LTS Termination Proof

by AProVE

Input

Integer Transition System

Proof

1 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:
l5 l5 l5: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28
l22 l22 l22: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28
l39 l39 l39: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28
l1 l1 l1: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28
l13 l13 l13: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28
l31 l31 l31: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28
l18 l18 l18: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28
l17 l17 l17: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28
l35 l35 l35: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28
l21 l21 l21: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28
l9 l9 l9: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28
l14 l14 l14: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28
l25 l25 l25: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28
l6 l6 l6: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28
l8 l8 l8: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28
l34 l34 l34: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28
l0 l0 l0: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28
l12 l12 l12: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28
l19 l19 l19: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28
l26 l26 l26: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28
l33 l33 l33: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28
l40 l40 l40: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28
l7 l7 l7: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28
l24 l24 l24: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28
l37 l37 l37: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28
l11 l11 l11: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28
l3 l3 l3: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28
l41 l41 l41: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28
l20 l20 l20: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28
l32 l32 l32: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28
l28 l28 l28: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28
l42 l42 l42: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28
l2 l2 l2: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28
l23 l23 l23: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28
l4 l4 l4: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28
l38 l38 l38: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28
l10 l10 l10: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28
l36 l36 l36: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28
l29 l29 l29: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28
l16 l16 l16: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28
l15 l15 l15: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28
l30 l30 l30: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28
and for every transition t, a duplicate t is considered.

2 SCC Decomposition

We consider subproblems for each of the 3 SCC(s) of the program graph.

2.1 SCC Subproblem 1/3

Here we consider the SCC { l5, l23, l7, l6 }.

2.1.1 Transition Removal

We remove transition 7 using the following ranking functions, which are bounded by 0.

l5: x7 + x9
l6: x7 + x9
l7: x7 + x9
l23: x7 + x9

2.1.2 Transition Removal

We remove transition 34 using the following ranking functions, which are bounded by 0.

l5: 4⋅x9 − 4⋅x6 − 2
l6: −4⋅x6 + 4⋅x9 + 1
l7: −4⋅x6 + 4⋅x9 − 1
l23: −4⋅x6 + 4⋅x9

2.1.3 Transition Removal

We remove transitions 6, 25, 41 using the following ranking functions, which are bounded by 0.

l5: 2
l6: 1
l7: 3
l23: 0

2.1.4 Trivial Cooperation Program

There are no more "sharp" transitions in the cooperation program. Hence the cooperation termination is proved.

2.2 SCC Subproblem 2/3

Here we consider the SCC { l24, l35 }.

2.2.1 Transition Removal

We remove transition 53 using the following ranking functions, which are bounded by 0.

l24: x6 + x9
l35: x6 + x9

2.2.2 Transition Removal

We remove transition 54 using the following ranking functions, which are bounded by 0.

l24: 0
l35: −1

2.2.3 Trivial Cooperation Program

There are no more "sharp" transitions in the cooperation program. Hence the cooperation termination is proved.

2.3 SCC Subproblem 3/3

Here we consider the SCC { l22, l39, l1, l13, l31, l18, l17, l21, l9, l14, l25, l8, l0, l12, l19, l26, l33, l40, l37, l11, l3, l41, l20, l32, l28, l2, l4, l38, l10, l36, l29, l16, l15, l30 }.

2.3.1 Transition Removal

We remove transitions 29, 43 using the following ranking functions, which are bounded by 0.

l0: −3 − 3⋅x7 + 3⋅x9
l1: −3 − 3⋅x7 + 3⋅x9
l2: −3 − 3⋅x7 + 3⋅x9
l4: −3 − 3⋅x7 + 3⋅x9
l9: −3 − 3⋅x7 + 3⋅x9
l3: −3 − 3⋅x7 + 3⋅x9
l8: −3 − 3⋅x7 + 3⋅x9
l10: −3 − 3⋅x7 + 3⋅x9
l12: −3 − 3⋅x7 + 3⋅x9
l18: −3 − 3⋅x7 + 3⋅x9
l14: −3 − 3⋅x7 + 3⋅x9
l16: −3 − 3⋅x7 + 3⋅x9
l13: −3 − 3⋅x7 + 3⋅x9
l17: −3 − 3⋅x7 + 3⋅x9
l19: −3⋅x7 + 3⋅x9
l15: −3⋅x7 + 3⋅x9
l21: −3⋅x7 + 3⋅x9
l20: −3⋅x7 + 3⋅x9
l25: −3⋅x7 + 3⋅x9
l26: −3⋅x7 + 3⋅x9
l31: −3⋅x7 + 3⋅x9
l29: −3⋅x7 + 3⋅x9
l32: −3⋅x7 + 3⋅x9
l33: −3⋅x7 + 3⋅x9
l36: −3⋅x7 + 3⋅x9
l22: −3⋅x7 + 3⋅x9
l28: −3⋅x7 + 3⋅x9
l30: −3⋅x7 + 3⋅x9
l11: −3 − 3⋅x7 + 3⋅x9
l37: −3 − 3⋅x7 + 3⋅x9
l38: −3 − 3⋅x7 + 3⋅x9
l39: −3 − 3⋅x7 + 3⋅x9
l40: −3 − 3⋅x7 + 3⋅x9
l41: −3 − 3⋅x7 + 3⋅x9

2.3.2 Transition Removal

We remove transitions 1, 9, 12, 5, 4, 8, 11, 10, 14, 15, 26, 17, 20, 19, 16, 23, 22, 27, 18, 58, 61, 64, 21, 24, 13 using the following ranking functions, which are bounded by 0.

l0: 4
l1: 3
l2: 4
l4: 5
l9: 8
l3: 6
l8: 7
l10: 9
l12: 10
l18: 14
l14: 11
l16: 12
l13: 12
l17: 13
l15: −1
l19: −1
l21: −1
l20: −1
l25: −1
l26: −1
l31: −1
l29: −1
l32: −1
l33: −1
l36: −1
l22: −1
l28: −1
l30: −1
l11: 0
l37: 1
l38: 1
l39: 2
l40: 2
l41: 3

