YES Input TRS: 1: 0(1(0(2(x1)))) -> 0(0(3(1(2(x1))))) 2: 0(1(3(4(x1)))) -> 0(4(1(0(3(x1))))) 3: 0(1(3(4(x1)))) -> 0(4(1(1(3(x1))))) 4: 0(1(3(4(x1)))) -> 0(4(1(3(1(x1))))) 5: 0(2(1(4(x1)))) -> 0(4(1(2(3(x1))))) 6: 0(2(1(4(x1)))) -> 0(4(1(3(2(x1))))) 7: 0(2(1(4(x1)))) -> 2(0(4(1(4(x1))))) 8: 0(2(1(4(x1)))) -> 5(5(0(4(1(2(x1)))))) 9: 0(2(1(5(x1)))) -> 5(0(4(1(2(x1))))) 10: 0(2(2(4(x1)))) -> 0(4(2(2(5(x1))))) 11: 0(2(2(4(x1)))) -> 0(4(2(5(2(x1))))) 12: 3(4(0(2(x1)))) -> 3(0(4(5(2(x1))))) 13: 3(4(0(2(x1)))) -> 3(5(0(4(2(x1))))) 14: 0(0(1(4(5(x1))))) -> 0(4(1(0(3(5(x1)))))) 15: 0(1(0(2(4(x1))))) -> 2(0(0(4(1(1(x1)))))) 16: 0(1(2(3(4(x1))))) -> 2(0(4(1(0(3(x1)))))) 17: 0(1(3(3(4(x1))))) -> 0(0(3(1(3(4(x1)))))) 18: 0(1(4(0(2(x1))))) -> 0(4(1(5(0(2(x1)))))) 19: 0(1(4(1(5(x1))))) -> 2(5(0(4(1(1(x1)))))) 20: 0(1(4(3(4(x1))))) -> 0(4(0(3(1(4(x1)))))) 21: 0(1(4(3(4(x1))))) -> 3(0(4(1(5(4(x1)))))) 22: 0(1(4(3(5(x1))))) -> 5(4(5(0(3(1(x1)))))) 23: 0(1(5(0(2(x1))))) -> 0(0(4(1(2(5(x1)))))) 24: 0(1(5(1(4(x1))))) -> 4(5(0(3(1(1(x1)))))) 25: 0(2(1(4(4(x1))))) -> 0(4(1(2(4(3(x1)))))) 26: 0(2(1(4(5(x1))))) -> 0(4(1(2(5(2(x1)))))) 27: 0(2(1(5(4(x1))))) -> 5(0(2(0(4(1(x1)))))) 28: 0(2(4(1(5(x1))))) -> 5(0(4(1(5(2(x1)))))) 29: 0(2(4(3(5(x1))))) -> 0(4(5(2(5(3(x1)))))) 30: 0(2(5(1(4(x1))))) -> 0(0(5(4(1(2(x1)))))) 31: 3(0(1(3(2(x1))))) -> 0(3(1(0(3(2(x1)))))) 32: 3(0(2(1(4(x1))))) -> 4(0(4(1(3(2(x1)))))) 33: 3(0(2(1(5(x1))))) -> 5(3(2(0(4(1(x1)))))) 34: 3(0(4(0(2(x1))))) -> 0(3(4(0(4(2(x1)))))) 35: 3(0(4(0(2(x1))))) -> 0(4(1(2(0(3(x1)))))) 36: 3(0(5(1(4(x1))))) -> 3(0(4(1(1(5(x1)))))) 37: 3(0(5(1(5(x1))))) -> 0(4(1(3(5(5(x1)))))) 38: 3(2(4(1(2(x1))))) -> 3(1(2(2(5(4(x1)))))) 39: 3(2(4(1(5(x1))))) -> 3(1(4(5(2(5(x1)))))) 40: 3(4(0(1(2(x1))))) -> 0(4(2(0(3(1(x1)))))) 41: 3(4(0(1(4(x1))))) -> 0(4(1(5(3(4(x1)))))) 42: 3(4(0(1(5(x1))))) -> 0(4(1(5(5(3(x1)))))) 43: 3(4(0(2(4(x1))))) -> 0(3(4(0(4(2(x1)))))) 