/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(dbl(X)) -> dbl(active(X)) active(dbl(0())) -> mark(0()) active(dbl(s(X))) -> mark(s(s(dbl(X)))) active(dbls(X)) -> dbls(active(X)) active(dbls(cons(X,Y))) -> mark(cons(dbl(X),dbls(Y))) active(dbls(nil())) -> mark(nil()) active(from(X)) -> mark(cons(X,from(s(X)))) active(indx(X1,X2)) -> indx(active(X1),X2) active(indx(cons(X,Y),Z)) -> mark(cons(sel(X,Z),indx(Y,Z))) active(indx(nil(),X)) -> mark(nil()) active(sel(X1,X2)) -> sel(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(0(),cons(X,Y))) -> mark(X) active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) dbl(mark(X)) -> mark(dbl(X)) dbl(ok(X)) -> ok(dbl(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(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(dbl(X)) -> dbl(proper(X)) proper(dbls(X)) -> dbls(proper(X)) proper(from(X)) -> from(proper(X)) proper(indx(X1,X2)) -> indx(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(s(X)) -> s(proper(X)) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) s(ok(X)) -> ok(s(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)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {active/1,cons/2,dbl/1,dbls/1,from/1,indx/2,proper/1,s/1,sel/2,top/1} / {0/0,mark/1,nil/0,ok/1} - Obligation: runtime complexity wrt. defined symbols {active,cons,dbl,dbls,from,indx,proper,s,sel ,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(dbl(X)) -> dbl(active(X)) active(dbl(0())) -> mark(0()) active(dbl(s(X))) -> mark(s(s(dbl(X)))) active(dbls(X)) -> dbls(active(X)) active(dbls(cons(X,Y))) -> mark(cons(dbl(X),dbls(Y))) active(dbls(nil())) -> mark(nil()) active(from(X)) -> mark(cons(X,from(s(X)))) active(indx(X1,X2)) -> indx(active(X1),X2) active(indx(cons(X,Y),Z)) -> mark(cons(sel(X,Z),indx(Y,Z))) active(indx(nil(),X)) -> mark(nil()) active(sel(X1,X2)) -> sel(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(0(),cons(X,Y))) -> mark(X) active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) dbl(mark(X)) -> mark(dbl(X)) dbl(ok(X)) -> ok(dbl(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(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(dbl(X)) -> dbl(proper(X)) proper(dbls(X)) -> dbls(proper(X)) proper(from(X)) -> from(proper(X)) proper(indx(X1,X2)) -> indx(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(s(X)) -> s(proper(X)) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) s(ok(X)) -> ok(s(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)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {active/1,cons/2,dbl/1,dbls/1,from/1,indx/2,proper/1,s/1,sel/2,top/1} / {0/0,mark/1,nil/0,ok/1} - Obligation: runtime complexity wrt. defined symbols {active,cons,dbl,dbls,from,indx,proper,s,sel ,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(dbl(X)) -> dbl(active(X)) active(dbl(0())) -> mark(0()) active(dbl(s(X))) -> mark(s(s(dbl(X)))) active(dbls(X)) -> dbls(active(X)) active(dbls(cons(X,Y))) -> mark(cons(dbl(X),dbls(Y))) active(dbls(nil())) -> mark(nil()) active(from(X)) -> mark(cons(X,from(s(X)))) active(indx(X1,X2)) -> indx(active(X1),X2) active(indx(cons(X,Y),Z)) -> mark(cons(sel(X,Z),indx(Y,Z))) active(indx(nil(),X)) -> mark(nil()) active(sel(X1,X2)) -> sel(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(0(),cons(X,Y))) -> mark(X) active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) dbl(mark(X)) -> mark(dbl(X)) dbl(ok(X)) -> ok(dbl(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(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(dbl(X)) -> dbl(proper(X)) proper(dbls(X)) -> dbls(proper(X)) proper(from(X)) -> from(proper(X)) proper(indx(X1,X2)) -> indx(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(s(X)) -> s(proper(X)) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) s(ok(X)) -> ok(s(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)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {active/1,cons/2,dbl/1,dbls/1,from/1,indx/2,proper/1,s/1,sel/2,top/1} / {0/0,mark/1,nil/0,ok/1} - Obligation: runtime complexity wrt. defined symbols {active,cons,dbl,dbls,from,indx,proper,s,sel ,top} and constructors {0,mark,nil,ok} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: cons(x,y){x -> ok(x),y -> ok(y)} = cons(ok(x),ok(y)) ->^+ ok(cons(x,y)) = C[cons(x,y) = cons(x,y){}] WORST_CASE(Omega(n^1),?)