KoAT2 Proof Output

Initial Problem

Start: eval_speedSimpleMultipleDep_start
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: eval_speedSimpleMultipleDep_0, eval_speedSimpleMultipleDep_1, eval_speedSimpleMultipleDep_2, eval_speedSimpleMultipleDep_3, eval_speedSimpleMultipleDep_4, eval_speedSimpleMultipleDep_5, eval_speedSimpleMultipleDep_6, eval_speedSimpleMultipleDep_7, eval_speedSimpleMultipleDep_bb0_in, eval_speedSimpleMultipleDep_bb1_in, eval_speedSimpleMultipleDep_bb2_in, eval_speedSimpleMultipleDep_bb3_in, eval_speedSimpleMultipleDep_start, eval_speedSimpleMultipleDep_stop
Transitions:
t₂: eval_speedSimpleMultipleDep_0(X₀, X₁, X₂, X₃) → eval_speedSimpleMultipleDep_1(X₀, X₁, X₂, X₃)
t₃: eval_speedSimpleMultipleDep_1(X₀, X₁, X₂, X₃) → eval_speedSimpleMultipleDep_2(X₀, X₁, X₂, X₃)
t₄: eval_speedSimpleMultipleDep_2(X₀, X₁, X₂, X₃) → eval_speedSimpleMultipleDep_3(X₀, X₁, X₂, X₃)
t₅: eval_speedSimpleMultipleDep_3(X₀, X₁, X₂, X₃) → eval_speedSimpleMultipleDep_4(X₀, X₁, X₂, X₃)
t₆: eval_speedSimpleMultipleDep_4(X₀, X₁, X₂, X₃) → eval_speedSimpleMultipleDep_5(X₀, X₁, X₂, X₃)
t₇: eval_speedSimpleMultipleDep_5(X₀, X₁, X₂, X₃) → eval_speedSimpleMultipleDep_6(X₀, X₁, X₂, X₃)
t₈: eval_speedSimpleMultipleDep_6(X₀, X₁, X₂, X₃) → eval_speedSimpleMultipleDep_7(X₀, X₁, X₂, X₃)
t₉: eval_speedSimpleMultipleDep_7(X₀, X₁, X₂, X₃) → eval_speedSimpleMultipleDep_bb1_in(X₀, X₁, 0, 0)
t₁: eval_speedSimpleMultipleDep_bb0_in(X₀, X₁, X₂, X₃) → eval_speedSimpleMultipleDep_0(X₀, X₁, X₂, X₃)
t₁₀: eval_speedSimpleMultipleDep_bb1_in(X₀, X₁, X₂, X₃) → eval_speedSimpleMultipleDep_bb2_in(X₀, X₁, X₂, X₃) :|: 1+X₂ ≤ X₁
t₁₁: eval_speedSimpleMultipleDep_bb1_in(X₀, X₁, X₂, X₃) → eval_speedSimpleMultipleDep_bb3_in(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₂
t₁₂: eval_speedSimpleMultipleDep_bb2_in(X₀, X₁, X₂, X₃) → eval_speedSimpleMultipleDep_bb1_in(X₀, X₁, X₂, 1+X₃) :|: 1+X₃ ≤ X₀
t₁₃: eval_speedSimpleMultipleDep_bb2_in(X₀, X₁, X₂, X₃) → eval_speedSimpleMultipleDep_bb1_in(X₀, X₁, 1+X₂, 1+X₃) :|: 1+X₃ ≤ X₀ ∧ X₀ ≤ X₃
t₁₄: eval_speedSimpleMultipleDep_bb2_in(X₀, X₁, X₂, X₃) → eval_speedSimpleMultipleDep_bb1_in(X₀, X₁, X₂, 0) :|: 1+X₃ ≤ X₀ ∧ X₀ ≤ X₃
t₁₅: eval_speedSimpleMultipleDep_bb2_in(X₀, X₁, X₂, X₃) → eval_speedSimpleMultipleDep_bb1_in(X₀, X₁, 1+X₂, 0) :|: X₀ ≤ X₃
t₁₆: eval_speedSimpleMultipleDep_bb3_in(X₀, X₁, X₂, X₃) → eval_speedSimpleMultipleDep_stop(X₀, X₁, X₂, X₃)
t₀: eval_speedSimpleMultipleDep_start(X₀, X₁, X₂, X₃) → eval_speedSimpleMultipleDep_bb0_in(X₀, X₁, X₂, X₃)

