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


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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


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

(0) DCpxTrs
(1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms]
(2) CpxRelTRS
(3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 198 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), 27 ms]
    (12) CpxTypedWeightedCompleteTrs
    (13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
    (14) CpxRNTS
    (15) InliningProof [UPPER BOUND(ID), 147 ms]
    (16) CpxRNTS
    (17) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (18) CpxRNTS
    (19) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 2 ms]
    (20) CpxRNTS
    (21) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (22) CpxRNTS
    (23) IntTrsBoundProof [UPPER BOUND(ID), 95 ms]
    (24) CpxRNTS
    (25) IntTrsBoundProof [UPPER BOUND(ID), 3 ms]
    (26) CpxRNTS
    (27) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (28) CpxRNTS
    (29) IntTrsBoundProof [UPPER BOUND(ID), 128 ms]
    (30) CpxRNTS
    (31) IntTrsBoundProof [UPPER BOUND(ID), 42 ms]
    (32) CpxRNTS
    (33) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (34) CpxRNTS
    (35) IntTrsBoundProof [UPPER BOUND(ID), 157 ms]
    (36) CpxRNTS
    (37) IntTrsBoundProof [UPPER BOUND(ID), 52 ms]
    (38) CpxRNTS
    (39) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (40) CpxRNTS
    (41) IntTrsBoundProof [UPPER BOUND(ID), 97 ms]
    (42) CpxRNTS
    (43) IntTrsBoundProof [UPPER BOUND(ID), 0 ms]
    (44) CpxRNTS
    (45) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (46) CpxRNTS
    (47) IntTrsBoundProof [UPPER BOUND(ID), 291 ms]
    (48) CpxRNTS
    (49) IntTrsBoundProof [UPPER BOUND(ID), 83 ms]
    (50) CpxRNTS
    (51) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (52) CpxRNTS
    (53) IntTrsBoundProof [UPPER BOUND(ID), 1030 ms]
    (54) CpxRNTS
    (55) IntTrsBoundProof [UPPER BOUND(ID), 420 ms]
    (56) CpxRNTS
    (57) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (58) CpxRNTS
    (59) IntTrsBoundProof [UPPER BOUND(ID), 168 ms]
    (60) CpxRNTS
    (61) IntTrsBoundProof [UPPER BOUND(ID), 4 ms]
    (62) CpxRNTS
    (63) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (64) CpxRNTS
    (65) IntTrsBoundProof [UPPER BOUND(ID), 458 ms]
    (66) CpxRNTS
    (67) IntTrsBoundProof [UPPER BOUND(ID), 17 ms]
    (68) CpxRNTS
    (69) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (70) CpxRNTS
    (71) IntTrsBoundProof [UPPER BOUND(ID), 187 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), 146 ms]
    (78) CpxRNTS
    (79) IntTrsBoundProof [UPPER BOUND(ID), 0 ms]
    (80) CpxRNTS
    (81) FinalProof [FINISHED, 0 ms]
    (82) BOUNDS(1, n^2)
(83) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
(84) TRS for Loop Detection
    (85) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
    (86) BEST
        (87) proven lower bound
            (88) LowerBoundPropagationProof [FINISHED, 0 ms]
            (89) BOUNDS(n^1, INF)
        (90) TRS for Loop Detection


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

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


The TRS R consists of the following rules:

   and(tt, X) -> activate(X)
   plus(N, 0) -> N
   plus(N, s(M)) -> s(plus(N, M))
   activate(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(tt) -> tt
   encArg(0) -> 0
   encArg(s(x_1)) -> s(encArg(x_1))
   encArg(cons_and(x_1, x_2)) -> and(encArg(x_1), encArg(x_2))
   encArg(cons_plus(x_1, x_2)) -> plus(encArg(x_1), encArg(x_2))
   encArg(cons_activate(x_1)) -> activate(encArg(x_1))
   encode_and(x_1, x_2) -> and(encArg(x_1), encArg(x_2))
   encode_tt -> tt
   encode_activate(x_1) -> activate(encArg(x_1))
   encode_plus(x_1, x_2) -> plus(encArg(x_1), encArg(x_2))
   encode_0 -> 0
   encode_s(x_1) -> s(encArg(x_1))


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

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


The TRS R consists of the following rules:

   and(tt, X) -> activate(X)
   plus(N, 0) -> N
   plus(N, s(M)) -> s(plus(N, M))
   activate(X) -> X

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

   encArg(tt) -> tt
   encArg(0) -> 0
   encArg(s(x_1)) -> s(encArg(x_1))
   encArg(cons_and(x_1, x_2)) -> and(encArg(x_1), encArg(x_2))
   encArg(cons_plus(x_1, x_2)) -> plus(encArg(x_1), encArg(x_2))
   encArg(cons_activate(x_1)) -> activate(encArg(x_1))
   encode_and(x_1, x_2) -> and(encArg(x_1), encArg(x_2))
   encode_tt -> tt
   encode_activate(x_1) -> activate(encArg(x_1))
   encode_plus(x_1, x_2) -> plus(encArg(x_1), encArg(x_2))
   encode_0 -> 0
   encode_s(x_1) -> s(encArg(x_1))

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

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

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


The TRS R consists of the following rules:

   and(tt, X) -> activate(X)
   plus(N, 0) -> N
   plus(N, s(M)) -> s(plus(N, M))
   activate(X) -> X

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

   encArg(tt) -> tt
   encArg(0) -> 0
   encArg(s(x_1)) -> s(encArg(x_1))
   encArg(cons_and(x_1, x_2)) -> and(encArg(x_1), encArg(x_2))
   encArg(cons_plus(x_1, x_2)) -> plus(encArg(x_1), encArg(x_2))
   encArg(cons_activate(x_1)) -> activate(encArg(x_1))
   encode_and(x_1, x_2) -> and(encArg(x_1), encArg(x_2))
   encode_tt -> tt
   encode_activate(x_1) -> activate(encArg(x_1))
   encode_plus(x_1, x_2) -> plus(encArg(x_1), encArg(x_2))
   encode_0 -> 0
   encode_s(x_1) -> s(encArg(x_1))

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

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

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


The TRS R consists of the following rules:

   and(tt, X) -> activate(X) [1]
   plus(N, 0) -> N [1]
   plus(N, s(M)) -> s(plus(N, M)) [1]
   activate(X) -> X [1]
   encArg(tt) -> tt [0]
   encArg(0) -> 0 [0]
   encArg(s(x_1)) -> s(encArg(x_1)) [0]
   encArg(cons_and(x_1, x_2)) -> and(encArg(x_1), encArg(x_2)) [0]
   encArg(cons_plus(x_1, x_2)) -> plus(encArg(x_1), encArg(x_2)) [0]
   encArg(cons_activate(x_1)) -> activate(encArg(x_1)) [0]
   encode_and(x_1, x_2) -> and(encArg(x_1), encArg(x_2)) [0]
   encode_tt -> tt [0]
   encode_activate(x_1) -> activate(encArg(x_1)) [0]
   encode_plus(x_1, x_2) -> plus(encArg(x_1), encArg(x_2)) [0]
   encode_0 -> 0 [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:

   and(tt, X) -> activate(X) [1]
   plus(N, 0) -> N [1]
   plus(N, s(M)) -> s(plus(N, M)) [1]
   activate(X) -> X [1]
   encArg(tt) -> tt [0]
   encArg(0) -> 0 [0]
   encArg(s(x_1)) -> s(encArg(x_1)) [0]
   encArg(cons_and(x_1, x_2)) -> and(encArg(x_1), encArg(x_2)) [0]
   encArg(cons_plus(x_1, x_2)) -> plus(encArg(x_1), encArg(x_2)) [0]
   encArg(cons_activate(x_1)) -> activate(encArg(x_1)) [0]
   encode_and(x_1, x_2) -> and(encArg(x_1), encArg(x_2)) [0]
   encode_tt -> tt [0]
   encode_activate(x_1) -> activate(encArg(x_1)) [0]
   encode_plus(x_1, x_2) -> plus(encArg(x_1), encArg(x_2)) [0]
   encode_0 -> 0 [0]
   encode_s(x_1) -> s(encArg(x_1)) [0]

The TRS has the following type information:
and :: tt:0:s:cons_and:cons_plus:cons_activate -> tt:0:s:cons_and:cons_plus:cons_activate -> tt:0:s:cons_and:cons_plus:cons_activate
tt :: tt:0:s:cons_and:cons_plus:cons_activate
activate :: tt:0:s:cons_and:cons_plus:cons_activate -> tt:0:s:cons_and:cons_plus:cons_activate
plus :: tt:0:s:cons_and:cons_plus:cons_activate -> tt:0:s:cons_and:cons_plus:cons_activate -> tt:0:s:cons_and:cons_plus:cons_activate
0 :: tt:0:s:cons_and:cons_plus:cons_activate
s :: tt:0:s:cons_and:cons_plus:cons_activate -> tt:0:s:cons_and:cons_plus:cons_activate
encArg :: tt:0:s:cons_and:cons_plus:cons_activate -> tt:0:s:cons_and:cons_plus:cons_activate
cons_and :: tt:0:s:cons_and:cons_plus:cons_activate -> tt:0:s:cons_and:cons_plus:cons_activate -> tt:0:s:cons_and:cons_plus:cons_activate
cons_plus :: tt:0:s:cons_and:cons_plus:cons_activate -> tt:0:s:cons_and:cons_plus:cons_activate -> tt:0:s:cons_and:cons_plus:cons_activate
cons_activate :: tt:0:s:cons_and:cons_plus:cons_activate -> tt:0:s:cons_and:cons_plus:cons_activate
encode_and :: tt:0:s:cons_and:cons_plus:cons_activate -> tt:0:s:cons_and:cons_plus:cons_activate -> tt:0:s:cons_and:cons_plus:cons_activate
encode_tt :: tt:0:s:cons_and:cons_plus:cons_activate
encode_activate :: tt:0:s:cons_and:cons_plus:cons_activate -> tt:0:s:cons_and:cons_plus:cons_activate
encode_plus :: tt:0:s:cons_and:cons_plus:cons_activate -> tt:0:s:cons_and:cons_plus:cons_activate -> tt:0:s:cons_and:cons_plus:cons_activate
encode_0 :: tt:0:s:cons_and:cons_plus:cons_activate
encode_s :: tt:0:s:cons_and:cons_plus:cons_activate -> tt:0:s:cons_and:cons_plus:cons_activate

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:

   plus_2
   and_2
   activate_1
   encArg_1
   encode_and_2
   encode_tt
   encode_activate_1
   encode_plus_2
   encode_0
   encode_s_1

Due to the following rules being added:

   encArg(v0) -> null_encArg [0]
   encode_and(v0, v1) -> null_encode_and [0]
   encode_tt -> null_encode_tt [0]
   encode_activate(v0) -> null_encode_activate [0]
   encode_plus(v0, v1) -> null_encode_plus [0]
   encode_0 -> null_encode_0 [0]
   encode_s(v0) -> null_encode_s [0]
   plus(v0, v1) -> null_plus [0]
   and(v0, v1) -> null_and [0]

And the following fresh constants:    null_encArg, null_encode_and, null_encode_tt, null_encode_activate, null_encode_plus, null_encode_0, null_encode_s, null_plus, null_and

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

(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:

   and(tt, X) -> activate(X) [1]
   plus(N, 0) -> N [1]
   plus(N, s(M)) -> s(plus(N, M)) [1]
   activate(X) -> X [1]
   encArg(tt) -> tt [0]
   encArg(0) -> 0 [0]
   encArg(s(x_1)) -> s(encArg(x_1)) [0]
   encArg(cons_and(x_1, x_2)) -> and(encArg(x_1), encArg(x_2)) [0]
   encArg(cons_plus(x_1, x_2)) -> plus(encArg(x_1), encArg(x_2)) [0]
   encArg(cons_activate(x_1)) -> activate(encArg(x_1)) [0]
   encode_and(x_1, x_2) -> and(encArg(x_1), encArg(x_2)) [0]
   encode_tt -> tt [0]
   encode_activate(x_1) -> activate(encArg(x_1)) [0]
   encode_plus(x_1, x_2) -> plus(encArg(x_1), encArg(x_2)) [0]
   encode_0 -> 0 [0]
   encode_s(x_1) -> s(encArg(x_1)) [0]
   encArg(v0) -> null_encArg [0]
   encode_and(v0, v1) -> null_encode_and [0]
   encode_tt -> null_encode_tt [0]
   encode_activate(v0) -> null_encode_activate [0]
   encode_plus(v0, v1) -> null_encode_plus [0]
   encode_0 -> null_encode_0 [0]
   encode_s(v0) -> null_encode_s [0]
   plus(v0, v1) -> null_plus [0]
   and(v0, v1) -> null_and [0]

The TRS has the following type information:
and :: tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and -> tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and -> tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and
tt :: tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and
activate :: tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and -> tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and
plus :: tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and -> tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and -> tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and
0 :: tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and
s :: tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and -> tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and
encArg :: tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and -> tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and
cons_and :: tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and -> tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and -> tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and
cons_plus :: tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and -> tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and -> tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and
cons_activate :: tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and -> tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and
encode_and :: tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and -> tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and -> tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and
encode_tt :: tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and
encode_activate :: tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and -> tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and
encode_plus :: tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and -> tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and -> tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and
encode_0 :: tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and
encode_s :: tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and -> tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and
null_encArg :: tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and
null_encode_and :: tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and
null_encode_tt :: tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and
null_encode_activate :: tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and
null_encode_plus :: tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and
null_encode_0 :: tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and
null_encode_s :: tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and
null_plus :: tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and
null_and :: tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and

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:

   and(tt, X) -> activate(X) [1]
   plus(N, 0) -> N [1]
   plus(N, s(M)) -> s(plus(N, M)) [1]
   activate(X) -> X [1]
   encArg(tt) -> tt [0]
   encArg(0) -> 0 [0]
   encArg(s(x_1)) -> s(encArg(x_1)) [0]
   encArg(cons_and(x_1, x_2)) -> and(encArg(x_1), encArg(x_2)) [0]
   encArg(cons_plus(x_1, x_2)) -> plus(encArg(x_1), encArg(x_2)) [0]
   encArg(cons_activate(tt)) -> activate(tt) [0]
   encArg(cons_activate(0)) -> activate(0) [0]
   encArg(cons_activate(s(x_163))) -> activate(s(encArg(x_163))) [0]
   encArg(cons_activate(cons_and(x_164, x_231))) -> activate(and(encArg(x_164), encArg(x_231))) [0]
   encArg(cons_activate(cons_plus(x_165, x_232))) -> activate(plus(encArg(x_165), encArg(x_232))) [0]
   encArg(cons_activate(cons_activate(x_166))) -> activate(activate(encArg(x_166))) [0]
   encArg(cons_activate(x_1)) -> activate(null_encArg) [0]
   encode_and(x_1, x_2) -> and(encArg(x_1), encArg(x_2)) [0]
   encode_tt -> tt [0]
   encode_activate(tt) -> activate(tt) [0]
   encode_activate(0) -> activate(0) [0]
   encode_activate(s(x_199)) -> activate(s(encArg(x_199))) [0]
   encode_activate(cons_and(x_1100, x_249)) -> activate(and(encArg(x_1100), encArg(x_249))) [0]
   encode_activate(cons_plus(x_1101, x_250)) -> activate(plus(encArg(x_1101), encArg(x_250))) [0]
   encode_activate(cons_activate(x_1102)) -> activate(activate(encArg(x_1102))) [0]
   encode_activate(x_1) -> activate(null_encArg) [0]
   encode_plus(x_1, x_2) -> plus(encArg(x_1), encArg(x_2)) [0]
   encode_0 -> 0 [0]
   encode_s(x_1) -> s(encArg(x_1)) [0]
   encArg(v0) -> null_encArg [0]
   encode_and(v0, v1) -> null_encode_and [0]
   encode_tt -> null_encode_tt [0]
   encode_activate(v0) -> null_encode_activate [0]
   encode_plus(v0, v1) -> null_encode_plus [0]
   encode_0 -> null_encode_0 [0]
   encode_s(v0) -> null_encode_s [0]
   plus(v0, v1) -> null_plus [0]
   and(v0, v1) -> null_and [0]

