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 = x28x29 = x29x30 = x30x31 = x31
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 = x28x29 = x29x30 = x30x31 = x31
l77 l77 l77: 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 = x28x29 = x29x30 = x30x31 = x31
l48 l48 l48: 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 = x28x29 = x29x30 = x30x31 = x31
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 = x28x29 = x29x30 = x30x31 = x31
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 = x28x29 = x29x30 = x30x31 = x31
l52 l52 l52: 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 = x28x29 = x29x30 = x30x31 = x31
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 = x28x29 = x29x30 = x30x31 = x31
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 = x28x29 = x29x30 = x30x31 = x31
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 = x28x29 = x29x30 = x30x31 = x31
l76 l76 l76: 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 = x28x29 = x29x30 = x30x31 = x31
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 = x28x29 = x29x30 = x30x31 = x31
l46 l46 l46: 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 = x28x29 = x29x30 = x30x31 = x31
l53 l53 l53: 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 = x28x29 = x29x30 = x30x31 = x31
l81 l81 l81: 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 = x28x29 = x29x30 = x30x31 = x31
l82 l82 l82: 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 = x28x29 = x29x30 = x30x31 = x31
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 = x28x29 = x29x30 = x30x31 = x31
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 = x28x29 = x29x30 = x30x31 = x31
l47 l47 l47: 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 = x28x29 = x29x30 = x30x31 = x31
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 = x28x29 = x29x30 = x30x31 = x31
l58 l58 l58: 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 = x28x29 = x29x30 = x30x31 = x31
l75 l75 l75: 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 = x28x29 = x29x30 = x30x31 = x31
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 = x28x29 = x29x30 = x30x31 = x31
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 = x28x29 = x29x30 = x30x31 = x31
l84 l84 l84: 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 = x28x29 = x29x30 = x30x31 = x31
l79 l79 l79: 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 = x28x29 = x29x30 = x30x31 = x31
l67 l67 l67: 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 = x28x29 = x29x30 = x30x31 = x31
l49 l49 l49: 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 = x28x29 = x29x30 = x30x31 = x31
l63 l63 l63: 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 = x28x29 = x29x30 = x30x31 = x31
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 = x28x29 = x29x30 = x30x31 = x31
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 = x28x29 = x29x30 = x30x31 = x31
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 = x28x29 = x29x30 = x30x31 = x31
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 = x28x29 = x29x30 = x30x31 = x31
l72 l72 l72: 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 = x28x29 = x29x30 = x30x31 = x31
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 = x28x29 = x29x30 = x30x31 = x31
l70 l70 l70: 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 = x28x29 = x29x30 = x30x31 = x31
l44 l44 l44: 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 = x28x29 = x29x30 = x30x31 = x31
l51 l51 l51: 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 = x28x29 = x29x30 = x30x31 = x31
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 = x28x29 = x29x30 = x30x31 = x31
l65 l65 l65: 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 = x28x29 = x29x30 = x30x31 = x31
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 = x28x29 = x29x30 = x30x31 = x31
l56 l56 l56: 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 = x28x29 = x29x30 = x30x31 = x31
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 = x28x29 = x29x30 = x30x31 = x31
l43 l43 l43: 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 = x28x29 = x29x30 = x30x31 = x31
l60 l60 l60: 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 = x28x29 = x29x30 = x30x31 = x31
l69 l69 l69: 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 = x28x29 = x29x30 = x30x31 = x31
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 = x28x29 = x29x30 = x30x31 = x31
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 = x28x29 = x29x30 = x30x31 = x31
l86 l86 l86: 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 = x28x29 = x29x30 = x30x31 = x31
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 = x28x29 = x29x30 = x30x31 = x31
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 = x28x29 = x29x30 = x30x31 = x31
l73 l73 l73: 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 = x28x29 = x29x30 = x30x31 = x31
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 = x28x29 = x29x30 = x30x31 = x31
l55 l55 l55: 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 = x28x29 = x29x30 = x30x31 = x31
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 = x28x29 = x29x30 = x30x31 = x31
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 = x28x29 = x29x30 = x30x31 = x31
l74 l74 l74: 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 = x28x29 = x29x30 = x30x31 = x31
l27 l27 l27: 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 = x28x29 = x29x30 = x30x31 = x31
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 = x28x29 = x29x30 = x30x31 = x31
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 = x28x29 = x29x30 = x30x31 = x31
l68 l68 l68: 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 = x28x29 = x29x30 = x30x31 = x31
l61 l61 l61: 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 = x28x29 = x29x30 = x30x31 = x31
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 = x28x29 = x29x30 = x30x31 = x31
l54 l54 l54: 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 = x28x29 = x29x30 = x30x31 = x31
l71 l71 l71: 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 = x28x29 = x29x30 = x30x31 = x31
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 = x28x29 = x29x30 = x30x31 = x31
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 = x28x29 = x29x30 = x30x31 = x31
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 = x28x29 = x29x30 = x30x31 = x31
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 = x28x29 = x29x30 = x30x31 = x31
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 = x28x29 = x29x30 = x30x31 = x31
l80 l80 l80: 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 = x28x29 = x29x30 = x30x31 = x31
l62 l62 l62: 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 = x28x29 = x29x30 = x30x31 = x31
l83 l83 l83: 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 = x28x29 = x29x30 = x30x31 = x31
l45 l45 l45: 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 = x28x29 = x29x30 = x30x31 = x31
l59 l59 l59: 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 = x28x29 = x29x30 = x30x31 = x31
l87 l87 l87: 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 = x28x29 = x29x30 = x30x31 = x31
l66 l66 l66: 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 = x28x29 = x29x30 = x30x31 = x31
l57 l57 l57: 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 = x28x29 = x29x30 = x30x31 = x31
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 = x28x29 = x29x30 = x30x31 = x31
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 = x28x29 = x29x30 = x30x31 = x31
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 = x28x29 = x29x30 = x30x31 = x31
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 = x28x29 = x29x30 = x30x31 = x31
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 = x28x29 = x29x30 = x30x31 = x31
l64 l64 l64: 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 = x28x29 = x29x30 = x30x31 = x31
l50 l50 l50: 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 = x28x29 = x29x30 = x30x31 = x31
l85 l85 l85: 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 = x28x29 = x29x30 = x30x31 = x31
l78 l78 l78: 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 = x28x29 = x29x30 = x30x31 = x31
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 { l44, l46, l45, l47 }.

2.1.1 Transition Removal

We remove transition 47 using the following ranking functions, which are bounded by 0.

l44: −1 − x5 + x11
l45: x5 + x11
l46: −1 − x5 + x11
l47: x5 + x11

2.1.2 Transition Removal

We remove transitions 43, 45, 44, 136 using the following ranking functions, which are bounded by 0.

l44: 2
l45: 1
l46: 3
l47: 0

2.1.3 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 { l39, l38, l37, l34, l33 }.

2.2.1 Transition Removal

We remove transition 39 using the following ranking functions, which are bounded by 0.

l33: −1 − x5 + x11
l34: −1 − x5 + x11
l38: −1 − x5 + x11
l39: x5 + x11
l37: x5 + x11

2.2.2 Transition Removal

We remove transitions 32, 36, 35, 48, 34, 37 using the following ranking functions, which are bounded by 0.

l33: 2
l34: 1
l38: 3
l37: 0
l39: −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 { l5, l22, l77, l48, l18, l17, l52, l35, l21, l6, l76, l53, l81, l82, l19, l40, l58, l75, l11, l84, l67, l79, l49, l63, l28, l42, l2, l72, l23, l4, l70, l51, l16, l65, l30, l56, l69, l60, l1, l13, l86, l31, l9, l73, l14, l25, l55, l8, l74, l27, l0, l61, l68, l12, l26, l54, l71, l7, l24, l41, l3, l20, l80, l62, l83, l59, l66, l57, l10, l36, l29, l64, l15, l50, l85, l78 }.

2.3.1 Transition Removal

We remove transition 21 using the following ranking functions, which are bounded by 0.

l0: −1 − x8 + x11
l1: −1 − x8 + x11
l2: −1 − x8 + x11
l30: −1 − x8 + x11
l31: −1 − x8 + x11
l40: −1 − x8 + x11
l51: −1 − x8 + x11
l49: −1 − x8 + x11
l48: −1 − x8 + x11
l58: −1 − x8 + x11
l50: −1 − x8 + x11
l57: −1 − x8 + x11
l53: −1 − x8 + x11
l42: −1 − x8 + x11
l41: −1 − x8 + x11
l25: −1 − x8 + x11
l24: −1 − x8 + x11
l22: −1 − x8 + x11
l21: −1 − x8 + x11
l7: −1 − x8 + x11
l6: −1 − x8 + x11
l70: −1 − x8 + x11
l9: −1 − x8 + x11
l84: −1 − x8 + x11
l73: −1 − x8 + x11
l74: −1 − x8 + x11
l75: −1 − x8 + x11
l76: −1 − x8 + x11
l83: −1 − x8 + x11
l81: −1 − x8 + x11
l72: −1 − x8 + x11
l71: −1 − x8 + x11
l65: −1 − x8 + x11
l64: −1 − x8 + x11
l61: −1 − x8 + x11
l63: −1 − x8 + x11
l62: −1 − x8 + x11
l85: −1 − x8 + x11
l86: −1 − x8 + x11
l67: −1 − x8 + x11
l66: −1 − x8 + x11
l78: −1 − x8 + x11
l77: −1 − x8 + x11
l80: −1 − x8 + x11
l82: −1 − x8 + x11
l79: −1 − x8 + x11
l68: −1 − x8 + x11
l69: −1 − x8 + x11
l8: −1 − x8 + x11
l4: −1 − x8 + x11
l23: −1 − x8 + x11
l11: −1 − x8 + x11
l29: −1 − x8 + x11
l27: −1 − x8 + x11
l26: −1 − x8 + x11
l28: −1 − x8 + x11
l10: −2 − x8 + x11
l20: −2 − x8 + x11
l19: −2 − x8 + x11
l13: −2 − x8 + x11
l12: −2 − x8 + x11
l14: −2 − x8 + x11
l17: −2 − x8 + x11
l18: −2 − x8 + x11
l3: −1 − x8 + x11
l5: −1 − x8 + x11
l16: −1 − x8 + x11
l15: −1 − x8 + x11
l36: −1 − x8 + x11
l35: −1 − x8 + x11
l59: −1 − x8 + x11
l60: −1 − x8 + x11
l52: −1 − x8 + x11
l54: −1 − x8 + x11
l55: −1 − x8 + x11
l56: −1 − x8 + x11

2.3.2 Transition Removal

We remove transition 15 using the following ranking functions, which are bounded by 0.

l0: −2 − x7 + x11
l1: −2 − x7 + x11
l2: −2 − x7 + x11
l30: −2 − x7 + x11
l31: −2 − x7 + x11
l40: −2 − x7 + x11
l51: −2 − x7 + x11
l49: −2 − x7 + x11
l48: −2 − x7 + x11
l58: −2 − x7 + x11
l50: −2 − x7 + x11
l57: −2 − x7 + x11
l53: −2 − x7 + x11
l42: −2 − x7 + x11
l41: −2 − x7 + x11
l25: −2 − x7 + x11
l24: −2 − x7 + x11
l22: −2 − x7 + x11
l21: −2 − x7 + x11
l7: −2 − x7 + x11
l6: −2 − x7 + x11
l70: −2 − x7 + x11
l9: −2 − x7 + x11
l84: −2 − x7 + x11
l73: −2 − x7 + x11
l74: −2 − x7 + x11
l75: −2 − x7 + x11
l76: −2 − x7 + x11
l83: −2 − x7 + x11
l81: −2 − x7 + x11
l72: −2 − x7 + x11
l71: −2 − x7 + x11
l65: −2 − x7 + x11
l64: −2 − x7 + x11
l61: −2 − x7 + x11
l63: −2 − x7 + x11
l62: −2 − x7 + x11
l85: −2 − x7 + x11
l86: −2 − x7 + x11
l67: −2 − x7 + x11
l66: −2 − x7 + x11
l78: −2 − x7 + x11
l77: −2 − x7 + x11
l80: −2 − x7 + x11
l82: −2 − x7 + x11
l79: −2 − x7 + x11
l68: −2 − x7 + x11
l69: −2 − x7 + x11
l8: −2 − x7 + x11
l4: −2 − x7 + x11
l23: −2 − x7 + x11
l11: −2 − x7 + x11
l29: −2 − x7 + x11
l27: −2 − x7 + x11
l26: −2 − x7 + x11
l28: −2 − x7 + x11
l10: −2 − x7 + x11
l20: x7 + x11
l19: x7 + x11
l13: x7 + x11
l12: −1 − x7 + x11
l14: −1 − x7 + x11
l17: −1 − x7 + x11
l18: −1 − x7 + x11
l3: −2 − x7 + x11
l5: −2 − x7 + x11
l16: −2 − x7 + x11
l15: −2 − x7 + x11
l36: −2 − x7 + x11
l35: −2 − x7 + x11
l59: −2 − x7 + x11
l60: −2 − x7 + x11
l52: −2 − x7 + x11
l54: −2 − x7 + x11
l55: −2 − x7 + x11
l56: −2 − x7 + x11

2.3.3 Transition Removal

We remove transitions 132, 127, 115, 97, 24, 84 using the following ranking functions, which are bounded by 0.

l0: x7 + x11
l1: x7 + x11
l2: x7 + x11
l30: x7 + x11
l31: x7 + x11
l40: x7 + x11
l51: x7 + x11
l49: x7 + x11
l48: x7 + x11
l58: x7 + x11
l50: x7 + x11
l57: x7 + x11
l53: x7 + x11
l42: x7 + x11
l41: x7 + x11
l25: x7 + x11
l24: x7 + x11
l22: x7 + x11
l21: x7 + x11
l7: x7 + x11
l6: x7 + x11
l70: x7 + x11
l9: x7 + x11
l84: x7 + x11
l73: x7 + x11
l74: x7 + x11
l75: x7 + x11
l76: x7 + x11
l83: x7 + x11
l81: x7 + x11
l72: x7 + x11
l71: x7 + x11
l65: x7 + x11
l64: x7 + x11
l61: x7 + x11
l63: x7 + x11
l62: x7 + x11
l85: x7 + x11
l86: x7 + x11
l67: x7 + x11
l66: x7 + x11
l78: x7 + x11
l77: x7 + x11
l80: x7 + x11
l82: x7 + x11
l79: x7 + x11
l68: x7 + x11
l69: x7 + x11
l8: x7 + x11
l4: x7 + x11
l23: x7 + x11
l11: x7 + x11
l29: x7 + x11
l27: x7 + x11
l26: x7 + x11
l28: x7 + x11
l10: x7 + x11
l20: x7 + x11
l19: x7 + x11
l13: x7 + x11
l12: −1 − x7 + x11
l14: −1 − x7 + x11
l17: −1 − x7 + x11
l18: −1 − x7 + x11
l3: x7 + x11
l5: x7 + x11
l16: x7 + x11
l15: x7 + x11
l36: x7 + x11
l35: x7 + x11
l59: x7 + x11
l60: x7 + x11
l52: x7 + x11
l54: x7 + x11
l55: x7 + x11
l56: x7 + x11

2.3.4 Transition Removal

We remove transition 31 using the following ranking functions, which are bounded by 0.

