0.95/0.98 YES 0.95/1.08 Input TRS: 0.95/1.08 1: 0(1(0(2(x1)))) -> 0(0(3(1(2(x1))))) 0.95/1.08 2: 0(1(3(4(x1)))) -> 0(4(1(0(3(x1))))) 0.95/1.08 3: 0(1(3(4(x1)))) -> 0(4(1(1(3(x1))))) 0.95/1.08 4: 0(1(3(4(x1)))) -> 0(4(1(3(1(x1))))) 0.95/1.08 5: 0(2(1(4(x1)))) -> 0(4(1(2(3(x1))))) 0.95/1.08 6: 0(2(1(4(x1)))) -> 0(4(1(3(2(x1))))) 0.95/1.08 7: 0(2(1(4(x1)))) -> 2(0(4(1(4(x1))))) 0.95/1.08 8: 0(2(1(4(x1)))) -> 5(5(0(4(1(2(x1)))))) 0.95/1.08 9: 0(2(1(5(x1)))) -> 5(0(4(1(2(x1))))) 0.95/1.08 10: 0(2(2(4(x1)))) -> 0(4(2(2(5(x1))))) 0.95/1.08 11: 0(2(2(4(x1)))) -> 0(4(2(5(2(x1))))) 0.95/1.08 12: 3(4(0(2(x1)))) -> 3(0(4(5(2(x1))))) 0.95/1.08 13: 3(4(0(2(x1)))) -> 3(5(0(4(2(x1))))) 0.95/1.08 14: 0(0(1(4(5(x1))))) -> 0(4(1(0(3(5(x1)))))) 0.95/1.08 15: 0(1(0(2(4(x1))))) -> 2(0(0(4(1(1(x1)))))) 0.95/1.08 16: 0(1(2(3(4(x1))))) -> 2(0(4(1(0(3(x1)))))) 0.95/1.08 17: 0(1(3(3(4(x1))))) -> 0(0(3(1(3(4(x1)))))) 0.95/1.08 18: 0(1(4(0(2(x1))))) -> 0(4(1(5(0(2(x1)))))) 0.95/1.08 19: 0(1(4(1(5(x1))))) -> 2(5(0(4(1(1(x1)))))) 0.95/1.08 20: 0(1(4(3(4(x1))))) -> 0(4(0(3(1(4(x1)))))) 0.95/1.08 21: 0(1(4(3(4(x1))))) -> 3(0(4(1(5(4(x1)))))) 0.95/1.08 22: 0(1(4(3(5(x1))))) -> 5(4(5(0(3(1(x1)))))) 0.95/1.08 23: 0(1(5(0(2(x1))))) -> 0(0(4(1(2(5(x1)))))) 0.95/1.08 24: 0(1(5(1(4(x1))))) -> 4(5(0(3(1(1(x1)))))) 0.95/1.08 25: 0(2(1(4(4(x1))))) -> 0(4(1(2(4(3(x1)))))) 0.95/1.08 26: 0(2(1(4(5(x1))))) -> 0(4(1(2(5(2(x1)))))) 0.95/1.08 27: 0(2(1(5(4(x1))))) -> 5(0(2(0(4(1(x1)))))) 0.95/1.08 28: 0(2(4(1(5(x1))))) -> 5(0(4(1(5(2(x1)))))) 0.95/1.08 29: 0(2(4(3(5(x1))))) -> 0(4(5(2(5(3(x1)))))) 0.95/1.08 30: 0(2(5(1(4(x1))))) -> 0(0(5(4(1(2(x1)))))) 0.95/1.08 31: 3(0(1(3(2(x1))))) -> 0(3(1(0(3(2(x1)))))) 0.95/1.08 32: 3(0(2(1(4(x1))))) -> 4(0(4(1(3(2(x1)))))) 0.95/1.08 33: 3(0(2(1(5(x1))))) -> 5(3(2(0(4(1(x1)))))) 0.95/1.08 34: 3(0(4(0(2(x1))))) -> 0(3(4(0(4(2(x1)))))) 0.95/1.08 35: 3(0(4(0(2(x1))))) -> 0(4(1(2(0(3(x1)))))) 