YES Input TRS: 1: 0(1(0(0(x1)))) -> 2(0(2(0(0(1(x1)))))) 2: 1(0(0(1(x1)))) -> 1(0(3(0(1(x1))))) 3: 1(0(0(4(x1)))) -> 1(4(0(2(0(x1))))) 4: 1(0(0(4(x1)))) -> 1(4(0(3(2(0(x1)))))) 5: 1(0(1(0(x1)))) -> 1(3(0(0(3(1(x1)))))) 6: 1(0(1(4(x1)))) -> 1(0(3(1(2(4(x1)))))) 7: 1(0(1(5(x1)))) -> 1(0(2(1(5(x1))))) 8: 1(0(4(1(x1)))) -> 1(0(3(4(1(x1))))) 9: 1(0(5(0(x1)))) -> 1(2(5(2(0(0(x1)))))) 10: 1(2(0(4(x1)))) -> 1(3(4(2(0(x1))))) 11: 1(3(0(4(x1)))) -> 1(3(4(2(0(x1))))) 12: 1(4(1(0(x1)))) -> 1(4(0(2(1(x1))))) 13: 1(4(1(0(x1)))) -> 1(4(0(3(1(x1))))) 14: 1(4(5(0(x1)))) -> 4(0(2(1(2(5(x1)))))) 15: 1(5(0(1(x1)))) -> 0(1(3(1(3(5(x1)))))) 16: 1(5(0(1(x1)))) -> 1(5(0(3(1(3(x1)))))) 17: 4(1(0(0(x1)))) -> 0(2(4(2(0(1(x1)))))) 18: 4(1(0(0(x1)))) -> 0(3(4(3(0(1(x1)))))) 19: 4(1(0(5(x1)))) -> 4(0(2(1(5(x1))))) 20: 4(1(2(0(x1)))) -> 3(0(2(1(3(4(x1)))))) 21: 4(5(0(0(x1)))) -> 3(0(4(0(5(x1))))) 22: 5(0(0(4(x1)))) -> 5(4(0(2(0(x1))))) 23: 5(0(1(4(x1)))) -> 1(5(4(3(0(x1))))) 24: 5(4(1(5(x1)))) -> 4(3(1(5(5(x1))))) 25: 1(0(1(4(5(x1))))) -> 1(3(1(5(4(0(x1)))))) 26: 1(0(4(0(4(x1))))) -> 1(0(4(3(4(0(x1)))))) 27: 1(1(1(0(0(x1))))) -> 1(1(0(0(3(1(x1)))))) 28: 1(1(4(5(0(x1))))) -> 1(1(3(4(0(5(x1)))))) 29: 1(2(0(5(0(x1))))) -> 5(2(1(0(2(0(x1)))))) 30: 1(4(5(0(0(x1))))) -> 4(0(5(0(2(1(x1)))))) 31: 1(4(5(2(0(x1))))) -> 0(3(1(2(5(4(x1)))))) 32: 1(5(0(4(5(x1))))) -> 3(4(0(5(1(5(x1)))))) 33: 4(1(0(0(1(x1))))) -> 1(0(4(0(3(1(x1)))))) 34: 4(1(2(0(0(x1))))) -> 4(2(0(0(2(1(x1)))))) 35: 4(1(3(0(5(x1))))) -> 3(2(4(0(1(5(x1)))))) 36: 4(1(5(3(1(x1))))) -> 2(1(5(4(3(1(x1)))))) 37: 4(4(1(0(1(x1))))) -> 1(3(4(4(0(1(x1)))))) 38: 4(5(0(1(0(x1))))) -> 4(0(0(5(3(1(x1)))))) 39: 4(5(1(1(0(x1))))) -> 1(1(3(4(0(5(x1)))))) 40: 4(5(1(1(0(x1))))) -> 4(0(2(1(5(1(x1)))))) 41: 4(5(1(5(1(x1))))) -> 4(1(5(5(3(1(x1)))))) 42: 4(5(5(0(4(x1))))) -> 5(4(0(5(4(2(x1)))))) 43: 5(0(0(4(1(x1))))) -> 5(4(0(3(0(1(x1)))))) 44: 5(0(0(4(5(x1))))) -> 0(3(4(0(5(5(x1)))))) 45: 5(0(0(4(5(x1))))) -> 4(0(0(3(5(5(x1)))))) 46: 5(0(4(1(0(x1))))) -> 5(0(4(0(3(1(x1)))))) 47: 5(1(5(0(1(x1))))) -> 5(0(3(5(1(1(x1)))))) 48: 5(4(1(1(0(x1))))) -> 1(2(4(0(1(5(x1)))))) 49: 5(4(5(1(0(x1))))) -> 5(5(1(3(4(0(x1)))))) 50: 5(5(2(0(4(x1))))) -> 