg(cons_p(x_1)) -> p(encArg(x_1))
encode_cond1(x_1, x_2, x_3) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3))
encode_true -> true
encode_cond2(x_1, x_2, x_3) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3))
encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2))
encode_0 -> 0'
encode_p(x_1) -> p(encArg(x_1))
encode_false -> false
encode_s(x_1) -> s(encArg(x_1))

Types:
cond1 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
true :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
cond2 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
gr :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
0' :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
p :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
false :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
s :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
encArg :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
cons_cond1 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
cons_cond2 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
cons_gr :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
cons_p :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
encode_cond1 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
encode_true :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
encode_cond2 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
encode_gr :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
encode_0 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
encode_p :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
encode_false :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
encode_s :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
hole_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p1_4 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4 :: Nat -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p


Lemmas:
gr(gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(+(1, n4_4)), gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(+(1, n4_4))) -> *3_4, rt in Omega(n4_4)


Generator Equations:
gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(0) <=> true
gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(+(x, 1)) <=> s(gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(x))


The following defined symbols remain to be analysed:
cond2, cond1, encArg

They will be analysed ascendingly in the following order:
cond1 = cond2
cond1 < encArg
cond2 < encArg

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

(107) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
cond2(gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(0), gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(b), gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(n1218_4)) -> *3_4, rt in Omega(n1218_4)

Induction Base:
cond2(gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(0), gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(b), gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(0))

Induction Step:
cond2(gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(0), gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(b), gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(+(n1218_4, 1))) ->_R^Omega(1)
cond2(gr(gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(+(n1218_4, 1)), 0'), gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(b), p(gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(+(n1218_4, 1)))) ->_R^Omega(1)
cond2(true, gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(b), p(gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(+(1, n1218_4)))) ->_R^Omega(1)
cond2(true, gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(b), gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(n1218_4)) ->_IH
*3_4

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

(108)
Obligation:
Innermost TRS:
Rules:
cond1(true, x, y) -> cond2(gr(y, 0'), x, y)
cond2(true, x, y) -> cond2(gr(y, 0'), x, p(y))
cond2(false, x, y) -> cond1(gr(x, 0'), p(x), y)
gr(0', x) -> false
gr(s(x), 0') -> true
gr(s(x), s(y)) -> gr(x, y)
p(0') -> 0'
p(s(x)) -> x
encArg(true) -> true
encArg(0') -> 0'
encArg(false) -> false
encArg(s(x_1)) -> s(encArg(x_1))
encArg(cons_cond1(x_1, x_2, x_3)) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3))
encArg(cons_cond2(x_1, x_2, x_3)) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3))
encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2))
encArg(cons_p(x_1)) -> p(encArg(x_1))
encode_cond1(x_1, x_2, x_3) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3))
encode_true -> true
encode_cond2(x_1, x_2, x_3) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3))
encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2))
encode_0 -> 0'
encode_p(x_1) -> p(encArg(x_1))
encode_false -> false
encode_s(x_1) -> s(encArg(x_1))

Types:
cond1 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
true :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
cond2 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
gr :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
0' :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
p :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
false :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
s :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
encArg :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
cons_cond1 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
cons_cond2 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
cons_gr :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
cons_p :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
encode_cond1 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
encode_true :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
encode_cond2 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
encode_gr :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
encode_0 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
encode_p :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
encode_false :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
encode_s :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
hole_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p1_4 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p
gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4 :: Nat -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p


Lemmas:
gr(gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(+(1, n4_4)), gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(+(1, n4_4))) -> *3_4, rt in Omega(n4_4)
cond2(gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(0), gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(b), gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(n1218_4)) -> *3_4, rt in Omega(n1218_4)


Generator Equations:
gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(0) <=> true
gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(+(x, 1)) <=> s(gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(x))


The following defined symbols remain to be analysed:
cond1, encArg

They will be analysed ascendingly in the following order:
cond1 = cond2
cond1 < encArg
cond2 < encArg

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

(109) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
encArg(gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(n3769_4)) -> gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(n3769_4), rt in Omega(0)

Induction Base:
encArg(gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(0)) ->_R^Omega(0)
true

Induction Step:
encArg(gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(+(n3769_4, 1))) ->_R^Omega(0)
s(encArg(gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(n3769_4))) ->_IH
s(gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(c3770_4))

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

(110)
BOUNDS(1, INF)