/export/starexec/sandbox2/solver/bin/starexec_run_tct_rc /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1),O(n^1)) * Step 1: Sum. WORST_CASE(Omega(n^1),O(n^1)) + Considered Problem: - Strict TRS: __(X1,mark(X2)) -> mark(__(X1,X2)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) active(__(X,nil())) -> mark(X) active(__(X1,X2)) -> __(X1,active(X2)) active(__(X1,X2)) -> __(active(X1),X2) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil(),X)) -> mark(X) active(and(X1,X2)) -> and(active(X1),X2) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(isNeList(V)) active(isList(__(V1,V2))) -> mark(and(isList(V1),isList(V2))) active(isList(nil())) -> mark(tt()) active(isNeList(V)) -> mark(isQid(V)) active(isNeList(__(V1,V2))) -> mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) -> mark(and(isNeList(V1),isList(V2))) active(isNePal(V)) -> mark(isQid(V)) active(isNePal(__(I,__(P,I)))) -> mark(and(isQid(I),isPal(P))) active(isPal(V)) -> mark(isNePal(V)) active(isPal(nil())) -> mark(tt()) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) and(mark(X1),X2) -> mark(and(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(a()) -> ok(a()) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(nil()) -> ok(nil()) proper(o()) -> ok(o()) proper(tt()) -> ok(tt()) proper(u()) -> ok(u()) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {__/2,active/1,and/2,isList/1,isNeList/1,isNePal/1,isPal/1,isQid/1,proper/1,top/1} / {a/0,e/0,i/0,mark/1 ,nil/0,o/0,ok/1,tt/0,u/0} - Obligation: runtime complexity wrt. defined symbols {__,active,and,isList,isNeList,isNePal,isPal,isQid,proper ,top} and constructors {a,e,i,mark,nil,o,ok,tt,u} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () ** Step 1.a:1: Sum. WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: __(X1,mark(X2)) -> mark(__(X1,X2)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) active(__(X,nil())) -> mark(X) active(__(X1,X2)) -> __(X1,active(X2)) active(__(X1,X2)) -> __(active(X1),X2) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil(),X)) -> mark(X) active(and(X1,X2)) -> and(active(X1),X2) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(isNeList(V)) active(isList(__(V1,V2))) -> mark(and(isList(V1),isList(V2))) active(isList(nil())) -> mark(tt()) active(isNeList(V)) -> mark(isQid(V)) active(isNeList(__(V1,V2))) -> mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) -> mark(and(isNeList(V1),isList(V2))) active(isNePal(V)) -> mark(isQid(V)) active(isNePal(__(I,__(P,I)))) -> mark(and(isQid(I),isPal(P))) active(isPal(V)) -> mark(isNePal(V)) active(isPal(nil())) -> mark