Start: l0
Program_Vars: X₀, X₁
Temp_Vars: C
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁) → l1(X₀, X₁)
t₁: l1(X₀, X₁) → l1(X₀-1, X₁) :|: 0 ≤ X₀
t₂: l1(X₀, X₁) → l2(X₀, C) :|: X₀+1 ≤ 0
Eliminate variables {C,X₁} that do not contribute to the problem
Found invariant 1+X₀ ≤ 0 for location l2
Start: l0
Program_Vars: X₀
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₇: l0(X₀) → l1(X₀)
t₈: l1(X₀) → l1(X₀-1) :|: 0 ≤ X₀
t₉: l1(X₀) → l2(X₀) :|: X₀+1 ≤ 0
Found invariant 1+X₀ ≤ 0 for location l2
Termination: true
Formula:
relevant size-bounds w.r.t. t₇:
X₀: X₀ {O(n)}
Runtime-bound of t₇: 1 {O(1)}
Results in: 2⋅X₀+4 {O(n)}
Overall timebound:2⋅X₀+6 {O(n)}
t₇: 1 {O(1)}
t₈: 2⋅X₀+4 {O(n)}
t₉: 1 {O(1)}
Overall costbound: 2⋅X₀+6 {O(n)}
t₇: 1 {O(1)}
t₈: 2⋅X₀+4 {O(n)}
t₉: 1 {O(1)}
t₇, X₀: X₀ {O(n)}
t₈, X₀: X₀+1 {O(n)}
t₉, X₀: 2⋅X₀+1 {O(n)}