Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, X₅)
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 < X₀
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₁, X₃, X₄, X₅) :|: X₀ ≤ 0
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₄, X₅, X₂, X₃, X₄, X₅)
t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀-1, X₁+2, X₂, X₃, X₄, X₅)
t₅: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 < X₂
t₆: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₂, X₄, X₅) :|: X₂ ≤ 0
t₇: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂-1, X₃, X₄, X₅)
t₈: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 < X₃
t₉: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l8(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₃ ≤ 0
t₁₀: l7(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃-1, X₄, X₅)
t₁₁: l8(X₀, X₁, X₂, X₃, X₄, X₅) → l9(X₀, X₁, X₂, X₃, X₄, X₅)

Preprocessing

Found invariant X₅ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ X₃ ≤ X₁ ∧ X₀+X₃ ≤ 0 ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₀+X₂ ≤ 0 ∧ X₀ ≤ 0 for location l6

Found invariant 1 ≤ 0 for location l7

Found invariant X₅ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l5

Found invariant X₅ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ X₃ ≤ X₁ ∧ X₀+X₃ ≤ 0 ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₀+X₂ ≤ 0 ∧ X₀ ≤ 0 for location l8

Found invariant X₅ ≤ X₁ ∧ X₀ ≤ X₄ for location l1

Found invariant X₅ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₁ ∧ X₀ ≤ 0 for location l4

Found invariant X₅ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ X₃ ≤ X₁ ∧ X₀+X₃ ≤ 0 ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₀+X₂ ≤ 0 ∧ X₀ ≤ 0 for location l9

Found invariant X₅ ≤ X₁ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 1 ≤ X₀ for location l3

Cut unsatisfiable transition t₈: l6→l7

Cut unsatisfiable transition t₁₀: l7→l6

Cut unreachable locations [l7] from the program graph

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, X₅)
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 < X₀ ∧ X₅ ≤ X₁ ∧ X₀ ≤ X₄
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₁, X₃, X₄, X₅) :|: X₀ ≤ 0 ∧ X₅ ≤ X₁ ∧ X₀ ≤ X₄
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₄, X₅, X₂, X₃, X₄, X₅)
t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀-1, X₁+2, X₂, X₃, X₄, X₅) :|: X₅ ≤ X₁ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 1 ≤ X₀
t₅: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 < X₂ ∧ X₅ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₁ ∧ X₀ ≤ 0
t₆: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₂, X₄, X₅) :|: X₂ ≤ 0 ∧ X₅ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₁ ∧ X₀ ≤ 0
t₇: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂-1, X₃, X₄, X₅) :|: X₅ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0
t₉: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l8(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₃ ≤ 0 ∧ X₅ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ X₃ ≤ X₁ ∧ X₀+X₃ ≤ 0 ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₀+X₂ ≤ 0 ∧ X₀ ≤ 0
t₁₁: l8(X₀, X₁, X₂, X₃, X₄, X₅) → l9(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₅ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ X₃ ≤ X₁ ∧ X₀+X₃ ≤ 0 ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₀+X₂ ≤ 0 ∧ X₀ ≤ 0

Found invariant X₅ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ X₃ ≤ X₁ ∧ X₀+X₃ ≤ 0 ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₀+X₂ ≤ 0 ∧ X₀ ≤ 0 for location l6

Found invariant X₅ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l5

Found invariant X₅ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ X₃ ≤ X₁ ∧ X₀+X₃ ≤ 0 ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₀+X₂ ≤ 0 ∧ X₀ ≤ 0 for location l8

Found invariant X₅ ≤ X₁ ∧ X₀ ≤ X₄ for location l1

Found invariant X₅ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₁ ∧ X₀ ≤ 0 for location l4

Found invariant X₅ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ X₃ ≤ X₁ ∧ X₀+X₃ ≤ 0 ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₀+X₂ ≤ 0 ∧ X₀ ≤ 0 for location l9

Found invariant X₅ ≤ X₁ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 1 ≤ X₀ for location l3

Time-Bound by TWN-Loops:

TWN-Loops: t₂ 2⋅X₄+4 {O(n)}

TWN-Loops:

entry: t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₄, X₅, X₂, X₃, X₄, X₅)
results in twn-loop: twn:Inv: [X₅ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₅ ≤ X₁ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 1 ≤ X₀] , (X₀,X₁,X₂,X₃,X₄,X₅) -> (X₀-1,X₁+2,X₂,X₃,X₄,X₅) :|: 0 < X₀
order: [X₀; X₁; X₄; X₅]
closed-form:
X₀: X₀ + [[n != 0]] * -1 * n^1
X₁: X₁ + [[n != 0]] * 2 * n^1
X₄: X₄
X₅: X₅

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. t₁:
X₀: X₄ {O(n)}
Runtime-bound of t₁: 1 {O(1)}
Results in: 2⋅X₄+4 {O(n)}

2⋅X₄+4 {O(n)}

Time-Bound by TWN-Loops:

TWN-Loops: t₄ 2⋅X₄+4 {O(n)}

relevant size-bounds w.r.t. t₁:
X₀: X₄ {O(n)}
Runtime-bound of t₁: 1 {O(1)}
Results in: 2⋅X₄+4 {O(n)}

2⋅X₄+4 {O(n)}

Found invariant X₅ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ X₃ ≤ X₁ ∧ X₀+X₃ ≤ 0 ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₀+X₂ ≤ 0 ∧ X₀ ≤ 0 for location l6

Found invariant X₅ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l5

Found invariant X₅ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ X₃ ≤ X₁ ∧ X₀+X₃ ≤ 0 ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₀+X₂ ≤ 0 ∧ X₀ ≤ 0 for location l8

Found invariant X₅ ≤ X₁ ∧ X₀ ≤ X₄ for location l1

Found invariant X₅ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₁ ∧ X₀ ≤ 0 for location l4

Found invariant X₅ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ X₃ ≤ X₁ ∧ X₀+X₃ ≤ 0 ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₀+X₂ ≤ 0 ∧ X₀ ≤ 0 for location l9

Found invariant X₅ ≤ X₁ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 1 ≤ X₀ for location l3

Time-Bound by TWN-Loops:

TWN-Loops: t₅ 4⋅X₅+8⋅X₄+20 {O(n)}

TWN-Loops:

entry: t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₁, X₃, X₄, X₅) :|: X₀ ≤ 0 ∧ X₅ ≤ X₁ ∧ X₀ ≤ X₄
results in twn-loop: twn:Inv: [X₅ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₁ ∧ X₀ ≤ 0 ∧ X₅ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0] , (X₀,X₁,X₂,X₃,X₄,X₅) -> (X₀,X₁,X₂-1,X₃,X₄,X₅) :|: 0 < X₂
order: [X₀; X₁; X₂; X₄; X₅]
closed-form:
X₀: X₀
X₁: X₁
X₂: X₂ + [[n != 0]] * -1 * n^1
X₄: X₄
X₅: X₅

Termination: true
Formula:

1 < 0
∨ 0 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1

Stabilization-Threshold for: 0 < X₂
alphas_abs: X₂
M: 0
N: 1
Bound: 2⋅X₂+2 {O(n)}

relevant size-bounds w.r.t. t₃:
X₂: 2⋅X₅+4⋅X₄+8 {O(n)}
Runtime-bound of t₃: 1 {O(1)}
Results in: 4⋅X₅+8⋅X₄+20 {O(n)}

4⋅X₅+8⋅X₄+20 {O(n)}

Time-Bound by TWN-Loops:

TWN-Loops: t₇ 4⋅X₅+8⋅X₄+20 {O(n)}

relevant size-bounds w.r.t. t₃:
X₂: 2⋅X₅+4⋅X₄+8 {O(n)}
Runtime-bound of t₃: 1 {O(1)}
Results in: 4⋅X₅+8⋅X₄+20 {O(n)}

