Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁) → l1(X₀, 1)
t₁: l1(X₀, X₁) → l1(X₀-1, 2⋅X₁) :|: 0 < X₀
t₂: l1(X₀, X₁) → l2(X₀, X₁) :|: X₀ ≤ 0
t₃: l2(X₀, X₁) → l2(X₀, X₁-1) :|: 0 < X₁
Found invariant 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l2
Found invariant 1 ≤ X₁ for location l1
Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁) → l1(X₀, 1)
t₁: l1(X₀, X₁) → l1(X₀-1, 2⋅X₁) :|: 0 < X₀ ∧ 1 ≤ X₁
t₂: l1(X₀, X₁) → l2(X₀, X₁) :|: X₀ ≤ 0 ∧ 1 ≤ X₁
t₃: l2(X₀, X₁) → l2(X₀, X₁-1) :|: 0 < X₁ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0
Found invariant 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l2
Found invariant 1 ≤ X₁ for location l1
Termination: true
Formula:
relevant size-bounds w.r.t. t₀:
X₀: X₀ {O(n)}
Runtime-bound of t₀: 1 {O(1)}
Results in: 2⋅X₀+4 {O(n)}
Found invariant 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l2
Found invariant 1 ≤ X₁ for location l1
Termination: true
Formula:
relevant size-bounds w.r.t. t₂:
X₁: 2^(2⋅X₀+4)+1 {O(EXP)}
Runtime-bound of t₂: 1 {O(1)}
Results in: 2⋅2^(2⋅X₀+4)+6 {O(EXP)}
Found invariant 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l2
Found invariant 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location n_l2___1
Found invariant 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location n_l2___2
Found invariant 1 ≤ X₁ for location l1
Found invariant 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l2
Found invariant 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location n_l2___1
Found invariant 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location n_l2___2
Found invariant 1 ≤ X₁ for location l1
Termination: true
Formula:
relevant size-bounds w.r.t. t₄₂:
X₁: 2^(2⋅X₀+4)+1 {O(EXP)}
Runtime-bound of t₄₂: 1 {O(1)}
Results in: 2⋅2^(2⋅X₀+4)+7 {O(EXP)}
Overall timebound:2⋅2^(2⋅X₀+4)+2⋅X₀+12 {O(EXP)}
t₀: 1 {O(1)}
t₁: 2⋅X₀+4 {O(n)}
t₂: 1 {O(1)}
t₃: 2⋅2^(2⋅X₀+4)+6 {O(EXP)}
Overall costbound: 2⋅2^(2⋅X₀+4)+2⋅X₀+12 {O(EXP)}
t₀: 1 {O(1)}
t₁: 2⋅X₀+4 {O(n)}
t₂: 1 {O(1)}
t₃: 2⋅2^(2⋅X₀+4)+6 {O(EXP)}
t₀, X₀: X₀ {O(n)}
t₀, X₁: 1 {O(1)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: 2^(2⋅X₀+4) {O(EXP)}
t₂, X₀: 2⋅X₀ {O(n)}
t₂, X₁: 2^(2⋅X₀+4)+1 {O(EXP)}
t₃, X₀: 2⋅X₀ {O(n)}
t₃, X₁: 2^(2⋅X₀+4)+1 {O(EXP)}