0.00/0.41 YES 0.00/0.41 Input TRS: 0.00/0.41 1: tower(0(x1)) -> s(0(p(s(p(s(x1)))))) 0.00/0.41 2: tower(s(x1)) -> p(s(p(s(twoto(p(s(p(s(tower(p(s(p(s(x1)))))))))))))) 0.00/0.41 3: twoto(0(x1)) -> s(0(x1)) 0.00/0.41 4: twoto(s(x1)) -> p(p(s(p(p(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))))))))))))))))))) 0.00/0.41 5: twice(0(x1)) -> 0(x1) 0.00/0.41 6: twice(s(x1)) -> p(p(p(s(s(s(s(s(twice(p(p(p(s(s(s(x1))))))))))))))) 0.00/0.41 7: p(p(s(x1))) -> p(x1) 0.00/0.41 8: p(s(x1)) -> x1 0.00/0.41 9: p(0(x1)) -> 0(s(s(s(s(s(s(s(s(x1))))))))) 0.00/0.41 Number of strict rules: 9 0.00/0.41 Direct POLO(bPol) ... removes: 1 0.00/0.41 tower w: x1 + 1 0.00/0.41 s w: x1 0.00/0.41 twice w: x1 0.00/0.41 p w: x1 0.00/0.41 0 w: x1 + 1 0.00/0.41 twoto w: x1 0.00/0.41 Number of strict rules: 8 0.00/0.41 Direct POLO(bPol) ... failed. 0.00/0.41 Uncurrying p 0.00/0.41 2: tower(s(x1)) -> p^1_s(p^1_s(twoto(p^1_s(p^1_s(tower(p^1_s(p^1_s(x1)))))))) 0.00/0.41 3: twoto(0(x1)) -> s(0(x1)) 0.00/0.41 4: twoto(s(x1)) -> p(p^1_s(p(p(p^1_s(s(p^1_s(s(p^1_s(s(p^1_s(twice(p^1_s(p^1_s(p(p(p^1_s(s(s(twoto(p^1_s(p^1_s(x1)))))))))))))))))))))) 0.00/0.41 5: twice(0(x1)) -> 0(x1) 0.00/0.41 6: twice(s(x1)) -> p(p(p^1_s(s(s(s(s(twice(p(p(p^1_s(s(s(x1))))))))))))) 0.00/0.41 7: p(p^1_s(x1)) -> p(x1) 0.00/0.41 8: p^1_s(x1) -> x1 0.00/0.41 9: p^1_0(x1) -> 0(s(s(s(s(s(s(s(s(x1))))))))) 0.00/0.41 10: p(0(_1)) ->= p^1_0(_1) 0.00/0.41 11: p(s(_1)) ->= p^1_s(_1) 0.00/0.41 Number of strict rules: 8 0.00/0.41 Direct POLO(bPol) ... failed. 0.00/0.41 Dependency Pairs: 0.00/0.41 #1: #tower(s(x1)) -> #p^1_s(p^1_s(twoto(p^1_s(p^1_s(tower(p^1_s(p^1_s(x1)))))))) 0.00/0.41 #2: #tower(s(x1)) -> #p^1_s(twoto(p^1_s(p^1_s(tower(p^1_s(p^1_s(x1))))))) 0.00/0.41 #3: #tower(s(x1)) -> #twoto(p^1_s(p^1_s(tower(p^1_s(p^1_s(x1)))))) 0.00/0.41 #4: #tower(s(x1)) -> #p^1_s(p^1_s(tower(p^1_s(p^1_s(x1))))) 0.00/0.41 #5: #tower(s(x1)) -> #p^1_s(tower(p^1_s(p^1_s(x1)))) 0.00/0.41 #6: #tower(s(x1)) -> #tower(p^1_s(p^1_s(x1))) 0.00/0.41 #7: #tower(s(x1)) -> #p^1_s(p^1_s(x1)) 0.00/0.41 #8: #tower(s(x1)) -> #p^1_s(x1) 0.00/0.41 #9: #twice(s(x1)) -> #p(p(p^1_s(s(s(s(s(twice(p(p(p^1_s(s(s(x1))))))))))))) 0.00/0.41 #10: #twice(s(x1)) -> #p(p^1_s(s(s(s(s(twice(p(p(p^1_s(s(s(x1)))))))))))) 0.00/0.41 #11: #twice(s(x1)) -> #p^1_s(s(s(s(s(twice(p(p(p^1_s(s(s(x1))))))))))) 0.00/0.41 #12: #twice(s(x1)) -> #twice(p(p(p^1_s(s(s(x1)))))) 0.00/0.41 #13: #twice(s(x1)) -> #p(p(p^1_s(s(s(x1))))) 0.00/0.41 #14: #twice(s(x1)) -> #p(p^1_s(s(s(x1)))) 0.00/0.41 #15: #twice(s(x1)) -> #p^1_s(s(s(x1))) 0.00/0.41 #16: #p(s(_1)) ->? #p^1_s(_1) 0.00/0.41 #17: #p(p^1_s(x1)) -> #p(x1) 0.00/0.41 #18: #p(0(_1)) ->? #p^1_0(_1) 0.00/0.41 #19: #twoto(s(x1)) -> #p(p^1_s(p(p(p^1_s(s(p^1_s(s(p^1_s(s(p^1_s(twice(p^1_s(p^1_s(p(p(p^1_s(s(s(twoto(p^1_s(p^1_s(x1)))))))))))))))))))))) 0.00/0.41 #20: #twoto(s(x1)) -> #p^1_s(p(p(p^1_s(s(p^1_s(s(p^1_s(s(p^1_s(twice(p^1_s(p^1_s(p(p(p^1_s(s(s(twoto(p^1_s(p^1_s(x1))))))))))))))))))))) 0.00/0.41 #21: #twoto(s(x1)) -> #p(p(p^1_s(s(p^1_s(s(p^1_s(s(p^1_s(twice(p^1_s(p^1_s(p(p(p^1_s(s(s(twoto(p^1_s(p^1_s(x1)))))))))))))))))))) 0.00/0.41 #22: #twoto(s(x1)) -> #p(p^1_s(s(p^1_s(s(p^1_s(s(p^1_s(twice(p^1_s(p^1_s(p(p(p^1_s(s(s(twoto(p^1_s(p^1_s(x1))))))))))))))))))) 0.00/0.41 #23: #twoto(s(x1)) -> #p^1_s(s(p^1_s(s(p^1_s(s(p^1_s(twice(p^1_s(p^1_s(p(p(p^1_s(s(s(twoto(p^1_s(p^1_s(x1)))))))))))))))))) 0.00/0.41 #24: #twoto(s(x1)) -> #p^1_s(s(p^1_s(s(p^1_s(twice(p^1_s(p^1_s(p(p(p^1_s(s(s(twoto(p^1_s(p^1_s(x1)))))))))))))))) 0.00/0.41 #25: #twoto(s(x1)) -> #p^1_s(s(p^1_s(twice(p^1_s(p^1_s(p(p(p^1_s(s(s(twoto(p^1_s(p^1_s(x1)))))))))))))) 0.00/0.41 #26: #twoto(s(x1)) -> #p^1_s(twice(p^1_s(p^1_s(p(p(p^1_s(s(s(twoto(p^1_s(p^1_s(x1)))))))))))) 0.00/0.41 #27: #twoto(s(x1)) -> #twice(p^1_s(p^1_s(p(p(p^1_s(s(s(twoto(p^1_s(p^1_s(x1))))))))))) 0.00/0.41 #28: #twoto(s(x1)) -> #p^1_s(p^1_s(p(p(p^1_s(s(s(twoto(p^1_s(p^1_s(x1)))))))))) 0.00/0.41 #29: #twoto(s(x1)) -> #p^1_s(p(p(p^1_s(s(s(twoto(p^1_s(p^1_s(x1))))))))) 0.00/0.41 #30: #twoto(s(x1)) -> #p(p(p^1_s(s(s(twoto(p^1_s(p^1_s(x1)))))))) 0.00/0.41 #31: #twoto(s(x1)) -> #p(p^1_s(s(s(twoto(p^1_s(p^1_s(x1))))))) 0.00/0.41 #32: #twoto(s(x1)) -> #p^1_s(s(s(twoto(p^1_s(p^1_s(x1)))))) 0.00/0.41 #33: #twoto(s(x1)) -> #twoto(p^1_s(p^1_s(x1))) 0.00/0.41 #34: #twoto(s(x1)) -> #p^1_s(p^1_s(x1)) 0.00/0.41 #35: #twoto(s(x1)) -> #p^1_s(x1) 0.00/0.41 Number of SCCs: 4, DPs: 4 0.00/0.41 SCC { #17 } 0.00/0.41 POLO(Sum)... succeeded. 