YES Input TRS: 1: 0(1(2(3(x1)))) -> 2(0(3(1(2(x1))))) 2: 0(1(2(3(x1)))) -> 2(0(3(1(3(x1))))) 3: 0(1(2(3(x1)))) -> 2(0(3(2(1(x1))))) 4: 0(1(2(3(x1)))) -> 2(1(0(3(0(x1))))) 5: 0(1(2(3(x1)))) -> 2(1(3(0(2(x1))))) 6: 0(1(2(3(x1)))) -> 2(1(4(3(0(x1))))) 7: 0(1(2(3(x1)))) -> 2(3(0(2(1(x1))))) 8: 0(1(2(3(x1)))) -> 2(0(3(2(1(1(x1)))))) 9: 0(1(2(3(x1)))) -> 2(0(3(3(2(1(x1)))))) 10: 0(1(2(3(x1)))) -> 2(1(3(0(3(0(x1)))))) 11: 0(1(5(3(x1)))) -> 2(1(0(3(3(5(x1)))))) 12: 0(1(5(3(x1)))) -> 2(1(0(3(4(5(x1)))))) 13: 0(5(2(3(x1)))) -> 2(0(3(3(5(x1))))) 14: 0(5(2(3(x1)))) -> 2(0(0(3(5(3(x1)))))) 15: 0(0(1(2(3(x1))))) -> 0(2(0(3(1(0(x1)))))) 16: 0(0(1(2(3(x1))))) -> 2(1(1(3(0(0(x1)))))) 17: 0(0(4(2(3(x1))))) -> 0(3(4(0(3(2(x1)))))) 18: 0(0(4(2(3(x1))))) -> 3(0(0(2(4(4(x1)))))) 19: 0(0(5(2(3(x1))))) -> 0(3(5(2(4(0(x1)))))) 20: 0(1(0(2(3(x1))))) -> 3(2(4(1(0(0(x1)))))) 21: 0(1(0(5(3(x1))))) -> 0(1(1(5(0(3(x1)))))) 22: 0(1(0(5(3(x1))))) -> 1(5(0(0(3(4(x1)))))) 23: 0(1(2(1(3(x1))))) -> 2(1(0(0(3(1(x1)))))) 24: 0(1(2(2(3(x1))))) -> 2(0(3(3(1(2(x1)))))) 25: 0(1(2(3(3(x1))))) -> 2(0(3(3(4(1(x1)))))) 26: 0(1(2(5(3(x1))))) -> 2(5(0(3(1(0(x1)))))) 27: 0(4(5(5(3(x1))))) -> 5(0(3(4(1(5(x1)))))) 28: 0(4(5(5(3(x1))))) -> 5(4(0(3(3(5(x1)))))) 29: 0(5(2(1(3(x1))))) -> 2(1(0(3(3(5(x1)))))) 30: 0(5(4(2(3(x1))))) -> 2(0(3(4(5(1(x1)))))) 31: 1(0(0(5(3(x1))))) -> 0(3(1(3(5(0(x1)))))) 32: 1(0(1(2(3(x1))))) -> 1(1(1(2(3(0(x1)))))) 33: 1(0(1(2(3(x1))))) -> 1(2(0(3(5(1(x1)))))) 34: 1(5(3(5(3(x1))))) -> 5(5(0(3(3(1(x1)))))) 35: 4(0(1(2(3(x1))))) -> 2(1(4(4(0(3(x1)))))) 36: 4(0(1(2(3(x1))))) -> 4(3(2(1(0(0(x1)))))) 37: 5(0(0(5(3(x1))))) -> 3(0(3(5(5(0(x1)))))) 38: 5(0(1(2(3(x1))))) -> 3(0(3(1(2(5(x1)))))) 39: 5(0(1(2(3(x1))))) -> 4(5(3(0(2(1(x1)))))) 40: 5(0(1(2(3(x1))))) -> 5(1(0(3(0(2(x1)))))) 41: 5(0(1(2(3(x1))))) -> 5(1(0(3(1(2(x1)))))) 42: 5(0(4(2(3(x1))))) -> 0(2(4(1(5(3(x1)))))) 43: 5(0(4(2(3(x1))))) -> 0(3(3(5(2(4(x1)))))) 44: 5(0(4(2(3(x1))))) -> 2(4(4(0(3(5(x1)))))) 45: 5(0(5(2(3(x1))))) -> 5(0(3(5(4(2(x1)))))) 46: 5(3(0(5(3(x1))))) -> 5(5(3(0(0(3(x1)))))) 47: 5(3(1(2(3(x1))))) -> 2(0(3(1(5(3(x1)))))) 48: 5(3(1(2(3(x1))))) -> 