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, X₃, X₄
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₁₂: l0(X₀, X₁, X₃, X₄) → l2(X₀, X₁, X₃, X₄)
t₁₃: l1(X₀, X₁, X₃, X₄) → l3(X₀, X₁, X₃, X₄) :|: 0 < X₁
t₁₄: l1(X₀, X₁, X₃, X₄) → l4(X₀, X₁, X₃, X₄) :|: X₁ ≤ 0
t₁₅: l2(X₀, X₁, X₃, X₄) → l1(X₃, X₄, X₃, X₄)
t₁₆: l3(X₀, X₁, X₃, X₄) → l1(X₁-1, X₀, X₃, X₄) :|: 1 ≤ X₁
t₁₇: l4(X₀, X₁, X₃, X₄) → l5(X₀, X₁, X₃, X₄) :|: X₁ ≤ 0

MPRF for transition t₁₃: l1(X₀, X₁, X₃, X₄) → l3(X₀, X₁, X₃, X₄) :|: 0 < X₁ of depth 2:

new bound:

16⋅X₄+8⋅X₃+9 {O(n)}

MPRF:

l3 [X₀+X₁-2 ; X₀ ]
l1 [X₀+X₁-1 ; X₁ ]

MPRF for transition t₁₆: l3(X₀, X₁, X₃, X₄) → l1(X₁-1, X₀, X₃, X₄) :|: 1 ≤ X₁ of depth 2:

new bound:

16⋅X₄+8⋅X₃+17 {O(n)}

MPRF:

l3 [X₀+X₁-1 ; 0 ]
l1 [X₀+X₁-1 ; X₁-1 ]

All Bounds

Timebounds

Overall timebound:16⋅X₃+32⋅X₄+30 {O(n)}
t₁₂: 1 {O(1)}
t₁₃: 16⋅X₄+8⋅X₃+9 {O(n)}
t₁₄: 1 {O(1)}
t₁₅: 1 {O(1)}
t₁₆: 16⋅X₄+8⋅X₃+17 {O(n)}
t₁₇: 1 {O(1)}

Costbounds

Overall costbound: 16⋅X₃+32⋅X₄+30 {O(n)}
t₁₂: 1 {O(1)}
t₁₃: 16⋅X₄+8⋅X₃+9 {O(n)}
t₁₄: 1 {O(1)}
t₁₅: 1 {O(1)}
t₁₆: 16⋅X₄+8⋅X₃+17 {O(n)}
t₁₇: 1 {O(1)}

Sizebounds

t₁₂, X₀: X₀ {O(n)}
t₁₂, X₁: X₁ {O(n)}
t₁₂, X₃: X₃ {O(n)}
t₁₂, X₄: X₄ {O(n)}
t₁₃, X₀: X₃+X₄ {O(n)}
t₁₃, X₁: X₃+X₄ {O(n)}
t₁₃, X₃: X₃ {O(n)}
t₁₃, X₄: X₄ {O(n)}
t₁₄, X₀: 2⋅X₃+X₄ {O(n)}
t₁₄, X₁: 2⋅X₄+X₃ {O(n)}
t₁₄, X₃: 2⋅X₃ {O(n)}
t₁₄, X₄: 2⋅X₄ {O(n)}
t₁₅, X₀: X₃ {O(n)}
t₁₅, X₁: X₄ {O(n)}
t₁₅, X₃: X₃ {O(n)}
t₁₅, X₄: X₄ {O(n)}
t₁₆, X₀: X₃+X₄ {O(n)}
t₁₆, X₁: X₃+X₄ {O(n)}
t₁₆, X₃: X₃ {O(n)}
t₁₆, X₄: X₄ {O(n)}
t₁₇, X₀: 2⋅X₃+X₄ {O(n)}
t₁₇, X₁: 2⋅X₄+X₃ {O(n)}
t₁₇, X₃: 2⋅X₃ {O(n)}
t₁₇, X₄: 2⋅X₄ {O(n)}