Preprocessing

Found invariant 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ for location l2

Found invariant 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location l3

Probabilistic Analysis

Probabilistic Program after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3
Transitions:
g₀:l0(X₀,X₁,X₂) → t₁:l1(X₀,X₁,X₂) :|:
g₂:l1(X₀,X₁,X₂) → t₃:l2(X₀,X₁,X₂) :|: 1 ≤ X₀ ∧ X₀ ≤ X₂
g₄:l2(X₀,X₁,X₂) → t₅:l1(3⋅X₀,X₁,2⋅X₂) :|: X₁ ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂
g₆:l2(X₀,X₁,X₂) → [1/2]:t₇:l1(X₀-1,X₁,1+X₂) :+: [1/2]:t₈:l1(X₀,X₁,X₂) :|: 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂
g₉:l1(X₀,X₁,X₂) → t₁₀:l3(X₀,X₁,X₂) :|: 1 ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
g₁₁:l3(X₀,X₁,X₂) → t₁₂:l3(X₀,X₁,X₂-1) :|: 1 ≤ X₂ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0

Run classical analysis on SCC: [l0]

Classical Approximation after Lifting Classical Results

All Bounds
Timebounds

Overall timebound:inf {Infinity}
g₀: 1 {O(1)}
g₂: inf {Infinity}
g₄: inf {Infinity}
g₆: inf {Infinity}
g₉: 1 {O(1)}
g₁₁: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
g₀: inf {Infinity}
g₂: inf {Infinity}
g₄: inf {Infinity}
g₆: inf {Infinity}
g₉: inf {Infinity}
g₁₁: inf {Infinity}

Sizebounds

(g₀,l1), X₀: X₀ {O(n)}
(g₀,l1), X₁: X₁ {O(n)}
(g₀,l1), X₂: X₂ {O(n)}

Run probabilistic analysis on SCC: [l0]

Run classical analysis on SCC: [l1; l2]

Classical Approximation after Lifting Classical Results

All Bounds
Timebounds

Overall timebound:inf {Infinity}
g₀: 1 {O(1)}
g₂: inf {Infinity}
g₄: inf {Infinity}
g₆: inf {Infinity}
g₉: 1 {O(1)}
g₁₁: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
g₀: inf {Infinity}
g₂: inf {Infinity}
g₄: inf {Infinity}
g₆: inf {Infinity}
g₉: inf {Infinity}
g₁₁: inf {Infinity}

Sizebounds

(g₀,l1), X₀: X₀ {O(n)}
(g₀,l1), X₁: X₁ {O(n)}
(g₀,l1), X₂: X₂ {O(n)}
(g₂,l2), X₁: X₁ {O(n)}
(g₄,l1), X₁: X₁ {O(n)}
(g₆,l1), X₁: 2⋅X₁ {O(n)}
(g₉,l3), X₀: 0 {O(1)}
(g₉,l3), X₁: 2⋅X₁ {O(n)}

Run probabilistic analysis on SCC: [l1; l2]

Analysing control-flow refined program

Run classical analysis on SCC: [l1]

Classical Approximation after Lifting Classical Results

All Bounds
Timebounds

Overall timebound:inf {Infinity}
g₀: 1 {O(1)}
g₉: 1 {O(1)}
g₁₁: inf {Infinity}
g₁₄: 1 {O(1)}
g₁₆: 1 {O(1)}
g₁₈: 1 {O(1)}
g₂₁: 1 {O(1)}
g₂₃: inf {Infinity}
g₂₅: 1 {O(1)}
g₂₈: inf {Infinity}
g₃₀: inf {Infinity}
g₃₂: inf {Infinity}
g₃₅: inf {Infinity}
g₃₇: inf {Infinity}
g₃₉: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
g₀: inf {Infinity}
g₉: inf {Infinity}
g₁₁: inf {Infinity}
g₁₄: inf {Infinity}
g₁₆: inf {Infinity}
g₁₈: inf {Infinity}
g₂₁: inf {Infinity}
g₂₃: inf {Infinity}
g₂₅: inf {Infinity}
g₂₈: inf {Infinity}
g₃₀: inf {Infinity}
g₃₂: inf {Infinity}
g₃₅: inf {Infinity}
g₃₇: inf {Infinity}
g₃₉: inf {Infinity}

Sizebounds

(g₀,l1), X₀: X₀ {O(n)}
(g₀,l1), X₁: X₁ {O(n)}
(g₀,l1), X₂: X₂ {O(n)}
(g₉,l3), X₀: 0 {O(1)}
(g₉,l3), X₁: X₁ {O(n)}
(g₉,l3), X₂: X₂ {O(n)}
(g₁₄,l2_v1), X₀: X₀ {O(n)}
(g₁₄,l2_v1), X₁: X₁ {O(n)}
(g₁₄,l2_v1), X₂: X₂ {O(n)}
(g₁₆,l3), X₀: 0 {O(1)}
(g₁₆,l3), X₁: X₁ {O(n)}
(g₁₆,l3), X₂: X₂ {O(n)}

Run probabilistic analysis on SCC: [l1]

Run classical analysis on SCC: [l2_v1]

