YES Input TRS: 1: 0(0(1(x1))) -> 0(0(2(1(2(x1))))) 2: 0(0(1(x1))) -> 0(0(3(1(4(x1))))) 3: 0(1(0(x1))) -> 0(0(1(2(4(x1))))) 4: 0(1(0(x1))) -> 2(1(2(0(0(x1))))) 5: 0(1(0(x1))) -> 0(0(1(2(2(4(x1)))))) 6: 0(1(0(x1))) -> 0(0(2(4(1(4(x1)))))) 7: 0(4(0(x1))) -> 3(4(3(2(0(0(x1)))))) 8: 0(0(1(0(x1)))) -> 0(0(0(1(4(x1))))) 9: 0(0(4(1(x1)))) -> 0(0(2(1(4(x1))))) 10: 0(0(4(1(x1)))) -> 0(0(2(1(4(3(x1)))))) 11: 0(1(0(4(x1)))) -> 0(0(3(4(1(2(x1)))))) 12: 0(1(3(0(x1)))) -> 0(0(3(1(4(x1))))) 13: 0(1(3(0(x1)))) -> 0(3(0(1(2(x1))))) 14: 0(1(3(0(x1)))) -> 0(0(1(3(2(5(x1)))))) 15: 0(1(4(0(x1)))) -> 0(2(0(3(1(4(x1)))))) 16: 0(1(5(1(x1)))) -> 2(1(1(4(5(0(x1)))))) 17: 0(1(5(4(x1)))) -> 1(2(4(2(5(0(x1)))))) 18: 0(1(5(4(x1)))) -> 4(1(0(3(2(5(x1)))))) 19: 0(1(5(4(x1)))) -> 5(0(2(4(1(4(x1)))))) 20: 0(3(0(1(x1)))) -> 0(0(3(1(2(2(x1)))))) 21: 0(3(1(0(x1)))) -> 0(0(3(1(4(x1))))) 22: 0(4(0(1(x1)))) -> 0(0(2(1(4(x1))))) 23: 0(4(5(1(x1)))) -> 1(2(4(2(5(0(x1)))))) 24: 0(4(5(1(x1)))) -> 3(1(4(5(0(2(x1)))))) 25: 0(4(5(1(x1)))) -> 3(2(5(1(4(0(x1)))))) 26: 0(4(5(1(x1)))) -> 5(3(0(5(1(4(x1)))))) 27: 0(4(5(1(x1)))) -> 5(5(0(5(1(4(x1)))))) 28: 0(4(5(4(x1)))) -> 5(2(4(4(0(4(x1)))))) 29: 0(5(1(0(x1)))) -> 0(0(5(1(2(x1))))) 30: 3(5(0(1(x1)))) -> 3(0(2(1(2(5(x1)))))) 31: 3(5(1(0(x1)))) -> 0(5(1(3(2(x1))))) 32: 3(5(1(0(x1)))) -> 2(1(2(0(5(3(x1)))))) 33: 3(5(1(0(x1)))) -> 3(1(2(2(0(5(x1)))))) 34: 3(5(1(0(x1)))) -> 5(1(3(2(0(2(x1)))))) 35: 0(1(3(3(0(x1))))) -> 3(3(2(0(0(1(x1)))))) 36: 0(1(3(5(1(x1))))) -> 1(1(3(4(5(0(x1)))))) 37: 0(1(3(5(1(x1))))) -> 1(1(5(0(3(3(x1)))))) 38: 0(1(5(2(0(x1))))) -> 5(0(3(1(0(2(x1)))))) 39: 0(1(5(4(1(x1))))) -> 5(3(4(1(0(1(x1)))))) 40: 0(1(5(4(4(x1))))) -> 4(5(2(1(4(0(x1)))))) 41: 0(1(5(4(4(x1))))) -> 5(0(4(3(4(1(x1)))))) 42: 0(3(1(0(4(x1))))) -> 0(0(3(1(2(4(x1)))))) 43: 0(4(3(3(0(x1))))) -> 0(2(3(4(0(3(x1)))))) 44: 0(4(5(2(0(x1))))) -> 0(2(2(5(0(4(x1)))))) 45: 0(5(1(5(1(x1))))) -> 5(5(3(0(1(1(x1)))))) 46: 3(0(1(5(4(x1))))) -> 0(5(3(4(1(2(x1)))))) 47: 3(5(0(1(0(x1))))) -> 5(1(2(0(0(3(x1)))))) 48: 3(5(4(0(0(x1))))) -> 5(0(3(0(4(4(x1)))))) 49: 3(5(5(0(1(x1))))) -> 5(5(0(3(1(2(x1)))))) Number of strict rules: 49 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #0(0(1(x1))) -> #0(0(3(1(4(x1))))) #2: #0(0(1(x1))) -> #0(3(1(4(x1)))) #3: #0(0(1(x1))) -> #3(1(4(x1))) #4: #0(4(3(3(0(x1))))) -> #0(2(3(4(0(3(x1)))))) #5: #0(4(3(3(0(x1))))) -> #3(4(0(3(x1)))) #6: #0(4(3(3(0(x1))))) -> #0(3(x1)) #7: #0(4(3(3(0(x1))))) -> #3(x1) #8: #0(5(1(0(x1)))) -> #0(0(5(1(2(x1))))) #9: #0(5(1(0(x1)))) -> #0(5(1(2(x1)))) #10: #0(1(3(3(0(x1))))) -> #3(3(2(0(0(1(x1)))))) #11: #0(1(3(3(0(x1))))) -> #3(2(0(0(1(x1))))) #12: #0(1(3(3(0(x1))))) -> #0(0(1(x1))) #13: #0(1(3(3(0(x1))))) -> #0(1(x1)) #14: #3(0(1(5(4(x1))))) -> #0(5(3(4(1(2(x1)))))) #15: #3(0(1(5(4(x1))))) -> #3(4(1(2(x1)))) #16: #0(3(1(0(4(x1))))) -> #0(0(3(1(2(4(x1)))))) #17: #0(3(1(0(4(x1))))) -> #0(3(1(2(4(x1))))) #18: #0(3(1(0(4(x1))))) -> #3(1(2(4(x1)))) #19: #0(1(5(4(4(x1))))) -> #0(4(3(4(1(x1))))) #20: #0(1(5(4(4(x1))))) -> #3(4(1(x1))) #21: #0(1(3(5(1(x1))))) -> #0(3(3(x1))) #22: #0(1(3(5(1(x1))))) -> #3(3(x1)) #23: #0(1(3(5(1(x1))))) -> #3(x1) #24: #3(5(0(1(0(x1))))) -> #0(0(3(x1))) #25: #3(5(0(1(0(x1))))) -> #0(3(x1)) #26: #3(5(0(1(0(x1))))) -> #3(x1) #27: #3(5(4(0(0(x1))))) -> #0(3(0(4(4(x1))))) #28: #3(5(4(0(0(x1))))) -> #3(0(4(4(x1)))) #29: #3(5(4(0(0(x1))))) -> #0(4(4(x1))) #30: #0(1(5(2(0(x1))))) -> #0(3(1(0(2(x1))))) #31: #0(1(5(2(0(x1))))) -> #3(1(0(2(x1)))) #32: #0(1(5(2(0(x1))))) -> #0(2(x1)) #33: #0(1(0(x1))) -> #0(0(2(4(1(4(x1)))))) #34: #0(1(0(x1))) -> #0(2(4(1(4(x1))))) #35: #0(1(5(4(4(x1))))) -> #0(x1) #36: #0(1(3(0(x1)))) -> #0(3(0(1(2(x1))))) #37: #0(1(3(0(x1)))) -> #3(0(1(2(x1)))) #38: #0(1(3(0(x1)))) -> #0(1(2(x1))) #39: #0(0(4(1(x1)))) -> #0(0(2(1(4(x1))))) #40: #0(0(4(1(x1)))) -> #0(2(1(4(x1)))) #41: #0(1(0(4(x1)))) -> #0(0(3(4(1(2(x1)))))) #42: #0(1(0(4(x1)))) -> #0(3(4(1(2(x1))))) #43: #0(1(0(4(x1)))) -> #3(4(1(2(x1)))) #44: #0(4(5(1(x1)))) -> #3(1(4(5(0(2(x1)))))) #45: #0(4(5(1(x1)))) -> #0(2(x1)) #46: #0(4(5(1(x1)))) -> #0(x1) #47: #0(5(1(5(1(x1))))) -> #3(0(1(1(x1)))) #48: #0(5(1(5(1(x1))))) -> #0(1(1(x1))) #49: #0(1(3(0(x1)))) -> #0(0(3(1(4(x1))))) #50: #0(1(3(0(x1)))) -> #0(3(1(4(x1)))) #51: #0(1(3(0(x1)))) -> #3(1(4(x1))) #52: #3(5(1(0(x1)))) -> #0(5(1(3(2(x1))))) #53: #3(5(1(0(x1)))) -> #3(2(x1)) #54: #0(1(3(0(x1)))) -> #0(0(1(3(2(5(x1)))))) #55: #0(1(3(0(x1)))) -> #0(1(3(2(5(x1))))) #56: #0(1(3(0(x1)))) -> #3(2(5(x1))) #57: #3(5(0(1(x1)))) -> #3(0(2(1(2(5(x1)))))) #58: #3(5(0(1(x1)))) -> #0(2(1(2(5(x1))))) #59: #3(5(5(0(1(x1))))) -> #0(3(1(2(x1)))) #60: #3(5(5(0(1(x1))))) -> #3(1(2(x1))) #61: #0(4(5(1(x1)))) -> #3(2(5(1(4(0(x1)))))) #62: #0(4(5(1(x1)))) -> #0(x1) #63: #0(3(0(1(x1)))) -> #0(0(3(1(2(2(x1)))))) #64: #0(3(0(1(x1)))) -> #0(3(1(2(2(x1))))) #65: #0(3(0(1(x1)))) -> #3(1(2(2(x1)))) #66: #0(4(0(x1))) -> #3(4(3(2(0(0(x1)))))) #67: #0(4(0(x1))) -> #3(2(0(0(x1)))) #68: #0(4(0(x1))) -> #0(0(x1)) #69: #0(1(5(4(1(x1))))) -> #3(4(1(0(1(x1))))) #70: #0(1(5(4(1(x1))))) -> #0(1(x1)) #71: #0(0(4(1(x1)))) -> #0(0(2(1(4(3(x1)))))) #72: #0(0(4(1(x1)))) -> #0(2(1(4(3(x1))))) #73: #0(0(4(1(x1)))) -> #3(x1) #74: #3(5(1(0(x1)))) -> #3(1(2(2(0(5(x1)))))) #75: #3(5(1(0(x1)))) -> #0(5(x1)) #76: #0(1(0(x1))) -> #0(0(1(2(2(4(x1)))))) #77: #0(1(0(x1))) -> #0(1(2(2(4(x1))))) #78: #0(4(5(2(0(x1))))) -> #0(2(2(5(0(4(x1)))))) #79: #0(4(5(2(0(x1))))) -> #0(4(x1)) #80: #0(4(5(4(x1)))) -> #0(4(x1)) #81: #0(4(0(1(x1)))) -> #0(0(2(1(4(x1))))) #82: #0(4(0(1(x1)))) -> #0(2(1(4(x1)))) #83: #3(5(1(0(x1)))) -> #3(2(0(2(x1)))) #84: #3(5(1(0(x1)))) -> #0(2(x1)) #85: #0(4(5(1(x1)))) -> #0(5(1(4(x1)))) #86: #0(1(5(4(x1)))) -> #0(x1) #87: #3(5(1(0(x1)))) -> #0(5(3(x1))) #88: #3(5(1(0(x1)))) -> #3(x1) #89: #0(1(5(4(x1)))) -> #0(2(4(1(4(x1))))) #90: #0(4(5(1(x1)))) -> #3(0(5(1(4(x1))))) #91: #0(4(5(1(x1)))) -> #0(5(1(4(x1)))) #92: #0(1(3(5(1(x1))))) -> #3(4(5(0(x1)))) #93: #0(1(3(5(1(x1))))) -> #0(x1) #94: #0(3(1(0(x1)))) -> #0(0(3(1(4(x1))))) #95: #0(3(1(0(x1)))) -> #0(3(1(4(x1)))) #96: #0(3(1(0(x1)))) -> #3(1(4(x1))) #97: #0(1(5(1(x1)))) -> #0(x1) #98: #0(1(0(x1))) -> #0(0(1(2(4(x1))))) #99: #0(1(0(x1))) -> #0(1(2(4(x1)))) #100: #0(0(1(x1))) -> #0(0(2(1(2(x1))))) #101: #0(0(1(x1))) -> #0(2(1(2(x1)))) #102: #0(0(1(0(x1)))) -> #0(0(0(1(4(x1))))) #103: #0(0(1(0(x1)))) -> #0(0(1(4(x1)))) #104: #0(0(1(0(x1)))) -> #0(1(4(x1))) #105: #0(1(4(0(x1)))) -> #0(2(0(3(1(4(x1)))))) #106: #0(1(4(0(x1)))) -> #0(3(1(4(x1)))) #107: #0(1(4(0(x1)))) -> #3(1(4(x1))) #108: #0(1(0(x1))) -> #0(0(x1)) #109: #0(1(5(4(x1)))) -> #0(3(2(5(x1)))) #110: #0(1(5(4(x1)))) -> #3(2(5(x1))) Number of SCCs: 2, DPs: 12 SCC { #26 #88 } POLO(Sum)... succeeded. #0 w: 0 1 w: x1 4 w: 0 5 w: x1 3 w: 0 0 w: x1 + 1 #3 w: x1 2 w: 0 USABLE RULES: { } Removed DPs: #26 #88 Number of SCCs: 1, DPs: 10 SCC { #13 #35 #46 #62 #70 #79 #80 #86 #93 #97 } POLO(Sum)... succeeded. #0 w: x1 1 w: x1 + 30613 4 w: x1 + 38551 5 w: x1 3 w: x1 0 w: x1 + 1 #3 w: 0 2 w: x1 + 5853 USABLE RULES: { } Removed DPs: #13 #35 #46 #62 #70 #79 #80 #86 #93 #97 Number of SCCs: 0, DPs: 0