Initial Problem
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, X₅, X₃, X₄, 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, X₅, X₃, 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(X₀, 3⋅X₁-4⋅X₂, 4⋅X₁-3⋅X₂, 5⋅X₃, 5⋅X₄-(X₀)², X₅) :|: 1 < (X₁)² ∧ 0 < X₀*X₂+2⋅X₀
Preprocessing
Found invariant X₂ ≤ 1+X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ for location l1
Problem after Preprocessing
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, X₅, X₃, X₄, X₅)
t₁: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀+X₂, X₁, X₂-1, X₃, X₄, X₅) :|: 0 < X₂ ∧ X₂ ≤ 1+X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₅, X₃, X₄, X₅) :|: X₂ ≤ 0 ∧ X₂ ≤ 1+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
t₃: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, 3⋅X₁-4⋅X₂, 4⋅X₁-3⋅X₂, 5⋅X₃, 5⋅X₄-(X₀)², X₅) :|: 1 < (X₁)² ∧ 0 < X₀*X₂+2⋅X₀
Analysing control-flow refined program
Found invariant X₅ ≤ X₂ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ for location n_l2___6
Found invariant 1+X₅ ≤ X₂ ∧ 0 ≤ X₅ ∧ 1 ≤ X₂+X₅ ∧ X₂ ≤ 1+X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ for location n_l1___4
Found invariant X₅ ≤ X₂ ∧ 1 ≤ X₅ ∧ 2 ≤ X₂+X₅ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₂ for location n_l2___5
Found invariant 1 ≤ X₅ ∧ 1 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₂ for location n_l1___7
Found invariant 0 ≤ X₅ ∧ 0 ≤ X₂+X₅ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₂ for location n_l1___2
Found invariant 1 ≤ X₅ for location n_l2___3
Found invariant X₅ ≤ X₂ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ for location l1
Found invariant X₅ ≤ X₂ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ for location n_l2___6
Found invariant 1+X₅ ≤ X₂ ∧ 0 ≤ X₅ ∧ 1 ≤ X₂+X₅ ∧ X₂ ≤ 1+X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ for location n_l1___4
Found invariant X₅ ≤ X₂ ∧ 1 ≤ X₅ ∧ 2 ≤ X₂+X₅ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₂ for location n_l2___5
Found invariant 1 ≤ X₅ ∧ 1 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₂ for location n_l1___7
Found invariant 0 ≤ X₅ ∧ 0 ≤ X₂+X₅ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₂ for location n_l1___2
Found invariant 1 ≤ X₅ for location n_l2___3
Found invariant X₅ ≤ X₂ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ for location l1
Time-Bound by TWN-Loops:
TWN-Loops: t₁₄₀ 14⋅X₅+8⋅X₃+14 {O(n)}
TWN-Loops:
entry: t₁₄₂: l1(X₀, X₁, X₂, X₃, X₄, X₅) → n_l1___7(X₀+X₂, X₁, X₂-1, X₃, X₁, X₅) :|: X₃ ≤ X₀ ∧ X₂ ≤ 1+X₅ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₅ ∧ X₅ ≤ X₂ ∧ X₀ ≤ X₃ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₁ ∧ X₂ ≤ 1+X₅ ∧ 0 < X₂ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₁ ∧ X₅ ≤ X₂ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃
results in twn-loop: twn:Inv: [1 ≤ X₅ ∧ 1 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₂] , (X₀,X₁,X₂,X₃,X₄,X₅) -> (X₀+X₂,X₁,X₂-1,X₃,X₁,X₅) :|: X₃ ≤ X₀ ∧ X₂ ≤ 1+X₅ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₁ ∧ 0 < X₅ ∧ X₂ ≤ 1+X₅ ∧ 0 < X₂ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₁
