Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars: nondef.0
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₀, X₁, X₂, X₃, X₄, X₅)
t₃: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ ≤ 0
t₄: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ < 2⋅X₁
t₅: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: 2⋅X₁ < X₀
t₂: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 < X₀ ∧ X₀ ≤ 2⋅X₁ ∧ 2⋅X₁ ≤ X₀
t₁₀: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, X₃, X₄, X₅)
t₉: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₂, X₃, X₂, X₃, X₄, X₅)
t₆: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₀-1, X₃, X₄, X₅)
t₈: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, nondef.0, X₄, X₅)
t₁: l7(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₅, X₄, X₂, X₃, X₄, X₅)

Preprocessing

Found invariant X₀ ≤ X₅ for location l2

Found invariant 2 ≤ X₅ ∧ 3 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₅ ∧ 3 ≤ X₁+X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location l6

Found invariant 2 ≤ X₅ ∧ 3 ≤ X₁+X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location l5

Found invariant X₀ ≤ X₅ for location l1

Found invariant 2 ≤ X₅ ∧ 3 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₅ ∧ 3 ≤ X₁+X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location l4

Found invariant X₀ ≤ X₅ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars: nondef.0
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₀, X₁, X₂, X₃, X₄, X₅)
t₃: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ ≤ 0 ∧ X₀ ≤ X₅
t₄: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ < 2⋅X₁ ∧ X₀ ≤ X₅
t₅: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: 2⋅X₁ < X₀ ∧ X₀ ≤ X₅
t₂: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 < X₀ ∧ X₀ ≤ 2⋅X₁ ∧ 2⋅X₁ ≤ X₀ ∧ X₀ ≤ X₅
t₁₀: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ ≤ X₅
t₉: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₂, X₃, X₂, X₃, X₄, X₅) :|: 2 ≤ X₅ ∧ 3 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₅ ∧ 3 ≤ X₁+X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₆: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₀-1, X₃, X₄, X₅) :|: 2 ≤ X₅ ∧ 3 ≤ X₁+X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₈: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, nondef.0, X₄, X₅) :|: 2 ≤ X₅ ∧ 3 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₅ ∧ 3 ≤ X₁+X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₁: l7(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₅, X₄, X₂, X₃, X₄, X₅)

Analysing control-flow refined program

Cut unsatisfiable transition t₁₇₁: n_l2___4→n_l5___3

Cut unreachable locations [n_l4___1; n_l5___3; n_l6___2] from the program graph

Found invariant X₅ ≤ 1+X₂ ∧ X₅ ≤ X₀ ∧ 2 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 3 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₅ ∧ 3 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 3 ≤ X₀+X₄ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l6___6

Found invariant X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ for location l2

Found invariant X₅ ≤ 1+X₂ ∧ X₅ ≤ X₀ ∧ 2 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 3 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₅ ∧ 3 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 3 ≤ X₀+X₄ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l4___5

Found invariant X₅ ≤ X₀ ∧ 2 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ 3 ≤ X₁+X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ 3 ≤ X₀+X₄ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l5___7

Found invariant X₅ ≤ 1+X₀ ∧ X₀ ≤ X₅ for location l1

Found invariant X₅ ≤ 1+X₀ ∧ X₀ ≤ X₅ for location l3

Found invariant X₅ ≤ 1+X₂ ∧ X₅ ≤ 1+X₀ ∧ 2 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 3 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₅ ∧ 3 ≤ X₀+X₅ ∧ 1+X₀ ≤ X₅ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₀+X₄ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ for location n_l2___4

CFR: Improvement to new bound with the following program:

new bound:

0 {O(1)}

cfr-program:

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars: Arg1_P, Arg5_P, NoDet0
Locations: l0, l1, l2, l3, l7, n_l2___4, n_l4___5, n_l5___7, n_l6___6
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₀, X₁, X₂, X₃, X₄, X₅)
t₃: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ ≤ 0 ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄
t₄: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ < 2⋅X₁ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄
t₅: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: 2⋅X₁ < X₀ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄
t₁₇₂: l2(X₀, X₁, X₂, X₃, X₄, X₅) → n_l5___7(X₀, Arg1_P, X₂, X₃, X₄, X₅) :|: X₀ ≤ X₅ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₅ ∧ 0 < X₀ ∧ X₀ ≤ 2⋅X₁ ∧ 2⋅X₁ ≤ X₀ ∧ X₀ ≤ 2⋅Arg1_P ∧ 2⋅Arg1_P ≤ X₀ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄
t₁₀: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ ≤ X₅ ∧ X₅ ≤ 1+X₀ ∧ X₀ ≤ X₅
t₁: l7(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₅, X₄, X₂, X₃, X₄, X₅)
t₁₈₆: n_l2___4(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ < 2⋅X₁ ∧ X₀ ≤ X₅ ∧ X₅ ≤ 1+X₂ ∧ X₅ ≤ 1+X₀ ∧ 2 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 3 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₅ ∧ 3 ≤ X₀+X₅ ∧ 1+X₀ ≤ X₅ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₀+X₄ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀
t₁₈₇: n_l2___4(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: 2⋅X₁ < X₀ ∧ X₀ ≤ X₅ ∧ X₅ ≤ 1+X₂ ∧ X₅ ≤ 1+X₀ ∧ 2 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 3 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₅ ∧ 3 ≤ X₀+X₅ ∧ 1+X₀ ≤ X₅ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₀+X₄ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀
t₁₇₄: n_l4___5(X₀, X₁, X₂, X₃, X₄, X₅) → n_l2___4(X₀-1, X₃, X₀-1, X₃, X₄, X₅) :|: 2 ≤ X₅ ∧ X₂+1 ≤ X₅ ∧ X₅ ≤ 1+X₂ ∧ 2⋅X₁ ≤ X₅ ∧ X₅ ≤ 2⋅X₁ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ 2⋅X₄ ≤ X₅ ∧ X₅ ≤ 2⋅X₄ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₀ ≤ X₂+1 ∧ 1+X₂ ≤ X₀ ∧ X₅ ≤ 1+X₂ ∧ X₅ ≤ X₀ ∧ 2 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 3 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₅ ∧ 3 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 3 ≤ X₀+X₄ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₁₇₆: n_l5___7(X₀, X₁, X₂, X₃, X₄, X₅) → n_l6___6(X₀, X₁, X₀-1, X₃, X₄, X₅) :|: 0 < 2⋅X₄ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₁ ∧ X₀ ≤ 2⋅X₄ ∧ 2⋅X₄ ≤ X₀ ∧ 2⋅X₄ ≤ X₅ ∧ X₅ ≤ 2⋅X₄ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ 2 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ 3 ≤ X₁+X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ 3 ≤ X₀+X₄ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₁₇₈: n_l6___6(X₀, X₁, X₂, X₃, X₄, X₅) → n_l4___5(X₀, X₁, X₀-1, NoDet0, X₄, Arg5_P) :|: 2 ≤ X₅ ∧ X₂+1 ≤ X₅ ∧ X₅ ≤ 1+X₂ ∧ 2⋅X₁ ≤ X₅ ∧ X₅ ≤ 2⋅X₁ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ 2⋅X₄ ≤ X₅ ∧ X₅ ≤ 2⋅X₄ ∧ X₀ ≤ Arg5_P ∧ 1 ≤ X₁ ∧ 2 ≤ X₀ ∧ X₅ ≤ Arg5_P ∧ Arg5_P ≤ X₅ ∧ X₀ ≤ X₂+1 ∧ 1+X₂ ≤ X₀ ∧ X₅ ≤ 1+X₂ ∧ X₅ ≤ X₀ ∧ 2 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 3 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₅ ∧ 3 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 3 ≤ X₀+X₄ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀

All Bounds

Timebounds

Overall timebound:12 {O(1)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₁₇₂: 1 {O(1)}
t₁₀: 1 {O(1)}
t₁: 1 {O(1)}
t₁₈₆: 1 {O(1)}
t₁₈₇: 1 {O(1)}
t₁₇₄: 1 {O(1)}
t₁₇₆: 1 {O(1)}
t₁₇₈: 1 {O(1)}

Costbounds

Overall costbound: 12 {O(1)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₁₇₂: 1 {O(1)}
t₁₀: 1 {O(1)}
t₁: 1 {O(1)}
t₁₈₆: 1 {O(1)}
t₁₈₇: 1 {O(1)}
t₁₇₄: 1 {O(1)}
t₁₇₆: 1 {O(1)}
t₁₇₈: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₀, X₄: X₄ {O(n)}
t₀, X₅: X₅ {O(n)}
t₃, X₀: X₅ {O(n)}
t₃, X₁: X₄ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₃ {O(n)}
t₃, X₄: X₄ {O(n)}
t₃, X₅: X₅ {O(n)}
t₄, X₀: 2⋅X₅ {O(n)}
t₄, X₂: X₂+X₅ {O(n)}
t₄, X₄: 2⋅X₄ {O(n)}
t₄, X₅: 2⋅X₅ {O(n)}
t₅, X₀: 2⋅X₅ {O(n)}
t₅, X₂: X₂+X₅ {O(n)}
t₅, X₄: 2⋅X₄ {O(n)}
t₅, X₅: 2⋅X₅ {O(n)}
t₁₀, X₀: 5⋅X₅ {O(n)}
t₁₀, X₂: 2⋅X₅+3⋅X₂ {O(n)}
t₁₀, X₄: 5⋅X₄ {O(n)}
t₁₀, X₅: 5⋅X₅ {O(n)}
t₁, X₀: X₅ {O(n)}
t₁, X₁: X₄ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₁, X₅: X₅ {O(n)}