Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars: G, H
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l1(4, 0, 0, X₃, X₄, X₅)
t₆: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, 1+X₁, G, H, X₄, G) :|: 1+X₁ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₂, X₂, X₅) :|: 1 ≤ X₂
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₂, X₂, X₅) :|: X₂+1 ≤ 0
t₁: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, 0, 0, 0, X₅) :|: X₀ ≤ X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂
t₄: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, 1+X₁, G, H, X₄, G)
t₅: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, 1+X₁, G, H, X₄, G)

Preprocessing

Cut unreachable locations [l4; l5] from the program graph

Eliminate variables {H,X₃,X₄,X₅} that do not contribute to the problem

Found invariant X₁ ≤ 4 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 8 ∧ 0 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ 4+X₁ ∧ X₀ ≤ 4 ∧ 4 ≤ X₀ for location l2

Found invariant X₁ ≤ 4 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 8 ∧ 0 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ 4+X₁ ∧ X₀ ≤ 4 ∧ 4 ≤ X₀ for location l1

Found invariant X₂ ≤ 0 ∧ 4+X₂ ≤ X₁ ∧ X₁+X₂ ≤ 4 ∧ 4+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 4 ∧ 0 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ 4+X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ 4+X₂ ∧ X₁ ≤ 4 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 8 ∧ 4 ≤ X₁ ∧ 8 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 4 ∧ 4 ≤ X₀ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars: G
Locations: l0, l1, l2, l3
Transitions:
t₁₂: l0(X₀, X₁, X₂) → l1(4, 0, 0)
t₁₃: l1(X₀, X₁, X₂) → l1(X₀, 1+X₁, G) :|: 1+X₁ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₁ ≤ 4 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 8 ∧ 0 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ 4+X₁ ∧ X₀ ≤ 4 ∧ 4 ≤ X₀
t₁₄: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: 1 ≤ X₂ ∧ X₁ ≤ 4 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 8 ∧ 0 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ 4+X₁ ∧ X₀ ≤ 4 ∧ 4 ≤ X₀
t₁₅: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₂+1 ≤ 0 ∧ X₁ ≤ 4 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 8 ∧ 0 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ 4+X₁ ∧ X₀ ≤ 4 ∧ 4 ≤ X₀
t₁₆: l1(X₀, X₁, X₂) → l3(X₀, X₁, 0) :|: X₀ ≤ X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₁ ≤ 4 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 8 ∧ 0 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ 4+X₁ ∧ X₀ ≤ 4 ∧ 4 ≤ X₀

MPRF for transition t₁₃: l1(X₀, X₁, X₂) → l1(X₀, 1+X₁, G) :|: 1+X₁ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₁ ≤ 4 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 8 ∧ 0 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ 4+X₁ ∧ X₀ ≤ 4 ∧ 4 ≤ X₀ of depth 1:

new bound:

5 {O(1)}

All Bounds

Timebounds

Overall timebound:9 {O(1)}
t₁₂: 1 {O(1)}
t₁₃: 5 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: 1 {O(1)}
t₁₆: 1 {O(1)}

Costbounds

Overall costbound: 9 {O(1)}
t₁₂: 1 {O(1)}
t₁₃: 5 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: 1 {O(1)}
t₁₆: 1 {O(1)}

Sizebounds

t₁₂, X₀: 4 {O(1)}
t₁₂, X₁: 0 {O(1)}
t₁₂, X₂: 0 {O(1)}
t₁₃, X₀: 4 {O(1)}
t₁₃, X₁: 4 {O(1)}
t₁₄, X₀: 4 {O(1)}
t₁₄, X₁: 4 {O(1)}
t₁₅, X₀: 4 {O(1)}
t₁₅, X₁: 4 {O(1)}
t₁₆, X₀: 4 {O(1)}
t₁₆, X₁: 4 {O(1)}
t₁₆, X₂: 0 {O(1)}