l0: −1 + x1x6
l1: −1 + x1x6
l2: −1 + x1x6
l30: −1 + x1x6
l31: x1x6
l40: x1x6
l51: −1 + x1x6
l49: −1 + x1x6
l48: −1 + x1x6
l58: −1 + x1x6
l50: −1 + x1x6
l57: −1 + x1x6
l53: −1 + x1x6
l42: −1 + x1x6
l41: −1 + x1x6
l25: −1 + x1x6
l24: −1 + x1x6
l22: −1 + x1x6
l21: −1 + x1x6
l7: −1 + x1x6
l6: −1 + x1x6
l70: −1 + x1x6
l9: −1 + x1x6
l84: −1 + x1x6
l73: −1 + x1x6
l74: −1 + x1x6
l75: −1 + x1x6
l76: −1 + x1x6
l83: −1 + x1x6
l81: −1 + x1x6
l72: −1 + x1x6
l71: −1 + x1x6
l65: −1 + x1x6
l64: −1 + x1x6
l61: −1 + x1x6
l63: −1 + x1x6
l62: −1 + x1x6
l85: −1 + x1x6
l86: −1 + x1x6
l67: −1 + x1x6
l66: −1 + x1x6
l78: −1 + x1x6
l77: −1 + x1x6
l80: −1 + x1x6
l82: −1 + x1x6
l79: −1 + x1x6
l68: −1 + x1x6
l69: −1 + x1x6
l8: −1 + x1x6
l4: −1 + x1x6
l23: −1 + x1x6
l11: −1 + x1x6
l29: −1 + x1x6
l27: −1 + x1x6
l26: −1 + x1x6
l28: −1 + x1x6
l10: −1 + x1x6
l20: −1 + x1x6
l19: −1 + x1x6
l13: −1 + x1x6
l12: −1 + x1x6
l14: −1 + x1x6
l17: −1 + x1x6
l18: −1 + x1x6
l3: −1 + x1x6
l5: −1 + x1x6
l16: −1 + x1x6
l15: −1 + x1x6
l36: −1 + x1x6
l35: −1 + x1x6
l59: −1 + x1x6
l60: −1 + x1x6
l52: −1 + x1x6
l54: −1 + x1x6
l55: −1 + x1x6
l56: −1 + x1x6

2.3.5 Transition Removal

We remove transition 20 using the following ranking functions, which are bounded by 0.

l0: −3 + x8x11
l1: −3 + x8x11
l2: −3 + x8x11
l30: x8x11
l40: −1 + x3x4 − 2⋅x5 + x8 + x11
l31: −1 + x3x4 − 2⋅x5 + x8 + x11
l51: −1 + x3x4 − 2⋅x5 + x8 + x11
l49: −1 + x3x4 − 2⋅x5 + x8 + x11
l48: −1 + x3x4 − 2⋅x5 + x8 + x11
l58: −1 + x3x4 − 2⋅x5 + x8 + x11
l50: −1 + x3x4 − 2⋅x5 + x8 + x11
l57: −1 + x3x4 − 2⋅x5 + x8 + x11
l53: −1 + x3x4 − 2⋅x5 + x8 + x11
l42: −1 + x3x4 − 2⋅x5 + x8 + x11
l41: −1 + x3x4 − 2⋅x5 + x8 + x11
l25: −1 + x3x4 − 2⋅x5 + x8 + x11
l24: −1 + x3x4 − 2⋅x5 + x8 + x11
l22: −3 + x8x11
l21: −3 + x8x11
l7: −3 + x8x11
l6: −3 + x8x11
l70: −3 + x8x11
l9: −3 + x8x11
l84: −3 + x8x11
l73: −3 + x8x11
l74: −3 + x8x11
l75: −3 + x8x11
l76: −3 + x8x11
l83: −3 + x8x11
l81: −3 + x8x11
l72: −3 + x8x11
l71: −3 + x8x11
l65: −3 + x8x11
l64: −3 + x8x11
l61: −3 + x8x11
l63: −3 + x8x11
l62: −3 + x8x11
l85: −3 + x8x11
l86: −3 + x8x11
l67: −3 + x8x11
l66: −3 + x8x11
l78: −3 + x8x11
l77: −3 + x8x11
l80: −3 + x8x11
l82: −3 + x8x11
l79: −3 + x8x11
l68: −3 + x8x11
l69: −3 + x8x11
l8: −3 + x8x11
l4: −3 + x8x11
l23: x8x11
l11: x8x11
l29: x8x11
l27: x8x11
l26: x8x11
l28: x8x11
l10: 1 + x8x11
l20: 1 + x8x11
l19: 1 + x8x11
l13: 1 + x8x11
l12: 1 + x8x11
l14: 1 + x8x11
l17: 1 + x8x11
l18: 1 + x8x11
l3: −3 + x8x11
l5: −3 + x8x11
l16: −3 + x8x11
l15: −3 + x8x11
l36: −3 + x3x4 − 2⋅x5 + x8 + x11
l35: −3 + x3x4 − 2⋅x5 + x8 + x11
l59: −3 + x3x4 − 2⋅x5 + x8 + x11
l60: −1 + x3x4 − 2⋅x5 + x8 + x11
l52: −3 + x3x4 − 2⋅x5 + x8 + x11
l54: −3 + x3x4 − 2⋅x5 + x8 + x11
l55: −3 + x3x4 − 2⋅x5 + x8 + x11
l56: −1 + x3x4 − 2⋅x5 + x8 + x11

2.3.6 Transition Removal

We remove transitions 1, 27, 71, 133, 6, 53, 25, 29, 28, 8, 16, 14, 54, 18, 17, 9, 12, 87, 80, 68 using the following ranking functions, which are bounded by 0.

l0: 17
l1: 16
l2: 17
l30: 18
l40: −1 − 6⋅x5 + 6⋅x11
l31: −1 − 6⋅x5 + 6⋅x11
l51: −1 − 6⋅x5 + 6⋅x11
l49: 5 − 6⋅x5 + 6⋅x11
l48: 5 − 6⋅x5 + 6⋅x11
l58: 5 − 6⋅x5 + 6⋅x11
l50: 5 − 6⋅x5 + 6⋅x11
l57: 5 − 6⋅x5 + 6⋅x11
l53: 5 − 6⋅x5 + 6⋅x11
l42: x5 + x11
l41: x5 + x11
l25: x5 + x11
l24: x5 + x11
l22: −1
l21: −1
l7: −1
l6: −1
l70: −1
l9: −1
l84: −1
l73: −1
l74: −1
l75: −1
l76: −1
l83: −1
l81: −1
l72: −1
l71: −1
l65: −1
l64: −1
l61: 16
l63: 16
l62: 16
l85: −1
l86: −1
l67: −1
l66: −1
l78: −1
l77: −1
l80: −1
l82: −1
l79: −1
l68: −1
l69: −1
l8: 10
l4: 10
l11: 0
l23: −1
l29: 17
l27: 17
l26: 17
l28: 17
l10: 1
l20: 4
l19: 2
l13: 3
l12: 4
l14: 4
l17: 5
l18: 5
l3: 10
l5: 10
l16: −1
l15: −1
l36: −1 − x5 + x11
l35: −1 − x5 + x11
l59: −1 − x5 + x11
l60: −1 − x5 + x11
l52: −1 − 6⋅x5 + 6⋅x11
l54: −1 − 6⋅x5 + 6⋅x11
l55: −1 − 6⋅x5 + 6⋅x11
l56: −1 − 6⋅x5 + 6⋅x11

2.3.7 Transition Removal

We remove transitions 13, 10, 7, 2 using the following ranking functions, which are bounded by 0.

l2: x5 + x11
l0: x5 + x11
l40: −1 + 3⋅x1 + x3 + x4 − 3⋅x5x6x7 + 4⋅x8 + x9 + x10 + x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l31: −1 + 3⋅x1 + x3 + x4 − 3⋅x5x6x7 + 4⋅x8 + x9 + x10 + x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l51: −2 + 3⋅x1 + x3 + x4 − 3⋅x5x6x7 + 4⋅x8 + x9 + x10 + x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l49: −4 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l48: −4 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l58: −4 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l50: −2 + 3⋅x1 + x3 + x4 − 3⋅x5x6x7 + 4⋅x8 + x9 + x10 + x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l57: −4 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l53: −4 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l42: −4 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l41: −4 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l25: −4 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l24: −4 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l22: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l21: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l7: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l6: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l70: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l9: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l84: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l73: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l74: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l75: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l76: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l83: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l81: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l72: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l71: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l65: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l64: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l1: −1 + 11⋅x1 + 12⋅x2 + 13⋅x3 + 14⋅x4 − 2⋅x5 + 15⋅x6 + x7 + 16⋅x8 + 17⋅x9 + 18⋅x10 + x11 + 19⋅x12 + 20⋅x13 + 21⋅x14 + 22⋅x15 + 23⋅x16 + 24⋅x17 + 25⋅x18 + 26⋅x19 + 27⋅x20 + 28⋅x21 + 29⋅x22 + 30⋅x23 + 31⋅x24 + 32⋅x25 + 33⋅x26 + 34⋅x27 + 35⋅x28 + 36⋅x29 + 37⋅x30 + 38⋅x31
l61: −1 + 11⋅x1 + 12⋅x2 + 13⋅x3 + 14⋅x4 − 2⋅x5 + 15⋅x6 + x7 + 16⋅x8 + 17⋅x9 + 18⋅x10 + x11 + 19⋅x12 + 20⋅x13 + 21⋅x14 + 22⋅x15 + 23⋅x16 + 24⋅x17 + 25⋅x18 + 26⋅x19 + 27⋅x20 + 28⋅x21 + 29⋅x22 + 30⋅x23 + 31⋅x24 + 32⋅x25 + 33⋅x26 + 34⋅x27 + 35⋅x28 + 36⋅x29 + 37⋅x30 + 38⋅x31
l63: −1 + 11⋅x1 + 12⋅x2 + 13⋅x3 + 14⋅x4 − 2⋅x5 + 15⋅x6 + x7 + 16⋅x8 + 17⋅x9 + 18⋅x10 + x11 + 19⋅x12 + 20⋅x13 + 21⋅x14 + 22⋅x15 + 23⋅x16 + 24⋅x17 + 25⋅x18 + 26⋅x19 + 27⋅x20 + 28⋅x21 + 29⋅x22 + 30⋅x23 + 31⋅x24 + 32⋅x25 + 33⋅x26 + 34⋅x27 + 35⋅x28 + 36⋅x29 + 37⋅x30 + 38⋅x31
l62: −1 + 11⋅x1 + 12⋅x2 + 13⋅x3 + 14⋅x4 − 2⋅x5 + 15⋅x6 + x7 + 16⋅x8 + 17⋅x9 + 18⋅x10 + x11 + 19⋅x12 + 20⋅x13 + 21⋅x14 + 22⋅x15 + 23⋅x16 + 24⋅x17 + 25⋅x18 + 26⋅x19 + 27⋅x20 + 28⋅x21 + 29⋅x22 + 30⋅x23 + 31⋅x24 + 32⋅x25 + 33⋅x26 + 34⋅x27 + 35⋅x28 + 36⋅x29 + 37⋅x30 + 38⋅x31
l85: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l86: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l67: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l66: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l78: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l77: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l80: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l82: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l79: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l68: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l69: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l4: x5 + x11
l8: x5 + x11
l27: −1 + 39⋅x1 + 40⋅x2 + 41⋅x3 + 42⋅x4 − 2⋅x5 + 43⋅x6 + x7 + 44⋅x8 + 45⋅x9 + 46⋅x10 + x11 + 47⋅x12 + 48⋅x13 + 49⋅x14 + 50⋅x15 + 51⋅x16 + 52⋅x17 + 53⋅x18 + 54⋅x19 + 55⋅x20 + 56⋅x21 + 57⋅x22 + 58⋅x23 + 59⋅x24 + 60⋅x25 + 61⋅x26 + 62⋅x27 + 63⋅x28 + 64⋅x29 + 65⋅x30 + 66⋅x31
l29: −1 + 39⋅x1 + 40⋅x2 + 41⋅x3 + 42⋅x4 − 2⋅x5 + 43⋅x6 + x7 + 44⋅x8 + 45⋅x9 + 46⋅x10 + x11 + 47⋅x12 + 48⋅x13 + 49⋅x14 + 50⋅x15 + 51⋅x16 + 52⋅x17 + 53⋅x18 + 54⋅x19 + 55⋅x20 + 56⋅x21 + 57⋅x22 + 58⋅x23 + 59⋅x24 + 60⋅x25 + 61⋅x26 + 62⋅x27 + 63⋅x28 + 64⋅x29 + 65⋅x30 + 66⋅x31
l26: −1 + 39⋅x1 + 40⋅x2 + 41⋅x3 + 42⋅x4 − 2⋅x5 + 43⋅x6 + x7 + 44⋅x8 + 45⋅x9 + 46⋅x10 + x11 + 47⋅x12 + 48⋅x13 + 49⋅x14 + 50⋅x15 + 51⋅x16 + 52⋅x17 + 53⋅x18 + 54⋅x19 + 55⋅x20 + 56⋅x21 + 57⋅x22 + 58⋅x23 + 59⋅x24 + 60⋅x25 + 61⋅x26 + 62⋅x27 + 63⋅x28 + 64⋅x29 + 65⋅x30 + 66⋅x31
l28: −1 + 39⋅x1 + 40⋅x2 + 41⋅x3 + 42⋅x4 − 2⋅x5 + 43⋅x6 + x7 + 44⋅x8 + 45⋅x9 + 46⋅x10 + x11 + 47⋅x12 + 48⋅x13 + 49⋅x14 + 50⋅x15 + 51⋅x16 + 52⋅x17 + 53⋅x18 + 54⋅x19 + 55⋅x20 + 56⋅x21 + 57⋅x22 + 58⋅x23 + 59⋅x24 + 60⋅x25 + 61⋅x26 + 62⋅x27 + 63⋅x28 + 64⋅x29 + 65⋅x30 + 66⋅x31
l14: −2⋅x5 + 2⋅x11
l12: −2⋅x5 + 2⋅x11
l18: −2⋅x5 + 2⋅x11
l17: −2⋅x5 + 2⋅x11
l3: −1 − x5 + x11
l5: −1 − x5 + x11
l16: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l15: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l36: −7 + 3⋅x1 + x3 + x4x5x6 + x7 + 4⋅x8 + x9 + x10 − 3⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l35: −7 + 3⋅x1 + x3 + x4x5x6 + x7 + 4⋅x8 + x9 + x10 − 3⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l59: −5 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l60: −5 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l52: −5 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l54: −5 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l55: −5 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l56: −5 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + x9 − 2⋅x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31

2.3.8 Transition Removal

We remove transitions 75, 56, 55 using the following ranking functions, which are bounded by 0.

