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