Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars: G, H
Locations: l0, l1, l2, l3, l4
Transitions:
t₆: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l1(10, 0, 10, G, 10, H)
t₀: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁+1, X₂, X₃, X₄, X₅) :|: X₁+1 ≤ X₀
t₅: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, 0, X₂, X₃, X₄, X₅) :|: X₀ ≤ X₁
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁+1, X₂, X₃, X₄, X₅) :|: X₁+1 ≤ X₀
t₄: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, 0, X₂, X₃, X₄, X₅) :|: X₀ ≤ X₁
t₂: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁+1, X₂, X₃, X₄, X₅) :|: X₁+1 ≤ X₀
t₃: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ ≤ X₁

Preprocessing

Eliminate variables {G,H,X₂,X₃,X₄,X₅} that do not contribute to the problem

Found invariant 0 ≤ X₁ ∧ 10 ≤ X₀+X₁ ∧ X₀ ≤ 10+X₁ ∧ X₀ ≤ 10 ∧ 10 ≤ X₀ for location l2

Found invariant X₁ ≤ 10 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 20 ∧ 0 ≤ X₁ ∧ 10 ≤ X₀+X₁ ∧ X₀ ≤ 10+X₁ ∧ X₀ ≤ 10 ∧ 10 ≤ X₀ for location l1

Found invariant 10 ≤ X₁ ∧ 20 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 10 ∧ 10 ≤ X₀ for location l4

Found invariant 0 ≤ X₁ ∧ 10 ≤ X₀+X₁ ∧ X₀ ≤ 10+X₁ ∧ X₀ ≤ 10 ∧ 10 ≤ X₀ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2, l3, l4
Transitions:
t₁₇: l0(X₀, X₁) → l1(10, 0)
t₁₈: l1(X₀, X₁) → l1(X₀, X₁+1) :|: X₁+1 ≤ X₀ ∧ X₁ ≤ 10 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 20 ∧ 0 ≤ X₁ ∧ 10 ≤ X₀+X₁ ∧ X₀ ≤ 10+X₁ ∧ X₀ ≤ 10 ∧ 10 ≤ X₀
t₁₉: l1(X₀, X₁) → l2(X₀, 0) :|: X₀ ≤ X₁ ∧ X₁ ≤ 10 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 20 ∧ 0 ≤ X₁ ∧ 10 ≤ X₀+X₁ ∧ X₀ ≤ 10+X₁ ∧ X₀ ≤ 10 ∧ 10 ≤ X₀
t₂₀: l2(X₀, X₁) → l2(X₀, X₁+1) :|: X₁+1 ≤ X₀ ∧ 0 ≤ X₁ ∧ 10 ≤ X₀+X₁ ∧ X₀ ≤ 10+X₁ ∧ X₀ ≤ 10 ∧ 10 ≤ X₀
t₂₁: l2(X₀, X₁) → l3(X₀, 0) :|: X₀ ≤ X₁ ∧ 0 ≤ X₁ ∧ 10 ≤ X₀+X₁ ∧ X₀ ≤ 10+X₁ ∧ X₀ ≤ 10 ∧ 10 ≤ X₀
t₂₂: l3(X₀, X₁) → l3(X₀, X₁+1) :|: X₁+1 ≤ X₀ ∧ 0 ≤ X₁ ∧ 10 ≤ X₀+X₁ ∧ X₀ ≤ 10+X₁ ∧ X₀ ≤ 10 ∧ 10 ≤ X₀
t₂₃: l3(X₀, X₁) → l4(X₀, X₁) :|: X₀ ≤ X₁ ∧ 0 ≤ X₁ ∧ 10 ≤ X₀+X₁ ∧ X₀ ≤ 10+X₁ ∧ X₀ ≤ 10 ∧ 10 ≤ X₀

Found invariant X₁ ≤ 10 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 20 ∧ 0 ≤ X₁ ∧ 10 ≤ X₀+X₁ ∧ X₀ ≤ 10+X₁ ∧ X₀ ≤ 10 ∧ 10 ≤ X₀ for location l2

