YES Input TRS: 1: 0(1(2(x1))) -> 0(2(1(0(x1)))) 2: 0(1(2(x1))) -> 1(0(2(3(x1)))) 3: 0(1(2(x1))) -> 0(2(4(1(5(x1))))) 4: 0(1(2(x1))) -> 0(3(2(1(0(x1))))) 5: 0(1(2(x1))) -> 1(0(3(2(3(x1))))) 6: 0(1(2(x1))) -> 0(1(3(4(2(3(x1)))))) 7: 0(5(2(x1))) -> 0(2(4(5(3(x1))))) 8: 0(5(2(x1))) -> 5(4(2(3(0(4(x1)))))) 9: 2(0(1(x1))) -> 3(0(2(1(x1)))) 10: 2(0(1(x1))) -> 0(2(1(1(4(x1))))) 11: 2(0(1(x1))) -> 0(3(2(4(1(x1))))) 12: 2(0(1(x1))) -> 3(0(2(1(4(x1))))) 13: 2(0(1(x1))) -> 0(2(2(3(4(1(x1)))))) 14: 2(0(1(x1))) -> 0(3(2(3(1(1(x1)))))) 15: 2(0(1(x1))) -> 4(0(4(2(1(4(x1)))))) 16: 2(5(1(x1))) -> 0(2(1(5(1(x1))))) 17: 2(5(1(x1))) -> 1(4(5(4(2(x1))))) 18: 2(5(1(x1))) -> 5(0(2(1(4(x1))))) 19: 2(5(1(x1))) -> 5(2(1(4(1(x1))))) 20: 2(5(1(x1))) -> 1(5(0(2(4(1(x1)))))) 21: 2(5(1(x1))) -> 5(2(1(1(1(1(x1)))))) 22: 0(1(2(1(x1)))) -> 3(1(4(0(2(1(x1)))))) 23: 0(1(3(1(x1)))) -> 5(0(3(1(1(x1))))) 24: 0(1(3(1(x1)))) -> 1(0(3(4(2(1(x1)))))) 25: 0(1(5(1(x1)))) -> 5(0(3(1(1(x1))))) 26: 0(2(1(2(x1)))) -> 0(2(2(1(5(x1))))) 27: 0(2(5(1(x1)))) -> 1(1(5(0(2(1(x1)))))) 28: 0(5(3(1(x1)))) -> 0(1(4(4(3(5(x1)))))) 29: 0(5(5(2(x1)))) -> 5(4(2(3(5(0(x1)))))) 30: 2(0(1(2(x1)))) -> 0(2(3(2(1(1(x1)))))) 31: 2(0(1(2(x1)))) -> 4(0(2(1(1(2(x1)))))) 32: 2(0(4(1(x1)))) -> 3(0(2(4(1(x1))))) 33: 2(0(5(1(x1)))) -> 5(4(2(1(0(x1))))) 34: 2(2(5(1(x1)))) -> 3(2(2(4(5(1(x1)))))) 35: 2(4(0(1(x1)))) -> 1(0(2(4(4(x1))))) 36: 2(4(0(1(x1)))) -> 3(0(0(2(4(1(x1)))))) 37: 2(4(0(1(x1)))) -> 5(4(0(2(1(1(x1)))))) 38: 2(5(2(1(x1)))) -> 1(5(2(2(3(1(x1)))))) 39: 2(5(4(1(x1)))) -> 4(5(2(1(4(4(x1)))))) 40: 2(5(5(1(x1)))) -> 1(5(4(2(4(5(x1)))))) 41: 2(5(5(2(x1)))) -> 5(5(2(3(2(x1))))) 42: 0(1(3(0(1(x1))))) -> 0(3(1(0(1(1(x1)))))) 43: 0(2(4(3(1(x1))))) -> 1(3(4(2(3(0(x1)))))) 44: 0(2(4(3(1(x1))))) -> 4(0(3(2(1(0(x1)))))) 45: 0(2(5(3(1(x1))))) -> 5(0(2(3(5(1(x1)))))) 46: 2(0(5(4(1(x1))))) -> 0(4(5(3(2(1(x1)))))) 47: 2(2(0(1(2(x1))))) -> 2(4(0(2(2(1(x1)))))) 48: 2(4(0(5(1(x1))))) -> 1(4(5(0(4(2(x1)))))) 49: 2(4(2(3(1(x1))))) -> 4(2(2(3(3(1(x1)))))) 50: 2(5(2(0(1(x1))))) -> 0(2(4(1(5(2(x1)))))) Number of strict rules: 50 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #0(1(2(x1))) -> #0(2(3(x1))) #2: #0(1(2(x1))) -> #2(3(x1)) #3: #0(2(4(3(1(x1))))) -> #2(3(0(x1))) #4: #0(2(4(3(1(x1))))) -> #0(x1) #5: #0(5(5(2(x1)))) -> #2(3(5(0(x1)))) #6: #0(5(5(2(x1)))) -> #0(x1) #7: #2(4(0(1(x1)))) -> #0(2(4(4(x1)))) #8: #2(4(0(1(x1)))) -> #2(4(4(x1))) #9: #2(0(5(4(1(x1))))) -> #0(4(5(3(2(1(x1)))))) #10: #2(0(5(4(1(x1))))) -> #2(1(x1)) #11: #0(1(3(0(1(x1))))) -> #0(3(1(0(1(1(x1)))))) #12: #0(1(3(0(1(x1))))) -> #0(1(1(x1))) #13: #2(5(5(2(x1)))) -> #2(3(2(x1))) #14: #2(4(0(1(x1)))) -> #0(2(1(1(x1)))) #15: #2(4(0(1(x1)))) -> #2(1(1(x1))) #16: #2(2(0(1(2(x1))))) -> #2(4(0(2(2(1(x1)))))) #17: #2(2(0(1(2(x1))))) -> #0(2(2(1(x1)))) #18: #2(2(0(1(2(x1))))) -> #2(2(1(x1))) #19: #2(2(0(1(2(x1))))) -> #2(1(x1)) #20: #2(4(0(5(1(x1))))) -> #0(4(2(x1))) #21: #2(4(0(5(1(x1))))) -> #2(x1) #22: #2(5(2(1(x1)))) -> #2(2(3(1(x1)))) #23: #2(5(2(1(x1)))) -> #2(3(1(x1))) #24: #0(1(2(x1))) -> #0(1(3(4(2(3(x1)))))) #25: #0(1(2(x1))) -> #2(3(x1)) #26: #2(5(5(1(x1)))) -> #2(4(5(x1))) #27: #2(0(1(x1))) -> #0(2(2(3(4(1(x1)))))) #28: #2(0(1(x1))) -> #2(2(3(4(1(x1))))) #29: #2(0(1(x1))) -> #2(3(4(1(x1)))) #30: #2(0(1(x1))) -> #0(2(1(x1))) #31: #2(0(1(x1))) -> #2(1(x1)) #32: #2(0(1(x1))) -> #0(3(2(4(1(x1))))) #33: #2(0(1(x1))) -> #2(4(1(x1))) #34: #0(1(3(1(x1)))) -> #0(3(4(2(1(x1))))) #35: #0(1(3(1(x1)))) -> #2(1(x1)) #36: #0(1(3(1(x1)))) -> #0(3(1(1(x1)))) #37: #0(2(5(3(1(x1))))) -> #0(2(3(5(1(x1))))) #38: #0(2(5(3(1(x1))))) -> #2(3(5(1(x1)))) #39: #2(0(1(x1))) -> #0(2(1(4(x1)))) #40: #2(0(1(x1))) -> #2(1(4(x1))) #41: #2(0(1(2(x1)))) -> #0(2(1(1(2(x1))))) #42: #2(0(1(2(x1)))) -> #2(1(1(2(x1)))) #43: #2(0(1(x1))) -> #0(3(2(3(1(1(x1)))))) #44: #2(0(1(x1))) -> #2(3(1(1(x1)))) #45: #2(0(1(2(x1)))) -> #0(2(3(2(1(1(x1)))))) #46: #2(0(1(2(x1)))) -> #2(3(2(1(1(x1))))) #47: #2(0(1(2(x1)))) -> #2(1(1(x1))) #48: #2(4(2(3(1(x1))))) -> #2(2(3(3(1(x1))))) #49: #2(4(2(3(1(x1))))) -> #2(3(3(1(x1)))) #50: #0(1(5(1(x1)))) -> #0(3(1(1(x1)))) #51: #2(5(1(x1))) -> #0(2(4(1(x1)))) #52: #2(5(1(x1))) -> #2(4(1(x1))) #53: #0(5(2(x1))) -> #0(2(4(5(3(x1))))) #54: #0(5(2(x1))) -> #2(4(5(3(x1)))) #55: #2(5(4(1(x1)))) -> #2(1(4(4(x1)))) #56: #2(0(1(x1))) -> #0(2(1(1(4(x1))))) #57: #2(0(1(x1))) -> #2(1(1(4(x1)))) #58: #2(0(5(1(x1)))) -> #2(1(0(x1))) #59: #2(0(5(1(x1)))) -> #0(x1) #60: #0(1(2(x1))) -> #0(3(2(3(x1)))) #61: #0(1(2(x1))) -> #2(3(x1)) #62: #0(2(4(3(1(x1))))) -> #0(3(2(1(0(x1))))) #63: #0(2(4(3(1(x1))))) -> #2(1(0(x1))) #64: #0(2(4(3(1(x1))))) -> #0(x1) #65: #0(5(3(1(x1)))) -> #0(1(4(4(3(5(x1)))))) #66: #0(1(2(1(x1)))) -> #0(2(1(x1))) #67: #2(2(5(1(x1)))) -> #2(2(4(5(1(x1))))) #68: #2(2(5(1(x1)))) -> #2(4(5(1(x1)))) #69: #0(2(5(1(x1)))) -> #0(2(1(x1))) #70: #0(2(5(1(x1)))) -> #2(1(x1)) #71: #2(5(1(x1))) -> #2(x1) #72: #2(0(4(1(x1)))) -> #0(2(4(1(x1)))) #73: #2(0(4(1(x1)))) -> #2(4(1(x1))) #74: #2(5(1(x1))) -> #2(1(4(1(x1)))) #75: #0(2(1(2(x1)))) -> #0(2(2(1(5(x1))))) #76: #0(2(1(2(x1)))) -> #2(2(1(5(x1)))) #77: #0(2(1(2(x1)))) -> #2(1(5(x1))) #78: #2(4(0(1(x1)))) -> #0(0(2(4(1(x1))))) #79: #2(4(0(1(x1)))) -> #0(2(4(1(x1)))) #80: #2(4(0(1(x1)))) -> #2(4(1(x1))) #81: #2(5(1(x1))) -> #2(1(1(1(1(x1))))) #82: #2(5(1(x1))) -> #0(2(1(5(1(x1))))) #83: #2(5(1(x1))) -> #2(1(5(1(x1)))) #84: #0(1(2(x1))) -> #0(2(4(1(5(x1))))) #85: #0(1(2(x1))) -> #2(4(1(5(x1)))) #86: #0(1(2(x1))) -> #0(2(1(0(x1)))) #87: #0(1(2(x1))) -> #2(1(0(x1))) #88: #0(1(2(x1))) -> #0(x1) #89: #0(5(2(x1))) -> #2(3(0(4(x1)))) #90: #0(5(2(x1))) -> #0(4(x1)) #91: #2(0(1(x1))) -> #0(4(2(1(4(x1))))) #92: #2(0(1(x1))) -> #2(1(4(x1))) #93: #0(1(2(x1))) -> #0(3(2(1(0(x1))))) #94: #0(1(2(x1))) -> #2(1(0(x1))) #95: #0(1(2(x1))) -> #0(x1) #96: #2(5(2(0(1(x1))))) -> #0(2(4(1(5(2(x1)))))) #97: #2(5(2(0(1(x1))))) -> #2(4(1(5(2(x1))))) #98: #2(5(2(0(1(x1))))) -> #2(x1) #99: #2(5(1(x1))) -> #0(2(1(4(x1)))) #100: #2(5(1(x1))) -> #2(1(4(x1))) Number of SCCs: 2, DPs: 8 SCC { #21 #71 #98 } POLO(Sum)... succeeded. #0 w: 0 1 w: x1 + 1 4 w: x1 5 w: x1 3 w: 0 #2 w: x1 0 w: x1 2 w: x1 + 7757 USABLE RULES: { } Removed DPs: #21 #71 #98 Number of SCCs: 1, DPs: 5 SCC { #4 #6 #64 #88 #95 } POLO(Sum)... succeeded. #0 w: x1 1 w: x1 + 1 4 w: x1 + 23675 5 w: x1 + 8855 3 w: x1 #2 w: 0 0 w: 0 2 w: x1 + 1 USABLE RULES: { } Removed DPs: #4 #6 #64 #88 #95 Number of SCCs: 0, DPs: 0