l2: 1
l0: 0
l40: −1 + 3⋅x1 + x3 + x4 − 3⋅x5x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 + x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l31: −1 + 3⋅x1 + x3 + x4 − 3⋅x5x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 + x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l51: −2 + 3⋅x1 + x3 + x4 − 3⋅x5x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 + x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l49: −4 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l48: −4 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l58: −4 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l50: −2 + 3⋅x1 + x3 + x4 − 3⋅x5x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 + x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l57: −4 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l53: −4 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l42: −4 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l41: −4 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l25: −4 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l24: −4 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l22: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l21: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l7: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l6: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l70: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l9: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l84: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l73: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l74: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l75: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l76: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l83: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l81: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l72: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l71: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l65: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l64: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l1: −1 + 11⋅x1 + 12⋅x2 + 13⋅x3 + 14⋅x4 − 2⋅x5 + 15⋅x6 + x7 + 16⋅x8 + 17⋅x9 + 18⋅x10 + x11 + 19⋅x12 + 20⋅x13 + 21⋅x14 + 22⋅x15 + 23⋅x16 + 24⋅x17 + 25⋅x18 + 26⋅x19 + 27⋅x20 + 28⋅x21 + 29⋅x22 + 30⋅x23 + 31⋅x24 + 32⋅x25 + 33⋅x26 + 34⋅x27 + 35⋅x28 + 36⋅x29 + 37⋅x30 + 38⋅x31
l61: −3 + 11⋅x1 + 12⋅x2 + 13⋅x3 + 14⋅x4 − 2⋅x5 + 15⋅x6 + x7 + 16⋅x8 + 17⋅x9 + 18⋅x10 + x11 + 19⋅x12 + 20⋅x13 + 21⋅x14 + 22⋅x15 + 23⋅x16 + 24⋅x17 + 25⋅x18 + 26⋅x19 + 27⋅x20 + 28⋅x21 + 29⋅x22 + 30⋅x23 + 31⋅x24 + 32⋅x25 + 33⋅x26 + 34⋅x27 + 35⋅x28 + 36⋅x29 + 37⋅x30 + 38⋅x31
l63: −3 + 11⋅x1 + 12⋅x2 + 13⋅x3 + 14⋅x4 − 2⋅x5 + 15⋅x6 + x7 + 16⋅x8 + 17⋅x9 + 18⋅x10 + x11 + 19⋅x12 + 20⋅x13 + 21⋅x14 + 22⋅x15 + 23⋅x16 + 24⋅x17 + 25⋅x18 + 26⋅x19 + 27⋅x20 + 28⋅x21 + 29⋅x22 + 30⋅x23 + 31⋅x24 + 32⋅x25 + 33⋅x26 + 34⋅x27 + 35⋅x28 + 36⋅x29 + 37⋅x30 + 38⋅x31
l62: −3 + 11⋅x1 + 12⋅x2 + 13⋅x3 + 14⋅x4 − 2⋅x5 + 15⋅x6 + x7 + 16⋅x8 + 17⋅x9 + 18⋅x10 + x11 + 19⋅x12 + 20⋅x13 + 21⋅x14 + 22⋅x15 + 23⋅x16 + 24⋅x17 + 25⋅x18 + 26⋅x19 + 27⋅x20 + 28⋅x21 + 29⋅x22 + 30⋅x23 + 31⋅x24 + 32⋅x25 + 33⋅x26 + 34⋅x27 + 35⋅x28 + 36⋅x29 + 37⋅x30 + 38⋅x31
l85: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l86: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l67: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l66: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l78: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l77: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l80: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l82: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l79: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l68: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l69: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l4: −2 + 39⋅x1 + 40⋅x2 + 41⋅x3 + 42⋅x4 + x5 + 43⋅x6 − 2⋅x7 + 44⋅x8 + 45⋅x9 + 46⋅x10 + 47⋅x11 + 48⋅x12 + 49⋅x13 + 50⋅x14 + 51⋅x15 + 52⋅x16 + 53⋅x17 + 54⋅x18 + 55⋅x19 + 56⋅x20 + 57⋅x21 + 58⋅x22 + 59⋅x23 + 60⋅x24 + 61⋅x25 + 62⋅x26 + 63⋅x27 + 64⋅x28 + 65⋅x29 + 66⋅x30 + 67⋅x31
l8: −2 + 39⋅x1 + 40⋅x2 + 41⋅x3 + 42⋅x4 + x5 + 43⋅x6 − 2⋅x7 + 44⋅x8 + 45⋅x9 + 46⋅x10 + 47⋅x11 + 48⋅x12 + 49⋅x13 + 50⋅x14 + 51⋅x15 + 52⋅x16 + 53⋅x17 + 54⋅x18 + 55⋅x19 + 56⋅x20 + 57⋅x21 + 58⋅x22 + 59⋅x23 + 60⋅x24 + 61⋅x25 + 62⋅x26 + 63⋅x27 + 64⋅x28 + 65⋅x29 + 66⋅x30 + 67⋅x31
l27: −1 + 68⋅x1 + 69⋅x2 + 70⋅x3 + 71⋅x4 − 2⋅x5 + 72⋅x6 + x7 + 73⋅x8 + 74⋅x9 + 75⋅x10 + x11 + 76⋅x12 + 77⋅x13 + 78⋅x14 + 79⋅x15 + 80⋅x16 + 81⋅x17 + 82⋅x18 + 83⋅x19 + 84⋅x20 + 85⋅x21 + 86⋅x22 + 87⋅x23 + 88⋅x24 + 89⋅x25 + 90⋅x26 + 91⋅x27 + 92⋅x28 + 93⋅x29 + 94⋅x30 + 95⋅x31
l29: −3 + 68⋅x1 + 69⋅x2 + 70⋅x3 + 71⋅x4 − 2⋅x5 + 72⋅x6 + x7 + 73⋅x8 + 74⋅x9 + 75⋅x10 + x11 + 76⋅x12 + 77⋅x13 + 78⋅x14 + 79⋅x15 + 80⋅x16 + 81⋅x17 + 82⋅x18 + 83⋅x19 + 84⋅x20 + 85⋅x21 + 86⋅x22 + 87⋅x23 + 88⋅x24 + 89⋅x25 + 90⋅x26 + 91⋅x27 + 92⋅x28 + 93⋅x29 + 94⋅x30 + 95⋅x31
l26: −3 + 68⋅x1 + 69⋅x2 + 70⋅x3 + 71⋅x4 − 2⋅x5 + 72⋅x6 + x7 + 73⋅x8 + 74⋅x9 + 75⋅x10 + x11 + 76⋅x12 + 77⋅x13 + 78⋅x14 + 79⋅x15 + 80⋅x16 + 81⋅x17 + 82⋅x18 + 83⋅x19 + 84⋅x20 + 85⋅x21 + 86⋅x22 + 87⋅x23 + 88⋅x24 + 89⋅x25 + 90⋅x26 + 91⋅x27 + 92⋅x28 + 93⋅x29 + 94⋅x30 + 95⋅x31
l28: −3 + 68⋅x1 + 69⋅x2 + 70⋅x3 + 71⋅x4 − 2⋅x5 + 72⋅x6 + x7 + 73⋅x8 + 74⋅x9 + 75⋅x10 + x11 + 76⋅x12 + 77⋅x13 + 78⋅x14 + 79⋅x15 + 80⋅x16 + 81⋅x17 + 82⋅x18 + 83⋅x19 + 84⋅x20 + 85⋅x21 + 86⋅x22 + 87⋅x23 + 88⋅x24 + 89⋅x25 + 90⋅x26 + 91⋅x27 + 92⋅x28 + 93⋅x29 + 94⋅x30 + 95⋅x31
l14: 1
l12: 0
l18: 1
l17: 0
l3: −1 + 39⋅x1 + 40⋅x2 + 41⋅x3 + 42⋅x4x5 + 43⋅x6 + 44⋅x8 + 45⋅x9 + 46⋅x10 + 47⋅x11 + 48⋅x12 + 49⋅x13 + 50⋅x14 + 51⋅x15 + 52⋅x16 + 53⋅x17 + 54⋅x18 + 55⋅x19 + 56⋅x20 + 57⋅x21 + 58⋅x22 + 59⋅x23 + 60⋅x24 + 61⋅x25 + 62⋅x26 + 63⋅x27 + 64⋅x28 + 65⋅x29 + 66⋅x30 + 67⋅x31
l5: −1 + 39⋅x1 + 40⋅x2 + 41⋅x3 + 42⋅x4x5 + 43⋅x6 + 44⋅x8 + 45⋅x9 + 46⋅x10 + 47⋅x11 + 48⋅x12 + 49⋅x13 + 50⋅x14 + 51⋅x15 + 52⋅x16 + 53⋅x17 + 54⋅x18 + 55⋅x19 + 56⋅x20 + 57⋅x21 + 58⋅x22 + 59⋅x23 + 60⋅x24 + 61⋅x25 + 62⋅x26 + 63⋅x27 + 64⋅x28 + 65⋅x29 + 66⋅x30 + 67⋅x31
l16: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l15: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l36: −7 + 3⋅x1 + x3 + x4x5x6 + x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 − 3⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l35: −7 + 3⋅x1 + x3 + x4x5x6 + x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 − 3⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l59: −5 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l60: −5 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l52: −5 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l54: −5 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l55: −5 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l56: −5 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + x9 − 2⋅x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31

2.3.9 Transition Removal

We remove transitions 134, 60, 3 using the following ranking functions, which are bounded by 0.

l40: −1 + 3⋅x1 + x3 + x4 − 3⋅x5x6x7 + 4⋅x8 + x9 + x10 + x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l31: −1 + 3⋅x1 + x3 + x4 − 3⋅x5x6x7 + 4⋅x8 + x9 + x10 + x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l51: −2 + 3⋅x1 + x3 + x4 − 3⋅x5x6x7 + 4⋅x8 + x9 + x10 + x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l49: −4 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l48: −4 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l58: −4 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l50: −2 + 3⋅x1 + x3 + x4 − 3⋅x5x6x7 + 4⋅x8 + x9 + x10 + x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l57: −4 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l53: −4 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l42: −4 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l41: −4 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l25: −4 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l24: −4 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l22: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l21: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l7: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l6: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l70: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l9: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l84: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l73: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l74: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l75: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l76: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l83: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l81: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l72: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l71: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l65: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l64: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l1: x5 + x11
l61: x5 + x11
l63: −1 − x5 + x11
l62: −1 − x5 + x11
l85: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l86: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l67: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l66: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l78: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l77: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l80: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l82: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l79: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l68: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l69: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l4: 0
l8: −1
l27: −1 + 11⋅x1 + 12⋅x2 + 13⋅x3 + 14⋅x4 − 2⋅x5 + 15⋅x6 + x7 + 16⋅x8 + 17⋅x9 + 18⋅x10 + x11 + 19⋅x12 + 20⋅x13 + 21⋅x14 + 22⋅x15 + 23⋅x16 + 24⋅x17 + 25⋅x18 + 26⋅x19 + 27⋅x20 + 28⋅x21 + 29⋅x22 + 30⋅x23 + 31⋅x24 + 32⋅x25 + 33⋅x26 + 34⋅x27 + 35⋅x28 + 36⋅x29 + 37⋅x30 + 38⋅x31
l29: −3 + 11⋅x1 + 12⋅x2 + 13⋅x3 + 14⋅x4 − 2⋅x5 + 15⋅x6 + x7 + 16⋅x8 + 17⋅x9 + 18⋅x10 + x11 + 19⋅x12 + 20⋅x13 + 21⋅x14 + 22⋅x15 + 23⋅x16 + 24⋅x17 + 25⋅x18 + 26⋅x19 + 27⋅x20 + 28⋅x21 + 29⋅x22 + 30⋅x23 + 31⋅x24 + 32⋅x25 + 33⋅x26 + 34⋅x27 + 35⋅x28 + 36⋅x29 + 37⋅x30 + 38⋅x31
l26: −3 + 11⋅x1 + 12⋅x2 + 13⋅x3 + 14⋅x4 − 2⋅x5 + 15⋅x6 + x7 + 16⋅x8 + 17⋅x9 + 18⋅x10 + x11 + 19⋅x12 + 20⋅x13 + 21⋅x14 + 22⋅x15 + 23⋅x16 + 24⋅x17 + 25⋅x18 + 26⋅x19 + 27⋅x20 + 28⋅x21 + 29⋅x22 + 30⋅x23 + 31⋅x24 + 32⋅x25 + 33⋅x26 + 34⋅x27 + 35⋅x28 + 36⋅x29 + 37⋅x30 + 38⋅x31
l28: −3 + 11⋅x1 + 12⋅x2 + 13⋅x3 + 14⋅x4 − 2⋅x5 + 15⋅x6 + x7 + 16⋅x8 + 17⋅x9 + 18⋅x10 + x11 + 19⋅x12 + 20⋅x13 + 21⋅x14 + 22⋅x15 + 23⋅x16 + 24⋅x17 + 25⋅x18 + 26⋅x19 + 27⋅x20 + 28⋅x21 + 29⋅x22 + 30⋅x23 + 31⋅x24 + 32⋅x25 + 33⋅x26 + 34⋅x27 + 35⋅x28 + 36⋅x29 + 37⋅x30 + 38⋅x31
l3: 1
l5: 1
l16: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l15: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l36: −7 + 3⋅x1 + x3 + x4x5x6 + x7 + 4⋅x8 + x9 + x10 − 3⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l35: −7 + 3⋅x1 + x3 + x4x5x6 + x7 + 4⋅x8 + x9 + x10 − 3⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l59: −5 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l60: −5 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l52: −5 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l54: −5 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l55: −5 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l56: −5 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 − 2⋅x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31

2.3.10 Transition Removal

We remove transition 4 using the following ranking functions, which are bounded by 0.

l40: −1 + 3⋅x1 + x3 + x4 − 3⋅x5x6x7 + 4⋅x8 + x9 + x10 + x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l31: −1 + 3⋅x1 + x3 + x4 − 3⋅x5x6x7 + 4⋅x8 + x9 + x10 + x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l51: −2 + 3⋅x1 + x3 + x4 − 3⋅x5x6x7 + 4⋅x8 + x9 + x10 + x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l49: −4 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l48: −4 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l58: −4 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l50: −2 + 3⋅x1 + x3 + x4 − 3⋅x5x6x7 + 4⋅x8 + x9 + x10 + x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l57: −4 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l53: −4 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l42: −4 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l41: −4 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l25: −4 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l24: −4 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l22: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l21: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l7: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l6: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l70: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l9: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l84: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l73: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l74: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l75: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l76: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l83: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l81: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l72: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l71: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l65: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l64: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l1: −2 + 11⋅x1 + 12⋅x2 + 13⋅x3 + 14⋅x4 + x5 + 15⋅x6 − 2⋅x7 + 16⋅x8 + 17⋅x9 + 18⋅x10 + x11 + 19⋅x12 + 20⋅x13 + 21⋅x14 + 22⋅x15 + 23⋅x16 + 24⋅x17 + 25⋅x18 + 26⋅x19 + 27⋅x20 + 28⋅x21 + 29⋅x22 + 30⋅x23 + 31⋅x24 + 32⋅x25 + 33⋅x26 + 34⋅x27 + 35⋅x28 + 36⋅x29 + 37⋅x30 + 38⋅x31
l61: −2 + 11⋅x1 + 12⋅x2 + 13⋅x3 + 14⋅x4 + x5 + 15⋅x6 − 2⋅x7 + 16⋅x8 + 17⋅x9 + 18⋅x10 + x11 + 19⋅x12 + 20⋅x13 + 21⋅x14 + 22⋅x15 + 23⋅x16 + 24⋅x17 + 25⋅x18 + 26⋅x19 + 27⋅x20 + 28⋅x21 + 29⋅x22 + 30⋅x23 + 31⋅x24 + 32⋅x25 + 33⋅x26 + 34⋅x27 + 35⋅x28 + 36⋅x29 + 37⋅x30 + 38⋅x31
l63: −1 + 11⋅x1 + 12⋅x2 + 13⋅x3 + 14⋅x4 + x5 + 15⋅x6 − 2⋅x7 + 16⋅x8 + 17⋅x9 + 18⋅x10 + x11 + 19⋅x12 + 20⋅x13 + 21⋅x14 + 22⋅x15 + 23⋅x16 + 24⋅x17 + 25⋅x18 + 26⋅x19 + 27⋅x20 + 28⋅x21 + 29⋅x22 + 30⋅x23 + 31⋅x24 + 32⋅x25 + 33⋅x26 + 34⋅x27 + 35⋅x28 + 36⋅x29 + 37⋅x30 + 38⋅x31
l62: −1 + 11⋅x1 + 12⋅x2 + 13⋅x3 + 14⋅x4 + x5 + 15⋅x6 − 2⋅x7 + 16⋅x8 + 17⋅x9 + 18⋅x10 + x11 + 19⋅x12 + 20⋅x13 + 21⋅x14 + 22⋅x15 + 23⋅x16 + 24⋅x17 + 25⋅x18 + 26⋅x19 + 27⋅x20 + 28⋅x21 + 29⋅x22 + 30⋅x23 + 31⋅x24 + 32⋅x25 + 33⋅x26 + 34⋅x27 + 35⋅x28 + 36⋅x29 + 37⋅x30 + 38⋅x31
l85: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l86: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l67: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l66: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l78: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l77: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l80: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l82: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l79: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l68: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l69: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l27: −1 + 39⋅x1 + 40⋅x2 + 41⋅x3 + 42⋅x4 − 2⋅x5 + 43⋅x6 + x7 + 44⋅x8 + 45⋅x9 + 46⋅x10 + x11 + 47⋅x12 + 48⋅x13 + 49⋅x14 + 50⋅x15 + 51⋅x16 + 52⋅x17 + 53⋅x18 + 54⋅x19 + 55⋅x20 + 56⋅x21 + 57⋅x22 + 58⋅x23 + 59⋅x24 + 60⋅x25 + 61⋅x26 + 62⋅x27 + 63⋅x28 + 64⋅x29 + 65⋅x30 + 66⋅x31
l29: −3 + 39⋅x1 + 40⋅x2 + 41⋅x3 + 42⋅x4 − 2⋅x5 + 43⋅x6 + x7 + 44⋅x8 + 45⋅x9 + 46⋅x10 + x11 + 47⋅x12 + 48⋅x13 + 49⋅x14 + 50⋅x15 + 51⋅x16 + 52⋅x17 + 53⋅x18 + 54⋅x19 + 55⋅x20 + 56⋅x21 + 57⋅x22 + 58⋅x23 + 59⋅x24 + 60⋅x25 + 61⋅x26 + 62⋅x27 + 63⋅x28 + 64⋅x29 + 65⋅x30 + 66⋅x31
l26: −3 + 39⋅x1 + 40⋅x2 + 41⋅x3 + 42⋅x4 − 2⋅x5 + 43⋅x6 + x7 + 44⋅x8 + 45⋅x9 + 46⋅x10 + x11 + 47⋅x12 + 48⋅x13 + 49⋅x14 + 50⋅x15 + 51⋅x16 + 52⋅x17 + 53⋅x18 + 54⋅x19 + 55⋅x20 + 56⋅x21 + 57⋅x22 + 58⋅x23 + 59⋅x24 + 60⋅x25 + 61⋅x26 + 62⋅x27 + 63⋅x28 + 64⋅x29 + 65⋅x30 + 66⋅x31
l28: −3 + 39⋅x1 + 40⋅x2 + 41⋅x3 + 42⋅x4 − 2⋅x5 + 43⋅x6 + x7 + 44⋅x8 + 45⋅x9 + 46⋅x10 + x11 + 47⋅x12 + 48⋅x13 + 49⋅x14 + 50⋅x15 + 51⋅x16 + 52⋅x17 + 53⋅x18 + 54⋅x19 + 55⋅x20 + 56⋅x21 + 57⋅x22 + 58⋅x23 + 59⋅x24 + 60⋅x25 + 61⋅x26 + 62⋅x27 + 63⋅x28 + 64⋅x29 + 65⋅x30 + 66⋅x31
l5: −1 + x5x7
l3: −1 + x5x7
l16: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l15: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l36: −7 + 3⋅x1 + x3 + x4x5x6 + x7 + 4⋅x8 + x9 + x10 − 3⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l35: −7 + 3⋅x1 + x3 + x4x5x6 + x7 + 4⋅x8 + x9 + x10 − 3⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l59: −5 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l60: −5 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l52: −5 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l54: −5 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l55: −5 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l56: −5 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 − 2⋅x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31

