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 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41x42 = x42x43 = x43x44 = x44x45 = x45x46 = x46x47 = x47x48 = x48x49 = x49x50 = x50x51 = x51x52 = x52x53 = x53x54 = x54x55 = x55
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 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41x42 = x42x43 = x43x44 = x44x45 = x45x46 = x46x47 = x47x48 = x48x49 = x49x50 = x50x51 = x51x52 = x52x53 = x53x54 = x54x55 = x55
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 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41x42 = x42x43 = x43x44 = x44x45 = x45x46 = x46x47 = x47x48 = x48x49 = x49x50 = x50x51 = x51x52 = x52x53 = x53x54 = x54x55 = x55
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 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41x42 = x42x43 = x43x44 = x44x45 = x45x46 = x46x47 = x47x48 = x48x49 = x49x50 = x50x51 = x51x52 = x52x53 = x53x54 = x54x55 = x55
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 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41x42 = x42x43 = x43x44 = x44x45 = x45x46 = x46x47 = x47x48 = x48x49 = x49x50 = x50x51 = x51x52 = x52x53 = x53x54 = x54x55 = x55
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 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41x42 = x42x43 = x43x44 = x44x45 = x45x46 = x46x47 = x47x48 = x48x49 = x49x50 = x50x51 = x51x52 = x52x53 = x53x54 = x54x55 = x55
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 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41x42 = x42x43 = x43x44 = x44x45 = x45x46 = x46x47 = x47x48 = x48x49 = x49x50 = x50x51 = x51x52 = x52x53 = x53x54 = x54x55 = x55
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 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41x42 = x42x43 = x43x44 = x44x45 = x45x46 = x46x47 = x47x48 = x48x49 = x49x50 = x50x51 = x51x52 = x52x53 = x53x54 = x54x55 = x55
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 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41x42 = x42x43 = x43x44 = x44x45 = x45x46 = x46x47 = x47x48 = x48x49 = x49x50 = x50x51 = x51x52 = x52x53 = x53x54 = x54x55 = x55
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 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41x42 = x42x43 = x43x44 = x44x45 = x45x46 = x46x47 = x47x48 = x48x49 = x49x50 = x50x51 = x51x52 = x52x53 = x53x54 = x54x55 = x55
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 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41x42 = x42x43 = x43x44 = x44x45 = x45x46 = x46x47 = x47x48 = x48x49 = x49x50 = x50x51 = x51x52 = x52x53 = x53x54 = x54x55 = x55
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 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41x42 = x42x43 = x43x44 = x44x45 = x45x46 = x46x47 = x47x48 = x48x49 = x49x50 = x50x51 = x51x52 = x52x53 = x53x54 = x54x55 = x55
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 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41x42 = x42x43 = x43x44 = x44x45 = x45x46 = x46x47 = x47x48 = x48x49 = x49x50 = x50x51 = x51x52 = x52x53 = x53x54 = x54x55 = x55
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 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41x42 = x42x43 = x43x44 = x44x45 = x45x46 = x46x47 = x47x48 = x48x49 = x49x50 = x50x51 = x51x52 = x52x53 = x53x54 = x54x55 = x55
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 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41x42 = x42x43 = x43x44 = x44x45 = x45x46 = x46x47 = x47x48 = x48x49 = x49x50 = x50x51 = x51x52 = x52x53 = x53x54 = x54x55 = x55
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 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41x42 = x42x43 = x43x44 = x44x45 = x45x46 = x46x47 = x47x48 = x48x49 = x49x50 = x50x51 = x51x52 = x52x53 = x53x54 = x54x55 = x55
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 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41x42 = x42x43 = x43x44 = x44x45 = x45x46 = x46x47 = x47x48 = x48x49 = x49x50 = x50x51 = x51x52 = x52x53 = x53x54 = x54x55 = x55
l32 l32 l32: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30x31 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41x42 = x42x43 = x43x44 = x44x45 = x45x46 = x46x47 = x47x48 = x48x49 = x49x50 = x50x51 = x51x52 = x52x53 = x53x54 = x54x55 = x55
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 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41x42 = x42x43 = x43x44 = x44x45 = x45x46 = x46x47 = x47x48 = x48x49 = x49x50 = x50x51 = x51x52 = x52x53 = x53x54 = x54x55 = x55
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 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41x42 = x42x43 = x43x44 = x44x45 = x45x46 = x46x47 = x47x48 = x48x49 = x49x50 = x50x51 = x51x52 = x52x53 = x53x54 = x54x55 = x55
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 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41x42 = x42x43 = x43x44 = x44x45 = x45x46 = x46x47 = x47x48 = x48x49 = x49x50 = x50x51 = x51x52 = x52x53 = x53x54 = x54x55 = x55
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 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41x42 = x42x43 = x43x44 = x44x45 = x45x46 = x46x47 = x47x48 = x48x49 = x49x50 = x50x51 = x51x52 = x52x53 = x53x54 = x54x55 = x55
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 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41x42 = x42x43 = x43x44 = x44x45 = x45x46 = x46x47 = x47x48 = x48x49 = x49x50 = x50x51 = x51x52 = x52x53 = x53x54 = x54x55 = x55
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 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41x42 = x42x43 = x43x44 = x44x45 = x45x46 = x46x47 = x47x48 = x48x49 = x49x50 = x50x51 = x51x52 = x52x53 = x53x54 = x54x55 = x55
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 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41x42 = x42x43 = x43x44 = x44x45 = x45x46 = x46x47 = x47x48 = x48x49 = x49x50 = x50x51 = x51x52 = x52x53 = x53x54 = x54x55 = x55
