Initial Problem
Start: evalnestedLoopstart
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇
Temp_Vars:
Locations: evalnestedLoopbb4in, evalnestedLoopbb5in, evalnestedLoopbb6in, evalnestedLoopbb7in, evalnestedLoopbb8in, evalnestedLoopbb9in, evalnestedLoopentryin, evalnestedLoopreturnin, evalnestedLoopstart, evalnestedLoopstop
Transitions:
t₉: evalnestedLoopbb4in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → evalnestedLoopbb6in(X₀, X₁, X₂, X₃, X₄, X₅, 1+X₄, X₅)
t₁₂: evalnestedLoopbb5in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → evalnestedLoopbb6in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, 1+X₇)
t₁₀: evalnestedLoopbb6in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → evalnestedLoopbb5in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₇ ≤ X₂
t₁₁: evalnestedLoopbb6in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → evalnestedLoopbb7in(X₀, X₁, X₂, X₃, X₆, X₇, X₆, X₇) :|: X₂ ≤ X₇
t₇: evalnestedLoopbb7in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → evalnestedLoopbb4in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₄ ≤ X₁
t₈: evalnestedLoopbb7in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → evalnestedLoopbb8in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₁ ≤ X₄
t₁₃: evalnestedLoopbb8in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → evalnestedLoopbb9in(X₀, X₁, X₂, 1+X₅, X₄, X₅, X₆, X₇)
t₅: evalnestedLoopbb9in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → evalnestedLoopbb7in(X₀, X₁, X₂, X₃, 0, X₃, X₆, X₇) :|: 1+X₃ ≤ X₀
t₆: evalnestedLoopbb9in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → evalnestedLoopreturnin(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₀ ≤ X₃
t₁: evalnestedLoopentryin(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → evalnestedLoopbb9in(X₀, X₁, X₂, 0, X₄, X₅, X₆, X₇) :|: 0 ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₂
t₂: evalnestedLoopentryin(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → evalnestedLoopreturnin(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₀ ≤ 0
t₃: evalnestedLoopentryin(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → evalnestedLoopreturnin(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₁ ≤ 0
t₄: evalnestedLoopentryin(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → evalnestedLoopreturnin(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₂ ≤ 0
t₁₄: evalnestedLoopreturnin(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → evalnestedLoopstop(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₀: evalnestedLoopstart(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → evalnestedLoopentryin(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
Preprocessing
Found invariant 0 ≤ X₅ ∧ 0 ≤ X₄+X₅ ∧ 0 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 0 ≤ X₂+X₅ ∧ 0 ≤ X₁+X₅ ∧ 1 ≤ X₀+X₅ ∧ X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location evalnestedLoopbb7in
