YES Input TRS: 1: 0(1(1(x1))) -> 1(2(1(2(0(x1))))) 2: 0(3(1(x1))) -> 1(3(2(2(0(x1))))) 3: 0(3(1(x1))) -> 3(2(1(2(0(x1))))) 4: 0(3(1(x1))) -> 1(3(3(3(2(0(x1)))))) 5: 0(4(1(x1))) -> 2(1(2(0(4(x1))))) 6: 0(0(4(5(x1)))) -> 0(0(2(5(4(x1))))) 7: 0(1(4(1(x1)))) -> 0(1(2(2(4(1(x1)))))) 8: 0(1(4(5(x1)))) -> 4(0(1(2(5(4(x1)))))) 9: 0(1(5(1(x1)))) -> 1(2(2(5(0(1(x1)))))) 10: 0(1(5(3(x1)))) -> 0(5(3(2(1(x1))))) 11: 0(2(4(1(x1)))) -> 1(3(3(2(0(4(x1)))))) 12: 0(2(4(1(x1)))) -> 4(2(1(2(0(4(x1)))))) 13: 0(2(4(5(x1)))) -> 0(2(2(5(0(4(x1)))))) 14: 0(3(1(5(x1)))) -> 0(1(2(5(3(x1))))) 15: 0(3(1(5(x1)))) -> 1(2(5(3(0(4(x1)))))) 16: 0(3(5(1(x1)))) -> 1(2(5(3(0(x1))))) 17: 0(3(5(1(x1)))) -> 0(5(2(1(2(3(x1)))))) 18: 0(3(5(5(x1)))) -> 0(3(2(5(5(x1))))) 19: 0(4(0(1(x1)))) -> 2(0(4(4(0(1(x1)))))) 20: 0(4(1(5(x1)))) -> 1(2(5(0(4(x1))))) 21: 0(4(3(5(x1)))) -> 0(4(3(2(5(4(x1)))))) 22: 0(4(5(1(x1)))) -> 2(5(4(4(0(1(x1)))))) 23: 3(0(1(5(x1)))) -> 3(1(4(0(5(4(x1)))))) 24: 3(0(3(1(x1)))) -> 1(3(3(2(0(x1))))) 25: 3(0(3(5(x1)))) -> 3(2(5(0(2(3(x1)))))) 26: 3(3(0(1(x1)))) -> 0(1(3(2(2(3(x1)))))) 27: 3(4(5(1(x1)))) -> 3(2(5(4(2(1(x1)))))) 28: 4(1(3(5(x1)))) -> 1(2(5(3(4(4(x1)))))) 29: 4(1(5(1(x1)))) -> 4(4(5(1(2(1(x1)))))) 30: 4(4(1(5(x1)))) -> 4(1(2(5(4(x1))))) 31: 0(1(4(5(5(x1))))) -> 0(5(1(4(2(5(x1)))))) 32: 0(2(1(4(5(x1))))) -> 0(0(1(2(5(4(x1)))))) 33: 0(2(1(5(5(x1))))) -> 0(1(2(2(5(5(x1)))))) 34: 0(4(2(4(1(x1))))) -> 1(3(2(0(4(4(x1)))))) 35: 0(4(5(4(3(x1))))) -> 2(5(0(4(4(3(x1)))))) 36: 0(5(1(5(1(x1))))) -> 0(5(1(1(2(5(x1)))))) 37: 0(5(2(1(5(x1))))) -> 1(2(5(5(0(4(x1)))))) 38: 0(5(2(4(1(x1))))) -> 4(5(2(1(2(0(x1)))))) 39: 3(0(1(4(1(x1))))) -> 0(4(4(1(3(1(x1)))))) 40: 3(0(1(4(1(x1))))) -> 4(3(2(0(1(1(x1)))))) 41: 3(0(3(5(5(x1))))) -> 3(3(2(5(0(5(x1)))))) 42: 3(0(5(3(1(x1))))) -> 1(0(3(3(2(5(x1)))))) 43: 4(0(1(4(1(x1))))) -> 4(4(0(1(3(1(x1)))))) 44: 4(0(1(5(1(x1))))) -> 0(1(2(5(4(1(x1)))))) 45: 4(0(2(4(5(x1))))) -> 4(0(2(5(0(4(x1)))))) 46: 4(1(1(5(1(x1))))) -> 1(1(2(5(4(1(x1)))))) 47: 4(5(1(4(1(x1))))) -> 4(4(1(2(1(5(x1)))))) 