YES Input TRS: 1: 1(4(x1)) -> 3(1(1(2(2(4(x1)))))) 2: 5(4(x1)) -> 4(2(3(1(1(1(x1)))))) 3: 0(3(0(x1))) -> 2(1(1(0(2(0(x1)))))) 4: 0(5(5(x1))) -> 1(0(1(3(4(2(x1)))))) 5: 1(5(4(x1))) -> 0(2(5(2(0(4(x1)))))) 6: 3(5(4(x1))) -> 4(1(3(4(2(3(x1)))))) 7: 4(1(4(x1))) -> 3(3(2(2(3(1(x1)))))) 8: 5(4(0(x1))) -> 2(4(0(4(4(0(x1)))))) 9: 5(4(0(x1))) -> 5(1(5(2(1(0(x1)))))) 10: 5(4(4(x1))) -> 4(1(1(3(2(4(x1)))))) 11: 5(5(4(x1))) -> 3(4(4(1(2(2(x1)))))) 12: 0(5(5(0(x1)))) -> 0(2(0(0(3(0(x1)))))) 13: 0(5(5(4(x1)))) -> 0(1(3(4(3(4(x1)))))) 14: 1(4(5(4(x1)))) -> 0(4(5(0(2(1(x1)))))) 15: 1(4(5(5(x1)))) -> 0(0(1(3(4(1(x1)))))) 16: 2(5(4(0(x1)))) -> 0(4(1(2(4(0(x1)))))) 17: 4(3(0(5(x1)))) -> 3(3(2(3(5(5(x1)))))) 18: 5(4(0(0(x1)))) -> 1(0(4(0(2(2(x1)))))) 19: 5(4(0(2(x1)))) -> 3(0(4(5(0(2(x1)))))) Number of strict rules: 19 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #5(4(x1)) -> #4(2(3(1(1(1(x1)))))) #2: #5(4(x1)) -> #2(3(1(1(1(x1))))) #3: #5(4(x1)) -> #3(1(1(1(x1)))) #4: #5(4(x1)) -> #1(1(1(x1))) #5: #5(4(x1)) -> #1(1(x1)) #6: #5(4(x1)) -> #1(x1) #7: #3(5(4(x1))) -> #4(1(3(4(2(3(x1)))))) #8: #3(5(4(x1))) -> #1(3(4(2(3(x1))))) #9: #3(5(4(x1))) -> #3(4(2(3(x1)))) #10: #3(5(4(x1))) -> #4(2(3(x1))) #11: #3(5(4(x1))) -> #2(3(x1)) #12: #3(5(4(x1))) -> #3(x1) #13: #0(5(5(4(x1)))) -> #0(1(3(4(3(4(x1)))))) #14: #0(5(5(4(x1)))) -> #1(3(4(3(4(x1))))) #15: #0(5(5(4(x1)))) -> #3(4(3(4(x1)))) #16: #0(5(5(4(x1)))) -> #4(3(4(x1))) #17: #0(5(5(4(x1)))) -> #3(4(x1)) #18: #5(4(0(x1))) -> #5(1(5(2(1(0(x1)))))) #19: #5(4(0(x1))) -> #1(5(2(1(0(x1))))) #20: #5(4(0(x1))) -> #5(2(1(0(x1)))) #21: #5(4(0(x1))) -> #2(1(0(x1))) #22: #5(4(0(x1))) -> #1(0(x1)) #23: #5(5(4(x1))) -> #3(4(4(1(2(2(x1)))))) #24: #5(5(4(x1))) -> #4(4(1(2(2(x1))))) #25: #5(5(4(x1))) -> #4(1(2(2(x1)))) #26: #5(5(4(x1))) -> #1(2(2(x1))) #27: #5(5(4(x1))) -> #2(2(x1)) #28: #5(5(4(x1))) -> #2(x1) #29: #0(5(5(0(x1)))) -> #0(2(0(0(3(0(x1)))))) #30: #0(5(5(0(x1)))) -> #2(0(0(3(0(x1))))) #31: #0(5(5(0(x1)))) -> #0(0(3(0(x1)))) #32: #0(5(5(0(x1)))) -> #0(3(0(x1))) #33: #0(5(5(0(x1)))) -> #3(0(x1)) #34: #1(4(5(4(x1)))) -> #0(4(5(0(2(1(x1)))))) #35: #1(4(5(4(x1)))) -> #4(5(0(2(1(x1))))) #36: #1(4(5(4(x1)))) -> #5(0(2(1(x1)))) #37: #1(4(5(4(x1)))) -> #0(2(1(x1))) #38: #1(4(5(4(x1)))) -> #2(1(x1)) #39: #1(4(5(4(x1)))) -> #1(x1) #40: #4(1(4(x1))) -> #3(3(2(2(3(1(x1)))))) #41: #4(1(4(x1))) -> #3(2(2(3(1(x1))))) #42: #4(1(4(x1))) -> #2(2(3(1(x1)))) #43: #4(1(4(x1))) -> #2(3(1(x1))) #44: #4(1(4(x1))) -> #3(1(x1)) #45: #4(1(4(x1))) -> #1(x1) #46: #5(4(4(x1))) -> #4(1(1(3(2(4(x1)))))) #47: #5(4(4(x1))) -> #1(1(3(2(4(x1))))) #48: #5(4(4(x1))) -> #1(3(2(4(x1)))) #49: #5(4(4(x1))) -> #3(2(4(x1))) #50: #5(4(4(x1))) -> #2(4(x1)) #51: #1(5(4(x1))) -> #0(2(5(2(0(4(x1)))))) #52: #1(5(4(x1))) -> #2(5(2(0(4(x1))))) #53: #1(5(4(x1))) -> #5(2(0(4(x1)))) #54: #1(5(4(x1))) -> #2(0(4(x1))) #55: #1(5(4(x1))) -> #0(4(x1)) #56: #4(3(0(5(x1)))) -> #3(3(2(3(5(5(x1)))))) #57: #4(3(0(5(x1)))) -> #3(2(3(5(5(x1))))) #58: #4(3(0(5(x1)))) -> #2(3(5(5(x1)))) #59: #4(3(0(5(x1)))) -> #3(5(5(x1))) #60: #4(3(0(5(x1)))) -> #5(5(x1)) #61: #5(4(0(2(x1)))) -> #3(0(4(5(0(2(x1)))))) #62: #5(4(0(2(x1)))) -> #0(4(5(0(2(x1))))) #63: #5(4(0(2(x1)))) -> #4(5(0(2(x1)))) #64: #5(4(0(2(x1)))) -> #5(0(2(x1))) #65: #2(5(4(0(x1)))) -> #0(4(1(2(4(0(x1)))))) #66: #2(5(4(0(x1)))) -> #4(1(2(4(0(x1))))) #67: #2(5(4(0(x1)))) -> #1(2(4(0(x1)))) #68: #2(5(4(0(x1)))) -> #2(4(0(x1))) #69: #0(3(0(x1))) -> #2(1(1(0(2(0(x1)))))) #70: #0(3(0(x1))) -> #1(1(0(2(0(x1))))) #71: #0(3(0(x1))) -> #1(0(2(0(x1)))) #72: #0(3(0(x1))) -> #0(2(0(x1))) #73: #0(3(0(x1))) -> #2(0(x1)) #74: #1(4(x1)) -> #3(1(1(2(2(4(x1)))))) #75: #1(4(x1)) -> #1(1(2(2(4(x1))))) #76: #1(4(x1)) -> #1(2(2(4(x1)))) #77: #1(4(x1)) -> #2(2(4(x1))) #78: #1(4(x1)) -> #2(4(x1)) #79: #5(4(0(x1))) -> #2(4(0(4(4(0(x1)))))) #80: #5(4(0(x1))) -> #4(0(4(4(0(x1))))) #81: #5(4(0(x1))) -> #0(4(4(0(x1)))) #82: #5(4(0(x1))) -> #4(4(0(x1))) #83: #1(4(5(5(x1)))) -> #0(0(1(3(4(1(x1)))))) #84: #1(4(5(5(x1)))) -> #0(1(3(4(1(x1))))) #85: #1(4(5(5(x1)))) -> #1(3(4(1(x1)))) #86: #1(4(5(5(x1)))) -> #3(4(1(x1))) #87: #1(4(5(5(x1)))) -> #4(1(x1)) #88: #1(4(5(5(x1)))) -> #1(x1) #89: #0(5(5(x1))) -> #1(0(1(3(4(2(x1)))))) #90: #0(5(5(x1))) -> #0(1(3(4(2(x1))))) #91: #0(5(5(x1))) -> #1(3(4(2(x1)))) #92: #0(5(5(x1))) -> #3(4(2(x1))) #93: #0(5(5(x1))) -> #4(2(x1)) #94: #0(5(5(x1))) -> #2(x1) #95: #5(4(0(0(x1)))) -> #1(0(4(0(2(2(x1)))))) #96: #5(4(0(0(x1)))) -> #0(4(0(2(2(x1))))) #97: #5(4(0(0(x1)))) -> #4(0(2(2(x1)))) #98: #5(4(0(0(x1)))) -> #0(2(2(x1))) #99: #5(4(0(0(x1)))) -> #2(2(x1)) #100: #5(4(0(0(x1)))) -> #2(x1) Number of SCCs: 2, DPs: 5 SCC { #12 } POLO(Sum)... succeeded. #0 w: 0 1 w: 0 4 w: x1 + 1 5 w: x1 3 w: 0 #2 w: 0 #4 w: 0 0 w: 0 #3 w: x1 #5 w: 0 2 w: 0 #1 w: 0 USABLE RULES: { } Removed DPs: #12 Number of SCCs: 1, DPs: 4 SCC { #39 #45 #87 #88 } POLO(Sum)... succeeded. #0 w: 0 1 w: x1 + 8367 4 w: x1 + 28532 5 w: x1 + 8366 3 w: x1 + 1 #2 w: 0 #4 w: x1 + 36896 0 w: 20164 #3 w: 0 #5 w: 0 2 w: 20164 #1 w: x1 USABLE RULES: { 1 3 5 7 14..17 } Removed DPs: #39 #45 #87 #88 Number of SCCs: 0, DPs: 0