0.95/1.08 36: 3(0(5(1(4(x1))))) -> 3(0(4(1(1(5(x1)))))) 0.95/1.08 37: 3(0(5(1(5(x1))))) -> 0(4(1(3(5(5(x1)))))) 0.95/1.08 38: 3(2(4(1(2(x1))))) -> 3(1(2(2(5(4(x1)))))) 0.95/1.08 39: 3(2(4(1(5(x1))))) -> 3(1(4(5(2(5(x1)))))) 0.95/1.08 40: 3(4(0(1(2(x1))))) -> 0(4(2(0(3(1(x1)))))) 0.95/1.08 41: 3(4(0(1(4(x1))))) -> 0(4(1(5(3(4(x1)))))) 0.95/1.08 42: 3(4(0(1(5(x1))))) -> 0(4(1(5(5(3(x1)))))) 0.95/1.08 43: 3(4(0(2(4(x1))))) -> 0(3(4(0(4(2(x1)))))) 0.95/1.08 44: 3(4(1(2(4(x1))))) -> 0(4(1(2(4(3(x1)))))) 0.95/1.08 45: 3(4(1(3(5(x1))))) -> 4(3(0(3(1(5(x1)))))) 0.95/1.08 46: 3(4(3(0(2(x1))))) -> 3(3(0(4(1(2(x1)))))) 0.95/1.08 47: 3(4(5(0(2(x1))))) -> 0(3(0(4(2(5(x1)))))) 0.95/1.08 48: 3(5(0(2(2(x1))))) -> 0(3(2(5(2(5(x1)))))) 0.95/1.08 49: 3(5(2(1(4(x1))))) -> 3(5(1(0(4(2(x1)))))) 0.95/1.08 Number of strict rules: 49 0.95/1.08 Direct POLO(bPol) ... failed. 0.95/1.08 Uncurrying 0 0.95/1.08 1: 0^1_1(0^1_2(x1)) -> 0(0(3(1(2(x1))))) 0.95/1.08 2: 0^1_1(3(4(x1))) -> 0^1_4(1(0(3(x1)))) 0.95/1.08 3: 0^1_1(3(4(x1))) -> 0^1_4(1(1(3(x1)))) 0.95/1.08 4: 0^1_1(3(4(x1))) -> 0^1_4(1(3(1(x1)))) 0.95/1.08 5: 0^1_2(1(4(x1))) -> 0^1_4(1(2(3(x1)))) 0.95/1.08 6: 0^1_2(1(4(x1))) -> 0^1_4(1(3(2(x1)))) 0.95/1.08 7: 0^1_2(1(4(x1))) -> 2(0^1_4(1(4(x1)))) 0.95/1.08 8: 0^1_2(1(4(x1))) -> 5(5(0^1_4(1(2(x1))))) 0.95/1.08 9: 0^1_2(1(5(x1))) -> 5(0^1_4(1(2(x1)))) 0.95/1.08 10: 0^1_2(2(4(x1))) -> 0^1_4(2(2(5(x1)))) 0.95/1.08 11: 0^1_2(2(4(x1))) -> 0^1_4(2(5(2(x1)))) 0.95/1.08 12: 3(4(0^1_2(x1))) -> 3(0^1_4(5(2(x1)))) 0.95/1.08 13: 3(4(0^1_2(x1))) -> 3(5(0^1_4(2(x1)))) 0.95/1.08 14: 0(0^1_1(4(5(x1)))) -> 0^1_4(1(0(3(5(x1))))) 0.95/1.08 15: 0^1_1(0^1_2(4(x1))) -> 2(0^2_4(1(1(x1)))) 0.95/1.08 16: 0^1_1(2(3(4(x1)))) -> 2(0^1_4(1(0(3(x1))))) 0.95/1.08 17: 0^1_1(3(3(4(x1)))) -> 0(0(3(1(3(4(x1)))))) 0.95/1.08 18: 0^1_1(4(0^1_2(x1))) -> 0^1_4(1(5(0^1_2(x1)))) 0.95/1.08 19: 0^1_1(4(1(5(x1)))) -> 2(5(0^1_4(1(1(x1))))) 0.95/1.08 