Initial Problem

Start: start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇
Temp_Vars: I, J, K
Locations: f1, f19, f2, f27, f34, f36, f43, f49, f8, start
Transitions:
t₃: f19(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f19(X₀, X₁, X₂, X₃, 1+X₄, X₅, X₆, J) :|: X₄ ≤ X₀
t₁₇: f19(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f27(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₀ ≤ X₄
t₂₁: f2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₀ ≤ X₁
t₀: f2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f8(X₀, X₁, 0, X₁, X₄, X₅, X₆, X₇) :|: 1+X₁ ≤ X₀
t₄: f27(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f27(X₀, X₁, X₂, X₃, 1+X₄, X₅, X₆, J) :|: X₄ ≤ X₀
t₁₆: f27(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f34(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₀ ≤ X₄
t₁₂: f34(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f2(X₀, 1+X₁, 0, X₃, X₄, X₅, X₆, X₇) :|: 0 ≤ X₂ ∧ X₂ ≤ 0
t₅: f34(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f36(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₂ ≤ 0
t₆: f34(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f36(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1 ≤ X₂
t₁₅: f36(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f2(X₀, 1+X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₀ ≤ X₃
t₁₁: f36(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f36(X₀, X₁, X₂, 1+X₃, X₄, X₅, X₆, 0) :|: X₃ ≤ X₀
t₇: f36(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f43(X₀, X₁, X₂, X₃, X₄, X₅, X₆, J) :|: 1+I ≤ 0 ∧ X₃ ≤ X₀
t₈: f36(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f43(X₀, X₁, X₂, X₃, X₄, X₅, X₆, J) :|: 1 ≤ I ∧ X₃ ≤ X₀
t₉: f43(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f43(X₀, X₁, X₂, X₃, 1+X₄, X₅, X₆, X₇) :|: X₄ ≤ X₀
t₁₄: f43(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f49(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₀ ≤ X₄
t₁₃: f49(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f36(X₀, X₁, X₂, 1+X₃, X₄, X₅, X₆, X₇) :|: 1+X₀ ≤ X₄
t₁₀: f49(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f49(X₀, X₁, X₂, X₃, 1+X₄, X₅, X₆, X₇) :|: X₄ ≤ X₀
t₁₉: f8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f19(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₀ ≤ X₄ ∧ 1+X₃ ≤ X₁
t₂₀: f8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f19(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₀ ≤ X₄ ∧ 1+X₁ ≤ X₃
t₁₈: f8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f34(X₀, X₁, X₂, X₁, X₄, X₅, X₆, X₇) :|: 1+X₀ ≤ X₄ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃
t₁: f8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f8(X₀, X₁, X₂, X₃, 1+X₄, J, I, X₇) :|: J ≤ I ∧ X₄ ≤ X₀
t₂: f8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f8(X₀, X₁, J, X₄, 1+X₄, I, K, X₇) :|: 1+K ≤ I ∧ X₄ ≤ X₀
t₂₂: start(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)

Preprocessing

Cut unsatisfiable transition [t₃: f19→f19; t₄: f27→f27; t₁₀: f49→f49]

Eliminate variables [X₅; X₆; X₇] that do not contribute to the problem

Found invariant 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ for location f49

Found invariant 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ for location f19

Found invariant X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ 1+X₀ ∧ 1+X₁ ≤ X₀ for location f36

Found invariant 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ for location f27

Found invariant X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ for location f8

Found invariant 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ for location f43

Found invariant X₀ ≤ X₁ for location f1

Found invariant 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ for location f34

Cut unsatisfiable transition [t₆₂: f43→f43]

