/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(eq(X,Y)) -> mark(false()) active(eq(0(),0())) -> mark(true()) active(eq(s(X),s(Y))) -> mark(eq(X,Y)) active(inf(X)) -> inf(active(X)) active(inf(X)) -> mark(cons(X,inf(s(X)))) active(length(X)) -> length(active(X)) active(length(cons(X,L))) -> mark(s(length(L))) active(length(nil())) -> mark(0()) active(take(X1,X2)) -> take(X1,active(X2)) active(take(X1,X2)) -> take(active(X1),X2) active(take(0(),X)) -> mark(nil()) active(take(s(X),cons(Y,L))) -> mark(cons(Y,take(X,L))) any(X) -> s(X) any(proper(X)) -> any(any(any(X))) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) eq(ok(X1),ok(X2)) -> ok(eq(X1,X2)) inf(mark(X)) -> mark(inf(X)) inf(ok(X)) -> ok(inf(X)) length(mark(X)) -> mark(length(X)) length(ok(X)) -> ok(length(X)) proper(0()) -> ok(0()) proper(cons(any(X1),X2)) -> cons(any(any(proper(X1))),any(proper(X2))) proper(eq(X1,X2)) -> eq(proper(X1),proper(X2)) proper(false()) -> ok(false()) proper(inf(X)) -> inf(proper(X)) proper(length(X)) -> length(proper(X)) proper(nil()) -> ok(nil()) proper(s(X)) -> s(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(true()) -> ok(true()) s(ok(X)) -> ok(s(X)) take(X1,mark(X2)) -> mark(take(X1,X2)) take(mark(X1),X2) -> mark(take(X1,X2)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {active/1,any/1,cons/2,eq/2,inf/1,length/1,proper/1,s/1,take/2,top/1} / {0/0,false/0,mark/1,nil/0,ok/1 ,true/0} - Obligation: runtime complexity wrt. defined symbols {active,any,cons,eq,inf,length,proper,s,take ,top} and constructors {0,false,mark,nil,ok,true} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: Sum. WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: active(eq(X,Y)) -> mark(false()) active(eq(0(),0())) -> mark(true()) active(eq(s(X),s(Y))) -> mark(eq(X,Y)) active(inf(X)) -> inf(active(X)) active(inf(X)) -> mark(cons(X,inf(s(X)))) active(length(X)) -> length(active(X)) active(length(cons(X,L))) -> mark(s(length(L))) active(length(nil())) -> mark(0()) active(take(X1,X2)) -> take(X1,active(X2)) active(take(X1,X2)) -> take(active(X1),X2) active(take(0(),X)) -> mark(nil()) active(take(s(X),cons(Y,L))) -> mark(cons(Y,take(X,L))) any(X) -> s(X) any(proper(X)) -> any(any(any(X))) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) eq(ok(X1),ok(X2)) -> ok(eq(X1,X2)) inf(mark(X)) -> mark(inf(X)) inf(ok(X)) -> ok(inf(X)) length(mark(X)) -> mark(length(X)) length(ok(X)) -> ok(length(X)) proper(0()) -> ok(0()) proper(cons(any(X1),X2)) -> cons(any(any(proper(X1))),any(proper(X2))) proper(eq(X1,X2)) -> eq(proper(X1),proper(X2)) proper(false()) -> ok(false()) proper(inf(X)) -> inf(proper(X)) proper(length(X)) -> length(proper(X)) proper(nil()) -> ok(nil()) proper(s(X)) -> s(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(true()) -> ok(true()) s(ok(X)) -> ok(s(X)) take(X1,mark(X2)) -> mark(take(X1,X2)) take(mark(X1),X2) -> mark(take(X1,X2)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {active/1,any/1,cons/2,eq/2,inf/1,length/1,proper/1,s/1,take/2,top/1} / {0/0,false/0,mark/1,nil/0,ok/1 ,true/0} - Obligation: runtime complexity wrt. defined symbols {active,any,cons,eq,inf,length,proper,s,take ,top} and constructors {0,false,mark,nil,ok,true} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 3: DecreasingLoops. WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: active(eq(X,Y)) -> mark(false()) active(eq(0(),0())) -> mark(true()) active(eq(s(X),s(Y))) -> mark(eq(X,Y)) active(inf(X)) -> inf(active(X)) active(inf(X)) -> mark(cons(X,inf(s(X)))) active(length(X)) -> length(active(X)) active(length(cons(X,L))) -> mark(s(length(L))) active(length(nil())) -> mark(0()) active(take(X1,X2)) -> take(X1,active(X2)) active(take(X1,X2)) -> take(active(X1),X2) active(take(0(),X)) -> mark(nil()) active(take(s(X),cons(Y,L))) -> mark(cons(Y,take(X,L))) any(X) -> s(X) any(proper(X)) -> any(any(any(X))) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) eq(ok(X1),ok(X2)) -> ok(eq(X1,X2)) inf(mark(X)) -> mark(inf(X)) inf(ok(X)) -> ok(inf(X)) length(mark(X)) -> mark(length(X)) length(ok(X)) -> ok(length(X)) proper(0()) -> ok(0()) proper(cons(any(X1),X2)) -> cons(any(any(proper(X1))),any(proper(X2))) proper(eq(X1,X2)) -> eq(proper(X1),proper(X2)) proper(false()) -> ok(false()) proper(inf(X)) -> inf(proper(X)) proper(length(X)) -> length(proper(X)) proper(nil()) -> ok(nil()) proper(s(X)) -> s(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(true()) -> ok(true()) s(ok(X)) -> ok(s(X)) take(X1,mark(X2)) -> mark(take(X1,X2)) take(mark(X1),X2) -> mark(take(X1,X2)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {active/1,any/1,cons/2,eq/2,inf/1,length/1,proper/1,s/1,take/2,top/1} / {0/0,false/0,mark/1,nil/0,ok/1 ,true/0} - Obligation: runtime complexity wrt. defined symbols {active,any,cons,eq,inf,length,proper,s,take ,top} and constructors {0,false,mark,nil,ok,true} + 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),?)