20: 0^1_1(4(3(4(x1)))) -> 0^1_4(0(3(1(4(x1))))) 0.95/1.08 21: 0^1_1(4(3(4(x1)))) -> 3(0^1_4(1(5(4(x1))))) 0.95/1.08 22: 0^1_1(4(3(5(x1)))) -> 5(4(5(0(3(1(x1)))))) 0.95/1.08 23: 0^1_1(5(0^1_2(x1))) -> 0^2_4(1(2(5(x1)))) 0.95/1.08 24: 0^1_1(5(1(4(x1)))) -> 4(5(0(3(1(1(x1)))))) 0.95/1.08 25: 0^1_2(1(4(4(x1)))) -> 0^1_4(1(2(4(3(x1))))) 0.95/1.08 26: 0^1_2(1(4(5(x1)))) -> 0^1_4(1(2(5(2(x1))))) 0.95/1.08 27: 0^1_2(1(5(4(x1)))) -> 5(0^1_2(0^1_4(1(x1)))) 0.95/1.08 28: 0^1_2(4(1(5(x1)))) -> 5(0^1_4(1(5(2(x1))))) 0.95/1.08 29: 0^1_2(4(3(5(x1)))) -> 0^1_4(5(2(5(3(x1))))) 0.95/1.08 30: 0^1_2(5(1(4(x1)))) -> 0^2_5(4(1(2(x1)))) 0.95/1.08 31: 3(0^1_1(3(2(x1)))) -> 0(3(1(0(3(2(x1)))))) 0.95/1.08 32: 3(0^1_2(1(4(x1)))) -> 4(0^1_4(1(3(2(x1))))) 0.95/1.08 33: 3(0^1_2(1(5(x1)))) -> 5(3(2(0^1_4(1(x1))))) 0.95/1.08 34: 3(0^1_4(0^1_2(x1))) -> 0(3(4(0^1_4(2(x1))))) 0.95/1.08 35: 3(0^1_4(0^1_2(x1))) -> 0^1_4(1(2(0(3(x1))))) 0.95/1.08 36: 3(0^1_5(1(4(x1)))) -> 3(0^1_4(1(1(5(x1))))) 0.95/1.08 37: 3(0^1_5(1(5(x1)))) -> 0^1_4(1(3(5(5(x1))))) 0.95/1.08 38: 3(2(4(1(2(x1))))) -> 3(1(2(2(5(4(x1)))))) 0.95/1.08 39: 3(2(4(1(5(x1))))) -> 3(1(4(5(2(5(x1)))))) 0.95/1.08 40: 3(4(0^1_1(2(x1)))) -> 0^1_4(2(0(3(1(x1))))) 0.95/1.08 41: 3(4(0^1_1(4(x1)))) -> 0^1_4(1(5(3(4(x1))))) 0.95/1.08 42: 3(4(0^1_1(5(x1)))) -> 0^1_4(1(5(5(3(x1))))) 0.95/1.08 43: 3(4(0^1_2(4(x1)))) -> 0(3(4(0^1_4(2(x1))))) 0.95/1.08 44: 3(4(1(2(4(x1))))) -> 0^1_4(1(2(4(3(x1))))) 0.95/1.08 45: 3(4(1(3(5(x1))))) -> 4(3(0(3(1(5(x1)))))) 0.95/1.08 46: 3(4(3(0^1_2(x1)))) -> 3(3(0^1_4(1(2(x1))))) 0.95/1.08 47: 3(4(5(0^1_2(x1)))) -> 0(3(0^1_4(2(5(x1))))) 0.95/1.08 48: 3(5(0^1_2(2(x1)))) -> 0(3(2(5(2(5(x1)))))) 0.95/1.08 49: 3(5(2(1(4(x1))))) -> 3(5(1(0^1_4(2(x1))))) 0.95/1.08 50: 0(2(_1)) ->= 0^1_2(_1) 0.95/1.08 51: 0(1(_1)) ->= 0^1_1(_1) 0.95/1.08 52: 0(4(_1)) ->= 0^1_4(_1) 0.95/1.08 53: 0(0^1_4(_1)) ->= 0^2_4(_1) 0.95/1.08 54: 0(5(_1)) ->= 0^1_5(_1) 0.95/1.08 55: 0(0^1_5(_1)) ->= 0^2_5(_1) 0.95/1.08 Number of strict rules: 49 0.95/1.08 Direct POLO(bPol) ... failed. 