The TRS has the following type information:
and :: tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and -> tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and -> tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and
tt :: tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and
activate :: tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and -> tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and
plus :: tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and -> tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and -> tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and
0 :: tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and
s :: tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and -> tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and
encArg :: tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and -> tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and
cons_and :: tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and -> tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and -> tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and
cons_plus :: tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and -> tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and -> tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and
cons_activate :: tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and -> tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and
encode_and :: tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and -> tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and -> tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and
encode_tt :: tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and
encode_activate :: tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and -> tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and
encode_plus :: tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and -> tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and -> tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and
encode_0 :: tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and
encode_s :: tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and -> tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and
null_encArg :: tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and
null_encode_and :: tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and
null_encode_tt :: tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and
null_encode_activate :: tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and
null_encode_plus :: tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and
null_encode_0 :: tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and
null_encode_s :: tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and
null_plus :: tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and
null_and :: tt:0:s:cons_and:cons_plus:cons_activate:null_encArg:null_encode_and:null_encode_tt:null_encode_activate:null_encode_plus:null_encode_0:null_encode_s:null_plus:null_and

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:

   tt => 1
   0 => 0
   null_encArg => 0
   null_encode_and => 0
   null_encode_tt => 0
   null_encode_activate => 0
   null_encode_plus => 0
   null_encode_0 => 0
   null_encode_s => 0
   null_plus => 0
   null_and => 0

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

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

   activate(z) -{ 1 }-> X :|: X >= 0, z = X
   and(z, z') -{ 1 }-> activate(X) :|: z' = X, z = 1, X >= 0
   and(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   encArg(z) -{ 0 }-> plus(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> and(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> activate(plus(encArg(x_165), encArg(x_232))) :|: z = 1 + (1 + x_165 + x_232), x_232 >= 0, x_165 >= 0
   encArg(z) -{ 0 }-> activate(and(encArg(x_164), encArg(x_231))) :|: x_164 >= 0, x_231 >= 0, z = 1 + (1 + x_164 + x_231)
   encArg(z) -{ 0 }-> activate(activate(encArg(x_166))) :|: x_166 >= 0, z = 1 + (1 + x_166)
   encArg(z) -{ 0 }-> activate(1) :|: z = 1 + 1
   encArg(z) -{ 0 }-> activate(0) :|: z = 1 + 0
   encArg(z) -{ 0 }-> activate(0) :|: z = 1 + x_1, x_1 >= 0
   encArg(z) -{ 0 }-> activate(1 + encArg(x_163)) :|: x_163 >= 0, z = 1 + (1 + x_163)
   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_activate(z) -{ 0 }-> activate(plus(encArg(x_1101), encArg(x_250))) :|: x_250 >= 0, x_1101 >= 0, z = 1 + x_1101 + x_250
   encode_activate(z) -{ 0 }-> activate(and(encArg(x_1100), encArg(x_249))) :|: x_1100 >= 0, x_249 >= 0, z = 1 + x_1100 + x_249
   encode_activate(z) -{ 0 }-> activate(activate(encArg(x_1102))) :|: x_1102 >= 0, z = 1 + x_1102
   encode_activate(z) -{ 0 }-> activate(1) :|: z = 1
   encode_activate(z) -{ 0 }-> activate(0) :|: z = 0
   encode_activate(z) -{ 0 }-> activate(0) :|: x_1 >= 0, z = x_1
   encode_activate(z) -{ 0 }-> activate(1 + encArg(x_199)) :|: x_199 >= 0, z = 1 + x_199
   encode_activate(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_and(z, z') -{ 0 }-> and(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2
   encode_and(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   encode_plus(z, z') -{ 0 }-> plus(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2
   encode_plus(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   encode_s(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_s(z) -{ 0 }-> 1 + encArg(x_1) :|: x_1 >= 0, z = x_1
   encode_tt -{ 0 }-> 1 :|: 
   encode_tt -{ 0 }-> 0 :|: 
   plus(z, z') -{ 1 }-> N :|: z = N, z' = 0, N >= 0
   plus(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   plus(z, z') -{ 1 }-> 1 + plus(N, M) :|: z' = 1 + M, z = N, M >= 0, N >= 0


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

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

   activate(z) -{ 1 }-> X :|: X >= 0, z = X
   and(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   and(z, z') -{ 1 }-> activate(X) :|: z' = X, z = 1, X >= 0

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

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

   activate(z) -{ 1 }-> X :|: X >= 0, z = X
   and(z, z') -{ 2 }-> X' :|: z' = X, z = 1, X >= 0, X' >= 0, X = X'
   and(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   encArg(z) -{ 1 }-> X :|: z = 1 + 1, X >= 0, 1 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + x_1, x_1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 0 }-> plus(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> and(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> activate(plus(encArg(x_165), encArg(x_232))) :|: z = 1 + (1 + x_165 + x_232), x_232 >= 0, x_165 >= 0
   encArg(z) -{ 0 }-> activate(and(encArg(x_164), encArg(x_231))) :|: x_164 >= 0, x_231 >= 0, z = 1 + (1 + x_164 + x_231)
   encArg(z) -{ 0 }-> activate(activate(encArg(x_166))) :|: x_166 >= 0, z = 1 + (1 + x_166)
   encArg(z) -{ 0 }-> activate(1 + encArg(x_163)) :|: x_163 >= 0, z = 1 + (1 + x_163)
   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_activate(z) -{ 1 }-> X :|: z = 1, X >= 0, 1 = X
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: x_1 >= 0, z = x_1, X >= 0, 0 = X
   encode_activate(z) -{ 0 }-> activate(plus(encArg(x_1101), encArg(x_250))) :|: x_250 >= 0, x_1101 >= 0, z = 1 + x_1101 + x_250
   encode_activate(z) -{ 0 }-> activate(and(encArg(x_1100), encArg(x_249))) :|: x_1100 >= 0, x_249 >= 0, z = 1 + x_1100 + x_249
   encode_activate(z) -{ 0 }-> activate(activate(encArg(x_1102))) :|: x_1102 >= 0, z = 1 + x_1102
   encode_activate(z) -{ 0 }-> activate(1 + encArg(x_199)) :|: x_199 >= 0, z = 1 + x_199
   encode_activate(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_and(z, z') -{ 0 }-> and(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2
   encode_and(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   encode_plus(z, z') -{ 0 }-> plus(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2
   encode_plus(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   encode_s(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_s(z) -{ 0 }-> 1 + encArg(x_1) :|: x_1 >= 0, z = x_1
   encode_tt -{ 0 }-> 1 :|: 
   encode_tt -{ 0 }-> 0 :|: 
   plus(z, z') -{ 1 }-> N :|: z = N, z' = 0, N >= 0
   plus(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   plus(z, z') -{ 1 }-> 1 + plus(N, M) :|: z' = 1 + M, z = N, M >= 0, N >= 0


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

(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:

   activate(z) -{ 1 }-> z :|: z >= 0
   and(z, z') -{ 2 }-> z' :|: z = 1, z' >= 0
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encArg(z) -{ 1 }-> X :|: z = 1 + 1, X >= 0, 1 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 0 }-> plus(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> and(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> activate(plus(encArg(x_165), encArg(x_232))) :|: z = 1 + (1 + x_165 + x_232), x_232 >= 0, x_165 >= 0
   encArg(z) -{ 0 }-> activate(and(encArg(x_164), encArg(x_231))) :|: x_164 >= 0, x_231 >= 0, z = 1 + (1 + x_164 + x_231)
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_activate(z) -{ 1 }-> X :|: z = 1, X >= 0, 1 = X
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 0 }-> activate(plus(encArg(x_1101), encArg(x_250))) :|: x_250 >= 0, x_1101 >= 0, z = 1 + x_1101 + x_250
   encode_activate(z) -{ 0 }-> activate(and(encArg(x_1100), encArg(x_249))) :|: x_1100 >= 0, x_249 >= 0, z = 1 + x_1100 + x_249
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_and(z, z') -{ 0 }-> and(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_plus(z, z') -{ 0 }-> plus(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   encode_tt -{ 0 }-> 1 :|: 
   encode_tt -{ 0 }-> 0 :|: 
   plus(z, z') -{ 1 }-> z :|: z' = 0, z >= 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 1 }-> 1 + plus(z, z' - 1) :|: z' - 1 >= 0, z >= 0


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

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

   { encode_0 }
   { activate }
   { and }
   { encode_tt }
   { plus }
   { encArg }
   { encode_and }
   { encode_activate }
   { encode_plus }
   { encode_s }

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   and(z, z') -{ 2 }-> z' :|: z = 1, z' >= 0
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encArg(z) -{ 1 }-> X :|: z = 1 + 1, X >= 0, 1 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 0 }-> plus(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> and(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> activate(plus(encArg(x_165), encArg(x_232))) :|: z = 1 + (1 + x_165 + x_232), x_232 >= 0, x_165 >= 0
   encArg(z) -{ 0 }-> activate(and(encArg(x_164), encArg(x_231))) :|: x_164 >= 0, x_231 >= 0, z = 1 + (1 + x_164 + x_231)
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_activate(z) -{ 1 }-> X :|: z = 1, X >= 0, 1 = X
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 0 }-> activate(plus(encArg(x_1101), encArg(x_250))) :|: x_250 >= 0, x_1101 >= 0, z = 1 + x_1101 + x_250
   encode_activate(z) -{ 0 }-> activate(and(encArg(x_1100), encArg(x_249))) :|: x_1100 >= 0, x_249 >= 0, z = 1 + x_1100 + x_249
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_and(z, z') -{ 0 }-> and(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_plus(z, z') -{ 0 }-> plus(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   encode_tt -{ 0 }-> 1 :|: 
   encode_tt -{ 0 }-> 0 :|: 
   plus(z, z') -{ 1 }-> z :|: z' = 0, z >= 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 1 }-> 1 + plus(z, z' - 1) :|: z' - 1 >= 0, z >= 0

Function symbols to be analyzed: {encode_0}, {activate}, {and}, {encode_tt}, {plus}, {encArg}, {encode_and}, {encode_activate}, {encode_plus}, {encode_s}

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

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   and(z, z') -{ 2 }-> z' :|: z = 1, z' >= 0
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encArg(z) -{ 1 }-> X :|: z = 1 + 1, X >= 0, 1 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 0 }-> plus(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> and(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> activate(plus(encArg(x_165), encArg(x_232))) :|: z = 1 + (1 + x_165 + x_232), x_232 >= 0, x_165 >= 0
   encArg(z) -{ 0 }-> activate(and(encArg(x_164), encArg(x_231))) :|: x_164 >= 0, x_231 >= 0, z = 1 + (1 + x_164 + x_231)
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_activate(z) -{ 1 }-> X :|: z = 1, X >= 0, 1 = X
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 0 }-> activate(plus(encArg(x_1101), encArg(x_250))) :|: x_250 >= 0, x_1101 >= 0, z = 1 + x_1101 + x_250
   encode_activate(z) -{ 0 }-> activate(and(encArg(x_1100), encArg(x_249))) :|: x_1100 >= 0, x_249 >= 0, z = 1 + x_1100 + x_249
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_and(z, z') -{ 0 }-> and(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_plus(z, z') -{ 0 }-> plus(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   encode_tt -{ 0 }-> 1 :|: 
   encode_tt -{ 0 }-> 0 :|: 
   plus(z, z') -{ 1 }-> z :|: z' = 0, z >= 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 1 }-> 1 + plus(z, z' - 1) :|: z' - 1 >= 0, z >= 0

Function symbols to be analyzed: {encode_0}, {activate}, {and}, {encode_tt}, {plus}, {encArg}, {encode_and}, {encode_activate}, {encode_plus}, {encode_s}

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

(23) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   and(z, z') -{ 2 }-> z' :|: z = 1, z' >= 0
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encArg(z) -{ 1 }-> X :|: z = 1 + 1, X >= 0, 1 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 0 }-> plus(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> and(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> activate(plus(encArg(x_165), encArg(x_232))) :|: z = 1 + (1 + x_165 + x_232), x_232 >= 0, x_165 >= 0
   encArg(z) -{ 0 }-> activate(and(encArg(x_164), encArg(x_231))) :|: x_164 >= 0, x_231 >= 0, z = 1 + (1 + x_164 + x_231)
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_activate(z) -{ 1 }-> X :|: z = 1, X >= 0, 1 = X
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 0 }-> activate(plus(encArg(x_1101), encArg(x_250))) :|: x_250 >= 0, x_1101 >= 0, z = 1 + x_1101 + x_250
   encode_activate(z) -{ 0 }-> activate(and(encArg(x_1100), encArg(x_249))) :|: x_1100 >= 0, x_249 >= 0, z = 1 + x_1100 + x_249
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_and(z, z') -{ 0 }-> and(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_plus(z, z') -{ 0 }-> plus(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   encode_tt -{ 0 }-> 1 :|: 
   encode_tt -{ 0 }-> 0 :|: 
   plus(z, z') -{ 1 }-> z :|: z' = 0, z >= 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 1 }-> 1 + plus(z, z' - 1) :|: z' - 1 >= 0, z >= 0

Function symbols to be analyzed: {encode_0}, {activate}, {and}, {encode_tt}, {plus}, {encArg}, {encode_and}, {encode_activate}, {encode_plus}, {encode_s}
Previous analysis results are:
  encode_0: runtime: ?, size: O(1) [0]

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

(25) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   and(z, z') -{ 2 }-> z' :|: z = 1, z' >= 0
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encArg(z) -{ 1 }-> X :|: z = 1 + 1, X >= 0, 1 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 0 }-> plus(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> and(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> activate(plus(encArg(x_165), encArg(x_232))) :|: z = 1 + (1 + x_165 + x_232), x_232 >= 0, x_165 >= 0
   encArg(z) -{ 0 }-> activate(and(encArg(x_164), encArg(x_231))) :|: x_164 >= 0, x_231 >= 0, z = 1 + (1 + x_164 + x_231)
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_activate(z) -{ 1 }-> X :|: z = 1, X >= 0, 1 = X
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 0 }-> activate(plus(encArg(x_1101), encArg(x_250))) :|: x_250 >= 0, x_1101 >= 0, z = 1 + x_1101 + x_250
   encode_activate(z) -{ 0 }-> activate(and(encArg(x_1100), encArg(x_249))) :|: x_1100 >= 0, x_249 >= 0, z = 1 + x_1100 + x_249
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_and(z, z') -{ 0 }-> and(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_plus(z, z') -{ 0 }-> plus(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   encode_tt -{ 0 }-> 1 :|: 
   encode_tt -{ 0 }-> 0 :|: 
   plus(z, z') -{ 1 }-> z :|: z' = 0, z >= 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 1 }-> 1 + plus(z, z' - 1) :|: z' - 1 >= 0, z >= 0

Function symbols to be analyzed: {activate}, {and}, {encode_tt}, {plus}, {encArg}, {encode_and}, {encode_activate}, {encode_plus}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [0], size: O(1) [0]

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

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   and(z, z') -{ 2 }-> z' :|: z = 1, z' >= 0
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encArg(z) -{ 1 }-> X :|: z = 1 + 1, X >= 0, 1 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 0 }-> plus(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> and(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> activate(plus(encArg(x_165), encArg(x_232))) :|: z = 1 + (1 + x_165 + x_232), x_232 >= 0, x_165 >= 0
   encArg(z) -{ 0 }-> activate(and(encArg(x_164), encArg(x_231))) :|: x_164 >= 0, x_231 >= 0, z = 1 + (1 + x_164 + x_231)
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_activate(z) -{ 1 }-> X :|: z = 1, X >= 0, 1 = X
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 0 }-> activate(plus(encArg(x_1101), encArg(x_250))) :|: x_250 >= 0, x_1101 >= 0, z = 1 + x_1101 + x_250
   encode_activate(z) -{ 0 }-> activate(and(encArg(x_1100), encArg(x_249))) :|: x_1100 >= 0, x_249 >= 0, z = 1 + x_1100 + x_249
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_and(z, z') -{ 0 }-> and(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_plus(z, z') -{ 0 }-> plus(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   encode_tt -{ 0 }-> 1 :|: 
   encode_tt -{ 0 }-> 0 :|: 
   plus(z, z') -{ 1 }-> z :|: z' = 0, z >= 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 1 }-> 1 + plus(z, z' - 1) :|: z' - 1 >= 0, z >= 0

