Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4
Transitions:
t₅: l0(X₀, X₁, X₂, X₃) → l1(X₀, 999, X₂, 1)
t₁: l1(X₀, X₁, X₂, X₃) → l1(X₀, X₁-1, X₂, X₃) :|: 0 ≤ X₁
t₄: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, 999, X₃) :|: X₁+1 ≤ 0
t₂: l2(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂-1, X₃) :|: 0 ≤ X₂
t₃: l2(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₂+1 ≤ 0
t₆: l3(X₀, X₁, X₂, X₃) → l1(X₀, 999, X₂, X₃) :|: X₀+1 ≤ 0
t₀: l3(X₀, X₁, X₂, X₃) → l3(X₀-1, X₁, X₂, X₃) :|: 0 ≤ X₀

Preprocessing

Cut unreachable locations [l3] from the program graph

Eliminate variables {X₀,X₃} that do not contribute to the problem

Found invariant X₁ ≤ 999 ∧ X₁ ≤ 1000+X₀ ∧ X₀+X₁ ≤ 998 ∧ 0 ≤ 1+X₁ ∧ 0 ≤ 2+X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 ∧ 0 ≤ 1+X₀ for location l2

Found invariant X₀ ≤ 999 ∧ 0 ≤ 1+X₀ for location l1

Found invariant 1+X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 2+X₀+X₁ ≤ 0 ∧ 0 ≤ 1+X₁ ∧ 0 ≤ 2+X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 ∧ 0 ≤ 1+X₀ for location l4

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2, l4
Transitions:
t₁₃: l0(X₀, X₁) → l1(999, X₁)
t₁₄: l1(X₀, X₁) → l1(X₀-1, X₁) :|: 0 ≤ X₀ ∧ X₀ ≤ 999 ∧ 0 ≤ 1+X₀
t₁₅: l1(X₀, X₁) → l2(X₀, 999) :|: X₀+1 ≤ 0 ∧ X₀ ≤ 999 ∧ 0 ≤ 1+X₀
t₁₆: l2(X₀, X₁) → l2(X₀, X₁-1) :|: 0 ≤ X₁ ∧ X₁ ≤ 999 ∧ X₁ ≤ 1000+X₀ ∧ X₀+X₁ ≤ 998 ∧ 0 ≤ 1+X₁ ∧ 0 ≤ 2+X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 ∧ 0 ≤ 1+X₀
t₁₇: l2(X₀, X₁) → l4(X₀, X₁) :|: X₁+1 ≤ 0 ∧ X₁ ≤ 999 ∧ X₁ ≤ 1000+X₀ ∧ X₀+X₁ ≤ 998 ∧ 0 ≤ 1+X₁ ∧ 0 ≤ 2+X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 ∧ 0 ≤ 1+X₀

MPRF for transition t₁₄: l1(X₀, X₁) → l1(X₀-1, X₁) :|: 0 ≤ X₀ ∧ X₀ ≤ 999 ∧ 0 ≤ 1+X₀ of depth 1:

new bound:

1000 {O(1)}

MPRF for transition t₁₆: l2(X₀, X₁) → l2(X₀, X₁-1) :|: 0 ≤ X₁ ∧ X₁ ≤ 999 ∧ X₁ ≤ 1000+X₀ ∧ X₀+X₁ ≤ 998 ∧ 0 ≤ 1+X₁ ∧ 0 ≤ 2+X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 ∧ 0 ≤ 1+X₀ of depth 1:

new bound:

1000 {O(1)}

All Bounds

Timebounds

Overall timebound:2003 {O(1)}
t₁₃: 1 {O(1)}
t₁₄: 1000 {O(1)}
t₁₅: 1 {O(1)}
t₁₆: 1000 {O(1)}
t₁₇: 1 {O(1)}

Costbounds

Overall costbound: 2003 {O(1)}
t₁₃: 1 {O(1)}
t₁₄: 1000 {O(1)}
t₁₅: 1 {O(1)}
t₁₆: 1000 {O(1)}
t₁₇: 1 {O(1)}

Sizebounds

t₁₃, X₀: 999 {O(1)}
t₁₃, X₁: X₁ {O(n)}
t₁₄, X₀: 998 {O(1)}
t₁₄, X₁: X₁ {O(n)}
t₁₅, X₀: 1 {O(1)}
t₁₅, X₁: 999 {O(1)}
t₁₆, X₀: 1 {O(1)}
t₁₆, X₁: 998 {O(1)}
t₁₇, X₀: 1 {O(1)}
t₁₇, X₁: 1 {O(1)}