Initial Problem

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

Preprocessing

Found invariant 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location h

Found invariant 1 ≤ X₁ for location g

Problem after Preprocessing

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

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

new bound:

X₀ {O(n)}

• g: [X₀]

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

new bound:

2^(X₀)+2 {O(EXP)}

• h: [1+X₁]

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

Found invariant 1 ≤ X₁ for location g

Found invariant 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location h_v1

All Bounds

Timebounds

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

Costbounds

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

Sizebounds

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