0.95/1.08 Dependency Pairs: 0.95/1.08 #1: #0^1_1(3(4(x1))) -> #0(3(x1)) 0.95/1.08 #2: #0^1_1(3(4(x1))) -> #3(x1) 0.95/1.08 #3: #3(4(0^1_2(4(x1)))) -> #0(3(4(0^1_4(2(x1))))) 0.95/1.08 #4: #3(4(0^1_2(4(x1)))) -> #3(4(0^1_4(2(x1)))) 0.95/1.08 #5: #0^1_2(4(3(5(x1)))) -> #3(x1) 0.95/1.08 #6: #3(0^1_4(0^1_2(x1))) -> #0(3(x1)) 0.95/1.08 #7: #3(0^1_4(0^1_2(x1))) -> #3(x1) 0.95/1.08 #8: #3(4(3(0^1_2(x1)))) -> #3(3(0^1_4(1(2(x1))))) 0.95/1.08 #9: #3(4(3(0^1_2(x1)))) -> #3(0^1_4(1(2(x1)))) 0.95/1.08 #10: #3(4(0^1_1(5(x1)))) -> #3(x1) 0.95/1.08 #11: #3(4(0^1_1(4(x1)))) -> #3(4(x1)) 0.95/1.08 #12: #3(0^1_5(1(5(x1)))) -> #3(5(5(x1))) 0.95/1.08 #13: #3(4(5(0^1_2(x1)))) -> #0(3(0^1_4(2(5(x1))))) 0.95/1.08 #14: #3(4(5(0^1_2(x1)))) -> #3(0^1_4(2(5(x1)))) 0.95/1.08 #15: #3(5(0^1_2(2(x1)))) -> #0(3(2(5(2(5(x1)))))) 0.95/1.08 #16: #3(5(0^1_2(2(x1)))) -> #3(2(5(2(5(x1))))) 0.95/1.08 #17: #3(2(4(1(2(x1))))) -> #3(1(2(2(5(4(x1)))))) 0.95/1.08 #18: #0^1_2(1(4(x1))) -> #3(2(x1)) 0.95/1.08 #19: #3(4(0^1_1(2(x1)))) -> #0(3(1(x1))) 0.95/1.08 #20: #3(4(0^1_1(2(x1)))) -> #3(1(x1)) 0.95/1.08 #21: #0(1(_1)) ->? #0^1_1(_1) 0.95/1.08 #22: #3(4(0^1_2(x1))) -> #3(5(0^1_4(2(x1)))) 0.95/1.08 #23: #0^1_1(5(1(4(x1)))) -> #0(3(1(1(x1)))) 0.95/1.08 #24: #0^1_1(5(1(4(x1)))) -> #3(1(1(x1))) 0.95/1.08 #25: #3(4(1(3(5(x1))))) -> #3(0(3(1(5(x1))))) 0.95/1.08 #26: #3(4(1(3(5(x1))))) -> #0(3(1(5(x1)))) 0.95/1.08 #27: #3(4(1(3(5(x1))))) -> #3(1(5(x1))) 0.95/1.08 #28: #3(4(0^1_2(x1))) -> #3(0^1_4(5(2(x1)))) 0.95/1.08 #29: #3(0^1_1(3(2(x1)))) -> #0(3(1(0(3(2(x1)))))) 0.95/1.08 #30: #3(0^1_1(3(2(x1)))) -> #3(1(0(3(2(x1))))) 0.95/1.08 #31: #3(0^1_1(3(2(x1)))) -> #0(3(2(x1))) 0.95/1.08 #32: #0(0^1_1(4(5(x1)))) -> #0(3(5(x1))) 0.95/1.08 #33: #0(0^1_1(4(5(x1)))) -> #3(5(x1)) 0.95/1.08 #34: #3(5(2(1(4(x1))))) -> #3(5(1(0^1_4(2(x1))))) 