Found invariant X₁ ≤ 10 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 20 ∧ 0 ≤ X₁ ∧ 10 ≤ X₀+X₁ ∧ X₀ ≤ 10+X₁ ∧ X₀ ≤ 10 ∧ 10 ≤ X₀ for location l1

Found invariant X₁ ≤ 10 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 20 ∧ 10 ≤ X₁ ∧ 20 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 10 ∧ 10 ≤ X₀ for location l4

Found invariant X₁ ≤ 10 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 20 ∧ 0 ≤ X₁ ∧ 10 ≤ X₀+X₁ ∧ X₀ ≤ 10+X₁ ∧ X₀ ≤ 10 ∧ 10 ≤ X₀ for location l3

Time-Bound by TWN-Loops:

TWN-Loops: t₁₈ 26 {O(1)}

TWN-Loops:

entry: t₁₇: l0(X₀, X₁) → l1(10, 0)
results in twn-loop: twn:Inv: [X₁ ≤ 10 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 20 ∧ 0 ≤ X₁ ∧ 10 ≤ X₀+X₁ ∧ X₀ ≤ 10+X₁ ∧ X₀ ≤ 10 ∧ 10 ≤ X₀] , (X₀,X₁) -> (X₀,X₁+1) :|: X₁+1 ≤ X₀
order: [X₀; X₁]
closed-form:
X₀: X₀
X₁: X₁ + [[n != 0]] * n^1

Termination: true
Formula:

1 < 0
∨ X₁+1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁+1 ≤ X₀ ∧ X₀ ≤ X₁+1

Stabilization-Threshold for: X₁+1 ≤ X₀
alphas_abs: X₁+1+X₀
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+4 {O(n)}

relevant size-bounds w.r.t. t₁₇:
X₀: 10 {O(1)}
X₁: 0 {O(1)}
Runtime-bound of t₁₇: 1 {O(1)}
Results in: 26 {O(1)}

26 {O(1)}

Found invariant X₁ ≤ 10 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 20 ∧ 0 ≤ X₁ ∧ 10 ≤ X₀+X₁ ∧ X₀ ≤ 10+X₁ ∧ X₀ ≤ 10 ∧ 10 ≤ X₀ for location l2

Found invariant X₁ ≤ 10 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 20 ∧ 0 ≤ X₁ ∧ 10 ≤ X₀+X₁ ∧ X₀ ≤ 10+X₁ ∧ X₀ ≤ 10 ∧ 10 ≤ X₀ for location l1

Found invariant X₁ ≤ 10 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 20 ∧ 10 ≤ X₁ ∧ 20 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 10 ∧ 10 ≤ X₀ for location l4

Found invariant X₁ ≤ 10 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 20 ∧ 0 ≤ X₁ ∧ 10 ≤ X₀+X₁ ∧ X₀ ≤ 10+X₁ ∧ X₀ ≤ 10 ∧ 10 ≤ X₀ for location l3

Time-Bound by TWN-Loops:

TWN-Loops: t₂₀ 26 {O(1)}

TWN-Loops:

entry: t₁₉: l1(X₀, X₁) → l2(X₀, 0) :|: X₀ ≤ X₁ ∧ X₁ ≤ 10 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 20 ∧ 0 ≤ X₁ ∧ 10 ≤ X₀+X₁ ∧ X₀ ≤ 10+X₁ ∧ X₀ ≤ 10 ∧ 10 ≤ X₀
results in twn-loop: twn:Inv: [0 ≤ X₁ ∧ 10 ≤ X₀+X₁ ∧ X₀ ≤ 10+X₁ ∧ X₀ ≤ 10 ∧ 10 ≤ X₀] , (X₀,X₁) -> (X₀,X₁+1) :|: X₁+1 ≤ X₀
order: [X₀; X₁]
closed-form:
X₀: X₀
X₁: X₁ + [[n != 0]] * n^1

Termination: true
Formula:

1 < 0
∨ X₁+1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁+1 ≤ X₀ ∧ X₀ ≤ X₁+1