Found invariant 0 ≤ X₇ ∧ 1 ≤ X₆+X₇ ∧ 0 ≤ X₅+X₇ ∧ X₅ ≤ X₇ ∧ 0 ≤ X₄+X₇ ∧ 0 ≤ X₃+X₇ ∧ X₃ ≤ X₇ ∧ 0 ≤ X₂+X₇ ∧ 1 ≤ X₁+X₇ ∧ 1 ≤ X₀+X₇ ∧ X₆ ≤ 1+X₄ ∧ X₆ ≤ X₁ ∧ 1 ≤ X₆ ∧ 1 ≤ X₅+X₆ ∧ 1 ≤ X₄+X₆ ∧ 1+X₄ ≤ X₆ ∧ 1 ≤ X₃+X₆ ∧ 1 ≤ X₂+X₆ ∧ 2 ≤ X₁+X₆ ∧ 2 ≤ X₀+X₆ ∧ 0 ≤ X₅ ∧ 0 ≤ X₄+X₅ ∧ 0 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 0 ≤ X₂+X₅ ∧ 1 ≤ X₁+X₅ ∧ 1 ≤ X₀+X₅ ∧ 1+X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location evalnestedLoopbb6in
Found invariant 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location evalnestedLoopbb9in
Found invariant 1+X₇ ≤ X₂ ∧ 0 ≤ X₇ ∧ 1 ≤ X₆+X₇ ∧ 0 ≤ X₅+X₇ ∧ X₅ ≤ X₇ ∧ 0 ≤ X₄+X₇ ∧ 0 ≤ X₃+X₇ ∧ X₃ ≤ X₇ ∧ 1 ≤ X₂+X₇ ∧ 1 ≤ X₁+X₇ ∧ 1 ≤ X₀+X₇ ∧ X₆ ≤ 1+X₄ ∧ X₆ ≤ X₁ ∧ 1 ≤ X₆ ∧ 1 ≤ X₅+X₆ ∧ 1 ≤ X₄+X₆ ∧ 1+X₄ ≤ X₆ ∧ 1 ≤ X₃+X₆ ∧ 2 ≤ X₂+X₆ ∧ 2 ≤ X₁+X₆ ∧ 2 ≤ X₀+X₆ ∧ 1+X₅ ≤ X₂ ∧ 0 ≤ X₅ ∧ 0 ≤ X₄+X₅ ∧ 0 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 1 ≤ X₂+X₅ ∧ 1 ≤ X₁+X₅ ∧ 1 ≤ X₀+X₅ ∧ 1+X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location evalnestedLoopbb5in
Found invariant 0 ≤ X₅ ∧ 0 ≤ X₄+X₅ ∧ 0 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 0 ≤ X₂+X₅ ∧ 0 ≤ X₁+X₅ ∧ 1 ≤ X₀+X₅ ∧ X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location evalnestedLoopbb8in
Found invariant 0 ≤ X₅ ∧ 0 ≤ X₄+X₅ ∧ 0 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 0 ≤ X₂+X₅ ∧ 1 ≤ X₁+X₅ ∧ 1 ≤ X₀+X₅ ∧ 1+X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location evalnestedLoopbb4in
Problem after Preprocessing
Start: evalnestedLoopstart
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇
Temp_Vars:
Locations: evalnestedLoopbb4in, evalnestedLoopbb5in, evalnestedLoopbb6in, evalnestedLoopbb7in, evalnestedLoopbb8in, evalnestedLoopbb9in, evalnestedLoopentryin, evalnestedLoopreturnin, evalnestedLoopstart, evalnestedLoopstop
Transitions:
t₉: evalnestedLoopbb4in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → evalnestedLoopbb6in(X₀, X₁, X₂, X₃, X₄, X₅, 1+X₄, X₅) :|: 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₁+X₄ ∧ 1+X₄ ≤ X₁ ∧ 1 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₂+X₅ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ 0 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 0 ≤ X₄ ∧ 0 ≤ X₄+X₅ ∧ 0 ≤ X₅
t₁₂: evalnestedLoopbb5in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → evalnestedLoopbb6in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, 1+X₇) :|: X₆ ≤ 1+X₄ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₀+X₇ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₁+X₄ ∧ 1+X₄ ≤ X₁ ∧ 1 ≤ X₁+X₅ ∧ 1 ≤ X₁+X₇ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂+X₃ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₂+X₅ ∧ 1+X₅ ≤ X₂ ∧ 1 ≤ X₂+X₇ ∧ 1+X₇ ≤ X₂ ∧ 1 ≤ X₃+X₆ ∧ 1 ≤ X₄+X₆ ∧ 1+X₄ ≤ X₆ ∧ 1 ≤ X₅+X₆ ∧ 1 ≤ X₆ ∧ 1 ≤ X₆+X₇ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀+X₆ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₆ ∧ 2 ≤ X₂+X₆ ∧ X₆ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₇ ∧ X₃ ≤ X₅ ∧ X₃ ≤ X₇ ∧ 0 ≤ X₄ ∧ 0 ≤ X₄+X₅ ∧ 0 ≤ X₄+X₇ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₇ ∧ X₅ ≤ X₇ ∧ 0 ≤ X₇