order: [X₂; X₀; X₁; X₃; X₄; X₅]
closed-form:
X₂: X₂ + [[n != 0]] * -1 * n^1
X₀: X₀ + [[n != 0]] * X₂ * n^1 + [[n != 0, n != 1]] * -1/2 * n^2 + [[n != 0, n != 1]] * 1/2 * n^1
X₁: X₁
X₃: X₃
X₄: [[n == 0]] * X₄ + [[n != 0]] * X₁
X₅: X₅
Termination: true
Formula:
0 < 1 ∧ 0 < X₅ ∧ 1 < 0
∨ 1 < 0 ∧ 0 < 1 ∧ 0 < X₅ ∧ 2+2⋅X₃ < 2⋅X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0
∨ 1 < 0 ∧ 0 < 1 ∧ 0 < X₅ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0 ∧ 2+2⋅X₃ ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2+2⋅X₃
∨ X₂ < 1+X₅ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 < X₅ ∧ 1 < 0
∨ 1 < 0 ∧ X₂ < 1+X₅ ∧ 0 < X₅ ∧ 2+2⋅X₃ < 2⋅X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0
∨ 1 < 0 ∧ X₂ < 1+X₅ ∧ 0 < X₅ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0 ∧ 2+2⋅X₃ ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2+2⋅X₃
∨ 0 ≤ 1 ∧ 1 ≤ 0 ∧ X₂ ≤ 1+X₅ ∧ 1+X₅ ≤ X₂ ∧ 0 < X₅ ∧ 1 < 0
∨ 1 < 0 ∧ X₂ ≤ 1+X₅ ∧ 1+X₅ ≤ X₂ ∧ 0 < X₅ ∧ 2+2⋅X₃ < 2⋅X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0
∨ 1 < 0 ∧ X₂ ≤ 1+X₅ ∧ 1+X₅ ≤ X₂ ∧ 0 < X₅ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0 ∧ 2+2⋅X₃ ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2+2⋅X₃
∨ 0 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < 1 ∧ 0 < X₅ ∧ 1 < 0
∨ 1 < 0 ∧ 0 < X₂ ∧ 0 < 1 ∧ 0 < X₅ ∧ 0 < 2⋅X₂+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 0 < X₂ ∧ 0 < 1 ∧ 0 < X₅ ∧ 2+2⋅X₃ < 2⋅X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0
∨ 1 < 0 ∧ 0 < X₂ ∧ 0 < 1 ∧ 0 < X₅ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0 ∧ 2+2⋅X₃ ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2+2⋅X₃
∨ 0 < X₂ ∧ X₂ < 1+X₅ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 < X₅ ∧ 1 < 0
∨ 1 < 0 ∧ 0 < X₂ ∧ X₂ < 1+X₅ ∧ 0 < X₅ ∧ 0 < 2⋅X₂+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 0 < X₂ ∧ X₂ < 1+X₅ ∧ 0 < X₅ ∧ 2+2⋅X₃ < 2⋅X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0
∨ 1 < 0 ∧ 0 < X₂ ∧ X₂ < 1+X₅ ∧ 0 < X₅ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0 ∧ 2+2⋅X₃ ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2+2⋅X₃
∨ 0 < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ X₂ ≤ 1+X₅ ∧ 1+X₅ ≤ X₂ ∧ 0 < X₅ ∧ 1 < 0
∨ 1 < 0 ∧ 0 < X₂ ∧ X₂ ≤ 1+X₅ ∧ 1+X₅ ≤ X₂ ∧ 0 < X₅ ∧ 0 < 2⋅X₂+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 0 < X₂ ∧ X₂ ≤ 1+X₅ ∧ 1+X₅ ≤ X₂ ∧ 0 < X₅ ∧ 2+2⋅X₃ < 2⋅X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0
∨ 1 < 0 ∧ 0 < X₂ ∧ X₂ ≤ 1+X₅ ∧ 1+X₅ ≤ X₂ ∧ 0 < X₅ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0 ∧ 2+2⋅X₃ ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2+2⋅X₃
∨ 0 < 2⋅X₂+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < 1 ∧ 0 < X₅ ∧ 1 < 0
∨ 1 < 0 ∧ 0 < 1 ∧ 0 < X₅ ∧ 0 < 2⋅X₂+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < 2⋅X₂+1 ∧ 1 < 0 ∧ 0 < 1 ∧ 0 < X₅ ∧ 2+2⋅X₃ < 2⋅X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0
