KoAT2 Proof Output

Initial Problem

Preprocessing

Found invariant 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₀ for location l2

Found invariant 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₀ for location l5

Found invariant 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₀+X₄ ∧ 0 ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀ for location l6

Found invariant X₄ ≤ X₀ for location l1

Found invariant 0 ≤ X₅ ∧ 0 ≤ X₄+X₅ ∧ 1 ≤ X₀+X₅ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₀ for location l4

Found invariant 0 ≤ X₅ ∧ 0 ≤ X₄+X₅ ∧ 1 ≤ X₀+X₅ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₀ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, X₃, X₀, 0)
t₁: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄-1, X₁+X₂) :|: 1 ≤ X₄ ∧ X₄ ≤ X₀
t₆: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, X₁+X₂, X₄, X₅) :|: 1 ≤ X₀ ∧ 1 ≤ X₀+X₄ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄
t₂: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅-1) :|: 1 ≤ X₅ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₄ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄
t₇: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1 ≤ X₀ ∧ 1 ≤ X₀+X₄ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄
t₃: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₃, X₀, X₃, X₄, X₅) :|: 1 ≤ X₀ ∧ 1 ≤ X₀+X₄ ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₀+X₅ ∧ 0 ≤ X₄ ∧ 0 ≤ X₄+X₅ ∧ 0 ≤ X₅
t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₀, X₃, X₃, X₄, X₅) :|: 1 ≤ X₀ ∧ 1 ≤ X₀+X₄ ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₀+X₅ ∧ 0 ≤ X₄ ∧ 0 ≤ X₄+X₅ ∧ 0 ≤ X₅
t₅: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1 ≤ X₀ ∧ 1 ≤ X₀+X₄ ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₀+X₅ ∧ 0 ≤ X₄ ∧ 0 ≤ X₄+X₅ ∧ 0 ≤ X₅
t₈: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃-1, X₄, X₅) :|: 1 ≤ X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₄ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄
t₉: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₀+X₁+X₂, X₃, X₄, X₅) :|: 1 ≤ X₀ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀+X₄ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ 0 ≤ X₄
t₁₀: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₀, X₁, X₃, X₄, X₅) :|: 1 ≤ X₀ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀+X₄ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ 0 ≤ X₄

MPRF for transition t₁: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄-1, X₁+X₂) :|: 1 ≤ X₄ ∧ X₄ ≤ X₀ of depth 1:

new bound:

X₀ {O(n)}

MPRF:

• l1: [X₄]
• l2: [X₄]
• l3: [X₄]
• l4: [X₄]

MPRF for transition t₆: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, X₁+X₂, X₄, X₅) :|: 1 ≤ X₀ ∧ 1 ≤ X₀+X₄ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ of depth 1:

new bound:

X₀ {O(n)}

MPRF:

• l1: [X₄]
• l2: [1+X₄]
• l3: [1+X₄]
• l4: [1+X₄]

MPRF for transition t₂: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅-1) :|: 1 ≤ X₅ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₄ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ of depth 1:

new bound:

2⋅2^(X₀)⋅X₀⋅X₁+2⋅2^(X₀)⋅X₀⋅X₂+2⋅2^(X₀)⋅X₀⋅X₃+2^(X₀)⋅4⋅X₀⋅X₀+X₁+X₂ {O(EXP)}

MPRF:

• l1: [X₁+X₂]
• l2: [X₅]
• l3: [X₅]
• l4: [X₅]

MPRF for transition t₃: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₃, X₀, X₃, X₄, X₅) :|: 1 ≤ X₀ ∧ 1 ≤ X₀+X₄ ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₀+X₅ ∧ 0 ≤ X₄ ∧ 0 ≤ X₄+X₅ ∧ 0 ≤ X₅ of depth 1:

new bound:

2⋅2^(X₀)⋅X₀⋅X₁+2⋅2^(X₀)⋅X₀⋅X₂+2⋅2^(X₀)⋅X₀⋅X₃+2^(X₀)⋅4⋅X₀⋅X₀+X₁+X₂ {O(EXP)}

MPRF:

• l1: [X₁+X₂]
• l2: [X₅]
• l3: [1+X₅]
• l4: [X₅]

MPRF for transition t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₀, X₃, X₃, X₄, X₅) :|: 1 ≤ X₀ ∧ 1 ≤ X₀+X₄ ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₀+X₅ ∧ 0 ≤ X₄ ∧ 0 ≤ X₄+X₅ ∧ 0 ≤ X₅ of depth 1:

new bound:

2⋅2^(X₀)⋅X₀⋅X₁+2⋅2^(X₀)⋅X₀⋅X₂+2⋅2^(X₀)⋅X₀⋅X₃+2^(X₀)⋅4⋅X₀⋅X₀+X₁+X₂ {O(EXP)}

MPRF:

• l1: [X₁+X₂]
• l2: [X₅]
• l3: [1+X₅]
• l4: [X₅]

MPRF for transition t₅: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1 ≤ X₀ ∧ 1 ≤ X₀+X₄ ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₀+X₅ ∧ 0 ≤ X₄ ∧ 0 ≤ X₄+X₅ ∧ 0 ≤ X₅ of depth 1:

new bound:

2⋅2^(X₀)⋅X₀⋅X₁+2⋅2^(X₀)⋅X₀⋅X₂+2⋅2^(X₀)⋅X₀⋅X₃+2^(X₀)⋅4⋅X₀⋅X₀+X₁+X₂ {O(EXP)}

MPRF:

• l1: [X₁+X₂]
• l2: [X₅]
• l3: [1+X₅]
• l4: [1+X₅]

Found invariant 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₀ for location l2

Found invariant 0 ≤ X₅ ∧ 0 ≤ X₄+X₅ ∧ 1 ≤ X₂+X₅ ∧ 1 ≤ X₀+X₅ ∧ 1+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ for location l3_v2

Found invariant 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₀+X₄ ∧ 0 ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀ for location l6

Found invariant 0 ≤ X₅ ∧ 0 ≤ X₄+X₅ ∧ 1 ≤ X₂+X₅ ∧ 1 ≤ X₀+X₅ ∧ 1+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ for location l2_v1

Found invariant 0 ≤ X₅ ∧ 0 ≤ X₄+X₅ ∧ 1 ≤ X₁+X₅ ∧ 1 ≤ X₀+X₅ ∧ 1+X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l3_v3

Found invariant 0 ≤ X₅ ∧ 0 ≤ X₄+X₅ ∧ 1 ≤ X₁+X₅ ∧ 1 ≤ X₀+X₅ ∧ 1+X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l4_v1

Found invariant 0 ≤ X₅ ∧ 0 ≤ X₄+X₅ ∧ 1 ≤ X₂+X₅ ∧ 1 ≤ X₀+X₅ ∧ 1+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ for location l4_v2

Found invariant 0 ≤ X₅ ∧ 0 ≤ X₄+X₅ ∧ 1 ≤ X₁+X₅ ∧ 1 ≤ X₀+X₅ ∧ 1+X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l2_v2

Found invariant 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₀ for location l5

Found invariant X₄ ≤ X₀ for location l1

Found invariant 0 ≤ X₅ ∧ 0 ≤ X₄+X₅ ∧ 1 ≤ X₀+X₅ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₀ for location l3_v1

MPRF for transition t₈: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃-1, X₄, X₅) :|: 1 ≤ X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₄ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ of depth 1:

new bound:

2⋅2^(X₀)⋅X₁+2⋅2^(X₀)⋅X₂+2⋅2^(X₀)⋅X₃+2^(X₀)⋅4⋅X₀ {O(EXP)}

MPRF:

• l5: [X₃]
• l6: [X₃]

MPRF for transition t₉: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₀+X₁+X₂, X₃, X₄, X₅) :|: 1 ≤ X₀ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀+X₄ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ 0 ≤ X₄ of depth 1:

new bound:

2⋅2^(X₀)⋅X₁+2⋅2^(X₀)⋅X₂+2⋅2^(X₀)⋅X₃+2^(X₀)⋅4⋅X₀ {O(EXP)}

MPRF:

• l5: [X₃]
• l6: [1+X₃]

MPRF for transition t₁₀: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₀, X₁, X₃, X₄, X₅) :|: 1 ≤ X₀ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀+X₄ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ 0 ≤ X₄ of depth 1:

new bound:

2⋅2^(X₀)⋅X₁+2⋅2^(X₀)⋅X₂+2⋅2^(X₀)⋅X₃+2^(X₀)⋅4⋅X₀ {O(EXP)}

MPRF:

• l5: [X₃]
• l6: [1+X₃]

Found invariant 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₀ for location l2

Found invariant 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₀+X₄ ∧ 0 ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀ for location l6_v1

Found invariant 1+X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 0 ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l5_v1

Found invariant 1+X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 0 ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l6_v2

Found invariant 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₀ for location l5