Function symbols to be analyzed: {activate}, {and}, {encode_tt}, {plus}, {encArg}, {encode_and}, {encode_activate}, {encode_plus}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [0], size: O(1) [0]

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

(29) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   and(z, z') -{ 2 }-> z' :|: z = 1, z' >= 0
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encArg(z) -{ 1 }-> X :|: z = 1 + 1, X >= 0, 1 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 0 }-> plus(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> and(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> activate(plus(encArg(x_165), encArg(x_232))) :|: z = 1 + (1 + x_165 + x_232), x_232 >= 0, x_165 >= 0
   encArg(z) -{ 0 }-> activate(and(encArg(x_164), encArg(x_231))) :|: x_164 >= 0, x_231 >= 0, z = 1 + (1 + x_164 + x_231)
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_activate(z) -{ 1 }-> X :|: z = 1, X >= 0, 1 = X
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 0 }-> activate(plus(encArg(x_1101), encArg(x_250))) :|: x_250 >= 0, x_1101 >= 0, z = 1 + x_1101 + x_250
   encode_activate(z) -{ 0 }-> activate(and(encArg(x_1100), encArg(x_249))) :|: x_1100 >= 0, x_249 >= 0, z = 1 + x_1100 + x_249
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_and(z, z') -{ 0 }-> and(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_plus(z, z') -{ 0 }-> plus(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   encode_tt -{ 0 }-> 1 :|: 
   encode_tt -{ 0 }-> 0 :|: 
   plus(z, z') -{ 1 }-> z :|: z' = 0, z >= 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 1 }-> 1 + plus(z, z' - 1) :|: z' - 1 >= 0, z >= 0

Function symbols to be analyzed: {activate}, {and}, {encode_tt}, {plus}, {encArg}, {encode_and}, {encode_activate}, {encode_plus}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [0], size: O(1) [0]
  activate: runtime: ?, size: O(n^1) [z]

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

(31) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   and(z, z') -{ 2 }-> z' :|: z = 1, z' >= 0
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encArg(z) -{ 1 }-> X :|: z = 1 + 1, X >= 0, 1 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 0 }-> plus(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> and(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> activate(plus(encArg(x_165), encArg(x_232))) :|: z = 1 + (1 + x_165 + x_232), x_232 >= 0, x_165 >= 0
   encArg(z) -{ 0 }-> activate(and(encArg(x_164), encArg(x_231))) :|: x_164 >= 0, x_231 >= 0, z = 1 + (1 + x_164 + x_231)
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_activate(z) -{ 1 }-> X :|: z = 1, X >= 0, 1 = X
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 0 }-> activate(plus(encArg(x_1101), encArg(x_250))) :|: x_250 >= 0, x_1101 >= 0, z = 1 + x_1101 + x_250
   encode_activate(z) -{ 0 }-> activate(and(encArg(x_1100), encArg(x_249))) :|: x_1100 >= 0, x_249 >= 0, z = 1 + x_1100 + x_249
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_and(z, z') -{ 0 }-> and(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_plus(z, z') -{ 0 }-> plus(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   encode_tt -{ 0 }-> 1 :|: 
   encode_tt -{ 0 }-> 0 :|: 
   plus(z, z') -{ 1 }-> z :|: z' = 0, z >= 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 1 }-> 1 + plus(z, z' - 1) :|: z' - 1 >= 0, z >= 0

Function symbols to be analyzed: {and}, {encode_tt}, {plus}, {encArg}, {encode_and}, {encode_activate}, {encode_plus}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [0], size: O(1) [0]
  activate: runtime: O(1) [1], size: O(n^1) [z]

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

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   and(z, z') -{ 2 }-> z' :|: z = 1, z' >= 0
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encArg(z) -{ 1 }-> X :|: z = 1 + 1, X >= 0, 1 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 0 }-> plus(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> and(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> activate(plus(encArg(x_165), encArg(x_232))) :|: z = 1 + (1 + x_165 + x_232), x_232 >= 0, x_165 >= 0
   encArg(z) -{ 0 }-> activate(and(encArg(x_164), encArg(x_231))) :|: x_164 >= 0, x_231 >= 0, z = 1 + (1 + x_164 + x_231)
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_activate(z) -{ 1 }-> X :|: z = 1, X >= 0, 1 = X
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 0 }-> activate(plus(encArg(x_1101), encArg(x_250))) :|: x_250 >= 0, x_1101 >= 0, z = 1 + x_1101 + x_250
   encode_activate(z) -{ 0 }-> activate(and(encArg(x_1100), encArg(x_249))) :|: x_1100 >= 0, x_249 >= 0, z = 1 + x_1100 + x_249
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_and(z, z') -{ 0 }-> and(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_plus(z, z') -{ 0 }-> plus(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   encode_tt -{ 0 }-> 1 :|: 
   encode_tt -{ 0 }-> 0 :|: 
   plus(z, z') -{ 1 }-> z :|: z' = 0, z >= 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 1 }-> 1 + plus(z, z' - 1) :|: z' - 1 >= 0, z >= 0

Function symbols to be analyzed: {and}, {encode_tt}, {plus}, {encArg}, {encode_and}, {encode_activate}, {encode_plus}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [0], size: O(1) [0]
  activate: runtime: O(1) [1], size: O(n^1) [z]

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

(35) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   and(z, z') -{ 2 }-> z' :|: z = 1, z' >= 0
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encArg(z) -{ 1 }-> X :|: z = 1 + 1, X >= 0, 1 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 0 }-> plus(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> and(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> activate(plus(encArg(x_165), encArg(x_232))) :|: z = 1 + (1 + x_165 + x_232), x_232 >= 0, x_165 >= 0
   encArg(z) -{ 0 }-> activate(and(encArg(x_164), encArg(x_231))) :|: x_164 >= 0, x_231 >= 0, z = 1 + (1 + x_164 + x_231)
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_activate(z) -{ 1 }-> X :|: z = 1, X >= 0, 1 = X
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 0 }-> activate(plus(encArg(x_1101), encArg(x_250))) :|: x_250 >= 0, x_1101 >= 0, z = 1 + x_1101 + x_250
   encode_activate(z) -{ 0 }-> activate(and(encArg(x_1100), encArg(x_249))) :|: x_1100 >= 0, x_249 >= 0, z = 1 + x_1100 + x_249
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_and(z, z') -{ 0 }-> and(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_plus(z, z') -{ 0 }-> plus(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   encode_tt -{ 0 }-> 1 :|: 
   encode_tt -{ 0 }-> 0 :|: 
   plus(z, z') -{ 1 }-> z :|: z' = 0, z >= 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 1 }-> 1 + plus(z, z' - 1) :|: z' - 1 >= 0, z >= 0

Function symbols to be analyzed: {and}, {encode_tt}, {plus}, {encArg}, {encode_and}, {encode_activate}, {encode_plus}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [0], size: O(1) [0]
  activate: runtime: O(1) [1], size: O(n^1) [z]
  and: runtime: ?, size: O(n^1) [z']

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

(37) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   and(z, z') -{ 2 }-> z' :|: z = 1, z' >= 0
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encArg(z) -{ 1 }-> X :|: z = 1 + 1, X >= 0, 1 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 0 }-> plus(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> and(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> activate(plus(encArg(x_165), encArg(x_232))) :|: z = 1 + (1 + x_165 + x_232), x_232 >= 0, x_165 >= 0
   encArg(z) -{ 0 }-> activate(and(encArg(x_164), encArg(x_231))) :|: x_164 >= 0, x_231 >= 0, z = 1 + (1 + x_164 + x_231)
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_activate(z) -{ 1 }-> X :|: z = 1, X >= 0, 1 = X
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 0 }-> activate(plus(encArg(x_1101), encArg(x_250))) :|: x_250 >= 0, x_1101 >= 0, z = 1 + x_1101 + x_250
   encode_activate(z) -{ 0 }-> activate(and(encArg(x_1100), encArg(x_249))) :|: x_1100 >= 0, x_249 >= 0, z = 1 + x_1100 + x_249
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_and(z, z') -{ 0 }-> and(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_plus(z, z') -{ 0 }-> plus(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   encode_tt -{ 0 }-> 1 :|: 
   encode_tt -{ 0 }-> 0 :|: 
   plus(z, z') -{ 1 }-> z :|: z' = 0, z >= 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 1 }-> 1 + plus(z, z' - 1) :|: z' - 1 >= 0, z >= 0

Function symbols to be analyzed: {encode_tt}, {plus}, {encArg}, {encode_and}, {encode_activate}, {encode_plus}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [0], size: O(1) [0]
  activate: runtime: O(1) [1], size: O(n^1) [z]
  and: runtime: O(1) [2], size: O(n^1) [z']

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

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   and(z, z') -{ 2 }-> z' :|: z = 1, z' >= 0
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encArg(z) -{ 1 }-> X :|: z = 1 + 1, X >= 0, 1 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 0 }-> plus(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> and(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> activate(plus(encArg(x_165), encArg(x_232))) :|: z = 1 + (1 + x_165 + x_232), x_232 >= 0, x_165 >= 0
   encArg(z) -{ 0 }-> activate(and(encArg(x_164), encArg(x_231))) :|: x_164 >= 0, x_231 >= 0, z = 1 + (1 + x_164 + x_231)
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_activate(z) -{ 1 }-> X :|: z = 1, X >= 0, 1 = X
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 0 }-> activate(plus(encArg(x_1101), encArg(x_250))) :|: x_250 >= 0, x_1101 >= 0, z = 1 + x_1101 + x_250
   encode_activate(z) -{ 0 }-> activate(and(encArg(x_1100), encArg(x_249))) :|: x_1100 >= 0, x_249 >= 0, z = 1 + x_1100 + x_249
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_and(z, z') -{ 0 }-> and(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_plus(z, z') -{ 0 }-> plus(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   encode_tt -{ 0 }-> 1 :|: 
   encode_tt -{ 0 }-> 0 :|: 
   plus(z, z') -{ 1 }-> z :|: z' = 0, z >= 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 1 }-> 1 + plus(z, z' - 1) :|: z' - 1 >= 0, z >= 0

Function symbols to be analyzed: {encode_tt}, {plus}, {encArg}, {encode_and}, {encode_activate}, {encode_plus}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [0], size: O(1) [0]
  activate: runtime: O(1) [1], size: O(n^1) [z]
  and: runtime: O(1) [2], size: O(n^1) [z']

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

(41) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   and(z, z') -{ 2 }-> z' :|: z = 1, z' >= 0
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encArg(z) -{ 1 }-> X :|: z = 1 + 1, X >= 0, 1 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 0 }-> plus(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> and(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> activate(plus(encArg(x_165), encArg(x_232))) :|: z = 1 + (1 + x_165 + x_232), x_232 >= 0, x_165 >= 0
   encArg(z) -{ 0 }-> activate(and(encArg(x_164), encArg(x_231))) :|: x_164 >= 0, x_231 >= 0, z = 1 + (1 + x_164 + x_231)
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_activate(z) -{ 1 }-> X :|: z = 1, X >= 0, 1 = X
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 0 }-> activate(plus(encArg(x_1101), encArg(x_250))) :|: x_250 >= 0, x_1101 >= 0, z = 1 + x_1101 + x_250
   encode_activate(z) -{ 0 }-> activate(and(encArg(x_1100), encArg(x_249))) :|: x_1100 >= 0, x_249 >= 0, z = 1 + x_1100 + x_249
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_and(z, z') -{ 0 }-> and(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_plus(z, z') -{ 0 }-> plus(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   encode_tt -{ 0 }-> 1 :|: 
   encode_tt -{ 0 }-> 0 :|: 
   plus(z, z') -{ 1 }-> z :|: z' = 0, z >= 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 1 }-> 1 + plus(z, z' - 1) :|: z' - 1 >= 0, z >= 0

Function symbols to be analyzed: {encode_tt}, {plus}, {encArg}, {encode_and}, {encode_activate}, {encode_plus}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [0], size: O(1) [0]
  activate: runtime: O(1) [1], size: O(n^1) [z]
  and: runtime: O(1) [2], size: O(n^1) [z']
  encode_tt: runtime: ?, size: O(1) [1]

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

(43) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: encode_tt
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:

   activate(z) -{ 1 }-> z :|: z >= 0
   and(z, z') -{ 2 }-> z' :|: z = 1, z' >= 0
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encArg(z) -{ 1 }-> X :|: z = 1 + 1, X >= 0, 1 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 0 }-> plus(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> and(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> activate(plus(encArg(x_165), encArg(x_232))) :|: z = 1 + (1 + x_165 + x_232), x_232 >= 0, x_165 >= 0
   encArg(z) -{ 0 }-> activate(and(encArg(x_164), encArg(x_231))) :|: x_164 >= 0, x_231 >= 0, z = 1 + (1 + x_164 + x_231)
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_activate(z) -{ 1 }-> X :|: z = 1, X >= 0, 1 = X
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 0 }-> activate(plus(encArg(x_1101), encArg(x_250))) :|: x_250 >= 0, x_1101 >= 0, z = 1 + x_1101 + x_250
   encode_activate(z) -{ 0 }-> activate(and(encArg(x_1100), encArg(x_249))) :|: x_1100 >= 0, x_249 >= 0, z = 1 + x_1100 + x_249
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_and(z, z') -{ 0 }-> and(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_plus(z, z') -{ 0 }-> plus(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   encode_tt -{ 0 }-> 1 :|: 
   encode_tt -{ 0 }-> 0 :|: 
   plus(z, z') -{ 1 }-> z :|: z' = 0, z >= 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 1 }-> 1 + plus(z, z' - 1) :|: z' - 1 >= 0, z >= 0

Function symbols to be analyzed: {plus}, {encArg}, {encode_and}, {encode_activate}, {encode_plus}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [0], size: O(1) [0]
  activate: runtime: O(1) [1], size: O(n^1) [z]
  and: runtime: O(1) [2], size: O(n^1) [z']
  encode_tt: runtime: O(1) [0], size: O(1) [1]

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

(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:

   activate(z) -{ 1 }-> z :|: z >= 0
   and(z, z') -{ 2 }-> z' :|: z = 1, z' >= 0
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encArg(z) -{ 1 }-> X :|: z = 1 + 1, X >= 0, 1 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 0 }-> plus(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> and(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> activate(plus(encArg(x_165), encArg(x_232))) :|: z = 1 + (1 + x_165 + x_232), x_232 >= 0, x_165 >= 0
   encArg(z) -{ 0 }-> activate(and(encArg(x_164), encArg(x_231))) :|: x_164 >= 0, x_231 >= 0, z = 1 + (1 + x_164 + x_231)
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_activate(z) -{ 1 }-> X :|: z = 1, X >= 0, 1 = X
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 0 }-> activate(plus(encArg(x_1101), encArg(x_250))) :|: x_250 >= 0, x_1101 >= 0, z = 1 + x_1101 + x_250
   encode_activate(z) -{ 0 }-> activate(and(encArg(x_1100), encArg(x_249))) :|: x_1100 >= 0, x_249 >= 0, z = 1 + x_1100 + x_249
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_and(z, z') -{ 0 }-> and(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_plus(z, z') -{ 0 }-> plus(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   encode_tt -{ 0 }-> 1 :|: 
   encode_tt -{ 0 }-> 0 :|: 
   plus(z, z') -{ 1 }-> z :|: z' = 0, z >= 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 1 }-> 1 + plus(z, z' - 1) :|: z' - 1 >= 0, z >= 0

Function symbols to be analyzed: {plus}, {encArg}, {encode_and}, {encode_activate}, {encode_plus}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [0], size: O(1) [0]
  activate: runtime: O(1) [1], size: O(n^1) [z]
  and: runtime: O(1) [2], size: O(n^1) [z']
  encode_tt: runtime: O(1) [0], size: O(1) [1]