4⋅X₅+8⋅X₄+20 {O(n)}

All Bounds

Timebounds

Overall timebound:20⋅X₄+8⋅X₅+54 {O(n)}
t₀: 1 {O(1)}
t₂: 2⋅X₄+4 {O(n)}
t₃: 1 {O(1)}
t₁: 1 {O(1)}
t₄: 2⋅X₄+4 {O(n)}
t₅: 4⋅X₅+8⋅X₄+20 {O(n)}
t₆: 1 {O(1)}
t₇: 4⋅X₅+8⋅X₄+20 {O(n)}
t₉: 1 {O(1)}
t₁₁: 1 {O(1)}

Costbounds

Overall costbound: 20⋅X₄+8⋅X₅+54 {O(n)}
t₀: 1 {O(1)}
t₂: 2⋅X₄+4 {O(n)}
t₃: 1 {O(1)}
t₁: 1 {O(1)}
t₄: 2⋅X₄+4 {O(n)}
t₅: 4⋅X₅+8⋅X₄+20 {O(n)}
t₆: 1 {O(1)}
t₇: 4⋅X₅+8⋅X₄+20 {O(n)}
t₉: 1 {O(1)}
t₁₁: 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)}
t₂, X₀: X₄ {O(n)}
t₂, X₁: 4⋅X₄+X₅+8 {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₂, X₄: X₄ {O(n)}
t₂, X₅: X₅ {O(n)}
t₃, X₀: 2⋅X₄ {O(n)}
t₃, X₁: 2⋅X₅+4⋅X₄+8 {O(n)}
t₃, X₂: 2⋅X₅+4⋅X₄+8 {O(n)}
t₃, X₃: 2⋅X₃ {O(n)}
t₃, X₄: 2⋅X₄ {O(n)}
t₃, X₅: 2⋅X₅ {O(n)}
t₁, X₀: X₄ {O(n)}
t₁, X₁: X₅ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₁, X₅: X₅ {O(n)}
t₄, X₀: X₄ {O(n)}
t₄, X₁: 4⋅X₄+X₅+8 {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₄, X₄: X₄ {O(n)}
t₄, X₅: X₅ {O(n)}
t₅, X₀: 2⋅X₄ {O(n)}
t₅, X₁: 2⋅X₅+4⋅X₄+8 {O(n)}
t₅, X₂: 2⋅X₅+4⋅X₄+8 {O(n)}
t₅, X₃: 2⋅X₃ {O(n)}
t₅, X₄: 2⋅X₄ {O(n)}
t₅, X₅: 2⋅X₅ {O(n)}
t₆, X₀: 4⋅X₄ {O(n)}
t₆, X₁: 4⋅X₅+8⋅X₄+16 {O(n)}
t₆, X₂: 4⋅X₅+8⋅X₄+16 {O(n)}
t₆, X₃: 4⋅X₅+8⋅X₄+16 {O(n)}
t₆, X₄: 4⋅X₄ {O(n)}
t₆, X₅: 4⋅X₅ {O(n)}
t₇, X₀: 2⋅X₄ {O(n)}
t₇, X₁: 2⋅X₅+4⋅X₄+8 {O(n)}
t₇, X₂: 2⋅X₅+4⋅X₄+8 {O(n)}
t₇, X₃: 2⋅X₃ {O(n)}
t₇, X₄: 2⋅X₄ {O(n)}
t₇, X₅: 2⋅X₅ {O(n)}
t₉, X₀: 4⋅X₄ {O(n)}
t₉, X₁: 4⋅X₅+8⋅X₄+16 {O(n)}
t₉, X₂: 4⋅X₅+8⋅X₄+16 {O(n)}
t₉, X₃: 4⋅X₅+8⋅X₄+16 {O(n)}
t₉, X₄: 4⋅X₄ {O(n)}
t₉, X₅: 4⋅X₅ {O(n)}
t₁₁, X₀: 4⋅X₄ {O(n)}
t₁₁, X₁: 4⋅X₅+8⋅X₄+16 {O(n)}
t₁₁, X₂: 4⋅X₅+8⋅X₄+16 {O(n)}
t₁₁, X₃: 4⋅X₅+8⋅X₄+16 {O(n)}
t₁₁, X₄: 4⋅X₄ {O(n)}
t₁₁, X₅: 4⋅X₅ {O(n)}