t₁₀: evalnestedLoopbb6in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → evalnestedLoopbb5in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₇ ≤ X₂ ∧ X₆ ≤ 1+X₄ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₀+X₇ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₁+X₄ ∧ 1+X₄ ≤ X₁ ∧ 1 ≤ X₁+X₅ ∧ 1 ≤ X₁+X₇ ∧ 1 ≤ X₂+X₆ ∧ 1 ≤ X₃+X₆ ∧ 1 ≤ X₄+X₆ ∧ 1+X₄ ≤ X₆ ∧ 1 ≤ X₅+X₆ ∧ 1 ≤ X₆ ∧ 1 ≤ X₆+X₇ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₆ ∧ 2 ≤ X₁+X₆ ∧ X₆ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₂+X₅ ∧ 0 ≤ X₂+X₇ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₇ ∧ X₃ ≤ X₅ ∧ X₃ ≤ X₇ ∧ 0 ≤ X₄ ∧ 0 ≤ X₄+X₅ ∧ 0 ≤ X₄+X₇ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₇ ∧ X₅ ≤ X₇ ∧ 0 ≤ X₇
t₁₁: evalnestedLoopbb6in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → evalnestedLoopbb7in(X₀, X₁, X₂, X₃, X₆, X₇, X₆, X₇) :|: X₂ ≤ X₇ ∧ X₆ ≤ 1+X₄ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₀+X₇ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₁+X₄ ∧ 1+X₄ ≤ X₁ ∧ 1 ≤ X₁+X₅ ∧ 1 ≤ X₁+X₇ ∧ 1 ≤ X₂+X₆ ∧ 1 ≤ X₃+X₆ ∧ 1 ≤ X₄+X₆ ∧ 1+X₄ ≤ X₆ ∧ 1 ≤ X₅+X₆ ∧ 1 ≤ X₆ ∧ 1 ≤ X₆+X₇ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₆ ∧ 2 ≤ X₁+X₆ ∧ X₆ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₂+X₅ ∧ 0 ≤ X₂+X₇ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₇ ∧ X₃ ≤ X₅ ∧ X₃ ≤ X₇ ∧ 0 ≤ X₄ ∧ 0 ≤ X₄+X₅ ∧ 0 ≤ X₄+X₇ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₇ ∧ X₅ ≤ X₇ ∧ 0 ≤ X₇
t₇: evalnestedLoopbb7in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → evalnestedLoopbb4in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₄ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₀+X₅ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₁+X₄ ∧ X₄ ≤ X₁ ∧ 0 ≤ X₁+X₅ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₂+X₅ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ 0 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 0 ≤ X₄ ∧ 0 ≤ X₄+X₅ ∧ 0 ≤ X₅
t₈: evalnestedLoopbb7in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → evalnestedLoopbb8in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₁ ≤ X₄ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₀+X₅ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₁+X₄ ∧ X₄ ≤ X₁ ∧ 0 ≤ X₁+X₅ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₂+X₅ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ 0 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 0 ≤ X₄ ∧ 0 ≤ X₄+X₅ ∧ 0 ≤ X₅
t₁₃: evalnestedLoopbb8in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → evalnestedLoopbb9in(X₀, X₁, X₂, 1+X₅, X₄, X₅, X₆, X₇) :|: 1 ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₀+X₅ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₁+X₄ ∧ X₄ ≤ X₁ ∧ 0 ≤ X₁+X₅ ∧ X₁ ≤ X₄ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₂+X₅ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ 0 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 0 ≤ X₄ ∧ 0 ≤ X₄+X₅ ∧ 0 ≤ X₅
t₅: evalnestedLoopbb9in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → evalnestedLoopbb7in(X₀, X₁, X₂, X₃, 0, X₃, X₆, X₇) :|: 1+X₃ ≤ X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀+X₂ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
