YES Input TRS: 1: 2(5(3(0(x1)))) -> 1(0(0(1(3(0(4(5(1(2(x1)))))))))) 2: 1(3(5(4(3(x1))))) -> 2(1(4(1(4(0(3(0(1(1(x1)))))))))) 3: 5(1(3(5(0(x1))))) -> 5(1(4(3(0(4(4(5(2(1(x1)))))))))) 4: 5(4(4(2(5(x1))))) -> 4(3(1(1(1(1(5(3(3(5(x1)))))))))) 5: 2(2(5(0(5(4(x1)))))) -> 2(1(4(1(3(3(2(2(5(4(x1)))))))))) 6: 3(0(5(5(4(3(x1)))))) -> 3(3(0(3(2(3(5(5(1(0(x1)))))))))) 7: 3(5(4(3(5(2(x1)))))) -> 2(0(5(2(0(5(2(2(3(2(x1)))))))))) 8: 4(4(2(5(5(0(x1)))))) -> 4(4(0(0(3(3(3(2(2(3(x1)))))))))) 9: 4(5(3(5(5(0(x1)))))) -> 4(2(2(3(0(2(4(1(1(5(x1)))))))))) 10: 5(4(5(1(1(2(x1)))))) -> 5(4(0(3(3(3(3(2(5(5(x1)))))))))) 11: 5(5(5(5(5(3(x1)))))) -> 5(5(0(1(4(0(0(5(0(1(x1)))))))))) 12: 3(5(0(0(5(4(3(x1))))))) -> 0(1(2(1(1(5(5(2(1(0(x1)))))))))) 13: 3(5(4(2(5(2(3(x1))))))) -> 4(0(4(0(0(2(2(3(4(4(x1)))))))))) 14: 3(5(4(5(1(4(0(x1))))))) -> 1(1(1(0(0(3(3(1(2(5(x1)))))))))) Number of strict rules: 14 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #1(3(5(4(3(x1))))) -> #2(1(4(1(4(0(3(0(1(1(x1)))))))))) #2: #1(3(5(4(3(x1))))) -> #1(4(1(4(0(3(0(1(1(x1))))))))) #3: #1(3(5(4(3(x1))))) -> #4(1(4(0(3(0(1(1(x1)))))))) #4: #1(3(5(4(3(x1))))) -> #1(4(0(3(0(1(1(x1))))))) #5: #1(3(5(4(3(x1))))) -> #4(0(3(0(1(1(x1)))))) #6: #1(3(5(4(3(x1))))) -> #3(0(1(1(x1)))) #7: #1(3(5(4(3(x1))))) -> #1(1(x1)) #8: #1(3(5(4(3(x1))))) -> #1(x1) #9: #3(0(5(5(4(3(x1)))))) -> #3(3(0(3(2(3(5(5(1(0(x1)))))))))) #10: #3(0(5(5(4(3(x1)))))) -> #3(0(3(2(3(5(5(1(0(x1))))))))) #11: #3(0(5(5(4(3(x1)))))) -> #3(2(3(5(5(1(0(x1))))))) #12: #3(0(5(5(4(3(x1)))))) -> #2(3(5(5(1(0(x1)))))) #13: #3(0(5(5(4(3(x1)))))) -> #3(5(5(1(0(x1))))) #14: #3(0(5(5(4(3(x1)))))) -> #5(5(1(0(x1)))) #15: #3(0(5(5(4(3(x1)))))) -> #5(1(0(x1))) #16: #3(0(5(5(4(3(x1)))))) -> #1(0(x1)) #17: #3(5(4(2(5(2(3(x1))))))) -> #4(0(4(0(0(2(2(3(4(4(x1)))))))))) #18: #3(5(4(2(5(2(3(x1))))))) -> #4(0(0(2(2(3(4(4(x1)))))))) #19: #3(5(4(2(5(2(3(x1))))))) -> #2(2(3(4(4(x1))))) #20: #3(5(4(2(5(2(3(x1))))))) -> #2(3(4(4(x1)))) #21: #3(5(4(2(5(2(3(x1))))))) -> #3(4(4(x1))) #22: #3(5(4(2(5(2(3(x1))))))) -> #4(4(x1)) #23: #3(5(4(2(5(2(3(x1))))))) -> #4(x1) #24: #4(5(3(5(5(0(x1)))))) -> #4(2(2(3(0(2(4(1(1(5(x1)))))))))) #25: #4(5(3(5(5(0(x1)))))) -> #2(2(3(0(2(4(1(1(5(x1))))))))) #26: #4(5(3(5(5(0(x1)))))) -> #2(3(0(2(4(1(1(5(x1)))))))) #27: #4(5(3(5(5(0(x1)))))) -> #3(0(2(4(1(1(5(x1))))))) #28: #4(5(3(5(5(0(x1)))))) -> #2(4(1(1(5(x1))))) #29: #4(5(3(5(5(0(x1)))))) -> #4(1(1(5(x1)))) #30: #4(5(3(5(5(0(x1)))))) -> #1(1(5(x1))) #31: #4(5(3(5(5(0(x1)))))) -> #1(5(x1)) #32: #4(5(3(5(5(0(x1)))))) -> #5(x1) #33: #5(5(5(5(5(3(x1)))))) -> #5(5(0(1(4(0(0(5(0(1(x1)))))))))) #34: #5(5(5(5(5(3(x1)))))) -> #5(0(1(4(0(0(5(0(1(x1))))))))) #35: #5(5(5(5(5(3(x1)))))) -> #1(4(0(0(5(0(1(x1))))))) #36: #5(5(5(5(5(3(x1)))))) -> #4(0(0(5(0(1(x1)))))) #37: #5(5(5(5(5(3(x1)))))) -> #5(0(1(x1))) #38: #5(5(5(5(5(3(x1)))))) -> #1(x1) #39: #3(5(0(0(5(4(3(x1))))))) -> #1(2(1(1(5(5(2(1(0(x1))))))))) #40: #3(5(0(0(5(4(3(x1))))))) -> #2(1(1(5(5(2(1(0(x1)))))))) #41: #3(5(0(0(5(4(3(x1))))))) -> #1(1(5(5(2(1(0(x1))))))) #42: #3(5(0(0(5(4(3(x1))))))) -> #1(5(5(2(1(0(x1)))))) #43: #3(5(0(0(5(4(3(x1))))))) -> #5(5(2(1(0(x1))))) #44: #3(5(0(0(5(4(3(x1))))))) -> #5(2(1(0(x1)))) #45: #3(5(0(0(5(4(3(x1))))))) -> #2(1(0(x1))) #46: #3(5(0(0(5(4(3(x1))))))) -> #1(0(x1)) #47: #3(5(4(5(1(4(0(x1))))))) -> #1(1(1(0(0(3(3(1(2(5(x1)))))))))) #48: #3(5(4(5(1(4(0(x1))))))) -> #1(1(0(0(3(3(1(2(5(x1))))))))) #49: #3(5(4(5(1(4(0(x1))))))) -> #1(0(0(3(3(1(2(5(x1)))))))) #50: #3(5(4(5(1(4(0(x1))))))) -> #3(3(1(2(5(x1))))) #51: #3(5(4(5(1(4(0(x1))))))) -> #3(1(2(5(x1)))) #52: #3(5(4(5(1(4(0(x1))))))) -> #1(2(5(x1))) #53: #3(5(4(5(1(4(0(x1))))))) -> #2(5(x1)) #54: #3(5(4(5(1(4(0(x1))))))) -> #5(x1) #55: #3(5(4(3(5(2(x1)))))) -> #2(0(5(2(0(5(2(2(3(2(x1)))))))))) #56: #3(5(4(3(5(2(x1)))))) -> #5(2(0(5(2(2(3(2(x1)))))))) #57: #3(5(4(3(5(2(x1)))))) -> #2(0(5(2(2(3(2(x1))))))) #58: #3(5(4(3(5(2(x1)))))) -> #5(2(2(3(2(x1))))) #59: #3(5(4(3(5(2(x1)))))) -> #2(2(3(2(x1)))) #60: #3(5(4(3(5(2(x1)))))) -> #2(3(2(x1))) #61: #3(5(4(3(5(2(x1)))))) -> #3(2(x1)) #62: #5(4(5(1(1(2(x1)))))) -> #5(4(0(3(3(3(3(2(5(5(x1)))))))))) #63: #5(4(5(1(1(2(x1)))))) -> #4(0(3(3(3(3(2(5(5(x1))))))))) #64: #5(4(5(1(1(2(x1)))))) -> #3(3(3(3(2(5(5(x1))))))) #65: #5(4(5(1(1(2(x1)))))) -> #3(3(3(2(5(5(x1)))))) #66: #5(4(5(1(1(2(x1)))))) -> #3(3(2(5(5(x1))))) #67: #5(4(5(1(1(2(x1)))))) -> #3(2(5(5(x1)))) #68: #5(4(5(1(1(2(x1)))))) -> #2(5(5(x1))) #69: #5(4(5(1(1(2(x1)))))) -> #5(5(x1)) #70: #5(4(5(1(1(2(x1)))))) -> #5(x1) #71: #2(2(5(0(5(4(x1)))))) -> #2(1(4(1(3(3(2(2(5(4(x1)))))))))) #72: #2(2(5(0(5(4(x1)))))) -> #1(4(1(3(3(2(2(5(4(x1))))))))) #73: #2(2(5(0(5(4(x1)))))) -> #4(1(3(3(2(2(5(4(x1)))))))) #74: #2(2(5(0(5(4(x1)))))) -> #1(3(3(2(2(5(4(x1))))))) #75: #2(2(5(0(5(4(x1)))))) -> #3(3(2(2(5(4(x1)))))) #76: #2(2(5(0(5(4(x1)))))) -> #3(2(2(5(4(x1))))) #77: #2(2(5(0(5(4(x1)))))) -> #2(2(5(4(x1)))) #78: #2(2(5(0(5(4(x1)))))) -> #2(5(4(x1))) #79: #5(1(3(5(0(x1))))) -> #5(1(4(3(0(4(4(5(2(1(x1)))))))))) #80: #5(1(3(5(0(x1))))) -> #1(4(3(0(4(4(5(2(1(x1))))))))) #81: #5(1(3(5(0(x1))))) -> #4(3(0(4(4(5(2(1(x1)))))))) #82: #5(1(3(5(0(x1))))) -> #3(0(4(4(5(2(1(x1))))))) #83: #5(1(3(5(0(x1))))) -> #4(4(5(2(1(x1))))) #84: #5(1(3(5(0(x1))))) -> #4(5(2(1(x1)))) #85: #5(1(3(5(0(x1))))) -> #5(2(1(x1))) #86: #5(1(3(5(0(x1))))) -> #2(1(x1)) #87: #5(1(3(5(0(x1))))) -> #1(x1) #88: #2(5(3(0(x1)))) -> #1(0(0(1(3(0(4(5(1(2(x1)))))))))) #89: #2(5(3(0(x1)))) -> #1(3(0(4(5(1(2(x1))))))) #90: #2(5(3(0(x1)))) -> #3(0(4(5(1(2(x1)))))) #91: #2(5(3(0(x1)))) -> #4(5(1(2(x1)))) #92: #2(5(3(0(x1)))) -> #5(1(2(x1))) #93: #2(5(3(0(x1)))) -> #1(2(x1)) #94: #2(5(3(0(x1)))) -> #2(x1) #95: #4(4(2(5(5(0(x1)))))) -> #4(4(0(0(3(3(3(2(2(3(x1)))))))))) #96: #4(4(2(5(5(0(x1)))))) -> #4(0(0(3(3(3(2(2(3(x1))))))))) #97: #4(4(2(5(5(0(x1)))))) -> #3(3(3(2(2(3(x1)))))) #98: #4(4(2(5(5(0(x1)))))) -> #3(3(2(2(3(x1))))) #99: #4(4(2(5(5(0(x1)))))) -> #3(2(2(3(x1)))) #100: #4(4(2(5(5(0(x1)))))) -> #2(2(3(x1))) #101: #4(4(2(5(5(0(x1)))))) -> #2(3(x1)) #102: #4(4(2(5(5(0(x1)))))) -> #3(x1) #103: #5(4(4(2(5(x1))))) -> #4(3(1(1(1(1(5(3(3(5(x1)))))))))) #104: #5(4(4(2(5(x1))))) -> #3(1(1(1(1(5(3(3(5(x1))))))))) #105: #5(4(4(2(5(x1))))) -> #1(1(1(1(5(3(3(5(x1)))))))) #106: #5(4(4(2(5(x1))))) -> #1(1(1(5(3(3(5(x1))))))) #107: #5(4(4(2(5(x1))))) -> #1(1(5(3(3(5(x1)))))) #108: #5(4(4(2(5(x1))))) -> #1(5(3(3(5(x1))))) #109: #5(4(4(2(5(x1))))) -> #5(3(3(5(x1)))) #110: #5(4(4(2(5(x1))))) -> #3(3(5(x1))) #111: #5(4(4(2(5(x1))))) -> #3(5(x1)) Number of SCCs: 3, DPs: 9 SCC { #94 } POLO(Sum)... succeeded. 1 w: 0 4 w: 0 5 w: x1 3 w: x1 #2 w: x1 #4 w: 0 0 w: x1 + 1 #3 w: 0 #5 w: 0 2 w: 0 #1 w: 0 USABLE RULES: { } Removed DPs: #94 Number of SCCs: 2, DPs: 8 SCC { #8 } POLO(Sum)... succeeded. 1 w: 0 4 w: x1 + 2437 5 w: x1 3 w: x1 + 1 #2 w: 0 #4 w: 0 0 w: 1 #3 w: 0 #5 w: 0 2 w: 0 #1 w: x1 USABLE RULES: { } Removed DPs: #8 Number of SCCs: 1, DPs: 7 SCC { #22 #23 #32 #54 #70 #102 #111 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... succeeded. 1 w: max(x1 - 414158, 0) 4 w: max(x1 + 144055, 0) 5 w: max(x1 + 828316, 0) 3 w: max(x1 - 882337, 0) #2 w: 0 #4 w: max(x1 + 54022, 0) 0 w: max(x1 - 774293, 0) #3 w: max(x1 + 882340, 0) #5 w: max(x1 + 882339, 0) 2 w: max(x1 - 18008, 0) #1 w: 0 USABLE RULES: { 1..14 } Removed DPs: #22 #23 #32 #54 #70 #102 #111 Number of SCCs: 0, DPs: 0