2.3.3 Transition Removal

We remove transition 59 using the following ranking functions, which are bounded by 0.

l2: −1 + 2⋅x1 + 3⋅x2 + 4⋅x5 + 5⋅x6 + 6⋅x7x8 + 7⋅x9 + 8⋅x10 + 9⋅x11 + 10⋅x12 + 11⋅x13 + 12⋅x14 + 13⋅x15 + 14⋅x16 + 15⋅x17 + 16⋅x18 + 17⋅x19 + 18⋅x20 + 19⋅x21 + 20⋅x22 + 21⋅x23 + 22⋅x24 + 23⋅x25 + 24⋅x26 + 25⋅x27 + 26⋅x28
l0: −2 + 2⋅x1 + 3⋅x2 + 4⋅x5 + 5⋅x6 + 6⋅x7x8 + 7⋅x9 + 8⋅x10 + 9⋅x11 + 10⋅x12 + 11⋅x13 + 12⋅x14 + 13⋅x15 + 14⋅x16 + 15⋅x17 + 16⋅x18 + 17⋅x19 + 18⋅x20 + 19⋅x21 + 20⋅x22 + 21⋅x23 + 22⋅x24 + 23⋅x25 + 24⋅x26 + 25⋅x27 + 26⋅x28
l15: −3 + x1 + 27⋅x2 + 28⋅x3 + 29⋅x4 − 4⋅x5 − 2⋅x6 + x7 + 30⋅x8 + x9 + 31⋅x10 + 32⋅x12 + 33⋅x13 + 34⋅x14 + 35⋅x15 + 36⋅x16 + 37⋅x17 + 38⋅x18 + 39⋅x19 + 40⋅x20 + 41⋅x21 + 42⋅x22 + 43⋅x23 + 44⋅x24 + 45⋅x25 + 46⋅x26 + 47⋅x27
l19: −5 + x1 + 27⋅x2 + 28⋅x3 + 29⋅x4 − 4⋅x5 − 2⋅x6 + x7 + 30⋅x8 + x9 + 31⋅x10 + 32⋅x12 + 33⋅x13 + 34⋅x14 + 35⋅x15 + 36⋅x16 + 37⋅x17 + 38⋅x18 + 39⋅x19 + 40⋅x20 + 41⋅x21 + 42⋅x22 + 43⋅x23 + 44⋅x24 + 45⋅x25 + 46⋅x26 + 47⋅x27
l21: −3 + x1 + 27⋅x2 + 28⋅x3 + 29⋅x4 − 4⋅x5 − 2⋅x6 + x7 + 30⋅x8 + x9 + 31⋅x10 + 32⋅x12 + 33⋅x13 + 34⋅x14 + 35⋅x15 + 36⋅x16 + 37⋅x17 + 38⋅x18 + 39⋅x19 + 40⋅x20 + 41⋅x21 + 42⋅x22 + 43⋅x23 + 44⋅x24 + 45⋅x25 + 46⋅x26 + 47⋅x27
l20: −3 + x1 + 27⋅x2 + 28⋅x3 + 29⋅x4 − 4⋅x5 − 2⋅x6 + x7 + 30⋅x8 + x9 + 31⋅x10 + 32⋅x12 + 33⋅x13 + 34⋅x14 + 35⋅x15 + 36⋅x16 + 37⋅x17 + 38⋅x18 + 39⋅x19 + 40⋅x20 + 41⋅x21 + 42⋅x22 + 43⋅x23 + 44⋅x24 + 45⋅x25 + 46⋅x26 + 47⋅x27
l25: −3 + x1 + 27⋅x2 + 28⋅x3 + 29⋅x4 − 4⋅x5 − 2⋅x6 + x7 + 30⋅x8 + x9 + 31⋅x10 + 32⋅x12 + 33⋅x13 + 34⋅x14 + 35⋅x15 + 36⋅x16 + 37⋅x17 + 38⋅x18 + 39⋅x19 + 40⋅x20 + 41⋅x21 + 42⋅x22 + 43⋅x23 + 44⋅x24 + 45⋅x25 + 46⋅x26 + 47⋅x27
l26: −3 + x1 + 27⋅x2 + 28⋅x3 + 29⋅x4 − 4⋅x5 − 2⋅x6 + x7 + 30⋅x8 + x9 + 31⋅x10 + 32⋅x12 + 33⋅x13 + 34⋅x14 + 35⋅x15 + 36⋅x16 + 37⋅x17 + 38⋅x18 + 39⋅x19 + 40⋅x20 + 41⋅x21 + 42⋅x22 + 43⋅x23 + 44⋅x24 + 45⋅x25 + 46⋅x26 + 47⋅x27
l31: −3 + x1 + 27⋅x2 + 28⋅x3 + 29⋅x4 − 4⋅x5 − 2⋅x6 + x7 + 30⋅x8 + x9 + 31⋅x10 + 32⋅x12 + 33⋅x13 + 34⋅x14 + 35⋅x15 + 36⋅x16 + 37⋅x17 + 38⋅x18 + 39⋅x19 + 40⋅x20 + 41⋅x21 + 42⋅x22 + 43⋅x23 + 44⋅x24 + 45⋅x25 + 46⋅x26 + 47⋅x27
l29: −1 + x1 + 27⋅x2 + 28⋅x3 + 29⋅x4 − 4⋅x5 − 2⋅x6 + x7 + 30⋅x8 + x9 + 31⋅x10 + 32⋅x12 + 33⋅x13 + 34⋅x14 + 35⋅x15 + 36⋅x16 + 37⋅x17 + 38⋅x18 + 39⋅x19 + 40⋅x20 + 41⋅x21 + 42⋅x22 + 43⋅x23 + 44⋅x24 + 45⋅x25 + 46⋅x26 + 47⋅x27