0.00/0.41 tower w: 0 0.00/0.41 s w: 0 0.00/0.41 #p^1_0 w: 0 0.00/0.41 twice w: 0 0.00/0.41 #p^1_s w: 0 0.00/0.41 p^1_0 w: 0 0.00/0.41 p^1_s w: x1 + 1 0.00/0.41 #p w: x1 0.00/0.41 p w: 0 0.00/0.41 0 w: 0 0.00/0.41 #tower w: 0 0.00/0.41 twoto w: 0 0.00/0.41 #twice w: 0 0.00/0.41 #twoto w: 0 0.00/0.41 USABLE RULES: { } 0.00/0.41 Removed DPs: #17 0.00/0.41 Number of SCCs: 3, DPs: 3 0.00/0.41 SCC { #6 } 0.00/0.41 POLO(Sum)... succeeded. 0.00/0.41 tower w: 0 0.00/0.41 s w: x1 + 3 0.00/0.41 #p^1_0 w: 0 0.00/0.41 twice w: 0 0.00/0.41 #p^1_s w: 0 0.00/0.41 p^1_0 w: 0 0.00/0.41 p^1_s w: x1 + 1 0.00/0.41 #p w: 0 0.00/0.41 p w: 0 0.00/0.41 0 w: 0 0.00/0.41 #tower w: x1 0.00/0.41 twoto w: 0 0.00/0.41 #twice w: 0 0.00/0.41 #twoto w: 0 0.00/0.41 USABLE RULES: { 8 } 0.00/0.41 Removed DPs: #6 0.00/0.41 Number of SCCs: 2, DPs: 2 0.00/0.41 SCC { #33 } 0.00/0.41 POLO(Sum)... succeeded. 0.00/0.41 tower w: 0 0.00/0.41 s w: x1 + 3 0.00/0.41 #p^1_0 w: 0 0.00/0.41 twice w: 0 0.00/0.41 #p^1_s w: 0 0.00/0.41 p^1_0 w: 0 0.00/0.41 p^1_s w: x1 + 1 0.00/0.41 #p w: 0 0.00/0.41 p w: 0 0.00/0.41 0 w: 0 0.00/0.41 #tower w: x1 0.00/0.41 twoto w: 0 0.00/0.41 #twice w: 0 0.00/0.41 #twoto w: x1 0.00/0.41 USABLE RULES: { 8 } 0.00/0.41 Removed DPs: #33 0.00/0.41 Number of SCCs: 1, DPs: 1 0.00/0.41 SCC { #12 } 0.00/0.41 POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... succeeded. 0.00/0.41 tower w: max(x1 - 1, 0) 0.00/0.41 s w: max(x1 + 5, 0) 0.00/0.41 #p^1_0 w: 0 0.00/0.41 twice w: 0 0.00/0.41 #p^1_s w: 0 0.00/0.41 p^1_0 w: 0 0.00/0.41 p^1_s w: max(x1 + 1, 0) 0.00/0.41 #p w: max(x1 - 1, 0) 0.00/0.41 p w: max(x1 - 4, 0) 0.00/0.41 0 w: 0 0.00/0.41 #tower w: 0 0.00/0.41 twoto w: max(x1 - 1, 0) 0.00/0.41 #twice w: max(x1 + 1, 0) 0.00/0.41 #twoto w: 0 0.00/0.41 USABLE RULES: { 7..11 } 0.00/0.41 Removed DPs: #12 0.00/0.41 Number of SCCs: 0, DPs: 0 0.00/0.41 EOF