Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄)
t₂: l1(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: 0 ≤ X₀ ∧ 0 ≤ X₁
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₀ < 0
t₄: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₁ < 0
t₁: l2(X₀, X₁, X₂, X₃, X₄) → l1(X₃, X₄, X₂, X₃, X₄)
t₅: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₁-1, X₀-1, X₂, X₃, X₄)
t₆: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄)

Preprocessing

Eliminate variables {X₂} that do not contribute to the problem

Found invariant 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₁₃: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₁₄: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 0 ≤ X₀ ∧ 0 ≤ X₁
t₁₅: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ < 0
t₁₆: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₁ < 0
t₁₇: l2(X₀, X₁, X₂, X₃) → l1(X₂, X₃, X₂, X₃)
t₁₈: l3(X₀, X₁, X₂, X₃) → l1(X₁-1, X₀-1, X₂, X₃) :|: 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₁₉: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)

MPRF for transition t₁₄: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 0 ≤ X₀ ∧ 0 ≤ X₁ of depth 1:

new bound:

X₂+X₃+1 {O(n)}

MPRF for transition t₁₈: l3(X₀, X₁, X₂, X₃) → l1(X₁-1, X₀-1, X₂, X₃) :|: 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₂+X₃+1 {O(n)}

All Bounds

Timebounds

Overall timebound:2⋅X₂+2⋅X₃+7 {O(n)}
t₁₃: 1 {O(1)}
t₁₄: X₂+X₃+1 {O(n)}
t₁₅: 1 {O(1)}
t₁₆: 1 {O(1)}
t₁₇: 1 {O(1)}
t₁₈: X₂+X₃+1 {O(n)}
t₁₉: 1 {O(1)}

Costbounds

Overall costbound: 2⋅X₂+2⋅X₃+7 {O(n)}
t₁₃: 1 {O(1)}
t₁₄: X₂+X₃+1 {O(n)}
t₁₅: 1 {O(1)}
t₁₆: 1 {O(1)}
t₁₇: 1 {O(1)}
t₁₈: X₂+X₃+1 {O(n)}
t₁₉: 1 {O(1)}

Sizebounds

t₁₃, X₀: X₀ {O(n)}
t₁₃, X₁: X₁ {O(n)}
t₁₃, X₂: X₂ {O(n)}
t₁₃, X₃: X₃ {O(n)}
t₁₄, X₀: X₂+X₃+1 {O(n)}
t₁₄, X₁: X₂+X₃+1 {O(n)}
t₁₄, X₂: X₂ {O(n)}
t₁₄, X₃: X₃ {O(n)}
t₁₅, X₀: 2⋅X₂+X₃+1 {O(n)}
t₁₅, X₁: 2⋅X₃+X₂+1 {O(n)}
t₁₅, X₂: 2⋅X₂ {O(n)}
t₁₅, X₃: 2⋅X₃ {O(n)}
t₁₆, X₀: 2⋅X₂+X₃+1 {O(n)}
t₁₆, X₁: 2⋅X₃+X₂+1 {O(n)}
t₁₆, X₂: 2⋅X₂ {O(n)}
t₁₆, X₃: 2⋅X₃ {O(n)}
t₁₇, X₀: X₂ {O(n)}
t₁₇, X₁: X₃ {O(n)}
t₁₇, X₂: X₂ {O(n)}
t₁₇, X₃: X₃ {O(n)}
t₁₈, X₀: X₂+X₃+1 {O(n)}
t₁₈, X₁: X₂+X₃+1 {O(n)}
t₁₈, X₂: X₂ {O(n)}
t₁₈, X₃: X₃ {O(n)}
t₁₉, X₀: 2⋅X₃+4⋅X₂+2 {O(n)}
t₁₉, X₁: 2⋅X₂+4⋅X₃+2 {O(n)}
t₁₉, X₂: 4⋅X₂ {O(n)}
t₁₉, X₃: 4⋅X₃ {O(n)}