KoAT2 Proof Output

Initial Problem

Start: evalrealheapsortstep1start
Program_Vars: X₀, X₁, X₂
Temp_Vars: D, E, F
Locations: evalrealheapsortstep1bb2in, evalrealheapsortstep1bb3in, evalrealheapsortstep1bb4in, evalrealheapsortstep1bb5in, evalrealheapsortstep1bb6in, evalrealheapsortstep1entryin, evalrealheapsortstep1returnin, evalrealheapsortstep1start, evalrealheapsortstep1stop
Transitions:
t₁₃: evalrealheapsortstep1bb2in(X₀, X₁, X₂) → evalrealheapsortstep1bb3in(X₀, X₁, -1) :|: 0 ≤ 1+X₂ ∧ 1+X₂ ≤ 0
t₁₄: evalrealheapsortstep1bb2in(X₀, X₁, X₂) → evalrealheapsortstep1bb3in(X₀, X₁, D-1) :|: 0 ≤ 1+2⋅D ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1+X₂ ≤ 0 ∧ 0 ≤ D ∧ D ≤ 0
t₁₅: evalrealheapsortstep1bb2in(X₀, X₁, X₂) → evalrealheapsortstep1bb3in(X₀, X₁, D-1) :|: 2⋅D ≤ 2+X₂ ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1+X₂ ≤ 2⋅D ∧ 1+X₂ ≤ 0 ∧ D ≤ 0
t₁₆: evalrealheapsortstep1bb2in(X₀, X₁, X₂) → evalrealheapsortstep1bb3in(X₀, X₁, -1) :|: 0 ≤ 1+2⋅D ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1+X₂ ≤ 0 ∧ 0 ≤ D ∧ D ≤ 0
t₁₇: evalrealheapsortstep1bb2in(X₀, X₁, X₂) → evalrealheapsortstep1bb3in(X₀, X₁, D-1) :|: 0 ≤ 1+2⋅D ∧ 0 ≤ 1+2⋅E ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1+X₂ ≤ 0 ∧ 0 ≤ D ∧ D ≤ 0 ∧ 0 ≤ E ∧ E ≤ 0
t₁₈: evalrealheapsortstep1bb2in(X₀, X₁, X₂) → evalrealheapsortstep1bb3in(X₀, X₁, D-1) :|: 2⋅D ≤ 2+X₂ ∧ 0 ≤ 1+2⋅E ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1+X₂ ≤ 2⋅D ∧ 1+X₂ ≤ 0 ∧ D ≤ 0 ∧ 0 ≤ E ∧ E ≤ 0
t₁₉: evalrealheapsortstep1bb2in(X₀, X₁, X₂) → evalrealheapsortstep1bb3in(X₀, X₁, -1) :|: 2⋅D ≤ 2+X₂ ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1+X₂ ≤ 2⋅D ∧ 1+X₂ ≤ 0 ∧ D ≤ 0
t₂₀: evalrealheapsortstep1bb2in(X₀, X₁, X₂) → evalrealheapsortstep1bb3in(X₀, X₁, D-1) :|: 2⋅E ≤ 2+X₂ ∧ 0 ≤ 1+2⋅D ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1+X₂ ≤ 2⋅E ∧ 1+X₂ ≤ 0 ∧ 0 ≤ D ∧ D ≤ 0 ∧ E ≤ 0