Problem after Preprocessing

Start: start
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars: I, J, K
Locations: f1, f19, f2, f27, f34, f36, f43, f49, f8, start
Transitions:
t₅₁: f19(X₀, X₁, X₂, X₃, X₄) → f27(X₀, X₁, X₂, X₃, X₄) :|: 1+X₀ ≤ X₄ ∧ 1+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ X₃ ≤ X₀
t₅₂: f2(X₀, X₁, X₂, X₃, X₄) → f1(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ X₁
t₅₃: f2(X₀, X₁, X₂, X₃, X₄) → f8(X₀, X₁, 0, X₁, X₄) :|: 1+X₁ ≤ X₀
t₅₄: f27(X₀, X₁, X₂, X₃, X₄) → f34(X₀, X₁, X₂, X₃, X₄) :|: 1+X₀ ≤ X₄ ∧ 1+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ X₃ ≤ X₀
t₅₅: f34(X₀, X₁, X₂, X₃, X₄) → f2(X₀, 1+X₁, 0, X₃, X₄) :|: 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ X₃ ≤ X₀
t₅₆: f34(X₀, X₁, X₂, X₃, X₄) → f36(X₀, X₁, X₂, X₃, X₄) :|: 1+X₂ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ X₃ ≤ X₀
t₅₇: f34(X₀, X₁, X₂, X₃, X₄) → f36(X₀, X₁, X₂, X₃, X₄) :|: 1 ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ X₃ ≤ X₀
t₅₈: f36(X₀, X₁, X₂, X₃, X₄) → f2(X₀, 1+X₁, X₂, X₃, X₄) :|: 1+X₀ ≤ X₃ ∧ X₃ ≤ 1+X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ X₃ ≤ X₄
t₅₉: f36(X₀, X₁, X₂, X₃, X₄) → f36(X₀, X₁, X₂, 1+X₃, X₄) :|: X₃ ≤ X₀ ∧ X₃ ≤ 1+X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ X₃ ≤ X₄
t₆₀: f36(X₀, X₁, X₂, X₃, X₄) → f43(X₀, X₁, X₂, X₃, X₄) :|: 1+I ≤ 0 ∧ X₃ ≤ X₀ ∧ X₃ ≤ 1+X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ X₃ ≤ X₄
t₆₁: f36(X₀, X₁, X₂, X₃, X₄) → f43(X₀, X₁, X₂, X₃, X₄) :|: 1 ≤ I ∧ X₃ ≤ X₀ ∧ X₃ ≤ 1+X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ X₃ ≤ X₄
t₆₃: f43(X₀, X₁, X₂, X₃, X₄) → f49(X₀, X₁, X₂, X₃, X₄) :|: 1+X₀ ≤ X₄ ∧ 1+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ X₃ ≤ X₀
t₆₄: f49(X₀, X₁, X₂, X₃, X₄) → f36(X₀, X₁, X₂, 1+X₃, X₄) :|: 1+X₀ ≤ X₄ ∧ 1+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ X₃ ≤ X₀
t₆₅: f8(X₀, X₁, X₂, X₃, X₄) → f19(X₀, X₁, X₂, X₃, X₄) :|: 1+X₀ ≤ X₄ ∧ 1+X₃ ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ X₃ ≤ X₀
t₆₆: f8(X₀, X₁, X₂, X₃, X₄) → f19(X₀, X₁, X₂, X₃, X₄) :|: 1+X₀ ≤ X₄ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₀ ∧ X₃ ≤ X₀
t₆₇: f8(X₀, X₁, X₂, X₃, X₄) → f34(X₀, X₁, X₂, X₁, X₄) :|: 1+X₀ ≤ X₄ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ 1+X₁ ≤ X₀ ∧ X₃ ≤ X₀
t₆₈: f8(X₀, X₁, X₂, X₃, X₄) → f8(X₀, X₁, X₂, X₃, 1+X₄) :|: J ≤ I ∧ X₄ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ X₃ ≤ X₀
t₆₉: f8(X₀, X₁, X₂, X₃, X₄) → f8(X₀, X₁, J, X₄, 1+X₄) :|: 1+K ≤ I ∧ X₄ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ X₃ ≤ X₀
t₇₀: start(X₀, X₁, X₂, X₃, X₄) → f2(X₀, X₁, X₂, X₃, X₄)

