WORST_CASE(?,?)
proof of input_65f60NoxdN.trs
# AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished


The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, EXP).

(0) CpxTRS
(1) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms]
(2) CdtProblem
(3) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
(4) CdtProblem
(5) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms]
(6) CdtProblem
(7) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
(8) CpxRelTRS
(9) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
(10) CpxWeightedTrs
(11) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
(12) CpxTypedWeightedTrs
(13) CompletionProof [UPPER BOUND(ID), 0 ms]
(14) CpxTypedWeightedCompleteTrs
(15) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
(16) CpxTypedWeightedCompleteTrs
(17) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
(18) CpxRNTS
(19) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
(20) CpxRNTS
(21) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms]
(22) CpxRNTS
(23) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(24) CpxRNTS
(25) IntTrsBoundProof [UPPER BOUND(ID), 160 ms]
(26) CpxRNTS
(27) IntTrsBoundProof [UPPER BOUND(ID), 23 ms]
(28) CpxRNTS
(29) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(30) CpxRNTS
(31) IntTrsBoundProof [UPPER BOUND(ID), 108 ms]
(32) CpxRNTS
(33) IntTrsBoundProof [UPPER BOUND(ID), 14 ms]
(34) CpxRNTS
(35) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(36) CpxRNTS
(37) IntTrsBoundProof [UPPER BOUND(ID), 200 ms]
(38) CpxRNTS
(39) IntTrsBoundProof [UPPER BOUND(ID), 22 ms]
(40) CpxRNTS
(41) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(42) CpxRNTS
(43) IntTrsBoundProof [UPPER BOUND(ID), 87 ms]
(44) CpxRNTS
(45) IntTrsBoundProof [UPPER BOUND(ID), 63 ms]
(46) CpxRNTS
(47) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(48) CpxRNTS
(49) IntTrsBoundProof [UPPER BOUND(ID), 119 ms]
(50) CpxRNTS
(51) IntTrsBoundProof [UPPER BOUND(ID), 2 ms]
(52) CpxRNTS
(53) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(54) CpxRNTS
(55) IntTrsBoundProof [UPPER BOUND(ID), 58 ms]
(56) CpxRNTS
(57) IntTrsBoundProof [UPPER BOUND(ID), 53 ms]
(58) CpxRNTS
(59) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(60) CpxRNTS
(61) IntTrsBoundProof [UPPER BOUND(ID), 495 ms]
(62) CpxRNTS
(63) IntTrsBoundProof [UPPER BOUND(ID), 367 ms]
(64) CpxRNTS
(65) FinalProof [FINISHED, 0 ms]
(66) BOUNDS(1, EXP)


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

(0)
Obligation:
The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, EXP).


The TRS R consists of the following rules:

   f(X) -> cons(X, n__f(g(X)))
   g(0) -> s(0)
   g(s(X)) -> s(s(g(X)))
   sel(0, cons(X, Y)) -> X
   sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
   f(X) -> n__f(X)
   activate(n__f(X)) -> f(X)
   activate(X) -> X

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

(1) CpxTrsToCdtProof (UPPER BOUND(ID))
Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT
----------------------------------------

(2)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   f(z0) -> cons(z0, n__f(g(z0)))
   f(z0) -> n__f(z0)
   g(0) -> s(0)
   g(s(z0)) -> s(s(g(z0)))
   sel(0, cons(z0, z1)) -> z0
   sel(s(z0), cons(z1, z2)) -> sel(z0, activate(z2))
   activate(n__f(z0)) -> f(z0)
   activate(z0) -> z0
Tuples:
   F(z0) -> c(G(z0))
   F(z0) -> c1
   G(0) -> c2
   G(s(z0)) -> c3(G(z0))
   SEL(0, cons(z0, z1)) -> c4
   SEL(s(z0), cons(z1, z2)) -> c5(SEL(z0, activate(z2)), ACTIVATE(z2))
   ACTIVATE(n__f(z0)) -> c6(F(z0))
   ACTIVATE(z0) -> c7
S tuples:
   F(z0) -> c(G(z0))
   F(z0) -> c1
   G(0) -> c2
   G(s(z0)) -> c3(G(z0))
   SEL(0, cons(z0, z1)) -> c4
   SEL(s(z0), cons(z1, z2)) -> c5(SEL(z0, activate(z2)), ACTIVATE(z2))
   ACTIVATE(n__f(z0)) -> c6(F(z0))
   ACTIVATE(z0) -> c7
K tuples:none
Defined Rule Symbols:   f_1, g_1, sel_2, activate_1

Defined Pair Symbols:   F_1, G_1, SEL_2, ACTIVATE_1

Compound Symbols:   c_1, c1, c2, c3_1, c4, c5_2, c6_1, c7


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

(3) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 4 trailing nodes:
   ACTIVATE(z0) -> c7
   SEL(0, cons(z0, z1)) -> c4
   G(0) -> c2
   F(z0) -> c1

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

(4)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   f(z0) -> cons(z0, n__f(g(z0)))
   f(z0) -> n__f(z0)
   g(0) -> s(0)
   g(s(z0)) -> s(s(g(z0)))
   sel(0, cons(z0, z1)) -> z0
   sel(s(z0), cons(z1, z2)) -> sel(z0, activate(z2))
   activate(n__f(z0)) -> f(z0)
   activate(z0) -> z0
Tuples:
   F(z0) -> c(G(z0))
   G(s(z0)) -> c3(G(z0))
   SEL(s(z0), cons(z1, z2)) -> c5(SEL(z0, activate(z2)), ACTIVATE(z2))
   ACTIVATE(n__f(z0)) -> c6(F(z0))
S tuples:
   F(z0) -> c(G(z0))
   G(s(z0)) -> c3(G(z0))
   SEL(s(z0), cons(z1, z2)) -> c5(SEL(z0, activate(z2)), ACTIVATE(z2))
   ACTIVATE(n__f(z0)) -> c6(F(z0))
K tuples:none
Defined Rule Symbols:   f_1, g_1, sel_2, activate_1

Defined Pair Symbols:   F_1, G_1, SEL_2, ACTIVATE_1

Compound Symbols:   c_1, c3_1, c5_2, c6_1


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

(5) CdtUsableRulesProof (BOTH BOUNDS(ID, ID))
The following rules are not usable and were removed:
   sel(0, cons(z0, z1)) -> z0
   sel(s(z0), cons(z1, z2)) -> sel(z0, activate(z2))

