Initial Problem

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

Preprocessing

Found invariant X₀ ≤ 0 for location l2

Found invariant X₀ ≤ 0 for location l5

Found invariant 1 ≤ X₀ for location l1

Problem after Preprocessing

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

MPRF for transition t₄: l1(X₀) → l4(X₀-1) :|: 1 ≤ X₀ of depth 1:

new bound:

X₀ {O(n)}

MPRF:

l4 [X₀ ]
l1 [X₀ ]

MPRF for transition t₂: l4(X₀) → l1(X₀) :|: 1 ≤ X₀ of depth 1:

new bound:

X₀ {O(n)}

MPRF:

l4 [X₀ ]
l1 [X₀-1 ]

All Bounds

Timebounds

Overall timebound:2⋅X₀+4 {O(n)}
t₀: 1 {O(1)}
t₄: X₀ {O(n)}
t₅: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₀ {O(n)}
t₃: 1 {O(1)}

Costbounds

Overall costbound: 2⋅X₀+4 {O(n)}
t₀: 1 {O(1)}
t₄: X₀ {O(n)}
t₅: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₀ {O(n)}
t₃: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₄, X₀: X₀ {O(n)}
t₅, X₀: 2⋅X₀ {O(n)}
t₁, X₀: X₀ {O(n)}
t₂, X₀: X₀ {O(n)}
t₃, X₀: 2⋅X₀ {O(n)}