Classical Approximation after Lifting Classical Results

All Bounds
Timebounds

Overall timebound:inf {Infinity}
g₀: 1 {O(1)}
g₉: 1 {O(1)}
g₁₁: inf {Infinity}
g₁₄: 1 {O(1)}
g₁₆: 1 {O(1)}
g₁₈: 1 {O(1)}
g₂₁: 2 {O(1)}
g₂₃: inf {Infinity}
g₂₅: 1 {O(1)}
g₂₈: inf {Infinity}
g₃₀: inf {Infinity}
g₃₂: inf {Infinity}
g₃₅: inf {Infinity}
g₃₇: inf {Infinity}
g₃₉: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
g₀: inf {Infinity}
g₉: inf {Infinity}
g₁₁: inf {Infinity}
g₁₄: inf {Infinity}
g₁₆: inf {Infinity}
g₁₈: inf {Infinity}
g₂₁: inf {Infinity}
g₂₃: inf {Infinity}
g₂₅: inf {Infinity}
g₂₈: inf {Infinity}
g₃₀: inf {Infinity}
g₃₂: inf {Infinity}
g₃₅: inf {Infinity}
g₃₇: inf {Infinity}
g₃₉: inf {Infinity}

Sizebounds

(g₀,l1), X₀: X₀ {O(n)}
(g₀,l1), X₁: X₁ {O(n)}
(g₀,l1), X₂: X₂ {O(n)}
(g₉,l3), X₀: 0 {O(1)}
(g₉,l3), X₁: X₁ {O(n)}
(g₉,l3), X₂: X₂ {O(n)}
(g₁₄,l2_v1), X₀: X₀ {O(n)}
(g₁₄,l2_v1), X₁: X₁ {O(n)}
(g₁₄,l2_v1), X₂: X₂ {O(n)}
(g₁₆,l3), X₀: 0 {O(1)}
(g₁₆,l3), X₁: X₁ {O(n)}
(g₁₆,l3), X₂: X₂ {O(n)}
(g₁₈,l1_v1), X₀: 3⋅X₀ {O(n)}
(g₁₈,l1_v1), X₁: X₁ {O(n)}
(g₁₈,l1_v1), X₂: 2⋅X₂ {O(n)}
(g₂₁,l1_v2), X₀: 2⋅X₀ {O(n)}
(g₂₁,l1_v2), X₁: 2⋅X₁ {O(n)}
(g₂₁,l1_v2), X₂: 2⋅X₂+1 {O(n)}
(g₂₁,l1_v3), X₀: 2⋅X₀ {O(n)}
(g₂₁,l1_v3), X₁: 2⋅X₁ {O(n)}
(g₂₁,l1_v3), X₂: 2⋅X₂+1 {O(n)}

Run probabilistic analysis on SCC: [l2_v1]

Run classical analysis on SCC: [l1_v1; l2_v4]

TWN: t₃₆: l1_v1→l2_v4

cycle: [t₃₆: l1_v1→l2_v4; t₃₈: l2_v4→l1_v1]
loop: (1 ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 0,(X₀,X₁,X₂) -> (3⋅X₀,X₁,2⋅X₂)
order: [X₀; X₁; X₂]
closed-form:
X₀: X₀ * 3^n
X₁: X₁
X₂: X₂ * 2^n

Termination: true
Formula:

0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₀ ≤ 0 ∧ 1+X₁ ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
∨ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₁ ≤ 0 ∧ 1 ≤ X₂ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₁ ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
∨ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ X₂ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
∨ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
∨ 1 ≤ 0 ∧ 1+X₀ ≤ 0 ∧ 1+X₁ ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 ≤ 0 ∧ 1+X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
∨ 1 ≤ 0 ∧ 1+X₁ ≤ 0 ∧ 1 ≤ X₂ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 ≤ 0 ∧ 1+X₁ ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
∨ 1 ≤ 0 ∧ 1 ≤ X₂ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
∨ 1 ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
∨ 1 ≤ X₀ ∧ 1+X₀ ≤ 0 ∧ 1+X₁ ≤ 0
∨ 1 ≤ X₀ ∧ 1+X₀ ≤ 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
∨ 1 ≤ X₀ ∧ 1+X₁ ≤ 0 ∧ 1 ≤ X₂ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 ≤ X₀ ∧ 1+X₁ ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
∨ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
∨ 1 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ ≤ 0

Stabilization-Threshold for: X₀ ≤ X₂
alphas_abs: 1+X₂
M: 0
N: 1
Bound: 2⋅X₂+4 {O(n)}

TWN - Lifting for [36: l1_v1->l2_v4; 38: l2_v4->l1_v1] of 2⋅X₂+8 {O(n)}

relevant size-bounds w.r.t. t₁₇: l2_v1→l1_v1:
X₂: 2⋅X₂ {O(n)}
Runtime-bound of t₁₇: 1 {O(1)}
Results in: 4⋅X₂+8 {O(n)}

Classical Approximation after Lifting Classical Results

All Bounds
Timebounds

Overall timebound:inf {Infinity}
g₀: 1 {O(1)}
g₉: 1 {O(1)}
g₁₁: inf {Infinity}
g₁₄: 1 {O(1)}
g₁₆: 1 {O(1)}
g₁₈: 1 {O(1)}
g₂₁: 2 {O(1)}
g₂₃: inf {Infinity}
g₂₅: 1 {O(1)}
g₂₈: inf {Infinity}
g₃₀: inf {Infinity}
g₃₂: inf {Infinity}
g₃₅: inf {Infinity}
g₃₇: 4⋅X₂+8 {O(n)}
g₃₉: 4⋅X₂+8 {O(n)}

