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) → l3(X₀, X₁, X₂, X₃, X₄)
t₅: l1(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: X₁ ≤ (X₀)²+(X₄)⁵
t₆: l1(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ 0 ∧ 0 ≤ X₀
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: (X₀)²+(X₄)⁵ < X₁ ∧ X₀ < 0
t₄: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: (X₀)²+(X₄)⁵ < X₁ ∧ 0 < X₀
t₈: l2(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄)
t₁: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₂, X₃, X₂, X₃, X₄) :|: 0 < X₄
t₂: l3(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: X₄ ≤ 0
t₇: l4(X₀, X₁, X₂, X₃, X₄) → l1(4⋅X₀, 9⋅X₁-8⋅(X₄)³, X₂, X₃, X₄)
Found invariant 1 ≤ X₄ for location l1
Found invariant 1 ≤ X₄ for location l4
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) → l3(X₀, X₁, X₂, X₃, X₄)
t₅: l1(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: X₁ ≤ (X₀)²+(X₄)⁵ ∧ 1 ≤ X₄
t₆: l1(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 ≤ X₄
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: (X₀)²+(X₄)⁵ < X₁ ∧ X₀ < 0 ∧ 1 ≤ X₄
t₄: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: (X₀)²+(X₄)⁵ < X₁ ∧ 0 < X₀ ∧ 1 ≤ X₄
t₈: l2(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄)
t₁: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₂, X₃, X₂, X₃, X₄) :|: 0 < X₄
t₂: l3(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: X₄ ≤ 0
t₇: l4(X₀, X₁, X₂, X₃, X₄) → l1(4⋅X₀, 9⋅X₁-8⋅(X₄)³, X₂, X₃, X₄) :|: 1 ≤ X₄
Found invariant 1 ≤ X₄ for location l1
Found invariant 1 ≤ X₄ for location l4
Termination: true
Formula:
relevant size-bounds w.r.t. t₁:
X₁: X₃ {O(n)}
Runtime-bound of t₁: 1 {O(1)}
Results in: 2⋅X₃+6 {O(n)}
knowledge_propagation leads to new time bound 2⋅X₃+7 {O(n)} for transition t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: (X₀)²+(X₄)⁵ < X₁ ∧ X₀ < 0 ∧ 1 ≤ X₄
knowledge_propagation leads to new time bound 2⋅X₃+7 {O(n)} for transition t₄: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: (X₀)²+(X₄)⁵ < X₁ ∧ 0 < X₀ ∧ 1 ≤ X₄
Overall timebound:6⋅X₃+26 {O(n)}
t₀: 1 {O(1)}
t₃: 2⋅X₃+7 {O(n)}
t₄: 2⋅X₃+7 {O(n)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₈: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₇: 2⋅X₃+6 {O(n)}
Overall costbound: 6⋅X₃+26 {O(n)}
t₀: 1 {O(1)}
t₃: 2⋅X₃+7 {O(n)}
t₄: 2⋅X₃+7 {O(n)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₈: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₇: 2⋅X₃+6 {O(n)}
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)}
t₃, X₀: 2⋅4^(2⋅X₃+6)⋅X₂ {O(EXP)}
t₃, X₂: 2⋅X₂ {O(n)}
t₃, X₃: 2⋅X₃ {O(n)}
t₃, X₄: 2⋅X₄ {O(n)}
t₄, X₀: 2⋅4^(2⋅X₃+6)⋅X₂ {O(EXP)}
t₄, X₂: 2⋅X₂ {O(n)}
t₄, X₃: 2⋅X₃ {O(n)}
t₄, X₄: 2⋅X₄ {O(n)}
t₅, X₀: 2⋅4^(2⋅X₃+6)⋅X₂+X₂ {O(EXP)}
t₅, X₂: 3⋅X₂ {O(n)}
t₅, X₃: 3⋅X₃ {O(n)}
t₅, X₄: 3⋅X₄ {O(n)}
t₆, X₀: 0 {O(1)}
t₆, X₂: 3⋅X₂ {O(n)}
t₆, X₃: 3⋅X₃ {O(n)}
t₆, X₄: 3⋅X₄ {O(n)}
t₈, X₀: 2⋅4^(2⋅X₃+6)⋅X₂+X₀+X₂ {O(EXP)}
t₈, X₂: 7⋅X₂ {O(n)}
t₈, X₃: 7⋅X₃ {O(n)}
t₈, X₄: 7⋅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)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₂, X₄: X₄ {O(n)}
t₇, X₀: 2⋅4^(2⋅X₃+6)⋅X₂ {O(EXP)}
t₇, X₂: 2⋅X₂ {O(n)}
t₇, X₃: 2⋅X₃ {O(n)}
t₇, X₄: 2⋅X₄ {O(n)}