YES Input TRS: 1: 0(1(0(2(x1)))) -> 2(0(3(1(0(x1))))) 2: 0(1(0(2(x1)))) -> 2(0(0(3(1(2(x1)))))) 3: 0(1(0(2(x1)))) -> 2(0(3(1(0(4(x1)))))) 4: 0(1(0(2(x1)))) -> 2(2(0(3(1(0(x1)))))) 5: 0(1(0(2(x1)))) -> 2(3(1(0(0(2(x1)))))) 6: 0(1(0(2(x1)))) -> 2(3(1(0(3(0(x1)))))) 7: 0(1(0(2(x1)))) -> 4(1(0(3(0(2(x1)))))) 8: 0(1(0(2(x1)))) -> 4(1(0(4(0(2(x1)))))) 9: 0(1(4(2(x1)))) -> 2(3(1(0(4(x1))))) 10: 0(1(4(2(x1)))) -> 2(4(0(3(1(x1))))) 11: 0(1(4(2(x1)))) -> 3(2(1(0(4(x1))))) 12: 0(1(4(2(x1)))) -> 3(2(1(4(0(x1))))) 13: 0(1(4(2(x1)))) -> 4(0(3(1(2(x1))))) 14: 0(1(4(2(x1)))) -> 4(1(0(3(2(x1))))) 15: 0(1(4(2(x1)))) -> 4(1(0(4(2(x1))))) 16: 0(1(4(2(x1)))) -> 4(1(0(5(2(x1))))) 17: 0(1(4(2(x1)))) -> 2(0(3(1(0(4(x1)))))) 18: 0(1(4(2(x1)))) -> 2(0(3(1(4(4(x1)))))) 19: 0(1(4(2(x1)))) -> 2(3(1(4(0(4(x1)))))) 20: 0(1(4(2(x1)))) -> 2(4(3(0(4(1(x1)))))) 21: 0(1(4(2(x1)))) -> 2(4(3(1(0(3(x1)))))) 22: 0(1(4(2(x1)))) -> 3(2(1(0(4(1(x1)))))) 23: 0(1(4(2(x1)))) -> 3(2(2(1(4(0(x1)))))) 24: 0(1(4(2(x1)))) -> 3(2(3(1(0(4(x1)))))) 25: 0(1(4(2(x1)))) -> 3(2(3(1(4(0(x1)))))) 26: 0(1(4(2(x1)))) -> 4(0(3(1(3(2(x1)))))) 27: 0(1(4(2(x1)))) -> 4(0(3(1(4(2(x1)))))) 28: 0(1(4(2(x1)))) -> 4(1(0(4(3(2(x1)))))) 29: 0(1(4(2(x1)))) -> 4(1(0(4(5(2(x1)))))) 30: 0(1(4(2(x1)))) -> 4(1(0(5(3(2(x1)))))) 31: 0(1(4(2(x1)))) -> 4(1(1(0(5(2(x1)))))) 32: 0(1(4(2(x1)))) -> 4(1(3(0(5(2(x1)))))) 33: 0(1(4(2(x1)))) -> 4(3(0(3(1(2(x1)))))) 34: 0(1(4(2(x1)))) -> 4(4(0(3(1(2(x1)))))) 35: 0(0(1(0(2(x1))))) -> 1(0(0(2(0(4(x1)))))) 36: 0(0(1(0(2(x1))))) -> 1(0(4(0(0(2(x1)))))) 37: 0(0(1(0(2(x1))))) -> 2(1(0(3(0(0(x1)))))) 38: 0(0(1(4(2(x1))))) -> 0(0(3(1(2(4(x1)))))) 39: 0(0(1(4(2(x1))))) -> 0(2(3(1(0(4(x1)))))) 40: 0(0(1(4(2(x1))))) -> 0(2(4(0(3(1(x1)))))) 41: 0(0(1(4(2(x1))))) -> 0(3(1(0(2(4(x1)))))) 42: 0(0(1(4(2(x1))))) -> 1(0(3(4(0(2(x1)))))) 