Initial Problem

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁) → l1(X₀, 1)
t₁: l1(X₀, X₁) → l1(X₀-1, 2⋅X₁) :|: 0 < X₀
t₂: l1(X₀, X₁) → l2(X₀, X₁) :|: X₀ ≤ 0
t₃: l2(X₀, X₁) → l2(X₀, X₁-1) :|: 0 < X₁

Preprocessing

Found invariant 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l2

Found invariant 1 ≤ X₁ for location l1

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁) → l1(X₀, 1)
t₁: l1(X₀, X₁) → l1(X₀-1, 2⋅X₁) :|: 0 < X₀ ∧ 1 ≤ X₁
t₂: l1(X₀, X₁) → l2(X₀, X₁) :|: X₀ ≤ 0 ∧ 1 ≤ X₁
t₃: l2(X₀, X₁) → l2(X₀, X₁-1) :|: 0 < X₁ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0

MPRF for transition t₁: l1(X₀, X₁) → l1(X₀-1, 2⋅X₁) :|: 0 < X₀ ∧ 1 ≤ X₁ of depth 1:

new bound:

X₀ {O(n)}

l1 [X₀ ]

MPRF for transition t₃: l2(X₀, X₁) → l2(X₀, X₁-1) :|: 0 < X₁ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 of depth 1:

new bound:

2^(X₀)+2 {O(EXP)}

l2 [X₁+1 ]

Analysing control-flow refined program

Found invariant 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l2

Found invariant 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location n_l2___1

Found invariant 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location n_l2___2

Found invariant 1 ≤ X₁ for location l1

MPRF for transition t₃₃: n_l2___1(X₀, X₁) → n_l2___1(X₀, X₁-1) :|: X₀ ≤ 0 ∧ 0 < X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 of depth 1:

new bound:

2^(X₀)+2 {O(EXP)}

n_l2___1 [X₁+1 ]

CFR did not improve the program. Rolling back

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)}