2.3.11 Transition Removal

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

l40: −1 + 3⋅x1x3 + 2⋅x4 − 3⋅x5x6x7 + 4⋅x8 + x9 + x10 + x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l31: −1 + 3⋅x1x3 + 2⋅x4 − 3⋅x5x6x7 + 4⋅x8 + x9 + x10 + x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l51: −2 + 3⋅x1x3 + 2⋅x4 − 3⋅x5x6x7 + 4⋅x8 + x9 + x10 + x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l49: −4 + 3⋅x1x3 + 2⋅x4x5x6x7 + 4⋅x8 + x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l48: −4 + 3⋅x1x3 + 2⋅x4x5x6x7 + 4⋅x8 + x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l58: −4 + 3⋅x1x3 + 2⋅x4x5x6x7 + 4⋅x8 + x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l50: −2 + 3⋅x1x3 + 2⋅x4 − 3⋅x5x6x7 + 4⋅x8 + x9 + x10 + x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l57: −4 + 3⋅x1x3 + 2⋅x4x5x6x7 + 4⋅x8 + x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l53: −4 + 3⋅x1x3 + 2⋅x4x5x6x7 + 4⋅x8 + x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l42: −4 + 3⋅x1x3 + 2⋅x4x5x6x7 + 4⋅x8 + x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l41: −4 + 3⋅x1x3 + 2⋅x4x5x6x7 + 4⋅x8 + x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l25: −4 + 3⋅x1x3 + 2⋅x4x5x6x7 + 4⋅x8 + x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l24: −4 + 3⋅x1x3 + 2⋅x4x5x6x7 + 4⋅x8 + x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l22: −5 + 3⋅x1 + x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l21: −5 + 3⋅x1 + x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l7: −5 + 3⋅x1 + x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l6: −5 + 3⋅x1 + x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l70: −5 + 3⋅x1 + x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l9: −5 + 3⋅x1 + x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l84: −5 + 3⋅x1 + x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l73: −5 + 3⋅x1 + x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l74: −5 + 3⋅x1 + x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l75: −5 + 3⋅x1 + x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l76: −5 + 3⋅x1 + x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l83: −5 + 3⋅x1 + x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l81: −5 + 3⋅x1 + x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l72: −5 + 3⋅x1 + x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l71: −5 + 3⋅x1 + x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l65: −5 + 3⋅x1 + x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l64: −5 + 3⋅x1 + x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l1: −4 + 11⋅x1 + 12⋅x2 + 13⋅x3 + 14⋅x4 + x5 + 15⋅x6 + x7 + 16⋅x8 + 17⋅x9 + 18⋅x10 − 2⋅x11 + 19⋅x12 + 20⋅x13 + 21⋅x14 + 22⋅x15 + 23⋅x16 + 24⋅x17 + 25⋅x18 + 26⋅x19 + 27⋅x20 + 28⋅x21 + 29⋅x22 + 30⋅x23 + 31⋅x24 + 32⋅x25 + 33⋅x26 + 34⋅x27 + 35⋅x28 + 36⋅x29 + 37⋅x30 + 38⋅x31
l61: −4 + 11⋅x1 + 12⋅x2 + 13⋅x3 + 14⋅x4 + x5 + 15⋅x6 + x7 + 16⋅x8 + 17⋅x9 + 18⋅x10 − 2⋅x11 + 19⋅x12 + 20⋅x13 + 21⋅x14 + 22⋅x15 + 23⋅x16 + 24⋅x17 + 25⋅x18 + 26⋅x19 + 27⋅x20 + 28⋅x21 + 29⋅x22 + 30⋅x23 + 31⋅x24 + 32⋅x25 + 33⋅x26 + 34⋅x27 + 35⋅x28 + 36⋅x29 + 37⋅x30 + 38⋅x31
l63: −3 + 11⋅x1 + 12⋅x2 + 13⋅x3 + 14⋅x4 + x5 + 15⋅x6 + x7 + 16⋅x8 + 17⋅x9 + 18⋅x10 − 2⋅x11 + 19⋅x12 + 20⋅x13 + 21⋅x14 + 22⋅x15 + 23⋅x16 + 24⋅x17 + 25⋅x18 + 26⋅x19 + 27⋅x20 + 28⋅x21 + 29⋅x22 + 30⋅x23 + 31⋅x24 + 32⋅x25 + 33⋅x26 + 34⋅x27 + 35⋅x28 + 36⋅x29 + 37⋅x30 + 38⋅x31
l62: −3 + 11⋅x1 + 12⋅x2 + 13⋅x3 + 14⋅x4 + x5 + 15⋅x6 + x7 + 16⋅x8 + 17⋅x9 + 18⋅x10 − 2⋅x11 + 19⋅x12 + 20⋅x13 + 21⋅x14 + 22⋅x15 + 23⋅x16 + 24⋅x17 + 25⋅x18 + 26⋅x19 + 27⋅x20 + 28⋅x21 + 29⋅x22 + 30⋅x23 + 31⋅x24 + 32⋅x25 + 33⋅x26 + 34⋅x27 + 35⋅x28 + 36⋅x29 + 37⋅x30 + 38⋅x31
l85: −5 + 3⋅x1 + x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l86: −5 + 3⋅x1 + x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l67: −5 + 3⋅x1 + x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l66: −5 + 3⋅x1 + x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l78: −5 + 3⋅x1 + x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l77: −5 + 3⋅x1 + x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l80: −5 + 3⋅x1 + x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l82: −5 + 3⋅x1 + x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l79: −5 + 3⋅x1 + x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l68: −5 + 3⋅x1 + x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l69: −5 + 3⋅x1 + x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l27: −1 + 39⋅x1 + 40⋅x2 + 41⋅x3 + 42⋅x4 − 2⋅x5 + 43⋅x6 + x7 + 44⋅x8 + 45⋅x9 + 46⋅x10 + x11 + 47⋅x12 + 48⋅x13 + 49⋅x14 + 50⋅x15 + 51⋅x16 + 52⋅x17 + 53⋅x18 + 54⋅x19 + 55⋅x20 + 56⋅x21 + 57⋅x22 + 58⋅x23 + 59⋅x24 + 60⋅x25 + 61⋅x26 + 62⋅x27 + 63⋅x28 + 64⋅x29 + 65⋅x30 + 66⋅x31
l29: −3 + 39⋅x1 + 40⋅x2 + 41⋅x3 + 42⋅x4 − 2⋅x5 + 43⋅x6 + x7 + 44⋅x8 + 45⋅x9 + 46⋅x10 + x11 + 47⋅x12 + 48⋅x13 + 49⋅x14 + 50⋅x15 + 51⋅x16 + 52⋅x17 + 53⋅x18 + 54⋅x19 + 55⋅x20 + 56⋅x21 + 57⋅x22 + 58⋅x23 + 59⋅x24 + 60⋅x25 + 61⋅x26 + 62⋅x27 + 63⋅x28 + 64⋅x29 + 65⋅x30 + 66⋅x31
l26: −3 + 39⋅x1 + 40⋅x2 + 41⋅x3 + 42⋅x4 − 2⋅x5 + 43⋅x6 + x7 + 44⋅x8 + 45⋅x9 + 46⋅x10 + x11 + 47⋅x12 + 48⋅x13 + 49⋅x14 + 50⋅x15 + 51⋅x16 + 52⋅x17 + 53⋅x18 + 54⋅x19 + 55⋅x20 + 56⋅x21 + 57⋅x22 + 58⋅x23 + 59⋅x24 + 60⋅x25 + 61⋅x26 + 62⋅x27 + 63⋅x28 + 64⋅x29 + 65⋅x30 + 66⋅x31
l28: −3 + 39⋅x1 + 40⋅x2 + 41⋅x3 + 42⋅x4 − 2⋅x5 + 43⋅x6 + x7 + 44⋅x8 + 45⋅x9 + 46⋅x10 + x11 + 47⋅x12 + 48⋅x13 + 49⋅x14 + 50⋅x15 + 51⋅x16 + 52⋅x17 + 53⋅x18 + 54⋅x19 + 55⋅x20 + 56⋅x21 + 57⋅x22 + 58⋅x23 + 59⋅x24 + 60⋅x25 + 61⋅x26 + 62⋅x27 + 63⋅x28 + 64⋅x29 + 65⋅x30 + 66⋅x31
l5: 0
l3: −1
l16: −5 + 3⋅x1 + x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l15: −5 + 3⋅x1 + x3x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l36: −7 + 3⋅x1x3 + 2⋅x4x5x6 + x7 + 4⋅x8 + x9 + x10 − 3⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l35: −7 + 3⋅x1x3 + 2⋅x4x5x6 + x7 + 4⋅x8 + x9 + x10 − 3⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l59: −5 + 3⋅x1x3 + 2⋅x4x5x6x7 + 4⋅x8 + x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l60: −5 + 3⋅x1x3 + 2⋅x4x5x6x7 + 4⋅x8 + x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l52: −5 + 3⋅x1x3 + 2⋅x4x5x6x7 + 4⋅x8 + x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l54: −5 + 3⋅x1x3 + 2⋅x4x5x6x7 + 4⋅x8 + x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l55: −5 + 3⋅x1x3 + 2⋅x4x5x6x7 + 4⋅x8 + x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l56: −5 + 3⋅x1x3 + 2⋅x4x5x6x7 + 4⋅x8 − 2⋅x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31

2.3.12 Transition Removal

We remove transitions 81, 131, 85, 26 using the following ranking functions, which are bounded by 0.

l40: −2 + 3⋅x1 + x3 + x4 − 3⋅x5 + x6x7 + 4⋅x8 + x9 + x10 + x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l31: −2 + 3⋅x1 + x3 + x4 − 3⋅x5 + x6x7 + 4⋅x8 + x9 + x10 + x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l51: −1 + 3⋅x1 + x3 + x4 − 3⋅x5 + x6x7 + 4⋅x8 + x9 + x10 + x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l49: −3 + 3⋅x1 + x3 + x4x5 + x6x7 + 4⋅x8 + x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l48: −3 + 3⋅x1 + x3 + x4x5 + x6x7 + 4⋅x8 + x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l58: −3 + 3⋅x1 + x3 + x4x5 + x6x7 + 4⋅x8 + x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l50: −1 + 3⋅x1 + x3 + x4 − 3⋅x5 + x6x7 + 4⋅x8 + x9 + x10 + x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l57: −3 + 3⋅x1 + x3 + x4x5 + x6x7 + 4⋅x8 + x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l53: −3 + 3⋅x1 + x3 + x4x5 + x6x7 + 4⋅x8 + x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l42: −3 + 3⋅x1 + x3 + x4x5 + x6x7 + 4⋅x8 + x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l41: −3 + 3⋅x1 + x3 + x4x5 + x6x7 + 4⋅x8 + x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l25: −3 + 3⋅x1 + x3 + x4x5 + x6x7 + 4⋅x8 + x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l24: −3 + 3⋅x1 + x3 + x4x5 + x6x7 + 4⋅x8 + x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l22: −4 + 3⋅x1 + 2⋅x3 + x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l21: −4 + 3⋅x1 + 2⋅x3 + x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l7: −4 + 3⋅x1 + 2⋅x3 + x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l6: −4 + 3⋅x1 + 2⋅x3 + x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l70: −4 + 3⋅x1 + 2⋅x3 + x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l9: −4 + 3⋅x1 + 2⋅x3 + x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l84: −4 + 3⋅x1 + 2⋅x3 + x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l73: −4 + 3⋅x1 + 2⋅x3 + x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l74: −4 + 3⋅x1 + 2⋅x3 + x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l75: −4 + 3⋅x1 + 2⋅x3 + x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l76: −4 + 3⋅x1 + 2⋅x3 + x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l83: −4 + 3⋅x1 + 2⋅x3 + x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l81: −4 + 3⋅x1 + 2⋅x3 + x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l72: −4 + 3⋅x1 + 2⋅x3 + x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l71: −4 + 3⋅x1 + 2⋅x3 + x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l65: −4 + 3⋅x1 + 2⋅x3 + x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l64: −4 + 3⋅x1 + 2⋅x3 + x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l1: 0
l61: −1
l63: 1
l62: 2
l85: −4 + 3⋅x1 + 2⋅x3 + x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l86: −4 + 3⋅x1 + 2⋅x3 + x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l67: −4 + 3⋅x1 + 2⋅x3 + x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l66: −4 + 3⋅x1 + 2⋅x3 + x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l78: −4 + 3⋅x1 + 2⋅x3 + x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l77: −4 + 3⋅x1 + 2⋅x3 + x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l80: −4 + 3⋅x1 + 2⋅x3 + x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l82: −4 + 3⋅x1 + 2⋅x3 + x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l79: −4 + 3⋅x1 + 2⋅x3 + x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l68: −4 + 3⋅x1 + 2⋅x3 + x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l69: −4 + 3⋅x1 + 2⋅x3 + x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l27: x5 + x11
l29: x5 + x11
l26: −1 − x5 + x11
l28: −1 − x5 + x11
l16: −4 + 3⋅x1 + 2⋅x3 + x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l15: −4 + 3⋅x1 + 2⋅x3 + x6x7 + 4⋅x8 + x9 + x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l36: −6 + 3⋅x1 + x3 + x4x5 + x6 + x7 + 4⋅x8 + x9 + x10 − 3⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l35: −6 + 3⋅x1 + x3 + x4x5 + x6 + x7 + 4⋅x8 + x9 + x10 − 3⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l59: −4 + 3⋅x1 + x3 + x4x5 + x6x7 + 4⋅x8 + x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l60: −4 + 3⋅x1 + x3 + x4x5 + x6x7 + 4⋅x8 + x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l52: −4 + 3⋅x1 + x3 + x4x5 + x6x7 + 4⋅x8 + x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l54: −4 + 3⋅x1 + x3 + x4x5 + x6x7 + 4⋅x8 + x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l55: −4 + 3⋅x1 + x3 + x4x5 + x6x7 + 4⋅x8 + x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 − 3⋅x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l56: −4 + 3⋅x1 + x3 + x4x5 + x6x7 + 4⋅x8 − 2⋅x9 + x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31