5(5(3(4(2(0(x1)))))) Number of strict rules: 50 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #1(0(0(1(x1)))) -> #1(0(3(0(1(x1))))) #2: #1(0(0(1(x1)))) -> #0(3(0(1(x1)))) #3: #5(0(0(4(1(x1))))) -> #5(4(0(3(0(1(x1)))))) #4: #5(0(0(4(1(x1))))) -> #4(0(3(0(1(x1))))) #5: #5(0(0(4(1(x1))))) -> #0(3(0(1(x1)))) #6: #5(0(0(4(1(x1))))) -> #0(1(x1)) #7: #1(2(0(5(0(x1))))) -> #5(2(1(0(2(0(x1)))))) #8: #1(2(0(5(0(x1))))) -> #1(0(2(0(x1)))) #9: #1(2(0(5(0(x1))))) -> #0(2(0(x1))) #10: #4(1(3(0(5(x1))))) -> #4(0(1(5(x1)))) #11: #4(1(3(0(5(x1))))) -> #0(1(5(x1))) #12: #4(1(3(0(5(x1))))) -> #1(5(x1)) #13: #5(0(4(1(0(x1))))) -> #5(0(4(0(3(1(x1)))))) #14: #5(0(4(1(0(x1))))) -> #0(4(0(3(1(x1))))) #15: #5(0(4(1(0(x1))))) -> #4(0(3(1(x1)))) #16: #5(0(4(1(0(x1))))) -> #0(3(1(x1))) #17: #5(0(4(1(0(x1))))) -> #1(x1) #18: #4(5(5(0(4(x1))))) -> #5(4(0(5(4(2(x1)))))) #19: #4(5(5(0(4(x1))))) -> #4(0(5(4(2(x1))))) #20: #4(5(5(0(4(x1))))) -> #0(5(4(2(x1)))) #21: #4(5(5(0(4(x1))))) -> #5(4(2(x1))) #22: #4(5(5(0(4(x1))))) -> #4(2(x1)) #23: #4(5(1(5(1(x1))))) -> #4(1(5(5(3(1(x1)))))) #24: #4(5(1(5(1(x1))))) -> #1(5(5(3(1(x1))))) #25: #4(5(1(5(1(x1))))) -> #5(5(3(1(x1)))) #26: #4(5(1(5(1(x1))))) -> #5(3(1(x1))) #27: #4(4(1(0(1(x1))))) -> #1(3(4(4(0(1(x1)))))) #28: #4(4(1(0(1(x1))))) -> #4(4(0(1(x1)))) #29: #4(4(1(0(1(x1))))) -> #4(0(1(x1))) #30: #5(1(5(0(1(x1))))) -> #5(0(3(5(1(1(x1)))))) #31: #5(1(5(0(1(x1))))) -> #0(3(5(1(1(x1))))) #32: #5(1(5(0(1(x1))))) -> #5(1(1(x1))) #33: #5(1(5(0(1(x1))))) -> #1(1(x1)) #34: #5(4(1(1(0(x1))))) -> #1(2(4(0(1(5(x1)))))) #35: #5(4(1(1(0(x1))))) -> #4(0(1(5(x1)))) #36: #5(4(1(1(0(x1))))) -> #0(1(5(x1))) #37: #5(4(1(1(0(x1))))) -> #1(5(x1)) #38: #5(4(1(1(0(x1))))) -> #5(x1) #39: #4(5(0(1(0(x1))))) -> #4(0(0(5(3(1(x1)))))) #40: #4(5(0(1(0(x1))))) -> #0(0(5(3(1(x1))))) #41: #4(5(0(1(0(x1))))) -> #0(5(3(1(x1)))) #42: #4(5(0(1(0(x1))))) -> #5(3(1(x1))) #43: #4(5(0(1(0(x1))))) -> #1(x1) #44: #1(0(1(4(x1)))) -> #1(0(3(1(2(4(x1)))))) #45: #1(0(1(4(x1)))) -> #0(3(1(2(4(x1))))) #46: #1(0(1(4(x1)))) -> #1(2(4(x1))) #47: #4(5(1(1(0(x1))))) -> #4(0(2(1(5(1(x1)))))) #48: #4(5(1(1(0(x1))))) -> #0(2(1(5(1(x1))))) #49: #4(5(1(1(0(x1))))) -> #1(5(1(x1))) #50: #4(5(1(1(0(x1))))) -> #5(1(x1)) #51: #4(5(1(1(0(x1))))) -> #1(x1) #52: #1(4(1(0(x1)))) -> #1(4(0(3(1(x1))))) #53: #1(4(1(0(x1)))) -> #4(0(3(1(x1)))) #54: #1(4(1(0(x1)))) -> #0(3(1(x1))) #55: #1(4(1(0(x1)))) -> #1(x1) #56: #1(0(5(0(x1)))) -> #1(2(5(2(0(0(x1)))))) #57: #1(0(5(0(x1)))) -> #5(2(0(0(x1)))) #58: #1(0(5(0(x1)))) -> #0(0(x1)) #59: #1(3(0(4(x1)))) -> #1(3(4(2(0(x1))))) #60: #1(3(0(4(x1)))) -> #4(2(0(x1))) #61: #1(3(0(4(x1)))) -> #0(x1) #62: #5(4(1(5(x1)))) -> #4(3(1(5(5(x1))))) #63: #5(4(1(5(x1)))) -> #1(5(5(x1))) #64: #5(4(1(5(x1)))) -> #5(5(x1)) #65: #5(0(1(4(x1)))) -> #1(5(4(3(0(x1))))) #66: #5(0(1(4(x1)))) -> #5(4(3(0(x1)))) #67: #5(0(1(4(x1)))) -> #4(3(0(x1))) #68: #5(0(1(4(x1)))) -> #0(x1) #69: #5(0(0(4(5(x1))))) -> #4(0(0(3(5(5(x1)))))) #70: #5(0(0(4(5(x1))))) -> #0(0(3(5(5(x1))))) #71: #5(0(0(4(5(x1))))) -> #0(3(5(5(x1)))) #72: #5(0(0(4(5(x1))))) -> #5(5(x1)) #73: #1(4(1(0(x1)))) -> #1(4(0(2(1(x1))))) #74: #1(4(1(0(x1)))) -> #4(0(2(1(x1)))) #75: #1(4(1(0(x1)))) -> #0(2(1(x1))) #76: #1(4(1(0(x1)))) -> #1(x1) #77: #1(4(5(2(0(x1))))) -> #0(3(1(2(5(4(x1)))))) #78: #1(4(5(2(0(x1))))) -> #1(2(5(4(x1)))) #79: #1(4(5(2(0(x1))))) -> #5(4(x1)) #80: #1(4(5(2(0(x1))))) -> #4(x1) #81: #1(4(5(0(x1)))) -> #4(0(2(1(2(5(x1)))))) #82: #1(4(5(0(x1)))) -> #0(2(1(2(5(x1))))) #83: #1(4(5(0(x1)))) -> #1(2(5(x1))) #84: #1(4(5(0(x1)))) -> #5(x1) #85: #1(4(5(0(0(x1))))) -> #4(0(5(0(2(1(x1)))))) #86: #1(4(5(0(0(x1))))) -> #0(5(0(2(1(x1))))) #87: #1(4(5(0(0(x1))))) -> #5(0(2(1(x1)))) #88: #1(4(5(0(0(x1))))) -> #0(2(1(x1))) #89: #1(4(5(0(0(x1))))) -> #1(x1) #90: #5(4(5(1(0(x1))))) -> #5(5(1(3(4(0(x1)))))) #91: #5(4(5(1(0(x1))))) -> #5(1(3(4(0(x1))))) #92: #5(4(5(1(0(x1))))) -> #1(3(4(0(x1)))) #93: #5(4(5(1(0(x1))))) -> #4(0(x1)) #94: #1(0(1(4(5(x1))))) -> #1(3(1(5(4(0(x1)))))) #95: #1(0(1(4(5(x1))))) -> #1(5(4(0(x1)))) #96: #1(0(1(4(5(x1))))) -> #5(4(0(x1))) #97: #1(0(1(4(5(x1))))) -> #4(0(x1)) #98: #1(0(1(4(5(x1))))) -> #0(x1) #99: #4(1(2(0(x1)))) -> #0(2(1(3(4(x1))))) #100: #4(1(2(0(x1)))) -> #1(3(4(x1))) #101: #4(1(2(0(x1)))) -> #4(x1) #102: #1(0(1(5(x1)))) -> #1(0(2(1(5(x1))))) #103: #1(0(1(5(x1)))) -> #0(2(1(5(x1)))) #104: #4(5(1(1(0(x1))))) -> #1(1(3(4(0(5(x1)))))) #105: #4(5(1(1(0(x1))))) -> #1(3(4(0(5(x1))))) #106: #4(5(1(1(0(x1))))) -> #4(0(5(x1))) #107: #4(5(1(1(0(x1))))) -> #0(5(x1)) #108: #4(5(1(1(0(x1))))) -> #5(x1) #109: #1(2(0(4(x1)))) -> #1(3(4(2(0(x1))))) #110: #1(2(0(4(x1)))) -> #4(2(0(x1))) #111: #1(2(0(4(x1)))) -> #0(x1) #112: #4(1(0(0(1(x1))))) -> #1(0(4(0(3(1(x1)))))) #113: #4(1(0(0(1(x1))))) -> #0(4(0(3(1(x1))))) #114: #4(1(0(0(1(x1))))) -> #4(0(3(1(x1)))) #115: #4(1(0(0(1(x1))))) -> #0(3(1(x1))) #116: #1(0(1(0(x1)))) -> #1(3(0(0(3(1(x1)))))) #117: #1(0(1(0(x1)))) -> #0(0(3(1(x1)))) #118: #1(0(1(0(x1)))) -> #0(3(1(x1))) #119: #1(0(1(0(x1)))) -> #1(x1) #120: #5(0(0(4(5(x1))))) -> #0(3(4(0(5(5(x1)))))) #121: #5(0(0(4(5(x1))))) -> #4(0(5(5(x1)))) #122: #5(0(0(4(5(x1))))) -> #0(5(5(x1))) #123: #5(0(0(4(5(x1))))) -> #5(5(x1)) #124: #1(1(4(5(0(x1))))) -> #1(1(3(4(0(5(x1)))))) #125: #1(1(4(5(0(x1))))) -> #1(3(4(0(5(x1))))) #126: #1(1(4(5(0(x1))))) -> #4(0(5(x1))) #127: #1(1(4(5(0(x1))))) -> #0(5(x1)) #128: #1(1(4(5(0(x1))))) -> #5(x1) #129: #5(0(0(4(x1)))) -> #5(4(0(2(0(x1))))) #130: #5(0(0(4(x1)))) -> #4(0(2(0(x1)))) #131: #5(0(0(4(x1)))) -> #0(2(0(x1))) #132: #5(0(0(4(x1)))) -> #0(x1) #133: #4(1(2(0(0(x1))))) -> #4(2(0(0(2(1(x1)))))) #134: #4(1(2(0(0(x1))))) -> #0(0(2(1(x1)))) #135: #4(1(2(0(0(x1))))) -> #0(2(1(x1))) #136: #4(1(2(0(0(x1))))) -> #1(x1) #137: #1(1(1(0(0(x1))))) -> #1(1(0(0(3(1(x1)))))) #138: #1(1(1(0(0(x1))))) -> #1(0(0(3(1(x1))))) #139: #1(1(1(0(0(x1))))) -> #0(0(3(1(x1)))) #140: #1(1(1(0(0(x1))))) -> #0(3(1(x1))) #141: #1(1(1(0(0(x1))))) -> #1(x1) #142: #4(1(0(0(x1)))) -> #0(2(4(2(0(1(x1)))))) #143: #4(1(0(0(x1)))) -> #4(2(0(1(x1)))) #144: #4(1(0(0(x1)))) -> #0(1(x1)) #145: #4(1(0(0(x1)))) -> #1(x1) #146: #1(5(0(4(5(x1))))) -> #4(0(5(1(5(x1))))) #147: #1(5(0(4(5(x1))))) -> #0(5(1(5(x1)))) #148: #1(5(0(4(5(x1))))) -> #5(1(5(x1))) #149: #1(5(0(4(5(x1))))) -> #1(5(x1)) #150: #4(1(0(5(x1)))) -> #4(0(2(1(5(x1))))) #151: #4(1(0(5(x1)))) -> #0(2(1(5(x1)))) #152: #4(1(0(5(x1)))) -> #1(5(x1)) #153: #1(0(4(0(4(x1))))) -> #1(0(4(3(4(0(x1)))))) #154: #1(0(4(0(4(x1))))) -> #0(4(3(4(0(x1))))) #155: #1(0(4(0(4(x1))))) -> #4(3(4(0(x1)))) #156: #1(0(4(0(4(x1))))) -> #4(0(x1)) #157: #1(0(4(0(4(x1))))) -> #0(x1) #158: #4(1(5(3(1(x1))))) -> #1(5(4(3(1(x1))))) #159: #4(1(5(3(1(x1))))) -> #5(4(3(1(x1)))) #160: #4(1(5(3(1(x1))))) -> #4(3(1(x1))) #161: #4(5(0(0(x1)))) -> #0(4(0(5(x1)))) #162: #4(5(0(0(x1)))) -> #4(0(5(x1))) #163: #4(5(0(0(x1)))) -> #0(5(x1)) #164: #4(5(0(0(x1)))) -> #5(x1) #165: #1(5(0(1(x1)))) -> #1(5(0(3(1(3(x1)))))) #166: #1(5(0(1(x1)))) -> #5(0(3(1(3(x1))))) #167: #1(5(0(1(x1)))) -> #0(3(1(3(x1)))) #168: #1(5(0(1(x1)))) -> #1(3(x1)) #169: #1(0(0(4(x1)))) -> #1(4(0(2(0(x1))))) #170: #1(0(0(4(x1)))) -> #4(0(2(0(x1)))) #171: #1(0(0(4(x1)))) -> #0(2(0(x1))) #172: #1(0(0(4(x1)))) -> #0(x1) #173: #0(1(0(0(x1)))) -> #0(2(0(0(1(x1))))) #174: #0(1(0(0(x1)))) -> #0(0(1(x1))) #175: #0(1(0(0(x1)))) -> #0(1(x1)) #176: #0(1(0(0(x1)))) -> #1(x1) #177: #1(0(4(1(x1)))) -> #1(0(3(4(1(x1))))) #178: #1(0(4(1(x1)))) -> #0(3(4(1(x1)))) #179: #1(5(0(1(x1)))) -> #0(1(3(1(3(5(x1)))))) #180: #1(5(0(1(x1)))) -> #1(3(1(3(5(x1))))) #181: #1(5(0(1(x1)))) -> #1(3(5(x1))) #182: #1(5(0(1(x1)))) -> #5(x1) #183: #1(0(0(4(x1)))) -> #1(4(0(3(2(0(x1)))))) #184: #1(0(0(4(x1)))) -> #4(0(3(2(0(x1))))) #185: #1(0(0(4(x1)))) -> #0(3(2(0(x1)))) #186: #1(0(0(4(x1)))) -> #0(x1) #187: #5(5(2(0(4(x1))))) -> #5(5(3(4(2(0(x1)))))) #188: #5(5(2(0(4(x1))))) -> #5(3(4(2(0(x1))))) #189: #5(5(2(0(4(x1))))) -> #4(2(0(x1))) #190: #5(5(2(0(4(x1))))) -> #0(x1) #191: #4(1(0(0(x1)))) -> #0(3(4(3(0(1(x1)))))) #192: #4(1(0(0(x1)))) -> #4(3(0(1(x1)))) #193: #4(1(0(0(x1)))) -> #0(1(x1)) #194: #4(1(0(0(x1)))) -> #1(x1) Number of SCCs: 1, DPs: 46 SCC { #6 #12 #17 #33 #37 #38 #43 #49..51 #55 #61 #64 #68 #72 #76 #79 #80 #84 #89 #98 #101 #108 #111 #119 #123 #128 #132 #136 #141 #144 #145 #148 #149 #152 #157 #164 #168 #172 #175 #176 #182 #186 #190 #193 #194 } POLO(Sum)... succeeded. #0 w: x1 1 w: x1 + 250 4 w: x1 + 17498 5 w: x1 + 1 3 w: x1 #4 w: x1 + 337 0 w: x1 + 88 #5 w: x1 + 513 2 w: x1 #1 w: x1 + 425 USABLE RULES: { 1..50 } Removed DPs: #6 #12 #17 #33 #37 #38 #43 #49..51 #55 #61 #64 #68 #72 #76 #79 #80 #84 #89 #98 #101 #108 #111 #119 #123 #128 #132 #136 #141 #144 #145 #148 #149 #152 #157 #164 #168 #172 #175 #176 #182 #186 #190 #193 #194 Number of SCCs: 0, DPs: 0