∨ 0 < 2⋅X₂+1 ∧ 1 < 0 ∧ 0 < 1 ∧ 0 < X₅ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0 ∧ 2+2⋅X₃ ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2+2⋅X₃
∨ 0 < 2⋅X₂+1 ∧ X₂ < 1+X₅ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 < X₅ ∧ 1 < 0
∨ 1 < 0 ∧ X₂ < 1+X₅ ∧ 0 < X₅ ∧ 0 < 2⋅X₂+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < 2⋅X₂+1 ∧ 1 < 0 ∧ X₂ < 1+X₅ ∧ 0 < X₅ ∧ 2+2⋅X₃ < 2⋅X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0
∨ 0 < 2⋅X₂+1 ∧ 1 < 0 ∧ X₂ < 1+X₅ ∧ 0 < X₅ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0 ∧ 2+2⋅X₃ ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2+2⋅X₃
∨ 0 < 2⋅X₂+1 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ X₂ ≤ 1+X₅ ∧ 1+X₅ ≤ X₂ ∧ 0 < X₅ ∧ 1 < 0
∨ 1 < 0 ∧ X₂ ≤ 1+X₅ ∧ 1+X₅ ≤ X₂ ∧ 0 < X₅ ∧ 0 < 2⋅X₂+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < 2⋅X₂+1 ∧ 1 < 0 ∧ X₂ ≤ 1+X₅ ∧ 1+X₅ ≤ X₂ ∧ 0 < X₅ ∧ 2+2⋅X₃ < 2⋅X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0
∨ 0 < 2⋅X₂+1 ∧ 1 < 0 ∧ X₂ ≤ 1+X₅ ∧ 1+X₅ ≤ X₂ ∧ 0 < X₅ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0 ∧ 2+2⋅X₃ ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2+2⋅X₃
∨ 0 < 2⋅X₂+1 ∧ 0 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < 1 ∧ 0 < X₅ ∧ 1 < 0
∨ 0 < X₂ ∧ 0 < 1 ∧ 0 < X₅ ∧ 0 < 2⋅X₂+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < 2⋅X₂+1 ∧ 0 < X₂ ∧ 0 < 1 ∧ 0 < X₅ ∧ 2+2⋅X₃ < 2⋅X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0
∨ 0 < 2⋅X₂+1 ∧ 0 < X₂ ∧ 0 < 1 ∧ 0 < X₅ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0 ∧ 2+2⋅X₃ ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2+2⋅X₃
∨ 0 < 2⋅X₂+1 ∧ 0 < X₂ ∧ X₂ < 1+X₅ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 < X₅ ∧ 1 < 0
∨ 0 < X₂ ∧ X₂ < 1+X₅ ∧ 0 < X₅ ∧ 0 < 2⋅X₂+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < 2⋅X₂+1 ∧ 0 < X₂ ∧ X₂ < 1+X₅ ∧ 0 < X₅ ∧ 2+2⋅X₃ < 2⋅X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0
∨ 0 < 2⋅X₂+1 ∧ 0 < X₂ ∧ X₂ < 1+X₅ ∧ 0 < X₅ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0 ∧ 2+2⋅X₃ ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2+2⋅X₃
∨ 0 < 2⋅X₂+1 ∧ 0 < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ X₂ ≤ 1+X₅ ∧ 1+X₅ ≤ X₂ ∧ 0 < X₅ ∧ 1 < 0
∨ 0 < X₂ ∧ X₂ ≤ 1+X₅ ∧ 1+X₅ ≤ X₂ ∧ 0 < X₅ ∧ 0 < 2⋅X₂+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < 2⋅X₂+1 ∧ 0 < X₂ ∧ X₂ ≤ 1+X₅ ∧ 1+X₅ ≤ X₂ ∧ 0 < X₅ ∧ 2+2⋅X₃ < 2⋅X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0
∨ 0 < 2⋅X₂+1 ∧ 0 < X₂ ∧ X₂ ≤ 1+X₅ ∧ 1+X₅ ≤ X₂ ∧ 0 < X₅ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0 ∧ 2+2⋅X₃ ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2+2⋅X₃
∨ 2⋅X₃ < 2⋅X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0 ∧ 0 < 1 ∧ 0 < X₅ ∧ 1 < 0
∨ 2⋅X₃ < 2⋅X₀ ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0 ∧ 1 < 0 ∧ 0 < 1 ∧ 0 < X₅ ∧ 0 < 2⋅X₂+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2⋅X₃ < 2⋅X₀ ∧ 1 < 0 ∧ 0 < 1 ∧ 0 < X₅ ∧ 2+2⋅X₃ < 2⋅X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0