2.3.13 Transition Removal

We remove transitions 51, 23, 52 using the following ranking functions, which are bounded by 0.

l40: −1 + 3⋅x1 + x3 + x4 − 3⋅x5x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 + x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l31: −1 + 3⋅x1 + x3 + x4 − 3⋅x5x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 + x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l51: −2 + 3⋅x1 + x3 + x4 − 3⋅x5x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 + x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l49: −4 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l48: −4 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l58: −4 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l50: −2 + 3⋅x1 + x3 + x4 − 3⋅x5x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 + x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l57: −4 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l53: −4 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l42: −4 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l41: −4 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l25: −4 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l24: −4 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l22: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l21: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l7: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l6: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l70: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l9: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l84: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l73: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l74: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l75: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l76: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l83: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l81: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l72: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l71: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l65: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l64: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l85: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l86: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l67: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l66: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l78: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l77: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l80: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l82: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l79: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l68: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l69: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l27: 0
l29: −1
l26: 1
l28: 2
l16: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l15: −5 + 3⋅x1 + 2⋅x3x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 − 2⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l36: −7 + 3⋅x1 + x3 + x4x5x6 + x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 − 3⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l35: −7 + 3⋅x1 + x3 + x4x5x6 + x7 + 4⋅x8 + 2⋅x9 − 2⋅x10 − 3⋅x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l59: −5 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l60: −5 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l52: −5 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l54: −5 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l55: −5 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + 2⋅x9 − 2⋅x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20x21 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31
l56: −5 + 3⋅x1 + x3 + x4x5x6x7 + 4⋅x8 + x9 − 2⋅x10x11 + 5⋅x18 + 6⋅x19 + 7⋅x20 + 8⋅x23 + 9⋅x24 + x30 + 10⋅x31

2.3.14 Transition Removal

We remove transitions 49, 69, 70, 50, 74, 73, 57, 67, 82, 72, 79, 40, 86, 22, 88, 93, 98, 119, 118, 101, 103, 111, 116, 120, 128, 83, 33, 76, 78, 77, 59, 62, 61, 63, 65, 64 using the following ranking functions, which are bounded by 0.

l40: 0
l31: −1
l51: 1
l49: 2
l48: 3
l58: 5
l50: 2
l57: 3
l53: 4
l42: 6
l41: 7
l25: 8
l24: 9
l22: 10
l21: 10
l7: 11
l6: 11
l70: 12
l9: 12
l84: 17
l73: 13
l74: 13
l75: 14
l76: 14
l83: 15
l81: 15
l72: 16
l71: 16
l65: 18
l64: 18
l85: 18
l86: 18
l67: 18
l66: 18
l78: 16
l77: 16
l80: 15
l82: 15
l79: 15
l68: 12
l69: 12
l16: 11
l15: 11
l36: 10
l35: 11
l59: 8
l60: 9
l52: 5
l54: 6
l55: 7
l56: 8

2.3.15 Transition Removal

We remove transitions 112, 102, 99, 92, 89 using the following ranking functions, which are bounded by 0.

l21: x5 + x11
l22: x5 + x11
l6: 1 + x5x7
l7: x5x7
l9: x5 + x11
l70: x5 + x11
l74: x5 + x11
l73: x5 + x11
l76: −1 + 2⋅x1 + 3⋅x2 + 4⋅x3 + 5⋅x4 − 2⋅x5 + 6⋅x6 + 7⋅x7 + 8⋅x8 + 9⋅x9 + 10⋅x10 + 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 + 28⋅x29 + 29⋅x30 + 30⋅x31
l75: −1 + 2⋅x1 + 3⋅x2 + 4⋅x3 + 5⋅x4 − 2⋅x5 + 6⋅x6 + 7⋅x7 + 8⋅x8 + 9⋅x9 + 10⋅x10 + 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 + 28⋅x29 + 29⋅x30 + 30⋅x31
l81: x5 + x11
l83: x5 + x11
l71: −1 + 31⋅x1 + 32⋅x2 + 33⋅x3 + 34⋅x4 − 2⋅x5 + 35⋅x6 + x7 + 36⋅x8 + 37⋅x9 + 38⋅x10 + x11 + 39⋅x12 + 40⋅x13 + 41⋅x14 + 42⋅x15 + 43⋅x16 + 44⋅x17 + 45⋅x18 + 46⋅x19 + 47⋅x20 + 48⋅x21 + 49⋅x22 + 50⋅x23 + 51⋅x24 + 52⋅x25 + 53⋅x26 + 54⋅x27 + 55⋅x28 + 56⋅x29 + 57⋅x30 + 58⋅x31
l72: −3 + 31⋅x1 + 32⋅x2 + 33⋅x3 + 34⋅x4 − 2⋅x5 + 35⋅x6 + x7 + 36⋅x8 + 37⋅x9 + 38⋅x10 + x11 + 39⋅x12 + 40⋅x13 + 41⋅x14 + 42⋅x15 + 43⋅x16 + 44⋅x17 + 45⋅x18 + 46⋅x19 + 47⋅x20 + 48⋅x21 + 49⋅x22 + 50⋅x23 + 51⋅x24 + 52⋅x25 + 53⋅x26 + 54⋅x27 + 55⋅x28 + 56⋅x29 + 57⋅x30 + 58⋅x31
l64: −3 + 59⋅x1 + 60⋅x2 + 61⋅x3 + 62⋅x4 − 2⋅x5 + 63⋅x6 − 2⋅x7 + 64⋅x8 + 65⋅x9 + 66⋅x10 + x11 + 67⋅x12 + 68⋅x14 + 69⋅x15 + 70⋅x16 + 71⋅x17 + 72⋅x18 + 73⋅x19 + 74⋅x20 + 75⋅x21 + 76⋅x22 + 77⋅x23 + 78⋅x24 + 79⋅x28 + 80⋅x29 + 81⋅x30 + 82⋅x31
l65: −3 + 59⋅x1 + 60⋅x2 + 61⋅x3 + 62⋅x4 − 2⋅x5 + 63⋅x6 − 2⋅x7 + 64⋅x8 + 65⋅x9 + 66⋅x10 + x11 + 67⋅x12 + 68⋅x14 + 69⋅x15 + 70⋅x16 + 71⋅x17 + 72⋅x18 + 73⋅x19 + 74⋅x20 + 75⋅x21 + 76⋅x22 + 77⋅x23 + 78⋅x24 + 79⋅x28 + 80⋅x29 + 81⋅x30 + 82⋅x31
l85: −5 + 59⋅x1 + 60⋅x2 + 61⋅x3 + 62⋅x4 − 2⋅x5 + 63⋅x6 − 2⋅x7 + 64⋅x8 + 65⋅x9 + 66⋅x10 + x11 + 67⋅x12 + 68⋅x14 + 69⋅x15 + 70⋅x16 + 71⋅x17 + 72⋅x18 + 73⋅x19 + 74⋅x20 + 75⋅x21 + 76⋅x22 + 77⋅x23 + 78⋅x24 + 79⋅x28 + 80⋅x29 + 81⋅x30 + 82⋅x31
l86: −5 + 59⋅x1 + 60⋅x2 + 61⋅x3 + 62⋅x4 − 2⋅x5 + 63⋅x6 − 2⋅x7 + 64⋅x8 + 65⋅x9 + 66⋅x10 + x11 + 67⋅x12 + 68⋅x14 + 69⋅x15 + 70⋅x16 + 71⋅x17 + 72⋅x18 + 73⋅x19 + 74⋅x20 + 75⋅x21 + 76⋅x22 + 77⋅x23 + 78⋅x24 + 79⋅x28 + 80⋅x29 + 81⋅x30 + 82⋅x31
l67: −3 + 59⋅x1 + 60⋅x2 + 61⋅x3 + 62⋅x4 − 2⋅x5 + 63⋅x6 − 2⋅x7 + 64⋅x8 + 65⋅x9 + 66⋅x10 + x11 + 67⋅x12 + 68⋅x14 + 69⋅x15 + 70⋅x16 + 71⋅x17 + 72⋅x18 + 73⋅x19 + 74⋅x20 + 75⋅x21 + 76⋅x22 + 77⋅x23 + 78⋅x24 + 79⋅x28 + 80⋅x29 + 81⋅x30 + 82⋅x31
l66: −3 + 59⋅x1 + 60⋅x2 + 61⋅x3 + 62⋅x4 − 2⋅x5 + 63⋅x6 − 2⋅x7 + 64⋅x8 + 65⋅x9 + 66⋅x10 + x11 + 67⋅x12 + 68⋅x14 + 69⋅x15 + 70⋅x16 + 71⋅x17 + 72⋅x18 + 73⋅x19 + 74⋅x20 + 75⋅x21 + 76⋅x22 + 77⋅x23 + 78⋅x24 + 79⋅x28 + 80⋅x29 + 81⋅x30 + 82⋅x31
l78: −3 + 31⋅x1 + 32⋅x2 + 33⋅x3 + 34⋅x4 − 2⋅x5 + 35⋅x6 + x7 + 36⋅x8 + 37⋅x9 + 38⋅x10 + x11 + 39⋅x12 + 40⋅x13 + 41⋅x14 + 42⋅x15 + 43⋅x16 + 44⋅x17 + 45⋅x18 + 46⋅x19 + 47⋅x20 + 48⋅x21 + 49⋅x22 + 50⋅x23 + 51⋅x24 + 52⋅x25 + 53⋅x26 + 54⋅x27 + 55⋅x28 + 56⋅x29 + 57⋅x30 + 58⋅x31
l77: −3 + 31⋅x1 + 32⋅x2 + 33⋅x3 + 34⋅x4 − 2⋅x5 + 35⋅x6 + x7 + 36⋅x8 + 37⋅x9 + 38⋅x10 + x11 + 39⋅x12 + 40⋅x13 + 41⋅x14 + 42⋅x15 + 43⋅x16 + 44⋅x17 + 45⋅x18 + 46⋅x19 + 47⋅x20 + 48⋅x21 + 49⋅x22 + 50⋅x23 + 51⋅x24 + 52⋅x25 + 53⋅x26 + 54⋅x27 + 55⋅x28 + 56⋅x29 + 57⋅x30 + 58⋅x31
l80: −1 − x5 + x11
l82: −1 − x5 + x11
l79: −1 − x5 + x11
l68: −1 − x5 + x11
l69: −1 − x5 + x11
l16: x5x7
l15: x5x7

2.3.16 Transition Removal

We remove transitions 130, 125, 113, 107, 110, 106, 109, 108, 96, 135 using the following ranking functions, which are bounded by 0.

