18.67/18.81 YES 18.67/18.81 Input TRS: 18.67/18.81 1: 0(1(2(x1))) -> 2(1(0(3(x1)))) 18.67/18.81 2: 0(1(2(x1))) -> 2(1(3(0(x1)))) 18.67/18.81 3: 0(1(2(x1))) -> 2(1(3(0(4(x1))))) 18.67/18.81 4: 0(1(2(x1))) -> 2(1(3(4(0(x1))))) 18.67/18.81 5: 0(1(2(x1))) -> 2(1(3(4(0(4(x1)))))) 18.67/18.81 6: 0(0(1(2(x1)))) -> 0(2(1(0(3(x1))))) 18.67/18.81 7: 0(1(1(2(x1)))) -> 1(0(4(1(2(x1))))) 18.67/18.81 8: 0(1(1(2(x1)))) -> 1(2(1(0(3(x1))))) 18.67/18.81 9: 0(1(2(0(x1)))) -> 2(1(0(3(0(3(x1)))))) 18.67/18.81 10: 0(1(2(5(x1)))) -> 2(1(0(3(5(x1))))) 18.67/18.81 11: 0(1(2(5(x1)))) -> 5(1(0(3(2(x1))))) 18.67/18.81 12: 0(1(4(2(x1)))) -> 2(1(3(4(0(x1))))) 18.67/18.81 13: 0(1(4(2(x1)))) -> 2(4(1(0(3(x1))))) 18.67/18.81 14: 0(1(4(2(x1)))) -> 0(2(1(0(3(4(x1)))))) 18.67/18.81 15: 2(1(1(5(x1)))) -> 2(5(1(4(1(x1))))) 18.67/18.81 16: 2(1(1(5(x1)))) -> 5(1(3(2(1(x1))))) 18.67/18.81 17: 2(1(2(0(x1)))) -> 2(2(1(0(3(x1))))) 18.67/18.81 18: 2(3(5(5(x1)))) -> 5(1(0(3(2(5(x1)))))) 18.67/18.81 19: 2(5(3(2(x1)))) -> 5(1(3(2(2(x1))))) 18.67/18.81 20: 5(1(2(0(x1)))) -> 2(5(1(0(3(x1))))) 18.67/18.81 21: 0(1(0(1(2(x1))))) -> 0(2(1(1(3(0(x1)))))) 18.67/18.81 22: 0(1(1(2(5(x1))))) -> 0(1(3(5(1(2(x1)))))) 18.67/18.81 23: 0(1(1(4(2(x1))))) -> 4(1(0(3(2(1(x1)))))) 18.67/18.81 24: 0(1(1(5(0(x1))))) -> 0(1(0(5(4(1(x1)))))) 18.67/18.81 25: 0(1(1(5(4(x1))))) -> 1(4(1(0(3(5(x1)))))) 18.67/18.81 26: 0(1(2(3(5(x1))))) -> 0(1(3(4(5(2(x1)))))) 18.67/18.81 27: 0(1(2(3(5(x1))))) -> 0(2(5(1(0(3(x1)))))) 18.67/18.81 28: 0(1(2(3(5(x1))))) -> 1(0(3(0(2(5(x1)))))) 18.67/18.81 29: 0(1(2(3(5(x1))))) -> 5(1(3(0(2(0(x1)))))) 18.67/18.81 30: 0(1(4(0(2(x1))))) -> 4(0(1(3(0(2(x1)))))) 18.67/18.81 31: 0(1(4(0(2(x1))))) -> 4(0(2(1(3(0(x1)))))) 18.67/18.81 32: 0(4(5(3(5(x1))))) -> 5(1(0(3(4(5(x1)))))) 18.67/18.81 33: 2(1(0(1(5(x1))))) -> 1(0(3(2(5(1(x1)))))) 18.67/18.81 34: 2(1(4(3(5(x1))))) -> 1(3(5(4(4(2(x1)))))) 18.67/18.81 35: 2(1(4(3(5(x1))))) -> 5(4(4(1(3(2(x1)))))) 18.67/18.81 36: 2(1(4(5(0(x1))))) -> 2(4(1(0(3(5(x1)))))) 18.67/18.81 37: 2(2(3(5(0(x1))))) -> 5(2(4(2(0(3(x1)))))) 18.67/18.81 38: 2(2(4(3(5(x1))))) -> 5(1(3(4(2(2(x1)))))) 18.67/18.81 39: 2(3(1(1(2(x1))))) -> 1(3(2(1(2(0(x1)))))) 18.67/18.81 40: 2(3(1(1(2(x1))))) -> 4(1(2(2(1(3(x1)))))) 18.67/18.81 41: 2(3(2(0(5(x1))))) -> 2(2(1(0(3(5(x1)))))) 