43: 0(0(1(4(2(x1))))) -> 2(0(0(3(1(4(x1)))))) 44: 0(0(1(4(2(x1))))) -> 2(1(0(4(0(0(x1)))))) 45: 0(1(2(0(2(x1))))) -> 2(0(1(0(4(2(x1)))))) 46: 0(1(2(4(2(x1))))) -> 2(3(1(0(2(4(x1)))))) 47: 0(1(2(4(2(x1))))) -> 4(1(0(2(2(4(x1)))))) 48: 0(1(3(4(2(x1))))) -> 2(3(1(4(4(0(x1)))))) 49: 0(1(3(4(2(x1))))) -> 2(4(3(0(4(1(x1)))))) 50: 0(1(3(4(2(x1))))) -> 3(2(1(0(4(0(x1)))))) 51: 0(1(3(4(2(x1))))) -> 4(0(3(3(1(2(x1)))))) 52: 0(1(3(4(2(x1))))) -> 4(1(4(0(3(2(x1)))))) 53: 0(1(4(0(2(x1))))) -> 2(0(3(1(0(4(x1)))))) 54: 0(1(5(0(2(x1))))) -> 0(2(3(1(0(5(x1)))))) 55: 0(1(5(0(2(x1))))) -> 3(0(5(1(0(2(x1)))))) 56: 0(1(5(0(2(x1))))) -> 5(1(3(0(0(2(x1)))))) 57: 0(1(5(4(2(x1))))) -> 0(4(4(1(2(5(x1)))))) 58: 0(1(5(4(2(x1))))) -> 1(0(4(5(1(2(x1)))))) 59: 0(1(5(4(2(x1))))) -> 2(0(4(4(5(1(x1)))))) 60: 0(1(5(4(2(x1))))) -> 4(0(2(3(1(5(x1)))))) 61: 0(1(5(4(2(x1))))) -> 4(1(0(2(5(2(x1)))))) 62: 0(1(5(4(2(x1))))) -> 4(1(0(5(2(5(x1)))))) 63: 0(1(5(4(2(x1))))) -> 4(2(1(3(0(5(x1)))))) 64: 0(1(5(4(2(x1))))) -> 4(3(1(0(2(5(x1)))))) 65: 0(1(5(4(2(x1))))) -> 4(4(0(5(1(2(x1)))))) 66: 0(1(5(4(2(x1))))) -> 4(4(2(1(0(5(x1)))))) 67: 0(1(5(4(2(x1))))) -> 5(0(4(5(2(1(x1)))))) 68: 0(1(5(4(2(x1))))) -> 5(1(2(0(4(3(x1)))))) 69: 0(1(5(4(2(x1))))) -> 5(3(1(0(4(2(x1)))))) 70: 0(2(1(4(2(x1))))) -> 0(4(4(1(2(2(x1)))))) 71: 0(2(1(4(2(x1))))) -> 3(2(2(1(4(0(x1)))))) 72: 0(2(1(4(2(x1))))) -> 4(1(0(3(2(2(x1)))))) 73: 5(0(1(4(2(x1))))) -> 2(0(4(3(5(1(x1)))))) 74: 5(0(1(4(2(x1))))) -> 2(4(0(3(1(5(x1)))))) 75: 5(0(1(4(2(x1))))) -> 4(1(0(5(3(2(x1)))))) 76: 5(0(1(4(2(x1))))) -> 5(2(1(1(0(4(x1)))))) 77: 5(0(2(0(2(x1))))) -> 5(0(3(0(2(2(x1)))))) 78: 5(0(2(0(2(x1))))) -> 5(0(4(0(2(2(x1)))))) 79: 5(0(2(4(2(x1))))) -> 5(4(0(3(2(2(x1)))))) 80: 5(1(5(0(2(x1))))) -> 5(2(1(4(5(0(x1)))))) 81: 5(1(5(4(2(x1))))) -> 5(2(1(0(4(5(x1)))))) 82: 