Initial Problem

Start: eval_ax_start
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: eval_ax_bb0_in, eval_ax_bb1_in, eval_ax_bb2_in, eval_ax_bb3_in, eval_ax_bb4_in, eval_ax_bb5_in, eval_ax_start, eval_ax_stop
Transitions:
t₁: eval_ax_bb0_in(X₀, X₁, X₂, X₃, X₄) → eval_ax_bb1_in(0, X₁, X₂, X₃, X₄)
t₂: eval_ax_bb1_in(X₀, X₁, X₂, X₃, X₄) → eval_ax_bb2_in(X₀, 0, X₂, X₃, X₄)
t₃: eval_ax_bb2_in(X₀, X₁, X₂, X₃, X₄) → eval_ax_bb3_in(X₀, X₁, X₂, X₃, X₄) :|: 2+X₁ ≤ X₄
t₄: eval_ax_bb2_in(X₀, X₁, X₂, X₃, X₄) → eval_ax_bb4_in(X₀, X₁, X₂, X₃, X₄) :|: X₄ ≤ 1+X₁
t₅: eval_ax_bb3_in(X₀, X₁, X₂, X₃, X₄) → eval_ax_bb2_in(X₀, 1+X₁, X₂, X₃, X₄)
t₆: eval_ax_bb4_in(X₀, X₁, X₂, X₃, X₄) → eval_ax_bb1_in(1+X₀, X₁, X₂, X₃, X₄) :|: X₄ ≤ 1+X₁ ∧ 3+X₀ ≤ X₄
t₇: eval_ax_bb4_in(X₀, X₁, X₂, X₃, X₄) → eval_ax_bb5_in(X₀, X₁, X₂, X₃, X₄) :|: 2+X₁ ≤ X₄
t₈: eval_ax_bb4_in(X₀, X₁, X₂, X₃, X₄) → eval_ax_bb5_in(X₀, X₁, X₂, X₃, X₄) :|: X₄ ≤ 2+X₀
t₉: eval_ax_bb5_in(X₀, X₁, X₂, X₃, X₄) → eval_ax_stop(X₀, X₁, X₂, X₃, X₄)
t₀: eval_ax_start(X₀, X₁, X₂, X₃, X₄) → eval_ax_bb0_in(X₀, X₁, X₂, X₃, X₄)

Preprocessing

Cut unsatisfiable transition [t₇: eval_ax_bb4_in→eval_ax_bb5_in]

Eliminate variables [X₂; X₃] that do not contribute to the problem

Found invariant X₂ ≤ 1+X₁ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location eval_ax_bb4_in

Found invariant 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location eval_ax_bb2_in

Found invariant 2 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location eval_ax_bb3_in

Found invariant X₂ ≤ 1+X₁ ∧ X₂ ≤ 2+X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location eval_ax_bb5_in

Found invariant 0 ≤ X₀ for location eval_ax_bb1_in

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

Problem after Preprocessing

Start: eval_ax_start
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: eval_ax_bb0_in, eval_ax_bb1_in, eval_ax_bb2_in, eval_ax_bb3_in, eval_ax_bb4_in, eval_ax_bb5_in, eval_ax_start, eval_ax_stop
Transitions:
t₁₉: eval_ax_bb0_in(X₀, X₁, X₂) → eval_ax_bb1_in(0, X₁, X₂)
t₂₀: eval_ax_bb1_in(X₀, X₁, X₂) → eval_ax_bb2_in(X₀, 0, X₂) :|: 0 ≤ X₀
t₂₁: eval_ax_bb2_in(X₀, X₁, X₂) → eval_ax_bb3_in(X₀, X₁, X₂) :|: 2+X₁ ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁
t₂₂: eval_ax_bb2_in(X₀, X₁, X₂) → eval_ax_bb4_in(X₀, X₁, X₂) :|: X₂ ≤ 1+X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁
t₂₃: eval_ax_bb3_in(X₀, X₁, X₂) → eval_ax_bb2_in(X₀, 1+X₁, X₂) :|: 2 ≤ X₀+X₂ ∧ 2 ≤ X₁+X₂ ∧ 2+X₁ ≤ X₂ ∧ 2 ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁
t₂₄: eval_ax_bb4_in(X₀, X₁, X₂) → eval_ax_bb1_in(1+X₀, X₁, X₂) :|: X₂ ≤ 1+X₁ ∧ 3+X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁
t₂₅: eval_ax_bb4_in(X₀, X₁, X₂) → eval_ax_bb5_in(X₀, X₁, X₂) :|: X₂ ≤ 2+X₀ ∧ X₂ ≤ 1+X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁
t₂₆: eval_ax_bb5_in(X₀, X₁, X₂) → eval_ax_stop(X₀, X₁, X₂) :|: X₂ ≤ 2+X₀ ∧ X₂ ≤ 1+X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁
t₂₇: eval_ax_start(X₀, X₁, X₂) → eval_ax_bb0_in(X₀, X₁, X₂)

MPRF for transition t₂₄: eval_ax_bb4_in(X₀, X₁, X₂) → eval_ax_bb1_in(1+X₀, X₁, X₂) :|: X₂ ≤ 1+X₁ ∧ 3+X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁ of depth 1:

new bound:

X₂+2 {O(n)}

• eval_ax_bb1_in: [X₂-2-X₀]
• eval_ax_bb2_in: [X₂-2-X₀]
• eval_ax_bb3_in: [X₂-2-X₀]
• eval_ax_bb4_in: [X₂-2-X₀]

knowledge_propagation leads to new time bound X₂+3 {O(n)} for transition t₂₀: eval_ax_bb1_in(X₀, X₁, X₂) → eval_ax_bb2_in(X₀, 0, X₂) :|: 0 ≤ X₀

MPRF for transition t₂₁: eval_ax_bb2_in(X₀, X₁, X₂) → eval_ax_bb3_in(X₀, X₁, X₂) :|: 2+X₁ ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁ of depth 1:

new bound:

X₂⋅X₂+3⋅X₂ {O(n^2)}

• eval_ax_bb1_in: [X₂]
• eval_ax_bb2_in: [X₂-1-X₁]
• eval_ax_bb3_in: [X₂-2-X₁]
• eval_ax_bb4_in: [X₂-1-X₁]

MPRF for transition t₂₂: eval_ax_bb2_in(X₀, X₁, X₂) → eval_ax_bb4_in(X₀, X₁, X₂) :|: X₂ ≤ 1+X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁ of depth 1:

new bound:

X₂+3 {O(n)}

• eval_ax_bb1_in: [1]
• eval_ax_bb2_in: [1]
• eval_ax_bb3_in: [1]
• eval_ax_bb4_in: [0]

MPRF for transition t₂₃: eval_ax_bb3_in(X₀, X₁, X₂) → eval_ax_bb2_in(X₀, 1+X₁, X₂) :|: 2 ≤ X₀+X₂ ∧ 2 ≤ X₁+X₂ ∧ 2+X₁ ≤ X₂ ∧ 2 ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁ of depth 1:

new bound:

X₂⋅X₂+3⋅X₂ {O(n^2)}

• eval_ax_bb1_in: [X₂]
• eval_ax_bb2_in: [X₂-1-X₁]
• eval_ax_bb3_in: [X₂-1-X₁]
• eval_ax_bb4_in: [X₂-1-X₁]

Found invariant X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location eval_ax_bb2_in

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

Found invariant 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location eval_ax_bb2_in_v1

Found invariant X₂ ≤ 1+X₁ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location eval_ax_bb4_in

Found invariant X₂ ≤ 1+X₁ ∧ X₂ ≤ 2+X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location eval_ax_bb5_in

Found invariant 0 ≤ X₀ for location eval_ax_bb1_in

Found invariant 2 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location eval_ax_bb3_in_v1

Found invariant 3 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 2+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location eval_ax_bb3_in_v2

All Bounds

Timebounds

Overall timebound:2⋅X₂⋅X₂+9⋅X₂+12 {O(n^2)}
t₁₉: 1 {O(1)}
t₂₀: X₂+3 {O(n)}
t₂₁: X₂⋅X₂+3⋅X₂ {O(n^2)}
t₂₂: X₂+3 {O(n)}
t₂₃: X₂⋅X₂+3⋅X₂ {O(n^2)}
t₂₄: X₂+2 {O(n)}
t₂₅: 1 {O(1)}
t₂₆: 1 {O(1)}
t₂₇: 1 {O(1)}

Costbounds

Overall costbound: 2⋅X₂⋅X₂+9⋅X₂+12 {O(n^2)}
t₁₉: 1 {O(1)}
t₂₀: X₂+3 {O(n)}
t₂₁: X₂⋅X₂+3⋅X₂ {O(n^2)}
t₂₂: X₂+3 {O(n)}
t₂₃: X₂⋅X₂+3⋅X₂ {O(n^2)}
t₂₄: X₂+2 {O(n)}
t₂₅: 1 {O(1)}
t₂₆: 1 {O(1)}
t₂₇: 1 {O(1)}

Sizebounds

t₁₉, X₀: 0 {O(1)}
t₁₉, X₁: X₁ {O(n)}
t₁₉, X₂: X₂ {O(n)}
t₂₀, X₀: X₂+2 {O(n)}
t₂₀, X₁: 0 {O(1)}
t₂₀, X₂: X₂ {O(n)}
t₂₁, X₀: X₂+2 {O(n)}
t₂₁, X₁: X₂+1 {O(n)}
t₂₁, X₂: X₂ {O(n)}
t₂₂, X₀: X₂+2 {O(n)}
t₂₂, X₁: X₂+1 {O(n)}
t₂₂, X₂: X₂ {O(n)}
t₂₃, X₀: X₂+2 {O(n)}
t₂₃, X₁: X₂+1 {O(n)}
t₂₃, X₂: X₂ {O(n)}
t₂₄, X₀: X₂+2 {O(n)}
t₂₄, X₁: X₂+1 {O(n)}
t₂₄, X₂: X₂ {O(n)}
t₂₅, X₀: X₂+2 {O(n)}
t₂₅, X₁: X₂+1 {O(n)}
t₂₅, X₂: X₂ {O(n)}
t₂₆, X₀: X₂+2 {O(n)}
t₂₆, X₁: X₂+1 {O(n)}
t₂₆, X₂: X₂ {O(n)}
t₂₇, X₀: X₀ {O(n)}
t₂₇, X₁: X₁ {O(n)}
t₂₇, X₂: X₂ {O(n)}