l32: −1 + x1 + 27⋅x2 + 28⋅x3 + 29⋅x4 − 4⋅x5 − 2⋅x6 + x7 + 30⋅x8 + x9 + 31⋅x10 + 32⋅x12 + 33⋅x13 + 34⋅x14 + 35⋅x15 + 36⋅x16 + 37⋅x17 + 38⋅x18 + 39⋅x19 + 40⋅x20 + 41⋅x21 + 42⋅x22 + 43⋅x23 + 44⋅x24 + 45⋅x25 + 46⋅x26 + 47⋅x27
l33: −1 + x1 + 27⋅x2 + 28⋅x3 + 29⋅x4 − 4⋅x5 − 2⋅x6 + x7 + 30⋅x8 + x9 + 31⋅x10 + 32⋅x12 + 33⋅x13 + 34⋅x14 + 35⋅x15 + 36⋅x16 + 37⋅x17 + 38⋅x18 + 39⋅x19 + 40⋅x20 + 41⋅x21 + 42⋅x22 + 43⋅x23 + 44⋅x24 + 45⋅x25 + 46⋅x26 + 47⋅x27
l36: −5 + x1 + 27⋅x2 + 28⋅x3 + 29⋅x4 − 4⋅x5 − 2⋅x6 + x7 + 30⋅x8 + x9 + 31⋅x10 + 32⋅x12 + 33⋅x13 + 34⋅x14 + 35⋅x15 + 36⋅x16 + 37⋅x17 + 38⋅x18 + 39⋅x19 + 40⋅x20 + 41⋅x21 + 42⋅x22 + 43⋅x23 + 44⋅x24 + 45⋅x25 + 46⋅x26 + 47⋅x27
l22: −3 + x1 + 27⋅x2 + 28⋅x3 + 29⋅x4 − 4⋅x5 − 2⋅x6 + x7 + 30⋅x8 + x9 + 31⋅x10 + 32⋅x12 + 33⋅x13 + 34⋅x14 + 35⋅x15 + 36⋅x16 + 37⋅x17 + 38⋅x18 + 39⋅x19 + 40⋅x20 + 41⋅x21 + 42⋅x22 + 43⋅x23 + 44⋅x24 + 45⋅x25 + 46⋅x26 + 47⋅x27
l28: −3 + x1 + 27⋅x2 + 28⋅x3 + 29⋅x4 − 4⋅x5 − 2⋅x6 + x7 + 30⋅x8 + x9 + 31⋅x10 + 32⋅x12 + 33⋅x13 + 34⋅x14 + 35⋅x15 + 36⋅x16 + 37⋅x17 + 38⋅x18 + 39⋅x19 + 40⋅x20 + 41⋅x21 + 42⋅x22 + 43⋅x23 + 44⋅x24 + 45⋅x25 + 46⋅x26 + 47⋅x27
l30: −3 + x1 + 27⋅x2 + 28⋅x3 + 29⋅x4 − 4⋅x5 − 2⋅x6 + x7 + 30⋅x8 + x9 + 31⋅x10 + 32⋅x12 + 33⋅x13 + 34⋅x14 + 35⋅x15 + 36⋅x16 + 37⋅x17 + 38⋅x18 + 39⋅x19 + 40⋅x20 + 41⋅x21 + 42⋅x22 + 43⋅x23 + 44⋅x24 + 45⋅x25 + 46⋅x26 + 47⋅x27
l38: x8 + x9
l37: x8 + x9
l40: −1 + 48⋅x1 + 49⋅x2 + 50⋅x5 + 51⋅x6 + 52⋅x7 − 2⋅x8 + x9 + 53⋅x10 + 54⋅x11 + 55⋅x12 + 56⋅x13 + 57⋅x14 + 58⋅x15 + 59⋅x16 + 60⋅x17 + 61⋅x18 + 62⋅x19 + 63⋅x20 + 64⋅x21 + 65⋅x22 + 66⋅x23 + 67⋅x24 + 68⋅x25 + 69⋅x26 + 70⋅x27 + 71⋅x28
l39: −1 + 48⋅x1 + 49⋅x2 + 50⋅x5 + 51⋅x6 + 52⋅x7 − 2⋅x8 + x9 + 53⋅x10 + 54⋅x11 + 55⋅x12 + 56⋅x13 + 57⋅x14 + 58⋅x15 + 59⋅x16 + 60⋅x17 + 61⋅x18 + 62⋅x19 + 63⋅x20 + 64⋅x21 + 65⋅x22 + 66⋅x23 + 67⋅x24 + 68⋅x25 + 69⋅x26 + 70⋅x27 + 71⋅x28
l1: −3 + 72⋅x1 + 73⋅x2 + 74⋅x5 + 75⋅x6 + x7 − 2⋅x8 + 76⋅x9 + 77⋅x10 + 78⋅x11 + 79⋅x12 + 80⋅x13 + 81⋅x14 + 82⋅x15 + 83⋅x16 + 84⋅x17 + 85⋅x18 + 86⋅x19 + 87⋅x20 + 88⋅x21 + 89⋅x22 + 90⋅x23 + 91⋅x24 + 92⋅x25 + 93⋅x26 + 94⋅x27 + 95⋅x28
l41: −3 + 72⋅x1 + 73⋅x2 + 74⋅x5 + 75⋅x6 + x7 − 2⋅x8 + 76⋅x9 + 77⋅x10 + 78⋅x11 + 79⋅x12 + 80⋅x13 + 81⋅x14 + 82⋅x15 + 83⋅x16 + 84⋅x17 + 85⋅x18 + 86⋅x19 + 87⋅x20 + 88⋅x21 + 89⋅x22 + 90⋅x23 + 91⋅x24 + 92⋅x25 + 93⋅x26 + 94⋅x27 + 95⋅x28

