Initial Problem

Start: f
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: f, g, h, i
Transitions:
t₀: f(X₀, X₁, X₂) → g(X₀, 1, 1)
t₁: g(X₀, X₁, X₂) → g(X₀-1, 2⋅X₁, X₂) :|: 1 ≤ X₀
t₂: g(X₀, X₁, X₂) → h(X₀, X₁, X₂) :|: X₀ ≤ 0
t₃: h(X₀, X₁, X₂) → h(X₀, X₁-1, 2⋅X₂) :|: 1 ≤ X₁
t₄: h(X₀, X₁, X₂) → i(X₀, X₁, X₂) :|: X₁ ≤ 0
t₅: i(X₀, X₁, X₂) → i(X₀, X₁, X₂-1) :|: 1 ≤ X₂

Preprocessing

Found invariant 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location h

Found invariant X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location g

Found invariant 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location i

Problem after Preprocessing

Start: f
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: f, g, h, i
Transitions:
t₀: f(X₀, X₁, X₂) → g(X₀, 1, 1)
t₁: g(X₀, X₁, X₂) → g(X₀-1, 2⋅X₁, X₂) :|: 1 ≤ X₀ ∧ X₂ ≤ 1 ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₂ ≤ X₁
t₂: g(X₀, X₁, X₂) → h(X₀, X₁, X₂) :|: X₀ ≤ 0 ∧ X₂ ≤ 1 ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₂ ≤ X₁
t₃: h(X₀, X₁, X₂) → h(X₀, X₁-1, 2⋅X₂) :|: 1 ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₁ ∧ 0 ≤ X₁
t₄: h(X₀, X₁, X₂) → i(X₀, X₁, X₂) :|: X₁ ≤ 0 ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₁ ∧ 0 ≤ X₁
t₅: i(X₀, X₁, X₂) → i(X₀, X₁, X₂-1) :|: 1 ≤ X₂ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₁ ∧ X₀+X₁ ≤ 0 ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₂ ∧ 0 ≤ X₂

MPRF for transition t₁: g(X₀, X₁, X₂) → g(X₀-1, 2⋅X₁, X₂) :|: 1 ≤ X₀ ∧ X₂ ≤ 1 ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₂ ≤ X₁ of depth 1:

new bound:

X₀ {O(n)}

• g: [X₀]

MPRF for transition t₃: h(X₀, X₁, X₂) → h(X₀, X₁-1, 2⋅X₂) :|: 1 ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₁ ∧ 0 ≤ X₁ of depth 1:

new bound:

2^(X₀)+2 {O(EXP)}

• h: [1+X₁]

Cut unsatisfiable transition [t₄: h→i; t₃₆: h→i]

Found invariant X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ X₀+X₂ ≤ 1 ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 for location h

Found invariant X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location g

Found invariant 2 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location h_v1

Found invariant 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location i

MPRF for transition t₅: i(X₀, X₁, X₂) → i(X₀, X₁, X₂-1) :|: 1 ≤ X₂ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₁ ∧ X₀+X₁ ≤ 0 ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₂ ∧ 0 ≤ X₂ of depth 1:

new bound:

2^(2^(X₀))⋅4+1 {O(EXP^O(EXP))}

• i: [1+X₂]

Found invariant 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location h

Found invariant 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location i_v1

Found invariant X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location g

Found invariant 2 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2+X₁ ≤ X₂ ∧ 2+X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location i

All Bounds

Timebounds

Overall timebound:2^(2^(X₀))⋅4+2^(X₀)+X₀+6 {O(EXP^O(EXP))}
t₀: 1 {O(1)}
t₁: X₀ {O(n)}
t₂: 1 {O(1)}
t₃: 2^(X₀)+2 {O(EXP)}
t₄: 1 {O(1)}
t₅: 2^(2^(X₀))⋅4+1 {O(EXP^O(EXP))}

Costbounds

Overall costbound: 2^(2^(X₀))⋅4+2^(X₀)+X₀+6 {O(EXP^O(EXP))}
t₀: 1 {O(1)}
t₁: X₀ {O(n)}
t₂: 1 {O(1)}
t₃: 2^(X₀)+2 {O(EXP)}
t₄: 1 {O(1)}
t₅: 2^(2^(X₀))⋅4+1 {O(EXP^O(EXP))}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: 1 {O(1)}
t₀, X₂: 1 {O(1)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: 2^(X₀) {O(EXP)}
t₁, X₂: 1 {O(1)}
t₂, X₀: 2⋅X₀ {O(n)}
t₂, X₁: 2^(X₀)+1 {O(EXP)}
t₂, X₂: 1 {O(1)}
t₃, X₀: 2⋅X₀ {O(n)}
t₃, X₁: 2^(X₀)+1 {O(EXP)}
t₃, X₂: 2^(2^(X₀))⋅4 {O(EXP^O(EXP))}
t₄, X₀: 2⋅X₀ {O(n)}
t₄, X₁: 0 {O(1)}
t₄, X₂: 2^(2^(X₀))⋅4 {O(EXP^O(EXP))}
t₅, X₀: 2⋅X₀ {O(n)}
t₅, X₁: 0 {O(1)}
t₅, X₂: 2^(2^(X₀))⋅4 {O(EXP^O(EXP))}