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 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41x42 = x42x43 = x43x44 = x44x45 = x45x46 = x46x47 = x47x48 = x48x49 = x49x50 = x50x51 = x51x52 = x52x53 = x53x54 = x54x55 = x55
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 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41x42 = x42x43 = x43x44 = x44x45 = x45x46 = x46x47 = x47x48 = x48x49 = x49x50 = x50x51 = x51x52 = x52x53 = x53x54 = x54x55 = x55
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 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41x42 = x42x43 = x43x44 = x44x45 = x45x46 = x46x47 = x47x48 = x48x49 = x49x50 = x50x51 = x51x52 = x52x53 = x53x54 = x54x55 = x55
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 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41x42 = x42x43 = x43x44 = x44x45 = x45x46 = x46x47 = x47x48 = x48x49 = x49x50 = x50x51 = x51x52 = x52x53 = x53x54 = x54x55 = x55
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 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41x42 = x42x43 = x43x44 = x44x45 = x45x46 = x46x47 = x47x48 = x48x49 = x49x50 = x50x51 = x51x52 = x52x53 = x53x54 = x54x55 = x55
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 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41x42 = x42x43 = x43x44 = x44x45 = x45x46 = x46x47 = x47x48 = x48x49 = x49x50 = x50x51 = x51x52 = x52x53 = x53x54 = x54x55 = x55
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 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41x42 = x42x43 = x43x44 = x44x45 = x45x46 = x46x47 = x47x48 = x48x49 = x49x50 = x50x51 = x51x52 = x52x53 = x53x54 = x54x55 = x55
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 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41x42 = x42x43 = x43x44 = x44x45 = x45x46 = x46x47 = x47x48 = x48x49 = x49x50 = x50x51 = x51x52 = x52x53 = x53x54 = x54x55 = x55
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 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41x42 = x42x43 = x43x44 = x44x45 = x45x46 = x46x47 = x47x48 = x48x49 = x49x50 = x50x51 = x51x52 = x52x53 = x53x54 = x54x55 = x55
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 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41x42 = x42x43 = x43x44 = x44x45 = x45x46 = x46x47 = x47x48 = x48x49 = x49x50 = x50x51 = x51x52 = x52x53 = x53x54 = x54x55 = x55
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 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41x42 = x42x43 = x43x44 = x44x45 = x45x46 = x46x47 = x47x48 = x48x49 = x49x50 = x50x51 = x51x52 = x52x53 = x53x54 = x54x55 = x55
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 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41x42 = x42x43 = x43x44 = x44x45 = x45x46 = x46x47 = x47x48 = x48x49 = x49x50 = x50x51 = x51x52 = x52x53 = x53x54 = x54x55 = x55
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 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41x42 = x42x43 = x43x44 = x44x45 = x45x46 = x46x47 = x47x48 = x48x49 = x49x50 = x50x51 = x51x52 = x52x53 = x53x54 = x54x55 = x55
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 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41x42 = x42x43 = x43x44 = x44x45 = x45x46 = x46x47 = x47x48 = x48x49 = x49x50 = x50x51 = x51x52 = x52x53 = x53x54 = x54x55 = x55
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 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41x42 = x42x43 = x43x44 = x44x45 = x45x46 = x46x47 = x47x48 = x48x49 = x49x50 = x50x51 = x51x52 = x52x53 = x53x54 = x54x55 = x55
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 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41x42 = x42x43 = x43x44 = x44x45 = x45x46 = x46x47 = x47x48 = x48x49 = x49x50 = x50x51 = x51x52 = x52x53 = x53x54 = x54x55 = x55
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 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41x42 = x42x43 = x43x44 = x44x45 = x45x46 = x46x47 = x47x48 = x48x49 = x49x50 = x50x51 = x51x52 = x52x53 = x53x54 = x54x55 = x55
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 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41x42 = x42x43 = x43x44 = x44x45 = x45x46 = x46x47 = x47x48 = x48x49 = x49x50 = x50x51 = x51x52 = x52x53 = x53x54 = x54x55 = x55
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 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41x42 = x42x43 = x43x44 = x44x45 = x45x46 = x46x47 = x47x48 = x48x49 = x49x50 = x50x51 = x51x52 = x52x53 = x53x54 = x54x55 = x55
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 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41x42 = x42x43 = x43x44 = x44x45 = x45x46 = x46x47 = x47x48 = x48x49 = x49x50 = x50x51 = x51x52 = x52x53 = x53x54 = x54x55 = x55
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 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41x42 = x42x43 = x43x44 = x44x45 = x45x46 = x46x47 = x47x48 = x48x49 = x49x50 = x50x51 = x51x52 = x52x53 = x53x54 = x54x55 = x55
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 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41x42 = x42x43 = x43x44 = x44x45 = x45x46 = x46x47 = x47x48 = x48x49 = x49x50 = x50x51 = x51x52 = x52x53 = x53x54 = x54x55 = x55
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 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41x42 = x42x43 = x43x44 = x44x45 = x45x46 = x46x47 = x47x48 = x48x49 = x49x50 = x50x51 = x51x52 = x52x53 = x53x54 = x54x55 = x55
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 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41x42 = x42x43 = x43x44 = x44x45 = x45x46 = x46x47 = x47x48 = x48x49 = x49x50 = x50x51 = x51x52 = x52x53 = x53x54 = x54x55 = x55
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 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41x42 = x42x43 = x43x44 = x44x45 = x45x46 = x46x47 = x47x48 = x48x49 = x49x50 = x50x51 = x51x52 = x52x53 = x53x54 = x54x55 = x55
and for every transition t, a duplicate t is considered.

