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, l4
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉) → l1(0, 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(U, X₁+1, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉) :|: X₁ ≤ 63
t₆: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉) → l4(X₀, X₁, 7, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉) :|: 64 ≤ X₁
t₃: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉) → l2(X₀, X₁, X₂-1, 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, G1, H1, I1+J1, K1+J1, J1) :|: 0 ≤ X₂
t₄: 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) :|: X₂+1 ≤ 0
t₅: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉) → l2(X₀, X₁, 7, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉) :|: X₂+1 ≤ 0
t₂: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉) → l4(X₀, X₁, X₂-1, 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, G1, H1, I1+J1, K1+J1, J1) :|: 0 ≤ X₂

Preprocessing

Eliminate variables {A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,U,V,W,X,Y,Z,X₀,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 X₂ ≤ 7 ∧ 57+X₂ ≤ X₁ ∧ X₁+X₂ ≤ 71 ∧ 0 ≤ 1+X₂ ∧ 63 ≤ X₁+X₂ ∧ X₁ ≤ 65+X₂ ∧ X₁ ≤ 64 ∧ 64 ≤ X₁ for location l2

Found invariant X₁ ≤ 64 ∧ 0 ≤ X₁ for location l1

Found invariant X₂ ≤ 7 ∧ 57+X₂ ≤ X₁ ∧ X₁+X₂ ≤ 71 ∧ 0 ≤ 1+X₂ ∧ 63 ≤ X₁+X₂ ∧ X₁ ≤ 65+X₂ ∧ X₁ ≤ 64 ∧ 64 ≤ X₁ for location l4

Found invariant 1+X₂ ≤ 0 ∧ 65+X₂ ≤ X₁ ∧ X₁+X₂ ≤ 63 ∧ 0 ≤ 1+X₂ ∧ 63 ≤ X₁+X₂ ∧ X₁ ≤ 65+X₂ ∧ X₁ ≤ 64 ∧ 64 ≤ X₁ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3, l4
Transitions:
t₁₇: l0(X₁, X₂) → l1(0, X₂)
t₁₈: l1(X₁, X₂) → l1(X₁+1, X₂) :|: X₁ ≤ 63 ∧ X₁ ≤ 64 ∧ 0 ≤ X₁
t₁₉: l1(X₁, X₂) → l4(X₁, 7) :|: 64 ≤ X₁ ∧ X₁ ≤ 64 ∧ 0 ≤ X₁
t₂₀: l2(X₁, X₂) → l2(X₁, X₂-1) :|: 0 ≤ X₂ ∧ X₂ ≤ 7 ∧ 57+X₂ ≤ X₁ ∧ X₁+X₂ ≤ 71 ∧ 0 ≤ 1+X₂ ∧ 63 ≤ X₁+X₂ ∧ X₁ ≤ 65+X₂ ∧ X₁ ≤ 64 ∧ 64 ≤ X₁
t₂₁: l2(X₁, X₂) → l3(X₁, X₂) :|: X₂+1 ≤ 0 ∧ X₂ ≤ 7 ∧ 57+X₂ ≤ X₁ ∧ X₁+X₂ ≤ 71 ∧ 0 ≤ 1+X₂ ∧ 63 ≤ X₁+X₂ ∧ X₁ ≤ 65+X₂ ∧ X₁ ≤ 64 ∧ 64 ≤ X₁
t₂₃: l4(X₁, X₂) → l2(X₁, 7) :|: X₂+1 ≤ 0 ∧ X₂ ≤ 7 ∧ 57+X₂ ≤ X₁ ∧ X₁+X₂ ≤ 71 ∧ 0 ≤ 1+X₂ ∧ 63 ≤ X₁+X₂ ∧ X₁ ≤ 65+X₂ ∧ X₁ ≤ 64 ∧ 64 ≤ X₁
t₂₂: l4(X₁, X₂) → l4(X₁, X₂-1) :|: 0 ≤ X₂ ∧ X₂ ≤ 7 ∧ 57+X₂ ≤ X₁ ∧ X₁+X₂ ≤ 71 ∧ 0 ≤ 1+X₂ ∧ 63 ≤ X₁+X₂ ∧ X₁ ≤ 65+X₂ ∧ X₁ ≤ 64 ∧ 64 ≤ X₁