2.3.4 Transition Removal

We remove transition 60 using the following ranking functions, which are bounded by 0.

l2: −1 + 2⋅x1 + 3⋅x2 + 4⋅x5 + 5⋅x6 + 6⋅x7x8 + 7⋅x9 + 8⋅x10 + 9⋅x11 + 10⋅x12 + 11⋅x13 + 12⋅x14 + 13⋅x15 + 14⋅x16 + 15⋅x17 + 16⋅x18 + 17⋅x19 + 18⋅x20 + 19⋅x21 + 20⋅x22 + 21⋅x23 + 22⋅x24 + 23⋅x25 + 24⋅x26 + 25⋅x27 + 26⋅x28
l0: −2 + 2⋅x1 + 3⋅x2 + 4⋅x5 + 5⋅x6 + 6⋅x7x8 + 7⋅x9 + 8⋅x10 + 9⋅x11 + 10⋅x12 + 11⋅x13 + 12⋅x14 + 13⋅x15 + 14⋅x16 + 15⋅x17 + 16⋅x18 + 17⋅x19 + 18⋅x20 + 19⋅x21 + 20⋅x22 + 21⋅x23 + 22⋅x24 + 23⋅x25 + 24⋅x26 + 25⋅x27 + 26⋅x28
l15: −3 + x1 + 27⋅x2 + 28⋅x3 + 29⋅x4 − 4⋅x5 − 2⋅x6 + x7 + 30⋅x8 − 2⋅x9 + 31⋅x10 + 32⋅x12 + 33⋅x13 + 34⋅x14 + 35⋅x15 + 36⋅x16 + 37⋅x17 + 38⋅x18 + 39⋅x19 + 40⋅x20 + 41⋅x21 + 42⋅x22 + 43⋅x23 + 44⋅x24 + 45⋅x25 + 46⋅x26 + 47⋅x27
l19: −5 + x1 + 27⋅x2 + 28⋅x3 + 29⋅x4 − 4⋅x5 − 2⋅x6 + x7 + 30⋅x8 − 2⋅x9 + 31⋅x10 + 32⋅x12 + 33⋅x13 + 34⋅x14 + 35⋅x15 + 36⋅x16 + 37⋅x17 + 38⋅x18 + 39⋅x19 + 40⋅x20 + 41⋅x21 + 42⋅x22 + 43⋅x23 + 44⋅x24 + 45⋅x25 + 46⋅x26 + 47⋅x27
l21: −3 + x1 + 27⋅x2 + 28⋅x3 + 29⋅x4 − 4⋅x5 − 2⋅x6 + x7 + 30⋅x8 − 2⋅x9 + 31⋅x10 + 32⋅x12 + 33⋅x13 + 34⋅x14 + 35⋅x15 + 36⋅x16 + 37⋅x17 + 38⋅x18 + 39⋅x19 + 40⋅x20 + 41⋅x21 + 42⋅x22 + 43⋅x23 + 44⋅x24 + 45⋅x25 + 46⋅x26 + 47⋅x27
l20: −3 + x1 + 27⋅x2 + 28⋅x3 + 29⋅x4 − 4⋅x5 − 2⋅x6 + x7 + 30⋅x8 − 2⋅x9 + 31⋅x10 + 32⋅x12 + 33⋅x13 + 34⋅x14 + 35⋅x15 + 36⋅x16 + 37⋅x17 + 38⋅x18 + 39⋅x19 + 40⋅x20 + 41⋅x21 + 42⋅x22 + 43⋅x23 + 44⋅x24 + 45⋅x25 + 46⋅x26 + 47⋅x27
l25: −3 + x1 + 27⋅x2 + 28⋅x3 + 29⋅x4 − 4⋅x5 − 2⋅x6 + x7 + 30⋅x8 − 2⋅x9 + 31⋅x10 + 32⋅x12 + 33⋅x13 + 34⋅x14 + 35⋅x15 + 36⋅x16 + 37⋅x17 + 38⋅x18 + 39⋅x19 + 40⋅x20 + 41⋅x21 + 42⋅x22 + 43⋅x23 + 44⋅x24 + 45⋅x25 + 46⋅x26 + 47⋅x27
l26: −3 + x1 + 27⋅x2 + 28⋅x3 + 29⋅x4 − 4⋅x5 − 2⋅x6 + x7 + 30⋅x8 − 2⋅x9 + 31⋅x10 + 32⋅x12 + 33⋅x13 + 34⋅x14 + 35⋅x15 + 36⋅x16 + 37⋅x17 + 38⋅x18 + 39⋅x19 + 40⋅x20 + 41⋅x21 + 42⋅x22 + 43⋅x23 + 44⋅x24 + 45⋅x25 + 46⋅x26 + 47⋅x27
l31: −3 + x1 + 27⋅x2 + 28⋅x3 + 29⋅x4 − 4⋅x5 − 2⋅x6 + x7 + 30⋅x8 − 2⋅x9 + 31⋅x10 + 32⋅x12 + 33⋅x13 + 34⋅x14 + 35⋅x15 + 36⋅x16 + 37⋅x17 + 38⋅x18 + 39⋅x19 + 40⋅x20 + 41⋅x21 + 42⋅x22 + 43⋅x23 + 44⋅x24 + 45⋅x25 + 46⋅x26 + 47⋅x27
l29: −1 + x1 + 27⋅x2 + 28⋅x3 + 29⋅x4 − 4⋅x5 − 2⋅x6 + x7 + 30⋅x8 − 2⋅x9 + 31⋅x10 + 32⋅x12 + 33⋅x13 + 34⋅x14 + 35⋅x15 + 36⋅x16 + 37⋅x17 + 38⋅x18 + 39⋅x19 + 40⋅x20 + 41⋅x21 + 42⋅x22 + 43⋅x23 + 44⋅x24 + 45⋅x25 + 46⋅x26 + 47⋅x27
