/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES Input TRS: 1: active(from(X)) -> mark(cons(X,from(s(X)))) 2: active(first(0(),Z)) -> mark(nil()) 3: active(first(s(X),cons(Y,Z))) -> mark(cons(Y,first(X,Z))) 4: active(sel(0(),cons(X,Z))) -> mark(X) 5: active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z)) 6: active(from(X)) -> from(active(X)) 7: active(cons(X1,X2)) -> cons(active(X1),X2) 8: active(s(X)) -> s(active(X)) 9: active(first(X1,X2)) -> first(active(X1),X2) 10: active(first(X1,X2)) -> first(X1,active(X2)) 11: active(sel(X1,X2)) -> sel(active(X1),X2) 12: active(sel(X1,X2)) -> sel(X1,active(X2)) 13: from(mark(X)) -> mark(from(X)) 14: cons(mark(X1),X2) -> mark(cons(X1,X2)) 15: s(mark(X)) -> mark(s(X)) 16: first(mark(X1),X2) -> mark(first(X1,X2)) 17: first(X1,mark(X2)) -> mark(first(X1,X2)) 18: sel(mark(X1),X2) -> mark(sel(X1,X2)) 19: sel(X1,mark(X2)) -> mark(sel(X1,X2)) 20: proper(from(X)) -> from(proper(X)) 21: proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) 22: proper(s(X)) -> s(proper(X)) 23: proper(first(X1,X2)) -> first(proper(X1),proper(X2)) 24: proper(0()) -> ok(0()) 25: proper(nil()) -> ok(nil()) 26: proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) 27: from(ok(X)) -> ok(from(X)) 28: cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) 29: s(ok(X)) -> ok(s(X)) 30: first(ok(X1),ok(X2)) -> ok(first(X1,X2)) 31: sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) 32: top(mark(X)) -> top(proper(X)) 33: top(ok(X)) -> top(active(X)) Number of strict rules: 33 Direct poly ... failed. Freezing ... failed. Dependency Pairs: #1: #s(ok(X)) -> #s(X) #2: #active(from(X)) -> #from(active(X)) #3: #active(from(X)) -> #active(X) #4: #from(mark(X)) -> #from(X) #5: #active(first(X1,X2)) -> #first(active(X1),X2) #6: #active(first(X1,X2)) -> #active(X1) #7: #active(sel(X1,X2)) -> #sel(active(X1),X2) #8: #active(sel(X1,X2)) -> #active(X1) #9: #proper(first(X1,X2)) -> #first(proper(X1),proper(X2)) #10: #proper(first(X1,X2)) -> #proper(X1) #11: #proper(first(X1,X2)) -> #proper(X2) #12: #active(sel(X1,X2)) -> #sel(X1,active(X2)) #13: #active(sel(X1,X2)) -> #active(X2) #14: #sel(ok(X1),ok(X2)) -> #sel(X1,X2) #15: #cons(mark(X1),X2) -> #cons(X1,X2) #16: #first(ok(X1),ok(X2)) -> #first(X1,X2) #17: #proper(from(X)) -> #from(proper(X)) #18: #proper(from(X)) -> #proper(X) #19: #active(cons(X1,X2)) -> #cons(active(X1),X2) #20: #active(cons(X1,X2)) -> #active(X1) #21: #active(first(X1,X2)) -> #first(X1,active(X2)) #22: #active(first(X1,X2)) -> #active(X2) #23: #top(ok(X)) -> #top(active(X)) #24: #top(ok(X)) -> #active(X) #25: #active(sel(s(X),cons(Y,Z))) -> #sel(X,Z) #26: #cons(ok(X1),ok(X2)) -> #cons(X1,X2) #27: #proper(s(X)) -> #s(proper(X)) #28: #proper(s(X)) -> #proper(X) #29: #from(ok(X)) -> #from(X) #30: #first(X1,mark(X2)) -> #first(X1,X2) #31: #top(mark(X)) -> #top(proper(X)) #32: #top(mark(X)) -> #proper(X) #33: #sel(X1,mark(X2)) -> #sel(X1,X2) #34: #proper(sel(X1,X2)) -> #sel(proper(X1),proper(X2)) #35: #proper(sel(X1,X2)) -> #proper(X1) #36: #proper(sel(X1,X2)) -> #proper(X2) #37: #proper(cons(X1,X2)) -> #cons(proper(X1),proper(X2)) #38: #proper(cons(X1,X2)) -> #proper(X1) #39: #proper(cons(X1,X2)) -> #proper(X2) #40: #first(mark(X1),X2) -> #first(X1,X2) #41: #active(first(s(X),cons(Y,Z))) -> #cons(Y,first(X,Z)) #42: #active(first(s(X),cons(Y,Z))) -> #first(X,Z) #43: #active(from(X)) -> #cons(X,from(s(X))) #44: #active(from(X)) -> #from(s(X)) #45: #active(from(X)) -> #s(X) #46: #active(s(X)) -> #s(active(X)) #47: #active(s(X)) -> #active(X) #48: #s(mark(X)) -> #s(X) #49: #sel(mark(X1),X2) -> #sel(X1,X2) Number of SCCs: 8, DPs: 29 SCC { #4 #29 } Sum... succeeded. #cons(x1,x2) w: (0) s(x1) w: (0) top(x1) w: (0) #top(x1) w: (0) proper(x1) w: (0) ok(x1) w: (1 + x1) 0() w: (0) #sel(x1,x2) w: (0) from(x1) w: (0) sel(x1,x2) w: (0) #s(x1) w: (0) #first(x1,x2) w: (0) nil() w: (0) mark(x1) w: (1 + x1) first(x1,x2) w: (0) #proper(x1) w: (0) #from(x1) w: (x1) active(x1) w: (0) cons(x1,x2) w: (0) #active(x1) w: (0) USABLE RULES: { } Removed DPs: #4 #29 Number of SCCs: 7, DPs: 27 SCC { #1 #48 } Sum... succeeded. #cons(x1,x2) w: (0) s(x1) w: (0) top(x1) w: (0) #top(x1) w: (0) proper(x1) w: (0) ok(x1) w: (1 + x1) 0() w: (0) #sel(x1,x2) w: (0) from(x1) w: (0) sel(x1,x2) w: (0) #s(x1) w: (x1) #first(x1,x2) w: (0) nil() w: (0) mark(x1) w: (1 + x1) first(x1,x2) w: (0) #proper(x1) w: (0) #from(x1) w: (0) active(x1) w: (0) cons(x1,x2) w: (0) #active(x1) w: (0) USABLE RULES: { } Removed DPs: #1 #48 Number of SCCs: 6, DPs: 25 SCC { #23 #31 } Sum... Max... QLPOpS... NegMaxSum... QWPOpSMaxSum... succeeded. #cons(x1,x2) 0[x2,x1] w: (max{1 + x2, 1 + x1}) s(x1) 4[x1] w: (x1) top(x1) 0[] w: (1) #top(x1) 0[x1] w: (x1) proper(x1) x1 w: (x1) ok(x1) x1 w: (x1) 0() 7 w: (841) #sel(x1,x2) 0[] w: (x2) from(x1) 4[x1] w: (21035 + x1) sel(x1,x2) 1[x1,x2] w: (18589 + x2 + x1) #s(x1) 0[] w: (x1) #first(x1,x2) 0[x2,x1] w: (1 + x2 + x1) nil() 6 w: (842) mark(x1) 0[x1] w: (x1) first(x1,x2) 3[x2,x1] w: (19179 + x2 + x1) #proper(x1) 0[] w: (x1) #from(x1) 0[] w: (x1) active(x1) x1 w: (x1) cons(x1,x2) 3[x1] w: (max{x2, 18588 + x1}) #active(x1) 0[] w: (x1) USABLE RULES: { 1..31 } Removed DPs: #31 Number of SCCs: 6, DPs: 24 SCC { #23 } Sum... succeeded. #cons(x1,x2) w: (0) s(x1) w: (x1) top(x1) w: (0) #top(x1) w: (x1) proper(x1) w: (3) ok(x1) w: (2 + x1) 0() w: (1) #sel(x1,x2) w: (0) from(x1) w: (x1) sel(x1,x2) w: (x2) #s(x1) w: (0) #first(x1,x2) w: (0) nil() w: (1) mark(x1) w: (0) first(x1,x2) w: (x1) #proper(x1) w: (0) #from(x1) w: (0) active(x1) w: (1 + x1) cons(x1,x2) w: (x1) #active(x1) w: (0) USABLE RULES: { 1..31 } Removed DPs: #23 Number of SCCs: 5, DPs: 23 SCC { #15 #26 } Sum... succeeded. #cons(x1,x2) w: (28223 + x2) s(x1) w: (x1) top(x1) w: (0) #top(x1) w: (x1) proper(x1) w: (2) ok(x1) w: (1 + x1) 0() w: (1) #sel(x1,x2) w: (0) from(x1) w: (x1) sel(x1,x2) w: (x2) #s(x1) w: (0) #first(x1,x2) w: (0) nil() w: (1) mark(x1) w: (0) first(x1,x2) w: (x1) #proper(x1) w: (0) #from(x1) w: (0) active(x1) w: (6879 + x1) cons(x1,x2) w: (x1) #active(x1) w: (0) USABLE RULES: { 1..31 } Removed DPs: #26 Number of SCCs: 5, DPs: 22 SCC { #15 } Sum... succeeded. #cons(x1,x2) w: (28223 + x1) s(x1) w: (x1) top(x1) w: (0) #top(x1) w: (0) proper(x1) w: (1) ok(x1) w: (x1) 0() w: (1) #sel(x1,x2) w: (0) from(x1) w: (0) sel(x1,x2) w: (0) #s(x1) w: (0) #first(x1,x2) w: (0) nil() w: (0) mark(x1) w: (2 + x1) first(x1,x2) w: (0) #proper(x1) w: (0) #from(x1) w: (0) active(x1) w: (1) cons(x1,x2) w: (0) #active(x1) w: (0) USABLE RULES: { 15 24 25 29 } Removed DPs: #15 Number of SCCs: 4, DPs: 21 SCC { #14 #33 #49 } Sum... succeeded. #cons(x1,x2) w: (28223) s(x1) w: (x1) top(x1) w: (0) #top(x1) w: (0) proper(x1) w: (1) ok(x1) w: (x1) 0() w: (1) #sel(x1,x2) w: (5598 + x1) from(x1) w: (0) sel(x1,x2) w: (0) #s(x1) w: (0) #first(x1,x2) w: (0) nil() w: (0) mark(x1) w: (2 + x1) first(x1,x2) w: (0) #proper(x1) w: (0) #from(x1) w: (0) active(x1) w: (1) cons(x1,x2) w: (0) #active(x1) w: (0) USABLE RULES: { 15 24 25 29 } Removed DPs: #49 Number of SCCs: 4, DPs: 20 SCC { #14 #33 } Sum... succeeded. #cons(x1,x2) w: (28223) s(x1) w: (x1) top(x1) w: (0) #top(x1) w: (0) proper(x1) w: (1) ok(x1) w: (x1) 0() w: (1) #sel(x1,x2) w: (5598 + x2) from(x1) w: (0) sel(x1,x2) w: (0) #s(x1) w: (0) #first(x1,x2) w: (0) nil() w: (0) mark(x1) w: (2 + x1) first(x1,x2) w: (0) #proper(x1) w: (0) #from(x1) w: (0) active(x1) w: (1) cons(x1,x2) w: (0) #active(x1) w: (0) USABLE RULES: { 15 24 29 } Removed DPs: #33 Number of SCCs: 4, DPs: 19 SCC { #14 } Sum... succeeded. #cons(x1,x2) w: (28223) s(x1) w: (x1) top(x1) w: (0) #top(x1) w: (0) proper(x1) w: (1 + x1) ok(x1) w: (1 + x1) 0() w: (1) #sel(x1,x2) w: (5598 + x1) from(x1) w: (2) sel(x1,x2) w: (1 + x1) #s(x1) w: (0) #first(x1,x2) w: (0) nil() w: (0) mark(x1) w: (4) first(x1,x2) w: (0) #proper(x1) w: (0) #from(x1) w: (0) active(x1) w: (1 + x1) cons(x1,x2) w: (1 + x2) #active(x1) w: (0) USABLE RULES: { 15 24 } Removed DPs: #14 Number of SCCs: 3, DPs: 18 SCC { #16 #30 #40 } Sum... succeeded. #cons(x1,x2) w: (28223) s(x1) w: (x1) top(x1) w: (0) #top(x1) w: (0) proper(x1) w: (1 + x1) ok(x1) w: (1 + x1) 0() w: (1) #sel(x1,x2) w: (5598) from(x1) w: (1) sel(x1,x2) w: (1 + x1) #s(x1) w: (0) #first(x1,x2) w: (x2 + x1) nil() w: (0) mark(x1) w: (4 + x1) first(x1,x2) w: (0) #proper(x1) w: (0) #from(x1) w: (0) active(x1) w: (1 + x1) cons(x1,x2) w: (1 + x2) #active(x1) w: (0) USABLE RULES: { 24 } Removed DPs: #16 #30 #40 Number of SCCs: 2, DPs: 15 SCC { #3 #6 #8 #13 #20 #22 #47 } Sum... succeeded. #cons(x1,x2) w: (28223) s(x1) w: (1 + x1) top(x1) w: (0) #top(x1) w: (0) proper(x1) w: (1 + x1) ok(x1) w: (29275) 0() w: (29273) #sel(x1,x2) w: (5598) from(x1) w: (1 + x1) sel(x1,x2) w: (1 + x2 + x1) #s(x1) w: (0) #first(x1,x2) w: (0) nil() w: (2743) mark(x1) w: (14461 + x1) first(x1,x2) w: (1 + x2 + x1) #proper(x1) w: (0) #from(x1) w: (0) active(x1) w: (14459) cons(x1,x2) w: (1 + x2 + x1) #active(x1) w: (x1) USABLE RULES: { 13..17 27..30 } Removed DPs: #3 #6 #8 #13 #20 #22 #47 Number of SCCs: 1, DPs: 8 SCC { #10 #11 #18 #28 #35 #36 #38 #39 } Sum... succeeded. #cons(x1,x2) w: (28223) s(x1) w: (1 + x1) top(x1) w: (0) #top(x1) w: (0) proper(x1) w: (1) ok(x1) w: (1770) 0() w: (21095) #sel(x1,x2) w: (5598) from(x1) w: (1 + x1) sel(x1,x2) w: (1 + x2 + x1) #s(x1) w: (0) #first(x1,x2) w: (0) nil() w: (1) mark(x1) w: (14460) first(x1,x2) w: (1 + x2 + x1) #proper(x1) w: (x1) #from(x1) w: (0) active(x1) w: (10636) cons(x1,x2) w: (1 + x2 + x1) #active(x1) w: (0) USABLE RULES: { 18 31 } Removed DPs: #10 #11 #18 #28 #35 #36 #38 #39 Number of SCCs: 0, DPs: 0