Found invariant X₂ ≤ 7 ∧ 57+X₂ ≤ X₁ ∧ X₁+X₂ ≤ 71 ∧ 0 ≤ 1+X₂ ∧ 63 ≤ X₁+X₂ ∧ X₁ ≤ 65+X₂ ∧ X₁ ≤ 64 ∧ 64 ≤ X₁ for location l2

Found invariant X₁ ≤ 64 ∧ 0 ≤ X₁ for location l1

Found invariant X₂ ≤ 7 ∧ 57+X₂ ≤ X₁ ∧ X₁+X₂ ≤ 71 ∧ 0 ≤ 1+X₂ ∧ 63 ≤ X₁+X₂ ∧ X₁ ≤ 65+X₂ ∧ X₁ ≤ 64 ∧ 64 ≤ X₁ for location l4

Found invariant 1+X₂ ≤ 0 ∧ 65+X₂ ≤ X₁ ∧ X₁+X₂ ≤ 63 ∧ 0 ≤ 1+X₂ ∧ 63 ≤ X₁+X₂ ∧ X₁ ≤ 65+X₂ ∧ X₁ ≤ 64 ∧ 64 ≤ X₁ for location l3

Time-Bound by TWN-Loops:

TWN-Loops: t₁₈ 130 {O(1)}

TWN-Loops:

entry: t₁₇: l0(X₁, X₂) → l1(0, X₂)
results in twn-loop: twn:Inv: [X₁ ≤ 64 ∧ 0 ≤ X₁] , (X₁,X₂) -> (X₁+1,X₂) :|: X₁ ≤ 63
order: [X₁]
closed-form:
X₁: X₁ + [[n != 0]] * n^1

Termination: true
Formula:

1 < 0
∨ X₁ < 63 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ 63 ∧ 63 ≤ X₁

Stabilization-Threshold for: X₁ ≤ 63
alphas_abs: 63
M: 0
N: 1
Bound: 128 {O(1)}

relevant size-bounds w.r.t. t₁₇:
Runtime-bound of t₁₇: 1 {O(1)}
Results in: 130 {O(1)}

130 {O(1)}

Found invariant X₂ ≤ 7 ∧ 57+X₂ ≤ X₁ ∧ X₁+X₂ ≤ 71 ∧ 0 ≤ 1+X₂ ∧ 63 ≤ X₁+X₂ ∧ X₁ ≤ 65+X₂ ∧ X₁ ≤ 64 ∧ 64 ≤ X₁ for location l2

Found invariant X₁ ≤ 64 ∧ 0 ≤ X₁ for location l1

Found invariant X₂ ≤ 7 ∧ 57+X₂ ≤ X₁ ∧ X₁+X₂ ≤ 71 ∧ 0 ≤ 1+X₂ ∧ 63 ≤ X₁+X₂ ∧ X₁ ≤ 65+X₂ ∧ X₁ ≤ 64 ∧ 64 ≤ X₁ for location l4

Found invariant 1+X₂ ≤ 0 ∧ 65+X₂ ≤ X₁ ∧ X₁+X₂ ≤ 63 ∧ 0 ≤ 1+X₂ ∧ 63 ≤ X₁+X₂ ∧ X₁ ≤ 65+X₂ ∧ X₁ ≤ 64 ∧ 64 ≤ X₁ for location l3

Time-Bound by TWN-Loops:

TWN-Loops: t₂₂ 18 {O(1)}

TWN-Loops:

entry: t₁₉: l1(X₁, X₂) → l4(X₁, 7) :|: 64 ≤ X₁ ∧ X₁ ≤ 64 ∧ 0 ≤ X₁
results in twn-loop: twn:Inv: [X₂ ≤ 7 ∧ 57+X₂ ≤ X₁ ∧ X₁+X₂ ≤ 71 ∧ 0 ≤ 1+X₂ ∧ 63 ≤ X₁+X₂ ∧ X₁ ≤ 65+X₂ ∧ X₁ ≤ 64 ∧ 64 ≤ X₁] , (X₁,X₂) -> (X₁,X₂-1) :|: 0 ≤ X₂
order: [X₁; X₂]
closed-form:
X₁: X₁
X₂: X₂ + [[n != 0]] * -1 * n^1

Termination: true
Formula:

1 < 0
∨ 0 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₂ ∧ X₂ ≤ 0

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

relevant size-bounds w.r.t. t₁₉:
X₂: 7 {O(1)}
Runtime-bound of t₁₉: 1 {O(1)}
Results in: 18 {O(1)}

18 {O(1)}

Found invariant X₂ ≤ 7 ∧ 57+X₂ ≤ X₁ ∧ X₁+X₂ ≤ 71 ∧ 0 ≤ 1+X₂ ∧ 63 ≤ X₁+X₂ ∧ X₁ ≤ 65+X₂ ∧ X₁ ≤ 64 ∧ 64 ≤ X₁ for location l2

Found invariant X₁ ≤ 64 ∧ 0 ≤ X₁ for location l1

Found invariant X₂ ≤ 7 ∧ 57+X₂ ≤ X₁ ∧ X₁+X₂ ≤ 71 ∧ 0 ≤ 1+X₂ ∧ 63 ≤ X₁+X₂ ∧ X₁ ≤ 65+X₂ ∧ X₁ ≤ 64 ∧ 64 ≤ X₁ for location l4

Found invariant 1+X₂ ≤ 0 ∧ 65+X₂ ≤ X₁ ∧ X₁+X₂ ≤ 63 ∧ 0 ≤ 1+X₂ ∧ 63 ≤ X₁+X₂ ∧ X₁ ≤ 65+X₂ ∧ X₁ ≤ 64 ∧ 64 ≤ X₁ for location l3

Time-Bound by TWN-Loops:

TWN-Loops: t₂₀ 18 {O(1)}

TWN-Loops:

entry: t₂₃: l4(X₁, X₂) → l2(X₁, 7) :|: X₂+1 ≤ 0 ∧ X₂ ≤ 7 ∧ 57+X₂ ≤ X₁ ∧ X₁+X₂ ≤ 71 ∧ 0 ≤ 1+X₂ ∧ 63 ≤ X₁+X₂ ∧ X₁ ≤ 65+X₂ ∧ X₁ ≤ 64 ∧ 64 ≤ X₁
results in twn-loop: twn:Inv: [X₂ ≤ 7 ∧ 57+X₂ ≤ X₁ ∧ X₁+X₂ ≤ 71 ∧ 0 ≤ 1+X₂ ∧ 63 ≤ X₁+X₂ ∧ X₁ ≤ 65+X₂ ∧ X₁ ≤ 64 ∧ 64 ≤ X₁] , (X₁,X₂) -> (X₁,X₂-1) :|: 0 ≤ X₂
order: [X₁; X₂]
closed-form:
X₁: X₁
X₂: X₂ + [[n != 0]] * -1 * n^1

Termination: true
Formula:

1 < 0
∨ 0 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₂ ∧ X₂ ≤ 0

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

relevant size-bounds w.r.t. t₂₃:
X₂: 7 {O(1)}
Runtime-bound of t₂₃: 1 {O(1)}
Results in: 18 {O(1)}

18 {O(1)}

All Bounds

Timebounds

Overall timebound:170 {O(1)}
t₁₇: 1 {O(1)}
t₁₈: 130 {O(1)}
t₁₉: 1 {O(1)}
t₂₀: 18 {O(1)}
t₂₁: 1 {O(1)}
t₂₂: 18 {O(1)}
t₂₃: 1 {O(1)}

Costbounds

Overall costbound: 170 {O(1)}
t₁₇: 1 {O(1)}
t₁₈: 130 {O(1)}
t₁₉: 1 {O(1)}
t₂₀: 18 {O(1)}
t₂₁: 1 {O(1)}
t₂₂: 18 {O(1)}
t₂₃: 1 {O(1)}

Sizebounds

t₁₇, X₁: 0 {O(1)}
t₁₇, X₂: X₂ {O(n)}
t₁₈, X₁: 64 {O(1)}
t₁₈, X₂: X₂ {O(n)}
t₁₉, X₁: 64 {O(1)}
t₁₉, X₂: 7 {O(1)}
t₂₀, X₁: 64 {O(1)}
t₂₀, X₂: 6 {O(1)}
t₂₁, X₁: 64 {O(1)}
t₂₁, X₂: 1 {O(1)}
t₂₂, X₁: 64 {O(1)}
t₂₂, X₂: 6 {O(1)}
t₂₃, X₁: 64 {O(1)}
t₂₃, X₂: 7 {O(1)}