Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars: D
Locations: l0, l1, l2, l3
Transitions:
t₀: l0(X₀, X₁, X₂) → l1(0, D, 0)
t₁: l1(X₀, X₁, X₂) → l1(X₀, X₁, X₂+1) :|: X₂ ≤ 49
t₄: l1(X₀, X₁, X₂) → l2(0, X₁, X₂) :|: 50 ≤ X₂
t₂: l2(X₀, X₁, X₂) → l2(X₀+1, X₁, X₂) :|: X₀ ≤ 49
t₃: l2(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: 50 ≤ X₀
Eliminate variables {D,X₁} that do not contribute to the problem
Found invariant X₂ ≤ 50 ∧ X₂ ≤ 50+X₀ ∧ X₀+X₂ ≤ 100 ∧ 50 ≤ X₂ ∧ 50 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 50 ∧ 0 ≤ X₀ for location l2
Found invariant X₂ ≤ 50 ∧ X₂ ≤ 50+X₀ ∧ X₀+X₂ ≤ 50 ∧ 0 ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location l1
Found invariant X₂ ≤ 50 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 100 ∧ 50 ≤ X₂ ∧ 100 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 50 ∧ 50 ≤ X₀ for location l3
Start: l0
Program_Vars: X₀, X₂
Temp_Vars:
Locations: l0, l1, l2, l3
Transitions:
t₁₂: l0(X₀, X₂) → l1(0, 0)
t₁₃: l1(X₀, X₂) → l1(X₀, X₂+1) :|: X₂ ≤ 49 ∧ X₂ ≤ 50 ∧ X₂ ≤ 50+X₀ ∧ X₀+X₂ ≤ 50 ∧ 0 ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
t₁₄: l1(X₀, X₂) → l2(0, X₂) :|: 50 ≤ X₂ ∧ X₂ ≤ 50 ∧ X₂ ≤ 50+X₀ ∧ X₀+X₂ ≤ 50 ∧ 0 ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
t₁₅: l2(X₀, X₂) → l2(X₀+1, X₂) :|: X₀ ≤ 49 ∧ X₂ ≤ 50 ∧ X₂ ≤ 50+X₀ ∧ X₀+X₂ ≤ 100 ∧ 50 ≤ X₂ ∧ 50 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 50 ∧ 0 ≤ X₀
t₁₆: l2(X₀, X₂) → l3(X₀, X₂) :|: 50 ≤ X₀ ∧ X₂ ≤ 50 ∧ X₂ ≤ 50+X₀ ∧ X₀+X₂ ≤ 100 ∧ 50 ≤ X₂ ∧ 50 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 50 ∧ 0 ≤ X₀
Found invariant X₂ ≤ 50 ∧ X₂ ≤ 50+X₀ ∧ X₀+X₂ ≤ 100 ∧ 50 ≤ X₂ ∧ 50 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 50 ∧ 0 ≤ X₀ for location l2
Found invariant X₂ ≤ 50 ∧ X₂ ≤ 50+X₀ ∧ X₀+X₂ ≤ 50 ∧ 0 ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location l1
Found invariant X₂ ≤ 50 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 100 ∧ 50 ≤ X₂ ∧ 100 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 50 ∧ 50 ≤ X₀ for location l3
Termination: true
Formula:
relevant size-bounds w.r.t. t₁₂:
X₂: 0 {O(1)}
Runtime-bound of t₁₂: 1 {O(1)}
Results in: 102 {O(1)}
Found invariant X₂ ≤ 50 ∧ X₂ ≤ 50+X₀ ∧ X₀+X₂ ≤ 100 ∧ 50 ≤ X₂ ∧ 50 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 50 ∧ 0 ≤ X₀ for location l2
Found invariant X₂ ≤ 50 ∧ X₂ ≤ 50+X₀ ∧ X₀+X₂ ≤ 50 ∧ 0 ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location l1
Found invariant X₂ ≤ 50 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 100 ∧ 50 ≤ X₂ ∧ 100 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 50 ∧ 50 ≤ X₀ for location l3
Termination: true
Formula:
relevant size-bounds w.r.t. t₁₄:
X₀: 0 {O(1)}
Runtime-bound of t₁₄: 1 {O(1)}
Results in: 102 {O(1)}
Overall timebound:207 {O(1)}
t₁₂: 1 {O(1)}
t₁₃: 102 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: 102 {O(1)}
t₁₆: 1 {O(1)}
Overall costbound: 207 {O(1)}
t₁₂: 1 {O(1)}
t₁₃: 102 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: 102 {O(1)}
t₁₆: 1 {O(1)}
t₁₂, X₀: 0 {O(1)}
t₁₂, X₂: 0 {O(1)}
t₁₃, X₀: 0 {O(1)}
t₁₃, X₂: 50 {O(1)}
t₁₄, X₀: 0 {O(1)}
t₁₄, X₂: 50 {O(1)}
t₁₅, X₀: 50 {O(1)}
t₁₅, X₂: 50 {O(1)}
t₁₆, X₀: 50 {O(1)}
t₁₆, X₂: 50 {O(1)}