0.00/0.45 YES 0.00/0.45 Input TRS: 0.00/0.45 1: thrice(0(x1)) -> p(s(p(p(p(s(s(s(0(p(s(p(s(x1))))))))))))) 0.00/0.45 2: thrice(s(x1)) -> p(p(s(s(half(p(p(s(s(p(s(sixtimes(p(s(p(p(s(s(x1)))))))))))))))))) 0.00/0.45 3: half(0(x1)) -> p(p(s(s(p(s(0(p(s(s(s(s(x1)))))))))))) 0.00/0.45 4: half(s(x1)) -> p(s(p(p(s(s(p(p(s(s(half(p(p(s(s(p(s(x1))))))))))))))))) 0.00/0.45 5: half(s(s(x1))) -> p(s(p(s(s(p(p(s(s(half(p(p(s(s(p(s(x1)))))))))))))))) 0.00/0.45 6: sixtimes(0(x1)) -> p(s(p(s(0(s(s(s(s(s(p(s(p(s(x1)))))))))))))) 0.00/0.45 7: sixtimes(s(x1)) -> p(p(s(s(s(s(s(s(s(p(p(s(p(s(s(s(sixtimes(p(s(p(p(p(s(s(s(x1))))))))))))))))))))))))) 0.00/0.45 8: p(p(s(x1))) -> p(x1) 0.00/0.45 9: p(s(x1)) -> x1 0.00/0.45 10: p(0(x1)) -> 0(s(s(s(s(x1))))) 0.00/0.45 11: 0(x1) -> x1 0.00/0.45 Number of strict rules: 11 0.00/0.45 Direct POLO(bPol) ... removes: 1 3 11 6 2 0.00/0.45 s w: x1 0.00/0.45 half w: x1 + 1 0.00/0.45 p w: x1 0.00/0.45 0 w: x1 + 1 0.00/0.45 sixtimes w: x1 + 1 0.00/0.45 thrice w: x1 + 3 0.00/0.45 Number of strict rules: 6 0.00/0.45 Direct POLO(bPol) ... failed. 0.00/0.45 Uncurrying p 0.00/0.45 4: half(s(x1)) -> p^1_s(p(p^1_s(s(p(p^1_s(s(half(p(p^1_s(s(p^1_s(x1)))))))))))) 0.00/0.45 5: half(s(s(x1))) -> p^1_s(p^1_s(s(p(p^1_s(s(half(p(p^1_s(s(p^1_s(x1))))))))))) 0.00/0.45 7: sixtimes(s(x1)) -> p(p^1_s(s(s(s(s(s(s(p(p^1_s(p^1_s(s(s(sixtimes(p^1_s(p(p(p^1_s(s(s(x1)))))))))))))))))))) 0.00/0.45 8: p(p^1_s(x1)) -> p(x1) 0.00/0.45 9: p^1_s(x1) -> x1 0.00/0.45 10: p^1_0(x1) -> 0(s(s(s(s(x1))))) 0.00/0.45 12: p(0(_1)) ->= p^1_0(_1) 0.00/0.45 13: p(s(_1)) ->= p^1_s(_1) 0.00/0.45 Number of strict rules: 6 0.00/0.45 Direct POLO(bPol) ... failed. 0.00/0.45 Dependency Pairs: 0.00/0.45 #1: #p(s(_1)) ->? #p^1_s(_1) 0.00/0.45 #2: #p(0(_1)) ->? #p^1_0(_1) 0.00/0.45 #3: #sixtimes(s(x1)) -> #p(p^1_s(s(s(s(s(s(s(p(p^1_s(p^1_s(s(s(sixtimes(p^1_s(p(p(p^1_s(s(s(x1)))))))))))))))))))) 0.00/0.45 #4: #sixtimes(s(x1)) -> #p^1_s(s(s(s(s(s(s(p(p^1_s(p^1_s(s(s(sixtimes(p^1_s(p(p(p^1_s(s(s(x1))))))))))))))))))) 0.00/0.45 #5: #sixtimes(s(x1)) -> #p(p^1_s(p^1_s(s(s(sixtimes(p^1_s(p(p(p^1_s(s(s(x1)))))))))))) 0.00/0.45 #6: #sixtimes(s(x1)) -> #p^1_s(p^1_s(s(s(sixtimes(p^1_s(p(p(p^1_s(s(s(x1))))))))))) 0.00/0.45 #7: #sixtimes(s(x1)) -> #p^1_s(s(s(sixtimes(p^1_s(p(p(p^1_s(s(s(x1)))))))))) 0.00/0.45 #8: #sixtimes(s(x1)) -> #sixtimes(p^1_s(p(p(p^1_s(s(s(x1))))))) 0.00/0.45 #9: #sixtimes(s(x1)) -> #p^1_s(p(p(p^1_s(s(s(x1)))))) 0.00/0.45 #10: #sixtimes(s(x1)) -> #p(p(p^1_s(s(s(x1))))) 0.00/0.45 #11: #sixtimes(s(x1)) -> #p(p^1_s(s(s(x1)))) 0.00/0.45 #12: #sixtimes(s(x1)) -> #p^1_s(s(s(x1))) 0.00/0.45 #13: #half(s(s(x1))) -> #p^1_s(p^1_s(s(p(p^1_s(s(half(p(p^1_s(s(p^1_s(x1))))))))))) 0.00/0.45 #14: #half(s(s(x1))) -> #p^1_s(s(p(p^1_s(s(half(p(p^1_s(s(p^1_s(x1)))))))))) 0.00/0.45 #15: #half(s(s(x1))) -> #p(p^1_s(s(half(p(p^1_s(s(p^1_s(x1)))))))) 0.00/0.45 #16: #half(s(s(x1))) -> #p^1_s(s(half(p(p^1_s(s(p^1_s(x1))))))) 0.00/0.45 #17: #half(s(s(x1))) -> #half(p(p^1_s(s(p^1_s(x1))))) 0.00/0.45 #18: #half(s(s(x1))) -> #p(p^1_s(s(p^1_s(x1)))) 0.00/0.45 #19: #half(s(s(x1))) -> #p^1_s(s(p^1_s(x1))) 0.00/0.45 #20: #half(s(s(x1))) -> #p^1_s(x1) 0.00/0.45 #21: #p(p^1_s(x1)) -> #p(x1) 0.00/0.45 #22: #half(s(x1)) -> #p^1_s(p(p^1_s(s(p(p^1_s(s(half(p(p^1_s(s(p^1_s(x1)))))))))))) 0.00/0.45 #23: #half(s(x1)) -> #p(p^1_s(s(p(p^1_s(s(half(p(p^1_s(s(p^1_s(x1))))))))))) 0.00/0.45 #24: #half(s(x1)) -> #p^1_s(s(p(p^1_s(s(half(p(p^1_s(s(p^1_s(x1)))))))))) 0.00/0.45 #25: #half(s(x1)) -> #p(p^1_s(s(half(p(p^1_s(s(p^1_s(x1)))))))) 0.00/0.45 #26: #half(s(x1)) -> #p^1_s(s(half(p(p^1_s(s(p^1_s(x1))))))) 0.00/0.45 #27: #half(s(x1)) -> #half(p(p^1_s(s(p^1_s(x1))))) 0.00/0.45 #28: #half(s(x1)) -> #p(p^1_s(s(p^1_s(x1)))) 0.00/0.45 #29: #half(s(x1)) -> #p^1_s(s(p^1_s(x1))) 0.00/0.45 #30: #half(s(x1)) -> #p^1_s(x1) 0.00/0.45 Number of SCCs: 3, DPs: 4 0.00/0.45 SCC { #21 } 0.00/0.45 POLO(Sum)... succeeded. 0.00/0.45 s w: 0 0.00/0.45 #p^1_0 w: 0 0.00/0.45 #p^1_s w: 0 0.00/0.45 p^1_0 w: 0 0.00/0.45 #sixtimes w: 0 0.00/0.45 p^1_s w: x1 + 1 0.00/0.45 #half w: 0 0.00/0.45 #p w: x1 0.00/0.45 half w: 0 0.00/0.45 p w: 0 0.00/0.45 0 w: 0 0.00/0.45 sixtimes w: 0 0.00/0.45 thrice w: 0 0.00/0.45 USABLE RULES: { } 0.00/0.45 Removed DPs: #21 0.00/0.45 Number of SCCs: 2, DPs: 3 0.00/0.45 SCC { #8 } 0.00/0.45 POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... succeeded. 0.00/0.45 s w: max(x1 + 6, 0) 0.00/0.45 #p^1_0 w: max(x1 - 1, 0) 0.00/0.45 #p^1_s w: 0 0.00/0.45 p^1_0 w: 0 0.00/0.45 #sixtimes w: max(x1 + 1, 0) 0.00/0.45 p^1_s w: max(x1 + 1, 0) 0.00/0.45 #half w: 0 0.00/0.45 #p w: 0 0.00/0.45 half w: max(x1 - 1, 0) 0.00/0.45 p w: max(x1 - 5, 0) 0.00/0.45 0 w: 0 0.00/0.45 sixtimes w: max(x1 - 1, 0) 0.00/0.45 thrice w: max(x1 - 1, 0) 0.00/0.45 USABLE RULES: { 8..10 12 13 } 0.00/0.45 Removed DPs: #8 0.00/0.45 Number of SCCs: 1, DPs: 2 0.00/0.45 SCC { #17 #27 } 0.00/0.45 POLO(Sum)... succeeded. 0.00/0.45 s w: x1 + 1 0.00/0.45 #p^1_0 w: 0 0.00/0.45 #p^1_s w: 0 0.00/0.45 p^1_0 w: 1 0.00/0.45 #sixtimes w: 0 0.00/0.45 p^1_s w: x1 0.00/0.45 #half w: x1 0.00/0.45 #p w: 0 0.00/0.45 half w: 0 0.00/0.45 p w: x1 0.00/0.45 0 w: 1 0.00/0.45 sixtimes w: 0 0.00/0.45 thrice w: 0 0.00/0.45 USABLE RULES: { 8..10 12 13 } 0.00/0.45 Removed DPs: #17 0.00/0.45 Number of SCCs: 1, DPs: 1 0.00/0.45 SCC { #27 } 0.00/0.45 POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... succeeded. 0.00/0.45 s w: max(x1 + 6, 0) 0.00/0.45 #p^1_0 w: max(x1 - 1, 0) 0.00/0.45 #p^1_s w: 0 0.00/0.45 p^1_0 w: 0 0.00/0.45 #sixtimes w: max(x1 + 1, 0) 0.00/0.45 p^1_s w: max(x1 + 1, 0) 0.00/0.45 #half w: max(x1 + 6, 0) 0.00/0.45 #p w: 0 0.00/0.45 half w: max(x1 - 1, 0) 0.00/0.45 p w: max(x1 - 5, 0) 0.00/0.45 0 w: 0 0.00/0.45 sixtimes w: max(x1 - 1, 0) 0.00/0.45 thrice w: max(x1 - 1, 0) 0.00/0.45 USABLE RULES: { 8..10 12 13 } 0.00/0.45 Removed DPs: #27 0.00/0.45 Number of SCCs: 0, DPs: 0 0.00/0.45 EOF