Initial Problem

Start: f3
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅
Temp_Vars: A1, B1, Q, R, S, T, U, V, W, X, Y, Z
Locations: f1, f3, f4
Transitions:
t₀: f1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅) → f1(X₀, 1+X₁, X₃, Q, X₃, R, X₁, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅) :|: 1+X₁ ≤ X₀ ∧ 0 ≤ X₁
t₁: f1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅) → f4(R, S, U, X, W, X₅, X₆, Q, T, V, Y, Z, X₂, X₁₃, X₁₄, X₁₅) :|: 2 ≤ Q ∧ Q ≤ S ∧ X₀ ≤ X₁ ∧ 0 ≤ X₁
t₃: f3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅) → f1(R, 2, U, S, U, X₅, X₆, R, T, U, X₁₀, X₁₁, X₁₂, Q, T, V) :|: 2 ≤ R
t₂: f3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅) → f4(T, V, S, Y, X, X₅, X₆, R, U, W, Z, B1, X₁₄, Q, X₁₄, X₁₅) :|: A1 ≤ 0 ∧ R ≤ 0
t₄: f3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅) → f4(R, S, U, Y, X, X₅, X₆, 1, T, W, Z, B1, X₃, Q, V, X₁₅)

Preprocessing

Eliminate variables [B1; U; W; X; Y; Z; X₂; X₃; X₄; X₅; X₆; X₇; X₈; X₉; X₁₀; X₁₁; X₁₂; X₁₃; X₁₄; X₁₅] 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: A1, Q, R, S, T, V
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(R, S) :|: 2 ≤ Q ∧ Q ≤ S ∧ X₀ ≤ X₁ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₁ ≤ X₀
t₉: f3(X₀, X₁) → f1(R, 2) :|: 2 ≤ R
t₁₀: f3(X₀, X₁) → f4(T, V) :|: A1 ≤ 0 ∧ R ≤ 0
t₁₁: f3(X₀, X₁) → f4(R, S)

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)}