18.67/18.81 42: 2(3(3(1(5(x1))))) -> 1(3(5(1(3(2(x1)))))) 18.67/18.81 43: 2(5(0(3(5(x1))))) -> 5(2(1(3(0(5(x1)))))) 18.67/18.81 44: 4(2(0(1(2(x1))))) -> 4(2(2(1(3(0(x1)))))) 18.67/18.81 45: 5(0(1(2(2(x1))))) -> 4(1(5(2(0(2(x1)))))) 18.67/18.81 46: 5(1(4(2(2(x1))))) -> 5(1(3(2(4(2(x1)))))) 18.67/18.81 47: 5(1(4(3(2(x1))))) -> 4(5(1(3(4(2(x1)))))) 18.67/18.81 48: 5(5(4(3(2(x1))))) -> 5(1(3(4(5(2(x1)))))) 18.67/18.81 Number of strict rules: 48 18.67/18.81 Direct POLO(bPol) ... failed. 18.67/18.81 Uncurrying ... failed. 18.67/18.81 Dependency Pairs: 18.67/18.81 #1: #0(1(2(x1))) -> #2(1(3(0(x1)))) 18.67/18.81 #2: #0(1(2(x1))) -> #0(x1) 18.67/18.81 #3: #2(5(0(3(5(x1))))) -> #5(2(1(3(0(5(x1)))))) 18.67/18.81 #4: #2(5(0(3(5(x1))))) -> #2(1(3(0(5(x1))))) 18.67/18.81 #5: #2(5(0(3(5(x1))))) -> #0(5(x1)) 18.67/18.81 #6: #0(1(2(3(5(x1))))) -> #5(1(3(0(2(0(x1)))))) 18.67/18.81 #7: #0(1(2(3(5(x1))))) -> #0(2(0(x1))) 18.67/18.81 #8: #0(1(2(3(5(x1))))) -> #2(0(x1)) 18.67/18.81 #9: #0(1(2(3(5(x1))))) -> #0(x1) 18.67/18.81 #10: #2(1(4(3(5(x1))))) -> #5(4(4(1(3(2(x1)))))) 18.67/18.81 #11: #2(1(4(3(5(x1))))) -> #4(4(1(3(2(x1))))) 18.67/18.81 #12: #2(1(4(3(5(x1))))) -> #4(1(3(2(x1)))) 18.67/18.81 #13: #2(1(4(3(5(x1))))) -> #2(x1) 18.67/18.81 #14: #5(1(4(2(2(x1))))) -> #5(1(3(2(4(2(x1)))))) 18.67/18.81 #15: #5(1(4(2(2(x1))))) -> #2(4(2(x1))) 18.67/18.81 #16: #5(1(4(2(2(x1))))) -> #4(2(x1)) 18.67/18.81 #17: #2(3(3(1(5(x1))))) -> #5(1(3(2(x1)))) 18.67/18.81 #18: #2(3(3(1(5(x1))))) -> #2(x1) 18.67/18.81 #19: #2(3(2(0(5(x1))))) -> #2(2(1(0(3(5(x1)))))) 18.67/18.81 #20: #2(3(2(0(5(x1))))) -> #2(1(0(3(5(x1))))) 18.67/18.81 #21: #2(3(2(0(5(x1))))) -> #0(3(5(x1))) 18.67/18.81 #22: #2(2(3(5(0(x1))))) -> #5(2(4(2(0(3(x1)))))) 18.67/18.81 #23: #2(2(3(5(0(x1))))) -> #2(4(2(0(3(x1))))) 18.67/18.81 #24: #2(2(3(5(0(x1))))) -> #4(2(0(3(x1)))) 18.67/18.81 #25: #2(2(3(5(0(x1))))) -> #2(0(3(x1))) 18.67/18.81 #26: #2(2(3(5(0(x1))))) -> #0(3(x1)) 18.67/18.81 #27: #5(1(4(3(2(x1))))) -> #4(5(1(3(4(2(x1)))))) 18.67/18.81 #28: #5(1(4(3(2(x1))))) -> #5(1(3(4(2(x1))))) 18.67/18.81 #29: #5(1(4(3(2(x1))))) -> #4(2(x1)) 18.67/18.81 #30: #5(5(4(3(2(x1))))) -> #5(1(3(4(5(2(x1)))))) 18.67/18.81 #31: #5(5(4(3(2(x1))))) -> #4(5(2(x1))) 18.67/18.81 #32: #5(5(4(3(2(x1))))) -> #5(2(x1)) 18.67/18.81 #33: #2(2(4(3(5(x1))))) -> #5(1(3(4(2(2(x1)))))) 18.67/18.81 #34: #2(2(4(3(5(x1))))) -> #4(2(2(x1))) 18.67/18.81 #35: #2(2(4(3(5(x1))))) -> #2(2(x1)) 18.67/18.81 #36: #2(2(4(3(5(x1))))) -> #2(x1) 18.67/18.81 #37: #0(0(1(2(x1)))) -> #0(2(1(0(3(x1))))) 18.67/18.81 #38: #0(0(1(2(x1)))) -> #2(1(0(3(x1)))) 18.67/18.81 #39: #0(0(1(2(x1)))) -> #0(3(x1)) 18.67/18.81 #40: #2(3(1(1(2(x1))))) -> #4(1(2(2(1(3(x1)))))) 18.67/18.81 #41: #2(3(1(1(2(x1))))) -> #2(2(1(3(x1)))) 18.67/18.81 #42: #2(3(1(1(2(x1))))) -> #2(1(3(x1))) 18.67/18.81 #43: #0(1(4(2(x1)))) -> #2(4(1(0(3(x1))))) 18.67/18.81 #44: #0(1(4(2(x1)))) -> #4(1(0(3(x1)))) 18.67/18.81 #45: #0(1(4(2(x1)))) -> #0(3(x1)) 18.67/18.81 #46: #0(1(2(0(x1)))) -> #2(1(0(3(0(3(x1)))))) 18.67/18.81 #47: #0(1(2(0(x1)))) -> #0(3(0(3(x1)))) 18.67/18.81 #48: #0(1(2(0(x1)))) -> #0(3(x1)) 18.67/18.81 #49: #0(1(2(5(x1)))) -> #5(1(0(3(2(x1))))) 18.67/18.81 #50: #0(1(2(5(x1)))) -> #0(3(2(x1))) 18.67/18.81 #51: #0(1(2(5(x1)))) -> #2(x1) 18.67/18.81 #52: #0(1(1(5(0(x1))))) -> #0(1(0(5(4(1(x1)))))) 18.67/18.81 #53: #0(1(1(5(0(x1))))) -> #0(5(4(1(x1)))) 18.67/18.81 #54: #0(1(1(5(0(x1))))) -> #5(4(1(x1))) 18.67/18.81 #55: #0(1(1(5(0(x1))))) -> #4(1(x1)) 18.67/18.81 #56: #0(1(1(4(2(x1))))) -> #4(1(0(3(2(1(x1)))))) 18.67/18.81 #57: #0(1(1(4(2(x1))))) -> #0(3(2(1(x1)))) 18.67/18.81 #58: #0(1(1(4(2(x1))))) -> #2(1(x1)) 18.67/18.81 #59: #5(0(1(2(2(x1))))) -> #4(1(5(2(0(2(x1)))))) 18.67/18.81 #60: #5(0(1(2(2(x1))))) -> #5(2(0(2(x1)))) 18.67/18.81 #61: #5(0(1(2(2(x1))))) -> #2(0(2(x1))) 18.67/18.81 #62: #5(0(1(2(2(x1))))) -> #0(2(x1)) 18.67/18.81 #63: #0(1(4(2(x1)))) -> #2(1(3(4(0(x1))))) 18.67/18.81 #64: #0(1(4(2(x1)))) -> #4(0(x1)) 18.67/18.81 #65: #0(1(4(2(x1)))) -> #0(x1) 18.67/18.81 #66: #0(1(4(0(2(x1))))) -> #4(0(2(1(3(0(x1)))))) 18.67/18.81 #67: #0(1(4(0(2(x1))))) -> #0(2(1(3(0(x1))))) 18.67/18.81 #68: #0(1(4(0(2(x1))))) -> #2(1(3(0(x1)))) 18.67/18.81 #69: #0(1(4(0(2(x1))))) -> #0(x1) 18.67/18.81 #70: #0(1(4(2(x1)))) -> #0(2(1(0(3(4(x1)))))) 18.67/18.81 #71: #0(1(4(2(x1)))) -> #2(1(0(3(4(x1))))) 18.67/18.81 #72: #0(1(4(2(x1)))) -> #0(3(4(x1))) 18.67/18.81 #73: #0(1(4(2(x1)))) -> #4(x1) 18.67/18.81 #74: #0(1(4(0(2(x1))))) -> #4(0(1(3(0(2(x1)))))) 18.67/18.81 #75: #0(1(4(0(2(x1))))) -> #0(1(3(0(2(x1))))) 18.67/18.81 #76: #0(1(1(5(4(x1))))) -> #4(1(0(3(5(x1))))) 18.67/18.81 #77: #0(1(1(5(4(x1))))) -> #0(3(5(x1))) 18.67/18.81 #78: #0(1(1(5(4(x1))))) -> #5(x1) 18.67/18.81 #79: #5(1(2(0(x1)))) -> #2(5(1(0(3(x1))))) 18.67/18.81 #80: #5(1(2(0(x1)))) -> #5(1(0(3(x1)))) 18.67/18.81 #81: #5(1(2(0(x1)))) -> #0(3(x1)) 18.67/18.81 #82: #0(1(1(2(x1)))) -> #0(4(1(2(x1)))) 18.67/18.81 #83: #0(1(1(2(x1)))) -> #4(1(2(x1))) 18.67/18.81 #84: #2(3(1(1(2(x1))))) -> #2(1(2(0(x1)))) 18.67/18.81 #85: #2(3(1(1(2(x1))))) -> #2(0(x1)) 18.67/18.81 #86: #2(3(1(1(2(x1))))) -> #0(x1) 18.67/18.81 #87: #0(1(2(5(x1)))) -> #2(1(0(3(5(x1))))) 18.67/18.81 #88: #0(1(2(5(x1)))) -> #0(3(5(x1))) 18.67/18.81 #89: #2(1(0(1(5(x1))))) -> #0(3(2(5(1(x1))))) 18.67/18.81 #90: #2(1(0(1(5(x1))))) -> #2(5(1(x1))) 18.67/18.81 #91: #2(1(0(1(5(x1))))) -> #5(1(x1)) 18.67/18.81 #92: #0(1(2(x1))) -> #2(1(3(4(0(4(x1)))))) 18.67/18.81 #93: #0(1(2(x1))) -> #4(0(4(x1))) 18.67/18.81 #94: #0(1(2(x1))) -> #0(4(x1)) 18.67/18.81 #95: #0(1(2(x1))) -> #4(x1) 18.67/18.81 #96: #4(2(0(1(2(x1))))) -> #4(2(2(1(3(0(x1)))))) 18.67/18.81 #97: #4(2(0(1(2(x1))))) -> #2(2(1(3(0(x1))))) 18.67/18.81 #98: #4(2(0(1(2(x1))))) -> #2(1(3(0(x1)))) 18.67/18.81 #99: #4(2(0(1(2(x1))))) -> #0(x1) 18.67/18.81 #100: #0(1(2(3(5(x1))))) -> #0(3(0(2(5(x1))))) 18.67/18.81 #101: #0(1(2(3(5(x1))))) -> #0(2(5(x1))) 18.67/18.81 #102: #0(1(2(3(5(x1))))) -> #2(5(x1)) 18.67/18.81 #103: #0(1(1(2(5(x1))))) -> #0(1(3(5(1(2(x1)))))) 18.67/18.81 #104: #0(1(1(2(5(x1))))) -> #5(1(2(x1))) 18.67/18.81 #105: #0(1(1(2(5(x1))))) -> #2(x1) 18.67/18.81 #106: #2(1(4(3(5(x1))))) -> #5(4(4(2(x1)))) 18.67/18.81 #107: #2(1(4(3(5(x1))))) -> #4(4(2(x1))) 18.67/18.81 #108: #2(1(4(3(5(x1))))) -> #4(2(x1)) 18.67/18.81 #109: #2(1(4(3(5(x1))))) -> #2(x1) 18.67/18.81 #110: #0(1(2(3(5(x1))))) -> #0(2(5(1(0(3(x1)))))) 18.67/18.81 #111: #0(1(2(3(5(x1))))) -> #2(5(1(0(3(x1))))) 18.67/18.81 #112: #0(1(2(3(5(x1))))) -> #5(1(0(3(x1)))) 18.67/18.81 #113: #0(1(2(3(5(x1))))) -> #0(3(x1)) 18.67/18.81 #114: #2(1(2(0(x1)))) -> #2(2(1(0(3(x1))))) 18.67/18.81 #115: #2(1(2(0(x1)))) -> #2(1(0(3(x1)))) 18.67/18.81 #116: #2(1(2(0(x1)))) -> #0(3(x1)) 18.67/18.81 #117: #0(4(5(3(5(x1))))) -> #5(1(0(3(4(5(x1)))))) 18.67/18.81 #118: #0(4(5(3(5(x1))))) -> #0(3(4(5(x1)))) 18.67/18.81 #119: #0(4(5(3(5(x1))))) -> #4(5(x1)) 