5(4(1(4(2(x1))))) -> 3(2(1(4(4(5(x1)))))) 83: 5(4(1(4(2(x1))))) -> 4(4(3(5(1(2(x1)))))) 84: 5(4(2(0(2(x1))))) -> 3(0(5(2(2(4(x1)))))) 85: 5(4(2(0(2(x1))))) -> 4(0(5(3(2(2(x1)))))) 86: 5(4(2(0(2(x1))))) -> 5(2(2(2(4(0(x1)))))) 87: 5(4(2(0(2(x1))))) -> 5(3(2(2(4(0(x1)))))) 88: 5(4(2(0(2(x1))))) -> 5(4(2(2(4(0(x1)))))) 89: 5(4(2(4(2(x1))))) -> 0(4(4(5(2(2(x1)))))) 90: 5(4(2(4(2(x1))))) -> 5(4(4(3(2(2(x1)))))) 91: 5(4(5(4(2(x1))))) -> 4(5(0(4(5(2(x1)))))) Number of strict rules: 91 Direct POLO(bPol) ... failed. Uncurrying 0 1: 0^1_1(0^1_2(x1)) -> 2(0^1_3(1(0(x1)))) 2: 0^1_1(0^1_2(x1)) -> 2(0^2_3(1(2(x1)))) 3: 0^1_1(0^1_2(x1)) -> 2(0^1_3(1(0^1_4(x1)))) 4: 0^1_1(0^1_2(x1)) -> 2(2(0^1_3(1(0(x1))))) 5: 0^1_1(0^1_2(x1)) -> 2(3(1(0(0^1_2(x1))))) 6: 0^1_1(0^1_2(x1)) -> 2(3(1(0^1_3(0(x1))))) 7: 0^1_1(0^1_2(x1)) -> 4(1(0^1_3(0^1_2(x1)))) 8: 0^1_1(0^1_2(x1)) -> 4(1(0^1_4(0^1_2(x1)))) 9: 0^1_1(4(2(x1))) -> 2(3(1(0^1_4(x1)))) 10: 0^1_1(4(2(x1))) -> 2(4(0^1_3(1(x1)))) 11: 0^1_1(4(2(x1))) -> 3(2(1(0^1_4(x1)))) 12: 0^1_1(4(2(x1))) -> 3(2(1(4(0(x1))))) 13: 0^1_1(4(2(x1))) -> 4(0^1_3(1(2(x1)))) 14: 0^1_1(4(2(x1))) -> 4(1(0^1_3(2(x1)))) 15: 0^1_1(4(2(x1))) -> 4(1(0^1_4(2(x1)))) 16: 0^1_1(4(2(x1))) -> 4(1(0(5(2(x1))))) 17: 0^1_1(4(2(x1))) -> 2(0^1_3(1(0^1_4(x1)))) 18: 0^1_1(4(2(x1))) -> 2(0^1_3(1(4(4(x1))))) 19: 0^1_1(4(2(x1))) -> 2(3(1(4(0^1_4(x1))))) 20: 0^1_1(4(2(x1))) -> 2(4(3(0^1_4(1(x1))))) 21: 0^1_1(4(2(x1))) -> 2(4(3(1(0^1_3(x1))))) 22: 0^1_1(4(2(x1))) -> 3(2(1(0^1_4(1(x1))))) 23: 0^1_1(4(2(x1))) -> 3(2(2(1(4(0(x1)))))) 24: 0^1_1(4(2(x1))) -> 3(2(3(1(0^1_4(x1))))) 25: 0^1_1(4(2(x1))) -> 3(2(3(1(4(0(x1)))))) 26: 0^1_1(4(2(x1))) -> 4(0^1_3(1(3(2(x1))))) 27: 0^1_1(4(2(x1))) -> 4(0^1_3(1(4(2(x1))))) 28: 0^1_1(4(2(x1))) -> 4(1(0^1_4(3(2(x1))))) 29: 0^1_1(4(2(x1))) -> 4(1(0^1_4(5(2(x1))))) 30: 