3(3(0(2(1(5(x1)))))) Number of strict rules: 48 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #0(1(2(3(x1)))) -> #0(3(1(3(x1)))) #2: #0(1(2(3(x1)))) -> #1(3(x1)) #3: #5(0(4(2(3(x1))))) -> #0(3(3(5(2(4(x1)))))) #4: #5(0(4(2(3(x1))))) -> #5(2(4(x1))) #5: #5(0(4(2(3(x1))))) -> #4(x1) #6: #0(5(2(1(3(x1))))) -> #1(0(3(3(5(x1))))) #7: #0(5(2(1(3(x1))))) -> #0(3(3(5(x1)))) #8: #0(5(2(1(3(x1))))) -> #5(x1) #9: #4(0(1(2(3(x1))))) -> #1(4(4(0(3(x1))))) #10: #4(0(1(2(3(x1))))) -> #4(4(0(3(x1)))) #11: #4(0(1(2(3(x1))))) -> #4(0(3(x1))) #12: #4(0(1(2(3(x1))))) -> #0(3(x1)) #13: #5(3(0(5(3(x1))))) -> #5(5(3(0(0(3(x1)))))) #14: #5(3(0(5(3(x1))))) -> #5(3(0(0(3(x1))))) #15: #5(3(0(5(3(x1))))) -> #0(0(3(x1))) #16: #5(3(0(5(3(x1))))) -> #0(3(x1)) #17: #5(0(4(2(3(x1))))) -> #0(2(4(1(5(3(x1)))))) #18: #5(0(4(2(3(x1))))) -> #4(1(5(3(x1)))) #19: #5(0(4(2(3(x1))))) -> #1(5(3(x1))) #20: #5(0(4(2(3(x1))))) -> #5(3(x1)) #21: #5(0(1(2(3(x1))))) -> #5(1(0(3(1(2(x1)))))) #22: #5(0(1(2(3(x1))))) -> #1(0(3(1(2(x1))))) #23: #5(0(1(2(3(x1))))) -> #0(3(1(2(x1)))) #24: #5(0(1(2(3(x1))))) -> #1(2(x1)) #25: #5(0(0(5(3(x1))))) -> #0(3(5(5(0(x1))))) #26: #5(0(0(5(3(x1))))) -> #5(5(0(x1))) #27: #5(0(0(5(3(x1))))) -> #5(0(x1)) #28: #5(0(0(5(3(x1))))) -> #0(x1) #29: #5(3(1(2(3(x1))))) -> #0(3(1(5(3(x1))))) #30: #5(3(1(2(3(x1))))) -> #1(5(3(x1))) #31: #5(3(1(2(3(x1))))) -> #5(3(x1)) #32: #5(3(1(2(3(x1))))) -> #0(2(1(5(x1)))) #33: #5(3(1(2(3(x1))))) -> #1(5(x1)) #34: #5(3(1(2(3(x1))))) -> #5(x1) #35: #5(0(1(2(3(x1))))) -> #0(3(1(2(5(x1))))) #36: #5(0(1(2(3(x1))))) -> #1(2(5(x1))) #37: #5(0(1(2(3(x1))))) -> #5(x1) #38: #0(1(2(3(x1)))) -> #1(4(3(0(x1)))) #39: #0(1(2(3(x1)))) -> #4(3(0(x1))) #40: #0(1(2(3(x1)))) -> #0(x1) #41: #5(0(1(2(3(x1))))) -> #5(1(0(3(0(2(x1)))))) #42: #5(0(1(2(3(x1))))) -> #1(0(3(0(2(x1))))) #43: #5(0(1(2(3(x1))))) -> #0(3(0(2(x1)))) #44: #5(0(1(2(3(x1))))) -> #0(2(x1)) #45: #0(5(2(3(x1)))) -> #0(3(3(5(x1)))) #46: #0(5(2(3(x1)))) -> #5(x1) #47: #0(1(2(3(x1)))) -> #0(3(3(2(1(x1))))) #48: #0(1(2(3(x1)))) -> #1(x1) #49: #0(1(5(3(x1)))) -> #1(0(3(3(5(x1))))) #50: #0(1(5(3(x1)))) -> #0(3(3(5(x1)))) #51: #0(1(5(3(x1)))) -> #5(x1) #52: #0(1(2(2(3(x1))))) -> #0(3(3(1(2(x1))))) #53: #0(1(2(2(3(x1))))) -> #1(2(x1)) #54: #0(1(2(1(3(x1))))) -> #1(0(0(3(1(x1))))) #55: #0(1(2(1(3(x1))))) -> #0(0(3(1(x1)))) #56: #0(1(2(1(3(x1))))) -> #0(3(1(x1))) #57: #0(1(2(1(3(x1))))) -> #1(x1) #58: #5(0(5(2(3(x1))))) -> #5(0(3(5(4(2(x1)))))) #59: #5(0(5(2(3(x1))))) -> #0(3(5(4(2(x1))))) #60: #5(0(5(2(3(x1))))) -> #5(4(2(x1))) #61: #5(0(5(2(3(x1))))) -> #4(2(x1)) #62: #0(1(5(3(x1)))) -> #1(0(3(4(5(x1))))) #63: #0(1(5(3(x1)))) -> #0(3(4(5(x1)))) #64: #0(1(5(3(x1)))) -> #4(5(x1)) #65: #0(1(5(3(x1)))) -> #5(x1) #66: #1(0(0(5(3(x1))))) -> #0(3(1(3(5(0(x1)))))) #67: #1(0(0(5(3(x1))))) -> #1(3(5(0(x1)))) #68: #1(0(0(5(3(x1))))) -> #5(0(x1)) #69: #1(0(0(5(3(x1))))) -> #0(x1) #70: #0(5(2(3(x1)))) -> #0(0(3(5(3(x1))))) #71: #0(5(2(3(x1)))) -> #0(3(5(3(x1)))) #72: #0(5(2(3(x1)))) -> #5(3(x1)) #73: #0(5(4(2(3(x1))))) -> #0(3(4(5(1(x1))))) #74: #0(5(4(2(3(x1))))) -> #4(5(1(x1))) #75: #0(5(4(2(3(x1))))) -> #5(1(x1)) #76: #0(5(4(2(3(x1))))) -> #1(x1) #77: #0(1(2(3(3(x1))))) -> #0(3(3(4(1(x1))))) #78: #0(1(2(3(3(x1))))) -> #4(1(x1)) #79: #0(1(2(3(3(x1))))) -> #1(x1) #80: #0(1(0(2(3(x1))))) -> #4(1(0(0(x1)))) #81: #0(1(0(2(3(x1))))) -> #1(0(0(x1))) #82: #0(1(0(2(3(x1))))) -> #0(0(x1)) #83: #0(1(0(2(3(x1))))) -> #0(x1) #84: #0(1(2(3(x1)))) -> #0(2(1(x1))) #85: #0(1(2(3(x1)))) -> #1(x1) #86: #5(0(1(2(3(x1))))) -> #4(5(3(0(2(1(x1)))))) #87: #5(0(1(2(3(x1))))) -> #5(3(0(2(1(x1))))) #88: #5(0(1(2(3(x1))))) -> #0(2(1(x1))) #89: #5(0(1(2(3(x1))))) -> #1(x1) #90: #0(1(2(3(x1)))) -> #1(3(0(3(0(x1))))) #91: #0(1(2(3(x1)))) -> #0(3(0(x1))) #92: #0(1(2(3(x1)))) -> #0(x1) #93: #1(0(1(2(3(x1))))) -> #1(2(0(3(5(1(x1)))))) #94: #1(0(1(2(3(x1))))) -> #0(3(5(1(x1)))) #95: #1(0(1(2(3(x1))))) -> #5(1(x1)) #96: #1(0(1(2(3(x1))))) -> #1(x1) #97: #0(1(2(3(x1)))) -> #1(3(0(2(x1)))) #98: #0(1(2(3(x1)))) -> #0(2(x1)) #99: #5(0(4(2(3(x1))))) -> #4(4(0(3(5(x1))))) #100: #5(0(4(2(3(x1))))) -> #4(0(3(5(x1)))) #101: #5(0(4(2(3(x1))))) -> #0(3(5(x1))) #102: #5(0(4(2(3(x1))))) -> #5(x1) #103: #0(4(5(5(3(x1))))) -> #5(4(0(3(3(5(x1)))))) #104: #0(4(5(5(3(x1))))) -> #4(0(3(3(5(x1))))) #105: #0(4(5(5(3(x1))))) -> #0(3(3(5(x1)))) #106: #0(4(5(5(3(x1))))) -> #5(x1) #107: #0(1(0(5(3(x1))))) -> #1(5(0(0(3(4(x1)))))) #108: #0(1(0(5(3(x1))))) -> #5(0(0(3(4(x1))))) #109: #0(1(0(5(3(x1))))) -> #0(0(3(4(x1)))) #110: #0(1(0(5(3(x1))))) -> #0(3(4(x1))) #111: #0(1(0(5(3(x1))))) -> #4(x1) #112: #1(5(3(5(3(x1))))) -> #5(5(0(3(3(1(x1)))))) #113: #1(5(3(5(3(x1))))) -> #5(0(3(3(1(x1))))) #114: #1(5(3(5(3(x1))))) -> #0(3(3(1(x1)))) #115: #1(5(3(5(3(x1))))) -> #1(x1) #116: #0(4(5(5(3(x1))))) -> #5(0(3(4(1(5(x1)))))) #117: #0(4(5(5(3(x1))))) -> #0(3(4(1(5(x1))))) #118: #0(4(5(5(3(x1))))) -> #4(1(5(x1))) #119: #0(4(5(5(3(x1))))) -> #1(5(x1)) #120: #0(4(5(5(3(x1))))) -> #5(x1) #121: #0(0(4(2(3(x1))))) -> #0(3(4(0(3(2(x1)))))) #122: #0(0(4(2(3(x1))))) -> #4(0(3(2(x1)))) #123: #0(0(4(2(3(x1))))) -> #0(3(2(x1))) #124: #1(0(1(2(3(x1))))) -> #1(1(1(2(3(0(x1)))))) #125: #1(0(1(2(3(x1))))) -> #1(1(2(3(0(x1))))) #126: #1(0(1(2(3(x1))))) -> #1(2(3(0(x1)))) #127: #1(0(1(2(3(x1))))) -> #0(x1) #128: #0(0(5(2(3(x1))))) -> #0(3(5(2(4(0(x1)))))) #129: #0(0(5(2(3(x1))))) -> #5(2(4(0(x1)))) #130: #0(0(5(2(3(x1))))) -> #4(0(x1)) #131: #0(0(5(2(3(x1))))) -> #0(x1) #132: #0(1(2(5(3(x1))))) -> #5(0(3(1(0(x1))))) #133: #0(1(2(5(3(x1))))) -> #0(3(1(0(x1)))) #134: #0(1(2(5(3(x1))))) -> #1(0(x1)) #135: #0(1(2(5(3(x1))))) -> #0(x1) #136: #4(0(1(2(3(x1))))) -> #4(3(2(1(0(0(x1)))))) #137: #4(0(1(2(3(x1))))) -> #1(0(0(x1))) #138: #4(0(1(2(3(x1))))) -> #0(0(x1)) #139: #4(0(1(2(3(x1))))) -> #0(x1) #140: #0(1(0(5(3(x1))))) -> #0(1(1(5(0(3(x1)))))) #141: #0(1(0(5(3(x1))))) -> #1(1(5(0(3(x1))))) #142: #0(1(0(5(3(x1))))) -> #1(5(0(3(x1)))) #143: #0(1(0(5(3(x1))))) -> #5(0(3(x1))) #144: #0(1(0(5(3(x1))))) -> #0(3(x1)) #145: #0(0(1(2(3(x1))))) -> #1(1(3(0(0(x1))))) #146: #0(0(1(2(3(x1))))) -> #1(3(0(0(x1)))) #147: #0(0(1(2(3(x1))))) -> #0(0(x1)) #148: #0(0(1(2(3(x1))))) -> #0(x1) #149: #0(1(2(3(x1)))) -> #0(3(2(1(x1)))) #150: #0(1(2(3(x1)))) -> #1(x1) #151: #0(1(2(3(x1)))) -> #0(3(1(2(x1)))) #152: #0(1(2(3(x1)))) -> #1(2(x1)) #153: #0(1(2(3(x1)))) -> #0(3(2(1(1(x1))))) #154: #0(1(2(3(x1)))) -> #1(1(x1)) #155: #0(1(2(3(x1)))) -> #1(x1) #156: #0(0(1(2(3(x1))))) -> #0(2(0(3(1(0(x1)))))) #157: #0(0(1(2(3(x1))))) -> #0(3(1(0(x1)))) #158: #0(0(1(2(3(x1))))) -> #1(0(x1)) #159: #0(0(1(2(3(x1))))) -> #0(x1) #160: #0(1(2(3(x1)))) -> #1(0(3(0(x1)))) #161: #0(1(2(3(x1)))) -> #0(3(0(x1))) #162: #0(1(2(3(x1)))) -> #0(x1) #163: #0(0(4(2(3(x1))))) -> #0(0(2(4(4(x1))))) #164: #0(0(4(2(3(x1))))) -> #0(2(4(4(x1)))) #165: #0(0(4(2(3(x1))))) -> #4(4(x1)) #166: #0(0(4(2(3(x1))))) -> #4(x1) Number of SCCs: 1, DPs: 51 SCC { #5 #8 #19 #20 #27 #28 #30 #31 #33 #34 #37 #40 #46 #48 #51 #57 #65 #68 #69 #72 #76 #79 #81..83 #85 #89 #92 #96 #102 #106 #111 #115 #119 #120 #127 #130 #131 #134 #135 #137..139 #147 #148 #150 #155 #158 #159 #162 #166 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... succeeded. #0 w: [1,1;0,0] * x1 1 w: x1 4 w: [0,0;0,1] * x1 5 w: [1,1;1,1] * x1 + [0;1] 3 w: [1,1;0,0] * x1 #4 w: [1,1;0,0] * x1 0 w: [0,0;0,1] * x1 #5 w: [1,1;0,0] * x1 + [1;0] 2 w: [0,0;1,0] * x1 #1 w: [0,1;0,0] * x1 USABLE RULES: { 1..48 } Removed DPs: #5 #27 #28 #69 #76 #89 #106 #111 #115 #119 #120 #130 #131 Number of SCCs: 2, DPs: 27 SCC { #20 #31 #34 #37 #102 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... succeeded. #0 w: [0;0] 1 w: [1,1;0,0] * x1 + [603965;91552] 4 w: [1,0;0,0] * x1 + [393562;91566] 5 w: [1,1;0,1] * x1 + [733352;37833] 3 w: [0,0;1,1] * x1 + [1;0] #4 w: [0;0] 0 w: [1,0;1,0] * x1 + [0;1] #5 w: [0,1;0,1] * x1 + [1;0] 2 w: [0,1;0,1] * x1 + [210430;0] #1 w: [0;0] USABLE RULES: { 1..48 } Removed DPs: #20 #31 #34 #37 #102 Number of SCCs: 1, DPs: 22 SCC { #40 #48 #57 #79 #82 #83 #85 #92 #96 #127 #134 #135 #138 #139 #147 #148 #150 #155 #158 #159 #162 #166 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... succeeded. #0 w: [1,0;1,1] * x1 + [3;0] 1 w: [1,1;0,0] * x1 4 w: [0,1;0,0] * x1 5 w: [0,0;0,1] * x1 + [1;0] 3 w: [0,0;1,1] * x1 + [0;1] #4 w: [1,1;0,1] * x1 0 w: [1,0;1,0] * x1 #5 w: [1;0] 2 w: [0,1;1,1] * x1 #1 w: [1,1;0,1] * x1 USABLE RULES: { 1..48 } Removed DPs: #40 #48 #57 #79 #82 #83 #85 #92 #96 #127 #134 #135 #138 #139 #147 #148 #150 #155 #158 #159 #162 #166 Number of SCCs: 0, DPs: 0