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