Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1
Transitions:
t₀: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂) :|: 1 ≤ X₂
t₁: l1(X₀, X₁, X₂) → l1(-2⋅X₀, 3⋅X₁-2⋅(X₂)³, X₂) :|: 1+X₀ ≤ 0 ∧ 1+(X₀)²+(X₂)⁵ ≤ X₁
t₂: l1(X₀, X₁, X₂) → l1(-2⋅X₀, 3⋅X₁-2⋅(X₂)³, X₂) :|: 1 ≤ X₀ ∧ 1+(X₀)²+(X₂)⁵ ≤ X₁

Preprocessing

Found invariant 1 ≤ X₂ for location l1

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1
Transitions:
t₀: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂) :|: 1 ≤ X₂
t₁: l1(X₀, X₁, X₂) → l1(-2⋅X₀, 3⋅X₁-2⋅(X₂)³, X₂) :|: 1+X₀ ≤ 0 ∧ 1+(X₀)²+(X₂)⁵ ≤ X₁ ∧ 1 ≤ X₂
t₂: l1(X₀, X₁, X₂) → l1(-2⋅X₀, 3⋅X₁-2⋅(X₂)³, X₂) :|: 1 ≤ X₀ ∧ 1+(X₀)²+(X₂)⁵ ≤ X₁ ∧ 1 ≤ X₂

TWN: t₁: l1→l1

Show Graph

Termination: true
Formula:

TWN - Lifting for [1: l1->l1; 2: l1->l1] of 32⋅log(X₂)+4⋅log(X₁)+29 {O(log(n))}

All Bounds

Timebounds

Overall timebound:64⋅log(X₂)+8⋅log(X₁)+59 {O(log(n))}
t₀: 1 {O(1)}
t₁: 32⋅log(X₂)+4⋅log(X₁)+29 {O(log(n))}
t₂: 32⋅log(X₂)+4⋅log(X₁)+29 {O(log(n))}

Costbounds

Overall costbound: 64⋅log(X₂)+8⋅log(X₁)+59 {O(log(n))}
t₀: 1 {O(1)}
t₁: 32⋅log(X₂)+4⋅log(X₁)+29 {O(log(n))}
t₂: 32⋅log(X₂)+4⋅log(X₁)+29 {O(log(n))}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₁, X₀: 2^(24⋅log(X₂))⋅2^(64⋅log(X₂))⋅2^(8⋅log(X₁))⋅9671406556917033397649408⋅X₀ {O(EXP)}
t₁, X₁: 3990838394187339929534246675572349035227⋅3^(24⋅log(X₂))⋅3^(64⋅log(X₂))⋅3^(8⋅log(X₁))⋅X₁+3990838394187339929534246675572349035227⋅3^(24⋅log(X₂))⋅3^(64⋅log(X₂))⋅3^(8⋅log(X₁))⋅X₂⋅X₂⋅X₂+X₂⋅X₂⋅X₂ {O(EXP)}
t₁, X₂: X₂ {O(n)}
t₂, X₀: 2^(24⋅log(X₂))⋅2^(64⋅log(X₂))⋅2^(8⋅log(X₁))⋅9671406556917033397649408⋅X₀ {O(EXP)}
t₂, X₁: 3990838394187339929534246675572349035227⋅3^(24⋅log(X₂))⋅3^(64⋅log(X₂))⋅3^(8⋅log(X₁))⋅X₁+3990838394187339929534246675572349035227⋅3^(24⋅log(X₂))⋅3^(64⋅log(X₂))⋅3^(8⋅log(X₁))⋅X₂⋅X₂⋅X₂+X₂⋅X₂⋅X₂ {O(EXP)}
t₂, X₂: X₂ {O(n)}