Initial Problem

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1
Transitions:
t₀: l0(X₀, X₁) → l1(X₀, X₁) :|: 0 < X₀
t₁: l1(X₀, X₁) → l1(3⋅X₀, 2⋅X₁) :|: X₀ < X₁

Preprocessing

Found invariant 1 ≤ X₀ for location l1

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1
Transitions:
t₀: l0(X₀, X₁) → l1(X₀, X₁) :|: 0 < X₀
t₁: l1(X₀, X₁) → l1(3⋅X₀, 2⋅X₁) :|: X₀ < X₁ ∧ 1 ≤ X₀

TWN: t₁: l1→l1

cycle: [t₁: l1→l1]
loop: (X₀ < X₁,(X₀,X₁) -> (3⋅X₀,2⋅X₁)
order: [X₀; X₁]
closed-form:
X₀: X₀ * 3^n
X₁: X₁ * 2^n

Termination: true
Formula:

X₀ < 0
∨ 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 t₁: l1→l1 of 2⋅X₁+4 {O(n)}

relevant size-bounds w.r.t. t₀:
X₁: X₁ {O(n)}
Runtime-bound of t₀: 1 {O(1)}
Results in: 2⋅X₁+4 {O(n)}

All Bounds

Timebounds

Overall timebound:2⋅X₁+5 {O(n)}
t₀: 1 {O(1)}
t₁: 2⋅X₁+4 {O(n)}

Costbounds

Overall costbound: 2⋅X₁+5 {O(n)}
t₀: 1 {O(1)}
t₁: 2⋅X₁+4 {O(n)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₁, X₀: 3^(2⋅X₁+4)⋅X₀ {O(EXP)}
t₁, X₁: 2^(2⋅X₁+4)⋅X₁ {O(EXP)}