48: 4(5(2(3(1(x1))))) -> 4(3(1(2(2(5(x1)))))) 49: 4(5(4(3(1(x1))))) -> 4(1(2(5(3(4(x1)))))) 50: 4(5(5(3(1(x1))))) -> 1(3(2(5(5(4(x1)))))) Number of strict rules: 50 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #0(3(1(x1))) -> #3(2(2(0(x1)))) #2: #0(3(1(x1))) -> #0(x1) #3: #4(0(1(4(1(x1))))) -> #4(4(0(1(3(1(x1)))))) #4: #4(0(1(4(1(x1))))) -> #4(0(1(3(1(x1))))) #5: #4(0(1(4(1(x1))))) -> #0(1(3(1(x1)))) #6: #4(0(1(4(1(x1))))) -> #3(1(x1)) #7: #4(1(5(1(x1)))) -> #4(4(5(1(2(1(x1)))))) #8: #4(1(5(1(x1)))) -> #4(5(1(2(1(x1))))) #9: #0(4(5(4(3(x1))))) -> #0(4(4(3(x1)))) #10: #0(4(5(4(3(x1))))) -> #4(4(3(x1))) #11: #4(1(1(5(1(x1))))) -> #4(1(x1)) #12: #3(0(5(3(1(x1))))) -> #0(3(3(2(5(x1))))) #13: #3(0(5(3(1(x1))))) -> #3(3(2(5(x1)))) #14: #3(0(5(3(1(x1))))) -> #3(2(5(x1))) #15: #3(0(3(5(5(x1))))) -> #3(3(2(5(0(5(x1)))))) #16: #3(0(3(5(5(x1))))) -> #3(2(5(0(5(x1))))) #17: #3(0(3(5(5(x1))))) -> #0(5(x1)) #18: #0(5(2(1(5(x1))))) -> #0(4(x1)) #19: #0(5(2(1(5(x1))))) -> #4(x1) #20: #4(5(1(4(1(x1))))) -> #4(4(1(2(1(5(x1)))))) #21: #4(5(1(4(1(x1))))) -> #4(1(2(1(5(x1))))) #22: #4(5(2(3(1(x1))))) -> #4(3(1(2(2(5(x1)))))) #23: #4(5(2(3(1(x1))))) -> #3(1(2(2(5(x1))))) #24: #0(5(2(4(1(x1))))) -> #4(5(2(1(2(0(x1)))))) #25: #0(5(2(4(1(x1))))) -> #0(x1) #26: #0(0(4(5(x1)))) -> #0(0(2(5(4(x1))))) #27: #0(0(4(5(x1)))) -> #0(2(5(4(x1)))) #28: #0(0(4(5(x1)))) -> #4(x1) #29: #3(0(1(4(1(x1))))) -> #4(3(2(0(1(1(x1)))))) #30: #3(0(1(4(1(x1))))) -> #3(2(0(1(1(x1))))) #31: #3(0(1(4(1(x1))))) -> #0(1(1(x1))) #32: #0(2(4(5(x1)))) -> #0(2(2(5(0(4(x1)))))) #33: #0(2(4(5(x1)))) -> #0(4(x1)) #34: #0(2(4(5(x1)))) -> #4(x1) #35: #0(1(5(1(x1)))) -> #0(1(x1)) #36: #0(2(4(1(x1)))) -> #3(3(2(0(4(x1))))) #37: #0(2(4(1(x1)))) -> #3(2(0(4(x1)))) #38: #0(2(4(1(x1)))) -> #0(4(x1)) #39: #0(2(4(1(x1)))) -> #4(x1) #40: #3(0(3(1(x1)))) -> #3(3(2(0(x1)))) #41: #3(0(3(1(x1)))) -> #3(2(0(x1))) #42: #3(0(3(1(x1)))) -> #0(x1) #43: #3(0(1(5(x1)))) -> #3(1(4(0(5(4(x1)))))) #44: #3(0(1(5(x1)))) -> #4(0(5(4(x1)))) #45: #3(0(1(5(x1)))) -> #0(5(4(x1))) #46: #3(0(1(5(x1)))) -> #4(x1) #47: #4(0(2(4(5(x1))))) -> #4(0(2(5(0(4(x1)))))) #48: #4(0(2(4(5(x1))))) -> #0(2(5(0(4(x1))))) #49: #4(0(2(4(5(x1))))) -> #0(4(x1)) #50: #4(0(2(4(5(x1))))) -> #4(x1) #51: #0(2(4(1(x1)))) -> #4(2(1(2(0(4(x1)))))) #52: #0(2(4(1(x1)))) -> #0(4(x1)) #53: #0(2(4(1(x1)))) -> #4(x1) #54: #0(1(4(5(5(x1))))) -> #0(5(1(4(2(5(x1)))))) #55: #0(1(4(5(5(x1))))) -> #4(2(5(x1))) #56: #0(3(1(5(x1)))) -> #0(1(2(5(3(x1))))) #57: #0(3(1(5(x1)))) -> #3(x1) #58: #4(4(1(5(x1)))) -> #4(1(2(5(4(x1))))) #59: #4(4(1(5(x1)))) -> #4(x1) #60: #4(5(4(3(1(x1))))) -> #4(1(2(5(3(4(x1)))))) #61: #4(5(4(3(1(x1))))) -> #3(4(x1)) #62: #4(5(4(3(1(x1))))) -> #4(x1) #63: #3(0(3(5(x1)))) -> #3(2(5(0(2(3(x1)))))) #64: #3(0(3(5(x1)))) -> #0(2(3(x1))) #65: #3(0(3(5(x1)))) -> #3(x1) #66: #0(4(1(5(x1)))) -> #0(4(x1)) #67: #0(4(1(5(x1)))) -> #4(x1) #68: #0(1(4(1(x1)))) -> #0(1(2(2(4(1(x1)))))) #69: #3(0(1(4(1(x1))))) -> #0(4(4(1(3(1(x1)))))) #70: #3(0(1(4(1(x1))))) -> #4(4(1(3(1(x1))))) #71: #3(0(1(4(1(x1))))) -> #4(1(3(1(x1)))) #72: #3(0(1(4(1(x1))))) -> #3(1(x1)) #73: #0(1(5(3(x1)))) -> #0(5(3(2(1(x1))))) #74: #0(1(5(3(x1)))) -> #3(2(1(x1))) #75: #0(2(1(5(5(x1))))) -> #0(1(2(2(5(5(x1)))))) #76: #0(4(1(x1))) -> #0(4(x1)) #77: #0(4(1(x1))) -> #4(x1) #78: #4(0(1(5(1(x1))))) -> #0(1(2(5(4(1(x1)))))) #79: #4(0(1(5(1(x1))))) -> #4(1(x1)) #80: #4(1(3(5(x1)))) -> #3(4(4(x1))) #81: #4(1(3(5(x1)))) -> #4(4(x1)) #82: #4(1(3(5(x1)))) -> #4(x1) #83: #0(4(5(1(x1)))) -> #4(4(0(1(x1)))) #84: #0(4(5(1(x1)))) -> #4(0(1(x1))) #85: #0(4(5(1(x1)))) -> #0(1(x1)) #86: #0(4(2(4(1(x1))))) -> #3(2(0(4(4(x1))))) #87: #0(4(2(4(1(x1))))) -> #0(4(4(x1))) #88: #0(4(2(4(1(x1))))) -> #4(4(x1)) #89: #0(4(2(4(1(x1))))) -> #4(x1) #90: #3(4(5(1(x1)))) -> #3(2(5(4(2(1(x1)))))) #91: #3(4(5(1(x1)))) -> #4(2(1(x1))) #92: #0(3(5(1(x1)))) -> #0(5(2(1(2(3(x1)))))) #93: #0(3(5(1(x1)))) -> #3(x1) #94: #0(2(1(4(5(x1))))) -> #0(0(1(2(5(4(x1)))))) #95: #0(2(1(4(5(x1))))) -> #0(1(2(5(4(x1))))) #96: #0(2(1(4(5(x1))))) -> #4(x1) #97: #0(4(0(1(x1)))) -> #0(4(4(0(1(x1))))) #98: #0(4(0(1(x1)))) -> #4(4(0(1(x1)))) #99: #3(3(0(1(x1)))) -> #0(1(3(2(2(3(x1)))))) #100: #3(3(0(1(x1)))) -> #3(2(2(3(x1)))) #101: #3(3(0(1(x1)))) -> #3(x1) #102: #0(5(1(5(1(x1))))) -> #0(5(1(1(2(5(x1)))))) #103: #0(4(3(5(x1)))) -> #0(4(3(2(5(4(x1)))))) #104: #0(4(3(5(x1)))) -> #4(3(2(5(4(x1))))) #105: #0(4(3(5(x1)))) -> #3(2(5(4(x1)))) #106: #0(4(3(5(x1)))) -> #4(x1) #107: #0(3(5(1(x1)))) -> #3(0(x1)) #108: #0(3(5(1(x1)))) -> #0(x1) #109: #0(3(1(x1))) -> #3(2(1(2(0(x1))))) #110: #0(3(1(x1))) -> #0(x1) #111: #0(1(1(x1))) -> #0(x1) #112: #0(1(4(5(x1)))) -> #4(0(1(2(5(4(x1)))))) #113: #0(1(4(5(x1)))) -> #0(1(2(5(4(x1))))) #114: #0(1(4(5(x1)))) -> #4(x1) #115: #0(3(1(5(x1)))) -> #3(0(4(x1))) #116: #0(3(1(5(x1)))) -> #0(4(x1)) #117: #0(3(1(5(x1)))) -> #4(x1) #118: #0(3(1(x1))) -> #3(3(3(2(0(x1))))) #119: #0(3(1(x1))) -> #3(3(2(0(x1)))) #120: #0(3(1(x1))) -> #3(2(0(x1))) #121: #0(3(1(x1))) -> #0(x1) #122: #4(5(5(3(1(x1))))) -> #3(2(5(5(4(x1))))) #123: #4(5(5(3(1(x1))))) -> #4(x1) #124: #0(3(5(5(x1)))) -> #0(3(2(5(5(x1))))) #125: #0(3(5(5(x1)))) -> #3(2(5(5(x1)))) Number of SCCs: 2, DPs: 49 SCC { #97 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... succeeded. #0 w: [1,0;1,0] * x1 1 w: [0,1;0,1] * x1 + [9;1] 4 w: [0,1;1,0] * x1 5 w: [6109;6109] 3 w: [0,1;0,1] * x1 + [6;7] #4 w: [0;0] 0 w: [1,1;1,1] * x1 + [22;24] #3 w: [0;0] 2 w: [1,0;0,0] * x1 USABLE RULES: { 1..50 } Removed DPs: #97 Number of SCCs: 1, DPs: 48 SCC { #2 #11 #17..19 #25 #28 #31 #33..35 #38 #39 #42 #46 #49 #50 #52 #53 #57 #59 #62 #65..67 #76 #77 #79 #81 #82 #84 #85 #87..89 #93 #96 #101 #106..108 #110 #111 #114 #116 #117 #121 #123 } POLO(Sum)... succeeded. #0 w: x1 1 w: x1 + 1 4 w: x1 5 w: x1 + 1 3 w: x1 #4 w: x1 0 w: x1 #3 w: x1 + 1 2 w: x1 USABLE RULES: { 1..50 } Removed DPs: #2 #11 #17..19 #25 #28 #31 #33..35 #38 #39 #42 #46 #49 #50 #52 #53 #57 #59 #62 #65..67 #76 #77 #79 #81 #82 #84 #85 #87..89 #93 #96 #101 #106..108 #110 #111 #114 #116 #117 #121 #123 Number of SCCs: 0, DPs: 0