MPRF for transition t₅₁: f19(X₀, X₁, X₂, X₃, X₄) → f27(X₀, X₁, X₂, X₃, X₄) :|: 1+X₀ ≤ X₄ ∧ 1+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ X₃ ≤ X₀ of depth 1:

new bound:

X₀+X₁+1 {O(n)}

• f19: [1+X₀-X₁]
• f2: [1+X₀-X₁]
• f27: [X₀-X₁]
• f34: [X₀-X₁]
• f36: [X₀-X₁]
• f43: [X₀-X₁]
• f49: [X₀-X₁]
• f8: [1+X₀-X₁]

MPRF for transition t₅₃: f2(X₀, X₁, X₂, X₃, X₄) → f8(X₀, X₁, 0, X₁, X₄) :|: 1+X₁ ≤ X₀ of depth 1:

new bound:

X₀+X₁+2 {O(n)}

• f19: [1+X₀-X₁]
• f2: [2+X₀-X₁]
• f27: [1+X₀-X₁]
• f34: [1+X₀-X₁]
• f36: [1+X₀-X₁]
• f43: [1+X₀-X₁]
• f49: [1+X₀-X₁]
• f8: [1+X₀-X₁]

MPRF for transition t₅₄: f27(X₀, X₁, X₂, X₃, X₄) → f34(X₀, X₁, X₂, X₃, X₄) :|: 1+X₀ ≤ X₄ ∧ 1+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ X₃ ≤ X₀ of depth 1:

new bound:

X₀+X₁+1 {O(n)}

• f19: [1+X₀-X₁]
• f2: [1+X₀-X₁]
• f27: [1+X₀-X₁]
• f34: [X₀-X₁]
• f36: [X₀-X₁]
• f43: [X₀-X₁]
• f49: [X₀-X₁]
• f8: [1+X₀-X₁]

MPRF for transition t₅₅: f34(X₀, X₁, X₂, X₃, X₄) → f2(X₀, 1+X₁, 0, X₃, X₄) :|: 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ X₃ ≤ X₀ of depth 1:

new bound:

X₀+X₁ {O(n)}

• f19: [X₀-X₁]
• f2: [X₀-X₁]
• f27: [X₀-X₁]
• f34: [X₀-X₁]
• f36: [X₀-X₁]
• f43: [X₀-X₁]
• f49: [X₀-X₁]
• f8: [X₀-X₁]

MPRF for transition t₅₆: f34(X₀, X₁, X₂, X₃, X₄) → f36(X₀, X₁, X₂, X₃, X₄) :|: 1+X₂ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ X₃ ≤ X₀ of depth 1:

new bound:

X₀+X₁+1 {O(n)}

• f19: [1+X₀-X₁]
• f2: [1+X₀-X₁]
• f27: [1+X₀-X₁]
• f34: [1+X₀-X₁]
• f36: [X₀-X₁]
• f43: [X₀-X₁]
• f49: [X₀-X₁]
• f8: [1+X₀-X₁]

MPRF for transition t₅₇: f34(X₀, X₁, X₂, X₃, X₄) → f36(X₀, X₁, X₂, X₃, X₄) :|: 1 ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ X₃ ≤ X₀ of depth 1:

new bound:

X₀+X₁ {O(n)}

• f19: [X₀-X₁]
• f2: [X₀-X₁]
• f27: [X₀-X₁]
• f34: [X₀-X₁]
• f36: [X₀-1-X₁]
• f43: [X₀-1-X₁]
• f49: [X₀-1-X₁]
• f8: [X₀-X₁]

MPRF for transition t₅₈: f36(X₀, X₁, X₂, X₃, X₄) → f2(X₀, 1+X₁, X₂, X₃, X₄) :|: 1+X₀ ≤ X₃ ∧ X₃ ≤ 1+X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ X₃ ≤ X₄ of depth 1:

new bound:

X₀+X₁ {O(n)}

• f19: [X₀-X₁]
• f2: [X₀-X₁]
• f27: [X₀-X₁]
• f34: [X₀-X₁]
• f36: [X₀-X₁]
• f43: [X₀-X₁]
• f49: [X₀-X₁]
• f8: [X₀-X₁]

MPRF for transition t₆₅: f8(X₀, X₁, X₂, X₃, X₄) → f19(X₀, X₁, X₂, X₃, X₄) :|: 1+X₀ ≤ X₄ ∧ 1+X₃ ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ X₃ ≤ X₀ of depth 1:

new bound:

X₀+X₁+1 {O(n)}

• f19: [X₀-X₁]
• f2: [1+X₀-X₁]
• f27: [X₀-X₁]
• f34: [X₀-X₁]
• f36: [X₀-X₁]
• f43: [X₀-X₁]
• f49: [X₀-X₁]
• f8: [1+X₀-X₁]

MPRF for transition t₆₆: f8(X₀, X₁, X₂, X₃, X₄) → f19(X₀, X₁, X₂, X₃, X₄) :|: 1+X₀ ≤ X₄ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₀ ∧ X₃ ≤ X₀ of depth 1:

new bound:

X₀+X₁ {O(n)}

• f19: [X₀-1-X₁]
• f2: [X₀-X₁]
• f27: [X₀-1-X₁]
• f34: [X₀-1-X₁]
• f36: [X₀-1-X₁]
• f43: [X₀-1-X₁]
• f49: [X₀-1-X₁]
• f8: [X₀-X₁]

MPRF for transition t₆₇: f8(X₀, X₁, X₂, X₃, X₄) → f34(X₀, X₁, X₂, X₁, X₄) :|: 1+X₀ ≤ X₄ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ 1+X₁ ≤ X₀ ∧ X₃ ≤ X₀ of depth 1:

new bound:

X₀+X₁+1 {O(n)}

• f19: [X₀-X₁]
• f2: [1+X₀-X₁]
• f27: [X₀-X₁]
• f34: [X₀-X₁]
• f36: [X₀-X₁]
• f43: [X₀-X₁]
• f49: [X₀-X₁]
• f8: [1+X₀-X₁]

MPRF for transition t₆₈: f8(X₀, X₁, X₂, X₃, X₄) → f8(X₀, X₁, X₂, X₃, 1+X₄) :|: J ≤ I ∧ X₄ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ X₃ ≤ X₀ of depth 1:

new bound:

X₀+X₄+1 {O(n)}

• f19: [1+X₀-X₄]
• f2: [1+X₀-X₄]
• f27: [1+X₀-X₄]
• f34: [1+X₀-X₄]
• f36: [1+X₀-X₄]
• f43: [1+X₀-X₄]
• f49: [1+X₀-X₄]
• f8: [1+X₀-X₄]

MPRF for transition t₆₉: f8(X₀, X₁, X₂, X₃, X₄) → f8(X₀, X₁, J, X₄, 1+X₄) :|: 1+K ≤ I ∧ X₄ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ X₃ ≤ X₀ of depth 1:

new bound:

X₀+X₄+1 {O(n)}

• f19: [1+X₀-X₄]
• f2: [1+X₀-X₄]
• f27: [1+X₀-X₄]
• f34: [1+X₀-X₄]
• f36: [1+X₀-X₄]
• f43: [1+X₀-X₄]
• f49: [1+X₀-X₄]
• f8: [1+X₀-X₄]

MPRF for transition t₅₉: f36(X₀, X₁, X₂, X₃, X₄) → f36(X₀, X₁, X₂, 1+X₃, X₄) :|: X₃ ≤ X₀ ∧ X₃ ≤ 1+X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ X₃ ≤ X₄ of depth 1:

new bound:

20⋅X₁⋅X₁+45⋅X₀⋅X₀+45⋅X₀⋅X₄+45⋅X₁⋅X₄+65⋅X₀⋅X₁+21⋅X₄+43⋅X₁+54⋅X₀+14 {O(n^2)}

• f19: [2⋅X₄-X₀-X₃]
• f2: [0]
• f27: [2⋅X₄-X₀-X₃]
• f34: [2⋅X₄-X₀-X₃]
• f36: [1+X₄-X₃]
• f43: [X₄-X₃]
• f49: [X₄-X₃]
• f8: [0]

MPRF for transition t₆₀: f36(X₀, X₁, X₂, X₃, X₄) → f43(X₀, X₁, X₂, X₃, X₄) :|: 1+I ≤ 0 ∧ X₃ ≤ X₀ ∧ X₃ ≤ 1+X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ X₃ ≤ X₄ of depth 1:

new bound:

20⋅X₁⋅X₁+27⋅X₀⋅X₄+27⋅X₁⋅X₄+33⋅X₀⋅X₀+53⋅X₀⋅X₁+37⋅X₁+40⋅X₀+9⋅X₄+10 {O(n^2)}

• f19: [2+X₀-X₃]
• f2: [0]
• f27: [2+X₀-X₃]
• f34: [2+X₀-X₃]
• f36: [2+X₀-X₃]
• f43: [1+X₀-X₃]
• f49: [1+X₀-X₃]
• f8: [0]

MPRF for transition t₆₁: f36(X₀, X₁, X₂, X₃, X₄) → f43(X₀, X₁, X₂, X₃, X₄) :|: 1 ≤ I ∧ X₃ ≤ X₀ ∧ X₃ ≤ 1+X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ X₃ ≤ X₄ of depth 1:

new bound:

20⋅X₁⋅X₁+36⋅X₀⋅X₀+36⋅X₀⋅X₄+36⋅X₁⋅X₄+56⋅X₀⋅X₁+15⋅X₄+40⋅X₁+45⋅X₀+12 {O(n^2)}

• f19: [1+X₄-X₃]
• f2: [0]
• f27: [1+X₄-X₃]
• f34: [1+X₄-X₃]
• f36: [1+X₄-X₃]
• f43: [X₄-X₃]
• f49: [X₄-X₃]
• f8: [0]

MPRF for transition t₆₃: f43(X₀, X₁, X₂, X₃, X₄) → f49(X₀, X₁, X₂, X₃, X₄) :|: 1+X₀ ≤ X₄ ∧ 1+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ X₃ ≤ X₀ of depth 1:

new bound:

20⋅X₁⋅X₁+27⋅X₀⋅X₄+27⋅X₁⋅X₄+33⋅X₀⋅X₀+53⋅X₀⋅X₁+34⋅X₁+37⋅X₀+9⋅X₄+8 {O(n^2)}

• f19: [1+X₀-X₃]
• f2: [0]
• f27: [1+X₀-X₃]
• f34: [1+X₀-X₃]
• f36: [1+X₀-X₃]
• f43: [1+X₀-X₃]
• f49: [X₀-X₃]
• f8: [0]

MPRF for transition t₆₄: f49(X₀, X₁, X₂, X₃, X₄) → f36(X₀, X₁, X₂, 1+X₃, X₄) :|: 1+X₀ ≤ X₄ ∧ 1+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ X₃ ≤ X₀ of depth 1:

new bound:

20⋅X₁⋅X₁+36⋅X₀⋅X₀+36⋅X₀⋅X₄+36⋅X₁⋅X₄+56⋅X₀⋅X₁+15⋅X₄+37⋅X₁+42⋅X₀+10 {O(n^2)}

• f19: [X₄-X₃]
• f2: [0]
• f27: [X₄-X₃]
• f34: [X₄-X₃]
• f36: [1+X₀-X₃]
• f43: [1+X₀-X₃]
• f49: [1+X₀-X₃]
• f8: [0]

Cut unsatisfiable transition [t₅₈: f36→f2; t₁₆₇: f36→f2]

Found invariant 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ for location f49_v1

Found invariant 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ for location f19