t₆: evalnestedLoopbb9in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → evalnestedLoopreturnin(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₀ ≤ X₃ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀+X₂ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
t₁: evalnestedLoopentryin(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → evalnestedLoopbb9in(X₀, X₁, X₂, 0, X₄, X₅, X₆, X₇) :|: 0 ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₂
t₂: evalnestedLoopentryin(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → evalnestedLoopreturnin(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₀ ≤ 0
t₃: evalnestedLoopentryin(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → evalnestedLoopreturnin(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₁ ≤ 0
t₄: evalnestedLoopentryin(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → evalnestedLoopreturnin(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₂ ≤ 0
t₁₄: evalnestedLoopreturnin(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → evalnestedLoopstop(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₀: evalnestedLoopstart(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → evalnestedLoopentryin(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
MPRF for transition t₅: evalnestedLoopbb9in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → evalnestedLoopbb7in(X₀, X₁, X₂, X₃, 0, X₃, X₆, X₇) :|: 1+X₃ ≤ X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀+X₂ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃ of depth 1:
new bound:
X₀+1 {O(n)}
MPRF:
• evalnestedLoopbb4in: [X₀-X₅]
• evalnestedLoopbb5in: [X₀-X₇]
• evalnestedLoopbb6in: [X₀-X₇]
• evalnestedLoopbb7in: [X₀-X₅]
• evalnestedLoopbb8in: [X₀-X₅]
• evalnestedLoopbb9in: [1+X₀-X₃]
MPRF for transition t₈: evalnestedLoopbb7in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → evalnestedLoopbb8in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₁ ≤ X₄ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₀+X₅ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₁+X₄ ∧ X₄ ≤ X₁ ∧ 0 ≤ X₁+X₅ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₂+X₅ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ 0 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 0 ≤ X₄ ∧ 0 ≤ X₄+X₅ ∧ 0 ≤ X₅ of depth 1:
new bound:
X₀+1 {O(n)}
MPRF:
• evalnestedLoopbb4in: [1+X₀-X₃]
• evalnestedLoopbb5in: [1+X₀-X₃]
• evalnestedLoopbb6in: [1+X₀-X₃]
• evalnestedLoopbb7in: [1+X₀-X₃]
• evalnestedLoopbb8in: [X₀-X₃]
• evalnestedLoopbb9in: [1+X₀-X₃]
MPRF for transition t₁₀: evalnestedLoopbb6in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → evalnestedLoopbb5in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₇ ≤ X₂ ∧ X₆ ≤ 1+X₄ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₀+X₇ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₁+X₄ ∧ 1+X₄ ≤ X₁ ∧ 1 ≤ X₁+X₅ ∧ 1 ≤ X₁+X₇ ∧ 1 ≤ X₂+X₆ ∧ 1 ≤ X₃+X₆ ∧ 1 ≤ X₄+X₆ ∧ 1+X₄ ≤ X₆ ∧ 1 ≤ X₅+X₆ ∧ 1 ≤ X₆ ∧ 1 ≤ X₆+X₇ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₆ ∧ 2 ≤ X₁+X₆ ∧ X₆ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₂+X₅ ∧ 0 ≤ X₂+X₇ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₇ ∧ X₃ ≤ X₅ ∧ X₃ ≤ X₇ ∧ 0 ≤ X₄ ∧ 0 ≤ X₄+X₅ ∧ 0 ≤ X₄+X₇ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₇ ∧ X₅ ≤ X₇ ∧ 0 ≤ X₇ of depth 1:
new bound:
X₂+1 {O(n)}
MPRF:
• evalnestedLoopbb4in: [1+X₂-X₅]
• evalnestedLoopbb5in: [X₂-X₇]
• evalnestedLoopbb6in: [1+X₂-X₇]
• evalnestedLoopbb7in: [1+X₂-X₅]
• evalnestedLoopbb8in: [X₂-X₅]
• evalnestedLoopbb9in: [1+X₂-X₃]
MPRF for transition t₁₂: evalnestedLoopbb5in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → evalnestedLoopbb6in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, 1+X₇) :|: X₆ ≤ 1+X₄ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₀+X₇ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₁+X₄ ∧ 1+X₄ ≤ X₁ ∧ 1 ≤ X₁+X₅ ∧ 1 ≤ X₁+X₇ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂+X₃ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₂+X₅ ∧ 1+X₅ ≤ X₂ ∧ 1 ≤ X₂+X₇ ∧ 1+X₇ ≤ X₂ ∧ 1 ≤ X₃+X₆ ∧ 1 ≤ X₄+X₆ ∧ 1+X₄ ≤ X₆ ∧ 1 ≤ X₅+X₆ ∧ 1 ≤ X₆ ∧ 1 ≤ X₆+X₇ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀+X₆ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₆ ∧ 2 ≤ X₂+X₆ ∧ X₆ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₇ ∧ X₃ ≤ X₅ ∧ X₃ ≤ X₇ ∧ 0 ≤ X₄ ∧ 0 ≤ X₄+X₅ ∧ 0 ≤ X₄+X₇ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₇ ∧ X₅ ≤ X₇ ∧ 0 ≤ X₇ of depth 1:
new bound:
X₂ {O(n)}
MPRF:
• evalnestedLoopbb4in: [X₂-X₅]
• evalnestedLoopbb5in: [X₂-X₇]
• evalnestedLoopbb6in: [X₂-X₇]
• evalnestedLoopbb7in: [X₂-X₅]
• evalnestedLoopbb8in: [X₂-X₅]
• evalnestedLoopbb9in: [X₂-X₃]
MPRF for transition t₁₃: evalnestedLoopbb8in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → evalnestedLoopbb9in(X₀, X₁, X₂, 1+X₅, X₄, X₅, X₆, X₇) :|: 1 ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₀+X₅ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₁+X₄ ∧ X₄ ≤ X₁ ∧ 0 ≤ X₁+X₅ ∧ X₁ ≤ X₄ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₂+X₅ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ 0 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 0 ≤ X₄ ∧ 0 ≤ X₄+X₅ ∧ 0 ≤ X₅ of depth 1:
new bound:
X₀ {O(n)}
MPRF:
• evalnestedLoopbb4in: [X₀-X₃]
• evalnestedLoopbb5in: [X₀-X₃]
• evalnestedLoopbb6in: [X₀-X₃]
• evalnestedLoopbb7in: [X₀-X₃]
• evalnestedLoopbb8in: [X₀-X₃]
• evalnestedLoopbb9in: [X₀-X₃]
MPRF for transition t₇: evalnestedLoopbb7in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → evalnestedLoopbb4in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₄ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₀+X₅ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₁+X₄ ∧ X₄ ≤ X₁ ∧ 0 ≤ X₁+X₅ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₂+X₅ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ 0 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 0 ≤ X₄ ∧ 0 ≤ X₄+X₅ ∧ 0 ≤ X₅ of depth 1:
new bound:
X₀⋅X₁+X₀+X₁+1 {O(n^2)}
MPRF:
• evalnestedLoopbb4in: [X₁-X₄]
• evalnestedLoopbb5in: [1+X₁-X₆]
• evalnestedLoopbb6in: [1+X₁-X₆]
• evalnestedLoopbb7in: [1+X₁-X₄]
• evalnestedLoopbb8in: [X₁-X₄]
• evalnestedLoopbb9in: [1+X₁]
