Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars: D
Locations: l0, l1, l2, l3
Transitions:
t₀: l0(X₀, X₁, X₂) → l1(0, D, 0)
t₁: l1(X₀, X₁, X₂) → l1(X₀, X₁, X₂+1) :|: X₂ ≤ 49
t₄: l1(X₀, X₁, X₂) → l2(0, X₁, X₂) :|: 50 ≤ X₂
t₂: l2(X₀, X₁, X₂) → l2(X₀+1, X₁, X₂) :|: X₀ ≤ 49
t₃: l2(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: 50 ≤ X₀

Preprocessing

Eliminate variables {D,X₁} that do not contribute to the problem

Found invariant X₂ ≤ 50 ∧ X₂ ≤ 50+X₀ ∧ X₀+X₂ ≤ 100 ∧ 50 ≤ X₂ ∧ 50 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 50 ∧ 0 ≤ X₀ for location l2

Found invariant X₂ ≤ 50 ∧ X₂ ≤ 50+X₀ ∧ X₀+X₂ ≤ 50 ∧ 0 ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location l1

Found invariant X₂ ≤ 50 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 100 ∧ 50 ≤ X₂ ∧ 100 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 50 ∧ 50 ≤ X₀ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₂
Temp_Vars:
Locations: l0, l1, l2, l3
Transitions:
t₁₂: l0(X₀, X₂) → l1(0, 0)
t₁₃: l1(X₀, X₂) → l1(X₀, X₂+1) :|: X₂ ≤ 49 ∧ X₂ ≤ 50 ∧ X₂ ≤ 50+X₀ ∧ X₀+X₂ ≤ 50 ∧ 0 ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
t₁₄: l1(X₀, X₂) → l2(0, X₂) :|: 50 ≤ X₂ ∧ X₂ ≤ 50 ∧ X₂ ≤ 50+X₀ ∧ X₀+X₂ ≤ 50 ∧ 0 ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
t₁₅: l2(X₀, X₂) → l2(X₀+1, X₂) :|: X₀ ≤ 49 ∧ X₂ ≤ 50 ∧ X₂ ≤ 50+X₀ ∧ X₀+X₂ ≤ 100 ∧ 50 ≤ X₂ ∧ 50 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 50 ∧ 0 ≤ X₀
t₁₆: l2(X₀, X₂) → l3(X₀, X₂) :|: 50 ≤ X₀ ∧ X₂ ≤ 50 ∧ X₂ ≤ 50+X₀ ∧ X₀+X₂ ≤ 100 ∧ 50 ≤ X₂ ∧ 50 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 50 ∧ 0 ≤ X₀

Found invariant X₂ ≤ 50 ∧ X₂ ≤ 50+X₀ ∧ X₀+X₂ ≤ 100 ∧ 50 ≤ X₂ ∧ 50 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 50 ∧ 0 ≤ X₀ for location l2

Found invariant X₂ ≤ 50 ∧ X₂ ≤ 50+X₀ ∧ X₀+X₂ ≤ 50 ∧ 0 ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location l1

Found invariant X₂ ≤ 50 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 100 ∧ 50 ≤ X₂ ∧ 100 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 50 ∧ 50 ≤ X₀ for location l3

Time-Bound by TWN-Loops:

TWN-Loops: t₁₃ 102 {O(1)}

TWN-Loops:

entry: t₁₂: l0(X₀, X₂) → l1(0, 0)
results in twn-loop: twn:Inv: [X₂ ≤ 50 ∧ X₂ ≤ 50+X₀ ∧ X₀+X₂ ≤ 50 ∧ 0 ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀] , (X₀,X₂) -> (X₀,X₂+1) :|: X₂ ≤ 49
order: [X₀; X₂]
closed-form:
X₀: X₀
X₂: X₂ + [[n != 0]] * n^1

Termination: true
Formula:

1 < 0
∨ X₂ < 49 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₂ ≤ 49 ∧ 49 ≤ X₂

Stabilization-Threshold for: X₂ ≤ 49
alphas_abs: X₂+49
M: 0
N: 1
Bound: 2⋅X₂+100 {O(n)}

relevant size-bounds w.r.t. t₁₂:
X₂: 0 {O(1)}
Runtime-bound of t₁₂: 1 {O(1)}
Results in: 102 {O(1)}

102 {O(1)}

Found invariant X₂ ≤ 50 ∧ X₂ ≤ 50+X₀ ∧ X₀+X₂ ≤ 100 ∧ 50 ≤ X₂ ∧ 50 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 50 ∧ 0 ≤ X₀ for location l2

Found invariant X₂ ≤ 50 ∧ X₂ ≤ 50+X₀ ∧ X₀+X₂ ≤ 50 ∧ 0 ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location l1

Found invariant X₂ ≤ 50 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 100 ∧ 50 ≤ X₂ ∧ 100 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 50 ∧ 50 ≤ X₀ for location l3

Time-Bound by TWN-Loops:

TWN-Loops: t₁₅ 102 {O(1)}

TWN-Loops:

entry: t₁₄: l1(X₀, X₂) → l2(0, X₂) :|: 50 ≤ X₂ ∧ X₂ ≤ 50 ∧ X₂ ≤ 50+X₀ ∧ X₀+X₂ ≤ 50 ∧ 0 ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
results in twn-loop: twn:Inv: [X₂ ≤ 50 ∧ X₂ ≤ 50+X₀ ∧ X₀+X₂ ≤ 100 ∧ 50 ≤ X₂ ∧ 50 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 50 ∧ 0 ≤ X₀] , (X₀,X₂) -> (X₀+1,X₂) :|: X₀ ≤ 49
order: [X₀; X₂]
closed-form:
X₀: X₀ + [[n != 0]] * n^1
X₂: X₂

Termination: true
Formula:

1 < 0
∨ X₀ < 49 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ 49 ∧ 49 ≤ X₀

Stabilization-Threshold for: X₀ ≤ 49
alphas_abs: X₀+49
M: 0
N: 1
Bound: 2⋅X₀+100 {O(n)}

relevant size-bounds w.r.t. t₁₄:
X₀: 0 {O(1)}
Runtime-bound of t₁₄: 1 {O(1)}
Results in: 102 {O(1)}

102 {O(1)}

All Bounds

Timebounds

Overall timebound:207 {O(1)}
t₁₂: 1 {O(1)}
t₁₃: 102 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: 102 {O(1)}
t₁₆: 1 {O(1)}

Costbounds

Overall costbound: 207 {O(1)}
t₁₂: 1 {O(1)}
t₁₃: 102 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: 102 {O(1)}
t₁₆: 1 {O(1)}

Sizebounds

t₁₂, X₀: 0 {O(1)}
t₁₂, X₂: 0 {O(1)}
t₁₃, X₀: 0 {O(1)}
t₁₃, X₂: 50 {O(1)}
t₁₄, X₀: 0 {O(1)}
t₁₄, X₂: 50 {O(1)}
t₁₅, X₀: 50 {O(1)}
t₁₅, X₂: 50 {O(1)}
t₁₆, X₀: 50 {O(1)}
t₁₆, X₂: 50 {O(1)}