/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(cons(X1,X2)) -> cons(active(X1),X2) active(tail(X)) -> tail(active(X)) active(tail(cons(X,XS))) -> mark(XS) active(zeros()) -> mark(cons(0(),zeros())) cons(mark(X1),X2) -> mark(cons(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) proper(0()) -> ok(0()) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(tail(X)) -> tail(proper(X)) proper(zeros()) -> ok(zeros()) tail(mark(X)) -> mark(tail(X)) tail(ok(X)) -> ok(tail(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {active/1,cons/2,proper/1,tail/1,top/1} / {0/0,mark/1,ok/1,zeros/0} - Obligation: runtime complexity wrt. defined symbols {active,cons,proper,tail,top} and constructors {0,mark,ok,zeros} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () ** Step 1.a:1: Sum. WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: active(cons(X1,X2)) -> cons(active(X1),X2) active(tail(X)) -> tail(active(X)) active(tail(cons(X,XS))) -> mark(XS) active(zeros()) -> mark(cons(0(),zeros())) cons(mark(X1),X2) -> mark(cons(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) proper(0()) -> ok(0()) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(tail(X)) -> tail(proper(X)) proper(zeros()) -> ok(zeros()) tail(mark(X)) -> mark(tail(X)) tail(ok(X)) -> ok(tail(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {active/1,cons/2,proper/1,tail/1,top/1} / {0/0,mark/1,ok/1,zeros/0} - Obligation: runtime complexity wrt. defined symbols {active,cons,proper,tail,top} and constructors {0,mark,ok,zeros} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () ** Step 1.a:2: DecreasingLoops. WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: active(cons(X1,X2)) -> cons(active(X1),X2) active(tail(X)) -> tail(active(X)) active(tail(cons(X,XS))) -> mark(XS) active(zeros()) -> mark(cons(0(),zeros())) cons(mark(X1),X2) -> mark(cons(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) proper(0()) -> ok(0()) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(tail(X)) -> tail(proper(X)) proper(zeros()) -> ok(zeros()) tail(mark(X)) -> mark(tail(X)) tail(ok(X)) -> ok(tail(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {active/1,cons/2,proper/1,tail/1,top/1} / {0/0,mark/1,ok/1,zeros/0} - Obligation: runtime complexity wrt. defined symbols {active,cons,proper,tail,top} and constructors {0,mark,ok,zeros} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: cons(x,y){x -> mark(x)} = cons(mark(x),y) ->^+ mark(cons(x,y)) = C[cons(x,y) = cons(x,y){}] ** Step 1.b:1: Bounds. WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: active(cons(X1,X2)) -> cons(active(X1),X2) active(tail(X)) -> tail(active(X)) active(tail(cons(X,XS))) -> mark(XS) active(zeros()) -> mark(cons(0(),zeros())) cons(mark(X1),X2) -> mark(cons(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) proper(0()) -> ok(0()) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(tail(X)) -> tail(proper(X)) proper(zeros()) -> ok(zeros()) tail(mark(X)) -> mark(tail(X)) tail(ok(X)) -> ok(tail(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {active/1,cons/2,proper/1,tail/1,top/1} / {0/0,mark/1,ok/1,zeros/0} - Obligation: runtime complexity wrt. defined symbols {active,cons,proper,tail,top} and constructors {0,mark,ok,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() -> 11 0_2() -> 18 0_3() -> 27 active_0(1) -> 2 active_0(4) -> 2 active_0(5) -> 2 active_0(9) -> 2 active_1(1) -> 15 active_1(4) -> 15 active_1(5) -> 15 active_1(9) -> 15 active_2(11) -> 16 active_2(12) -> 16 active_3(26) -> 22 active_4(18) -> 28 active_4(29) -> 30 active_5(27) -> 31 cons_0(1,1) -> 3 cons_0(1,4) -> 3 cons_0(1,5) -> 3 cons_0(1,9) -> 3 cons_0(4,1) -> 3 cons_0(4,4) -> 3 cons_0(4,5) -> 3 cons_0(4,9) -> 3 cons_0(5,1) -> 3 cons_0(5,4) -> 3 cons_0(5,5) -> 3 cons_0(5,9) -> 3 cons_0(9,1) -> 3 cons_0(9,4) -> 3 cons_0(9,5) -> 3 cons_0(9,9) -> 3 cons_1(1,1) -> 13 cons_1(1,4) -> 13 cons_1(1,5) -> 13 cons_1(1,9) -> 13 cons_1(4,1) -> 13 cons_1(4,4) -> 13 cons_1(4,5) -> 13 cons_1(4,9) -> 13 cons_1(5,1) -> 13 cons_1(5,4) -> 13 cons_1(5,5) -> 13 cons_1(5,9) -> 13 cons_1(9,1) -> 13 cons_1(9,4) -> 13 cons_1(9,5) -> 13 cons_1(9,9) -> 13 cons_1(11,12) -> 10 cons_2(18,19) -> 17 cons_2(20,21) -> 16 cons_3(18,19) -> 26 cons_3(23,24) -> 22 cons_4(27,25) -> 29 cons_4(28,19) -> 22 cons_5(31,25) -> 30 mark_0(1) -> 4 mark_0(4) -> 4 mark_0(5) -> 4 mark_0(9) -> 4 mark_1(10) -> 2 mark_1(10) -> 15 mark_1(13) -> 3 mark_1(13) -> 13 mark_1(14) -> 7 mark_1(14) -> 14 mark_2(17) -> 16 ok_0(1) -> 5 ok_0(4) -> 5 ok_0(5) -> 5 ok_0(9) -> 5 ok_1(11) -> 6 ok_1(11) -> 15 ok_1(12) -> 6 ok_1(12) -> 15 ok_1(13) -> 3 ok_1(13) -> 13 ok_1(14) -> 7 ok_1(14) -> 14 ok_2(18) -> 20 ok_2(19) -> 21 ok_3(25) -> 24 ok_3(26) -> 16 ok_3(27) -> 23 ok_4(29) -> 22 proper_0(1) -> 6 proper_0(4) -> 6 proper_0(5) -> 6 proper_0(9) -> 6 proper_1(1) -> 15 proper_1(4) -> 15 proper_1(5) -> 15 proper_1(9) -> 15 proper_2(10) -> 16 proper_2(11) -> 20 proper_2(12) -> 21 proper_3(17) -> 22 proper_3(18) -> 23 proper_3(19) -> 24 tail_0(1) -> 7 tail_0(4) -> 7 tail_0(5) -> 7 tail_0(9) -> 7 tail_1(1) -> 14 tail_1(4) -> 14 tail_1(5) -> 14 tail_1(9) -> 14 top_0(1) -> 8 top_0(4) -> 8 top_0(5) -> 8 top_0(9) -> 8 top_1(15) -> 8 top_2(16) -> 8 top_3(22) -> 8 top_4(30) -> 8 zeros_0() -> 9 zeros_1() -> 12 zeros_2() -> 19 zeros_3() -> 25 ** Step 1.b:2: EmptyProcessor. WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: active(cons(X1,X2)) -> cons(active(X1),X2) active(tail(X)) -> tail(active(X)) active(tail(cons(X,XS))) -> mark(XS) active(zeros()) -> mark(cons(0(),zeros())) cons(mark(X1),X2) -> mark(cons(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) proper(0()) -> ok(0()) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(tail(X)) -> tail(proper(X)) proper(zeros()) -> ok(zeros()) tail(mark(X)) -> mark(tail(X)) tail(ok(X)) -> ok(tail(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {active/1,cons/2,proper/1,tail/1,top/1} / {0/0,mark/1,ok/1,zeros/0} - Obligation: runtime complexity wrt. defined symbols {active,cons,proper,tail,top} and constructors {0,mark,ok,zeros} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(Omega(n^1),O(n^1))