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