Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 < X₂
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₂ ≤ 0
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₃, X₄, X₆, X₃, X₄, X₅, X₆)
t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(3⋅X₀-4⋅X₁, 4⋅X₀+3⋅X₁, X₂+X₀-1, X₃, X₄, X₅, X₆)
t₅: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆)

Preprocessing

Eliminate variables {X₅} that do not contribute to the problem

Found invariant X₂ ≤ 0 for location l5

Found invariant X₂ ≤ 0 for location l4

Found invariant 1 ≤ X₂ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₆
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₁₂: l0(X₀, X₁, X₂, X₃, X₄, X₆) → l2(X₀, X₁, X₂, X₃, X₄, X₆)
t₁₃: l1(X₀, X₁, X₂, X₃, X₄, X₆) → l3(X₀, X₁, X₂, X₃, X₄, X₆) :|: 0 < X₂
t₁₄: l1(X₀, X₁, X₂, X₃, X₄, X₆) → l4(X₀, X₁, X₂, X₃, X₄, X₆) :|: X₂ ≤ 0
t₁₅: l2(X₀, X₁, X₂, X₃, X₄, X₆) → l1(X₃, X₄, X₆, X₃, X₄, X₆)
t₁₆: l3(X₀, X₁, X₂, X₃, X₄, X₆) → l1(3⋅X₀-4⋅X₁, 4⋅X₀+3⋅X₁, X₂+X₀-1, X₃, X₄, X₆) :|: 1 ≤ X₂
t₁₇: l4(X₀, X₁, X₂, X₃, X₄, X₆) → l5(X₀, X₁, X₂, X₃, X₄, X₆) :|: X₂ ≤ 0

MPRF for transition t₁₃: l1(X₀, X₁, X₂, X₃, X₄, X₆) → l3(X₀, X₁, X₂, X₃, X₄, X₆) :|: 0 < X₂ of depth 4:

new bound:

1246⋅X₃+2136⋅X₄+9078⋅X₆+8901 {O(n)}

MPRF:

l3 [100⋅X₂-10⋅X₀-20⋅X₁-199 ; -7⋅X₀-24⋅X₁ ; 4⋅X₀+X₂-4⋅X₁-2 ; X₀+2⋅X₂-2 ]
l1 [100⋅X₂-10⋅X₀-20⋅X₁-99 ; 3⋅X₀-4⋅X₁ ; X₀+X₂-1 ; X₂ ]

MPRF for transition t₁₆: l3(X₀, X₁, X₂, X₃, X₄, X₆) → l1(3⋅X₀-4⋅X₁, 4⋅X₀+3⋅X₁, X₂+X₀-1, X₃, X₄, X₆) :|: 1 ≤ X₂ of depth 4:

new bound:

1246⋅X₃+2136⋅X₄+9078⋅X₆+8901 {O(n)}

MPRF:

l3 [100⋅X₂-10⋅X₀-20⋅X₁-99 ; 3⋅X₀-4⋅X₁ ; X₀+X₂-1 ; X₂ ]
l1 [100⋅X₂-10⋅X₀-20⋅X₁-99 ; 3⋅X₀-4⋅X₁ ; X₀+X₂-1 ; X₂ ]

All Bounds

Timebounds

Overall timebound:18156⋅X₆+2492⋅X₃+4272⋅X₄+17806 {O(n)}
t₁₂: 1 {O(1)}
t₁₃: 1246⋅X₃+2136⋅X₄+9078⋅X₆+8901 {O(n)}
t₁₄: 1 {O(1)}
t₁₅: 1 {O(1)}
t₁₆: 1246⋅X₃+2136⋅X₄+9078⋅X₆+8901 {O(n)}
t₁₇: 1 {O(1)}

Costbounds

Overall costbound: 18156⋅X₆+2492⋅X₃+4272⋅X₄+17806 {O(n)}
t₁₂: 1 {O(1)}
t₁₃: 1246⋅X₃+2136⋅X₄+9078⋅X₆+8901 {O(n)}
t₁₄: 1 {O(1)}
t₁₅: 1 {O(1)}
t₁₆: 1246⋅X₃+2136⋅X₄+9078⋅X₆+8901 {O(n)}
t₁₇: 1 {O(1)}

