2.78/2.72 YES 2.78/2.72 Input TRS: 2.78/2.72 1: 0(5(0(x1))) -> 3(4(3(3(2(0(4(4(4(0(x1)))))))))) 2.78/2.72 2: 0(2(5(0(x1)))) -> 0(2(1(1(5(2(1(4(1(3(x1)))))))))) 2.78/2.72 3: 0(5(0(5(x1)))) -> 3(2(0(2(0(4(4(1(5(4(x1)))))))))) 2.78/2.72 4: 2(5(5(3(x1)))) -> 4(3(0(2(1(0(1(3(4(3(x1)))))))))) 2.78/2.72 5: 5(5(5(0(x1)))) -> 4(1(2(1(2(3(5(0(1(3(x1)))))))))) 2.78/2.72 6: 0(5(1(5(0(x1))))) -> 3(4(0(1(4(5(2(2(3(1(x1)))))))))) 2.78/2.72 7: 3(0(0(5(3(x1))))) -> 1(3(4(3(5(2(4(1(3(3(x1)))))))))) 2.78/2.72 8: 3(5(5(0(0(x1))))) -> 1(4(1(0(0(4(4(0(4(1(x1)))))))))) 2.78/2.72 9: 0(2(5(1(5(0(x1)))))) -> 2(1(0(1(5(2(4(0(2(0(x1)))))))))) 2.78/2.72 10: 0(2(5(5(1(4(x1)))))) -> 4(0(1(1(1(1(0(4(1(5(x1)))))))))) 2.78/2.72 11: 0(5(3(1(2(5(x1)))))) -> 0(2(3(1(1(2(4(4(5(5(x1)))))))))) 2.78/2.72 12: 0(5(5(1(5(1(x1)))))) -> 0(5(1(1(3(3(4(2(1(0(x1)))))))))) 2.78/2.72 13: 4(5(5(4(2(0(x1)))))) -> 2(4(0(1(3(4(4(4(1(0(x1)))))))))) 2.78/2.72 14: 5(0(0(3(5(2(x1)))))) -> 4(4(2(3(0(1(2(0(5(2(x1)))))))))) 2.78/2.72 15: 5(1(5(0(2(5(x1)))))) -> 5(0(0(1(4(2(3(2(1(5(x1)))))))))) 2.78/2.72 16: 5(2(0(2(5(5(x1)))))) -> 5(5(4(4(4(5(4(4(1(4(x1)))))))))) 2.78/2.72 17: 5(5(0(2(5(0(x1)))))) -> 2(0(5(0(2(1(0(0(3(0(x1)))))))))) 2.78/2.72 18: 5(5(0(3(4(5(x1)))))) -> 2(0(5(5(2(1(3(2(3(2(x1)))))))))) 2.78/2.72 19: 5(5(3(5(0(5(x1)))))) -> 5(4(4(3(5(1(3(3(4(5(x1)))))))))) 2.78/2.72 20: 0(4(4(0(0(5(1(x1))))))) -> 1(3(2(0(4(1(5(1(1(2(x1)))))))))) 2.78/2.72 21: 0(4(4(2(5(5(5(x1))))))) -> 0(2(4(5(5(4(2(0(1(1(x1)))))))))) 2.78/2.72 22: 1(0(2(5(2(0(0(x1))))))) -> 3(1(4(4(0(3(0(1(2(2(x1)))))))))) 2.78/2.72 23: 1(2(0(4(2(5(0(x1))))))) -> 4(2(4(0(3(2(2(4(1(0(x1)))))))))) 2.78/2.72 24: 1(2(5(5(0(3(3(x1))))))) -> 3(4(1(2(0(3(3(1(0(3(x1)))))))))) 2.78/2.72 25: 1(5(5(3(3(3(4(x1))))))) -> 1(5(1(0(0(2(2(2(3(5(x1)))))))))) 2.78/2.72 26: 2(5(4(5(2(5(1(x1))))))) -> 4(3(2(1(4(2(2(4(5(2(x1)))))))))) 2.78/2.72 27: 3(2(3(5(1(5(2(x1))))))) -> 2(0(3(2(3(2(1(5(5(1(x1)))))))))) 2.78/2.72 28: 3(3(4(2(5(5(2(x1))))))) -> 1(2(3(3(4(4(1(4(0(1(x1)))))))))) 2.78/2.72 29: 3(5(0(5(5(5(0(x1))))))) -> 0(0(3(0(3(5(0(3(2(0(x1)))))))))) 2.78/2.72 30: 4(3(1(2(5(2(4(x1))))))) -> 2(3(1(1(4(3(4(4(2(4(x1)))))))))) 2.78/2.72 31: 4(5(5(3(1(0(5(x1))))))) -> 1(1(5(2(0(3(3(3(2(1(x1)))))))))) 2.78/2.72 32: 