(tt()) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) and(mark(X1),X2) -> mark(and(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(a()) -> ok(a()) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(nil()) -> ok(nil()) proper(o()) -> ok(o()) proper(tt()) -> ok(tt()) proper(u()) -> ok(u()) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {__/2,active/1,and/2,isList/1,isNeList/1,isNePal/1,isPal/1,isQid/1,proper/1,top/1} / {a/0,e/0,i/0,mark/1 ,nil/0,o/0,ok/1,tt/0,u/0} - Obligation: runtime complexity wrt. defined symbols {__,active,and,isList,isNeList,isNePal,isPal,isQid,proper ,top} and constructors {a,e,i,mark,nil,o,ok,tt,u} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () ** Step 1.a:2: DecreasingLoops. WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: __(X1,mark(X2)) -> mark(__(X1,X2)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) active(__(X,nil())) -> mark(X) active(__(X1,X2)) -> __(X1,active(X2)) active(__(X1,X2)) -> __(active(X1),X2) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil(),X)) -> mark(X) active(and(X1,X2)) -> and(active(X1),X2) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(isNeList(V)) active(isList(__(V1,V2))) -> mark(and(isList(V1),isList(V2))) active(isList(nil())) -> mark(tt()) active(isNeList(V)) -> mark(isQid(V)) active(isNeList(__(V1,V2))) -> mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) -> mark(and(isNeList(V1),isList(V2))) active(isNePal(V)) -> mark(isQid(V)) active(isNePal(__(I,__(P,I)))) -> mark(and(isQid(I),isPal(P))) active(isPal(V)) -> mark(isNePal(V)) active(isPal(nil())) -> mark(tt()) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) and(mark(X1),X2) -> mark(and(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(a()) -> ok(a()) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(nil()) -> ok(nil()) proper(o()) -> ok(o()) proper(tt()) -> ok(tt()) proper(u()) -> ok(u()) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {__/2,active/1,and/2,isList/1,isNeList/1,isNePal/1,isPal/1,isQid/1,proper/1,top/1} / {a/0,e/0,i/0,mark/1 ,nil/0,o/0,ok/1,tt/0,u/0} - Obligation: runtime complexity wrt. defined symbols {__,active,and,isList,isNeList,isNePal,isPal,isQid,proper ,top} and constructors {a,e,i,mark,nil,o,ok,tt,u} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: __(x,y){y -> mark(y)} = __(x,mark(y)) ->^+ mark(__(x,y)) = C[__(x,y) = __(x,y){}] ** Step 1.b:1: Bounds. WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: __(X1,mark(X2)) -> mark(__(X1,X2)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) active(__(X,nil())) -> mark(X) active(__(X1,X2)) -> __(X1,active(X2)) active(__(X1,X2)) -> __(active(X1),X2) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil(),X)) -> mark(X) active(and(X1,X2)) -> and(active(X1),X2) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(isNeList(V)) active(isList(__(V1,V2))) -> mark(and(isList(V1),isList(V2))) active(isList(nil())) -> mark(tt()) active(isNeList(V)) -> mark(isQid(V)) active(isNeList(__(V1,V2))) -> mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) -> mark(and(isNeList(V1),isList(V2))) active(isNePal(V)) -> mark(isQid(V)) active(isNePal(__(I,__(P,I)))) -> mark(and(isQid(I),isPal(P))) active(isPal(V)) -> mark(isNePal(V)) active(isPal(nil())) -> mark(tt()) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) and(mark(X1),X2) -> mark(and(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(a()) -> ok(a()) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(nil()) -> ok(nil()) proper(o()) -> ok(o()) proper(tt()) -> ok(tt()) proper(u()) -> ok(u()) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {__/2,active/1,and/2,isList/1,isNeList/1,isNePal/1,isPal/1,isQid/1,proper/1,top/1} / {a/0,e/0,i/0,mark/1 ,nil/0,o/0,ok/1,tt/0,u/0} - Obligation: runtime complexity wrt. defined symbols {__,active,and,isList,isNeList,isNePal,isPal,isQid,proper ,top} and constructors {a,e,i,mark,nil,o,ok,tt,u} + Applied Processor: Bounds {initialAutomaton = perSymbol, enrichment = match} + Details: The problem is match-bounded by 2. The enriched problem is compatible with follwoing automaton. ___0(2,2) -> 1 ___0(2,5) -> 1 ___0(2,6) -> 1 ___0(2,12) -> 1 ___0(2,13) -> 1 ___0(2,14) -> 1 ___0(2,15) -> 1 ___0(2,18) -> 1 ___0(2,19) -> 1 ___0(5,2) -> 1 ___0(5,5) -> 1 ___0(5,6) -> 1 ___0(5,12) -> 1 ___0(5,13) -> 1 ___0(5,14) -> 1 ___0(5,15) -> 1 ___0(5,18) -> 1 ___0(5,19) -> 1 ___0(6,2) -> 1 ___0(6,5) -> 1 ___0(6,6) -> 1 ___0(6,12) -> 1 ___0(6,13) -> 1 ___0(6,14) -> 1 ___0(6,15) -> 1 ___0(6,18) -> 1 ___0(6,19) -> 1 ___0(12,2) -> 1 ___0(12,5) -> 1 ___0(12,6) -> 1 ___0(12,12) -> 1 ___0(12,13) -> 1 ___0(12,14) -> 1 ___0(12,15) -> 1 ___0(12,18) -> 1 ___0(12,19) -> 1 ___0(13,2) -> 1 ___0(13,5) -> 1 ___0(13,6) -> 1 ___0(13,12) -> 1 ___0(13,13) -> 1 ___0(13,14) -> 1 ___0(13,15) -> 1 ___0(13,18) -> 1 ___0(13,19) -> 1 ___0(14,2) -> 1 ___0(14,5) -> 1 ___0(14,6) -> 1 ___0(14,12) -> 1 ___0(14,13) -> 1 ___0(14,14) -> 1 ___0(14,15) -> 1 ___0(14,18) -> 1 ___0(14,19) -> 1 ___0(15,2) -> 1 ___0(15,5) -> 1 ___0(15,6) -> 1 ___0(15,12) -> 1 ___0(15,13) -> 1 ___0(15,14) -> 1 ___0(15,15) -> 1 ___0(15,18) -> 1 ___0(15,19) -> 1 ___0(18,2) -> 1 ___0(18,5) -> 1 ___0(18,6) -> 1 ___0(18,12) -> 