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

(6)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__f(z0)) -> f(z0)
   activate(z0) -> z0
   f(z0) -> cons(z0, n__f(g(z0)))
   f(z0) -> n__f(z0)
   g(0) -> s(0)
   g(s(z0)) -> s(s(g(z0)))
Tuples:
   F(z0) -> c(G(z0))
   G(s(z0)) -> c3(G(z0))
   SEL(s(z0), cons(z1, z2)) -> c5(SEL(z0, activate(z2)), ACTIVATE(z2))
   ACTIVATE(n__f(z0)) -> c6(F(z0))
S tuples:
   F(z0) -> c(G(z0))
   G(s(z0)) -> c3(G(z0))
   SEL(s(z0), cons(z1, z2)) -> c5(SEL(z0, activate(z2)), ACTIVATE(z2))
   ACTIVATE(n__f(z0)) -> c6(F(z0))
K tuples:none
Defined Rule Symbols:   activate_1, f_1, g_1

Defined Pair Symbols:   F_1, G_1, SEL_2, ACTIVATE_1

Compound Symbols:   c_1, c3_1, c5_2, c6_1


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

(7) CdtToCpxRelTrsProof (BOTH BOUNDS(ID, ID))
Converted S to standard rules, and D \ S as well as R to relative rules.
----------------------------------------

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


The TRS R consists of the following rules:

   F(z0) -> c(G(z0))
   G(s(z0)) -> c3(G(z0))
   SEL(s(z0), cons(z1, z2)) -> c5(SEL(z0, activate(z2)), ACTIVATE(z2))
   ACTIVATE(n__f(z0)) -> c6(F(z0))

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

   activate(n__f(z0)) -> f(z0)
   activate(z0) -> z0
   f(z0) -> cons(z0, n__f(g(z0)))
   f(z0) -> n__f(z0)
   g(0) -> s(0)
   g(s(z0)) -> s(s(g(z0)))

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

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

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


The TRS R consists of the following rules:

   F(z0) -> c(G(z0)) [1]
   G(s(z0)) -> c3(G(z0)) [1]
   SEL(s(z0), cons(z1, z2)) -> c5(SEL(z0, activate(z2)), ACTIVATE(z2)) [1]
   ACTIVATE(n__f(z0)) -> c6(F(z0)) [1]
   activate(n__f(z0)) -> f(z0) [0]
   activate(z0) -> z0 [0]
   f(z0) -> cons(z0, n__f(g(z0))) [0]
   f(z0) -> n__f(z0) [0]
   g(0) -> s(0) [0]
   g(s(z0)) -> s(s(g(z0))) [0]

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

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

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

   F(z0) -> c(G(z0)) [1]
   G(s(z0)) -> c3(G(z0)) [1]
   SEL(s(z0), cons(z1, z2)) -> c5(SEL(z0, activate(z2)), ACTIVATE(z2)) [1]
   ACTIVATE(n__f(z0)) -> c6(F(z0)) [1]
   activate(n__f(z0)) -> f(z0) [0]
   activate(z0) -> z0 [0]
   f(z0) -> cons(z0, n__f(g(z0))) [0]
   f(z0) -> n__f(z0) [0]
   g(0) -> s(0) [0]
   g(s(z0)) -> s(s(g(z0))) [0]

The TRS has the following type information:
F :: s:0 -> c
c :: c3 -> c
G :: s:0 -> c3
s :: s:0 -> s:0
c3 :: c3 -> c3
SEL :: s:0 -> cons:n__f -> c5
cons :: s:0 -> cons:n__f -> cons:n__f
c5 :: c5 -> c6 -> c5
activate :: cons:n__f -> cons:n__f
ACTIVATE :: cons:n__f -> c6
n__f :: s:0 -> cons:n__f
c6 :: c -> c6
f :: s:0 -> cons:n__f
g :: s:0 -> s:0
0 :: s:0

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

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

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

(b) The following defined symbols do not have to be completely defined, as they can never occur inside other defined symbols:

   F_1
   G_1
   SEL_2
   ACTIVATE_1

(c) The following functions are completely defined:

   activate_1
   f_1
   g_1

Due to the following rules being added:

   activate(v0) -> const3 [0]
   f(v0) -> const3 [0]
   g(v0) -> 0 [0]

And the following fresh constants:    const3, const, const1, const2, const4

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

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

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

   F(z0) -> c(G(z0)) [1]
   G(s(z0)) -> c3(G(z0)) [1]
   SEL(s(z0), cons(z1, z2)) -> c5(SEL(z0, activate(z2)), ACTIVATE(z2)) [1]
   ACTIVATE(n__f(z0)) -> c6(F(z0)) [1]
   activate(n__f(z0)) -> f(z0) [0]
   activate(z0) -> z0 [0]
   f(z0) -> cons(z0, n__f(g(z0))) [0]
   f(z0) -> n__f(z0) [0]
   g(0) -> s(0) [0]
   g(s(z0)) -> s(s(g(z0))) [0]
   activate(v0) -> const3 [0]
   f(v0) -> const3 [0]
   g(v0) -> 0 [0]

The TRS has the following type information:
F :: s:0 -> c
c :: c3 -> c
G :: s:0 -> c3
s :: s:0 -> s:0
c3 :: c3 -> c3
SEL :: s:0 -> cons:n__f:const3 -> c5
cons :: s:0 -> cons:n__f:const3 -> cons:n__f:const3
c5 :: c5 -> c6 -> c5
activate :: cons:n__f:const3 -> cons:n__f:const3
ACTIVATE :: cons:n__f:const3 -> c6
n__f :: s:0 -> cons:n__f:const3
c6 :: c -> c6
f :: s:0 -> cons:n__f:const3
g :: s:0 -> s:0
0 :: s:0
const3 :: cons:n__f:const3
const :: c
const1 :: c3
const2 :: c5
const4 :: c6

