Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars: D
Locations: l0, l1, l2
Transitions:
t₃: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
t₀: l1(X₀, X₁, X₂) → l1(1+X₀, X₁, X₂) :|: 1+X₀ ≤ X₁
t₁: l1(X₀, X₁, X₂) → l1(1+X₀, X₁, X₂) :|: 1+X₁ ≤ X₀ ∧ X₁ ≤ X₀
t₂: l1(X₀, X₁, X₂) → l2(X₀, X₁, D) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀
Eliminate variables {D,X₂} that do not contribute to the problem
Found invariant X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l2
Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₁₃: l0(X₀, X₁) → l1(X₀, X₁)
t₁₄: l1(X₀, X₁) → l1(1+X₀, X₁) :|: 1+X₀ ≤ X₁
t₁₅: l1(X₀, X₁) → l1(1+X₀, X₁) :|: 1+X₁ ≤ X₀ ∧ X₁ ≤ X₀
t₁₆: l1(X₀, X₁) → l2(X₀, X₁) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀
Found invariant X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l2
Cut unsatisfiable transition t₇₁: n_l1___1→l2
Found invariant X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l2
Found invariant X₀ ≤ X₁ for location n_l1___2
Found invariant 2+X₁ ≤ X₀ for location n_l1___1
Found invariant X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l2
Found invariant X₀ ≤ X₁ for location n_l1___2
Found invariant 2+X₁ ≤ X₀ for location n_l1___1
Found invariant X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l2
Found invariant X₀ ≤ X₁ for location n_l1___2
Found invariant 2+X₁ ≤ X₀ for location n_l1___1
Termination: true
Formula:
relevant size-bounds w.r.t. t₆₄:
X₀: X₀+1 {O(n)}
X₁: X₁ {O(n)}
Runtime-bound of t₆₄: 1 {O(1)}
Results in: 4⋅X₀+4⋅X₁+10 {O(n)}
Overall timebound:inf {Infinity}
t₁₃: 1 {O(1)}
t₁₄: inf {Infinity}
t₁₅: inf {Infinity}
t₁₆: 1 {O(1)}
Overall costbound: inf {Infinity}
t₁₃: 1 {O(1)}
t₁₄: inf {Infinity}
t₁₅: inf {Infinity}
t₁₆: 1 {O(1)}
t₁₃, X₀: X₀ {O(n)}
t₁₃, X₁: X₁ {O(n)}
t₁₄, X₁: X₁ {O(n)}
t₁₅, X₁: X₁ {O(n)}
t₁₆, X₁: 2⋅X₁ {O(n)}