Found invariant 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₀+X₄ ∧ 0 ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀ for location l5_v2

Found invariant X₄ ≤ X₀ for location l1

Found invariant 0 ≤ X₅ ∧ 0 ≤ X₄+X₅ ∧ 1 ≤ X₀+X₅ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₀ for location l4

Found invariant 0 ≤ X₅ ∧ 0 ≤ X₄+X₅ ∧ 1 ≤ X₀+X₅ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₀ for location l3

All Bounds

Timebounds

Overall timebound:16⋅2^(X₀)⋅X₀⋅X₀+2⋅2^(X₀)⋅X₁+2⋅2^(X₀)⋅X₂+2⋅2^(X₀)⋅X₃+2^(X₀)⋅4⋅X₀+2^(X₀)⋅4⋅X₁+2^(X₀)⋅4⋅X₂+2^(X₀)⋅4⋅X₃+2^(X₀)⋅8⋅X₀+2^(X₀)⋅8⋅X₀⋅X₁+2^(X₀)⋅8⋅X₀⋅X₂+2^(X₀)⋅8⋅X₀⋅X₃+2⋅X₀+4⋅X₁+4⋅X₂+2 {O(EXP)}
t₀: 1 {O(1)}
t₁: X₀ {O(n)}
t₂: 2⋅2^(X₀)⋅X₀⋅X₁+2⋅2^(X₀)⋅X₀⋅X₂+2⋅2^(X₀)⋅X₀⋅X₃+2^(X₀)⋅4⋅X₀⋅X₀+X₁+X₂ {O(EXP)}
t₃: 2⋅2^(X₀)⋅X₀⋅X₁+2⋅2^(X₀)⋅X₀⋅X₂+2⋅2^(X₀)⋅X₀⋅X₃+2^(X₀)⋅4⋅X₀⋅X₀+X₁+X₂ {O(EXP)}
t₄: 2⋅2^(X₀)⋅X₀⋅X₁+2⋅2^(X₀)⋅X₀⋅X₂+2⋅2^(X₀)⋅X₀⋅X₃+2^(X₀)⋅4⋅X₀⋅X₀+X₁+X₂ {O(EXP)}
t₅: 2⋅2^(X₀)⋅X₀⋅X₁+2⋅2^(X₀)⋅X₀⋅X₂+2⋅2^(X₀)⋅X₀⋅X₃+2^(X₀)⋅4⋅X₀⋅X₀+X₁+X₂ {O(EXP)}
t₆: X₀ {O(n)}
t₇: 1 {O(1)}
t₈: 2⋅2^(X₀)⋅X₁+2⋅2^(X₀)⋅X₂+2⋅2^(X₀)⋅X₃+2^(X₀)⋅4⋅X₀ {O(EXP)}
t₉: 2⋅2^(X₀)⋅X₁+2⋅2^(X₀)⋅X₂+2⋅2^(X₀)⋅X₃+2^(X₀)⋅4⋅X₀ {O(EXP)}
t₁₀: 2⋅2^(X₀)⋅X₁+2⋅2^(X₀)⋅X₂+2⋅2^(X₀)⋅X₃+2^(X₀)⋅4⋅X₀ {O(EXP)}

