Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, 1, X₂, X₃) :|: 0 ≤ X₀
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ < 0
t₁: l2(X₀, X₁, X₂, X₃) → l1(X₂, X₁, X₂, X₃)
t₅: l3(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₁
t₄: l3(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: X₁ < X₀
t₈: l4(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃)
t₇: l5(X₀, X₁, X₂, X₃) → l1(X₀-1, X₁, X₂, X₃)
t₆: l6(X₀, X₁, X₂, X₃) → l3(X₀, 2⋅X₁, X₂, X₃)

Preprocessing

Eliminate variables {X₃} that do not contribute to the problem

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

Found invariant X₀ ≤ X₂ ∧ 1+X₀ ≤ 0 for location l7

Found invariant 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l5

Found invariant X₀ ≤ X₂ for location l1

Found invariant X₀ ≤ X₂ ∧ 1+X₀ ≤ 0 for location l4

Found invariant 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₁₇: l0(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₁₈: l1(X₀, X₁, X₂) → l3(X₀, 1, X₂) :|: 0 ≤ X₀ ∧ X₀ ≤ X₂
t₁₉: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₀ < 0 ∧ X₀ ≤ X₂
t₂₀: l2(X₀, X₁, X₂) → l1(X₂, X₁, X₂)
t₂₁: l3(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₀ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₂₂: l3(X₀, X₁, X₂) → l6(X₀, X₁, X₂) :|: X₁ < X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₂₃: l4(X₀, X₁, X₂) → l7(X₀, X₁, X₂) :|: X₀ ≤ X₂ ∧ 1+X₀ ≤ 0
t₂₄: l5(X₀, X₁, X₂) → l1(X₀-1, X₁, X₂) :|: 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀
t₂₅: l6(X₀, X₁, X₂) → l3(X₀, 2⋅X₁, X₂) :|: 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀

MPRF for transition t₁₈: l1(X₀, X₁, X₂) → l3(X₀, 1, X₂) :|: 0 ≤ X₀ ∧ X₀ ≤ X₂ of depth 1:

new bound:

X₂+1 {O(n)}

MPRF for transition t₂₁: l3(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₀ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₂+1 {O(n)}

MPRF for transition t₂₄: l5(X₀, X₁, X₂) → l1(X₀-1, X₁, X₂) :|: 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₂+1 {O(n)}

MPRF for transition t₂₂: l3(X₀, X₁, X₂) → l6(X₀, X₁, X₂) :|: X₁ < X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₂⋅X₂+2⋅X₂ {O(n^2)}

MPRF for transition t₂₅: l6(X₀, X₁, X₂) → l3(X₀, 2⋅X₁, X₂) :|: 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₂⋅X₂+3⋅X₂+1 {O(n^2)}

Chain transitions t₂₄: l5→l1 and t₁₉: l1→l4 to t₅₃: l5→l4

Chain transitions t₂₀: l2→l1 and t₁₉: l1→l4 to t₅₄: l2→l4

Chain transitions t₂₀: l2→l1 and t₁₈: l1→l3 to t₅₅: l2→l3

Chain transitions t₂₄: l5→l1 and t₁₈: l1→l3 to t₅₆: l5→l3

Chain transitions t₂₅: l6→l3 and t₂₂: l3→l6 to t₅₇: l6→l6

Chain transitions t₅₆: l5→l3 and t₂₂: l3→l6 to t₅₈: l5→l6

Chain transitions t₅₆: l5→l3 and t₂₁: l3→l5 to t₅₉: l5→l5

Chain transitions t₂₅: l6→l3 and t₂₁: l3→l5 to t₆₀: l6→l5

Chain transitions t₅₅: l2→l3 and t₂₁: l3→l5 to t₆₁: l2→l5

Chain transitions t₅₅: l2→l3 and t₂₂: l3→l6 to t₆₂: l2→l6

Analysing control-flow refined program

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

Found invariant X₀ ≤ X₂ ∧ 1+X₀ ≤ 0 for location l7

Found invariant 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l5

Found invariant X₀ ≤ X₂ for location l1

Found invariant X₀ ≤ X₂ ∧ 1+X₀ ≤ 0 for location l4

Found invariant 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l3

MPRF for transition t₅₈: l5(X₀, X₁, X₂) -{3}> l6(X₀-1, 1, X₂) :|: 1 ≤ X₀ ∧ 2 < X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 1+X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 0 ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₂+3 {O(n)}

MPRF for transition t₅₉: l5(X₀, X₁, X₂) -{3}> l5(X₀-1, 1, X₂) :|: 1 ≤ X₀ ∧ X₀ ≤ 2 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 1+X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 0 ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₂+3 {O(n)}

MPRF for transition t₆₀: l6(X₀, X₁, X₂) -{2}> l5(X₀, 2⋅X₁, X₂) :|: X₀ ≤ 2⋅X₁ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ 2⋅X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ 2⋅X₁ ∧ 1 ≤ X₀+2⋅X₁ ∧ 0 ≤ X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₂+2 {O(n)}

