Initial Problem

Start: f2
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: f2, f3, f300
Transitions:
t₃: f2(X₀, X₁, X₂, X₃, X₄) → f3(0, X₁, 0, 0, 0) :|: X₁ ≤ 0
t₂: f2(X₀, X₁, X₂, X₃, X₄) → f300(1, X₁, X₂, X₃, X₄) :|: 1 ≤ X₁
t₁: f300(X₀, X₁, X₂, X₃, X₄) → f3(X₀, X₁, 0, 0, 0) :|: 101 ≤ X₀
t₀: f300(X₀, X₁, X₂, X₃, X₄) → f300(1+X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ 100 ∧ 1 ≤ X₁

Preprocessing

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

Found invariant 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ 100+X₁ ∧ X₀ ≤ 101 ∧ 1 ≤ X₀ for location f300

Found invariant X₀ ≤ 101 ∧ 0 ≤ X₀ for location f3

Problem after Preprocessing

Start: f2
Program_Vars: X₀, X₁
Temp_Vars:
Locations: f2, f3, f300
Transitions:
t₇: f2(X₀, X₁) → f3(0, X₁) :|: X₁ ≤ 0
t₈: f2(X₀, X₁) → f300(1, X₁) :|: 1 ≤ X₁
t₉: f300(X₀, X₁) → f3(X₀, X₁) :|: 101 ≤ X₀ ∧ X₀ ≤ 101 ∧ X₀ ≤ 100+X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁
t₁₀: f300(X₀, X₁) → f300(1+X₀, X₁) :|: X₀ ≤ 100 ∧ 1 ≤ X₁ ∧ X₀ ≤ 101 ∧ X₀ ≤ 100+X₁ ∧ 1 ≤ X₀ ∧ 2 ≤ X₀+X₁

MPRF for transition t₁₀: f300(X₀, X₁) → f300(1+X₀, X₁) :|: X₀ ≤ 100 ∧ 1 ≤ X₁ ∧ X₀ ≤ 101 ∧ X₀ ≤ 100+X₁ ∧ 1 ≤ X₀ ∧ 2 ≤ X₀+X₁ of depth 1:

new bound:

102 {O(1)}

• f300: [101-X₀]

All Bounds

Timebounds

Overall timebound:105 {O(1)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₉: 1 {O(1)}
t₁₀: 102 {O(1)}

Costbounds

Overall costbound: 105 {O(1)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₉: 1 {O(1)}
t₁₀: 102 {O(1)}

Sizebounds

t₇, X₀: 0 {O(1)}
t₇, X₁: X₁ {O(n)}
t₈, X₀: 1 {O(1)}
t₈, X₁: X₁ {O(n)}
t₉, X₀: 101 {O(1)}
t₉, X₁: X₁ {O(n)}
t₁₀, X₀: 101 {O(1)}
t₁₀, X₁: X₁ {O(n)}