Costbounds

Overall costbound: 16⋅2^(X₀)⋅X₀⋅X₀+2⋅2^(X₀)⋅X₁+2⋅2^(X₀)⋅X₂+2⋅2^(X₀)⋅X₃+2^(X₀)⋅4⋅X₀+2^(X₀)⋅4⋅X₁+2^(X₀)⋅4⋅X₂+2^(X₀)⋅4⋅X₃+2^(X₀)⋅8⋅X₀+2^(X₀)⋅8⋅X₀⋅X₁+2^(X₀)⋅8⋅X₀⋅X₂+2^(X₀)⋅8⋅X₀⋅X₃+2⋅X₀+4⋅X₁+4⋅X₂+2 {O(EXP)}
t₀: 1 {O(1)}
t₁: X₀ {O(n)}
t₂: 2⋅2^(X₀)⋅X₀⋅X₁+2⋅2^(X₀)⋅X₀⋅X₂+2⋅2^(X₀)⋅X₀⋅X₃+2^(X₀)⋅4⋅X₀⋅X₀+X₁+X₂ {O(EXP)}
t₃: 2⋅2^(X₀)⋅X₀⋅X₁+2⋅2^(X₀)⋅X₀⋅X₂+2⋅2^(X₀)⋅X₀⋅X₃+2^(X₀)⋅4⋅X₀⋅X₀+X₁+X₂ {O(EXP)}
t₄: 2⋅2^(X₀)⋅X₀⋅X₁+2⋅2^(X₀)⋅X₀⋅X₂+2⋅2^(X₀)⋅X₀⋅X₃+2^(X₀)⋅4⋅X₀⋅X₀+X₁+X₂ {O(EXP)}
t₅: 2⋅2^(X₀)⋅X₀⋅X₁+2⋅2^(X₀)⋅X₀⋅X₂+2⋅2^(X₀)⋅X₀⋅X₃+2^(X₀)⋅4⋅X₀⋅X₀+X₁+X₂ {O(EXP)}
t₆: X₀ {O(n)}
t₇: 1 {O(1)}
t₈: 2⋅2^(X₀)⋅X₁+2⋅2^(X₀)⋅X₂+2⋅2^(X₀)⋅X₃+2^(X₀)⋅4⋅X₀ {O(EXP)}
t₉: 2⋅2^(X₀)⋅X₁+2⋅2^(X₀)⋅X₂+2⋅2^(X₀)⋅X₃+2^(X₀)⋅4⋅X₀ {O(EXP)}
t₁₀: 2⋅2^(X₀)⋅X₁+2⋅2^(X₀)⋅X₂+2⋅2^(X₀)⋅X₃+2^(X₀)⋅4⋅X₀ {O(EXP)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₀, X₄: X₀ {O(n)}
t₀, X₅: 0 {O(1)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: 2⋅2^(X₀)⋅X₀+2^(X₀)⋅X₁+2^(X₀)⋅X₂+2^(X₀)⋅X₃ {O(EXP)}
t₁, X₂: 2⋅2^(X₀)⋅X₀+2^(X₀)⋅X₁+2^(X₀)⋅X₂+2^(X₀)⋅X₃ {O(EXP)}
t₁, X₃: 2⋅2^(X₀)⋅X₀+2^(X₀)⋅X₁+2^(X₀)⋅X₂+2^(X₀)⋅X₃ {O(EXP)}
t₁, X₄: X₀ {O(n)}
t₁, X₅: 2⋅2^(X₀)⋅X₁+2⋅2^(X₀)⋅X₂+2⋅2^(X₀)⋅X₃+2^(X₀)⋅4⋅X₀+X₁+X₂ {O(EXP)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: 2⋅2^(X₀)⋅X₁+2⋅2^(X₀)⋅X₂+2⋅2^(X₀)⋅X₃+2^(X₀)⋅4⋅X₀ {O(EXP)}
t₂, X₂: 2⋅2^(X₀)⋅X₁+2⋅2^(X₀)⋅X₂+2⋅2^(X₀)⋅X₃+2^(X₀)⋅4⋅X₀ {O(EXP)}
t₂, X₃: 2⋅2^(X₀)⋅X₀+2^(X₀)⋅X₁+2^(X₀)⋅X₂+2^(X₀)⋅X₃ {O(EXP)}
t₂, X₄: X₀ {O(n)}
