YES Input TRS: 1: 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 2: 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 3: 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 4: 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 5: 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 6: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 7: 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 8: 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 9: 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 10: 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 11: 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 12: 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 13: 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 14: 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 15: 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 16: 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 17: 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) 18: 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 19: 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 20: 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 21: 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 22: 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 23: 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 24: 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 25: 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 26: 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 27: 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 28: 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 29: 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 30: 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 31: 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 32: 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 33: 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 34: 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 35: 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 36: 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 37: 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 38: 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 39: 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 40: 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 41: 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 42: 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 43: 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 44: 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 45: 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 46: 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 47: 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 48: 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 49: 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 50: 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 51: 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 52: 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 53: 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 54: 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 55: 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 56: 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 57: 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 58: 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) Number of strict rules: 58 Direct POLO(bPol) ... removes: 18 50 4 8 54 1 3 16 21 36 26 19 32 17 27 34 22 28 44 5 33 10 39 7 20 25 49 52 30 14 31 12 45 23 24 57 11 9 13 51 40 55 6 38 58 48 53 37 41 42 46 35 29 43 2 1 w: x1 4 w: x1 + 13544 5 w: x1 + 27087 3 w: x1 0 w: x1 + 40631 2 w: x1 Number of strict rules: 3 Direct POLO(bPol) ... failed. Uncurrying 4 15: 4^1_0(0(1(3(1(x1))))) -> 3(2(2(1(2(0(5(4(4^1_1(x1))))))))) 47: 4^1_1(2(5(4^1_0(0(x1))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 56: 5(3(0(1(4^1_3(1(x1)))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 59: 4(0(_1)) ->= 4^1_0(_1) 60: 4(1(_1)) ->= 4^1_1(_1) 61: 4(3(_1)) ->= 4^1_3(_1) Number of strict rules: 3 Direct POLO(bPol) ... failed. Dependency Pairs: #1: #4^1_1(2(5(4^1_0(0(x1))))) -> #4(5(1(3(0(3(2(0(4(x1))))))))) #2: #4^1_1(2(5(4^1_0(0(x1))))) -> #5(1(3(0(3(2(0(4(x1)))))))) #3: #4^1_1(2(5(4^1_0(0(x1))))) -> #4(x1) #4: #4(0(_1)) ->? #4^1_0(_1) #5: #4(1(_1)) ->? #4^1_1(_1) #6: #4^1_0(0(1(3(1(x1))))) -> #5(4(4^1_1(x1))) #7: #4^1_0(0(1(3(1(x1))))) -> #4(4^1_1(x1)) #8: #4^1_0(0(1(3(1(x1))))) -> #4^1_1(x1) Number of SCCs: 1, DPs: 4 SCC { #3..5 #8 } POLO(Sum)... succeeded. 1 w: x1 + 8366 4 w: 0 5 w: x1 3 w: x1 4^1_1 w: 0 #4 w: x1 0 w: x1 + 20653 #4^1_1 w: x1 + 8365 4^1_0 w: x1 #5 w: 0 2 w: x1 4^1_3 w: 0 #4^1_0 w: x1 + 20652 USABLE RULES: { } Removed DPs: #3..5 #8 Number of SCCs: 0, DPs: 0