YES Input TRS: 1: 0(1(2(x1))) -> 1(3(0(2(x1)))) 2: 0(1(2(x1))) -> 3(1(2(0(x1)))) 3: 0(1(2(x1))) -> 2(0(4(1(3(x1))))) 4: 0(1(2(x1))) -> 3(0(2(1(3(x1))))) 5: 0(1(2(x1))) -> 3(3(0(2(1(x1))))) 6: 0(1(2(x1))) -> 1(3(3(0(2(3(x1)))))) 7: 0(1(2(x1))) -> 2(0(4(3(1(3(x1)))))) 8: 0(1(2(x1))) -> 3(0(1(3(1(2(x1)))))) 9: 0(1(2(x1))) -> 3(0(5(3(1(2(x1)))))) 10: 0(5(2(x1))) -> 1(5(0(2(x1)))) 11: 0(5(2(x1))) -> 3(5(0(2(x1)))) 12: 0(5(2(x1))) -> 3(0(5(1(2(x1))))) 13: 0(5(2(x1))) -> 3(5(3(0(2(x1))))) 14: 0(5(2(x1))) -> 1(5(5(3(0(2(x1)))))) 15: 0(5(2(x1))) -> 5(0(4(3(1(2(x1)))))) 16: 1(5(2(x1))) -> 5(3(1(2(x1)))) 17: 1(5(2(x1))) -> 1(5(3(1(2(x1))))) 18: 0(0(5(4(x1)))) -> 5(3(0(4(0(0(x1)))))) 19: 0(1(0(1(x1)))) -> 1(1(3(0(3(0(x1)))))) 20: 0(1(1(2(x1)))) -> 2(1(1(3(0(2(x1)))))) 21: 0(1(2(5(x1)))) -> 3(0(5(1(2(x1))))) 22: 0(1(2(5(x1)))) -> 3(5(3(1(2(0(x1)))))) 23: 0(1(3(2(x1)))) -> 3(0(2(1(3(5(x1)))))) 24: 0(1(4(2(x1)))) -> 3(0(0(4(1(2(x1)))))) 25: 0(1(4(2(x1)))) -> 4(0(1(3(1(2(x1)))))) 26: 0(5(2(4(x1)))) -> 5(5(3(0(2(4(x1)))))) 27: 0(5(2(5(x1)))) -> 0(2(3(5(5(x1))))) 28: 0(5(3(2(x1)))) -> 3(0(2(1(5(x1))))) 29: 0(5(3(2(x1)))) -> 5(3(1(4(0(2(x1)))))) 30: 1(0(3(4(x1)))) -> 1(0(4(1(3(x1))))) 31: 1(5(3(2(x1)))) -> 3(1(3(5(2(x1))))) 32: 5(0(1(2(x1)))) -> 1(5(0(4(1(2(x1)))))) 33: 5(1(0(2(x1)))) -> 3(1(5(0(2(x1))))) 34: 5(1(1(2(x1)))) -> 1(3(5(2(1(3(x1)))))) 35: 5(1(5(2(x1)))) -> 1(3(5(5(2(x1))))) 36: 0(0(1(3(2(x1))))) -> 0(3(1(2(0(3(x1)))))) 37: 0(0(5(3(2(x1))))) -> 0(3(0(3(2(5(x1)))))) 38: 0(1(0(3(4(x1))))) -> 4(0(1(3(0(3(x1)))))) 39: 0(1(0(5(4(x1))))) -> 3(0(4(0(1(5(x1)))))) 40: 0(1(2(4(4(x1))))) -> 0(4(1(2(1(4(x1)))))) 41: 0(1(5(3(2(x1))))) -> 1(2(3(0(4(5(x1)))))) 42: 0(5(4(2(4(x1))))) -> 4(5(3(0(4(2(x1)))))) 43: 0(5(4(4(2(x1))))) -> 0(4(4(3(5(2(x1)))))) 44: 1(0(1(3(4(x1))))) -> 4(1(1(3(0(3(x1)))))) 45: 1(0(3(4(5(x1))))) -> 2(1(3(0(4(5(x1)))))) 46: 1(1(3(4(2(x1))))) -> 2(5(1(3(1(4(x1)))))) 47: 1(5(3(2(2(x1))))) -> 2(3(5(3(1(2(x1)))))) 48: 5(0(5(2(4(x1))))) -> 5(1(5(0(4(2(x1)))))) 49: 5(1(0(5(2(x1))))) -> 1(5(0(2(3(5(x1)))))) 50: 5(1(1(2(1(x1))))) -> 3(1(2(5(1(1(x1)))))) Number of strict rules: 50 