Initial Problem

Start: f1
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars: G, H, I
Locations: f0, f1, f2
Transitions:
t₁: f0(X₀, X₁, X₂, X₃, X₄, X₅) → f0(X₀, X₁, X₂-1, G, 0, H) :|: 1 ≤ X₀ ∧ 3 ≤ X₂
t₂: f0(X₀, X₁, X₂, X₃, X₄, X₅) → f0(X₀-1, X₁, I, G, H, X₅) :|: 1+H ≤ 0 ∧ 1 ≤ X₀
t₃: f0(X₀, X₁, X₂, X₃, X₄, X₅) → f0(X₀-1, X₁, I, G, H, X₅) :|: 1 ≤ H ∧ 1 ≤ X₀
t₀: f0(X₀, X₁, X₂, X₃, X₄, X₅) → f2(X₀, G, X₂, X₃, X₄, X₅) :|: X₀ ≤ 0
t₄: f1(X₀, X₁, X₂, X₃, X₄, X₅) → f0(X₀, X₁, X₂, X₃, X₄, X₅)

Preprocessing

Eliminate variables [G; X₁; X₃; X₄; X₅] that do not contribute to the problem

Found invariant X₀ ≤ 0 for location f2

Problem after Preprocessing

Start: f1
Program_Vars: X₀, X₁
Temp_Vars: H, I
Locations: f0, f1, f2
Transitions:
t₉: f0(X₀, X₁) → f0(X₀, X₁-1) :|: 1 ≤ X₀ ∧ 3 ≤ X₁
t₁₀: f0(X₀, X₁) → f0(X₀-1, I) :|: 1+H ≤ 0 ∧ 1 ≤ X₀
t₁₁: f0(X₀, X₁) → f0(X₀-1, I) :|: 1 ≤ H ∧ 1 ≤ X₀
t₁₂: f0(X₀, X₁) → f2(X₀, X₁) :|: X₀ ≤ 0
t₁₃: f1(X₀, X₁) → f0(X₀, X₁)

MPRF for transition t₁₀: f0(X₀, X₁) → f0(X₀-1, I) :|: 1+H ≤ 0 ∧ 1 ≤ X₀ of depth 1:

new bound:

X₀ {O(n)}

• f0: [X₀]

MPRF for transition t₁₁: f0(X₀, X₁) → f0(X₀-1, I) :|: 1 ≤ H ∧ 1 ≤ X₀ of depth 1:

new bound:

X₀ {O(n)}

• f0: [X₀]

Found invariant 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location f0_v2

Found invariant 0 ≤ X₀ for location f0_v1

Found invariant X₀ ≤ 0 for location f2

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₉: inf {Infinity}
t₁₀: X₀ {O(n)}
t₁₁: X₀ {O(n)}
t₁₂: 1 {O(1)}
t₁₃: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₉: inf {Infinity}
t₁₀: X₀ {O(n)}
t₁₁: X₀ {O(n)}
t₁₂: 1 {O(1)}
t₁₃: 1 {O(1)}

Sizebounds

t₉, X₀: X₀ {O(n)}
t₁₀, X₀: X₀ {O(n)}
t₁₁, X₀: X₀ {O(n)}
t₁₂, X₀: 3⋅X₀ {O(n)}
t₁₃, X₀: X₀ {O(n)}
t₁₃, X₁: X₁ {O(n)}