MPRF for transition t₉: evalnestedLoopbb4in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → evalnestedLoopbb6in(X₀, X₁, X₂, X₃, X₄, X₅, 1+X₄, X₅) :|: 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₁+X₄ ∧ 1+X₄ ≤ X₁ ∧ 1 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₂+X₅ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ 0 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 0 ≤ X₄ ∧ 0 ≤ X₄+X₅ ∧ 0 ≤ X₅ of depth 1:
new bound:
X₀⋅X₁+X₁ {O(n^2)}
MPRF:
• evalnestedLoopbb4in: [X₁-X₄]
• evalnestedLoopbb5in: [X₁-X₆]
• evalnestedLoopbb6in: [X₁-X₆]
• evalnestedLoopbb7in: [X₁-X₄]
• evalnestedLoopbb8in: [X₄-X₁]
• evalnestedLoopbb9in: [X₁]
MPRF for transition t₁₁: evalnestedLoopbb6in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → evalnestedLoopbb7in(X₀, X₁, X₂, X₃, X₆, X₇, X₆, X₇) :|: X₂ ≤ X₇ ∧ X₆ ≤ 1+X₄ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₀+X₇ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₁+X₄ ∧ 1+X₄ ≤ X₁ ∧ 1 ≤ X₁+X₅ ∧ 1 ≤ X₁+X₇ ∧ 1 ≤ X₂+X₆ ∧ 1 ≤ X₃+X₆ ∧ 1 ≤ X₄+X₆ ∧ 1+X₄ ≤ X₆ ∧ 1 ≤ X₅+X₆ ∧ 1 ≤ X₆ ∧ 1 ≤ X₆+X₇ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₆ ∧ 2 ≤ X₁+X₆ ∧ X₆ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₂+X₅ ∧ 0 ≤ X₂+X₇ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₇ ∧ X₃ ≤ X₅ ∧ X₃ ≤ X₇ ∧ 0 ≤ X₄ ∧ 0 ≤ X₄+X₅ ∧ 0 ≤ X₄+X₇ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₇ ∧ X₅ ≤ X₇ ∧ 0 ≤ X₇ of depth 1:
new bound:
X₀⋅X₁+X₁ {O(n^2)}
MPRF:
• evalnestedLoopbb4in: [X₁-X₄]
• evalnestedLoopbb5in: [X₁-X₄]
• evalnestedLoopbb6in: [X₁-X₄]
• evalnestedLoopbb7in: [X₁-X₄]
• evalnestedLoopbb8in: [X₁-X₄]
• evalnestedLoopbb9in: [X₁]
Found invariant X₅ ≤ X₃ ∧ 1+X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₄+X₅ ∧ X₄ ≤ X₅ ∧ 0 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 0 ≤ X₂+X₅ ∧ 0 ≤ X₁+X₅ ∧ 1 ≤ X₀+X₅ ∧ X₄ ≤ 0 ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location evalnestedLoopbb7in
Found invariant X₇ ≤ X₂ ∧ 1 ≤ X₇ ∧ 2 ≤ X₆+X₇ ∧ X₆ ≤ X₇ ∧ 1 ≤ X₅+X₇ ∧ 1+X₅ ≤ X₇ ∧ 1 ≤ X₄+X₇ ∧ 1+X₄ ≤ X₇ ∧ 1 ≤ X₃+X₇ ∧ 1+X₃ ≤ X₇ ∧ 2 ≤ X₂+X₇ ∧ 2 ≤ X₁+X₇ ∧ 2 ≤ X₀+X₇ ∧ X₆ ≤ 1 ∧ X₆ ≤ 1+X₅ ∧ X₆ ≤ 1+X₄ ∧ X₄+X₆ ≤ 1 ∧ X₆ ≤ 1+X₃ ∧ X₆ ≤ X₂ ∧ X₆ ≤ X₁ ∧ X₆ ≤ X₀ ∧ 1 ≤ X₆ ∧ 1 ≤ X₅+X₆ ∧ 1 ≤ X₄+X₆ ∧ 1+X₄ ≤ X₆ ∧ 1 ≤ X₃+X₆ ∧ 2 ≤ X₂+X₆ ∧ 2 ≤ X₁+X₆ ∧ 2 ≤ X₀+X₆ ∧ X₅ ≤ X₃ ∧ 1+X₅ ≤ X₂ ∧ 1+X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₄+X₅ ∧ X₄ ≤ X₅ ∧ 0 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 1 ≤ X₂+X₅ ∧ 1 ≤ X₁+X₅ ∧ 1 ≤ X₀+X₅ ∧ X₄ ≤ 0 ∧ X₄ ≤ X₃ ∧ 1+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location evalnestedLoopbb6in
Found invariant X₇ ≤ X₅ ∧ X₇ ≤ X₃ ∧ 1+X₇ ≤ X₀ ∧ 0 ≤ X₇ ∧ 1 ≤ X₆+X₇ ∧ X₆ ≤ 1+X₇ ∧ 0 ≤ X₅+X₇ ∧ X₅ ≤ X₇ ∧ 0 ≤ X₄+X₇ ∧ X₄ ≤ X₇ ∧ 0 ≤ X₃+X₇ ∧ X₃ ≤ X₇ ∧ 0 ≤ X₂+X₇ ∧ 1 ≤ X₁+X₇ ∧ 1 ≤ X₀+X₇ ∧ X₆ ≤ 1 ∧ X₆ ≤ 1+X₅ ∧ X₆ ≤ 1+X₄ ∧ X₄+X₆ ≤ 1 ∧ X₆ ≤ 1+X₃ ∧ X₆ ≤ 1+X₂ ∧ X₆ ≤ X₁ ∧ X₆ ≤ X₀ ∧ 1 ≤ X₆ ∧ 1 ≤ X₅+X₆ ∧ 1 ≤ X₄+X₆ ∧ 1+X₄ ≤ X₆ ∧ 1 ≤ X₃+X₆ ∧ 1 ≤ X₂+X₆ ∧ 2 ≤ X₁+X₆ ∧ 2 ≤ X₀+X₆ ∧ X₅ ≤ X₃ ∧ 1+X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₄+X₅ ∧ X₄ ≤ X₅ ∧ 0 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 0 ≤ X₂+X₅ ∧ 1 ≤ X₁+X₅ ∧ 1 ≤ X₀+X₅ ∧ X₄ ≤ 0 ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₂ ∧ 1+X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location evalnestedLoopbb6in_v2