Costbounds

Overall costbound: inf {Infinity}
g₀: inf {Infinity}
g₉: inf {Infinity}
g₁₁: inf {Infinity}
g₁₄: inf {Infinity}
g₁₆: inf {Infinity}
g₁₈: inf {Infinity}
g₂₁: inf {Infinity}
g₂₃: inf {Infinity}
g₂₅: inf {Infinity}
g₂₈: inf {Infinity}
g₃₀: inf {Infinity}
g₃₂: inf {Infinity}
g₃₅: inf {Infinity}
g₃₇: inf {Infinity}
g₃₉: inf {Infinity}

Sizebounds

(g₀,l1), X₀: X₀ {O(n)}
(g₀,l1), X₁: X₁ {O(n)}
(g₀,l1), X₂: X₂ {O(n)}
(g₉,l3), X₀: 0 {O(1)}
(g₉,l3), X₁: X₁ {O(n)}
(g₉,l3), X₂: X₂ {O(n)}
(g₁₄,l2_v1), X₀: X₀ {O(n)}
(g₁₄,l2_v1), X₁: X₁ {O(n)}
(g₁₄,l2_v1), X₂: X₂ {O(n)}
(g₁₆,l3), X₀: 0 {O(1)}
(g₁₆,l3), X₁: X₁ {O(n)}
(g₁₆,l3), X₂: X₂ {O(n)}
(g₁₈,l1_v1), X₀: 3⋅X₀ {O(n)}
(g₁₈,l1_v1), X₁: X₁ {O(n)}
(g₁₈,l1_v1), X₂: 2⋅X₂ {O(n)}
(g₂₁,l1_v2), X₀: X₀ {O(n)}
(g₂₁,l1_v2), X₁: X₁ {O(n)}
(g₂₁,l1_v2), X₂: 2⋅X₂+1 {O(n)}
(g₂₁,l1_v3), X₀: X₀ {O(n)}
(g₂₁,l1_v3), X₁: X₁ {O(n)}
(g₂₁,l1_v3), X₂: X₂ {O(n)}
(g₃₇,l2_v4), X₀: 3⋅3^(4⋅X₂+8)⋅X₀ {O(EXP)}
(g₃₇,l2_v4), X₁: X₁ {O(n)}
(g₃₇,l2_v4), X₂: 2⋅2^(4⋅X₂+8)⋅X₂ {O(EXP)}
(g₃₉,l1_v1), X₀: 3⋅3^(4⋅X₂+8)⋅X₀ {O(EXP)}
(g₃₉,l1_v1), X₁: X₁ {O(n)}
(g₃₉,l1_v1), X₂: 2⋅2^(4⋅X₂+8)⋅X₂ {O(EXP)}

Run probabilistic analysis on SCC: [l1_v1; l2_v4]

Run classical analysis on SCC: [l1_v3; l2_v3]

Classical Approximation after Lifting Classical Results

All Bounds
Timebounds

Overall timebound:inf {Infinity}
g₀: 1 {O(1)}
g₉: 1 {O(1)}
g₁₁: inf {Infinity}
g₁₄: 1 {O(1)}
g₁₆: 1 {O(1)}
g₁₈: 1 {O(1)}
g₂₁: 2 {O(1)}
g₂₃: inf {Infinity}
g₂₅: 1 {O(1)}
g₂₈: inf {Infinity}
g₃₀: inf {Infinity}
g₃₂: inf {Infinity}
g₃₅: inf {Infinity}
g₃₇: 4⋅X₂+8 {O(n)}
g₃₉: 4⋅X₂+8 {O(n)}

Costbounds

Overall costbound: inf {Infinity}
g₀: inf {Infinity}
g₉: inf {Infinity}
g₁₁: inf {Infinity}
g₁₄: inf {Infinity}
g₁₆: inf {Infinity}
g₁₈: inf {Infinity}
g₂₁: inf {Infinity}
g₂₃: inf {Infinity}
g₂₅: inf {Infinity}
g₂₈: inf {Infinity}
g₃₀: inf {Infinity}
g₃₂: inf {Infinity}
g₃₅: inf {Infinity}
g₃₇: inf {Infinity}
g₃₉: inf {Infinity}