t₂₁: evalrealheapsortstep1bb2in(X₀, X₁, X₂) → evalrealheapsortstep1bb3in(X₀, X₁, D-1) :|: 2⋅D ≤ 2+X₂ ∧ 2⋅E ≤ 2+X₂ ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1+X₂ ≤ 2⋅D ∧ 1+X₂ ≤ 2⋅E ∧ 1+X₂ ≤ 0 ∧ D ≤ 0 ∧ E ≤ 0
t₂₂: evalrealheapsortstep1bb2in(X₀, X₁, X₂) → evalrealheapsortstep1bb3in(X₀, X₁, -1) :|: 0 ≤ 1+2⋅D ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1+X₂ ≤ 0 ∧ 0 ≤ D ∧ D ≤ 0
t₂₃: evalrealheapsortstep1bb2in(X₀, X₁, X₂) → evalrealheapsortstep1bb3in(X₀, X₁, D-1) :|: 0 ≤ 1+2⋅D ∧ 0 ≤ 1+2⋅E ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1+X₂ ≤ 0 ∧ 0 ≤ D ∧ D ≤ 0 ∧ 0 ≤ E ∧ E ≤ 0
t₂₄: evalrealheapsortstep1bb2in(X₀, X₁, X₂) → evalrealheapsortstep1bb3in(X₀, X₁, D-1) :|: 2⋅D ≤ 2+X₂ ∧ 0 ≤ 1+2⋅E ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1+X₂ ≤ 2⋅D ∧ 1+X₂ ≤ 0 ∧ D ≤ 0 ∧ 0 ≤ E ∧ E ≤ 0
t₂₅: evalrealheapsortstep1bb2in(X₀, X₁, X₂) → evalrealheapsortstep1bb3in(X₀, X₁, -1) :|: 0 ≤ 1+2⋅D ∧ 0 ≤ 1+2⋅E ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1+X₂ ≤ 0 ∧ 0 ≤ D ∧ D ≤ 0 ∧ 0 ≤ E ∧ E ≤ 0
t₂₆: evalrealheapsortstep1bb2in(X₀, X₁, X₂) → evalrealheapsortstep1bb3in(X₀, X₁, D-1) :|: 2⋅D ≤ 1+X₂ ∧ 2⋅E ≤ 1+X₂ ∧ 2⋅F ≤ 1+X₂ ∧ X₂ ≤ 2⋅D ∧ 0 ≤ D ∧ X₂ ≤ 2⋅E ∧ 0 ≤ E ∧ X₂ ≤ 2⋅F ∧ 0 ≤ F ∧ 0 ≤ X₂
t₂₇: evalrealheapsortstep1bb2in(X₀, X₁, X₂) → evalrealheapsortstep1bb3in(X₀, X₁, D-1) :|: 2⋅D ≤ 2+X₂ ∧ 2⋅E ≤ 1+X₂ ∧ 2⋅F ≤ 1+X₂ ∧ 1+X₂ ≤ 2⋅D ∧ 2+X₂ ≤ 0 ∧ D ≤ 0 ∧ X₂ ≤ 2⋅E ∧ 0 ≤ E ∧ X₂ ≤ 2⋅F ∧ 0 ≤ F ∧ 0 ≤ X₂
t₂₈: evalrealheapsortstep1bb2in(X₀, X₁, X₂) → evalrealheapsortstep1bb3in(X₀, X₁, -1) :|: 2⋅E ≤ 2+X₂ ∧ 0 ≤ 1+2⋅D ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1+X₂ ≤ 2⋅E ∧ 1+X₂ ≤ 0 ∧ 0 ≤ D ∧ D ≤ 0 ∧ E ≤ 0
t₂₉: evalrealheapsortstep1bb2in(X₀, X₁, X₂) → evalrealheapsortstep1bb3in(X₀, X₁, D-1) :|: 2⋅F ≤ 2+X₂ ∧ 2⋅D ≤ 1+X₂ ∧ 2⋅E ≤ 1+X₂ ∧ 1+X₂ ≤ 2⋅F ∧ 2+X₂ ≤ 0 ∧ X₂ ≤ 2⋅D ∧ 0 ≤ D ∧ X₂ ≤ 2⋅E ∧ 0 ≤ E ∧ F ≤ 0 ∧ 0 ≤ X₂
