KoAT2 Proof Output

Initial Problem

Preprocessing

Found invariant X₄ ≤ X₃ ∧ 1+X₄ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 0 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location eval_speedSingleSingle2_bb3_in

Found invariant X₄ ≤ X₃ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₁+X₄ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ for location eval_speedSingleSingle2_1

Found invariant X₄ ≤ X₃ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 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 eval_speedSingleSingle2_bb2_in

Found invariant X₄ ≤ X₃ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 0 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 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 eval_speedSingleSingle2_bb4_in

Found invariant X₄ ≤ X₃ ∧ 1+X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location eval_speedSingleSingle2_bb5_in

Found invariant X₄ ≤ X₃ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₁+X₄ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ for location eval_speedSingleSingle2_bb1_in

Found invariant X₄ ≤ X₃ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₁+X₄ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ for location eval_speedSingleSingle2_0

Problem after Preprocessing

Start: eval_speedSingleSingle2_start
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars: nondef.0
Locations: eval_speedSingleSingle2_0, eval_speedSingleSingle2_1, eval_speedSingleSingle2_bb0_in, eval_speedSingleSingle2_bb1_in, eval_speedSingleSingle2_bb2_in, eval_speedSingleSingle2_bb3_in, eval_speedSingleSingle2_bb4_in, eval_speedSingleSingle2_bb5_in, eval_speedSingleSingle2_bb6_in, eval_speedSingleSingle2_start, eval_speedSingleSingle2_stop
Transitions:
t₆: eval_speedSingleSingle2_0(X₀, X₁, X₂, X₃, X₄) → eval_speedSingleSingle2_1(nondef.0, X₁, X₂, X₃, X₄) :|: 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₁+X₄ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ X₄ ≤ X₃ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₄
t₇: eval_speedSingleSingle2_1(X₀, X₁, X₂, X₃, X₄) → eval_speedSingleSingle2_bb2_in(X₀, X₁, X₂, X₃, X₄) :|: 1 ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₁+X₄ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ X₄ ≤ X₃ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₄
t₈: eval_speedSingleSingle2_1(X₀, X₁, X₂, X₃, X₄) → eval_speedSingleSingle2_bb6_in(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ 0 ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₁+X₄ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ X₄ ≤ X₃ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₄
t₃: eval_speedSingleSingle2_bb0_in(X₀, X₁, X₂, X₃, X₄) → eval_speedSingleSingle2_bb1_in(X₀, X₁, X₂, 0, 0) :|: 0 ≤ X₁ ∧ 0 ≤ X₂
t₁: eval_speedSingleSingle2_bb0_in(X₀, X₁, X₂, X₃, X₄) → eval_speedSingleSingle2_bb6_in(X₀, X₁, X₂, X₃, X₄) :|: 1+X₂ ≤ 0
t₂: eval_speedSingleSingle2_bb0_in(X₀, X₁, X₂, X₃, X₄) → eval_speedSingleSingle2_bb6_in(X₀, X₁, X₂, X₃, X₄) :|: 1+X₁ ≤ 0
t₄: eval_speedSingleSingle2_bb1_in(X₀, X₁, X₂, X₃, X₄) → eval_speedSingleSingle2_0(X₀, X₁, X₂, X₃, X₄) :|: 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₁+X₄ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ X₄ ≤ X₃ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₄
t₉: eval_speedSingleSingle2_bb2_in(X₀, X₁, X₂, X₃, X₄) → eval_speedSingleSingle2_bb3_in(X₀, X₁, X₂, X₃, X₄) :|: 1+X₃ ≤ X₂ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀+X₄ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₁+X₄ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ X₄ ≤ X₃ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₄
t₁₀: eval_speedSingleSingle2_bb2_in(X₀, X₁, X₂, X₃, X₄) → eval_speedSingleSingle2_bb4_in(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀+X₄ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₁+X₄ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ X₄ ≤ X₃ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₄
t₁₁: eval_speedSingleSingle2_bb3_in(X₀, X₁, X₂, X₃, X₄) → eval_speedSingleSingle2_bb1_in(X₀, X₁, X₂, 1+X₃, 1+X₄) :|: 1 ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂+X₃ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₂+X₄ ∧ 1+X₄ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₁+X₄ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ X₄ ≤ X₃ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₄
t₁₂: eval_speedSingleSingle2_bb4_in(X₀, X₁, X₂, X₃, X₄) → eval_speedSingleSingle2_bb5_in(X₀, X₁, X₂, X₃, X₄) :|: 1+X₄ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀+X₄ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₁+X₄ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂+X₄ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₄ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ X₄ ≤ X₃ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₄
t₁₃: eval_speedSingleSingle2_bb4_in(X₀, X₁, X₂, X₃, X₄) → eval_speedSingleSingle2_bb6_in(X₀, X₁, X₂, X₃, X₄) :|: X₁ ≤ X₄ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀+X₄ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₁+X₄ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂+X₄ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₄ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ X₄ ≤ X₃ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₄
t₁₄: eval_speedSingleSingle2_bb5_in(X₀, X₁, X₂, X₃, X₄) → eval_speedSingleSingle2_bb1_in(X₀, X₁, X₂, 1+X₃, 1+X₄) :|: 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₁+X₃ ∧ 1+X₃ ≤ X₁ ∧ 1 ≤ X₁+X₄ ∧ 1+X₄ ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂+X₄ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₄ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ X₄ ≤ X₃ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₄
t₁₅: eval_speedSingleSingle2_bb6_in(X₀, X₁, X₂, X₃, X₄) → eval_speedSingleSingle2_stop(X₀, X₁, X₂, X₃, X₄)
t₀: eval_speedSingleSingle2_start(X₀, X₁, X₂, X₃, X₄) → eval_speedSingleSingle2_bb0_in(X₀, X₁, X₂, X₃, X₄)

