Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l1(30, 30, 1, 0, 2, X₅, X₆, X₇, X₈)
t₁: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l1(X₀, X₁, X₂+X₃, X₂, X₄+1, X₂, X₆, X₇, X₈) :|: X₄ ≤ X₁
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₂, X₂, X₂) :|: 1+X₁ ≤ X₄

Preprocessing

Eliminate variables {X₀,X₂,X₃,X₅,X₆,X₇,X₈} that do not contribute to the problem

Found invariant X₄ ≤ 31 ∧ X₄ ≤ 1+X₁ ∧ X₁+X₄ ≤ 61 ∧ 31 ≤ X₄ ∧ 61 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ X₁ ≤ 30 ∧ 30 ≤ X₁ for location l2

Found invariant X₄ ≤ 31 ∧ X₄ ≤ 1+X₁ ∧ X₁+X₄ ≤ 61 ∧ 2 ≤ X₄ ∧ 32 ≤ X₁+X₄ ∧ X₁ ≤ 28+X₄ ∧ X₁ ≤ 30 ∧ 30 ≤ X₁ for location l1

Problem after Preprocessing

Start: l0
Program_Vars: X₁, X₄
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₇: l0(X₁, X₄) → l1(30, 2)
t₈: l1(X₁, X₄) → l1(X₁, X₄+1) :|: X₄ ≤ X₁ ∧ X₄ ≤ 31 ∧ X₄ ≤ 1+X₁ ∧ X₁+X₄ ≤ 61 ∧ 2 ≤ X₄ ∧ 32 ≤ X₁+X₄ ∧ X₁ ≤ 28+X₄ ∧ X₁ ≤ 30 ∧ 30 ≤ X₁
t₉: l1(X₁, X₄) → l2(X₁, X₄) :|: 1+X₁ ≤ X₄ ∧ X₄ ≤ 31 ∧ X₄ ≤ 1+X₁ ∧ X₁+X₄ ≤ 61 ∧ 2 ≤ X₄ ∧ 32 ≤ X₁+X₄ ∧ X₁ ≤ 28+X₄ ∧ X₁ ≤ 30 ∧ 30 ≤ X₁

MPRF for transition t₈: l1(X₁, X₄) → l1(X₁, X₄+1) :|: X₄ ≤ X₁ ∧ X₄ ≤ 31 ∧ X₄ ≤ 1+X₁ ∧ X₁+X₄ ≤ 61 ∧ 2 ≤ X₄ ∧ 32 ≤ X₁+X₄ ∧ X₁ ≤ 28+X₄ ∧ X₁ ≤ 30 ∧ 30 ≤ X₁ of depth 1:

new bound:

34 {O(1)}

MPRF:

l1 [32-X₄ ]

All Bounds

Timebounds

Overall timebound:36 {O(1)}
t₇: 1 {O(1)}
t₈: 34 {O(1)}
t₉: 1 {O(1)}

Costbounds

Overall costbound: 36 {O(1)}
t₇: 1 {O(1)}
t₈: 34 {O(1)}
t₉: 1 {O(1)}

Sizebounds

t₇, X₁: 30 {O(1)}
t₇, X₄: 2 {O(1)}
t₈, X₁: 30 {O(1)}
t₈, X₄: 31 {O(1)}
t₉, X₁: 30 {O(1)}
t₉, X₄: 31 {O(1)}