Initial Problem

Start: f0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: f0, f19, f28, f36, f8
Transitions:
t₅: f0(X₀, X₁, X₂, X₃) → f19(X₀, 999, X₂, 1)
t₁: f19(X₀, X₁, X₂, X₃) → f19(X₀, X₁-1, X₂, X₃) :|: 0 ≤ X₁
t₄: f19(X₀, X₁, X₂, X₃) → f28(X₀, X₁, 999, X₃) :|: 1+X₁ ≤ 0
t₂: f28(X₀, X₁, X₂, X₃) → f28(X₀, X₁, X₂-1, X₃) :|: 0 ≤ X₂
t₃: f28(X₀, X₁, X₂, X₃) → f36(X₀, X₁, X₂, X₃) :|: 1+X₂ ≤ 0
t₆: f8(X₀, X₁, X₂, X₃) → f19(X₀, 999, X₂, X₃) :|: 1+X₀ ≤ 0
t₀: f8(X₀, X₁, X₂, X₃) → f8(X₀-1, X₁, X₂, X₃) :|: 0 ≤ X₀

Preprocessing

Cut unreachable locations [f8] from the program graph

Eliminate variables [X₀; X₃] that do not contribute to the problem

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 f36

Found invariant X₀ ≤ 999 ∧ 0 ≤ 1+X₀ for location f19

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 f28

Problem after Preprocessing

Start: f0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: f0, f19, f28, f36
Transitions:
t₁₃: f0(X₀, X₁) → f19(999, X₁)
t₁₄: f19(X₀, X₁) → f19(X₀-1, X₁) :|: 0 ≤ X₀ ∧ X₀ ≤ 999 ∧ 0 ≤ 1+X₀
t₁₅: f19(X₀, X₁) → f28(X₀, 999) :|: 1+X₀ ≤ 0 ∧ X₀ ≤ 999 ∧ 0 ≤ 1+X₀
t₁₆: f28(X₀, X₁) → f28(X₀, X₁-1) :|: 0 ≤ X₁ ∧ X₁ ≤ 1000+X₀ ∧ X₁ ≤ 999 ∧ X₀+X₁ ≤ 998 ∧ 0 ≤ 2+X₀+X₁ ∧ 0 ≤ 1+X₀ ∧ 0 ≤ 1+X₁ ∧ 1+X₀ ≤ 0 ∧ X₀ ≤ X₁
t₁₇: f28(X₀, X₁) → f36(X₀, X₁) :|: 1+X₁ ≤ 0 ∧ X₁ ≤ 1000+X₀ ∧ X₁ ≤ 999 ∧ X₀+X₁ ≤ 998 ∧ 0 ≤ 2+X₀+X₁ ∧ 0 ≤ 1+X₀ ∧ 0 ≤ 1+X₁ ∧ 1+X₀ ≤ 0 ∧ X₀ ≤ X₁

MPRF for transition t₁₄: f19(X₀, X₁) → f19(X₀-1, X₁) :|: 0 ≤ X₀ ∧ X₀ ≤ 999 ∧ 0 ≤ 1+X₀ of depth 1:

new bound:

1000 {O(1)}

MPRF:

• f19: [1+X₀]

MPRF for transition t₁₆: f28(X₀, X₁) → f28(X₀, X₁-1) :|: 0 ≤ X₁ ∧ X₁ ≤ 1000+X₀ ∧ X₁ ≤ 999 ∧ X₀+X₁ ≤ 998 ∧ 0 ≤ 2+X₀+X₁ ∧ 0 ≤ 1+X₀ ∧ 0 ≤ 1+X₁ ∧ 1+X₀ ≤ 0 ∧ X₀ ≤ X₁ of depth 1:

new bound:

1000 {O(1)}

MPRF:

• f28: [1+X₁]

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)}