t₂, X₅: 2⋅2^(X₀)⋅X₁+2⋅2^(X₀)⋅X₂+2⋅2^(X₀)⋅X₃+2^(X₀)⋅4⋅X₀+X₁+X₂ {O(EXP)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: 2⋅2^(X₀)⋅X₀+2^(X₀)⋅X₁+2^(X₀)⋅X₂+2^(X₀)⋅X₃ {O(EXP)}
t₃, X₂: X₀ {O(n)}
t₃, X₃: 2⋅2^(X₀)⋅X₀+2^(X₀)⋅X₁+2^(X₀)⋅X₂+2^(X₀)⋅X₃ {O(EXP)}
t₃, X₄: X₀ {O(n)}
t₃, X₅: 2⋅2^(X₀)⋅X₁+2⋅2^(X₀)⋅X₂+2⋅2^(X₀)⋅X₃+2^(X₀)⋅4⋅X₀+X₁+X₂ {O(EXP)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₀ {O(n)}
t₄, X₂: 2⋅2^(X₀)⋅X₀+2^(X₀)⋅X₁+2^(X₀)⋅X₂+2^(X₀)⋅X₃ {O(EXP)}
t₄, X₃: 2⋅2^(X₀)⋅X₀+2^(X₀)⋅X₁+2^(X₀)⋅X₂+2^(X₀)⋅X₃ {O(EXP)}
t₄, X₄: X₀ {O(n)}
t₄, X₅: 2⋅2^(X₀)⋅X₁+2⋅2^(X₀)⋅X₂+2⋅2^(X₀)⋅X₃+2^(X₀)⋅4⋅X₀+X₁+X₂ {O(EXP)}
t₅, X₀: X₀ {O(n)}
t₅, X₁: 2⋅2^(X₀)⋅X₀+2^(X₀)⋅X₁+2^(X₀)⋅X₂+2^(X₀)⋅X₃ {O(EXP)}
t₅, X₂: 2⋅2^(X₀)⋅X₀+2^(X₀)⋅X₁+2^(X₀)⋅X₂+2^(X₀)⋅X₃ {O(EXP)}
t₅, X₃: 2⋅2^(X₀)⋅X₀+2^(X₀)⋅X₁+2^(X₀)⋅X₂+2^(X₀)⋅X₃ {O(EXP)}
t₅, X₄: X₀ {O(n)}
t₅, X₅: 2⋅2^(X₀)⋅X₁+2⋅2^(X₀)⋅X₂+2⋅2^(X₀)⋅X₃+2^(X₀)⋅4⋅X₀+X₁+X₂ {O(EXP)}
t₆, X₀: X₀ {O(n)}
t₆, X₁: 2⋅2^(X₀)⋅X₀+2^(X₀)⋅X₁+2^(X₀)⋅X₂+2^(X₀)⋅X₃ {O(EXP)}
t₆, X₂: 2⋅2^(X₀)⋅X₀+2^(X₀)⋅X₁+2^(X₀)⋅X₂+2^(X₀)⋅X₃ {O(EXP)}
t₆, X₃: 2⋅2^(X₀)⋅X₀+2^(X₀)⋅X₁+2^(X₀)⋅X₂+2^(X₀)⋅X₃ {O(EXP)}
t₆, X₄: X₀ {O(n)}
t₆, X₅: 2^(X₀)⋅4⋅X₁+2^(X₀)⋅4⋅X₂+2^(X₀)⋅4⋅X₃+2^(X₀)⋅8⋅X₀+2⋅X₁+2⋅X₂ {O(EXP)}
t₇, X₀: 2⋅X₀ {O(n)}
t₇, X₁: 2⋅2^(X₀)⋅X₁+2⋅2^(X₀)⋅X₂+2⋅2^(X₀)⋅X₃+2^(X₀)⋅4⋅X₀ {O(EXP)}
t₇, X₂: 2⋅2^(X₀)⋅X₁+2⋅2^(X₀)⋅X₂+2⋅2^(X₀)⋅X₃+2^(X₀)⋅4⋅X₀ {O(EXP)}
t₇, X₃: 2⋅2^(X₀)⋅X₁+2⋅2^(X₀)⋅X₂+2⋅2^(X₀)⋅X₃+2^(X₀)⋅4⋅X₀ {O(EXP)}
t₇, X₄: 2⋅X₀ {O(n)}
t₇, X₅: 2^(X₀)⋅4⋅X₁+2^(X₀)⋅4⋅X₂+2^(X₀)⋅4⋅X₃+2^(X₀)⋅8⋅X₀+2⋅X₁+2⋅X₂ {O(EXP)}
t₈, X₀: 2⋅X₀ {O(n)}
t₈, X₁: 2⋅2^(X₀)⋅X₁+2⋅2^(X₀)⋅X₂+2⋅2^(X₀)⋅X₃+2^(X₀)⋅4⋅X₀+2⋅X₀ {O(EXP)}
