* Step 1: Bounds WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) dbl(mark(X)) -> mark(dbl(X)) dbl(ok(X)) -> ok(dbl(X)) dbl1(mark(X)) -> mark(dbl1(X)) dbl1(ok(X)) -> ok(dbl1(X)) dbls(mark(X)) -> mark(dbls(X)) dbls(ok(X)) -> ok(dbls(X)) from(ok(X)) -> ok(from(X)) indx(mark(X1),X2) -> mark(indx(X1,X2)) indx(ok(X1),ok(X2)) -> ok(indx(X1,X2)) proper(0()) -> ok(0()) proper(01()) -> ok(01()) proper(nil()) -> ok(nil()) quote(mark(X)) -> mark(quote(X)) quote(ok(X)) -> ok(quote(X)) s(ok(X)) -> ok(s(X)) s1(mark(X)) -> mark(s1(X)) s1(ok(X)) -> ok(s1(X)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) sel1(X1,mark(X2)) -> mark(sel1(X1,X2)) sel1(mark(X1),X2) -> mark(sel1(X1,X2)) sel1(ok(X1),ok(X2)) -> ok(sel1(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {cons/2,dbl/1,dbl1/1,dbls/1,from/1,indx/2,proper/1,quote/1,s/1,s1/1,sel/2,sel1/2,top/1} / {0/0,01/0,active/1 ,mark/1,nil/0,ok/1} - Obligation: innermost runtime complexity wrt. defined symbols {cons,dbl,dbl1,dbls,from,indx,proper,quote,s,s1,sel,sel1 ,top} and constructors {0,01,active,mark,nil,ok} + Applied Processor: Bounds {initialAutomaton = minimal, enrichment = match} + Details: The problem is match-bounded by 2. The enriched problem is compatible with follwoing automaton. 0_0() -> 2 0_1() -> 3 01_0() -> 2 01_1() -> 3 active_0(2) -> 2 active_1(2) -> 5 active_2(3) -> 6 cons_0(2,2) -> 1 cons_1(2,2) -> 3 dbl_0(2) -> 1 dbl_1(2) -> 4 dbl1_0(2) -> 1 dbl1_1(2) -> 4 dbls_0(2) -> 1 dbls_1(2) -> 4 from_0(2) -> 1 from_1(2) -> 3 indx_0(2,2) -> 1 indx_1(2,2) -> 4 mark_0(2) -> 2 mark_1(4) -> 1 mark_1(4) -> 4 nil_0() -> 2 nil_1() -> 3 ok_0(2) -> 2 ok_1(3) -> 1 ok_1(3) -> 3 ok_1(3) -> 5 ok_1(4) -> 1 ok_1(4) -> 4 proper_0(2) -> 1 proper_1(2) -> 5 quote_0(2) -> 1 quote_1(2) -> 4 s_0(2) -> 1 s_1(2) -> 3 s1_0(2) -> 1 s1_1(2) -> 4 sel_0(2,2) -> 1 sel_1(2,2) -> 4 sel1_0(2,2) -> 1 sel1_1(2,2) -> 4 top_0(2) -> 1 top_1(5) -> 1 top_2(6) -> 1 * Step 2: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) dbl(mark(X)) -> mark(dbl(X)) dbl(ok(X)) -> ok(dbl(X)) dbl1(mark(X)) -> mark(dbl1(X)) dbl1(ok(X)) -> ok(dbl1(X)) dbls(mark(X)) -> mark(dbls(X)) dbls(ok(X)) -> ok(dbls(X)) from(ok(X)) -> ok(from(X)) indx(mark(X1),X2) -> mark(indx(X1,X2)) indx(ok(X1),ok(X2)) -> ok(indx(X1,X2)) proper(0()) -> ok(0()) proper(01()) -> ok(01()) proper(nil()) -> ok(nil()) quote(mark(X)) -> mark(quote(X)) quote(ok(X)) -> ok(quote(X)) s(ok(X)) -> ok(s(X)) s1(mark(X)) -> mark(s1(X)) s1(ok(X)) -> ok(s1(X)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) sel1(X1,mark(X2)) -> mark(sel1(X1,X2)) sel1(mark(X1),X2) -> mark(sel1(X1,X2)) sel1(ok(X1),ok(X2)) -> ok(sel1(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {cons/2,dbl/1,dbl1/1,dbls/1,from/1,indx/2,proper/1,quote/1,s/1,s1/1,sel/2,sel1/2,top/1} / {0/0,01/0,active/1 ,mark/1,nil/0,ok/1} - Obligation: innermost runtime complexity wrt. defined symbols {cons,dbl,dbl1,dbls,from,indx,proper,quote,s,s1,sel,sel1 ,top} and constructors {0,01,active,mark,nil,ok} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(n^1))