∨ 2⋅X₃ < 2⋅X₀ ∧ 1 < 0 ∧ 0 < 1 ∧ 0 < X₅ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0 ∧ 2+2⋅X₃ ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2+2⋅X₃
∨ 2⋅X₃ < 2⋅X₀ ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0 ∧ X₂ < 1+X₅ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 < X₅ ∧ 1 < 0
∨ 2⋅X₃ < 2⋅X₀ ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0 ∧ 1 < 0 ∧ X₂ < 1+X₅ ∧ 0 < X₅ ∧ 0 < 2⋅X₂+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2⋅X₃ < 2⋅X₀ ∧ 1 < 0 ∧ X₂ < 1+X₅ ∧ 0 < X₅ ∧ 2+2⋅X₃ < 2⋅X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0
∨ 2⋅X₃ < 2⋅X₀ ∧ 1 < 0 ∧ X₂ < 1+X₅ ∧ 0 < X₅ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0 ∧ 2+2⋅X₃ ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2+2⋅X₃
∨ 2⋅X₃ < 2⋅X₀ ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ X₂ ≤ 1+X₅ ∧ 1+X₅ ≤ X₂ ∧ 0 < X₅ ∧ 1 < 0
∨ 2⋅X₃ < 2⋅X₀ ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0 ∧ 1 < 0 ∧ X₂ ≤ 1+X₅ ∧ 1+X₅ ≤ X₂ ∧ 0 < X₅ ∧ 0 < 2⋅X₂+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2⋅X₃ < 2⋅X₀ ∧ 1 < 0 ∧ X₂ ≤ 1+X₅ ∧ 1+X₅ ≤ X₂ ∧ 0 < X₅ ∧ 2+2⋅X₃ < 2⋅X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0
∨ 2⋅X₃ < 2⋅X₀ ∧ 1 < 0 ∧ X₂ ≤ 1+X₅ ∧ 1+X₅ ≤ X₂ ∧ 0 < X₅ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0 ∧ 2+2⋅X₃ ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2+2⋅X₃
∨ 2⋅X₃ < 2⋅X₀ ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0 ∧ 0 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < 1 ∧ 0 < X₅ ∧ 1 < 0
∨ 2⋅X₃ < 2⋅X₀ ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0 ∧ 0 < X₂ ∧ 0 < 1 ∧ 0 < X₅ ∧ 0 < 2⋅X₂+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2⋅X₃ < 2⋅X₀ ∧ 0 < X₂ ∧ 0 < 1 ∧ 0 < X₅ ∧ 2+2⋅X₃ < 2⋅X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0
∨ 2⋅X₃ < 2⋅X₀ ∧ 0 < X₂ ∧ 0 < 1 ∧ 0 < X₅ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0 ∧ 2+2⋅X₃ ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2+2⋅X₃
∨ 2⋅X₃ < 2⋅X₀ ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0 ∧ 0 < X₂ ∧ X₂ < 1+X₅ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 < X₅ ∧ 1 < 0
∨ 2⋅X₃ < 2⋅X₀ ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0 ∧ 0 < X₂ ∧ X₂ < 1+X₅ ∧ 0 < X₅ ∧ 0 < 2⋅X₂+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2⋅X₃ < 2⋅X₀ ∧ 0 < X₂ ∧ X₂ < 1+X₅ ∧ 0 < X₅ ∧ 2+2⋅X₃ < 2⋅X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0
∨ 2⋅X₃ < 2⋅X₀ ∧ 0 < X₂ ∧ X₂ < 1+X₅ ∧ 0 < X₅ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0 ∧ 2+2⋅X₃ ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2+2⋅X₃
∨ 2⋅X₃ < 2⋅X₀ ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0 ∧ 0 < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ X₂ ≤ 1+X₅ ∧ 1+X₅ ≤ X₂ ∧ 0 < X₅ ∧ 1 < 0
∨ 2⋅X₃ < 2⋅X₀ ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0 ∧ 0 < X₂ ∧ X₂ ≤ 1+X₅ ∧ 1+X₅ ≤ X₂ ∧ 0 < X₅ ∧ 0 < 2⋅X₂+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2⋅X₃ < 2⋅X₀ ∧ 0 < X₂ ∧ X₂ ≤ 1+X₅ ∧ 1+X₅ ≤ X₂ ∧ 0 < X₅ ∧ 2+2⋅X₃ < 2⋅X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0
