Initial Problem
Start: l0
Program_Vars: X₀, X₁
Temp_Vars: nondef.0
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁) → l2(X₀, X₁)
t₂: l1(X₀, X₁) → l3(X₀, X₁) :|: X₁ < 40
t₃: l1(X₀, X₁) → l4(X₀, X₁) :|: 40 ≤ X₁
t₁: l2(X₀, X₁) → l1(nondef.0, 0)
t₄: l3(X₀, X₁) → l1(X₀, X₁+1) :|: X₀ ≤ 0 ∧ 0 ≤ X₀
t₅: l3(X₀, X₁) → l1(X₀, X₁+2) :|: X₀ < 0
t₆: l3(X₀, X₁) → l1(X₀, X₁+2) :|: 0 < X₀
t₇: l4(X₀, X₁) → l5(X₀, X₁)
Preprocessing
Found invariant 40 ≤ X₁ for location l5
Found invariant 0 ≤ X₁ for location l1
Found invariant 40 ≤ X₁ for location l4
Found invariant X₁ ≤ 39 ∧ 0 ≤ X₁ for location l3
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁
Temp_Vars: nondef.0
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁) → l2(X₀, X₁)
t₂: l1(X₀, X₁) → l3(X₀, X₁) :|: X₁ < 40 ∧ 0 ≤ X₁
t₃: l1(X₀, X₁) → l4(X₀, X₁) :|: 40 ≤ X₁ ∧ 0 ≤ X₁
t₁: l2(X₀, X₁) → l1(nondef.0, 0)
t₄: l3(X₀, X₁) → l1(X₀, X₁+1) :|: X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ X₁ ≤ 39 ∧ 0 ≤ X₁
t₅: l3(X₀, X₁) → l1(X₀, X₁+2) :|: X₀ < 0 ∧ X₁ ≤ 39 ∧ 0 ≤ X₁
t₆: l3(X₀, X₁) → l1(X₀, X₁+2) :|: 0 < X₀ ∧ X₁ ≤ 39 ∧ 0 ≤ X₁
t₇: l4(X₀, X₁) → l5(X₀, X₁) :|: 40 ≤ X₁
MPRF for transition t₂: l1(X₀, X₁) → l3(X₀, X₁) :|: X₁ < 40 ∧ 0 ≤ X₁ of depth 1:
new bound:
40 {O(1)}
MPRF for transition t₄: l3(X₀, X₁) → l1(X₀, X₁+1) :|: X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ X₁ ≤ 39 ∧ 0 ≤ X₁ of depth 1:
new bound:
40 {O(1)}
MPRF for transition t₅: l3(X₀, X₁) → l1(X₀, X₁+2) :|: X₀ < 0 ∧ X₁ ≤ 39 ∧ 0 ≤ X₁ of depth 1:
new bound:
40 {O(1)}
MPRF for transition t₆: l3(X₀, X₁) → l1(X₀, X₁+2) :|: 0 < X₀ ∧ X₁ ≤ 39 ∧ 0 ≤ X₁ of depth 1:
new bound:
40 {O(1)}
All Bounds
Timebounds
Overall timebound:164 {O(1)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 40 {O(1)}
t₃: 1 {O(1)}
t₄: 40 {O(1)}
t₅: 40 {O(1)}
t₆: 40 {O(1)}
t₇: 1 {O(1)}
Costbounds
Overall costbound: 164 {O(1)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 40 {O(1)}
t₃: 1 {O(1)}
t₄: 40 {O(1)}
t₅: 40 {O(1)}
t₆: 40 {O(1)}
t₇: 1 {O(1)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₁, X₁: 0 {O(1)}
t₂, X₁: 39 {O(1)}
t₃, X₁: 122 {O(1)}
t₄, X₀: 0 {O(1)}
t₄, X₁: 40 {O(1)}
t₅, X₁: 41 {O(1)}
t₆, X₁: 41 {O(1)}
t₇, X₁: 122 {O(1)}