Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars: G
Locations: l0, l1, l2, l3, l4
Transitions:
t₅: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l1(4, G, 0, X₃, G, 4) :|: 1 ≤ G
t₀: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀-2, X₁-1, X₂+1, G, X₄, X₅) :|: 1 ≤ X₀ ∧ 1 ≤ G
t₁: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀-2, X₁, X₂, G, X₄, X₅) :|: G ≤ 0 ∧ 1 ≤ X₀ ∧ X₁+1 ≤ X₀
t₄: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ ≤ 0
t₂: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, X₅)
t₃: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅)

Preprocessing

Cut unreachable locations [l3; l4] from the program graph

Eliminate variables {X₂,X₃,X₄,X₅} that do not contribute to the problem

Found invariant 0 ≤ 3+X₁ ∧ 0 ≤ 4+X₀+X₁ ∧ X₀ ≤ 3+X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ 1+X₀ for location l2

Found invariant 0 ≤ 3+X₁ ∧ 0 ≤ 4+X₀+X₁ ∧ X₀ ≤ 3+X₁ ∧ X₀ ≤ 4 ∧ 0 ≤ 1+X₀ for location l1

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars: G
Locations: l0, l1, l2
Transitions:
t₁₃: l0(X₀, X₁) → l1(4, G) :|: 1 ≤ G
t₁₄: l1(X₀, X₁) → l1(X₀-2, X₁-1) :|: 1 ≤ X₀ ∧ 1 ≤ G ∧ 0 ≤ 3+X₁ ∧ 0 ≤ 4+X₀+X₁ ∧ X₀ ≤ 3+X₁ ∧ X₀ ≤ 4 ∧ 0 ≤ 1+X₀
t₁₅: l1(X₀, X₁) → l1(X₀-2, X₁) :|: G ≤ 0 ∧ 1 ≤ X₀ ∧ X₁+1 ≤ X₀ ∧ 0 ≤ 3+X₁ ∧ 0 ≤ 4+X₀+X₁ ∧ X₀ ≤ 3+X₁ ∧ X₀ ≤ 4 ∧ 0 ≤ 1+X₀
t₁₆: l1(X₀, X₁) → l2(X₀, X₁) :|: X₀ ≤ 0 ∧ 0 ≤ 3+X₁ ∧ 0 ≤ 4+X₀+X₁ ∧ X₀ ≤ 3+X₁ ∧ X₀ ≤ 4 ∧ 0 ≤ 1+X₀
t₁₇: l2(X₀, X₁) → l2(X₀, X₁) :|: 0 ≤ 3+X₁ ∧ 0 ≤ 4+X₀+X₁ ∧ X₀ ≤ 3+X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ 1+X₀

Analysing control-flow refined program

Cut unsatisfiable transition t₁₆: l1→l2

Cut unsatisfiable transition t₆₉: n_l1___1→n_l1___1

Cut unsatisfiable transition t₇₀: n_l1___1→n_l1___2

Cut unsatisfiable transition t₇₁: n_l1___2→n_l1___1

Cut unsatisfiable transition t₇₂: n_l1___2→n_l1___2

Cut unsatisfiable transition t₈₇: n_l1___3→l2

Cut unsatisfiable transition t₈₈: n_l1___4→l2

Found invariant 0 ≤ 1+X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location l2

Found invariant 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ 2+X₁ ∧ X₀ ≤ 2 ∧ 2 ≤ X₀ for location n_l1___4

Found invariant 0 ≤ 1+X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l1___2

Found invariant X₁ ≤ 3 ∧ X₁ ≤ 1+X₀ ∧ X₀+X₁ ≤ 5 ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ X₀ ≤ 2 ∧ 2 ≤ X₀ for location n_l1___3

Found invariant 1 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ X₀ ≤ 3+X₁ ∧ X₀ ≤ 4 ∧ 4 ≤ X₀ for location l1

Found invariant X₁ ≤ 1 ∧ X₁ ≤ 1+X₀ ∧ X₀+X₁ ≤ 1 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l1___1

CFR: Improvement to new bound with the following program:

new bound:

0 {O(1)}

cfr-program:

Start: l0
Program_Vars: X₀, X₁
Temp_Vars: Arg0_P, Arg1_P, G
Locations: l0, l1, l2, n_l1___1, n_l1___2, n_l1___3, n_l1___4
Transitions:
t₁₃: l0(X₀, X₁) → l1(4, G) :|: 1 ≤ G
t₇₇: l1(X₀, X₁) → n_l1___3(Arg0_P, Arg1_P) :|: X₀ ≤ 4 ∧ 1 ≤ X₀ ∧ X₀ ≤ 3+X₁ ∧ X₀ ≤ 4 ∧ 4 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 3+X₁ ∧ Arg0_P ≤ 1+Arg1_P ∧ 0 ≤ 1+Arg0_P ∧ Arg0_P ≤ 2 ∧ Arg1_P ≤ 1+Arg0_P ∧ X₀ ≤ Arg0_P+2 ∧ 2+Arg0_P ≤ X₀ ∧ X₁ ≤ Arg1_P ∧ Arg1_P ≤ X₁ ∧ 1 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ X₀ ≤ 3+X₁ ∧ X₀ ≤ 4 ∧ 4 ≤ X₀
t₇₈: l1(X₀, X₁) → n_l1___4(X₀-2, X₁-1) :|: X₀ ≤ 4 ∧ 1 ≤ X₀ ∧ X₀ ≤ 3+X₁ ∧ X₀ ≤ 4 ∧ 4 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 3+X₁ ∧ X₀ ≤ 4 ∧ 1 ≤ X₀ ∧ X₀ ≤ 3+X₁ ∧ 1 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ X₀ ≤ 3+X₁ ∧ X₀ ≤ 4 ∧ 4 ≤ X₀
t₁₇: l2(X₀, X₁) → l2(X₀, X₁) :|: 0 ≤ 3+X₁ ∧ 0 ≤ 4+X₀+X₁ ∧ X₀ ≤ 3+X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ 1+X₀ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
t₈₅: n_l1___1(X₀, X₁) → l2(X₀, X₁) :|: X₀ ≤ 0 ∧ 0 ≤ 3+X₁ ∧ 0 ≤ 4+X₀+X₁ ∧ X₀ ≤ 3+X₁ ∧ X₀ ≤ 4 ∧ 0 ≤ 1+X₀ ∧ X₁ ≤ 1 ∧ X₁ ≤ 1+X₀ ∧ X₀+X₁ ≤ 1 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
t₈₆: n_l1___2(X₀, X₁) → l2(X₀, X₁) :|: X₀ ≤ 0 ∧ 0 ≤ 3+X₁ ∧ 0 ≤ 4+X₀+X₁ ∧ X₀ ≤ 3+X₁ ∧ X₀ ≤ 4 ∧ 0 ≤ 1+X₀ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
t₇₃: n_l1___3(X₀, X₁) → n_l1___1(Arg0_P, Arg1_P) :|: X₀ ≤ 4 ∧ 1 ≤ X₀ ∧ X₀ ≤ 3+X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 3+X₁ ∧ 0 ≤ 1+X₀ ∧ X₀ ≤ 2+X₁ ∧ X₀ ≤ 2 ∧ 0 ≤ 1+X₀ ∧ X₀ ≤ 1+X₁ ∧ X₀ ≤ 2 ∧ X₁ ≤ 1+X₀ ∧ Arg0_P ≤ 1+Arg1_P ∧ 0 ≤ 1+Arg0_P ∧ Arg0_P ≤ 2 ∧ Arg1_P ≤ 1+Arg0_P ∧ X₀ ≤ Arg0_P+2 ∧ 2+Arg0_P ≤ X₀ ∧ X₁ ≤ Arg1_P ∧ Arg1_P ≤ X₁ ∧ X₁ ≤ 3 ∧ X₁ ≤ 1+X₀ ∧ X₀+X₁ ≤ 5 ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ X₀ ≤ 2 ∧ 2 ≤ X₀
t₇₄: n_l1___3(X₀, X₁) → n_l1___2(X₀-2, X₁-1) :|: X₀ ≤ 4 ∧ 1 ≤ X₀ ∧ X₀ ≤ 3+X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 3+X₁ ∧ 0 ≤ 1+X₀ ∧ X₀ ≤ 2+X₁ ∧ X₀ ≤ 2 ∧ 0 ≤ 1+X₀ ∧ X₀ ≤ 1+X₁ ∧ X₀ ≤ 2 ∧ X₁ ≤ 1+X₀ ∧ X₀ ≤ 4 ∧ 1 ≤ X₀ ∧ X₀ ≤ 3+X₁ ∧ X₁ ≤ 3 ∧ X₁ ≤ 1+X₀ ∧ X₀+X₁ ≤ 5 ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ X₀ ≤ 2 ∧ 2 ≤ X₀
t₇₅: n_l1___4(X₀, X₁) → n_l1___1(Arg0_P, Arg1_P) :|: X₀ ≤ 4 ∧ 1 ≤ X₀ ∧ X₀ ≤ 3+X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 3+X₁ ∧ 0 ≤ 1+X₀ ∧ X₀ ≤ 2+X₁ ∧ X₀ ≤ 2 ∧ Arg0_P ≤ 1+Arg1_P ∧ 0 ≤ 1+Arg0_P ∧ Arg0_P ≤ 2 ∧ Arg1_P ≤ 1+Arg0_P ∧ X₀ ≤ Arg0_P+2 ∧ 2+Arg0_P ≤ X₀ ∧ X₁ ≤ Arg1_P ∧ Arg1_P ≤ X₁ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ 2+X₁ ∧ X₀ ≤ 2 ∧ 2 ≤ X₀
t₇₆: n_l1___4(X₀, X₁) → n_l1___2(X₀-2, X₁-1) :|: X₀ ≤ 4 ∧ 1 ≤ X₀ ∧ X₀ ≤ 3+X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 3+X₁ ∧ 0 ≤ 1+X₀ ∧ X₀ ≤ 2+X₁ ∧ X₀ ≤ 2 ∧ X₀ ≤ 4 ∧ 1 ≤ X₀ ∧ X₀ ≤ 3+X₁ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ 2+X₁ ∧ X₀ ≤ 2 ∧ 2 ≤ X₀

