* Step 1: Bounds WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: add(X1,mark(X2)) -> mark(add(X1,X2)) add(mark(X1),X2) -> mark(add(X1,X2)) add(ok(X1),ok(X2)) -> ok(add(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) dbl(mark(X)) -> mark(dbl(X)) dbl(ok(X)) -> ok(dbl(X)) first(X1,mark(X2)) -> mark(first(X1,X2)) first(mark(X1),X2) -> mark(first(X1,X2)) first(ok(X1),ok(X2)) -> ok(first(X1,X2)) proper(0()) -> ok(0()) proper(nil()) -> ok(nil()) recip(mark(X)) -> mark(recip(X)) recip(ok(X)) -> ok(recip(X)) s(ok(X)) -> ok(s(X)) sqr(mark(X)) -> mark(sqr(X)) sqr(ok(X)) -> ok(sqr(X)) terms(mark(X)) -> mark(terms(X)) terms(ok(X)) -> ok(terms(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {add/2,cons/2,dbl/1,first/2,proper/1,recip/1,s/1,sqr/1,terms/1,top/1} / {0/0,active/1,mark/1,nil/0,ok/1} - Obligation: innermost runtime complexity wrt. defined symbols {add,cons,dbl,first,proper,recip,s,sqr,terms ,top} and constructors {0,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 active_0(2) -> 2 active_1(2) -> 4 active_2(3) -> 5 add_0(2,2) -> 1 add_1(2,2) -> 3 cons_0(2,2) -> 1 cons_1(2,2) -> 3 dbl_0(2) -> 1 dbl_1(2) -> 3 first_0(2,2) -> 1 first_1(2,2) -> 3 mark_0(2) -> 2 mark_1(3) -> 1 mark_1(3) -> 3 nil_0() -> 2 nil_1() -> 3 ok_0(2) -> 2 ok_1(3) -> 1 ok_1(3) -> 3 ok_1(3) -> 4 proper_0(2) -> 1 proper_1(2) -> 4 recip_0(2) -> 1 recip_1(2) -> 3 s_0(2) -> 1 s_1(2) -> 3 sqr_0(2) -> 1 sqr_1(2) -> 3 terms_0(2) -> 1 terms_1(2) -> 3 top_0(2) -> 1 top_1(4) -> 1 top_2(5) -> 1 * Step 2: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: add(X1,mark(X2)) -> mark(add(X1,X2)) add(mark(X1),X2) -> mark(add(X1,X2)) add(ok(X1),ok(X2)) -> ok(add(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) dbl(mark(X)) -> mark(dbl(X)) dbl(ok(X)) -> ok(dbl(X)) first(X1,mark(X2)) -> mark(first(X1,X2)) first(mark(X1),X2) -> mark(first(X1,X2)) first(ok(X1),ok(X2)) -> ok(first(X1,X2)) proper(0()) -> ok(0()) proper(nil()) -> ok(nil()) recip(mark(X)) -> mark(recip(X)) recip(ok(X)) -> ok(recip(X)) s(ok(X)) -> ok(s(X)) sqr(mark(X)) -> mark(sqr(X)) sqr(ok(X)) -> ok(sqr(X)) terms(mark(X)) -> mark(terms(X)) terms(ok(X)) -> ok(terms(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {add/2,cons/2,dbl/1,first/2,proper/1,recip/1,s/1,sqr/1,terms/1,top/1} / {0/0,active/1,mark/1,nil/0,ok/1} - Obligation: innermost runtime complexity wrt. defined symbols {add,cons,dbl,first,proper,recip,s,sqr,terms ,top} and constructors {0,active,mark,nil,ok} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(n^1))