YES Input TRS: 1: 0(1(2(x1))) -> 0(0(2(1(x1)))) 2: 0(1(2(x1))) -> 0(2(1(3(x1)))) 3: 0(1(2(x1))) -> 0(0(2(1(4(4(x1)))))) 4: 0(3(1(x1))) -> 0(1(3(4(0(x1))))) 5: 0(3(1(x1))) -> 0(1(3(4(4(x1))))) 6: 0(3(1(x1))) -> 1(3(4(4(4(0(x1)))))) 7: 0(3(2(x1))) -> 0(2(1(3(x1)))) 8: 0(3(2(x1))) -> 0(2(3(4(x1)))) 9: 0(3(2(x1))) -> 0(0(2(4(3(x1))))) 10: 0(3(2(x1))) -> 0(2(1(4(3(x1))))) 11: 0(3(2(x1))) -> 0(2(4(3(3(x1))))) 12: 0(3(2(x1))) -> 0(2(1(3(3(4(x1)))))) 13: 0(3(2(x1))) -> 0(2(3(4(5(5(x1)))))) 14: 0(3(2(x1))) -> 2(4(4(3(4(0(x1)))))) 15: 0(4(1(x1))) -> 0(1(4(4(x1)))) 16: 0(4(1(x1))) -> 0(2(1(4(x1)))) 17: 0(4(2(x1))) -> 0(2(1(4(x1)))) 18: 0(4(2(x1))) -> 0(2(3(4(x1)))) 19: 0(4(2(x1))) -> 0(2(4(3(x1)))) 20: 2(0(1(x1))) -> 5(0(2(1(x1)))) 21: 2(3(1(x1))) -> 1(3(5(2(x1)))) 22: 2(3(1(x1))) -> 0(2(1(3(5(x1))))) 23: 2(3(1(x1))) -> 1(4(3(5(2(x1))))) 24: 0(2(0(1(x1)))) -> 5(0(0(2(1(x1))))) 25: 0(3(1(1(x1)))) -> 0(1(4(1(3(4(x1)))))) 26: 0(3(2(1(x1)))) -> 0(0(3(4(2(1(x1)))))) 27: 0(3(2(2(x1)))) -> 1(3(4(0(2(2(x1)))))) 28: 0(4(1(2(x1)))) -> 1(4(0(2(5(x1))))) 29: 0(4(3(2(x1)))) -> 2(3(4(4(0(0(x1)))))) 30: 0(5(3(1(x1)))) -> 0(1(4(3(5(4(x1)))))) 31: 0(5(3(1(x1)))) -> 0(1(5(3(4(0(x1)))))) 32: 0(5(3(2(x1)))) -> 0(2(4(5(3(x1))))) 33: 0(5(3(2(x1)))) -> 0(2(5(3(3(x1))))) 34: 2(0(3(1(x1)))) -> 2(0(1(3(5(2(x1)))))) 35: 2(0(4(1(x1)))) -> 2(0(1(4(5(x1))))) 36: 2(5(3(2(x1)))) -> 2(5(2(3(3(x1))))) 37: 2(5(4(2(x1)))) -> 0(2(5(2(4(x1))))) 38: 0(0(3(2(1(x1))))) -> 0(0(1(3(5(2(x1)))))) 39: 0(1(0(3(2(x1))))) -> 0(1(4(3(2(0(x1)))))) 40: 0(1(0(3(2(x1))))) -> 2(3(1(0(0(5(x1)))))) 41: 0(3(2(5(1(x1))))) -> 0(2(5(1(3(3(x1)))))) 42: 0(5(1(1(2(x1))))) -> 0(2(4(1(1(5(x1)))))) 43: 0(5(1(2(2(x1))))) -> 0(2(5(2(1(2(x1)))))) 44: 0(5(3(2(1(x1))))) -> 0(1(3(4(2(5(x1)))))) 45: 0(5(5(3(2(x1))))) -> 0(2(5(1(3(5(x1)))))) 46: 2(0(3(1(1(x1))))) -> 2(1(0(1(3(4(x1)))))) 47: 2(2(0(3(1(x1))))) -> 1(3(0(2(5(2(x1)))))) 48: 2(2(0(5(1(x1))))) -> 2(0(2(1(5(1(x1)))))) 49: 2(5(5(4(1(x1))))) -> 5(5(2(1(3(4(x1)))))) Number of strict rules: 49 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #0(1(2(x1))) -> #0(2(1(3(x1)))) #2: #0(1(2(x1))) -> #2(1(3(x1))) #3: #0(5(1(2(2(x1))))) -> #0(2(5(2(1(2(x1)))))) #4: #0(5(1(2(2(x1))))) -> #2(5(2(1(2(x1))))) #5: #0(5(1(2(2(x1))))) -> #2(1(2(x1))) #6: #0(4(3(2(x1)))) -> #2(3(4(4(0(0(x1)))))) #7: #0(4(3(2(x1)))) -> #0(0(x1)) #8: #0(4(3(2(x1)))) -> #0(x1) #9: #2(0(4(1(x1)))) -> #2(0(1(4(5(x1))))) #10: #2(0(4(1(x1)))) -> #0(1(4(5(x1)))) #11: #2(0(3(1(1(x1))))) -> #2(1(0(1(3(4(x1)))))) #12: #2(0(3(1(1(x1))))) -> #0(1(3(4(x1)))) #13: #0(5(1(1(2(x1))))) -> #0(2(4(1(1(5(x1)))))) #14: #0(5(1(1(2(x1))))) -> #2(4(1(1(5(x1))))) #15: #0(3(2(5(1(x1))))) -> #0(2(5(1(3(3(x1)))))) #16: #0(3(2(5(1(x1))))) -> #2(5(1(3(3(x1))))) #17: #2(5(4(2(x1)))) -> #0(2(5(2(4(x1))))) #18: #2(5(4(2(x1)))) -> #2(5(2(4(x1)))) #19: #2(5(4(2(x1)))) -> #2(4(x1)) #20: #2(2(0(3(1(x1))))) -> #0(2(5(2(x1)))) #21: #2(2(0(3(1(x1))))) -> #2(5(2(x1))) #22: #2(2(0(3(1(x1))))) -> #2(x1) #23: #2(2(0(5(1(x1))))) -> #2(0(2(1(5(1(x1)))))) #24: #2(2(0(5(1(x1))))) -> #0(2(1(5(1(x1))))) #25: #2(2(0(5(1(x1))))) -> #2(1(5(1(x1)))) #26: #0(0(3(2(1(x1))))) -> #0(0(1(3(5(2(x1)))))) #27: #0(0(3(2(1(x1))))) -> #0(1(3(5(2(x1))))) #28: #0(0(3(2(1(x1))))) -> #2(x1) #29: #0(3(1(x1))) -> #0(x1) #30: #0(1(0(3(2(x1))))) -> #2(3(1(0(0(5(x1)))))) #31: #0(1(0(3(2(x1))))) -> #0(0(5(x1))) #32: #0(1(0(3(2(x1))))) -> #0(5(x1)) #33: #0(3(2(x1))) -> #0(2(3(4(5(5(x1)))))) #34: #0(3(2(x1))) -> #2(3(4(5(5(x1))))) #35: #0(3(2(x1))) -> #0(0(2(4(3(x1))))) #36: #0(3(2(x1))) -> #0(2(4(3(x1)))) #37: #0(3(2(x1))) -> #2(4(3(x1))) #38: #0(3(2(x1))) -> #0(2(4(3(3(x1))))) #39: #0(3(2(x1))) -> #2(4(3(3(x1)))) #40: #0(2(0(1(x1)))) -> #0(0(2(1(x1)))) #41: #0(2(0(1(x1)))) -> #0(2(1(x1))) #42: #0(2(0(1(x1)))) -> #2(1(x1)) #43: #2(3(1(x1))) -> #2(x1) #44: #0(5(5(3(2(x1))))) -> #0(2(5(1(3(5(x1)))))) #45: #0(5(5(3(2(x1))))) -> #2(5(1(3(5(x1))))) #46: #0(3(2(x1))) -> #0(2(1(3(3(4(x1)))))) #47: #0(3(2(x1))) -> #2(1(3(3(4(x1))))) #48: #0(5(3(1(x1)))) -> #0(1(5(3(4(0(x1)))))) #49: #0(5(3(1(x1)))) -> #0(x1) #50: #0(3(2(x1))) -> #2(4(4(3(4(0(x1)))))) #51: #0(3(2(x1))) -> #0(x1) #52: #0(5(3(1(x1)))) -> #0(1(4(3(5(4(x1)))))) #53: #2(5(5(4(1(x1))))) -> #2(1(3(4(x1)))) #54: #0(3(1(1(x1)))) -> #0(1(4(1(3(4(x1)))))) #55: #2(0(1(x1))) -> #0(2(1(x1))) #56: #2(0(1(x1))) -> #2(1(x1)) #57: #0(3(2(x1))) -> #0(2(1(3(x1)))) #58: #0(3(2(x1))) -> #2(1(3(x1))) #59: #0(1(0(3(2(x1))))) -> #0(1(4(3(2(0(x1)))))) #60: #0(1(0(3(2(x1))))) -> #2(0(x1)) #61: #0(1(0(3(2(x1))))) -> #0(x1) #62: #0(3(2(x1))) -> #0(2(1(4(3(x1))))) #63: #0(3(2(x1))) -> #2(1(4(3(x1)))) #64: #0(5(3(2(x1)))) -> #0(2(5(3(3(x1))))) #65: #0(5(3(2(x1)))) -> #2(5(3(3(x1)))) #66: #0(3(1(x1))) -> #0(1(3(4(4(x1))))) #67: #0(5(3(2(1(x1))))) -> #0(1(3(4(2(5(x1)))))) #68: #0(5(3(2(1(x1))))) -> #2(5(x1)) #69: #0(4(1(2(x1)))) -> #0(2(5(x1))) #70: #0(4(1(2(x1)))) -> #2(5(x1)) #71: #2(3(1(x1))) -> #0(2(1(3(5(x1))))) #72: #2(3(1(x1))) -> #2(1(3(5(x1)))) #73: #2(0(3(1(x1)))) -> #2(0(1(3(5(2(x1)))))) #74: #2(0(3(1(x1)))) -> #0(1(3(5(2(x1))))) #75: #2(0(3(1(x1)))) -> #2(x1) #76: #0(3(2(2(x1)))) -> #0(2(2(x1))) #77: #0(4(2(x1))) -> #0(2(1(4(x1)))) #78: #0(4(2(x1))) -> #2(1(4(x1))) #79: #0(5(3(2(x1)))) -> #0(2(4(5(3(x1))))) #80: #0(5(3(2(x1)))) -> #2(4(5(3(x1)))) #81: #0(4(2(x1))) -> #0(2(4(3(x1)))) #82: #0(4(2(x1))) -> #2(4(3(x1))) #83: #0(3(2(1(x1)))) -> #0(0(3(4(2(1(x1)))))) #84: #0(3(2(1(x1)))) -> #0(3(4(2(1(x1))))) #85: #2(5(3(2(x1)))) -> #2(5(2(3(3(x1))))) #86: #2(5(3(2(x1)))) -> #2(3(3(x1))) #87: #2(3(1(x1))) -> #2(x1) #88: #0(4(1(x1))) -> #0(2(1(4(x1)))) #89: #0(4(1(x1))) -> #2(1(4(x1))) #90: #0(1(2(x1))) -> #0(0(2(1(4(4(x1)))))) #91: #0(1(2(x1))) -> #0(2(1(4(4(x1))))) #92: #0(1(2(x1))) -> #2(1(4(4(x1)))) #93: #0(1(2(x1))) -> #0(0(2(1(x1)))) #94: #0(1(2(x1))) -> #0(2(1(x1))) #95: #0(1(2(x1))) -> #2(1(x1)) #96: #0(3(2(x1))) -> #0(2(3(4(x1)))) #97: #0(3(2(x1))) -> #2(3(4(x1))) #98: #0(4(1(x1))) -> #0(1(4(4(x1)))) #99: #0(3(1(x1))) -> #0(1(3(4(0(x1))))) #100: #0(3(1(x1))) -> #0(x1) #101: #0(4(2(x1))) -> #0(2(3(4(x1)))) #102: #0(4(2(x1))) -> #2(3(4(x1))) Number of SCCs: 2, DPs: 11 SCC { #22 #43 #75 #87 } POLO(Sum)... succeeded. #0 w: 0 1 w: x1 + 1 4 w: 0 5 w: 0 3 w: x1 #2 w: x1 0 w: x1 2 w: x1 USABLE RULES: { } Removed DPs: #22 #43 #75 #87 Number of SCCs: 1, DPs: 7 SCC { #8 #29 #32 #49 #51 #61 #100 } POLO(Sum)... succeeded. #0 w: x1 1 w: x1 + 1 4 w: x1 5 w: x1 + 1542 3 w: x1 #2 w: 0 0 w: x1 + 2437 2 w: x1 + 1 USABLE RULES: { } Removed DPs: #8 #29 #32 #49 #51 #61 #100 Number of SCCs: 0, DPs: 0