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

(47) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   and(z, z') -{ 2 }-> z' :|: z = 1, z' >= 0
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encArg(z) -{ 1 }-> X :|: z = 1 + 1, X >= 0, 1 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 0 }-> plus(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> and(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> activate(plus(encArg(x_165), encArg(x_232))) :|: z = 1 + (1 + x_165 + x_232), x_232 >= 0, x_165 >= 0
   encArg(z) -{ 0 }-> activate(and(encArg(x_164), encArg(x_231))) :|: x_164 >= 0, x_231 >= 0, z = 1 + (1 + x_164 + x_231)
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_activate(z) -{ 1 }-> X :|: z = 1, X >= 0, 1 = X
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 0 }-> activate(plus(encArg(x_1101), encArg(x_250))) :|: x_250 >= 0, x_1101 >= 0, z = 1 + x_1101 + x_250
   encode_activate(z) -{ 0 }-> activate(and(encArg(x_1100), encArg(x_249))) :|: x_1100 >= 0, x_249 >= 0, z = 1 + x_1100 + x_249
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_and(z, z') -{ 0 }-> and(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_plus(z, z') -{ 0 }-> plus(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   encode_tt -{ 0 }-> 1 :|: 
   encode_tt -{ 0 }-> 0 :|: 
   plus(z, z') -{ 1 }-> z :|: z' = 0, z >= 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 1 }-> 1 + plus(z, z' - 1) :|: z' - 1 >= 0, z >= 0

Function symbols to be analyzed: {plus}, {encArg}, {encode_and}, {encode_activate}, {encode_plus}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [0], size: O(1) [0]
  activate: runtime: O(1) [1], size: O(n^1) [z]
  and: runtime: O(1) [2], size: O(n^1) [z']
  encode_tt: runtime: O(1) [0], size: O(1) [1]
  plus: runtime: ?, size: O(n^1) [z + z']

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

(49) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   and(z, z') -{ 2 }-> z' :|: z = 1, z' >= 0
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encArg(z) -{ 1 }-> X :|: z = 1 + 1, X >= 0, 1 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 0 }-> plus(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> and(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> activate(plus(encArg(x_165), encArg(x_232))) :|: z = 1 + (1 + x_165 + x_232), x_232 >= 0, x_165 >= 0
   encArg(z) -{ 0 }-> activate(and(encArg(x_164), encArg(x_231))) :|: x_164 >= 0, x_231 >= 0, z = 1 + (1 + x_164 + x_231)
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_activate(z) -{ 1 }-> X :|: z = 1, X >= 0, 1 = X
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 0 }-> activate(plus(encArg(x_1101), encArg(x_250))) :|: x_250 >= 0, x_1101 >= 0, z = 1 + x_1101 + x_250
   encode_activate(z) -{ 0 }-> activate(and(encArg(x_1100), encArg(x_249))) :|: x_1100 >= 0, x_249 >= 0, z = 1 + x_1100 + x_249
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_and(z, z') -{ 0 }-> and(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_plus(z, z') -{ 0 }-> plus(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   encode_tt -{ 0 }-> 1 :|: 
   encode_tt -{ 0 }-> 0 :|: 
   plus(z, z') -{ 1 }-> z :|: z' = 0, z >= 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 1 }-> 1 + plus(z, z' - 1) :|: z' - 1 >= 0, z >= 0

Function symbols to be analyzed: {encArg}, {encode_and}, {encode_activate}, {encode_plus}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [0], size: O(1) [0]
  activate: runtime: O(1) [1], size: O(n^1) [z]
  and: runtime: O(1) [2], size: O(n^1) [z']
  encode_tt: runtime: O(1) [0], size: O(1) [1]
  plus: runtime: O(n^1) [1 + z'], size: O(n^1) [z + 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:

   activate(z) -{ 1 }-> z :|: z >= 0
   and(z, z') -{ 2 }-> z' :|: z = 1, z' >= 0
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encArg(z) -{ 1 }-> X :|: z = 1 + 1, X >= 0, 1 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 0 }-> plus(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> and(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> activate(plus(encArg(x_165), encArg(x_232))) :|: z = 1 + (1 + x_165 + x_232), x_232 >= 0, x_165 >= 0
   encArg(z) -{ 0 }-> activate(and(encArg(x_164), encArg(x_231))) :|: x_164 >= 0, x_231 >= 0, z = 1 + (1 + x_164 + x_231)
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_activate(z) -{ 1 }-> X :|: z = 1, X >= 0, 1 = X
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 0 }-> activate(plus(encArg(x_1101), encArg(x_250))) :|: x_250 >= 0, x_1101 >= 0, z = 1 + x_1101 + x_250
   encode_activate(z) -{ 0 }-> activate(and(encArg(x_1100), encArg(x_249))) :|: x_1100 >= 0, x_249 >= 0, z = 1 + x_1100 + x_249
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_and(z, z') -{ 0 }-> and(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_plus(z, z') -{ 0 }-> plus(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   encode_tt -{ 0 }-> 1 :|: 
   encode_tt -{ 0 }-> 0 :|: 
   plus(z, z') -{ 1 }-> z :|: z' = 0, z >= 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 1 + z' }-> 1 + s :|: s >= 0, s <= z + (z' - 1), z' - 1 >= 0, z >= 0

Function symbols to be analyzed: {encArg}, {encode_and}, {encode_activate}, {encode_plus}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [0], size: O(1) [0]
  activate: runtime: O(1) [1], size: O(n^1) [z]
  and: runtime: O(1) [2], size: O(n^1) [z']
  encode_tt: runtime: O(1) [0], size: O(1) [1]
  plus: runtime: O(n^1) [1 + z'], size: O(n^1) [z + z']

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

(53) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: encArg
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 5 + 3*z

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   and(z, z') -{ 2 }-> z' :|: z = 1, z' >= 0
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encArg(z) -{ 1 }-> X :|: z = 1 + 1, X >= 0, 1 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 0 }-> plus(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> and(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> activate(plus(encArg(x_165), encArg(x_232))) :|: z = 1 + (1 + x_165 + x_232), x_232 >= 0, x_165 >= 0
   encArg(z) -{ 0 }-> activate(and(encArg(x_164), encArg(x_231))) :|: x_164 >= 0, x_231 >= 0, z = 1 + (1 + x_164 + x_231)
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_activate(z) -{ 1 }-> X :|: z = 1, X >= 0, 1 = X
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 0 }-> activate(plus(encArg(x_1101), encArg(x_250))) :|: x_250 >= 0, x_1101 >= 0, z = 1 + x_1101 + x_250
   encode_activate(z) -{ 0 }-> activate(and(encArg(x_1100), encArg(x_249))) :|: x_1100 >= 0, x_249 >= 0, z = 1 + x_1100 + x_249
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_and(z, z') -{ 0 }-> and(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_plus(z, z') -{ 0 }-> plus(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   encode_tt -{ 0 }-> 1 :|: 
   encode_tt -{ 0 }-> 0 :|: 
   plus(z, z') -{ 1 }-> z :|: z' = 0, z >= 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 1 + z' }-> 1 + s :|: s >= 0, s <= z + (z' - 1), z' - 1 >= 0, z >= 0

Function symbols to be analyzed: {encArg}, {encode_and}, {encode_activate}, {encode_plus}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [0], size: O(1) [0]
  activate: runtime: O(1) [1], size: O(n^1) [z]
  and: runtime: O(1) [2], size: O(n^1) [z']
  encode_tt: runtime: O(1) [0], size: O(1) [1]
  plus: runtime: O(n^1) [1 + z'], size: O(n^1) [z + z']
  encArg: runtime: ?, size: O(n^1) [5 + 3*z]

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

(55) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   and(z, z') -{ 2 }-> z' :|: z = 1, z' >= 0
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encArg(z) -{ 1 }-> X :|: z = 1 + 1, X >= 0, 1 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 0 }-> plus(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> and(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> activate(plus(encArg(x_165), encArg(x_232))) :|: z = 1 + (1 + x_165 + x_232), x_232 >= 0, x_165 >= 0
   encArg(z) -{ 0 }-> activate(and(encArg(x_164), encArg(x_231))) :|: x_164 >= 0, x_231 >= 0, z = 1 + (1 + x_164 + x_231)
   encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> activate(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_activate(z) -{ 1 }-> X :|: z = 1, X >= 0, 1 = X
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 0 }-> activate(plus(encArg(x_1101), encArg(x_250))) :|: x_250 >= 0, x_1101 >= 0, z = 1 + x_1101 + x_250
   encode_activate(z) -{ 0 }-> activate(and(encArg(x_1100), encArg(x_249))) :|: x_1100 >= 0, x_249 >= 0, z = 1 + x_1100 + x_249
   encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> activate(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_and(z, z') -{ 0 }-> and(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_plus(z, z') -{ 0 }-> plus(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   encode_tt -{ 0 }-> 1 :|: 
   encode_tt -{ 0 }-> 0 :|: 
   plus(z, z') -{ 1 }-> z :|: z' = 0, z >= 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 1 + z' }-> 1 + s :|: s >= 0, s <= z + (z' - 1), z' - 1 >= 0, z >= 0

Function symbols to be analyzed: {encode_and}, {encode_activate}, {encode_plus}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [0], size: O(1) [0]
  activate: runtime: O(1) [1], size: O(n^1) [z]
  and: runtime: O(1) [2], size: O(n^1) [z']
  encode_tt: runtime: O(1) [0], size: O(1) [1]
  plus: runtime: O(n^1) [1 + z'], size: O(n^1) [z + z']
  encArg: runtime: O(n^2) [1 + 3*z + 3*z^2], size: O(n^1) [5 + 3*z]

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

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   and(z, z') -{ 2 }-> z' :|: z = 1, z' >= 0
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encArg(z) -{ 1 }-> X :|: z = 1 + 1, X >= 0, 1 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 4 + s10 + 3*x_165 + 3*x_165^2 + 3*x_232 + 3*x_232^2 }-> s12 :|: s9 >= 0, s9 <= 3 * x_165 + 5, s10 >= 0, s10 <= 3 * x_232 + 5, s11 >= 0, s11 <= s9 + s10, s12 >= 0, s12 <= s11, z = 1 + (1 + x_165 + x_232), x_232 >= 0, x_165 >= 0
   encArg(z) -{ 9 + -9*z + 3*z^2 }-> s15 :|: s13 >= 0, s13 <= 3 * (z - 2) + 5, s14 >= 0, s14 <= s13, s15 >= 0, s15 <= s14, z - 2 >= 0
   encArg(z) -{ 3 + s1 + 3*x_1 + 3*x_1^2 + 3*x_2 + 3*x_2^2 }-> s2 :|: s'' >= 0, s'' <= 3 * x_1 + 5, s1 >= 0, s1 <= 3 * x_2 + 5, s2 >= 0, s2 <= s'' + s1, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 4 + 3*x_1 + 3*x_1^2 + 3*x_2 + 3*x_2^2 }-> s27 :|: s25 >= 0, s25 <= 3 * x_1 + 5, s26 >= 0, s26 <= 3 * x_2 + 5, s27 >= 0, s27 <= s26, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 5 + 3*x_164 + 3*x_164^2 + 3*x_231 + 3*x_231^2 }-> s34 :|: s31 >= 0, s31 <= 3 * x_164 + 5, s32 >= 0, s32 <= 3 * x_231 + 5, s33 >= 0, s33 <= s32, s34 >= 0, s34 <= s33, x_164 >= 0, x_231 >= 0, z = 1 + (1 + x_164 + x_231)
   encArg(z) -{ 8 + -9*z + 3*z^2 }-> s8 :|: s7 >= 0, s7 <= 3 * (z - 2) + 5, s8 >= 0, s8 <= 1 + s7, z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 1 + -3*z + 3*z^2 }-> 1 + s' :|: s' >= 0, s' <= 3 * (z - 1) + 5, z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_activate(z) -{ 1 }-> X :|: z = 1, X >= 0, 1 = X
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 2 + -3*z + 3*z^2 }-> s17 :|: s16 >= 0, s16 <= 3 * (z - 1) + 5, s17 >= 0, s17 <= 1 + s16, z - 1 >= 0
   encode_activate(z) -{ 4 + s19 + 3*x_1101 + 3*x_1101^2 + 3*x_250 + 3*x_250^2 }-> s21 :|: s18 >= 0, s18 <= 3 * x_1101 + 5, s19 >= 0, s19 <= 3 * x_250 + 5, s20 >= 0, s20 <= s18 + s19, s21 >= 0, s21 <= s20, x_250 >= 0, x_1101 >= 0, z = 1 + x_1101 + x_250
   encode_activate(z) -{ 3 + -3*z + 3*z^2 }-> s24 :|: s22 >= 0, s22 <= 3 * (z - 1) + 5, s23 >= 0, s23 <= s22, s24 >= 0, s24 <= s23, z - 1 >= 0
   encode_activate(z) -{ 5 + 3*x_1100 + 3*x_1100^2 + 3*x_249 + 3*x_249^2 }-> s38 :|: s35 >= 0, s35 <= 3 * x_1100 + 5, s36 >= 0, s36 <= 3 * x_249 + 5, s37 >= 0, s37 <= s36, s38 >= 0, s38 <= s37, x_1100 >= 0, x_249 >= 0, z = 1 + x_1100 + x_249
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_and(z, z') -{ 4 + 3*z + 3*z^2 + 3*z' + 3*z'^2 }-> s30 :|: s28 >= 0, s28 <= 3 * z + 5, s29 >= 0, s29 <= 3 * z' + 5, s30 >= 0, s30 <= s29, z >= 0, z' >= 0
   encode_and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_plus(z, z') -{ 3 + s4 + 3*z + 3*z^2 + 3*z' + 3*z'^2 }-> s5 :|: s3 >= 0, s3 <= 3 * z + 5, s4 >= 0, s4 <= 3 * z' + 5, s5 >= 0, s5 <= s3 + s4, z >= 0, z' >= 0
   encode_plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 1 + 3*z + 3*z^2 }-> 1 + s6 :|: s6 >= 0, s6 <= 3 * z + 5, z >= 0
   encode_tt -{ 0 }-> 1 :|: 
   encode_tt -{ 0 }-> 0 :|: 
   plus(z, z') -{ 1 }-> z :|: z' = 0, z >= 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 1 + z' }-> 1 + s :|: s >= 0, s <= z + (z' - 1), z' - 1 >= 0, z >= 0

Function symbols to be analyzed: {encode_and}, {encode_activate}, {encode_plus}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [0], size: O(1) [0]
  activate: runtime: O(1) [1], size: O(n^1) [z]
  and: runtime: O(1) [2], size: O(n^1) [z']
  encode_tt: runtime: O(1) [0], size: O(1) [1]
  plus: runtime: O(n^1) [1 + z'], size: O(n^1) [z + z']
  encArg: runtime: O(n^2) [1 + 3*z + 3*z^2], size: O(n^1) [5 + 3*z]

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

(59) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: encode_and
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 5 + 3*z'

