Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars: E
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l1(0, X₁, X₂, X₃)
t₁: l1(X₀, X₁, X₂, X₃) → l1(X₀+1, X₁, X₂, X₃) :|: X₀ ≤ 3
t₂: l1(X₀, X₁, X₂, X₃) → l1(X₀+1, X₀, X₀+1, E) :|: X₀ ≤ 3
t₃: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: 4 ≤ X₀ ∧ E+1 ≤ 0
t₄: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: 4 ≤ X₀

Preprocessing

Eliminate variables {X₁,X₂,X₃} that do not contribute to the problem

Found invariant X₀ ≤ 4 ∧ 4 ≤ X₀ for location l2

Found invariant X₀ ≤ 4 ∧ 0 ≤ X₀ for location l1

Problem after Preprocessing

Start: l0
Program_Vars: X₀
Temp_Vars: E
Locations: l0, l1, l2
Transitions:
t₁₁: l0(X₀) → l1(0)
t₁₂: l1(X₀) → l1(X₀+1) :|: X₀ ≤ 3 ∧ X₀ ≤ 4 ∧ 0 ≤ X₀
t₁₃: l1(X₀) → l1(X₀+1) :|: X₀ ≤ 3 ∧ X₀ ≤ 4 ∧ 0 ≤ X₀
t₁₄: l1(X₀) → l2(X₀) :|: 4 ≤ X₀ ∧ E+1 ≤ 0 ∧ X₀ ≤ 4 ∧ 0 ≤ X₀
t₁₅: l1(X₀) → l2(X₀) :|: 4 ≤ X₀ ∧ X₀ ≤ 4 ∧ 0 ≤ X₀

MPRF for transition t₁₂: l1(X₀) → l1(X₀+1) :|: X₀ ≤ 3 ∧ X₀ ≤ 4 ∧ 0 ≤ X₀ of depth 1:

new bound:

4 {O(1)}

MPRF:

l1 [4-X₀ ]

MPRF for transition t₁₃: l1(X₀) → l1(X₀+1) :|: X₀ ≤ 3 ∧ X₀ ≤ 4 ∧ 0 ≤ X₀ of depth 1:

new bound:

4 {O(1)}

MPRF:

l1 [4-X₀ ]

All Bounds

Timebounds

Overall timebound:11 {O(1)}
t₁₁: 1 {O(1)}
t₁₂: 4 {O(1)}
t₁₃: 4 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: 1 {O(1)}

Costbounds

Overall costbound: 11 {O(1)}
t₁₁: 1 {O(1)}
t₁₂: 4 {O(1)}
t₁₃: 4 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: 1 {O(1)}

Sizebounds

t₁₁, X₀: 0 {O(1)}
t₁₂, X₀: 4 {O(1)}
t₁₃, X₀: 4 {O(1)}
t₁₄, X₀: 4 {O(1)}
t₁₅, X₀: 4 {O(1)}