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

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

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

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

   F(z0) -> c(G(z0)) [1]
   G(s(z0)) -> c3(G(z0)) [1]
   SEL(s(z0), cons(z1, n__f(z0'))) -> c5(SEL(z0, f(z0')), ACTIVATE(n__f(z0'))) [1]
   SEL(s(z0), cons(z1, z2)) -> c5(SEL(z0, z2), ACTIVATE(z2)) [1]
   SEL(s(z0), cons(z1, z2)) -> c5(SEL(z0, const3), ACTIVATE(z2)) [1]
   ACTIVATE(n__f(z0)) -> c6(F(z0)) [1]
   activate(n__f(z0)) -> f(z0) [0]
   activate(z0) -> z0 [0]
   f(z0) -> cons(z0, n__f(g(z0))) [0]
   f(z0) -> n__f(z0) [0]
   g(0) -> s(0) [0]
   g(s(z0)) -> s(s(g(z0))) [0]
   activate(v0) -> const3 [0]
   f(v0) -> const3 [0]
   g(v0) -> 0 [0]

The TRS has the following type information:
F :: s:0 -> c
c :: c3 -> c
G :: s:0 -> c3
s :: s:0 -> s:0
c3 :: c3 -> c3
SEL :: s:0 -> cons:n__f:const3 -> c5
cons :: s:0 -> cons:n__f:const3 -> cons:n__f:const3
c5 :: c5 -> c6 -> c5
activate :: cons:n__f:const3 -> cons:n__f:const3
ACTIVATE :: cons:n__f:const3 -> c6
n__f :: s:0 -> cons:n__f:const3
c6 :: c -> c6
f :: s:0 -> cons:n__f:const3
g :: s:0 -> s:0
0 :: s:0
const3 :: cons:n__f:const3
const :: c
const1 :: c3
const2 :: c5
const4 :: c6

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

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

   0 => 0
   const3 => 0
   const => 0
   const1 => 0
   const2 => 0
   const4 => 0

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

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

   ACTIVATE(z) -{ 1 }-> 1 + F(z0) :|: z = 1 + z0, z0 >= 0
   F(z) -{ 1 }-> 1 + G(z0) :|: z = z0, z0 >= 0
   G(z) -{ 1 }-> 1 + G(z0) :|: z = 1 + z0, z0 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z0, z2) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z0, f(z0')) + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z = 1 + z0, z0 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z0, 0) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 0
   activate(z) -{ 0 }-> z0 :|: z = z0, z0 >= 0
   activate(z) -{ 0 }-> f(z0) :|: z = 1 + z0, z0 >= 0
   activate(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   f(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   f(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   f(z) -{ 0 }-> 1 + z0 + (1 + g(z0)) :|: z = z0, z0 >= 0
   g(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   g(z) -{ 0 }-> 1 + 0 :|: z = 0
   g(z) -{ 0 }-> 1 + (1 + g(z0)) :|: z = 1 + z0, z0 >= 0


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

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

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

   ACTIVATE(z) -{ 1 }-> 1 + F(z - 1) :|: z - 1 >= 0
   F(z) -{ 1 }-> 1 + G(z) :|: z >= 0
   G(z) -{ 1 }-> 1 + G(z - 1) :|: z - 1 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, z2) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, f(z0')) + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   activate(z) -{ 0 }-> z :|: z >= 0
   activate(z) -{ 0 }-> f(z - 1) :|: z - 1 >= 0
   activate(z) -{ 0 }-> 0 :|: z >= 0
   f(z) -{ 0 }-> 0 :|: z >= 0
   f(z) -{ 0 }-> 1 + z :|: z >= 0
   f(z) -{ 0 }-> 1 + z + (1 + g(z)) :|: z >= 0
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + 0 :|: z = 0
   g(z) -{ 0 }-> 1 + (1 + g(z - 1)) :|: z - 1 >= 0


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

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

   { g }
   { G }
   { f }
   { F }
   { activate }
   { ACTIVATE }
   { SEL }

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

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

   ACTIVATE(z) -{ 1 }-> 1 + F(z - 1) :|: z - 1 >= 0
   F(z) -{ 1 }-> 1 + G(z) :|: z >= 0
   G(z) -{ 1 }-> 1 + G(z - 1) :|: z - 1 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, z2) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, f(z0')) + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   activate(z) -{ 0 }-> z :|: z >= 0
   activate(z) -{ 0 }-> f(z - 1) :|: z - 1 >= 0
   activate(z) -{ 0 }-> 0 :|: z >= 0
   f(z) -{ 0 }-> 0 :|: z >= 0
   f(z) -{ 0 }-> 1 + z :|: z >= 0
   f(z) -{ 0 }-> 1 + z + (1 + g(z)) :|: z >= 0
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + 0 :|: z = 0
   g(z) -{ 0 }-> 1 + (1 + g(z - 1)) :|: z - 1 >= 0

Function symbols to be analyzed: {g}, {G}, {f}, {F}, {activate}, {ACTIVATE}, {SEL}

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

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

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

   ACTIVATE(z) -{ 1 }-> 1 + F(z - 1) :|: z - 1 >= 0
   F(z) -{ 1 }-> 1 + G(z) :|: z >= 0
   G(z) -{ 1 }-> 1 + G(z - 1) :|: z - 1 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, z2) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, f(z0')) + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   activate(z) -{ 0 }-> z :|: z >= 0
   activate(z) -{ 0 }-> f(z - 1) :|: z - 1 >= 0
   activate(z) -{ 0 }-> 0 :|: z >= 0
   f(z) -{ 0 }-> 0 :|: z >= 0
   f(z) -{ 0 }-> 1 + z :|: z >= 0
   f(z) -{ 0 }-> 1 + z + (1 + g(z)) :|: z >= 0
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + 0 :|: z = 0
   g(z) -{ 0 }-> 1 + (1 + g(z - 1)) :|: z - 1 >= 0

Function symbols to be analyzed: {g}, {G}, {f}, {F}, {activate}, {ACTIVATE}, {SEL}

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

(25) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   ACTIVATE(z) -{ 1 }-> 1 + F(z - 1) :|: z - 1 >= 0
   F(z) -{ 1 }-> 1 + G(z) :|: z >= 0
   G(z) -{ 1 }-> 1 + G(z - 1) :|: z - 1 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, z2) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, f(z0')) + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   activate(z) -{ 0 }-> z :|: z >= 0
   activate(z) -{ 0 }-> f(z - 1) :|: z - 1 >= 0
   activate(z) -{ 0 }-> 0 :|: z >= 0
   f(z) -{ 0 }-> 0 :|: z >= 0
   f(z) -{ 0 }-> 1 + z :|: z >= 0
   f(z) -{ 0 }-> 1 + z + (1 + g(z)) :|: z >= 0
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + 0 :|: z = 0
   g(z) -{ 0 }-> 1 + (1 + g(z - 1)) :|: z - 1 >= 0

