Initial Problem

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

Preprocessing

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

Found invariant 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location g

Problem after Preprocessing

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

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

new bound:

X₂ {O(n)}

• g: [X₂]

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

new bound:

2⋅2^(X₂)+2 {O(EXP)}

• h: [1+X₁]

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

Found invariant 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location g

Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location h_v1

All Bounds

Timebounds

Overall timebound:2⋅2^(X₂)+X₂+4 {O(EXP)}
t₀: 1 {O(1)}
t₁: X₂ {O(n)}
t₂: 1 {O(1)}
t₃: 2⋅2^(X₂)+2 {O(EXP)}

Costbounds

Overall costbound: 2⋅2^(X₂)+X₂+4 {O(EXP)}
t₀: 1 {O(1)}
t₁: X₂ {O(n)}
t₂: 1 {O(1)}
t₃: 2⋅2^(X₂)+2 {O(EXP)}

Sizebounds

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