Found invariant 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ for location f43_v1

Found invariant X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ 1+X₀ ∧ 1+X₁ ≤ X₀ for location f36_v1

Found invariant 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ for location f36

Found invariant 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ for location f27

Found invariant X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ for location f8

Found invariant X₀ ≤ X₁ for location f1

Found invariant 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ for location f34

All Bounds

Timebounds

Overall timebound:100⋅X₁⋅X₁+171⋅X₀⋅X₄+171⋅X₁⋅X₄+183⋅X₀⋅X₀+283⋅X₀⋅X₁+201⋅X₁+230⋅X₀+71⋅X₄+65 {O(n^2)}
t₅₁: X₀+X₁+1 {O(n)}
t₅₂: 1 {O(1)}
t₅₃: X₀+X₁+2 {O(n)}
t₅₄: X₀+X₁+1 {O(n)}
t₅₅: X₀+X₁ {O(n)}
t₅₆: X₀+X₁+1 {O(n)}
t₅₇: X₀+X₁ {O(n)}
t₅₈: X₀+X₁ {O(n)}
t₅₉: 20⋅X₁⋅X₁+45⋅X₀⋅X₀+45⋅X₀⋅X₄+45⋅X₁⋅X₄+65⋅X₀⋅X₁+21⋅X₄+43⋅X₁+54⋅X₀+14 {O(n^2)}
t₆₀: 20⋅X₁⋅X₁+27⋅X₀⋅X₄+27⋅X₁⋅X₄+33⋅X₀⋅X₀+53⋅X₀⋅X₁+37⋅X₁+40⋅X₀+9⋅X₄+10 {O(n^2)}
t₆₁: 20⋅X₁⋅X₁+36⋅X₀⋅X₀+36⋅X₀⋅X₄+36⋅X₁⋅X₄+56⋅X₀⋅X₁+15⋅X₄+40⋅X₁+45⋅X₀+12 {O(n^2)}
t₆₃: 20⋅X₁⋅X₁+27⋅X₀⋅X₄+27⋅X₁⋅X₄+33⋅X₀⋅X₀+53⋅X₀⋅X₁+34⋅X₁+37⋅X₀+9⋅X₄+8 {O(n^2)}
t₆₄: 20⋅X₁⋅X₁+36⋅X₀⋅X₀+36⋅X₀⋅X₄+36⋅X₁⋅X₄+56⋅X₀⋅X₁+15⋅X₄+37⋅X₁+42⋅X₀+10 {O(n^2)}
t₆₅: X₀+X₁+1 {O(n)}
t₆₆: X₀+X₁ {O(n)}
t₆₇: X₀+X₁+1 {O(n)}
t₆₈: X₀+X₄+1 {O(n)}
t₆₉: X₀+X₄+1 {O(n)}
t₇₀: 1 {O(1)}