Function symbols to be analyzed: {g}, {G}, {f}, {F}, {activate}, {ACTIVATE}, {SEL}
Previous analysis results are:
  g: runtime: ?, size: O(n^1) [1 + 2*z]

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

(27) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   ACTIVATE(z) -{ 1 }-> 1 + F(z - 1) :|: z - 1 >= 0
   F(z) -{ 1 }-> 1 + G(z) :|: z >= 0
   G(z) -{ 1 }-> 1 + G(z - 1) :|: z - 1 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, z2) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, f(z0')) + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   activate(z) -{ 0 }-> z :|: z >= 0
   activate(z) -{ 0 }-> f(z - 1) :|: z - 1 >= 0
   activate(z) -{ 0 }-> 0 :|: z >= 0
   f(z) -{ 0 }-> 0 :|: z >= 0
   f(z) -{ 0 }-> 1 + z :|: z >= 0
   f(z) -{ 0 }-> 1 + z + (1 + g(z)) :|: z >= 0
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + 0 :|: z = 0
   g(z) -{ 0 }-> 1 + (1 + g(z - 1)) :|: z - 1 >= 0

Function symbols to be analyzed: {G}, {f}, {F}, {activate}, {ACTIVATE}, {SEL}
Previous analysis results are:
  g: runtime: O(1) [0], size: O(n^1) [1 + 2*z]

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

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

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

   ACTIVATE(z) -{ 1 }-> 1 + F(z - 1) :|: z - 1 >= 0
   F(z) -{ 1 }-> 1 + G(z) :|: z >= 0
   G(z) -{ 1 }-> 1 + G(z - 1) :|: z - 1 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, z2) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, f(z0')) + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   activate(z) -{ 0 }-> z :|: z >= 0
   activate(z) -{ 0 }-> f(z - 1) :|: z - 1 >= 0
   activate(z) -{ 0 }-> 0 :|: z >= 0
   f(z) -{ 0 }-> 0 :|: z >= 0
   f(z) -{ 0 }-> 1 + z :|: z >= 0
   f(z) -{ 0 }-> 1 + z + (1 + s) :|: s >= 0, s <= 2 * z + 1, z >= 0
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + 0 :|: z = 0
   g(z) -{ 0 }-> 1 + (1 + s') :|: s' >= 0, s' <= 2 * (z - 1) + 1, z - 1 >= 0

Function symbols to be analyzed: {G}, {f}, {F}, {activate}, {ACTIVATE}, {SEL}
Previous analysis results are:
  g: runtime: O(1) [0], size: O(n^1) [1 + 2*z]

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

(31) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   ACTIVATE(z) -{ 1 }-> 1 + F(z - 1) :|: z - 1 >= 0
   F(z) -{ 1 }-> 1 + G(z) :|: z >= 0
   G(z) -{ 1 }-> 1 + G(z - 1) :|: z - 1 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, z2) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, f(z0')) + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   activate(z) -{ 0 }-> z :|: z >= 0
   activate(z) -{ 0 }-> f(z - 1) :|: z - 1 >= 0
   activate(z) -{ 0 }-> 0 :|: z >= 0
   f(z) -{ 0 }-> 0 :|: z >= 0
   f(z) -{ 0 }-> 1 + z :|: z >= 0
   f(z) -{ 0 }-> 1 + z + (1 + s) :|: s >= 0, s <= 2 * z + 1, z >= 0
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + 0 :|: z = 0
   g(z) -{ 0 }-> 1 + (1 + s') :|: s' >= 0, s' <= 2 * (z - 1) + 1, z - 1 >= 0

Function symbols to be analyzed: {G}, {f}, {F}, {activate}, {ACTIVATE}, {SEL}
Previous analysis results are:
  g: runtime: O(1) [0], size: O(n^1) [1 + 2*z]
  G: runtime: ?, size: O(1) [0]

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

(33) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   ACTIVATE(z) -{ 1 }-> 1 + F(z - 1) :|: z - 1 >= 0
   F(z) -{ 1 }-> 1 + G(z) :|: z >= 0
   G(z) -{ 1 }-> 1 + G(z - 1) :|: z - 1 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, z2) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, f(z0')) + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   activate(z) -{ 0 }-> z :|: z >= 0
   activate(z) -{ 0 }-> f(z - 1) :|: z - 1 >= 0
   activate(z) -{ 0 }-> 0 :|: z >= 0
   f(z) -{ 0 }-> 0 :|: z >= 0
   f(z) -{ 0 }-> 1 + z :|: z >= 0
   f(z) -{ 0 }-> 1 + z + (1 + s) :|: s >= 0, s <= 2 * z + 1, z >= 0
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + 0 :|: z = 0
   g(z) -{ 0 }-> 1 + (1 + s') :|: s' >= 0, s' <= 2 * (z - 1) + 1, z - 1 >= 0

Function symbols to be analyzed: {f}, {F}, {activate}, {ACTIVATE}, {SEL}
Previous analysis results are:
  g: runtime: O(1) [0], size: O(n^1) [1 + 2*z]
  G: runtime: O(n^1) [z], size: O(1) [0]

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

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

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

   ACTIVATE(z) -{ 1 }-> 1 + F(z - 1) :|: z - 1 >= 0
   F(z) -{ 1 + z }-> 1 + s'' :|: s'' >= 0, s'' <= 0, z >= 0
   G(z) -{ z }-> 1 + s1 :|: s1 >= 0, s1 <= 0, z - 1 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, z2) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, f(z0')) + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   activate(z) -{ 0 }-> z :|: z >= 0
   activate(z) -{ 0 }-> f(z - 1) :|: z - 1 >= 0
   activate(z) -{ 0 }-> 0 :|: z >= 0
   f(z) -{ 0 }-> 0 :|: z >= 0
   f(z) -{ 0 }-> 1 + z :|: z >= 0
   f(z) -{ 0 }-> 1 + z + (1 + s) :|: s >= 0, s <= 2 * z + 1, z >= 0
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + 0 :|: z = 0
   g(z) -{ 0 }-> 1 + (1 + s') :|: s' >= 0, s' <= 2 * (z - 1) + 1, z - 1 >= 0