0.95/1.08 #35: #0^1_2(1(4(4(x1)))) -> #3(x1) 0.95/1.08 #36: #0^1_1(4(3(4(x1)))) -> #0(3(1(4(x1)))) 0.95/1.08 #37: #0^1_1(4(3(4(x1)))) -> #3(1(4(x1))) 0.95/1.08 #38: #3(2(4(1(5(x1))))) -> #3(1(4(5(2(5(x1)))))) 0.95/1.08 #39: #3(0^1_2(1(5(x1)))) -> #3(2(0^1_4(1(x1)))) 0.95/1.08 #40: #0^1_2(1(4(x1))) -> #3(x1) 0.95/1.08 #41: #3(4(1(2(4(x1))))) -> #3(x1) 0.95/1.08 #42: #0^1_1(4(3(5(x1)))) -> #0(3(1(x1))) 0.95/1.08 #43: #0^1_1(4(3(5(x1)))) -> #3(1(x1)) 0.95/1.08 #44: #3(0^1_4(0^1_2(x1))) -> #0(3(4(0^1_4(2(x1))))) 0.95/1.08 #45: #3(0^1_4(0^1_2(x1))) -> #3(4(0^1_4(2(x1)))) 0.95/1.08 #46: #0^1_2(1(5(4(x1)))) -> #0^1_2(0^1_4(1(x1))) 0.95/1.08 #47: #0^1_1(3(3(4(x1)))) -> #0(0(3(1(3(4(x1)))))) 0.95/1.08 #48: #0^1_1(3(3(4(x1)))) -> #0(3(1(3(4(x1))))) 0.95/1.08 #49: #0^1_1(3(3(4(x1)))) -> #3(1(3(4(x1)))) 0.95/1.08 #50: #3(0^1_2(1(4(x1)))) -> #3(2(x1)) 0.95/1.08 #51: #3(0^1_5(1(4(x1)))) -> #3(0^1_4(1(1(5(x1))))) 0.95/1.08 #52: #0^1_1(4(3(4(x1)))) -> #3(0^1_4(1(5(4(x1))))) 0.95/1.08 #53: #0^1_1(2(3(4(x1)))) -> #0(3(x1)) 0.95/1.08 #54: #0^1_1(2(3(4(x1)))) -> #3(x1) 0.95/1.08 #55: #0^1_1(3(4(x1))) -> #3(x1) 0.95/1.08 #56: #0^1_1(0^1_2(x1)) -> #0(0(3(1(2(x1))))) 0.95/1.08 #57: #0^1_1(0^1_2(x1)) -> #0(3(1(2(x1)))) 0.95/1.08 #58: #0^1_1(0^1_2(x1)) -> #3(1(2(x1))) 0.95/1.08 #59: #0^1_1(3(4(x1))) -> #3(1(x1)) 0.95/1.08 #60: #0(2(_1)) ->? #0^1_2(_1) 0.95/1.08 Number of SCCs: 1, DPs: 4 0.95/1.08 SCC { #7 #10 #11 #41 } 0.95/1.08 POLO(Sum)... succeeded. 0.95/1.08 #0 w: 0 0.95/1.08 1 w: x1 0.95/1.08 4 w: x1 + 1 0.95/1.08 5 w: x1 + 1 0.95/1.08 #0^1_2 w: 0 0.95/1.08 3 w: 0 0.95/1.08 0^1_4 w: x1 0.95/1.08 0 w: 0 0.95/1.08 0^1_5 w: 0 0.95/1.08 0^2_4 w: 0 0.95/1.08 #3 w: x1 0.95/1.08 0^2_5 w: 0 0.95/1.08 0^1_1 w: x1 0.95/1.08 #0^1_1 w: 0 0.95/1.08 2 w: x1 0.95/1.08 0^1_2 w: x1 + 1 0.95/1.08 USABLE RULES: { } 0.95/1.08 Removed DPs: #7 #10 #11 #41 0.95/1.08 Number of SCCs: 0, DPs: 0 0.95/1.08 EOF