2 SCC Decomposition

We consider subproblems for each of the 2 SCC(s) of the program graph.

2.1 SCC Subproblem 1/2

Here we consider the SCC { l37, l49 }.

2.1.1 Transition Removal

We remove transition 78 using the following ranking functions, which are bounded by 0.

l37: −1 − x10 + x14
l49: −1 − x10 + x14

2.1.2 Transition Removal

We remove transition 79 using the following ranking functions, which are bounded by 0.

l49: 0
l37: −1

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 2/2

Here we consider the SCC { l5, l7, l10, l6, l11, l8, l0, l12, l9 }.

2.2.1 Transition Removal

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

l0: 2⋅x3 + x11
l6: −1 + 2⋅x3 + x11
l5: 2⋅x3 + x11
l12: 2⋅x4 + x12
l11: 2⋅x4 + x12
l10: 2⋅x4 + x12
l9: 2⋅x4 + x12
l8: 2⋅x4 + x12
l7: −1 + 2⋅x3 + x11

2.2.2 Transition Removal

We remove transitions 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8 using the following ranking functions, which are bounded by 0.

l5: 0
l0: −1
l12: 1
l11: 2
l10: 3
l9: 4
l8: 5
l7: 6
l6: 7

2.2.3 Trivial Cooperation Program

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

Tool configuration

AProVE