Initial Problem

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

Preprocessing

Eliminate variables {X₂,X₃,X₄,X₅,X₆} that do not contribute to the problem

Found invariant 1+X₁ ≤ 0 for location l1

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₈: l0(X₀, X₁) → l1(X₀, X₁) :|: X₁+1 ≤ 0
t₉: l0(X₀, X₁) → l2(X₀, X₁) :|: 0 ≤ X₁
t₁₀: l1(X₀, X₁) → l1(X₀+X₁, X₁) :|: 0 ≤ X₀ ∧ 1+X₁ ≤ 0
t₁₁: l1(X₀, X₁) → l2(X₀, X₁) :|: X₀+1 ≤ 0 ∧ 1+X₁ ≤ 0

MPRF for transition t₁₀: l1(X₀, X₁) → l1(X₀+X₁, X₁) :|: 0 ≤ X₀ ∧ 1+X₁ ≤ 0 of depth 1:

new bound:

X₀+1 {O(n)}

MPRF:

l1 [X₀+1 ]

All Bounds

Timebounds

Overall timebound:X₀+4 {O(n)}
t₈: 1 {O(1)}
t₉: 1 {O(1)}
t₁₀: X₀+1 {O(n)}
t₁₁: 1 {O(1)}

Costbounds

Overall costbound: X₀+4 {O(n)}
t₈: 1 {O(1)}
t₉: 1 {O(1)}
t₁₀: X₀+1 {O(n)}
t₁₁: 1 {O(1)}

Sizebounds

t₈, X₀: X₀ {O(n)}
t₈, X₁: X₁ {O(n)}
t₉, X₀: X₀ {O(n)}
t₉, X₁: X₁ {O(n)}
t₁₀, X₀: 2⋅X₁+X₀ {O(n)}
t₁₀, X₁: X₁ {O(n)}
t₁₁, X₀: 2⋅X₀+2⋅X₁ {O(n)}
t₁₁, X₁: 2⋅X₁ {O(n)}