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   and(z, z') -{ 2 }-> z' :|: z = 1, z' >= 0
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encArg(z) -{ 1 }-> X :|: z = 1 + 1, X >= 0, 1 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 4 + s10 + 3*x_165 + 3*x_165^2 + 3*x_232 + 3*x_232^2 }-> s12 :|: s9 >= 0, s9 <= 3 * x_165 + 5, s10 >= 0, s10 <= 3 * x_232 + 5, s11 >= 0, s11 <= s9 + s10, s12 >= 0, s12 <= s11, z = 1 + (1 + x_165 + x_232), x_232 >= 0, x_165 >= 0
   encArg(z) -{ 9 + -9*z + 3*z^2 }-> s15 :|: s13 >= 0, s13 <= 3 * (z - 2) + 5, s14 >= 0, s14 <= s13, s15 >= 0, s15 <= s14, z - 2 >= 0
   encArg(z) -{ 3 + s1 + 3*x_1 + 3*x_1^2 + 3*x_2 + 3*x_2^2 }-> s2 :|: s'' >= 0, s'' <= 3 * x_1 + 5, s1 >= 0, s1 <= 3 * x_2 + 5, s2 >= 0, s2 <= s'' + s1, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 4 + 3*x_1 + 3*x_1^2 + 3*x_2 + 3*x_2^2 }-> s27 :|: s25 >= 0, s25 <= 3 * x_1 + 5, s26 >= 0, s26 <= 3 * x_2 + 5, s27 >= 0, s27 <= s26, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 5 + 3*x_164 + 3*x_164^2 + 3*x_231 + 3*x_231^2 }-> s34 :|: s31 >= 0, s31 <= 3 * x_164 + 5, s32 >= 0, s32 <= 3 * x_231 + 5, s33 >= 0, s33 <= s32, s34 >= 0, s34 <= s33, x_164 >= 0, x_231 >= 0, z = 1 + (1 + x_164 + x_231)
   encArg(z) -{ 8 + -9*z + 3*z^2 }-> s8 :|: s7 >= 0, s7 <= 3 * (z - 2) + 5, s8 >= 0, s8 <= 1 + s7, z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 1 + -3*z + 3*z^2 }-> 1 + s' :|: s' >= 0, s' <= 3 * (z - 1) + 5, z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_activate(z) -{ 1 }-> X :|: z = 1, X >= 0, 1 = X
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 2 + -3*z + 3*z^2 }-> s17 :|: s16 >= 0, s16 <= 3 * (z - 1) + 5, s17 >= 0, s17 <= 1 + s16, z - 1 >= 0
   encode_activate(z) -{ 4 + s19 + 3*x_1101 + 3*x_1101^2 + 3*x_250 + 3*x_250^2 }-> s21 :|: s18 >= 0, s18 <= 3 * x_1101 + 5, s19 >= 0, s19 <= 3 * x_250 + 5, s20 >= 0, s20 <= s18 + s19, s21 >= 0, s21 <= s20, x_250 >= 0, x_1101 >= 0, z = 1 + x_1101 + x_250
   encode_activate(z) -{ 3 + -3*z + 3*z^2 }-> s24 :|: s22 >= 0, s22 <= 3 * (z - 1) + 5, s23 >= 0, s23 <= s22, s24 >= 0, s24 <= s23, z - 1 >= 0
   encode_activate(z) -{ 5 + 3*x_1100 + 3*x_1100^2 + 3*x_249 + 3*x_249^2 }-> s38 :|: s35 >= 0, s35 <= 3 * x_1100 + 5, s36 >= 0, s36 <= 3 * x_249 + 5, s37 >= 0, s37 <= s36, s38 >= 0, s38 <= s37, x_1100 >= 0, x_249 >= 0, z = 1 + x_1100 + x_249
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_and(z, z') -{ 4 + 3*z + 3*z^2 + 3*z' + 3*z'^2 }-> s30 :|: s28 >= 0, s28 <= 3 * z + 5, s29 >= 0, s29 <= 3 * z' + 5, s30 >= 0, s30 <= s29, z >= 0, z' >= 0
   encode_and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_plus(z, z') -{ 3 + s4 + 3*z + 3*z^2 + 3*z' + 3*z'^2 }-> s5 :|: s3 >= 0, s3 <= 3 * z + 5, s4 >= 0, s4 <= 3 * z' + 5, s5 >= 0, s5 <= s3 + s4, z >= 0, z' >= 0
   encode_plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 1 + 3*z + 3*z^2 }-> 1 + s6 :|: s6 >= 0, s6 <= 3 * z + 5, z >= 0
   encode_tt -{ 0 }-> 1 :|: 
   encode_tt -{ 0 }-> 0 :|: 
   plus(z, z') -{ 1 }-> z :|: z' = 0, z >= 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 1 + z' }-> 1 + s :|: s >= 0, s <= z + (z' - 1), z' - 1 >= 0, z >= 0

Function symbols to be analyzed: {encode_and}, {encode_activate}, {encode_plus}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [0], size: O(1) [0]
  activate: runtime: O(1) [1], size: O(n^1) [z]
  and: runtime: O(1) [2], size: O(n^1) [z']
  encode_tt: runtime: O(1) [0], size: O(1) [1]
  plus: runtime: O(n^1) [1 + z'], size: O(n^1) [z + z']
  encArg: runtime: O(n^2) [1 + 3*z + 3*z^2], size: O(n^1) [5 + 3*z]
  encode_and: runtime: ?, size: O(n^1) [5 + 3*z']

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

(61) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using KoAT for: encode_and
after applying outer abstraction to obtain an ITS,
resulting in: O(n^2) with polynomial bound: 4 + 3*z + 3*z^2 + 3*z' + 3*z'^2

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   and(z, z') -{ 2 }-> z' :|: z = 1, z' >= 0
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encArg(z) -{ 1 }-> X :|: z = 1 + 1, X >= 0, 1 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 4 + s10 + 3*x_165 + 3*x_165^2 + 3*x_232 + 3*x_232^2 }-> s12 :|: s9 >= 0, s9 <= 3 * x_165 + 5, s10 >= 0, s10 <= 3 * x_232 + 5, s11 >= 0, s11 <= s9 + s10, s12 >= 0, s12 <= s11, z = 1 + (1 + x_165 + x_232), x_232 >= 0, x_165 >= 0
   encArg(z) -{ 9 + -9*z + 3*z^2 }-> s15 :|: s13 >= 0, s13 <= 3 * (z - 2) + 5, s14 >= 0, s14 <= s13, s15 >= 0, s15 <= s14, z - 2 >= 0
   encArg(z) -{ 3 + s1 + 3*x_1 + 3*x_1^2 + 3*x_2 + 3*x_2^2 }-> s2 :|: s'' >= 0, s'' <= 3 * x_1 + 5, s1 >= 0, s1 <= 3 * x_2 + 5, s2 >= 0, s2 <= s'' + s1, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 4 + 3*x_1 + 3*x_1^2 + 3*x_2 + 3*x_2^2 }-> s27 :|: s25 >= 0, s25 <= 3 * x_1 + 5, s26 >= 0, s26 <= 3 * x_2 + 5, s27 >= 0, s27 <= s26, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 5 + 3*x_164 + 3*x_164^2 + 3*x_231 + 3*x_231^2 }-> s34 :|: s31 >= 0, s31 <= 3 * x_164 + 5, s32 >= 0, s32 <= 3 * x_231 + 5, s33 >= 0, s33 <= s32, s34 >= 0, s34 <= s33, x_164 >= 0, x_231 >= 0, z = 1 + (1 + x_164 + x_231)
   encArg(z) -{ 8 + -9*z + 3*z^2 }-> s8 :|: s7 >= 0, s7 <= 3 * (z - 2) + 5, s8 >= 0, s8 <= 1 + s7, z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 1 + -3*z + 3*z^2 }-> 1 + s' :|: s' >= 0, s' <= 3 * (z - 1) + 5, z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_activate(z) -{ 1 }-> X :|: z = 1, X >= 0, 1 = X
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 2 + -3*z + 3*z^2 }-> s17 :|: s16 >= 0, s16 <= 3 * (z - 1) + 5, s17 >= 0, s17 <= 1 + s16, z - 1 >= 0
   encode_activate(z) -{ 4 + s19 + 3*x_1101 + 3*x_1101^2 + 3*x_250 + 3*x_250^2 }-> s21 :|: s18 >= 0, s18 <= 3 * x_1101 + 5, s19 >= 0, s19 <= 3 * x_250 + 5, s20 >= 0, s20 <= s18 + s19, s21 >= 0, s21 <= s20, x_250 >= 0, x_1101 >= 0, z = 1 + x_1101 + x_250
   encode_activate(z) -{ 3 + -3*z + 3*z^2 }-> s24 :|: s22 >= 0, s22 <= 3 * (z - 1) + 5, s23 >= 0, s23 <= s22, s24 >= 0, s24 <= s23, z - 1 >= 0
   encode_activate(z) -{ 5 + 3*x_1100 + 3*x_1100^2 + 3*x_249 + 3*x_249^2 }-> s38 :|: s35 >= 0, s35 <= 3 * x_1100 + 5, s36 >= 0, s36 <= 3 * x_249 + 5, s37 >= 0, s37 <= s36, s38 >= 0, s38 <= s37, x_1100 >= 0, x_249 >= 0, z = 1 + x_1100 + x_249
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_and(z, z') -{ 4 + 3*z + 3*z^2 + 3*z' + 3*z'^2 }-> s30 :|: s28 >= 0, s28 <= 3 * z + 5, s29 >= 0, s29 <= 3 * z' + 5, s30 >= 0, s30 <= s29, z >= 0, z' >= 0
   encode_and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_plus(z, z') -{ 3 + s4 + 3*z + 3*z^2 + 3*z' + 3*z'^2 }-> s5 :|: s3 >= 0, s3 <= 3 * z + 5, s4 >= 0, s4 <= 3 * z' + 5, s5 >= 0, s5 <= s3 + s4, z >= 0, z' >= 0
   encode_plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 1 + 3*z + 3*z^2 }-> 1 + s6 :|: s6 >= 0, s6 <= 3 * z + 5, z >= 0
   encode_tt -{ 0 }-> 1 :|: 
   encode_tt -{ 0 }-> 0 :|: 
   plus(z, z') -{ 1 }-> z :|: z' = 0, z >= 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 1 + z' }-> 1 + s :|: s >= 0, s <= z + (z' - 1), z' - 1 >= 0, z >= 0

Function symbols to be analyzed: {encode_activate}, {encode_plus}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [0], size: O(1) [0]
  activate: runtime: O(1) [1], size: O(n^1) [z]
  and: runtime: O(1) [2], size: O(n^1) [z']
  encode_tt: runtime: O(1) [0], size: O(1) [1]
  plus: runtime: O(n^1) [1 + z'], size: O(n^1) [z + z']
  encArg: runtime: O(n^2) [1 + 3*z + 3*z^2], size: O(n^1) [5 + 3*z]
  encode_and: runtime: O(n^2) [4 + 3*z + 3*z^2 + 3*z' + 3*z'^2], size: O(n^1) [5 + 3*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:

   activate(z) -{ 1 }-> z :|: z >= 0
   and(z, z') -{ 2 }-> z' :|: z = 1, z' >= 0
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encArg(z) -{ 1 }-> X :|: z = 1 + 1, X >= 0, 1 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 4 + s10 + 3*x_165 + 3*x_165^2 + 3*x_232 + 3*x_232^2 }-> s12 :|: s9 >= 0, s9 <= 3 * x_165 + 5, s10 >= 0, s10 <= 3 * x_232 + 5, s11 >= 0, s11 <= s9 + s10, s12 >= 0, s12 <= s11, z = 1 + (1 + x_165 + x_232), x_232 >= 0, x_165 >= 0
   encArg(z) -{ 9 + -9*z + 3*z^2 }-> s15 :|: s13 >= 0, s13 <= 3 * (z - 2) + 5, s14 >= 0, s14 <= s13, s15 >= 0, s15 <= s14, z - 2 >= 0
   encArg(z) -{ 3 + s1 + 3*x_1 + 3*x_1^2 + 3*x_2 + 3*x_2^2 }-> s2 :|: s'' >= 0, s'' <= 3 * x_1 + 5, s1 >= 0, s1 <= 3 * x_2 + 5, s2 >= 0, s2 <= s'' + s1, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 4 + 3*x_1 + 3*x_1^2 + 3*x_2 + 3*x_2^2 }-> s27 :|: s25 >= 0, s25 <= 3 * x_1 + 5, s26 >= 0, s26 <= 3 * x_2 + 5, s27 >= 0, s27 <= s26, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 5 + 3*x_164 + 3*x_164^2 + 3*x_231 + 3*x_231^2 }-> s34 :|: s31 >= 0, s31 <= 3 * x_164 + 5, s32 >= 0, s32 <= 3 * x_231 + 5, s33 >= 0, s33 <= s32, s34 >= 0, s34 <= s33, x_164 >= 0, x_231 >= 0, z = 1 + (1 + x_164 + x_231)
   encArg(z) -{ 8 + -9*z + 3*z^2 }-> s8 :|: s7 >= 0, s7 <= 3 * (z - 2) + 5, s8 >= 0, s8 <= 1 + s7, z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 1 + -3*z + 3*z^2 }-> 1 + s' :|: s' >= 0, s' <= 3 * (z - 1) + 5, z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_activate(z) -{ 1 }-> X :|: z = 1, X >= 0, 1 = X
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 2 + -3*z + 3*z^2 }-> s17 :|: s16 >= 0, s16 <= 3 * (z - 1) + 5, s17 >= 0, s17 <= 1 + s16, z - 1 >= 0
   encode_activate(z) -{ 4 + s19 + 3*x_1101 + 3*x_1101^2 + 3*x_250 + 3*x_250^2 }-> s21 :|: s18 >= 0, s18 <= 3 * x_1101 + 5, s19 >= 0, s19 <= 3 * x_250 + 5, s20 >= 0, s20 <= s18 + s19, s21 >= 0, s21 <= s20, x_250 >= 0, x_1101 >= 0, z = 1 + x_1101 + x_250
   encode_activate(z) -{ 3 + -3*z + 3*z^2 }-> s24 :|: s22 >= 0, s22 <= 3 * (z - 1) + 5, s23 >= 0, s23 <= s22, s24 >= 0, s24 <= s23, z - 1 >= 0
   encode_activate(z) -{ 5 + 3*x_1100 + 3*x_1100^2 + 3*x_249 + 3*x_249^2 }-> s38 :|: s35 >= 0, s35 <= 3 * x_1100 + 5, s36 >= 0, s36 <= 3 * x_249 + 5, s37 >= 0, s37 <= s36, s38 >= 0, s38 <= s37, x_1100 >= 0, x_249 >= 0, z = 1 + x_1100 + x_249
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_and(z, z') -{ 4 + 3*z + 3*z^2 + 3*z' + 3*z'^2 }-> s30 :|: s28 >= 0, s28 <= 3 * z + 5, s29 >= 0, s29 <= 3 * z' + 5, s30 >= 0, s30 <= s29, z >= 0, z' >= 0
   encode_and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_plus(z, z') -{ 3 + s4 + 3*z + 3*z^2 + 3*z' + 3*z'^2 }-> s5 :|: s3 >= 0, s3 <= 3 * z + 5, s4 >= 0, s4 <= 3 * z' + 5, s5 >= 0, s5 <= s3 + s4, z >= 0, z' >= 0
   encode_plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 1 + 3*z + 3*z^2 }-> 1 + s6 :|: s6 >= 0, s6 <= 3 * z + 5, z >= 0
   encode_tt -{ 0 }-> 1 :|: 
   encode_tt -{ 0 }-> 0 :|: 
   plus(z, z') -{ 1 }-> z :|: z' = 0, z >= 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 1 + z' }-> 1 + s :|: s >= 0, s <= z + (z' - 1), z' - 1 >= 0, z >= 0

Function symbols to be analyzed: {encode_activate}, {encode_plus}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [0], size: O(1) [0]
  activate: runtime: O(1) [1], size: O(n^1) [z]
  and: runtime: O(1) [2], size: O(n^1) [z']
  encode_tt: runtime: O(1) [0], size: O(1) [1]
  plus: runtime: O(n^1) [1 + z'], size: O(n^1) [z + z']
  encArg: runtime: O(n^2) [1 + 3*z + 3*z^2], size: O(n^1) [5 + 3*z]
  encode_and: runtime: O(n^2) [4 + 3*z + 3*z^2 + 3*z' + 3*z'^2], size: O(n^1) [5 + 3*z']

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

(65) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: encode_activate
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 7 + 3*z

