/export/starexec/sandbox/solver/bin/starexec_run_tct_rc /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1),O(n^1)) * Step 1: Sum. WORST_CASE(Omega(n^1),O(n^1)) + Considered Problem: - Strict TRS: active(and(X1,X2)) -> and(active(X1),X2) active(and(tt(),X)) -> mark(X) active(cons(X1,X2)) -> cons(active(X1),X2) active(length(X)) -> length(active(X)) active(length(cons(N,L))) -> mark(s(length(L))) active(length(nil())) -> mark(0()) active(s(X)) -> s(active(X)) active(take(X1,X2)) -> take(X1,active(X2)) active(take(X1,X2)) -> take(active(X1),X2) active(take(0(),IL)) -> mark(nil()) active(take(s(M),cons(N,IL))) -> mark(cons(N,take(M,IL))) active(zeros()) -> mark(cons(0(),zeros())) and(mark(X1),X2) -> mark(and(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) length(mark(X)) -> mark(length(X)) length(ok(X)) -> ok(length(X)) proper(0()) -> ok(0()) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(length(X)) -> length(proper(X)) proper(nil()) -> ok(nil()) proper(s(X)) -> s(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(zeros()) -> ok(zeros()) s(mark(X)) -> mark(s(X)) s(ok(X)) -> ok(s(X)) take(X1,mark(X2)) -> mark(take(X1,X2)) take(mark(X1),X2) -> mark(take(X1,X2)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {active/1,and/2,cons/2,length/1,proper/1,s/1,take/2,top/1} / {0/0,mark/1,nil/0,ok/1,tt/0,zeros/0} - Obligation: runtime complexity wrt. defined symbols {active,and,cons,length,proper,s,take,top} and constructors {0,mark ,nil,ok,tt,zeros} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () ** Step 1.a:1: Sum. WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: active(and(X1,X2)) -> and(active(X1),X2) active(and(tt(),X)) -> mark(X) active(cons(X1,X2)) -> cons(active(X1),X2) active(length(X)) -> length(active(X)) active(length(cons(N,L))) -> mark(s(length(L))) active(length(nil())) -> mark(0()) active(s(X)) -> s(active(X)) active(take(X1,X2)) -> take(X1,active(X2)) active(take(X1,X2)) -> take(active(X1),X2) active(take(0(),IL)) -> mark(nil()) active(take(s(M),cons(N,IL))) -> mark(cons(N,take(M,IL))) active(zeros()) -> mark(cons(0(),zeros())) and(mark(X1),X2) -> mark(and(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) length(mark(X)) -> mark(length(X)) length(ok(X)) -> ok(length(X)) proper(0()) -> ok(0()) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(length(X)) -> length(proper(X)) proper(nil()) -> ok(nil()) proper(s(X)) -> s(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(zeros()) -> ok(zeros()) s(mark(X)) -> mark(s(X)) s(ok(X)) -> ok(s(X)) take(X1,mark(X2)) -> mark(take(X1,X2)) take(mark(X1),X2) -> mark(take(X1,X2)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {active/1,and/2,cons/2,length/1,proper/1,s/1,take/2,top/1} / {0/0,mark/1,nil/0,ok/1,tt/0,zeros/0} - Obligation: runtime complexity wrt. defined symbols {active,and,cons,length,proper,s,take,top} and constructors {0,mark ,nil,ok,tt,zeros} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () ** Step 1.a:2: DecreasingLoops. WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: active(and(X1,X2)) -> and(active(X1),X2) active(and(tt(),X)) -> mark(X) active(cons(X1,X2)) -> cons(active(X1),X2) active(length(X)) -> length(active(X)) active(length(cons(N,L))) -> mark(s(length(L))) active(length(nil())) -> mark(0()) active(s(X)) -> s(active(X)) active(take(X1,X2)) -> take(X1,active(X2)) active(take(X1,X2)) -> take(active(X1),X2) active(take(0(),IL)) -> mark(nil()) active(take(s(M),cons(N,IL))) -> mark(cons(N,take(M,IL))) active(zeros()) -> mark(cons(0(),zeros())) and(mark(X1),X2) -> mark(and(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) length(mark(X)) -> mark(length(X)) length(ok(X)) -> ok(length(X)) proper(0()) -> ok(0()) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(length(X)) -> length(proper(X)) proper(nil()) -> ok(nil()) proper(s(X)) -> s(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(zeros()) -> ok(zeros()) s(mark(X)) -> mark(s(X)) s(ok(X)) -> ok(s(X)) take(X1,mark(X2)) -> mark(take(X1,X2)) take(mark(X1),X2) -> mark(take(X1,X2)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {active/1,and/2,cons/2,length/1,proper/1,s/1,take/2,top/1} / {0/0,mark/1,nil/0,ok/1,tt/0,zeros/0} - Obligation: runtime complexity wrt. defined symbols {active,and,cons,length,proper,s,take,top} and constructors {0,mark ,nil,ok,tt,zeros} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: and(x,y){x -> mark(x)} = and(mark(x),y) ->^+ mark(and(x,y)) = C[and(x,y) = and(x,y){}] ** Step 1.b:1: Bounds. WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: active(and(X1,X2)) -> and(active(X1),X2) active(and(tt(),X)) -> mark(X) active(cons(X1,X2)) -> cons(active(X1),X2) active(length(X)) -> length(active(X)) active(length(cons(N,L))) -> mark(s(length(L))) active(length(nil())) -> mark(0()) active(s(X)) -> s(active(X)) active(take(X1,X2)) -> take(X1,active(X2)) active(take(X1,X2)) -> take(active(X1),X2) active(take(0(),IL)) -> mark(nil()) active(take(s(M),cons(N,IL))) -> mark(cons(N,take(M,IL))) active(zeros()) -> mark(cons(0(),zeros())) and(mark(X1),X2) -> mark(and(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) length(mark(X)) -> mark(length(X)) length(ok(X)) -> ok(length(X)) proper(0()) -> ok(0()) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(length(X)) -> length(proper(X)) proper(nil()) -> ok(nil()) proper(s(X)) -> s(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(zeros()) -> ok(zeros()) s(mark(X)) -> mark(s(X)) s(ok(X)) -> ok(s(X)) take(X1,mark(X2)) -> mark(take(X1,X2)) take(mark(X1),X2) -> mark(take(X1,X2)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {active/1,and/2,cons/2,length/1,proper/1,s/1,take/2,top/1} / {0/0,mark/1,nil/0,ok/1,tt/0,zeros/0} - Obligation: runtime complexity wrt. defined symbols {active,and,cons,length,proper,s,take,top} and constructors {0,mark ,nil,ok,tt,zeros} + Applied Processor: Bounds {initialAutomaton = perSymbol, enrichment = match} + Details: The problem is match-bounded by 5. The enriched problem is compatible with follwoing automaton. 0_0() -> 1 0_1() -> 16 0_2() -> 26 0_3() -> 37 active_0(1) -> 2 active_0(6) -> 2 active_0(7) -> 2 active_0(8) -> 2 active_0(13) -> 2 active_0(14) -> 2 active_1(1) -> 23 active_1(6) -> 23 active_1(7) -> 23 active_1(8) -> 23 active_1(13) -> 23 active_1(14) -> 23 active_2(16) -> 24 active_2(17) -> 24 active_3(32) -> 31 active_4(26) -> 36 active_4(30) -> 36 active_4(38) -> 39 active_5(37) -> 40 and_0(1,1) -> 3 and_0(1,6) -> 3 and_0(1,7) -> 3 and_0(1,8) -> 3 and_0(1,13) -> 3 and_0(1,14) -> 3 and_0(6,1) -> 3 and_0(6,6) -> 3 and_0(6,7) -> 3 and_0(6,8) -> 3 and_0(6,13) -> 3 and_0(6,14) -> 3 and_0(7,1) -> 3 and_0(7,6) -> 3 and_0(7,7) -> 3 and_0(7,8) -> 3 and_0(7,13) -> 3 and_0(7,14) -> 3 and_0(8,1) -> 3 and_0(8,6) -> 3 and_0(8,7) -> 3 and_0(8,8) -> 3 and_0(8,13) -> 3 and_0(8,14) -> 3 and_0(13,1) -> 3 and_0(13,6) -> 3 and_0(13,7) -> 3 and_0(13,8) -> 3 and_0(13,13) -> 3 and_0(13,14) -> 3 and_0(14,1) -> 3 and_0(14,6) -> 3 and_0(14,7) -> 3 and_0(14,8) -> 3 and_0(14,13) -> 3 and_0(14,14) -> 3 and_1(1,1) -> 18 and_1(1,6) -> 18 and_1(1,7) -> 18 and_1(1,8) -> 18 and_1(1,13) -> 18 and_1(1,14) -> 18 and_1(6,1) -> 18 and_1(6,6) -> 18 and_1(6,7) -> 18 and_1(6,8) -> 18 and_1(6,13) -> 18 and_1(6,14) -> 18 and_1(7,1) -> 18 and_1(7,6) -> 18 and_1(7,7) -> 18 and_1(7,8) -> 18 and_1(7,13) -> 18 and_1(7,14) -> 18 and_1(8,1) -> 18 and_1(8,6) -> 18 and_1(8,7) -> 18 and_1(8,8) -> 18 and_1(8,13) -> 18 and_1(8,14) -> 18 and_1(13,1) -> 18 and_1(13,6) -> 18 and_1(13,7) -> 18 and_1(13,8) -> 18 and_1(13,13) -> 18 and_1(13,14) -> 18 and_1(14,1) -> 18 and_1(14,6) -> 18 and_1(14,7) -> 18 and_1(14,8) -> 18 and_1(14,13) -> 18 and_1(14,14) -> 18 cons_0(1,1) -> 4 cons_0(1,6) -> 4 cons_0(1,7) -> 4 cons_0(1,8) -> 4 cons_0(1,13) -> 4 cons_0(1,14) -> 4 cons_0(6,1) -> 4 cons_0(6,6) -> 4 cons_0(6,7) -> 4 cons_0(6,8) -> 4 cons_0(6,13) -> 4 cons_0(6,14) -> 4 cons_0(7,1) -> 4 cons_0(7,6) -> 4 cons_0(7,7) -> 4 cons_0(7,8) -> 4 cons_0(7,13) -> 4 cons_0(7,14) -> 4 cons_0(8,1) -> 4 cons_0(8,6) -> 4 cons_0(8,7) -> 4 cons_0(8,8) -> 4 cons_0(8,13) -> 4 cons_0(8,14) -> 4 cons_0(13,1) -> 4 cons_0(13,6) -> 4 cons_0(13,7) -> 4 cons_0(13,8) -> 4 cons_0(13,13) -> 4 cons_0(13,14) -> 4 