l21: −1 + 4⋅x1 + 5⋅x2 + 6⋅x3 + 7⋅x4 + 8⋅x5 + 9⋅x6 + 10⋅x7 + 11⋅x8 + 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 + 32⋅x29 + 33⋅x30 + 34⋅x31
l22: −1 + 4⋅x1 + 5⋅x2 + 6⋅x3 + 7⋅x4 + 8⋅x5 + 9⋅x6 + 10⋅x7 + 11⋅x8 + 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 + 32⋅x29 + 33⋅x30 + 34⋅x31
l6: −1 + 35⋅x1 + 36⋅x2 + 37⋅x3 + 38⋅x4 + x5 + 39⋅x6 + x7 + 40⋅x8 + 41⋅x9 + 42⋅x10 + 43⋅x11 + 44⋅x12 + 45⋅x13 + 46⋅x14 + 47⋅x15 + 48⋅x16 + 49⋅x17 + 50⋅x18 + 51⋅x19 + 52⋅x20 + 53⋅x21 + 54⋅x22 + 55⋅x23 + 56⋅x24 + 57⋅x25 + 58⋅x26 + 59⋅x27 + 60⋅x28 + 61⋅x29 + 62⋅x30 + 63⋅x31
l7: −2 + 35⋅x1 + 36⋅x2 + 37⋅x3 + 38⋅x4 + x5 + 39⋅x6 + x7 + 40⋅x8 + 41⋅x9 + 42⋅x10 + 43⋅x11 + 44⋅x12 + 45⋅x13 + 46⋅x14 + 47⋅x15 + 48⋅x16 + 49⋅x17 + 50⋅x18 + 51⋅x19 + 52⋅x20 + 53⋅x21 + 54⋅x22 + 55⋅x23 + 56⋅x24 + 57⋅x25 + 58⋅x26 + 59⋅x27 + 60⋅x28 + 61⋅x29 + 62⋅x30 + 63⋅x31
l9: 0
l70: −1
l74: 1
l73: 0
l76: −1 + 64⋅x1 + 65⋅x2 + 66⋅x3 + 67⋅x4 − 2⋅x5 + 68⋅x6 + 69⋅x7 + 70⋅x8 + 71⋅x9 + 72⋅x10 + x11 + 73⋅x12 + 74⋅x13 + 75⋅x14 + 76⋅x15 + 77⋅x16 + 78⋅x17 + 79⋅x18 + 80⋅x19 + 81⋅x20 + 82⋅x21 + 83⋅x22 + 84⋅x23 + 85⋅x24 + 86⋅x25 + 87⋅x26 + 88⋅x27 + 89⋅x28 + 90⋅x29 + 91⋅x30 + 92⋅x31
l75: −3 + 64⋅x1 + 65⋅x2 + 66⋅x3 + 67⋅x4 − 2⋅x5 + 68⋅x6 + 69⋅x7 + 70⋅x8 + 71⋅x9 + 72⋅x10 + x11 + 73⋅x12 + 74⋅x13 + 75⋅x14 + 76⋅x15 + 77⋅x16 + 78⋅x17 + 79⋅x18 + 80⋅x19 + 81⋅x20 + 82⋅x21 + 83⋅x22 + 84⋅x23 + 85⋅x24 + 86⋅x25 + 87⋅x26 + 88⋅x27 + 89⋅x28 + 90⋅x29 + 91⋅x30 + 92⋅x31
l81: 0
l83: −1
l71: −1 + 93⋅x1 + 94⋅x2 + 95⋅x3 + 96⋅x4 − 2⋅x5 + 97⋅x6 + x7 + 98⋅x8 + 99⋅x9 + 100⋅x10 + x11 + 101⋅x12 + 102⋅x13 + 103⋅x14 + 104⋅x15 + 105⋅x16 + 106⋅x17 + 107⋅x18 + 108⋅x19 + 109⋅x20 + 110⋅x21 + 111⋅x22 + 112⋅x23 + 113⋅x24 + 114⋅x25 + 115⋅x26 + 116⋅x27 + 117⋅x28 + 118⋅x29 + 119⋅x30 + 120⋅x31
l72: −3 + 93⋅x1 + 94⋅x2 + 95⋅x3 + 96⋅x4 − 2⋅x5 + 97⋅x6 + x7 + 98⋅x8 + 99⋅x9 + 100⋅x10 + x11 + 101⋅x12 + 102⋅x13 + 103⋅x14 + 104⋅x15 + 105⋅x16 + 106⋅x17 + 107⋅x18 + 108⋅x19 + 109⋅x20 + 110⋅x21 + 111⋅x22 + 112⋅x23 + 113⋅x24 + 114⋅x25 + 115⋅x26 + 116⋅x27 + 117⋅x28 + 118⋅x29 + 119⋅x30 + 120⋅x31
l64: −1 + 121⋅x1 + 122⋅x2 + 123⋅x3 + 124⋅x4 − 2⋅x5 + 125⋅x6 − 2⋅x7 + 126⋅x8 + 127⋅x9 + 128⋅x10 + x11 + 129⋅x12 + 130⋅x14 + 131⋅x15 + 132⋅x16 + 133⋅x17 + 134⋅x18 + 135⋅x19 + 136⋅x20 + 137⋅x21 + 138⋅x22 + 139⋅x23 + 140⋅x24 + 141⋅x28 + 142⋅x29 + 143⋅x30 + 144⋅x31
l65: −3 + 121⋅x1 + 122⋅x2 + 123⋅x3 + 124⋅x4 − 2⋅x5 + 125⋅x6 − 2⋅x7 + 126⋅x8 + 127⋅x9 + 128⋅x10 + x11 + 129⋅x12 + 130⋅x14 + 131⋅x15 + 132⋅x16 + 133⋅x17 + 134⋅x18 + 135⋅x19 + 136⋅x20 + 137⋅x21 + 138⋅x22 + 139⋅x23 + 140⋅x24 + 141⋅x28 + 142⋅x29 + 143⋅x30 + 144⋅x31
l85: −3 + 121⋅x1 + 122⋅x2 + 123⋅x3 + 124⋅x4 − 2⋅x5 + 125⋅x6 − 2⋅x7 + 126⋅x8 + 127⋅x9 + 128⋅x10 + x11 + 129⋅x12 + 130⋅x14 + 131⋅x15 + 132⋅x16 + 133⋅x17 + 134⋅x18 + 135⋅x19 + 136⋅x20 + 137⋅x21 + 138⋅x22 + 139⋅x23 + 140⋅x24 + 141⋅x28 + 142⋅x29 + 143⋅x30 + 144⋅x31
l86: −3 + 121⋅x1 + 122⋅x2 + 123⋅x3 + 124⋅x4 − 2⋅x5 + 125⋅x6 − 2⋅x7 + 126⋅x8 + 127⋅x9 + 128⋅x10 + x11 + 129⋅x12 + 130⋅x14 + 131⋅x15 + 132⋅x16 + 133⋅x17 + 134⋅x18 + 135⋅x19 + 136⋅x20 + 137⋅x21 + 138⋅x22 + 139⋅x23 + 140⋅x24 + 141⋅x28 + 142⋅x29 + 143⋅x30 + 144⋅x31
l67: −3 + 121⋅x1 + 122⋅x2 + 123⋅x3 + 124⋅x4 − 2⋅x5 + 125⋅x6 − 2⋅x7 + 126⋅x8 + 127⋅x9 + 128⋅x10 + x11 + 129⋅x12 + 130⋅x14 + 131⋅x15 + 132⋅x16 + 133⋅x17 + 134⋅x18 + 135⋅x19 + 136⋅x20 + 137⋅x21 + 138⋅x22 + 139⋅x23 + 140⋅x24 + 141⋅x28 + 142⋅x29 + 143⋅x30 + 144⋅x31
l66: −3 + 121⋅x1 + 122⋅x2 + 123⋅x3 + 124⋅x4 − 2⋅x5 + 125⋅x6 − 2⋅x7 + 126⋅x8 + 127⋅x9 + 128⋅x10 + x11 + 129⋅x12 + 130⋅x14 + 131⋅x15 + 132⋅x16 + 133⋅x17 + 134⋅x18 + 135⋅x19 + 136⋅x20 + 137⋅x21 + 138⋅x22 + 139⋅x23 + 140⋅x24 + 141⋅x28 + 142⋅x29 + 143⋅x30 + 144⋅x31
l78: −3 + 93⋅x1 + 94⋅x2 + 95⋅x3 + 96⋅x4 − 2⋅x5 + 97⋅x6 + x7 + 98⋅x8 + 99⋅x9 + 100⋅x10 + x11 + 101⋅x12 + 102⋅x13 + 103⋅x14 + 104⋅x15 + 105⋅x16 + 106⋅x17 + 107⋅x18 + 108⋅x19 + 109⋅x20 + 110⋅x21 + 111⋅x22 + 112⋅x23 + 113⋅x24 + 114⋅x25 + 115⋅x26 + 116⋅x27 + 117⋅x28 + 118⋅x29 + 119⋅x30 + 120⋅x31
l77: −3 + 93⋅x1 + 94⋅x2 + 95⋅x3 + 96⋅x4 − 2⋅x5 + 97⋅x6 + x7 + 98⋅x8 + 99⋅x9 + 100⋅x10 + x11 + 101⋅x12 + 102⋅x13 + 103⋅x14 + 104⋅x15 + 105⋅x16 + 106⋅x17 + 107⋅x18 + 108⋅x19 + 109⋅x20 + 110⋅x21 + 111⋅x22 + 112⋅x23 + 113⋅x24 + 114⋅x25 + 115⋅x26 + 116⋅x27 + 117⋅x28 + 118⋅x29 + 119⋅x30 + 120⋅x31
l80: 1
l82: 3
l79: 2
l68: 1
l69: 2
l16: −2 + 35⋅x1 + 36⋅x2 + 37⋅x3 + 38⋅x4 + x5 + 39⋅x6 + x7 + 40⋅x8 + 41⋅x9 + 42⋅x10 + 43⋅x11 + 44⋅x12 + 45⋅x13 + 46⋅x14 + 47⋅x15 + 48⋅x16 + 49⋅x17 + 50⋅x18 + 51⋅x19 + 52⋅x20 + 53⋅x21 + 54⋅x22 + 55⋅x23 + 56⋅x24 + 57⋅x25 + 58⋅x26 + 59⋅x27 + 60⋅x28 + 61⋅x29 + 62⋅x30 + 63⋅x31
l15: −2 + 35⋅x1 + 36⋅x2 + 37⋅x3 + 38⋅x4 + x5 + 39⋅x6 + x7 + 40⋅x8 + 41⋅x9 + 42⋅x10 + 43⋅x11 + 44⋅x12 + 45⋅x13 + 46⋅x14 + 47⋅x15 + 48⋅x16 + 49⋅x17 + 50⋅x18 + 51⋅x19 + 52⋅x20 + 53⋅x21 + 54⋅x22 + 55⋅x23 + 56⋅x24 + 57⋅x25 + 58⋅x26 + 59⋅x27 + 60⋅x28 + 61⋅x29 + 62⋅x30 + 63⋅x31

2.3.17 Transition Removal

We remove transition 104 using the following ranking functions, which are bounded by 0.

l21: −1 + 2⋅x1 + 3⋅x2 + 4⋅x3 + 5⋅x4 + 6⋅x5 + 7⋅x6 + 8⋅x7 + 9⋅x8 + 10⋅x9 + 11⋅x10 + 12⋅x11 + 13⋅x12 + 14⋅x13 + 15⋅x14 + 16⋅x15 + 17⋅x16 + 18⋅x17 + 19⋅x18 + 20⋅x19 + 21⋅x20 + 22⋅x21 + 23⋅x22 + 24⋅x23 + 25⋅x24 + 26⋅x25 + 27⋅x26 + 28⋅x27 + 29⋅x28 + 30⋅x29 + 31⋅x30 + 32⋅x31
l22: −1 + 2⋅x1 + 3⋅x2 + 4⋅x3 + 5⋅x4 + 6⋅x5 + 7⋅x6 + 8⋅x7 + 9⋅x8 + 10⋅x9 + 11⋅x10 + 12⋅x11 + 13⋅x12 + 14⋅x13 + 15⋅x14 + 16⋅x15 + 17⋅x16 + 18⋅x17 + 19⋅x18 + 20⋅x19 + 21⋅x20 + 22⋅x21 + 23⋅x22 + 24⋅x23 + 25⋅x24 + 26⋅x25 + 27⋅x26 + 28⋅x27 + 29⋅x28 + 30⋅x29 + 31⋅x30 + 32⋅x31
l6: −1 + 33⋅x1 + 34⋅x2 + 35⋅x3 + 36⋅x4 + x5 + 37⋅x6 + x7 + 38⋅x8 + 39⋅x9 + 40⋅x10 + 41⋅x11 + 42⋅x12 + 43⋅x13 + 44⋅x14 + 45⋅x15 + 46⋅x16 + 47⋅x17 + 48⋅x18 + 49⋅x19 + 50⋅x20 + 51⋅x21 + 52⋅x22 + 53⋅x23 + 54⋅x24 + 55⋅x25 + 56⋅x26 + 57⋅x27 + 58⋅x28 + 59⋅x29 + 60⋅x30 + 61⋅x31
l7: −2 + 33⋅x1 + 34⋅x2 + 35⋅x3 + 36⋅x4 + x5 + 37⋅x6 + x7 + 38⋅x8 + 39⋅x9 + 40⋅x10 + 41⋅x11 + 42⋅x12 + 43⋅x13 + 44⋅x14 + 45⋅x15 + 46⋅x16 + 47⋅x17 + 48⋅x18 + 49⋅x19 + 50⋅x20 + 51⋅x21 + 52⋅x22 + 53⋅x23 + 54⋅x24 + 55⋅x25 + 56⋅x26 + 57⋅x27 + 58⋅x28 + 59⋅x29 + 60⋅x30 + 61⋅x31
l76: x5 + x11
l75: x5 + x11
l71: −1 + 62⋅x1 + 63⋅x2 + 64⋅x3 + 65⋅x4 − 2⋅x5 + 66⋅x6 + x7 + 67⋅x8 + 68⋅x9 + 69⋅x10 + x11 + 70⋅x12 + 71⋅x13 + 72⋅x14 + 73⋅x15 + 74⋅x16 + 75⋅x17 + 76⋅x18 + 77⋅x19 + 78⋅x20 + 79⋅x21 + 80⋅x22 + 81⋅x23 + 82⋅x24 + 83⋅x25 + 84⋅x26 + 85⋅x27 + 86⋅x28 + 87⋅x29 + 88⋅x30 + 89⋅x31
l72: −3 + 62⋅x1 + 63⋅x2 + 64⋅x3 + 65⋅x4 − 2⋅x5 + 66⋅x6 + x7 + 67⋅x8 + 68⋅x9 + 69⋅x10 + x11 + 70⋅x12 + 71⋅x13 + 72⋅x14 + 73⋅x15 + 74⋅x16 + 75⋅x17 + 76⋅x18 + 77⋅x19 + 78⋅x20 + 79⋅x21 + 80⋅x22 + 81⋅x23 + 82⋅x24 + 83⋅x25 + 84⋅x26 + 85⋅x27 + 86⋅x28 + 87⋅x29 + 88⋅x30 + 89⋅x31
l64: −1 + 90⋅x1 + 91⋅x2 + 92⋅x3 + 93⋅x4 − 2⋅x5 + 94⋅x6 − 2⋅x7 + 95⋅x8 + 96⋅x9 + 97⋅x10 + x11 + 98⋅x12 + 99⋅x14 + 100⋅x15 + 101⋅x16 + 102⋅x17 + 103⋅x18 + 104⋅x19 + 105⋅x20 + 106⋅x21 + 107⋅x22 + 108⋅x23 + 109⋅x24 + 110⋅x28 + 111⋅x29 + 112⋅x30 + 113⋅x31
l65: −3 + 90⋅x1 + 91⋅x2 + 92⋅x3 + 93⋅x4 − 2⋅x5 + 94⋅x6 − 2⋅x7 + 95⋅x8 + 96⋅x9 + 97⋅x10 + x11 + 98⋅x12 + 99⋅x14 + 100⋅x15 + 101⋅x16 + 102⋅x17 + 103⋅x18 + 104⋅x19 + 105⋅x20 + 106⋅x21 + 107⋅x22 + 108⋅x23 + 109⋅x24 + 110⋅x28 + 111⋅x29 + 112⋅x30 + 113⋅x31
l85: −3 + 90⋅x1 + 91⋅x2 + 92⋅x3 + 93⋅x4 − 2⋅x5 + 94⋅x6 − 2⋅x7 + 95⋅x8 + 96⋅x9 + 97⋅x10 + x11 + 98⋅x12 + 99⋅x14 + 100⋅x15 + 101⋅x16 + 102⋅x17 + 103⋅x18 + 104⋅x19 + 105⋅x20 + 106⋅x21 + 107⋅x22 + 108⋅x23 + 109⋅x24 + 110⋅x28 + 111⋅x29 + 112⋅x30 + 113⋅x31
l86: −3 + 90⋅x1 + 91⋅x2 + 92⋅x3 + 93⋅x4 − 2⋅x5 + 94⋅x6 − 2⋅x7 + 95⋅x8 + 96⋅x9 + 97⋅x10 + x11 + 98⋅x12 + 99⋅x14 + 100⋅x15 + 101⋅x16 + 102⋅x17 + 103⋅x18 + 104⋅x19 + 105⋅x20 + 106⋅x21 + 107⋅x22 + 108⋅x23 + 109⋅x24 + 110⋅x28 + 111⋅x29 + 112⋅x30 + 113⋅x31
l67: −3 + 90⋅x1 + 91⋅x2 + 92⋅x3 + 93⋅x4 − 2⋅x5 + 94⋅x6 − 2⋅x7 + 95⋅x8 + 96⋅x9 + 97⋅x10 + x11 + 98⋅x12 + 99⋅x14 + 100⋅x15 + 101⋅x16 + 102⋅x17 + 103⋅x18 + 104⋅x19 + 105⋅x20 + 106⋅x21 + 107⋅x22 + 108⋅x23 + 109⋅x24 + 110⋅x28 + 111⋅x29 + 112⋅x30 + 113⋅x31
l66: −3 + 90⋅x1 + 91⋅x2 + 92⋅x3 + 93⋅x4 − 2⋅x5 + 94⋅x6 − 2⋅x7 + 95⋅x8 + 96⋅x9 + 97⋅x10 + x11 + 98⋅x12 + 99⋅x14 + 100⋅x15 + 101⋅x16 + 102⋅x17 + 103⋅x18 + 104⋅x19 + 105⋅x20 + 106⋅x21 + 107⋅x22 + 108⋅x23 + 109⋅x24 + 110⋅x28 + 111⋅x29 + 112⋅x30 + 113⋅x31
l78: −3 + 62⋅x1 + 63⋅x2 + 64⋅x3 + 65⋅x4 − 2⋅x5 + 66⋅x6 + x7 + 67⋅x8 + 68⋅x9 + 69⋅x10 + x11 + 70⋅x12 + 71⋅x13 + 72⋅x14 + 73⋅x15 + 74⋅x16 + 75⋅x17 + 76⋅x18 + 77⋅x19 + 78⋅x20 + 79⋅x21 + 80⋅x22 + 81⋅x23 + 82⋅x24 + 83⋅x25 + 84⋅x26 + 85⋅x27 + 86⋅x28 + 87⋅x29 + 88⋅x30 + 89⋅x31
l77: −3 + 62⋅x1 + 63⋅x2 + 64⋅x3 + 65⋅x4 − 2⋅x5 + 66⋅x6 + x7 + 67⋅x8 + 68⋅x9 + 69⋅x10 + x11 + 70⋅x12 + 71⋅x13 + 72⋅x14 + 73⋅x15 + 74⋅x16 + 75⋅x17 + 76⋅x18 + 77⋅x19 + 78⋅x20 + 79⋅x21 + 80⋅x22 + 81⋅x23 + 82⋅x24 + 83⋅x25 + 84⋅x26 + 85⋅x27 + 86⋅x28 + 87⋅x29 + 88⋅x30 + 89⋅x31
l16: −2 + 33⋅x1 + 34⋅x2 + 35⋅x3 + 36⋅x4 + x5 + 37⋅x6 + x7 + 38⋅x8 + 39⋅x9 + 40⋅x10 + 41⋅x11 + 42⋅x12 + 43⋅x13 + 44⋅x14 + 45⋅x15 + 46⋅x16 + 47⋅x17 + 48⋅x18 + 49⋅x19 + 50⋅x20 + 51⋅x21 + 52⋅x22 + 53⋅x23 + 54⋅x24 + 55⋅x25 + 56⋅x26 + 57⋅x27 + 58⋅x28 + 59⋅x29 + 60⋅x30 + 61⋅x31
l15: −2 + 33⋅x1 + 34⋅x2 + 35⋅x3 + 36⋅x4 + x5 + 37⋅x6 + x7 + 38⋅x8 + 39⋅x9 + 40⋅x10 + 41⋅x11 + 42⋅x12 + 43⋅x13 + 44⋅x14 + 45⋅x15 + 46⋅x16 + 47⋅x17 + 48⋅x18 + 49⋅x19 + 50⋅x20 + 51⋅x21 + 52⋅x22 + 53⋅x23 + 54⋅x24 + 55⋅x25 + 56⋅x26 + 57⋅x27 + 58⋅x28 + 59⋅x29 + 60⋅x30 + 61⋅x31