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   and(z, z') -{ 2 }-> z' :|: z = 1, z' >= 0
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encArg(z) -{ 1 }-> X :|: z = 1 + 1, X >= 0, 1 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 4 + s10 + 3*x_165 + 3*x_165^2 + 3*x_232 + 3*x_232^2 }-> s12 :|: s9 >= 0, s9 <= 3 * x_165 + 5, s10 >= 0, s10 <= 3 * x_232 + 5, s11 >= 0, s11 <= s9 + s10, s12 >= 0, s12 <= s11, z = 1 + (1 + x_165 + x_232), x_232 >= 0, x_165 >= 0
   encArg(z) -{ 9 + -9*z + 3*z^2 }-> s15 :|: s13 >= 0, s13 <= 3 * (z - 2) + 5, s14 >= 0, s14 <= s13, s15 >= 0, s15 <= s14, z - 2 >= 0
   encArg(z) -{ 3 + s1 + 3*x_1 + 3*x_1^2 + 3*x_2 + 3*x_2^2 }-> s2 :|: s'' >= 0, s'' <= 3 * x_1 + 5, s1 >= 0, s1 <= 3 * x_2 + 5, s2 >= 0, s2 <= s'' + s1, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 4 + 3*x_1 + 3*x_1^2 + 3*x_2 + 3*x_2^2 }-> s27 :|: s25 >= 0, s25 <= 3 * x_1 + 5, s26 >= 0, s26 <= 3 * x_2 + 5, s27 >= 0, s27 <= s26, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 5 + 3*x_164 + 3*x_164^2 + 3*x_231 + 3*x_231^2 }-> s34 :|: s31 >= 0, s31 <= 3 * x_164 + 5, s32 >= 0, s32 <= 3 * x_231 + 5, s33 >= 0, s33 <= s32, s34 >= 0, s34 <= s33, x_164 >= 0, x_231 >= 0, z = 1 + (1 + x_164 + x_231)
   encArg(z) -{ 8 + -9*z + 3*z^2 }-> s8 :|: s7 >= 0, s7 <= 3 * (z - 2) + 5, s8 >= 0, s8 <= 1 + s7, z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 1 + -3*z + 3*z^2 }-> 1 + s' :|: s' >= 0, s' <= 3 * (z - 1) + 5, z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_activate(z) -{ 1 }-> X :|: z = 1, X >= 0, 1 = X
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 2 + -3*z + 3*z^2 }-> s17 :|: s16 >= 0, s16 <= 3 * (z - 1) + 5, s17 >= 0, s17 <= 1 + s16, z - 1 >= 0
   encode_activate(z) -{ 4 + s19 + 3*x_1101 + 3*x_1101^2 + 3*x_250 + 3*x_250^2 }-> s21 :|: s18 >= 0, s18 <= 3 * x_1101 + 5, s19 >= 0, s19 <= 3 * x_250 + 5, s20 >= 0, s20 <= s18 + s19, s21 >= 0, s21 <= s20, x_250 >= 0, x_1101 >= 0, z = 1 + x_1101 + x_250
   encode_activate(z) -{ 3 + -3*z + 3*z^2 }-> s24 :|: s22 >= 0, s22 <= 3 * (z - 1) + 5, s23 >= 0, s23 <= s22, s24 >= 0, s24 <= s23, z - 1 >= 0
   encode_activate(z) -{ 5 + 3*x_1100 + 3*x_1100^2 + 3*x_249 + 3*x_249^2 }-> s38 :|: s35 >= 0, s35 <= 3 * x_1100 + 5, s36 >= 0, s36 <= 3 * x_249 + 5, s37 >= 0, s37 <= s36, s38 >= 0, s38 <= s37, x_1100 >= 0, x_249 >= 0, z = 1 + x_1100 + x_249
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_and(z, z') -{ 4 + 3*z + 3*z^2 + 3*z' + 3*z'^2 }-> s30 :|: s28 >= 0, s28 <= 3 * z + 5, s29 >= 0, s29 <= 3 * z' + 5, s30 >= 0, s30 <= s29, z >= 0, z' >= 0
   encode_and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_plus(z, z') -{ 3 + s4 + 3*z + 3*z^2 + 3*z' + 3*z'^2 }-> s5 :|: s3 >= 0, s3 <= 3 * z + 5, s4 >= 0, s4 <= 3 * z' + 5, s5 >= 0, s5 <= s3 + s4, z >= 0, z' >= 0
   encode_plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 1 + 3*z + 3*z^2 }-> 1 + s6 :|: s6 >= 0, s6 <= 3 * z + 5, z >= 0
   encode_tt -{ 0 }-> 1 :|: 
   encode_tt -{ 0 }-> 0 :|: 
   plus(z, z') -{ 1 }-> z :|: z' = 0, z >= 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 1 + z' }-> 1 + s :|: s >= 0, s <= z + (z' - 1), z' - 1 >= 0, z >= 0

Function symbols to be analyzed: {encode_activate}, {encode_plus}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [0], size: O(1) [0]
  activate: runtime: O(1) [1], size: O(n^1) [z]
  and: runtime: O(1) [2], size: O(n^1) [z']
  encode_tt: runtime: O(1) [0], size: O(1) [1]
  plus: runtime: O(n^1) [1 + z'], size: O(n^1) [z + z']
  encArg: runtime: O(n^2) [1 + 3*z + 3*z^2], size: O(n^1) [5 + 3*z]
  encode_and: runtime: O(n^2) [4 + 3*z + 3*z^2 + 3*z' + 3*z'^2], size: O(n^1) [5 + 3*z']
  encode_activate: runtime: ?, size: O(n^1) [7 + 3*z]

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

(67) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using KoAT for: encode_activate
after applying outer abstraction to obtain an ITS,
resulting in: O(n^2) with polynomial bound: 22 + 15*z + 18*z^2

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   and(z, z') -{ 2 }-> z' :|: z = 1, z' >= 0
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encArg(z) -{ 1 }-> X :|: z = 1 + 1, X >= 0, 1 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 4 + s10 + 3*x_165 + 3*x_165^2 + 3*x_232 + 3*x_232^2 }-> s12 :|: s9 >= 0, s9 <= 3 * x_165 + 5, s10 >= 0, s10 <= 3 * x_232 + 5, s11 >= 0, s11 <= s9 + s10, s12 >= 0, s12 <= s11, z = 1 + (1 + x_165 + x_232), x_232 >= 0, x_165 >= 0
   encArg(z) -{ 9 + -9*z + 3*z^2 }-> s15 :|: s13 >= 0, s13 <= 3 * (z - 2) + 5, s14 >= 0, s14 <= s13, s15 >= 0, s15 <= s14, z - 2 >= 0
   encArg(z) -{ 3 + s1 + 3*x_1 + 3*x_1^2 + 3*x_2 + 3*x_2^2 }-> s2 :|: s'' >= 0, s'' <= 3 * x_1 + 5, s1 >= 0, s1 <= 3 * x_2 + 5, s2 >= 0, s2 <= s'' + s1, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 4 + 3*x_1 + 3*x_1^2 + 3*x_2 + 3*x_2^2 }-> s27 :|: s25 >= 0, s25 <= 3 * x_1 + 5, s26 >= 0, s26 <= 3 * x_2 + 5, s27 >= 0, s27 <= s26, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 5 + 3*x_164 + 3*x_164^2 + 3*x_231 + 3*x_231^2 }-> s34 :|: s31 >= 0, s31 <= 3 * x_164 + 5, s32 >= 0, s32 <= 3 * x_231 + 5, s33 >= 0, s33 <= s32, s34 >= 0, s34 <= s33, x_164 >= 0, x_231 >= 0, z = 1 + (1 + x_164 + x_231)
   encArg(z) -{ 8 + -9*z + 3*z^2 }-> s8 :|: s7 >= 0, s7 <= 3 * (z - 2) + 5, s8 >= 0, s8 <= 1 + s7, z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 1 + -3*z + 3*z^2 }-> 1 + s' :|: s' >= 0, s' <= 3 * (z - 1) + 5, z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_activate(z) -{ 1 }-> X :|: z = 1, X >= 0, 1 = X
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 2 + -3*z + 3*z^2 }-> s17 :|: s16 >= 0, s16 <= 3 * (z - 1) + 5, s17 >= 0, s17 <= 1 + s16, z - 1 >= 0
   encode_activate(z) -{ 4 + s19 + 3*x_1101 + 3*x_1101^2 + 3*x_250 + 3*x_250^2 }-> s21 :|: s18 >= 0, s18 <= 3 * x_1101 + 5, s19 >= 0, s19 <= 3 * x_250 + 5, s20 >= 0, s20 <= s18 + s19, s21 >= 0, s21 <= s20, x_250 >= 0, x_1101 >= 0, z = 1 + x_1101 + x_250
   encode_activate(z) -{ 3 + -3*z + 3*z^2 }-> s24 :|: s22 >= 0, s22 <= 3 * (z - 1) + 5, s23 >= 0, s23 <= s22, s24 >= 0, s24 <= s23, z - 1 >= 0
   encode_activate(z) -{ 5 + 3*x_1100 + 3*x_1100^2 + 3*x_249 + 3*x_249^2 }-> s38 :|: s35 >= 0, s35 <= 3 * x_1100 + 5, s36 >= 0, s36 <= 3 * x_249 + 5, s37 >= 0, s37 <= s36, s38 >= 0, s38 <= s37, x_1100 >= 0, x_249 >= 0, z = 1 + x_1100 + x_249
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_and(z, z') -{ 4 + 3*z + 3*z^2 + 3*z' + 3*z'^2 }-> s30 :|: s28 >= 0, s28 <= 3 * z + 5, s29 >= 0, s29 <= 3 * z' + 5, s30 >= 0, s30 <= s29, z >= 0, z' >= 0
   encode_and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_plus(z, z') -{ 3 + s4 + 3*z + 3*z^2 + 3*z' + 3*z'^2 }-> s5 :|: s3 >= 0, s3 <= 3 * z + 5, s4 >= 0, s4 <= 3 * z' + 5, s5 >= 0, s5 <= s3 + s4, z >= 0, z' >= 0
   encode_plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 1 + 3*z + 3*z^2 }-> 1 + s6 :|: s6 >= 0, s6 <= 3 * z + 5, z >= 0
   encode_tt -{ 0 }-> 1 :|: 
   encode_tt -{ 0 }-> 0 :|: 
   plus(z, z') -{ 1 }-> z :|: z' = 0, z >= 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 1 + z' }-> 1 + s :|: s >= 0, s <= z + (z' - 1), z' - 1 >= 0, z >= 0

Function symbols to be analyzed: {encode_plus}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [0], size: O(1) [0]
  activate: runtime: O(1) [1], size: O(n^1) [z]
  and: runtime: O(1) [2], size: O(n^1) [z']
  encode_tt: runtime: O(1) [0], size: O(1) [1]
  plus: runtime: O(n^1) [1 + z'], size: O(n^1) [z + z']
  encArg: runtime: O(n^2) [1 + 3*z + 3*z^2], size: O(n^1) [5 + 3*z]
  encode_and: runtime: O(n^2) [4 + 3*z + 3*z^2 + 3*z' + 3*z'^2], size: O(n^1) [5 + 3*z']
  encode_activate: runtime: O(n^2) [22 + 15*z + 18*z^2], size: O(n^1) [7 + 3*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:

   activate(z) -{ 1 }-> z :|: z >= 0
   and(z, z') -{ 2 }-> z' :|: z = 1, z' >= 0
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encArg(z) -{ 1 }-> X :|: z = 1 + 1, X >= 0, 1 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 4 + s10 + 3*x_165 + 3*x_165^2 + 3*x_232 + 3*x_232^2 }-> s12 :|: s9 >= 0, s9 <= 3 * x_165 + 5, s10 >= 0, s10 <= 3 * x_232 + 5, s11 >= 0, s11 <= s9 + s10, s12 >= 0, s12 <= s11, z = 1 + (1 + x_165 + x_232), x_232 >= 0, x_165 >= 0
   encArg(z) -{ 9 + -9*z + 3*z^2 }-> s15 :|: s13 >= 0, s13 <= 3 * (z - 2) + 5, s14 >= 0, s14 <= s13, s15 >= 0, s15 <= s14, z - 2 >= 0
   encArg(z) -{ 3 + s1 + 3*x_1 + 3*x_1^2 + 3*x_2 + 3*x_2^2 }-> s2 :|: s'' >= 0, s'' <= 3 * x_1 + 5, s1 >= 0, s1 <= 3 * x_2 + 5, s2 >= 0, s2 <= s'' + s1, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 4 + 3*x_1 + 3*x_1^2 + 3*x_2 + 3*x_2^2 }-> s27 :|: s25 >= 0, s25 <= 3 * x_1 + 5, s26 >= 0, s26 <= 3 * x_2 + 5, s27 >= 0, s27 <= s26, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 5 + 3*x_164 + 3*x_164^2 + 3*x_231 + 3*x_231^2 }-> s34 :|: s31 >= 0, s31 <= 3 * x_164 + 5, s32 >= 0, s32 <= 3 * x_231 + 5, s33 >= 0, s33 <= s32, s34 >= 0, s34 <= s33, x_164 >= 0, x_231 >= 0, z = 1 + (1 + x_164 + x_231)
   encArg(z) -{ 8 + -9*z + 3*z^2 }-> s8 :|: s7 >= 0, s7 <= 3 * (z - 2) + 5, s8 >= 0, s8 <= 1 + s7, z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 1 + -3*z + 3*z^2 }-> 1 + s' :|: s' >= 0, s' <= 3 * (z - 1) + 5, z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_activate(z) -{ 1 }-> X :|: z = 1, X >= 0, 1 = X
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 2 + -3*z + 3*z^2 }-> s17 :|: s16 >= 0, s16 <= 3 * (z - 1) + 5, s17 >= 0, s17 <= 1 + s16, z - 1 >= 0
   encode_activate(z) -{ 4 + s19 + 3*x_1101 + 3*x_1101^2 + 3*x_250 + 3*x_250^2 }-> s21 :|: s18 >= 0, s18 <= 3 * x_1101 + 5, s19 >= 0, s19 <= 3 * x_250 + 5, s20 >= 0, s20 <= s18 + s19, s21 >= 0, s21 <= s20, x_250 >= 0, x_1101 >= 0, z = 1 + x_1101 + x_250
   encode_activate(z) -{ 3 + -3*z + 3*z^2 }-> s24 :|: s22 >= 0, s22 <= 3 * (z - 1) + 5, s23 >= 0, s23 <= s22, s24 >= 0, s24 <= s23, z - 1 >= 0
   encode_activate(z) -{ 5 + 3*x_1100 + 3*x_1100^2 + 3*x_249 + 3*x_249^2 }-> s38 :|: s35 >= 0, s35 <= 3 * x_1100 + 5, s36 >= 0, s36 <= 3 * x_249 + 5, s37 >= 0, s37 <= s36, s38 >= 0, s38 <= s37, x_1100 >= 0, x_249 >= 0, z = 1 + x_1100 + x_249
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_and(z, z') -{ 4 + 3*z + 3*z^2 + 3*z' + 3*z'^2 }-> s30 :|: s28 >= 0, s28 <= 3 * z + 5, s29 >= 0, s29 <= 3 * z' + 5, s30 >= 0, s30 <= s29, z >= 0, z' >= 0
   encode_and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_plus(z, z') -{ 3 + s4 + 3*z + 3*z^2 + 3*z' + 3*z'^2 }-> s5 :|: s3 >= 0, s3 <= 3 * z + 5, s4 >= 0, s4 <= 3 * z' + 5, s5 >= 0, s5 <= s3 + s4, z >= 0, z' >= 0
   encode_plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 1 + 3*z + 3*z^2 }-> 1 + s6 :|: s6 >= 0, s6 <= 3 * z + 5, z >= 0
   encode_tt -{ 0 }-> 1 :|: 
   encode_tt -{ 0 }-> 0 :|: 
   plus(z, z') -{ 1 }-> z :|: z' = 0, z >= 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 1 + z' }-> 1 + s :|: s >= 0, s <= z + (z' - 1), z' - 1 >= 0, z >= 0

Function symbols to be analyzed: {encode_plus}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [0], size: O(1) [0]
  activate: runtime: O(1) [1], size: O(n^1) [z]
  and: runtime: O(1) [2], size: O(n^1) [z']
  encode_tt: runtime: O(1) [0], size: O(1) [1]
  plus: runtime: O(n^1) [1 + z'], size: O(n^1) [z + z']
  encArg: runtime: O(n^2) [1 + 3*z + 3*z^2], size: O(n^1) [5 + 3*z]
  encode_and: runtime: O(n^2) [4 + 3*z + 3*z^2 + 3*z' + 3*z'^2], size: O(n^1) [5 + 3*z']
  encode_activate: runtime: O(n^2) [22 + 15*z + 18*z^2], size: O(n^1) [7 + 3*z]

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

(71) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: encode_plus
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 10 + 3*z + 3*z'