t₃₀: evalrealheapsortstep1bb2in(X₀, X₁, X₂) → evalrealheapsortstep1bb3in(X₀, X₁, D-1) :|: 2⋅D ≤ 2+X₂ ∧ 2⋅F ≤ 2+X₂ ∧ 2⋅E ≤ 1+X₂ ∧ 1+X₂ ≤ 2⋅D ∧ 1+X₂ ≤ 2⋅F ∧ 2+X₂ ≤ 0 ∧ D ≤ 0 ∧ X₂ ≤ 2⋅E ∧ 0 ≤ E ∧ F ≤ 0 ∧ 0 ≤ X₂
t₃₁: evalrealheapsortstep1bb2in(X₀, X₁, X₂) → evalrealheapsortstep1bb3in(X₀, X₁, -1) :|: 2⋅D ≤ 2+X₂ ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1+X₂ ≤ 2⋅D ∧ 1+X₂ ≤ 0 ∧ D ≤ 0
t₃₂: evalrealheapsortstep1bb2in(X₀, X₁, X₂) → evalrealheapsortstep1bb3in(X₀, X₁, D-1) :|: 2⋅E ≤ 2+X₂ ∧ 0 ≤ 1+2⋅D ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1+X₂ ≤ 2⋅E ∧ 1+X₂ ≤ 0 ∧ 0 ≤ D ∧ D ≤ 0 ∧ E ≤ 0
t₃₃: evalrealheapsortstep1bb2in(X₀, X₁, X₂) → evalrealheapsortstep1bb3in(X₀, X₁, D-1) :|: 2⋅D ≤ 2+X₂ ∧ 2⋅E ≤ 2+X₂ ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1+X₂ ≤ 2⋅D ∧ 1+X₂ ≤ 2⋅E ∧ 1+X₂ ≤ 0 ∧ D ≤ 0 ∧ E ≤ 0
t₃₄: evalrealheapsortstep1bb2in(X₀, X₁, X₂) → evalrealheapsortstep1bb3in(X₀, X₁, -1) :|: 2⋅D ≤ 2+X₂ ∧ 0 ≤ 1+2⋅E ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1+X₂ ≤ 2⋅D ∧ 1+X₂ ≤ 0 ∧ D ≤ 0 ∧ 0 ≤ E ∧ E ≤ 0
t₃₅: evalrealheapsortstep1bb2in(X₀, X₁, X₂) → evalrealheapsortstep1bb3in(X₀, X₁, D-1) :|: 2⋅E ≤ 2+X₂ ∧ 2⋅D ≤ 1+X₂ ∧ 2⋅F ≤ 1+X₂ ∧ 1+X₂ ≤ 2⋅E ∧ 2+X₂ ≤ 0 ∧ X₂ ≤ 2⋅D ∧ 0 ≤ D ∧ E ≤ 0 ∧ X₂ ≤ 2⋅F ∧ 0 ≤ F ∧ 0 ≤ X₂
t₃₆: evalrealheapsortstep1bb2in(X₀, X₁, X₂) → evalrealheapsortstep1bb3in(X₀, X₁, D-1) :|: 2⋅D ≤ 2+X₂ ∧ 2⋅E ≤ 2+X₂ ∧ 2⋅F ≤ 1+X₂ ∧ 1+X₂ ≤ 2⋅D ∧ 1+X₂ ≤ 2⋅E ∧ 2+X₂ ≤ 0 ∧ D ≤ 0 ∧ E ≤ 0 ∧ X₂ ≤ 2⋅F ∧ 0 ≤ F ∧ 0 ≤ X₂
t₃₇: evalrealheapsortstep1bb2in(X₀, X₁, X₂) → evalrealheapsortstep1bb3in(X₀, X₁, -1) :|: 2⋅D ≤ 2+X₂ ∧ 2⋅E ≤ 2+X₂ ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1+X₂ ≤ 2⋅D ∧ 1+X₂ ≤ 2⋅E ∧ 1+X₂ ≤ 0 ∧ D ≤ 0 ∧ E ≤ 0
t₃₈: evalrealheapsortstep1bb2in(X₀, X₁, X₂) → evalrealheapsortstep1bb3in(X₀, X₁, D-1) :|: 2⋅E ≤ 2+X₂ ∧ 2⋅F ≤ 2+X₂ ∧ 2⋅D ≤ 1+X₂ ∧ 1+X₂ ≤ 2⋅E ∧ 1+X₂ ≤ 2⋅F ∧ 2+X₂ ≤ 0 ∧ X₂ ≤ 2⋅D ∧ 0 ≤ D ∧ E ≤ 0 ∧ F ≤ 0 ∧ 0 ≤ X₂
