YES Input TRS: 1: 4(2(4(x1))) -> 2(0(0(5(3(3(5(2(0(4(x1)))))))))) 2: 4(4(2(4(2(x1))))) -> 2(0(5(2(1(4(0(2(0(1(x1)))))))))) 3: 0(5(4(2(4(3(x1)))))) -> 5(1(5(5(3(5(3(0(0(0(x1)))))))))) 4: 1(1(4(5(3(3(x1)))))) -> 1(3(1(1(3(0(1(2(2(1(x1)))))))))) 5: 3(1(4(3(1(2(x1)))))) -> 0(0(1(1(4(2(3(0(0(3(x1)))))))))) 6: 3(2(4(2(4(1(x1)))))) -> 0(2(1(1(1(5(3(1(3(3(x1)))))))))) 7: 3(3(0(4(1(2(x1)))))) -> 3(5(1(2(0(2(0(5(3(1(x1)))))))))) 8: 4(1(4(5(0(5(4(x1))))))) -> 4(1(5(3(1(0(5(3(1(0(x1)))))))))) 9: 4(4(0(5(4(2(2(x1))))))) -> 4(0(4(3(4(4(4(5(4(1(x1)))))))))) 10: 5(4(5(3(2(4(3(x1))))))) -> 2(5(5(5(0(4(5(0(1(4(x1)))))))))) Number of strict rules: 10 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #4(4(2(4(2(x1))))) -> #0(5(2(1(4(0(2(0(1(x1))))))))) #2: #4(4(2(4(2(x1))))) -> #5(2(1(4(0(2(0(1(x1)))))))) #3: #4(4(2(4(2(x1))))) -> #1(4(0(2(0(1(x1)))))) #4: #4(4(2(4(2(x1))))) -> #4(0(2(0(1(x1))))) #5: #4(4(2(4(2(x1))))) -> #0(2(0(1(x1)))) #6: #4(4(2(4(2(x1))))) -> #0(1(x1)) #7: #4(4(2(4(2(x1))))) -> #1(x1) #8: #3(2(4(2(4(1(x1)))))) -> #0(2(1(1(1(5(3(1(3(3(x1)))))))))) #9: #3(2(4(2(4(1(x1)))))) -> #1(1(1(5(3(1(3(3(x1)))))))) #10: #3(2(4(2(4(1(x1)))))) -> #1(1(5(3(1(3(3(x1))))))) #11: #3(2(4(2(4(1(x1)))))) -> #1(5(3(1(3(3(x1)))))) #12: #3(2(4(2(4(1(x1)))))) -> #5(3(1(3(3(x1))))) #13: #3(2(4(2(4(1(x1)))))) -> #3(1(3(3(x1)))) #14: #3(2(4(2(4(1(x1)))))) -> #1(3(3(x1))) #15: #3(2(4(2(4(1(x1)))))) -> #3(3(x1)) #16: #3(2(4(2(4(1(x1)))))) -> #3(x1) #17: #4(4(0(5(4(2(2(x1))))))) -> #4(0(4(3(4(4(4(5(4(1(x1)))))))))) #18: #4(4(0(5(4(2(2(x1))))))) -> #0(4(3(4(4(4(5(4(1(x1))))))))) #19: #4(4(0(5(4(2(2(x1))))))) -> #4(3(4(4(4(5(4(1(x1)))))))) #20: #4(4(0(5(4(2(2(x1))))))) -> #3(4(4(4(5(4(1(x1))))))) #21: #4(4(0(5(4(2(2(x1))))))) -> #4(4(4(5(4(1(x1)))))) #22: #4(4(0(5(4(2(2(x1))))))) -> #4(4(5(4(1(x1))))) #23: #4(4(0(5(4(2(2(x1))))))) -> #4(5(4(1(x1)))) #24: #4(4(0(5(4(2(2(x1))))))) -> #5(4(1(x1))) #25: #4(4(0(5(4(2(2(x1))))))) -> #4(1(x1)) #26: #4(4(0(5(4(2(2(x1))))))) -> #1(x1) #27: #3(3(0(4(1(2(x1)))))) -> #3(5(1(2(0(2(0(5(3(1(x1)))))))))) #28: #3(3(0(4(1(2(x1)))))) -> #5(1(2(0(2(0(5(3(1(x1))))))))) #29: #3(3(0(4(1(2(x1)))))) -> #1(2(0(2(0(5(3(1(x1)))))))) #30: #3(3(0(4(1(2(x1)))))) -> #0(2(0(5(3(1(x1)))))) #31: #3(3(0(4(1(2(x1)))))) -> #0(5(3(1(x1)))) #32: #3(3(0(4(1(2(x1)))))) -> #5(3(1(x1))) #33: #3(3(0(4(1(2(x1)))))) -> #3(1(x1)) #34: #3(3(0(4(1(2(x1)))))) -> #1(x1) #35: #5(4(5(3(2(4(3(x1))))))) -> #5(5(5(0(4(5(0(1(4(x1))))))))) #36: #5(4(5(3(2(4(3(x1))))))) -> #5(5(0(4(5(0(1(4(x1)))))))) #37: #5(4(5(3(2(4(3(x1))))))) -> #5(0(4(5(0(1(4(x1))))))) #38: #5(4(5(3(2(4(3(x1))))))) -> #0(4(5(0(1(4(x1)))))) #39: #5(4(5(3(2(4(3(x1))))))) -> #4(5(0(1(4(x1))))) #40: #5(4(5(3(2(4(3(x1))))))) -> #5(0(1(4(x1)))) #41: #5(4(5(3(2(4(3(x1))))))) -> #0(1(4(x1))) #42: #5(4(5(3(2(4(3(x1))))))) -> #1(4(x1)) #43: #5(4(5(3(2(4(3(x1))))))) -> #4(x1) #44: #3(1(4(3(1(2(x1)))))) -> #0(0(1(1(4(2(3(0(0(3(x1)))))))))) #45: #3(1(4(3(1(2(x1)))))) -> #0(1(1(4(2(3(0(0(3(x1))))))))) #46: #3(1(4(3(1(2(x1)))))) -> #1(1(4(2(3(0(0(3(x1)))))))) #47: #3(1(4(3(1(2(x1)))))) -> #1(4(2(3(0(0(3(x1))))))) #48: #3(1(4(3(1(2(x1)))))) -> #4(2(3(0(0(3(x1)))))) #49: #3(1(4(3(1(2(x1)))))) -> #3(0(0(3(x1)))) #50: #3(1(4(3(1(2(x1)))))) -> #0(0(3(x1))) #51: #3(1(4(3(1(2(x1)))))) -> #0(3(x1)) #52: #3(1(4(3(1(2(x1)))))) -> #3(x1) #53: #0(5(4(2(4(3(x1)))))) -> #5(1(5(5(3(5(3(0(0(0(x1)))))))))) #54: #0(5(4(2(4(3(x1)))))) -> #1(5(5(3(5(3(0(0(0(x1))))))))) #55: #0(5(4(2(4(3(x1)))))) -> #5(5(3(5(3(0(0(0(x1)))))))) #56: #0(5(4(2(4(3(x1)))))) -> #5(3(5(3(0(0(0(x1))))))) #57: #0(5(4(2(4(3(x1)))))) -> #3(5(3(0(0(0(x1)))))) #58: #0(5(4(2(4(3(x1)))))) -> #5(3(0(0(0(x1))))) #59: #0(5(4(2(4(3(x1)))))) -> #3(0(0(0(x1)))) #60: #0(5(4(2(4(3(x1)))))) -> #0(0(0(x1))) #61: #0(5(4(2(4(3(x1)))))) -> #0(0(x1)) #62: #0(5(4(2(4(3(x1)))))) -> #0(x1) #63: #4(2(4(x1))) -> #0(0(5(3(3(5(2(0(4(x1))))))))) #64: #4(2(4(x1))) -> #0(5(3(3(5(2(0(4(x1)))))))) #65: #4(2(4(x1))) -> #5(3(3(5(2(0(4(x1))))))) #66: #4(2(4(x1))) -> #3(3(5(2(0(4(x1)))))) #67: #4(2(4(x1))) -> #3(5(2(0(4(x1))))) #68: #4(2(4(x1))) -> #5(2(0(4(x1)))) #69: #4(2(4(x1))) -> #0(4(x1)) #70: #4(1(4(5(0(5(4(x1))))))) -> #4(1(5(3(1(0(5(3(1(0(x1)))))))))) #71: #4(1(4(5(0(5(4(x1))))))) -> #1(5(3(1(0(5(3(1(0(x1))))))))) #72: #4(1(4(5(0(5(4(x1))))))) -> #5(3(1(0(5(3(1(0(x1)))))))) #73: #4(1(4(5(0(5(4(x1))))))) -> #3(1(0(5(3(1(0(x1))))))) #74: #4(1(4(5(0(5(4(x1))))))) -> #1(0(5(3(1(0(x1)))))) #75: #4(1(4(5(0(5(4(x1))))))) -> #0(5(3(1(0(x1))))) #76: #4(1(4(5(0(5(4(x1))))))) -> #5(3(1(0(x1)))) #77: #4(1(4(5(0(5(4(x1))))))) -> #3(1(0(x1))) #78: #4(1(4(5(0(5(4(x1))))))) -> #1(0(x1)) #79: #4(1(4(5(0(5(4(x1))))))) -> #0(x1) #80: #1(1(4(5(3(3(x1)))))) -> #1(3(1(1(3(0(1(2(2(1(x1)))))))))) #81: #1(1(4(5(3(3(x1)))))) -> #3(1(1(3(0(1(2(2(1(x1))))))))) #82: #1(1(4(5(3(3(x1)))))) -> #1(1(3(0(1(2(2(1(x1)))))))) #83: #1(1(4(5(3(3(x1)))))) -> #1(3(0(1(2(2(1(x1))))))) #84: #1(1(4(5(3(3(x1)))))) -> #3(0(1(2(2(1(x1)))))) #85: #1(1(4(5(3(3(x1)))))) -> #0(1(2(2(1(x1))))) #86: #1(1(4(5(3(3(x1)))))) -> #1(2(2(1(x1)))) #87: #1(1(4(5(3(3(x1)))))) -> #1(x1) Number of SCCs: 3, DPs: 6 SCC { #87 } POLO(Sum)... succeeded. #0 w: 0 1 w: x1 4 w: x1 5 w: x1 + 21238 3 w: x1 + 1 #4 w: 0 0 w: 0 #3 w: 0 #5 w: 0 2 w: 0 #1 w: x1 USABLE RULES: { } Removed DPs: #87 Number of SCCs: 2, DPs: 5 SCC { #62 } POLO(Sum)... succeeded. #0 w: x1 1 w: 0 4 w: x1 + 2437 5 w: x1 + 21238 3 w: x1 + 1 #4 w: 0 0 w: 0 #3 w: 0 #5 w: 0 2 w: x1 #1 w: 0 USABLE RULES: { } Removed DPs: #62 Number of SCCs: 1, DPs: 4 SCC { #15 #16 #33 #52 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... succeeded. #0 w: max(x1 - 1, 0) 1 w: max(x1 - 2633055, 0) 4 w: max(x1 + 2922239, 0) 5 w: max(x1 - 1573514, 0) 3 w: max(x1 + 160391, 0) #4 w: max(x1 - 1, 0) 0 w: max(x1 - 64396, 0) #3 w: max(x1 - 160392, 0) #5 w: max(x1 - 1, 0) 2 w: max(x1 + 4656143, 0) #1 w: max(x1 - 1, 0) USABLE RULES: { 1..10 } Removed DPs: #15 #16 #33 #52 Number of SCCs: 0, DPs: 0