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, X₂₇, X₂₈, X₂₉, X₃₀
Temp_Vars: F1, G1, H1, I1, J1, K1, L1, M1, N1, O1, P1
Locations: l0, l1, l2, l3
Transitions:
t₆: 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, X₂₇, X₂₈, X₂₉, X₃₀) → l3(X₀, X₁, X₂, X₃, L1, X₅, 1, 4, 1, 4, X₁₀, X₁₁, X₁₂, F1, 2, 3, G1, H1, 4, J1, 0, K1, M1, M1, M1, M1, N1, O1, P1, 4, X₃₀) :|: X₅+1 ≤ I1
t₇: 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, X₂₇, X₂₈, X₂₉, X₃₀) → l3(X₀, X₁, X₂, X₃, L1, X₅, 1, 4, 1, 4, X₁₀, X₁₁, X₁₂, F1, 2, 3, G1, H1, 4, J1, 0, K1, M1, M1, M1, M1, N1, O1, P1, 4, X₃₀) :|: I1+1 ≤ X₅
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, X₂₇, X₂₈, X₂₉, X₃₀) → l1(X₀, X₁, X₀, X₀, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆, X₂₇, X₂₈, X₂₉, X₃₀) :|: X₁+1 ≤ X₀
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, X₂₇, X₂₈, X₂₉, X₃₀) → l1(X₀, X₁, X₀, X₀, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆, X₂₇, X₂₈, X₂₉, X₃₀) :|: X₀+1 ≤ X₁
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, X₂₇, X₂₈, X₂₉, X₃₀) → l1(X₀, X₁, X₀, X₀, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆, X₂₇, X₂₈, X₂₉, X₃₀) :|: 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, X₂₇, X₂₈, X₂₉, X₃₀) → l1(X₀, X₁, X₀, X₀, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆, X₂₇, X₂₈, X₂₉, X₃₀) :|: X₀+1 ≤ X₁
t₈: l3(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, X₂₇, X₂₈, X₂₉, X₃₀) → l2(J1, X₁, J1, J1, X₄, X₄, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, F1, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, G1, X₂₆, X₂₇, X₂₈, X₂₉, H1) :|: X₁+1 ≤ J1 ∧ 0 ≤ X₆ ∧ 1 ≤ X₇ ∧ X₄ ≤ X₅ ∧ X₅ ≤ X₄
t₉: l3(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, X₂₇, X₂₈, X₂₉, X₃₀) → l2(J1, X₁, J1, J1, X₄, X₄, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, F1, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, G1, X₂₆, X₂₇, X₂₈, X₂₉, H1) :|: J1+1 ≤ X₁ ∧ 0 ≤ X₆ ∧ 1 ≤ X₇ ∧ X₄ ≤ X₅ ∧ X₅ ≤ X₄
t₄: l3(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, X₂₇, X₂₈, X₂₉, X₃₀) → l3(X₀, X₁, X₂, X₃, H1, X₅, 1+X₆, X₇-1, 1+X₆, X₇-1, F1, G1, X₇-1, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆, X₂₇, X₂₈, X₂₉, X₃₀) :|: X₅+1 ≤ X₄ ∧ 0 ≤ X₆ ∧ 1 ≤ X₇
t₅: l3(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, X₂₇, X₂₈, X₂₉, X₃₀) → l3(X₀, X₁, X₂, X₃, H1, X₅, 1+X₆, X₇-1, 1+X₆, X₇-1, F1, G1, X₇-1, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆, X₂₇, X₂₈, X₂₉, X₃₀) :|: X₄+1 ≤ X₅ ∧ 0 ≤ X₆ ∧ 1 ≤ X₇

Preprocessing

Eliminate variables {F1,G1,K1,M1,N1,O1,P1,X₂,X₃,X₈,X₉,X₁₀,X₁₁,X₁₂,X₁₃,X₁₄,X₁₅,X₁₆,X₁₇,X₁₈,X₁₉,X₂₀,X₂₁,X₂₂,X₂₃,X₂₄,X₂₅,X₂₆,X₂₇,X₂₈,X₂₉,X₃₀} that do not contribute to the problem

Found invariant X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 1 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 3+X₅ ∧ X₄ ≤ 4 ∧ 1 ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ for location l2

Found invariant X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 1 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 3+X₅ ∧ X₄ ≤ 4 ∧ 1 ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ for location l1

