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