MPRF for transition t₅₇: l6(X₀, X₁, X₂) -{2}> l6(X₀, 2⋅X₁, X₂) :|: 2⋅X₁ < X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ 2⋅X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ 2⋅X₁ ∧ 1 ≤ X₀+2⋅X₁ ∧ 0 ≤ X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₂⋅X₂+3⋅X₂+2 {O(n^2)}

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

Analysing control-flow refined program

Found invariant 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l6___3

Found invariant 3 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 6 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 3 ≤ X₀ for location n_l6___1

Found invariant X₀ ≤ X₂ ∧ 1+X₀ ≤ 0 for location l7

Found invariant 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l5

Found invariant 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l3___2

Found invariant X₀ ≤ X₂ for location l1

Found invariant X₀ ≤ X₂ ∧ 1+X₀ ≤ 0 for location l4

Found invariant 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 1 ∧ X₁ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l3

knowledge_propagation leads to new time bound X₂+1 {O(n)} for transition t₁₄₇: l3(X₀, X₁, X₂) → n_l6___3(X₀, X₁, X₂) :|: X₁ ≤ 1 ∧ X₁ < X₀ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 1 ∧ X₁ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀

knowledge_propagation leads to new time bound X₂+1 {O(n)} for transition t₁₄₉: n_l6___3(X₀, X₁, X₂) → n_l3___2(X₀, 2⋅X₁, X₂) :|: 1 < X₀ ∧ X₁ ≤ 1 ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀

MPRF for transition t₁₄₆: n_l3___2(X₀, X₁, X₂) → n_l6___1(X₀, X₁, X₂) :|: 2 ≤ X₁ ∧ 2+X₁ ≤ 2⋅X₀ ∧ X₁ < X₀ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

2⋅X₂⋅X₂+4⋅X₂ {O(n^2)}

MPRF for transition t₁₄₈: n_l6___1(X₀, X₁, X₂) → n_l3___2(X₀, 2⋅X₁, X₂) :|: X₁ < X₀ ∧ 2 ≤ X₁ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 3 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 6 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 3 ≤ X₀ of depth 1:

new bound:

X₂⋅X₂+2⋅X₂ {O(n^2)}

MPRF for transition t₁₅₃: n_l3___2(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₀ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₂+1 {O(n)}

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:2⋅X₂⋅X₂+8⋅X₂+8 {O(n^2)}
t₁₇: 1 {O(1)}
t₁₈: X₂+1 {O(n)}
t₁₉: 1 {O(1)}
t₂₀: 1 {O(1)}
t₂₁: X₂+1 {O(n)}
t₂₂: X₂⋅X₂+2⋅X₂ {O(n^2)}
t₂₃: 1 {O(1)}
t₂₄: X₂+1 {O(n)}
t₂₅: X₂⋅X₂+3⋅X₂+1 {O(n^2)}

Costbounds

Overall costbound: 2⋅X₂⋅X₂+8⋅X₂+8 {O(n^2)}
t₁₇: 1 {O(1)}
t₁₈: X₂+1 {O(n)}
t₁₉: 1 {O(1)}
t₂₀: 1 {O(1)}
t₂₁: X₂+1 {O(n)}
t₂₂: X₂⋅X₂+2⋅X₂ {O(n^2)}
t₂₃: 1 {O(1)}
t₂₄: X₂+1 {O(n)}
t₂₅: X₂⋅X₂+3⋅X₂+1 {O(n^2)}

Sizebounds

t₁₇, X₀: X₀ {O(n)}
t₁₇, X₁: X₁ {O(n)}
t₁₇, X₂: X₂ {O(n)}
t₁₈, X₀: X₂+1 {O(n)}
t₁₈, X₁: 1 {O(1)}
t₁₈, X₂: X₂ {O(n)}
t₁₉, X₀: 2⋅X₂+1 {O(n)}
t₁₉, X₁: 2^(X₂⋅X₂+3⋅X₂+1)+X₁+1 {O(EXP)}
t₁₉, X₂: 2⋅X₂ {O(n)}
t₂₀, X₀: X₂ {O(n)}
t₂₀, X₁: X₁ {O(n)}
t₂₀, X₂: X₂ {O(n)}
t₂₁, X₀: X₂+1 {O(n)}
t₂₁, X₁: 2^(X₂⋅X₂+3⋅X₂+1)+1 {O(EXP)}
t₂₁, X₂: X₂ {O(n)}
t₂₂, X₀: X₂+1 {O(n)}
t₂₂, X₁: 2^(X₂⋅X₂+3⋅X₂+1) {O(EXP)}
t₂₂, X₂: X₂ {O(n)}
t₂₃, X₀: 2⋅X₂+1 {O(n)}
t₂₃, X₁: 2^(X₂⋅X₂+3⋅X₂+1)+X₁+1 {O(EXP)}
t₂₃, X₂: 2⋅X₂ {O(n)}
t₂₄, X₀: X₂+1 {O(n)}
t₂₄, X₁: 2^(X₂⋅X₂+3⋅X₂+1)+1 {O(EXP)}
t₂₄, X₂: X₂ {O(n)}
t₂₅, X₀: X₂+1 {O(n)}
t₂₅, X₁: 2^(X₂⋅X₂+3⋅X₂+1) {O(EXP)}
t₂₅, X₂: X₂ {O(n)}