cons_0(14,1) -> 4 cons_0(14,6) -> 4 cons_0(14,7) -> 4 cons_0(14,8) -> 4 cons_0(14,13) -> 4 cons_0(14,14) -> 4 cons_1(1,1) -> 19 cons_1(1,6) -> 19 cons_1(1,7) -> 19 cons_1(1,8) -> 19 cons_1(1,13) -> 19 cons_1(1,14) -> 19 cons_1(6,1) -> 19 cons_1(6,6) -> 19 cons_1(6,7) -> 19 cons_1(6,8) -> 19 cons_1(6,13) -> 19 cons_1(6,14) -> 19 cons_1(7,1) -> 19 cons_1(7,6) -> 19 cons_1(7,7) -> 19 cons_1(7,8) -> 19 cons_1(7,13) -> 19 cons_1(7,14) -> 19 cons_1(8,1) -> 19 cons_1(8,6) -> 19 cons_1(8,7) -> 19 cons_1(8,8) -> 19 cons_1(8,13) -> 19 cons_1(8,14) -> 19 cons_1(13,1) -> 19 cons_1(13,6) -> 19 cons_1(13,7) -> 19 cons_1(13,8) -> 19 cons_1(13,13) -> 19 cons_1(13,14) -> 19 cons_1(14,1) -> 19 cons_1(14,6) -> 19 cons_1(14,7) -> 19 cons_1(14,8) -> 19 cons_1(14,13) -> 19 cons_1(14,14) -> 19 cons_1(16,17) -> 15 cons_2(26,27) -> 25 cons_2(28,29) -> 24 cons_3(26,27) -> 32 cons_3(30,27) -> 32 cons_3(33,34) -> 31 cons_4(36,27) -> 31 cons_4(37,35) -> 38 cons_5(40,35) -> 39 length_0(1) -> 5 length_0(6) -> 5 length_0(7) -> 5 length_0(8) -> 5 length_0(13) -> 5 length_0(14) -> 5 length_1(1) -> 20 length_1(6) -> 20 length_1(7) -> 20 length_1(8) -> 20 length_1(13) -> 20 length_1(14) -> 20 mark_0(1) -> 6 mark_0(6) -> 6 mark_0(7) -> 6 mark_0(8) -> 6 mark_0(13) -> 6 mark_0(14) -> 6 mark_1(15) -> 2 mark_1(15) -> 23 mark_1(18) -> 3 mark_1(18) -> 18 mark_1(19) -> 4 mark_1(19) -> 19 mark_1(20) -> 5 mark_1(20) -> 20 mark_1(21) -> 10 mark_1(21) -> 21 mark_1(22) -> 11 mark_1(22) -> 22 mark_2(25) -> 24 nil_0() -> 7 nil_1() -> 16 nil_2() -> 30 ok_0(1) -> 8 ok_0(6) -> 8 ok_0(7) -> 8 ok_0(8) -> 8 ok_0(13) -> 8 ok_0(14) -> 8 ok_1(16) -> 9 ok_1(16) -> 23 ok_1(17) -> 9 ok_1(17) -> 23 ok_1(18) -> 3 ok_1(18) -> 18 ok_1(19) -> 4 ok_1(19) -> 19 ok_1(20) -> 5 ok_1(20) -> 20 ok_1(21) -> 10 ok_1(21) -> 21 ok_1(22) -> 11 ok_1(22) -> 22 ok_2(26) -> 28 ok_2(27) -> 29 ok_2(30) -> 28 ok_3(32) -> 24 ok_3(35) -> 34 ok_3(37) -> 33 ok_4(38) -> 31 proper_0(1) -> 9 proper_0(6) -> 9 proper_0(7) -> 9 proper_0(8) -> 9 proper_0(13) -> 9 proper_0(14) -> 9 proper_1(1) -> 23 proper_1(6) -> 23 proper_1(7) -> 23 proper_1(8) -> 23 proper_1(13) -> 23 proper_1(14) -> 23 proper_2(15) -> 24 proper_2(16) -> 28 proper_2(17) -> 29 proper_3(25) -> 31 proper_3(26) -> 33 proper_3(27) -> 34 s_0(1) -> 10 s_0(6) -> 10 s_0(7) -> 10 s_0(8) -> 10 s_0(13) -> 10 s_0(14) -> 10 s_1(1) -> 21 s_1(6) -> 21 s_1(7) -> 21 s_1(8) -> 21 s_1(13) -> 21 s_1(14) -> 21 take_0(1,1) -> 11 take_0(1,6) -> 11 take_0(1,7) -> 11 take_0(1,8) -> 11 take_0(1,13) -> 11 take_0(1,14) -> 11 take_0(6,1) -> 11 take_0(6,6) -> 11 take_0(6,7) -> 11 take_0(6,8) -> 11 take_0(6,13) -> 11 take_0(6,14) -> 11 take_0(7,1) -> 11 take_0(7,6) -> 11 take_0(7,7) -> 11 take_0(7,8) -> 11 take_0(7,13) -> 11 take_0(7,14) -> 