/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: active(add(X1,X2)) -> add(X1,active(X2)) active(add(X1,X2)) -> add(active(X1),X2) active(add(0(),X)) -> mark(X) active(add(s(X),Y)) -> mark(s(add(X,Y))) active(cons(X1,X2)) -> cons(active(X1),X2) active(dbl(X)) -> dbl(active(X)) active(dbl(0())) -> mark(0()) active(dbl(s(X))) -> mark(s(s(dbl(X)))) active(first(X1,X2)) -> first(X1,active(X2)) active(first(X1,X2)) -> first(active(X1),X2) active(first(0(),X)) -> mark(nil()) active(first(s(X),cons(Y,Z))) -> mark(cons(Y,first(X,Z))) active(half(X)) -> half(active(X)) active(half(0())) -> mark(0()) active(half(dbl(X))) -> mark(X) active(half(s(0()))) -> mark(0()) active(half(s(s(X)))) -> mark(s(half(X))) active(recip(X)) -> recip(active(X)) active(s(X)) -> s(active(X)) active(sqr(X)) -> sqr(active(X)) active(sqr(0())) -> mark(0()) active(sqr(s(X))) -> mark(s(add(sqr(X),dbl(X)))) active(terms(N)) -> mark(cons(recip(sqr(N)),terms(s(N)))) active(terms(X)) -> terms(active(X)) 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)) half(mark(X)) -> mark(half(X)) half(ok(X)) -> ok(half(X)) proper(0()) -> ok(0()) proper(add(X1,X2)) -> add(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(dbl(X)) -> dbl(proper(X)) proper(first(X1,X2)) -> first(proper(X1),proper(X2)) proper(half(X)) -> half(proper(X)) proper(nil()) -> ok(nil()) proper(recip(X)) -> recip(proper(X)) proper(s(X)) -> s(proper(X)) proper(sqr(X)) -> sqr(proper(X)) proper(terms(X)) -> terms(proper(X)) recip(mark(X)) -> mark(recip(X)) recip(ok(X)) -> ok(recip(X)) s(mark(X)) -> mark(s(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: {active/1,add/2,cons/2,dbl/1,first/2,half/1,proper/1,recip/1,s/1,sqr/1,terms/1,top/1} / {0/0,mark/1,nil/0 ,ok/1} - Obligation: runtime complexity wrt. defined symbols {active,add,cons,dbl,first,half,proper,recip,s,sqr,terms ,top} and constructors {0,mark,nil,ok} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: Sum. WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: active(add(X1,X2)) -> add(X1,active(X2)) active(add(X1,X2)) -> add(active(X1),X2) active(add(0(),X)) -> mark(X) active(add(s(X),Y)) -> mark(s(add(X,Y))) active(cons(X1,X2)) -> cons(active(X1),X2) active(dbl(X)) -> dbl(active(X)) active(dbl(0())) -> mark(0()) active(dbl(s(X))) -> mark(s(s(dbl(X)))) active(first(X1,X2)) -> first(X1,active(X2)) active(first(X1,X2)) -> first(active(X1),X2) active(first(0(),X)) -> mark(nil()) active(first(s(X),cons(Y,Z))) -> mark(cons(Y,first(X,Z))) active(half(X)) -> half(active(X)) active(half(0())) -> mark(0()) active(half(dbl(X))) -> mark(X) active(half(s(0()))) -> mark(0()) active(half(s(s(X)))) -> mark(s(half(X))) active(recip(X)) -> recip(active(X)) active(s(X)) -> s(active(X)) active(sqr(X)) -> sqr(active(X)) active(sqr(0())) -> mark(0()) active(sqr(s(X))) -> mark(s(add(sqr(X),dbl(X)))) active(terms(N)) -> mark(cons(recip(sqr(N)),terms(s(N)))) active(terms(X)) -> terms(active(X)) 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)) half(mark(X)) -> mark(half(X)) half(ok(X)) -> ok(half(X)) proper(0()) -> ok(0()) proper(add(X1,X2)) -> add(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(dbl(X)) -> dbl(proper(X)) proper(first(X1,X2)) -> first(proper(X1),proper(X2)) proper(half(X)) -> half(proper(X)) proper(nil()) -> ok(nil()) proper(recip(X)) -> recip(proper(X)) proper(s(X)) -> s(proper(X)) proper(sqr(X)) -> sqr(proper(X)) proper(terms(X)) -> terms(proper(X)) recip(mark(X)) -> mark(recip(X)) recip(ok(X)) -> ok(recip(X)) s(mark(X)) -> mark(s(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: {active/1,add/2,cons/2,dbl/1,first/2,half/1,proper/1,recip/1,s/1,sqr/1,terms/1,top/1} / {0/0,mark/1,nil/0 ,ok/1} - Obligation: runtime complexity wrt. defined symbols {active,add,cons,dbl,first,half,proper,recip,s,sqr,terms ,top} and constructors {0,mark,nil,ok} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 3: DecreasingLoops. WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: active(add(X1,X2)) -> add(X1,active(X2)) active(add(X1,X2)) -> add(active(X1),X2) active(add(0(),X)) -> mark(X) active(add(s(X),Y)) -> mark(s(add(X,Y))) active(cons(X1,X2)) -> cons(active(X1),X2) active(dbl(X)) -> dbl(active(X)) active(dbl(0())) -> mark(0()) active(dbl(s(X))) -> mark(s(s(dbl(X)))) active(first(X1,X2)) -> first(X1,active(X2)) active(first(X1,X2)) -> first(active(X1),X2) active(first(0(),X)) -> mark(nil()) active(first(s(X),cons(Y,Z))) -> mark(cons(Y,first(X,Z))) active(half(X)) -> half(active(X)) active(half(0())) -> mark(0()) active(half(dbl(X))) -> mark(X) active(half(s(0()))) -> mark(0()) active(half(s(s(X)))) -> mark(s(half(X))) active(recip(X)) -> recip(active(X)) active(s(X)) -> s(active(X)) active(sqr(X)) -> sqr(active(X)) active(sqr(0())) -> mark(0()) active(sqr(s(X))) -> mark(s(add(sqr(X),dbl(X)))) active(terms(N)) -> mark(cons(recip(sqr(N)),terms(s(N)))) active(terms(X)) -> terms(active(X)) 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)) half(mark(X)) -> mark(half(X)) half(ok(X)) -> ok(half(X)) proper(0()) -> ok(0()) proper(add(X1,X2)) -> add(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(dbl(X)) -> dbl(proper(X)) proper(first(X1,X2)) -> first(proper(X1),proper(X2)) proper(half(X)) -> half(proper(X)) proper(nil()) -> ok(nil()) proper(recip(X)) -> recip(proper(X)) proper(s(X)) -> s(proper(X)) proper(sqr(X)) -> sqr(proper(X)) proper(terms(X)) -> terms(proper(X)) recip(mark(X)) -> mark(recip(X)) recip(ok(X)) -> ok(recip(X)) s(mark(X)) -> mark(s(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: {active/1,add/2,cons/2,dbl/1,first/2,half/1,proper/1,recip/1,s/1,sqr/1,terms/1,top/1} / {0/0,mark/1,nil/0 ,ok/1} - Obligation: runtime complexity wrt. defined symbols {active,add,cons,dbl,first,half,proper,recip,s,sqr,terms ,top} and constructors {0,mark,nil,ok} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: add(x,y){y -> mark(y)} = add(x,mark(y)) ->^+ mark(add(x,y)) = C[add(x,y) = add(x,y){}] WORST_CASE(Omega(n^1),?)