t₈, X₂: 16⋅2^(X₀)⋅2^(X₀)⋅X₀⋅X₀+16⋅2^(X₀)⋅2^(X₀)⋅X₀⋅X₁+16⋅2^(X₀)⋅2^(X₀)⋅X₀⋅X₂+16⋅2^(X₀)⋅2^(X₀)⋅X₀⋅X₃+16⋅2^(X₀)⋅X₀⋅X₀+2⋅2^(X₀)⋅X₁+2⋅2^(X₀)⋅X₂+2⋅2^(X₀)⋅X₃+2^(X₀)⋅2^(X₀)⋅4⋅X₁⋅X₁+2^(X₀)⋅2^(X₀)⋅4⋅X₂⋅X₂+2^(X₀)⋅2^(X₀)⋅4⋅X₃⋅X₃+2^(X₀)⋅2^(X₀)⋅8⋅X₁⋅X₂+2^(X₀)⋅2^(X₀)⋅8⋅X₁⋅X₃+2^(X₀)⋅2^(X₀)⋅8⋅X₂⋅X₃+2^(X₀)⋅4⋅X₀+2^(X₀)⋅4⋅X₁+2^(X₀)⋅4⋅X₂+2^(X₀)⋅4⋅X₃+2^(X₀)⋅8⋅X₀+2^(X₀)⋅8⋅X₀⋅X₁+2^(X₀)⋅8⋅X₀⋅X₂+2^(X₀)⋅8⋅X₀⋅X₃+6⋅X₀ {O(EXP)}
t₈, X₃: 2⋅2^(X₀)⋅X₁+2⋅2^(X₀)⋅X₂+2⋅2^(X₀)⋅X₃+2^(X₀)⋅4⋅X₀ {O(EXP)}
t₈, X₄: 2⋅X₀ {O(n)}
t₈, X₅: 2^(X₀)⋅4⋅X₁+2^(X₀)⋅4⋅X₂+2^(X₀)⋅4⋅X₃+2^(X₀)⋅8⋅X₀+2⋅X₁+2⋅X₂ {O(EXP)}
t₉, X₀: 2⋅X₀ {O(n)}
t₉, X₁: 2⋅2^(X₀)⋅X₁+2⋅2^(X₀)⋅X₂+2⋅2^(X₀)⋅X₃+2^(X₀)⋅4⋅X₀+2⋅X₀ {O(EXP)}
t₉, X₂: 16⋅2^(X₀)⋅2^(X₀)⋅X₀⋅X₀+16⋅2^(X₀)⋅2^(X₀)⋅X₀⋅X₁+16⋅2^(X₀)⋅2^(X₀)⋅X₀⋅X₂+16⋅2^(X₀)⋅2^(X₀)⋅X₀⋅X₃+16⋅2^(X₀)⋅X₀⋅X₀+2⋅2^(X₀)⋅X₁+2⋅2^(X₀)⋅X₂+2⋅2^(X₀)⋅X₃+2^(X₀)⋅2^(X₀)⋅4⋅X₁⋅X₁+2^(X₀)⋅2^(X₀)⋅4⋅X₂⋅X₂+2^(X₀)⋅2^(X₀)⋅4⋅X₃⋅X₃+2^(X₀)⋅2^(X₀)⋅8⋅X₁⋅X₂+2^(X₀)⋅2^(X₀)⋅8⋅X₁⋅X₃+2^(X₀)⋅2^(X₀)⋅8⋅X₂⋅X₃+2^(X₀)⋅4⋅X₀+2^(X₀)⋅4⋅X₁+2^(X₀)⋅4⋅X₂+2^(X₀)⋅4⋅X₃+2^(X₀)⋅8⋅X₀+2^(X₀)⋅8⋅X₀⋅X₁+2^(X₀)⋅8⋅X₀⋅X₂+2^(X₀)⋅8⋅X₀⋅X₃+6⋅X₀ {O(EXP)}
t₉, X₃: 2⋅2^(X₀)⋅X₁+2⋅2^(X₀)⋅X₂+2⋅2^(X₀)⋅X₃+2^(X₀)⋅4⋅X₀ {O(EXP)}
t₉, X₄: 2⋅X₀ {O(n)}
t₉, X₅: 2^(X₀)⋅4⋅X₁+2^(X₀)⋅4⋅X₂+2^(X₀)⋅4⋅X₃+2^(X₀)⋅8⋅X₀+2⋅X₁+2⋅X₂ {O(EXP)}
t₁₀, X₀: 2⋅X₀ {O(n)}
t₁₀, X₁: 2⋅X₀ {O(n)}
t₁₀, X₂: 2⋅2^(X₀)⋅X₁+2⋅2^(X₀)⋅X₂+2⋅2^(X₀)⋅X₃+2^(X₀)⋅4⋅X₀+2⋅X₀ {O(EXP)}
t₁₀, X₃: 2⋅2^(X₀)⋅X₁+2⋅2^(X₀)⋅X₂+2⋅2^(X₀)⋅X₃+2^(X₀)⋅4⋅X₀ {O(EXP)}
t₁₀, X₄: 2⋅X₀ {O(n)}
t₁₀, X₅: 2^(X₀)⋅4⋅X₁+2^(X₀)⋅4⋅X₂+2^(X₀)⋅4⋅X₃+2^(X₀)⋅8⋅X₀+2⋅X₁+2⋅X₂ {O(EXP)}