l32: −1 + x1 + 27⋅x2 + 28⋅x3 + 29⋅x4 − 4⋅x5 − 2⋅x6 + x7 + 30⋅x8 − 2⋅x9 + 31⋅x10 + 32⋅x12 + 33⋅x13 + 34⋅x14 + 35⋅x15 + 36⋅x16 + 37⋅x17 + 38⋅x18 + 39⋅x19 + 40⋅x20 + 41⋅x21 + 42⋅x22 + 43⋅x23 + 44⋅x24 + 45⋅x25 + 46⋅x26 + 47⋅x27
l33: −1 + x1 + 27⋅x2 + 28⋅x3 + 29⋅x4 − 4⋅x5 − 2⋅x6 + x7 + 30⋅x8 − 2⋅x9 + 31⋅x10 + 32⋅x12 + 33⋅x13 + 34⋅x14 + 35⋅x15 + 36⋅x16 + 37⋅x17 + 38⋅x18 + 39⋅x19 + 40⋅x20 + 41⋅x21 + 42⋅x22 + 43⋅x23 + 44⋅x24 + 45⋅x25 + 46⋅x26 + 47⋅x27
l36: −5 + x1 + 27⋅x2 + 28⋅x3 + 29⋅x4 − 4⋅x5 − 2⋅x6 + x7 + 30⋅x8 − 2⋅x9 + 31⋅x10 + 32⋅x12 + 33⋅x13 + 34⋅x14 + 35⋅x15 + 36⋅x16 + 37⋅x17 + 38⋅x18 + 39⋅x19 + 40⋅x20 + 41⋅x21 + 42⋅x22 + 43⋅x23 + 44⋅x24 + 45⋅x25 + 46⋅x26 + 47⋅x27
l22: −3 + x1 + 27⋅x2 + 28⋅x3 + 29⋅x4 − 4⋅x5 − 2⋅x6 + x7 + 30⋅x8 − 2⋅x9 + 31⋅x10 + 32⋅x12 + 33⋅x13 + 34⋅x14 + 35⋅x15 + 36⋅x16 + 37⋅x17 + 38⋅x18 + 39⋅x19 + 40⋅x20 + 41⋅x21 + 42⋅x22 + 43⋅x23 + 44⋅x24 + 45⋅x25 + 46⋅x26 + 47⋅x27
l28: −3 + x1 + 27⋅x2 + 28⋅x3 + 29⋅x4 − 4⋅x5 − 2⋅x6 + x7 + 30⋅x8 − 2⋅x9 + 31⋅x10 + 32⋅x12 + 33⋅x13 + 34⋅x14 + 35⋅x15 + 36⋅x16 + 37⋅x17 + 38⋅x18 + 39⋅x19 + 40⋅x20 + 41⋅x21 + 42⋅x22 + 43⋅x23 + 44⋅x24 + 45⋅x25 + 46⋅x26 + 47⋅x27
l30: −3 + x1 + 27⋅x2 + 28⋅x3 + 29⋅x4 − 4⋅x5 − 2⋅x6 + x7 + 30⋅x8 − 2⋅x9 + 31⋅x10 + 32⋅x12 + 33⋅x13 + 34⋅x14 + 35⋅x15 + 36⋅x16 + 37⋅x17 + 38⋅x18 + 39⋅x19 + 40⋅x20 + 41⋅x21 + 42⋅x22 + 43⋅x23 + 44⋅x24 + 45⋅x25 + 46⋅x26 + 47⋅x27
l38: 1
l37: 0
l40: −1 + 48⋅x1 + 49⋅x2 + 50⋅x5 + 51⋅x6 + 52⋅x7x9 + 53⋅x10 + 54⋅x11 + 55⋅x12 + 56⋅x13 + 57⋅x14 + 58⋅x15 + 59⋅x16 + 60⋅x17 + 61⋅x18 + 62⋅x19 + 63⋅x20 + 64⋅x21 + 65⋅x22 + 66⋅x23 + 67⋅x24 + 68⋅x25 + 69⋅x26 + 70⋅x27 + 71⋅x28
l39: −1 + 48⋅x1 + 49⋅x2 + 50⋅x5 + 51⋅x6 + 52⋅x7x9 + 53⋅x10 + 54⋅x11 + 55⋅x12 + 56⋅x13 + 57⋅x14 + 58⋅x15 + 59⋅x16 + 60⋅x17 + 61⋅x18 + 62⋅x19 + 63⋅x20 + 64⋅x21 + 65⋅x22 + 66⋅x23 + 67⋅x24 + 68⋅x25 + 69⋅x26 + 70⋅x27 + 71⋅x28
l1: −2 + 72⋅x1 + 73⋅x2 + 74⋅x5 + 75⋅x6x7x8 + 76⋅x9 + 77⋅x10 + 78⋅x11 + 79⋅x12 + 80⋅x13 + 81⋅x14 + 82⋅x15 + 83⋅x16 + 84⋅x17 + 85⋅x18 + 86⋅x19 + 87⋅x20 + 88⋅x21 + 89⋅x22 + 90⋅x23 + 91⋅x24 + 92⋅x25 + 93⋅x26 + 94⋅x27 + 95⋅x28
l41: −2 + 72⋅x1 + 73⋅x2 + 74⋅x5 + 75⋅x6x7x8 + 76⋅x9 + 77⋅x10 + 78⋅x11 + 79⋅x12 + 80⋅x13 + 81⋅x14 + 82⋅x15 + 83⋅x16 + 84⋅x17 + 85⋅x18 + 86⋅x19 + 87⋅x20 + 88⋅x21 + 89⋅x22 + 90⋅x23 + 91⋅x24 + 92⋅x25 + 93⋅x26 + 94⋅x27 + 95⋅x28

