Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars: E
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃)
t₆: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₃+1 ≤ X₁
t₅: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₃
t₇: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: E+1 ≤ 0
t₈: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 1 ≤ E
t₉: l2(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃)
t₁₀: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂+1, X₃+1)
t₁₁: l4(X₀, X₁, X₂, X₃) → l6(X₃-1, X₁, X₂, X₃) :|: 1 ≤ X₂
t₁₂: l4(X₀, X₁, X₂, X₃) → l6(X₃, X₁, X₂, X₃) :|: X₂ ≤ 0
t₄: l5(X₀, X₁, X₂, X₃) → l1(X₀, X₁, 0, X₀+1)
t₂: l6(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₀+1 ≤ X₁
t₃: l6(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₀
t₁₃: l7(X₀, X₁, X₂, X₃) → l9(X₀, X₁, X₂, X₃)
t₁: l8(X₀, X₁, X₂, X₃) → l6(0, X₁, X₂, X₃)

Preprocessing

Found invariant 1+X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 2+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l2

Found invariant 0 ≤ X₀ for location l6

Found invariant X₁ ≤ X₀ ∧ 0 ≤ X₀ for location l7

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

Found invariant X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l1

Found invariant X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l4

Found invariant X₁ ≤ X₀ ∧ 0 ≤ X₀ for location l9

Found invariant 1+X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 2+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars: E
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃)
t₆: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₃+1 ≤ X₁ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₅: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₃ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₇: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: E+1 ≤ 0 ∧ 1+X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 2+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₈: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 1 ≤ E ∧ 1+X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 2+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₉: l2(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: 1+X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 2+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₁₀: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂+1, X₃+1) :|: 1+X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 2+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₁₁: l4(X₀, X₁, X₂, X₃) → l6(X₃-1, X₁, X₂, X₃) :|: 1 ≤ X₂ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₁₂: l4(X₀, X₁, X₂, X₃) → l6(X₃, X₁, X₂, X₃) :|: X₂ ≤ 0 ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₄: l5(X₀, X₁, X₂, X₃) → l1(X₀, X₁, 0, X₀+1) :|: 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₂: l6(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₀+1 ≤ X₁ ∧ 0 ≤ X₀
t₃: l6(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₀ ∧ 0 ≤ X₀
t₁₃: l7(X₀, X₁, X₂, X₃) → l9(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₀ ∧ 0 ≤ X₀
t₁: l8(X₀, X₁, X₂, X₃) → l6(0, X₁, X₂, X₃)

MPRF for transition t₂: l6(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₀+1 ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₁ {O(n)}

MPRF for transition t₄: l5(X₀, X₁, X₂, X₃) → l1(X₀, X₁, 0, X₀+1) :|: 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₁ {O(n)}

MPRF for transition t₅: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₃ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₁ {O(n)}

MPRF for transition t₆: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₃+1 ≤ X₁ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

2⋅X₁+1 {O(n)}

MPRF for transition t₇: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: E+1 ≤ 0 ∧ 1+X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 2+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₁ {O(n)}

MPRF for transition t₈: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 1 ≤ E ∧ 1+X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 2+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₁+1 {O(n)}

MPRF for transition t₉: l2(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: 1+X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 2+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₁ {O(n)}

MPRF for transition t₁₀: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂+1, X₃+1) :|: 1+X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 2+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

2⋅X₁+2 {O(n)}

MPRF for transition t₁₁: l4(X₀, X₁, X₂, X₃) → l6(X₃-1, X₁, X₂, X₃) :|: 1 ≤ X₂ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₁ {O(n)}

MPRF for transition t₁₂: l4(X₀, X₁, X₂, X₃) → l6(X₃, X₁, X₂, X₃) :|: X₂ ≤ 0 ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₁ {O(n)}

All Bounds

Timebounds

Overall timebound:12⋅X₁+8 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₁ {O(n)}
t₃: 1 {O(1)}
t₄: X₁ {O(n)}
t₅: X₁ {O(n)}
t₆: 2⋅X₁+1 {O(n)}
t₇: X₁ {O(n)}
t₈: X₁+1 {O(n)}
t₉: X₁ {O(n)}
t₁₀: 2⋅X₁+2 {O(n)}
t₁₁: X₁ {O(n)}
t₁₂: X₁ {O(n)}
t₁₃: 1 {O(1)}

Costbounds

Overall costbound: 12⋅X₁+8 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₁ {O(n)}
t₃: 1 {O(1)}
t₄: X₁ {O(n)}
t₅: X₁ {O(n)}
t₆: 2⋅X₁+1 {O(n)}
t₇: X₁ {O(n)}
t₈: X₁+1 {O(n)}
t₉: X₁ {O(n)}
t₁₀: 2⋅X₁+2 {O(n)}
t₁₁: X₁ {O(n)}
t₁₂: X₁ {O(n)}
t₁₃: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₁, X₀: 0 {O(1)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₂, X₀: 3⋅X₁+2 {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: 4⋅X₁+X₂+4 {O(n)}
t₂, X₃: 12⋅X₁+X₃+8 {O(n)}
t₃, X₀: 3⋅X₁+2 {O(n)}
t₃, X₁: 2⋅X₁ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: 6⋅X₁+X₃+4 {O(n)}
t₄, X₀: 3⋅X₁+2 {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: 0 {O(1)}
t₄, X₃: 3⋅X₁+2 {O(n)}
t₅, X₀: 6⋅X₁+4 {O(n)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: 2⋅X₁+2 {O(n)}
t₅, X₃: 3⋅X₁+2 {O(n)}
t₆, X₀: 3⋅X₁+2 {O(n)}
t₆, X₁: X₁ {O(n)}
t₆, X₂: 2⋅X₁+2 {O(n)}
t₆, X₃: 3⋅X₁+2 {O(n)}
t₇, X₀: 3⋅X₁+2 {O(n)}
t₇, X₁: X₁ {O(n)}
t₇, X₂: 2⋅X₁+2 {O(n)}
t₇, X₃: 3⋅X₁+2 {O(n)}
t₈, X₀: 3⋅X₁+2 {O(n)}
t₈, X₁: X₁ {O(n)}
t₈, X₂: 2⋅X₁+2 {O(n)}
t₈, X₃: 3⋅X₁+2 {O(n)}
t₉, X₀: 3⋅X₁+2 {O(n)}
t₉, X₁: X₁ {O(n)}
t₉, X₂: 2⋅X₁+2 {O(n)}
t₉, X₃: 3⋅X₁+2 {O(n)}
t₁₀, X₀: 3⋅X₁+2 {O(n)}
t₁₀, X₁: X₁ {O(n)}
t₁₀, X₂: 2⋅X₁+2 {O(n)}
t₁₀, X₃: 3⋅X₁+2 {O(n)}
t₁₁, X₀: 3⋅X₁+2 {O(n)}
t₁₁, X₁: X₁ {O(n)}
t₁₁, X₂: 4⋅X₁+4 {O(n)}
t₁₁, X₃: 6⋅X₁+4 {O(n)}
t₁₂, X₀: 3⋅X₁+2 {O(n)}
t₁₂, X₁: X₁ {O(n)}
t₁₂, X₂: 0 {O(1)}
t₁₂, X₃: 6⋅X₁+4 {O(n)}
t₁₃, X₀: 3⋅X₁+2 {O(n)}
t₁₃, X₁: 2⋅X₁ {O(n)}
t₁₃, X₂: X₂ {O(n)}
t₁₃, X₃: 6⋅X₁+X₃+4 {O(n)}