Found invariant 0 ≤ 1+X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location l2

Found invariant 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ 2+X₁ ∧ X₀ ≤ 2 ∧ 2 ≤ X₀ for location n_l1___4

Found invariant 0 ≤ 1+X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l1___2

Found invariant X₁ ≤ 3 ∧ X₁ ≤ 1+X₀ ∧ X₀+X₁ ≤ 5 ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ X₀ ≤ 2 ∧ 2 ≤ X₀ for location n_l1___3

Found invariant 1 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ X₀ ≤ 3+X₁ ∧ X₀ ≤ 4 ∧ 4 ≤ X₀ for location l1

Found invariant X₁ ≤ 1 ∧ X₁ ≤ 1+X₀ ∧ X₀+X₁ ≤ 1 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l1___1

Analysing control-flow refined program

Found invariant 0 ≤ 1+X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location l2

Found invariant 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ 2+X₁ ∧ X₀ ≤ 2 ∧ 2 ≤ X₀ for location n_l1___4

Found invariant 0 ≤ 1+X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l1___2

Found invariant X₁ ≤ 3 ∧ X₁ ≤ 1+X₀ ∧ X₀+X₁ ≤ 5 ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ X₀ ≤ 2 ∧ 2 ≤ X₀ for location n_l1___3

Found invariant 1 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ X₀ ≤ 3+X₁ ∧ X₀ ≤ 4 ∧ 4 ≤ X₀ for location l1

Found invariant X₁ ≤ 1 ∧ X₁ ≤ 1+X₀ ∧ X₀+X₁ ≤ 1 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l1___1

Found invariant 0 ≤ 1+X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location l2

Found invariant 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ 2+X₁ ∧ X₀ ≤ 2 ∧ 2 ≤ X₀ for location n_l1___4

Found invariant 0 ≤ 1+X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l1___2

Found invariant X₁ ≤ 3 ∧ X₁ ≤ 1+X₀ ∧ X₀+X₁ ≤ 5 ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ X₀ ≤ 2 ∧ 2 ≤ X₀ for location n_l1___3

Found invariant 1 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ X₀ ≤ 3+X₁ ∧ X₀ ≤ 4 ∧ 4 ≤ X₀ for location l1

Found invariant X₁ ≤ 1 ∧ X₁ ≤ 1+X₀ ∧ X₀+X₁ ≤ 1 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l1___1

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₁₃: 1 {O(1)}
t₇₇: 1 {O(1)}
t₇₈: 1 {O(1)}
t₁₇: inf {Infinity}
t₈₅: 1 {O(1)}
t₈₆: 1 {O(1)}
t₇₃: 1 {O(1)}
t₇₄: 1 {O(1)}
t₇₅: 1 {O(1)}
t₇₆: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₁₃: 1 {O(1)}
t₇₇: 1 {O(1)}
t₇₈: 1 {O(1)}
t₁₇: inf {Infinity}
t₈₅: 1 {O(1)}
t₈₆: 1 {O(1)}
t₇₃: 1 {O(1)}
t₇₄: 1 {O(1)}
t₇₅: 1 {O(1)}
t₇₆: 1 {O(1)}

Sizebounds

t₁₃, X₀: 4 {O(1)}
t₇₇, X₀: 2 {O(1)}
t₇₇, X₁: 3 {O(1)}
t₇₈, X₀: 2 {O(1)}
t₁₇, X₀: 0 {O(1)}
t₈₅, X₀: 0 {O(1)}
t₈₅, X₁: 1 {O(1)}
t₈₆, X₀: 0 {O(1)}
t₇₃, X₀: 0 {O(1)}
t₇₃, X₁: 1 {O(1)}
t₇₄, X₀: 0 {O(1)}
t₇₄, X₁: 2 {O(1)}
t₇₅, X₀: 0 {O(1)}
t₇₅, X₁: 1 {O(1)}
t₇₆, X₀: 0 {O(1)}