/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),?) * Step 1: Sum. WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: a__2ndsneg(X1,X2) -> 2ndsneg(X1,X2) a__2ndsneg(0(),Z) -> rnil() a__2ndsneg(s(N),cons(X,cons(Y,Z))) -> rcons(negrecip(mark(Y)),a__2ndspos(mark(N),mark(Z))) a__2ndspos(X1,X2) -> 2ndspos(X1,X2) a__2ndspos(0(),Z) -> rnil() a__2ndspos(s(N),cons(X,cons(Y,Z))) -> rcons(posrecip(mark(Y)),a__2ndsneg(mark(N),mark(Z))) a__from(X) -> cons(mark(X),from(s(X))) a__from(X) -> from(X) a__pi(X) -> a__2ndspos(mark(X),a__from(0())) a__pi(X) -> pi(X) a__plus(X1,X2) -> plus(X1,X2) a__plus(0(),Y) -> mark(Y) a__plus(s(X),Y) -> s(a__plus(mark(X),mark(Y))) a__square(X) -> a__times(mark(X),mark(X)) a__square(X) -> square(X) a__times(X1,X2) -> times(X1,X2) a__times(0(),Y) -> 0() a__times(s(X),Y) -> a__plus(mark(Y),a__times(mark(X),mark(Y))) mark(0()) -> 0() mark(2ndsneg(X1,X2)) -> a__2ndsneg(mark(X1),mark(X2)) mark(2ndspos(X1,X2)) -> a__2ndspos(mark(X1),mark(X2)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(from(X)) -> a__from(mark(X)) mark(negrecip(X)) -> negrecip(mark(X)) mark(nil()) -> nil() mark(pi(X)) -> a__pi(mark(X)) mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2)) mark(posrecip(X)) -> posrecip(mark(X)) mark(rcons(X1,X2)) -> rcons(mark(X1),mark(X2)) mark(rnil()) -> rnil() mark(s(X)) -> s(mark(X)) mark(square(X)) -> a__square(mark(X)) mark(times(X1,X2)) -> a__times(mark(X1),mark(X2)) - Signature: {a__2ndsneg/2,a__2ndspos/2,a__from/1,a__pi/1,a__plus/2,a__square/1,a__times/2,mark/1} / {0/0,2ndsneg/2 ,2ndspos/2,cons/2,from/1,negrecip/1,nil/0,pi/1,plus/2,posrecip/1,rcons/2,rnil/0,s/1,square/1,times/2} - Obligation: runtime complexity wrt. defined symbols {a__2ndsneg,a__2ndspos,a__from,a__pi,a__plus,a__square,a__times ,mark} and constructors {0,2ndsneg,2ndspos,cons,from,negrecip,nil,pi,plus,posrecip,rcons,rnil,s,square ,times} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: Sum. WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: a__2ndsneg(X1,X2) -> 2ndsneg(X1,X2) a__2ndsneg(0(),Z) -> rnil() a__2ndsneg(s(N),cons(X,cons(Y,Z))) -> rcons(negrecip(mark(Y)),a__2ndspos(mark(N),mark(Z))) a__2ndspos(X1,X2) -> 2ndspos(X1,X2) a__2ndspos(0(),Z) -> rnil() a__2ndspos(s(N),cons(X,cons(Y,Z))) -> rcons(posrecip(mark(Y)),a__2ndsneg(mark(N),mark(Z))) a__from(X) -> cons(mark(X),from(s(X))) a__from(X) -> from(X) a__pi(X) -> a__2ndspos(mark(X),a__from(0())) a__pi(X) -> pi(X) a__plus(X1,X2) -> plus(X1,X2) a__plus(0(),Y) -> mark(Y) a__plus(s(X),Y) -> s(a__plus(mark(X),mark(Y))) a__square(X) -> a__times(mark(X),mark(X)) a__square(X) -> square(X) a__times(X1,X2) -> times(X1,X2) a__times(0(),Y) -> 0() a__times(s(X),Y) -> a__plus(mark(Y),a__times(mark(X),mark(Y))) mark(0()) -> 