44: 3(4(1(2(4(x1))))) -> 0(4(1(2(4(3(x1)))))) 45: 3(4(1(3(5(x1))))) -> 4(3(0(3(1(5(x1)))))) 46: 3(4(3(0(2(x1))))) -> 3(3(0(4(1(2(x1)))))) 47: 3(4(5(0(2(x1))))) -> 0(3(0(4(2(5(x1)))))) 48: 3(5(0(2(2(x1))))) -> 0(3(2(5(2(5(x1)))))) 49: 3(5(2(1(4(x1))))) -> 3(5(1(0(4(2(x1)))))) Number of strict rules: 49 Direct POLO(bPol) ... failed. Uncurrying 0 1: 0^1_1(0^1_2(x1)) -> 0(0(3(1(2(x1))))) 2: 0^1_1(3(4(x1))) -> 0^1_4(1(0(3(x1)))) 3: 0^1_1(3(4(x1))) -> 0^1_4(1(1(3(x1)))) 4: 0^1_1(3(4(x1))) -> 0^1_4(1(3(1(x1)))) 5: 0^1_2(1(4(x1))) -> 0^1_4(1(2(3(x1)))) 6: 0^1_2(1(4(x1))) -> 0^1_4(1(3(2(x1)))) 7: 0^1_2(1(4(x1))) -> 2(0^1_4(1(4(x1)))) 8: 0^1_2(1(4(x1))) -> 5(5(0^1_4(1(2(x1))))) 9: 0^1_2(1(5(x1))) -> 5(0^1_4(1(2(x1)))) 10: 0^1_2(2(4(x1))) -> 0^1_4(2(2(5(x1)))) 11: 0^1_2(2(4(x1))) -> 0^1_4(2(5(2(x1)))) 12: 3(4(0^1_2(x1))) -> 3(0^1_4(5(2(x1)))) 13: 3(4(0^1_2(x1))) -> 3(5(0^1_4(2(x1)))) 14: 0(0^1_1(4(5(x1)))) -> 0^1_4(1(0(3(5(x1))))) 15: 0^1_1(0^1_2(4(x1))) -> 2(0^2_4(1(1(x1)))) 16: 0^1_1(2(3(4(x1)))) -> 2(0^1_4(1(0(3(x1))))) 17: 0^1_1(3(3(4(x1)))) -> 0(0(3(1(3(4(x1)))))) 18: 0^1_1(4(0^1_2(x1))) -> 0^1_4(1(5(0^1_2(x1)))) 19: 0^1_1(4(1(5(x1)))) -> 2(5(0^1_4(1(1(x1))))) 20: 0^1_1(4(3(4(x1)))) -> 0^1_4(0(3(1(4(x1))))) 21: 0^1_1(4(3(4(x1)))) -> 3(0^1_4(1(5(4(x1))))) 22: 0^1_1(4(3(5(x1)))) -> 5(4(5(0(3(1(x1)))))) 23: 0^1_1(5(0^1_2(x1))) -> 0^2_4(1(2(5(x1)))) 24: 0^1_1(5(1(4(x1)))) -> 4(5(0(3(1(1(x1)))))) 25: 0^1_2(1(4(4(x1)))) -> 0^1_4(1(2(4(3(x1))))) 26: 0^1_2(1(4(5(x1)))) -> 0^1_4(1(2(5(2(x1))))) 27: 0^1_2(1(5(4(x1)))) -> 5(0^1_2(0^1_4(1(x1)))) 28: 0^1_2(4(1(5(x1)))) -> 5(0^1_4(1(5(2(x1))))) 29: 0^1_2(4(3(5(x1)))) -> 0^1_4(5(2(5(3(x1))))) 30: 0^1_2(5(1(4(x1)))) -> 0^2_5(4(1(2(x1)))) 31: 3(0^1_1(3(2(x1)))) -> 0(3(1(0(3(2(x1)))))) 32: 3(0^1_2(1(4(x1)))) -> 4(0^1_4(1(3(2(x1))))) 33: 3(0^1_2(1(5(x1)))) -> 5(3(2(0^1_4(1(x1))))) 34: 3(0^1_4(0^1_2(x1))) -> 0(3(4(0^1_4(2(x1))))) 35: 