2.3.18 Transition Removal

We remove transition 19 using the following ranking functions, which are bounded by 0.

l21: 1
l22: 0
l6: −1 + 2⋅x1 + 3⋅x2 + 4⋅x3 + 5⋅x4 + x5 + 6⋅x6 + x7 + 7⋅x8 + 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 + 28⋅x29 + 29⋅x30 + 30⋅x31
l7: −2 + 2⋅x1 + 3⋅x2 + 4⋅x3 + 5⋅x4 + x5 + 6⋅x6 + x7 + 7⋅x8 + 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 + 28⋅x29 + 29⋅x30 + 30⋅x31
l76: −1 + 31⋅x1 + 32⋅x2 + 33⋅x3 + 34⋅x4 + 35⋅x5 + 36⋅x6 + 37⋅x7 + 38⋅x8 + 39⋅x9 + 40⋅x10 + 41⋅x11 + 42⋅x12 + 43⋅x13 + 44⋅x14 + 45⋅x15 + 46⋅x16 + 47⋅x17 + 48⋅x18 + 49⋅x19 + 50⋅x20 + 51⋅x21 + 52⋅x22 + 53⋅x23 + 54⋅x24 + 55⋅x25 + 56⋅x26 + 57⋅x27 + 58⋅x28 + 59⋅x29 + 60⋅x30 + 61⋅x31
l75: −1 + 31⋅x1 + 32⋅x2 + 33⋅x3 + 34⋅x4 + 35⋅x5 + 36⋅x6 + 37⋅x7 + 38⋅x8 + 39⋅x9 + 40⋅x10 + 41⋅x11 + 42⋅x12 + 43⋅x13 + 44⋅x14 + 45⋅x15 + 46⋅x16 + 47⋅x17 + 48⋅x18 + 49⋅x19 + 50⋅x20 + 51⋅x21 + 52⋅x22 + 53⋅x23 + 54⋅x24 + 55⋅x25 + 56⋅x26 + 57⋅x27 + 58⋅x28 + 59⋅x29 + 60⋅x30 + 61⋅x31
l71: −1 + 62⋅x1 + 63⋅x2 + 64⋅x3 + 65⋅x4 − 2⋅x5 + 66⋅x6 + x7 + 67⋅x8 + 68⋅x9 + 69⋅x10 + x11 + 70⋅x12 + 71⋅x13 + 72⋅x14 + 73⋅x15 + 74⋅x16 + 75⋅x17 + 76⋅x18 + 77⋅x19 + 78⋅x20 + 79⋅x21 + 80⋅x22 + 81⋅x23 + 82⋅x24 + 83⋅x25 + 84⋅x26 + 85⋅x27 + 86⋅x28 + 87⋅x29 + 88⋅x30 + 89⋅x31
l72: −3 + 62⋅x1 + 63⋅x2 + 64⋅x3 + 65⋅x4 − 2⋅x5 + 66⋅x6 + x7 + 67⋅x8 + 68⋅x9 + 69⋅x10 + x11 + 70⋅x12 + 71⋅x13 + 72⋅x14 + 73⋅x15 + 74⋅x16 + 75⋅x17 + 76⋅x18 + 77⋅x19 + 78⋅x20 + 79⋅x21 + 80⋅x22 + 81⋅x23 + 82⋅x24 + 83⋅x25 + 84⋅x26 + 85⋅x27 + 86⋅x28 + 87⋅x29 + 88⋅x30 + 89⋅x31
l64: −1 + 90⋅x1 + 91⋅x2 + 92⋅x3 + 93⋅x4 − 2⋅x5 + 94⋅x6 − 2⋅x7 + 95⋅x8 + 96⋅x9 + 97⋅x10 + x11 + 98⋅x12 + 99⋅x14 + 100⋅x15 + 101⋅x16 + 102⋅x17 + 103⋅x18 + 104⋅x19 + 105⋅x20 + 106⋅x21 + 107⋅x22 + 108⋅x23 + 109⋅x24 + 110⋅x28 + 111⋅x29 + 112⋅x30 + 113⋅x31
l65: −3 + 90⋅x1 + 91⋅x2 + 92⋅x3 + 93⋅x4 − 2⋅x5 + 94⋅x6 − 2⋅x7 + 95⋅x8 + 96⋅x9 + 97⋅x10 + x11 + 98⋅x12 + 99⋅x14 + 100⋅x15 + 101⋅x16 + 102⋅x17 + 103⋅x18 + 104⋅x19 + 105⋅x20 + 106⋅x21 + 107⋅x22 + 108⋅x23 + 109⋅x24 + 110⋅x28 + 111⋅x29 + 112⋅x30 + 113⋅x31
l85: −3 + 90⋅x1 + 91⋅x2 + 92⋅x3 + 93⋅x4 − 2⋅x5 + 94⋅x6 − 2⋅x7 + 95⋅x8 + 96⋅x9 + 97⋅x10 + x11 + 98⋅x12 + 99⋅x14 + 100⋅x15 + 101⋅x16 + 102⋅x17 + 103⋅x18 + 104⋅x19 + 105⋅x20 + 106⋅x21 + 107⋅x22 + 108⋅x23 + 109⋅x24 + 110⋅x28 + 111⋅x29 + 112⋅x30 + 113⋅x31
l86: −3 + 90⋅x1 + 91⋅x2 + 92⋅x3 + 93⋅x4 − 2⋅x5 + 94⋅x6 − 2⋅x7 + 95⋅x8 + 96⋅x9 + 97⋅x10 + x11 + 98⋅x12 + 99⋅x14 + 100⋅x15 + 101⋅x16 + 102⋅x17 + 103⋅x18 + 104⋅x19 + 105⋅x20 + 106⋅x21 + 107⋅x22 + 108⋅x23 + 109⋅x24 + 110⋅x28 + 111⋅x29 + 112⋅x30 + 113⋅x31
l67: −3 + 90⋅x1 + 91⋅x2 + 92⋅x3 + 93⋅x4 − 2⋅x5 + 94⋅x6 − 2⋅x7 + 95⋅x8 + 96⋅x9 + 97⋅x10 + x11 + 98⋅x12 + 99⋅x14 + 100⋅x15 + 101⋅x16 + 102⋅x17 + 103⋅x18 + 104⋅x19 + 105⋅x20 + 106⋅x21 + 107⋅x22 + 108⋅x23 + 109⋅x24 + 110⋅x28 + 111⋅x29 + 112⋅x30 + 113⋅x31
l66: −3 + 90⋅x1 + 91⋅x2 + 92⋅x3 + 93⋅x4 − 2⋅x5 + 94⋅x6 − 2⋅x7 + 95⋅x8 + 96⋅x9 + 97⋅x10 + x11 + 98⋅x12 + 99⋅x14 + 100⋅x15 + 101⋅x16 + 102⋅x17 + 103⋅x18 + 104⋅x19 + 105⋅x20 + 106⋅x21 + 107⋅x22 + 108⋅x23 + 109⋅x24 + 110⋅x28 + 111⋅x29 + 112⋅x30 + 113⋅x31
l78: −3 + 62⋅x1 + 63⋅x2 + 64⋅x3 + 65⋅x4 − 2⋅x5 + 66⋅x6 + x7 + 67⋅x8 + 68⋅x9 + 69⋅x10 + x11 + 70⋅x12 + 71⋅x13 + 72⋅x14 + 73⋅x15 + 74⋅x16 + 75⋅x17 + 76⋅x18 + 77⋅x19 + 78⋅x20 + 79⋅x21 + 80⋅x22 + 81⋅x23 + 82⋅x24 + 83⋅x25 + 84⋅x26 + 85⋅x27 + 86⋅x28 + 87⋅x29 + 88⋅x30 + 89⋅x31
l77: −3 + 62⋅x1 + 63⋅x2 + 64⋅x3 + 65⋅x4 − 2⋅x5 + 66⋅x6 + x7 + 67⋅x8 + 68⋅x9 + 69⋅x10 + x11 + 70⋅x12 + 71⋅x13 + 72⋅x14 + 73⋅x15 + 74⋅x16 + 75⋅x17 + 76⋅x18 + 77⋅x19 + 78⋅x20 + 79⋅x21 + 80⋅x22 + 81⋅x23 + 82⋅x24 + 83⋅x25 + 84⋅x26 + 85⋅x27 + 86⋅x28 + 87⋅x29 + 88⋅x30 + 89⋅x31
l16: −2 + 2⋅x1 + 3⋅x2 + 4⋅x3 + 5⋅x4 + x5 + 6⋅x6 + x7 + 7⋅x8 + 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 + 28⋅x29 + 29⋅x30 + 30⋅x31
l15: −2 + 2⋅x1 + 3⋅x2 + 4⋅x3 + 5⋅x4 + x5 + 6⋅x6 + x7 + 7⋅x8 + 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 + 28⋅x29 + 29⋅x30 + 30⋅x31

2.3.19 Transition Removal

We remove transition 121 using the following ranking functions, which are bounded by 0.

l6: −1 + 2⋅x1 + 3⋅x2 + 4⋅x3 + 5⋅x4 + x5 + 6⋅x6 + x7 + 7⋅x8 + 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 + 28⋅x29 + 29⋅x30 + 30⋅x31
l7: −2 + 2⋅x1 + 3⋅x2 + 4⋅x3 + 5⋅x4 + x5 + 6⋅x6 + x7 + 7⋅x8 + 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 + 28⋅x29 + 29⋅x30 + 30⋅x31
l76: 1
l75: 0
l71: −1 + 31⋅x1 + 32⋅x2 + 33⋅x3 + 34⋅x4 − 2⋅x5 + 35⋅x6 + x7 + 36⋅x8 + 37⋅x9 + 38⋅x10 + x11 + 39⋅x12 + 40⋅x13 + 41⋅x14 + 42⋅x15 + 43⋅x16 + 44⋅x17 + 45⋅x18 + 46⋅x19 + 47⋅x20 + 48⋅x21 + 49⋅x22 + 50⋅x23 + 51⋅x24 + 52⋅x25 + 53⋅x26 + 54⋅x27 + 55⋅x28 + 56⋅x29 + 57⋅x30 + 58⋅x31
l72: −3 + 31⋅x1 + 32⋅x2 + 33⋅x3 + 34⋅x4 − 2⋅x5 + 35⋅x6 + x7 + 36⋅x8 + 37⋅x9 + 38⋅x10 + x11 + 39⋅x12 + 40⋅x13 + 41⋅x14 + 42⋅x15 + 43⋅x16 + 44⋅x17 + 45⋅x18 + 46⋅x19 + 47⋅x20 + 48⋅x21 + 49⋅x22 + 50⋅x23 + 51⋅x24 + 52⋅x25 + 53⋅x26 + 54⋅x27 + 55⋅x28 + 56⋅x29 + 57⋅x30 + 58⋅x31
l64: −1 + 59⋅x1 + 60⋅x2 + 61⋅x3 + 62⋅x4 − 2⋅x5 + 63⋅x6 − 2⋅x7 + 64⋅x8 + 65⋅x9 + 66⋅x10 + x11 + 67⋅x12 + 68⋅x14 + 69⋅x15 + 70⋅x16 + 71⋅x17 + 72⋅x18 + 73⋅x19 + 74⋅x20 + 75⋅x21 + 76⋅x22 + 77⋅x23 + 78⋅x24 + 79⋅x28 + 80⋅x29 + 81⋅x30 + 82⋅x31
l65: −3 + 59⋅x1 + 60⋅x2 + 61⋅x3 + 62⋅x4 − 2⋅x5 + 63⋅x6 − 2⋅x7 + 64⋅x8 + 65⋅x9 + 66⋅x10 + x11 + 67⋅x12 + 68⋅x14 + 69⋅x15 + 70⋅x16 + 71⋅x17 + 72⋅x18 + 73⋅x19 + 74⋅x20 + 75⋅x21 + 76⋅x22 + 77⋅x23 + 78⋅x24 + 79⋅x28 + 80⋅x29 + 81⋅x30 + 82⋅x31
l85: −3 + 59⋅x1 + 60⋅x2 + 61⋅x3 + 62⋅x4 − 2⋅x5 + 63⋅x6 − 2⋅x7 + 64⋅x8 + 65⋅x9 + 66⋅x10 + x11 + 67⋅x12 + 68⋅x14 + 69⋅x15 + 70⋅x16 + 71⋅x17 + 72⋅x18 + 73⋅x19 + 74⋅x20 + 75⋅x21 + 76⋅x22 + 77⋅x23 + 78⋅x24 + 79⋅x28 + 80⋅x29 + 81⋅x30 + 82⋅x31
l86: −3 + 59⋅x1 + 60⋅x2 + 61⋅x3 + 62⋅x4 − 2⋅x5 + 63⋅x6 − 2⋅x7 + 64⋅x8 + 65⋅x9 + 66⋅x10 + x11 + 67⋅x12 + 68⋅x14 + 69⋅x15 + 70⋅x16 + 71⋅x17 + 72⋅x18 + 73⋅x19 + 74⋅x20 + 75⋅x21 + 76⋅x22 + 77⋅x23 + 78⋅x24 + 79⋅x28 + 80⋅x29 + 81⋅x30 + 82⋅x31
l67: −3 + 59⋅x1 + 60⋅x2 + 61⋅x3 + 62⋅x4 − 2⋅x5 + 63⋅x6 − 2⋅x7 + 64⋅x8 + 65⋅x9 + 66⋅x10 + x11 + 67⋅x12 + 68⋅x14 + 69⋅x15 + 70⋅x16 + 71⋅x17 + 72⋅x18 + 73⋅x19 + 74⋅x20 + 75⋅x21 + 76⋅x22 + 77⋅x23 + 78⋅x24 + 79⋅x28 + 80⋅x29 + 81⋅x30 + 82⋅x31
l66: −3 + 59⋅x1 + 60⋅x2 + 61⋅x3 + 62⋅x4 − 2⋅x5 + 63⋅x6 − 2⋅x7 + 64⋅x8 + 65⋅x9 + 66⋅x10 + x11 + 67⋅x12 + 68⋅x14 + 69⋅x15 + 70⋅x16 + 71⋅x17 + 72⋅x18 + 73⋅x19 + 74⋅x20 + 75⋅x21 + 76⋅x22 + 77⋅x23 + 78⋅x24 + 79⋅x28 + 80⋅x29 + 81⋅x30 + 82⋅x31
l78: −3 + 31⋅x1 + 32⋅x2 + 33⋅x3 + 34⋅x4 − 2⋅x5 + 35⋅x6 + x7 + 36⋅x8 + 37⋅x9 + 38⋅x10 + x11 + 39⋅x12 + 40⋅x13 + 41⋅x14 + 42⋅x15 + 43⋅x16 + 44⋅x17 + 45⋅x18 + 46⋅x19 + 47⋅x20 + 48⋅x21 + 49⋅x22 + 50⋅x23 + 51⋅x24 + 52⋅x25 + 53⋅x26 + 54⋅x27 + 55⋅x28 + 56⋅x29 + 57⋅x30 + 58⋅x31
l77: −3 + 31⋅x1 + 32⋅x2 + 33⋅x3 + 34⋅x4 − 2⋅x5 + 35⋅x6 + x7 + 36⋅x8 + 37⋅x9 + 38⋅x10 + x11 + 39⋅x12 + 40⋅x13 + 41⋅x14 + 42⋅x15 + 43⋅x16 + 44⋅x17 + 45⋅x18 + 46⋅x19 + 47⋅x20 + 48⋅x21 + 49⋅x22 + 50⋅x23 + 51⋅x24 + 52⋅x25 + 53⋅x26 + 54⋅x27 + 55⋅x28 + 56⋅x29 + 57⋅x30 + 58⋅x31
l16: −2 + 2⋅x1 + 3⋅x2 + 4⋅x3 + 5⋅x4 + x5 + 6⋅x6 + x7 + 7⋅x8 + 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 + 28⋅x29 + 29⋅x30 + 30⋅x31
l15: −2 + 2⋅x1 + 3⋅x2 + 4⋅x3 + 5⋅x4 + x5 + 6⋅x6 + x7 + 7⋅x8 + 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 + 28⋅x29 + 29⋅x30 + 30⋅x31

