Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₄: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₁, X₁, X₃, X₄, X₅, X₆) :|: X₀+(X₁)² ≤ 0
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 < X₀+(X₁)²
t₆: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, (X₂)², X₄, X₅, X₆)
t₁: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₄, X₅, X₂, X₃, X₄, X₅, X₆) :|: X₆ < 0
t₂: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₁, X₅, X₃, X₄, X₅, X₆) :|: 0 ≤ X₆
t₅: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀+(X₁)²*X₆, X₁-2⋅(X₆)², X₂, X₃, X₄, X₅, X₆)
t₇: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 < X₃
t₈: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₃ ≤ 0
t₉: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₃-1, X₄, X₅, X₆)
t₁₀: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
Found invariant X₂ ≤ X₅ for location l2
Found invariant X₂ ≤ X₅ ∧ 1 ≤ X₃ for location l6
Found invariant X₂ ≤ X₅ ∧ X₃ ≤ 0 ∧ 0 ≤ X₃ for location l7
Found invariant X₂ ≤ X₅ ∧ 0 ≤ X₃ for location l5
Found invariant X₂ ≤ X₅ ∧ X₃ ≤ 0 ∧ 0 ≤ X₃ for location l8
Found invariant 1+X₆ ≤ 0 ∧ X₁ ≤ X₅ for location l1
Found invariant 1+X₆ ≤ 0 ∧ X₁ ≤ X₅ for location l4
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₄: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₁, X₁, X₃, X₄, X₅, X₆) :|: X₀+(X₁)² ≤ 0 ∧ 1+X₆ ≤ 0 ∧ X₁ ≤ X₅
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 < X₀+(X₁)² ∧ 1+X₆ ≤ 0 ∧ X₁ ≤ X₅
t₆: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, (X₂)², X₄, X₅, X₆) :|: X₂ ≤ X₅
t₁: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₄, X₅, X₂, X₃, X₄, X₅, X₆) :|: X₆ < 0
t₂: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₁, X₅, X₃, X₄, X₅, X₆) :|: 0 ≤ X₆
t₅: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀+(X₁)²*X₆, X₁-2⋅(X₆)², X₂, X₃, X₄, X₅, X₆) :|: 1+X₆ ≤ 0 ∧ X₁ ≤ X₅
t₇: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 < X₃ ∧ X₂ ≤ X₅ ∧ 0 ≤ X₃
t₈: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₃ ≤ 0 ∧ X₂ ≤ X₅ ∧ 0 ≤ X₃
t₉: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₃-1, X₄, X₅, X₆) :|: X₂ ≤ X₅ ∧ 1 ≤ X₃
t₁₀: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₂ ≤ X₅ ∧ X₃ ≤ 0 ∧ 0 ≤ X₃
cycle: [t₃: l1→l4; t₅: l4→l1]
Termination: true
Formula:
Chain transitions t₅: l4→l1 and t₃: l1→l4 to t₇₂: l4→l4
Chain transitions t₁: l3→l1 and t₃: l1→l4 to t₇₃: l3→l4
Chain transitions t₁: l3→l1 and t₄: l1→l2 to t₇₄: l3→l2
Chain transitions t₅: l4→l1 and t₄: l1→l2 to t₇₅: l4→l2
Found invariant X₂ ≤ X₅ for location l2
Found invariant X₂ ≤ X₅ ∧ 1 ≤ X₃ for location l6
Found invariant X₂ ≤ X₅ ∧ X₃ ≤ 0 ∧ 0 ≤ X₃ for location l7
Found invariant X₂ ≤ X₅ ∧ 0 ≤ X₃ for location l5
Found invariant X₂ ≤ X₅ ∧ X₃ ≤ 0 ∧ 0 ≤ X₃ for location l8
Found invariant 1+X₆ ≤ 0 ∧ X₁ ≤ X₅ for location l1
Found invariant 1+X₆ ≤ 0 ∧ X₁ ≤ X₅ for location l4
cycle: [t₇₂: l4→l4]
Termination: true
Formula:
Found invariant X₂ ≤ X₅ for location l2
Found invariant X₂ ≤ X₅ ∧ 1 ≤ X₃ for location l6
Found invariant 1+X₆ ≤ 0 ∧ X₁ ≤ X₅ for location n_l4___2
