Initial Problem

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁) → l6(X₀, X₁)
t₉: l1(X₀, X₁) → l3(X₀-X₁, X₁)
t₁₀: l2(X₀, X₁) → l3(X₀, X₁-X₀)
t₄: l3(X₀, X₁) → l4(X₀, X₁) :|: X₁+1 ≤ X₀
t₅: l3(X₀, X₁) → l4(X₀, X₁) :|: X₀+1 ≤ X₁
t₆: l3(X₀, X₁) → l5(X₀, X₁) :|: X₁ ≤ X₀ ∧ X₀ ≤ X₁
t₇: l4(X₀, X₁) → l1(X₀, X₁) :|: X₁+1 ≤ X₀
t₈: l4(X₀, X₁) → l2(X₀, X₁) :|: X₀ ≤ X₁
t₁₁: l5(X₀, X₁) → l7(X₀, X₁)
t₃: l6(X₀, X₁) → l3(X₁, X₀) :|: 1 ≤ X₀ ∧ 1 ≤ X₁
t₁: l6(X₀, X₁) → l5(X₀, X₁) :|: X₀ ≤ 0
t₂: l6(X₀, X₁) → l5(X₀, X₁) :|: X₁ ≤ 0

Preprocessing

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

Found invariant 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l1

Found invariant 1 ≤ X₀+X₁ for location l4

Found invariant 1 ≤ X₀+X₁ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁) → l6(X₀, X₁)
t₉: l1(X₀, X₁) → l3(X₀-X₁, X₁) :|: 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁₀: l2(X₀, X₁) → l3(X₀, X₁-X₀) :|: 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ X₁
t₄: l3(X₀, X₁) → l4(X₀, X₁) :|: X₁+1 ≤ X₀ ∧ 1 ≤ X₀+X₁
t₅: l3(X₀, X₁) → l4(X₀, X₁) :|: X₀+1 ≤ X₁ ∧ 1 ≤ X₀+X₁
t₆: l3(X₀, X₁) → l5(X₀, X₁) :|: X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀+X₁
t₇: l4(X₀, X₁) → l1(X₀, X₁) :|: X₁+1 ≤ X₀ ∧ 1 ≤ X₀+X₁
t₈: l4(X₀, X₁) → l2(X₀, X₁) :|: X₀ ≤ X₁ ∧ 1 ≤ X₀+X₁
t₁₁: l5(X₀, X₁) → l7(X₀, X₁)
t₃: l6(X₀, X₁) → l3(X₁, X₀) :|: 1 ≤ X₀ ∧ 1 ≤ X₁
t₁: l6(X₀, X₁) → l5(X₀, X₁) :|: X₀ ≤ 0
t₂: l6(X₀, X₁) → l5(X₀, X₁) :|: X₁ ≤ 0

Chain transitions t₇: l4→l1 and t₉: l1→l3 to t₁₄₁: l4→l3

Chain transitions t₈: l4→l2 and t₁₀: l2→l3 to t₁₄₂: l4→l3

Chain transitions t₃: l6→l3 and t₆: l3→l5 to t₁₄₃: l6→l5

Chain transitions t₁₄₂: l4→l3 and t₆: l3→l5 to t₁₄₄: l4→l5

Chain transitions t₁₄₂: l4→l3 and t₅: l3→l4 to t₁₄₅: l4→l4

Chain transitions t₃: l6→l3 and t₅: l3→l4 to t₁₄₆: l6→l4

Chain transitions t₁₄₁: l4→l3 and t₅: l3→l4 to t₁₄₇: l4→l4

Chain transitions t₁₄₁: l4→l3 and t₆: l3→l5 to t₁₄₈: l4→l5

Chain transitions t₁₄₁: l4→l3 and t₄: l3→l4 to t₁₄₉: l4→l4

Chain transitions t₁₄₂: l4→l3 and t₄: l3→l4 to t₁₅₀: l4→l4

Chain transitions t₃: l6→l3 and t₄: l3→l4 to t₁₅₁: l6→l4

Analysing control-flow refined program

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

Found invariant 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l1

Found invariant 1 ≤ X₀+X₁ for location l4

Found invariant 1 ≤ X₀+X₁ for location l3

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

Analysing control-flow refined program

Found invariant 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l4___3

Found invariant 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l4___4

Found invariant 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l1___2

Found invariant 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l2___1

Found invariant 2 ≤ X₀+X₁ for location l3

MPRF for transition t₃₃₈: n_l1___2(X₀, X₁) → l3(X₀-X₁, X₁) :|: 1 ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₁+1 {O(n)}

MPRF for transition t₃₃₉: n_l2___1(X₀, X₁) → l3(X₀, X₁-X₀) :|: 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₀ {O(n)}

MPRF for transition t₃₄₀: l3(X₀, X₁) → n_l4___3(X₀, X₁) :|: 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+2⋅X₁ ∧ 1 ≤ 2⋅X₀+X₁ ∧ 0 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₁ of depth 1:

new bound:

X₀+1 {O(n)}

MPRF for transition t₃₄₁: l3(X₀, X₁) → n_l4___4(X₀, X₁) :|: 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+2⋅X₁ ∧ 1 ≤ 2⋅X₀+X₁ ∧ 0 ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₁ of depth 1:

new bound:

X₁ {O(n)}

MPRF for transition t₃₄₂: n_l4___3(X₀, X₁) → n_l2___1(X₀, X₁) :|: 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₀ {O(n)}

