Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅)
t₄: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 < X₀
t₅: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₀, X₂, X₃, X₄, X₅) :|: X₀ ≤ 0
t₁₀: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₀, X₁, X₂, X₃, X₄, X₅)
t₁: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₃, X₁, X₂, X₃, X₄, X₅) :|: 0 < X₄ ∧ 0 < X₃
t₂: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₄ ≤ 0
t₃: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₃ ≤ 0
t₆: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀-1, X₁, X₂, X₃, X₄, X₅)
t₈: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₄ ≤ X₁
t₇: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁ < X₄
t₉: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁+1, X₂, X₃, X₄, X₅)

Preprocessing

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

Found invariant 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 1 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location l6

Found invariant 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 1 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location l5

Found invariant 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₀ for location l1

Found invariant 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ for location l4

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₃, X₄
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₂₂: l0(X₀, X₁, X₃, X₄) → l3(X₀, X₁, X₃, X₄)
t₂₃: l1(X₀, X₁, X₃, X₄) → l4(X₀, X₁, X₃, X₄) :|: 0 < X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₀
t₂₄: l1(X₀, X₁, X₃, X₄) → l5(X₀, X₀, X₃, X₄) :|: X₀ ≤ 0 ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₀
t₂₅: l2(X₀, X₁, X₃, X₄) → l7(X₀, X₁, X₃, X₄)
t₂₆: l3(X₀, X₁, X₃, X₄) → l1(X₃, X₁, X₃, X₄) :|: 0 < X₄ ∧ 0 < X₃
t₂₇: l3(X₀, X₁, X₃, X₄) → l2(X₀, X₁, X₃, X₄) :|: X₄ ≤ 0
t₂₈: l3(X₀, X₁, X₃, X₄) → l2(X₀, X₁, X₃, X₄) :|: X₃ ≤ 0
t₂₉: l4(X₀, X₁, X₃, X₄) → l1(X₀-1, X₁, X₃, X₄) :|: 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀
t₃₁: l5(X₀, X₁, X₃, X₄) → l2(X₀, X₁, X₃, X₄) :|: X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 1 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
t₃₀: l5(X₀, X₁, X₃, X₄) → l6(X₀, X₁, X₃, X₄) :|: X₁ < X₄ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 1 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
t₃₂: l6(X₀, X₁, X₃, X₄) → l5(X₀, X₁+1, X₃, X₄) :|: 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 1 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀

Found invariant 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 1 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location l6

Found invariant 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 1 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location l5

Found invariant 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₀ for location l1

Found invariant 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ for location l4

Time-Bound by TWN-Loops:

TWN-Loops: t₂₃ 2⋅X₃+4 {O(n)}

TWN-Loops:

entry: t₂₆: l3(X₀, X₁, X₃, X₄) → l1(X₃, X₁, X₃, X₄) :|: 0 < X₄ ∧ 0 < X₃
results in twn-loop: twn:Inv: [1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀] , (X₀,X₁,X₃,X₄) -> (X₀-1,X₁,X₃,X₄) :|: 0 < X₀
order: [X₀; X₃; X₄]
closed-form:
X₀: X₀ + [[n != 0]] * -1 * n^1
X₃: X₃
X₄: X₄

Termination: true
Formula:

1 < 0
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1

Stabilization-Threshold for: 0 < X₀
alphas_abs: X₀
M: 0
N: 1
Bound: 2⋅X₀+2 {O(n)}

relevant size-bounds w.r.t. t₂₆:
X₀: X₃ {O(n)}
Runtime-bound of t₂₆: 1 {O(1)}
Results in: 2⋅X₃+4 {O(n)}

2⋅X₃+4 {O(n)}

Time-Bound by TWN-Loops:

TWN-Loops: t₂₉ 2⋅X₃+4 {O(n)}

relevant size-bounds w.r.t. t₂₆:
X₀: X₃ {O(n)}
Runtime-bound of t₂₆: 1 {O(1)}
Results in: 2⋅X₃+4 {O(n)}

2⋅X₃+4 {O(n)}

Found invariant 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 1 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location l6

Found invariant 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 1 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location l5

Found invariant 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₀ for location l1

Found invariant 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ for location l4

Time-Bound by TWN-Loops:

TWN-Loops: t₃₀ 2⋅X₄+4 {O(n)}

TWN-Loops:

entry: t₂₄: l1(X₀, X₁, X₃, X₄) → l5(X₀, X₀, X₃, X₄) :|: X₀ ≤ 0 ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₀
results in twn-loop: twn:Inv: [1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 1 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 1 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀] , (X₀,X₁,X₃,X₄) -> (X₀,X₁+1,X₃,X₄) :|: X₁ < X₄
order: [X₀; X₁; X₃; X₄]
closed-form:
X₀: X₀
X₁: X₁ + [[n != 0]] * n^1
X₃: X₃
X₄: X₄