Stabilization-Threshold for: X₁+1 ≤ X₀
alphas_abs: X₁+1+X₀
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+4 {O(n)}

relevant size-bounds w.r.t. t₁₉:
X₀: 10 {O(1)}
X₁: 0 {O(1)}
Runtime-bound of t₁₉: 1 {O(1)}
Results in: 26 {O(1)}

26 {O(1)}

Found invariant X₁ ≤ 10 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 20 ∧ 0 ≤ X₁ ∧ 10 ≤ X₀+X₁ ∧ X₀ ≤ 10+X₁ ∧ X₀ ≤ 10 ∧ 10 ≤ X₀ for location l2

Found invariant X₁ ≤ 10 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 20 ∧ 0 ≤ X₁ ∧ 10 ≤ X₀+X₁ ∧ X₀ ≤ 10+X₁ ∧ X₀ ≤ 10 ∧ 10 ≤ X₀ for location l1

Found invariant X₁ ≤ 10 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 20 ∧ 10 ≤ X₁ ∧ 20 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 10 ∧ 10 ≤ X₀ for location l4

Found invariant X₁ ≤ 10 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 20 ∧ 0 ≤ X₁ ∧ 10 ≤ X₀+X₁ ∧ X₀ ≤ 10+X₁ ∧ X₀ ≤ 10 ∧ 10 ≤ X₀ for location l3

Time-Bound by TWN-Loops:

TWN-Loops: t₂₂ 26 {O(1)}

TWN-Loops:

entry: t₂₁: l2(X₀, X₁) → l3(X₀, 0) :|: X₀ ≤ X₁ ∧ 0 ≤ X₁ ∧ 10 ≤ X₀+X₁ ∧ X₀ ≤ 10+X₁ ∧ X₀ ≤ 10 ∧ 10 ≤ X₀
results in twn-loop: twn:Inv: [0 ≤ X₁ ∧ 10 ≤ X₀+X₁ ∧ X₀ ≤ 10+X₁ ∧ X₀ ≤ 10 ∧ 10 ≤ X₀] , (X₀,X₁) -> (X₀,X₁+1) :|: X₁+1 ≤ X₀
order: [X₀; X₁]
closed-form:
X₀: X₀
X₁: X₁ + [[n != 0]] * n^1

Termination: true
Formula:

1 < 0
∨ X₁+1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁+1 ≤ X₀ ∧ X₀ ≤ X₁+1

Stabilization-Threshold for: X₁+1 ≤ X₀
alphas_abs: X₁+1+X₀
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+4 {O(n)}

relevant size-bounds w.r.t. t₂₁:
X₀: 10 {O(1)}
X₁: 0 {O(1)}
Runtime-bound of t₂₁: 1 {O(1)}
Results in: 26 {O(1)}

26 {O(1)}

All Bounds

Timebounds

Overall timebound:82 {O(1)}
t₁₇: 1 {O(1)}
t₁₈: 26 {O(1)}
t₁₉: 1 {O(1)}
t₂₀: 26 {O(1)}
t₂₁: 1 {O(1)}
t₂₂: 26 {O(1)}
t₂₃: 1 {O(1)}

Costbounds

Overall costbound: 82 {O(1)}
t₁₇: 1 {O(1)}
t₁₈: 26 {O(1)}
t₁₉: 1 {O(1)}
t₂₀: 26 {O(1)}
t₂₁: 1 {O(1)}
t₂₂: 26 {O(1)}
t₂₃: 1 {O(1)}

Sizebounds

t₁₇, X₀: 10 {O(1)}
t₁₇, X₁: 0 {O(1)}
t₁₈, X₀: 10 {O(1)}
t₁₈, X₁: 10 {O(1)}
t₁₉, X₀: 10 {O(1)}
t₁₉, X₁: 0 {O(1)}
t₂₀, X₀: 10 {O(1)}
t₂₀, X₁: 10 {O(1)}
t₂₁, X₀: 10 {O(1)}
t₂₁, X₁: 0 {O(1)}
t₂₂, X₀: 10 {O(1)}
t₂₂, X₁: 10 {O(1)}
t₂₃, X₀: 10 {O(1)}
t₂₃, X₁: 10 {O(1)}