11 take_0(8,1) -> 11 take_0(8,6) -> 11 take_0(8,7) -> 11 take_0(8,8) -> 11 take_0(8,13) -> 11 take_0(8,14) -> 11 take_0(13,1) -> 11 take_0(13,6) -> 11 take_0(13,7) -> 11 take_0(13,8) -> 11 take_0(13,13) -> 11 take_0(13,14) -> 11 take_0(14,1) -> 11 take_0(14,6) -> 11 take_0(14,7) -> 11 take_0(14,8) -> 11 take_0(14,13) -> 11 take_0(14,14) -> 11 take_1(1,1) -> 22 take_1(1,6) -> 22 take_1(1,7) -> 22 take_1(1,8) -> 22 take_1(1,13) -> 22 take_1(1,14) -> 22 take_1(6,1) -> 22 take_1(6,6) -> 22 take_1(6,7) -> 22 take_1(6,8) -> 22 take_1(6,13) -> 22 take_1(6,14) -> 22 take_1(7,1) -> 22 take_1(7,6) -> 22 take_1(7,7) -> 22 take_1(7,8) -> 22 take_1(7,13) -> 22 take_1(7,14) -> 22 take_1(8,1) -> 22 take_1(8,6) -> 22 take_1(8,7) -> 22 take_1(8,8) -> 22 take_1(8,13) -> 22 take_1(8,14) -> 22 take_1(13,1) -> 22 take_1(13,6) -> 22 take_1(13,7) -> 22 take_1(13,8) -> 22 take_1(13,13) -> 22 take_1(13,14) -> 22 take_1(14,1) -> 22 take_1(14,6) -> 22 take_1(14,7) -> 22 take_1(14,8) -> 22 take_1(14,13) -> 22 take_1(14,14) -> 22 top_0(1) -> 12 top_0(6) -> 12 top_0(7) -> 12 top_0(8) -> 12 top_0(13) -> 12 top_0(14) -> 12 top_1(23) -> 12 top_2(24) -> 12 top_3(31) -> 12 top_4(39) -> 12 tt_0() -> 13 tt_1() -> 16 tt_2() -> 30 zeros_0() -> 14 zeros_1() -> 17 zeros_2() -> 27 zeros_3() -> 35 ** Step 1.b:2: EmptyProcessor. WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: active(and(X1,X2)) -> and(active(X1),X2) active(and(tt(),X)) -> mark(X) active(cons(X1,X2)) -> cons(active(X1),X2) active(length(X)) -> length(active(X)) active(length(cons(N,L))) -> mark(s(length(L))) active(length(nil())) -> mark(0()) active(s(X)) -> s(active(X)) active(take(X1,X2)) -> take(X1,active(X2)) active(take(X1,X2)) -> take(active(X1),X2) active(take(0(),IL)) -> mark(nil()) active(take(s(M),cons(N,IL))) -> mark(cons(N,take(M,IL))) active(zeros()) -> mark(cons(0(),zeros())) and(mark(X1),X2) -> mark(and(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) length(mark(X)) -> mark(length(X)) length(ok(X)) -> ok(length(X)) proper(0()) -> ok(0()) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(length(X)) -> length(proper(X)) proper(nil()) -> ok(nil()) proper(s(X)) -> s(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(zeros()) -> ok(zeros()) s(mark(X)) -> mark(s(X)) s(ok(X)) -> ok(s(X)) take(X1,mark(X2)) -> mark(take(X1,X2)) take(mark(X1),X2) -> mark(take(X1,X2)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {active/1,and/2,cons/2,length/1,proper/1,s/1,take/2,top/1} / {0/0,mark/1,nil/0,ok/1,tt/0,zeros/0} - Obligation: runtime complexity wrt. defined symbols {active,and,cons,length,proper,s,take,top} and constructors {0,mark ,nil,ok,tt,zeros} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(Omega(n^1),O(n^1))