YES Input TRS: 1: 0(0(1(x1))) -> 0(1(2(0(3(x1))))) 2: 0(0(1(x1))) -> 0(1(2(0(3(2(x1)))))) 3: 0(0(1(x1))) -> 1(2(0(0(3(2(x1)))))) 4: 0(1(0(x1))) -> 2(0(3(1(2(0(x1)))))) 5: 0(4(1(x1))) -> 4(0(3(1(x1)))) 6: 0(4(1(x1))) -> 2(4(0(3(2(1(x1)))))) 7: 0(4(1(x1))) -> 2(4(0(5(3(1(x1)))))) 8: 0(4(1(x1))) -> 4(2(1(2(0(3(x1)))))) 9: 4(1(0(x1))) -> 1(2(0(4(x1)))) 10: 0(0(1(1(x1)))) -> 1(2(0(0(3(1(x1)))))) 11: 0(0(2(1(x1)))) -> 2(2(0(3(0(1(x1)))))) 12: 0(0(4(1(x1)))) -> 1(4(0(3(0(3(x1)))))) 13: 0(0(5(1(x1)))) -> 0(0(3(1(2(5(x1)))))) 14: 0(1(1(0(x1)))) -> 1(2(0(0(1(2(x1)))))) 15: 0(1(4(1(x1)))) -> 0(1(2(4(1(2(x1)))))) 16: 0(1(5(0(x1)))) -> 1(2(5(0(0(3(x1)))))) 17: 0(2(4(1(x1)))) -> 4(0(5(3(1(2(x1)))))) 18: 0(4(1(0(x1)))) -> 0(4(0(1(2(x1))))) 19: 0(4(2(1(x1)))) -> 4(0(3(2(2(1(x1)))))) 20: 0(4(2(1(x1)))) -> 4(0(3(5(1(2(x1)))))) 21: 0(4(4(1(x1)))) -> 2(4(0(3(4(1(x1)))))) 22: 0(5(0(1(x1)))) -> 0(2(0(3(5(1(x1)))))) 23: 0(5(0(1(x1)))) -> 5(2(0(3(0(1(x1)))))) 24: 0(5(1(0(x1)))) -> 0(1(2(0(3(5(x1)))))) 25: 0(5(1(0(x1)))) -> 2(0(1(3(5(0(x1)))))) 26: 4(0(5(1(x1)))) -> 1(4(0(5(3(2(x1)))))) 27: 4(1(0(0(x1)))) -> 0(4(1(2(0(x1))))) 28: 4(1(0(1(x1)))) -> 1(1(2(0(4(x1))))) 29: 4(1(5(0(x1)))) -> 1(2(0(5(4(x1))))) 30: 4(1(5(0(x1)))) -> 1(4(0(3(5(x1))))) 31: 4(3(1(0(x1)))) -> 1(4(2(0(3(x1))))) 32: 4(3(1(0(x1)))) -> 2(0(2(1(3(4(x1)))))) 33: 4(3(1(0(x1)))) -> 2(1(4(2(0(3(x1)))))) 34: 4(3(1(0(x1)))) -> 2(2(4(0(1(3(x1)))))) 35: 5(0(1(0(x1)))) -> 0(3(5(1(2(0(x1)))))) 36: 5(0(1(0(x1)))) -> 1(5(2(0(3(0(x1)))))) 37: 5(4(1(0(x1)))) -> 0(1(2(4(5(2(x1)))))) 38: 0(0(5(5(1(x1))))) -> 1(0(0(3(5(5(x1)))))) 39: 0(1(0(5(0(x1))))) -> 0(1(5(2(0(0(x1)))))) 40: 0(2(5(0(1(x1))))) -> 2(0(3(5(0(1(x1)))))) 41: 0(3(1(0(0(x1))))) -> 0(0(3(0(1(2(x1)))))) 42: 0(4(1(4(1(x1))))) -> 4(4(0(1(2(1(x1)))))) 43: 0(5(5(4(1(x1))))) -> 4(1(0(5(5(3(x1)))))) 44: 4(1(5(0(0(x1))))) -> 1(2(0(4(5(0(x1)))))) 45: 4(1(5(5(0(x1))))) -> 5(1(3(0(5(4(x1)))))) 46: 4(3(1(0(1(x1))))) -> 1(1(2(3(0(4(x1)))))) 47: 4(3(1(1(0(x1))))) -> 1(2(0(1(4(3(x1)))))) 48: 4(3(1(5(0(x1))))) -> 5(1(0(3(2(4(x1)))))) 49: 4(4(1(0(5(x1))))) -> 4(0(5(3(4(1(x1)))))) Number of strict rules: 49 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #0(0(1(x1))) -> #0(1(2(0(3(2(x1)))))) #2: #0(0(1(x1))) -> #0(3(2(x1))) #3: #0(5(5(4(1(x1))))) -> #4(1(0(5(5(3(x1)))))) #4: #0(5(5(4(1(x1))))) -> #0(5(5(3(x1)))) #5: #0(5(5(4(1(x1))))) -> #5(5(3(x1))) #6: #0(5(5(4(1(x1))))) -> #5(3(x1)) #7: #4(1(5(0(x1)))) -> #0(5(4(x1))) #8: #4(1(5(0(x1)))) -> #5(4(x1)) #9: #4(1(5(0(x1)))) -> #4(x1) #10: #5(0(1(0(x1)))) -> #0(3(5(1(2(0(x1)))))) #11: #5(0(1(0(x1)))) -> #5(1(2(0(x1)))) #12: #4(3(1(0(1(x1))))) -> #0(4(x1)) #13: #4(3(1(0(1(x1))))) -> #4(x1) #14: #0(4(1(4(1(x1))))) -> #4(4(0(1(2(1(x1)))))) #15: #0(4(1(4(1(x1))))) -> #4(0(1(2(1(x1))))) #16: #0(4(1(4(1(x1))))) -> #0(1(2(1(x1)))) #17: #0(3(1(0(0(x1))))) -> #0(0(3(0(1(2(x1)))))) #18: #0(3(1(0(0(x1))))) -> #0(3(0(1(2(x1))))) #19: #0(3(1(0(0(x1))))) -> #0(1(2(x1))) #20: #5(4(1(0(x1)))) -> #0(1(2(4(5(2(x1)))))) #21: #5(4(1(0(x1)))) -> #4(5(2(x1))) #22: #5(4(1(0(x1)))) -> #5(2(x1)) #23: #4(3(1(1(0(x1))))) -> #0(1(4(3(x1)))) #24: #4(3(1(1(0(x1))))) -> #4(3(x1)) #25: #4(3(1(5(0(x1))))) -> #5(1(0(3(2(4(x1)))))) #26: #4(3(1(5(0(x1))))) -> #0(3(2(4(x1)))) #27: #4(3(1(5(0(x1))))) -> #4(x1) #28: #0(0(5(5(1(x1))))) -> #0(0(3(5(5(x1))))) #29: #0(0(5(5(1(x1))))) -> #0(3(5(5(x1)))) #30: #0(0(5(5(1(x1))))) -> #5(5(x1)) #31: #0(0(5(5(1(x1))))) -> #5(x1) #32: #0(4(1(x1))) -> #4(0(3(2(1(x1))))) #33: #0(4(1(x1))) -> #0(3(2(1(x1)))) #34: #0(2(5(0(1(x1))))) -> #0(3(5(0(1(x1))))) #35: #0(0(5(1(x1)))) -> #0(0(3(1(2(5(x1)))))) #36: #0(0(5(1(x1)))) -> #0(3(1(2(5(x1))))) #37: #0(0(5(1(x1)))) -> #5(x1) #38: #4(1(0(x1))) -> #0(4(x1)) #39: #4(1(0(x1))) -> #4(x1) #40: #0(0(2(1(x1)))) -> #0(3(0(1(x1)))) #41: #0(0(2(1(x1)))) -> #0(1(x1)) #42: #0(5(1(0(x1)))) -> #0(1(2(0(3(5(x1)))))) #43: #0(5(1(0(x1)))) -> #0(3(5(x1))) #44: #0(5(1(0(x1)))) -> #5(x1) #45: #0(5(0(1(x1)))) -> #5(2(0(3(0(1(x1)))))) #46: #0(5(0(1(x1)))) -> #0(3(0(1(x1)))) #47: #4(1(5(5(0(x1))))) -> #5(1(3(0(5(4(x1)))))) #48: #4(1(5(5(0(x1))))) -> #0(5(4(x1))) #49: #4(1(5(5(0(x1))))) -> #5(4(x1)) #50: #4(1(5(5(0(x1))))) -> #4(x1) #51: #0(0(4(1(x1)))) -> #4(0(3(0(3(x1))))) #52: #0(0(4(1(x1)))) -> #0(3(0(3(x1)))) #53: #0(0(4(1(x1)))) -> #0(3(x1)) #54: #4(3(1(0(x1)))) -> #4(2(0(3(x1)))) #55: #4(3(1(0(x1)))) -> #0(3(x1)) #56: #0(1(1(0(x1)))) -> #0(0(1(2(x1)))) #57: #0(1(1(0(x1)))) -> #0(1(2(x1))) #58: #4(1(5(0(x1)))) -> #4(0(3(5(x1)))) #59: #4(1(5(0(x1)))) -> #0(3(5(x1))) #60: #4(1(5(0(x1)))) -> #5(x1) #61: #4(4(1(0(5(x1))))) -> #4(0(5(3(4(1(x1)))))) #62: #4(4(1(0(5(x1))))) -> #0(5(3(4(1(x1))))) #63: #4(4(1(0(5(x1))))) -> #5(3(4(1(x1)))) #64: #4(4(1(0(5(x1))))) -> #4(1(x1)) #65: #0(5(1(0(x1)))) -> #0(1(3(5(0(x1))))) #66: #0(5(1(0(x1)))) -> #5(0(x1)) #67: #0(4(2(1(x1)))) -> #4(0(3(5(1(2(x1)))))) #68: #0(4(2(1(x1)))) -> #0(3(5(1(2(x1))))) #69: #0(4(2(1(x1)))) -> #5(1(2(x1))) #70: #0(4(1(x1))) -> #4(0(5(3(1(x1))))) #71: #0(4(1(x1))) -> #0(5(3(1(x1)))) #72: #0(4(1(x1))) -> #5(3(1(x1))) #73: #0(1(0(5(0(x1))))) -> #0(1(5(2(0(0(x1)))))) #74: #0(1(0(5(0(x1))))) -> #5(2(0(0(x1)))) #75: #0(1(0(5(0(x1))))) -> #0(0(x1)) #76: #0(0(1(1(x1)))) -> #0(0(3(1(x1)))) #77: #0(0(1(1(x1)))) -> #0(3(1(x1))) #78: #4(3(1(0(x1)))) -> #4(2(0(3(x1)))) #79: #4(3(1(0(x1)))) -> #0(3(x1)) #80: #0(4(1(x1))) -> #4(0(3(1(x1)))) #81: #0(4(1(x1))) -> #0(3(1(x1))) #82: #4(1(5(0(0(x1))))) -> #0(4(5(0(x1)))) #83: #4(1(5(0(0(x1))))) -> #4(5(0(x1))) #84: #4(1(5(0(0(x1))))) -> #5(0(x1)) #85: #4(1(0(1(x1)))) -> #0(4(x1)) #86: #4(1(0(1(x1)))) -> #4(x1) #87: #0(5(0(1(x1)))) -> #0(2(0(3(5(1(x1)))))) #88: #0(5(0(1(x1)))) -> #0(3(5(1(x1)))) #89: #0(5(0(1(x1)))) -> #5(1(x1)) #90: #4(3(1(0(x1)))) -> #4(0(1(3(x1)))) #91: #4(3(1(0(x1)))) -> #0(1(3(x1))) #92: #4(1(0(0(x1)))) -> #0(4(1(2(0(x1))))) #93: #4(1(0(0(x1)))) -> #4(1(2(0(x1)))) #94: #0(2(4(1(x1)))) -> #4(0(5(3(1(2(x1)))))) #95: #0(2(4(1(x1)))) -> #0(5(3(1(2(x1))))) #96: #0(2(4(1(x1)))) -> #5(3(1(2(x1)))) #97: #4(3(1(0(x1)))) -> #0(2(1(3(4(x1))))) #98: #4(3(1(0(x1)))) -> #4(x1) #99: #0(4(2(1(x1)))) -> #4(0(3(2(2(1(x1)))))) #100: #0(4(2(1(x1)))) -> #0(3(2(2(1(x1))))) #101: #4(0(5(1(x1)))) -> #4(0(5(3(2(x1))))) #102: #4(0(5(1(x1)))) -> #0(5(3(2(x1)))) #103: #4(0(5(1(x1)))) -> #5(3(2(x1))) #104: #5(0(1(0(x1)))) -> #5(2(0(3(0(x1))))) #105: #5(0(1(0(x1)))) -> #0(3(0(x1))) #106: #0(4(4(1(x1)))) -> #4(0(3(4(1(x1))))) #107: #0(4(4(1(x1)))) -> #0(3(4(1(x1)))) #108: #0(1(5(0(x1)))) -> #5(0(0(3(x1)))) #109: #0(1(5(0(x1)))) -> #0(0(3(x1))) #110: #0(1(5(0(x1)))) -> #0(3(x1)) #111: #0(0(1(x1))) -> #0(0(3(2(x1)))) #112: #0(0(1(x1))) -> #0(3(2(x1))) #113: #0(0(1(x1))) -> #0(1(2(0(3(x1))))) #114: #0(0(1(x1))) -> #0(3(x1)) #115: #0(4(1(x1))) -> #4(2(1(2(0(3(x1)))))) #116: #0(4(1(x1))) -> #0(3(x1)) #117: #0(1(4(1(x1)))) -> #0(1(2(4(1(2(x1)))))) #118: #0(1(4(1(x1)))) -> #4(1(2(x1))) #119: #0(1(0(x1))) -> #0(3(1(2(0(x1))))) #120: #0(4(1(0(x1)))) -> #0(4(0(1(2(x1))))) #121: #0(4(1(0(x1)))) -> #4(0(1(2(x1)))) #122: #0(4(1(0(x1)))) -> #0(1(2(x1))) Number of SCCs: 2, DPs: 11 SCC { #41 #75 } POLO(Sum)... succeeded. #0 w: x1 1 w: x1 + 1 4 w: x1 + 24696 5 w: x1 3 w: x1 #4 w: 0 0 w: x1 + 1 #5 w: 0 2 w: x1 USABLE RULES: { 1..49 } Removed DPs: #41 #75 Number of SCCs: 1, DPs: 9 SCC { #9 #13 #24 #27 #39 #50 #64 #86 #98 } POLO(Sum)... succeeded. #0 w: 0 1 w: x1 + 26051 4 w: x1 + 1 5 w: x1 3 w: x1 + 1 #4 w: x1 0 w: x1 + 38368 #5 w: 0 2 w: x1 USABLE RULES: { } Removed DPs: #9 #13 #24 #27 #39 #50 #64 #86 #98 Number of SCCs: 0, DPs: 0