Function symbols to be analyzed: {f}, {F}, {activate}, {ACTIVATE}, {SEL}
Previous analysis results are:
  g: runtime: O(1) [0], size: O(n^1) [1 + 2*z]
  G: runtime: O(n^1) [z], size: O(1) [0]

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

(37) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   ACTIVATE(z) -{ 1 }-> 1 + F(z - 1) :|: z - 1 >= 0
   F(z) -{ 1 + z }-> 1 + s'' :|: s'' >= 0, s'' <= 0, z >= 0
   G(z) -{ z }-> 1 + s1 :|: s1 >= 0, s1 <= 0, z - 1 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, z2) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, f(z0')) + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   activate(z) -{ 0 }-> z :|: z >= 0
   activate(z) -{ 0 }-> f(z - 1) :|: z - 1 >= 0
   activate(z) -{ 0 }-> 0 :|: z >= 0
   f(z) -{ 0 }-> 0 :|: z >= 0
   f(z) -{ 0 }-> 1 + z :|: z >= 0
   f(z) -{ 0 }-> 1 + z + (1 + s) :|: s >= 0, s <= 2 * z + 1, z >= 0
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + 0 :|: z = 0
   g(z) -{ 0 }-> 1 + (1 + s') :|: s' >= 0, s' <= 2 * (z - 1) + 1, z - 1 >= 0

Function symbols to be analyzed: {f}, {F}, {activate}, {ACTIVATE}, {SEL}
Previous analysis results are:
  g: runtime: O(1) [0], size: O(n^1) [1 + 2*z]
  G: runtime: O(n^1) [z], size: O(1) [0]
  f: runtime: ?, size: O(n^1) [3 + 3*z]

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

(39) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   ACTIVATE(z) -{ 1 }-> 1 + F(z - 1) :|: z - 1 >= 0
   F(z) -{ 1 + z }-> 1 + s'' :|: s'' >= 0, s'' <= 0, z >= 0
   G(z) -{ z }-> 1 + s1 :|: s1 >= 0, s1 <= 0, z - 1 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, z2) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, f(z0')) + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   activate(z) -{ 0 }-> z :|: z >= 0
   activate(z) -{ 0 }-> f(z - 1) :|: z - 1 >= 0
   activate(z) -{ 0 }-> 0 :|: z >= 0
   f(z) -{ 0 }-> 0 :|: z >= 0
   f(z) -{ 0 }-> 1 + z :|: z >= 0
   f(z) -{ 0 }-> 1 + z + (1 + s) :|: s >= 0, s <= 2 * z + 1, z >= 0
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + 0 :|: z = 0
   g(z) -{ 0 }-> 1 + (1 + s') :|: s' >= 0, s' <= 2 * (z - 1) + 1, z - 1 >= 0

Function symbols to be analyzed: {F}, {activate}, {ACTIVATE}, {SEL}
Previous analysis results are:
  g: runtime: O(1) [0], size: O(n^1) [1 + 2*z]
  G: runtime: O(n^1) [z], size: O(1) [0]
  f: runtime: O(1) [0], size: O(n^1) [3 + 3*z]

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

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

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

   ACTIVATE(z) -{ 1 }-> 1 + F(z - 1) :|: z - 1 >= 0
   F(z) -{ 1 + z }-> 1 + s'' :|: s'' >= 0, s'' <= 0, z >= 0
   G(z) -{ z }-> 1 + s1 :|: s1 >= 0, s1 <= 0, z - 1 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, s2) + ACTIVATE(1 + z0') :|: s2 >= 0, s2 <= 3 * z0' + 3, z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, z2) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   activate(z) -{ 0 }-> s3 :|: s3 >= 0, s3 <= 3 * (z - 1) + 3, z - 1 >= 0
   activate(z) -{ 0 }-> z :|: z >= 0
   activate(z) -{ 0 }-> 0 :|: z >= 0
   f(z) -{ 0 }-> 0 :|: z >= 0
   f(z) -{ 0 }-> 1 + z :|: z >= 0
   f(z) -{ 0 }-> 1 + z + (1 + s) :|: s >= 0, s <= 2 * z + 1, z >= 0
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + 0 :|: z = 0
   g(z) -{ 0 }-> 1 + (1 + s') :|: s' >= 0, s' <= 2 * (z - 1) + 1, z - 1 >= 0

Function symbols to be analyzed: {F}, {activate}, {ACTIVATE}, {SEL}
Previous analysis results are:
  g: runtime: O(1) [0], size: O(n^1) [1 + 2*z]
  G: runtime: O(n^1) [z], size: O(1) [0]
  f: runtime: O(1) [0], size: O(n^1) [3 + 3*z]

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

(43) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   ACTIVATE(z) -{ 1 }-> 1 + F(z - 1) :|: z - 1 >= 0
   F(z) -{ 1 + z }-> 1 + s'' :|: s'' >= 0, s'' <= 0, z >= 0
   G(z) -{ z }-> 1 + s1 :|: s1 >= 0, s1 <= 0, z - 1 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, s2) + ACTIVATE(1 + z0') :|: s2 >= 0, s2 <= 3 * z0' + 3, z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, z2) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   activate(z) -{ 0 }-> s3 :|: s3 >= 0, s3 <= 3 * (z - 1) + 3, z - 1 >= 0
   activate(z) -{ 0 }-> z :|: z >= 0
   activate(z) -{ 0 }-> 0 :|: z >= 0
   f(z) -{ 0 }-> 0 :|: z >= 0
   f(z) -{ 0 }-> 1 + z :|: z >= 0
   f(z) -{ 0 }-> 1 + z + (1 + s) :|: s >= 0, s <= 2 * z + 1, z >= 0
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + 0 :|: z = 0
   g(z) -{ 0 }-> 1 + (1 + s') :|: s' >= 0, s' <= 2 * (z - 1) + 1, z - 1 >= 0

Function symbols to be analyzed: {F}, {activate}, {ACTIVATE}, {SEL}
Previous analysis results are:
  g: runtime: O(1) [0], size: O(n^1) [1 + 2*z]
  G: runtime: O(n^1) [z], size: O(1) [0]
  f: runtime: O(1) [0], size: O(n^1) [3 + 3*z]
  F: runtime: ?, size: O(1) [1]