18.67/18.81 #120: #2(5(3(2(x1)))) -> #5(1(3(2(2(x1))))) 18.67/18.81 #121: #2(5(3(2(x1)))) -> #2(2(x1)) 18.67/18.81 #122: #0(1(2(3(5(x1))))) -> #0(1(3(4(5(2(x1)))))) 18.67/18.81 #123: #0(1(2(3(5(x1))))) -> #4(5(2(x1))) 18.67/18.81 #124: #0(1(2(3(5(x1))))) -> #5(2(x1)) 18.67/18.81 #125: #0(1(2(3(5(x1))))) -> #2(x1) 18.67/18.81 #126: #2(1(4(5(0(x1))))) -> #2(4(1(0(3(5(x1)))))) 18.67/18.81 #127: #2(1(4(5(0(x1))))) -> #4(1(0(3(5(x1))))) 18.67/18.81 #128: #2(1(4(5(0(x1))))) -> #0(3(5(x1))) 18.67/18.81 #129: #2(1(4(5(0(x1))))) -> #5(x1) 18.67/18.81 #130: #0(1(0(1(2(x1))))) -> #0(2(1(1(3(0(x1)))))) 18.67/18.81 #131: #0(1(0(1(2(x1))))) -> #2(1(1(3(0(x1))))) 18.67/18.81 #132: #0(1(0(1(2(x1))))) -> #0(x1) 18.67/18.81 #133: #2(1(1(5(x1)))) -> #5(1(3(2(1(x1))))) 18.67/18.81 #134: #2(1(1(5(x1)))) -> #2(1(x1)) 18.67/18.81 #135: #0(1(2(x1))) -> #2(1(3(0(4(x1))))) 18.67/18.81 #136: #0(1(2(x1))) -> #0(4(x1)) 18.67/18.81 #137: #0(1(2(x1))) -> #4(x1) 18.67/18.81 #138: #0(1(2(x1))) -> #2(1(0(3(x1)))) 18.67/18.81 #139: #0(1(2(x1))) -> #0(3(x1)) 18.67/18.81 #140: #0(1(1(2(x1)))) -> #2(1(0(3(x1)))) 18.67/18.81 #141: #0(1(1(2(x1)))) -> #0(3(x1)) 18.67/18.81 #142: #2(1(1(5(x1)))) -> #2(5(1(4(1(x1))))) 18.67/18.81 #143: #2(1(1(5(x1)))) -> #5(1(4(1(x1)))) 18.67/18.81 #144: #2(1(1(5(x1)))) -> #4(1(x1)) 18.67/18.81 #145: #0(1(2(x1))) -> #2(1(3(4(0(x1))))) 18.67/18.81 #146: #0(1(2(x1))) -> #4(0(x1)) 18.67/18.81 #147: #0(1(2(x1))) -> #0(x1) 18.67/18.81 #148: #2(3(5(5(x1)))) -> #5(1(0(3(2(5(x1)))))) 18.67/18.81 #149: #2(3(5(5(x1)))) -> #0(3(2(5(x1)))) 18.67/18.81 #150: #2(3(5(5(x1)))) -> #2(5(x1)) 18.67/18.81 Number of SCCs: 1, DPs: 30 18.67/18.81 SCC { #2 #9 #13 #16 #18 #29 #35 #36 #51 #58 #65 #69 #73 #78 #86 #91 #95 #99 #102 #105 #108 #109 #121 #125 #129 #132 #134 #137 #147 #150 } 18.67/18.81 POLO(Sum)... succeeded. 18.67/18.81 #0 w: x1 18.67/18.81 1 w: x1 18.67/18.81 4 w: x1 18.67/18.81 5 w: x1 + 2 18.67/18.81 3 w: x1 18.67/18.81 #2 w: x1 18.67/18.81 #4 w: x1 18.67/18.81 0 w: x1 18.67/18.81 #5 w: x1 + 1 18.67/18.81 2 w: x1 + 1 18.67/18.81 USABLE RULES: { 1..48 } 18.67/18.81 Removed DPs: #2 #9 #13 #16 #18 #29 #35 #36 #51 #58 #65 #69 #73 #78 #86 #91 #95 #99 #102 #105 #108 #109 #121 #125 #129 #132 #134 #137 #147 #150 18.67/18.81 Number of SCCs: 0, DPs: 0 18.67/18.81 EOF