Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆
Temp_Vars: B1, C1, D1, E1, F1, G1, H1, I1, J1
Locations: l0, l1, l2
Transitions:
t₄: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆) → l1(X₀, X₁, X₂, X₃, X₄, B1, 2, 1, 1, 2, X₁₀, X₁₁, X₁₂, 2, C1, D1, F1, G1, G1, G1, G1, H1, I1, 2, J1, 0, X₂₆) :|: E1+1 ≤ X₄
t₅: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆) → l1(X₀, X₁, X₂, X₃, X₄, B1, 2, 1, 1, 2, X₁₀, X₁₁, X₁₂, 2, C1, D1, F1, G1, G1, G1, G1, H1, I1, 2, J1, 0, X₂₆) :|: X₄+1 ≤ E1
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆) → l1(X₀, X₁, X₂, X₃, X₄, B1, X₆-1, 1+X₇, 1+X₇, X₆-1, C1, D1, X₆-1, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆) :|: X₅+1 ≤ X₄ ∧ 1 ≤ X₆ ∧ 0 ≤ X₇
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆) → l1(X₀, X₁, X₂, X₃, X₄, B1, X₆-1, 1+X₇, 1+X₇, X₆-1, C1, D1, X₆-1, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆) :|: X₄+1 ≤ X₅ ∧ 1 ≤ X₆ ∧ 0 ≤ X₇
t₆: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆) → l2(X₀, C1, C1, C1, X₅, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, B1, X₁₇, X₁₈, X₁₉, D1, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, F1) :|: C1+1 ≤ X₀ ∧ 1 ≤ X₆ ∧ 0 ≤ X₇ ∧ X₅ ≤ X₄ ∧ X₄ ≤ X₅
t₇: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆) → l2(X₀, C1, C1, C1, X₅, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, B1, X₁₇, X₁₈, X₁₉, D1, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, F1) :|: X₀+1 ≤ C1 ∧ 1 ≤ X₆ ∧ 0 ≤ X₇ ∧ X₅ ≤ X₄ ∧ X₄ ≤ X₅
t₀: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆) → l2(X₀, X₁, X₁, X₁, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆) :|: X₁+1 ≤ X₀
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆) → l2(X₀, X₁, X₁, X₁, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆) :|: X₀+1 ≤ X₁

Preprocessing

Eliminate variables {D1,F1,G1,H1,I1,J1,X₂,X₃,X₈,X₉,X₁₀,X₁₁,X₁₂,X₁₃,X₁₄,X₁₅,X₁₆,X₁₇,X₁₈,X₁₉,X₂₀,X₂₁,X₂₂,X₂₃,X₂₄,X₂₅,X₂₆} that do not contribute to the problem

Found invariant X₅ ≤ 2 ∧ X₅ ≤ 1+X₄ ∧ X₄+X₅ ≤ 3 ∧ 1 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ X₄ ≤ 1+X₅ ∧ X₄ ≤ 2 ∧ 1 ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ for location l2

Found invariant X₅ ≤ 3 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 3 ∧ 1 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ X₄ ≤ 1+X₅ ∧ X₄ ≤ 2 ∧ 0 ≤ X₄ for location l1

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars: B1, C1, E1
Locations: l0, l1, l2
Transitions:
t₂₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, B1, 2, 1) :|: E1+1 ≤ X₂
t₂₁: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, B1, 2, 1) :|: X₂+1 ≤ E1
t₂₂: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, B1, X₄-1, 1+X₅) :|: X₃+1 ≤ X₂ ∧ 1 ≤ X₄ ∧ 0 ≤ X₅ ∧ X₅ ≤ 3 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 3 ∧ 1 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ X₄ ≤ 1+X₅ ∧ X₄ ≤ 2 ∧ 0 ≤ X₄
t₂₃: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, B1, X₄-1, 1+X₅) :|: X₂+1 ≤ X₃ ∧ 1 ≤ X₄ ∧ 0 ≤ X₅ ∧ X₅ ≤ 3 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 3 ∧ 1 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ X₄ ≤ 1+X₅ ∧ X₄ ≤ 2 ∧ 0 ≤ X₄
t₂₄: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, C1, X₃, X₃, X₄, X₅) :|: C1+1 ≤ X₀ ∧ 1 ≤ X₄ ∧ 0 ≤ X₅ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ X₅ ≤ 3 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 3 ∧ 1 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ X₄ ≤ 1+X₅ ∧ X₄ ≤ 2 ∧ 0 ≤ X₄
t₂₅: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, C1, X₃, X₃, X₄, X₅) :|: X₀+1 ≤ C1 ∧ 1 ≤ X₄ ∧ 0 ≤ X₅ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ X₅ ≤ 3 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 3 ∧ 1 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ X₄ ≤ 1+X₅ ∧ X₄ ≤ 2 ∧ 0 ≤ X₄
t₂₆: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁+1 ≤ X₀ ∧ X₅ ≤ 2 ∧ X₅ ≤ 1+X₄ ∧ X₄+X₅ ≤ 3 ∧ 1 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ X₄ ≤ 1+X₅ ∧ X₄ ≤ 2 ∧ 1 ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃
t₂₇: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀+1 ≤ X₁ ∧ X₅ ≤ 2 ∧ X₅ ≤ 1+X₄ ∧ X₄+X₅ ≤ 3 ∧ 1 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ X₄ ≤ 1+X₅ ∧ X₄ ≤ 2 ∧ 1 ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃

MPRF for transition t₂₂: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, B1, X₄-1, 1+X₅) :|: X₃+1 ≤ X₂ ∧ 1 ≤ X₄ ∧ 0 ≤ X₅ ∧ X₅ ≤ 3 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 3 ∧ 1 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ X₄ ≤ 1+X₅ ∧ X₄ ≤ 2 ∧ 0 ≤ X₄ of depth 1:

new bound:

6 {O(1)}

MPRF for transition t₂₃: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, B1, X₄-1, 1+X₅) :|: X₂+1 ≤ X₃ ∧ 1 ≤ X₄ ∧ 0 ≤ X₅ ∧ X₅ ≤ 3 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 3 ∧ 1 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ X₄ ≤ 1+X₅ ∧ X₄ ≤ 2 ∧ 0 ≤ X₄ of depth 1:

new bound:

6 {O(1)}

Analysing control-flow refined program

Found invariant X₅ ≤ 2 ∧ X₅ ≤ 1+X₄ ∧ X₄+X₅ ≤ 3 ∧ 1 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ X₄ ≤ 1+X₅ ∧ X₄ ≤ 2 ∧ 1 ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ for location l2

Found invariant X₅ ≤ 3 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 3 ∧ 1 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ X₄ ≤ 1+X₅ ∧ X₄ ≤ 2 ∧ 0 ≤ X₄ for location l1

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₂₀: 1 {O(1)}
t₂₁: 1 {O(1)}
t₂₂: 6 {O(1)}
t₂₃: 6 {O(1)}
t₂₄: 1 {O(1)}
t₂₅: 1 {O(1)}
t₂₆: inf {Infinity}
t₂₇: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
t₂₀: 1 {O(1)}
t₂₁: 1 {O(1)}
t₂₂: 6 {O(1)}
t₂₃: 6 {O(1)}
t₂₄: 1 {O(1)}
t₂₅: 1 {O(1)}
t₂₆: inf {Infinity}
t₂₇: inf {Infinity}

Sizebounds

t₂₀, X₀: X₀ {O(n)}
t₂₀, X₁: X₁ {O(n)}
t₂₀, X₂: X₂ {O(n)}
t₂₀, X₄: 2 {O(1)}
t₂₀, X₅: 1 {O(1)}
t₂₁, X₀: X₀ {O(n)}
t₂₁, X₁: X₁ {O(n)}
t₂₁, X₂: X₂ {O(n)}
t₂₁, X₄: 2 {O(1)}
t₂₁, X₅: 1 {O(1)}
t₂₂, X₀: 2⋅X₀ {O(n)}
t₂₂, X₁: 2⋅X₁ {O(n)}
t₂₂, X₂: 2⋅X₂ {O(n)}
t₂₂, X₄: 1 {O(1)}
t₂₂, X₅: 3 {O(1)}
t₂₃, X₀: 2⋅X₀ {O(n)}
t₂₃, X₁: 2⋅X₁ {O(n)}
t₂₃, X₂: 2⋅X₂ {O(n)}
t₂₃, X₄: 1 {O(1)}
t₂₃, X₅: 3 {O(1)}
t₂₄, X₀: 6⋅X₀ {O(n)}
t₂₄, X₂: 6⋅X₂ {O(n)}
t₂₄, X₄: 2 {O(1)}
t₂₄, X₅: 2 {O(1)}
t₂₅, X₀: 6⋅X₀ {O(n)}
t₂₅, X₂: 6⋅X₂ {O(n)}
t₂₅, X₄: 2 {O(1)}
t₂₅, X₅: 2 {O(1)}
t₂₆, X₀: 6⋅X₀ {O(n)}
t₂₆, X₂: 6⋅X₂ {O(n)}
t₂₆, X₄: 2 {O(1)}
t₂₆, X₅: 2 {O(1)}
t₂₇, X₀: 6⋅X₀ {O(n)}
t₂₇, X₂: 6⋅X₂ {O(n)}
t₂₇, X₄: 2 {O(1)}
t₂₇, X₅: 2 {O(1)}