/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES Input TRS: 1: sq(0(x1)) -> p(s(p(s(p(p(p(p(s(s(s(s(0(p(s(p(s(x1))))))))))))))))) 2: sq(s(x1)) -> s(p(s(p(s(p(p(s(s(twice(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))))))))))))))))))))))) 3: twice(0(x1)) -> p(p(p(p(s(s(p(s(s(s(0(p(p(p(s(s(s(p(p(s(s(p(s(p(s(p(s(x1))))))))))))))))))))))))))) 4: twice(s(x1)) -> p(p(s(s(s(p(p(s(s(s(twice(p(s(p(s(x1))))))))))))))) 5: p(p(s(x1))) -> p(x1) 6: p(s(x1)) -> x1 7: p(0(x1)) -> 0(s(s(s(s(s(s(s(s(s(s(s(x1)))))))))))) 8: 0(x1) -> x1 Number of strict rules: 8 Direct poly ... removes: 8 1 s(x1) w: (x1) twice(x1) w: (x1) p(x1) w: (x1) 0(x1) w: (1 + x1) sq(x1) w: (28938 + x1) Number of strict rules: 6 Direct poly ... failed. Freezing p 2: sq(s(x1)) -> s(p❆1_s(p❆1_s(p(p❆1_s(s(twice(p❆1_s(p❆1_s(p(p(p❆1_s(s(s(sq(p(p(p(p(p(p❆1_s(s(s(s(s(s(x1)))))))))))))))))))))))))) 3: twice(0(x1)) -> p(p(p(p❆1_s(s(p❆1_s(s(s(0(p(p(p❆1_s(s(s(p(p❆1_s(s(p❆1_s(p❆1_s(p❆1_s(x1)))))))))))))))))))) 4: twice(s(x1)) -> p(p❆1_s(s(s(p(p❆1_s(s(s(twice(p❆1_s(p❆1_s(x1))))))))))) 5: p(p❆1_s(x1)) -> p(x1) 6: p❆1_s(x1) -> x1 7: p❆1_0(x1) -> 0(s(s(s(s(s(s(s(s(s(s(s(x1)))))))))))) 9: p(0(_1)) ->= p❆1_0(_1) 10: p(s(_1)) ->= p❆1_s(_1) Number of strict rules: 6 Direct poly ... failed. Dependency Pairs: #1: #sq(s(x1)) -> #p❆1_s(p❆1_s(p(p❆1_s(s(twice(p❆1_s(p❆1_s(p(p(p❆1_s(s(s(sq(p(p(p(p(p(p❆1_s(s(s(s(s(s(x1))))))))))))))))))))))))) #2: #sq(s(x1)) -> #p❆1_s(p(p❆1_s(s(twice(p❆1_s(p❆1_s(p(p(p❆1_s(s(s(sq(p(p(p(p(p(p❆1_s(s(s(s(s(s(x1)))))))))))))))))))))))) #3: #sq(s(x1)) -> #p(p❆1_s(s(twice(p❆1_s(p❆1_s(p(p(p❆1_s(s(s(sq(p(p(p(p(p(p❆1_s(s(s(s(s(s(x1))))))))))))))))))))))) #4: #sq(s(x1)) -> #p❆1_s(s(twice(p❆1_s(p❆1_s(p(p(p❆1_s(s(s(sq(p(p(p(p(p(p❆1_s(s(s(s(s(s(x1)))))))))))))))))))))) #5: #sq(s(x1)) -> #twice(p❆1_s(p❆1_s(p(p(p❆1_s(s(s(sq(p(p(p(p(p(p❆1_s(s(s(s(s(s(x1)))))))))))))))))))) #6: #sq(s(x1)) -> #p❆1_s(p❆1_s(p(p(p❆1_s(s(s(sq(p(p(p(p(p(p❆1_s(s(s(s(s(s(x1))))))))))))))))))) #7: #sq(s(x1)) -> #p❆1_s(p(p(p❆1_s(s(s(sq(p(p(p(p(p(p❆1_s(s(s(s(s(s(x1)))))))))))))))))) #8: #sq(s(x1)) -> #p(p(p❆1_s(s(s(sq(p(p(p(p(p(p❆1_s(s(s(s(s(s(x1))))))))))))))))) #9: #sq(s(x1)) -> #p(p❆1_s(s(s(sq(p(p(p(p(p(p❆1_s(s(s(s(s(s(x1)))))))))))))))) #10: #sq(s(x1)) -> #p❆1_s(s(s(sq(p(p(p(p(p(p❆1_s(s(s(s(s(s(x1))))))))))))))) #11: #sq(s(x1)) -> #sq(p(p(p(p(p(p❆1_s(s(s(s(s(s(x1)))))))))))) #12: #sq(s(x1)) -> #p(p(p(p(p(p❆1_s(s(s(s(s(s(x1))))))))))) #13: #sq(s(x1)) -> #p(p(p(p(p❆1_s(s(s(s(s(s(x1)))))))))) #14: #sq(s(x1)) -> #p(p(p(p❆1_s(s(s(s(s(s(x1))))))))) #15: #sq(s(x1)) -> #p(p(p❆1_s(s(s(s(s(s(x1)))))))) #16: #sq(s(x1)) -> #p(p❆1_s(s(s(s(s(s(x1))))))) #17: #sq(s(x1)) -> #p❆1_s(s(s(s(s(s(x1)))))) #18: #p(0(_1)) ->? #p❆1_0(_1) #19: #p(s(_1)) ->? #p❆1_s(_1) #20: #p(p❆1_s(x1)) -> #p(x1) #21: #twice(0(x1)) -> #p(p(p(p❆1_s(s(p❆1_s(s(s(0(p(p(p❆1_s(s(s(p(p❆1_s(s(p❆1_s(p❆1_s(p❆1_s(x1)))))))))))))))))))) #22: #twice(0(x1)) -> #p(p(p❆1_s(s(p❆1_s(s(s(0(p(p(p❆1_s(s(s(p(p❆1_s(s(p❆1_s(p❆1_s(p❆1_s(x1))))))))))))))))))) #23: #twice(0(x1)) -> #p(p❆1_s(s(p❆1_s(s(s(0(p(p(p❆1_s(s(s(p(p❆1_s(s(p❆1_s(p❆1_s(p❆1_s(x1)))))))))))))))))) #24: #twice(0(x1)) -> #p❆1_s(s(p❆1_s(s(s(0(p(p(p❆1_s(s(s(p(p❆1_s(s(p❆1_s(p❆1_s(p❆1_s(x1))))))))))))))))) #25: #twice(0(x1)) -> #p❆1_s(s(s(0(p(p(p❆1_s(s(s(p(p❆1_s(s(p❆1_s(p❆1_s(p❆1_s(x1))))))))))))))) #26: #twice(0(x1)) -> #p(p(p❆1_s(s(s(p(p❆1_s(s(p❆1_s(p❆1_s(p❆1_s(x1))))))))))) #27: #twice(0(x1)) -> #p(p❆1_s(s(s(p(p❆1_s(s(p❆1_s(p❆1_s(p❆1_s(x1)))))))))) #28: #twice(0(x1)) -> #p❆1_s(s(s(p(p❆1_s(s(p❆1_s(p❆1_s(p❆1_s(x1))))))))) #29: #twice(0(x1)) -> #p(p❆1_s(s(p❆1_s(p❆1_s(p❆1_s(x1)))))) #30: #twice(0(x1)) -> #p❆1_s(s(p❆1_s(p❆1_s(p❆1_s(x1))))) #31: #twice(0(x1)) -> #p❆1_s(p❆1_s(p❆1_s(x1))) #32: #twice(0(x1)) -> #p❆1_s(p❆1_s(x1)) #33: #twice(0(x1)) -> #p❆1_s(x1) #34: #twice(s(x1)) -> #p(p❆1_s(s(s(p(p❆1_s(s(s(twice(p❆1_s(p❆1_s(x1))))))))))) #35: #twice(s(x1)) -> #p❆1_s(s(s(p(p❆1_s(s(s(twice(p❆1_s(p❆1_s(x1)))))))))) #36: #twice(s(x1)) -> #p(p❆1_s(s(s(twice(p❆1_s(p❆1_s(x1))))))) #37: #twice(s(x1)) -> #p❆1_s(s(s(twice(p❆1_s(p❆1_s(x1)))))) #38: #twice(s(x1)) -> #twice(p❆1_s(p❆1_s(x1))) #39: #twice(s(x1)) -> #p❆1_s(p❆1_s(x1)) #40: #twice(s(x1)) -> #p❆1_s(x1) Number of SCCs: 3, DPs: 3 SCC { #20 } Sum... succeeded. s(x1) w: (0) twice(x1) w: (0) p❆1_s(x1) w: (1 + x1) #sq(x1) w: (0) #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) #twice(x1) w: (0) sq(x1) w: (0) USABLE RULES: { } Removed DPs: #20 Number of SCCs: 2, DPs: 2 SCC { #38 } Sum... succeeded. s(x1) w: (3 + x1) twice(x1) w: (0) p❆1_s(x1) w: (1 + x1) #sq(x1) w: (0) #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) #twice(x1) w: (x1) sq(x1) w: (0) USABLE RULES: { 6 } Removed DPs: #38 Number of SCCs: 1, DPs: 1 SCC { #11 } Sum... Max... QLPOpS... NegMaxSum... succeeded. s(x1) w: (max{0, 8 + x1}) twice(x1) w: (0) p❆1_s(x1) w: (max{0, 1 + x1}) #sq(x1) w: (max{0, -7 + x1}) #p❆1_0(x1) w: (0) #p(x1) w: (0) #p❆1_s(x1) w: (0) p(x1) w: (max{0, -7 + x1}) 0(x1) w: (0) p❆1_0(x1) w: (0) #twice(x1) w: (0) sq(x1) w: (0) USABLE RULES: { 5..7 9 10 } Removed DPs: #11 Number of SCCs: 0, DPs: 0