WORST_CASE(Omega(n^1), O(n^3))
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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^3).

(0) DCpxTrs
(1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms]
(2) CpxRelTRS
(3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 200 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), 559 ms]
    (12) CpxTypedWeightedCompleteTrs
    (13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
    (14) CpxRNTS
    (15) InliningProof [UPPER BOUND(ID), 422 ms]
    (16) CpxRNTS
    (17) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (18) CpxRNTS
    (19) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms]
    (20) CpxRNTS
    (21) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (22) CpxRNTS
    (23) IntTrsBoundProof [UPPER BOUND(ID), 64 ms]
    (24) CpxRNTS
    (25) IntTrsBoundProof [UPPER BOUND(ID), 4 ms]
    (26) CpxRNTS
    (27) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (28) CpxRNTS
    (29) IntTrsBoundProof [UPPER BOUND(ID), 48 ms]
    (30) CpxRNTS
    (31) IntTrsBoundProof [UPPER BOUND(ID), 22 ms]
    (32) CpxRNTS
    (33) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (34) CpxRNTS
    (35) IntTrsBoundProof [UPPER BOUND(ID), 292 ms]
    (36) CpxRNTS
    (37) IntTrsBoundProof [UPPER BOUND(ID), 126 ms]
    (38) CpxRNTS
    (39) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (40) CpxRNTS
    (41) IntTrsBoundProof [UPPER BOUND(ID), 27 ms]
    (42) CpxRNTS
    (43) IntTrsBoundProof [UPPER BOUND(ID), 3 ms]
    (44) CpxRNTS
    (45) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (46) CpxRNTS
    (47) IntTrsBoundProof [UPPER BOUND(ID), 127 ms]
    (48) CpxRNTS
    (49) IntTrsBoundProof [UPPER BOUND(ID), 62 ms]
    (50) CpxRNTS
    (51) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (52) CpxRNTS
    (53) IntTrsBoundProof [UPPER BOUND(ID), 1726 ms]
    (54) CpxRNTS
    (55) IntTrsBoundProof [UPPER BOUND(ID), 1009 ms]
    (56) CpxRNTS
    (57) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (58) CpxRNTS
    (59) IntTrsBoundProof [UPPER BOUND(ID), 799 ms]
    (60) CpxRNTS
    (61) IntTrsBoundProof [UPPER BOUND(ID), 309 ms]
    (62) CpxRNTS
    (63) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (64) CpxRNTS
    (65) IntTrsBoundProof [UPPER BOUND(ID), 308 ms]
    (66) CpxRNTS
    (67) IntTrsBoundProof [UPPER BOUND(ID), 87 ms]
    (68) CpxRNTS
    (69) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (70) CpxRNTS
    (71) IntTrsBoundProof [UPPER BOUND(ID), 117 ms]
    (72) CpxRNTS
    (73) IntTrsBoundProof [UPPER BOUND(ID), 0 ms]
    (74) CpxRNTS
    (75) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (76) CpxRNTS
    (77) IntTrsBoundProof [UPPER BOUND(ID), 87 ms]
    (78) CpxRNTS
    (79) IntTrsBoundProof [UPPER BOUND(ID), 0 ms]
    (80) CpxRNTS
    (81) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (82) CpxRNTS
    (83) IntTrsBoundProof [UPPER BOUND(ID), 167 ms]
    (84) CpxRNTS
    (85) IntTrsBoundProof [UPPER BOUND(ID), 0 ms]
    (86) CpxRNTS
    (87) FinalProof [FINISHED, 0 ms]
    (88) BOUNDS(1, n^3)
(89) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(90) CpxRelTRS
    (91) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (92) typed CpxTrs
    (93) OrderProof [LOWER BOUND(ID), 3 ms]
    (94) typed CpxTrs
    (95) RewriteLemmaProof [LOWER BOUND(ID), 495 ms]
    (96) BEST
        (97) proven lower bound
            (98) LowerBoundPropagationProof [FINISHED, 0 ms]
            (99) BOUNDS(n^1, INF)
        (100) typed CpxTrs
            (101) RewriteLemmaProof [LOWER BOUND(ID), 49 ms]
            (102) BOUNDS(1, INF)


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

(0)
Obligation:
The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^3).


The TRS R consists of the following rules:

   cond(true, x, y) -> cond(gr(x, y), 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_cond(x_1, x_2, x_3)) -> cond(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_cond(x_1, x_2, x_3) -> cond(encArg(x_1), encArg(x_2), encArg(x_3))
   encode_true -> true
   encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2))
   encode_p(x_1) -> p(encArg(x_1))
   encode_0 -> 0
   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^3).


The TRS R consists of the following rules:

   cond(true, x, y) -> cond(gr(x, y), 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_cond(x_1, x_2, x_3)) -> cond(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_cond(x_1, x_2, x_3) -> cond(encArg(x_1), encArg(x_2), encArg(x_3))
   encode_true -> true
   encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2))
   encode_p(x_1) -> p(encArg(x_1))
   encode_0 -> 0
   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^3).


The TRS R consists of the following rules:

   cond(true, x, y) -> cond(gr(x, y), 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_cond(x_1, x_2, x_3)) -> cond(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_cond(x_1, x_2, x_3) -> cond(encArg(x_1), encArg(x_2), encArg(x_3))
   encode_true -> true
   encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2))
   encode_p(x_1) -> p(encArg(x_1))
   encode_0 -> 0
   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^3).


The TRS R consists of the following rules:

   cond(true, x, y) -> cond(gr(x, y), 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_cond(x_1, x_2, x_3)) -> cond(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_cond(x_1, x_2, x_3) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encode_true -> true [0]
   encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2)) [0]
   encode_p(x_1) -> p(encArg(x_1)) [0]
   encode_0 -> 0 [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:

   cond(true, x, y) -> cond(gr(x, y), 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_cond(x_1, x_2, x_3)) -> cond(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_cond(x_1, x_2, x_3) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encode_true -> true [0]
   encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2)) [0]
   encode_p(x_1) -> p(encArg(x_1)) [0]
   encode_0 -> 0 [0]
   encode_false -> false [0]
   encode_s(x_1) -> s(encArg(x_1)) [0]

The TRS has the following type information:
cond :: true:0:false:s:cons_cond:cons_gr:cons_p -> true:0:false:s:cons_cond:cons_gr:cons_p -> true:0:false:s:cons_cond:cons_gr:cons_p -> true:0:false:s:cons_cond:cons_gr:cons_p
true :: true:0:false:s:cons_cond:cons_gr:cons_p
gr :: true:0:false:s:cons_cond:cons_gr:cons_p -> true:0:false:s:cons_cond:cons_gr:cons_p -> true:0:false:s:cons_cond:cons_gr:cons_p
p :: true:0:false:s:cons_cond:cons_gr:cons_p -> true:0:false:s:cons_cond:cons_gr:cons_p
0 :: true:0:false:s:cons_cond:cons_gr:cons_p
false :: true:0:false:s:cons_cond:cons_gr:cons_p
s :: true:0:false:s:cons_cond:cons_gr:cons_p -> true:0:false:s:cons_cond:cons_gr:cons_p
encArg :: true:0:false:s:cons_cond:cons_gr:cons_p -> true:0:false:s:cons_cond:cons_gr:cons_p
cons_cond :: true:0:false:s:cons_cond:cons_gr:cons_p -> true:0:false:s:cons_cond:cons_gr:cons_p -> true:0:false:s:cons_cond:cons_gr:cons_p -> true:0:false:s:cons_cond:cons_gr:cons_p
cons_gr :: true:0:false:s:cons_cond:cons_gr:cons_p -> true:0:false:s:cons_cond:cons_gr:cons_p -> true:0:false:s:cons_cond:cons_gr:cons_p
cons_p :: true:0:false:s:cons_cond:cons_gr:cons_p -> true:0:false:s:cons_cond:cons_gr:cons_p
encode_cond :: true:0:false:s:cons_cond:cons_gr:cons_p -> true:0:false:s:cons_cond:cons_gr:cons_p -> true:0:false:s:cons_cond:cons_gr:cons_p -> true:0:false:s:cons_cond:cons_gr:cons_p
encode_true :: true:0:false:s:cons_cond:cons_gr:cons_p
encode_gr :: true:0:false:s:cons_cond:cons_gr:cons_p -> true:0:false:s:cons_cond:cons_gr:cons_p -> true:0:false:s:cons_cond:cons_gr:cons_p
encode_p :: true:0:false:s:cons_cond:cons_gr:cons_p -> true:0:false:s:cons_cond:cons_gr:cons_p
encode_0 :: true:0:false:s:cons_cond:cons_gr:cons_p
encode_false :: true:0:false:s:cons_cond:cons_gr:cons_p
encode_s :: true:0:false:s:cons_cond:cons_gr:cons_p -> true:0:false:s:cons_cond: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
   cond_3
   encArg_1
   encode_cond_3
   encode_true
   encode_gr_2
   encode_p_1
   encode_0
   encode_false
   encode_s_1

Due to the following rules being added:

   encArg(v0) -> null_encArg [0]
   encode_cond(v0, v1, v2) -> null_encode_cond [0]
   encode_true -> null_encode_true [0]
   encode_gr(v0, v1) -> null_encode_gr [0]
   encode_p(v0) -> null_encode_p [0]
   encode_0 -> null_encode_0 [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]
   cond(v0, v1, v2) -> null_cond [0]

And the following fresh constants:    null_encArg, null_encode_cond, null_encode_true, null_encode_gr, null_encode_p, null_encode_0, null_encode_false, null_encode_s, null_gr, null_p, null_cond

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

(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:

   cond(true, x, y) -> cond(gr(x, y), 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_cond(x_1, x_2, x_3)) -> cond(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_cond(x_1, x_2, x_3) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encode_true -> true [0]
   encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2)) [0]
   encode_p(x_1) -> p(encArg(x_1)) [0]
   encode_0 -> 0 [0]
   encode_false -> false [0]
   encode_s(x_1) -> s(encArg(x_1)) [0]
   encArg(v0) -> null_encArg [0]
   encode_cond(v0, v1, v2) -> null_encode_cond [0]
   encode_true -> null_encode_true [0]
   encode_gr(v0, v1) -> null_encode_gr [0]
   encode_p(v0) -> null_encode_p [0]
   encode_0 -> null_encode_0 [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]
   cond(v0, v1, v2) -> null_cond [0]

The TRS has the following type information:
cond :: true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond -> true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond -> true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond -> true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond
true :: true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond
gr :: true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond -> true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond -> true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond
p :: true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond -> true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond
0 :: true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond
false :: true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond
s :: true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond -> true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond
encArg :: true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond -> true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond
cons_cond :: true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond -> true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond -> true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond -> true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond
cons_gr :: true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond -> true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond -> true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond
cons_p :: true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond -> true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond
encode_cond :: true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond -> true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond -> true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond -> true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond
encode_true :: true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond
encode_gr :: true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond -> true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond -> true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond
encode_p :: true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond -> true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond
encode_0 :: true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond
encode_false :: true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond
encode_s :: true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond -> true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond
null_encArg :: true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond
null_encode_cond :: true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond
null_encode_true :: true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond
null_encode_gr :: true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond
null_encode_p :: true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond
null_encode_0 :: true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond
null_encode_false :: true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond
null_encode_s :: true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond
null_gr :: true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond
null_p :: true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond
null_cond :: true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond

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:

   cond(true, 0, y) -> cond(false, 0, y) [3]
   cond(true, 0, y) -> cond(false, null_p, y) [2]
   cond(true, s(x'), 0) -> cond(true, x', 0) [3]
   cond(true, s(x'), 0) -> cond(true, null_p, 0) [2]
   cond(true, s(x''), s(y')) -> cond(gr(x'', y'), x'', s(y')) [3]
   cond(true, s(x''), s(y')) -> cond(gr(x'', y'), null_p, s(y')) [2]
   cond(true, 0, y) -> cond(null_gr, 0, y) [2]
   cond(true, s(x1), y) -> cond(null_gr, x1, y) [2]
   cond(true, x, y) -> cond(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_cond(x_1, x_2, x_3)) -> cond(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_1327))) -> p(s(encArg(x_1327))) [0]
   encArg(cons_p(cons_cond(x_1328, x_2163, x_381))) -> p(cond(encArg(x_1328), encArg(x_2163), encArg(x_381))) [0]
   encArg(cons_p(cons_gr(x_1329, x_2164))) -> p(gr(encArg(x_1329), encArg(x_2164))) [0]
   encArg(cons_p(cons_p(x_1330))) -> p(p(encArg(x_1330))) [0]
   encArg(cons_p(x_1)) -> p(null_encArg) [0]
   encode_cond(x_1, x_2, x_3) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encode_true -> true [0]
   encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2)) [0]
   encode_p(true) -> p(true) [0]
   encode_p(0) -> p(0) [0]
   encode_p(false) -> p(false) [0]
   encode_p(s(x_1659)) -> p(s(encArg(x_1659))) [0]
   encode_p(cons_cond(x_1660, x_2329, x_3164)) -> p(cond(encArg(x_1660), encArg(x_2329), encArg(x_3164))) [0]
   encode_p(cons_gr(x_1661, x_2330)) -> p(gr(encArg(x_1661), encArg(x_2330))) [0]
   encode_p(cons_p(x_1662)) -> p(p(encArg(x_1662))) [0]
   encode_p(x_1) -> p(null_encArg) [0]
   encode_0 -> 0 [0]
   encode_false -> false [0]
   encode_s(x_1) -> s(encArg(x_1)) [0]
   encArg(v0) -> null_encArg [0]
   encode_cond(v0, v1, v2) -> null_encode_cond [0]
   encode_true -> null_encode_true [0]
   encode_gr(v0, v1) -> null_encode_gr [0]
   encode_p(v0) -> null_encode_p [0]
   encode_0 -> null_encode_0 [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]
   cond(v0, v1, v2) -> null_cond [0]

The TRS has the following type information:
cond :: true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond -> true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond -> true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond -> true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond
true :: true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond
gr :: true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond -> true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond -> true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond
p :: true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond -> true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond
0 :: true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond
false :: true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond
s :: true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond -> true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond
encArg :: true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond -> true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond
cons_cond :: true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond -> true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond -> true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond -> true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond
cons_gr :: true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond -> true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond -> true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond
cons_p :: true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond -> true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond
encode_cond :: true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond -> true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond -> true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond -> true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond
encode_true :: true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond
encode_gr :: true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond -> true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond -> true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond
encode_p :: true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond -> true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond
encode_0 :: true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond
encode_false :: true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond
encode_s :: true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond -> true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond
null_encArg :: true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond
null_encode_cond :: true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond
null_encode_true :: true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond
null_encode_gr :: true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond
null_encode_p :: true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond
null_encode_0 :: true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond
null_encode_false :: true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond
null_encode_s :: true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond
null_gr :: true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond
null_p :: true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond
null_cond :: true:0:false:s:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_0:null_encode_false:null_encode_s:null_gr:null_p:null_cond

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_cond => 0
   null_encode_true => 0
   null_encode_gr => 0
   null_encode_p => 0
   null_encode_0 => 0
   null_encode_false => 0
   null_encode_s => 0
   null_gr => 0
   null_p => 0
   null_cond => 0

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

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

   cond(z, z', z'') -{ 3 }-> cond(gr(x'', y'), x'', 1 + y') :|: z = 2, z' = 1 + x'', y' >= 0, x'' >= 0, z'' = 1 + y'
   cond(z, z', z'') -{ 2 }-> cond(gr(x'', y'), 0, 1 + y') :|: z = 2, z' = 1 + x'', y' >= 0, x'' >= 0, z'' = 1 + y'
   cond(z, z', z'') -{ 3 }-> cond(2, x', 0) :|: z = 2, z'' = 0, z' = 1 + x', x' >= 0
   cond(z, z', z'') -{ 2 }-> cond(2, 0, 0) :|: z = 2, z'' = 0, z' = 1 + x', x' >= 0
   cond(z, z', z'') -{ 3 }-> cond(1, 0, y) :|: z = 2, z'' = y, y >= 0, z' = 0
   cond(z, z', z'') -{ 2 }-> cond(1, 0, y) :|: z = 2, z'' = y, y >= 0, z' = 0
   cond(z, z', z'') -{ 2 }-> cond(0, x1, y) :|: z = 2, x1 >= 0, z'' = y, y >= 0, z' = 1 + x1
   cond(z, z', z'') -{ 2 }-> cond(0, 0, y) :|: z = 2, z'' = y, y >= 0, z' = 0
   cond(z, z', z'') -{ 1 }-> cond(0, 0, y) :|: z = 2, z' = x, z'' = y, x >= 0, y >= 0
   cond(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   encArg(z) -{ 0 }-> p(p(encArg(x_1330))) :|: z = 1 + (1 + x_1330), x_1330 >= 0
   encArg(z) -{ 0 }-> p(gr(encArg(x_1329), encArg(x_2164))) :|: x_2164 >= 0, z = 1 + (1 + x_1329 + x_2164), x_1329 >= 0
   encArg(z) -{ 0 }-> p(cond(encArg(x_1328), encArg(x_2163), encArg(x_381))) :|: x_1328 >= 0, x_381 >= 0, z = 1 + (1 + x_1328 + x_2163 + x_381), x_2163 >= 0
   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_1327)) :|: x_1327 >= 0, z = 1 + (1 + x_1327)
   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 }-> cond(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_cond(z, z', z'') -{ 0 }-> cond(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_cond(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_1662))) :|: x_1662 >= 0, z = 1 + x_1662
   encode_p(z) -{ 0 }-> p(gr(encArg(x_1661), encArg(x_2330))) :|: z = 1 + x_1661 + x_2330, x_2330 >= 0, x_1661 >= 0
   encode_p(z) -{ 0 }-> p(cond(encArg(x_1660), encArg(x_2329), encArg(x_3164))) :|: x_3164 >= 0, x_1660 >= 0, x_2329 >= 0, z = 1 + x_1660 + x_2329 + x_3164
   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_1659)) :|: z = 1 + x_1659, x_1659 >= 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:

   cond(z, z', z'') -{ 3 }-> cond(gr(x'', y'), x'', 1 + y') :|: z = 2, z' = 1 + x'', y' >= 0, x'' >= 0, z'' = 1 + y'
   cond(z, z', z'') -{ 2 }-> cond(gr(x'', y'), 0, 1 + y') :|: z = 2, z' = 1 + x'', y' >= 0, x'' >= 0, z'' = 1 + y'
   cond(z, z', z'') -{ 3 }-> cond(2, x', 0) :|: z = 2, z'' = 0, z' = 1 + x', x' >= 0
   cond(z, z', z'') -{ 2 }-> cond(2, 0, 0) :|: z = 2, z'' = 0, z' = 1 + x', x' >= 0
   cond(z, z', z'') -{ 3 }-> cond(1, 0, y) :|: z = 2, z'' = y, y >= 0, z' = 0
   cond(z, z', z'') -{ 2 }-> cond(1, 0, y) :|: z = 2, z'' = y, y >= 0, z' = 0
   cond(z, z', z'') -{ 2 }-> cond(0, x1, y) :|: z = 2, x1 >= 0, z'' = y, y >= 0, z' = 1 + x1
   cond(z, z', z'') -{ 2 }-> cond(0, 0, y) :|: z = 2, z'' = y, y >= 0, z' = 0
   cond(z, z', z'') -{ 1 }-> cond(0, 0, y) :|: z = 2, z' = x, z'' = y, x >= 0, y >= 0
   cond(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_1330))) :|: z = 1 + (1 + x_1330), x_1330 >= 0
   encArg(z) -{ 0 }-> p(gr(encArg(x_1329), encArg(x_2164))) :|: x_2164 >= 0, z = 1 + (1 + x_1329 + x_2164), x_1329 >= 0
   encArg(z) -{ 0 }-> p(cond(encArg(x_1328), encArg(x_2163), encArg(x_381))) :|: x_1328 >= 0, x_381 >= 0, z = 1 + (1 + x_1328 + x_2163 + x_381), x_2163 >= 0
   encArg(z) -{ 0 }-> p(1 + encArg(x_1327)) :|: x_1327 >= 0, z = 1 + (1 + x_1327)
   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 }-> cond(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_cond(z, z', z'') -{ 0 }-> cond(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_cond(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_1662))) :|: x_1662 >= 0, z = 1 + x_1662
   encode_p(z) -{ 0 }-> p(gr(encArg(x_1661), encArg(x_2330))) :|: z = 1 + x_1661 + x_2330, x_2330 >= 0, x_1661 >= 0
   encode_p(z) -{ 0 }-> p(cond(encArg(x_1660), encArg(x_2329), encArg(x_3164))) :|: x_3164 >= 0, x_1660 >= 0, x_2329 >= 0, z = 1 + x_1660 + x_2329 + x_3164
   encode_p(z) -{ 0 }-> p(1 + encArg(x_1659)) :|: z = 1 + x_1659, x_1659 >= 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:

   cond(z, z', z'') -{ 2 }-> cond(gr(z' - 1, z'' - 1), 0, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 3 }-> cond(gr(z' - 1, z'' - 1), z' - 1, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 2 }-> cond(2, 0, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 3 }-> cond(2, z' - 1, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 3 }-> cond(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 2 }-> cond(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 2 }-> cond(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 1 }-> cond(0, 0, z'') :|: z = 2, z' >= 0, z'' >= 0
   cond(z, z', z'') -{ 2 }-> cond(0, z' - 1, z'') :|: z = 2, z' - 1 >= 0, z'' >= 0
   cond(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_1329), encArg(x_2164))) :|: x_2164 >= 0, z = 1 + (1 + x_1329 + x_2164), x_1329 >= 0
   encArg(z) -{ 0 }-> p(cond(encArg(x_1328), encArg(x_2163), encArg(x_381))) :|: x_1328 >= 0, x_381 >= 0, z = 1 + (1 + x_1328 + x_2163 + x_381), x_2163 >= 0
   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 }-> cond(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_cond(z, z', z'') -{ 0 }-> cond(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_cond(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_1661), encArg(x_2330))) :|: z = 1 + x_1661 + x_2330, x_2330 >= 0, x_1661 >= 0
   encode_p(z) -{ 0 }-> p(cond(encArg(x_1660), encArg(x_2329), encArg(x_3164))) :|: x_3164 >= 0, x_1660 >= 0, x_2329 >= 0, z = 1 + x_1660 + x_2329 + x_3164
   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 }
   { p }
   { cond }
   { encArg }
   { encode_p }
   { encode_gr }
   { encode_s }
   { encode_cond }

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

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

   cond(z, z', z'') -{ 2 }-> cond(gr(z' - 1, z'' - 1), 0, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 3 }-> cond(gr(z' - 1, z'' - 1), z' - 1, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 2 }-> cond(2, 0, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 3 }-> cond(2, z' - 1, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 3 }-> cond(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 2 }-> cond(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 2 }-> cond(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 1 }-> cond(0, 0, z'') :|: z = 2, z' >= 0, z'' >= 0
   cond(z, z', z'') -{ 2 }-> cond(0, z' - 1, z'') :|: z = 2, z' - 1 >= 0, z'' >= 0
   cond(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_1329), encArg(x_2164))) :|: x_2164 >= 0, z = 1 + (1 + x_1329 + x_2164), x_1329 >= 0
   encArg(z) -{ 0 }-> p(cond(encArg(x_1328), encArg(x_2163), encArg(x_381))) :|: x_1328 >= 0, x_381 >= 0, z = 1 + (1 + x_1328 + x_2163 + x_381), x_2163 >= 0
   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 }-> cond(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_cond(z, z', z'') -{ 0 }-> cond(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_cond(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_1661), encArg(x_2330))) :|: z = 1 + x_1661 + x_2330, x_2330 >= 0, x_1661 >= 0
   encode_p(z) -{ 0 }-> p(cond(encArg(x_1660), encArg(x_2329), encArg(x_3164))) :|: x_3164 >= 0, x_1660 >= 0, x_2329 >= 0, z = 1 + x_1660 + x_2329 + x_3164
   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}, {p}, {cond}, {encArg}, {encode_p}, {encode_gr}, {encode_s}, {encode_cond}

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

(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:

   cond(z, z', z'') -{ 2 }-> cond(gr(z' - 1, z'' - 1), 0, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 3 }-> cond(gr(z' - 1, z'' - 1), z' - 1, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 2 }-> cond(2, 0, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 3 }-> cond(2, z' - 1, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 3 }-> cond(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 2 }-> cond(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 2 }-> cond(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 1 }-> cond(0, 0, z'') :|: z = 2, z' >= 0, z'' >= 0
   cond(z, z', z'') -{ 2 }-> cond(0, z' - 1, z'') :|: z = 2, z' - 1 >= 0, z'' >= 0
   cond(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_1329), encArg(x_2164))) :|: x_2164 >= 0, z = 1 + (1 + x_1329 + x_2164), x_1329 >= 0
   encArg(z) -{ 0 }-> p(cond(encArg(x_1328), encArg(x_2163), encArg(x_381))) :|: x_1328 >= 0, x_381 >= 0, z = 1 + (1 + x_1328 + x_2163 + x_381), x_2163 >= 0
   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 }-> cond(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_cond(z, z', z'') -{ 0 }-> cond(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_cond(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_1661), encArg(x_2330))) :|: z = 1 + x_1661 + x_2330, x_2330 >= 0, x_1661 >= 0
   encode_p(z) -{ 0 }-> p(cond(encArg(x_1660), encArg(x_2329), encArg(x_3164))) :|: x_3164 >= 0, x_1660 >= 0, x_2329 >= 0, z = 1 + x_1660 + x_2329 + x_3164
   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}, {p}, {cond}, {encArg}, {encode_p}, {encode_gr}, {encode_s}, {encode_cond}

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

(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:

   cond(z, z', z'') -{ 2 }-> cond(gr(z' - 1, z'' - 1), 0, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 3 }-> cond(gr(z' - 1, z'' - 1), z' - 1, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 2 }-> cond(2, 0, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 3 }-> cond(2, z' - 1, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 3 }-> cond(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 2 }-> cond(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 2 }-> cond(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 1 }-> cond(0, 0, z'') :|: z = 2, z' >= 0, z'' >= 0
   cond(z, z', z'') -{ 2 }-> cond(0, z' - 1, z'') :|: z = 2, z' - 1 >= 0, z'' >= 0
   cond(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_1329), encArg(x_2164))) :|: x_2164 >= 0, z = 1 + (1 + x_1329 + x_2164), x_1329 >= 0
   encArg(z) -{ 0 }-> p(cond(encArg(x_1328), encArg(x_2163), encArg(x_381))) :|: x_1328 >= 0, x_381 >= 0, z = 1 + (1 + x_1328 + x_2163 + x_381), x_2163 >= 0
   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 }-> cond(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_cond(z, z', z'') -{ 0 }-> cond(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_cond(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_1661), encArg(x_2330))) :|: z = 1 + x_1661 + x_2330, x_2330 >= 0, x_1661 >= 0
   encode_p(z) -{ 0 }-> p(cond(encArg(x_1660), encArg(x_2329), encArg(x_3164))) :|: x_3164 >= 0, x_1660 >= 0, x_2329 >= 0, z = 1 + x_1660 + x_2329 + x_3164
   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}, {p}, {cond}, {encArg}, {encode_p}, {encode_gr}, {encode_s}, {encode_cond}
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:

   cond(z, z', z'') -{ 2 }-> cond(gr(z' - 1, z'' - 1), 0, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 3 }-> cond(gr(z' - 1, z'' - 1), z' - 1, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 2 }-> cond(2, 0, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 3 }-> cond(2, z' - 1, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 3 }-> cond(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 2 }-> cond(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 2 }-> cond(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 1 }-> cond(0, 0, z'') :|: z = 2, z' >= 0, z'' >= 0
   cond(z, z', z'') -{ 2 }-> cond(0, z' - 1, z'') :|: z = 2, z' - 1 >= 0, z'' >= 0
   cond(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_1329), encArg(x_2164))) :|: x_2164 >= 0, z = 1 + (1 + x_1329 + x_2164), x_1329 >= 0
   encArg(z) -{ 0 }-> p(cond(encArg(x_1328), encArg(x_2163), encArg(x_381))) :|: x_1328 >= 0, x_381 >= 0, z = 1 + (1 + x_1328 + x_2163 + x_381), x_2163 >= 0
   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 }-> cond(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_cond(z, z', z'') -{ 0 }-> cond(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_cond(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_1661), encArg(x_2330))) :|: z = 1 + x_1661 + x_2330, x_2330 >= 0, x_1661 >= 0
   encode_p(z) -{ 0 }-> p(cond(encArg(x_1660), encArg(x_2329), encArg(x_3164))) :|: x_3164 >= 0, x_1660 >= 0, x_2329 >= 0, z = 1 + x_1660 + x_2329 + x_3164
   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}, {p}, {cond}, {encArg}, {encode_p}, {encode_gr}, {encode_s}, {encode_cond}
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:

   cond(z, z', z'') -{ 2 }-> cond(gr(z' - 1, z'' - 1), 0, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 3 }-> cond(gr(z' - 1, z'' - 1), z' - 1, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 2 }-> cond(2, 0, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 3 }-> cond(2, z' - 1, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 3 }-> cond(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 2 }-> cond(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 2 }-> cond(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 1 }-> cond(0, 0, z'') :|: z = 2, z' >= 0, z'' >= 0
   cond(z, z', z'') -{ 2 }-> cond(0, z' - 1, z'') :|: z = 2, z' - 1 >= 0, z'' >= 0
   cond(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_1329), encArg(x_2164))) :|: x_2164 >= 0, z = 1 + (1 + x_1329 + x_2164), x_1329 >= 0
   encArg(z) -{ 0 }-> p(cond(encArg(x_1328), encArg(x_2163), encArg(x_381))) :|: x_1328 >= 0, x_381 >= 0, z = 1 + (1 + x_1328 + x_2163 + x_381), x_2163 >= 0
   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 }-> cond(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_cond(z, z', z'') -{ 0 }-> cond(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_cond(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_1661), encArg(x_2330))) :|: z = 1 + x_1661 + x_2330, x_2330 >= 0, x_1661 >= 0
   encode_p(z) -{ 0 }-> p(cond(encArg(x_1660), encArg(x_2329), encArg(x_3164))) :|: x_3164 >= 0, x_1660 >= 0, x_2329 >= 0, z = 1 + x_1660 + x_2329 + x_3164
   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}, {p}, {cond}, {encArg}, {encode_p}, {encode_gr}, {encode_s}, {encode_cond}
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:

   cond(z, z', z'') -{ 2 }-> cond(gr(z' - 1, z'' - 1), 0, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 3 }-> cond(gr(z' - 1, z'' - 1), z' - 1, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 2 }-> cond(2, 0, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 3 }-> cond(2, z' - 1, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 3 }-> cond(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 2 }-> cond(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 2 }-> cond(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 1 }-> cond(0, 0, z'') :|: z = 2, z' >= 0, z'' >= 0
   cond(z, z', z'') -{ 2 }-> cond(0, z' - 1, z'') :|: z = 2, z' - 1 >= 0, z'' >= 0
   cond(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_1329), encArg(x_2164))) :|: x_2164 >= 0, z = 1 + (1 + x_1329 + x_2164), x_1329 >= 0
   encArg(z) -{ 0 }-> p(cond(encArg(x_1328), encArg(x_2163), encArg(x_381))) :|: x_1328 >= 0, x_381 >= 0, z = 1 + (1 + x_1328 + x_2163 + x_381), x_2163 >= 0
   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 }-> cond(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_cond(z, z', z'') -{ 0 }-> cond(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_cond(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_1661), encArg(x_2330))) :|: z = 1 + x_1661 + x_2330, x_2330 >= 0, x_1661 >= 0
   encode_p(z) -{ 0 }-> p(cond(encArg(x_1660), encArg(x_2329), encArg(x_3164))) :|: x_3164 >= 0, x_1660 >= 0, x_2329 >= 0, z = 1 + x_1660 + x_2329 + x_3164
   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}, {p}, {cond}, {encArg}, {encode_p}, {encode_gr}, {encode_s}, {encode_cond}
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:

   cond(z, z', z'') -{ 2 }-> cond(gr(z' - 1, z'' - 1), 0, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 3 }-> cond(gr(z' - 1, z'' - 1), z' - 1, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 2 }-> cond(2, 0, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 3 }-> cond(2, z' - 1, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 3 }-> cond(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 2 }-> cond(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 2 }-> cond(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 1 }-> cond(0, 0, z'') :|: z = 2, z' >= 0, z'' >= 0
   cond(z, z', z'') -{ 2 }-> cond(0, z' - 1, z'') :|: z = 2, z' - 1 >= 0, z'' >= 0
   cond(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_1329), encArg(x_2164))) :|: x_2164 >= 0, z = 1 + (1 + x_1329 + x_2164), x_1329 >= 0
   encArg(z) -{ 0 }-> p(cond(encArg(x_1328), encArg(x_2163), encArg(x_381))) :|: x_1328 >= 0, x_381 >= 0, z = 1 + (1 + x_1328 + x_2163 + x_381), x_2163 >= 0
   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 }-> cond(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_cond(z, z', z'') -{ 0 }-> cond(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_cond(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_1661), encArg(x_2330))) :|: z = 1 + x_1661 + x_2330, x_2330 >= 0, x_1661 >= 0
   encode_p(z) -{ 0 }-> p(cond(encArg(x_1660), encArg(x_2329), encArg(x_3164))) :|: x_3164 >= 0, x_1660 >= 0, x_2329 >= 0, z = 1 + x_1660 + x_2329 + x_3164
   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}, {p}, {cond}, {encArg}, {encode_p}, {encode_gr}, {encode_s}, {encode_cond}
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:

   cond(z, z', z'') -{ 2 }-> cond(gr(z' - 1, z'' - 1), 0, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 3 }-> cond(gr(z' - 1, z'' - 1), z' - 1, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 2 }-> cond(2, 0, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 3 }-> cond(2, z' - 1, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 3 }-> cond(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 2 }-> cond(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 2 }-> cond(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 1 }-> cond(0, 0, z'') :|: z = 2, z' >= 0, z'' >= 0
   cond(z, z', z'') -{ 2 }-> cond(0, z' - 1, z'') :|: z = 2, z' - 1 >= 0, z'' >= 0
   cond(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_1329), encArg(x_2164))) :|: x_2164 >= 0, z = 1 + (1 + x_1329 + x_2164), x_1329 >= 0
   encArg(z) -{ 0 }-> p(cond(encArg(x_1328), encArg(x_2163), encArg(x_381))) :|: x_1328 >= 0, x_381 >= 0, z = 1 + (1 + x_1328 + x_2163 + x_381), x_2163 >= 0
   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 }-> cond(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_cond(z, z', z'') -{ 0 }-> cond(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_cond(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_1661), encArg(x_2330))) :|: z = 1 + x_1661 + x_2330, x_2330 >= 0, x_1661 >= 0
   encode_p(z) -{ 0 }-> p(cond(encArg(x_1660), encArg(x_2329), encArg(x_3164))) :|: x_3164 >= 0, x_1660 >= 0, x_2329 >= 0, z = 1 + x_1660 + x_2329 + x_3164
   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}, {p}, {cond}, {encArg}, {encode_p}, {encode_gr}, {encode_s}, {encode_cond}
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:

   cond(z, z', z'') -{ 2 }-> cond(gr(z' - 1, z'' - 1), 0, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 3 }-> cond(gr(z' - 1, z'' - 1), z' - 1, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 2 }-> cond(2, 0, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 3 }-> cond(2, z' - 1, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 3 }-> cond(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 2 }-> cond(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 2 }-> cond(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 1 }-> cond(0, 0, z'') :|: z = 2, z' >= 0, z'' >= 0
   cond(z, z', z'') -{ 2 }-> cond(0, z' - 1, z'') :|: z = 2, z' - 1 >= 0, z'' >= 0
   cond(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_1329), encArg(x_2164))) :|: x_2164 >= 0, z = 1 + (1 + x_1329 + x_2164), x_1329 >= 0
   encArg(z) -{ 0 }-> p(cond(encArg(x_1328), encArg(x_2163), encArg(x_381))) :|: x_1328 >= 0, x_381 >= 0, z = 1 + (1 + x_1328 + x_2163 + x_381), x_2163 >= 0
   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 }-> cond(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_cond(z, z', z'') -{ 0 }-> cond(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_cond(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_1661), encArg(x_2330))) :|: z = 1 + x_1661 + x_2330, x_2330 >= 0, x_1661 >= 0
   encode_p(z) -{ 0 }-> p(cond(encArg(x_1660), encArg(x_2329), encArg(x_3164))) :|: x_3164 >= 0, x_1660 >= 0, x_2329 >= 0, z = 1 + x_1660 + x_2329 + x_3164
   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}, {p}, {cond}, {encArg}, {encode_p}, {encode_gr}, {encode_s}, {encode_cond}
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:

   cond(z, z', z'') -{ 2 }-> cond(gr(z' - 1, z'' - 1), 0, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 3 }-> cond(gr(z' - 1, z'' - 1), z' - 1, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 2 }-> cond(2, 0, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 3 }-> cond(2, z' - 1, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 3 }-> cond(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 2 }-> cond(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 2 }-> cond(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 1 }-> cond(0, 0, z'') :|: z = 2, z' >= 0, z'' >= 0
   cond(z, z', z'') -{ 2 }-> cond(0, z' - 1, z'') :|: z = 2, z' - 1 >= 0, z'' >= 0
   cond(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_1329), encArg(x_2164))) :|: x_2164 >= 0, z = 1 + (1 + x_1329 + x_2164), x_1329 >= 0
   encArg(z) -{ 0 }-> p(cond(encArg(x_1328), encArg(x_2163), encArg(x_381))) :|: x_1328 >= 0, x_381 >= 0, z = 1 + (1 + x_1328 + x_2163 + x_381), x_2163 >= 0
   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 }-> cond(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_cond(z, z', z'') -{ 0 }-> cond(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_cond(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_1661), encArg(x_2330))) :|: z = 1 + x_1661 + x_2330, x_2330 >= 0, x_1661 >= 0
   encode_p(z) -{ 0 }-> p(cond(encArg(x_1660), encArg(x_2329), encArg(x_3164))) :|: x_3164 >= 0, x_1660 >= 0, x_2329 >= 0, z = 1 + x_1660 + x_2329 + x_3164
   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}, {p}, {cond}, {encArg}, {encode_p}, {encode_gr}, {encode_s}, {encode_cond}
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:

   cond(z, z', z'') -{ 4 + z'' }-> cond(s, z' - 1, 1 + (z'' - 1)) :|: s >= 0, s <= 2, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 3 + z'' }-> cond(s', 0, 1 + (z'' - 1)) :|: s' >= 0, s' <= 2, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 2 }-> cond(2, 0, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 3 }-> cond(2, z' - 1, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 3 }-> cond(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 2 }-> cond(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 2 }-> cond(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 1 }-> cond(0, 0, z'') :|: z = 2, z' >= 0, z'' >= 0
   cond(z, z', z'') -{ 2 }-> cond(0, z' - 1, z'') :|: z = 2, z' - 1 >= 0, z'' >= 0
   cond(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_1329), encArg(x_2164))) :|: x_2164 >= 0, z = 1 + (1 + x_1329 + x_2164), x_1329 >= 0
   encArg(z) -{ 0 }-> p(cond(encArg(x_1328), encArg(x_2163), encArg(x_381))) :|: x_1328 >= 0, x_381 >= 0, z = 1 + (1 + x_1328 + x_2163 + x_381), x_2163 >= 0
   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 }-> cond(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_cond(z, z', z'') -{ 0 }-> cond(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_cond(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_1661), encArg(x_2330))) :|: z = 1 + x_1661 + x_2330, x_2330 >= 0, x_1661 >= 0
   encode_p(z) -{ 0 }-> p(cond(encArg(x_1660), encArg(x_2329), encArg(x_3164))) :|: x_3164 >= 0, x_1660 >= 0, x_2329 >= 0, z = 1 + x_1660 + x_2329 + x_3164
   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}, {p}, {cond}, {encArg}, {encode_p}, {encode_gr}, {encode_s}, {encode_cond}
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:

   cond(z, z', z'') -{ 4 + z'' }-> cond(s, z' - 1, 1 + (z'' - 1)) :|: s >= 0, s <= 2, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 3 + z'' }-> cond(s', 0, 1 + (z'' - 1)) :|: s' >= 0, s' <= 2, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 2 }-> cond(2, 0, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 3 }-> cond(2, z' - 1, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 3 }-> cond(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 2 }-> cond(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 2 }-> cond(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 1 }-> cond(0, 0, z'') :|: z = 2, z' >= 0, z'' >= 0
   cond(z, z', z'') -{ 2 }-> cond(0, z' - 1, z'') :|: z = 2, z' - 1 >= 0, z'' >= 0
   cond(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_1329), encArg(x_2164))) :|: x_2164 >= 0, z = 1 + (1 + x_1329 + x_2164), x_1329 >= 0
   encArg(z) -{ 0 }-> p(cond(encArg(x_1328), encArg(x_2163), encArg(x_381))) :|: x_1328 >= 0, x_381 >= 0, z = 1 + (1 + x_1328 + x_2163 + x_381), x_2163 >= 0
   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 }-> cond(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_cond(z, z', z'') -{ 0 }-> cond(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_cond(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_1661), encArg(x_2330))) :|: z = 1 + x_1661 + x_2330, x_2330 >= 0, x_1661 >= 0
   encode_p(z) -{ 0 }-> p(cond(encArg(x_1660), encArg(x_2329), encArg(x_3164))) :|: x_3164 >= 0, x_1660 >= 0, x_2329 >= 0, z = 1 + x_1660 + x_2329 + x_3164
   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}, {p}, {cond}, {encArg}, {encode_p}, {encode_gr}, {encode_s}, {encode_cond}
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:

   cond(z, z', z'') -{ 4 + z'' }-> cond(s, z' - 1, 1 + (z'' - 1)) :|: s >= 0, s <= 2, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 3 + z'' }-> cond(s', 0, 1 + (z'' - 1)) :|: s' >= 0, s' <= 2, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 2 }-> cond(2, 0, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 3 }-> cond(2, z' - 1, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 3 }-> cond(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 2 }-> cond(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 2 }-> cond(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 1 }-> cond(0, 0, z'') :|: z = 2, z' >= 0, z'' >= 0
   cond(z, z', z'') -{ 2 }-> cond(0, z' - 1, z'') :|: z = 2, z' - 1 >= 0, z'' >= 0
   cond(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_1329), encArg(x_2164))) :|: x_2164 >= 0, z = 1 + (1 + x_1329 + x_2164), x_1329 >= 0
   encArg(z) -{ 0 }-> p(cond(encArg(x_1328), encArg(x_2163), encArg(x_381))) :|: x_1328 >= 0, x_381 >= 0, z = 1 + (1 + x_1328 + x_2163 + x_381), x_2163 >= 0
   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 }-> cond(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_cond(z, z', z'') -{ 0 }-> cond(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_cond(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_1661), encArg(x_2330))) :|: z = 1 + x_1661 + x_2330, x_2330 >= 0, x_1661 >= 0
   encode_p(z) -{ 0 }-> p(cond(encArg(x_1660), encArg(x_2329), encArg(x_3164))) :|: x_3164 >= 0, x_1660 >= 0, x_2329 >= 0, z = 1 + x_1660 + x_2329 + x_3164
   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}, {cond}, {encArg}, {encode_p}, {encode_gr}, {encode_s}, {encode_cond}
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:

   cond(z, z', z'') -{ 4 + z'' }-> cond(s, z' - 1, 1 + (z'' - 1)) :|: s >= 0, s <= 2, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 3 + z'' }-> cond(s', 0, 1 + (z'' - 1)) :|: s' >= 0, s' <= 2, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 2 }-> cond(2, 0, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 3 }-> cond(2, z' - 1, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 3 }-> cond(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 2 }-> cond(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 2 }-> cond(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 1 }-> cond(0, 0, z'') :|: z = 2, z' >= 0, z'' >= 0
   cond(z, z', z'') -{ 2 }-> cond(0, z' - 1, z'') :|: z = 2, z' - 1 >= 0, z'' >= 0
   cond(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_1329), encArg(x_2164))) :|: x_2164 >= 0, z = 1 + (1 + x_1329 + x_2164), x_1329 >= 0
   encArg(z) -{ 0 }-> p(cond(encArg(x_1328), encArg(x_2163), encArg(x_381))) :|: x_1328 >= 0, x_381 >= 0, z = 1 + (1 + x_1328 + x_2163 + x_381), x_2163 >= 0
   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 }-> cond(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_cond(z, z', z'') -{ 0 }-> cond(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_cond(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_1661), encArg(x_2330))) :|: z = 1 + x_1661 + x_2330, x_2330 >= 0, x_1661 >= 0
   encode_p(z) -{ 0 }-> p(cond(encArg(x_1660), encArg(x_2329), encArg(x_3164))) :|: x_3164 >= 0, x_1660 >= 0, x_2329 >= 0, z = 1 + x_1660 + x_2329 + x_3164
   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}, {cond}, {encArg}, {encode_p}, {encode_gr}, {encode_s}, {encode_cond}
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: p
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: z

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

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

   cond(z, z', z'') -{ 4 + z'' }-> cond(s, z' - 1, 1 + (z'' - 1)) :|: s >= 0, s <= 2, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 3 + z'' }-> cond(s', 0, 1 + (z'' - 1)) :|: s' >= 0, s' <= 2, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 2 }-> cond(2, 0, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 3 }-> cond(2, z' - 1, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 3 }-> cond(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 2 }-> cond(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 2 }-> cond(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 1 }-> cond(0, 0, z'') :|: z = 2, z' >= 0, z'' >= 0
   cond(z, z', z'') -{ 2 }-> cond(0, z' - 1, z'') :|: z = 2, z' - 1 >= 0, z'' >= 0
   cond(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_1329), encArg(x_2164))) :|: x_2164 >= 0, z = 1 + (1 + x_1329 + x_2164), x_1329 >= 0
   encArg(z) -{ 0 }-> p(cond(encArg(x_1328), encArg(x_2163), encArg(x_381))) :|: x_1328 >= 0, x_381 >= 0, z = 1 + (1 + x_1328 + x_2163 + x_381), x_2163 >= 0
   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 }-> cond(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_cond(z, z', z'') -{ 0 }-> cond(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_cond(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_1661), encArg(x_2330))) :|: z = 1 + x_1661 + x_2330, x_2330 >= 0, x_1661 >= 0
   encode_p(z) -{ 0 }-> p(cond(encArg(x_1660), encArg(x_2329), encArg(x_3164))) :|: x_3164 >= 0, x_1660 >= 0, x_2329 >= 0, z = 1 + x_1660 + x_2329 + x_3164
   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}, {cond}, {encArg}, {encode_p}, {encode_gr}, {encode_s}, {encode_cond}
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]
  p: runtime: ?, size: O(n^1) [z]

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

(49) 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

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

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

   cond(z, z', z'') -{ 4 + z'' }-> cond(s, z' - 1, 1 + (z'' - 1)) :|: s >= 0, s <= 2, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 3 + z'' }-> cond(s', 0, 1 + (z'' - 1)) :|: s' >= 0, s' <= 2, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 2 }-> cond(2, 0, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 3 }-> cond(2, z' - 1, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 3 }-> cond(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 2 }-> cond(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 2 }-> cond(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 1 }-> cond(0, 0, z'') :|: z = 2, z' >= 0, z'' >= 0
   cond(z, z', z'') -{ 2 }-> cond(0, z' - 1, z'') :|: z = 2, z' - 1 >= 0, z'' >= 0
   cond(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_1329), encArg(x_2164))) :|: x_2164 >= 0, z = 1 + (1 + x_1329 + x_2164), x_1329 >= 0
   encArg(z) -{ 0 }-> p(cond(encArg(x_1328), encArg(x_2163), encArg(x_381))) :|: x_1328 >= 0, x_381 >= 0, z = 1 + (1 + x_1328 + x_2163 + x_381), x_2163 >= 0
   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 }-> cond(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_cond(z, z', z'') -{ 0 }-> cond(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_cond(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_1661), encArg(x_2330))) :|: z = 1 + x_1661 + x_2330, x_2330 >= 0, x_1661 >= 0
   encode_p(z) -{ 0 }-> p(cond(encArg(x_1660), encArg(x_2329), encArg(x_3164))) :|: x_3164 >= 0, x_1660 >= 0, x_2329 >= 0, z = 1 + x_1660 + x_2329 + x_3164
   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: {cond}, {encArg}, {encode_p}, {encode_gr}, {encode_s}, {encode_cond}
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]
  p: runtime: O(1) [1], size: O(n^1) [z]

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

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

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

   cond(z, z', z'') -{ 4 + z'' }-> cond(s, z' - 1, 1 + (z'' - 1)) :|: s >= 0, s <= 2, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 3 + z'' }-> cond(s', 0, 1 + (z'' - 1)) :|: s' >= 0, s' <= 2, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 2 }-> cond(2, 0, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 3 }-> cond(2, z' - 1, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 3 }-> cond(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 2 }-> cond(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 2 }-> cond(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 1 }-> cond(0, 0, z'') :|: z = 2, z' >= 0, z'' >= 0
   cond(z, z', z'') -{ 2 }-> cond(0, z' - 1, z'') :|: z = 2, z' - 1 >= 0, z'' >= 0
   cond(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_1329), encArg(x_2164))) :|: x_2164 >= 0, z = 1 + (1 + x_1329 + x_2164), x_1329 >= 0
   encArg(z) -{ 0 }-> p(cond(encArg(x_1328), encArg(x_2163), encArg(x_381))) :|: x_1328 >= 0, x_381 >= 0, z = 1 + (1 + x_1328 + x_2163 + x_381), x_2163 >= 0
   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 }-> cond(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_cond(z, z', z'') -{ 0 }-> cond(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_cond(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_1661), encArg(x_2330))) :|: z = 1 + x_1661 + x_2330, x_2330 >= 0, x_1661 >= 0
   encode_p(z) -{ 0 }-> p(cond(encArg(x_1660), encArg(x_2329), encArg(x_3164))) :|: x_3164 >= 0, x_1660 >= 0, x_2329 >= 0, z = 1 + x_1660 + x_2329 + x_3164
   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: {cond}, {encArg}, {encode_p}, {encode_gr}, {encode_s}, {encode_cond}
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]
  p: runtime: O(1) [1], size: O(n^1) [z]

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

(53) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   cond(z, z', z'') -{ 4 + z'' }-> cond(s, z' - 1, 1 + (z'' - 1)) :|: s >= 0, s <= 2, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 3 + z'' }-> cond(s', 0, 1 + (z'' - 1)) :|: s' >= 0, s' <= 2, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 2 }-> cond(2, 0, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 3 }-> cond(2, z' - 1, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 3 }-> cond(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 2 }-> cond(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 2 }-> cond(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 1 }-> cond(0, 0, z'') :|: z = 2, z' >= 0, z'' >= 0
   cond(z, z', z'') -{ 2 }-> cond(0, z' - 1, z'') :|: z = 2, z' - 1 >= 0, z'' >= 0
   cond(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_1329), encArg(x_2164))) :|: x_2164 >= 0, z = 1 + (1 + x_1329 + x_2164), x_1329 >= 0
   encArg(z) -{ 0 }-> p(cond(encArg(x_1328), encArg(x_2163), encArg(x_381))) :|: x_1328 >= 0, x_381 >= 0, z = 1 + (1 + x_1328 + x_2163 + x_381), x_2163 >= 0
   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 }-> cond(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_cond(z, z', z'') -{ 0 }-> cond(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_cond(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_1661), encArg(x_2330))) :|: z = 1 + x_1661 + x_2330, x_2330 >= 0, x_1661 >= 0
   encode_p(z) -{ 0 }-> p(cond(encArg(x_1660), encArg(x_2329), encArg(x_3164))) :|: x_3164 >= 0, x_1660 >= 0, x_2329 >= 0, z = 1 + x_1660 + x_2329 + x_3164
   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: {cond}, {encArg}, {encode_p}, {encode_gr}, {encode_s}, {encode_cond}
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]
  p: runtime: O(1) [1], size: O(n^1) [z]
  cond: runtime: ?, size: O(1) [0]

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

(55) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: cond
after applying outer abstraction to obtain an ITS,
resulting in: O(n^2) with polynomial bound: 10 + 4*z' + z'*z'' + 2*z''

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

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

   cond(z, z', z'') -{ 4 + z'' }-> cond(s, z' - 1, 1 + (z'' - 1)) :|: s >= 0, s <= 2, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 3 + z'' }-> cond(s', 0, 1 + (z'' - 1)) :|: s' >= 0, s' <= 2, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 2 }-> cond(2, 0, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 3 }-> cond(2, z' - 1, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 3 }-> cond(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 2 }-> cond(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 2 }-> cond(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 1 }-> cond(0, 0, z'') :|: z = 2, z' >= 0, z'' >= 0
   cond(z, z', z'') -{ 2 }-> cond(0, z' - 1, z'') :|: z = 2, z' - 1 >= 0, z'' >= 0
   cond(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_1329), encArg(x_2164))) :|: x_2164 >= 0, z = 1 + (1 + x_1329 + x_2164), x_1329 >= 0
   encArg(z) -{ 0 }-> p(cond(encArg(x_1328), encArg(x_2163), encArg(x_381))) :|: x_1328 >= 0, x_381 >= 0, z = 1 + (1 + x_1328 + x_2163 + x_381), x_2163 >= 0
   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 }-> cond(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_cond(z, z', z'') -{ 0 }-> cond(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_cond(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_1661), encArg(x_2330))) :|: z = 1 + x_1661 + x_2330, x_2330 >= 0, x_1661 >= 0
   encode_p(z) -{ 0 }-> p(cond(encArg(x_1660), encArg(x_2329), encArg(x_3164))) :|: x_3164 >= 0, x_1660 >= 0, x_2329 >= 0, z = 1 + x_1660 + x_2329 + x_3164
   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_s}, {encode_cond}
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]
  p: runtime: O(1) [1], size: O(n^1) [z]
  cond: runtime: O(n^2) [10 + 4*z' + z'*z'' + 2*z''], size: O(1) [0]

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

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

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

   cond(z, z', z'') -{ 13 + 2*z'' }-> s1 :|: s1 >= 0, s1 <= 0, z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 12 + 2*z'' }-> s2 :|: s2 >= 0, s2 <= 0, z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 9 + 4*z' }-> s3 :|: s3 >= 0, s3 <= 0, z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 12 }-> s4 :|: s4 >= 0, s4 <= 0, z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 10 + 4*z' + z'*z'' + 2*z'' }-> s5 :|: s5 >= 0, s5 <= 0, s >= 0, s <= 2, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 13 + 3*z'' }-> s6 :|: s6 >= 0, s6 <= 0, s' >= 0, s' <= 2, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 12 + 2*z'' }-> s7 :|: s7 >= 0, s7 <= 0, z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 8 + 4*z' + z'*z'' + z'' }-> s8 :|: s8 >= 0, s8 <= 0, z = 2, z' - 1 >= 0, z'' >= 0
   cond(z, z', z'') -{ 11 + 2*z'' }-> s9 :|: s9 >= 0, s9 <= 0, z = 2, z' >= 0, z'' >= 0
   cond(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_1329), encArg(x_2164))) :|: x_2164 >= 0, z = 1 + (1 + x_1329 + x_2164), x_1329 >= 0
   encArg(z) -{ 0 }-> p(cond(encArg(x_1328), encArg(x_2163), encArg(x_381))) :|: x_1328 >= 0, x_381 >= 0, z = 1 + (1 + x_1328 + x_2163 + x_381), x_2163 >= 0
   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 }-> cond(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_cond(z, z', z'') -{ 0 }-> cond(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_cond(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_1661), encArg(x_2330))) :|: z = 1 + x_1661 + x_2330, x_2330 >= 0, x_1661 >= 0
   encode_p(z) -{ 0 }-> p(cond(encArg(x_1660), encArg(x_2329), encArg(x_3164))) :|: x_3164 >= 0, x_1660 >= 0, x_2329 >= 0, z = 1 + x_1660 + x_2329 + x_3164
   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_s}, {encode_cond}
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]
  p: runtime: O(1) [1], size: O(n^1) [z]
  cond: runtime: O(n^2) [10 + 4*z' + z'*z'' + 2*z''], size: O(1) [0]

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

(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:

   cond(z, z', z'') -{ 13 + 2*z'' }-> s1 :|: s1 >= 0, s1 <= 0, z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 12 + 2*z'' }-> s2 :|: s2 >= 0, s2 <= 0, z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 9 + 4*z' }-> s3 :|: s3 >= 0, s3 <= 0, z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 12 }-> s4 :|: s4 >= 0, s4 <= 0, z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 10 + 4*z' + z'*z'' + 2*z'' }-> s5 :|: s5 >= 0, s5 <= 0, s >= 0, s <= 2, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 13 + 3*z'' }-> s6 :|: s6 >= 0, s6 <= 0, s' >= 0, s' <= 2, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 12 + 2*z'' }-> s7 :|: s7 >= 0, s7 <= 0, z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 8 + 4*z' + z'*z'' + z'' }-> s8 :|: s8 >= 0, s8 <= 0, z = 2, z' - 1 >= 0, z'' >= 0
   cond(z, z', z'') -{ 11 + 2*z'' }-> s9 :|: s9 >= 0, s9 <= 0, z = 2, z' >= 0, z'' >= 0
   cond(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_1329), encArg(x_2164))) :|: x_2164 >= 0, z = 1 + (1 + x_1329 + x_2164), x_1329 >= 0
   encArg(z) -{ 0 }-> p(cond(encArg(x_1328), encArg(x_2163), encArg(x_381))) :|: x_1328 >= 0, x_381 >= 0, z = 1 + (1 + x_1328 + x_2163 + x_381), x_2163 >= 0
   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 }-> cond(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_cond(z, z', z'') -{ 0 }-> cond(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_cond(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_1661), encArg(x_2330))) :|: z = 1 + x_1661 + x_2330, x_2330 >= 0, x_1661 >= 0
   encode_p(z) -{ 0 }-> p(cond(encArg(x_1660), encArg(x_2329), encArg(x_3164))) :|: x_3164 >= 0, x_1660 >= 0, x_2329 >= 0, z = 1 + x_1660 + x_2329 + x_3164
   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_s}, {encode_cond}
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]
  p: runtime: O(1) [1], size: O(n^1) [z]
  cond: runtime: O(n^2) [10 + 4*z' + z'*z'' + 2*z''], size: O(1) [0]
  encArg: runtime: ?, size: O(n^1) [1 + z]