1 ___0(18,13) -> 1 ___0(18,14) -> 1 ___0(18,15) -> 1 ___0(18,18) -> 1 ___0(18,19) -> 1 ___0(19,2) -> 1 ___0(19,5) -> 1 ___0(19,6) -> 1 ___0(19,12) -> 1 ___0(19,13) -> 1 ___0(19,14) -> 1 ___0(19,15) -> 1 ___0(19,18) -> 1 ___0(19,19) -> 1 ___1(2,2) -> 20 ___1(2,5) -> 20 ___1(2,6) -> 20 ___1(2,12) -> 20 ___1(2,13) -> 20 ___1(2,14) -> 20 ___1(2,15) -> 20 ___1(2,18) -> 20 ___1(2,19) -> 20 ___1(5,2) -> 20 ___1(5,5) -> 20 ___1(5,6) -> 20 ___1(5,12) -> 20 ___1(5,13) -> 20 ___1(5,14) -> 20 ___1(5,15) -> 20 ___1(5,18) -> 20 ___1(5,19) -> 20 ___1(6,2) -> 20 ___1(6,5) -> 20 ___1(6,6) -> 20 ___1(6,12) -> 20 ___1(6,13) -> 20 ___1(6,14) -> 20 ___1(6,15) -> 20 ___1(6,18) -> 20 ___1(6,19) -> 20 ___1(12,2) -> 20 ___1(12,5) -> 20 ___1(12,6) -> 20 ___1(12,12) -> 20 ___1(12,13) -> 20 ___1(12,14) -> 20 ___1(12,15) -> 20 ___1(12,18) -> 20 ___1(12,19) -> 20 ___1(13,2) -> 20 ___1(13,5) -> 20 ___1(13,6) -> 20 ___1(13,12) -> 20 ___1(13,13) -> 20 ___1(13,14) -> 20 ___1(13,15) -> 20 ___1(13,18) -> 20 ___1(13,19) -> 20 ___1(14,2) -> 20 ___1(14,5) -> 20 ___1(14,6) -> 20 ___1(14,12) -> 20 ___1(14,13) -> 20 ___1(14,14) -> 20 ___1(14,15) -> 20 ___1(14,18) -> 20 ___1(14,19) -> 20 ___1(15,2) -> 20 ___1(15,5) -> 20 ___1(15,6) -> 20 ___1(15,12) -> 20 ___1(15,13) -> 20 ___1(15,14) -> 20 ___1(15,15) -> 20 ___1(15,18) -> 20 ___1(15,19) -> 20 ___1(18,2) -> 20 ___1(18,5) -> 20 ___1(18,6) -> 20 ___1(18,12) -> 20 ___1(18,13) -> 20 ___1(18,14) -> 20 ___1(18,15) -> 20 ___1(18,18) -> 20 ___1(18,19) -> 20 ___1(19,2) -> 20 ___1(19,5) -> 20 ___1(19,6) -> 20 ___1(19,12) -> 20 ___1(19,13) -> 20 ___1(19,14) -> 20 ___1(19,15) -> 20 ___1(19,18) -> 20 ___1(19,19) -> 20 a_0() -> 2 a_1() -> 27 active_0(2) -> 3 active_0(5) -> 3 active_0(6) -> 3 active_0(12) -> 3 active_0(13) -> 3 active_0(14) -> 3 active_0(15) -> 3 active_0(18) -> 3 active_0(19) -> 3 active_1(2) -> 28 active_1(5) -> 28 active_1(6) -> 28 active_1(12) -> 28 active_1(13) -> 28 active_1(14) -> 28 active_1(15) -> 28 active_1(18) -> 28 active_1(19) -> 28 active_2(27) -> 29 and_0(2,2) -> 4 and_0(2,5) -> 4 and_0(2,6) -> 4 and_0(2,12) -> 4 and_0(2,13) -> 4 and_0(2,14) -> 4 and_0(2,15) -> 4 and_0(2,18) -> 4 and_0(2,19) -> 4 and_0(5,2) -> 4 and_0(5,5) -> 4 and_0(5,6) -> 4 and_0(5,12) -> 4 and_0(5,13) -> 4 and_0(5,14) -> 4 and_0(5,15) -> 4 and_0(5,18) -> 4 and_0(5,19) -> 4 and_0(6,2) -> 4 and_0(6,5) -> 4 and_0(6,6) -> 4 and_0(6,12) -> 4 and_0(6,13) -> 4 and_0(6,14) -> 4 and_0(6,15) -> 4 and_0(6,18) -> 4 and_0(6,19) -> 4 and_0(12,2) -> 4 and_0(12,5) -> 4 and_0(12,6) -> 4 and_0(12,12) -> 4 and_0(12,13) -> 4 and_0(12,14) -> 4 and_0(12,15) -> 