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

(45) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   ACTIVATE(z) -{ 1 }-> 1 + F(z - 1) :|: z - 1 >= 0
   F(z) -{ 1 + z }-> 1 + s'' :|: s'' >= 0, s'' <= 0, z >= 0
   G(z) -{ z }-> 1 + s1 :|: s1 >= 0, s1 <= 0, z - 1 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, s2) + ACTIVATE(1 + z0') :|: s2 >= 0, s2 <= 3 * z0' + 3, z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, z2) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   activate(z) -{ 0 }-> s3 :|: s3 >= 0, s3 <= 3 * (z - 1) + 3, z - 1 >= 0
   activate(z) -{ 0 }-> z :|: z >= 0
   activate(z) -{ 0 }-> 0 :|: z >= 0
   f(z) -{ 0 }-> 0 :|: z >= 0
   f(z) -{ 0 }-> 1 + z :|: z >= 0
   f(z) -{ 0 }-> 1 + z + (1 + s) :|: s >= 0, s <= 2 * z + 1, z >= 0
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + 0 :|: z = 0
   g(z) -{ 0 }-> 1 + (1 + s') :|: s' >= 0, s' <= 2 * (z - 1) + 1, z - 1 >= 0

Function symbols to be analyzed: {activate}, {ACTIVATE}, {SEL}
Previous analysis results are:
  g: runtime: O(1) [0], size: O(n^1) [1 + 2*z]
  G: runtime: O(n^1) [z], size: O(1) [0]
  f: runtime: O(1) [0], size: O(n^1) [3 + 3*z]
  F: runtime: O(n^1) [1 + z], size: O(1) [1]

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

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

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

   ACTIVATE(z) -{ 1 + z }-> 1 + s4 :|: s4 >= 0, s4 <= 1, z - 1 >= 0
   F(z) -{ 1 + z }-> 1 + s'' :|: s'' >= 0, s'' <= 0, z >= 0
   G(z) -{ z }-> 1 + s1 :|: s1 >= 0, s1 <= 0, z - 1 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, s2) + ACTIVATE(1 + z0') :|: s2 >= 0, s2 <= 3 * z0' + 3, z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, z2) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   activate(z) -{ 0 }-> s3 :|: s3 >= 0, s3 <= 3 * (z - 1) + 3, z - 1 >= 0
   activate(z) -{ 0 }-> z :|: z >= 0
   activate(z) -{ 0 }-> 0 :|: z >= 0
   f(z) -{ 0 }-> 0 :|: z >= 0
   f(z) -{ 0 }-> 1 + z :|: z >= 0
   f(z) -{ 0 }-> 1 + z + (1 + s) :|: s >= 0, s <= 2 * z + 1, z >= 0
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + 0 :|: z = 0
   g(z) -{ 0 }-> 1 + (1 + s') :|: s' >= 0, s' <= 2 * (z - 1) + 1, z - 1 >= 0

Function symbols to be analyzed: {activate}, {ACTIVATE}, {SEL}
Previous analysis results are:
  g: runtime: O(1) [0], size: O(n^1) [1 + 2*z]
  G: runtime: O(n^1) [z], size: O(1) [0]
  f: runtime: O(1) [0], size: O(n^1) [3 + 3*z]
  F: runtime: O(n^1) [1 + z], size: O(1) [1]

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

(49) 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: 3*z

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

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

   ACTIVATE(z) -{ 1 + z }-> 1 + s4 :|: s4 >= 0, s4 <= 1, z - 1 >= 0
   F(z) -{ 1 + z }-> 1 + s'' :|: s'' >= 0, s'' <= 0, z >= 0
   G(z) -{ z }-> 1 + s1 :|: s1 >= 0, s1 <= 0, z - 1 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, s2) + ACTIVATE(1 + z0') :|: s2 >= 0, s2 <= 3 * z0' + 3, z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, z2) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   activate(z) -{ 0 }-> s3 :|: s3 >= 0, s3 <= 3 * (z - 1) + 3, z - 1 >= 0
   activate(z) -{ 0 }-> z :|: z >= 0
   activate(z) -{ 0 }-> 0 :|: z >= 0
   f(z) -{ 0 }-> 0 :|: z >= 0
   f(z) -{ 0 }-> 1 + z :|: z >= 0
   f(z) -{ 0 }-> 1 + z + (1 + s) :|: s >= 0, s <= 2 * z + 1, z >= 0
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + 0 :|: z = 0
   g(z) -{ 0 }-> 1 + (1 + s') :|: s' >= 0, s' <= 2 * (z - 1) + 1, z - 1 >= 0

Function symbols to be analyzed: {activate}, {ACTIVATE}, {SEL}
Previous analysis results are:
  g: runtime: O(1) [0], size: O(n^1) [1 + 2*z]
  G: runtime: O(n^1) [z], size: O(1) [0]
  f: runtime: O(1) [0], size: O(n^1) [3 + 3*z]
  F: runtime: O(n^1) [1 + z], size: O(1) [1]
  activate: runtime: ?, size: O(n^1) [3*z]

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

(51) 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: 0

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

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

   ACTIVATE(z) -{ 1 + z }-> 1 + s4 :|: s4 >= 0, s4 <= 1, z - 1 >= 0
   F(z) -{ 1 + z }-> 1 + s'' :|: s'' >= 0, s'' <= 0, z >= 0
   G(z) -{ z }-> 1 + s1 :|: s1 >= 0, s1 <= 0, z - 1 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, s2) + ACTIVATE(1 + z0') :|: s2 >= 0, s2 <= 3 * z0' + 3, z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, z2) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   activate(z) -{ 0 }-> s3 :|: s3 >= 0, s3 <= 3 * (z - 1) + 3, z - 1 >= 0
   activate(z) -{ 0 }-> z :|: z >= 0
   activate(z) -{ 0 }-> 0 :|: z >= 0
   f(z) -{ 0 }-> 0 :|: z >= 0
   f(z) -{ 0 }-> 1 + z :|: z >= 0
   f(z) -{ 0 }-> 1 + z + (1 + s) :|: s >= 0, s <= 2 * z + 1, z >= 0
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + 0 :|: z = 0
   g(z) -{ 0 }-> 1 + (1 + s') :|: s' >= 0, s' <= 2 * (z - 1) + 1, z - 1 >= 0

