Initial Problem

Start: f0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉
Temp_Vars: A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, U, V, W, X, Y, Z
Locations: f0, f118, f62, f7
Transitions:
t₀: f0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉) → f7(8, 0, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉)
t₃: f62(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉) → f118(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉) :|: 8 ≤ X₁
t₂: f62(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉) → f62(X₀, 1+X₁, U+V, W, X+Y, Z, A1+B1, C1, D1+E1, F1, D1+E1+U+V, U+V-D1-E1, A1+B1+X+Y, X+Y-A1-B1, -3196, G1, H1, I1+J1, J1+K1, J1) :|: X₁ ≤ 7
t₄: f7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉) → f62(X₀, 0, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉) :|: 8 ≤ X₁
t₁: f7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉) → f7(X₀, 1+X₁, U+V, W, X+Y, Z, A1+B1, C1, D1+E1, F1, D1+E1+U+V, U+V-D1-E1, A1+B1+X+Y, X+Y-A1-B1, -3196, G1, H1, I1+J1, J1+K1, J1) :|: X₁ ≤ 7

Preprocessing

Eliminate variables [A1; B1; C1; D1; E1; F1; G1; H1; I1; J1; K1; U; V; W; X; Y; Z; X₀; X₂; X₃; X₄; X₅; X₆; X₇; X₈; X₉; X₁₀; X₁₁; X₁₂; X₁₃; X₁₄; X₁₅; X₁₆; X₁₇; X₁₈; X₁₉] that do not contribute to the problem

Found invariant X₀ ≤ 8 ∧ 0 ≤ X₀ for location f62

Found invariant X₀ ≤ 8 ∧ 8 ≤ X₀ for location f118

Found invariant X₀ ≤ 8 ∧ 0 ≤ X₀ for location f7

Problem after Preprocessing

Start: f0
Program_Vars: X₀
Temp_Vars:
Locations: f0, f118, f62, f7
Transitions:
t₁₁: f0(X₀) → f7(0)
t₁₂: f62(X₀) → f118(X₀) :|: 8 ≤ X₀ ∧ X₀ ≤ 8 ∧ 0 ≤ X₀
t₁₃: f62(X₀) → f62(1+X₀) :|: X₀ ≤ 7 ∧ X₀ ≤ 8 ∧ 0 ≤ X₀
t₁₄: f7(X₀) → f62(0) :|: 8 ≤ X₀ ∧ X₀ ≤ 8 ∧ 0 ≤ X₀
t₁₅: f7(X₀) → f7(1+X₀) :|: X₀ ≤ 7 ∧ X₀ ≤ 8 ∧ 0 ≤ X₀

MPRF for transition t₁₅: f7(X₀) → f7(1+X₀) :|: X₀ ≤ 7 ∧ X₀ ≤ 8 ∧ 0 ≤ X₀ of depth 1:

new bound:

9 {O(1)}

MPRF:

• f7: [9-X₀]

MPRF for transition t₁₃: f62(X₀) → f62(1+X₀) :|: X₀ ≤ 7 ∧ X₀ ≤ 8 ∧ 0 ≤ X₀ of depth 1:

new bound:

9 {O(1)}

MPRF:

• f62: [9-X₀]

All Bounds

Timebounds

Overall timebound:21 {O(1)}
t₁₁: 1 {O(1)}
t₁₂: 1 {O(1)}
t₁₃: 9 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: 9 {O(1)}

Costbounds

Overall costbound: 21 {O(1)}
t₁₁: 1 {O(1)}
t₁₂: 1 {O(1)}
t₁₃: 9 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: 9 {O(1)}

Sizebounds

t₁₁, X₀: 0 {O(1)}
t₁₂, X₀: 8 {O(1)}
t₁₃, X₀: 8 {O(1)}
t₁₄, X₀: 0 {O(1)}
t₁₅, X₀: 8 {O(1)}