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 = x22
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 = x22
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 = x22
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 = x22
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 = x22
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 = x22
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 = x22
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 = x22
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 = x22
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 = x22
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 = x22
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 = x22
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 = x22
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 = x22
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 = x22
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 = x22
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 = x22
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 = x22
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 = x22
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 = x22
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 = x22
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 = x22
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 = x22
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 = x22
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 = x22
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 = x22
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 = x22
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 = x22
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 = x22
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 = x22
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 = x22
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 = x22
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 = x22
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 = x22
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 = x22
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 = x22
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 = x22
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 = x22
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 = x22
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 = x22
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 = x22
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 = x22
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 = x22
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 = x22
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 = x22
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 = x22
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 = x22
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 = x22
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 = x22
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 = x22
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 = x22
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 = x22
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 = x22
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 = x22
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 = x22
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 = x22
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 = x22
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 = x22
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 = x22
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 = x22
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 = x22
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 = x22
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 = x22
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 = x22
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 = x22
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 = x22
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 = x22
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 = x22
and for every transition t, a duplicate t is considered.

2 SCC Decomposition

There exist no SCC in the program graph.

Tool configuration

AProVE