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

(61) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using KoAT for: encArg
after applying outer abstraction to obtain an ITS,
resulting in: O(n^3) with polynomial bound: 49 + 165*z + 56*z^2 + 6*z^3

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

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

   cond(z, z', z'') -{ 13 + 2*z'' }-> s1 :|: s1 >= 0, s1 <= 0, z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 12 + 2*z'' }-> s2 :|: s2 >= 0, s2 <= 0, z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 9 + 4*z' }-> s3 :|: s3 >= 0, s3 <= 0, z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 12 }-> s4 :|: s4 >= 0, s4 <= 0, z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 10 + 4*z' + z'*z'' + 2*z'' }-> s5 :|: s5 >= 0, s5 <= 0, s >= 0, s <= 2, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 13 + 3*z'' }-> s6 :|: s6 >= 0, s6 <= 0, s' >= 0, s' <= 2, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 12 + 2*z'' }-> s7 :|: s7 >= 0, s7 <= 0, z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 8 + 4*z' + z'*z'' + z'' }-> s8 :|: s8 >= 0, s8 <= 0, z = 2, z' - 1 >= 0, z'' >= 0
   cond(z, z', z'') -{ 11 + 2*z'' }-> s9 :|: s9 >= 0, s9 <= 0, z = 2, z' >= 0, z'' >= 0
   cond(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_1329), encArg(x_2164))) :|: x_2164 >= 0, z = 1 + (1 + x_1329 + x_2164), x_1329 >= 0
   encArg(z) -{ 0 }-> p(cond(encArg(x_1328), encArg(x_2163), encArg(x_381))) :|: x_1328 >= 0, x_381 >= 0, z = 1 + (1 + x_1328 + x_2163 + x_381), x_2163 >= 0
   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 }-> cond(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_cond(z, z', z'') -{ 0 }-> cond(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_cond(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_1661), encArg(x_2330))) :|: z = 1 + x_1661 + x_2330, x_2330 >= 0, x_1661 >= 0
   encode_p(z) -{ 0 }-> p(cond(encArg(x_1660), encArg(x_2329), encArg(x_3164))) :|: x_3164 >= 0, x_1660 >= 0, x_2329 >= 0, z = 1 + x_1660 + x_2329 + x_3164
   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_s}, {encode_cond}
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]
  p: runtime: O(1) [1], size: O(n^1) [z]
  cond: runtime: O(n^2) [10 + 4*z' + z'*z'' + 2*z''], size: O(1) [0]
  encArg: runtime: O(n^3) [49 + 165*z + 56*z^2 + 6*z^3], 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:

   cond(z, z', z'') -{ 13 + 2*z'' }-> s1 :|: s1 >= 0, s1 <= 0, z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 12 + 2*z'' }-> s2 :|: s2 >= 0, s2 <= 0, z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 9 + 4*z' }-> s3 :|: s3 >= 0, s3 <= 0, z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 12 }-> s4 :|: s4 >= 0, s4 <= 0, z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 10 + 4*z' + z'*z'' + 2*z'' }-> s5 :|: s5 >= 0, s5 <= 0, s >= 0, s <= 2, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 13 + 3*z'' }-> s6 :|: s6 >= 0, s6 <= 0, s' >= 0, s' <= 2, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 12 + 2*z'' }-> s7 :|: s7 >= 0, s7 <= 0, z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 8 + 4*z' + z'*z'' + z'' }-> s8 :|: s8 >= 0, s8 <= 0, z = 2, z' - 1 >= 0, z'' >= 0
   cond(z, z', z'') -{ 11 + 2*z'' }-> s9 :|: s9 >= 0, s9 <= 0, z = 2, z' >= 0, z'' >= 0
   cond(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encArg(z) -{ 157 + 4*s12 + s12*s13 + 2*s13 + 165*x_1 + 56*x_1^2 + 6*x_1^3 + 165*x_2 + 56*x_2^2 + 6*x_2^3 + 165*x_3 + 56*x_3^2 + 6*x_3^3 }-> s14 :|: s11 >= 0, s11 <= x_1 + 1, s12 >= 0, s12 <= x_2 + 1, s13 >= 0, s13 <= x_3 + 1, s14 >= 0, s14 <= 0, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 100 + s16 + 165*x_1 + 56*x_1^2 + 6*x_1^3 + 165*x_2 + 56*x_2^2 + 6*x_2^3 }-> s17 :|: s15 >= 0, s15 <= x_1 + 1, s16 >= 0, s16 <= x_2 + 1, s17 >= 0, s17 <= 2, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ -104 + 13*z + 20*z^2 + 6*z^3 }-> s27 :|: s26 >= 0, s26 <= z - 2 + 1, s27 >= 0, s27 <= 1 + s26, z - 2 >= 0
   encArg(z) -{ 158 + 4*s29 + s29*s30 + 2*s30 + 165*x_1328 + 56*x_1328^2 + 6*x_1328^3 + 165*x_2163 + 56*x_2163^2 + 6*x_2163^3 + 165*x_381 + 56*x_381^2 + 6*x_381^3 }-> s32 :|: s28 >= 0, s28 <= x_1328 + 1, s29 >= 0, s29 <= x_2163 + 1, s30 >= 0, s30 <= x_381 + 1, s31 >= 0, s31 <= 0, s32 >= 0, s32 <= s31, x_1328 >= 0, x_381 >= 0, z = 1 + (1 + x_1328 + x_2163 + x_381), x_2163 >= 0
   encArg(z) -{ 101 + s34 + 165*x_1329 + 56*x_1329^2 + 6*x_1329^3 + 165*x_2164 + 56*x_2164^2 + 6*x_2164^3 }-> s36 :|: s33 >= 0, s33 <= x_1329 + 1, s34 >= 0, s34 <= x_2164 + 1, s35 >= 0, s35 <= 2, s36 >= 0, s36 <= s35, x_2164 >= 0, z = 1 + (1 + x_1329 + x_2164), x_1329 >= 0
   encArg(z) -{ -103 + 13*z + 20*z^2 + 6*z^3 }-> s39 :|: s37 >= 0, s37 <= z - 2 + 1, s38 >= 0, s38 <= s37, s39 >= 0, s39 <= s38, 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) -{ -66 + 71*z + 38*z^2 + 6*z^3 }-> 1 + s10 :|: s10 >= 0, s10 <= z - 1 + 1, z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_cond(z, z', z'') -{ 157 + 4*s19 + s19*s20 + 2*s20 + 165*z + 56*z^2 + 6*z^3 + 165*z' + 56*z'^2 + 6*z'^3 + 165*z'' + 56*z''^2 + 6*z''^3 }-> s21 :|: s18 >= 0, s18 <= z + 1, s19 >= 0, s19 <= z' + 1, s20 >= 0, s20 <= z'' + 1, s21 >= 0, s21 <= 0, z >= 0, z'' >= 0, z' >= 0
   encode_cond(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_gr(z, z') -{ 100 + s23 + 165*z + 56*z^2 + 6*z^3 + 165*z' + 56*z'^2 + 6*z'^3 }-> s24 :|: s22 >= 0, s22 <= z + 1, s23 >= 0, s23 <= z' + 1, s24 >= 0, s24 <= 2, z >= 0, z' >= 0
   encode_gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_p(z) -{ -65 + 71*z + 38*z^2 + 6*z^3 }-> s41 :|: s40 >= 0, s40 <= z - 1 + 1, s41 >= 0, s41 <= 1 + s40, z - 1 >= 0
   encode_p(z) -{ 158 + 4*s43 + s43*s44 + 2*s44 + 165*x_1660 + 56*x_1660^2 + 6*x_1660^3 + 165*x_2329 + 56*x_2329^2 + 6*x_2329^3 + 165*x_3164 + 56*x_3164^2 + 6*x_3164^3 }-> s46 :|: s42 >= 0, s42 <= x_1660 + 1, s43 >= 0, s43 <= x_2329 + 1, s44 >= 0, s44 <= x_3164 + 1, s45 >= 0, s45 <= 0, s46 >= 0, s46 <= s45, x_3164 >= 0, x_1660 >= 0, x_2329 >= 0, z = 1 + x_1660 + x_2329 + x_3164
   encode_p(z) -{ 101 + s48 + 165*x_1661 + 56*x_1661^2 + 6*x_1661^3 + 165*x_2330 + 56*x_2330^2 + 6*x_2330^3 }-> s50 :|: s47 >= 0, s47 <= x_1661 + 1, s48 >= 0, s48 <= x_2330 + 1, s49 >= 0, s49 <= 2, s50 >= 0, s50 <= s49, z = 1 + x_1661 + x_2330, x_2330 >= 0, x_1661 >= 0
   encode_p(z) -{ -64 + 71*z + 38*z^2 + 6*z^3 }-> s53 :|: s51 >= 0, s51 <= z - 1 + 1, s52 >= 0, s52 <= s51, s53 >= 0, s53 <= s52, 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) -{ 49 + 165*z + 56*z^2 + 6*z^3 }-> 1 + s25 :|: s25 >= 0, s25 <= 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_s}, {encode_cond}
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]
  p: runtime: O(1) [1], size: O(n^1) [z]
  cond: runtime: O(n^2) [10 + 4*z' + z'*z'' + 2*z''], size: O(1) [0]
  encArg: runtime: O(n^3) [49 + 165*z + 56*z^2 + 6*z^3], 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:

   cond(z, z', z'') -{ 13 + 2*z'' }-> s1 :|: s1 >= 0, s1 <= 0, z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 12 + 2*z'' }-> s2 :|: s2 >= 0, s2 <= 0, z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 9 + 4*z' }-> s3 :|: s3 >= 0, s3 <= 0, z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 12 }-> s4 :|: s4 >= 0, s4 <= 0, z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 10 + 4*z' + z'*z'' + 2*z'' }-> s5 :|: s5 >= 0, s5 <= 0, s >= 0, s <= 2, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 13 + 3*z'' }-> s6 :|: s6 >= 0, s6 <= 0, s' >= 0, s' <= 2, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 12 + 2*z'' }-> s7 :|: s7 >= 0, s7 <= 0, z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 8 + 4*z' + z'*z'' + z'' }-> s8 :|: s8 >= 0, s8 <= 0, z = 2, z' - 1 >= 0, z'' >= 0
   cond(z, z', z'') -{ 11 + 2*z'' }-> s9 :|: s9 >= 0, s9 <= 0, z = 2, z' >= 0, z'' >= 0
   cond(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encArg(z) -{ 157 + 4*s12 + s12*s13 + 2*s13 + 165*x_1 + 56*x_1^2 + 6*x_1^3 + 165*x_2 + 56*x_2^2 + 6*x_2^3 + 165*x_3 + 56*x_3^2 + 6*x_3^3 }-> s14 :|: s11 >= 0, s11 <= x_1 + 1, s12 >= 0, s12 <= x_2 + 1, s13 >= 0, s13 <= x_3 + 1, s14 >= 0, s14 <= 0, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 100 + s16 + 165*x_1 + 56*x_1^2 + 6*x_1^3 + 165*x_2 + 56*x_2^2 + 6*x_2^3 }-> s17 :|: s15 >= 0, s15 <= x_1 + 1, s16 >= 0, s16 <= x_2 + 1, s17 >= 0, s17 <= 2, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ -104 + 13*z + 20*z^2 + 6*z^3 }-> s27 :|: s26 >= 0, s26 <= z - 2 + 1, s27 >= 0, s27 <= 1 + s26, z - 2 >= 0
   encArg(z) -{ 158 + 4*s29 + s29*s30 + 2*s30 + 165*x_1328 + 56*x_1328^2 + 6*x_1328^3 + 165*x_2163 + 56*x_2163^2 + 6*x_2163^3 + 165*x_381 + 56*x_381^2 + 6*x_381^3 }-> s32 :|: s28 >= 0, s28 <= x_1328 + 1, s29 >= 0, s29 <= x_2163 + 1, s30 >= 0, s30 <= x_381 + 1, s31 >= 0, s31 <= 0, s32 >= 0, s32 <= s31, x_1328 >= 0, x_381 >= 0, z = 1 + (1 + x_1328 + x_2163 + x_381), x_2163 >= 0
   encArg(z) -{ 101 + s34 + 165*x_1329 + 56*x_1329^2 + 6*x_1329^3 + 165*x_2164 + 56*x_2164^2 + 6*x_2164^3 }-> s36 :|: s33 >= 0, s33 <= x_1329 + 1, s34 >= 0, s34 <= x_2164 + 1, s35 >= 0, s35 <= 2, s36 >= 0, s36 <= s35, x_2164 >= 0, z = 1 + (1 + x_1329 + x_2164), x_1329 >= 0
   encArg(z) -{ -103 + 13*z + 20*z^2 + 6*z^3 }-> s39 :|: s37 >= 0, s37 <= z - 2 + 1, s38 >= 0, s38 <= s37, s39 >= 0, s39 <= s38, 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) -{ -66 + 71*z + 38*z^2 + 6*z^3 }-> 1 + s10 :|: s10 >= 0, s10 <= z - 1 + 1, z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_cond(z, z', z'') -{ 157 + 4*s19 + s19*s20 + 2*s20 + 165*z + 56*z^2 + 6*z^3 + 165*z' + 56*z'^2 + 6*z'^3 + 165*z'' + 56*z''^2 + 6*z''^3 }-> s21 :|: s18 >= 0, s18 <= z + 1, s19 >= 0, s19 <= z' + 1, s20 >= 0, s20 <= z'' + 1, s21 >= 0, s21 <= 0, z >= 0, z'' >= 0, z' >= 0
   encode_cond(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_gr(z, z') -{ 100 + s23 + 165*z + 56*z^2 + 6*z^3 + 165*z' + 56*z'^2 + 6*z'^3 }-> s24 :|: s22 >= 0, s22 <= z + 1, s23 >= 0, s23 <= z' + 1, s24 >= 0, s24 <= 2, z >= 0, z' >= 0
   encode_gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_p(z) -{ -65 + 71*z + 38*z^2 + 6*z^3 }-> s41 :|: s40 >= 0, s40 <= z - 1 + 1, s41 >= 0, s41 <= 1 + s40, z - 1 >= 0
   encode_p(z) -{ 158 + 4*s43 + s43*s44 + 2*s44 + 165*x_1660 + 56*x_1660^2 + 6*x_1660^3 + 165*x_2329 + 56*x_2329^2 + 6*x_2329^3 + 165*x_3164 + 56*x_3164^2 + 6*x_3164^3 }-> s46 :|: s42 >= 0, s42 <= x_1660 + 1, s43 >= 0, s43 <= x_2329 + 1, s44 >= 0, s44 <= x_3164 + 1, s45 >= 0, s45 <= 0, s46 >= 0, s46 <= s45, x_3164 >= 0, x_1660 >= 0, x_2329 >= 0, z = 1 + x_1660 + x_2329 + x_3164
   encode_p(z) -{ 101 + s48 + 165*x_1661 + 56*x_1661^2 + 6*x_1661^3 + 165*x_2330 + 56*x_2330^2 + 6*x_2330^3 }-> s50 :|: s47 >= 0, s47 <= x_1661 + 1, s48 >= 0, s48 <= x_2330 + 1, s49 >= 0, s49 <= 2, s50 >= 0, s50 <= s49, z = 1 + x_1661 + x_2330, x_2330 >= 0, x_1661 >= 0
   encode_p(z) -{ -64 + 71*z + 38*z^2 + 6*z^3 }-> s53 :|: s51 >= 0, s51 <= z - 1 + 1, s52 >= 0, s52 <= s51, s53 >= 0, s53 <= s52, 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) -{ 49 + 165*z + 56*z^2 + 6*z^3 }-> 1 + s25 :|: s25 >= 0, s25 <= 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_s}, {encode_cond}
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]
  p: runtime: O(1) [1], size: O(n^1) [z]
  cond: runtime: O(n^2) [10 + 4*z' + z'*z'' + 2*z''], size: O(1) [0]
  encArg: runtime: O(n^3) [49 + 165*z + 56*z^2 + 6*z^3], 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^3) with polynomial bound: 271 + 976*z + 357*z^2 + 42*z^3