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #0(1(2(x1))) -> #1(2(0(x1))) #2: #0(1(2(x1))) -> #0(x1) #3: #0(5(4(4(2(x1))))) -> #0(4(4(3(5(2(x1)))))) #4: #0(5(4(4(2(x1))))) -> #5(2(x1)) #5: #0(5(3(2(x1)))) -> #5(3(1(4(0(2(x1)))))) #6: #0(5(3(2(x1)))) -> #1(4(0(2(x1)))) #7: #0(5(3(2(x1)))) -> #0(2(x1)) #8: #5(1(5(2(x1)))) -> #1(3(5(5(2(x1))))) #9: #5(1(5(2(x1)))) -> #5(5(2(x1))) #10: #1(1(3(4(2(x1))))) -> #5(1(3(1(4(x1))))) #11: #1(1(3(4(2(x1))))) -> #1(3(1(4(x1)))) #12: #1(1(3(4(2(x1))))) -> #1(4(x1)) #13: #0(5(4(2(4(x1))))) -> #5(3(0(4(2(x1))))) #14: #0(5(4(2(4(x1))))) -> #0(4(2(x1))) #15: #0(1(5(3(2(x1))))) -> #1(2(3(0(4(5(x1)))))) #16: #0(1(5(3(2(x1))))) -> #0(4(5(x1))) #17: #0(1(5(3(2(x1))))) -> #5(x1) #18: #0(0(5(3(2(x1))))) -> #0(3(0(3(2(5(x1)))))) #19: #0(0(5(3(2(x1))))) -> #0(3(2(5(x1)))) #20: #0(0(5(3(2(x1))))) -> #5(x1) #21: #1(5(3(2(2(x1))))) -> #5(3(1(2(x1)))) #22: #1(5(3(2(2(x1))))) -> #1(2(x1)) #23: #5(0(5(2(4(x1))))) -> #5(1(5(0(4(2(x1)))))) #24: #5(0(5(2(4(x1))))) -> #1(5(0(4(2(x1))))) #25: #5(0(5(2(4(x1))))) -> #5(0(4(2(x1)))) #26: #5(0(5(2(4(x1))))) -> #0(4(2(x1))) #27: #0(1(0(3(4(x1))))) -> #0(1(3(0(3(x1))))) #28: #0(1(0(3(4(x1))))) -> #1(3(0(3(x1)))) #29: #0(1(0(3(4(x1))))) -> #0(3(x1)) #30: #0(1(2(x1))) -> #1(3(3(0(2(3(x1)))))) #31: #0(1(2(x1))) -> #0(2(3(x1))) #32: #0(1(2(4(4(x1))))) -> #0(4(1(2(1(4(x1)))))) #33: #0(1(2(4(4(x1))))) -> #1(2(1(4(x1)))) #34: #0(1(2(4(4(x1))))) -> #1(4(x1)) #35: #0(5(2(x1))) -> #5(3(0(2(x1)))) #36: #0(5(2(x1))) -> #0(2(x1)) #37: #0(1(2(x1))) -> #0(5(3(1(2(x1))))) #38: #0(1(2(x1))) -> #5(3(1(2(x1)))) #39: #0(5(2(x1))) -> #5(0(2(x1))) #40: #0(5(2(x1))) -> #0(2(x1)) #41: #0(1(4(2(x1)))) -> #0(0(4(1(2(x1))))) #42: #0(1(4(2(x1)))) -> #0(4(1(2(x1)))) #43: #0(1(4(2(x1)))) -> #1(2(x1)) #44: #0(1(3(2(x1)))) -> #0(2(1(3(5(x1))))) #45: #0(1(3(2(x1)))) -> #1(3(5(x1))) #46: #0(1(3(2(x1)))) -> #5(x1) #47: #1(0(3(4(5(x1))))) -> #1(3(0(4(5(x1))))) #48: #1(0(3(4(5(x1))))) -> #0(4(5(x1))) #49: #0(5(2(x1))) -> #0(5(1(2(x1)))) #50: #0(5(2(x1))) -> #5(1(2(x1))) #51: #0(5(2(x1))) -> #1(2(x1)) #52: #1(5(3(2(x1)))) -> #1(3(5(2(x1)))) #53: #1(5(3(2(x1)))) -> #5(2(x1)) #54: #0(5(2(x1))) -> #1(5(5(3(0(2(x1)))))) #55: #0(5(2(x1))) -> #5(5(3(0(2(x1))))) #56: #0(5(2(x1))) -> #5(3(0(2(x1)))) #57: #0(5(2(x1))) -> #0(2(x1)) #58: #1(0(3(4(x1)))) -> #1(0(4(1(3(x1))))) #59: #1(0(3(4(x1)))) -> #0(4(1(3(x1)))) #60: #1(0(3(4(x1)))) -> #1(3(x1)) #61: #5(1(0(5(2(x1))))) -> #1(5(0(2(3(5(x1)))))) #62: #5(1(0(5(2(x1))))) -> #5(0(2(3(5(x1))))) #63: #5(1(0(5(2(x1))))) -> #0(2(3(5(x1)))) #64: #5(1(0(5(2(x1))))) -> #5(x1) #65: #0(1(4(2(x1)))) -> #0(1(3(1(2(x1))))) #66: #0(1(4(2(x1)))) -> #1(3(1(2(x1)))) #67: #0(1(4(2(x1)))) -> #1(2(x1)) #68: #0(1(1(2(x1)))) -> #1(1(3(0(2(x1))))) #69: #0(1(1(2(x1)))) -> #1(3(0(2(x1)))) #70: #0(1(1(2(x1)))) -> #0(2(x1)) #71: #0(1(2(x1))) -> #0(4(3(1(3(x1))))) #72: #0(1(2(x1))) -> #1(3(x1)) #73: #0(1(0(5(4(x1))))) -> #0(4(0(1(5(x1))))) #74: #0(1(0(5(4(x1))))) -> #0(1(5(x1))) #75: #0(1(0(5(4(x1))))) -> #1(5(x1)) #76: #0(1(0(5(4(x1))))) -> #5(x1) #77: #0(5(2(x1))) -> #1(5(0(2(x1)))) #78: #0(5(2(x1))) -> #5(0(2(x1))) #79: #0(5(2(x1))) -> #0(2(x1)) #80: #5(1(0(2(x1)))) -> #1(5(0(2(x1)))) #81: #5(1(0(2(x1)))) -> #5(0(2(x1))) #82: #0(1(2(x1))) -> #0(2(1(x1))) #83: #0(1(2(x1))) -> #1(x1) #84: #1(0(1(3(4(x1))))) -> #1(1(3(0(3(x1))))) #85: #1(0(1(3(4(x1))))) -> #1(3(0(3(x1)))) #86: #1(0(1(3(4(x1))))) -> #0(3(x1)) #87: #0(5(3(2(x1)))) -> #0(2(1(5(x1)))) #88: #0(5(3(2(x1)))) -> #1(5(x1)) #89: #0(5(3(2(x1)))) -> #5(x1) #90: #0(1(2(5(x1)))) -> #5(3(1(2(0(x1))))) #91: #0(1(2(5(x1)))) -> #1(2(0(x1))) #92: #0(1(2(5(x1)))) -> #0(x1) #93: #5(1(1(2(x1)))) -> #1(3(5(2(1(3(x1)))))) #94: #5(1(1(2(x1)))) -> #5(2(1(3(x1)))) #95: #5(1(1(2(x1)))) -> #1(3(x1)) #96: #0(5(2(5(x1)))) -> #0(2(3(5(5(x1))))) #97: #0(5(2(5(x1)))) -> #5(5(x1)) #98: #1(5(2(x1))) -> #1(5(3(1(2(x1))))) #99: #1(5(2(x1))) -> #5(3(1(2(x1)))) #100: #1(5(2(x1))) -> #1(2(x1)) #101: #5(0(1(2(x1)))) -> #1(5(0(4(1(2(x1)))))) #102: #5(0(1(2(x1)))) -> #5(0(4(1(2(x1))))) #103: #5(0(1(2(x1)))) -> #0(4(1(2(x1)))) #104: #0(1(0(1(x1)))) -> #1(1(3(0(3(0(x1)))))) #105: #0(1(0(1(x1)))) -> #1(3(0(3(0(x1))))) #106: #0(1(0(1(x1)))) -> #0(3(0(x1))) #107: #0(1(0(1(x1)))) -> #0(x1) #108: #0(5(2(4(x1)))) -> #5(5(3(0(2(4(x1)))))) #109: #0(5(2(4(x1)))) -> #5(3(0(2(4(x1))))) #110: #0(5(2(4(x1)))) -> #0(2(4(x1))) #111: #0(0(1(3(2(x1))))) -> #0(3(1(2(0(3(x1)))))) #112: #0(0(1(3(2(x1))))) -> #1(2(0(3(x1)))) #113: #0(0(1(3(2(x1))))) -> #0(3(x1)) #114: #0(1(2(5(x1)))) -> #0(5(1(2(x1)))) #115: #0(1(2(5(x1)))) -> #5(1(2(x1))) #116: #0(1(2(5(x1)))) -> #1(2(x1)) #117: #1(5(2(x1))) -> #5(3(1(2(x1)))) #118: #1(5(2(x1))) -> #1(2(x1)) #119: #0(1(2(x1))) -> #0(4(1(3(x1)))) #120: #0(1(2(x1))) -> #1(3(x1)) #121: #0(1(2(x1))) -> #1(3(0(2(x1)))) #122: #0(1(2(x1))) -> #0(2(x1)) #123: #0(1(2(x1))) -> #0(1(3(1(2(x1))))) #124: #0(1(2(x1))) -> #1(3(1(2(x1)))) #125: #0(5(2(x1))) -> #5(0(4(3(1(2(x1)))))) #126: #0(5(2(x1))) -> #0(4(3(1(2(x1))))) #127: #0(5(2(x1))) -> #1(2(x1)) #128: #0(1(2(x1))) -> #0(2(1(3(x1)))) #129: #0(1(2(x1))) -> #1(3(x1)) #130: #5(1(1(2(1(x1))))) -> #1(2(5(1(1(x1))))) #131: #5(1(1(2(1(x1))))) -> #5(1(1(x1))) #132: #5(1(1(2(1(x1))))) -> #1(1(x1)) #133: #0(0(5(4(x1)))) -> #5(3(0(4(0(0(x1)))))) #134: #0(0(5(4(x1)))) -> #0(4(0(0(x1)))) #135: #0(0(5(4(x1)))) -> #0(0(x1)) #136: #0(0(5(4(x1)))) -> #0(x1) Number of SCCs: 3, DPs: 7 SCC { #64 } POLO(Sum)... succeeded. #0 w: 0 1 w: x1 4 w: 0 5 w: x1 3 w: 0 0 w: x1 #5 w: x1 2 w: x1 + 1 #1 w: 0 USABLE RULES: { } Removed DPs: #64 Number of SCCs: 2, DPs: 6 SCC { #131 } POLO(Sum)... succeeded. #0 w: 0 1 w: x1 + 30401 4 w: 0 5 w: x1 3 w: 0 0 w: x1 + 30401 #5 w: x1 2 w: x1 + 30401 #1 w: 0 USABLE RULES: { 16 17 30..35 44..50 } Removed DPs: #131 Number of SCCs: 1, DPs: 5 SCC { #2 #92 #107 #135 #136 } POLO(Sum)... succeeded. #0 w: x1 1 w: x1 4 w: x1 5 w: x1 3 w: 0 0 w: x1 + 31742 #5 w: x1 2 w: x1 #1 w: 0 USABLE RULES: { 1..50 } Removed DPs: #107 #136 Number of SCCs: 1, DPs: 3 SCC { #2 #92 #135 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... succeeded. #0 w: [1,0;1,0] * x1 1 w: [1,0;1,0] * x1 + [1;6073] 4 w: [0,1;0,0] * x1 + [1;1] 5 w: [1,0;1,0] * x1 + [0;6073] 3 w: [0;5544] 0 w: [0,1;0,0] * x1 + [1;6075] #5 w: [0;0] 2 w: [1,0;0,0] * x1 + [0;1] #1 w: [0;0] USABLE RULES: { 1..50 } Removed DPs: #2 #92 #135 Number of SCCs: 0, DPs: 0