Sizebounds

(g₀,l1), X₀: X₀ {O(n)}
(g₀,l1), X₁: X₁ {O(n)}
(g₀,l1), X₂: X₂ {O(n)}
(g₉,l3), X₀: 0 {O(1)}
(g₉,l3), X₁: X₁ {O(n)}
(g₉,l3), X₂: X₂ {O(n)}
(g₁₄,l2_v1), X₀: X₀ {O(n)}
(g₁₄,l2_v1), X₁: X₁ {O(n)}
(g₁₄,l2_v1), X₂: X₂ {O(n)}
(g₁₆,l3), X₀: 0 {O(1)}
(g₁₆,l3), X₁: X₁ {O(n)}
(g₁₆,l3), X₂: X₂ {O(n)}
(g₁₈,l1_v1), X₀: 3⋅X₀ {O(n)}
(g₁₈,l1_v1), X₁: X₁ {O(n)}
(g₁₈,l1_v1), X₂: 2⋅X₂ {O(n)}
(g₂₁,l1_v2), X₀: X₀ {O(n)}
(g₂₁,l1_v2), X₁: X₁ {O(n)}
(g₂₁,l1_v2), X₂: 2⋅X₂+1 {O(n)}
(g₂₁,l1_v3), X₀: X₀ {O(n)}
(g₂₁,l1_v3), X₁: X₁ {O(n)}
(g₂₁,l1_v3), X₂: X₂ {O(n)}
(g₃₂,l2_v3), X₀: X₀ {O(n)}
(g₃₂,l2_v3), X₁: X₁ {O(n)}
(g₃₂,l2_v3), X₂: X₂ {O(n)}
(g₃₅,l1_v2), X₀: 2⋅X₀ {O(n)}
(g₃₅,l1_v2), X₁: 2⋅X₁ {O(n)}
(g₃₅,l1_v2), X₂: 2⋅X₂+1 {O(n)}
(g₃₅,l1_v3), X₀: 2⋅X₀ {O(n)}
(g₃₅,l1_v3), X₁: 2⋅X₁ {O(n)}
(g₃₅,l1_v3), X₂: 2⋅X₂+1 {O(n)}
(g₃₇,l2_v4), X₀: 3⋅3^(4⋅X₂+8)⋅X₀ {O(EXP)}
(g₃₇,l2_v4), X₁: X₁ {O(n)}
(g₃₇,l2_v4), X₂: 2⋅2^(4⋅X₂+8)⋅X₂ {O(EXP)}
(g₃₉,l1_v1), X₀: 3⋅3^(4⋅X₂+8)⋅X₀ {O(EXP)}
(g₃₉,l1_v1), X₁: X₁ {O(n)}
(g₃₉,l1_v1), X₂: 2⋅2^(4⋅X₂+8)⋅X₂ {O(EXP)}

Run probabilistic analysis on SCC: [l1_v3; l2_v3]

Plrf for transition g₃₂:l1_v3(X₀,X₁,X₂) → t₃₁:l2_v3(X₀,X₁,X₂) :|: 1 ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 0 ≤ X₀ ∧ 2⋅X₀ ≤ 3⋅X₂:

new bound:

X₁+1 {O(n)}

PLRF:

• l1_v2: X₁-1
• l1_v3: 1+X₁
• l2_v3: X₁

Use expected size bounds for entry point (g₂₁:l2_v1→[t₁₉:1/2:l1_v2; t₂₀:1/2:l1_v3],l1_v3)
Use classical time bound for entry point (g₂₁:l2_v1→[t₁₉:1/2:l1_v2; t₂₀:1/2:l1_v3],l1_v3)

Plrf for transition g₃₅:l2_v3(X₀,X₁,X₂) → [1/2]:t₃₃:l1_v2(X₀-1,X₁,1+X₂) :+: [1/2]:t₃₄:l1_v3(X₀,X₁,X₂) :|: 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂:

new bound:

2⋅X₂ {O(n)}

PLRF:

• l1_v2: 0
• l1_v3: 2⋅X₂
• l2_v3: 1+X₂

Use expected size bounds for entry point (g₂₁:l2_v1→[t₁₉:1/2:l1_v2; t₂₀:1/2:l1_v3],l1_v3)
Use classical time bound for entry point (g₂₁:l2_v1→[t₁₉:1/2:l1_v2; t₂₀:1/2:l1_v3],l1_v3)

Run classical analysis on SCC: [l1_v2; l1_v4; l2_v2]

MPRF for transition t₂₂: l1_v2(X₀,X₁,X₂) → l2_v2(X₀,X₁,X₂) :|: 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 2+X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ 2⋅X₀ ≤ 3⋅X₂ ∧ 1 ≤ X₀ ∧ X₀ ≤ X₂ of depth 1:

new bound:

2⋅X₀+2 {O(n)}

MPRF:

• l1_v2: [1+X₀]
• l1_v4: [X₀]
• l2_v2: [X₀]

MPRF for transition t₂₆: l2_v2(X₀,X₁,X₂) → l1_v2(X₀-1,X₁,1+X₂) :|: 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ of depth 1:

new bound:

2⋅X₀ {O(n)}

MPRF:

• l1_v2: [X₀]
• l1_v4: [X₀]
• l2_v2: [X₀]

Classical Approximation after Lifting Classical Results

All Bounds
Timebounds

Overall timebound:inf {Infinity}
g₀: 1 {O(1)}
g₉: 1 {O(1)}
g₁₁: inf {Infinity}
g₁₄: 1 {O(1)}
g₁₆: 1 {O(1)}
g₁₈: 1 {O(1)}
g₂₁: 2 {O(1)}
g₂₃: 2⋅X₀+2 {O(n)}
g₂₅: 1 {O(1)}
g₂₈: inf {Infinity}
g₃₀: inf {Infinity}
g₃₂: X₁+1 {O(n)}
g₃₅: 2⋅X₂ {O(n)}
g₃₇: 4⋅X₂+8 {O(n)}
g₃₉: 4⋅X₂+8 {O(n)}

Costbounds

Overall costbound: inf {Infinity}
g₀: inf {Infinity}
g₉: inf {Infinity}
g₁₁: inf {Infinity}
g₁₄: inf {Infinity}
g₁₆: inf {Infinity}
g₁₈: inf {Infinity}
g₂₁: inf {Infinity}
g₂₃: inf {Infinity}
g₂₅: inf {Infinity}
g₂₈: inf {Infinity}
g₃₀: inf {Infinity}
g₃₂: inf {Infinity}
g₃₅: inf {Infinity}
g₃₇: inf {Infinity}
g₃₉: inf {Infinity}