4 and_0(12,18) -> 4 and_0(12,19) -> 4 and_0(13,2) -> 4 and_0(13,5) -> 4 and_0(13,6) -> 4 and_0(13,12) -> 4 and_0(13,13) -> 4 and_0(13,14) -> 4 and_0(13,15) -> 4 and_0(13,18) -> 4 and_0(13,19) -> 4 and_0(14,2) -> 4 and_0(14,5) -> 4 and_0(14,6) -> 4 and_0(14,12) -> 4 and_0(14,13) -> 4 and_0(14,14) -> 4 and_0(14,15) -> 4 and_0(14,18) -> 4 and_0(14,19) -> 4 and_0(15,2) -> 4 and_0(15,5) -> 4 and_0(15,6) -> 4 and_0(15,12) -> 4 and_0(15,13) -> 4 and_0(15,14) -> 4 and_0(15,15) -> 4 and_0(15,18) -> 4 and_0(15,19) -> 4 and_0(18,2) -> 4 and_0(18,5) -> 4 and_0(18,6) -> 4 and_0(18,12) -> 4 and_0(18,13) -> 4 and_0(18,14) -> 4 and_0(18,15) -> 4 and_0(18,18) -> 4 and_0(18,19) -> 4 and_0(19,2) -> 4 and_0(19,5) -> 4 and_0(19,6) -> 4 and_0(19,12) -> 4 and_0(19,13) -> 4 and_0(19,14) -> 4 and_0(19,15) -> 4 and_0(19,18) -> 4 and_0(19,19) -> 4 and_1(2,2) -> 21 and_1(2,5) -> 21 and_1(2,6) -> 21 and_1(2,12) -> 21 and_1(2,13) -> 21 and_1(2,14) -> 21 and_1(2,15) -> 21 and_1(2,18) -> 21 and_1(2,19) -> 21 and_1(5,2) -> 21 and_1(5,5) -> 21 and_1(5,6) -> 21 and_1(5,12) -> 21 and_1(5,13) -> 21 and_1(5,14) -> 21 and_1(5,15) -> 21 and_1(5,18) -> 21 and_1(5,19) -> 21 and_1(6,2) -> 21 and_1(6,5) -> 21 and_1(6,6) -> 21 and_1(6,12) -> 21 and_1(6,13) -> 21 and_1(6,14) -> 21 and_1(6,15) -> 21 and_1(6,18) -> 21 and_1(6,19) -> 21 and_1(12,2) -> 21 and_1(12,5) -> 21 and_1(12,6) -> 21 and_1(12,12) -> 21 and_1(12,13) -> 21 and_1(12,14) -> 21 and_1(12,15) -> 21 and_1(12,18) -> 21 and_1(12,19) -> 21 and_1(13,2) -> 21 and_1(13,5) -> 21 and_1(13,6) -> 21 and_1(13,12) -> 21 and_1(13,13) -> 21 and_1(13,14) -> 21 and_1(13,15) -> 21 and_1(13,18) -> 21 and_1(13,19) -> 21 and_1(14,2) -> 21 and_1(14,5) -> 21 and_1(14,6) -> 21 and_1(14,12) -> 21 and_1(14,13) -> 21 and_1(14,14) -> 21 and_1(14,15) -> 21 and_1(14,18) -> 21 and_1(14,19) -> 21 and_1(15,2) -> 21 and_1(15,5) -> 21 and_1(15,6) -> 21 and_1(15,12) -> 21 and_1(15,13) -> 21 and_1(15,14) -> 21 and_1(15,15) -> 21 and_1(15,18) -> 21 and_1(15,19) -> 21 and_1(18,2) -> 21 and_1(18,5) -> 21 and_1(18,6) -> 21 and_1(18,12) -> 21 and_1(18,13) -> 21 and_1(18,14) -> 21 and_1(18,15) -> 21 and_1(18,18) -> 21 and_1(18,19) -> 21 and_1(19,2) -> 21 and_1(19,5) -> 21 and_1(19,6) -> 21 and_1(19,12) -> 21 and_1(19,13) -> 21 and_1(19,14) -> 21 and_1(19,15) -> 21 and_1(19,18) -> 21 and_1(19,19) -> 21 e_0() -> 5 e_1() -> 27 i_0() -> 6 i_1() -> 27 isList_0(2) -> 7 isList_0(5) -> 7 isList_0(6) -> 7 isList_0(12) -> 7 isList_0(13) -> 7 isList_0(14) -> 7 isList_0(15) -> 7 isList_0(18) -> 7 isList_0(19) -> 7 isList_1(2) -> 22 isList_1(5) -> 22 isList_1(6) -> 22 isList_1(12) -> 