Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇
Temp_Vars: I
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l1(I, 0, X₂, X₃, X₄, X₅, X₆, X₇)
t₁: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l1(X₀, X₁+1, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₁+1 ≤ X₂
t₉: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l2(X₀, X₁, X₂, X₂, 0, X₅, X₆, X₇) :|: X₂ ≤ X₁
t₂: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l3(X₀, X₁, X₂, X₃, X₄, X₄, X₄+1, X₇) :|: 2+X₄ ≤ X₃
t₈: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l4(X₀, X₁, X₂, X₃, 0, X₅, X₆, X₇) :|: X₃ ≤ X₄+1
t₇: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l2(X₀, X₁, X₂, X₃, X₄+1, X₅, X₆, I) :|: X₃ ≤ X₆
t₃: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆+1, X₇) :|: X₆+1 ≤ X₃
t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l3(X₀, X₁, X₂, X₃, X₄, X₆, X₆+1, X₇) :|: X₆+1 ≤ X₃
t₅: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l4(X₀, X₁, X₂, X₃, X₄+1, X₅, X₆, X₇) :|: 2+X₄ ≤ X₃
t₆: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₃ ≤ X₄+1
Eliminate variables {I,X₀,X₅,X₇} that do not contribute to the problem
Found invariant X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 0 ≤ X₁+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁ for location l2
Found invariant X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ X₃ ≤ 1+X₄ ∧ X₂ ≤ 1+X₄ ∧ 0 ≤ X₁+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁ for location l5
Found invariant 0 ≤ X₁ for location l1
Found invariant X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 0 ≤ X₁+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁ for location l4
Found invariant X₆ ≤ X₃ ∧ X₆ ≤ X₂ ∧ X₆ ≤ X₁ ∧ 1 ≤ X₆ ∧ 1 ≤ X₄+X₆ ∧ 1+X₄ ≤ X₆ ∧ 3 ≤ X₃+X₆ ∧ 3 ≤ X₂+X₆ ∧ 3 ≤ X₁+X₆ ∧ 2+X₄ ≤ X₃ ∧ 2+X₄ ≤ X₂ ∧ 2+X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 2 ≤ X₁ for location l3
Start: l0
Program_Vars: X₁, X₂, X₃, X₄, X₆
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₂₃: l0(X₁, X₂, X₃, X₄, X₆) → l1(0, X₂, X₃, X₄, X₆)
t₂₄: l1(X₁, X₂, X₃, X₄, X₆) → l1(X₁+1, X₂, X₃, X₄, X₆) :|: X₁+1 ≤ X₂ ∧ 0 ≤ X₁
t₂₅: l1(X₁, X₂, X₃, X₄, X₆) → l2(X₁, X₂, X₂, 0, X₆) :|: X₂ ≤ X₁ ∧ 0 ≤ X₁
t₂₆: l2(X₁, X₂, X₃, X₄, X₆) → l3(X₁, X₂, X₃, X₄, X₄+1) :|: 2+X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 0 ≤ X₁+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁
t₂₇: l2(X₁, X₂, X₃, X₄, X₆) → l4(X₁, X₂, X₃, 0, X₆) :|: X₃ ≤ X₄+1 ∧ X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 0 ≤ X₁+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁
t₃₀: l3(X₁, X₂, X₃, X₄, X₆) → l2(X₁, X₂, X₃, X₄+1, X₆) :|: X₃ ≤ X₆ ∧ X₆ ≤ X₃ ∧ X₆ ≤ X₂ ∧ X₆ ≤ X₁ ∧ 1 ≤ X₆ ∧ 1 ≤ X₄+X₆ ∧ 1+X₄ ≤ X₆ ∧ 3 ≤ X₃+X₆ ∧ 3 ≤ X₂+X₆ ∧ 3 ≤ X₁+X₆ ∧ 2+X₄ ≤ X₃ ∧ 2+X₄ ≤ X₂ ∧ 2+X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 2 ≤ X₁
t₂₈: l3(X₁, X₂, X₃, X₄, X₆) → l3(X₁, X₂, X₃, X₄, X₆+1) :|: X₆+1 ≤ X₃ ∧ X₆ ≤ X₃ ∧ X₆ ≤ X₂ ∧ X₆ ≤ X₁ ∧ 1 ≤ X₆ ∧ 1 ≤ X₄+X₆ ∧ 1+X₄ ≤ X₆ ∧ 3 ≤ X₃+X₆ ∧ 3 ≤ X₂+X₆ ∧ 3 ≤ X₁+X₆ ∧ 2+X₄ ≤ X₃ ∧ 2+X₄ ≤ X₂ ∧ 2+X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 2 ≤ X₁
t₂₉: l3(X₁, X₂, X₃, X₄, X₆) → l3(X₁, X₂, X₃, X₄, X₆+1) :|: X₆+1 ≤ X₃ ∧ X₆ ≤ X₃ ∧ X₆ ≤ X₂ ∧ X₆ ≤ X₁ ∧ 1 ≤ X₆ ∧ 1 ≤ X₄+X₆ ∧ 1+X₄ ≤ X₆ ∧ 3 ≤ X₃+X₆ ∧ 3 ≤ X₂+X₆ ∧ 3 ≤ X₁+X₆ ∧ 2+X₄ ≤ X₃ ∧ 2+X₄ ≤ X₂ ∧ 2+X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 2 ≤ X₁
t₃₁: l4(X₁, X₂, X₃, X₄, X₆) → l4(X₁, X₂, X₃, X₄+1, X₆) :|: 2+X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 0 ≤ X₁+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁
t₃₂: l4(X₁, X₂, X₃, X₄, X₆) → l5(X₁, X₂, X₃, X₄, X₆) :|: X₃ ≤ X₄+1 ∧ X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 0 ≤ X₁+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁
Found invariant X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 0 ≤ X₁+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁ for location l2
Found invariant X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ X₃ ≤ 1+X₄ ∧ X₂ ≤ 1+X₄ ∧ 0 ≤ X₁+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁ for location l5
Found invariant 0 ≤ X₁ for location l1
Found invariant X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 0 ≤ X₁+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁ for location l4
Found invariant X₆ ≤ X₃ ∧ X₆ ≤ X₂ ∧ X₆ ≤ X₁ ∧ 1 ≤ X₆ ∧ 1 ≤ X₄+X₆ ∧ 1+X₄ ≤ X₆ ∧ 3 ≤ X₃+X₆ ∧ 3 ≤ X₂+X₆ ∧ 3 ≤ X₁+X₆ ∧ 2+X₄ ≤ X₃ ∧ 2+X₄ ≤ X₂ ∧ 2+X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 2 ≤ X₁ for location l3
Termination: true
Formula:
relevant size-bounds w.r.t. t₂₃:
X₂: X₂ {O(n)}
Runtime-bound of t₂₃: 1 {O(1)}
Results in: 2⋅X₂+4 {O(n)}
Found invariant X₄ ≤ 0 ∧ X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 0 ≤ X₁+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁ for location l2
Found invariant X₆ ≤ 1+X₄ ∧ 1+X₆ ≤ X₃ ∧ 1+X₆ ≤ X₂ ∧ 1+X₆ ≤ X₁ ∧ 1 ≤ X₆ ∧ 1 ≤ X₄+X₆ ∧ 1+X₄ ≤ X₆ ∧ 3 ≤ X₃+X₆ ∧ 3 ≤ X₂+X₆ ∧ 3 ≤ X₁+X₆ ∧ 2+X₄ ≤ X₃ ∧ 2+X₄ ≤ X₂ ∧ 2+X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 2 ≤ X₁ for location n_l3___3
Found invariant X₆ ≤ X₃ ∧ X₆ ≤ X₂ ∧ X₆ ≤ X₁ ∧ 2 ≤ X₆ ∧ 3 ≤ X₄+X₆ ∧ 1+X₄ ≤ X₆ ∧ 4 ≤ X₃+X₆ ∧ X₃ ≤ X₆ ∧ 4 ≤ X₂+X₆ ∧ X₂ ≤ X₆ ∧ 4 ≤ X₁+X₆ ∧ 1+X₄ ≤ X₃ ∧ 1+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 3 ≤ X₃+X₄ ∧ 3 ≤ X₂+X₄ ∧ 3 ≤ X₁+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 2 ≤ X₁ for location n_l2___1