5(0(5(3(1(0(5(x1))))))) -> 5(2(4(4(2(1(3(5(1(5(x1)))))))))) 2.78/2.72 33: 5(0(5(3(5(1(5(x1))))))) -> 5(1(1(2(4(0(0(3(2(5(x1)))))))))) 2.78/2.72 34: 5(1(5(3(3(0(5(x1))))))) -> 4(4(3(2(2(2(5(0(1(1(x1)))))))))) 2.78/2.72 35: 5(2(0(2(5(3(3(x1))))))) -> 5(2(0(5(1(1(3(2(0(3(x1)))))))))) 2.78/2.72 Number of strict rules: 35 2.78/2.72 Direct POLO(bPol) ... removes: 18 4 15 8 1 3 21 26 19 17 34 22 28 5 33 10 30 14 31 12 23 24 9 13 6 29 2.78/2.72 1 w: x1 2.78/2.72 4 w: x1 2.78/2.72 5 w: x1 + 1 2.78/2.72 3 w: x1 2.78/2.72 0 w: x1 2.78/2.72 2 w: x1 2.78/2.72 Number of strict rules: 9 2.78/2.72 Direct POLO(bPol) ... failed. 2.78/2.72 Uncurrying ... failed. 2.78/2.72 Dependency Pairs: 2.78/2.72 #1: #0(2(5(0(x1)))) -> #0(2(1(1(5(2(1(4(1(3(x1)))))))))) 2.78/2.72 #2: #0(2(5(0(x1)))) -> #1(1(5(2(1(4(1(3(x1)))))))) 2.78/2.72 #3: #0(2(5(0(x1)))) -> #1(5(2(1(4(1(3(x1))))))) 2.78/2.72 #4: #0(2(5(0(x1)))) -> #5(2(1(4(1(3(x1)))))) 2.78/2.72 #5: #0(2(5(0(x1)))) -> #1(4(1(3(x1)))) 2.78/2.72 #6: #0(2(5(0(x1)))) -> #1(3(x1)) 2.78/2.72 #7: #0(2(5(0(x1)))) -> #3(x1) 2.78/2.72 #8: #5(2(0(2(5(3(3(x1))))))) -> #5(2(0(5(1(1(3(2(0(3(x1)))))))))) 2.78/2.72 #9: #5(2(0(2(5(3(3(x1))))))) -> #0(5(1(1(3(2(0(3(x1)))))))) 2.78/2.72 #10: #5(2(0(2(5(3(3(x1))))))) -> #5(1(1(3(2(0(3(x1))))))) 2.78/2.72 #11: #5(2(0(2(5(3(3(x1))))))) -> #1(1(3(2(0(3(x1)))))) 2.78/2.72 #12: #5(2(0(2(5(3(3(x1))))))) -> #1(3(2(0(3(x1))))) 2.78/2.72 #13: #5(2(0(2(5(3(3(x1))))))) -> #3(2(0(3(x1)))) 2.78/2.72 #14: #5(2(0(2(5(3(3(x1))))))) -> #0(3(x1)) 2.78/2.72 #15: #0(5(3(1(2(5(x1)))))) -> #0(2(3(1(1(2(4(4(5(5(x1)))))))))) 2.78/2.72 #16: #0(5(3(1(2(5(x1)))))) -> #3(1(1(2(4(4(5(5(x1)))))))) 2.78/2.72 #17: #0(5(3(1(2(5(x1)))))) -> #1(1(2(4(4(5(5(x1))))))) 2.78/2.72 #18: #0(5(3(1(2(5(x1)))))) -> #1(2(4(4(5(5(x1)))))) 2.78/2.72 #19: #0(5(3(1(2(5(x1)))))) -> #5(5(x1)) 2.78/2.72 #20: #1(5(5(3(3(3(4(x1))))))) -> #1(5(1(0(0(2(2(2(3(5(x1)))))))))) 2.78/2.72 #21: #1(5(5(3(3(3(4(x1))))))) -> #5(1(0(0(2(2(2(3(5(x1))))))))) 2.78/2.72 #22: #1(5(5(3(3(3(4(x1))))))) -> #1(0(0(2(2(2(3(5(x1)))))))) 2.78/2.72 #23: #1(5(5(3(3(3(4(x1))))))) -> #0(0(2(2(2(3(5(x1))))))) 2.78/2.72 #24: #1(5(5(3(3(3(4(x1))))))) -> #0(2(2(2(3(5(x1)))))) 2.78/2.72 #25: #1(5(5(3(3(3(4(x1))))))) -> #3(5(x1)) 2.78/2.72 #26: #1(5(5(3(3(3(4(x1))))))) -> #5(x1) 2.78/2.72 #27: #0(4(4(0(0(5(1(x1))))))) -> #1(3(2(0(4(1(5(1(1(2(x1)))))))))) 2.78/2.72 #28: #0(4(4(0(0(5(1(x1))))))) -> #3(2(0(4(1(5(1(1(2(x1))))))))) 2.78/2.72 #29: #0(4(4(0(0(5(1(x1))))))) -> #0(4(1(5(1(1(2(x1))))))) 2.78/2.72 #30: #0(4(4(0(0(5(1(x1))))))) -> #1(5(1(1(2(x1))))) 2.78/2.72 #31: #0(4(4(0(0(5(1(x1))))))) -> #5(1(1(2(x1)))) 2.78/2.72 #32: #0(4(4(0(0(5(1(x1))))))) -> #1(1(2(x1))) 2.78/2.72 #33: #0(4(4(0(0(5(1(x1))))))) -> #1(2(x1)) 2.78/2.72 #34: #3(0(0(5(3(x1))))) -> #1(3(4(3(5(2(4(1(3(3(x1)))))))))) 2.78/2.72 #35: #3(0(0(5(3(x1))))) -> #3(4(3(5(2(4(1(3(3(x1))))))))) 2.78/2.72 #36: #3(0(0(5(3(x1))))) -> #3(5(2(4(1(3(3(x1))))))) 2.78/2.72 #37: #3(0(0(5(3(x1))))) -> #5(2(4(1(3(3(x1)))))) 2.78/2.72 #38: #3(0(0(5(3(x1))))) -> #1(3(3(x1))) 2.78/2.72 #39: #3(0(0(5(3(x1))))) -> #3(3(x1)) 2.78/2.72 #40: #3(2(3(5(1(5(2(x1))))))) -> #0(3(2(3(2(1(5(5(1(x1))))))))) 2.78/2.72 #41: #3(2(3(5(1(5(2(x1))))))) -> #3(2(3(2(1(5(5(1(x1)))))))) 2.78/2.72 #42: #3(2(3(5(1(5(2(x1))))))) -> #3(2(1(5(5(1(x1)))))) 2.78/2.72 #43: #3(2(3(5(1(5(2(x1))))))) -> #1(5(5(1(x1)))) 2.78/2.72 #44: #3(2(3(5(1(5(2(x1))))))) -> #5(5(1(x1))) 2.78/2.72 #45: #3(2(3(5(1(5(2(x1))))))) -> #5(1(x1)) 2.78/2.72 #46: #3(2(3(5(1(5(2(x1))))))) -> #1(x1) 2.78/2.72 #47: #5(0(5(3(1(0(5(x1))))))) -> #5(2(4(4(2(1(3(5(1(5(x1)))))))))) 2.78/2.72 #48: #5(0(5(3(1(0(5(x1))))))) -> #1(3(5(1(5(x1))))) 2.78/2.72 #49: #5(0(5(3(1(0(5(x1))))))) -> #3(5(1(5(x1)))) 2.78/2.72 #50: #5(0(5(3(1(0(5(x1))))))) -> #5(1(5(x1))) 2.78/2.72 #51: #5(0(5(3(1(0(5(x1))))))) -> #1(5(x1)) 2.78/2.72 #52: #5(2(0(2(5(5(x1)))))) -> #5(5(4(4(4(5(4(4(1(4(x1)))))))))) 2.78/2.72 #53: #5(2(0(2(5(5(x1)))))) -> #5(4(4(4(5(4(4(1(4(x1))))))))) 2.78/2.72 #54: #5(2(0(2(5(5(x1)))))) -> #5(4(4(1(4(x1))))) 2.78/2.72 #55: #5(2(0(2(5(5(x1)))))) -> #1(4(x1)) 2.78/2.72 Number of SCCs: 1, DPs: 2 2.78/2.72 SCC { #26 #51 } 2.78/2.72 POLO(Sum)... succeeded. 2.78/2.72 #0 w: 0 2.78/2.72 1 w: x1 2.78/2.72 4 w: x1 2.78/2.72 5 w: x1 + 1 2.78/2.72 3 w: x1 2.78/2.72 0 w: x1 2.78/2.72 #3 w: 0 2.78/2.72 #5 w: x1 + 1 2.78/2.72 2 w: x1 2.78/2.72 #1 w: x1 2.78/2.72 USABLE RULES: { 2 7 11 16 25 27 32 35 } 2.78/2.72 Removed DPs: #26 #51 2.78/2.72 Number of SCCs: 0, DPs: 0 2.78/2.72 EOF