Preprocessing

Cut unsatisfiable transition [t₁₃: eval_speedSimpleMultipleDep_bb2_in→eval_speedSimpleMultipleDep_bb1_in; t₁₄: eval_speedSimpleMultipleDep_bb2_in→eval_speedSimpleMultipleDep_bb1_in]

Found invariant 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂ for location eval_speedSimpleMultipleDep_bb1_in

Found invariant 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location eval_speedSimpleMultipleDep_bb2_in

Found invariant 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₂ for location eval_speedSimpleMultipleDep_stop

Found invariant 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₂ for location eval_speedSimpleMultipleDep_bb3_in

Problem after Preprocessing

Start: eval_speedSimpleMultipleDep_start
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: eval_speedSimpleMultipleDep_0, eval_speedSimpleMultipleDep_1, eval_speedSimpleMultipleDep_2, eval_speedSimpleMultipleDep_3, eval_speedSimpleMultipleDep_4, eval_speedSimpleMultipleDep_5, eval_speedSimpleMultipleDep_6, eval_speedSimpleMultipleDep_7, eval_speedSimpleMultipleDep_bb0_in, eval_speedSimpleMultipleDep_bb1_in, eval_speedSimpleMultipleDep_bb2_in, eval_speedSimpleMultipleDep_bb3_in, eval_speedSimpleMultipleDep_start, eval_speedSimpleMultipleDep_stop
Transitions:
t₂: eval_speedSimpleMultipleDep_0(X₀, X₁, X₂, X₃) → eval_speedSimpleMultipleDep_1(X₀, X₁, X₂, X₃)
t₃: eval_speedSimpleMultipleDep_1(X₀, X₁, X₂, X₃) → eval_speedSimpleMultipleDep_2(X₀, X₁, X₂, X₃)
t₄: eval_speedSimpleMultipleDep_2(X₀, X₁, X₂, X₃) → eval_speedSimpleMultipleDep_3(X₀, X₁, X₂, X₃)
t₅: eval_speedSimpleMultipleDep_3(X₀, X₁, X₂, X₃) → eval_speedSimpleMultipleDep_4(X₀, X₁, X₂, X₃)
t₆: eval_speedSimpleMultipleDep_4(X₀, X₁, X₂, X₃) → eval_speedSimpleMultipleDep_5(X₀, X₁, X₂, X₃)
t₇: eval_speedSimpleMultipleDep_5(X₀, X₁, X₂, X₃) → eval_speedSimpleMultipleDep_6(X₀, X₁, X₂, X₃)
t₈: eval_speedSimpleMultipleDep_6(X₀, X₁, X₂, X₃) → eval_speedSimpleMultipleDep_7(X₀, X₁, X₂, X₃)
t₉: eval_speedSimpleMultipleDep_7(X₀, X₁, X₂, X₃) → eval_speedSimpleMultipleDep_bb1_in(X₀, X₁, 0, 0)
t₁: eval_speedSimpleMultipleDep_bb0_in(X₀, X₁, X₂, X₃) → eval_speedSimpleMultipleDep_0(X₀, X₁, X₂, X₃)
t₁₀: eval_speedSimpleMultipleDep_bb1_in(X₀, X₁, X₂, X₃) → eval_speedSimpleMultipleDep_bb2_in(X₀, X₁, X₂, X₃) :|: 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
t₁₁: eval_speedSimpleMultipleDep_bb1_in(X₀, X₁, X₂, X₃) → eval_speedSimpleMultipleDep_bb3_in(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
t₁₂: eval_speedSimpleMultipleDep_bb2_in(X₀, X₁, X₂, X₃) → eval_speedSimpleMultipleDep_bb1_in(X₀, X₁, X₂, 1+X₃) :|: 1+X₃ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
t₁₅: eval_speedSimpleMultipleDep_bb2_in(X₀, X₁, X₂, X₃) → eval_speedSimpleMultipleDep_bb1_in(X₀, X₁, 1+X₂, 0) :|: X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
t₁₆: eval_speedSimpleMultipleDep_bb3_in(X₀, X₁, X₂, X₃) → eval_speedSimpleMultipleDep_stop(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
t₀: eval_speedSimpleMultipleDep_start(X₀, X₁, X₂, X₃) → eval_speedSimpleMultipleDep_bb0_in(X₀, X₁, X₂, X₃)

MPRF for transition t₁₅: eval_speedSimpleMultipleDep_bb2_in(X₀, X₁, X₂, X₃) → eval_speedSimpleMultipleDep_bb1_in(X₀, X₁, 1+X₂, 0) :|: X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃ of depth 1:

new bound:

X₁ {O(n)}

MPRF:

• eval_speedSimpleMultipleDep_bb1_in: [X₁-X₂]
• eval_speedSimpleMultipleDep_bb2_in: [X₁-X₂]

MPRF for transition t₁₂: eval_speedSimpleMultipleDep_bb2_in(X₀, X₁, X₂, X₃) → eval_speedSimpleMultipleDep_bb1_in(X₀, X₁, X₂, 1+X₃) :|: 1+X₃ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃ of depth 1:

new bound:

X₀⋅X₁+X₀ {O(n^2)}

MPRF:

• eval_speedSimpleMultipleDep_bb1_in: [X₀-X₃]
• eval_speedSimpleMultipleDep_bb2_in: [X₀-X₃]

TWN: t₁₂: eval_speedSimpleMultipleDep_bb2_in→eval_speedSimpleMultipleDep_bb1_in

cycle: [t₁₂: eval_speedSimpleMultipleDep_bb2_in→eval_speedSimpleMultipleDep_bb1_in; t₁₀: eval_speedSimpleMultipleDep_bb1_in→eval_speedSimpleMultipleDep_bb2_in]
original loop: (1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃,(X₀,X₁,X₂,X₃) -> (X₀,X₁,X₂,1+X₃))
transformed loop: (1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃,(X₀,X₁,X₂,X₃) -> (X₀,X₁,X₂,1+X₃))
loop: (1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃,(X₀,X₁,X₂,X₃) -> (X₀,X₁,X₂,1+X₃))
order: [X₃; X₂; X₁; X₀]
closed-form:

X₃: X₃ + [[n != 0]]⋅n^1
X₂: X₂
X₁: X₁
X₀: X₀

Termination: true
Formula:

0 ≤ 1 ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ 0 ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₁+X₃ ∧ 2+X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ 1 ≤ 0 ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃

Stabilization-Threshold for: 1+X₃ ≤ X₀

alphas_abs: X₀+X₃
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₃+2 {O(n)}

original loop: (1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃,(X₀,X₁,X₂,X₃) -> (X₀,X₁,X₂,1+X₃))
transformed loop: (1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃,(X₀,X₁,X₂,X₃) -> (X₀,X₁,X₂,1+X₃))
loop: (1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃,(X₀,X₁,X₂,X₃) -> (X₀,X₁,X₂,1+X₃))
order: [X₃; X₂; X₁; X₀]
closed-form:

X₃: X₃ + [[n != 0]]⋅n^1
X₂: X₂
X₁: X₁
X₀: X₀

Termination: true
Formula:

Stabilization-Threshold for: 1+X₃ ≤ X₀

alphas_abs: X₀+X₃
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₃+2 {O(n)}

TWN - Lifting for [10: eval_speedSimpleMultipleDep_bb1_in->eval_speedSimpleMultipleDep_bb2_in; 12: eval_speedSimpleMultipleDep_bb2_in->eval_speedSimpleMultipleDep_bb1_in] of 2⋅X₀+2⋅X₃+4 {O(n)}

relevant size-bounds w.r.t. t₉: eval_speedSimpleMultipleDep_7→eval_speedSimpleMultipleDep_bb1_in:
X₀: X₀ {O(n)}
X₃: 0 {O(1)}
Runtime-bound of t₉: 1 {O(1)}
Results in: 2⋅X₀+4 {O(n)}

TWN - Lifting for [10: eval_speedSimpleMultipleDep_bb1_in->eval_speedSimpleMultipleDep_bb2_in; 12: eval_speedSimpleMultipleDep_bb2_in->eval_speedSimpleMultipleDep_bb1_in] of 2⋅X₀+2⋅X₃+4 {O(n)}

relevant size-bounds w.r.t. t₁₅: eval_speedSimpleMultipleDep_bb2_in→eval_speedSimpleMultipleDep_bb1_in:
X₀: X₀ {O(n)}
X₃: 0 {O(1)}
Runtime-bound of t₁₅: X₁ {O(n)}
Results in: 2⋅X₀⋅X₁+4⋅X₁ {O(n^2)}

Found invariant X₃ ≤ 0 ∧ 2+X₃ ≤ X₂ ∧ 3+X₃ ≤ X₁ ∧ X₀+X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 3 ≤ X₁+X₃ ∧ X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 2+X₀ ≤ X₂ ∧ 3 ≤ X₁ ∧ 3+X₀ ≤ X₁ ∧ X₀ ≤ 0 for location eval_speedSimpleMultipleDep_bb2_in_v6

Found invariant X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location eval_speedSimpleMultipleDep_bb2_in_v1

Found invariant X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location eval_speedSimpleMultipleDep_bb1_in_v3