t₃₉: evalrealheapsortstep1bb2in(X₀, X₁, X₂) → evalrealheapsortstep1bb3in(X₀, X₁, D-1) :|: 2⋅D ≤ 2+X₂ ∧ 2⋅E ≤ 2+X₂ ∧ 2⋅F ≤ 2+X₂ ∧ 1+X₂ ≤ 2⋅D ∧ 1+X₂ ≤ 2⋅E ∧ 1+X₂ ≤ 2⋅F ∧ 2+X₂ ≤ 0 ∧ D ≤ 0 ∧ E ≤ 0 ∧ F ≤ 0
t₆: evalrealheapsortstep1bb3in(X₀, X₁, X₂) → evalrealheapsortstep1bb4in(X₀, X₁, X₂) :|: 1 ≤ X₂
t₅: evalrealheapsortstep1bb3in(X₀, X₁, X₂) → evalrealheapsortstep1bb5in(X₀, X₁, X₂) :|: X₂ ≤ 0
t₇: evalrealheapsortstep1bb4in(X₀, X₁, X₂) → evalrealheapsortstep1bb2in(X₀, X₁, X₂) :|: 0 ≤ 1+X₂ ∧ 1+X₂ ≤ 0
t₈: evalrealheapsortstep1bb4in(X₀, X₁, X₂) → evalrealheapsortstep1bb2in(X₀, X₁, X₂) :|: 2⋅D ≤ 1+X₂ ∧ X₂ ≤ 2⋅D ∧ 0 ≤ D ∧ 0 ≤ X₂
t₉: evalrealheapsortstep1bb4in(X₀, X₁, X₂) → evalrealheapsortstep1bb2in(X₀, X₁, X₂) :|: 2⋅D ≤ 2+X₂ ∧ 1+X₂ ≤ 2⋅D ∧ 2+X₂ ≤ 0 ∧ D ≤ 0
t₁₀: evalrealheapsortstep1bb4in(X₀, X₁, X₂) → evalrealheapsortstep1bb5in(X₀, X₁, X₂) :|: 0 ≤ 1+X₂ ∧ 1+X₂ ≤ 0
t₁₁: evalrealheapsortstep1bb4in(X₀, X₁, X₂) → evalrealheapsortstep1bb5in(X₀, X₁, X₂) :|: 2⋅D ≤ 1+X₂ ∧ X₂ ≤ 2⋅D ∧ 0 ≤ D ∧ 0 ≤ X₂
t₁₂: evalrealheapsortstep1bb4in(X₀, X₁, X₂) → evalrealheapsortstep1bb5in(X₀, X₁, X₂) :|: 2⋅D ≤ 2+X₂ ∧ 1+X₂ ≤ 2⋅D ∧ 2+X₂ ≤ 0 ∧ D ≤ 0
t₄₀: evalrealheapsortstep1bb5in(X₀, X₁, X₂) → evalrealheapsortstep1bb6in(X₀, 1+X₁, X₂)
t₃: evalrealheapsortstep1bb6in(X₀, X₁, X₂) → evalrealheapsortstep1bb3in(X₀, X₁, X₁) :|: 1+X₁ ≤ X₀
t₄: evalrealheapsortstep1bb6in(X₀, X₁, X₂) → evalrealheapsortstep1returnin(X₀, X₁, X₂) :|: X₀ ≤ X₁
t₁: evalrealheapsortstep1entryin(X₀, X₁, X₂) → evalrealheapsortstep1bb6in(X₀, 1, X₂) :|: 3 ≤ X₀
t₂: evalrealheapsortstep1entryin(X₀, X₁, X₂) → evalrealheapsortstep1returnin(X₀, X₁, X₂) :|: X₀ ≤ 2
t₄₁: evalrealheapsortstep1returnin(X₀, X₁, X₂) → evalrealheapsortstep1stop(X₀, X₁, X₂)
t₀: evalrealheapsortstep1start(X₀, X₁, X₂) → evalrealheapsortstep1entryin(X₀, X₁, X₂)

