YES Input TRS: 1: 0(0(1(2(x1)))) -> 2(3(1(0(0(x1))))) 2: 0(0(1(2(x1)))) -> 3(1(0(0(2(x1))))) 3: 0(0(1(2(x1)))) -> 0(0(2(3(1(1(x1)))))) 4: 0(1(0(4(x1)))) -> 3(1(4(0(0(x1))))) 5: 0(1(0(4(x1)))) -> 3(4(0(0(3(1(x1)))))) 6: 0(1(0(4(x1)))) -> 4(3(1(0(5(0(x1)))))) 7: 0(1(0(4(x1)))) -> 5(0(4(3(1(0(x1)))))) 8: 0(1(0(5(x1)))) -> 3(5(3(1(0(0(x1)))))) 9: 0(1(0(5(x1)))) -> 5(3(1(0(0(2(x1)))))) 10: 0(1(4(2(x1)))) -> 2(3(1(4(0(x1))))) 11: 0(1(4(2(x1)))) -> 4(0(3(1(2(4(x1)))))) 12: 0(1(4(2(x1)))) -> 4(3(1(1(0(2(x1)))))) 13: 0(5(0(4(x1)))) -> 4(0(0(3(5(x1))))) 14: 0(5(0(4(x1)))) -> 5(0(0(3(4(x1))))) 15: 0(5(0(5(x1)))) -> 3(5(2(0(0(5(x1)))))) 16: 0(5(0(5(x1)))) -> 5(3(5(4(0(0(x1)))))) 17: 0(5(0(5(x1)))) -> 5(5(3(4(0(0(x1)))))) 18: 2(0(1(2(x1)))) -> 0(2(4(1(2(x1))))) 19: 2(0(1(2(x1)))) -> 2(5(0(2(2(1(x1)))))) 20: 2(0(1(2(x1)))) -> 3(1(3(2(2(0(x1)))))) 21: 2(0(4(2(x1)))) -> 4(0(2(2(1(x1))))) 22: 2(0(4(2(x1)))) -> 4(0(2(1(2(1(x1)))))) 23: 2(0(5(2(x1)))) -> 0(2(1(5(2(2(x1)))))) 24: 3(0(4(2(x1)))) -> 0(3(4(1(1(2(x1)))))) 25: 3(0(4(2(x1)))) -> 4(3(3(1(0(2(x1)))))) 26: 0(0(1(2(2(x1))))) -> 0(0(2(1(2(1(x1)))))) 27: 0(0(1(3(2(x1))))) -> 0(3(1(2(0(4(x1)))))) 28: 0(0(1(3(2(x1))))) -> 2(5(0(3(1(0(x1)))))) 29: 0(0(5(2(2(x1))))) -> 0(0(2(5(2(1(x1)))))) 30: 0(1(0(5(2(x1))))) -> 0(2(1(0(3(5(x1)))))) 31: 0(1(0(5(5(x1))))) -> 1(3(5(0(0(5(x1)))))) 32: 0(1(2(0(5(x1))))) -> 4(0(5(2(1(0(x1)))))) 33: 0(1(3(0(4(x1))))) -> 1(0(3(4(4(0(x1)))))) 34: 0(1(3(4(2(x1))))) -> 4(2(1(0(3(4(x1)))))) 35: 0(1(4(2(2(x1))))) -> 1(1(0(2(4(2(x1)))))) 36: 0(1(4(2(4(x1))))) -> 4(0(2(3(1(4(x1)))))) 37: 0(1(4(3(2(x1))))) -> 3(1(2(0(4(4(x1)))))) 38: 0(3(0(0(5(x1))))) -> 5(3(1(0(0(0(x1)))))) 39: 0(4(1(0(4(x1))))) -> 4(0(2(1(4(0(x1)))))) 40: 0(4(3(2(2(x1))))) -> 4(2(0(3(5(2(x1)))))) 41: 0(5(1(0(4(x1))))) -> 5(2(4(1(0(0(x1)))))) 42: 0(5(1(4(2(x1))))) -> 4(0(3(5(1(2(x1)))))) 43: 2(1(0(1(2(x1))))) -> 2(1(1(0(2(3(x1)))))) 44: 2(4(0(5(2(x1))))) -> 0(4(2(3(5(2(x1)))))) 45: 3(0(0(1(2(x1))))) -> 0(3(5(1(0(2(x1)))))) 46: 3(0(0(5(2(x1))))) -> 2(0(0(3(5(1(x1)))))) 47: 3(0(5(4(2(x1))))) -> 4(0(3(5(2(1(x1)))))) 48: 