Found invariant 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location evalnestedLoopbb9in
Found invariant X₅ ≤ X₃ ∧ 1+X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₄+X₅ ∧ X₄ ≤ X₅ ∧ 0 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 0 ≤ X₂+X₅ ∧ 1 ≤ X₁+X₅ ∧ 1 ≤ X₀+X₅ ∧ X₄ ≤ 0 ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₂ ∧ 1+X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location evalnestedLoopbb4in_v2
Found invariant 1+X₇ ≤ X₂ ∧ 0 ≤ X₇ ∧ 1 ≤ X₆+X₇ ∧ X₆ ≤ 1+X₇ ∧ 0 ≤ X₅+X₇ ∧ X₅ ≤ X₇ ∧ 0 ≤ X₄+X₇ ∧ X₄ ≤ X₇ ∧ 0 ≤ X₃+X₇ ∧ X₃ ≤ X₇ ∧ 1 ≤ X₂+X₇ ∧ 1 ≤ X₁+X₇ ∧ 1 ≤ X₀+X₇ ∧ X₆ ≤ 1 ∧ X₆ ≤ 1+X₅ ∧ X₆ ≤ 1+X₄ ∧ X₄+X₆ ≤ 1 ∧ X₆ ≤ 1+X₃ ∧ X₆ ≤ X₂ ∧ X₆ ≤ X₁ ∧ X₆ ≤ X₀ ∧ 1 ≤ X₆ ∧ 1 ≤ X₅+X₆ ∧ 1 ≤ X₄+X₆ ∧ 1+X₄ ≤ X₆ ∧ 1 ≤ X₃+X₆ ∧ 2 ≤ X₂+X₆ ∧ 2 ≤ X₁+X₆ ∧ 2 ≤ X₀+X₆ ∧ X₅ ≤ X₃ ∧ 1+X₅ ≤ X₂ ∧ 1+X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₄+X₅ ∧ X₄ ≤ X₅ ∧ 0 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 1 ≤ X₂+X₅ ∧ 1 ≤ X₁+X₅ ∧ 1 ≤ X₀+X₅ ∧ X₄ ≤ 0 ∧ X₄ ≤ X₃ ∧ 1+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location evalnestedLoopbb5in
Found invariant X₇ ≤ X₅ ∧ 0 ≤ X₇ ∧ 2 ≤ X₆+X₇ ∧ 0 ≤ X₅+X₇ ∧ X₅ ≤ X₇ ∧ 1 ≤ X₄+X₇ ∧ 0 ≤ X₃+X₇ ∧ X₃ ≤ X₇ ∧ 0 ≤ X₂+X₇ ∧ X₂ ≤ X₇ ∧ 2 ≤ X₁+X₇ ∧ 1 ≤ X₀+X₇ ∧ X₆ ≤ 1+X₄ ∧ X₆ ≤ X₁ ∧ 2 ≤ X₆ ∧ 2 ≤ X₅+X₆ ∧ 3 ≤ X₄+X₆ ∧ 1+X₄ ≤ X₆ ∧ 2 ≤ X₃+X₆ ∧ 2 ≤ X₂+X₆ ∧ 4 ≤ X₁+X₆ ∧ 3 ≤ X₀+X₆ ∧ 0 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 0 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 0 ≤ X₂+X₅ ∧ X₂ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ 1 ≤ X₀+X₅ ∧ 1+X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 3 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location evalnestedLoopbb6in_v1
Found invariant 0 ≤ X₅ ∧ 0 ≤ X₄+X₅ ∧ 0 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 0 ≤ X₂+X₅ ∧ 0 ≤ X₁+X₅ ∧ 1 ≤ X₀+X₅ ∧ X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location evalnestedLoopbb8in
Found invariant X₇ ≤ X₅ ∧ 0 ≤ X₇ ∧ 1 ≤ X₆+X₇ ∧ 0 ≤ X₅+X₇ ∧ X₅ ≤ X₇ ∧ 1 ≤ X₄+X₇ ∧ 0 ≤ X₃+X₇ ∧ X₃ ≤ X₇ ∧ 0 ≤ X₂+X₇ ∧ X₂ ≤ X₇ ∧ 2 ≤ X₁+X₇ ∧ 1 ≤ X₀+X₇ ∧ X₆ ≤ X₄ ∧ 1+X₆ ≤ X₁ ∧ 1 ≤ X₆ ∧ 1 ≤ X₅+X₆ ∧ 2 ≤ X₄+X₆ ∧ X₄ ≤ X₆ ∧ 1 ≤ X₃+X₆ ∧ 1 ≤ X₂+X₆ ∧ 3 ≤ X₁+X₆ ∧ 2 ≤ X₀+X₆ ∧ 0 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 0 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 0 ≤ X₂+X₅ ∧ X₂ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ 1 ≤ X₀+X₅ ∧ 1+X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 3 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location evalnestedLoopbb4in_v1
Found invariant X₇ ≤ X₅ ∧ 0 ≤ X₇ ∧ 1 ≤ X₆+X₇ ∧ 0 ≤ X₅+X₇ ∧ X₅ ≤ X₇ ∧ 1 ≤ X₄+X₇ ∧ 0 ≤ X₃+X₇ ∧ X₃ ≤ X₇ ∧ 0 ≤ X₂+X₇ ∧ X₂ ≤ X₇ ∧ 1 ≤ X₁+X₇ ∧ 1 ≤ X₀+X₇ ∧ X₆ ≤ X₄ ∧ X₆ ≤ X₁ ∧ 1 ≤ X₆ ∧ 1 ≤ X₅+X₆ ∧ 2 ≤ X₄+X₆ ∧ X₄ ≤ X₆ ∧ 1 ≤ X₃+X₆ ∧ 1 ≤ X₂+X₆ ∧ 2 ≤ X₁+X₆ ∧ 2 ≤ X₀+X₆ ∧ 0 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 0 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 0 ≤ X₂+X₅ ∧ X₂ ≤ X₅ ∧ 1 ≤ X₁+X₅ ∧ 1 ≤ X₀+X₅ ∧ X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location evalnestedLoopbb7in_v1