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

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

   cond(z, z', z'') -{ 13 + 2*z'' }-> s1 :|: s1 >= 0, s1 <= 0, z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 12 + 2*z'' }-> s2 :|: s2 >= 0, s2 <= 0, z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 9 + 4*z' }-> s3 :|: s3 >= 0, s3 <= 0, z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 12 }-> s4 :|: s4 >= 0, s4 <= 0, z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 10 + 4*z' + z'*z'' + 2*z'' }-> s5 :|: s5 >= 0, s5 <= 0, s >= 0, s <= 2, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 13 + 3*z'' }-> s6 :|: s6 >= 0, s6 <= 0, s' >= 0, s' <= 2, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 12 + 2*z'' }-> s7 :|: s7 >= 0, s7 <= 0, z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 8 + 4*z' + z'*z'' + z'' }-> s8 :|: s8 >= 0, s8 <= 0, z = 2, z' - 1 >= 0, z'' >= 0
   cond(z, z', z'') -{ 11 + 2*z'' }-> s9 :|: s9 >= 0, s9 <= 0, z = 2, z' >= 0, z'' >= 0
   cond(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encArg(z) -{ 157 + 4*s12 + s12*s13 + 2*s13 + 165*x_1 + 56*x_1^2 + 6*x_1^3 + 165*x_2 + 56*x_2^2 + 6*x_2^3 + 165*x_3 + 56*x_3^2 + 6*x_3^3 }-> s14 :|: s11 >= 0, s11 <= x_1 + 1, s12 >= 0, s12 <= x_2 + 1, s13 >= 0, s13 <= x_3 + 1, s14 >= 0, s14 <= 0, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 100 + s16 + 165*x_1 + 56*x_1^2 + 6*x_1^3 + 165*x_2 + 56*x_2^2 + 6*x_2^3 }-> s17 :|: s15 >= 0, s15 <= x_1 + 1, s16 >= 0, s16 <= x_2 + 1, s17 >= 0, s17 <= 2, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ -104 + 13*z + 20*z^2 + 6*z^3 }-> s27 :|: s26 >= 0, s26 <= z - 2 + 1, s27 >= 0, s27 <= 1 + s26, z - 2 >= 0
   encArg(z) -{ 158 + 4*s29 + s29*s30 + 2*s30 + 165*x_1328 + 56*x_1328^2 + 6*x_1328^3 + 165*x_2163 + 56*x_2163^2 + 6*x_2163^3 + 165*x_381 + 56*x_381^2 + 6*x_381^3 }-> s32 :|: s28 >= 0, s28 <= x_1328 + 1, s29 >= 0, s29 <= x_2163 + 1, s30 >= 0, s30 <= x_381 + 1, s31 >= 0, s31 <= 0, s32 >= 0, s32 <= s31, x_1328 >= 0, x_381 >= 0, z = 1 + (1 + x_1328 + x_2163 + x_381), x_2163 >= 0
   encArg(z) -{ 101 + s34 + 165*x_1329 + 56*x_1329^2 + 6*x_1329^3 + 165*x_2164 + 56*x_2164^2 + 6*x_2164^3 }-> s36 :|: s33 >= 0, s33 <= x_1329 + 1, s34 >= 0, s34 <= x_2164 + 1, s35 >= 0, s35 <= 2, s36 >= 0, s36 <= s35, x_2164 >= 0, z = 1 + (1 + x_1329 + x_2164), x_1329 >= 0
   encArg(z) -{ -103 + 13*z + 20*z^2 + 6*z^3 }-> s39 :|: s37 >= 0, s37 <= z - 2 + 1, s38 >= 0, s38 <= s37, s39 >= 0, s39 <= s38, 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) -{ -66 + 71*z + 38*z^2 + 6*z^3 }-> 1 + s10 :|: s10 >= 0, s10 <= z - 1 + 1, z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_cond(z, z', z'') -{ 157 + 4*s19 + s19*s20 + 2*s20 + 165*z + 56*z^2 + 6*z^3 + 165*z' + 56*z'^2 + 6*z'^3 + 165*z'' + 56*z''^2 + 6*z''^3 }-> s21 :|: s18 >= 0, s18 <= z + 1, s19 >= 0, s19 <= z' + 1, s20 >= 0, s20 <= z'' + 1, s21 >= 0, s21 <= 0, z >= 0, z'' >= 0, z' >= 0
   encode_cond(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_gr(z, z') -{ 100 + s23 + 165*z + 56*z^2 + 6*z^3 + 165*z' + 56*z'^2 + 6*z'^3 }-> s24 :|: s22 >= 0, s22 <= z + 1, s23 >= 0, s23 <= z' + 1, s24 >= 0, s24 <= 2, z >= 0, z' >= 0
   encode_gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_p(z) -{ -65 + 71*z + 38*z^2 + 6*z^3 }-> s41 :|: s40 >= 0, s40 <= z - 1 + 1, s41 >= 0, s41 <= 1 + s40, z - 1 >= 0
   encode_p(z) -{ 158 + 4*s43 + s43*s44 + 2*s44 + 165*x_1660 + 56*x_1660^2 + 6*x_1660^3 + 165*x_2329 + 56*x_2329^2 + 6*x_2329^3 + 165*x_3164 + 56*x_3164^2 + 6*x_3164^3 }-> s46 :|: s42 >= 0, s42 <= x_1660 + 1, s43 >= 0, s43 <= x_2329 + 1, s44 >= 0, s44 <= x_3164 + 1, s45 >= 0, s45 <= 0, s46 >= 0, s46 <= s45, x_3164 >= 0, x_1660 >= 0, x_2329 >= 0, z = 1 + x_1660 + x_2329 + x_3164
   encode_p(z) -{ 101 + s48 + 165*x_1661 + 56*x_1661^2 + 6*x_1661^3 + 165*x_2330 + 56*x_2330^2 + 6*x_2330^3 }-> s50 :|: s47 >= 0, s47 <= x_1661 + 1, s48 >= 0, s48 <= x_2330 + 1, s49 >= 0, s49 <= 2, s50 >= 0, s50 <= s49, z = 1 + x_1661 + x_2330, x_2330 >= 0, x_1661 >= 0
   encode_p(z) -{ -64 + 71*z + 38*z^2 + 6*z^3 }-> s53 :|: s51 >= 0, s51 <= z - 1 + 1, s52 >= 0, s52 <= s51, s53 >= 0, s53 <= s52, 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) -{ 49 + 165*z + 56*z^2 + 6*z^3 }-> 1 + s25 :|: s25 >= 0, s25 <= 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_s}, {encode_cond}
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]
  p: runtime: O(1) [1], size: O(n^1) [z]
  cond: runtime: O(n^2) [10 + 4*z' + z'*z'' + 2*z''], size: O(1) [0]
  encArg: runtime: O(n^3) [49 + 165*z + 56*z^2 + 6*z^3], size: O(n^1) [1 + z]
  encode_p: runtime: O(n^3) [271 + 976*z + 357*z^2 + 42*z^3], 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:

   cond(z, z', z'') -{ 13 + 2*z'' }-> s1 :|: s1 >= 0, s1 <= 0, z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 12 + 2*z'' }-> s2 :|: s2 >= 0, s2 <= 0, z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 9 + 4*z' }-> s3 :|: s3 >= 0, s3 <= 0, z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 12 }-> s4 :|: s4 >= 0, s4 <= 0, z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 10 + 4*z' + z'*z'' + 2*z'' }-> s5 :|: s5 >= 0, s5 <= 0, s >= 0, s <= 2, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 13 + 3*z'' }-> s6 :|: s6 >= 0, s6 <= 0, s' >= 0, s' <= 2, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 12 + 2*z'' }-> s7 :|: s7 >= 0, s7 <= 0, z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 8 + 4*z' + z'*z'' + z'' }-> s8 :|: s8 >= 0, s8 <= 0, z = 2, z' - 1 >= 0, z'' >= 0
   cond(z, z', z'') -{ 11 + 2*z'' }-> s9 :|: s9 >= 0, s9 <= 0, z = 2, z' >= 0, z'' >= 0
   cond(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encArg(z) -{ 157 + 4*s12 + s12*s13 + 2*s13 + 165*x_1 + 56*x_1^2 + 6*x_1^3 + 165*x_2 + 56*x_2^2 + 6*x_2^3 + 165*x_3 + 56*x_3^2 + 6*x_3^3 }-> s14 :|: s11 >= 0, s11 <= x_1 + 1, s12 >= 0, s12 <= x_2 + 1, s13 >= 0, s13 <= x_3 + 1, s14 >= 0, s14 <= 0, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 100 + s16 + 165*x_1 + 56*x_1^2 + 6*x_1^3 + 165*x_2 + 56*x_2^2 + 6*x_2^3 }-> s17 :|: s15 >= 0, s15 <= x_1 + 1, s16 >= 0, s16 <= x_2 + 1, s17 >= 0, s17 <= 2, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ -104 + 13*z + 20*z^2 + 6*z^3 }-> s27 :|: s26 >= 0, s26 <= z - 2 + 1, s27 >= 0, s27 <= 1 + s26, z - 2 >= 0
   encArg(z) -{ 158 + 4*s29 + s29*s30 + 2*s30 + 165*x_1328 + 56*x_1328^2 + 6*x_1328^3 + 165*x_2163 + 56*x_2163^2 + 6*x_2163^3 + 165*x_381 + 56*x_381^2 + 6*x_381^3 }-> s32 :|: s28 >= 0, s28 <= x_1328 + 1, s29 >= 0, s29 <= x_2163 + 1, s30 >= 0, s30 <= x_381 + 1, s31 >= 0, s31 <= 0, s32 >= 0, s32 <= s31, x_1328 >= 0, x_381 >= 0, z = 1 + (1 + x_1328 + x_2163 + x_381), x_2163 >= 0
   encArg(z) -{ 101 + s34 + 165*x_1329 + 56*x_1329^2 + 6*x_1329^3 + 165*x_2164 + 56*x_2164^2 + 6*x_2164^3 }-> s36 :|: s33 >= 0, s33 <= x_1329 + 1, s34 >= 0, s34 <= x_2164 + 1, s35 >= 0, s35 <= 2, s36 >= 0, s36 <= s35, x_2164 >= 0, z = 1 + (1 + x_1329 + x_2164), x_1329 >= 0
   encArg(z) -{ -103 + 13*z + 20*z^2 + 6*z^3 }-> s39 :|: s37 >= 0, s37 <= z - 2 + 1, s38 >= 0, s38 <= s37, s39 >= 0, s39 <= s38, 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) -{ -66 + 71*z + 38*z^2 + 6*z^3 }-> 1 + s10 :|: s10 >= 0, s10 <= z - 1 + 1, z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_cond(z, z', z'') -{ 157 + 4*s19 + s19*s20 + 2*s20 + 165*z + 56*z^2 + 6*z^3 + 165*z' + 56*z'^2 + 6*z'^3 + 165*z'' + 56*z''^2 + 6*z''^3 }-> s21 :|: s18 >= 0, s18 <= z + 1, s19 >= 0, s19 <= z' + 1, s20 >= 0, s20 <= z'' + 1, s21 >= 0, s21 <= 0, z >= 0, z'' >= 0, z' >= 0
   encode_cond(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_gr(z, z') -{ 100 + s23 + 165*z + 56*z^2 + 6*z^3 + 165*z' + 56*z'^2 + 6*z'^3 }-> s24 :|: s22 >= 0, s22 <= z + 1, s23 >= 0, s23 <= z' + 1, s24 >= 0, s24 <= 2, z >= 0, z' >= 0
   encode_gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_p(z) -{ -65 + 71*z + 38*z^2 + 6*z^3 }-> s41 :|: s40 >= 0, s40 <= z - 1 + 1, s41 >= 0, s41 <= 1 + s40, z - 1 >= 0
   encode_p(z) -{ 158 + 4*s43 + s43*s44 + 2*s44 + 165*x_1660 + 56*x_1660^2 + 6*x_1660^3 + 165*x_2329 + 56*x_2329^2 + 6*x_2329^3 + 165*x_3164 + 56*x_3164^2 + 6*x_3164^3 }-> s46 :|: s42 >= 0, s42 <= x_1660 + 1, s43 >= 0, s43 <= x_2329 + 1, s44 >= 0, s44 <= x_3164 + 1, s45 >= 0, s45 <= 0, s46 >= 0, s46 <= s45, x_3164 >= 0, x_1660 >= 0, x_2329 >= 0, z = 1 + x_1660 + x_2329 + x_3164
   encode_p(z) -{ 101 + s48 + 165*x_1661 + 56*x_1661^2 + 6*x_1661^3 + 165*x_2330 + 56*x_2330^2 + 6*x_2330^3 }-> s50 :|: s47 >= 0, s47 <= x_1661 + 1, s48 >= 0, s48 <= x_2330 + 1, s49 >= 0, s49 <= 2, s50 >= 0, s50 <= s49, z = 1 + x_1661 + x_2330, x_2330 >= 0, x_1661 >= 0
   encode_p(z) -{ -64 + 71*z + 38*z^2 + 6*z^3 }-> s53 :|: s51 >= 0, s51 <= z - 1 + 1, s52 >= 0, s52 <= s51, s53 >= 0, s53 <= s52, 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) -{ 49 + 165*z + 56*z^2 + 6*z^3 }-> 1 + s25 :|: s25 >= 0, s25 <= 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_s}, {encode_cond}
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]
  p: runtime: O(1) [1], size: O(n^1) [z]
  cond: runtime: O(n^2) [10 + 4*z' + z'*z'' + 2*z''], size: O(1) [0]
  encArg: runtime: O(n^3) [49 + 165*z + 56*z^2 + 6*z^3], size: O(n^1) [1 + z]
  encode_p: runtime: O(n^3) [271 + 976*z + 357*z^2 + 42*z^3], 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:

   cond(z, z', z'') -{ 13 + 2*z'' }-> s1 :|: s1 >= 0, s1 <= 0, z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 12 + 2*z'' }-> s2 :|: s2 >= 0, s2 <= 0, z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 9 + 4*z' }-> s3 :|: s3 >= 0, s3 <= 0, z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 12 }-> s4 :|: s4 >= 0, s4 <= 0, z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 10 + 4*z' + z'*z'' + 2*z'' }-> s5 :|: s5 >= 0, s5 <= 0, s >= 0, s <= 2, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 13 + 3*z'' }-> s6 :|: s6 >= 0, s6 <= 0, s' >= 0, s' <= 2, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 12 + 2*z'' }-> s7 :|: s7 >= 0, s7 <= 0, z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 8 + 4*z' + z'*z'' + z'' }-> s8 :|: s8 >= 0, s8 <= 0, z = 2, z' - 1 >= 0, z'' >= 0
   cond(z, z', z'') -{ 11 + 2*z'' }-> s9 :|: s9 >= 0, s9 <= 0, z = 2, z' >= 0, z'' >= 0
   cond(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encArg(z) -{ 157 + 4*s12 + s12*s13 + 2*s13 + 165*x_1 + 56*x_1^2 + 6*x_1^3 + 165*x_2 + 56*x_2^2 + 6*x_2^3 + 165*x_3 + 56*x_3^2 + 6*x_3^3 }-> s14 :|: s11 >= 0, s11 <= x_1 + 1, s12 >= 0, s12 <= x_2 + 1, s13 >= 0, s13 <= x_3 + 1, s14 >= 0, s14 <= 0, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 100 + s16 + 165*x_1 + 56*x_1^2 + 6*x_1^3 + 165*x_2 + 56*x_2^2 + 6*x_2^3 }-> s17 :|: s15 >= 0, s15 <= x_1 + 1, s16 >= 0, s16 <= x_2 + 1, s17 >= 0, s17 <= 2, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ -104 + 13*z + 20*z^2 + 6*z^3 }-> s27 :|: s26 >= 0, s26 <= z - 2 + 1, s27 >= 0, s27 <= 1 + s26, z - 2 >= 0
   encArg(z) -{ 158 + 4*s29 + s29*s30 + 2*s30 + 165*x_1328 + 56*x_1328^2 + 6*x_1328^3 + 165*x_2163 + 56*x_2163^2 + 6*x_2163^3 + 165*x_381 + 56*x_381^2 + 6*x_381^3 }-> s32 :|: s28 >= 0, s28 <= x_1328 + 1, s29 >= 0, s29 <= x_2163 + 1, s30 >= 0, s30 <= x_381 + 1, s31 >= 0, s31 <= 0, s32 >= 0, s32 <= s31, x_1328 >= 0, x_381 >= 0, z = 1 + (1 + x_1328 + x_2163 + x_381), x_2163 >= 0
   encArg(z) -{ 101 + s34 + 165*x_1329 + 56*x_1329^2 + 6*x_1329^3 + 165*x_2164 + 56*x_2164^2 + 6*x_2164^3 }-> s36 :|: s33 >= 0, s33 <= x_1329 + 1, s34 >= 0, s34 <= x_2164 + 1, s35 >= 0, s35 <= 2, s36 >= 0, s36 <= s35, x_2164 >= 0, z = 1 + (1 + x_1329 + x_2164), x_1329 >= 0
   encArg(z) -{ -103 + 13*z + 20*z^2 + 6*z^3 }-> s39 :|: s37 >= 0, s37 <= z - 2 + 1, s38 >= 0, s38 <= s37, s39 >= 0, s39 <= s38, 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) -{ -66 + 71*z + 38*z^2 + 6*z^3 }-> 1 + s10 :|: s10 >= 0, s10 <= z - 1 + 1, z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_cond(z, z', z'') -{ 157 + 4*s19 + s19*s20 + 2*s20 + 165*z + 56*z^2 + 6*z^3 + 165*z' + 56*z'^2 + 6*z'^3 + 165*z'' + 56*z''^2 + 6*z''^3 }-> s21 :|: s18 >= 0, s18 <= z + 1, s19 >= 0, s19 <= z' + 1, s20 >= 0, s20 <= z'' + 1, s21 >= 0, s21 <= 0, z >= 0, z'' >= 0, z' >= 0
   encode_cond(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_gr(z, z') -{ 100 + s23 + 165*z + 56*z^2 + 6*z^3 + 165*z' + 56*z'^2 + 6*z'^3 }-> s24 :|: s22 >= 0, s22 <= z + 1, s23 >= 0, s23 <= z' + 1, s24 >= 0, s24 <= 2, z >= 0, z' >= 0
   encode_gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_p(z) -{ -65 + 71*z + 38*z^2 + 6*z^3 }-> s41 :|: s40 >= 0, s40 <= z - 1 + 1, s41 >= 0, s41 <= 1 + s40, z - 1 >= 0
   encode_p(z) -{ 158 + 4*s43 + s43*s44 + 2*s44 + 165*x_1660 + 56*x_1660^2 + 6*x_1660^3 + 165*x_2329 + 56*x_2329^2 + 6*x_2329^3 + 165*x_3164 + 56*x_3164^2 + 6*x_3164^3 }-> s46 :|: s42 >= 0, s42 <= x_1660 + 1, s43 >= 0, s43 <= x_2329 + 1, s44 >= 0, s44 <= x_3164 + 1, s45 >= 0, s45 <= 0, s46 >= 0, s46 <= s45, x_3164 >= 0, x_1660 >= 0, x_2329 >= 0, z = 1 + x_1660 + x_2329 + x_3164
   encode_p(z) -{ 101 + s48 + 165*x_1661 + 56*x_1661^2 + 6*x_1661^3 + 165*x_2330 + 56*x_2330^2 + 6*x_2330^3 }-> s50 :|: s47 >= 0, s47 <= x_1661 + 1, s48 >= 0, s48 <= x_2330 + 1, s49 >= 0, s49 <= 2, s50 >= 0, s50 <= s49, z = 1 + x_1661 + x_2330, x_2330 >= 0, x_1661 >= 0
   encode_p(z) -{ -64 + 71*z + 38*z^2 + 6*z^3 }-> s53 :|: s51 >= 0, s51 <= z - 1 + 1, s52 >= 0, s52 <= s51, s53 >= 0, s53 <= s52, 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) -{ 49 + 165*z + 56*z^2 + 6*z^3 }-> 1 + s25 :|: s25 >= 0, s25 <= 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_s}, {encode_cond}
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]
  p: runtime: O(1) [1], size: O(n^1) [z]
  cond: runtime: O(n^2) [10 + 4*z' + z'*z'' + 2*z''], size: O(1) [0]
  encArg: runtime: O(n^3) [49 + 165*z + 56*z^2 + 6*z^3], size: O(n^1) [1 + z]
  encode_p: runtime: O(n^3) [271 + 976*z + 357*z^2 + 42*z^3], 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^3) with polynomial bound: 101 + 165*z + 56*z^2 + 6*z^3 + 166*z' + 56*z'^2 + 6*z'^3