0^1_1(4(2(x1))) -> 4(1(0(5(3(2(x1)))))) 31: 0^1_1(4(2(x1))) -> 4(1(1(0(5(2(x1)))))) 32: 0^1_1(4(2(x1))) -> 4(1(3(0(5(2(x1)))))) 33: 0^1_1(4(2(x1))) -> 4(3(0^1_3(1(2(x1))))) 34: 0^1_1(4(2(x1))) -> 4(4(0^1_3(1(2(x1))))) 35: 0(0^1_1(0^1_2(x1))) -> 1(0(0^1_2(0^1_4(x1)))) 36: 0(0^1_1(0^1_2(x1))) -> 1(0^1_4(0(0^1_2(x1)))) 37: 0(0^1_1(0^1_2(x1))) -> 2(1(0^1_3(0(0(x1))))) 38: 0(0^1_1(4(2(x1)))) -> 0^2_3(1(2(4(x1)))) 39: 0(0^1_1(4(2(x1)))) -> 0^1_2(3(1(0^1_4(x1)))) 40: 0(0^1_1(4(2(x1)))) -> 0^1_2(4(0^1_3(1(x1)))) 41: 0(0^1_1(4(2(x1)))) -> 0^1_3(1(0^1_2(4(x1)))) 42: 0(0^1_1(4(2(x1)))) -> 1(0^1_3(4(0^1_2(x1)))) 43: 0(0^1_1(4(2(x1)))) -> 2(0^2_3(1(4(x1)))) 44: 0(0^1_1(4(2(x1)))) -> 2(1(0^1_4(0(0(x1))))) 45: 0^1_1(2(0^1_2(x1))) -> 2(0^1_1(0^1_4(2(x1)))) 46: 0^1_1(2(4(2(x1)))) -> 2(3(1(0^1_2(4(x1))))) 47: 0^1_1(2(4(2(x1)))) -> 4(1(0^1_2(2(4(x1))))) 48: 0^1_1(3(4(2(x1)))) -> 2(3(1(4(4(0(x1)))))) 49: 0^1_1(3(4(2(x1)))) -> 2(4(3(0^1_4(1(x1))))) 50: 0^1_1(3(4(2(x1)))) -> 3(2(1(0^1_4(0(x1))))) 51: 0^1_1(3(4(2(x1)))) -> 4(0^1_3(3(1(2(x1))))) 52: 0^1_1(3(4(2(x1)))) -> 4(1(4(0^1_3(2(x1))))) 53: 0^1_1(4(0^1_2(x1))) -> 2(0^1_3(1(0^1_4(x1)))) 54: 0^1_1(5(0^1_2(x1))) -> 0^1_2(3(1(0(5(x1))))) 55: 0^1_1(5(0^1_2(x1))) -> 3(0(5(1(0^1_2(x1))))) 56: 0^1_1(5(0^1_2(x1))) -> 5(1(3(0(0^1_2(x1))))) 57: 0^1_1(5(4(2(x1)))) -> 0^1_4(4(1(2(5(x1))))) 58: 0^1_1(5(4(2(x1)))) -> 1(0^1_4(5(1(2(x1))))) 59: 0^1_1(5(4(2(x1)))) -> 2(0^1_4(4(5(1(x1))))) 60: 0^1_1(5(4(2(x1)))) -> 4(0^1_2(3(1(5(x1))))) 61: 0^1_1(5(4(2(x1)))) -> 4(1(0^1_2(5(2(x1))))) 62: 0^1_1(5(4(2(x1)))) -> 4(1(0(5(2(5(x1)))))) 63: 0^1_1(5(4(2(x1)))) -> 4(2(1(3(0(5(x1)))))) 64: 0^1_1(5(4(2(x1)))) -> 4(3(1(0^1_2(5(x1))))) 65: 0^1_1(5(4(2(x1)))) -> 4(4(0(5(1(2(x1)))))) 66: 0^1_1(5(4(2(x1)))) -> 4(4(2(1(0(5(x1)))))) 67: 0^1_1(5(4(2(x1)))) -> 5(0^1_4(5(2(1(x1))))) 