Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars: F, G
Locations: l0, l1, l2, l3
Transitions:
t₄: l0(X₀, X₁, X₂, X₃, X₄) → l1(0, X₁, X₂, F, G)
t₀: l1(X₀, X₁, X₂, X₃, X₄) → l1(X₀+1, X₁, X₂, X₃, X₄) :|: X₀ ≤ 9
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l2(X₀, 0, F, X₃, X₄) :|: 10 ≤ X₀
t₁: l2(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁+1, X₂, X₃, X₄) :|: X₁ ≤ 9
t₂: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: 10 ≤ X₁

Preprocessing

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

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 X₀ ≤ 10 ∧ 0 ≤ 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 l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2, l3
Transitions:
t₁₂: l0(X₀, X₁) → l1(0, X₁)
t₁₃: l1(X₀, X₁) → l1(X₀+1, X₁) :|: X₀ ≤ 9 ∧ X₀ ≤ 10 ∧ 0 ≤ X₀
t₁₄: l1(X₀, X₁) → l2(X₀, 0) :|: 10 ≤ X₀ ∧ X₀ ≤ 10 ∧ 0 ≤ X₀
t₁₅: l2(X₀, X₁) → l2(X₀, X₁+1) :|: X₁ ≤ 9 ∧ X₁ ≤ 10 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 20 ∧ 0 ≤ X₁ ∧ 10 ≤ X₀+X₁ ∧ X₀ ≤ 10+X₁ ∧ X₀ ≤ 10 ∧ 10 ≤ X₀
t₁₆: l2(X₀, X₁) → l3(X₀, X₁) :|: 10 ≤ X₁ ∧ X₁ ≤ 10 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 20 ∧ 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 X₀ ≤ 10 ∧ 0 ≤ 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 l3

Time-Bound by TWN-Loops:

TWN-Loops: t₁₃ 22 {O(1)}

TWN-Loops:

entry: t₁₂: l0(X₀, X₁) → l1(0, X₁)
results in twn-loop: twn:Inv: [X₀ ≤ 10 ∧ 0 ≤ X₀] , (X₀,X₁) -> (X₀+1,X₁) :|: X₀ ≤ 9
order: [X₀]
closed-form:
X₀: X₀ + [[n != 0]] * n^1

Termination: true
Formula:

1 < 0
∨ X₀ < 9 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ 9 ∧ 9 ≤ X₀

Stabilization-Threshold for: X₀ ≤ 9
alphas_abs: 9
M: 0
N: 1
Bound: 20 {O(1)}

relevant size-bounds w.r.t. t₁₂:
Runtime-bound of t₁₂: 1 {O(1)}
Results in: 22 {O(1)}

22 {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 X₀ ≤ 10 ∧ 0 ≤ 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 l3

Time-Bound by TWN-Loops:

TWN-Loops: t₁₅ 22 {O(1)}

TWN-Loops:

entry: t₁₄: l1(X₀, X₁) → l2(X₀, 0) :|: 10 ≤ X₀ ∧ X₀ ≤ 10 ∧ 0 ≤ X₀
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 ≤ 9
order: [X₀; X₁]
closed-form:
X₀: X₀
X₁: X₁ + [[n != 0]] * n^1

Termination: true
Formula:

1 < 0
∨ X₁ < 9 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ 9 ∧ 9 ≤ X₁

Stabilization-Threshold for: X₁ ≤ 9
alphas_abs: X₁+9
M: 0
N: 1
Bound: 2⋅X₁+20 {O(n)}

relevant size-bounds w.r.t. t₁₄:
X₁: 0 {O(1)}
Runtime-bound of t₁₄: 1 {O(1)}
Results in: 22 {O(1)}

22 {O(1)}

All Bounds

Timebounds

Overall timebound:47 {O(1)}
t₁₂: 1 {O(1)}
t₁₃: 22 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: 22 {O(1)}
t₁₆: 1 {O(1)}

Costbounds

Overall costbound: 47 {O(1)}
t₁₂: 1 {O(1)}
t₁₃: 22 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: 22 {O(1)}
t₁₆: 1 {O(1)}

Sizebounds

t₁₂, X₀: 0 {O(1)}
t₁₂, X₁: X₁ {O(n)}
t₁₃, X₀: 10 {O(1)}
t₁₃, X₁: X₁ {O(n)}
t₁₄, X₀: 10 {O(1)}
t₁₄, X₁: 0 {O(1)}
t₁₅, X₀: 10 {O(1)}
t₁₅, X₁: 10 {O(1)}
t₁₆, X₀: 10 {O(1)}
t₁₆, X₁: 10 {O(1)}