Sizebounds

(g₀,l1), X₀: X₀ {O(n)}
(g₀,l1), X₁: X₁ {O(n)}
(g₀,l1), X₂: X₂ {O(n)}
(g₉,l3), X₀: 0 {O(1)}
(g₉,l3), X₁: X₁ {O(n)}
(g₉,l3), X₂: X₂ {O(n)}
(g₁₄,l2_v1), X₀: X₀ {O(n)}
(g₁₄,l2_v1), X₁: X₁ {O(n)}
(g₁₄,l2_v1), X₂: X₂ {O(n)}
(g₁₆,l3), X₀: 0 {O(1)}
(g₁₆,l3), X₁: X₁ {O(n)}
(g₁₆,l3), X₂: X₂ {O(n)}
(g₁₈,l1_v1), X₀: 3⋅X₀ {O(n)}
(g₁₈,l1_v1), X₁: X₁ {O(n)}
(g₁₈,l1_v1), X₂: 2⋅X₂ {O(n)}
(g₂₁,l1_v2), X₀: X₀ {O(n)}
(g₂₁,l1_v2), X₁: X₁ {O(n)}
(g₂₁,l1_v2), X₂: 2⋅X₂+1 {O(n)}
(g₂₁,l1_v3), X₀: X₀ {O(n)}
(g₂₁,l1_v3), X₁: X₁ {O(n)}
(g₂₁,l1_v3), X₂: X₂ {O(n)}
(g₂₃,l2_v2), X₀: 2⋅X₀ {O(n)}
(g₂₃,l2_v2), X₁: 2⋅X₁ {O(n)}
(g₂₃,l2_v2), X₂: 2⋅X₀+2⋅X₂+2 {O(n)}
(g₂₅,l3), X₀: 0 {O(1)}
(g₂₅,l3), X₁: 4⋅X₁ {O(n)}
(g₂₅,l3), X₂: 2⋅X₀+4⋅X₂+4 {O(n)}
(g₂₈,l1_v2), X₀: 4⋅X₀ {O(n)}
(g₂₈,l1_v2), X₁: 4⋅X₁ {O(n)}
(g₂₈,l1_v2), X₂: 4⋅X₀+4⋅X₂+4 {O(n)}
(g₂₈,l1_v4), X₀: 4⋅X₀ {O(n)}
(g₂₈,l1_v4), X₁: 4⋅X₁ {O(n)}
(g₂₈,l1_v4), X₂: 4⋅X₀+4⋅X₂+4 {O(n)}
(g₃₀,l2_v2), X₀: 2⋅X₀ {O(n)}
(g₃₀,l2_v2), X₁: 2⋅X₁ {O(n)}
(g₃₀,l2_v2), X₂: 2⋅X₀+2⋅X₂+2 {O(n)}
(g₃₂,l2_v3), X₀: X₀ {O(n)}
(g₃₂,l2_v3), X₁: X₁ {O(n)}
(g₃₂,l2_v3), X₂: X₂ {O(n)}
(g₃₅,l1_v2), X₀: X₀ {O(n)}
(g₃₅,l1_v2), X₁: X₁ {O(n)}
(g₃₅,l1_v2), X₂: 2⋅X₂ {O(n)}
(g₃₅,l1_v3), X₀: X₀ {O(n)}
(g₃₅,l1_v3), X₁: X₁ {O(n)}
(g₃₅,l1_v3), X₂: 2⋅X₂ {O(n)}
(g₃₇,l2_v4), X₀: 3⋅3^(4⋅X₂+8)⋅X₀ {O(EXP)}
(g₃₇,l2_v4), X₁: X₁ {O(n)}
(g₃₇,l2_v4), X₂: 2⋅2^(4⋅X₂+8)⋅X₂ {O(EXP)}
(g₃₉,l1_v1), X₀: 3⋅3^(4⋅X₂+8)⋅X₀ {O(EXP)}
(g₃₉,l1_v1), X₁: X₁ {O(n)}
(g₃₉,l1_v1), X₂: 2⋅2^(4⋅X₂+8)⋅X₂ {O(EXP)}

Run probabilistic analysis on SCC: [l1_v2; l1_v4; l2_v2]

Plrf for transition g₂₈:l2_v2(X₀,X₁,X₂) → [1/2]:t₂₆:l1_v2(X₀-1,X₁,1+X₂) :+: [1/2]:t₂₇:l1_v4(X₀,X₁,X₂) :|: 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ X₀ ≤ X₂:

new bound:

4⋅X₀ {O(n)}

PLRF:

• l1_v2: 2⋅X₀
• l1_v4: 2⋅X₀
• l2_v2: 2⋅X₀

Use expected size bounds for entry point (g₂₁:l2_v1→[t₁₉:1/2:l1_v2; t₂₀:1/2:l1_v3],l1_v2)
Use classical time bound for entry point (g₂₁:l2_v1→[t₁₉:1/2:l1_v2; t₂₀:1/2:l1_v3],l1_v2)
Use expected size bounds for entry point (g₃₅:l2_v3→[t₃₃:1/2:l1_v2; t₃₄:1/2:l1_v3],l1_v2)
Use classical time bound for entry point (g₃₅:l2_v3→[t₃₃:1/2:l1_v2; t₃₄:1/2:l1_v3],l1_v2)

Plrf for transition g₃₀:l1_v4(X₀,X₁,X₂) → t₂₉:l2_v2(X₀,X₁,X₂) :|: 1 ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 2+X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ 2⋅X₀ ≤ 3⋅X₂:

new bound:

2⋅X₀ {O(n)}

PLRF:

• l1_v2: X₀
• l1_v4: 1+X₀
• l2_v2: X₀

Use expected size bounds for entry point (g₂₁:l2_v1→[t₁₉:1/2:l1_v2; t₂₀:1/2:l1_v3],l1_v2)
Use classical time bound for entry point (g₂₁:l2_v1→[t₁₉:1/2:l1_v2; t₂₀:1/2:l1_v3],l1_v2)
Use expected size bounds for entry point (g₃₅:l2_v3→[t₃₃:1/2:l1_v2; t₃₄:1/2:l1_v3],l1_v2)
Use classical time bound for entry point (g₃₅:l2_v3→[t₃₃:1/2:l1_v2; t₃₄:1/2:l1_v3],l1_v2)

CFR: Improvement to new bound with the following program:

method: PartialEvaluationProbabilistic new bound:

O(n)

cfr-program:

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l1_v1, l1_v2, l1_v3, l1_v4, l2_v1, l2_v2, l2_v3, l2_v4, l3
Transitions:
g₀:l0(X₀,X₁,X₂) → t₁:l1(X₀,X₁,X₂) :|:
g₉:l1(X₀,X₁,X₂) → t₁₀:l3(X₀,X₁,X₂) :|: 1 ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
g₁₁:l3(X₀,X₁,X₂) → t₁₂:l3(X₀,X₁,X₂-1) :|: 1 ≤ X₂ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
g₁₄:l1(X₀,X₁,X₂) → t₁₃:l2_v1(X₀,X₁,X₂) :|: 1 ≤ X₀ ∧ X₀ ≤ X₂
g₁₆:l1(X₀,X₁,X₂) → t₁₅:l3(X₀,X₁,X₂) :|: 1 ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
g₁₈:l2_v1(X₀,X₁,X₂) → t₁₇:l1_v1(3⋅X₀,X₁,2⋅X₂) :|: X₁ ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂
g₂₁:l2_v1(X₀,X₁,X₂) → [1/2]:t₁₉:l1_v2(X₀-1,X₁,1+X₂) :+: [1/2]:t₂₀:l1_v3(X₀,X₁,X₂) :|: 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂
g₂₃:l1_v2(X₀,X₁,X₂) → t₂₂:l2_v2(X₀,X₁,X₂) :|: 1 ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 2+X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ 2⋅X₀ ≤ 3⋅X₂
g₂₅:l1_v2(X₀,X₁,X₂) → t₂₄:l3(X₀,X₁,X₂) :|: 1 ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 1 ≤ X₂ ∧ 2+X₀ ≤ X₂ ∧ X₀ ≤ X₂ ∧ 2⋅X₀ ≤ 3⋅X₂
g₂₈:l2_v2(X₀,X₁,X₂) → [1/2]:t₂₆:l1_v2(X₀-1,X₁,1+X₂) :+: [1/2]:t₂₇:l1_v4(X₀,X₁,X₂) :|: 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ X₀ ≤ X₂
g₃₀:l1_v4(X₀,X₁,X₂) → t₂₉:l2_v2(X₀,X₁,X₂) :|: 1 ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 2+X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ 2⋅X₀ ≤ 3⋅X₂
g₃₂:l1_v3(X₀,X₁,X₂) → t₃₁:l2_v3(X₀,X₁,X₂) :|: 1 ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 0 ≤ X₀ ∧ 2⋅X₀ ≤ 3⋅X₂
g₃₅:l2_v3(X₀,X₁,X₂) → [1/2]:t₃₃:l1_v2(X₀-1,X₁,1+X₂) :+: [1/2]:t₃₄:l1_v3(X₀,X₁,X₂) :|: 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂
g₃₇:l1_v1(X₀,X₁,X₂) → t₃₆:l2_v4(X₀,X₁,X₂) :|: 1 ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₂ ∧ 3 ≤ X₀ ∧ 0 ≤ X₀ ∧ 2⋅X₀ ≤ 3⋅X₂ ∧ X₁ ≤ 0
g₃₉:l2_v4(X₀,X₁,X₂) → t₃₈:l1_v1(3⋅X₀,X₁,2⋅X₂) :|: X₁ ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀ ∧ X₀ ≤ X₂

Run classical analysis on SCC: [l3]

MPRF for transition t₁₂: l3(X₀,X₁,X₂) → l3(X₀,X₁,X₂-1) :|: 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 1 ≤ X₂ of depth 1:

new bound:

2⋅X₀+6⋅X₂+4 {O(n)}

MPRF:

• l3: [X₂]

Classical Approximation after Lifting Classical Results

All Bounds
Timebounds

Overall timebound:10⋅X₀+16⋅X₂+X₁+31 {O(n)}
g₀: 1 {O(1)}
g₉: 1 {O(1)}
g₁₁: 2⋅X₀+6⋅X₂+4 {O(n)}
g₁₄: 1 {O(1)}
g₁₆: 1 {O(1)}
g₁₈: 1 {O(1)}
g₂₁: 2 {O(1)}
g₂₃: 2⋅X₀+2 {O(n)}
g₂₅: 1 {O(1)}
g₂₈: 4⋅X₀ {O(n)}
g₃₀: 2⋅X₀ {O(n)}
g₃₂: X₁+1 {O(n)}
g₃₅: 2⋅X₂ {O(n)}
g₃₇: 4⋅X₂+8 {O(n)}
g₃₉: 4⋅X₂+8 {O(n)}

