/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Input TRS: 1: tower(0(x1)) -> s(0(p(s(p(s(x1)))))) 2: tower(s(x1)) -> p(s(p(s(twoto(p(s(p(s(tower(p(s(p(s(x1)))))))))))))) 3: twoto(0(x1)) -> s(0(x1)) 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)))))))))))))))))))))))))))))))) 5: twice(0(x1)) -> 0(x1) 6: twice(s(x1)) -> p(p(p(s(s(s(s(s(twice(p(p(p(s(s(s(x1))))))))))))))) 7: p(p(s(x1))) -> p(x1) 8: p(s(x1)) -> x1 9: p(0(x1)) -> 0(s(s(s(s(s(s(s(s(x1))))))))) Number of strict rules: 9 Direct poly ... removes: 1 tower(x1) w: (24897 + x1) s(x1) w: (x1) twice(x1) w: (x1) p(x1) w: (x1) 0(x1) w: (28312 + 2 * x1) twoto(x1) w: (x1) Number of strict rules: 8 Direct poly ... failed. Freezing p 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)))))))) 3: twoto(0(x1)) -> s(0(x1)) 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)))))))))))))))))))))) 5: twice(0(x1)) -> 0(x1) 6: twice(s(x1)) -> p(p(p❆1_s(s(s(s(s(twice(p(p(p❆1_s(s(s(x1))))))))))))) 7: p(p❆1_s(x1)) -> p(x1) 8: p❆1_s(x1) -> x1 9: p❆1_0(x1) -> 0(s(s(s(s(s(s(s(s(x1))))))))) 10: p(0(_1)) ->= p❆1_0(_1) 11: p(s(_1)) ->= p❆1_s(_1) Number of strict rules: 8 Direct poly ... failed. Dependency Pairs: #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)))))))) #2: #tower(s(x1)) -> #p❆1_s(twoto(p❆1_s(p❆1_s(tower(p❆1_s(p❆1_s(x1))))))) #3: #tower(s(x1)) -> #twoto(p❆1_s(p❆1_s(tower(p❆1_s(p❆1_s(x1)))))) #4: #tower(s(x1)) -> #p❆1_s(p❆1_s(tower(p❆1_s(p❆1_s(x1))))) #5: #tower(s(x1)) -> #p❆1_s(tower(p❆1_s(p❆1_s(x1)))) #6: #tower(s(x1)) -> #tower(p❆1_s(p❆1_s(x1))) #7: #tower(s(x1)) -> #p❆1_s(p❆1_s(x1)) #8: #tower(s(x1)) -> #p❆1_s(x1) #9: #twice(s(x1)) -> #p(p(p❆1_s(s(s(s(s(twice(p(p(p❆1_s(s(s(x1))))))))))))) #10: #twice(s(x1)) -> #p(p❆1_s(s(s(s(s(twice(p(p(p❆1_s(s(s(x1)))))))))))) #11: #twice(s(x1)) -> #p❆1_s(s(s(s(s(twice(p(p(p❆1_s(s(s(x1))))))))))) #12: #twice(s(x1)) -> #twice(p(p(p❆1_s(s(s(x1)))))) #13: #twice(s(x1)) -> #p(p(p❆1_s(s(s(x1))))) #14: #twice(s(x1)) -> #p(p❆1_s(s(s(x1)))) #15: #twice(s(x1)) -> #p❆1_s(s(s(x1))) #16: #p(s(_1)) ->? #p❆1_s(_1) #17: #p(p❆1_s(x1)) -> #p(x1) #18: #p(0(_1)) ->? #p❆1_0(_1) #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)))))))))))))))))))))) #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))))))))))))))))))))) #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)))))))))))))))))))) #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))))))))))))))))))) #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)))))))))))))))))) #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)))))))))))))))) #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)))))))))))))) #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)))))))))))) #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))))))))))) #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)))))))))) #29: #twoto(s(x1)) -> #p❆1_s(p(p(p❆1_s(s(s(twoto(p❆1_s(p❆1_s(x1))))))))) #30: #twoto(s(x1)) -> #p(p(p❆1_s(s(s(twoto(p❆1_s(p❆1_s(x1)))))))) #31: #twoto(s(x1)) -> #p(p❆1_s(s(s(twoto(p❆1_s(p❆1_s(x1))))))) #32: #twoto(s(x1)) -> #p❆1_s(s(s(twoto(p❆1_s(p❆1_s(x1)))))) #33: #twoto(s(x1)) -> #twoto(p❆1_s(p❆1_s(x1))) #34: #twoto(s(x1)) -> #p❆1_s(p❆1_s(x1)) #35: #twoto(s(x1)) -> #p❆1_s(x1) Number of SCCs: 4, DPs: 4 SCC { #17 } Sum... succeeded. tower(x1) w: (0) s(x1) w: (0) twice(x1) w: (0) p❆1_s(x1) w: (1 + x1) #p❆1_0(x1) w: (0) #p(x1) w: (x1) #p❆1_s(x1) w: (0) p(x1) w: (0) 0(x1) w: (0) p❆1_0(x1) w: (0) #tower(x1) w: (0) twoto(x1) w: (0) #twice(x1) w: (0) #twoto(x1) w: (0) USABLE RULES: { } Removed DPs: #17 Number of SCCs: 3, DPs: 3 SCC { #6 } Sum... succeeded. tower(x1) w: (0) s(x1) w: (3 + x1) twice(x1) w: (0) p❆1_s(x1) w: (1 + x1) #p❆1_0(x1) w: (0) #p(x1) w: (0) #p❆1_s(x1) w: (0) p(x1) w: (0) 0(x1) w: (0) p❆1_0(x1) w: (0) #tower(x1) w: (x1) twoto(x1) w: (0) #twice(x1) w: (0) #twoto(x1) w: (0) USABLE RULES: { 8 } Removed DPs: #6 Number of SCCs: 2, DPs: 2 SCC { #33 } Sum... succeeded. tower(x1) w: (0) s(x1) w: (3 + x1) twice(x1) w: (0) p❆1_s(x1) w: (1 + x1) #p❆1_0(x1) w: (0) #p(x1) w: (0) #p❆1_s(x1) w: (0) p(x1) w: (0) 0(x1) w: (0) p❆1_0(x1) w: (0) #tower(x1) w: (x1) twoto(x1) w: (0) #twice(x1) w: (0) #twoto(x1) w: (x1) USABLE RULES: { 8 } Removed DPs: #33 Number of SCCs: 1, DPs: 1 SCC { #12 } Sum... Max... QLPOpS... NegMaxSum... succeeded. tower(x1) w: (0) s(x1) w: (max{0, 46837 + x1}) twice(x1) w: (0) p❆1_s(x1) w: (max{0, 7720 + x1}) #p❆1_0(x1) w: (0) #p(x1) w: (0) #p❆1_s(x1) w: (0) p(x1) w: (max{0, -39117 + x1}) 0(x1) w: (0) p❆1_0(x1) w: (0) #tower(x1) w: (0) twoto(x1) w: (0) #twice(x1) w: (max{0, -23161 + x1}) #twoto(x1) w: (0) USABLE RULES: { 7..11 } Removed DPs: #12 Number of SCCs: 0, DPs: 0