Initial Problem

Start: f300
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃
Temp_Vars: O, P, Q, R
Locations: f11, f13, f16, f300
Transitions:
t₀: f11(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → f11(X₀, P, X₁, O, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) :|: 1 ≤ X₁ ∧ 0 ≤ X₀
t₁: f11(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → f11(X₀, P, X₁, O, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) :|: 1+X₁ ≤ 0 ∧ 0 ≤ X₀
t₃: f11(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → f13(X₀, 0, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, O, X₁₁, X₁₂, X₁₃) :|: 0 ≤ X₀ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
t₄: f16(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → f11(X₀, R, P, Q, X₄, X₅, X₆, X₇, X₈, X₉, O, X₉, X₉, X₁₃) :|: X₅ ≤ 1+X₆ ∧ 1 ≤ P ∧ 0 ≤ X₄
t₅: f16(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → f11(X₀, R, P, Q, X₄, X₅, X₆, X₇, X₈, X₉, O, X₉, X₉, X₁₃) :|: X₅ ≤ 1+X₆ ∧ 1+P ≤ 0 ∧ 0 ≤ X₄
t₂: f16(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → f16(X₀, X₁, X₂, X₃, X₄, X₅, 1+X₆, O, O, O, X₁₀, X₁₁, X₁₂, X₁₃) :|: 2+X₆ ≤ X₅ ∧ 0 ≤ X₄
t₇: f300(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → f13(X₀, 0, X₂, X₃, X₄, X₅, 0, X₇, X₈, 0, O, 0, 0, P) :|: X₅ ≤ 1
t₆: f300(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → f16(X₀, X₁, X₂, X₃, X₄, X₅, 1, O, O, O, X₁₀, X₁₁, X₁₂, P) :|: 2 ≤ X₅

Preprocessing

Eliminate variables [O; Q; X₂; X₃; X₇; X₈; X₉; X₁₀; X₁₁; X₁₂; X₁₃] that do not contribute to the problem

Found invariant 0 ≤ X₄ ∧ X₃ ≤ 1+X₄ ∧ 0 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ for location f13

Found invariant 1+X₄ ≤ X₃ ∧ 1 ≤ X₄ ∧ 3 ≤ X₃+X₄ ∧ X₃ ≤ 1+X₄ ∧ 1 ≤ X₂+X₄ ∧ 2 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 0 ≤ X₂ for location f11

Found invariant 1+X₄ ≤ X₃ ∧ 1 ≤ X₄ ∧ 3 ≤ X₃+X₄ ∧ 2 ≤ X₃ for location f16

Problem after Preprocessing

Start: f300
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars: P, R
Locations: f11, f13, f16, f300
Transitions:
t₁₄: f11(X₀, X₁, X₂, X₃, X₄) → f11(X₀, P, X₂, X₃, X₄) :|: 1 ≤ X₁ ∧ 0 ≤ X₀ ∧ X₃ ≤ 1+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₄ ≤ X₃ ∧ 1 ≤ X₄ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₃+X₄ ∧ 0 ≤ X₂
t₁₅: f11(X₀, X₁, X₂, X₃, X₄) → f11(X₀, P, X₂, X₃, X₄) :|: 1+X₁ ≤ 0 ∧ 0 ≤ X₀ ∧ X₃ ≤ 1+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₄ ≤ X₃ ∧ 1 ≤ X₄ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₃+X₄ ∧ 0 ≤ X₂
t₁₆: f11(X₀, X₁, X₂, X₃, X₄) → f13(X₀, 0, X₂, X₃, X₄) :|: 0 ≤ X₀ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ X₃ ≤ 1+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₄ ≤ X₃ ∧ 1 ≤ X₄ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₃+X₄ ∧ 0 ≤ X₂
t₁₇: f16(X₀, X₁, X₂, X₃, X₄) → f11(X₀, R, X₂, X₃, X₄) :|: X₃ ≤ 1+X₄ ∧ 1 ≤ P ∧ 0 ≤ X₂ ∧ 1+X₄ ≤ X₃ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₃+X₄
t₁₈: f16(X₀, X₁, X₂, X₃, X₄) → f11(X₀, R, X₂, X₃, X₄) :|: X₃ ≤ 1+X₄ ∧ 1+P ≤ 0 ∧ 0 ≤ X₂ ∧ 1+X₄ ≤ X₃ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₃+X₄
t₁₉: f16(X₀, X₁, X₂, X₃, X₄) → f16(X₀, X₁, X₂, X₃, 1+X₄) :|: 2+X₄ ≤ X₃ ∧ 0 ≤ X₂ ∧ 1+X₄ ≤ X₃ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₃+X₄
t₂₀: f300(X₀, X₁, X₂, X₃, X₄) → f13(X₀, 0, X₂, X₃, 0) :|: X₃ ≤ 1
t₂₁: f300(X₀, X₁, X₂, X₃, X₄) → f16(X₀, X₁, X₂, X₃, 1) :|: 2 ≤ X₃