2.3.5 Transition Removal

We remove transitions 32, 46, 65, 62 using the following ranking functions, which are bounded by 0.

l2: −1 + 2⋅x1 + 3⋅x2 + 4⋅x5 + 5⋅x6 + 6⋅x7x8 + 7⋅x9 + 8⋅x10 + 9⋅x11 + 10⋅x12 + 11⋅x13 + 12⋅x14 + 13⋅x15 + 14⋅x16 + 15⋅x17 + 16⋅x18 + 17⋅x19 + 18⋅x20 + 19⋅x21 + 20⋅x22 + 21⋅x23 + 22⋅x24 + 23⋅x25 + 24⋅x26 + 25⋅x27 + 26⋅x28
l0: −1 + 2⋅x1 + 3⋅x2 + 4⋅x5 + 5⋅x6 + 6⋅x7x8 + 7⋅x9 + 8⋅x10 + 9⋅x11 + 10⋅x12 + 11⋅x13 + 12⋅x14 + 13⋅x15 + 14⋅x16 + 15⋅x17 + 16⋅x18 + 17⋅x19 + 18⋅x20 + 19⋅x21 + 20⋅x22 + 21⋅x23 + 22⋅x24 + 23⋅x25 + 24⋅x26 + 25⋅x27 + 26⋅x28
l15: −2 − x6 + x9
l19: −2 − x6 + x9
l21: −1 − x6 + x9
l20: −1 − x6 + x9
l25: −1 − x6 + x9
l26: −1 − x6 + x9
l31: −1 − x6 + x9
l29: −1 − x6 + x9
l32: −1 − x6 + x9
l33: −1 − x6 + x9
l36: −1 − x6 + x9
l22: −1 − x6 + x9
l28: −2 − x6 + x9
l30: −2 − x6 + x9
l40: x8 + x9
l39: x8 + x9
l1: −1 + x7x8
l41: −1 + x7x8

2.3.6 Transition Removal

We remove transitions 63, 66 using the following ranking functions, which are bounded by 0.