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   and(z, z') -{ 2 }-> z' :|: z = 1, z' >= 0
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encArg(z) -{ 1 }-> X :|: z = 1 + 1, X >= 0, 1 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 4 + s10 + 3*x_165 + 3*x_165^2 + 3*x_232 + 3*x_232^2 }-> s12 :|: s9 >= 0, s9 <= 3 * x_165 + 5, s10 >= 0, s10 <= 3 * x_232 + 5, s11 >= 0, s11 <= s9 + s10, s12 >= 0, s12 <= s11, z = 1 + (1 + x_165 + x_232), x_232 >= 0, x_165 >= 0
   encArg(z) -{ 9 + -9*z + 3*z^2 }-> s15 :|: s13 >= 0, s13 <= 3 * (z - 2) + 5, s14 >= 0, s14 <= s13, s15 >= 0, s15 <= s14, z - 2 >= 0
   encArg(z) -{ 3 + s1 + 3*x_1 + 3*x_1^2 + 3*x_2 + 3*x_2^2 }-> s2 :|: s'' >= 0, s'' <= 3 * x_1 + 5, s1 >= 0, s1 <= 3 * x_2 + 5, s2 >= 0, s2 <= s'' + s1, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 4 + 3*x_1 + 3*x_1^2 + 3*x_2 + 3*x_2^2 }-> s27 :|: s25 >= 0, s25 <= 3 * x_1 + 5, s26 >= 0, s26 <= 3 * x_2 + 5, s27 >= 0, s27 <= s26, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 5 + 3*x_164 + 3*x_164^2 + 3*x_231 + 3*x_231^2 }-> s34 :|: s31 >= 0, s31 <= 3 * x_164 + 5, s32 >= 0, s32 <= 3 * x_231 + 5, s33 >= 0, s33 <= s32, s34 >= 0, s34 <= s33, x_164 >= 0, x_231 >= 0, z = 1 + (1 + x_164 + x_231)
   encArg(z) -{ 8 + -9*z + 3*z^2 }-> s8 :|: s7 >= 0, s7 <= 3 * (z - 2) + 5, s8 >= 0, s8 <= 1 + s7, z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 1 + -3*z + 3*z^2 }-> 1 + s' :|: s' >= 0, s' <= 3 * (z - 1) + 5, z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_activate(z) -{ 1 }-> X :|: z = 1, X >= 0, 1 = X
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 2 + -3*z + 3*z^2 }-> s17 :|: s16 >= 0, s16 <= 3 * (z - 1) + 5, s17 >= 0, s17 <= 1 + s16, z - 1 >= 0
   encode_activate(z) -{ 4 + s19 + 3*x_1101 + 3*x_1101^2 + 3*x_250 + 3*x_250^2 }-> s21 :|: s18 >= 0, s18 <= 3 * x_1101 + 5, s19 >= 0, s19 <= 3 * x_250 + 5, s20 >= 0, s20 <= s18 + s19, s21 >= 0, s21 <= s20, x_250 >= 0, x_1101 >= 0, z = 1 + x_1101 + x_250
   encode_activate(z) -{ 3 + -3*z + 3*z^2 }-> s24 :|: s22 >= 0, s22 <= 3 * (z - 1) + 5, s23 >= 0, s23 <= s22, s24 >= 0, s24 <= s23, z - 1 >= 0
   encode_activate(z) -{ 5 + 3*x_1100 + 3*x_1100^2 + 3*x_249 + 3*x_249^2 }-> s38 :|: s35 >= 0, s35 <= 3 * x_1100 + 5, s36 >= 0, s36 <= 3 * x_249 + 5, s37 >= 0, s37 <= s36, s38 >= 0, s38 <= s37, x_1100 >= 0, x_249 >= 0, z = 1 + x_1100 + x_249
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_and(z, z') -{ 4 + 3*z + 3*z^2 + 3*z' + 3*z'^2 }-> s30 :|: s28 >= 0, s28 <= 3 * z + 5, s29 >= 0, s29 <= 3 * z' + 5, s30 >= 0, s30 <= s29, z >= 0, z' >= 0
   encode_and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_plus(z, z') -{ 3 + s4 + 3*z + 3*z^2 + 3*z' + 3*z'^2 }-> s5 :|: s3 >= 0, s3 <= 3 * z + 5, s4 >= 0, s4 <= 3 * z' + 5, s5 >= 0, s5 <= s3 + s4, z >= 0, z' >= 0
   encode_plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 1 + 3*z + 3*z^2 }-> 1 + s6 :|: s6 >= 0, s6 <= 3 * z + 5, z >= 0
   encode_tt -{ 0 }-> 1 :|: 
   encode_tt -{ 0 }-> 0 :|: 
   plus(z, z') -{ 1 }-> z :|: z' = 0, z >= 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 1 + z' }-> 1 + s :|: s >= 0, s <= z + (z' - 1), z' - 1 >= 0, z >= 0

Function symbols to be analyzed: {encode_plus}, {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [0], size: O(1) [0]
  activate: runtime: O(1) [1], size: O(n^1) [z]
  and: runtime: O(1) [2], size: O(n^1) [z']
  encode_tt: runtime: O(1) [0], size: O(1) [1]
  plus: runtime: O(n^1) [1 + z'], size: O(n^1) [z + z']
  encArg: runtime: O(n^2) [1 + 3*z + 3*z^2], size: O(n^1) [5 + 3*z]
  encode_and: runtime: O(n^2) [4 + 3*z + 3*z^2 + 3*z' + 3*z'^2], size: O(n^1) [5 + 3*z']
  encode_activate: runtime: O(n^2) [22 + 15*z + 18*z^2], size: O(n^1) [7 + 3*z]
  encode_plus: runtime: ?, size: O(n^1) [10 + 3*z + 3*z']

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

(73) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using KoAT for: encode_plus
after applying outer abstraction to obtain an ITS,
resulting in: O(n^2) with polynomial bound: 8 + 3*z + 3*z^2 + 6*z' + 3*z'^2

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   and(z, z') -{ 2 }-> z' :|: z = 1, z' >= 0
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encArg(z) -{ 1 }-> X :|: z = 1 + 1, X >= 0, 1 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 4 + s10 + 3*x_165 + 3*x_165^2 + 3*x_232 + 3*x_232^2 }-> s12 :|: s9 >= 0, s9 <= 3 * x_165 + 5, s10 >= 0, s10 <= 3 * x_232 + 5, s11 >= 0, s11 <= s9 + s10, s12 >= 0, s12 <= s11, z = 1 + (1 + x_165 + x_232), x_232 >= 0, x_165 >= 0
   encArg(z) -{ 9 + -9*z + 3*z^2 }-> s15 :|: s13 >= 0, s13 <= 3 * (z - 2) + 5, s14 >= 0, s14 <= s13, s15 >= 0, s15 <= s14, z - 2 >= 0
   encArg(z) -{ 3 + s1 + 3*x_1 + 3*x_1^2 + 3*x_2 + 3*x_2^2 }-> s2 :|: s'' >= 0, s'' <= 3 * x_1 + 5, s1 >= 0, s1 <= 3 * x_2 + 5, s2 >= 0, s2 <= s'' + s1, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 4 + 3*x_1 + 3*x_1^2 + 3*x_2 + 3*x_2^2 }-> s27 :|: s25 >= 0, s25 <= 3 * x_1 + 5, s26 >= 0, s26 <= 3 * x_2 + 5, s27 >= 0, s27 <= s26, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 5 + 3*x_164 + 3*x_164^2 + 3*x_231 + 3*x_231^2 }-> s34 :|: s31 >= 0, s31 <= 3 * x_164 + 5, s32 >= 0, s32 <= 3 * x_231 + 5, s33 >= 0, s33 <= s32, s34 >= 0, s34 <= s33, x_164 >= 0, x_231 >= 0, z = 1 + (1 + x_164 + x_231)
   encArg(z) -{ 8 + -9*z + 3*z^2 }-> s8 :|: s7 >= 0, s7 <= 3 * (z - 2) + 5, s8 >= 0, s8 <= 1 + s7, z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 1 + -3*z + 3*z^2 }-> 1 + s' :|: s' >= 0, s' <= 3 * (z - 1) + 5, z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_activate(z) -{ 1 }-> X :|: z = 1, X >= 0, 1 = X
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 2 + -3*z + 3*z^2 }-> s17 :|: s16 >= 0, s16 <= 3 * (z - 1) + 5, s17 >= 0, s17 <= 1 + s16, z - 1 >= 0
   encode_activate(z) -{ 4 + s19 + 3*x_1101 + 3*x_1101^2 + 3*x_250 + 3*x_250^2 }-> s21 :|: s18 >= 0, s18 <= 3 * x_1101 + 5, s19 >= 0, s19 <= 3 * x_250 + 5, s20 >= 0, s20 <= s18 + s19, s21 >= 0, s21 <= s20, x_250 >= 0, x_1101 >= 0, z = 1 + x_1101 + x_250
   encode_activate(z) -{ 3 + -3*z + 3*z^2 }-> s24 :|: s22 >= 0, s22 <= 3 * (z - 1) + 5, s23 >= 0, s23 <= s22, s24 >= 0, s24 <= s23, z - 1 >= 0
   encode_activate(z) -{ 5 + 3*x_1100 + 3*x_1100^2 + 3*x_249 + 3*x_249^2 }-> s38 :|: s35 >= 0, s35 <= 3 * x_1100 + 5, s36 >= 0, s36 <= 3 * x_249 + 5, s37 >= 0, s37 <= s36, s38 >= 0, s38 <= s37, x_1100 >= 0, x_249 >= 0, z = 1 + x_1100 + x_249
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_and(z, z') -{ 4 + 3*z + 3*z^2 + 3*z' + 3*z'^2 }-> s30 :|: s28 >= 0, s28 <= 3 * z + 5, s29 >= 0, s29 <= 3 * z' + 5, s30 >= 0, s30 <= s29, z >= 0, z' >= 0
   encode_and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_plus(z, z') -{ 3 + s4 + 3*z + 3*z^2 + 3*z' + 3*z'^2 }-> s5 :|: s3 >= 0, s3 <= 3 * z + 5, s4 >= 0, s4 <= 3 * z' + 5, s5 >= 0, s5 <= s3 + s4, z >= 0, z' >= 0
   encode_plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 1 + 3*z + 3*z^2 }-> 1 + s6 :|: s6 >= 0, s6 <= 3 * z + 5, z >= 0
   encode_tt -{ 0 }-> 1 :|: 
   encode_tt -{ 0 }-> 0 :|: 
   plus(z, z') -{ 1 }-> z :|: z' = 0, z >= 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 1 + z' }-> 1 + s :|: s >= 0, s <= z + (z' - 1), z' - 1 >= 0, z >= 0

Function symbols to be analyzed: {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [0], size: O(1) [0]
  activate: runtime: O(1) [1], size: O(n^1) [z]
  and: runtime: O(1) [2], size: O(n^1) [z']
  encode_tt: runtime: O(1) [0], size: O(1) [1]
  plus: runtime: O(n^1) [1 + z'], size: O(n^1) [z + z']
  encArg: runtime: O(n^2) [1 + 3*z + 3*z^2], size: O(n^1) [5 + 3*z]
  encode_and: runtime: O(n^2) [4 + 3*z + 3*z^2 + 3*z' + 3*z'^2], size: O(n^1) [5 + 3*z']
  encode_activate: runtime: O(n^2) [22 + 15*z + 18*z^2], size: O(n^1) [7 + 3*z]
  encode_plus: runtime: O(n^2) [8 + 3*z + 3*z^2 + 6*z' + 3*z'^2], size: O(n^1) [10 + 3*z + 3*z']

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

(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:

   activate(z) -{ 1 }-> z :|: z >= 0
   and(z, z') -{ 2 }-> z' :|: z = 1, z' >= 0
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encArg(z) -{ 1 }-> X :|: z = 1 + 1, X >= 0, 1 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 4 + s10 + 3*x_165 + 3*x_165^2 + 3*x_232 + 3*x_232^2 }-> s12 :|: s9 >= 0, s9 <= 3 * x_165 + 5, s10 >= 0, s10 <= 3 * x_232 + 5, s11 >= 0, s11 <= s9 + s10, s12 >= 0, s12 <= s11, z = 1 + (1 + x_165 + x_232), x_232 >= 0, x_165 >= 0
   encArg(z) -{ 9 + -9*z + 3*z^2 }-> s15 :|: s13 >= 0, s13 <= 3 * (z - 2) + 5, s14 >= 0, s14 <= s13, s15 >= 0, s15 <= s14, z - 2 >= 0
   encArg(z) -{ 3 + s1 + 3*x_1 + 3*x_1^2 + 3*x_2 + 3*x_2^2 }-> s2 :|: s'' >= 0, s'' <= 3 * x_1 + 5, s1 >= 0, s1 <= 3 * x_2 + 5, s2 >= 0, s2 <= s'' + s1, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 4 + 3*x_1 + 3*x_1^2 + 3*x_2 + 3*x_2^2 }-> s27 :|: s25 >= 0, s25 <= 3 * x_1 + 5, s26 >= 0, s26 <= 3 * x_2 + 5, s27 >= 0, s27 <= s26, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 5 + 3*x_164 + 3*x_164^2 + 3*x_231 + 3*x_231^2 }-> s34 :|: s31 >= 0, s31 <= 3 * x_164 + 5, s32 >= 0, s32 <= 3 * x_231 + 5, s33 >= 0, s33 <= s32, s34 >= 0, s34 <= s33, x_164 >= 0, x_231 >= 0, z = 1 + (1 + x_164 + x_231)
   encArg(z) -{ 8 + -9*z + 3*z^2 }-> s8 :|: s7 >= 0, s7 <= 3 * (z - 2) + 5, s8 >= 0, s8 <= 1 + s7, z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 1 + -3*z + 3*z^2 }-> 1 + s' :|: s' >= 0, s' <= 3 * (z - 1) + 5, z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_activate(z) -{ 1 }-> X :|: z = 1, X >= 0, 1 = X
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 2 + -3*z + 3*z^2 }-> s17 :|: s16 >= 0, s16 <= 3 * (z - 1) + 5, s17 >= 0, s17 <= 1 + s16, z - 1 >= 0
   encode_activate(z) -{ 4 + s19 + 3*x_1101 + 3*x_1101^2 + 3*x_250 + 3*x_250^2 }-> s21 :|: s18 >= 0, s18 <= 3 * x_1101 + 5, s19 >= 0, s19 <= 3 * x_250 + 5, s20 >= 0, s20 <= s18 + s19, s21 >= 0, s21 <= s20, x_250 >= 0, x_1101 >= 0, z = 1 + x_1101 + x_250
   encode_activate(z) -{ 3 + -3*z + 3*z^2 }-> s24 :|: s22 >= 0, s22 <= 3 * (z - 1) + 5, s23 >= 0, s23 <= s22, s24 >= 0, s24 <= s23, z - 1 >= 0
   encode_activate(z) -{ 5 + 3*x_1100 + 3*x_1100^2 + 3*x_249 + 3*x_249^2 }-> s38 :|: s35 >= 0, s35 <= 3 * x_1100 + 5, s36 >= 0, s36 <= 3 * x_249 + 5, s37 >= 0, s37 <= s36, s38 >= 0, s38 <= s37, x_1100 >= 0, x_249 >= 0, z = 1 + x_1100 + x_249
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_and(z, z') -{ 4 + 3*z + 3*z^2 + 3*z' + 3*z'^2 }-> s30 :|: s28 >= 0, s28 <= 3 * z + 5, s29 >= 0, s29 <= 3 * z' + 5, s30 >= 0, s30 <= s29, z >= 0, z' >= 0
   encode_and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_plus(z, z') -{ 3 + s4 + 3*z + 3*z^2 + 3*z' + 3*z'^2 }-> s5 :|: s3 >= 0, s3 <= 3 * z + 5, s4 >= 0, s4 <= 3 * z' + 5, s5 >= 0, s5 <= s3 + s4, z >= 0, z' >= 0
   encode_plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 1 + 3*z + 3*z^2 }-> 1 + s6 :|: s6 >= 0, s6 <= 3 * z + 5, z >= 0
   encode_tt -{ 0 }-> 1 :|: 
   encode_tt -{ 0 }-> 0 :|: 
   plus(z, z') -{ 1 }-> z :|: z' = 0, z >= 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 1 + z' }-> 1 + s :|: s >= 0, s <= z + (z' - 1), z' - 1 >= 0, z >= 0

Function symbols to be analyzed: {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [0], size: O(1) [0]
  activate: runtime: O(1) [1], size: O(n^1) [z]
  and: runtime: O(1) [2], size: O(n^1) [z']
  encode_tt: runtime: O(1) [0], size: O(1) [1]
  plus: runtime: O(n^1) [1 + z'], size: O(n^1) [z + z']
  encArg: runtime: O(n^2) [1 + 3*z + 3*z^2], size: O(n^1) [5 + 3*z]
  encode_and: runtime: O(n^2) [4 + 3*z + 3*z^2 + 3*z' + 3*z'^2], size: O(n^1) [5 + 3*z']
  encode_activate: runtime: O(n^2) [22 + 15*z + 18*z^2], size: O(n^1) [7 + 3*z]
  encode_plus: runtime: O(n^2) [8 + 3*z + 3*z^2 + 6*z' + 3*z'^2], size: O(n^1) [10 + 3*z + 3*z']