MPRF for transition t₁₉: f16(X₀, X₁, X₂, X₃, X₄) → f16(X₀, X₁, X₂, X₃, 1+X₄) :|: 2+X₄ ≤ X₃ ∧ 0 ≤ X₂ ∧ 1+X₄ ≤ X₃ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₃+X₄ of depth 1:

new bound:

X₃+1 {O(n)}

MPRF:

• f16: [X₃-X₄]

Found invariant 1+X₄ ≤ X₃ ∧ 1 ≤ X₄ ∧ 3 ≤ X₃+X₄ ∧ X₃ ≤ 1+X₄ ∧ 1 ≤ X₂+X₄ ∧ 2 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 0 ≤ X₂ for location f11

Found invariant 1+X₄ ≤ X₃ ∧ 1 ≤ X₄ ∧ 3 ≤ X₃+X₄ ∧ 2 ≤ X₃ for location f16

Found invariant 0 ≤ X₄ ∧ X₃ ≤ 1+X₄ ∧ 0 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ for location f13

Found invariant 1+X₄ ≤ X₃ ∧ 1 ≤ X₄ ∧ 3 ≤ X₃+X₄ ∧ X₃ ≤ 1+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ 2 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ 0 ≤ X₀ for location f11_v1

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₁₄: inf {Infinity}
t₁₅: inf {Infinity}
t₁₆: 1 {O(1)}
t₁₇: 1 {O(1)}
t₁₈: 1 {O(1)}
t₁₉: X₃+1 {O(n)}
t₂₀: 1 {O(1)}
t₂₁: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₁₄: inf {Infinity}
t₁₅: inf {Infinity}
t₁₆: 1 {O(1)}
t₁₇: 1 {O(1)}
t₁₈: 1 {O(1)}
t₁₉: X₃+1 {O(n)}
t₂₀: 1 {O(1)}
t₂₁: 1 {O(1)}

Sizebounds

t₁₄, X₀: 4⋅X₀ {O(n)}
t₁₄, X₂: 4⋅X₂ {O(n)}
t₁₄, X₃: 4⋅X₃ {O(n)}
t₁₄, X₄: 2⋅X₃+6 {O(n)}
t₁₅, X₀: 4⋅X₀ {O(n)}
t₁₅, X₂: 4⋅X₂ {O(n)}
t₁₅, X₃: 4⋅X₃ {O(n)}
t₁₅, X₄: 2⋅X₃+6 {O(n)}
t₁₆, X₀: 12⋅X₀ {O(n)}
t₁₆, X₁: 0 {O(1)}
t₁₆, X₂: 12⋅X₂ {O(n)}
t₁₆, X₃: 12⋅X₃ {O(n)}
t₁₆, X₄: 6⋅X₃+18 {O(n)}
t₁₇, X₀: 2⋅X₀ {O(n)}
t₁₇, X₂: 2⋅X₂ {O(n)}
t₁₇, X₃: 2⋅X₃ {O(n)}
t₁₇, X₄: X₃+3 {O(n)}
t₁₈, X₀: 2⋅X₀ {O(n)}
t₁₈, X₂: 2⋅X₂ {O(n)}
t₁₈, X₃: 2⋅X₃ {O(n)}
t₁₈, X₄: X₃+3 {O(n)}
t₁₉, X₀: X₀ {O(n)}
t₁₉, X₁: X₁ {O(n)}
t₁₉, X₂: X₂ {O(n)}
t₁₉, X₃: X₃ {O(n)}
t₁₉, X₄: X₃+2 {O(n)}
t₂₀, X₀: X₀ {O(n)}
t₂₀, X₁: 0 {O(1)}
t₂₀, X₂: X₂ {O(n)}
t₂₀, X₃: X₃ {O(n)}
t₂₀, X₄: 0 {O(1)}
t₂₁, X₀: X₀ {O(n)}
t₂₁, X₁: X₁ {O(n)}
t₂₁, X₂: X₂ {O(n)}
t₂₁, X₃: X₃ {O(n)}
t₂₁, X₄: 1 {O(1)}