Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉
Temp_Vars: K, L
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l1(K, 0, 0, X₃, X₄, X₅, X₆, X₇, X₈, X₉)
t₁: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l1(X₀, X₁+1, X₂+1, 1, X₄, X₅, X₆, X₇, X₈, X₉) :|: X₂ ≤ 15
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l1(X₀, X₁, X₂+1, 0, X₄, X₅, X₆, X₇, X₈, X₉) :|: X₂ ≤ 15
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l2(X₀, X₁, X₂, X₃, X₁, X₁, K, L, L, L) :|: 16 ≤ X₂

Preprocessing

Eliminate variables {K,L,X₀,X₁,X₃,X₄,X₅,X₆,X₇,X₈,X₉} that do not contribute to the problem

Found invariant X₂ ≤ 16 ∧ 16 ≤ X₂ for location l2

Found invariant X₂ ≤ 16 ∧ 0 ≤ X₂ for location l1

Problem after Preprocessing

Start: l0
Program_Vars: X₂
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₉: l0(X₂) → l1(0)
t₁₀: l1(X₂) → l1(X₂+1) :|: X₂ ≤ 15 ∧ X₂ ≤ 16 ∧ 0 ≤ X₂
t₁₁: l1(X₂) → l1(X₂+1) :|: X₂ ≤ 15 ∧ X₂ ≤ 16 ∧ 0 ≤ X₂
t₁₂: l1(X₂) → l2(X₂) :|: 16 ≤ X₂ ∧ X₂ ≤ 16 ∧ 0 ≤ X₂

MPRF for transition t₁₀: l1(X₂) → l1(X₂+1) :|: X₂ ≤ 15 ∧ X₂ ≤ 16 ∧ 0 ≤ X₂ of depth 1:

new bound:

16 {O(1)}

MPRF:

l1 [16-X₂ ]

MPRF for transition t₁₁: l1(X₂) → l1(X₂+1) :|: X₂ ≤ 15 ∧ X₂ ≤ 16 ∧ 0 ≤ X₂ of depth 1:

new bound:

16 {O(1)}

MPRF:

l1 [16-X₂ ]

All Bounds

Timebounds

Overall timebound:34 {O(1)}
t₉: 1 {O(1)}
t₁₀: 16 {O(1)}
t₁₁: 16 {O(1)}
t₁₂: 1 {O(1)}

Costbounds

Overall costbound: 34 {O(1)}
t₉: 1 {O(1)}
t₁₀: 16 {O(1)}
t₁₁: 16 {O(1)}
t₁₂: 1 {O(1)}

Sizebounds

t₉, X₂: 0 {O(1)}
t₁₀, X₂: 16 {O(1)}
t₁₁, X₂: 16 {O(1)}
t₁₂, X₂: 16 {O(1)}