Initial Problem

Start: f3
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃
Temp_Vars: O, P, Q, R, S, T, U, V, W, X, Y
Locations: f1, f3, f4
Transitions:
t₀: f1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → f1(X₀, 1+X₁, X₃, O, X₃, P, X₁, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) :|: 1+X₁ ≤ X₀ ∧ 0 ≤ X₁
t₁: f1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → f4(P, Q, R, U, T, X₅, X₆, O, S, V, W, X₂, X₁₂, X₁₃) :|: 2 ≤ O ∧ O ≤ Q ∧ X₀ ≤ X₁ ∧ 0 ≤ X₁
t₃: f3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → f1(P, 2, R, Q, R, X₅, X₆, P, R, X₉, X₁₀, X₁₁, O, S) :|: 2 ≤ P
t₂: f3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → f4(R, S, Q, V, U, X₅, X₆, P, T, W, Y, 0, O, X₁₃) :|: P ≤ 0 ∧ X ≤ 0
t₄: f3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → f4(P, Q, R, U, T, X₅, X₆, 1, S, V, W, X₃, O, X₁₃)

Preprocessing

Eliminate variables [T; U; V; W; Y; X₂; X₃; X₄; X₅; X₆; X₇; X₈; X₉; X₁₀; X₁₁; X₁₂; X₁₃] that do not contribute to the problem

Found invariant X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location f1

Problem after Preprocessing

Start: f3
Program_Vars: X₀, X₁
Temp_Vars: O, P, Q, R, S, X
Locations: f1, f3, f4
Transitions:
t₇: f1(X₀, X₁) → f1(X₀, 1+X₁) :|: 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₁ ≤ X₀
t₈: f1(X₀, X₁) → f4(P, Q) :|: 2 ≤ O ∧ O ≤ Q ∧ X₀ ≤ X₁ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₁ ≤ X₀
t₉: f3(X₀, X₁) → f1(P, 2) :|: 2 ≤ P
t₁₀: f3(X₀, X₁) → f4(R, S) :|: P ≤ 0 ∧ X ≤ 0
t₁₁: f3(X₀, X₁) → f4(P, Q)

Found invariant X₁ ≤ 2 ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location f1

Found invariant X₁ ≤ X₀ ∧ 3 ≤ X₁ ∧ 6 ≤ X₀+X₁ ∧ 3 ≤ X₀ for location f1_v1

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₇: inf {Infinity}
t₈: 1 {O(1)}
t₉: 1 {O(1)}
t₁₀: 1 {O(1)}
t₁₁: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₇: inf {Infinity}
t₈: 1 {O(1)}
t₉: 1 {O(1)}
t₁₀: 1 {O(1)}
t₁₁: 1 {O(1)}

Sizebounds

t₉, X₁: 2 {O(1)}