Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l2, l3
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l1(0, X₁, X₂, X₃, X₄)
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l1(X₀+1, X₁, X₂, X₀, X₀) :|: X₀ ≤ 99
t₄: l1(X₀, X₁, X₂, X₃, X₄) → l2(X₀, 100, X₂, X₃, X₄) :|: 100 ≤ X₀
t₁: l2(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁+1, X₁, X₃, X₄) :|: X₁ ≤ 199
t₂: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: 200 ≤ X₁

Preprocessing

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

Found invariant X₁ ≤ 200 ∧ X₁ ≤ 100+X₀ ∧ X₀+X₁ ≤ 300 ∧ 100 ≤ X₁ ∧ 200 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 100 ∧ 100 ≤ X₀ for location l2

Found invariant X₀ ≤ 100 ∧ 0 ≤ X₀ for location l1

Found invariant X₁ ≤ 200 ∧ X₁ ≤ 100+X₀ ∧ X₀+X₁ ≤ 300 ∧ 200 ≤ X₁ ∧ 300 ≤ X₀+X₁ ∧ 100+X₀ ≤ X₁ ∧ X₀ ≤ 100 ∧ 100 ≤ 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 ≤ 99 ∧ X₀ ≤ 100 ∧ 0 ≤ X₀
t₁₄: l1(X₀, X₁) → l2(X₀, 100) :|: 100 ≤ X₀ ∧ X₀ ≤ 100 ∧ 0 ≤ X₀
t₁₅: l2(X₀, X₁) → l2(X₀, X₁+1) :|: X₁ ≤ 199 ∧ X₁ ≤ 200 ∧ X₁ ≤ 100+X₀ ∧ X₀+X₁ ≤ 300 ∧ 100 ≤ X₁ ∧ 200 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 100 ∧ 100 ≤ X₀
t₁₆: l2(X₀, X₁) → l3(X₀, X₁) :|: 200 ≤ X₁ ∧ X₁ ≤ 200 ∧ X₁ ≤ 100+X₀ ∧ X₀+X₁ ≤ 300 ∧ 100 ≤ X₁ ∧ 200 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 100 ∧ 100 ≤ X₀

Found invariant X₁ ≤ 200 ∧ X₁ ≤ 100+X₀ ∧ X₀+X₁ ≤ 300 ∧ 100 ≤ X₁ ∧ 200 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 100 ∧ 100 ≤ X₀ for location l2

Found invariant X₀ ≤ 100 ∧ 0 ≤ X₀ for location l1

Found invariant X₁ ≤ 200 ∧ X₁ ≤ 100+X₀ ∧ X₀+X₁ ≤ 300 ∧ 200 ≤ X₁ ∧ 300 ≤ X₀+X₁ ∧ 100+X₀ ≤ X₁ ∧ X₀ ≤ 100 ∧ 100 ≤ X₀ for location l3

Time-Bound by TWN-Loops:

TWN-Loops: t₁₃ 202 {O(1)}

TWN-Loops:

entry: t₁₂: l0(X₀, X₁) → l1(0, X₁)
results in twn-loop: twn:Inv: [X₀ ≤ 100 ∧ 0 ≤ X₀] , (X₀,X₁) -> (X₀+1,X₁) :|: X₀ ≤ 99
order: [X₀]
closed-form:
X₀: X₀ + [[n != 0]] * n^1

Termination: true
Formula:

1 < 0
∨ X₀ < 99 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ 99 ∧ 99 ≤ X₀

Stabilization-Threshold for: X₀ ≤ 99
alphas_abs: 99
M: 0
N: 1
Bound: 200 {O(1)}

relevant size-bounds w.r.t. t₁₂:
Runtime-bound of t₁₂: 1 {O(1)}
Results in: 202 {O(1)}

202 {O(1)}

Found invariant X₁ ≤ 200 ∧ X₁ ≤ 100+X₀ ∧ X₀+X₁ ≤ 300 ∧ 100 ≤ X₁ ∧ 200 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 100 ∧ 100 ≤ X₀ for location l2

Found invariant X₀ ≤ 100 ∧ 0 ≤ X₀ for location l1

Found invariant X₁ ≤ 200 ∧ X₁ ≤ 100+X₀ ∧ X₀+X₁ ≤ 300 ∧ 200 ≤ X₁ ∧ 300 ≤ X₀+X₁ ∧ 100+X₀ ≤ X₁ ∧ X₀ ≤ 100 ∧ 100 ≤ X₀ for location l3

Time-Bound by TWN-Loops:

TWN-Loops: t₁₅ 602 {O(1)}

TWN-Loops:

entry: t₁₄: l1(X₀, X₁) → l2(X₀, 100) :|: 100 ≤ X₀ ∧ X₀ ≤ 100 ∧ 0 ≤ X₀
results in twn-loop: twn:Inv: [X₁ ≤ 200 ∧ X₁ ≤ 100+X₀ ∧ X₀+X₁ ≤ 300 ∧ 100 ≤ X₁ ∧ 200 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 100 ∧ 100 ≤ X₀] , (X₀,X₁) -> (X₀,X₁+1) :|: X₁ ≤ 199
order: [X₀; X₁]
closed-form:
X₀: X₀
X₁: X₁ + [[n != 0]] * n^1

Termination: true
Formula:

1 < 0
∨ X₁ < 199 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ 199 ∧ 199 ≤ X₁

Stabilization-Threshold for: X₁ ≤ 199
alphas_abs: X₁+199
M: 0
N: 1
Bound: 2⋅X₁+400 {O(n)}

relevant size-bounds w.r.t. t₁₄:
X₁: 100 {O(1)}
Runtime-bound of t₁₄: 1 {O(1)}
Results in: 602 {O(1)}

602 {O(1)}

All Bounds

Timebounds

Overall timebound:807 {O(1)}
t₁₂: 1 {O(1)}
t₁₃: 202 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: 602 {O(1)}
t₁₆: 1 {O(1)}

Costbounds

Overall costbound: 807 {O(1)}
t₁₂: 1 {O(1)}
t₁₃: 202 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: 602 {O(1)}
t₁₆: 1 {O(1)}

Sizebounds

t₁₂, X₀: 0 {O(1)}
t₁₂, X₁: X₁ {O(n)}
t₁₃, X₀: 100 {O(1)}
t₁₃, X₁: X₁ {O(n)}
t₁₄, X₀: 100 {O(1)}
t₁₄, X₁: 100 {O(1)}
t₁₅, X₀: 100 {O(1)}
t₁₅, X₁: 200 {O(1)}
t₁₆, X₀: 100 {O(1)}
t₁₆, X₁: 200 {O(1)}