∨ 2⋅X₃ < 2⋅X₀ ∧ 0 < X₂ ∧ X₂ ≤ 1+X₅ ∧ 1+X₅ ≤ X₂ ∧ 0 < X₅ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0 ∧ 2+2⋅X₃ ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2+2⋅X₃
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0 ∧ 2⋅X₃ ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2⋅X₃ ∧ 0 < 1 ∧ 0 < X₅ ∧ 1 < 0
∨ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0 ∧ 2⋅X₃ ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2⋅X₃ ∧ 1 < 0 ∧ 0 < 1 ∧ 0 < X₅ ∧ 0 < 2⋅X₂+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2⋅X₃ ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2⋅X₃ ∧ 1 < 0 ∧ 0 < 1 ∧ 0 < X₅ ∧ 2+2⋅X₃ < 2⋅X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0
∨ 2⋅X₃ ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2⋅X₃ ∧ 1 < 0 ∧ 0 < 1 ∧ 0 < X₅ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0 ∧ 2+2⋅X₃ ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2+2⋅X₃
∨ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0 ∧ 2⋅X₃ ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2⋅X₃ ∧ X₂ < 1+X₅ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 < X₅ ∧ 1 < 0
∨ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0 ∧ 2⋅X₃ ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2⋅X₃ ∧ 1 < 0 ∧ X₂ < 1+X₅ ∧ 0 < X₅ ∧ 0 < 2⋅X₂+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2⋅X₃ ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2⋅X₃ ∧ 1 < 0 ∧ X₂ < 1+X₅ ∧ 0 < X₅ ∧ 2+2⋅X₃ < 2⋅X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0
∨ 2⋅X₃ ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2⋅X₃ ∧ 1 < 0 ∧ X₂ < 1+X₅ ∧ 0 < X₅ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0 ∧ 2+2⋅X₃ ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2+2⋅X₃
∨ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0 ∧ 2⋅X₃ ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2⋅X₃ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ X₂ ≤ 1+X₅ ∧ 1+X₅ ≤ X₂ ∧ 0 < X₅ ∧ 1 < 0
∨ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0 ∧ 2⋅X₃ ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2⋅X₃ ∧ 1 < 0 ∧ X₂ ≤ 1+X₅ ∧ 1+X₅ ≤ X₂ ∧ 0 < X₅ ∧ 0 < 2⋅X₂+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2⋅X₃ ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2⋅X₃ ∧ 1 < 0 ∧ X₂ ≤ 1+X₅ ∧ 1+X₅ ≤ X₂ ∧ 0 < X₅ ∧ 2+2⋅X₃ < 2⋅X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0
∨ 2⋅X₃ ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2⋅X₃ ∧ 1 < 0 ∧ X₂ ≤ 1+X₅ ∧ 1+X₅ ≤ X₂ ∧ 0 < X₅ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0 ∧ 2+2⋅X₃ ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2+2⋅X₃
∨ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0 ∧ 2⋅X₃ ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2⋅X₃ ∧ 0 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < 1 ∧ 0 < X₅ ∧ 1 < 0
∨ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0 ∧ 2⋅X₃ ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2⋅X₃ ∧ 0 < X₂ ∧ 0 < 1 ∧ 0 < X₅ ∧ 0 < 2⋅X₂+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2⋅X₃ ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2⋅X₃ ∧ 0 < X₂ ∧ 0 < 1 ∧ 0 < X₅ ∧ 2+2⋅X₃ < 2⋅X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0