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

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

   cond(z, z', z'') -{ 13 + 2*z'' }-> s1 :|: s1 >= 0, s1 <= 0, z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 12 + 2*z'' }-> s2 :|: s2 >= 0, s2 <= 0, z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 9 + 4*z' }-> s3 :|: s3 >= 0, s3 <= 0, z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 12 }-> s4 :|: s4 >= 0, s4 <= 0, z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 10 + 4*z' + z'*z'' + 2*z'' }-> s5 :|: s5 >= 0, s5 <= 0, s >= 0, s <= 2, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 13 + 3*z'' }-> s6 :|: s6 >= 0, s6 <= 0, s' >= 0, s' <= 2, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 12 + 2*z'' }-> s7 :|: s7 >= 0, s7 <= 0, z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 8 + 4*z' + z'*z'' + z'' }-> s8 :|: s8 >= 0, s8 <= 0, z = 2, z' - 1 >= 0, z'' >= 0
   cond(z, z', z'') -{ 11 + 2*z'' }-> s9 :|: s9 >= 0, s9 <= 0, z = 2, z' >= 0, z'' >= 0
   cond(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encArg(z) -{ 157 + 4*s12 + s12*s13 + 2*s13 + 165*x_1 + 56*x_1^2 + 6*x_1^3 + 165*x_2 + 56*x_2^2 + 6*x_2^3 + 165*x_3 + 56*x_3^2 + 6*x_3^3 }-> s14 :|: s11 >= 0, s11 <= x_1 + 1, s12 >= 0, s12 <= x_2 + 1, s13 >= 0, s13 <= x_3 + 1, s14 >= 0, s14 <= 0, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 100 + s16 + 165*x_1 + 56*x_1^2 + 6*x_1^3 + 165*x_2 + 56*x_2^2 + 6*x_2^3 }-> s17 :|: s15 >= 0, s15 <= x_1 + 1, s16 >= 0, s16 <= x_2 + 1, s17 >= 0, s17 <= 2, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ -104 + 13*z + 20*z^2 + 6*z^3 }-> s27 :|: s26 >= 0, s26 <= z - 2 + 1, s27 >= 0, s27 <= 1 + s26, z - 2 >= 0
   encArg(z) -{ 158 + 4*s29 + s29*s30 + 2*s30 + 165*x_1328 + 56*x_1328^2 + 6*x_1328^3 + 165*x_2163 + 56*x_2163^2 + 6*x_2163^3 + 165*x_381 + 56*x_381^2 + 6*x_381^3 }-> s32 :|: s28 >= 0, s28 <= x_1328 + 1, s29 >= 0, s29 <= x_2163 + 1, s30 >= 0, s30 <= x_381 + 1, s31 >= 0, s31 <= 0, s32 >= 0, s32 <= s31, x_1328 >= 0, x_381 >= 0, z = 1 + (1 + x_1328 + x_2163 + x_381), x_2163 >= 0
   encArg(z) -{ 101 + s34 + 165*x_1329 + 56*x_1329^2 + 6*x_1329^3 + 165*x_2164 + 56*x_2164^2 + 6*x_2164^3 }-> s36 :|: s33 >= 0, s33 <= x_1329 + 1, s34 >= 0, s34 <= x_2164 + 1, s35 >= 0, s35 <= 2, s36 >= 0, s36 <= s35, x_2164 >= 0, z = 1 + (1 + x_1329 + x_2164), x_1329 >= 0
   encArg(z) -{ -103 + 13*z + 20*z^2 + 6*z^3 }-> s39 :|: s37 >= 0, s37 <= z - 2 + 1, s38 >= 0, s38 <= s37, s39 >= 0, s39 <= s38, 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) -{ -66 + 71*z + 38*z^2 + 6*z^3 }-> 1 + s10 :|: s10 >= 0, s10 <= z - 1 + 1, z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_cond(z, z', z'') -{ 157 + 4*s19 + s19*s20 + 2*s20 + 165*z + 56*z^2 + 6*z^3 + 165*z' + 56*z'^2 + 6*z'^3 + 165*z'' + 56*z''^2 + 6*z''^3 }-> s21 :|: s18 >= 0, s18 <= z + 1, s19 >= 0, s19 <= z' + 1, s20 >= 0, s20 <= z'' + 1, s21 >= 0, s21 <= 0, z >= 0, z'' >= 0, z' >= 0
   encode_cond(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_gr(z, z') -{ 100 + s23 + 165*z + 56*z^2 + 6*z^3 + 165*z' + 56*z'^2 + 6*z'^3 }-> s24 :|: s22 >= 0, s22 <= z + 1, s23 >= 0, s23 <= z' + 1, s24 >= 0, s24 <= 2, z >= 0, z' >= 0
   encode_gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_p(z) -{ -65 + 71*z + 38*z^2 + 6*z^3 }-> s41 :|: s40 >= 0, s40 <= z - 1 + 1, s41 >= 0, s41 <= 1 + s40, z - 1 >= 0
   encode_p(z) -{ 158 + 4*s43 + s43*s44 + 2*s44 + 165*x_1660 + 56*x_1660^2 + 6*x_1660^3 + 165*x_2329 + 56*x_2329^2 + 6*x_2329^3 + 165*x_3164 + 56*x_3164^2 + 6*x_3164^3 }-> s46 :|: s42 >= 0, s42 <= x_1660 + 1, s43 >= 0, s43 <= x_2329 + 1, s44 >= 0, s44 <= x_3164 + 1, s45 >= 0, s45 <= 0, s46 >= 0, s46 <= s45, x_3164 >= 0, x_1660 >= 0, x_2329 >= 0, z = 1 + x_1660 + x_2329 + x_3164
   encode_p(z) -{ 101 + s48 + 165*x_1661 + 56*x_1661^2 + 6*x_1661^3 + 165*x_2330 + 56*x_2330^2 + 6*x_2330^3 }-> s50 :|: s47 >= 0, s47 <= x_1661 + 1, s48 >= 0, s48 <= x_2330 + 1, s49 >= 0, s49 <= 2, s50 >= 0, s50 <= s49, z = 1 + x_1661 + x_2330, x_2330 >= 0, x_1661 >= 0
   encode_p(z) -{ -64 + 71*z + 38*z^2 + 6*z^3 }-> s53 :|: s51 >= 0, s51 <= z - 1 + 1, s52 >= 0, s52 <= s51, s53 >= 0, s53 <= s52, 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) -{ 49 + 165*z + 56*z^2 + 6*z^3 }-> 1 + s25 :|: s25 >= 0, s25 <= 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}, {encode_cond}
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]
  p: runtime: O(1) [1], size: O(n^1) [z]
  cond: runtime: O(n^2) [10 + 4*z' + z'*z'' + 2*z''], size: O(1) [0]
  encArg: runtime: O(n^3) [49 + 165*z + 56*z^2 + 6*z^3], size: O(n^1) [1 + z]
  encode_p: runtime: O(n^3) [271 + 976*z + 357*z^2 + 42*z^3], size: O(n^1) [1 + z]
  encode_gr: runtime: O(n^3) [101 + 165*z + 56*z^2 + 6*z^3 + 166*z' + 56*z'^2 + 6*z'^3], 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:

   cond(z, z', z'') -{ 13 + 2*z'' }-> s1 :|: s1 >= 0, s1 <= 0, z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 12 + 2*z'' }-> s2 :|: s2 >= 0, s2 <= 0, z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 9 + 4*z' }-> s3 :|: s3 >= 0, s3 <= 0, z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 12 }-> s4 :|: s4 >= 0, s4 <= 0, z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 10 + 4*z' + z'*z'' + 2*z'' }-> s5 :|: s5 >= 0, s5 <= 0, s >= 0, s <= 2, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 13 + 3*z'' }-> s6 :|: s6 >= 0, s6 <= 0, s' >= 0, s' <= 2, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 12 + 2*z'' }-> s7 :|: s7 >= 0, s7 <= 0, z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 8 + 4*z' + z'*z'' + z'' }-> s8 :|: s8 >= 0, s8 <= 0, z = 2, z' - 1 >= 0, z'' >= 0
   cond(z, z', z'') -{ 11 + 2*z'' }-> s9 :|: s9 >= 0, s9 <= 0, z = 2, z' >= 0, z'' >= 0
   cond(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encArg(z) -{ 157 + 4*s12 + s12*s13 + 2*s13 + 165*x_1 + 56*x_1^2 + 6*x_1^3 + 165*x_2 + 56*x_2^2 + 6*x_2^3 + 165*x_3 + 56*x_3^2 + 6*x_3^3 }-> s14 :|: s11 >= 0, s11 <= x_1 + 1, s12 >= 0, s12 <= x_2 + 1, s13 >= 0, s13 <= x_3 + 1, s14 >= 0, s14 <= 0, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 100 + s16 + 165*x_1 + 56*x_1^2 + 6*x_1^3 + 165*x_2 + 56*x_2^2 + 6*x_2^3 }-> s17 :|: s15 >= 0, s15 <= x_1 + 1, s16 >= 0, s16 <= x_2 + 1, s17 >= 0, s17 <= 2, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ -104 + 13*z + 20*z^2 + 6*z^3 }-> s27 :|: s26 >= 0, s26 <= z - 2 + 1, s27 >= 0, s27 <= 1 + s26, z - 2 >= 0
   encArg(z) -{ 158 + 4*s29 + s29*s30 + 2*s30 + 165*x_1328 + 56*x_1328^2 + 6*x_1328^3 + 165*x_2163 + 56*x_2163^2 + 6*x_2163^3 + 165*x_381 + 56*x_381^2 + 6*x_381^3 }-> s32 :|: s28 >= 0, s28 <= x_1328 + 1, s29 >= 0, s29 <= x_2163 + 1, s30 >= 0, s30 <= x_381 + 1, s31 >= 0, s31 <= 0, s32 >= 0, s32 <= s31, x_1328 >= 0, x_381 >= 0, z = 1 + (1 + x_1328 + x_2163 + x_381), x_2163 >= 0
   encArg(z) -{ 101 + s34 + 165*x_1329 + 56*x_1329^2 + 6*x_1329^3 + 165*x_2164 + 56*x_2164^2 + 6*x_2164^3 }-> s36 :|: s33 >= 0, s33 <= x_1329 + 1, s34 >= 0, s34 <= x_2164 + 1, s35 >= 0, s35 <= 2, s36 >= 0, s36 <= s35, x_2164 >= 0, z = 1 + (1 + x_1329 + x_2164), x_1329 >= 0
   encArg(z) -{ -103 + 13*z + 20*z^2 + 6*z^3 }-> s39 :|: s37 >= 0, s37 <= z - 2 + 1, s38 >= 0, s38 <= s37, s39 >= 0, s39 <= s38, 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) -{ -66 + 71*z + 38*z^2 + 6*z^3 }-> 1 + s10 :|: s10 >= 0, s10 <= z - 1 + 1, z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_cond(z, z', z'') -{ 157 + 4*s19 + s19*s20 + 2*s20 + 165*z + 56*z^2 + 6*z^3 + 165*z' + 56*z'^2 + 6*z'^3 + 165*z'' + 56*z''^2 + 6*z''^3 }-> s21 :|: s18 >= 0, s18 <= z + 1, s19 >= 0, s19 <= z' + 1, s20 >= 0, s20 <= z'' + 1, s21 >= 0, s21 <= 0, z >= 0, z'' >= 0, z' >= 0
   encode_cond(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_gr(z, z') -{ 100 + s23 + 165*z + 56*z^2 + 6*z^3 + 165*z' + 56*z'^2 + 6*z'^3 }-> s24 :|: s22 >= 0, s22 <= z + 1, s23 >= 0, s23 <= z' + 1, s24 >= 0, s24 <= 2, z >= 0, z' >= 0
   encode_gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_p(z) -{ -65 + 71*z + 38*z^2 + 6*z^3 }-> s41 :|: s40 >= 0, s40 <= z - 1 + 1, s41 >= 0, s41 <= 1 + s40, z - 1 >= 0
   encode_p(z) -{ 158 + 4*s43 + s43*s44 + 2*s44 + 165*x_1660 + 56*x_1660^2 + 6*x_1660^3 + 165*x_2329 + 56*x_2329^2 + 6*x_2329^3 + 165*x_3164 + 56*x_3164^2 + 6*x_3164^3 }-> s46 :|: s42 >= 0, s42 <= x_1660 + 1, s43 >= 0, s43 <= x_2329 + 1, s44 >= 0, s44 <= x_3164 + 1, s45 >= 0, s45 <= 0, s46 >= 0, s46 <= s45, x_3164 >= 0, x_1660 >= 0, x_2329 >= 0, z = 1 + x_1660 + x_2329 + x_3164
   encode_p(z) -{ 101 + s48 + 165*x_1661 + 56*x_1661^2 + 6*x_1661^3 + 165*x_2330 + 56*x_2330^2 + 6*x_2330^3 }-> s50 :|: s47 >= 0, s47 <= x_1661 + 1, s48 >= 0, s48 <= x_2330 + 1, s49 >= 0, s49 <= 2, s50 >= 0, s50 <= s49, z = 1 + x_1661 + x_2330, x_2330 >= 0, x_1661 >= 0
   encode_p(z) -{ -64 + 71*z + 38*z^2 + 6*z^3 }-> s53 :|: s51 >= 0, s51 <= z - 1 + 1, s52 >= 0, s52 <= s51, s53 >= 0, s53 <= s52, 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) -{ 49 + 165*z + 56*z^2 + 6*z^3 }-> 1 + s25 :|: s25 >= 0, s25 <= 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}, {encode_cond}
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]
  p: runtime: O(1) [1], size: O(n^1) [z]
  cond: runtime: O(n^2) [10 + 4*z' + z'*z'' + 2*z''], size: O(1) [0]
  encArg: runtime: O(n^3) [49 + 165*z + 56*z^2 + 6*z^3], size: O(n^1) [1 + z]
  encode_p: runtime: O(n^3) [271 + 976*z + 357*z^2 + 42*z^3], size: O(n^1) [1 + z]
  encode_gr: runtime: O(n^3) [101 + 165*z + 56*z^2 + 6*z^3 + 166*z' + 56*z'^2 + 6*z'^3], size: O(1) [2]

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

(77) 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

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

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

   cond(z, z', z'') -{ 13 + 2*z'' }-> s1 :|: s1 >= 0, s1 <= 0, z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 12 + 2*z'' }-> s2 :|: s2 >= 0, s2 <= 0, z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 9 + 4*z' }-> s3 :|: s3 >= 0, s3 <= 0, z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 12 }-> s4 :|: s4 >= 0, s4 <= 0, z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 10 + 4*z' + z'*z'' + 2*z'' }-> s5 :|: s5 >= 0, s5 <= 0, s >= 0, s <= 2, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 13 + 3*z'' }-> s6 :|: s6 >= 0, s6 <= 0, s' >= 0, s' <= 2, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 12 + 2*z'' }-> s7 :|: s7 >= 0, s7 <= 0, z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 8 + 4*z' + z'*z'' + z'' }-> s8 :|: s8 >= 0, s8 <= 0, z = 2, z' - 1 >= 0, z'' >= 0
   cond(z, z', z'') -{ 11 + 2*z'' }-> s9 :|: s9 >= 0, s9 <= 0, z = 2, z' >= 0, z'' >= 0
   cond(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encArg(z) -{ 157 + 4*s12 + s12*s13 + 2*s13 + 165*x_1 + 56*x_1^2 + 6*x_1^3 + 165*x_2 + 56*x_2^2 + 6*x_2^3 + 165*x_3 + 56*x_3^2 + 6*x_3^3 }-> s14 :|: s11 >= 0, s11 <= x_1 + 1, s12 >= 0, s12 <= x_2 + 1, s13 >= 0, s13 <= x_3 + 1, s14 >= 0, s14 <= 0, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 100 + s16 + 165*x_1 + 56*x_1^2 + 6*x_1^3 + 165*x_2 + 56*x_2^2 + 6*x_2^3 }-> s17 :|: s15 >= 0, s15 <= x_1 + 1, s16 >= 0, s16 <= x_2 + 1, s17 >= 0, s17 <= 2, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ -104 + 13*z + 20*z^2 + 6*z^3 }-> s27 :|: s26 >= 0, s26 <= z - 2 + 1, s27 >= 0, s27 <= 1 + s26, z - 2 >= 0
   encArg(z) -{ 158 + 4*s29 + s29*s30 + 2*s30 + 165*x_1328 + 56*x_1328^2 + 6*x_1328^3 + 165*x_2163 + 56*x_2163^2 + 6*x_2163^3 + 165*x_381 + 56*x_381^2 + 6*x_381^3 }-> s32 :|: s28 >= 0, s28 <= x_1328 + 1, s29 >= 0, s29 <= x_2163 + 1, s30 >= 0, s30 <= x_381 + 1, s31 >= 0, s31 <= 0, s32 >= 0, s32 <= s31, x_1328 >= 0, x_381 >= 0, z = 1 + (1 + x_1328 + x_2163 + x_381), x_2163 >= 0
   encArg(z) -{ 101 + s34 + 165*x_1329 + 56*x_1329^2 + 6*x_1329^3 + 165*x_2164 + 56*x_2164^2 + 6*x_2164^3 }-> s36 :|: s33 >= 0, s33 <= x_1329 + 1, s34 >= 0, s34 <= x_2164 + 1, s35 >= 0, s35 <= 2, s36 >= 0, s36 <= s35, x_2164 >= 0, z = 1 + (1 + x_1329 + x_2164), x_1329 >= 0
   encArg(z) -{ -103 + 13*z + 20*z^2 + 6*z^3 }-> s39 :|: s37 >= 0, s37 <= z - 2 + 1, s38 >= 0, s38 <= s37, s39 >= 0, s39 <= s38, 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) -{ -66 + 71*z + 38*z^2 + 6*z^3 }-> 1 + s10 :|: s10 >= 0, s10 <= z - 1 + 1, z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_cond(z, z', z'') -{ 157 + 4*s19 + s19*s20 + 2*s20 + 165*z + 56*z^2 + 6*z^3 + 165*z' + 56*z'^2 + 6*z'^3 + 165*z'' + 56*z''^2 + 6*z''^3 }-> s21 :|: s18 >= 0, s18 <= z + 1, s19 >= 0, s19 <= z' + 1, s20 >= 0, s20 <= z'' + 1, s21 >= 0, s21 <= 0, z >= 0, z'' >= 0, z' >= 0
   encode_cond(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_gr(z, z') -{ 100 + s23 + 165*z + 56*z^2 + 6*z^3 + 165*z' + 56*z'^2 + 6*z'^3 }-> s24 :|: s22 >= 0, s22 <= z + 1, s23 >= 0, s23 <= z' + 1, s24 >= 0, s24 <= 2, z >= 0, z' >= 0
   encode_gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_p(z) -{ -65 + 71*z + 38*z^2 + 6*z^3 }-> s41 :|: s40 >= 0, s40 <= z - 1 + 1, s41 >= 0, s41 <= 1 + s40, z - 1 >= 0
   encode_p(z) -{ 158 + 4*s43 + s43*s44 + 2*s44 + 165*x_1660 + 56*x_1660^2 + 6*x_1660^3 + 165*x_2329 + 56*x_2329^2 + 6*x_2329^3 + 165*x_3164 + 56*x_3164^2 + 6*x_3164^3 }-> s46 :|: s42 >= 0, s42 <= x_1660 + 1, s43 >= 0, s43 <= x_2329 + 1, s44 >= 0, s44 <= x_3164 + 1, s45 >= 0, s45 <= 0, s46 >= 0, s46 <= s45, x_3164 >= 0, x_1660 >= 0, x_2329 >= 0, z = 1 + x_1660 + x_2329 + x_3164
   encode_p(z) -{ 101 + s48 + 165*x_1661 + 56*x_1661^2 + 6*x_1661^3 + 165*x_2330 + 56*x_2330^2 + 6*x_2330^3 }-> s50 :|: s47 >= 0, s47 <= x_1661 + 1, s48 >= 0, s48 <= x_2330 + 1, s49 >= 0, s49 <= 2, s50 >= 0, s50 <= s49, z = 1 + x_1661 + x_2330, x_2330 >= 0, x_1661 >= 0
   encode_p(z) -{ -64 + 71*z + 38*z^2 + 6*z^3 }-> s53 :|: s51 >= 0, s51 <= z - 1 + 1, s52 >= 0, s52 <= s51, s53 >= 0, s53 <= s52, 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) -{ 49 + 165*z + 56*z^2 + 6*z^3 }-> 1 + s25 :|: s25 >= 0, s25 <= 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}, {encode_cond}
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]
  p: runtime: O(1) [1], size: O(n^1) [z]
  cond: runtime: O(n^2) [10 + 4*z' + z'*z'' + 2*z''], size: O(1) [0]
  encArg: runtime: O(n^3) [49 + 165*z + 56*z^2 + 6*z^3], size: O(n^1) [1 + z]
  encode_p: runtime: O(n^3) [271 + 976*z + 357*z^2 + 42*z^3], size: O(n^1) [1 + z]
  encode_gr: runtime: O(n^3) [101 + 165*z + 56*z^2 + 6*z^3 + 166*z' + 56*z'^2 + 6*z'^3], size: O(1) [2]
  encode_s: runtime: ?, size: O(n^1) [2 + z]