Found invariant X₂ ≤ X₅ ∧ X₃ ≤ 0 ∧ 0 ≤ X₃ for location l7
Found invariant X₂ ≤ X₅ ∧ 0 ≤ X₃ for location l5
Found invariant X₂ ≤ X₅ ∧ X₃ ≤ 0 ∧ 0 ≤ X₃ for location l8
Found invariant 1+X₆ ≤ 0 ∧ X₅ ≤ X₁ ∧ X₁ ≤ X₅ ∧ X₄ ≤ X₀ ∧ X₀ ≤ X₄ for location l1
Found invariant 1+X₆ ≤ 0 for location n_l1___1
Chain transitions t₉: l6→l5 and t₈: l5→l7 to t₂₅₆: l6→l7
Chain transitions t₆: l2→l5 and t₈: l5→l7 to t₂₅₇: l2→l7
Chain transitions t₆: l2→l5 and t₇: l5→l6 to t₂₅₈: l2→l6
Chain transitions t₉: l6→l5 and t₇: l5→l6 to t₂₅₉: l6→l6
Found invariant X₂ ≤ X₅ for location l2
Found invariant X₂ ≤ X₅ ∧ 0 ≤ X₃ for location l6
Found invariant X₂ ≤ X₅ ∧ 0 ≤ X₃ for location l7
Found invariant X₂ ≤ X₅ ∧ 0 ≤ X₃ for location l5
Found invariant X₂ ≤ X₅ ∧ X₃ ≤ 0 ∧ 0 ≤ X₃ for location l8
Found invariant 1+X₆ ≤ 0 ∧ X₁ ≤ X₅ for location l1
Found invariant 1+X₆ ≤ 0 ∧ X₁ ≤ X₅ for location l4
new bound:
2⋅X₅⋅X₅+1 {O(n^2)}
Found invariant X₂ ≤ X₅ for location l2
Found invariant X₂ ≤ X₅ ∧ 0 ≤ X₃ for location n_l5___1
Found invariant X₂ ≤ X₅ ∧ 1 ≤ X₃ for location n_l6___2
Found invariant X₂ ≤ X₅ ∧ X₃ ≤ 0 ∧ 0 ≤ X₃ for location l7
Found invariant X₂ ≤ X₅ ∧ 0 ≤ X₃ for location l5
Found invariant X₂ ≤ X₅ ∧ X₃ ≤ 0 ∧ 0 ≤ X₃ for location l8
Found invariant 1+X₆ ≤ 0 ∧ X₁ ≤ X₅ for location l1
Found invariant 1+X₆ ≤ 0 ∧ X₁ ≤ X₅ for location l4
Overall timebound:inf {Infinity}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 12⋅X₆⋅X₆⋅X₆⋅X₆⋅X₆+12⋅X₅⋅X₆⋅X₆⋅X₆+24⋅X₆⋅X₆⋅X₆⋅X₆+24⋅X₅⋅X₆⋅X₆+6⋅X₅⋅X₅⋅X₆+6⋅X₅⋅X₅+6⋅X₄+6 {O(n^5)}
t₄: 1 {O(1)}
t₅: 12⋅X₆⋅X₆⋅X₆⋅X₆⋅X₆+12⋅X₅⋅X₆⋅X₆⋅X₆+24⋅X₆⋅X₆⋅X₆⋅X₆+24⋅X₅⋅X₆⋅X₆+6⋅X₅⋅X₅⋅X₆+6⋅X₅⋅X₅+6⋅X₄+6 {O(n^5)}
t₆: 1 {O(1)}
t₇: inf {Infinity}
t₈: 1 {O(1)}
t₉: inf {Infinity}
t₁₀: 1 {O(1)}
Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 12⋅X₆⋅X₆⋅X₆⋅X₆⋅X₆+12⋅X₅⋅X₆⋅X₆⋅X₆+24⋅X₆⋅X₆⋅X₆⋅X₆+24⋅X₅⋅X₆⋅X₆+6⋅X₅⋅X₅⋅X₆+6⋅X₅⋅X₅+6⋅X₄+6 {O(n^5)}
t₄: 1 {O(1)}
t₅: 12⋅X₆⋅X₆⋅X₆⋅X₆⋅X₆+12⋅X₅⋅X₆⋅X₆⋅X₆+24⋅X₆⋅X₆⋅X₆⋅X₆+24⋅X₅⋅X₆⋅X₆+6⋅X₅⋅X₅⋅X₆+6⋅X₅⋅X₅+6⋅X₄+6 {O(n^5)}
t₆: 1 {O(1)}
t₇: inf {Infinity}
t₈: 1 {O(1)}
t₉: inf {Infinity}
t₁₀: 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)}
t₀, X₅: X₅ {O(n)}
t₀, X₆: X₆ {O(n)}
t₁, X₀: X₄ {O(n)}
t₁, X₁: X₅ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₁, X₅: X₅ {O(n)}
t₁, X₆: X₆ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₅ {O(n)}
t₂, X₃: X₃ {O(n)}
t₂, X₄: X₄ {O(n)}
t₂, X₅: X₅ {O(n)}
t₂, X₆: X₆ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₃ {O(n)}
t₃, X₄: X₄ {O(n)}
t₃, X₅: X₅ {O(n)}
t₃, X₆: X₆ {O(n)}
t₄, X₃: 2⋅X₃ {O(n)}
t₄, X₄: 2⋅X₄ {O(n)}
t₄, X₅: 2⋅X₅ {O(n)}
t₄, X₆: 2⋅X₆ {O(n)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₃ {O(n)}
t₅, X₄: X₄ {O(n)}
t₅, X₅: X₅ {O(n)}
t₅, X₆: X₆ {O(n)}
t₆, X₄: 3⋅X₄ {O(n)}
t₆, X₅: 3⋅X₅ {O(n)}
t₆, X₆: 3⋅X₆ {O(n)}
t₇, X₄: 3⋅X₄ {O(n)}
t₇, X₅: 3⋅X₅ {O(n)}
t₇, X₆: 3⋅X₆ {O(n)}
t₈, X₃: 0 {O(1)}
t₈, X₄: 6⋅X₄ {O(n)}
t₈, X₅: 6⋅X₅ {O(n)}
t₈, X₆: 6⋅X₆ {O(n)}
t₉, X₄: 3⋅X₄ {O(n)}
t₉, X₅: 3⋅X₅ {O(n)}
t₉, X₆: 3⋅X₆ {O(n)}
t₁₀, X₃: 0 {O(1)}
t₁₀, X₄: 6⋅X₄ {O(n)}
t₁₀, X₅: 6⋅X₅ {O(n)}
t₁₀, X₆: 6⋅X₆ {O(n)}