∨ 2⋅X₃ ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2⋅X₃ ∧ 0 < X₂ ∧ 0 < 1 ∧ 0 < X₅ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0 ∧ 2+2⋅X₃ ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2+2⋅X₃
∨ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0 ∧ 2⋅X₃ ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2⋅X₃ ∧ 0 < X₂ ∧ X₂ < 1+X₅ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 < X₅ ∧ 1 < 0
∨ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0 ∧ 2⋅X₃ ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2⋅X₃ ∧ 0 < X₂ ∧ X₂ < 1+X₅ ∧ 0 < X₅ ∧ 0 < 2⋅X₂+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2⋅X₃ ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2⋅X₃ ∧ 0 < X₂ ∧ X₂ < 1+X₅ ∧ 0 < X₅ ∧ 2+2⋅X₃ < 2⋅X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0
∨ 2⋅X₃ ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2⋅X₃ ∧ 0 < X₂ ∧ X₂ < 1+X₅ ∧ 0 < X₅ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0 ∧ 2+2⋅X₃ ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2+2⋅X₃
∨ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0 ∧ 2⋅X₃ ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2⋅X₃ ∧ 0 < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ X₂ ≤ 1+X₅ ∧ 1+X₅ ≤ X₂ ∧ 0 < X₅ ∧ 1 < 0
∨ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0 ∧ 2⋅X₃ ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2⋅X₃ ∧ 0 < X₂ ∧ X₂ ≤ 1+X₅ ∧ 1+X₅ ≤ X₂ ∧ 0 < X₅ ∧ 0 < 2⋅X₂+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2⋅X₃ ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2⋅X₃ ∧ 0 < X₂ ∧ X₂ ≤ 1+X₅ ∧ 1+X₅ ≤ X₂ ∧ 0 < X₅ ∧ 2+2⋅X₃ < 2⋅X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0
∨ 2⋅X₃ ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2⋅X₃ ∧ 0 < X₂ ∧ X₂ ≤ 1+X₅ ∧ 1+X₅ ≤ X₂ ∧ 0 < X₅ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0 ∧ 2+2⋅X₃ ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2+2⋅X₃
Stabilization-Threshold for: X₃ ≤ X₀
alphas_abs: 1+2⋅X₀+2⋅X₂+2⋅X₃
M: 0
N: 2
Bound: 4⋅X₀+4⋅X₂+4⋅X₃+5 {O(n)}
Stabilization-Threshold for: 0 < X₂
alphas_abs: X₂
M: 0
N: 1
Bound: 2⋅X₂+2 {O(n)}
Stabilization-Threshold for: X₂ ≤ 1+X₅
alphas_abs: 1+X₂+X₅
M: 0
N: 1
Bound: 2⋅X₂+2⋅X₅+4 {O(n)}
relevant size-bounds w.r.t. t₁₄₂:
X₀: X₃+X₅ {O(n)}
X₂: X₅ {O(n)}
X₃: X₃ {O(n)}
X₅: X₅ {O(n)}
Runtime-bound of t₁₄₂: 1 {O(1)}
Results in: 14⋅X₅+8⋅X₃+14 {O(n)}
14⋅X₅+8⋅X₃+14 {O(n)}
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:inf {Infinity}
t₀: 1 {O(1)}
t₁: inf {Infinity}
t₂: inf {Infinity}
t₃: inf {Infinity}
t₄: inf {Infinity}
Costbounds
Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₁: inf {Infinity}
t₂: inf {Infinity}
t₃: inf {Infinity}
t₄: inf {Infinity}
Sizebounds
t₀, X₀: X₃ {O(n)}
t₀, X₁: X₄ {O(n)}
t₀, X₂: X₅ {O(n)}
t₀, X₃: X₃ {O(n)}
t₀, X₄: X₄ {O(n)}
t₀, X₅: X₅ {O(n)}
t₁, X₂: 5⋅X₅ {O(n)}
t₁, X₅: 2⋅X₅ {O(n)}
t₂, X₂: 3⋅X₅ {O(n)}
t₂, X₅: 2⋅X₅ {O(n)}
t₃, X₅: 2⋅X₅ {O(n)}
t₄, X₂: 4⋅X₅ {O(n)}
t₄, X₅: 2⋅X₅ {O(n)}