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

(79) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using KoAT for: encode_s
after applying outer abstraction to obtain an ITS,
resulting in: O(n^3) with polynomial bound: 49 + 165*z + 56*z^2 + 6*z^3

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

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

   cond(z, z', z'') -{ 13 + 2*z'' }-> s1 :|: s1 >= 0, s1 <= 0, z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 12 + 2*z'' }-> s2 :|: s2 >= 0, s2 <= 0, z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 9 + 4*z' }-> s3 :|: s3 >= 0, s3 <= 0, z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 12 }-> s4 :|: s4 >= 0, s4 <= 0, z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 10 + 4*z' + z'*z'' + 2*z'' }-> s5 :|: s5 >= 0, s5 <= 0, s >= 0, s <= 2, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 13 + 3*z'' }-> s6 :|: s6 >= 0, s6 <= 0, s' >= 0, s' <= 2, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 12 + 2*z'' }-> s7 :|: s7 >= 0, s7 <= 0, z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 8 + 4*z' + z'*z'' + z'' }-> s8 :|: s8 >= 0, s8 <= 0, z = 2, z' - 1 >= 0, z'' >= 0
   cond(z, z', z'') -{ 11 + 2*z'' }-> s9 :|: s9 >= 0, s9 <= 0, z = 2, z' >= 0, z'' >= 0
   cond(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encArg(z) -{ 157 + 4*s12 + s12*s13 + 2*s13 + 165*x_1 + 56*x_1^2 + 6*x_1^3 + 165*x_2 + 56*x_2^2 + 6*x_2^3 + 165*x_3 + 56*x_3^2 + 6*x_3^3 }-> s14 :|: s11 >= 0, s11 <= x_1 + 1, s12 >= 0, s12 <= x_2 + 1, s13 >= 0, s13 <= x_3 + 1, s14 >= 0, s14 <= 0, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 100 + s16 + 165*x_1 + 56*x_1^2 + 6*x_1^3 + 165*x_2 + 56*x_2^2 + 6*x_2^3 }-> s17 :|: s15 >= 0, s15 <= x_1 + 1, s16 >= 0, s16 <= x_2 + 1, s17 >= 0, s17 <= 2, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ -104 + 13*z + 20*z^2 + 6*z^3 }-> s27 :|: s26 >= 0, s26 <= z - 2 + 1, s27 >= 0, s27 <= 1 + s26, z - 2 >= 0
   encArg(z) -{ 158 + 4*s29 + s29*s30 + 2*s30 + 165*x_1328 + 56*x_1328^2 + 6*x_1328^3 + 165*x_2163 + 56*x_2163^2 + 6*x_2163^3 + 165*x_381 + 56*x_381^2 + 6*x_381^3 }-> s32 :|: s28 >= 0, s28 <= x_1328 + 1, s29 >= 0, s29 <= x_2163 + 1, s30 >= 0, s30 <= x_381 + 1, s31 >= 0, s31 <= 0, s32 >= 0, s32 <= s31, x_1328 >= 0, x_381 >= 0, z = 1 + (1 + x_1328 + x_2163 + x_381), x_2163 >= 0
   encArg(z) -{ 101 + s34 + 165*x_1329 + 56*x_1329^2 + 6*x_1329^3 + 165*x_2164 + 56*x_2164^2 + 6*x_2164^3 }-> s36 :|: s33 >= 0, s33 <= x_1329 + 1, s34 >= 0, s34 <= x_2164 + 1, s35 >= 0, s35 <= 2, s36 >= 0, s36 <= s35, x_2164 >= 0, z = 1 + (1 + x_1329 + x_2164), x_1329 >= 0
   encArg(z) -{ -103 + 13*z + 20*z^2 + 6*z^3 }-> s39 :|: s37 >= 0, s37 <= z - 2 + 1, s38 >= 0, s38 <= s37, s39 >= 0, s39 <= s38, 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) -{ -66 + 71*z + 38*z^2 + 6*z^3 }-> 1 + s10 :|: s10 >= 0, s10 <= z - 1 + 1, z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_cond(z, z', z'') -{ 157 + 4*s19 + s19*s20 + 2*s20 + 165*z + 56*z^2 + 6*z^3 + 165*z' + 56*z'^2 + 6*z'^3 + 165*z'' + 56*z''^2 + 6*z''^3 }-> s21 :|: s18 >= 0, s18 <= z + 1, s19 >= 0, s19 <= z' + 1, s20 >= 0, s20 <= z'' + 1, s21 >= 0, s21 <= 0, z >= 0, z'' >= 0, z' >= 0
   encode_cond(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_gr(z, z') -{ 100 + s23 + 165*z + 56*z^2 + 6*z^3 + 165*z' + 56*z'^2 + 6*z'^3 }-> s24 :|: s22 >= 0, s22 <= z + 1, s23 >= 0, s23 <= z' + 1, s24 >= 0, s24 <= 2, z >= 0, z' >= 0
   encode_gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_p(z) -{ -65 + 71*z + 38*z^2 + 6*z^3 }-> s41 :|: s40 >= 0, s40 <= z - 1 + 1, s41 >= 0, s41 <= 1 + s40, z - 1 >= 0
   encode_p(z) -{ 158 + 4*s43 + s43*s44 + 2*s44 + 165*x_1660 + 56*x_1660^2 + 6*x_1660^3 + 165*x_2329 + 56*x_2329^2 + 6*x_2329^3 + 165*x_3164 + 56*x_3164^2 + 6*x_3164^3 }-> s46 :|: s42 >= 0, s42 <= x_1660 + 1, s43 >= 0, s43 <= x_2329 + 1, s44 >= 0, s44 <= x_3164 + 1, s45 >= 0, s45 <= 0, s46 >= 0, s46 <= s45, x_3164 >= 0, x_1660 >= 0, x_2329 >= 0, z = 1 + x_1660 + x_2329 + x_3164
   encode_p(z) -{ 101 + s48 + 165*x_1661 + 56*x_1661^2 + 6*x_1661^3 + 165*x_2330 + 56*x_2330^2 + 6*x_2330^3 }-> s50 :|: s47 >= 0, s47 <= x_1661 + 1, s48 >= 0, s48 <= x_2330 + 1, s49 >= 0, s49 <= 2, s50 >= 0, s50 <= s49, z = 1 + x_1661 + x_2330, x_2330 >= 0, x_1661 >= 0
   encode_p(z) -{ -64 + 71*z + 38*z^2 + 6*z^3 }-> s53 :|: s51 >= 0, s51 <= z - 1 + 1, s52 >= 0, s52 <= s51, s53 >= 0, s53 <= s52, 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) -{ 49 + 165*z + 56*z^2 + 6*z^3 }-> 1 + s25 :|: s25 >= 0, s25 <= 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_cond}
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]
  p: runtime: O(1) [1], size: O(n^1) [z]
  cond: runtime: O(n^2) [10 + 4*z' + z'*z'' + 2*z''], size: O(1) [0]
  encArg: runtime: O(n^3) [49 + 165*z + 56*z^2 + 6*z^3], size: O(n^1) [1 + z]
  encode_p: runtime: O(n^3) [271 + 976*z + 357*z^2 + 42*z^3], size: O(n^1) [1 + z]
  encode_gr: runtime: O(n^3) [101 + 165*z + 56*z^2 + 6*z^3 + 166*z' + 56*z'^2 + 6*z'^3], size: O(1) [2]
  encode_s: runtime: O(n^3) [49 + 165*z + 56*z^2 + 6*z^3], size: O(n^1) [2 + z]

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

(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:

   cond(z, z', z'') -{ 13 + 2*z'' }-> s1 :|: s1 >= 0, s1 <= 0, z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 12 + 2*z'' }-> s2 :|: s2 >= 0, s2 <= 0, z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 9 + 4*z' }-> s3 :|: s3 >= 0, s3 <= 0, z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 12 }-> s4 :|: s4 >= 0, s4 <= 0, z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 10 + 4*z' + z'*z'' + 2*z'' }-> s5 :|: s5 >= 0, s5 <= 0, s >= 0, s <= 2, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 13 + 3*z'' }-> s6 :|: s6 >= 0, s6 <= 0, s' >= 0, s' <= 2, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 12 + 2*z'' }-> s7 :|: s7 >= 0, s7 <= 0, z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 8 + 4*z' + z'*z'' + z'' }-> s8 :|: s8 >= 0, s8 <= 0, z = 2, z' - 1 >= 0, z'' >= 0
   cond(z, z', z'') -{ 11 + 2*z'' }-> s9 :|: s9 >= 0, s9 <= 0, z = 2, z' >= 0, z'' >= 0
   cond(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encArg(z) -{ 157 + 4*s12 + s12*s13 + 2*s13 + 165*x_1 + 56*x_1^2 + 6*x_1^3 + 165*x_2 + 56*x_2^2 + 6*x_2^3 + 165*x_3 + 56*x_3^2 + 6*x_3^3 }-> s14 :|: s11 >= 0, s11 <= x_1 + 1, s12 >= 0, s12 <= x_2 + 1, s13 >= 0, s13 <= x_3 + 1, s14 >= 0, s14 <= 0, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 100 + s16 + 165*x_1 + 56*x_1^2 + 6*x_1^3 + 165*x_2 + 56*x_2^2 + 6*x_2^3 }-> s17 :|: s15 >= 0, s15 <= x_1 + 1, s16 >= 0, s16 <= x_2 + 1, s17 >= 0, s17 <= 2, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ -104 + 13*z + 20*z^2 + 6*z^3 }-> s27 :|: s26 >= 0, s26 <= z - 2 + 1, s27 >= 0, s27 <= 1 + s26, z - 2 >= 0
   encArg(z) -{ 158 + 4*s29 + s29*s30 + 2*s30 + 165*x_1328 + 56*x_1328^2 + 6*x_1328^3 + 165*x_2163 + 56*x_2163^2 + 6*x_2163^3 + 165*x_381 + 56*x_381^2 + 6*x_381^3 }-> s32 :|: s28 >= 0, s28 <= x_1328 + 1, s29 >= 0, s29 <= x_2163 + 1, s30 >= 0, s30 <= x_381 + 1, s31 >= 0, s31 <= 0, s32 >= 0, s32 <= s31, x_1328 >= 0, x_381 >= 0, z = 1 + (1 + x_1328 + x_2163 + x_381), x_2163 >= 0
   encArg(z) -{ 101 + s34 + 165*x_1329 + 56*x_1329^2 + 6*x_1329^3 + 165*x_2164 + 56*x_2164^2 + 6*x_2164^3 }-> s36 :|: s33 >= 0, s33 <= x_1329 + 1, s34 >= 0, s34 <= x_2164 + 1, s35 >= 0, s35 <= 2, s36 >= 0, s36 <= s35, x_2164 >= 0, z = 1 + (1 + x_1329 + x_2164), x_1329 >= 0
   encArg(z) -{ -103 + 13*z + 20*z^2 + 6*z^3 }-> s39 :|: s37 >= 0, s37 <= z - 2 + 1, s38 >= 0, s38 <= s37, s39 >= 0, s39 <= s38, 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) -{ -66 + 71*z + 38*z^2 + 6*z^3 }-> 1 + s10 :|: s10 >= 0, s10 <= z - 1 + 1, z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_cond(z, z', z'') -{ 157 + 4*s19 + s19*s20 + 2*s20 + 165*z + 56*z^2 + 6*z^3 + 165*z' + 56*z'^2 + 6*z'^3 + 165*z'' + 56*z''^2 + 6*z''^3 }-> s21 :|: s18 >= 0, s18 <= z + 1, s19 >= 0, s19 <= z' + 1, s20 >= 0, s20 <= z'' + 1, s21 >= 0, s21 <= 0, z >= 0, z'' >= 0, z' >= 0
   encode_cond(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_gr(z, z') -{ 100 + s23 + 165*z + 56*z^2 + 6*z^3 + 165*z' + 56*z'^2 + 6*z'^3 }-> s24 :|: s22 >= 0, s22 <= z + 1, s23 >= 0, s23 <= z' + 1, s24 >= 0, s24 <= 2, z >= 0, z' >= 0
   encode_gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_p(z) -{ -65 + 71*z + 38*z^2 + 6*z^3 }-> s41 :|: s40 >= 0, s40 <= z - 1 + 1, s41 >= 0, s41 <= 1 + s40, z - 1 >= 0
   encode_p(z) -{ 158 + 4*s43 + s43*s44 + 2*s44 + 165*x_1660 + 56*x_1660^2 + 6*x_1660^3 + 165*x_2329 + 56*x_2329^2 + 6*x_2329^3 + 165*x_3164 + 56*x_3164^2 + 6*x_3164^3 }-> s46 :|: s42 >= 0, s42 <= x_1660 + 1, s43 >= 0, s43 <= x_2329 + 1, s44 >= 0, s44 <= x_3164 + 1, s45 >= 0, s45 <= 0, s46 >= 0, s46 <= s45, x_3164 >= 0, x_1660 >= 0, x_2329 >= 0, z = 1 + x_1660 + x_2329 + x_3164
   encode_p(z) -{ 101 + s48 + 165*x_1661 + 56*x_1661^2 + 6*x_1661^3 + 165*x_2330 + 56*x_2330^2 + 6*x_2330^3 }-> s50 :|: s47 >= 0, s47 <= x_1661 + 1, s48 >= 0, s48 <= x_2330 + 1, s49 >= 0, s49 <= 2, s50 >= 0, s50 <= s49, z = 1 + x_1661 + x_2330, x_2330 >= 0, x_1661 >= 0
   encode_p(z) -{ -64 + 71*z + 38*z^2 + 6*z^3 }-> s53 :|: s51 >= 0, s51 <= z - 1 + 1, s52 >= 0, s52 <= s51, s53 >= 0, s53 <= s52, 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) -{ 49 + 165*z + 56*z^2 + 6*z^3 }-> 1 + s25 :|: s25 >= 0, s25 <= 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_cond}
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]
  p: runtime: O(1) [1], size: O(n^1) [z]
  cond: runtime: O(n^2) [10 + 4*z' + z'*z'' + 2*z''], size: O(1) [0]
  encArg: runtime: O(n^3) [49 + 165*z + 56*z^2 + 6*z^3], size: O(n^1) [1 + z]
  encode_p: runtime: O(n^3) [271 + 976*z + 357*z^2 + 42*z^3], size: O(n^1) [1 + z]
  encode_gr: runtime: O(n^3) [101 + 165*z + 56*z^2 + 6*z^3 + 166*z' + 56*z'^2 + 6*z'^3], size: O(1) [2]
  encode_s: runtime: O(n^3) [49 + 165*z + 56*z^2 + 6*z^3], size: O(n^1) [2 + z]

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

(83) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: encode_cond
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:

   cond(z, z', z'') -{ 13 + 2*z'' }-> s1 :|: s1 >= 0, s1 <= 0, z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 12 + 2*z'' }-> s2 :|: s2 >= 0, s2 <= 0, z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 9 + 4*z' }-> s3 :|: s3 >= 0, s3 <= 0, z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 12 }-> s4 :|: s4 >= 0, s4 <= 0, z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 10 + 4*z' + z'*z'' + 2*z'' }-> s5 :|: s5 >= 0, s5 <= 0, s >= 0, s <= 2, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 13 + 3*z'' }-> s6 :|: s6 >= 0, s6 <= 0, s' >= 0, s' <= 2, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 12 + 2*z'' }-> s7 :|: s7 >= 0, s7 <= 0, z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 8 + 4*z' + z'*z'' + z'' }-> s8 :|: s8 >= 0, s8 <= 0, z = 2, z' - 1 >= 0, z'' >= 0
   cond(z, z', z'') -{ 11 + 2*z'' }-> s9 :|: s9 >= 0, s9 <= 0, z = 2, z' >= 0, z'' >= 0
   cond(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encArg(z) -{ 157 + 4*s12 + s12*s13 + 2*s13 + 165*x_1 + 56*x_1^2 + 6*x_1^3 + 165*x_2 + 56*x_2^2 + 6*x_2^3 + 165*x_3 + 56*x_3^2 + 6*x_3^3 }-> s14 :|: s11 >= 0, s11 <= x_1 + 1, s12 >= 0, s12 <= x_2 + 1, s13 >= 0, s13 <= x_3 + 1, s14 >= 0, s14 <= 0, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 100 + s16 + 165*x_1 + 56*x_1^2 + 6*x_1^3 + 165*x_2 + 56*x_2^2 + 6*x_2^3 }-> s17 :|: s15 >= 0, s15 <= x_1 + 1, s16 >= 0, s16 <= x_2 + 1, s17 >= 0, s17 <= 2, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ -104 + 13*z + 20*z^2 + 6*z^3 }-> s27 :|: s26 >= 0, s26 <= z - 2 + 1, s27 >= 0, s27 <= 1 + s26, z - 2 >= 0
   encArg(z) -{ 158 + 4*s29 + s29*s30 + 2*s30 + 165*x_1328 + 56*x_1328^2 + 6*x_1328^3 + 165*x_2163 + 56*x_2163^2 + 6*x_2163^3 + 165*x_381 + 56*x_381^2 + 6*x_381^3 }-> s32 :|: s28 >= 0, s28 <= x_1328 + 1, s29 >= 0, s29 <= x_2163 + 1, s30 >= 0, s30 <= x_381 + 1, s31 >= 0, s31 <= 0, s32 >= 0, s32 <= s31, x_1328 >= 0, x_381 >= 0, z = 1 + (1 + x_1328 + x_2163 + x_381), x_2163 >= 0
   encArg(z) -{ 101 + s34 + 165*x_1329 + 56*x_1329^2 + 6*x_1329^3 + 165*x_2164 + 56*x_2164^2 + 6*x_2164^3 }-> s36 :|: s33 >= 0, s33 <= x_1329 + 1, s34 >= 0, s34 <= x_2164 + 1, s35 >= 0, s35 <= 2, s36 >= 0, s36 <= s35, x_2164 >= 0, z = 1 + (1 + x_1329 + x_2164), x_1329 >= 0
   encArg(z) -{ -103 + 13*z + 20*z^2 + 6*z^3 }-> s39 :|: s37 >= 0, s37 <= z - 2 + 1, s38 >= 0, s38 <= s37, s39 >= 0, s39 <= s38, 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) -{ -66 + 71*z + 38*z^2 + 6*z^3 }-> 1 + s10 :|: s10 >= 0, s10 <= z - 1 + 1, z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_cond(z, z', z'') -{ 157 + 4*s19 + s19*s20 + 2*s20 + 165*z + 56*z^2 + 6*z^3 + 165*z' + 56*z'^2 + 6*z'^3 + 165*z'' + 56*z''^2 + 6*z''^3 }-> s21 :|: s18 >= 0, s18 <= z + 1, s19 >= 0, s19 <= z' + 1, s20 >= 0, s20 <= z'' + 1, s21 >= 0, s21 <= 0, z >= 0, z'' >= 0, z' >= 0
   encode_cond(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_gr(z, z') -{ 100 + s23 + 165*z + 56*z^2 + 6*z^3 + 165*z' + 56*z'^2 + 6*z'^3 }-> s24 :|: s22 >= 0, s22 <= z + 1, s23 >= 0, s23 <= z' + 1, s24 >= 0, s24 <= 2, z >= 0, z' >= 0
   encode_gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_p(z) -{ -65 + 71*z + 38*z^2 + 6*z^3 }-> s41 :|: s40 >= 0, s40 <= z - 1 + 1, s41 >= 0, s41 <= 1 + s40, z - 1 >= 0
   encode_p(z) -{ 158 + 4*s43 + s43*s44 + 2*s44 + 165*x_1660 + 56*x_1660^2 + 6*x_1660^3 + 165*x_2329 + 56*x_2329^2 + 6*x_2329^3 + 165*x_3164 + 56*x_3164^2 + 6*x_3164^3 }-> s46 :|: s42 >= 0, s42 <= x_1660 + 1, s43 >= 0, s43 <= x_2329 + 1, s44 >= 0, s44 <= x_3164 + 1, s45 >= 0, s45 <= 0, s46 >= 0, s46 <= s45, x_3164 >= 0, x_1660 >= 0, x_2329 >= 0, z = 1 + x_1660 + x_2329 + x_3164
   encode_p(z) -{ 101 + s48 + 165*x_1661 + 56*x_1661^2 + 6*x_1661^3 + 165*x_2330 + 56*x_2330^2 + 6*x_2330^3 }-> s50 :|: s47 >= 0, s47 <= x_1661 + 1, s48 >= 0, s48 <= x_2330 + 1, s49 >= 0, s49 <= 2, s50 >= 0, s50 <= s49, z = 1 + x_1661 + x_2330, x_2330 >= 0, x_1661 >= 0
   encode_p(z) -{ -64 + 71*z + 38*z^2 + 6*z^3 }-> s53 :|: s51 >= 0, s51 <= z - 1 + 1, s52 >= 0, s52 <= s51, s53 >= 0, s53 <= s52, 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) -{ 49 + 165*z + 56*z^2 + 6*z^3 }-> 1 + s25 :|: s25 >= 0, s25 <= 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_cond}
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]
  p: runtime: O(1) [1], size: O(n^1) [z]
  cond: runtime: O(n^2) [10 + 4*z' + z'*z'' + 2*z''], size: O(1) [0]
  encArg: runtime: O(n^3) [49 + 165*z + 56*z^2 + 6*z^3], size: O(n^1) [1 + z]
  encode_p: runtime: O(n^3) [271 + 976*z + 357*z^2 + 42*z^3], size: O(n^1) [1 + z]
  encode_gr: runtime: O(n^3) [101 + 165*z + 56*z^2 + 6*z^3 + 166*z' + 56*z'^2 + 6*z'^3], size: O(1) [2]
  encode_s: runtime: O(n^3) [49 + 165*z + 56*z^2 + 6*z^3], size: O(n^1) [2 + z]
  encode_cond: runtime: ?, size: O(1) [0]