Costbounds

Overall costbound: 100⋅X₁⋅X₁+171⋅X₀⋅X₄+171⋅X₁⋅X₄+183⋅X₀⋅X₀+283⋅X₀⋅X₁+201⋅X₁+230⋅X₀+71⋅X₄+65 {O(n^2)}
t₅₁: X₀+X₁+1 {O(n)}
t₅₂: 1 {O(1)}
t₅₃: X₀+X₁+2 {O(n)}
t₅₄: X₀+X₁+1 {O(n)}
t₅₅: X₀+X₁ {O(n)}
t₅₆: X₀+X₁+1 {O(n)}
t₅₇: X₀+X₁ {O(n)}
t₅₈: X₀+X₁ {O(n)}
t₅₉: 20⋅X₁⋅X₁+45⋅X₀⋅X₀+45⋅X₀⋅X₄+45⋅X₁⋅X₄+65⋅X₀⋅X₁+21⋅X₄+43⋅X₁+54⋅X₀+14 {O(n^2)}
t₆₀: 20⋅X₁⋅X₁+27⋅X₀⋅X₄+27⋅X₁⋅X₄+33⋅X₀⋅X₀+53⋅X₀⋅X₁+37⋅X₁+40⋅X₀+9⋅X₄+10 {O(n^2)}
t₆₁: 20⋅X₁⋅X₁+36⋅X₀⋅X₀+36⋅X₀⋅X₄+36⋅X₁⋅X₄+56⋅X₀⋅X₁+15⋅X₄+40⋅X₁+45⋅X₀+12 {O(n^2)}
t₆₃: 20⋅X₁⋅X₁+27⋅X₀⋅X₄+27⋅X₁⋅X₄+33⋅X₀⋅X₀+53⋅X₀⋅X₁+34⋅X₁+37⋅X₀+9⋅X₄+8 {O(n^2)}
t₆₄: 20⋅X₁⋅X₁+36⋅X₀⋅X₀+36⋅X₀⋅X₄+36⋅X₁⋅X₄+56⋅X₀⋅X₁+15⋅X₄+37⋅X₁+42⋅X₀+10 {O(n^2)}
t₆₅: X₀+X₁+1 {O(n)}
t₆₆: X₀+X₁ {O(n)}
t₆₇: X₀+X₁+1 {O(n)}
t₆₈: X₀+X₄+1 {O(n)}
t₆₉: X₀+X₄+1 {O(n)}
t₇₀: 1 {O(1)}