Preprocessing

Cut unsatisfiable transition [t₇: evalrealheapsortstep1bb4in→evalrealheapsortstep1bb2in; t₉: evalrealheapsortstep1bb4in→evalrealheapsortstep1bb2in; t₁₀: evalrealheapsortstep1bb4in→evalrealheapsortstep1bb5in; t₁₂: evalrealheapsortstep1bb4in→evalrealheapsortstep1bb5in; t₁₄: evalrealheapsortstep1bb2in→evalrealheapsortstep1bb3in; t₁₅: evalrealheapsortstep1bb2in→evalrealheapsortstep1bb3in; t₁₆: evalrealheapsortstep1bb2in→evalrealheapsortstep1bb3in; t₁₇: evalrealheapsortstep1bb2in→evalrealheapsortstep1bb3in; t₁₈: evalrealheapsortstep1bb2in→evalrealheapsortstep1bb3in; t₁₉: evalrealheapsortstep1bb2in→evalrealheapsortstep1bb3in; t₂₀: evalrealheapsortstep1bb2in→evalrealheapsortstep1bb3in; t₂₁: evalrealheapsortstep1bb2in→evalrealheapsortstep1bb3in; t₂₂: evalrealheapsortstep1bb2in→evalrealheapsortstep1bb3in; t₂₃: evalrealheapsortstep1bb2in→evalrealheapsortstep1bb3in; t₂₄: evalrealheapsortstep1bb2in→evalrealheapsortstep1bb3in; t₂₅: evalrealheapsortstep1bb2in→evalrealheapsortstep1bb3in; t₂₇: evalrealheapsortstep1bb2in→evalrealheapsortstep1bb3in; t₂₈: evalrealheapsortstep1bb2in→evalrealheapsortstep1bb3in; t₂₉: evalrealheapsortstep1bb2in→evalrealheapsortstep1bb3in; t₃₀: evalrealheapsortstep1bb2in→evalrealheapsortstep1bb3in; t₃₁: evalrealheapsortstep1bb2in→evalrealheapsortstep1bb3in; t₃₂: evalrealheapsortstep1bb2in→evalrealheapsortstep1bb3in; t₃₃: evalrealheapsortstep1bb2in→evalrealheapsortstep1bb3in; t₃₄: evalrealheapsortstep1bb2in→evalrealheapsortstep1bb3in; t₃₅: evalrealheapsortstep1bb2in→evalrealheapsortstep1bb3in; t₃₆: evalrealheapsortstep1bb2in→evalrealheapsortstep1bb3in; t₃₇: evalrealheapsortstep1bb2in→evalrealheapsortstep1bb3in; t₃₈: evalrealheapsortstep1bb2in→evalrealheapsortstep1bb3in]

Found invariant 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 3 ≤ X₀ for location evalrealheapsortstep1bb4in

Found invariant 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 3 ≤ X₀ for location evalrealheapsortstep1bb5in

Found invariant X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 3 ≤ X₀ for location evalrealheapsortstep1bb6in

Found invariant 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 3 ≤ X₀ for location evalrealheapsortstep1bb3in

Found invariant 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 3 ≤ X₀ for location evalrealheapsortstep1bb2in

Cut unsatisfiable transition [t₁₃: evalrealheapsortstep1bb2in→evalrealheapsortstep1bb3in; t₃₉: evalrealheapsortstep1bb2in→evalrealheapsortstep1bb3in]

Problem after Preprocessing

MPRF for transition t₃: evalrealheapsortstep1bb6in(X₀, X₁, X₂) → evalrealheapsortstep1bb3in(X₀, X₁, X₁) :|: 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀ ∧ 4 ≤ X₀+X₁ ∧ X₁ ≤ X₀ of depth 1:

new bound:

X₀+2 {O(n)}

MPRF:

• evalrealheapsortstep1bb2in: [X₀-X₁]
• evalrealheapsortstep1bb3in: [X₀-X₁]
• evalrealheapsortstep1bb4in: [X₀-X₁]
• evalrealheapsortstep1bb5in: [X₀-X₁]
• evalrealheapsortstep1bb6in: [1+X₀-X₁]

MPRF for transition t₅: evalrealheapsortstep1bb3in(X₀, X₁, X₂) → evalrealheapsortstep1bb5in(X₀, X₁, X₂) :|: X₂ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₂ ∧ 4 ≤ X₀+X₁ ∧ 0 ≤ X₂ of depth 1:

new bound:

X₀+1 {O(n)}

MPRF:

• evalrealheapsortstep1bb2in: [X₀-X₁]
• evalrealheapsortstep1bb3in: [X₀-X₁]
• evalrealheapsortstep1bb4in: [X₀-X₁]
• evalrealheapsortstep1bb5in: [X₀-1-X₁]
• evalrealheapsortstep1bb6in: [X₀-X₁]

MPRF for transition t₁₁: evalrealheapsortstep1bb4in(X₀, X₁, X₂) → evalrealheapsortstep1bb5in(X₀, X₁, X₂) :|: 2⋅D ≤ 1+X₂ ∧ X₂ ≤ 2⋅D ∧ 0 ≤ D ∧ 0 ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀ ∧ 4 ≤ X₀+X₁ ∧ 4 ≤ X₀+X₂ of depth 1:

new bound:

X₀+1 {O(n)}

MPRF:

MPRF for transition t₄₀: evalrealheapsortstep1bb5in(X₀, X₁, X₂) → evalrealheapsortstep1bb6in(X₀, 1+X₁, X₂) :|: 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₂ ∧ 4 ≤ X₀+X₁ ∧ 0 ≤ X₂ of depth 1:

new bound:

X₀+1 {O(n)}

MPRF:

MPRF for transition t₆: evalrealheapsortstep1bb3in(X₀, X₁, X₂) → evalrealheapsortstep1bb4in(X₀, X₁, X₂) :|: 1 ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₂ ∧ 4 ≤ X₀+X₁ ∧ 0 ≤ X₂ of depth 1:

new bound:

2⋅X₀⋅X₀+7⋅X₀+8 {O(n^2)}

MPRF:

• evalrealheapsortstep1bb2in: [2⋅X₂]
• evalrealheapsortstep1bb3in: [1+2⋅X₂]
• evalrealheapsortstep1bb4in: [2⋅X₂]
• evalrealheapsortstep1bb5in: [2⋅X₂]
• evalrealheapsortstep1bb6in: [1+2⋅X₁]

MPRF for transition t₈: evalrealheapsortstep1bb4in(X₀, X₁, X₂) → evalrealheapsortstep1bb2in(X₀, X₁, X₂) :|: 2⋅D ≤ 1+X₂ ∧ X₂ ≤ 2⋅D ∧ 0 ≤ D ∧ 0 ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀ ∧ 4 ≤ X₀+X₁ ∧ 4 ≤ X₀+X₂ of depth 1:

new bound:

2⋅X₀⋅X₀+7⋅X₀+8 {O(n^2)}

MPRF:

• evalrealheapsortstep1bb2in: [X₂]
• evalrealheapsortstep1bb3in: [1+2⋅X₂]
• evalrealheapsortstep1bb4in: [1+X₂]
• evalrealheapsortstep1bb5in: [0]
• evalrealheapsortstep1bb6in: [1+2⋅X₁]

MPRF for transition t₂₆: evalrealheapsortstep1bb2in(X₀, X₁, X₂) → evalrealheapsortstep1bb3in(X₀, X₁, D-1) :|: 2⋅D ≤ 1+X₂ ∧ 2⋅E ≤ 1+X₂ ∧ 2⋅F ≤ 1+X₂ ∧ X₂ ≤ 2⋅D ∧ 0 ≤ D ∧ X₂ ≤ 2⋅E ∧ 0 ≤ E ∧ X₂ ≤ 2⋅F ∧ 0 ≤ F ∧ 0 ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀ ∧ 4 ≤ X₀+X₁ ∧ 4 ≤ X₀+X₂ of depth 1:

new bound:

2⋅X₀⋅X₀+6⋅X₀+6 {O(n^2)}

MPRF:

• evalrealheapsortstep1bb2in: [1+X₂]
• evalrealheapsortstep1bb3in: [2⋅X₂]
• evalrealheapsortstep1bb4in: [2⋅X₂]
• evalrealheapsortstep1bb5in: [2⋅X₂]
• evalrealheapsortstep1bb6in: [2⋅X₁]

