KoAT2 Proof Output

Initial Problem

Start: eval_non_linear13_start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars:
Locations: eval_non_linear13_bb0_in, eval_non_linear13_bb1_in, eval_non_linear13_bb2_in, eval_non_linear13_bb3_in, eval_non_linear13_bb4_in, eval_non_linear13_bb5_in, eval_non_linear13_start, eval_non_linear13_stop
Transitions:
t₁: eval_non_linear13_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_non_linear13_bb1_in(X₄, X₅, X₂, X₃, X₄, X₅, X₆)
t₂: eval_non_linear13_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_non_linear13_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1 ≤ X₀
t₃: eval_non_linear13_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_non_linear13_bb3_in(X₀, X₁, X₆, X₁, X₄, X₅, X₆) :|: X₀ ≤ 0
t₄: eval_non_linear13_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_non_linear13_bb1_in(X₀-1, 2⋅X₁, X₂, X₃, X₄, X₅, X₆)
t₅: eval_non_linear13_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_non_linear13_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1 ≤ X₂ ∧ 1+X₂ ≤ X₃
t₆: eval_non_linear13_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_non_linear13_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₃ ≤ X₂
t₇: eval_non_linear13_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_non_linear13_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₂ ≤ 0
t₈: eval_non_linear13_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_non_linear13_bb3_in(X₀, X₁, 3⋅X₂, 2⋅X₃, X₄, X₅, X₆)
t₉: eval_non_linear13_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_non_linear13_stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₀: eval_non_linear13_start(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_non_linear13_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆)

Preprocessing

Found invariant X₆ ≤ X₂ ∧ X₀ ≤ X₄ ∧ X₁ ≤ X₃ ∧ X₀ ≤ 0 for location eval_non_linear13_stop

Found invariant X₆ ≤ X₂ ∧ X₀ ≤ X₄ ∧ X₁ ≤ X₃ ∧ X₀ ≤ 0 for location eval_non_linear13_bb3_in

Found invariant X₆ ≤ X₂ ∧ X₀ ≤ X₄ ∧ X₁ ≤ X₃ ∧ X₀ ≤ 0 for location eval_non_linear13_bb5_in

Found invariant X₀ ≤ X₄ for location eval_non_linear13_bb1_in

Found invariant 1 ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 1 ≤ X₀ for location eval_non_linear13_bb2_in

Found invariant 1+X₆ ≤ X₃ ∧ X₆ ≤ X₂ ∧ X₀ ≤ X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ X₁ ≤ X₃ ∧ 2+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ X₀ ≤ 0 for location eval_non_linear13_bb4_in

Problem after Preprocessing

Start: eval_non_linear13_start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars:
Locations: eval_non_linear13_bb0_in, eval_non_linear13_bb1_in, eval_non_linear13_bb2_in, eval_non_linear13_bb3_in, eval_non_linear13_bb4_in, eval_non_linear13_bb5_in, eval_non_linear13_start, eval_non_linear13_stop
Transitions:
t₁: eval_non_linear13_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_non_linear13_bb1_in(X₄, X₅, X₂, X₃, X₄, X₅, X₆)
t₂: eval_non_linear13_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_non_linear13_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1 ≤ X₀ ∧ X₀ ≤ X₄
t₃: eval_non_linear13_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_non_linear13_bb3_in(X₀, X₁, X₆, X₁, X₄, X₅, X₆) :|: X₀ ≤ 0 ∧ X₀ ≤ X₄
t₄: eval_non_linear13_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_non_linear13_bb1_in(X₀-1, 2⋅X₁, X₂, X₃, X₄, X₅, X₆) :|: 1 ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ X₀ ≤ X₄
t₅: eval_non_linear13_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_non_linear13_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₄ ∧ X₁ ≤ X₃ ∧ X₆ ≤ X₂
t₆: eval_non_linear13_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_non_linear13_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₃ ≤ X₂ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₄ ∧ X₁ ≤ X₃ ∧ X₆ ≤ X₂
t₇: eval_non_linear13_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_non_linear13_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₂ ≤ 0 ∧ X₀ ≤ 0 ∧ X₀ ≤ X₄ ∧ X₁ ≤ X₃ ∧ X₆ ≤ X₂
t₈: eval_non_linear13_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_non_linear13_bb3_in(X₀, X₁, 3⋅X₂, 2⋅X₃, X₄, X₅, X₆) :|: 1+X₀ ≤ X₂ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 1+X₆ ≤ X₃ ∧ 2+X₀ ≤ X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₄ ∧ X₁ ≤ X₃ ∧ X₆ ≤ X₂
t₉: eval_non_linear13_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_non_linear13_stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₀ ≤ 0 ∧ X₀ ≤ X₄ ∧ X₁ ≤ X₃ ∧ X₆ ≤ X₂
t₀: eval_non_linear13_start(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_non_linear13_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆)

MPRF for transition t₂: eval_non_linear13_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_non_linear13_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1 ≤ X₀ ∧ X₀ ≤ X₄ of depth 1:

new bound:

X₄ {O(n)}

MPRF:

• eval_non_linear13_bb1_in: [X₀]
• eval_non_linear13_bb2_in: [X₀-1]

MPRF for transition t₄: eval_non_linear13_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_non_linear13_bb1_in(X₀-1, 2⋅X₁, X₂, X₃, X₄, X₅, X₆) :|: 1 ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ X₀ ≤ X₄ of depth 1:

new bound:

X₄ {O(n)}

MPRF:

• eval_non_linear13_bb1_in: [X₀]
• eval_non_linear13_bb2_in: [X₀]

