/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(first(0(),X)) -> mark(nil()) 2: active(first(s(X),cons(Y,Z))) -> mark(cons(Y,first(X,Z))) 3: active(from(X)) -> mark(cons(X,from(s(X)))) 4: active(first(X1,X2)) -> first(active(X1),X2) 5: active(first(X1,X2)) -> first(X1,active(X2)) 6: active(s(X)) -> s(active(X)) 7: active(cons(X1,X2)) -> cons(active(X1),X2) 8: active(from(X)) -> from(active(X)) 9: first(mark(X1),X2) -> mark(first(X1,X2)) 10: first(X1,mark(X2)) -> mark(first(X1,X2)) 11: s(mark(X)) -> mark(s(X)) 12: cons(mark(X1),X2) -> mark(cons(X1,X2)) 13: from(mark(X)) -> mark(from(X)) 14: proper(first(X1,X2)) -> first(proper(X1),proper(X2)) 15: proper(0()) -> ok(0()) 16: proper(nil()) -> ok(nil()) 17: proper(s(X)) -> s(proper(X)) 18: proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) 19: proper(from(X)) -> from(proper(X)) 20: first(ok(X1),ok(X2)) -> ok(first(X1,X2)) 21: s(ok(X)) -> ok(s(X)) 22: cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) 23: from(ok(X)) -> ok(from(X)) 24: top(mark(X)) -> top(proper(X)) 25: top(ok(X)) -> top(active(X)) Number of strict rules: 25 Direct poly ... failed. Freezing ... failed. Dependency Pairs: #1: #active(first(s(X),cons(Y,Z))) -> #cons(Y,first(X,Z)) #2: #active(first(s(X),cons(Y,Z))) -> #first(X,Z) #3: #active(s(X)) -> #s(active(X)) #4: #active(s(X)) -> #active(X) #5: #from(mark(X)) -> #from(X) #6: #first(mark(X1),X2) -> #first(X1,X2) #7: #s(mark(X)) -> #s(X) #8: #top(mark(X)) -> #top(proper(X)) #9: #top(mark(X)) -> #proper(X) #10: #from(ok(X)) -> #from(X) #11: #cons(mark(X1),X2) -> #cons(X1,X2) #12: #proper(first(X1,X2)) -> #first(proper(X1),proper(X2)) #13: #proper(first(X1,X2)) -> #proper(X1) #14: #proper(first(X1,X2)) -> #proper(X2) #15: #top(ok(X)) -> #top(active(X)) #16: #top(ok(X)) -> #active(X) #17: #first(ok(X1),ok(X2)) -> #first(X1,X2) #18: #active(cons(X1,X2)) -> #cons(active(X1),X2) #19: #active(cons(X1,X2)) -> #active(X1) #20: #first(X1,mark(X2)) -> #first(X1,X2) #21: #active(first(X1,X2)) -> #first(X1,active(X2)) #22: #active(first(X1,X2)) -> #active(X2) #23: #cons(ok(X1),ok(X2)) -> #cons(X1,X2) #24: #proper(s(X)) -> #s(proper(X)) #25: #proper(s(X)) -> #proper(X) #26: #proper(from(X)) -> #from(proper(X)) #27: #proper(from(X)) -> #proper(X) #28: #s(ok(X)) -> #s(X) #29: #active(from(X)) -> #cons(X,from(s(X))) #30: #active(from(X)) -> #from(s(X)) #31: #active(from(X)) -> #s(X) #32: #active(from(X)) -> #from(active(X)) #33: #active(from(X)) -> #active(X) #34: #active(first(X1,X2)) -> #first(active(X1),X2) #35: #active(first(X1,X2)) -> #active(X1) #36: #proper(cons(X1,X2)) -> #cons(proper(X1),proper(X2)) #37: #proper(cons(X1,X2)) -> #proper(X1) #38: #proper(cons(X1,X2)) -> #proper(X2) Number of SCCs: 7, DPs: 22 SCC { #7 #28 } 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) from(x1) 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: #7 #28 Number of SCCs: 6, DPs: 20 SCC { #5 #10 } 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) from(x1) 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: #5 #10 Number of SCCs: 5, DPs: 18 SCC { #8 #15 } Sum... succeeded. #cons(x1,x2) w: (0) s(x1) w: (20538 + x1) top(x1) w: (0) #top(x1) w: (x1) proper(x1) w: (x1) ok(x1) w: (x1) 0() w: (8946) from(x1) w: (23452 + x1) #s(x1) w: (0) #first(x1,x2) w: (0) nil() w: (162) mark(x1) w: (23451 + x1) first(x1,x2) w: (15923 + x2 + x1) #proper(x1) w: (0) #from(x1) w: (0) active(x1) w: (x1) cons(x1,x2) w: (1 + x1) #active(x1) w: (0) USABLE RULES: { 1..23 } Removed DPs: #8 Number of SCCs: 5, DPs: 17 SCC { #15 } Sum... succeeded. #cons(x1,x2) w: (0) s(x1) w: (1 + x1) top(x1) w: (0) #top(x1) w: (x1) proper(x1) w: (17888 + x1) ok(x1) w: (1 + x1) 0() w: (8946) from(x1) w: (1 + x1) #s(x1) w: (0) #first(x1,x2) w: (0) nil() w: (28224) mark(x1) w: (x1) first(x1,x2) w: (28224 + x2) #proper(x1) w: (0) #from(x1) w: (0) active(x1) w: (x1) cons(x1,x2) w: (1 + x1) #active(x1) w: (0) USABLE RULES: { 1..23 } Removed DPs: #15 Number of SCCs: 4, DPs: 16 SCC { #11 #23 } Sum... succeeded. #cons(x1,x2) w: (12329 + x1) s(x1) w: (1 + x1) top(x1) w: (0) #top(x1) w: (x1) proper(x1) w: (1 + x1) ok(x1) w: (1 + x1) 0() w: (20595) from(x1) w: (24389 + x1) #s(x1) w: (0) #first(x1,x2) w: (0) nil() w: (1) mark(x1) w: (x1) first(x1,x2) w: (1 + x2) #proper(x1) w: (0) #from(x1) w: (0) active(x1) w: (x1) cons(x1,x2) w: (1 + x1) #active(x1) w: (0) USABLE RULES: { 1..23 } Removed DPs: #23 Number of SCCs: 4, DPs: 15 SCC { #11 } Sum... succeeded. #cons(x1,x2) w: (12329 + x1) s(x1) w: (18005) top(x1) w: (0) #top(x1) w: (0) proper(x1) w: (x1) ok(x1) w: (19829 + x1) 0() w: (20596) from(x1) w: (24389) #s(x1) w: (0) #first(x1,x2) w: (0) nil() w: (1) mark(x1) w: (1 + x1) first(x1,x2) w: (1) #proper(x1) w: (0) #from(x1) w: (0) active(x1) w: (1 + x1) cons(x1,x2) w: (1) #active(x1) w: (0) USABLE RULES: { 1 } Removed DPs: #11 Number of SCCs: 3, DPs: 14 SCC { #6 #17 #20 } Sum... succeeded. #cons(x1,x2) w: (12329) s(x1) w: (18005) top(x1) w: (0) #top(x1) w: (0) proper(x1) w: (x1) ok(x1) w: (1 + x1) 0() w: (10336) from(x1) w: (24389) #s(x1) w: (0) #first(x1,x2) w: (16020 + x2) nil() w: (858) mark(x1) w: (3 + x1) first(x1,x2) w: (5) #proper(x1) w: (0) #from(x1) w: (0) active(x1) w: (20534 + x1) cons(x1,x2) w: (1) #active(x1) w: (0) USABLE RULES: { 1 } Removed DPs: #17 #20 Number of SCCs: 3, DPs: 12 SCC { #6 } Sum... succeeded. #cons(x1,x2) w: (12329) s(x1) w: (1) top(x1) w: (0) #top(x1) w: (0) proper(x1) w: (x1) ok(x1) w: (1 + x1) 0() w: (1) from(x1) w: (24389) #s(x1) w: (0) #first(x1,x2) w: (16020 + x1) nil() w: (1) mark(x1) w: (1 + x1) first(x1,x2) w: (1) #proper(x1) w: (0) #from(x1) w: (0) active(x1) w: (1 + x1) cons(x1,x2) w: (1) #active(x1) w: (0) USABLE RULES: { 1 } Removed DPs: #6 Number of SCCs: 2, DPs: 11 SCC { #4 #19 #22 #33 #35 } Sum... succeeded. #cons(x1,x2) w: (12329) s(x1) w: (2 + x1) top(x1) w: (0) #top(x1) w: (0) proper(x1) w: (x1) ok(x1) w: (16336) 0() w: (1) from(x1) w: (1 + x1) #s(x1) w: (0) #first(x1,x2) w: (16020) nil() w: (1) mark(x1) w: (2 + x1) first(x1,x2) w: (1 + x2 + x1) #proper(x1) w: (0) #from(x1) w: (0) active(x1) w: (x1) cons(x1,x2) w: (1 + x2 + x1) #active(x1) w: (x1) USABLE RULES: { } Removed DPs: #4 #19 #22 #33 #35 Number of SCCs: 1, DPs: 6 SCC { #13 #14 #25 #27 #37 #38 } Sum... succeeded. #cons(x1,x2) w: (12329) s(x1) w: (25532 + x1) top(x1) w: (0) #top(x1) w: (0) proper(x1) w: (x1) ok(x1) w: (14461) 0() w: (14459) from(x1) w: (15047 + x1) #s(x1) w: (0) #first(x1,x2) w: (16020) nil() w: (14460) mark(x1) w: (1 + x1) first(x1,x2) w: (1 + x2 + x1) #proper(x1) w: (x1) #from(x1) w: (0) active(x1) w: (x1) cons(x1,x2) w: (1 + x2 + x1) #active(x1) w: (0) USABLE RULES: { } Removed DPs: #13 #14 #25 #27 #37 #38 Number of SCCs: 0, DPs: 0