Initial Problem

Start: f5
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars:
Locations: f4, f5, f6
Transitions:
t₀: f4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f4(X₀+X₁, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 ≤ X₀
t₁: f4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f6(X₀, X₁, 0, 0, 0, 0, 0) :|: 1+X₀ ≤ 0
t₂: f5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1+X₁ ≤ 0
t₃: f5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f6(X₀, X₁, 0, 0, 0, 0, 0) :|: 0 ≤ X₁

Preprocessing

Eliminate variables [X₂; X₃; X₄; X₅; X₆] that do not contribute to the problem

Found invariant 1+X₁ ≤ 0 for location f4

Problem after Preprocessing

Start: f5
Program_Vars: X₀, X₁
Temp_Vars:
Locations: f4, f5, f6
Transitions:
t₆: f4(X₀, X₁) → f4(X₀+X₁, X₁) :|: 0 ≤ X₀ ∧ 1+X₁ ≤ 0
t₇: f4(X₀, X₁) → f6(X₀, X₁) :|: 1+X₀ ≤ 0 ∧ 1+X₁ ≤ 0
t₈: f5(X₀, X₁) → f4(X₀, X₁) :|: 1+X₁ ≤ 0
t₉: f5(X₀, X₁) → f6(X₀, X₁) :|: 0 ≤ X₁

MPRF for transition t₆: f4(X₀, X₁) → f4(X₀+X₁, X₁) :|: 0 ≤ X₀ ∧ 1+X₁ ≤ 0 of depth 1:

new bound:

X₀+1 {O(n)}

• f4: [1+X₀]

All Bounds

Timebounds

Overall timebound:X₀+4 {O(n)}
t₆: X₀+1 {O(n)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₉: 1 {O(1)}

Costbounds

Overall costbound: X₀+4 {O(n)}
t₆: X₀+1 {O(n)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₉: 1 {O(1)}

Sizebounds

t₆, X₀: 2⋅X₁+X₀ {O(n)}
t₆, X₁: X₁ {O(n)}
t₇, X₀: 2⋅X₀+2⋅X₁ {O(n)}
t₇, X₁: 2⋅X₁ {O(n)}
t₈, X₀: X₀ {O(n)}
t₈, X₁: X₁ {O(n)}
t₉, X₀: X₀ {O(n)}
t₉, X₁: X₁ {O(n)}