MPRF for transition t₃₄₃: n_l4___4(X₀, X₁) → n_l1___2(X₀, X₁) :|: 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₁+1 {O(n)}

CFR: Improvement to new bound with the following program:

new bound:

Infinite

cfr-program:

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l3, l5, l6, l7, n_l1___2, n_l2___1, n_l4___3, n_l4___4
Transitions:
t₀: l0(X₀, X₁) → l6(X₀, X₁)
t₆: l3(X₀, X₁) → l5(X₀, X₁) :|: X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₁
t₃₄₀: l3(X₀, X₁) → n_l4___3(X₀, X₁) :|: 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+2⋅X₁ ∧ 1 ≤ 2⋅X₀+X₁ ∧ 0 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₁
t₃₄₁: l3(X₀, X₁) → n_l4___4(X₀, X₁) :|: 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+2⋅X₁ ∧ 1 ≤ 2⋅X₀+X₁ ∧ 0 ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₁
t₁₁: l5(X₀, X₁) → l7(X₀, X₁)
t₃: l6(X₀, X₁) → l3(X₁, X₀) :|: 1 ≤ X₀ ∧ 1 ≤ X₁
t₁: l6(X₀, X₁) → l5(X₀, X₁) :|: X₀ ≤ 0
t₂: l6(X₀, X₁) → l5(X₀, X₁) :|: X₁ ≤ 0
t₃₃₈: n_l1___2(X₀, X₁) → l3(X₀-X₁, X₁) :|: 1 ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₃₃₉: n_l2___1(X₀, X₁) → l3(X₀, X₁-X₀) :|: 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₃₄₂: n_l4___3(X₀, X₁) → n_l2___1(X₀, X₁) :|: 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₃₄₃: n_l4___4(X₀, X₁) → n_l1___2(X₀, X₁) :|: 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀

CFR: Improvement to new bound with the following program:

new bound:

3⋅X₀+3⋅X₁+3 {O(n)}

cfr-program:

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l3, l5, l6, l7, n_l1___2, n_l2___1, n_l4___3, n_l4___4
Transitions:
t₀: l0(X₀, X₁) → l6(X₀, X₁)
t₆: l3(X₀, X₁) → l5(X₀, X₁) :|: X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₁
t₃₄₀: l3(X₀, X₁) → n_l4___3(X₀, X₁) :|: 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+2⋅X₁ ∧ 1 ≤ 2⋅X₀+X₁ ∧ 0 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₁
t₃₄₁: l3(X₀, X₁) → n_l4___4(X₀, X₁) :|: 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+2⋅X₁ ∧ 1 ≤ 2⋅X₀+X₁ ∧ 0 ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₁
t₁₁: l5(X₀, X₁) → l7(X₀, X₁)
t₃: l6(X₀, X₁) → l3(X₁, X₀) :|: 1 ≤ X₀ ∧ 1 ≤ X₁
t₁: l6(X₀, X₁) → l5(X₀, X₁) :|: X₀ ≤ 0
t₂: l6(X₀, X₁) → l5(X₀, X₁) :|: X₁ ≤ 0
t₃₃₈: n_l1___2(X₀, X₁) → l3(X₀-X₁, X₁) :|: 1 ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₃₃₉: n_l2___1(X₀, X₁) → l3(X₀, X₁-X₀) :|: 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₃₄₂: n_l4___3(X₀, X₁) → n_l2___1(X₀, X₁) :|: 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₃₄₃: n_l4___4(X₀, X₁) → n_l1___2(X₀, X₁) :|: 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀

All Bounds

Timebounds

Overall timebound:3⋅X₀+3⋅X₁+9 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₆: 1 {O(1)}
t₁₁: 1 {O(1)}
t₃₃₈: X₁+1 {O(n)}
t₃₃₉: X₀ {O(n)}
t₃₄₀: X₀+1 {O(n)}
t₃₄₁: X₁ {O(n)}
t₃₄₂: X₀ {O(n)}
t₃₄₃: X₁+1 {O(n)}

Costbounds

Overall costbound: 3⋅X₀+3⋅X₁+9 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₆: 1 {O(1)}
t₁₁: 1 {O(1)}
t₃₃₈: X₁+1 {O(n)}
t₃₃₉: X₀ {O(n)}
t₃₄₀: X₀+1 {O(n)}
t₃₄₁: X₁ {O(n)}
t₃₄₂: X₀ {O(n)}
t₃₄₃: X₁+1 {O(n)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₃, X₀: X₁ {O(n)}
t₃, X₁: X₀ {O(n)}
t₆, X₀: 3⋅X₁ {O(n)}
t₆, X₁: 3⋅X₀ {O(n)}
t₁₁, X₀: 2⋅X₀+3⋅X₁ {O(n)}
t₁₁, X₁: 2⋅X₁+3⋅X₀ {O(n)}
t₃₃₈, X₀: X₁ {O(n)}
t₃₃₈, X₁: X₀ {O(n)}
t₃₃₉, X₀: X₁ {O(n)}
t₃₃₉, X₁: X₀ {O(n)}
t₃₄₀, X₀: X₁ {O(n)}
t₃₄₀, X₁: X₀ {O(n)}
t₃₄₁, X₀: X₁ {O(n)}
t₃₄₁, X₁: X₀ {O(n)}
t₃₄₂, X₀: X₁ {O(n)}
t₃₄₂, X₁: X₀ {O(n)}
t₃₄₃, X₀: X₁ {O(n)}
t₃₄₃, X₁: X₀ {O(n)}