68: 0^1_1(5(4(2(x1)))) -> 5(1(2(0^1_4(3(x1))))) 69: 0^1_1(5(4(2(x1)))) -> 5(3(1(0^1_4(2(x1))))) 70: 0^1_2(1(4(2(x1)))) -> 0^1_4(4(1(2(2(x1))))) 71: 0^1_2(1(4(2(x1)))) -> 3(2(2(1(4(0(x1)))))) 72: 0^1_2(1(4(2(x1)))) -> 4(1(0^1_3(2(2(x1))))) 73: 5(0^1_1(4(2(x1)))) -> 2(0^1_4(3(5(1(x1))))) 74: 5(0^1_1(4(2(x1)))) -> 2(4(0^1_3(1(5(x1))))) 75: 5(0^1_1(4(2(x1)))) -> 4(1(0(5(3(2(x1)))))) 76: 5(0^1_1(4(2(x1)))) -> 5(2(1(1(0^1_4(x1))))) 77: 5(0^1_2(0^1_2(x1))) -> 5(0^1_3(0^1_2(2(x1)))) 78: 5(0^1_2(0^1_2(x1))) -> 5(0^1_4(0^1_2(2(x1)))) 79: 5(0^1_2(4(2(x1)))) -> 5(4(0^1_3(2(2(x1))))) 80: 5(1(5(0^1_2(x1)))) -> 5(2(1(4(5(0(x1)))))) 81: 5(1(5(4(2(x1))))) -> 5(2(1(0^1_4(5(x1))))) 82: 5(4(1(4(2(x1))))) -> 3(2(1(4(4(5(x1)))))) 83: 5(4(1(4(2(x1))))) -> 4(4(3(5(1(2(x1)))))) 84: 5(4(2(0^1_2(x1)))) -> 3(0(5(2(2(4(x1)))))) 85: 5(4(2(0^1_2(x1)))) -> 4(0(5(3(2(2(x1)))))) 86: 5(4(2(0^1_2(x1)))) -> 5(2(2(2(4(0(x1)))))) 87: 5(4(2(0^1_2(x1)))) -> 5(3(2(2(4(0(x1)))))) 88: 5(4(2(0^1_2(x1)))) -> 5(4(2(2(4(0(x1)))))) 89: 5(4(2(4(2(x1))))) -> 0^1_4(4(5(2(2(x1))))) 90: 5(4(2(4(2(x1))))) -> 5(4(4(3(2(2(x1)))))) 91: 5(4(5(4(2(x1))))) -> 4(5(0^1_4(5(2(x1))))) 92: 0(2(_1)) ->= 0^1_2(_1) 93: 0(1(_1)) ->= 0^1_1(_1) 94: 0(4(_1)) ->= 0^1_4(_1) 95: 0(3(_1)) ->= 0^1_3(_1) 96: 0(0^1_3(_1)) ->= 0^2_3(_1) Number of strict rules: 91 Direct POLO(bPol) ... removes: 18 4 15 8 1 77 3 21 36 68 26 19 17 27 34 22 28 72 33 10 39 7 20 52 49 14 79 69 96 45 78 70 24 94 76 57 11 9 13 51 40 67 59 6 38 58 74 53 73 37 41 95 42 35 29 43 2 1 w: x1 4 w: x1 5 w: x1 3 w: x1 0^1_4 w: x1 0^1_3 w: x1 + 22069 0 w: x1 + 22070 0^1_1 w: x1 + 22070 0^2_3 w: x1 + 10087 2 w: x1 0^1_2 w: x1 + 22070 Number of strict rules: 37 Direct POLO(bPol) ... removes: 50 16 63 32 44 5 64 25 62 30 56 12 23 61 75 48 71 47 46 66 1 w: x1 + 28495 4 w: x1 5 w: x1 3 