2.3.20 Transition Removal

We remove transition 94 using the following ranking functions, which are bounded by 0.

l6: −1 + x5
l7: −1 + x5
l71: −1 + 2⋅x1 + 3⋅x2 + 4⋅x3 + 5⋅x4 − 2⋅x5 + 6⋅x6 + x7 + 7⋅x8 + 8⋅x9 + 9⋅x10 + 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 + 27⋅x29 + 28⋅x30 + 29⋅x31
l72: −3 + 2⋅x1 + 3⋅x2 + 4⋅x3 + 5⋅x4 − 2⋅x5 + 6⋅x6 + x7 + 7⋅x8 + 8⋅x9 + 9⋅x10 + 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 + 27⋅x29 + 28⋅x30 + 29⋅x31
l64: −1 + 30⋅x1 + 31⋅x2 + 32⋅x3 + 33⋅x4 − 2⋅x5 + 34⋅x6 − 2⋅x7 + 35⋅x8 + 36⋅x9 + 37⋅x10 + x11 + 38⋅x12 + 39⋅x14 + 40⋅x15 + 41⋅x16 + 42⋅x17 + 43⋅x18 + 44⋅x19 + 45⋅x20 + 46⋅x21 + 47⋅x22 + 48⋅x23 + 49⋅x24 + 50⋅x28 + 51⋅x29 + 52⋅x30 + 53⋅x31
l65: −3 + 30⋅x1 + 31⋅x2 + 32⋅x3 + 33⋅x4 − 2⋅x5 + 34⋅x6 − 2⋅x7 + 35⋅x8 + 36⋅x9 + 37⋅x10 + x11 + 38⋅x12 + 39⋅x14 + 40⋅x15 + 41⋅x16 + 42⋅x17 + 43⋅x18 + 44⋅x19 + 45⋅x20 + 46⋅x21 + 47⋅x22 + 48⋅x23 + 49⋅x24 + 50⋅x28 + 51⋅x29 + 52⋅x30 + 53⋅x31
l85: −3 + 30⋅x1 + 31⋅x2 + 32⋅x3 + 33⋅x4 − 2⋅x5 + 34⋅x6 − 2⋅x7 + 35⋅x8 + 36⋅x9 + 37⋅x10 + x11 + 38⋅x12 + 39⋅x14 + 40⋅x15 + 41⋅x16 + 42⋅x17 + 43⋅x18 + 44⋅x19 + 45⋅x20 + 46⋅x21 + 47⋅x22 + 48⋅x23 + 49⋅x24 + 50⋅x28 + 51⋅x29 + 52⋅x30 + 53⋅x31
l86: −3 + 30⋅x1 + 31⋅x2 + 32⋅x3 + 33⋅x4 − 2⋅x5 + 34⋅x6 − 2⋅x7 + 35⋅x8 + 36⋅x9 + 37⋅x10 + x11 + 38⋅x12 + 39⋅x14 + 40⋅x15 + 41⋅x16 + 42⋅x17 + 43⋅x18 + 44⋅x19 + 45⋅x20 + 46⋅x21 + 47⋅x22 + 48⋅x23 + 49⋅x24 + 50⋅x28 + 51⋅x29 + 52⋅x30 + 53⋅x31
l67: −3 + 30⋅x1 + 31⋅x2 + 32⋅x3 + 33⋅x4 − 2⋅x5 + 34⋅x6 − 2⋅x7 + 35⋅x8 + 36⋅x9 + 37⋅x10 + x11 + 38⋅x12 + 39⋅x14 + 40⋅x15 + 41⋅x16 + 42⋅x17 + 43⋅x18 + 44⋅x19 + 45⋅x20 + 46⋅x21 + 47⋅x22 + 48⋅x23 + 49⋅x24 + 50⋅x28 + 51⋅x29 + 52⋅x30 + 53⋅x31
l66: −3 + 30⋅x1 + 31⋅x2 + 32⋅x3 + 33⋅x4 − 2⋅x5 + 34⋅x6 − 2⋅x7 + 35⋅x8 + 36⋅x9 + 37⋅x10 + x11 + 38⋅x12 + 39⋅x14 + 40⋅x15 + 41⋅x16 + 42⋅x17 + 43⋅x18 + 44⋅x19 + 45⋅x20 + 46⋅x21 + 47⋅x22 + 48⋅x23 + 49⋅x24 + 50⋅x28 + 51⋅x29 + 52⋅x30 + 53⋅x31
l78: −3 + 2⋅x1 + 3⋅x2 + 4⋅x3 + 5⋅x4 − 2⋅x5 + 6⋅x6 + x7 + 7⋅x8 + 8⋅x9 + 9⋅x10 + 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 + 27⋅x29 + 28⋅x30 + 29⋅x31
l77: −3 + 2⋅x1 + 3⋅x2 + 4⋅x3 + 5⋅x4 − 2⋅x5 + 6⋅x6 + x7 + 7⋅x8 + 8⋅x9 + 9⋅x10 + 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 + 27⋅x29 + 28⋅x30 + 29⋅x31
l16: −2 + x5
l15: −2 + x5

2.3.21 Transition Removal

We remove transitions 5, 117, 91, 11 using the following ranking functions, which are bounded by 0.

l6: 0
l7: −1
l71: x5 + x11
l72: x5 + x11
l64: −1 + 3⋅x1 + 4⋅x2 + 5⋅x3 + 6⋅x4 − 2⋅x5 + 7⋅x6 − 2⋅x7 + 8⋅x8 + 9⋅x9 + 10⋅x10 + x11 + 11⋅x12 + 12⋅x14 + 13⋅x15 + 14⋅x16 + 15⋅x17 + 16⋅x18 + 17⋅x19 + 18⋅x20 + 19⋅x21 + 20⋅x22 + 21⋅x23 + 22⋅x24 + 23⋅x28 + 24⋅x29 + 25⋅x30 + 26⋅x31
l65: −3 + 3⋅x1 + 4⋅x2 + 5⋅x3 + 6⋅x4 − 2⋅x5 + 7⋅x6 − 2⋅x7 + 8⋅x8 + 9⋅x9 + 10⋅x10 + x11 + 11⋅x12 + 12⋅x14 + 13⋅x15 + 14⋅x16 + 15⋅x17 + 16⋅x18 + 17⋅x19 + 18⋅x20 + 19⋅x21 + 20⋅x22 + 21⋅x23 + 22⋅x24 + 23⋅x28 + 24⋅x29 + 25⋅x30 + 26⋅x31
l85: −3 + 3⋅x1 + 4⋅x2 + 5⋅x3 + 6⋅x4 − 2⋅x5 + 7⋅x6 − 2⋅x7 + 8⋅x8 + 9⋅x9 + 10⋅x10 + x11 + 11⋅x12 + 12⋅x14 + 13⋅x15 + 14⋅x16 + 15⋅x17 + 16⋅x18 + 17⋅x19 + 18⋅x20 + 19⋅x21 + 20⋅x22 + 21⋅x23 + 22⋅x24 + 23⋅x28 + 24⋅x29 + 25⋅x30 + 26⋅x31
l86: −3 + 3⋅x1 + 4⋅x2 + 5⋅x3 + 6⋅x4 − 2⋅x5 + 7⋅x6 − 2⋅x7 + 8⋅x8 + 9⋅x9 + 10⋅x10 + x11 + 11⋅x12 + 12⋅x14 + 13⋅x15 + 14⋅x16 + 15⋅x17 + 16⋅x18 + 17⋅x19 + 18⋅x20 + 19⋅x21 + 20⋅x22 + 21⋅x23 + 22⋅x24 + 23⋅x28 + 24⋅x29 + 25⋅x30 + 26⋅x31
l67: −3 + 3⋅x1 + 4⋅x2 + 5⋅x3 + 6⋅x4 − 2⋅x5 + 7⋅x6 − 2⋅x7 + 8⋅x8 + 9⋅x9 + 10⋅x10 + x11 + 11⋅x12 + 12⋅x14 + 13⋅x15 + 14⋅x16 + 15⋅x17 + 16⋅x18 + 17⋅x19 + 18⋅x20 + 19⋅x21 + 20⋅x22 + 21⋅x23 + 22⋅x24 + 23⋅x28 + 24⋅x29 + 25⋅x30 + 26⋅x31
l66: −3 + 3⋅x1 + 4⋅x2 + 5⋅x3 + 6⋅x4 − 2⋅x5 + 7⋅x6 − 2⋅x7 + 8⋅x8 + 9⋅x9 + 10⋅x10 + x11 + 11⋅x12 + 12⋅x14 + 13⋅x15 + 14⋅x16 + 15⋅x17 + 16⋅x18 + 17⋅x19 + 18⋅x20 + 19⋅x21 + 20⋅x22 + 21⋅x23 + 22⋅x24 + 23⋅x28 + 24⋅x29 + 25⋅x30 + 26⋅x31
l78: −1 − x5 + x11
l77: −1 − x5 + x11
l16: 1
l15: 2

2.3.22 Transition Removal

We remove transitions 100, 114, 105 using the following ranking functions, which are bounded by 0.

l71: 0
l72: −1
l64: −1 + 3⋅x1 + 4⋅x2 + 5⋅x3 + 6⋅x4 − 2⋅x5 + 7⋅x6 − 2⋅x7 + 8⋅x8 + 9⋅x9 + 10⋅x10 + x11 + 11⋅x12 + 12⋅x14 + 13⋅x15 + 14⋅x16 + 15⋅x17 + 16⋅x18 + 17⋅x19 + 18⋅x20 + 19⋅x21 + 20⋅x22 + 21⋅x23 + 22⋅x24 + 23⋅x28 + 24⋅x29 + 25⋅x30 + 26⋅x31
l65: −3 + 3⋅x1 + 4⋅x2 + 5⋅x3 + 6⋅x4 − 2⋅x5 + 7⋅x6 − 2⋅x7 + 8⋅x8 + 9⋅x9 + 10⋅x10 + x11 + 11⋅x12 + 12⋅x14 + 13⋅x15 + 14⋅x16 + 15⋅x17 + 16⋅x18 + 17⋅x19 + 18⋅x20 + 19⋅x21 + 20⋅x22 + 21⋅x23 + 22⋅x24 + 23⋅x28 + 24⋅x29 + 25⋅x30 + 26⋅x31
l85: −3 + 3⋅x1 + 4⋅x2 + 5⋅x3 + 6⋅x4 − 2⋅x5 + 7⋅x6 − 2⋅x7 + 8⋅x8 + 9⋅x9 + 10⋅x10 + x11 + 11⋅x12 + 12⋅x14 + 13⋅x15 + 14⋅x16 + 15⋅x17 + 16⋅x18 + 17⋅x19 + 18⋅x20 + 19⋅x21 + 20⋅x22 + 21⋅x23 + 22⋅x24 + 23⋅x28 + 24⋅x29 + 25⋅x30 + 26⋅x31
l86: −3 + 3⋅x1 + 4⋅x2 + 5⋅x3 + 6⋅x4 − 2⋅x5 + 7⋅x6 − 2⋅x7 + 8⋅x8 + 9⋅x9 + 10⋅x10 + x11 + 11⋅x12 + 12⋅x14 + 13⋅x15 + 14⋅x16 + 15⋅x17 + 16⋅x18 + 17⋅x19 + 18⋅x20 + 19⋅x21 + 20⋅x22 + 21⋅x23 + 22⋅x24 + 23⋅x28 + 24⋅x29 + 25⋅x30 + 26⋅x31
l67: −3 + 3⋅x1 + 4⋅x2 + 5⋅x3 + 6⋅x4 − 2⋅x5 + 7⋅x6 − 2⋅x7 + 8⋅x8 + 9⋅x9 + 10⋅x10 + x11 + 11⋅x12 + 12⋅x14 + 13⋅x15 + 14⋅x16 + 15⋅x17 + 16⋅x18 + 17⋅x19 + 18⋅x20 + 19⋅x21 + 20⋅x22 + 21⋅x23 + 22⋅x24 + 23⋅x28 + 24⋅x29 + 25⋅x30 + 26⋅x31
l66: −3 + 3⋅x1 + 4⋅x2 + 5⋅x3 + 6⋅x4 − 2⋅x5 + 7⋅x6 − 2⋅x7 + 8⋅x8 + 9⋅x9 + 10⋅x10 + x11 + 11⋅x12 + 12⋅x14 + 13⋅x15 + 14⋅x16 + 15⋅x17 + 16⋅x18 + 17⋅x19 + 18⋅x20 + 19⋅x21 + 20⋅x22 + 21⋅x23 + 22⋅x24 + 23⋅x28 + 24⋅x29 + 25⋅x30 + 26⋅x31
l78: 1
l77: 2

2.3.23 Transition Removal

We remove transition 129 using the following ranking functions, which are bounded by 0.

l64: x5 + x11
l65: x5 + x11
l85: −1 − x5 + x11
l86: −1 − x5 + x11
l67: −1 − x5 + x11
l66: −1 − x5 + x11

2.3.24 Transition Removal

We remove transitions 90, 122, 124, 123, 126, 95 using the following ranking functions, which are bounded by 0.

l64: 0
l65: −1
l85: 1
l86: 2
l67: 3
l66: 4

2.3.25 Trivial Cooperation Program

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

Tool configuration

AProVE