Found invariant X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ X₃ ≤ 1+X₄ ∧ X₂ ≤ 1+X₄ ∧ 0 ≤ X₁+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁ for location l5
Found invariant X₆ ≤ X₃ ∧ X₆ ≤ X₂ ∧ X₆ ≤ X₁ ∧ 2 ≤ X₆ ∧ 2 ≤ X₄+X₆ ∧ 2+X₄ ≤ X₆ ∧ 4 ≤ X₃+X₆ ∧ 4 ≤ X₂+X₆ ∧ 4 ≤ X₁+X₆ ∧ 2+X₄ ≤ X₃ ∧ 2+X₄ ≤ X₂ ∧ 2+X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 2 ≤ X₁ for location n_l3___2
Found invariant 0 ≤ X₁ for location l1
Found invariant X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 0 ≤ X₁+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁ for location l4
Found invariant X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 0 ≤ X₁+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁ for location l2
Found invariant X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ X₃ ≤ 1+X₄ ∧ X₂ ≤ 1+X₄ ∧ 0 ≤ X₁+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁ for location l5
Found invariant 0 ≤ X₁ for location l1
Found invariant X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 0 ≤ X₁+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁ for location l4
Found invariant X₆ ≤ X₃ ∧ X₆ ≤ X₂ ∧ X₆ ≤ X₁ ∧ 1 ≤ X₆ ∧ 1 ≤ X₄+X₆ ∧ 1+X₄ ≤ X₆ ∧ 3 ≤ X₃+X₆ ∧ 3 ≤ X₂+X₆ ∧ 3 ≤ X₁+X₆ ∧ 2+X₄ ≤ X₃ ∧ 2+X₄ ≤ X₂ ∧ 2+X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 2 ≤ X₁ for location l3
Termination: true
Formula:
relevant size-bounds w.r.t. t₂₇:
X₃: 4⋅X₂ {O(n)}
X₄: 0 {O(1)}
Runtime-bound of t₂₇: 1 {O(1)}
Results in: 8⋅X₂+8 {O(n)}
Overall timebound:inf {Infinity}
t₂₃: 1 {O(1)}
t₂₄: 2⋅X₂+4 {O(n)}
t₂₅: 1 {O(1)}
t₂₆: inf {Infinity}
t₂₇: 1 {O(1)}
t₂₈: inf {Infinity}
t₂₉: inf {Infinity}
t₃₀: inf {Infinity}
t₃₁: 8⋅X₂+8 {O(n)}
t₃₂: 1 {O(1)}
Overall costbound: inf {Infinity}
t₂₃: 1 {O(1)}
t₂₄: 2⋅X₂+4 {O(n)}
t₂₅: 1 {O(1)}
t₂₆: inf {Infinity}
t₂₇: 1 {O(1)}
t₂₈: inf {Infinity}
t₂₉: inf {Infinity}
t₃₀: inf {Infinity}
t₃₁: 8⋅X₂+8 {O(n)}
t₃₂: 1 {O(1)}
t₂₃, X₁: 0 {O(1)}
t₂₃, X₂: X₂ {O(n)}
t₂₃, X₃: X₃ {O(n)}
t₂₃, X₄: X₄ {O(n)}
t₂₃, X₆: X₆ {O(n)}
t₂₄, X₁: 2⋅X₂+4 {O(n)}
t₂₄, X₂: X₂ {O(n)}
t₂₄, X₃: X₃ {O(n)}
t₂₄, X₄: X₄ {O(n)}
t₂₄, X₆: X₆ {O(n)}
t₂₅, X₁: 2⋅X₂+4 {O(n)}
t₂₅, X₂: 2⋅X₂ {O(n)}
t₂₅, X₃: 2⋅X₂ {O(n)}
t₂₅, X₄: 0 {O(1)}
t₂₅, X₆: 2⋅X₆ {O(n)}
t₂₆, X₁: 2⋅X₂+4 {O(n)}
t₂₆, X₂: 2⋅X₂ {O(n)}
t₂₆, X₃: 2⋅X₂ {O(n)}
t₂₇, X₁: 4⋅X₂+8 {O(n)}
t₂₇, X₂: 4⋅X₂ {O(n)}
t₂₇, X₃: 4⋅X₂ {O(n)}
t₂₇, X₄: 0 {O(1)}
t₂₈, X₁: 2⋅X₂+4 {O(n)}
t₂₈, X₂: 2⋅X₂ {O(n)}
t₂₈, X₃: 2⋅X₂ {O(n)}
t₂₉, X₁: 2⋅X₂+4 {O(n)}
t₂₉, X₂: 2⋅X₂ {O(n)}
t₂₉, X₃: 2⋅X₂ {O(n)}
t₃₀, X₁: 2⋅X₂+4 {O(n)}
t₃₀, X₂: 2⋅X₂ {O(n)}
t₃₀, X₃: 2⋅X₂ {O(n)}
t₃₁, X₁: 4⋅X₂+8 {O(n)}
t₃₁, X₂: 4⋅X₂ {O(n)}
t₃₁, X₃: 4⋅X₂ {O(n)}
t₃₁, X₄: 8⋅X₂+8 {O(n)}
t₃₂, X₁: 8⋅X₂+16 {O(n)}
t₃₂, X₂: 8⋅X₂ {O(n)}
t₃₂, X₃: 8⋅X₂ {O(n)}
t₃₂, X₄: 8⋅X₂+8 {O(n)}