MPRF for transition t₉: eval_speedSingleSingle2_bb2_in(X₀, X₁, X₂, X₃, X₄) → eval_speedSingleSingle2_bb3_in(X₀, X₁, X₂, X₃, X₄) :|: 1+X₃ ≤ X₂ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀+X₄ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₁+X₄ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ X₄ ≤ X₃ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₄ of depth 1:

new bound:

X₂ {O(n)}

MPRF:

• eval_speedSingleSingle2_0: [X₂-X₃]
• eval_speedSingleSingle2_1: [X₂-X₃]
• eval_speedSingleSingle2_bb1_in: [X₂-X₃]
• eval_speedSingleSingle2_bb2_in: [X₂-X₃]
• eval_speedSingleSingle2_bb3_in: [X₂-1-X₄]
• eval_speedSingleSingle2_bb4_in: [X₂-X₃]
• eval_speedSingleSingle2_bb5_in: [X₂-X₃]

MPRF for transition t₁₁: eval_speedSingleSingle2_bb3_in(X₀, X₁, X₂, X₃, X₄) → eval_speedSingleSingle2_bb1_in(X₀, X₁, X₂, 1+X₃, 1+X₄) :|: 1 ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂+X₃ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₂+X₄ ∧ 1+X₄ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₁+X₄ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ X₄ ≤ X₃ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₄ of depth 1:

new bound:

X₂ {O(n)}

MPRF:

• eval_speedSingleSingle2_0: [X₂-X₃]
• eval_speedSingleSingle2_1: [X₂-X₃]
• eval_speedSingleSingle2_bb1_in: [X₂-X₃]
• eval_speedSingleSingle2_bb2_in: [X₂-X₃]
• eval_speedSingleSingle2_bb3_in: [X₂-X₃]
• eval_speedSingleSingle2_bb4_in: [X₂-X₃]
• eval_speedSingleSingle2_bb5_in: [X₂-X₃]

MPRF for transition t₁₂: eval_speedSingleSingle2_bb4_in(X₀, X₁, X₂, X₃, X₄) → eval_speedSingleSingle2_bb5_in(X₀, X₁, X₂, X₃, X₄) :|: 1+X₄ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀+X₄ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₁+X₄ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂+X₄ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₄ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ X₄ ≤ X₃ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₄ of depth 1:

new bound:

X₁+1 {O(n)}

MPRF:

• eval_speedSingleSingle2_0: [1+X₁-X₄]
• eval_speedSingleSingle2_1: [1+X₁-X₄]
• eval_speedSingleSingle2_bb1_in: [1+X₁-X₃]
• eval_speedSingleSingle2_bb2_in: [1+X₁-X₃]
• eval_speedSingleSingle2_bb3_in: [1+X₁-X₄]
• eval_speedSingleSingle2_bb4_in: [1+X₁-X₄]
• eval_speedSingleSingle2_bb5_in: [X₁-X₃]

MPRF for transition t₁₄: eval_speedSingleSingle2_bb5_in(X₀, X₁, X₂, X₃, X₄) → eval_speedSingleSingle2_bb1_in(X₀, X₁, X₂, 1+X₃, 1+X₄) :|: 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₁+X₃ ∧ 1+X₃ ≤ X₁ ∧ 1 ≤ X₁+X₄ ∧ 1+X₄ ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂+X₄ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₄ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ X₄ ≤ X₃ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₄ of depth 1:

new bound:

X₁ {O(n)}

MPRF:

• eval_speedSingleSingle2_0: [X₁-X₄]
• eval_speedSingleSingle2_1: [X₁-X₃]
• eval_speedSingleSingle2_bb1_in: [X₁-X₃]
• eval_speedSingleSingle2_bb2_in: [X₁-X₄]
• eval_speedSingleSingle2_bb3_in: [X₁-X₄]
• eval_speedSingleSingle2_bb4_in: [X₁-X₃]
• eval_speedSingleSingle2_bb5_in: [X₁-X₃]

knowledge_propagation leads to new time bound X₁+X₂+1 {O(n)} for transition t₄: eval_speedSingleSingle2_bb1_in(X₀, X₁, X₂, X₃, X₄) → eval_speedSingleSingle2_0(X₀, X₁, X₂, X₃, X₄) :|: 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₁+X₄ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ X₄ ≤ X₃ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₄

knowledge_propagation leads to new time bound X₁+X₂+1 {O(n)} for transition t₆: eval_speedSingleSingle2_0(X₀, X₁, X₂, X₃, X₄) → eval_speedSingleSingle2_1(nondef.0, X₁, X₂, X₃, X₄) :|: 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₁+X₄ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ X₄ ≤ X₃ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₄

knowledge_propagation leads to new time bound X₁+X₂+1 {O(n)} for transition t₇: eval_speedSingleSingle2_1(X₀, X₁, X₂, X₃, X₄) → eval_speedSingleSingle2_bb2_in(X₀, X₁, X₂, X₃, X₄) :|: 1 ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₁+X₄ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ X₄ ≤ X₃ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₄

knowledge_propagation leads to new time bound X₁+X₂+1 {O(n)} for transition t₁₀: eval_speedSingleSingle2_bb2_in(X₀, X₁, X₂, X₃, X₄) → eval_speedSingleSingle2_bb4_in(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀+X₄ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₁+X₄ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ X₄ ≤ X₃ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₄

All Bounds

Timebounds

Overall timebound:6⋅X₁+6⋅X₂+12 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: X₁+X₂+1 {O(n)}
t₆: X₁+X₂+1 {O(n)}
t₇: X₁+X₂+1 {O(n)}
t₈: 1 {O(1)}
t₉: X₂ {O(n)}
t₁₀: X₁+X₂+1 {O(n)}
t₁₁: X₂ {O(n)}
t₁₂: X₁+1 {O(n)}
t₁₃: 1 {O(1)}
t₁₄: X₁ {O(n)}
t₁₅: 1 {O(1)}

Costbounds

Overall costbound: 6⋅X₁+6⋅X₂+12 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: X₁+X₂+1 {O(n)}
t₆: X₁+X₂+1 {O(n)}
t₇: X₁+X₂+1 {O(n)}
t₈: 1 {O(1)}
t₉: X₂ {O(n)}
t₁₀: X₁+X₂+1 {O(n)}
t₁₁: X₂ {O(n)}
t₁₂: X₁+1 {O(n)}
t₁₃: 1 {O(1)}
t₁₄: X₁ {O(n)}
t₁₅: 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)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {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)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₁ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: 0 {O(1)}
t₃, X₄: 0 {O(1)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₁+X₂ {O(n)}
t₄, X₄: X₁+X₂ {O(n)}
t₆, X₁: X₁ {O(n)}
t₆, X₂: X₂ {O(n)}
t₆, X₃: X₁+X₂ {O(n)}
t₆, X₄: X₁+X₂ {O(n)}
t₇, X₁: X₁ {O(n)}
t₇, X₂: X₂ {O(n)}
t₇, X₃: X₁+X₂ {O(n)}
t₇, X₄: X₁+X₂ {O(n)}
t₈, X₁: X₁ {O(n)}
t₈, X₂: X₂ {O(n)}
t₈, X₃: X₁+X₂ {O(n)}
t₈, X₄: X₁+X₂ {O(n)}
t₉, X₁: X₁ {O(n)}
t₉, X₂: X₂ {O(n)}
t₉, X₃: X₁+X₂ {O(n)}
t₉, X₄: X₁+X₂ {O(n)}
t₁₀, X₁: X₁ {O(n)}
t₁₀, X₂: X₂ {O(n)}
t₁₀, X₃: X₁+X₂ {O(n)}
t₁₀, X₄: X₁+X₂ {O(n)}
t₁₁, X₁: X₁ {O(n)}
t₁₁, X₂: X₂ {O(n)}
t₁₁, X₃: X₁+X₂ {O(n)}
t₁₁, X₄: X₁+X₂ {O(n)}
t₁₂, X₁: X₁ {O(n)}
t₁₂, X₂: X₂ {O(n)}
t₁₂, X₃: X₁+X₂ {O(n)}
t₁₂, X₄: X₁+X₂ {O(n)}
t₁₃, X₁: X₁ {O(n)}
t₁₃, X₂: X₂ {O(n)}
t₁₃, X₃: X₁+X₂ {O(n)}
t₁₃, X₄: X₁+X₂ {O(n)}
t₁₄, X₁: X₁ {O(n)}
t₁₄, X₂: X₂ {O(n)}
t₁₄, X₃: X₁+X₂ {O(n)}
t₁₄, X₄: X₁+X₂ {O(n)}
t₁₅, X₁: 4⋅X₁ {O(n)}
t₁₅, X₂: 4⋅X₂ {O(n)}
t₁₅, X₃: 2⋅X₁+2⋅X₂+2⋅X₃ {O(n)}
t₁₅, X₄: 2⋅X₁+2⋅X₂+2⋅X₄ {O(n)}