* Step 1: Bounds WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: 2ndsneg(X1,mark(X2)) -> mark(2ndsneg(X1,X2)) 2ndsneg(mark(X1),X2) -> mark(2ndsneg(X1,X2)) 2ndsneg(ok(X1),ok(X2)) -> ok(2ndsneg(X1,X2)) 2ndspos(X1,mark(X2)) -> mark(2ndspos(X1,X2)) 2ndspos(mark(X1),X2) -> mark(2ndspos(X1,X2)) 2ndspos(ok(X1),ok(X2)) -> ok(2ndspos(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) cons2(X1,mark(X2)) -> mark(cons2(X1,X2)) cons2(ok(X1),ok(X2)) -> ok(cons2(X1,X2)) from(mark(X)) -> mark(from(X)) from(ok(X)) -> ok(from(X)) negrecip(mark(X)) -> mark(negrecip(X)) negrecip(ok(X)) -> ok(negrecip(X)) pi(mark(X)) -> mark(pi(X)) pi(ok(X)) -> ok(pi(X)) plus(X1,mark(X2)) -> mark(plus(X1,X2)) plus(mark(X1),X2) -> mark(plus(X1,X2)) plus(ok(X1),ok(X2)) -> ok(plus(X1,X2)) posrecip(mark(X)) -> mark(posrecip(X)) posrecip(ok(X)) -> ok(posrecip(X)) proper(0()) -> ok(0()) proper(nil()) -> ok(nil()) proper(rnil()) -> ok(rnil()) rcons(X1,mark(X2)) -> mark(rcons(X1,X2)) rcons(mark(X1),X2) -> mark(rcons(X1,X2)) rcons(ok(X1),ok(X2)) -> ok(rcons(X1,X2)) s(mark(X)) -> mark(s(X)) s(ok(X)) -> ok(s(X)) square(mark(X)) -> mark(square(X)) square(ok(X)) -> ok(square(X)) times(X1,mark(X2)) -> mark(times(X1,X2)) times(mark(X1),X2) -> mark(times(X1,X2)) times(ok(X1),ok(X2)) -> ok(times(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {2ndsneg/2,2ndspos/2,cons/2,cons2/2,from/1,negrecip/1,pi/1,plus/2,posrecip/1,proper/1,rcons/2,s/1,square/1 ,times/2,top/1} / {0/0,active/1,mark/1,nil/0,ok/1,rnil/0} - Obligation: innermost runtime complexity wrt. defined symbols {2ndsneg,2ndspos,cons,cons2,from,negrecip,pi,plus,posrecip ,proper,rcons,s,square,times,top} and constructors {0,active,mark,nil,ok,rnil} + 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 2ndsneg_0(2,2) -> 1 2ndsneg_1(2,2) -> 3 2ndspos_0(2,2) -> 1 2ndspos_1(2,2) -> 3 active_0(2) -> 2 active_1(2) -> 4 active_2(3) -> 5 cons_0(2,2) -> 1 cons_1(2,2) -> 3 cons2_0(2,2) -> 1 cons2_1(2,2) -> 3 from_0(2) -> 1 from_1(2) -> 3 mark_0(2) -> 2 mark_1(3) -> 1 mark_1(3) -> 3 negrecip_0(2) -> 1 negrecip_1(2) -> 3 nil_0() -> 2 nil_1() -> 3 ok_0(2) -> 2 ok_1(3) -> 1 ok_1(3) -> 3 ok_1(3) -> 4 pi_0(2) -> 1 pi_1(2) -> 3 plus_0(2,2) -> 1 plus_1(2,2) -> 3 posrecip_0(2) -> 1 posrecip_1(2) -> 3 proper_0(2) -> 1 proper_1(2) -> 4 rcons_0(2,2) -> 1 rcons_1(2,2) -> 3 rnil_0() -> 2 rnil_1() -> 3 s_0(2) -> 1 s_1(2) -> 3 square_0(2) -> 1 square_1(2) -> 3 times_0(2,2) -> 1 times_1(2,2) -> 3 top_0(2) -> 1 top_1(4) -> 1 top_2(5) -> 1 * Step 2: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: 2ndsneg(X1,mark(X2)) -> mark(2ndsneg(X1,X2)) 2ndsneg(mark(X1),X2) -> mark(2ndsneg(X1,X2)) 2ndsneg(ok(X1),ok(X2)) -> ok(2ndsneg(X1,X2)) 2ndspos(X1,mark(X2)) -> mark(2ndspos(X1,X2)) 2ndspos(mark(X1),X2) -> mark(2ndspos(X1,X2)) 2ndspos(ok(X1),ok(X2)) -> ok(2ndspos(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) cons2(X1,mark(X2)) -> mark(cons2(X1,X2)) cons2(ok(X1),ok(X2)) -> ok(cons2(X1,X2)) from(mark(X)) -> mark(from(X)) from(ok(X)) -> ok(from(X)) negrecip(mark(X)) -> mark(negrecip(X)) negrecip(ok(X)) -> ok(negrecip(X)) pi(mark(X)) -> mark(pi(X)) pi(ok(X)) -> ok(pi(X)) plus(X1,mark(X2)) -> mark(plus(X1,X2)) plus(mark(X1),X2) -> mark(plus(X1,X2)) plus(ok(X1),ok(X2)) -> ok(plus(X1,X2)) posrecip(mark(X)) -> mark(posrecip(X)) posrecip(ok(X)) -> ok(posrecip(X)) proper(0()) -> ok(0()) proper(nil()) -> ok(nil()) proper(rnil()) -> ok(rnil()) rcons(X1,mark(X2)) -> mark(rcons(X1,X2)) rcons(mark(X1),X2) -> mark(rcons(X1,X2)) rcons(ok(X1),ok(X2)) -> ok(rcons(X1,X2)) s(mark(X)) -> mark(s(X)) s(ok(X)) -> ok(s(X)) square(mark(X)) -> mark(square(X)) square(ok(X)) -> ok(square(X)) times(X1,mark(X2)) -> mark(times(X1,X2)) times(mark(X1),X2) -> mark(times(X1,X2)) times(ok(X1),ok(X2)) -> ok(times(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {2ndsneg/2,2ndspos/2,cons/2,cons2/2,from/1,negrecip/1,pi/1,plus/2,posrecip/1,proper/1,rcons/2,s/1,square/1 ,times/2,top/1} / {0/0,active/1,mark/1,nil/0,ok/1,rnil/0} - Obligation: innermost runtime complexity wrt. defined symbols {2ndsneg,2ndspos,cons,cons2,from,negrecip,pi,plus,posrecip ,proper,rcons,s,square,times,top} and constructors {0,active,mark,nil,ok,rnil} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(n^1))