Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₃, X₄, X₂, X₃, X₄, X₅) :|: 0 < X₅
t₁: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀+X₂, X₁, X₂-1, X₃, X₄, X₅) :|: 0 < X₂
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₂, X₄, X₅) :|: X₂ ≤ 0
t₄: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₃, X₄, X₅, X₃, X₄, X₅-1) :|: 0 < X₅
t₃: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l2(5⋅X₀+(X₂)², 2⋅X₁, X₂, X₃, X₄, X₅) :|: X₀ < (X₁)² ∧ 0 < X₀
Found invariant 0 ≤ X₅ ∧ X₃ ≤ X₅ ∧ X₂ ≤ X₅ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0 for location l2
Found invariant 0 ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ for location l1
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₃, X₄, X₂, X₃, X₄, X₅) :|: 0 < X₅
t₁: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀+X₂, X₁, X₂-1, X₃, X₄, X₅) :|: 0 < X₂ ∧ 0 ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₂, X₄, X₅) :|: X₂ ≤ 0 ∧ 0 ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀
t₄: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₃, X₄, X₅, X₃, X₄, X₅-1) :|: 0 < X₅ ∧ 0 ≤ X₅ ∧ X₃ ≤ X₅ ∧ X₂ ≤ X₅ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0
t₃: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l2(5⋅X₀+(X₂)², 2⋅X₁, X₂, X₃, X₄, X₅) :|: X₀ < (X₁)² ∧ 0 < X₀ ∧ 0 ≤ X₅ ∧ X₃ ≤ X₅ ∧ X₂ ≤ X₅ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0
Found invariant 1 ≤ X₅ ∧ 1+X₃ ≤ X₅ ∧ 1+X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0 for location n_l2___6
Found invariant 0 ≤ X₅ ∧ X₃ ≤ X₅ ∧ 0 ≤ X₂+X₅ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₂ for location n_l1___3
Found invariant 0 ≤ X₅ ∧ 0 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 0 ≤ X₂+X₅ ∧ X₂ ≤ X₅ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ for location n_l2___1
Found invariant 0 ≤ X₅ ∧ 0 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 0 ≤ X₂+X₅ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ for location n_l2___2
Found invariant 1+X₅ ≤ X₂ ∧ 0 ≤ X₅ ∧ X₃ ≤ X₅ ∧ 1 ≤ X₂+X₅ ∧ X₂ ≤ 1+X₅ ∧ X₀ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₀+X₃ ≤ 0 ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ X₀ ≤ 0 for location n_l1___5
Found invariant 1 ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ for location l1
Found invariant 1 ≤ X₅ ∧ 1+X₃ ≤ X₅ ∧ 1+X₂ ≤ X₅ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0 for location n_l2___4
Found invariant 1 ≤ X₅ ∧ 1+X₃ ≤ X₅ ∧ 1+X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0 for location n_l2___6
Found invariant 0 ≤ X₅ ∧ X₃ ≤ X₅ ∧ 0 ≤ X₂+X₅ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₂ for location n_l1___3
Found invariant 0 ≤ X₅ ∧ 0 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 0 ≤ X₂+X₅ ∧ X₂ ≤ X₅ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ for location n_l2___1
Found invariant 0 ≤ X₅ ∧ 0 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 0 ≤ X₂+X₅ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ for location n_l2___2
Found invariant 1+X₅ ≤ X₂ ∧ 0 ≤ X₅ ∧ X₃ ≤ X₅ ∧ 1 ≤ X₂+X₅ ∧ X₂ ≤ 1+X₅ ∧ X₀ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₀+X₃ ≤ 0 ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ X₀ ≤ 0 for location n_l1___5
Found invariant 1 ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ for location l1
Found invariant 1 ≤ X₅ ∧ 1+X₃ ≤ X₅ ∧ 1+X₂ ≤ X₅ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0 for location n_l2___4
Termination: true
Formula:
relevant size-bounds w.r.t. t₀:
X₀: X₃ {O(n)}
X₂: X₂ {O(n)}
X₃: X₃ {O(n)}
Runtime-bound of t₀: 1 {O(1)}
Results in: 6⋅X₂+8⋅X₃+11 {O(n)}
Overall timebound:inf {Infinity}
t₀: 1 {O(1)}
t₁: inf {Infinity}
t₂: inf {Infinity}
t₃: inf {Infinity}
t₄: inf {Infinity}
Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₁: inf {Infinity}
t₂: inf {Infinity}
t₃: inf {Infinity}
t₄: inf {Infinity}
t₀, X₀: X₃ {O(n)}
t₀, X₁: X₄ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₀, X₄: X₄ {O(n)}
t₀, X₅: X₅ {O(n)}
t₁, X₁: 5⋅X₄ {O(n)}
t₁, X₂: 4⋅X₅+X₂ {O(n)}
t₁, X₃: 4⋅X₂+8⋅X₅+X₃ {O(n)}
t₁, X₄: 2⋅X₄ {O(n)}
t₁, X₅: 2⋅X₅ {O(n)}
t₂, X₁: 6⋅X₄ {O(n)}
t₂, X₂: 2⋅X₂+4⋅X₅ {O(n)}
t₂, X₃: 2⋅X₂+4⋅X₅ {O(n)}
t₂, X₄: 2⋅X₄ {O(n)}
t₂, X₅: 2⋅X₅ {O(n)}
t₃, X₂: 2⋅X₂+4⋅X₅ {O(n)}
t₃, X₃: 2⋅X₂+4⋅X₅ {O(n)}
t₃, X₄: 2⋅X₄ {O(n)}
t₃, X₅: 2⋅X₅ {O(n)}
t₄, X₀: 4⋅X₂+8⋅X₅ {O(n)}
t₄, X₁: 4⋅X₄ {O(n)}
t₄, X₂: 4⋅X₅ {O(n)}
t₄, X₃: 4⋅X₂+8⋅X₅ {O(n)}
t₄, X₄: 2⋅X₄ {O(n)}
t₄, X₅: 2⋅X₅ {O(n)}