w: x1 0^1_4 w: x1 0^1_3 w: 2 * x1 + 1 0 w: 2 * x1 + 1 0^1_1 w: 2 * x1 + 56991 0^2_3 w: x1 2 w: x1 0^1_2 w: 2 * x1 + 1 Number of strict rules: 17 Direct POLO(bPol) ... failed. Dependency Pairs: #1: #5(4(2(0^1_2(x1)))) -> #5(2(2(2(4(0(x1)))))) #2: #5(4(2(0^1_2(x1)))) -> #0(x1) #3: #5(4(1(4(2(x1))))) -> #5(1(2(x1))) #4: #5(4(5(4(2(x1))))) -> #5(0^1_4(5(2(x1)))) #5: #5(4(5(4(2(x1))))) -> #5(2(x1)) #6: #0^1_1(5(0^1_2(x1))) -> #0(5(1(0^1_2(x1)))) #7: #0^1_1(5(0^1_2(x1))) -> #5(1(0^1_2(x1))) #8: #5(4(2(4(2(x1))))) -> #5(4(4(3(2(2(x1)))))) #9: #5(1(5(4(2(x1))))) -> #5(2(1(0^1_4(5(x1))))) #10: #5(1(5(4(2(x1))))) -> #5(x1) #11: #0^1_1(4(2(x1))) -> #0(5(2(x1))) #12: #0^1_1(4(2(x1))) -> #5(2(x1)) #13: #5(4(2(4(2(x1))))) -> #5(2(2(x1))) #14: #5(4(1(4(2(x1))))) -> #5(x1) #15: #5(4(2(0^1_2(x1)))) -> #5(4(2(2(4(0(x1)))))) #16: #5(4(2(0^1_2(x1)))) -> #0(x1) #17: #0(1(_1)) ->? #0^1_1(_1) #18: #0^1_1(5(4(2(x1)))) -> #0(5(1(2(x1)))) #19: #0^1_1(5(4(2(x1)))) -> #5(1(2(x1))) #20: #5(4(2(0^1_2(x1)))) -> #0(5(2(2(4(x1))))) #21: #5(4(2(0^1_2(x1)))) -> #5(2(2(4(x1)))) #22: #5(4(2(0^1_2(x1)))) -> #5(3(2(2(4(0(x1)))))) #23: #5(4(2(0^1_2(x1)))) -> #0(x1) #24: #0^1_1(5(4(2(x1)))) -> #5(x1) #25: #5(4(2(0^1_2(x1)))) -> #0(5(3(2(2(x1))))) #26: #5(4(2(0^1_2(x1)))) -> #5(3(2(2(x1)))) #27: #0^1_1(5(0^1_2(x1))) -> #0(5(x1)) #28: #0^1_1(5(0^1_2(x1))) -> #5(x1) #29: #5(1(5(0^1_2(x1)))) -> #5(2(1(4(5(0(x1)))))) #30: #5(1(5(0^1_2(x1)))) -> #5(0(x1)) #31: #5(1(5(0^1_2(x1)))) -> #0(x1) Number of SCCs: 1, DPs: 9 SCC { #2 #10 #14 #16 #17 #23 #24 #28 #31 } POLO(Sum)... succeeded. #0 w: x1 + 1 1 w: x1 + 2438 4 w: x1 5 w: x1 3 w: 0 0^1_4 w: 0 0^1_3 w: 0 0 w: 0 0^1_1 w: 0 0^2_3 w: 0 #0^1_1 w: x1 #5 w: x1 2 w: x1 + 1 0^1_2 w: x1 + 1 USABLE RULES: { } Removed DPs: #2 #10 #14 #16 #17 #23 #24 #28 #31 Number of SCCs: 0, DPs: 0