0() mark(2ndsneg(X1,X2)) -> a__2ndsneg(mark(X1),mark(X2)) mark(2ndspos(X1,X2)) -> a__2ndspos(mark(X1),mark(X2)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(from(X)) -> a__from(mark(X)) mark(negrecip(X)) -> negrecip(mark(X)) mark(nil()) -> nil() mark(pi(X)) -> a__pi(mark(X)) mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2)) mark(posrecip(X)) -> posrecip(mark(X)) mark(rcons(X1,X2)) -> rcons(mark(X1),mark(X2)) mark(rnil()) -> rnil() mark(s(X)) -> s(mark(X)) mark(square(X)) -> a__square(mark(X)) mark(times(X1,X2)) -> a__times(mark(X1),mark(X2)) - Signature: {a__2ndsneg/2,a__2ndspos/2,a__from/1,a__pi/1,a__plus/2,a__square/1,a__times/2,mark/1} / {0/0,2ndsneg/2 ,2ndspos/2,cons/2,from/1,negrecip/1,nil/0,pi/1,plus/2,posrecip/1,rcons/2,rnil/0,s/1,square/1,times/2} - Obligation: runtime complexity wrt. defined symbols {a__2ndsneg,a__2ndspos,a__from,a__pi,a__plus,a__square,a__times ,mark} and constructors {0,2ndsneg,2ndspos,cons,from,negrecip,nil,pi,plus,posrecip,rcons,rnil,s,square ,times} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 3: DecreasingLoops. WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: a__2ndsneg(X1,X2) -> 2ndsneg(X1,X2) a__2ndsneg(0(),Z) -> rnil() a__2ndsneg(s(N),cons(X,cons(Y,Z))) -> rcons(negrecip(mark(Y)),a__2ndspos(mark(N),mark(Z))) a__2ndspos(X1,X2) -> 2ndspos(X1,X2) a__2ndspos(0(),Z) -> rnil() a__2ndspos(s(N),cons(X,cons(Y,Z))) -> rcons(posrecip(mark(Y)),a__2ndsneg(mark(N),mark(Z))) a__from(X) -> cons(mark(X),from(s(X))) a__from(X) -> from(X) a__pi(X) -> a__2ndspos(mark(X),a__from(0())) a__pi(X) -> pi(X) a__plus(X1,X2) -> plus(X1,X2) a__plus(0(),Y) -> mark(Y) a__plus(s(X),Y) -> s(a__plus(mark(X),mark(Y))) a__square(X) -> a__times(mark(X),mark(X)) a__square(X) -> square(X) a__times(X1,X2) -> times(X1,X2) a__times(0(),Y) -> 0() a__times(s(X),Y) -> a__plus(mark(Y),a__times(mark(X),mark(Y))) mark(0()) -> 0() mark(2ndsneg(X1,X2)) -> a__2ndsneg(mark(X1),mark(X2)) mark(2ndspos(X1,X2)) -> a__2ndspos(mark(X1),mark(X2)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(from(X)) -> a__from(mark(X)) mark(negrecip(X)) -> negrecip(mark(X)) mark(nil()) -> nil() mark(pi(X)) -> a__pi(mark(X)) mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2)) mark(posrecip(X)) -> posrecip(mark(X)) mark(rcons(X1,X2)) -> rcons(mark(X1),mark(X2)) mark(rnil()) -> rnil() mark(s(X)) -> s(mark(X)) mark(square(X)) -> a__square(mark(X)) mark(times(X1,X2)) -> a__times(mark(X1),mark(X2)) - Signature: {a__2ndsneg/2,a__2ndspos/2,a__from/1,a__pi/1,a__plus/2,a__square/1,a__times/2,mark/1} / {0/0,2ndsneg/2 ,2ndspos/2,cons/2,from/1,negrecip/1,nil/0,pi/1,plus/2,posrecip/1,rcons/2,rnil/0,s/1,square/1,times/2} - Obligation: runtime complexity wrt. defined symbols {a__2ndsneg,a__2ndspos,a__from,a__pi,a__plus,a__square,a__times ,mark} and constructors {0,2ndsneg,2ndspos,cons,from,negrecip,nil,pi,plus,posrecip,rcons,rnil,s,square ,times} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: mark(x){x -> 2ndsneg(x,y)} = mark(2ndsneg(x,y)) ->^+ a__2ndsneg(mark(x),mark(y)) = C[mark(x) = mark(x){}] WORST_CASE(Omega(n^1),?)