Termination: true
Formula:

1 < 0
∨ X₁ < X₄ ∧ 1 ≤ 0 ∧ 0 ≤ 1

Stabilization-Threshold for: X₁ < X₄
alphas_abs: X₁+X₄
M: 0
N: 1
Bound: 2⋅X₁+2⋅X₄+2 {O(n)}

relevant size-bounds w.r.t. t₂₄:
X₁: 0 {O(1)}
X₄: X₄ {O(n)}
Runtime-bound of t₂₄: 1 {O(1)}
Results in: 2⋅X₄+4 {O(n)}

2⋅X₄+4 {O(n)}

Time-Bound by TWN-Loops:

TWN-Loops: t₃₂ 2⋅X₄+4 {O(n)}

relevant size-bounds w.r.t. t₂₄:
X₁: 0 {O(1)}
X₄: X₄ {O(n)}
Runtime-bound of t₂₄: 1 {O(1)}
Results in: 2⋅X₄+4 {O(n)}

2⋅X₄+4 {O(n)}

All Bounds

Timebounds

Overall timebound:4⋅X₃+4⋅X₄+23 {O(n)}
t₂₂: 1 {O(1)}
t₂₃: 2⋅X₃+4 {O(n)}
t₂₄: 1 {O(1)}
t₂₅: 1 {O(1)}
t₂₆: 1 {O(1)}
t₂₇: 1 {O(1)}
t₂₈: 1 {O(1)}
t₂₉: 2⋅X₃+4 {O(n)}
t₃₀: 2⋅X₄+4 {O(n)}
t₃₁: 1 {O(1)}
t₃₂: 2⋅X₄+4 {O(n)}

Costbounds

Overall costbound: 4⋅X₃+4⋅X₄+23 {O(n)}
t₂₂: 1 {O(1)}
t₂₃: 2⋅X₃+4 {O(n)}
t₂₄: 1 {O(1)}
t₂₅: 1 {O(1)}
t₂₆: 1 {O(1)}
t₂₇: 1 {O(1)}
t₂₈: 1 {O(1)}
t₂₉: 2⋅X₃+4 {O(n)}
t₃₀: 2⋅X₄+4 {O(n)}
t₃₁: 1 {O(1)}
t₃₂: 2⋅X₄+4 {O(n)}

Sizebounds

t₂₂, X₀: X₀ {O(n)}
t₂₂, X₁: X₁ {O(n)}
t₂₂, X₃: X₃ {O(n)}
t₂₂, X₄: X₄ {O(n)}
t₂₃, X₀: X₃ {O(n)}
t₂₃, X₁: X₁ {O(n)}
t₂₃, X₃: X₃ {O(n)}
t₂₃, X₄: X₄ {O(n)}
t₂₄, X₀: 0 {O(1)}
t₂₄, X₁: 0 {O(1)}
t₂₄, X₃: X₃ {O(n)}
t₂₄, X₄: X₄ {O(n)}
t₂₅, X₀: 2⋅X₀ {O(n)}
t₂₅, X₁: 2⋅X₁+2⋅X₄+4 {O(n)}
t₂₅, X₃: 3⋅X₃ {O(n)}
t₂₅, X₄: 3⋅X₄ {O(n)}
t₂₆, X₀: X₃ {O(n)}
t₂₆, X₁: X₁ {O(n)}
t₂₆, X₃: X₃ {O(n)}
t₂₆, X₄: X₄ {O(n)}
t₂₇, X₀: X₀ {O(n)}
t₂₇, X₁: X₁ {O(n)}
t₂₇, X₃: X₃ {O(n)}
t₂₇, X₄: X₄ {O(n)}
t₂₈, X₀: X₀ {O(n)}
t₂₈, X₁: X₁ {O(n)}
t₂₈, X₃: X₃ {O(n)}
t₂₈, X₄: X₄ {O(n)}
t₂₉, X₀: X₃ {O(n)}
t₂₉, X₁: X₁ {O(n)}
t₂₉, X₃: X₃ {O(n)}
t₂₉, X₄: X₄ {O(n)}
t₃₀, X₀: 0 {O(1)}
t₃₀, X₁: 2⋅X₄+4 {O(n)}
t₃₀, X₃: X₃ {O(n)}
t₃₀, X₄: X₄ {O(n)}
t₃₁, X₀: 0 {O(1)}
t₃₁, X₁: 2⋅X₄+4 {O(n)}
t₃₁, X₃: X₃ {O(n)}
t₃₁, X₄: X₄ {O(n)}
t₃₂, X₀: 0 {O(1)}
t₃₂, X₁: 2⋅X₄+4 {O(n)}
t₃₂, X₃: X₃ {O(n)}
t₃₂, X₄: X₄ {O(n)}