Cut unreachable locations [evalrealheapsortstep1bb3in] from the program graph

Cut unsatisfiable transition [t₄: evalrealheapsortstep1bb6in→evalrealheapsortstep1returnin; t₂₀₈: evalrealheapsortstep1bb6in→evalrealheapsortstep1returnin]

Found invariant X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 3 ≤ X₀ for location evalrealheapsortstep1bb5in_v1

Found invariant 1+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 3 ≤ X₀ for location evalrealheapsortstep1bb4in_v2

Found invariant X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 3+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 3 ≤ X₀ for location evalrealheapsortstep1bb5in

Found invariant X₁ ≤ 1 ∧ 2+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 3 ≤ X₀ for location evalrealheapsortstep1bb6in

Found invariant 1+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 3 ≤ X₀ for location evalrealheapsortstep1bb5in_v2

Found invariant X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 3 ≤ X₀ for location evalrealheapsortstep1bb3in_v1

Found invariant X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 3 ≤ X₀ for location evalrealheapsortstep1bb4in_v1

Found invariant 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 3 ≤ X₀ for location evalrealheapsortstep1bb6in_v1

Found invariant X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 3 ≤ X₀ for location evalrealheapsortstep1bb2in_v1

Found invariant 1+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 3 ≤ X₀ for location evalrealheapsortstep1bb2in_v2

Found invariant 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 3 ≤ X₀ for location evalrealheapsortstep1bb3in_v2

Found invariant 2+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 3 ≤ X₁ ∧ 6 ≤ X₀+X₁ ∧ 3 ≤ X₀ for location evalrealheapsortstep1bb6in_v2

All Bounds

Timebounds

Overall timebound:6⋅X₀⋅X₀+24⋅X₀+32 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: X₀+2 {O(n)}
t₄: 1 {O(1)}
t₅: X₀+1 {O(n)}
t₆: 2⋅X₀⋅X₀+7⋅X₀+8 {O(n^2)}
t₈: 2⋅X₀⋅X₀+7⋅X₀+8 {O(n^2)}
t₁₁: X₀+1 {O(n)}
t₂₆: 2⋅X₀⋅X₀+6⋅X₀+6 {O(n^2)}
t₄₀: X₀+1 {O(n)}
t₄₁: 1 {O(1)}

Costbounds

Overall costbound: 6⋅X₀⋅X₀+24⋅X₀+32 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: X₀+2 {O(n)}
t₄: 1 {O(1)}
t₅: X₀+1 {O(n)}
t₆: 2⋅X₀⋅X₀+7⋅X₀+8 {O(n^2)}
t₈: 2⋅X₀⋅X₀+7⋅X₀+8 {O(n^2)}
t₁₁: X₀+1 {O(n)}
t₂₆: 2⋅X₀⋅X₀+6⋅X₀+6 {O(n^2)}
t₄₀: X₀+1 {O(n)}
t₄₁: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: 1 {O(1)}
t₁, X₂: X₂ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₀+2 {O(n)}
t₃, X₂: X₀+3 {O(n)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₀+2 {O(n)}
t₄, X₂: X₀+3 {O(n)}
t₅, X₀: X₀ {O(n)}
t₅, X₁: X₀+2 {O(n)}
t₅, X₂: 0 {O(1)}
t₆, X₀: X₀ {O(n)}
t₆, X₁: X₀+2 {O(n)}
t₆, X₂: X₀+3 {O(n)}
t₈, X₀: X₀ {O(n)}
t₈, X₁: X₀+2 {O(n)}
t₈, X₂: X₀+3 {O(n)}
t₁₁, X₀: X₀ {O(n)}
t₁₁, X₁: X₀+2 {O(n)}
t₁₁, X₂: X₀+3 {O(n)}
t₂₆, X₀: X₀ {O(n)}
t₂₆, X₁: X₀+2 {O(n)}
t₂₆, X₂: X₀+3 {O(n)}
t₄₀, X₀: X₀ {O(n)}
t₄₀, X₁: X₀+2 {O(n)}
t₄₀, X₂: X₀+3 {O(n)}
t₄₁, X₀: 2⋅X₀ {O(n)}
t₄₁, X₁: X₀+X₁+2 {O(n)}
t₄₁, X₂: X₀+X₂+3 {O(n)}