Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, X₅)
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 < X₁
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁ ≤ 0
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₃, X₄, X₂, X₃, X₄, X₅)
t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₁-1, X₀, X₂, X₃, X₄, X₅)
t₅: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅)

Preprocessing

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

Found invariant X₁ ≤ 0 for location l5

Found invariant X₁ ≤ 0 for location l4

Found invariant 1 ≤ X₁ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₁₁: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₁₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 0 < X₁
t₁₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₁ ≤ 0
t₁₄: l2(X₀, X₁, X₂, X₃) → l1(X₂, X₃, X₂, X₃)
t₁₅: l3(X₀, X₁, X₂, X₃) → l1(X₁-1, X₀, X₂, X₃) :|: 1 ≤ X₁
t₁₆: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₁ ≤ 0

MPRF for transition t₁₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 0 < X₁ of depth 2:

new bound:

16⋅X₃+8⋅X₂+9 {O(n)}

MPRF for transition t₁₅: l3(X₀, X₁, X₂, X₃) → l1(X₁-1, X₀, X₂, X₃) :|: 1 ≤ X₁ of depth 2:

new bound:

16⋅X₃+8⋅X₂+17 {O(n)}

All Bounds

Timebounds

Overall timebound:16⋅X₂+32⋅X₃+30 {O(n)}
t₁₁: 1 {O(1)}
t₁₂: 16⋅X₃+8⋅X₂+9 {O(n)}
t₁₃: 1 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: 16⋅X₃+8⋅X₂+17 {O(n)}
t₁₆: 1 {O(1)}

Costbounds

Overall costbound: 16⋅X₂+32⋅X₃+30 {O(n)}
t₁₁: 1 {O(1)}
t₁₂: 16⋅X₃+8⋅X₂+9 {O(n)}
t₁₃: 1 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: 16⋅X₃+8⋅X₂+17 {O(n)}
t₁₆: 1 {O(1)}

Sizebounds

t₁₁, X₀: X₀ {O(n)}
t₁₁, X₁: X₁ {O(n)}
t₁₁, X₂: X₂ {O(n)}
t₁₁, X₃: X₃ {O(n)}
t₁₂, X₀: X₂+X₃ {O(n)}
t₁₂, X₁: X₂+X₃ {O(n)}
t₁₂, X₂: X₂ {O(n)}
t₁₂, X₃: X₃ {O(n)}
t₁₃, X₀: 2⋅X₂+X₃ {O(n)}
t₁₃, X₁: 2⋅X₃+X₂ {O(n)}
t₁₃, X₂: 2⋅X₂ {O(n)}
t₁₃, X₃: 2⋅X₃ {O(n)}
t₁₄, X₀: X₂ {O(n)}
t₁₄, X₁: X₃ {O(n)}
t₁₄, X₂: X₂ {O(n)}
t₁₄, X₃: X₃ {O(n)}
t₁₅, X₀: X₂+X₃ {O(n)}
t₁₅, X₁: X₂+X₃ {O(n)}
t₁₅, X₂: X₂ {O(n)}
t₁₅, X₃: X₃ {O(n)}
t₁₆, X₀: 2⋅X₂+X₃ {O(n)}
t₁₆, X₁: 2⋅X₃+X₂ {O(n)}
t₁₆, X₂: 2⋅X₂ {O(n)}
t₁₆, X₃: 2⋅X₃ {O(n)}