YES Input TRS: 1: 5(5(x1)) -> 0(5(4(0(2(5(4(5(2(1(x1)))))))))) 2: 5(5(x1)) -> 3(4(1(1(1(1(4(4(0(4(x1)))))))))) 3: 2(5(5(x1))) -> 4(2(5(4(4(0(0(1(1(2(x1)))))))))) 4: 5(2(4(x1))) -> 0(5(0(2(3(3(4(2(4(2(x1)))))))))) 5: 5(5(2(x1))) -> 0(1(3(2(3(0(3(2(5(3(x1)))))))))) 6: 5(5(3(x1))) -> 0(3(5(4(4(1(0(1(5(0(x1)))))))))) 7: 5(5(5(x1))) -> 5(3(4(1(0(1(4(5(0(0(x1)))))))))) 8: 2(5(0(4(x1)))) -> 4(4(3(2(4(4(5(1(0(0(x1)))))))))) 9: 4(5(2(4(x1)))) -> 4(1(5(5(2(0(3(1(3(3(x1)))))))))) 10: 4(5(5(5(x1)))) -> 1(5(1(2(0(3(2(1(0(5(x1)))))))))) 11: 0(2(5(3(4(x1))))) -> 3(2(4(3(1(5(1(1(3(4(x1)))))))))) 12: 2(5(5(3(4(x1))))) -> 4(5(4(3(1(4(0(2(4(4(x1)))))))))) 13: 5(5(5(1(4(x1))))) -> 3(3(0(5(0(4(3(4(4(0(x1)))))))))) 14: 0(4(4(5(5(5(x1)))))) -> 0(4(4(4(3(3(4(1(3(1(x1)))))))))) 15: 1(2(4(5(2(4(x1)))))) -> 3(3(5(3(0(4(0(3(1(3(x1)))))))))) 16: 4(1(5(5(0(4(x1)))))) -> 1(0(3(0(4(2(4(4(3(4(x1)))))))))) 17: 4(2(5(5(1(5(x1)))))) -> 2(3(4(2(1(1(3(4(2(5(x1)))))))))) 18: 5(2(5(5(0(4(x1)))))) -> 0(4(2(3(3(5(2(1(4(4(x1)))))))))) 19: 5(5(2(4(5(0(x1)))))) -> 2(1(1(4(2(4(0(4(2(0(x1)))))))))) 20: 0(1(5(5(5(3(5(x1))))))) -> 5(3(2(5(1(0(1(2(0(5(x1)))))))))) 21: 4(4(5(2(4(2(2(x1))))))) -> 4(0(5(5(4(5(1(2(2(1(x1)))))))))) Number of strict rules: 21 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #5(5(x1)) -> #4(1(1(1(1(4(4(0(4(x1))))))))) #2: #5(5(x1)) -> #1(1(1(1(4(4(0(4(x1)))))))) #3: #5(5(x1)) -> #1(1(1(4(4(0(4(x1))))))) #4: #5(5(x1)) -> #1(1(4(4(0(4(x1)))))) #5: #5(5(x1)) -> #1(4(4(0(4(x1))))) #6: #5(5(x1)) -> #4(4(0(4(x1)))) #7: #5(5(x1)) -> #4(0(4(x1))) #8: #5(5(x1)) -> #0(4(x1)) #9: #5(5(x1)) -> #4(x1) #10: #5(5(3(x1))) -> #0(3(5(4(4(1(0(1(5(0(x1)))))))))) #11: #5(5(3(x1))) -> #5(4(4(1(0(1(5(0(x1)))))))) #12: #5(5(3(x1))) -> #4(4(1(0(1(5(0(x1))))))) #13: #5(5(3(x1))) -> #4(1(0(1(5(0(x1)))))) #14: #5(5(3(x1))) -> #1(0(1(5(0(x1))))) #15: #5(5(3(x1))) -> #0(1(5(0(x1)))) #16: #5(5(3(x1))) -> #1(5(0(x1))) #17: #5(5(3(x1))) -> #5(0(x1)) #18: #5(5(3(x1))) -> #0(x1) #19: #5(5(5(1(4(x1))))) -> #0(5(0(4(3(4(4(0(x1)))))))) #20: #5(5(5(1(4(x1))))) -> #5(0(4(3(4(4(0(x1))))))) #21: #5(5(5(1(4(x1))))) -> #0(4(3(4(4(0(x1)))))) #22: #5(5(5(1(4(x1))))) -> #4(3(4(4(0(x1))))) #23: #5(5(5(1(4(x1))))) -> #4(4(0(x1))) #24: #5(5(5(1(4(x1))))) -> #4(0(x1)) #25: #5(5(5(1(4(x1))))) -> #0(x1) #26: #4(5(2(4(x1)))) -> #4(1(5(5(2(0(3(1(3(3(x1)))))))))) #27: #4(5(2(4(x1)))) -> #1(5(5(2(0(3(1(3(3(x1))))))))) #28: #4(5(2(4(x1)))) -> #5(5(2(0(3(1(3(3(x1)))))))) #29: #4(5(2(4(x1)))) -> #5(2(0(3(1(3(3(x1))))))) #30: #4(5(2(4(x1)))) -> #2(0(3(1(3(3(x1)))))) #31: #4(5(2(4(x1)))) -> #0(3(1(3(3(x1))))) #32: #4(5(2(4(x1)))) -> #1(3(3(x1))) #33: #0(2(5(3(4(x1))))) -> #2(4(3(1(5(1(1(3(4(x1))))))))) #34: #0(2(5(3(4(x1))))) -> #4(3(1(5(1(1(3(4(x1)))))))) #35: #0(2(5(3(4(x1))))) -> #1(5(1(1(3(4(x1)))))) #36: #0(2(5(3(4(x1))))) -> #5(1(1(3(4(x1))))) #37: #0(2(5(3(4(x1))))) -> #1(1(3(4(x1)))) #38: #0(2(5(3(4(x1))))) -> #1(3(4(x1))) #39: #2(5(5(3(4(x1))))) -> #4(5(4(3(1(4(0(2(4(4(x1)))))))))) #40: #2(5(5(3(4(x1))))) -> #5(4(3(1(4(0(2(4(4(x1))))))))) #41: #2(5(5(3(4(x1))))) -> #4(3(1(4(0(2(4(4(x1)))))))) #42: #2(5(5(3(4(x1))))) -> #1(4(0(2(4(4(x1)))))) #43: #2(5(5(3(4(x1))))) -> #4(0(2(4(4(x1))))) #44: #2(5(5(3(4(x1))))) -> #0(2(4(4(x1)))) #45: #2(5(5(3(4(x1))))) -> #2(4(4(x1))) #46: #2(5(5(3(4(x1))))) -> #4(4(x1)) #47: #0(4(4(5(5(5(x1)))))) -> #0(4(4(4(3(3(4(1(3(1(x1)))))))))) #48: #0(4(4(5(5(5(x1)))))) -> #4(4(4(3(3(4(1(3(1(x1))))))))) #49: #0(4(4(5(5(5(x1)))))) -> #4(4(3(3(4(1(3(1(x1)))))))) #50: #0(4(4(5(5(5(x1)))))) -> #4(3(3(4(1(3(1(x1))))))) #51: #0(4(4(5(5(5(x1)))))) -> #4(1(3(1(x1)))) #52: #0(4(4(5(5(5(x1)))))) -> #1(3(1(x1))) #53: #0(4(4(5(5(5(x1)))))) -> #1(x1) #54: #0(1(5(5(5(3(5(x1))))))) -> #5(3(2(5(1(0(1(2(0(5(x1)))))))))) #55: #0(1(5(5(5(3(5(x1))))))) -> #2(5(1(0(1(2(0(5(x1)))))))) #56: #0(1(5(5(5(3(5(x1))))))) -> #5(1(0(1(2(0(5(x1))))))) #57: #0(1(5(5(5(3(5(x1))))))) -> #1(0(1(2(0(5(x1)))))) #58: #0(1(5(5(5(3(5(x1))))))) -> #0(1(2(0(5(x1))))) #59: #0(1(5(5(5(3(5(x1))))))) -> #1(2(0(5(x1)))) #60: #0(1(5(5(5(3(5(x1))))))) -> #2(0(5(x1))) #61: #0(1(5(5(5(3(5(x1))))))) -> #0(5(x1)) #62: #5(5(5(x1))) -> #5(3(4(1(0(1(4(5(0(0(x1)))))))))) #63: #5(5(5(x1))) -> #4(1(0(1(4(5(0(0(x1)))))))) #64: #5(5(5(x1))) -> #1(0(1(4(5(0(0(x1))))))) #65: #5(5(5(x1))) -> #0(1(4(5(0(0(x1)))))) #66: #5(5(5(x1))) -> #1(4(5(0(0(x1))))) #67: #5(5(5(x1))) -> #4(5(0(0(x1)))) #68: #5(5(5(x1))) -> #5(0(0(x1))) #69: #5(5(5(x1))) -> #0(0(x1)) #70: #5(5(5(x1))) -> #0(x1) #71: #4(5(5(5(x1)))) -> #1(5(1(2(0(3(2(1(0(5(x1)))))))))) #72: #4(5(5(5(x1)))) -> #5(1(2(0(3(2(1(0(5(x1))))))))) #73: #4(5(5(5(x1)))) -> #1(2(0(3(2(1(0(5(x1)))))))) #74: #4(5(5(5(x1)))) -> #2(0(3(2(1(0(5(x1))))))) #75: #4(5(5(5(x1)))) -> #0(3(2(1(0(5(x1)))))) #76: #4(5(5(5(x1)))) -> #2(1(0(5(x1)))) #77: #4(5(5(5(x1)))) -> #1(0(5(x1))) #78: #4(5(5(5(x1)))) -> #0(5(x1)) #79: #5(5(2(x1))) -> #0(1(3(2(3(0(3(2(5(3(x1)))))))))) #80: #5(5(2(x1))) -> #1(3(2(3(0(3(2(5(3(x1))))))))) #81: #5(5(2(x1))) -> #2(3(0(3(2(5(3(x1))))))) #82: #5(5(2(x1))) -> #0(3(2(5(3(x1))))) #83: #5(5(2(x1))) -> #2(5(3(x1))) #84: #5(5(2(x1))) -> #5(3(x1)) #85: #4(2(5(5(1(5(x1)))))) -> #2(3(4(2(1(1(3(4(2(5(x1)))))))))) #86: #4(2(5(5(1(5(x1)))))) -> #4(2(1(1(3(4(2(5(x1)))))))) #87: #4(2(5(5(1(5(x1)))))) -> #2(1(1(3(4(2(5(x1))))))) #88: #4(2(5(5(1(5(x1)))))) -> #1(1(3(4(2(5(x1)))))) #89: #4(2(5(5(1(5(x1)))))) -> #1(3(4(2(5(x1))))) #90: #4(2(5(5(1(5(x1)))))) -> #4(2(5(x1))) #91: #4(2(5(5(1(5(x1)))))) -> #2(5(x1)) #92: #5(5(2(4(5(0(x1)))))) -> #2(1(1(4(2(4(0(4(2(0(x1)))))))))) #93: #5(5(2(4(5(0(x1)))))) -> #1(1(4(2(4(0(4(2(0(x1))))))))) #94: #5(5(2(4(5(0(x1)))))) -> #1(4(2(4(0(4(2(0(x1)))))))) #95: #5(5(2(4(5(0(x1)))))) -> #4(2(4(0(4(2(0(x1))))))) #96: #5(5(2(4(5(0(x1)))))) -> #2(4(0(4(2(0(x1)))))) #97: #5(5(2(4(5(0(x1)))))) -> #4(0(4(2(0(x1))))) #98: #5(5(2(4(5(0(x1)))))) -> #0(4(2(0(x1)))) #99: #5(5(2(4(5(0(x1)))))) -> #4(2(0(x1))) #100: #5(5(2(4(5(0(x1)))))) -> #2(0(x1)) #101: #4(4(5(2(4(2(2(x1))))))) -> #4(0(5(5(4(5(1(2(2(1(x1)))))))))) #102: #4(4(5(2(4(2(2(x1))))))) -> #0(5(5(4(5(1(2(2(1(x1))))))))) #103: #4(4(5(2(4(2(2(x1))))))) -> #5(5(4(5(1(2(2(1(x1)))))))) #104: #4(4(5(2(4(2(2(x1))))))) -> #5(4(5(1(2(2(1(x1))))))) #105: #4(4(5(2(4(2(2(x1))))))) -> #4(5(1(2(2(1(x1)))))) #106: #4(4(5(2(4(2(2(x1))))))) -> #5(1(2(2(1(x1))))) #107: #4(4(5(2(4(2(2(x1))))))) -> #1(2(2(1(x1)))) #108: #4(4(5(2(4(2(2(x1))))))) -> #2(2(1(x1))) #109: #4(4(5(2(4(2(2(x1))))))) -> #2(1(x1)) #110: #4(4(5(2(4(2(2(x1))))))) -> #1(x1) #111: #4(1(5(5(0(4(x1)))))) -> #1(0(3(0(4(2(4(4(3(4(x1)))))))))) #112: #4(1(5(5(0(4(x1)))))) -> #0(3(0(4(2(4(4(3(4(x1))))))))) #113: #4(1(5(5(0(4(x1)))))) -> #0(4(2(4(4(3(4(x1))))))) #114: #4(1(5(5(0(4(x1)))))) -> #4(2(4(4(3(4(x1)))))) #115: #4(1(5(5(0(4(x1)))))) -> #2(4(4(3(4(x1))))) #116: #4(1(5(5(0(4(x1)))))) -> #4(4(3(4(x1)))) #117: #4(1(5(5(0(4(x1)))))) -> #4(3(4(x1))) #118: #2(5(5(x1))) -> #4(2(5(4(4(0(0(1(1(2(x1)))))))))) #119: #2(5(5(x1))) -> #2(5(4(4(0(0(1(1(2(x1))))))))) #120: #2(5(5(x1))) -> #5(4(4(0(0(1(1(2(x1)))))))) #121: #2(5(5(x1))) -> #4(4(0(0(1(1(2(x1))))))) #122: #2(5(5(x1))) -> #4(0(0(1(1(2(x1)))))) #123: #2(5(5(x1))) -> #0(0(1(1(2(x1))))) #124: #2(5(5(x1))) -> #0(1(1(2(x1)))) #125: #2(5(5(x1))) -> #1(1(2(x1))) #126: #2(5(5(x1))) -> #1(2(x1)) #127: #2(5(5(x1))) -> #2(x1) #128: #5(5(x1)) -> #0(5(4(0(2(5(4(5(2(1(x1)))))))))) #129: #5(5(x1)) -> #5(4(0(2(5(4(5(2(1(x1))))))))) #130: #5(5(x1)) -> #4(0(2(5(4(5(2(1(x1)))))))) #131: #5(5(x1)) -> #0(2(5(4(5(2(1(x1))))))) #132: #5(5(x1)) -> #2(5(4(5(2(1(x1)))))) #133: #5(5(x1)) -> #5(4(5(2(1(x1))))) #134: #5(5(x1)) -> #4(5(2(1(x1)))) #135: #5(5(x1)) -> #5(2(1(x1))) #136: #5(5(x1)) -> #2(1(x1)) #137: #5(5(x1)) -> #1(x1) #138: #2(5(0(4(x1)))) -> #4(4(3(2(4(4(5(1(0(0(x1)))))))))) #139: #2(5(0(4(x1)))) -> #4(3(2(4(4(5(1(0(0(x1))))))))) #140: #2(5(0(4(x1)))) -> #2(4(4(5(1(0(0(x1))))))) #141: #2(5(0(4(x1)))) -> #4(4(5(1(0(0(x1)))))) #142: #2(5(0(4(x1)))) -> #4(5(1(0(0(x1))))) #143: #2(5(0(4(x1)))) -> #5(1(0(0(x1)))) #144: #2(5(0(4(x1)))) -> #1(0(0(x1))) #145: #2(5(0(4(x1)))) -> #0(0(x1)) #146: #2(5(0(4(x1)))) -> #0(x1) #147: #1(2(4(5(2(4(x1)))))) -> #5(3(0(4(0(3(1(3(x1)))))))) #148: #1(2(4(5(2(4(x1)))))) -> #0(4(0(3(1(3(x1)))))) #149: #1(2(4(5(2(4(x1)))))) -> #4(0(3(1(3(x1))))) #150: #1(2(4(5(2(4(x1)))))) -> #0(3(1(3(x1)))) #151: #1(2(4(5(2(4(x1)))))) -> #1(3(x1)) #152: #5(2(4(x1))) -> #0(5(0(2(3(3(4(2(4(2(x1)))))))))) #153: #5(2(4(x1))) -> #5(0(2(3(3(4(2(4(2(x1))))))))) #154: #5(2(4(x1))) -> #0(2(3(3(4(2(4(2(x1)))))))) #155: #5(2(4(x1))) -> #2(3(3(4(2(4(2(x1))))))) #156: #5(2(4(x1))) -> #4(2(4(2(x1)))) #157: #5(2(4(x1))) -> #2(4(2(x1))) #158: #5(2(4(x1))) -> #4(2(x1)) #159: #5(2(4(x1))) -> #2(x1) #160: #5(2(5(5(0(4(x1)))))) -> #0(4(2(3(3(5(2(1(4(4(x1)))))))))) #161: #5(2(5(5(0(4(x1)))))) -> #4(2(3(3(5(2(1(4(4(x1))))))))) #162: #5(2(5(5(0(4(x1)))))) -> #2(3(3(5(2(1(4(4(x1)))))))) #163: #5(2(5(5(0(4(x1)))))) -> #5(2(1(4(4(x1))))) #164: #5(2(5(5(0(4(x1)))))) -> #2(1(4(4(x1)))) #165: #5(2(5(5(0(4(x1)))))) -> #1(4(4(x1))) #166: #5(2(5(5(0(4(x1)))))) -> #4(4(x1)) Number of SCCs: 2, DPs: 8 SCC { #17 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... succeeded. #0 w: 0 1 w: max(x1 - 125653, 0) 4 w: 354872 5 w: max(x1 + 208436, 0) 3 w: max(x1 - 88718, 0) #2 w: 0 #4 w: max(x1 - 1, 0) 0 w: max(x1 - 88718, 0) #5 w: max(x1 + 1, 0) 2 w: 354872 #1 w: 0 USABLE RULES: { 3 8..12 14..17 20 21 } Removed DPs: #17 Number of SCCs: 1, DPs: 7 SCC { #9 #28 #46 #90 #91 #103 #127 } POLO(Sum)... succeeded. #0 w: 0 1 w: x1 4 w: 3 5 w: x1 + 1 3 w: 0 #2 w: x1 + 3 #4 w: x1 + 1 0 w: 1 #5 w: x1 2 w: x1 + 1 #1 w: 0 USABLE RULES: { 1..21 } Removed DPs: #28 #46 #90 #91 #127 Number of SCCs: 1, DPs: 2 SCC { #9 #103 } POLO(Sum)... succeeded. #0 w: 0 1 w: 84765 4 w: x1 5 w: x1 + 28255 3 w: 56511 #2 w: 3 #4 w: x1 0 w: 113022 #5 w: x1 + 397 2 w: 113418 #1 w: 0 USABLE RULES: { 3 4 8..12 14..18 20 21 } Removed DPs: #9 #103 Number of SCCs: 0, DPs: 0