l2: −1 + 2⋅x1 + 3⋅x2 + 4⋅x5 + 5⋅x6 + 6⋅x7x8 + 7⋅x9 + 8⋅x10 + 9⋅x11 + 10⋅x12 + 11⋅x13 + 12⋅x14 + 13⋅x15 + 14⋅x16 + 15⋅x17 + 16⋅x18 + 17⋅x19 + 18⋅x20 + 19⋅x21 + 20⋅x22 + 21⋅x23 + 22⋅x24 + 23⋅x25 + 24⋅x26 + 25⋅x27 + 26⋅x28
l0: −2 + 2⋅x1 + 3⋅x2 + 4⋅x5 + 5⋅x6 + 6⋅x7x8 + 7⋅x9 + 8⋅x10 + 9⋅x11 + 10⋅x12 + 11⋅x13 + 12⋅x14 + 13⋅x15 + 14⋅x16 + 15⋅x17 + 16⋅x18 + 17⋅x19 + 18⋅x20 + 19⋅x21 + 20⋅x22 + 21⋅x23 + 22⋅x24 + 23⋅x25 + 24⋅x26 + 25⋅x27 + 26⋅x28
l15: −3 + x1 + 27⋅x2 + 28⋅x3 + 29⋅x4 − 2⋅x5 − 2⋅x6 − 2⋅x7 + 30⋅x8 + x9 + 31⋅x10 + 32⋅x12 + 33⋅x13 + 34⋅x14 + 35⋅x15 + 36⋅x16 + 37⋅x17 + 38⋅x18 + 39⋅x19 + 40⋅x20 + 41⋅x21 + 42⋅x22 + 43⋅x23 + 44⋅x24 + 45⋅x25 + 46⋅x26 + 47⋅x27
l19: −3 + x1 + 27⋅x2 + 28⋅x3 + 29⋅x4 − 2⋅x5 − 2⋅x6 − 2⋅x7 + 30⋅x8 + x9 + 31⋅x10 + 32⋅x12 + 33⋅x13 + 34⋅x14 + 35⋅x15 + 36⋅x16 + 37⋅x17 + 38⋅x18 + 39⋅x19 + 40⋅x20 + 41⋅x21 + 42⋅x22 + 43⋅x23 + 44⋅x24 + 45⋅x25 + 46⋅x26 + 47⋅x27
l20: −1 + x1 + 27⋅x2 + 28⋅x3 + 29⋅x4 − 2⋅x5 − 2⋅x6 − 2⋅x7 + 30⋅x8 + x9 + 31⋅x10 + 32⋅x12 + 33⋅x13 + 34⋅x14 + 35⋅x15 + 36⋅x16 + 37⋅x17 + 38⋅x18 + 39⋅x19 + 40⋅x20 + 41⋅x21 + 42⋅x22 + 43⋅x23 + 44⋅x24 + 45⋅x25 + 46⋅x26 + 47⋅x27
l21: −1 + x1 + 27⋅x2 + 28⋅x3 + 29⋅x4 − 2⋅x5 − 2⋅x6 − 2⋅x7 + 30⋅x8 + x9 + 31⋅x10 + 32⋅x12 + 33⋅x13 + 34⋅x14 + 35⋅x15 + 36⋅x16 + 37⋅x17 + 38⋅x18 + 39⋅x19 + 40⋅x20 + 41⋅x21 + 42⋅x22 + 43⋅x23 + 44⋅x24 + 45⋅x25 + 46⋅x26 + 47⋅x27
l25: −1 + x1 + 27⋅x2 + 28⋅x3 + 29⋅x4 − 2⋅x5 − 2⋅x6 − 2⋅x7 + 30⋅x8 + x9 + 31⋅x10 + 32⋅x12 + 33⋅x13 + 34⋅x14 + 35⋅x15 + 36⋅x16 + 37⋅x17 + 38⋅x18 + 39⋅x19 + 40⋅x20 + 41⋅x21 + 42⋅x22 + 43⋅x23 + 44⋅x24 + 45⋅x25 + 46⋅x26 + 47⋅x27
l26: −1 + x1 + 27⋅x2 + 28⋅x3 + 29⋅x4 − 2⋅x5 − 2⋅x6 − 2⋅x7 + 30⋅x8 + x9 + 31⋅x10 + 32⋅x12 + 33⋅x13 + 34⋅x14 + 35⋅x15 + 36⋅x16 + 37⋅x17 + 38⋅x18 + 39⋅x19 + 40⋅x20 + 41⋅x21 + 42⋅x22 + 43⋅x23 + 44⋅x24 + 45⋅x25 + 46⋅x26 + 47⋅x27
l31: −1 + x1 + 27⋅x2 + 28⋅x3 + 29⋅x4 − 2⋅x5 − 2⋅x6 − 2⋅x7 + 30⋅x8 + x9 + 31⋅x10 + 32⋅x12 + 33⋅x13 + 34⋅x14 + 35⋅x15 + 36⋅x16 + 37⋅x17 + 38⋅x18 + 39⋅x19 + 40⋅x20 + 41⋅x21 + 42⋅x22 + 43⋅x23 + 44⋅x24 + 45⋅x25 + 46⋅x26 + 47⋅x27
l29: −1 + x1 + 27⋅x2 + 28⋅x3 + 29⋅x4 − 2⋅x5 − 2⋅x6 − 2⋅x7 + 30⋅x8 + x9 + 31⋅x10 + 32⋅x12 + 33⋅x13 + 34⋅x14 + 35⋅x15 + 36⋅x16 + 37⋅x17 + 38⋅x18 + 39⋅x19 + 40⋅x20 + 41⋅x21 + 42⋅x22 + 43⋅x23 + 44⋅x24 + 45⋅x25 + 46⋅x26 + 47⋅x27
l32: −1 + x1 + 27⋅x2 + 28⋅x3 + 29⋅x4 − 2⋅x5 − 2⋅x6 − 2⋅x7 + 30⋅x8 + x9 + 31⋅x10 + 32⋅x12 + 33⋅x13 + 34⋅x14 + 35⋅x15 + 36⋅x16 + 37⋅x17 + 38⋅x18 + 39⋅x19 + 40⋅x20 + 41⋅x21 + 42⋅x22 + 43⋅x23 + 44⋅x24 + 45⋅x25 + 46⋅x26 + 47⋅x27
l33: −1 + x1 + 27⋅x2 + 28⋅x3 + 29⋅x4 − 2⋅x5 − 2⋅x6 − 2⋅x7 + 30⋅x8 + x9 + 31⋅x10 + 32⋅x12 + 33⋅x13 + 34⋅x14 + 35⋅x15 + 36⋅x16 + 37⋅x17 + 38⋅x18 + 39⋅x19 + 40⋅x20 + 41⋅x21 + 42⋅x22 + 43⋅x23 + 44⋅x24 + 45⋅x25 + 46⋅x26 + 47⋅x27
l36: −3 + x1 + 27⋅x2 + 28⋅x3 + 29⋅x4 − 2⋅x5 − 2⋅x6 − 2⋅x7 + 30⋅x8 + x9 + 31⋅x10 + 32⋅x12 + 33⋅x13 + 34⋅x14 + 35⋅x15 + 36⋅x16 + 37⋅x17 + 38⋅x18 + 39⋅x19 + 40⋅x20 + 41⋅x21 + 42⋅x22 + 43⋅x23 + 44⋅x24 + 45⋅x25 + 46⋅x26 + 47⋅x27
l22: −1 + x1 + 27⋅x2 + 28⋅x3 + 29⋅x4 − 2⋅x5 − 2⋅x6 − 2⋅x7 + 30⋅x8 + x9 + 31⋅x10 + 32⋅x12 + 33⋅x13 + 34⋅x14 + 35⋅x15 + 36⋅x16 + 37⋅x17 + 38⋅x18 + 39⋅x19 + 40⋅x20 + 41⋅x21 + 42⋅x22 + 43⋅x23 + 44⋅x24 + 45⋅x25 + 46⋅x26 + 47⋅x27
l28: −6 + x1 + 27⋅x2 + 28⋅x3 + 29⋅x4 − 2⋅x5 − 2⋅x6 + x7 + 30⋅x8 − 2⋅x9 + 31⋅x10 + 32⋅x12 + 33⋅x13 + 34⋅x14 + 35⋅x15 + 36⋅x16 + 37⋅x17 + 38⋅x18 + 39⋅x19 + 40⋅x20 + 41⋅x21 + 42⋅x22 + 43⋅x23 + 44⋅x24 + 45⋅x25 + 46⋅x26 + 47⋅x27
l30: −6 + x1 + 27⋅x2 + 28⋅x3 + 29⋅x4 − 2⋅x5 − 2⋅x6 + x7 + 30⋅x8 − 2⋅x9 + 31⋅x10 + 32⋅x12 + 33⋅x13 + 34⋅x14 + 35⋅x15 + 36⋅x16 + 37⋅x17 + 38⋅x18 + 39⋅x19 + 40⋅x20 + 41⋅x21 + 42⋅x22 + 43⋅x23 + 44⋅x24 + 45⋅x25 + 46⋅x26 + 47⋅x27
l40: 1
l39: 0
l1: 1
l41: 0

2.3.7 Transition Removal

We remove transitions 30, 42, 44, 28 using the following ranking functions, which are bounded by 0.

