Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3
Transitions:
t₀: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂) :|: 0 < X₀
t₁: l1(X₀, X₁, X₂) → l1(X₀+X₂, X₁, X₂-1) :|: 0 < X₂
t₂: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₂ ≤ 0
t₃: l2(X₀, X₁, X₂) → l2(X₀+(X₂)², X₁+1, X₂+1) :|: X₀ < (X₁)²
t₄: l2(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: (X₁)² ≤ X₀
t₅: l3(X₀, X₁, X₂) → l3(X₀-1, X₁, X₂) :|: 0 < X₀
Found invariant 1 ≤ X₀ for location l2
Found invariant 1 ≤ X₀ for location l1
Found invariant 0 ≤ X₀ for location l3
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3
Transitions:
t₀: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂) :|: 0 < X₀
t₁: l1(X₀, X₁, X₂) → l1(X₀+X₂, X₁, X₂-1) :|: 0 < X₂ ∧ 1 ≤ X₀
t₂: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₂ ≤ 0 ∧ 1 ≤ X₀
t₃: l2(X₀, X₁, X₂) → l2(X₀+(X₂)², X₁+1, X₂+1) :|: X₀ < (X₁)² ∧ 1 ≤ X₀
t₄: l2(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: (X₁)² ≤ X₀ ∧ 1 ≤ X₀
t₅: l3(X₀, X₁, X₂) → l3(X₀-1, X₁, X₂) :|: 0 < X₀ ∧ 0 ≤ X₀
new bound:
X₂ {O(n)}
cycle: [t₃: l2→l2]
Termination: true
Formula:
Found invariant X₂ ≤ 0 ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₀ for location l2
Found invariant 1 ≤ X₀ for location l1
Found invariant 0 ≤ X₀ for location l3
Found invariant 1 ≤ X₀ for location l2
Found invariant 0 ≤ X₀ for location n_l3___2
Found invariant 1 ≤ X₀ for location l1
Found invariant 0 ≤ X₀ for location n_l3___1
Found invariant 1 ≤ X₀ for location l3
Overall timebound:inf {Infinity}
t₀: 1 {O(1)}
t₁: X₂ {O(n)}
t₂: 1 {O(1)}
t₃: 48⋅X₁⋅X₁+72⋅X₂⋅X₂+24⋅X₀+48⋅X₁+48⋅X₂+24 {O(n^2)}
t₄: 1 {O(1)}
t₅: inf {Infinity}
Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₁: X₂ {O(n)}
t₂: 1 {O(1)}
t₃: 48⋅X₁⋅X₁+72⋅X₂⋅X₂+24⋅X₀+48⋅X₁+48⋅X₂+24 {O(n^2)}
t₄: 1 {O(1)}
t₅: inf {Infinity}
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₁, X₀: 2⋅X₂⋅X₂+2⋅X₂+X₀ {O(n^2)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₂, X₀: 2⋅X₂⋅X₂+2⋅X₀+2⋅X₂ {O(n^2)}
t₂, X₁: 2⋅X₁ {O(n)}
t₂, X₂: 2⋅X₂ {O(n)}
t₃, X₁: 48⋅X₁⋅X₁+72⋅X₂⋅X₂+24⋅X₀+48⋅X₂+50⋅X₁+24 {O(n^2)}
t₃, X₂: 48⋅X₁⋅X₁+72⋅X₂⋅X₂+24⋅X₀+48⋅X₁+50⋅X₂+24 {O(n^2)}
t₄, X₁: 48⋅X₁⋅X₁+72⋅X₂⋅X₂+24⋅X₀+48⋅X₂+52⋅X₁+24 {O(n^2)}
t₄, X₂: 48⋅X₁⋅X₁+72⋅X₂⋅X₂+24⋅X₀+48⋅X₁+52⋅X₂+24 {O(n^2)}
t₅, X₁: 48⋅X₁⋅X₁+72⋅X₂⋅X₂+24⋅X₀+48⋅X₂+52⋅X₁+24 {O(n^2)}
t₅, X₂: 48⋅X₁⋅X₁+72⋅X₂⋅X₂+24⋅X₀+48⋅X₁+52⋅X₂+24 {O(n^2)}