Initial Problem

Start: f3
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars: G, H
Locations: f2, f3, f4
Transitions:
t₀: f2(X₀, X₁, X₂, X₃, X₄, X₅) → f2(X₀-1, X₁-1, X₀, X₁, X₀-2, X₅) :|: 1 ≤ X₀ ∧ 1 ≤ X₁
t₂: f2(X₀, X₁, X₂, X₃, X₄, X₅) → f4(X₀, G, X₂, X₃, X₄, H) :|: G ≤ 0 ∧ X₁ ≤ 0
t₃: f2(X₀, X₁, X₂, X₃, X₄, X₅) → f4(X₀, X₁, X₂, X₃, X₄, H) :|: 1 ≤ X₁ ∧ X₀ ≤ 0
t₁: f3(X₀, X₁, X₂, X₃, X₄, X₅) → f2(X₀, X₁, X₂, X₃, X₄, X₅)

Preprocessing

Eliminate variables [H; X₂; X₃; X₄; X₅] that do not contribute to the problem

Problem after Preprocessing

Start: f3
Program_Vars: X₀, X₁
Temp_Vars: G
Locations: f2, f3, f4
Transitions:
t₇: f2(X₀, X₁) → f2(X₀-1, X₁-1) :|: 1 ≤ X₀ ∧ 1 ≤ X₁
t₈: f2(X₀, X₁) → f4(X₀, G) :|: G ≤ 0 ∧ X₁ ≤ 0
t₉: f2(X₀, X₁) → f4(X₀, X₁) :|: 1 ≤ X₁ ∧ X₀ ≤ 0
t₁₀: f3(X₀, X₁) → f2(X₀, X₁)

MPRF for transition t₇: f2(X₀, X₁) → f2(X₀-1, X₁-1) :|: 1 ≤ X₀ ∧ 1 ≤ X₁ of depth 1:

new bound:

X₀ {O(n)}

• f2: [X₀]

All Bounds

Timebounds

Overall timebound:X₀+3 {O(n)}
t₇: X₀ {O(n)}
t₈: 1 {O(1)}
t₉: 1 {O(1)}
t₁₀: 1 {O(1)}

Costbounds

Overall costbound: X₀+3 {O(n)}
t₇: X₀ {O(n)}
t₈: 1 {O(1)}
t₉: 1 {O(1)}
t₁₀: 1 {O(1)}

Sizebounds

t₇, X₀: X₀ {O(n)}
t₇, X₁: X₁ {O(n)}
t₈, X₀: 2⋅X₀ {O(n)}
t₉, X₀: 2⋅X₀ {O(n)}
t₉, X₁: 2⋅X₁ {O(n)}
t₁₀, X₀: X₀ {O(n)}
t₁₀, X₁: X₁ {O(n)}