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

(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: 6 + 3*z

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   and(z, z') -{ 2 }-> z' :|: z = 1, z' >= 0
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encArg(z) -{ 1 }-> X :|: z = 1 + 1, X >= 0, 1 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 4 + s10 + 3*x_165 + 3*x_165^2 + 3*x_232 + 3*x_232^2 }-> s12 :|: s9 >= 0, s9 <= 3 * x_165 + 5, s10 >= 0, s10 <= 3 * x_232 + 5, s11 >= 0, s11 <= s9 + s10, s12 >= 0, s12 <= s11, z = 1 + (1 + x_165 + x_232), x_232 >= 0, x_165 >= 0
   encArg(z) -{ 9 + -9*z + 3*z^2 }-> s15 :|: s13 >= 0, s13 <= 3 * (z - 2) + 5, s14 >= 0, s14 <= s13, s15 >= 0, s15 <= s14, z - 2 >= 0
   encArg(z) -{ 3 + s1 + 3*x_1 + 3*x_1^2 + 3*x_2 + 3*x_2^2 }-> s2 :|: s'' >= 0, s'' <= 3 * x_1 + 5, s1 >= 0, s1 <= 3 * x_2 + 5, s2 >= 0, s2 <= s'' + s1, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 4 + 3*x_1 + 3*x_1^2 + 3*x_2 + 3*x_2^2 }-> s27 :|: s25 >= 0, s25 <= 3 * x_1 + 5, s26 >= 0, s26 <= 3 * x_2 + 5, s27 >= 0, s27 <= s26, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 5 + 3*x_164 + 3*x_164^2 + 3*x_231 + 3*x_231^2 }-> s34 :|: s31 >= 0, s31 <= 3 * x_164 + 5, s32 >= 0, s32 <= 3 * x_231 + 5, s33 >= 0, s33 <= s32, s34 >= 0, s34 <= s33, x_164 >= 0, x_231 >= 0, z = 1 + (1 + x_164 + x_231)
   encArg(z) -{ 8 + -9*z + 3*z^2 }-> s8 :|: s7 >= 0, s7 <= 3 * (z - 2) + 5, s8 >= 0, s8 <= 1 + s7, z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 1 + -3*z + 3*z^2 }-> 1 + s' :|: s' >= 0, s' <= 3 * (z - 1) + 5, z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_activate(z) -{ 1 }-> X :|: z = 1, X >= 0, 1 = X
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 2 + -3*z + 3*z^2 }-> s17 :|: s16 >= 0, s16 <= 3 * (z - 1) + 5, s17 >= 0, s17 <= 1 + s16, z - 1 >= 0
   encode_activate(z) -{ 4 + s19 + 3*x_1101 + 3*x_1101^2 + 3*x_250 + 3*x_250^2 }-> s21 :|: s18 >= 0, s18 <= 3 * x_1101 + 5, s19 >= 0, s19 <= 3 * x_250 + 5, s20 >= 0, s20 <= s18 + s19, s21 >= 0, s21 <= s20, x_250 >= 0, x_1101 >= 0, z = 1 + x_1101 + x_250
   encode_activate(z) -{ 3 + -3*z + 3*z^2 }-> s24 :|: s22 >= 0, s22 <= 3 * (z - 1) + 5, s23 >= 0, s23 <= s22, s24 >= 0, s24 <= s23, z - 1 >= 0
   encode_activate(z) -{ 5 + 3*x_1100 + 3*x_1100^2 + 3*x_249 + 3*x_249^2 }-> s38 :|: s35 >= 0, s35 <= 3 * x_1100 + 5, s36 >= 0, s36 <= 3 * x_249 + 5, s37 >= 0, s37 <= s36, s38 >= 0, s38 <= s37, x_1100 >= 0, x_249 >= 0, z = 1 + x_1100 + x_249
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_and(z, z') -{ 4 + 3*z + 3*z^2 + 3*z' + 3*z'^2 }-> s30 :|: s28 >= 0, s28 <= 3 * z + 5, s29 >= 0, s29 <= 3 * z' + 5, s30 >= 0, s30 <= s29, z >= 0, z' >= 0
   encode_and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_plus(z, z') -{ 3 + s4 + 3*z + 3*z^2 + 3*z' + 3*z'^2 }-> s5 :|: s3 >= 0, s3 <= 3 * z + 5, s4 >= 0, s4 <= 3 * z' + 5, s5 >= 0, s5 <= s3 + s4, z >= 0, z' >= 0
   encode_plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 1 + 3*z + 3*z^2 }-> 1 + s6 :|: s6 >= 0, s6 <= 3 * z + 5, z >= 0
   encode_tt -{ 0 }-> 1 :|: 
   encode_tt -{ 0 }-> 0 :|: 
   plus(z, z') -{ 1 }-> z :|: z' = 0, z >= 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 1 + z' }-> 1 + s :|: s >= 0, s <= z + (z' - 1), z' - 1 >= 0, z >= 0

Function symbols to be analyzed: {encode_s}
Previous analysis results are:
  encode_0: runtime: O(1) [0], size: O(1) [0]
  activate: runtime: O(1) [1], size: O(n^1) [z]
  and: runtime: O(1) [2], size: O(n^1) [z']
  encode_tt: runtime: O(1) [0], size: O(1) [1]
  plus: runtime: O(n^1) [1 + z'], size: O(n^1) [z + z']
  encArg: runtime: O(n^2) [1 + 3*z + 3*z^2], size: O(n^1) [5 + 3*z]
  encode_and: runtime: O(n^2) [4 + 3*z + 3*z^2 + 3*z' + 3*z'^2], size: O(n^1) [5 + 3*z']
  encode_activate: runtime: O(n^2) [22 + 15*z + 18*z^2], size: O(n^1) [7 + 3*z]
  encode_plus: runtime: O(n^2) [8 + 3*z + 3*z^2 + 6*z' + 3*z'^2], size: O(n^1) [10 + 3*z + 3*z']
  encode_s: runtime: ?, size: O(n^1) [6 + 3*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^2) with polynomial bound: 1 + 3*z + 3*z^2

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   and(z, z') -{ 2 }-> z' :|: z = 1, z' >= 0
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encArg(z) -{ 1 }-> X :|: z = 1 + 1, X >= 0, 1 = X
   encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X
   encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X
   encArg(z) -{ 4 + s10 + 3*x_165 + 3*x_165^2 + 3*x_232 + 3*x_232^2 }-> s12 :|: s9 >= 0, s9 <= 3 * x_165 + 5, s10 >= 0, s10 <= 3 * x_232 + 5, s11 >= 0, s11 <= s9 + s10, s12 >= 0, s12 <= s11, z = 1 + (1 + x_165 + x_232), x_232 >= 0, x_165 >= 0
   encArg(z) -{ 9 + -9*z + 3*z^2 }-> s15 :|: s13 >= 0, s13 <= 3 * (z - 2) + 5, s14 >= 0, s14 <= s13, s15 >= 0, s15 <= s14, z - 2 >= 0
   encArg(z) -{ 3 + s1 + 3*x_1 + 3*x_1^2 + 3*x_2 + 3*x_2^2 }-> s2 :|: s'' >= 0, s'' <= 3 * x_1 + 5, s1 >= 0, s1 <= 3 * x_2 + 5, s2 >= 0, s2 <= s'' + s1, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 4 + 3*x_1 + 3*x_1^2 + 3*x_2 + 3*x_2^2 }-> s27 :|: s25 >= 0, s25 <= 3 * x_1 + 5, s26 >= 0, s26 <= 3 * x_2 + 5, s27 >= 0, s27 <= s26, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 5 + 3*x_164 + 3*x_164^2 + 3*x_231 + 3*x_231^2 }-> s34 :|: s31 >= 0, s31 <= 3 * x_164 + 5, s32 >= 0, s32 <= 3 * x_231 + 5, s33 >= 0, s33 <= s32, s34 >= 0, s34 <= s33, x_164 >= 0, x_231 >= 0, z = 1 + (1 + x_164 + x_231)
   encArg(z) -{ 8 + -9*z + 3*z^2 }-> s8 :|: s7 >= 0, s7 <= 3 * (z - 2) + 5, s8 >= 0, s8 <= 1 + s7, z - 2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 1 + -3*z + 3*z^2 }-> 1 + s' :|: s' >= 0, s' <= 3 * (z - 1) + 5, z - 1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_activate(z) -{ 1 }-> X :|: z = 1, X >= 0, 1 = X
   encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X
   encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X
   encode_activate(z) -{ 2 + -3*z + 3*z^2 }-> s17 :|: s16 >= 0, s16 <= 3 * (z - 1) + 5, s17 >= 0, s17 <= 1 + s16, z - 1 >= 0
   encode_activate(z) -{ 4 + s19 + 3*x_1101 + 3*x_1101^2 + 3*x_250 + 3*x_250^2 }-> s21 :|: s18 >= 0, s18 <= 3 * x_1101 + 5, s19 >= 0, s19 <= 3 * x_250 + 5, s20 >= 0, s20 <= s18 + s19, s21 >= 0, s21 <= s20, x_250 >= 0, x_1101 >= 0, z = 1 + x_1101 + x_250
   encode_activate(z) -{ 3 + -3*z + 3*z^2 }-> s24 :|: s22 >= 0, s22 <= 3 * (z - 1) + 5, s23 >= 0, s23 <= s22, s24 >= 0, s24 <= s23, z - 1 >= 0
   encode_activate(z) -{ 5 + 3*x_1100 + 3*x_1100^2 + 3*x_249 + 3*x_249^2 }-> s38 :|: s35 >= 0, s35 <= 3 * x_1100 + 5, s36 >= 0, s36 <= 3 * x_249 + 5, s37 >= 0, s37 <= s36, s38 >= 0, s38 <= s37, x_1100 >= 0, x_249 >= 0, z = 1 + x_1100 + x_249
   encode_activate(z) -{ 0 }-> 0 :|: z >= 0
   encode_and(z, z') -{ 4 + 3*z + 3*z^2 + 3*z' + 3*z'^2 }-> s30 :|: s28 >= 0, s28 <= 3 * z + 5, s29 >= 0, s29 <= 3 * z' + 5, s30 >= 0, s30 <= s29, z >= 0, z' >= 0
   encode_and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_plus(z, z') -{ 3 + s4 + 3*z + 3*z^2 + 3*z' + 3*z'^2 }-> s5 :|: s3 >= 0, s3 <= 3 * z + 5, s4 >= 0, s4 <= 3 * z' + 5, s5 >= 0, s5 <= s3 + s4, z >= 0, z' >= 0
   encode_plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_s(z) -{ 0 }-> 0 :|: z >= 0
   encode_s(z) -{ 1 + 3*z + 3*z^2 }-> 1 + s6 :|: s6 >= 0, s6 <= 3 * z + 5, z >= 0
   encode_tt -{ 0 }-> 1 :|: 
   encode_tt -{ 0 }-> 0 :|: 
   plus(z, z') -{ 1 }-> z :|: z' = 0, z >= 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 1 + z' }-> 1 + s :|: s >= 0, s <= z + (z' - 1), z' - 1 >= 0, z >= 0

Function symbols to be analyzed: 
Previous analysis results are:
  encode_0: runtime: O(1) [0], size: O(1) [0]
  activate: runtime: O(1) [1], size: O(n^1) [z]
  and: runtime: O(1) [2], size: O(n^1) [z']
  encode_tt: runtime: O(1) [0], size: O(1) [1]
  plus: runtime: O(n^1) [1 + z'], size: O(n^1) [z + z']
  encArg: runtime: O(n^2) [1 + 3*z + 3*z^2], size: O(n^1) [5 + 3*z]
  encode_and: runtime: O(n^2) [4 + 3*z + 3*z^2 + 3*z' + 3*z'^2], size: O(n^1) [5 + 3*z']
  encode_activate: runtime: O(n^2) [22 + 15*z + 18*z^2], size: O(n^1) [7 + 3*z]
  encode_plus: runtime: O(n^2) [8 + 3*z + 3*z^2 + 6*z' + 3*z'^2], size: O(n^1) [10 + 3*z + 3*z']
  encode_s: runtime: O(n^2) [1 + 3*z + 3*z^2], size: O(n^1) [6 + 3*z]

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

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

(82)
BOUNDS(1, n^2)

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

(83) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
Transformed a relative TRS into a decreasing-loop problem.
----------------------------------------

(84)
Obligation:
Analyzing the following TRS for decreasing loops:

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


The TRS R consists of the following rules:

   and(tt, X) -> activate(X)
   plus(N, 0) -> N
   plus(N, s(M)) -> s(plus(N, M))
   activate(X) -> X

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

   encArg(tt) -> tt
   encArg(0) -> 0
   encArg(s(x_1)) -> s(encArg(x_1))
   encArg(cons_and(x_1, x_2)) -> and(encArg(x_1), encArg(x_2))
   encArg(cons_plus(x_1, x_2)) -> plus(encArg(x_1), encArg(x_2))
   encArg(cons_activate(x_1)) -> activate(encArg(x_1))
   encode_and(x_1, x_2) -> and(encArg(x_1), encArg(x_2))
   encode_tt -> tt
   encode_activate(x_1) -> activate(encArg(x_1))
   encode_plus(x_1, x_2) -> plus(encArg(x_1), encArg(x_2))
   encode_0 -> 0
   encode_s(x_1) -> s(encArg(x_1))

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

(85) DecreasingLoopProof (LOWER BOUND(ID))
The following loop(s) give(s) rise to the lower bound Omega(n^1):

The rewrite sequence

plus(N, s(M)) ->^+ s(plus(N, M))

gives rise to a decreasing loop by considering the right hand sides subterm at position [0].

The pumping substitution is [M / s(M)].

The result substitution is [ ].




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

(86)
Complex Obligation (BEST)

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

(87)
Obligation:
Proved the lower bound n^1 for the following obligation:

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


The TRS R consists of the following rules:

   and(tt, X) -> activate(X)
   plus(N, 0) -> N
   plus(N, s(M)) -> s(plus(N, M))
   activate(X) -> X

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

   encArg(tt) -> tt
   encArg(0) -> 0
   encArg(s(x_1)) -> s(encArg(x_1))
   encArg(cons_and(x_1, x_2)) -> and(encArg(x_1), encArg(x_2))
   encArg(cons_plus(x_1, x_2)) -> plus(encArg(x_1), encArg(x_2))
   encArg(cons_activate(x_1)) -> activate(encArg(x_1))
   encode_and(x_1, x_2) -> and(encArg(x_1), encArg(x_2))
   encode_tt -> tt
   encode_activate(x_1) -> activate(encArg(x_1))
   encode_plus(x_1, x_2) -> plus(encArg(x_1), encArg(x_2))
   encode_0 -> 0
   encode_s(x_1) -> s(encArg(x_1))

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

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

(89)
BOUNDS(n^1, INF)

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

(90)
Obligation:
Analyzing the following TRS for decreasing loops:

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


The TRS R consists of the following rules:

   and(tt, X) -> activate(X)
   plus(N, 0) -> N
   plus(N, s(M)) -> s(plus(N, M))
   activate(X) -> X

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

   encArg(tt) -> tt
   encArg(0) -> 0
   encArg(s(x_1)) -> s(encArg(x_1))
   encArg(cons_and(x_1, x_2)) -> and(encArg(x_1), encArg(x_2))
   encArg(cons_plus(x_1, x_2)) -> plus(encArg(x_1), encArg(x_2))
   encArg(cons_activate(x_1)) -> activate(encArg(x_1))
   encode_and(x_1, x_2) -> and(encArg(x_1), encArg(x_2))
   encode_tt -> tt
   encode_activate(x_1) -> activate(encArg(x_1))
   encode_plus(x_1, x_2) -> plus(encArg(x_1), encArg(x_2))
   encode_0 -> 0
   encode_s(x_1) -> s(encArg(x_1))

Rewrite Strategy: INNERMOST