Found invariant X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 0 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 5+X₅ ∧ X₄ ≤ 5 ∧ 1 ≤ X₄ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars: H1, I1, J1, L1
Locations: l0, l1, l2, l3
Transitions:
t₂₁: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, L1, X₃, 1, 4) :|: X₃+1 ≤ I1
t₂₂: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, L1, X₃, 1, 4) :|: I1+1 ≤ X₃
t₂₃: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁+1 ≤ X₀ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 1 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 3+X₅ ∧ X₄ ≤ 4 ∧ 1 ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃
t₂₄: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀+1 ≤ X₁ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 1 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 3+X₅ ∧ X₄ ≤ 4 ∧ 1 ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃
t₂₅: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁+1 ≤ X₀ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 1 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 3+X₅ ∧ X₄ ≤ 4 ∧ 1 ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃
t₂₆: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀+1 ≤ X₁ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 1 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 3+X₅ ∧ X₄ ≤ 4 ∧ 1 ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃
t₂₇: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l2(J1, X₁, X₂, X₂, X₄, X₅) :|: X₁+1 ≤ J1 ∧ 0 ≤ X₄ ∧ 1 ≤ X₅ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 0 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 5+X₅ ∧ X₄ ≤ 5 ∧ 1 ≤ X₄
t₂₈: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l2(J1, X₁, X₂, X₂, X₄, X₅) :|: J1+1 ≤ X₁ ∧ 0 ≤ X₄ ∧ 1 ≤ X₅ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 0 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 5+X₅ ∧ X₄ ≤ 5 ∧ 1 ≤ X₄
t₂₉: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, H1, X₃, 1+X₄, X₅-1) :|: X₃+1 ≤ X₂ ∧ 0 ≤ X₄ ∧ 1 ≤ X₅ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 0 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 5+X₅ ∧ X₄ ≤ 5 ∧ 1 ≤ X₄
t₃₀: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, H1, X₃, 1+X₄, X₅-1) :|: X₂+1 ≤ X₃ ∧ 0 ≤ X₄ ∧ 1 ≤ X₅ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 0 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 5+X₅ ∧ X₄ ≤ 5 ∧ 1 ≤ X₄

MPRF for transition t₂₉: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, H1, X₃, 1+X₄, X₅-1) :|: X₃+1 ≤ X₂ ∧ 0 ≤ X₄ ∧ 1 ≤ X₅ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 0 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 5+X₅ ∧ X₄ ≤ 5 ∧ 1 ≤ X₄ of depth 1:

new bound:

14 {O(1)}

MPRF for transition t₃₀: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, H1, X₃, 1+X₄, X₅-1) :|: X₂+1 ≤ X₃ ∧ 0 ≤ X₄ ∧ 1 ≤ X₅ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 0 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 5+X₅ ∧ X₄ ≤ 5 ∧ 1 ≤ X₄ of depth 1:

new bound:

14 {O(1)}

Analysing control-flow refined program

Found invariant X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 1 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 3+X₅ ∧ X₄ ≤ 4 ∧ 1 ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ for location l2

Found invariant X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 1 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 3+X₅ ∧ X₄ ≤ 4 ∧ 1 ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ for location l1

Found invariant X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 0 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 5+X₅ ∧ X₄ ≤ 5 ∧ 1 ≤ X₄ for location l3

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₂₁: 1 {O(1)}
t₂₂: 1 {O(1)}
t₂₃: inf {Infinity}
t₂₄: inf {Infinity}
t₂₅: 1 {O(1)}
t₂₆: 1 {O(1)}
t₂₇: 1 {O(1)}
t₂₈: 1 {O(1)}
t₂₉: 14 {O(1)}
t₃₀: 14 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₂₁: 1 {O(1)}
t₂₂: 1 {O(1)}
t₂₃: inf {Infinity}
t₂₄: inf {Infinity}
t₂₅: 1 {O(1)}
t₂₆: 1 {O(1)}
t₂₇: 1 {O(1)}
t₂₈: 1 {O(1)}
t₂₉: 14 {O(1)}
t₃₀: 14 {O(1)}

Sizebounds

t₂₁, X₀: X₀ {O(n)}
t₂₁, X₁: X₁ {O(n)}
t₂₁, X₃: X₃ {O(n)}
t₂₁, X₄: 1 {O(1)}
t₂₁, X₅: 4 {O(1)}
t₂₂, X₀: X₀ {O(n)}
t₂₂, X₁: X₁ {O(n)}
t₂₂, X₃: X₃ {O(n)}
t₂₂, X₄: 1 {O(1)}
t₂₂, X₅: 4 {O(1)}
t₂₃, X₁: 6⋅X₁ {O(n)}
t₂₃, X₄: 4 {O(1)}
t₂₃, X₅: 4 {O(1)}
t₂₄, X₁: 6⋅X₁ {O(n)}
t₂₄, X₄: 4 {O(1)}
t₂₄, X₅: 4 {O(1)}
t₂₅, X₁: 6⋅X₁ {O(n)}
t₂₅, X₄: 4 {O(1)}
t₂₅, X₅: 4 {O(1)}
t₂₆, X₁: 6⋅X₁ {O(n)}
t₂₆, X₄: 4 {O(1)}
t₂₆, X₅: 4 {O(1)}
t₂₇, X₁: 6⋅X₁ {O(n)}
t₂₇, X₄: 4 {O(1)}
t₂₇, X₅: 4 {O(1)}
t₂₈, X₁: 6⋅X₁ {O(n)}
t₂₈, X₄: 4 {O(1)}
t₂₈, X₅: 4 {O(1)}
t₂₉, X₀: 2⋅X₀ {O(n)}
t₂₉, X₁: 2⋅X₁ {O(n)}
t₂₉, X₃: 2⋅X₃ {O(n)}
t₂₉, X₄: 5 {O(1)}
t₂₉, X₅: 3 {O(1)}
t₃₀, X₀: 2⋅X₀ {O(n)}
t₃₀, X₁: 2⋅X₁ {O(n)}
t₃₀, X₃: 2⋅X₃ {O(n)}
t₃₀, X₄: 5 {O(1)}
t₃₀, X₅: 3 {O(1)}