Found invariant X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ X₂+X₃ ≤ 1 ∧ 1+X₃ ≤ X₁ ∧ X₀+X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ X₀+X₂ ≤ 1 ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 for location eval_speedSimpleMultipleDep_bb1_in_v1

Found invariant X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location eval_speedSimpleMultipleDep_bb1_in_v2

Found invariant X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ X₂+X₃ ≤ 1 ∧ 2+X₃ ≤ X₁ ∧ X₀+X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1 ∧ 1+X₂ ≤ X₁ ∧ X₀+X₂ ≤ 1 ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2+X₀ ≤ X₁ ∧ X₀ ≤ 0 for location eval_speedSimpleMultipleDep_bb2_in_v5

Found invariant X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₂ for location eval_speedSimpleMultipleDep_stop

Found invariant X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location eval_speedSimpleMultipleDep_bb2_in_v4

Found invariant X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₂ for location eval_speedSimpleMultipleDep_bb3_in

Found invariant X₃ ≤ 0 ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ X₀+X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 2+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2+X₀ ≤ X₁ ∧ X₀ ≤ 0 for location eval_speedSimpleMultipleDep_bb1_in_v5

Found invariant X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ for location eval_speedSimpleMultipleDep_bb1_in

Found invariant X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location eval_speedSimpleMultipleDep_bb2_in_v3

Found invariant X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location eval_speedSimpleMultipleDep_bb1_in_v4

Cut unsatisfiable transition [t₉₅: eval_speedSimpleMultipleDep_bb2_in_v5→eval_speedSimpleMultipleDep_bb1_in_v4]

All Bounds

Timebounds

Overall timebound:3⋅X₀⋅X₁+3⋅X₀+5⋅X₁+16 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₉: 1 {O(1)}
t₁₀: 2⋅X₀⋅X₁+2⋅X₀+4⋅X₁+4 {O(n^2)}
t₁₁: 1 {O(1)}
t₁₂: X₀⋅X₁+X₀ {O(n^2)}
t₁₅: X₁ {O(n)}
t₁₆: 1 {O(1)}

Costbounds

Overall costbound: 3⋅X₀⋅X₁+3⋅X₀+5⋅X₁+16 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₉: 1 {O(1)}
t₁₀: 2⋅X₀⋅X₁+2⋅X₀+4⋅X₁+4 {O(n^2)}
t₁₁: 1 {O(1)}
t₁₂: X₀⋅X₁+X₀ {O(n^2)}
t₁₅: X₁ {O(n)}
t₁₆: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₁ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₃ {O(n)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₅, X₀: X₀ {O(n)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₃ {O(n)}
t₆, X₀: X₀ {O(n)}
t₆, X₁: X₁ {O(n)}
t₆, X₂: X₂ {O(n)}
t₆, X₃: X₃ {O(n)}
t₇, X₀: X₀ {O(n)}
t₇, X₁: X₁ {O(n)}
t₇, X₂: X₂ {O(n)}
t₇, X₃: X₃ {O(n)}
t₈, X₀: X₀ {O(n)}
t₈, X₁: X₁ {O(n)}
t₈, X₂: X₂ {O(n)}
t₈, X₃: X₃ {O(n)}
t₉, X₀: X₀ {O(n)}
t₉, X₁: X₁ {O(n)}
t₉, X₂: 0 {O(1)}
t₉, X₃: 0 {O(1)}
t₁₀, X₀: X₀ {O(n)}
t₁₀, X₁: X₁ {O(n)}
t₁₀, X₂: X₁ {O(n)}
t₁₀, X₃: X₀⋅X₁+X₀ {O(n^2)}
t₁₁, X₀: 2⋅X₀ {O(n)}
t₁₁, X₁: 2⋅X₁ {O(n)}
t₁₁, X₂: X₁ {O(n)}
t₁₁, X₃: 0 {O(1)}
t₁₂, X₀: X₀ {O(n)}
t₁₂, X₁: X₁ {O(n)}
t₁₂, X₂: X₁ {O(n)}
t₁₂, X₃: X₀⋅X₁+X₀ {O(n^2)}
t₁₅, X₀: X₀ {O(n)}
t₁₅, X₁: X₁ {O(n)}
t₁₅, X₂: X₁ {O(n)}
t₁₅, X₃: 0 {O(1)}
t₁₆, X₀: 2⋅X₀ {O(n)}
t₁₆, X₁: 2⋅X₁ {O(n)}
t₁₆, X₂: X₁ {O(n)}
t₁₆, X₃: 0 {O(1)}