YES Input TRS: 1: 0(1(1(2(x1)))) -> 0(1(0(3(1(2(x1)))))) 2: 0(2(3(1(x1)))) -> 0(3(2(0(1(x1))))) 3: 0(2(3(1(x1)))) -> 1(0(3(4(2(x1))))) 4: 0(2(3(1(x1)))) -> 4(0(3(2(1(x1))))) 5: 0(2(3(1(x1)))) -> 0(0(3(2(1(4(x1)))))) 6: 3(0(1(1(x1)))) -> 0(3(4(1(1(0(x1)))))) 7: 3(0(1(2(x1)))) -> 0(3(4(1(2(4(x1)))))) 8: 3(0(1(2(x1)))) -> 0(3(4(4(1(2(x1)))))) 9: 3(0(2(1(x1)))) -> 0(3(2(1(0(x1))))) 10: 3(0(2(1(x1)))) -> 0(3(2(1(4(x1))))) 11: 3(0(2(1(x1)))) -> 0(3(4(2(1(0(x1)))))) 12: 0(1(0(1(2(x1))))) -> 0(0(2(1(1(3(x1)))))) 13: 0(1(1(4(2(x1))))) -> 1(0(3(1(4(2(x1)))))) 14: 0(1(2(3(1(x1))))) -> 1(0(3(1(2(2(x1)))))) 15: 0(1(2(3(1(x1))))) -> 1(4(0(3(1(2(x1)))))) 16: 0(1(2(3(1(x1))))) -> 2(1(0(3(2(1(x1)))))) 17: 0(1(5(3(1(x1))))) -> 0(3(1(5(4(1(x1)))))) 18: 0(2(3(2(1(x1))))) -> 0(3(2(4(1(2(x1)))))) 19: 0(2(4(3(1(x1))))) -> 0(3(4(1(2(0(x1)))))) 20: 0(2(4(3(1(x1))))) -> 1(0(0(3(4(2(x1)))))) 21: 0(3(3(1(2(x1))))) -> 3(0(1(0(3(2(x1)))))) 22: 0(3(3(2(1(x1))))) -> 0(3(2(3(1(4(x1)))))) 23: 0(5(2(3(1(x1))))) -> 0(3(2(1(5(4(x1)))))) 24: 0(5(2(3(1(x1))))) -> 0(5(0(3(2(1(x1)))))) 25: 0(5(4(3(1(x1))))) -> 0(3(4(1(4(5(x1)))))) 26: 1(4(0(1(2(x1))))) -> 2(1(4(0(3(1(x1)))))) 27: 3(0(1(0(2(x1))))) -> 0(3(2(0(4(1(x1)))))) 28: 3(0(2(3(1(x1))))) -> 3(0(0(3(1(2(x1)))))) 29: 3(0(2(5(1(x1))))) -> 0(3(2(5(0(1(x1)))))) 30: 3(0(2(5(1(x1))))) -> 0(3(5(2(1(4(x1)))))) 31: 3(0(2(5(1(x1))))) -> 5(4(0(3(2(1(x1)))))) 32: 3(0(4(5(1(x1))))) -> 5(0(0(3(4(1(x1)))))) 33: 3(3(0(1(4(x1))))) -> 3(0(0(3(1(4(x1)))))) 34: 3(3(1(1(1(x1))))) -> 0(3(1(3(1(1(x1)))))) 35: 3(3(1(1(2(x1))))) -> 1(3(2(1(4(3(x1)))))) 36: 3(3(1(1(4(x1))))) -> 4(4(3(1(3(1(x1)))))) 37: 3(4(3(2(1(x1))))) -> 3(0(3(2(4(1(x1)))))) 38: 3(5(0(2(1(x1))))) -> 0(3(2(0(5(1(x1)))))) 39: 3(5(0(2(1(x1))))) -> 0(3(5(2(4(1(x1)))))) 40: 4(0(1(1(4(x1))))) -> 1(0(3(4(4(1(x1)))))) 41: 4(5(3(2(1(x1))))) -> 0(3(1(5(2(4(x1)))))) 42: 5(0(1(1(4(x1))))) -> 0(3(1(5(1(4(x1)))))) 43: 5(0(2(3(1(x1))))) -> 5(0(3(2(1(0(x1)))))) 44: 5(3(0(1(1(x1))))) -> 0(3(1(1(5(0(x1)))))) 45: 5(3(0(2(1(x1))))) -> 0(3(4(2(1(5(x1)))))) 46: 5(3(0(2(1(x1))))) -> 0(3(5(1(2(4(x1)))))) 47: 5(3(1(1(2(x1))))) -> 