Initial Problem

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

Preprocessing

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

Found invariant X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l2

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₁₃: l0(X₀, X₁) → l1(X₀, X₁)
t₁₄: l1(X₀, X₁) → l1(1+X₀, X₁) :|: 1+X₀ ≤ X₁
t₁₅: l1(X₀, X₁) → l1(1+X₀, X₁) :|: 1+X₁ ≤ X₀ ∧ X₁ ≤ X₀
t₁₆: l1(X₀, X₁) → l2(X₀, X₁) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀

Found invariant X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l2

Analysing control-flow refined program

Cut unsatisfiable transition t₇₁: n_l1___1→l2

Found invariant X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l2

Found invariant X₀ ≤ X₁ for location n_l1___2

Found invariant 2+X₁ ≤ X₀ for location n_l1___1

Found invariant X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l2

Found invariant X₀ ≤ X₁ for location n_l1___2

Found invariant 2+X₁ ≤ X₀ for location n_l1___1

Found invariant X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l2

Found invariant X₀ ≤ X₁ for location n_l1___2

Found invariant 2+X₁ ≤ X₀ for location n_l1___1

Time-Bound by TWN-Loops:

TWN-Loops: t₆₂ 4⋅X₀+4⋅X₁+10 {O(n)}

TWN-Loops:

entry: t₆₄: l1(X₀, X₁) → n_l1___2(X₀+1, X₁) :|: 1+X₀ ≤ X₁
results in twn-loop: twn:Inv: [X₀ ≤ X₁] , (X₀,X₁) -> (X₀+1,X₁) :|: X₀ ≤ X₁ ∧ 1+X₀ ≤ X₁
order: [X₀; X₁]
closed-form:
X₀: X₀ + [[n != 0]] * n^1
X₁: X₁

Termination: true
Formula:

1 < 0
∨ 1 < 0 ∧ X₀ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀
∨ 1+X₀ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 1+X₀ < X₁ ∧ X₀ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1+X₀ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₀ ≤ X₁ ∧ X₁ ≤ 1+X₀ ∧ 1 < 0
∨ 1+X₀ ≤ X₁ ∧ X₁ ≤ 1+X₀ ∧ X₀ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1+X₀ ≤ X₁ ∧ X₁ ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀

Stabilization-Threshold for: 1+X₀ ≤ X₁
alphas_abs: X₀+X₁
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+2 {O(n)}
Stabilization-Threshold for: X₀ ≤ X₁
alphas_abs: X₀+X₁
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+2 {O(n)}

relevant size-bounds w.r.t. t₆₄:
X₀: X₀+1 {O(n)}
X₁: X₁ {O(n)}
Runtime-bound of t₆₄: 1 {O(1)}
Results in: 4⋅X₀+4⋅X₁+10 {O(n)}

4⋅X₀+4⋅X₁+10 {O(n)}

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₁₃: 1 {O(1)}
t₁₄: inf {Infinity}
t₁₅: inf {Infinity}
t₁₆: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₁₃: 1 {O(1)}
t₁₄: inf {Infinity}
t₁₅: inf {Infinity}
t₁₆: 1 {O(1)}

Sizebounds

t₁₃, X₀: X₀ {O(n)}
t₁₃, X₁: X₁ {O(n)}
t₁₄, X₁: X₁ {O(n)}
t₁₅, X₁: X₁ {O(n)}
t₁₆, X₁: 2⋅X₁ {O(n)}