Function symbols to be analyzed: {ACTIVATE}, {SEL}
Previous analysis results are:
  g: runtime: O(1) [0], size: O(n^1) [1 + 2*z]
  G: runtime: O(n^1) [z], size: O(1) [0]
  f: runtime: O(1) [0], size: O(n^1) [3 + 3*z]
  F: runtime: O(n^1) [1 + z], size: O(1) [1]
  activate: runtime: O(1) [0], size: O(n^1) [3*z]

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

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

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

   ACTIVATE(z) -{ 1 + z }-> 1 + s4 :|: s4 >= 0, s4 <= 1, z - 1 >= 0
   F(z) -{ 1 + z }-> 1 + s'' :|: s'' >= 0, s'' <= 0, z >= 0
   G(z) -{ z }-> 1 + s1 :|: s1 >= 0, s1 <= 0, z - 1 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, s2) + ACTIVATE(1 + z0') :|: s2 >= 0, s2 <= 3 * z0' + 3, z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, z2) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   activate(z) -{ 0 }-> s3 :|: s3 >= 0, s3 <= 3 * (z - 1) + 3, z - 1 >= 0
   activate(z) -{ 0 }-> z :|: z >= 0
   activate(z) -{ 0 }-> 0 :|: z >= 0
   f(z) -{ 0 }-> 0 :|: z >= 0
   f(z) -{ 0 }-> 1 + z :|: z >= 0
   f(z) -{ 0 }-> 1 + z + (1 + s) :|: s >= 0, s <= 2 * z + 1, z >= 0
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + 0 :|: z = 0
   g(z) -{ 0 }-> 1 + (1 + s') :|: s' >= 0, s' <= 2 * (z - 1) + 1, z - 1 >= 0

Function symbols to be analyzed: {ACTIVATE}, {SEL}
Previous analysis results are:
  g: runtime: O(1) [0], size: O(n^1) [1 + 2*z]
  G: runtime: O(n^1) [z], size: O(1) [0]
  f: runtime: O(1) [0], size: O(n^1) [3 + 3*z]
  F: runtime: O(n^1) [1 + z], size: O(1) [1]
  activate: runtime: O(1) [0], size: O(n^1) [3*z]

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

(55) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   ACTIVATE(z) -{ 1 + z }-> 1 + s4 :|: s4 >= 0, s4 <= 1, z - 1 >= 0
   F(z) -{ 1 + z }-> 1 + s'' :|: s'' >= 0, s'' <= 0, z >= 0
   G(z) -{ z }-> 1 + s1 :|: s1 >= 0, s1 <= 0, z - 1 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, s2) + ACTIVATE(1 + z0') :|: s2 >= 0, s2 <= 3 * z0' + 3, z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, z2) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   activate(z) -{ 0 }-> s3 :|: s3 >= 0, s3 <= 3 * (z - 1) + 3, z - 1 >= 0
   activate(z) -{ 0 }-> z :|: z >= 0
   activate(z) -{ 0 }-> 0 :|: z >= 0
   f(z) -{ 0 }-> 0 :|: z >= 0
   f(z) -{ 0 }-> 1 + z :|: z >= 0
   f(z) -{ 0 }-> 1 + z + (1 + s) :|: s >= 0, s <= 2 * z + 1, z >= 0
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + 0 :|: z = 0
   g(z) -{ 0 }-> 1 + (1 + s') :|: s' >= 0, s' <= 2 * (z - 1) + 1, z - 1 >= 0

Function symbols to be analyzed: {ACTIVATE}, {SEL}
Previous analysis results are:
  g: runtime: O(1) [0], size: O(n^1) [1 + 2*z]
  G: runtime: O(n^1) [z], size: O(1) [0]
  f: runtime: O(1) [0], size: O(n^1) [3 + 3*z]
  F: runtime: O(n^1) [1 + z], size: O(1) [1]
  activate: runtime: O(1) [0], size: O(n^1) [3*z]
  ACTIVATE: runtime: ?, size: O(1) [2]

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

(57) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   ACTIVATE(z) -{ 1 + z }-> 1 + s4 :|: s4 >= 0, s4 <= 1, z - 1 >= 0
   F(z) -{ 1 + z }-> 1 + s'' :|: s'' >= 0, s'' <= 0, z >= 0
   G(z) -{ z }-> 1 + s1 :|: s1 >= 0, s1 <= 0, z - 1 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, s2) + ACTIVATE(1 + z0') :|: s2 >= 0, s2 <= 3 * z0' + 3, z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, z2) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   activate(z) -{ 0 }-> s3 :|: s3 >= 0, s3 <= 3 * (z - 1) + 3, z - 1 >= 0
   activate(z) -{ 0 }-> z :|: z >= 0
   activate(z) -{ 0 }-> 0 :|: z >= 0
   f(z) -{ 0 }-> 0 :|: z >= 0
   f(z) -{ 0 }-> 1 + z :|: z >= 0
   f(z) -{ 0 }-> 1 + z + (1 + s) :|: s >= 0, s <= 2 * z + 1, z >= 0
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + 0 :|: z = 0
   g(z) -{ 0 }-> 1 + (1 + s') :|: s' >= 0, s' <= 2 * (z - 1) + 1, z - 1 >= 0

Function symbols to be analyzed: {SEL}
Previous analysis results are:
  g: runtime: O(1) [0], size: O(n^1) [1 + 2*z]
  G: runtime: O(n^1) [z], size: O(1) [0]
  f: runtime: O(1) [0], size: O(n^1) [3 + 3*z]
  F: runtime: O(n^1) [1 + z], size: O(1) [1]
  activate: runtime: O(1) [0], size: O(n^1) [3*z]
  ACTIVATE: runtime: O(n^1) [1 + z], size: O(1) [2]