Sizebounds

t₁₂, X₀: X₀ {O(n)}
t₁₂, X₁: X₁ {O(n)}
t₁₂, X₂: X₂ {O(n)}
t₁₂, X₃: X₃ {O(n)}
t₁₂, X₄: X₄ {O(n)}
t₁₂, X₆: X₆ {O(n)}
t₁₃, X₀: 8^(1246⋅X₃+2136⋅X₄+9078⋅X₆+8901)⋅X₃+8^(1246⋅X₃+2136⋅X₄+9078⋅X₆+8901)⋅X₄ {O(EXP)}
t₁₃, X₁: 8^(1246⋅X₃+2136⋅X₄+9078⋅X₆+8901)⋅X₃+8^(1246⋅X₃+2136⋅X₄+9078⋅X₆+8901)⋅X₄ {O(EXP)}
t₁₃, X₂: 1246⋅8^(1246⋅X₃+2136⋅X₄+9078⋅X₆+8901)⋅X₃⋅X₃+2136⋅8^(1246⋅X₃+2136⋅X₄+9078⋅X₆+8901)⋅X₄⋅X₄+3382⋅8^(1246⋅X₃+2136⋅X₄+9078⋅X₆+8901)⋅X₃⋅X₄+8902⋅8^(1246⋅X₃+2136⋅X₄+9078⋅X₆+8901)⋅X₃+8902⋅8^(1246⋅X₃+2136⋅X₄+9078⋅X₆+8901)⋅X₄+8^(1246⋅X₃+2136⋅X₄+9078⋅X₆+8901)⋅9078⋅X₃⋅X₆+8^(1246⋅X₃+2136⋅X₄+9078⋅X₆+8901)⋅9078⋅X₄⋅X₆+X₆ {O(EXP)}
t₁₃, X₃: X₃ {O(n)}
t₁₃, X₄: X₄ {O(n)}
t₁₃, X₆: X₆ {O(n)}
t₁₄, X₀: 8^(1246⋅X₃+2136⋅X₄+9078⋅X₆+8901)⋅X₃+8^(1246⋅X₃+2136⋅X₄+9078⋅X₆+8901)⋅X₄+X₃ {O(EXP)}
t₁₄, X₁: 8^(1246⋅X₃+2136⋅X₄+9078⋅X₆+8901)⋅X₃+8^(1246⋅X₃+2136⋅X₄+9078⋅X₆+8901)⋅X₄+X₄ {O(EXP)}
t₁₄, X₂: 1246⋅8^(1246⋅X₃+2136⋅X₄+9078⋅X₆+8901)⋅X₃⋅X₃+2136⋅8^(1246⋅X₃+2136⋅X₄+9078⋅X₆+8901)⋅X₄⋅X₄+3382⋅8^(1246⋅X₃+2136⋅X₄+9078⋅X₆+8901)⋅X₃⋅X₄+8902⋅8^(1246⋅X₃+2136⋅X₄+9078⋅X₆+8901)⋅X₃+8902⋅8^(1246⋅X₃+2136⋅X₄+9078⋅X₆+8901)⋅X₄+8^(1246⋅X₃+2136⋅X₄+9078⋅X₆+8901)⋅9078⋅X₃⋅X₆+8^(1246⋅X₃+2136⋅X₄+9078⋅X₆+8901)⋅9078⋅X₄⋅X₆+2⋅X₆ {O(EXP)}
t₁₄, X₃: 2⋅X₃ {O(n)}
t₁₄, X₄: 2⋅X₄ {O(n)}
t₁₄, X₆: 2⋅X₆ {O(n)}
t₁₅, X₀: X₃ {O(n)}
t₁₅, X₁: X₄ {O(n)}
t₁₅, X₂: X₆ {O(n)}
t₁₅, X₃: X₃ {O(n)}
t₁₅, X₄: X₄ {O(n)}
t₁₅, X₆: X₆ {O(n)}
t₁₆, X₀: 8^(1246⋅X₃+2136⋅X₄+9078⋅X₆+8901)⋅X₃+8^(1246⋅X₃+2136⋅X₄+9078⋅X₆+8901)⋅X₄ {O(EXP)}
t₁₆, X₁: 8^(1246⋅X₃+2136⋅X₄+9078⋅X₆+8901)⋅X₃+8^(1246⋅X₃+2136⋅X₄+9078⋅X₆+8901)⋅X₄ {O(EXP)}
t₁₆, X₂: 1246⋅8^(1246⋅X₃+2136⋅X₄+9078⋅X₆+8901)⋅X₃⋅X₃+2136⋅8^(1246⋅X₃+2136⋅X₄+9078⋅X₆+8901)⋅X₄⋅X₄+3382⋅8^(1246⋅X₃+2136⋅X₄+9078⋅X₆+8901)⋅X₃⋅X₄+8902⋅8^(1246⋅X₃+2136⋅X₄+9078⋅X₆+8901)⋅X₃+8902⋅8^(1246⋅X₃+2136⋅X₄+9078⋅X₆+8901)⋅X₄+8^(1246⋅X₃+2136⋅X₄+9078⋅X₆+8901)⋅9078⋅X₃⋅X₆+8^(1246⋅X₃+2136⋅X₄+9078⋅X₆+8901)⋅9078⋅X₄⋅X₆+X₆ {O(EXP)}
t₁₆, X₃: X₃ {O(n)}
t₁₆, X₄: X₄ {O(n)}
t₁₆, X₆: X₆ {O(n)}
t₁₇, X₀: 8^(1246⋅X₃+2136⋅X₄+9078⋅X₆+8901)⋅X₃+8^(1246⋅X₃+2136⋅X₄+9078⋅X₆+8901)⋅X₄+X₃ {O(EXP)}
t₁₇, X₁: 8^(1246⋅X₃+2136⋅X₄+9078⋅X₆+8901)⋅X₃+8^(1246⋅X₃+2136⋅X₄+9078⋅X₆+8901)⋅X₄+X₄ {O(EXP)}
t₁₇, X₂: 1246⋅8^(1246⋅X₃+2136⋅X₄+9078⋅X₆+8901)⋅X₃⋅X₃+2136⋅8^(1246⋅X₃+2136⋅X₄+9078⋅X₆+8901)⋅X₄⋅X₄+3382⋅8^(1246⋅X₃+2136⋅X₄+9078⋅X₆+8901)⋅X₃⋅X₄+8902⋅8^(1246⋅X₃+2136⋅X₄+9078⋅X₆+8901)⋅X₃+8902⋅8^(1246⋅X₃+2136⋅X₄+9078⋅X₆+8901)⋅X₄+8^(1246⋅X₃+2136⋅X₄+9078⋅X₆+8901)⋅9078⋅X₃⋅X₆+8^(1246⋅X₃+2136⋅X₄+9078⋅X₆+8901)⋅9078⋅X₄⋅X₆+2⋅X₆ {O(EXP)}
t₁₇, X₃: 2⋅X₃ {O(n)}
t₁₇, X₄: 2⋅X₄ {O(n)}
t₁₇, X₆: 2⋅X₆ {O(n)}