l2: −1 + 2⋅x1 + 3⋅x2 + 4⋅x5 + 5⋅x6 + 6⋅x7x8 + 7⋅x9 + 8⋅x10 + 9⋅x11 + 10⋅x12 + 11⋅x13 + 12⋅x14 + 13⋅x15 + 14⋅x16 + 15⋅x17 + 16⋅x18 + 17⋅x19 + 18⋅x20 + 19⋅x21 + 20⋅x22 + 21⋅x23 + 22⋅x24 + 23⋅x25 + 24⋅x26 + 25⋅x27 + 26⋅x28
l0: −1 + 2⋅x1 + 3⋅x2 + 4⋅x5 + 5⋅x6 + 6⋅x7x8 + 7⋅x9 + 8⋅x10 + 9⋅x11 + 10⋅x12 + 11⋅x13 + 12⋅x14 + 13⋅x15 + 14⋅x16 + 15⋅x17 + 16⋅x18 + 17⋅x19 + 18⋅x20 + 19⋅x21 + 20⋅x22 + 21⋅x23 + 22⋅x24 + 23⋅x25 + 24⋅x26 + 25⋅x27 + 26⋅x28
l15: 1
l19: 0
l20: −1 − x7 + x9
l21: −1 − x7 + x9
l25: −1 − x7 + x9
l26: −1 − x7 + x9
l31: −1 − x7 + x9
l29: −1 − x7 + x9
l32: −1 − x7 + x9
l33: −1 − x7 + x9
l36: −1 − x7 + x9
l22: −1 − x7 + x9
l28: 0
l30: 1

2.3.8 Transition Removal

We remove transition 49 using the following ranking functions, which are bounded by 0.

l2: −1 + 2⋅x1 + 3⋅x2 + 4⋅x5 + 5⋅x6 + 6⋅x7x8 + 7⋅x9 + 8⋅x10 + 9⋅x11 + 10⋅x12 + 11⋅x13 + 12⋅x14 + 13⋅x15 + 14⋅x16 + 15⋅x17 + 16⋅x18 + 17⋅x19 + 18⋅x20 + 19⋅x21 + 20⋅x22 + 21⋅x23 + 22⋅x24 + 23⋅x25 + 24⋅x26 + 25⋅x27 + 26⋅x28
l0: −1 + 2⋅x1 + 3⋅x2 + 4⋅x5 + 5⋅x6 + 6⋅x7x8 + 7⋅x9 + 8⋅x10 + 9⋅x11 + 10⋅x12 + 11⋅x13 + 12⋅x14 + 13⋅x15 + 14⋅x16 + 15⋅x17 + 16⋅x18 + 17⋅x19 + 18⋅x20 + 19⋅x21 + 20⋅x22 + 21⋅x23 + 22⋅x24 + 23⋅x25 + 24⋅x26 + 25⋅x27 + 26⋅x28
l20: −1 + x1x5
l21: −1 + x1x5
l25: −1 + x1x5
l26: −1 + x1x5
l31: −1 + x1x5
l29: −1 + x1x5
l32: x1x5
l33: x1x5
l36: −1 + x1x5
l22: −1 + x1x5

2.3.9 Transition Removal

We remove transitions 35, 37, 36, 39, 38, 45, 47, 56, 31 using the following ranking functions, which are bounded by 0.

l2: −1 + 7⋅x1 + 8⋅x2 + 9⋅x5 + 10⋅x6 + 11⋅x7x8 + 12⋅x9 + 13⋅x10 + 14⋅x11 + 15⋅x12 + 16⋅x13 + 17⋅x14 + 18⋅x15 + 19⋅x16 + 20⋅x17 + 21⋅x18 + 22⋅x19 + 23⋅x20 + 24⋅x21 + 25⋅x22 + 26⋅x23 + 27⋅x24 + 28⋅x25 + 29⋅x26 + 30⋅x27 + 31⋅x28
l0: −2 + 7⋅x1 + 8⋅x2 + 9⋅x5 + 10⋅x6 + 11⋅x7x8 + 12⋅x9 + 13⋅x10 + 14⋅x11 + 15⋅x12 + 16⋅x13 + 17⋅x14 + 18⋅x15 + 19⋅x16 + 20⋅x17 + 21⋅x18 + 22⋅x19 + 23⋅x20 + 24⋅x21 + 25⋅x22 + 26⋅x23 + 27⋅x24 + 28⋅x25 + 29⋅x26 + 30⋅x27 + 31⋅x28
l20: 2
l21: 1
l25: 3
l26: 4
l31: 5
l29: 6
l33: x6 + x9
l32: x6 + x9
l36: x6 + x9
l22: x6 + x9

2.3.10 Transition Removal

We remove transitions 50, 55, 57 using the following ranking functions, which are bounded by 0.

l2: −1 + 3⋅x1 + 4⋅x2 + 5⋅x5 + 6⋅x6 + 7⋅x7x8 + 8⋅x9 + 9⋅x10 + 10⋅x11 + 11⋅x12 + 12⋅x13 + 13⋅x14 + 14⋅x15 + 15⋅x16 + 16⋅x17 + 17⋅x18 + 18⋅x19 + 19⋅x20 + 20⋅x21 + 21⋅x22 + 22⋅x23 + 23⋅x24 + 24⋅x25 + 25⋅x26 + 26⋅x27 + 27⋅x28
l0: −2 + 3⋅x1 + 4⋅x2 + 5⋅x5 + 6⋅x6 + 7⋅x7x8 + 8⋅x9 + 9⋅x10 + 10⋅x11 + 11⋅x12 + 12⋅x13 + 13⋅x14 + 14⋅x15 + 15⋅x16 + 16⋅x17 + 17⋅x18 + 18⋅x19 + 19⋅x20 + 20⋅x21 + 21⋅x22 + 22⋅x23 + 23⋅x24 + 24⋅x25 + 25⋅x26 + 26⋅x27 + 27⋅x28
l33: 0
l32: −1
l36: 1
l22: 2

2.3.11 Transition Removal

We remove transition 2 using the following ranking functions, which are bounded by 0.

l2: 2⋅x6 − 2⋅x8 + 1
l0: 2⋅x6 − 2⋅x8

2.3.12 Transition Removal

We remove transition 3 using the following ranking functions, which are bounded by 0.

l2: 0
l0: −1

2.3.13 Trivial Cooperation Program

There are no more "sharp" transitions in the cooperation program. Hence the cooperation termination is proved.

Tool configuration

AProVE