3(0^1_4(0^1_2(x1))) -> 0^1_4(1(2(0(3(x1))))) 36: 3(0^1_5(1(4(x1)))) -> 3(0^1_4(1(1(5(x1))))) 37: 3(0^1_5(1(5(x1)))) -> 0^1_4(1(3(5(5(x1))))) 38: 3(2(4(1(2(x1))))) -> 3(1(2(2(5(4(x1)))))) 39: 3(2(4(1(5(x1))))) -> 3(1(4(5(2(5(x1)))))) 40: 3(4(0^1_1(2(x1)))) -> 0^1_4(2(0(3(1(x1))))) 41: 3(4(0^1_1(4(x1)))) -> 0^1_4(1(5(3(4(x1))))) 42: 3(4(0^1_1(5(x1)))) -> 0^1_4(1(5(5(3(x1))))) 43: 3(4(0^1_2(4(x1)))) -> 0(3(4(0^1_4(2(x1))))) 44: 3(4(1(2(4(x1))))) -> 0^1_4(1(2(4(3(x1))))) 45: 3(4(1(3(5(x1))))) -> 4(3(0(3(1(5(x1)))))) 46: 3(4(3(0^1_2(x1)))) -> 3(3(0^1_4(1(2(x1))))) 47: 3(4(5(0^1_2(x1)))) -> 0(3(0^1_4(2(5(x1))))) 48: 3(5(0^1_2(2(x1)))) -> 0(3(2(5(2(5(x1)))))) 49: 3(5(2(1(4(x1))))) -> 3(5(1(0^1_4(2(x1))))) 50: 0(2(_1)) ->= 0^1_2(_1) 51: 0(1(_1)) ->= 0^1_1(_1) 52: 0(4(_1)) ->= 0^1_4(_1) 53: 0(0^1_4(_1)) ->= 0^2_4(_1) 54: 0(5(_1)) ->= 0^1_5(_1) 55: 0(0^1_5(_1)) ->= 0^2_5(_1) Number of strict rules: 49 Direct POLO(bPol) ... failed. Dependency Pairs: #1: #0^1_1(3(4(x1))) -> #0(3(x1)) #2: #0^1_1(3(4(x1))) -> #3(x1) #3: #3(4(0^1_2(4(x1)))) -> #0(3(4(0^1_4(2(x1))))) #4: #3(4(0^1_2(4(x1)))) -> #3(4(0^1_4(2(x1)))) #5: #0^1_2(4(3(5(x1)))) -> #3(x1) #6: #3(0^1_4(0^1_2(x1))) -> #0(3(x1)) #7: #3(0^1_4(0^1_2(x1))) -> #3(x1) #8: #3(4(3(0^1_2(x1)))) -> #3(3(0^1_4(1(2(x1))))) #9: #3(4(3(0^1_2(x1)))) -> #3(0^1_4(1(2(x1)))) #10: #3(4(0^1_1(5(x1)))) -> #3(x1) #11: #3(4(0^1_1(4(x1)))) -> #3(4(x1)) #12: #3(0^1_5(1(5(x1)))) -> #3(5(5(x1))) #13: #3(4(5(0^1_2(x1)))) -> #0(3(0^1_4(2(5(x1))))) #14: #3(4(5(0^1_2(x1)))) -> #3(0^1_4(2(5(x1)))) #15: #3(5(0^1_2(2(x1)))) -> #0(3(2(5(2(5(x1)))))) #16: #3(5(0^1_2(2(x1)))) -> #3(2(5(2(5(x1))))) #17: #3(2(4(1(2(x1))))) -> #3(1(2(2(5(4(x1)))))) #18: #0^1_2(1(4(x1))) -> #3(2(x1)) #19: #3(4(0^1_1(2(x1)))) -> #0(3(1(x1))) #20: #3(4(0^1_1(2(x1)))) -> #3(1(x1)) #21: #0(1(_1)) ->? #0^1_1(_1) #22: #3(4(0^1_2(x1))) -> #3(5(0^1_4(2(x1)))) #23: #0^1_1(5(1(4(x1)))) -> #0(3(1(1(x1)))) #24: #0^1_1(5(1(4(x1)))) -> #3(1(1(x1))) #25: #3(4(1(3(5(x1))))) -> #3(0(3(1(5(x1))))) #26: #3(4(1(3(5(x1))))) -> #0(3(1(5(x1)))) #27: #3(4(1(3(5(x1))))) -> #3(1(5(x1))) #28: #3(4(0^1_2(x1))) -> #3(0^1_4(5(2(x1)))) #29: #3(0^1_1(3(2(x1)))) -> #0(3(1(0(3(2(x1)))))) #30: #3(0^1_1(3(2(x1)))) -> #3(1(0(3(2(x1))))) #31: #3(0^1_1(3(2(x1)))) -> #0(3(2(x1))) #32: #0(0^1_1(4(5(x1)))) -> #0(3(5(x1))) #33: #0(0^1_1(4(5(x1)))) -> #3(5(x1)) #34: #3(5(2(1(4(x1))))) -> #3(5(1(0^1_4(2(x1))))) #35: #0^1_2(1(4(4(x1)))) -> #3(x1) #36: #0^1_1(4(3(4(x1)))) -> #0(3(1(4(x1)))) #37: #0^1_1(4(3(4(x1)))) -> #3(1(4(x1))) #38: #3(2(4(1(5(x1))))) -> #3(1(4(5(2(5(x1)))))) #39: #3(0^1_2(1(5(x1)))) -> #3(2(0^1_4(1(x1)))) #40: #0^1_2(1(4(x1))) -> #3(x1) #41: #3(4(1(2(4(x1))))) -> #3(x1) #42: #0^1_1(4(3(5(x1)))) -> #0(3(1(x1))) #43: #0^1_1(4(3(5(x1)))) -> #3(1(x1)) #44: #3(0^1_4(0^1_2(x1))) -> #0(3(4(0^1_4(2(x1))))) #45: #3(0^1_4(0^1_2(x1))) -> #3(4(0^1_4(2(x1)))) #46: #0^1_2(1(5(4(x1)))) -> #0^1_2(0^1_4(1(x1))) #47: #0^1_1(3(3(4(x1)))) -> #0(0(3(1(3(4(x1)))))) #48: #0^1_1(3(3(4(x1)))) -> #0(3(1(3(4(x1))))) #49: #0^1_1(3(3(4(x1)))) -> #3(1(3(4(x1)))) #50: #3(0^1_2(1(4(x1)))) -> #3(2(x1)) #51: #3(0^1_5(1(4(x1)))) -> #3(0^1_4(1(1(5(x1))))) #52: #0^1_1(4(3(4(x1)))) -> #3(0^1_4(1(5(4(x1))))) #53: #0^1_1(2(3(4(x1)))) -> #0(3(x1)) #54: #0^1_1(2(3(4(x1)))) -> #3(x1) #55: #0^1_1(3(4(x1))) -> #3(x1) #56: #0^1_1(0^1_2(x1)) -> #0(0(3(1(2(x1))))) #57: #0^1_1(0^1_2(x1)) -> #0(3(1(2(x1)))) #58: #0^1_1(0^1_2(x1)) -> #3(1(2(x1))) #59: #0^1_1(3(4(x1))) -> #3(1(x1)) #60: #0(2(_1)) ->? #0^1_2(_1) Number of SCCs: 1, DPs: 4 SCC { #7 #10 #11 #41 } POLO(Sum)... succeeded. #0 w: 0 1 w: x1 4 w: x1 + 5723 5 w: x1 + 1 #0^1_2 w: 0 3 w: 0 0^1_4 w: x1 0 w: 0 0^1_5 w: 0 0^2_4 w: 0 #3 w: x1 0^2_5 w: 0 0^1_1 w: x1 #0^1_1 w: 0 2 w: x1 + 2035 0^1_2 w: x1 + 1 USABLE RULES: { } Removed DPs: #7 #10 #11 #41 Number of SCCs: 0, DPs: 0