Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄)
t₂: l1(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: X₀ < (X₁)² ∧ 0 < X₀
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: (X₁)² ≤ X₀
t₄: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ 0
t₁: l2(X₀, X₁, X₂, X₃, X₄) → l1(X₂, X₃, X₂, X₃, X₄)
t₅: l3(X₀, X₁, X₂, X₃, X₄) → l1(5⋅X₀+(X₄)², 2⋅X₁, X₂, X₃, X₄)
t₆: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄)
Found invariant X₂ ≤ X₀ for location l5
Found invariant X₂ ≤ X₀ for location l1
Found invariant X₂ ≤ X₀ for location l4
Found invariant X₂ ≤ X₀ ∧ 1 ≤ X₀ for location l3
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄)
t₂: l1(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: X₀ < (X₁)² ∧ 0 < X₀ ∧ X₂ ≤ X₀
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: (X₁)² ≤ X₀ ∧ X₂ ≤ X₀
t₄: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ 0 ∧ X₂ ≤ X₀
t₁: l2(X₀, X₁, X₂, X₃, X₄) → l1(X₂, X₃, X₂, X₃, X₄)
t₅: l3(X₀, X₁, X₂, X₃, X₄) → l1(5⋅X₀+(X₄)², 2⋅X₁, X₂, X₃, X₄) :|: X₂ ≤ X₀ ∧ 1 ≤ X₀
t₆: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ X₀
Found invariant X₂ ≤ X₀ for location l5
Found invariant X₂ ≤ X₀ for location l1
Found invariant X₂ ≤ X₀ for location l4
Found invariant X₂ ≤ X₀ ∧ 1 ≤ X₀ for location l3
Termination: true
Formula:
relevant size-bounds w.r.t. t₁:
X₁: X₃ {O(n)}
X₄: X₄ {O(n)}
Runtime-bound of t₁: 1 {O(1)}
Results in: 4⋅X₄⋅X₄+8⋅X₃⋅X₃+16 {O(n^2)}
relevant size-bounds w.r.t. t₁:
X₁: X₃ {O(n)}
X₄: X₄ {O(n)}
Runtime-bound of t₁: 1 {O(1)}
Results in: 4⋅X₄⋅X₄+8⋅X₃⋅X₃+16 {O(n^2)}
Eliminate variables {X₄} that do not contribute to the problem
Found invariant X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ for location n_l3___3
Found invariant 1 ≤ X₂ for location n_l1___2
Found invariant X₂ ≤ X₀ for location l5
Found invariant X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ for location l1
Found invariant X₂ ≤ X₀ for location l4
Found invariant X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₀ for location n_l3___1
Overall timebound:16⋅X₃⋅X₃+8⋅X₄⋅X₄+37 {O(n^2)}
t₀: 1 {O(1)}
t₂: 4⋅X₄⋅X₄+8⋅X₃⋅X₃+16 {O(n^2)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₁: 1 {O(1)}
t₅: 4⋅X₄⋅X₄+8⋅X₃⋅X₃+16 {O(n^2)}
t₆: 1 {O(1)}
Overall costbound: 16⋅X₃⋅X₃+8⋅X₄⋅X₄+37 {O(n^2)}
t₀: 1 {O(1)}
t₂: 4⋅X₄⋅X₄+8⋅X₃⋅X₃+16 {O(n^2)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₁: 1 {O(1)}
t₅: 4⋅X₄⋅X₄+8⋅X₃⋅X₃+16 {O(n^2)}
t₆: 1 {O(1)}
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₀, X₄: X₄ {O(n)}
t₂, X₁: 2^(4⋅X₄⋅X₄+8⋅X₃⋅X₃+16)⋅X₃ {O(EXP)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₂, X₄: X₄ {O(n)}
t₃, X₁: 2^(4⋅X₄⋅X₄+8⋅X₃⋅X₃+16)⋅X₃+X₃ {O(EXP)}
t₃, X₂: 2⋅X₂ {O(n)}
t₃, X₃: 2⋅X₃ {O(n)}
t₃, X₄: 2⋅X₄ {O(n)}
t₄, X₁: 2^(4⋅X₄⋅X₄+8⋅X₃⋅X₃+16)⋅X₃+X₃ {O(EXP)}
t₄, X₂: 2⋅X₂ {O(n)}
t₄, X₃: 2⋅X₃ {O(n)}
t₄, X₄: 2⋅X₄ {O(n)}
t₁, X₀: X₂ {O(n)}
t₁, X₁: X₃ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₅, X₁: 2^(4⋅X₄⋅X₄+8⋅X₃⋅X₃+16)⋅X₃ {O(EXP)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₃ {O(n)}
t₅, X₄: X₄ {O(n)}
t₆, X₁: 2⋅2^(4⋅X₄⋅X₄+8⋅X₃⋅X₃+16)⋅X₃+2⋅X₃ {O(EXP)}
t₆, X₂: 4⋅X₂ {O(n)}
t₆, X₃: 4⋅X₃ {O(n)}
t₆, X₄: 4⋅X₄ {O(n)}