All Bounds
Timebounds
Overall timebound:3⋅X₀⋅X₁+2⋅X₂+3⋅X₁+4⋅X₀+11 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: X₀+1 {O(n)}
t₆: 1 {O(1)}
t₇: X₀⋅X₁+X₀+X₁+1 {O(n^2)}
t₈: X₀+1 {O(n)}
t₉: X₀⋅X₁+X₁ {O(n^2)}
t₁₀: X₂+1 {O(n)}
t₁₁: X₀⋅X₁+X₁ {O(n^2)}
t₁₂: X₂ {O(n)}
t₁₃: X₀ {O(n)}
t₁₄: 1 {O(1)}
Costbounds
Overall costbound: 3⋅X₀⋅X₁+2⋅X₂+3⋅X₁+4⋅X₀+11 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: X₀+1 {O(n)}
t₆: 1 {O(1)}
t₇: X₀⋅X₁+X₀+X₁+1 {O(n^2)}
t₈: X₀+1 {O(n)}
t₉: X₀⋅X₁+X₁ {O(n^2)}
t₁₀: X₂+1 {O(n)}
t₁₁: X₀⋅X₁+X₁ {O(n^2)}
t₁₂: X₂ {O(n)}
t₁₃: X₀ {O(n)}
t₁₄: 1 {O(1)}
Sizebounds
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)}
t₀, X₇: X₇ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: 0 {O(1)}
t₁, X₄: X₄ {O(n)}
t₁, X₅: X₅ {O(n)}
t₁, X₆: X₆ {O(n)}
t₁, X₇: X₇ {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)}
t₂, X₅: X₅ {O(n)}
t₂, X₆: X₆ {O(n)}
t₂, X₇: X₇ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₁ {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)}
t₃, X₇: X₇ {O(n)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₄, X₄: X₄ {O(n)}
t₄, X₅: X₅ {O(n)}
t₄, X₆: X₆ {O(n)}
t₄, X₇: X₇ {O(n)}
t₅, X₀: X₀ {O(n)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₀+X₂ {O(n)}
t₅, X₄: 0 {O(1)}
t₅, X₅: X₀+X₂ {O(n)}
t₅, X₆: 2⋅X₀⋅X₁+2⋅X₁+X₆+2 {O(n^2)}
t₅, X₇: 2⋅X₀+2⋅X₂+X₇ {O(n)}
t₆, X₀: 2⋅X₀ {O(n)}
t₆, X₁: 2⋅X₁ {O(n)}
t₆, X₂: 2⋅X₂ {O(n)}
t₆, X₃: X₀+X₂ {O(n)}
t₆, X₄: X₀⋅X₁+X₁+X₄ {O(n^2)}
t₆, X₅: X₀+X₂+X₅ {O(n)}
t₆, X₆: 2⋅X₀⋅X₁+2⋅X₁+2⋅X₆+2 {O(n^2)}
t₆, X₇: 2⋅X₀+2⋅X₂+2⋅X₇ {O(n)}
t₇, X₀: X₀ {O(n)}
t₇, X₁: X₁ {O(n)}
t₇, X₂: X₂ {O(n)}
t₇, X₃: X₀+X₂ {O(n)}
t₇, X₄: X₀⋅X₁+X₁ {O(n^2)}
t₇, X₅: X₀+X₂ {O(n)}
t₇, X₆: 4⋅X₀⋅X₁+4⋅X₁+X₆+4 {O(n^2)}
t₇, X₇: 4⋅X₀+4⋅X₂+X₇ {O(n)}
t₈, X₀: X₀ {O(n)}
t₈, X₁: X₁ {O(n)}
t₈, X₂: X₂ {O(n)}
t₈, X₃: 2⋅X₀+2⋅X₂ {O(n)}
t₈, X₄: X₀⋅X₁+X₁ {O(n^2)}
t₈, X₅: X₀+X₂ {O(n)}
t₈, X₆: 2⋅X₀⋅X₁+2⋅X₁+X₆+2 {O(n^2)}
t₈, X₇: 2⋅X₀+2⋅X₂+X₇ {O(n)}
t₉, X₀: X₀ {O(n)}
t₉, X₁: X₁ {O(n)}
t₉, X₂: X₂ {O(n)}
t₉, X₃: X₀+X₂ {O(n)}
t₉, X₄: X₀⋅X₁+X₁ {O(n^2)}
t₉, X₅: X₀+X₂ {O(n)}
t₉, X₆: X₀⋅X₁+X₁+1 {O(n^2)}
t₉, X₇: X₀+X₂ {O(n)}
t₁₀, X₀: X₀ {O(n)}
t₁₀, X₁: X₁ {O(n)}
t₁₀, X₂: X₂ {O(n)}
t₁₀, X₃: X₀+X₂ {O(n)}
t₁₀, X₄: X₀⋅X₁+X₁ {O(n^2)}
t₁₀, X₅: X₀+X₂ {O(n)}
t₁₀, X₆: X₀⋅X₁+X₁+1 {O(n^2)}
t₁₀, X₇: X₀+X₂ {O(n)}
t₁₁, X₀: X₀ {O(n)}
t₁₁, X₁: X₁ {O(n)}
t₁₁, X₂: X₂ {O(n)}
t₁₁, X₃: X₀+X₂ {O(n)}
t₁₁, X₄: X₀⋅X₁+X₁ {O(n^2)}
t₁₁, X₅: X₀+X₂ {O(n)}
t₁₁, X₆: 2⋅X₀⋅X₁+2⋅X₁+2 {O(n^2)}
t₁₁, X₇: 2⋅X₀+2⋅X₂ {O(n)}
t₁₂, X₀: X₀ {O(n)}
t₁₂, X₁: X₁ {O(n)}
t₁₂, X₂: X₂ {O(n)}
t₁₂, X₃: X₀+X₂ {O(n)}
t₁₂, X₄: X₀⋅X₁+X₁ {O(n^2)}
t₁₂, X₅: X₀+X₂ {O(n)}
t₁₂, X₆: X₀⋅X₁+X₁+1 {O(n^2)}
t₁₂, X₇: X₀+X₂ {O(n)}
t₁₃, X₀: X₀ {O(n)}
t₁₃, X₁: X₁ {O(n)}
t₁₃, X₂: X₂ {O(n)}
t₁₃, X₃: X₀+X₂ {O(n)}
t₁₃, X₄: X₀⋅X₁+X₁ {O(n^2)}
t₁₃, X₅: X₀+X₂ {O(n)}
t₁₃, X₆: 2⋅X₀⋅X₁+2⋅X₁+X₆+2 {O(n^2)}
t₁₃, X₇: 2⋅X₀+2⋅X₂+X₇ {O(n)}
t₁₄, X₀: 5⋅X₀ {O(n)}
t₁₄, X₁: 5⋅X₁ {O(n)}
t₁₄, X₂: 5⋅X₂ {O(n)}
t₁₄, X₃: 3⋅X₃+X₀+X₂ {O(n)}
t₁₄, X₄: X₀⋅X₁+4⋅X₄+X₁ {O(n^2)}
t₁₄, X₅: 4⋅X₅+X₀+X₂ {O(n)}
t₁₄, X₆: 2⋅X₀⋅X₁+2⋅X₁+5⋅X₆+2 {O(n^2)}
t₁₄, X₇: 2⋅X₀+2⋅X₂+5⋅X₇ {O(n)}