Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉
Temp_Vars: A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, U, V, W, X, Y, Z
Locations: l0, l1, l2, l3
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉) → l1(8, 0, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉)
t₁: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉) → l1(X₀, X₁+1, U+V, W, X+Y, Z, A1+B1, C1, D1+E1, F1, U+V+D1+E1, U+V-D1-E1, X+Y+A1+B1, X+Y-A1-B1, -3196, G1, H1, I1+J1, K1+J1, J1) :|: X₁ ≤ 7
t₄: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉) → l2(X₀, 0, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉) :|: 8 ≤ X₁
t₂: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉) → l2(X₀, X₁+1, U+V, W, X+Y, Z, A1+B1, C1, D1+E1, F1, U+V+D1+E1, U+V-D1-E1, X+Y+A1+B1, X+Y-A1-B1, -3196, G1, H1, I1+J1, K1+J1, J1) :|: X₁ ≤ 7
t₃: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉) :|: 8 ≤ X₁

Preprocessing

Eliminate variables {A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,U,V,W,X,Y,Z,X₀,X₂,X₃,X₄,X₅,X₆,X₇,X₈,X₉,X₁₀,X₁₁,X₁₂,X₁₃,X₁₄,X₁₅,X₁₆,X₁₇,X₁₈,X₁₉} that do not contribute to the problem

Found invariant X₁ ≤ 8 ∧ 0 ≤ X₁ for location l2

Found invariant X₁ ≤ 8 ∧ 0 ≤ X₁ for location l1

Found invariant X₁ ≤ 8 ∧ 8 ≤ X₁ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₁
Temp_Vars:
Locations: l0, l1, l2, l3
Transitions:
t₁₂: l0(X₁) → l1(0)
t₁₃: l1(X₁) → l1(X₁+1) :|: X₁ ≤ 7 ∧ X₁ ≤ 8 ∧ 0 ≤ X₁
t₁₄: l1(X₁) → l2(0) :|: 8 ≤ X₁ ∧ X₁ ≤ 8 ∧ 0 ≤ X₁
t₁₅: l2(X₁) → l2(X₁+1) :|: X₁ ≤ 7 ∧ X₁ ≤ 8 ∧ 0 ≤ X₁
t₁₆: l2(X₁) → l3(X₁) :|: 8 ≤ X₁ ∧ X₁ ≤ 8 ∧ 0 ≤ X₁

Found invariant X₁ ≤ 8 ∧ 0 ≤ X₁ for location l2

Found invariant X₁ ≤ 8 ∧ 0 ≤ X₁ for location l1

Found invariant X₁ ≤ 8 ∧ 8 ≤ X₁ for location l3

Time-Bound by TWN-Loops:

TWN-Loops: t₁₃ 18 {O(1)}

TWN-Loops:

entry: t₁₂: l0(X₁) → l1(0)
results in twn-loop: twn:Inv: [X₁ ≤ 8 ∧ 0 ≤ X₁] , (X₁) -> (X₁+1) :|: X₁ ≤ 7
order: [X₁]
closed-form:
X₁: X₁ + [[n != 0]] * n^1

Termination: true
Formula:

1 < 0
∨ X₁ < 7 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ 7 ∧ 7 ≤ X₁

Stabilization-Threshold for: X₁ ≤ 7
alphas_abs: 7
M: 0
N: 1
Bound: 16 {O(1)}

relevant size-bounds w.r.t. t₁₂:
Runtime-bound of t₁₂: 1 {O(1)}
Results in: 18 {O(1)}

18 {O(1)}

Found invariant X₁ ≤ 8 ∧ 0 ≤ X₁ for location l2

Found invariant X₁ ≤ 8 ∧ 0 ≤ X₁ for location l1

Found invariant X₁ ≤ 8 ∧ 8 ≤ X₁ for location l3

Time-Bound by TWN-Loops:

TWN-Loops: t₁₅ 18 {O(1)}

TWN-Loops:

entry: t₁₄: l1(X₁) → l2(0) :|: 8 ≤ X₁ ∧ X₁ ≤ 8 ∧ 0 ≤ X₁
results in twn-loop: twn:Inv: [X₁ ≤ 8 ∧ 0 ≤ X₁] , (X₁) -> (X₁+1) :|: X₁ ≤ 7
order: [X₁]
closed-form:
X₁: X₁ + [[n != 0]] * n^1

Termination: true
Formula:

1 < 0
∨ X₁ < 7 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ 7 ∧ 7 ≤ X₁

Stabilization-Threshold for: X₁ ≤ 7
alphas_abs: 7
M: 0
N: 1
Bound: 16 {O(1)}

relevant size-bounds w.r.t. t₁₄:
Runtime-bound of t₁₄: 1 {O(1)}
Results in: 18 {O(1)}

18 {O(1)}

All Bounds

Timebounds

Overall timebound:39 {O(1)}
t₁₂: 1 {O(1)}
t₁₃: 18 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: 18 {O(1)}
t₁₆: 1 {O(1)}

Costbounds

Overall costbound: 39 {O(1)}
t₁₂: 1 {O(1)}
t₁₃: 18 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: 18 {O(1)}
t₁₆: 1 {O(1)}

Sizebounds

t₁₂, X₁: 0 {O(1)}
t₁₃, X₁: 8 {O(1)}
t₁₄, X₁: 0 {O(1)}
t₁₅, X₁: 8 {O(1)}
t₁₆, X₁: 8 {O(1)}