Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₀ < X₁ ∧ 0 < X₀
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₀
t₄: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0
t₁: l2(X₀, X₁, X₂, X₃) → l1(X₂, X₃, X₂, X₃)
t₅: l3(X₀, X₁, X₂, X₃) → l1(3⋅X₀, 2⋅X₁, X₂, X₃)
t₆: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)

Preprocessing

Found invariant X₃ ≤ X₁ ∧ X₂ ≤ X₀ for location l5

Found invariant X₃ ≤ X₁ ∧ X₂ ≤ X₀ for location l1

Found invariant X₃ ≤ X₁ ∧ X₂ ≤ X₀ for location l4

Found invariant X₃ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₀ < X₁ ∧ 0 < X₀ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₀
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₀
t₄: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0 ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₀
t₁: l2(X₀, X₁, X₂, X₃) → l1(X₂, X₃, X₂, X₃)
t₅: l3(X₀, X₁, X₂, X₃) → l1(3⋅X₀, 2⋅X₁, X₂, X₃) :|: X₃ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₆: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₁ ∧ X₂ ≤ X₀

TWN: t₂: l1→l3

cycle: [t₂: l1→l3; t₅: l3→l1]
loop: (X₀ < X₁ ∧ 0 < X₀,(X₀,X₁) -> (3⋅X₀,2⋅X₁)
order: [X₀; X₁]
closed-form:
X₀: X₀ * 3^n
X₁: X₁ * 2^n

Termination: true
Formula:

0 < X₀ ∧ X₀ < 0
∨ 0 < X₀ ∧ 0 < X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀

Stabilization-Threshold for: X₀ < X₁
alphas_abs: X₁
M: 0
N: 1
Bound: 2⋅X₁+2 {O(n)}

TWN - Lifting for t₂: l1→l3 of 2⋅X₁+5 {O(n)}

relevant size-bounds w.r.t. t₁:
X₁: X₃ {O(n)}
Runtime-bound of t₁: 1 {O(1)}
Results in: 2⋅X₃+5 {O(n)}

TWN: t₅: l3→l1

TWN - Lifting for t₅: l3→l1 of 2⋅X₁+5 {O(n)}

relevant size-bounds w.r.t. t₁:
X₁: X₃ {O(n)}
Runtime-bound of t₁: 1 {O(1)}
Results in: 2⋅X₃+5 {O(n)}

All Bounds

Timebounds

Overall timebound:4⋅X₃+15 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 2⋅X₃+5 {O(n)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 2⋅X₃+5 {O(n)}
t₆: 1 {O(1)}

Costbounds

Overall costbound: 4⋅X₃+15 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 2⋅X₃+5 {O(n)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 2⋅X₃+5 {O(n)}
t₆: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₁, X₀: X₂ {O(n)}
t₁, X₁: X₃ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₂, X₀: 3^(2⋅X₃+5)⋅X₂ {O(EXP)}
t₂, X₁: 2^(2⋅X₃+5)⋅X₃ {O(EXP)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₃, X₀: 3^(2⋅X₃+5)⋅X₂+X₂ {O(EXP)}
t₃, X₁: 2^(2⋅X₃+5)⋅X₃+X₃ {O(EXP)}
t₃, X₂: 2⋅X₂ {O(n)}
t₃, X₃: 2⋅X₃ {O(n)}
t₄, X₀: X₂ {O(n)}
t₄, X₁: X₃ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₅, X₀: 3^(2⋅X₃+5)⋅X₂ {O(EXP)}
t₅, X₁: 2^(2⋅X₃+5)⋅X₃ {O(EXP)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₃ {O(n)}
t₆, X₀: 3^(2⋅X₃+5)⋅X₂+2⋅X₂ {O(EXP)}
t₆, X₁: 2^(2⋅X₃+5)⋅X₃+2⋅X₃ {O(EXP)}
t₆, X₂: 3⋅X₂ {O(n)}
t₆, X₃: 3⋅X₃ {O(n)}