Costbounds

Overall costbound: inf {Infinity}
g₀: inf {Infinity}
g₉: inf {Infinity}
g₁₁: inf {Infinity}
g₁₄: inf {Infinity}
g₁₆: inf {Infinity}
g₁₈: inf {Infinity}
g₂₁: inf {Infinity}
g₂₃: inf {Infinity}
g₂₅: inf {Infinity}
g₂₈: inf {Infinity}
g₃₀: inf {Infinity}
g₃₂: inf {Infinity}
g₃₅: inf {Infinity}
g₃₇: inf {Infinity}
g₃₉: inf {Infinity}

Sizebounds

(g₀,l1), X₀: X₀ {O(n)}
(g₀,l1), X₁: X₁ {O(n)}
(g₀,l1), X₂: X₂ {O(n)}
(g₉,l3), X₀: 0 {O(1)}
(g₉,l3), X₁: X₁ {O(n)}
(g₉,l3), X₂: X₂ {O(n)}
(g₁₁,l3), X₀: 0 {O(1)}
(g₁₁,l3), X₁: 6⋅X₁ {O(n)}
(g₁₁,l3), X₂: 2⋅X₀+6⋅X₂+4 {O(n)}
(g₁₄,l2_v1), X₀: X₀ {O(n)}
(g₁₄,l2_v1), X₁: X₁ {O(n)}
(g₁₄,l2_v1), X₂: X₂ {O(n)}
(g₁₆,l3), X₀: 0 {O(1)}
(g₁₆,l3), X₁: X₁ {O(n)}
(g₁₆,l3), X₂: X₂ {O(n)}
(g₁₈,l1_v1), X₀: 3⋅X₀ {O(n)}
(g₁₈,l1_v1), X₁: X₁ {O(n)}
(g₁₈,l1_v1), X₂: 2⋅X₂ {O(n)}
(g₂₁,l1_v2), X₀: X₀ {O(n)}
(g₂₁,l1_v2), X₁: X₁ {O(n)}
(g₂₁,l1_v2), X₂: 2⋅X₂+1 {O(n)}
(g₂₁,l1_v3), X₀: X₀ {O(n)}
(g₂₁,l1_v3), X₁: X₁ {O(n)}
(g₂₁,l1_v3), X₂: X₂ {O(n)}
(g₂₃,l2_v2), X₀: 2⋅X₀ {O(n)}
(g₂₃,l2_v2), X₁: 2⋅X₁ {O(n)}
(g₂₃,l2_v2), X₂: 2⋅X₀+2⋅X₂+2 {O(n)}
(g₂₅,l3), X₀: 0 {O(1)}
(g₂₅,l3), X₁: 4⋅X₁ {O(n)}
(g₂₅,l3), X₂: 2⋅X₀+4⋅X₂+4 {O(n)}
(g₂₈,l1_v2), X₀: 4⋅X₀ {O(n)}
(g₂₈,l1_v2), X₁: 4⋅X₁ {O(n)}
(g₂₈,l1_v2), X₂: 4⋅X₀+4⋅X₂+4 {O(n)}
(g₂₈,l1_v4), X₀: 4⋅X₀ {O(n)}
(g₂₈,l1_v4), X₁: 4⋅X₁ {O(n)}
(g₂₈,l1_v4), X₂: 4⋅X₀+4⋅X₂+4 {O(n)}
(g₃₀,l2_v2), X₀: 2⋅X₀ {O(n)}
(g₃₀,l2_v2), X₁: 2⋅X₁ {O(n)}
(g₃₀,l2_v2), X₂: 2⋅X₀+2⋅X₂+2 {O(n)}
(g₃₂,l2_v3), X₀: X₀ {O(n)}
(g₃₂,l2_v3), X₁: X₁ {O(n)}
(g₃₂,l2_v3), X₂: X₂ {O(n)}
(g₃₅,l1_v2), X₀: X₀ {O(n)}
(g₃₅,l1_v2), X₁: X₁ {O(n)}
(g₃₅,l1_v2), X₂: 2⋅X₂ {O(n)}
(g₃₅,l1_v3), X₀: X₀ {O(n)}
(g₃₅,l1_v3), X₁: X₁ {O(n)}
(g₃₅,l1_v3), X₂: X₂ {O(n)}
(g₃₇,l2_v4), X₀: 3⋅3^(4⋅X₂+8)⋅X₀ {O(EXP)}
(g₃₇,l2_v4), X₁: X₁ {O(n)}
(g₃₇,l2_v4), X₂: 2⋅2^(4⋅X₂+8)⋅X₂ {O(EXP)}
(g₃₉,l1_v1), X₀: 3⋅3^(4⋅X₂+8)⋅X₀ {O(EXP)}
(g₃₉,l1_v1), X₁: X₁ {O(n)}
(g₃₉,l1_v1), X₂: 2⋅2^(4⋅X₂+8)⋅X₂ {O(EXP)}

Run probabilistic analysis on SCC: [l3]

Results of Probabilistic Analysis

All Bounds

Timebounds

Overall timebound:10⋅X₀+16⋅X₂+X₁+31 {O(n)}
g₀: 1 {O(1)}
g₉: 1 {O(1)}
g₁₁: 2⋅X₀+6⋅X₂+4 {O(n)}
g₁₄: 1 {O(1)}
g₁₆: 1 {O(1)}
g₁₈: 1 {O(1)}
g₂₁: 2 {O(1)}
g₂₃: 2⋅X₀+2 {O(n)}
g₂₅: 1 {O(1)}
g₂₈: 4⋅X₀ {O(n)}
g₃₀: 2⋅X₀ {O(n)}
g₃₂: X₁+1 {O(n)}
g₃₅: 2⋅X₂ {O(n)}
g₃₇: 4⋅X₂+8 {O(n)}
g₃₉: 4⋅X₂+8 {O(n)}

