YES Input TRS: 1: 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(x1)))))))))) 2: 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(x1))))))))))))) 3: 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))) 4: 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))))) 5: 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))))))))) Number of strict rules: 5 Direct POLO(bPol) ... failed. Uncurrying 0^1_1 0 1: 0^1_1^1_2(1(x1)) -> 1(2(1(1(0^1_1^1_2(0^1_1^1_2(x1)))))) 2: 0^1_1^1_2(1(x1)) -> 1(2(1(1(0^1_1^1_2(0^1_1^1_2(0^1_1^1_2(x1))))))) 3: 0^1_1^1_2(1(x1)) -> 1(2(1(1(0^1_1^1_2(0^1_1^1_2(0^1_1^1_2(0^1_1^1_2(x1)))))))) 4: 0^1_1^1_2(1(x1)) -> 1(2(1(1(0^1_1^1_2(0^1_1^1_2(0^1_1^1_2(0^1_1^1_2(0^1_1^1_2(x1))))))))) 5: 0^1_1^1_2(1(x1)) -> 1(2(1(1(0^1_1^1_2(0^1_1^1_2(0^1_1^1_2(0^1_1^1_2(0^1_1^1_2(0^1_1^1_2(x1)))))))))) 6: 0(1(_1)) ->= 0^1_1(_1) 7: 0^1_1(2(_1)) ->= 0^1_1^1_2(_1) Number of strict rules: 5 Direct POLO(bPol) ... removes: 7 6 1 w: x1 0^1_1^1_2 w: x1 0 w: x1 + 2 0^1_1 w: x1 + 1 2 w: x1 Number of strict rules: 5 Direct POLO(bPol) ... failed. Dependency Pairs: #1: #0^1_1^1_2(1(x1)) -> #0^1_1^1_2(0^1_1^1_2(0^1_1^1_2(x1))) #2: #0^1_1^1_2(1(x1)) -> #0^1_1^1_2(0^1_1^1_2(x1)) #3: #0^1_1^1_2(1(x1)) -> #0^1_1^1_2(x1) #4: #0^1_1^1_2(1(x1)) -> #0^1_1^1_2(0^1_1^1_2(0^1_1^1_2(0^1_1^1_2(0^1_1^1_2(0^1_1^1_2(x1)))))) #5: #0^1_1^1_2(1(x1)) -> #0^1_1^1_2(0^1_1^1_2(0^1_1^1_2(0^1_1^1_2(0^1_1^1_2(x1))))) #6: #0^1_1^1_2(1(x1)) -> #0^1_1^1_2(0^1_1^1_2(0^1_1^1_2(0^1_1^1_2(x1)))) #7: #0^1_1^1_2(1(x1)) -> #0^1_1^1_2(0^1_1^1_2(0^1_1^1_2(x1))) #8: #0^1_1^1_2(1(x1)) -> #0^1_1^1_2(0^1_1^1_2(x1)) #9: #0^1_1^1_2(1(x1)) -> #0^1_1^1_2(x1) #10: #0^1_1^1_2(1(x1)) -> #0^1_1^1_2(0^1_1^1_2(0^1_1^1_2(0^1_1^1_2(x1)))) #11: #0^1_1^1_2(1(x1)) -> #0^1_1^1_2(0^1_1^1_2(0^1_1^1_2(x1))) #12: #0^1_1^1_2(1(x1)) -> #0^1_1^1_2(0^1_1^1_2(x1)) #13: #0^1_1^1_2(1(x1)) -> #0^1_1^1_2(x1) #14: #0^1_1^1_2(1(x1)) -> #0^1_1^1_2(0^1_1^1_2(x1)) #15: #0^1_1^1_2(1(x1)) -> #0^1_1^1_2(x1) #16: #0^1_1^1_2(1(x1)) -> #0^1_1^1_2(0^1_1^1_2(0^1_1^1_2(0^1_1^1_2(0^1_1^1_2(x1))))) #17: #0^1_1^1_2(1(x1)) -> #0^1_1^1_2(0^1_1^1_2(0^1_1^1_2(0^1_1^1_2(x1)))) #18: #0^1_1^1_2(1(x1)) -> #0^1_1^1_2(0^1_1^1_2(0^1_1^1_2(x1))) #19: #0^1_1^1_2(1(x1)) -> #0^1_1^1_2(0^1_1^1_2(x1)) #20: #0^1_1^1_2(1(x1)) -> #0^1_1^1_2(x1) Number of SCCs: 1, DPs: 20 SCC { #1..20 } POLO(Sum)... succeeded. 1 w: x1 + 38601 0^1_1^1_2 w: x1 + 7720 0 w: 0 #0^1_1^1_2 w: x1 0^1_1 w: 0 2 w: 5799 USABLE RULES: { 1..5 } Removed DPs: #1..20 Number of SCCs: 0, DPs: 0