Found invariant X₆ ≤ X₂ ∧ X₂ ≤ X₆ ∧ X₀ ≤ X₄ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₀ ≤ 0 for location eval_non_linear13_bb3_in

Found invariant X₆ ≤ X₂ ∧ X₀ ≤ X₄ ∧ X₁ ≤ X₃ ∧ X₀ ≤ 0 for location eval_non_linear13_bb5_in

Found invariant 3+X₆ ≤ X₃ ∧ 2+X₆ ≤ X₂ ∧ 1+X₆ ≤ X₁ ∧ 1 ≤ X₆ ∧ 5 ≤ X₃+X₆ ∧ 4 ≤ X₂+X₆ ∧ 3 ≤ X₁+X₆ ∧ 1+X₀ ≤ X₆ ∧ X₀ ≤ X₄ ∧ 4 ≤ X₃ ∧ 7 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 6 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 4+X₀ ≤ X₃ ∧ 3 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 3+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2+X₀ ≤ X₁ ∧ X₀ ≤ 0 for location eval_non_linear13_bb4_in_v2

Found invariant X₆ ≤ X₂ ∧ X₀ ≤ X₄ ∧ X₁ ≤ X₃ ∧ X₀ ≤ 0 for location eval_non_linear13_stop

Found invariant X₀ ≤ X₄ for location eval_non_linear13_bb1_in

Found invariant 1 ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 1 ≤ X₀ for location eval_non_linear13_bb2_in

Found invariant 1+X₆ ≤ X₃ ∧ X₆ ≤ X₂ ∧ 1+X₆ ≤ X₁ ∧ 1 ≤ X₆ ∧ 3 ≤ X₃+X₆ ∧ 2 ≤ X₂+X₆ ∧ X₂ ≤ X₆ ∧ 3 ≤ X₁+X₆ ∧ 1+X₀ ≤ X₆ ∧ X₀ ≤ X₄ ∧ X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2+X₀ ≤ X₁ ∧ X₀ ≤ 0 for location eval_non_linear13_bb4_in_v1

Found invariant 3+X₆ ≤ X₃ ∧ 2+X₆ ≤ X₂ ∧ 1+X₆ ≤ X₁ ∧ 1 ≤ X₆ ∧ 5 ≤ X₃+X₆ ∧ 4 ≤ X₂+X₆ ∧ 3 ≤ X₁+X₆ ∧ 1+X₀ ≤ X₆ ∧ X₀ ≤ X₄ ∧ 4 ≤ X₃ ∧ 7 ≤ X₂+X₃ ∧ 6 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 4+X₀ ≤ X₃ ∧ 3 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 3+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2+X₀ ≤ X₁ ∧ X₀ ≤ 0 for location eval_non_linear13_bb3_in_v1

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₄ {O(n)}
t₃: 1 {O(1)}
t₄: X₄ {O(n)}
t₅: inf {Infinity}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: inf {Infinity}
t₉: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₄ {O(n)}
t₃: 1 {O(1)}
t₄: X₄ {O(n)}
t₅: inf {Infinity}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: inf {Infinity}
t₉: 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)}
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: X₄ {O(n)}
t₂, X₁: 2^(X₄)⋅X₅ {O(EXP)}
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)}
t₃, X₀: 2⋅X₄ {O(n)}
t₃, X₁: 2^(X₄)⋅X₅+X₅ {O(EXP)}
t₃, X₂: 2⋅X₆ {O(n)}
t₃, X₃: 2^(X₄)⋅X₅+X₅ {O(EXP)}
t₃, X₄: 2⋅X₄ {O(n)}
t₃, X₅: 2⋅X₅ {O(n)}
t₃, X₆: 2⋅X₆ {O(n)}
t₄, X₀: X₄ {O(n)}
t₄, X₁: 2^(X₄)⋅X₅ {O(EXP)}
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)}
t₅, X₀: 2⋅X₄ {O(n)}
t₅, X₁: 2^(X₄)⋅X₅+X₅ {O(EXP)}
t₅, X₄: 2⋅X₄ {O(n)}
t₅, X₅: 2⋅X₅ {O(n)}
t₅, X₆: 2⋅X₆ {O(n)}
t₆, X₀: 4⋅X₄ {O(n)}
t₆, X₁: 2⋅2^(X₄)⋅X₅+2⋅X₅ {O(EXP)}
t₆, X₄: 4⋅X₄ {O(n)}
t₆, X₅: 4⋅X₅ {O(n)}
t₆, X₆: 4⋅X₆ {O(n)}
t₇, X₀: 2⋅X₄ {O(n)}
t₇, X₁: 2^(X₄)⋅X₅+X₅ {O(EXP)}
t₇, X₂: 2⋅X₆ {O(n)}
t₇, X₃: 2^(X₄)⋅X₅+X₅ {O(EXP)}
t₇, X₄: 2⋅X₄ {O(n)}
t₇, X₅: 2⋅X₅ {O(n)}
t₇, X₆: 2⋅X₆ {O(n)}
t₈, X₀: 2⋅X₄ {O(n)}
t₈, X₁: 2^(X₄)⋅X₅+X₅ {O(EXP)}
t₈, X₄: 2⋅X₄ {O(n)}
t₈, X₅: 2⋅X₅ {O(n)}
t₈, X₆: 2⋅X₆ {O(n)}
t₉, X₀: 6⋅X₄ {O(n)}
t₉, X₁: 2^(X₄)⋅3⋅X₅+3⋅X₅ {O(EXP)}
t₉, X₄: 6⋅X₄ {O(n)}
t₉, X₅: 6⋅X₅ {O(n)}
t₉, X₆: 6⋅X₆ {O(n)}