Sizebounds

t₅₁, X₀: X₀ {O(n)}
t₅₁, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₅₁, X₃: 14⋅X₁+26⋅X₀+27⋅X₄+18 {O(n)}
t₅₁, X₄: 2⋅X₀+3⋅X₄+2 {O(n)}
t₅₂, X₀: 3⋅X₀ {O(n)}
t₅₂, X₁: 4⋅X₀+7⋅X₁ {O(n)}
t₅₂, X₃: 162⋅X₀⋅X₀+162⋅X₀⋅X₄+162⋅X₁⋅X₄+242⋅X₀⋅X₁+80⋅X₁⋅X₁+207⋅X₄+260⋅X₁+342⋅X₀+X₃+138 {O(n^2)}
t₅₂, X₄: 4⋅X₀+7⋅X₄+4 {O(n)}
t₅₃, X₀: X₀ {O(n)}
t₅₃, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₅₃, X₂: 0 {O(1)}
t₅₃, X₃: 4⋅X₀+7⋅X₁ {O(n)}
t₅₃, X₄: 2⋅X₀+3⋅X₄+2 {O(n)}
t₅₄, X₀: X₀ {O(n)}
t₅₄, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₅₄, X₃: 14⋅X₁+26⋅X₀+27⋅X₄+18 {O(n)}
t₅₄, X₄: 2⋅X₀+3⋅X₄+2 {O(n)}
t₅₅, X₀: X₀ {O(n)}
t₅₅, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₅₅, X₂: 0 {O(1)}
t₅₅, X₃: 20⋅X₁+27⋅X₄+30⋅X₀+18 {O(n)}
t₅₅, X₄: 2⋅X₀+3⋅X₄+2 {O(n)}
t₅₆, X₀: X₀ {O(n)}
t₅₆, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₅₆, X₃: 20⋅X₁+27⋅X₄+30⋅X₀+18 {O(n)}
t₅₆, X₄: 2⋅X₀+3⋅X₄+2 {O(n)}
t₅₇, X₀: X₀ {O(n)}
t₅₇, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₅₇, X₃: 20⋅X₁+27⋅X₄+30⋅X₀+18 {O(n)}
t₅₇, X₄: 2⋅X₀+3⋅X₄+2 {O(n)}
t₅₈, X₀: X₀ {O(n)}
t₅₈, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₅₈, X₃: 162⋅X₀⋅X₀+162⋅X₀⋅X₄+162⋅X₁⋅X₄+242⋅X₀⋅X₁+80⋅X₁⋅X₁+180⋅X₄+240⋅X₁+312⋅X₀+120 {O(n^2)}
t₅₈, X₄: 2⋅X₀+3⋅X₄+2 {O(n)}
t₅₉, X₀: X₀ {O(n)}
t₅₉, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₅₉, X₃: 121⋅X₀⋅X₁+40⋅X₁⋅X₁+81⋅X₀⋅X₀+81⋅X₀⋅X₄+81⋅X₁⋅X₄+120⋅X₁+156⋅X₀+90⋅X₄+60 {O(n^2)}
t₅₉, X₄: 2⋅X₀+3⋅X₄+2 {O(n)}
t₆₀, X₀: X₀ {O(n)}
t₆₀, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₆₀, X₃: 121⋅X₀⋅X₁+40⋅X₁⋅X₁+81⋅X₀⋅X₀+81⋅X₀⋅X₄+81⋅X₁⋅X₄+120⋅X₁+156⋅X₀+90⋅X₄+60 {O(n^2)}
t₆₀, X₄: 2⋅X₀+3⋅X₄+2 {O(n)}
t₆₁, X₀: X₀ {O(n)}
t₆₁, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₆₁, X₃: 121⋅X₀⋅X₁+40⋅X₁⋅X₁+81⋅X₀⋅X₀+81⋅X₀⋅X₄+81⋅X₁⋅X₄+120⋅X₁+156⋅X₀+90⋅X₄+60 {O(n^2)}
t₆₁, X₄: 2⋅X₀+3⋅X₄+2 {O(n)}
t₆₃, X₀: X₀ {O(n)}
t₆₃, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₆₃, X₃: 121⋅X₀⋅X₁+40⋅X₁⋅X₁+81⋅X₀⋅X₀+81⋅X₀⋅X₄+81⋅X₁⋅X₄+120⋅X₁+156⋅X₀+90⋅X₄+60 {O(n^2)}
t₆₃, X₄: 2⋅X₀+3⋅X₄+2 {O(n)}
t₆₄, X₀: X₀ {O(n)}
t₆₄, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₆₄, X₃: 121⋅X₀⋅X₁+40⋅X₁⋅X₁+81⋅X₀⋅X₀+81⋅X₀⋅X₄+81⋅X₁⋅X₄+120⋅X₁+156⋅X₀+90⋅X₄+60 {O(n^2)}
t₆₄, X₄: 2⋅X₀+3⋅X₄+2 {O(n)}
t₆₅, X₀: X₀ {O(n)}
t₆₅, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₆₅, X₃: 10⋅X₀+7⋅X₁+9⋅X₄+6 {O(n)}
t₆₅, X₄: 2⋅X₀+3⋅X₄+2 {O(n)}
t₆₆, X₀: X₀ {O(n)}
t₆₆, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₆₆, X₃: 16⋅X₀+18⋅X₄+7⋅X₁+12 {O(n)}
t₆₆, X₄: 2⋅X₀+3⋅X₄+2 {O(n)}
t₆₇, X₀: X₀ {O(n)}
t₆₇, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₆₇, X₃: 4⋅X₀+6⋅X₁ {O(n)}
t₆₇, X₄: 2⋅X₀+3⋅X₄+2 {O(n)}
t₆₈, X₀: X₀ {O(n)}
t₆₈, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₆₈, X₃: 10⋅X₀+7⋅X₁+9⋅X₄+6 {O(n)}
t₆₈, X₄: 2⋅X₀+3⋅X₄+2 {O(n)}
t₆₉, X₀: X₀ {O(n)}
t₆₉, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₆₉, X₃: 6⋅X₀+9⋅X₄+6 {O(n)}
t₆₉, X₄: 2⋅X₀+3⋅X₄+2 {O(n)}
t₇₀, X₀: X₀ {O(n)}
t₇₀, X₁: X₁ {O(n)}
t₇₀, X₂: X₂ {O(n)}
t₇₀, X₃: X₃ {O(n)}
t₇₀, X₄: X₄ {O(n)}