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

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

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

   ACTIVATE(z) -{ 1 + z }-> 1 + s4 :|: s4 >= 0, s4 <= 1, z - 1 >= 0
   F(z) -{ 1 + z }-> 1 + s'' :|: s'' >= 0, s'' <= 0, z >= 0
   G(z) -{ z }-> 1 + s1 :|: s1 >= 0, s1 <= 0, z - 1 >= 0
   SEL(z, z') -{ 3 + z0' }-> 1 + SEL(z - 1, s2) + s5 :|: s5 >= 0, s5 <= 2, s2 >= 0, s2 <= 3 * z0' + 3, z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0
   SEL(z, z') -{ 2 + z2 }-> 1 + SEL(z - 1, z2) + s6 :|: s6 >= 0, s6 <= 2, z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 2 + z2 }-> 1 + SEL(z - 1, 0) + s7 :|: s7 >= 0, s7 <= 2, z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   activate(z) -{ 0 }-> s3 :|: s3 >= 0, s3 <= 3 * (z - 1) + 3, z - 1 >= 0
   activate(z) -{ 0 }-> z :|: z >= 0
   activate(z) -{ 0 }-> 0 :|: z >= 0
   f(z) -{ 0 }-> 0 :|: z >= 0
   f(z) -{ 0 }-> 1 + z :|: z >= 0
   f(z) -{ 0 }-> 1 + z + (1 + s) :|: s >= 0, s <= 2 * z + 1, z >= 0
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + 0 :|: z = 0
   g(z) -{ 0 }-> 1 + (1 + s') :|: s' >= 0, s' <= 2 * (z - 1) + 1, z - 1 >= 0

Function symbols to be analyzed: {SEL}
Previous analysis results are:
  g: runtime: O(1) [0], size: O(n^1) [1 + 2*z]
  G: runtime: O(n^1) [z], size: O(1) [0]
  f: runtime: O(1) [0], size: O(n^1) [3 + 3*z]
  F: runtime: O(n^1) [1 + z], size: O(1) [1]
  activate: runtime: O(1) [0], size: O(n^1) [3*z]
  ACTIVATE: runtime: O(n^1) [1 + z], size: O(1) [2]

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

(61) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   ACTIVATE(z) -{ 1 + z }-> 1 + s4 :|: s4 >= 0, s4 <= 1, z - 1 >= 0
   F(z) -{ 1 + z }-> 1 + s'' :|: s'' >= 0, s'' <= 0, z >= 0
   G(z) -{ z }-> 1 + s1 :|: s1 >= 0, s1 <= 0, z - 1 >= 0
   SEL(z, z') -{ 3 + z0' }-> 1 + SEL(z - 1, s2) + s5 :|: s5 >= 0, s5 <= 2, s2 >= 0, s2 <= 3 * z0' + 3, z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0
   SEL(z, z') -{ 2 + z2 }-> 1 + SEL(z - 1, z2) + s6 :|: s6 >= 0, s6 <= 2, z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 2 + z2 }-> 1 + SEL(z - 1, 0) + s7 :|: s7 >= 0, s7 <= 2, z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   activate(z) -{ 0 }-> s3 :|: s3 >= 0, s3 <= 3 * (z - 1) + 3, z - 1 >= 0
   activate(z) -{ 0 }-> z :|: z >= 0
   activate(z) -{ 0 }-> 0 :|: z >= 0
   f(z) -{ 0 }-> 0 :|: z >= 0
   f(z) -{ 0 }-> 1 + z :|: z >= 0
   f(z) -{ 0 }-> 1 + z + (1 + s) :|: s >= 0, s <= 2 * z + 1, z >= 0
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + 0 :|: z = 0
   g(z) -{ 0 }-> 1 + (1 + s') :|: s' >= 0, s' <= 2 * (z - 1) + 1, z - 1 >= 0

Function symbols to be analyzed: {SEL}
Previous analysis results are:
  g: runtime: O(1) [0], size: O(n^1) [1 + 2*z]
  G: runtime: O(n^1) [z], size: O(1) [0]
  f: runtime: O(1) [0], size: O(n^1) [3 + 3*z]
  F: runtime: O(n^1) [1 + z], size: O(1) [1]
  activate: runtime: O(1) [0], size: O(n^1) [3*z]
  ACTIVATE: runtime: O(n^1) [1 + z], size: O(1) [2]
  SEL: runtime: ?, size: O(1) [0]

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

(63) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using KoAT for: SEL
after applying outer abstraction to obtain an ITS,
resulting in: EXP with polynomial bound: ?

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

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

   ACTIVATE(z) -{ 1 + z }-> 1 + s4 :|: s4 >= 0, s4 <= 1, z - 1 >= 0
   F(z) -{ 1 + z }-> 1 + s'' :|: s'' >= 0, s'' <= 0, z >= 0
   G(z) -{ z }-> 1 + s1 :|: s1 >= 0, s1 <= 0, z - 1 >= 0
   SEL(z, z') -{ 3 + z0' }-> 1 + SEL(z - 1, s2) + s5 :|: s5 >= 0, s5 <= 2, s2 >= 0, s2 <= 3 * z0' + 3, z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0
   SEL(z, z') -{ 2 + z2 }-> 1 + SEL(z - 1, z2) + s6 :|: s6 >= 0, s6 <= 2, z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 2 + z2 }-> 1 + SEL(z - 1, 0) + s7 :|: s7 >= 0, s7 <= 2, z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   activate(z) -{ 0 }-> s3 :|: s3 >= 0, s3 <= 3 * (z - 1) + 3, z - 1 >= 0
   activate(z) -{ 0 }-> z :|: z >= 0
   activate(z) -{ 0 }-> 0 :|: z >= 0
   f(z) -{ 0 }-> 0 :|: z >= 0
   f(z) -{ 0 }-> 1 + z :|: z >= 0
   f(z) -{ 0 }-> 1 + z + (1 + s) :|: s >= 0, s <= 2 * z + 1, z >= 0
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + 0 :|: z = 0
   g(z) -{ 0 }-> 1 + (1 + s') :|: s' >= 0, s' <= 2 * (z - 1) + 1, z - 1 >= 0

Function symbols to be analyzed: 
Previous analysis results are:
  g: runtime: O(1) [0], size: O(n^1) [1 + 2*z]
  G: runtime: O(n^1) [z], size: O(1) [0]
  f: runtime: O(1) [0], size: O(n^1) [3 + 3*z]
  F: runtime: O(n^1) [1 + z], size: O(1) [1]
  activate: runtime: O(1) [0], size: O(n^1) [3*z]
  ACTIVATE: runtime: O(n^1) [1 + z], size: O(1) [2]
  SEL: runtime: EXP, size: O(1) [0]

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

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

(66)
BOUNDS(1, EXP)