Costbounds

Overall costbound: 14⋅X₀+18⋅X₂+X₁+33 {O(n)}
g₀: 1 {O(1)}
g₉: 1 {O(1)}
g₁₁: 2⋅X₀+6⋅X₂+4 {O(n)}
g₁₄: 1 {O(1)}
g₁₆: 1 {O(1)}
g₁₈: 1 {O(1)}
g₂₁: 4 {O(1)}
g₂₃: 2⋅X₀+2 {O(n)}
g₂₅: 1 {O(1)}
g₂₈: 8⋅X₀ {O(n)}
g₃₀: 2⋅X₀ {O(n)}
g₃₂: X₁+1 {O(n)}
g₃₅: 4⋅X₂ {O(n)}
g₃₇: 4⋅X₂+8 {O(n)}
g₃₉: 4⋅X₂+8 {O(n)}

Sizebounds

(g₀,l1), X₀: X₀ {O(n)}
(g₀,l1), X₁: X₁ {O(n)}
(g₀,l1), X₂: X₂ {O(n)}
(g₉,l3), X₀: 0 {O(1)}
(g₉,l3), X₁: X₁ {O(n)}
(g₉,l3), X₂: X₂ {O(n)}
(g₁₁,l3), X₀: 0 {O(1)}
(g₁₁,l3), X₁: 6⋅X₁ {O(n)}
(g₁₁,l3), X₂: 2⋅X₀+6⋅X₂+4 {O(n)}
(g₁₄,l2_v1), X₀: X₀ {O(n)}
(g₁₄,l2_v1), X₁: X₁ {O(n)}
(g₁₄,l2_v1), X₂: X₂ {O(n)}
(g₁₆,l3), X₀: 0 {O(1)}
(g₁₆,l3), X₁: X₁ {O(n)}
(g₁₆,l3), X₂: X₂ {O(n)}
(g₁₈,l1_v1), X₀: 3⋅X₀ {O(n)}
(g₁₈,l1_v1), X₁: X₁ {O(n)}
(g₁₈,l1_v1), X₂: 2⋅X₂ {O(n)}
(g₂₁,l1_v2), X₀: X₀ {O(n)}
(g₂₁,l1_v2), X₁: X₁ {O(n)}
(g₂₁,l1_v2), X₂: 2⋅X₂+1 {O(n)}
(g₂₁,l1_v3), X₀: X₀ {O(n)}
(g₂₁,l1_v3), X₁: X₁ {O(n)}
(g₂₁,l1_v3), X₂: X₂ {O(n)}
(g₂₃,l2_v2), X₀: 2⋅X₀ {O(n)}
(g₂₃,l2_v2), X₁: 2⋅X₁ {O(n)}
(g₂₃,l2_v2), X₂: 2⋅X₀+2⋅X₂+2 {O(n)}
(g₂₅,l3), X₀: 0 {O(1)}
(g₂₅,l3), X₁: 4⋅X₁ {O(n)}
(g₂₅,l3), X₂: 2⋅X₀+4⋅X₂+4 {O(n)}
(g₂₈,l1_v2), X₀: 4⋅X₀ {O(n)}
(g₂₈,l1_v2), X₁: 4⋅X₁ {O(n)}
(g₂₈,l1_v2), X₂: 4⋅X₀+4⋅X₂+4 {O(n)}
(g₂₈,l1_v4), X₀: 4⋅X₀ {O(n)}
(g₂₈,l1_v4), X₁: 4⋅X₁ {O(n)}
(g₂₈,l1_v4), X₂: 4⋅X₀+4⋅X₂+4 {O(n)}
(g₃₀,l2_v2), X₀: 2⋅X₀ {O(n)}
(g₃₀,l2_v2), X₁: 2⋅X₁ {O(n)}
(g₃₀,l2_v2), X₂: 2⋅X₀+2⋅X₂+2 {O(n)}
(g₃₂,l2_v3), X₀: X₀ {O(n)}
(g₃₂,l2_v3), X₁: X₁ {O(n)}
(g₃₂,l2_v3), X₂: X₂ {O(n)}
(g₃₅,l1_v2), X₀: X₀ {O(n)}
(g₃₅,l1_v2), X₁: X₁ {O(n)}
(g₃₅,l1_v2), X₂: 2⋅X₂ {O(n)}
(g₃₅,l1_v3), X₀: X₀ {O(n)}
(g₃₅,l1_v3), X₁: X₁ {O(n)}
(g₃₅,l1_v3), X₂: X₂ {O(n)}
(g₃₇,l2_v4), X₀: 3⋅3^(4⋅X₂+8)⋅X₀ {O(EXP)}
(g₃₇,l2_v4), X₁: X₁ {O(n)}
(g₃₇,l2_v4), X₂: 2⋅2^(4⋅X₂+8)⋅X₂ {O(EXP)}
(g₃₉,l1_v1), X₀: 3⋅3^(4⋅X₂+8)⋅X₀ {O(EXP)}
(g₃₉,l1_v1), X₁: X₁ {O(n)}
(g₃₉,l1_v1), X₂: 2⋅2^(4⋅X₂+8)⋅X₂ {O(EXP)}