3(2(0(1(2(x1))))) -> 2(1(3(1(0(2(x1)))))) 49: 3(2(0(5(2(x1))))) -> 2(0(2(3(4(5(x1)))))) 50: 3(2(0(5(2(x1))))) -> 5(3(0(2(2(2(x1)))))) Number of strict rules: 50 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #0(0(1(2(x1)))) -> #3(1(0(0(2(x1))))) #2: #0(0(1(2(x1)))) -> #0(0(2(x1))) #3: #0(0(1(2(x1)))) -> #0(2(x1)) #4: #2(1(0(1(2(x1))))) -> #2(1(1(0(2(3(x1)))))) #5: #2(1(0(1(2(x1))))) -> #0(2(3(x1))) #6: #2(1(0(1(2(x1))))) -> #2(3(x1)) #7: #2(1(0(1(2(x1))))) -> #3(x1) #8: #0(0(5(2(2(x1))))) -> #0(0(2(5(2(1(x1)))))) #9: #0(0(5(2(2(x1))))) -> #0(2(5(2(1(x1))))) #10: #0(0(5(2(2(x1))))) -> #2(5(2(1(x1)))) #11: #0(0(5(2(2(x1))))) -> #2(1(x1)) #12: #0(1(4(2(2(x1))))) -> #0(2(4(2(x1)))) #13: #0(1(4(2(2(x1))))) -> #2(4(2(x1))) #14: #3(0(0(5(2(x1))))) -> #2(0(0(3(5(1(x1)))))) #15: #3(0(0(5(2(x1))))) -> #0(0(3(5(1(x1))))) #16: #3(0(0(5(2(x1))))) -> #0(3(5(1(x1)))) #17: #3(0(0(5(2(x1))))) -> #3(5(1(x1))) #18: #0(5(1(4(2(x1))))) -> #0(3(5(1(2(x1))))) #19: #0(5(1(4(2(x1))))) -> #3(5(1(2(x1)))) #20: #0(5(1(0(4(x1))))) -> #2(4(1(0(0(x1))))) #21: #0(5(1(0(4(x1))))) -> #0(0(x1)) #22: #0(5(1(0(4(x1))))) -> #0(x1) #23: #0(1(4(3(2(x1))))) -> #3(1(2(0(4(4(x1)))))) #24: #0(1(4(3(2(x1))))) -> #2(0(4(4(x1)))) #25: #0(1(4(3(2(x1))))) -> #0(4(4(x1))) #26: #3(0(5(4(2(x1))))) -> #0(3(5(2(1(x1))))) #27: #3(0(5(4(2(x1))))) -> #3(5(2(1(x1)))) #28: #3(0(5(4(2(x1))))) -> #2(1(x1)) #29: #3(2(0(1(2(x1))))) -> #2(1(3(1(0(2(x1)))))) #30: #3(2(0(1(2(x1))))) -> #3(1(0(2(x1)))) #31: #3(2(0(1(2(x1))))) -> #0(2(x1)) #32: #0(3(0(0(5(x1))))) -> #3(1(0(0(0(x1))))) #33: #0(3(0(0(5(x1))))) -> #0(0(0(x1))) #34: #0(3(0(0(5(x1))))) -> #0(0(x1)) #35: #0(3(0(0(5(x1))))) -> #0(x1) #36: #0(1(0(4(x1)))) -> #3(1(0(5(0(x1))))) #37: #0(1(0(4(x1)))) -> #0(5(0(x1))) #38: #0(1(0(4(x1)))) -> #0(x1) #39: #0(4(3(2(2(x1))))) -> #2(0(3(5(2(x1))))) #40: #0(4(3(2(2(x1))))) -> #0(3(5(2(x1)))) #41: #0(4(3(2(2(x1))))) -> #3(5(2(x1))) #42: #0(5(0(4(x1)))) -> #0(0(3(5(x1)))) #43: #0(5(0(4(x1)))) -> #0(3(5(x1))) #44: #0(5(0(4(x1)))) -> #3(5(x1)) #45: #0(1(0(5(x1)))) -> #3(1(0(0(2(x1))))) #46: #0(1(0(5(x1)))) -> #0(0(2(x1))) #47: #0(1(0(5(x1)))) -> #0(2(x1)) #48: #0(1(0(5(x1)))) -> #2(x1) #49: #0(1(4(2(x1)))) -> #0(3(1(2(4(x1))))) #50: #0(1(4(2(x1)))) -> #3(1(2(4(x1)))) #51: #0(1(4(2(x1)))) -> #2(4(x1)) #52: #3(0(4(2(x1)))) -> #0(3(4(1(1(2(x1)))))) #53: #3(0(4(2(x1)))) -> #3(4(1(1(2(x1))))) #54: #2(0(5(2(x1)))) -> #0(2(1(5(2(2(x1)))))) #55: #2(0(5(2(x1)))) -> #2(1(5(2(2(x1))))) #56: #2(0(5(2(x1)))) -> #2(2(x1)) #57: #3(0(0(1(2(x1))))) -> #0(3(5(1(0(2(x1)))))) #58: #3(0(0(1(2(x1))))) -> #3(5(1(0(2(x1))))) #59: #3(0(0(1(2(x1))))) -> #0(2(x1)) #60: #0(1(4(2(x1)))) -> #3(1(1(0(2(x1))))) #61: #0(1(4(2(x1)))) -> #0(2(x1)) #62: #0(1(0(5(5(x1))))) -> #3(5(0(0(5(x1))))) #63: #0(1(0(5(5(x1))))) -> #0(0(5(x1))) #64: #0(1(0(5(5(x1))))) -> #0(5(x1)) #65: #0(5(0(4(x1)))) -> #0(0(3(4(x1)))) #66: #0(5(0(4(x1)))) -> #0(3(4(x1))) #67: #0(5(0(4(x1)))) -> #3(4(x1)) #68: #0(1(0(5(2(x1))))) -> #0(2(1(0(3(5(x1)))))) #69: #0(1(0(5(2(x1))))) -> #2(1(0(3(5(x1))))) #70: #0(1(0(5(2(x1))))) -> #0(3(5(x1))) #71: #0(1(0(5(2(x1))))) -> #3(5(x1)) #72: #3(2(0(5(2(x1))))) -> #2(0(2(3(4(5(x1)))))) #73: #3(2(0(5(2(x1))))) -> #0(2(3(4(5(x1))))) #74: #3(2(0(5(2(x1))))) -> #2(3(4(5(x1)))) #75: #3(2(0(5(2(x1))))) -> #3(4(5(x1))) #76: #3(0(4(2(x1)))) -> #3(3(1(0(2(x1))))) #77: #3(0(4(2(x1)))) -> #3(1(0(2(x1)))) #78: #3(0(4(2(x1)))) -> #0(2(x1)) #79: #2(0(1(2(x1)))) -> #3(1(3(2(2(0(x1)))))) #80: #2(0(1(2(x1)))) -> #3(2(2(0(x1)))) #81: #2(0(1(2(x1)))) -> #2(2(0(x1))) #82: #2(0(1(2(x1)))) -> #2(0(x1)) #83: #2(0(1(2(x1)))) -> #0(x1) #84: #0(1(0(4(x1)))) -> #0(4(3(1(0(x1))))) #85: #0(1(0(4(x1)))) -> #3(1(0(x1))) #86: #0(1(0(4(x1)))) -> #0(x1) #87: #0(4(1(0(4(x1))))) -> #0(2(1(4(0(x1))))) #88: #0(4(1(0(4(x1))))) -> #2(1(4(0(x1)))) #89: #0(4(1(0(4(x1))))) -> #0(x1) #90: #0(1(4(2(x1)))) -> #2(3(1(4(0(x1))))) #91: #0(1(4(2(x1)))) -> #3(1(4(0(x1)))) #92: #0(1(4(2(x1)))) -> #0(x1) #93: #0(1(3(0(4(x1))))) -> #0(3(4(4(0(x1))))) #94: #0(1(3(0(4(x1))))) -> #3(4(4(0(x1)))) #95: #0(1(3(0(4(x1))))) -> #0(x1) #96: #0(1(0(4(x1)))) -> #3(4(0(0(3(1(x1)))))) #97: #0(1(0(4(x1)))) -> #0(0(3(1(x1)))) #98: #0(1(0(4(x1)))) -> #0(3(1(x1))) #99: #0(1(0(4(x1)))) -> #3(1(x1)) #100: #2(4(0(5(2(x1))))) -> #0(4(2(3(5(2(x1)))))) #101: #2(4(0(5(2(x1))))) -> #2(3(5(2(x1)))) #102: #2(4(0(5(2(x1))))) -> #3(5(2(x1))) #103: #0(0(1(3(2(x1))))) -> #2(5(0(3(1(0(x1)))))) #104: #0(0(1(3(2(x1))))) -> #0(3(1(0(x1)))) #105: #0(0(1(3(2(x1))))) -> #3(1(0(x1))) #106: #0(0(1(3(2(x1))))) -> #0(x1) #107: #2(0(4(2(x1)))) -> #0(2(1(2(1(x1))))) #108: #2(0(4(2(x1)))) -> #2(1(2(1(x1)))) #109: #2(0(4(2(x1)))) -> #2(1(x1)) #110: #0(1(3(4(2(x1))))) -> #2(1(0(3(4(x1))))) #111: #0(1(3(4(2(x1))))) -> #0(3(4(x1))) #112: #0(1(3(4(2(x1))))) -> #3(4(x1)) #113: #0(0(1(3(2(x1))))) -> #0(3(1(2(0(4(x1)))))) #114: #0(0(1(3(2(x1))))) -> #3(1(2(0(4(x1))))) #115: #0(0(1(3(2(x1))))) -> #2(0(4(x1))) #116: #0(0(1(3(2(x1))))) -> #0(4(x1)) #117: #0(5(0(5(x1)))) -> #3(4(0(0(x1)))) #118: #0(5(0(5(x1)))) -> #0(0(x1)) #119: #0(5(0(5(x1)))) -> #0(x1) #120: #0(1(2(0(5(x1))))) -> #0(5(2(1(0(x1))))) #121: #0(1(2(0(5(x1))))) -> #2(1(0(x1))) #122: #0(1(2(0(5(x1))))) -> #0(x1) #123: #2(0(1(2(x1)))) -> #2(5(0(2(2(1(x1)))))) #124: #2(0(1(2(x1)))) -> #0(2(2(1(x1)))) #125: #2(0(1(2(x1)))) -> #2(2(1(x1))) #126: #2(0(1(2(x1)))) -> #2(1(x1)) #127: #0(0(1(2(2(x1))))) -> #0(0(2(1(2(1(x1)))))) #128: #0(0(1(2(2(x1))))) -> #0(2(1(2(1(x1))))) #129: #0(0(1(2(2(x1))))) -> #2(1(2(1(x1)))) #130: #0(0(1(2(2(x1))))) -> #2(1(x1)) #131: #0(1(4(2(4(x1))))) -> #0(2(3(1(4(x1))))) #132: #0(1(4(2(4(x1))))) -> #2(3(1(4(x1)))) #133: #0(1(4(2(4(x1))))) -> #3(1(4(x1))) #134: #2(0(4(2(x1)))) -> #0(2(2(1(x1)))) #135: #2(0(4(2(x1)))) -> #2(2(1(x1))) #136: #2(0(4(2(x1)))) -> #2(1(x1)) #137: #0(5(0(5(x1)))) -> #3(5(4(0(0(x1))))) #138: #0(5(0(5(x1)))) -> #0(0(x1)) #139: #0(5(0(5(x1)))) -> #0(x1) #140: #0(0(1(2(x1)))) -> #0(0(2(3(1(1(x1)))))) #141: #0(0(1(2(x1)))) -> #0(2(3(1(1(x1))))) #142: #0(0(1(2(x1)))) -> #2(3(1(1(x1)))) #143: #0(0(1(2(x1)))) -> #3(1(1(x1))) #144: #0(0(1(2(x1)))) -> #2(3(1(0(0(x1))))) #145: #0(0(1(2(x1)))) -> #3(1(0(0(x1)))) #146: #0(0(1(2(x1)))) -> #0(0(x1)) #147: #0(0(1(2(x1)))) -> #0(x1) #148: #0(1(0(5(x1)))) -> #3(5(3(1(0(0(x1)))))) #149: #0(1(0(5(x1)))) -> #3(1(0(0(x1)))) #150: #0(1(0(5(x1)))) -> #0(0(x1)) #151: #0(1(0(5(x1)))) -> #0(x1) #152: #0(5(0(5(x1)))) -> #3(5(2(0(0(5(x1)))))) #153: #0(5(0(5(x1)))) -> #2(0(0(5(x1)))) #154: #0(5(0(5(x1)))) -> #0(0(5(x1))) #155: #0(1(0(4(x1)))) -> #3(1(4(0(0(x1))))) #156: #0(1(0(4(x1)))) -> #0(0(x1)) #157: #0(1(0(4(x1)))) -> #0(x1) #158: #3(2(0(5(2(x1))))) -> #3(0(2(2(2(x1))))) #159: #3(2(0(5(2(x1))))) -> #0(2(2(2(x1)))) #160: #3(2(0(5(2(x1))))) -> #2(2(2(x1))) #161: #3(2(0(5(2(x1))))) -> #2(2(x1)) #162: #2(0(1(2(x1)))) -> #0(2(4(1(2(x1))))) #163: #2(0(1(2(x1)))) -> #2(4(1(2(x1)))) Number of SCCs: 2, DPs: 32 SCC { #7 #28 #109 #136 #161 } POLO(Sum)... succeeded. #0 w: 0 1 w: x1 4 w: x1 5 w: x1 3 w: x1 #2 w: x1 0 w: x1 + 1 #3 w: x1 2 w: x1 USABLE RULES: { 1..50 } Removed DPs: #7 #28 #109 #136 #161 Number of SCCs: 1, DPs: 27 SCC { #21 #22 #34 #35 #37 #38 #48 #64 #82 #83 #86 #89 #92 #95 #106 #116 #118 #119 #122 #138 #139 #146 #147 #150 #151 #156 #157 } POLO(Sum)... succeeded. #0 w: x1 1 w: x1 4 w: x1 5 w: x1 3 w: x1 #2 w: x1 0 w: x1 + 1 #3 w: 0 2 w: x1 USABLE RULES: { 1..50 } Removed DPs: #22 #34 #35 #38 #48 #64 #83 #86 #89 #95 #106 #116 #119 #122 #139 #147 #151 #157 Number of SCCs: 3, DPs: 3 SCC { #92 } POLO(Sum)... POLO(max)... succeeded. #0 w: x1 1 w: x1 4 w: x1 5 w: 0 3 w: 0 #2 w: 0 0 w: 0 #3 w: 0 2 w: x1 + 1 USABLE RULES: { } Removed DPs: #92 Number of SCCs: 2, DPs: 2 SCC { #82 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... succeeded. #0 w: [0;0] 1 w: [0,0;1,0] * x1 + [1;131642] 4 w: [58068;86387] 5 w: [480;143975] 3 w: [1,0;1,0] * x1 + [86388;58065] #2 w: [0,1;1,1] * x1 0 w: [0,0;0,1] * x1 + [144456;13921] #3 w: [0;0] 2 w: [1,1;1,0] * x1 + [1;45254] USABLE RULES: { 1..50 } Removed DPs: #82 Number of SCCs: 1, DPs: 1 SCC { #146 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... succeeded. #0 w: [0,1;1,1] * x1 1 w: [0,0;1,0] * x1 + [1;6] 4 w: [4;4] 5 w: [1;5] 3 w: [1,0;1,0] * x1 + [5;1] #2 w: [0,1;1,1] * x1 0 w: [0,0;0,1] * x1 + [9;1] #3 w: [0;0] 2 w: [1,1;1,0] * x1 + [1;1] USABLE RULES: { 1..50 } Removed DPs: #146 Number of SCCs: 0, DPs: 0