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

(85) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using KoAT for: encode_cond
after applying outer abstraction to obtain an ITS,
resulting in: O(n^3) with polynomial bound: 164 + 165*z + 56*z^2 + 6*z^3 + 170*z' + z'*z'' + 56*z'^2 + 6*z'^3 + 168*z'' + 56*z''^2 + 6*z''^3

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

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

   cond(z, z', z'') -{ 13 + 2*z'' }-> s1 :|: s1 >= 0, s1 <= 0, z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 12 + 2*z'' }-> s2 :|: s2 >= 0, s2 <= 0, z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 9 + 4*z' }-> s3 :|: s3 >= 0, s3 <= 0, z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 12 }-> s4 :|: s4 >= 0, s4 <= 0, z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 10 + 4*z' + z'*z'' + 2*z'' }-> s5 :|: s5 >= 0, s5 <= 0, s >= 0, s <= 2, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 13 + 3*z'' }-> s6 :|: s6 >= 0, s6 <= 0, s' >= 0, s' <= 2, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 12 + 2*z'' }-> s7 :|: s7 >= 0, s7 <= 0, z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 8 + 4*z' + z'*z'' + z'' }-> s8 :|: s8 >= 0, s8 <= 0, z = 2, z' - 1 >= 0, z'' >= 0
   cond(z, z', z'') -{ 11 + 2*z'' }-> s9 :|: s9 >= 0, s9 <= 0, z = 2, z' >= 0, z'' >= 0
   cond(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encArg(z) -{ 157 + 4*s12 + s12*s13 + 2*s13 + 165*x_1 + 56*x_1^2 + 6*x_1^3 + 165*x_2 + 56*x_2^2 + 6*x_2^3 + 165*x_3 + 56*x_3^2 + 6*x_3^3 }-> s14 :|: s11 >= 0, s11 <= x_1 + 1, s12 >= 0, s12 <= x_2 + 1, s13 >= 0, s13 <= x_3 + 1, s14 >= 0, s14 <= 0, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 100 + s16 + 165*x_1 + 56*x_1^2 + 6*x_1^3 + 165*x_2 + 56*x_2^2 + 6*x_2^3 }-> s17 :|: s15 >= 0, s15 <= x_1 + 1, s16 >= 0, s16 <= x_2 + 1, s17 >= 0, s17 <= 2, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ -104 + 13*z + 20*z^2 + 6*z^3 }-> s27 :|: s26 >= 0, s26 <= z - 2 + 1, s27 >= 0, s27 <= 1 + s26, z - 2 >= 0
   encArg(z) -{ 158 + 4*s29 + s29*s30 + 2*s30 + 165*x_1328 + 56*x_1328^2 + 6*x_1328^3 + 165*x_2163 + 56*x_2163^2 + 6*x_2163^3 + 165*x_381 + 56*x_381^2 + 6*x_381^3 }-> s32 :|: s28 >= 0, s28 <= x_1328 + 1, s29 >= 0, s29 <= x_2163 + 1, s30 >= 0, s30 <= x_381 + 1, s31 >= 0, s31 <= 0, s32 >= 0, s32 <= s31, x_1328 >= 0, x_381 >= 0, z = 1 + (1 + x_1328 + x_2163 + x_381), x_2163 >= 0
   encArg(z) -{ 101 + s34 + 165*x_1329 + 56*x_1329^2 + 6*x_1329^3 + 165*x_2164 + 56*x_2164^2 + 6*x_2164^3 }-> s36 :|: s33 >= 0, s33 <= x_1329 + 1, s34 >= 0, s34 <= x_2164 + 1, s35 >= 0, s35 <= 2, s36 >= 0, s36 <= s35, x_2164 >= 0, z = 1 + (1 + x_1329 + x_2164), x_1329 >= 0
   encArg(z) -{ -103 + 13*z + 20*z^2 + 6*z^3 }-> s39 :|: s37 >= 0, s37 <= z - 2 + 1, s38 >= 0, s38 <= s37, s39 >= 0, s39 <= s38, 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) -{ -66 + 71*z + 38*z^2 + 6*z^3 }-> 1 + s10 :|: s10 >= 0, s10 <= z - 1 + 1, z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_cond(z, z', z'') -{ 157 + 4*s19 + s19*s20 + 2*s20 + 165*z + 56*z^2 + 6*z^3 + 165*z' + 56*z'^2 + 6*z'^3 + 165*z'' + 56*z''^2 + 6*z''^3 }-> s21 :|: s18 >= 0, s18 <= z + 1, s19 >= 0, s19 <= z' + 1, s20 >= 0, s20 <= z'' + 1, s21 >= 0, s21 <= 0, z >= 0, z'' >= 0, z' >= 0
   encode_cond(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_gr(z, z') -{ 100 + s23 + 165*z + 56*z^2 + 6*z^3 + 165*z' + 56*z'^2 + 6*z'^3 }-> s24 :|: s22 >= 0, s22 <= z + 1, s23 >= 0, s23 <= z' + 1, s24 >= 0, s24 <= 2, z >= 0, z' >= 0
   encode_gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_p(z) -{ -65 + 71*z + 38*z^2 + 6*z^3 }-> s41 :|: s40 >= 0, s40 <= z - 1 + 1, s41 >= 0, s41 <= 1 + s40, z - 1 >= 0
   encode_p(z) -{ 158 + 4*s43 + s43*s44 + 2*s44 + 165*x_1660 + 56*x_1660^2 + 6*x_1660^3 + 165*x_2329 + 56*x_2329^2 + 6*x_2329^3 + 165*x_3164 + 56*x_3164^2 + 6*x_3164^3 }-> s46 :|: s42 >= 0, s42 <= x_1660 + 1, s43 >= 0, s43 <= x_2329 + 1, s44 >= 0, s44 <= x_3164 + 1, s45 >= 0, s45 <= 0, s46 >= 0, s46 <= s45, x_3164 >= 0, x_1660 >= 0, x_2329 >= 0, z = 1 + x_1660 + x_2329 + x_3164
   encode_p(z) -{ 101 + s48 + 165*x_1661 + 56*x_1661^2 + 6*x_1661^3 + 165*x_2330 + 56*x_2330^2 + 6*x_2330^3 }-> s50 :|: s47 >= 0, s47 <= x_1661 + 1, s48 >= 0, s48 <= x_2330 + 1, s49 >= 0, s49 <= 2, s50 >= 0, s50 <= s49, z = 1 + x_1661 + x_2330, x_2330 >= 0, x_1661 >= 0
   encode_p(z) -{ -64 + 71*z + 38*z^2 + 6*z^3 }-> s53 :|: s51 >= 0, s51 <= z - 1 + 1, s52 >= 0, s52 <= s51, s53 >= 0, s53 <= s52, 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) -{ 49 + 165*z + 56*z^2 + 6*z^3 }-> 1 + s25 :|: s25 >= 0, s25 <= 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]
  p: runtime: O(1) [1], size: O(n^1) [z]
  cond: runtime: O(n^2) [10 + 4*z' + z'*z'' + 2*z''], size: O(1) [0]
  encArg: runtime: O(n^3) [49 + 165*z + 56*z^2 + 6*z^3], size: O(n^1) [1 + z]
  encode_p: runtime: O(n^3) [271 + 976*z + 357*z^2 + 42*z^3], size: O(n^1) [1 + z]
  encode_gr: runtime: O(n^3) [101 + 165*z + 56*z^2 + 6*z^3 + 166*z' + 56*z'^2 + 6*z'^3], size: O(1) [2]
  encode_s: runtime: O(n^3) [49 + 165*z + 56*z^2 + 6*z^3], size: O(n^1) [2 + z]
  encode_cond: runtime: O(n^3) [164 + 165*z + 56*z^2 + 6*z^3 + 170*z' + z'*z'' + 56*z'^2 + 6*z'^3 + 168*z'' + 56*z''^2 + 6*z''^3], size: O(1) [0]

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

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

(88)
BOUNDS(1, n^3)

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

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

(90)
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:

   cond(true, x, y) -> cond(gr(x, y), 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_cond(x_1, x_2, x_3)) -> cond(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_cond(x_1, x_2, x_3) -> cond(encArg(x_1), encArg(x_2), encArg(x_3))
   encode_true -> true
   encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2))
   encode_p(x_1) -> p(encArg(x_1))
   encode_0 -> 0'
   encode_false -> false
   encode_s(x_1) -> s(encArg(x_1))

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

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

(92)
Obligation:
Innermost TRS:
Rules:
cond(true, x, y) -> cond(gr(x, y), 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_cond(x_1, x_2, x_3)) -> cond(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_cond(x_1, x_2, x_3) -> cond(encArg(x_1), encArg(x_2), encArg(x_3))
encode_true -> true
encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2))
encode_p(x_1) -> p(encArg(x_1))
encode_0 -> 0'
encode_false -> false
encode_s(x_1) -> s(encArg(x_1))

Types:
cond :: true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p
true :: true:0':false:s:cons_cond:cons_gr:cons_p
gr :: true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p
p :: true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p
0' :: true:0':false:s:cons_cond:cons_gr:cons_p
false :: true:0':false:s:cons_cond:cons_gr:cons_p
s :: true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p
encArg :: true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p
cons_cond :: true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p
cons_gr :: true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p
cons_p :: true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p
encode_cond :: true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p
encode_true :: true:0':false:s:cons_cond:cons_gr:cons_p
encode_gr :: true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p
encode_p :: true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p
encode_0 :: true:0':false:s:cons_cond:cons_gr:cons_p
encode_false :: true:0':false:s:cons_cond:cons_gr:cons_p
encode_s :: true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p
hole_true:0':false:s:cons_cond:cons_gr:cons_p1_4 :: true:0':false:s:cons_cond:cons_gr:cons_p
gen_true:0':false:s:cons_cond:cons_gr:cons_p2_4 :: Nat -> true:0':false:s:cons_cond:cons_gr:cons_p

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

(93) OrderProof (LOWER BOUND(ID))
Heuristically decided to analyse the following defined symbols:
cond, gr, encArg

They will be analysed ascendingly in the following order:
gr < cond
cond < encArg
gr < encArg

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

(94)
Obligation:
Innermost TRS:
Rules:
cond(true, x, y) -> cond(gr(x, y), 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_cond(x_1, x_2, x_3)) -> cond(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_cond(x_1, x_2, x_3) -> cond(encArg(x_1), encArg(x_2), encArg(x_3))
encode_true -> true
encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2))
encode_p(x_1) -> p(encArg(x_1))
encode_0 -> 0'
encode_false -> false
encode_s(x_1) -> s(encArg(x_1))

Types:
cond :: true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p
true :: true:0':false:s:cons_cond:cons_gr:cons_p
gr :: true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p
p :: true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p
0' :: true:0':false:s:cons_cond:cons_gr:cons_p
false :: true:0':false:s:cons_cond:cons_gr:cons_p
s :: true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p
encArg :: true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p
cons_cond :: true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p
cons_gr :: true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p
cons_p :: true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p
encode_cond :: true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p
encode_true :: true:0':false:s:cons_cond:cons_gr:cons_p
encode_gr :: true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p
encode_p :: true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p
encode_0 :: true:0':false:s:cons_cond:cons_gr:cons_p
encode_false :: true:0':false:s:cons_cond:cons_gr:cons_p
encode_s :: true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p
hole_true:0':false:s:cons_cond:cons_gr:cons_p1_4 :: true:0':false:s:cons_cond:cons_gr:cons_p
gen_true:0':false:s:cons_cond:cons_gr:cons_p2_4 :: Nat -> true:0':false:s:cons_cond:cons_gr:cons_p


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


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

They will be analysed ascendingly in the following order:
gr < cond
cond < encArg
gr < encArg

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

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

Induction Step:
gr(gen_true:0':false:s:cons_cond:cons_gr:cons_p2_4(+(1, +(n4_4, 1))), gen_true:0':false:s:cons_cond:cons_gr:cons_p2_4(+(1, +(n4_4, 1)))) ->_R^Omega(1)
gr(gen_true:0':false:s:cons_cond:cons_gr:cons_p2_4(+(1, n4_4)), gen_true:0':false:s:cons_cond: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).
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(96)
Complex Obligation (BEST)

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(97)
Obligation:
Proved the lower bound n^1 for the following obligation:

Innermost TRS:
Rules:
cond(true, x, y) -> cond(gr(x, y), 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_cond(x_1, x_2, x_3)) -> cond(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_cond(x_1, x_2, x_3) -> cond(encArg(x_1), encArg(x_2), encArg(x_3))
encode_true -> true
encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2))
encode_p(x_1) -> p(encArg(x_1))
encode_0 -> 0'
encode_false -> false
encode_s(x_1) -> s(encArg(x_1))

Types:
cond :: true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p
true :: true:0':false:s:cons_cond:cons_gr:cons_p
gr :: true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p
p :: true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p
0' :: true:0':false:s:cons_cond:cons_gr:cons_p
false :: true:0':false:s:cons_cond:cons_gr:cons_p
s :: true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p
encArg :: true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p
cons_cond :: true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p
cons_gr :: true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p
cons_p :: true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p
encode_cond :: true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p
encode_true :: true:0':false:s:cons_cond:cons_gr:cons_p
encode_gr :: true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p
encode_p :: true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p
encode_0 :: true:0':false:s:cons_cond:cons_gr:cons_p
encode_false :: true:0':false:s:cons_cond:cons_gr:cons_p
encode_s :: true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p
hole_true:0':false:s:cons_cond:cons_gr:cons_p1_4 :: true:0':false:s:cons_cond:cons_gr:cons_p
gen_true:0':false:s:cons_cond:cons_gr:cons_p2_4 :: Nat -> true:0':false:s:cons_cond:cons_gr:cons_p


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


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

They will be analysed ascendingly in the following order:
gr < cond
cond < encArg
gr < encArg

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(98) LowerBoundPropagationProof (FINISHED)
Propagated lower bound.
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(99)
BOUNDS(n^1, INF)

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(100)
Obligation:
Innermost TRS:
Rules:
cond(true, x, y) -> cond(gr(x, y), 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_cond(x_1, x_2, x_3)) -> cond(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_cond(x_1, x_2, x_3) -> cond(encArg(x_1), encArg(x_2), encArg(x_3))
encode_true -> true
encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2))
encode_p(x_1) -> p(encArg(x_1))
encode_0 -> 0'
encode_false -> false
encode_s(x_1) -> s(encArg(x_1))

Types:
cond :: true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p
true :: true:0':false:s:cons_cond:cons_gr:cons_p
gr :: true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p
p :: true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p
0' :: true:0':false:s:cons_cond:cons_gr:cons_p
false :: true:0':false:s:cons_cond:cons_gr:cons_p
s :: true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p
encArg :: true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p
cons_cond :: true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p
cons_gr :: true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p
cons_p :: true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p
encode_cond :: true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p
encode_true :: true:0':false:s:cons_cond:cons_gr:cons_p
encode_gr :: true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p
encode_p :: true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p
encode_0 :: true:0':false:s:cons_cond:cons_gr:cons_p
encode_false :: true:0':false:s:cons_cond:cons_gr:cons_p
encode_s :: true:0':false:s:cons_cond:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_gr:cons_p
hole_true:0':false:s:cons_cond:cons_gr:cons_p1_4 :: true:0':false:s:cons_cond:cons_gr:cons_p
gen_true:0':false:s:cons_cond:cons_gr:cons_p2_4 :: Nat -> true:0':false:s:cons_cond:cons_gr:cons_p


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


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


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

They will be analysed ascendingly in the following order:
cond < encArg

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(101) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
encArg(gen_true:0':false:s:cons_cond:cons_gr:cons_p2_4(n2271_4)) -> gen_true:0':false:s:cons_cond:cons_gr:cons_p2_4(n2271_4), rt in Omega(0)

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

Induction Step:
encArg(gen_true:0':false:s:cons_cond:cons_gr:cons_p2_4(+(n2271_4, 1))) ->_R^Omega(0)
s(encArg(gen_true:0':false:s:cons_cond:cons_gr:cons_p2_4(n2271_4))) ->_IH
s(gen_true:0':false:s:cons_cond:cons_gr:cons_p2_4(c2272_4))

We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0).
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(102)
BOUNDS(1, INF)