Initial Problem

Start: f0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈
Temp_Vars:
Locations: f0, f19, f7
Transitions:
t₀: f0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → f7(30, 30, 1, 0, 2, X₅, X₆, X₇, X₈)
t₂: f7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → f19(X₀, X₁, X₂, X₃, X₄, X₅, X₂, X₂, X₂) :|: 1+X₁ ≤ X₄
t₁: f7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → f7(X₀, X₁, X₂+X₃, X₂, 1+X₄, X₂, X₆, X₇, X₈) :|: X₄ ≤ X₁

Preprocessing

Eliminate variables [X₀; X₂; X₃; X₅; X₆; X₇; X₈] that do not contribute to the problem

Found invariant X₁ ≤ 31 ∧ X₁ ≤ 1+X₀ ∧ X₀+X₁ ≤ 61 ∧ 31 ≤ X₁ ∧ 61 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 30 ∧ 30 ≤ X₀ for location f19

Found invariant X₁ ≤ 31 ∧ X₁ ≤ 1+X₀ ∧ X₀+X₁ ≤ 61 ∧ 2 ≤ X₁ ∧ 32 ≤ X₀+X₁ ∧ X₀ ≤ 28+X₁ ∧ X₀ ≤ 30 ∧ 30 ≤ X₀ for location f7

Problem after Preprocessing

Start: f0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: f0, f19, f7
Transitions:
t₆: f0(X₀, X₁) → f7(30, 2)
t₇: f7(X₀, X₁) → f19(X₀, X₁) :|: 1+X₀ ≤ X₁ ∧ X₀+X₁ ≤ 61 ∧ X₁ ≤ 31 ∧ X₀ ≤ 30 ∧ X₀ ≤ 28+X₁ ∧ X₁ ≤ 1+X₀ ∧ 2 ≤ X₁ ∧ 30 ≤ X₀ ∧ 32 ≤ X₀+X₁
t₈: f7(X₀, X₁) → f7(X₀, 1+X₁) :|: X₁ ≤ X₀ ∧ X₀+X₁ ≤ 61 ∧ X₁ ≤ 31 ∧ X₀ ≤ 30 ∧ X₀ ≤ 28+X₁ ∧ X₁ ≤ 1+X₀ ∧ 2 ≤ X₁ ∧ 30 ≤ X₀ ∧ 32 ≤ X₀+X₁

MPRF for transition t₈: f7(X₀, X₁) → f7(X₀, 1+X₁) :|: X₁ ≤ X₀ ∧ X₀+X₁ ≤ 61 ∧ X₁ ≤ 31 ∧ X₀ ≤ 30 ∧ X₀ ≤ 28+X₁ ∧ X₁ ≤ 1+X₀ ∧ 2 ≤ X₁ ∧ 30 ≤ X₀ ∧ 32 ≤ X₀+X₁ of depth 1:

new bound:

34 {O(1)}

MPRF:

• f7: [32-X₁]

All Bounds

Timebounds

Overall timebound:36 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 34 {O(1)}

Costbounds

Overall costbound: 36 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 34 {O(1)}

Sizebounds

t₆, X₀: 30 {O(1)}
t₆, X₁: 2 {O(1)}
t₇, X₀: 30 {O(1)}
t₇, X₁: 31 {O(1)}
t₈, X₀: 30 {O(1)}
t₈, X₁: 31 {O(1)}