3(1(2(1(4(5(x1)))))) 48: 5(3(1(1(4(x1))))) -> 3(4(1(5(2(1(x1)))))) 49: 5(4(3(4(1(x1))))) -> 0(3(4(4(1(5(x1)))))) Number of strict rules: 49 Direct POLO(bPol) ... removes: 44 25 49 45 23 48 47 41 42 1 w: x1 + 24291 4 w: x1 5 w: 2 * x1 + 20540 3 w: x1 0 w: x1 2 w: x1 Number of strict rules: 40 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #0(2(3(1(x1)))) -> #0(3(2(0(1(x1))))) #2: #0(2(3(1(x1)))) -> #3(2(0(1(x1)))) #3: #0(2(3(1(x1)))) -> #0(1(x1)) #4: #5(0(2(3(1(x1))))) -> #5(0(3(2(1(0(x1)))))) #5: #5(0(2(3(1(x1))))) -> #0(3(2(1(0(x1))))) #6: #5(0(2(3(1(x1))))) -> #3(2(1(0(x1)))) #7: #5(0(2(3(1(x1))))) -> #1(0(x1)) #8: #5(0(2(3(1(x1))))) -> #0(x1) #9: #3(0(2(5(1(x1))))) -> #0(3(2(5(0(1(x1)))))) #10: #3(0(2(5(1(x1))))) -> #3(2(5(0(1(x1))))) #11: #3(0(2(5(1(x1))))) -> #5(0(1(x1))) #12: #3(0(2(5(1(x1))))) -> #0(1(x1)) #13: #3(3(1(1(2(x1))))) -> #1(3(2(1(4(3(x1)))))) #14: #3(3(1(1(2(x1))))) -> #3(2(1(4(3(x1))))) #15: #3(3(1(1(2(x1))))) -> #1(4(3(x1))) #16: #3(3(1(1(2(x1))))) -> #4(3(x1)) #17: #3(3(1(1(2(x1))))) -> #3(x1) #18: #5(3(0(2(1(x1))))) -> #0(3(5(1(2(4(x1)))))) #19: #5(3(0(2(1(x1))))) -> #3(5(1(2(4(x1))))) #20: #5(3(0(2(1(x1))))) -> #5(1(2(4(x1)))) #21: #5(3(0(2(1(x1))))) -> #1(2(4(x1))) #22: #5(3(0(2(1(x1))))) -> #4(x1) #23: #3(4(3(2(1(x1))))) -> #3(0(3(2(4(1(x1)))))) #24: #3(4(3(2(1(x1))))) -> #0(3(2(4(1(x1))))) #25: #3(4(3(2(1(x1))))) -> #3(2(4(1(x1)))) #26: #3(4(3(2(1(x1))))) -> #4(1(x1)) #27: #3(5(0(2(1(x1))))) -> #0(3(2(0(5(1(x1)))))) #28: #3(5(0(2(1(x1))))) -> #3(2(0(5(1(x1))))) #29: #3(5(0(2(1(x1))))) -> #0(5(1(x1))) #30: #3(5(0(2(1(x1))))) -> #5(1(x1)) #31: #3(0(1(1(x1)))) -> #0(3(4(1(1(0(x1)))))) #32: #3(0(1(1(x1)))) -> #3(4(1(1(0(x1))))) #33: #3(0(1(1(x1)))) -> #4(1(1(0(x1)))) #34: #3(0(1(1(x1)))) -> #1(1(0(x1))) #35: #3(0(1(1(x1)))) -> #1(0(x1)) #36: #3(0(1(1(x1)))) -> #0(x1) #37: #4(0(1(1(4(x1))))) -> #1(0(3(4(4(1(x1)))))) #38: #4(0(1(1(4(x1))))) -> #0(3(4(4(1(x1))))) #39: #4(0(1(1(4(x1))))) -> #3(4(4(1(x1)))) #40: #4(0(1(1(4(x1))))) -> #4(4(1(x1))) #41: #4(0(1(1(4(x1))))) -> #4(1(x1)) #42: #4(0(1(1(4(x1))))) -> #1(x1) #43: #0(1(1(4(2(x1))))) -> #1(0(3(1(4(2(x1)))))) #44: #0(1(1(4(2(x1))))) -> #0(3(1(4(2(x1))))) #45: #0(1(1(4(2(x1))))) -> #3(1(4(2(x1)))) #46: #3(0(2(1(x1)))) -> #0(3(2(1(0(x1))))) #47: #3(0(2(1(x1)))) -> #3(2(1(0(x1)))) #48: #3(0(2(1(x1)))) -> #1(0(x1)) #49: #3(0(2(1(x1)))) -> #0(x1) #50: #3(0(2(1(x1)))) -> #0(3(4(2(1(0(x1)))))) #51: #3(0(2(1(x1)))) -> #3(4(2(1(0(x1))))) #52: #3(0(2(1(x1)))) -> #4(2(1(0(x1)))) #53: #3(0(2(1(x1)))) -> #1(0(x1)) #54: #3(0(2(1(x1)))) -> #0(x1) #55: #0(5(2(3(1(x1))))) -> #0(5(0(3(2(1(x1)))))) #56: #0(5(2(3(1(x1))))) -> #5(0(3(2(1(x1))))) #57: #0(5(2(3(1(x1))))) -> #0(3(2(1(x1)))) #58: #0(5(2(3(1(x1))))) -> #3(2(1(x1))) #59: #0(1(0(1(2(x1))))) -> #0(0(2(1(1(3(x1)))))) #60: #0(1(0(1(2(x1))))) -> #0(2(1(1(3(x1))))) #61: #0(1(0(1(2(x1))))) -> #1(1(3(x1))) #62: #0(1(0(1(2(x1))))) -> #1(3(x1)) #63: #0(1(0(1(2(x1))))) -> #3(x1) #64: #3(0(2(5(1(x1))))) -> #5(4(0(3(2(1(x1)))))) #65: #3(0(2(5(1(x1))))) -> #4(0(3(2(1(x1))))) #66: #3(0(2(5(1(x1))))) -> #0(3(2(1(x1)))) #67: #3(0(2(5(1(x1))))) -> #3(2(1(x1))) #68: #0(1(2(3(1(x1))))) -> #1(0(3(1(2(2(x1)))))) #69: #0(1(2(3(1(x1))))) -> #0(3(1(2(2(x1))))) #70: #0(1(2(3(1(x1))))) -> #3(1(2(2(x1)))) #71: #0(1(2(3(1(x1))))) -> #1(2(2(x1))) #72: #3(0(2(5(1(x1))))) -> #0(3(5(2(1(4(x1)))))) #73: #3(0(2(5(1(x1))))) -> #3(5(2(1(4(x1))))) #74: #3(0(2(5(1(x1))))) -> #5(2(1(4(x1)))) #75: #3(0(2(5(1(x1))))) -> #1(4(x1)) #76: #3(0(2(5(1(x1))))) -> #4(x1) #77: #0(2(4(3(1(x1))))) -> #1(0(0(3(4(2(x1)))))) #78: #0(2(4(3(1(x1))))) -> #0(0(3(4(2(x1))))) #79: #0(2(4(3(1(x1))))) -> #0(3(4(2(x1)))) #80: #0(2(4(3(1(x1))))) -> #3(4(2(x1))) #81: #0(2(4(3(1(x1))))) -> #4(2(x1)) #82: #3(0(1(2(x1)))) -> #0(3(4(1(2(4(x1)))))) #83: #3(0(1(2(x1)))) -> #3(4(1(2(4(x1))))) #84: #3(0(1(2(x1)))) -> #4(1(2(4(x1)))) #85: #3(0(1(2(x1)))) -> #1(2(4(x1))) #86: #3(0(1(2(x1)))) -> #4(x1) #87: #3(5(0(2(1(x1))))) -> #0(3(5(2(4(1(x1)))))) #88: #3(5(0(2(1(x1))))) -> #3(5(2(4(1(x1))))) #89: #3(5(0(2(1(x1))))) -> #5(2(4(1(x1)))) #90: #3(5(0(2(1(x1))))) -> #4(1(x1)) #91: #3(0(2(1(x1)))) -> #0(3(2(1(4(x1))))) #92: #3(0(2(1(x1)))) -> #3(2(1(4(x1)))) #93: #3(0(2(1(x1)))) -> #1(4(x1)) #94: #3(0(2(1(x1)))) -> #4(x1) #95: #3(3(0(1(4(x1))))) -> #3(0(0(3(1(4(x1)))))) #96: #3(3(0(1(4(x1))))) -> #0(0(3(1(4(x1))))) #97: #3(3(0(1(4(x1))))) -> #0(3(1(4(x1)))) #98: #3(3(0(1(4(x1))))) -> #3(1(4(x1))) #99: #0(2(3(1(x1)))) -> #0(0(3(2(1(4(x1)))))) #100: #0(2(3(1(x1)))) -> #0(3(2(1(4(x1))))) #101: #0(2(3(1(x1)))) -> #3(2(1(4(x1)))) #102: #0(2(3(1(x1)))) -> #1(4(x1)) #103: #0(2(3(1(x1)))) -> #4(x1) #104: #3(0(2(3(1(x1))))) -> #3(0(0(3(1(2(x1)))))) #105: #3(0(2(3(1(x1))))) -> #0(0(3(1(2(x1))))) #106: #3(0(2(3(1(x1))))) -> #0(3(1(2(x1)))) #107: #3(0(2(3(1(x1))))) -> #3(1(2(x1))) #108: #3(0(2(3(1(x1))))) -> #1(2(x1)) #109: #0(3(3(2(1(x1))))) -> #0(3(2(3(1(4(x1)))))) #110: #0(3(3(2(1(x1))))) -> #3(2(3(1(4(x1))))) #111: #0(3(3(2(1(x1))))) -> #3(1(4(x1))) #112: #0(3(3(2(1(x1))))) -> #1(4(x1)) #113: #0(3(3(2(1(x1))))) -> #4(x1) #114: #3(3(1(1(1(x1))))) -> #0(3(1(3(1(1(x1)))))) #115: #3(3(1(1(1(x1))))) -> #3(1(3(1(1(x1))))) #116: #3(3(1(1(1(x1))))) -> #1(3(1(1(x1)))) #117: #3(3(1(1(1(x1))))) -> #3(1(1(x1))) #118: #3(0(1(0(2(x1))))) -> #0(3(2(0(4(1(x1)))))) #119: #3(0(1(0(2(x1))))) -> #3(2(0(4(1(x1))))) #120: #3(0(1(0(2(x1))))) -> #0(4(1(x1))) #121: #3(0(1(0(2(x1))))) -> #4(1(x1)) #122: #3(0(1(0(2(x1))))) -> #1(x1) #123: #0(1(5(3(1(x1))))) -> #0(3(1(5(4(1(x1)))))) #124: #0(1(5(3(1(x1))))) -> #3(1(5(4(1(x1))))) #125: #0(1(5(3(1(x1))))) -> #1(5(4(1(x1)))) #126: #0(1(5(3(1(x1))))) -> #5(4(1(x1))) #127: #0(1(5(3(1(x1))))) -> #4(1(x1)) #128: #3(0(4(5(1(x1))))) -> #5(0(0(3(4(1(x1)))))) #129: #3(0(4(5(1(x1))))) -> #0(0(3(4(1(x1))))) #130: #3(0(4(5(1(x1))))) -> #0(3(4(1(x1)))) #131: #3(0(4(5(1(x1))))) -> #3(4(1(x1))) #132: #3(0(4(5(1(x1))))) -> #4(1(x1)) #133: #0(2(4(3(1(x1))))) -> #0(3(4(1(2(0(x1)))))) #134: #0(2(4(3(1(x1))))) -> #3(4(1(2(0(x1))))) #135: #0(2(4(3(1(x1))))) -> #4(1(2(0(x1)))) #136: #0(2(4(3(1(x1))))) -> #1(2(0(x1))) #137: #0(2(4(3(1(x1))))) -> #0(x1) #138: #1(4(0(1(2(x1))))) -> #1(4(0(3(1(x1))))) #139: #1(4(0(1(2(x1))))) -> #4(0(3(1(x1)))) #140: #1(4(0(1(2(x1))))) -> #0(3(1(x1))) #141: #1(4(0(1(2(x1))))) -> #3(1(x1)) #142: #1(4(0(1(2(x1))))) -> #1(x1) #143: #3(3(1(1(4(x1))))) -> #4(4(3(1(3(1(x1)))))) #144: #3(3(1(1(4(x1))))) -> #4(3(1(3(1(x1))))) #145: #3(3(1(1(4(x1))))) -> #3(1(3(1(x1)))) #146: #3(3(1(1(4(x1))))) -> #1(3(1(x1))) #147: #3(3(1(1(4(x1))))) -> #3(1(x1)) #148: #3(3(1(1(4(x1))))) -> #1(x1) #149: #0(3(3(1(2(x1))))) -> #3(0(1(0(3(2(x1)))))) #150: #0(3(3(1(2(x1))))) -> #0(1(0(3(2(x1))))) #151: #0(3(3(1(2(x1))))) -> #1(0(3(2(x1)))) #152: #0(3(3(1(2(x1))))) -> #0(3(2(x1))) #153: #0(3(3(1(2(x1))))) -> #3(2(x1)) #154: #0(1(2(3(1(x1))))) -> #1(0(3(2(1(x1))))) #155: #0(1(2(3(1(x1))))) -> #0(3(2(1(x1)))) #156: #0(1(2(3(1(x1))))) -> #3(2(1(x1))) #157: #0(2(3(1(x1)))) -> #1(0(3(4(2(x1))))) #158: #0(2(3(1(x1)))) -> #0(3(4(2(x1)))) #159: #0(2(3(1(x1)))) -> #3(4(2(x1))) #160: #0(2(3(1(x1)))) -> #4(2(x1)) #161: #0(1(1(2(x1)))) -> #0(1(0(3(1(2(x1)))))) #162: #0(1(1(2(x1)))) -> #1(0(3(1(2(x1))))) #163: #0(1(1(2(x1)))) -> #0(3(1(2(x1)))) #164: #0(1(1(2(x1)))) -> #3(1(2(x1))) #165: #3(0(1(2(x1)))) -> #0(3(4(4(1(2(x1)))))) #166: #3(0(1(2(x1)))) -> #3(4(4(1(2(x1))))) #167: #3(0(1(2(x1)))) -> #4(4(1(2(x1)))) #168: #3(0(1(2(x1)))) -> #4(1(2(x1))) #169: #0(1(2(3(1(x1))))) -> #1(4(0(3(1(2(x1)))))) #170: #0(1(2(3(1(x1))))) -> #4(0(3(1(2(x1))))) #171: #0(1(2(3(1(x1))))) -> #0(3(1(2(x1)))) #172: #0(1(2(3(1(x1))))) -> #3(1(2(x1))) #173: #0(1(2(3(1(x1))))) -> #1(2(x1)) #174: #0(2(3(1(x1)))) -> #4(0(3(2(1(x1))))) #175: #0(2(3(1(x1)))) -> #0(3(2(1(x1)))) #176: #0(2(3(1(x1)))) -> #3(2(1(x1))) #177: #0(2(3(2(1(x1))))) -> #0(3(2(4(1(2(x1)))))) #178: #0(2(3(2(1(x1))))) -> #3(2(4(1(2(x1))))) #179: #0(2(3(2(1(x1))))) -> #4(1(2(x1))) #180: #0(2(3(2(1(x1))))) -> #1(2(x1)) Number of SCCs: 2, DPs: 9 SCC { #142 } POLO(Sum)... succeeded. #0 w: 0 1 w: x1 4 w: x1 5 w: 0 3 w: 0 #4 w: 0 0 w: x1 #3 w: 0 #5 w: 0 2 w: x1 + 1 #1 w: x1 USABLE RULES: { } Removed DPs: #142 Number of SCCs: 1, DPs: 8 SCC { #3 #12 #17 #36 #49 #54 #63 #137 } POLO(Sum)... succeeded. #0 w: x1 1 w: x1 + 1 4 w: x1 5 w: x1 3 w: x1 #4 w: 0 0 w: x1 #3 w: x1 + 1 #5 w: 0 2 w: x1 #1 w: 0 USABLE RULES: { 1..22 24 26..40 43 46 } Removed DPs: #12 #17 #36 #49 #54 #63 #137 Number of SCCs: 0, DPs: 0