YES Input TRS: 1: 0(5(0(x1))) -> 3(4(3(3(2(0(4(4(4(0(x1)))))))))) 2: 0(2(5(0(x1)))) -> 0(2(1(1(5(2(1(4(1(3(x1)))))))))) 3: 0(5(0(5(x1)))) -> 3(2(0(2(0(4(4(1(5(4(x1)))))))))) 4: 2(5(5(3(x1)))) -> 4(3(0(2(1(0(1(3(4(3(x1)))))))))) 5: 5(5(5(0(x1)))) -> 4(1(2(1(2(3(5(0(1(3(x1)))))))))) 6: 0(5(1(5(0(x1))))) -> 3(4(0(1(4(5(2(2(3(1(x1)))))))))) 7: 3(0(0(5(3(x1))))) -> 1(3(4(3(5(2(4(1(3(3(x1)))))))))) 8: 3(5(5(0(0(x1))))) -> 1(4(1(0(0(4(4(0(4(1(x1)))))))))) 9: 0(2(5(1(5(0(x1)))))) -> 2(1(0(1(5(2(4(0(2(0(x1)))))))))) 10: 0(2(5(5(1(4(x1)))))) -> 4(0(1(1(1(1(0(4(1(5(x1)))))))))) 11: 0(5(3(1(2(5(x1)))))) -> 0(2(3(1(1(2(4(4(5(5(x1)))))))))) 12: 0(5(5(1(5(1(x1)))))) -> 0(5(1(1(3(3(4(2(1(0(x1)))))))))) 13: 4(5(5(4(2(0(x1)))))) -> 2(4(0(1(3(4(4(4(1(0(x1)))))))))) 14: 5(0(0(3(5(2(x1)))))) -> 4(4(2(3(0(1(2(0(5(2(x1)))))))))) 15: 5(1(5(0(2(5(x1)))))) -> 5(0(0(1(4(2(3(2(1(5(x1)))))))))) 16: 5(2(0(2(5(5(x1)))))) -> 5(5(4(4(4(5(4(4(1(4(x1)))))))))) 17: 5(5(0(2(5(0(x1)))))) -> 2(0(5(0(2(1(0(0(3(0(x1)))))))))) 18: 5(5(0(3(4(5(x1)))))) -> 2(0(5(5(2(1(3(2(3(2(x1)))))))))) 19: 5(5(3(5(0(5(x1)))))) -> 5(4(4(3(5(1(3(3(4(5(x1)))))))))) 20: 0(4(4(0(0(5(1(x1))))))) -> 1(3(2(0(4(1(5(1(1(2(x1)))))))))) 21: 0(4(4(2(5(5(5(x1))))))) -> 0(2(4(5(5(4(2(0(1(1(x1)))))))))) 22: 1(0(2(5(2(0(0(x1))))))) -> 3(1(4(4(0(3(0(1(2(2(x1)))))))))) 23: 1(2(0(4(2(5(0(x1))))))) -> 4(2(4(0(3(2(2(4(1(0(x1)))))))))) 24: 1(2(5(5(0(3(3(x1))))))) -> 3(4(1(2(0(3(3(1(0(3(x1)))))))))) 25: 1(5(5(3(3(3(4(x1))))))) -> 1(5(1(0(0(2(2(2(3(5(x1)))))))))) 26: 2(5(4(5(2(5(1(x1))))))) -> 4(3(2(1(4(2(2(4(5(2(x1)))))))))) 27: 3(2(3(5(1(5(2(x1))))))) -> 2(0(3(2(3(2(1(5(5(1(x1)))))))))) 28: 3(3(4(2(5(5(2(x1))))))) -> 1(2(3(3(4(4(1(4(0(1(x1)))))))))) 29: 3(5(0(5(5(5(0(x1))))))) -> 0(0(3(0(3(5(0(3(2(0(x1)))))))))) 30: 4(3(1(2(5(2(4(x1))))))) -> 2(3(1(1(4(3(4(4(2(4(x1)))))))))) 31: 4(5(5(3(1(0(5(x1))))))) -> 1(1(5(2(0(3(3(3(2(1(x1)))))))))) 32: 5(0(5(3(1(0(5(x1))))))) -> 5(2(4(4(2(1(3(5(1(5(x1)))))))))) 33: 5(0(5(3(5(1(5(x1))))))) -> 5(1(1(2(4(0(0(3(2(5(x1)))))))))) 34: 5(1(5(3(3(0(5(x1))))))) -> 4(4(3(2(2(2(5(0(1(1(x1)))))))))) 35: 5(2(0(2(5(3(3(x1))))))) -> 5(2(0(5(1(1(3(2(0(3(x1)))))))))) Number of strict rules: 35 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 1 w: x1 4 w: x1 5 w: x1 + 8945 3 w: x1 0 w: x1 2 w: x1 Number of strict rules: 9 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #0(2(5(0(x1)))) -> #0(2(1(1(5(2(1(4(1(3(x1)))))))))) #2: #0(2(5(0(x1)))) -> #1(1(5(2(1(4(1(3(x1)))))))) #3: #0(2(5(0(x1)))) -> #1(5(2(1(4(1(3(x1))))))) #4: #0(2(5(0(x1)))) -> #5(2(1(4(1(3(x1)))))) #5: #0(2(5(0(x1)))) -> #1(4(1(3(x1)))) #6: #0(2(5(0(x1)))) -> #1(3(x1)) #7: #0(2(5(0(x1)))) -> #3(x1) #8: #5(2(0(2(5(3(3(x1))))))) -> #5(2(0(5(1(1(3(2(0(3(x1)))))))))) #9: #5(2(0(2(5(3(3(x1))))))) -> #0(5(1(1(3(2(0(3(x1)))))))) #10: #5(2(0(2(5(3(3(x1))))))) -> #5(1(1(3(2(0(3(x1))))))) #11: #5(2(0(2(5(3(3(x1))))))) -> #1(1(3(2(0(3(x1)))))) #12: #5(2(0(2(5(3(3(x1))))))) -> #1(3(2(0(3(x1))))) #13: #5(2(0(2(5(3(3(x1))))))) -> #3(2(0(3(x1)))) #14: #5(2(0(2(5(3(3(x1))))))) -> #0(3(x1)) #15: #0(5(3(1(2(5(x1)))))) -> #0(2(3(1(1(2(4(4(5(5(x1)))))))))) #16: #0(5(3(1(2(5(x1)))))) -> #3(1(1(2(4(4(5(5(x1)))))))) #17: #0(5(3(1(2(5(x1)))))) -> #1(1(2(4(4(5(5(x1))))))) #18: #0(5(3(1(2(5(x1)))))) -> #1(2(4(4(5(5(x1)))))) #19: #0(5(3(1(2(5(x1)))))) -> #5(5(x1)) #20: #1(5(5(3(3(3(4(x1))))))) -> #1(5(1(0(0(2(2(2(3(5(x1)))))))))) #21: #1(5(5(3(3(3(4(x1))))))) -> #5(1(0(0(2(2(2(3(5(x1))))))))) #22: #1(5(5(3(3(3(4(x1))))))) -> #1(0(0(2(2(2(3(5(x1)))))))) #23: #1(5(5(3(3(3(4(x1))))))) -> #0(0(2(2(2(3(5(x1))))))) #24: #1(5(5(3(3(3(4(x1))))))) -> #0(2(2(2(3(5(x1)))))) #25: #1(5(5(3(3(3(4(x1))))))) -> #3(5(x1)) #26: #1(5(5(3(3(3(4(x1))))))) -> #5(x1) #27: #0(4(4(0(0(5(1(x1))))))) -> #1(3(2(0(4(1(5(1(1(2(x1)))))))))) #28: #0(4(4(0(0(5(1(x1))))))) -> #3(2(0(4(1(5(1(1(2(x1))))))))) #29: #0(4(4(0(0(5(1(x1))))))) -> #0(4(1(5(1(1(2(x1))))))) #30: #0(4(4(0(0(5(1(x1))))))) -> #1(5(1(1(2(x1))))) #31: #0(4(4(0(0(5(1(x1))))))) -> #5(1(1(2(x1)))) #32: #0(4(4(0(0(5(1(x1))))))) -> #1(1(2(x1))) #33: #0(4(4(0(0(5(1(x1))))))) -> #1(2(x1)) #34: #3(0(0(5(3(x1))))) -> #1(3(4(3(5(2(4(1(3(3(x1)))))))))) #35: #3(0(0(5(3(x1))))) -> #3(4(3(5(2(4(1(3(3(x1))))))))) #36: #3(0(0(5(3(x1))))) -> #3(5(2(4(1(3(3(x1))))))) #37: #3(0(0(5(3(x1))))) -> #5(2(4(1(3(3(x1)))))) #38: #3(0(0(5(3(x1))))) -> #1(3(3(x1))) #39: #3(0(0(5(3(x1))))) -> #3(3(x1)) #40: #3(2(3(5(1(5(2(x1))))))) -> #0(3(2(3(2(1(5(5(1(x1))))))))) #41: #3(2(3(5(1(5(2(x1))))))) -> #3(2(3(2(1(5(5(1(x1)))))))) #42: #3(2(3(5(1(5(2(x1))))))) -> #3(2(1(5(5(1(x1)))))) #43: #3(2(3(5(1(5(2(x1))))))) -> #1(5(5(1(x1)))) #44: #3(2(3(5(1(5(2(x1))))))) -> #5(5(1(x1))) #45: #3(2(3(5(1(5(2(x1))))))) -> #5(1(x1)) #46: #3(2(3(5(1(5(2(x1))))))) -> #1(x1) #47: #5(0(5(3(1(0(5(x1))))))) -> #5(2(4(4(2(1(3(5(1(5(x1)))))))))) #48: #5(0(5(3(1(0(5(x1))))))) -> #1(3(5(1(5(x1))))) #49: #5(0(5(3(1(0(5(x1))))))) -> #3(5(1(5(x1)))) #50: #5(0(5(3(1(0(5(x1))))))) -> #5(1(5(x1))) #51: #5(0(5(3(1(0(5(x1))))))) -> #1(5(x1)) #52: #5(2(0(2(5(5(x1)))))) -> #5(5(4(4(4(5(4(4(1(4(x1)))))))))) #53: #5(2(0(2(5(5(x1)))))) -> #5(4(4(4(5(4(4(1(4(x1))))))))) #54: #5(2(0(2(5(5(x1)))))) -> #5(4(4(1(4(x1))))) #55: #5(2(0(2(5(5(x1)))))) -> #1(4(x1)) Number of SCCs: 1, DPs: 2 SCC { #26 #51 } POLO(Sum)... succeeded. #0 w: 0 1 w: x1 4 w: x1 5 w: x1 + 2998 3 w: x1 0 w: x1 #3 w: 0 #5 w: x1 2 w: x1 #1 w: x1 + 2997 USABLE RULES: { 2 7 11 16 25 27 32 35 } Removed DPs: #26 #51 Number of SCCs: 0, DPs: 0