Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars: D
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁, X₂) → l1(X₀, 0, X₂) :|: 128 ≤ X₀
t₁: l0(X₀, X₁, X₂) → l2(X₀, 0, D) :|: X₀ ≤ 127
t₃: l2(X₀, X₁, X₂) → l1(X₀, X₁, X₂) :|: 36 ≤ X₁
t₂: l2(X₀, X₁, X₂) → l2(X₀, X₁+1, X₂+1) :|: X₁ ≤ 35

Preprocessing

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

Found invariant X₁ ≤ 36 ∧ X₀+X₁ ≤ 163 ∧ 0 ≤ X₁ ∧ X₀ ≤ 127+X₁ ∧ X₀ ≤ 127 for location l2

Found invariant X₁ ≤ 36 ∧ 0 ≤ X₁ for location l1

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₈: l0(X₀, X₁) → l1(X₀, 0) :|: 128 ≤ X₀
t₉: l0(X₀, X₁) → l2(X₀, 0) :|: X₀ ≤ 127
t₁₁: l2(X₀, X₁) → l1(X₀, X₁) :|: 36 ≤ X₁ ∧ X₁ ≤ 36 ∧ X₀+X₁ ≤ 163 ∧ 0 ≤ X₁ ∧ X₀ ≤ 127+X₁ ∧ X₀ ≤ 127
t₁₀: l2(X₀, X₁) → l2(X₀, X₁+1) :|: X₁ ≤ 35 ∧ X₁ ≤ 36 ∧ X₀+X₁ ≤ 163 ∧ 0 ≤ X₁ ∧ X₀ ≤ 127+X₁ ∧ X₀ ≤ 127

Found invariant X₁ ≤ 36 ∧ X₀+X₁ ≤ 163 ∧ 0 ≤ X₁ ∧ X₀ ≤ 127+X₁ ∧ X₀ ≤ 127 for location l2

Found invariant X₁ ≤ 36 ∧ 0 ≤ X₁ for location l1

Time-Bound by TWN-Loops:

TWN-Loops: t₁₀ 74 {O(1)}

TWN-Loops:

entry: t₉: l0(X₀, X₁) → l2(X₀, 0) :|: X₀ ≤ 127
results in twn-loop: twn:Inv: [X₁ ≤ 36 ∧ X₀+X₁ ≤ 163 ∧ 0 ≤ X₁ ∧ X₀ ≤ 127+X₁ ∧ X₀ ≤ 127] , (X₀,X₁) -> (X₀,X₁+1) :|: X₁ ≤ 35
order: [X₀; X₁]
closed-form:
X₀: X₀
X₁: X₁ + [[n != 0]] * n^1

Termination: true
Formula:

1 < 0
∨ X₁ < 35 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ 35 ∧ 35 ≤ X₁

Stabilization-Threshold for: X₁ ≤ 35
alphas_abs: 35
M: 0
N: 1
Bound: 72 {O(1)}

relevant size-bounds w.r.t. t₉:
Runtime-bound of t₉: 1 {O(1)}
Results in: 74 {O(1)}

74 {O(1)}

All Bounds

Timebounds

Overall timebound:77 {O(1)}
t₈: 1 {O(1)}
t₉: 1 {O(1)}
t₁₀: 74 {O(1)}
t₁₁: 1 {O(1)}

Costbounds

Overall costbound: 77 {O(1)}
t₈: 1 {O(1)}
t₉: 1 {O(1)}
t₁₀: 74 {O(1)}
t₁₁: 1 {O(1)}

Sizebounds

t₈, X₀: X₀ {O(n)}
t₈, X₁: 0 {O(1)}
t₉, X₀: X₀ {O(n)}
t₉, X₁: 0 {O(1)}
t₁₀, X₀: X₀ {O(n)}
t₁₀, X₁: 36 {O(1)}
t₁₁, X₀: X₀ {O(n)}
t₁₁, X₁: 36 {O(1)}