22 isList_1(13) -> 22 isList_1(14) -> 22 isList_1(15) -> 22 isList_1(18) -> 22 isList_1(19) -> 22 isNeList_0(2) -> 8 isNeList_0(5) -> 8 isNeList_0(6) -> 8 isNeList_0(12) -> 8 isNeList_0(13) -> 8 isNeList_0(14) -> 8 isNeList_0(15) -> 8 isNeList_0(18) -> 8 isNeList_0(19) -> 8 isNeList_1(2) -> 23 isNeList_1(5) -> 23 isNeList_1(6) -> 23 isNeList_1(12) -> 23 isNeList_1(13) -> 23 isNeList_1(14) -> 23 isNeList_1(15) -> 23 isNeList_1(18) -> 23 isNeList_1(19) -> 23 isNePal_0(2) -> 9 isNePal_0(5) -> 9 isNePal_0(6) -> 9 isNePal_0(12) -> 9 isNePal_0(13) -> 9 isNePal_0(14) -> 9 isNePal_0(15) -> 9 isNePal_0(18) -> 9 isNePal_0(19) -> 9 isNePal_1(2) -> 24 isNePal_1(5) -> 24 isNePal_1(6) -> 24 isNePal_1(12) -> 24 isNePal_1(13) -> 24 isNePal_1(14) -> 24 isNePal_1(15) -> 24 isNePal_1(18) -> 24 isNePal_1(19) -> 24 isPal_0(2) -> 10 isPal_0(5) -> 10 isPal_0(6) -> 10 isPal_0(12) -> 10 isPal_0(13) -> 10 isPal_0(14) -> 10 isPal_0(15) -> 10 isPal_0(18) -> 10 isPal_0(19) -> 10 isPal_1(2) -> 25 isPal_1(5) -> 25 isPal_1(6) -> 25 isPal_1(12) -> 25 isPal_1(13) -> 25 isPal_1(14) -> 25 isPal_1(15) -> 25 isPal_1(18) -> 25 isPal_1(19) -> 25 isQid_0(2) -> 11 isQid_0(5) -> 11 isQid_0(6) -> 11 isQid_0(12) -> 11 isQid_0(13) -> 11 isQid_0(14) -> 11 isQid_0(15) -> 11 isQid_0(18) -> 11 isQid_0(19) -> 11 isQid_1(2) -> 26 isQid_1(5) -> 26 isQid_1(6) -> 26 isQid_1(12) -> 26 isQid_1(13) -> 26 isQid_1(14) -> 26 isQid_1(15) -> 26 isQid_1(18) -> 26 isQid_1(19) -> 26 mark_0(2) -> 12 mark_0(5) -> 12 mark_0(6) -> 12 mark_0(12) -> 12 mark_0(13) -> 12 mark_0(14) -> 12 mark_0(15) -> 12 mark_0(18) -> 12 mark_0(19) -> 12 mark_1(20) -> 1 mark_1(20) -> 20 mark_1(21) -> 4 mark_1(21) -> 21 nil_0() -> 13 nil_1() -> 27 o_0() -> 14 o_1() -> 27 ok_0(2) -> 15 ok_0(5) -> 15 ok_0(6) -> 15 ok_0(12) -> 15 ok_0(13) -> 15 ok_0(14) -> 15 ok_0(15) -> 15 ok_0(18) -> 15 ok_0(19) -> 15 ok_1(20) -> 1 ok_1(20) -> 20 ok_1(21) -> 4 ok_1(21) -> 21 ok_1(22) -> 7 ok_1(22) -> 22 ok_1(23) -> 8 ok_1(23) -> 23 ok_1(24) -> 9 ok_1(24) -> 24 ok_1(25) -> 10 ok_1(25) -> 25 ok_1(26) -> 11 ok_1(26) -> 26 ok_1(27) -> 16 ok_1(27) -> 28 proper_0(2) -> 16 proper_0(5) -> 16 proper_0(6) -> 16 proper_0(12) -> 16 proper_0(13) -> 16 proper_0(14) -> 16 proper_0(15) -> 16 proper_0(18) -> 16 proper_0(19) -> 16 proper_1(2) -> 28 proper_1(5) -> 28 proper_1(6) -> 28 proper_1(12) -> 28 proper_1(13) -> 28 proper_1(14) -> 28 proper_1(15) -> 28 proper_1(18) -> 28 proper_1(19) -> 28 top_0(2) -> 17 top_0(5) -> 17 top_0(6) -> 17 top_0(12) -> 17 top_0(13) -> 17 top_0(14) -> 17 top_0(15) -> 17 top_0(18) -> 17 top_0(19) -> 17 top_1(28) -> 17 top_2(29) -> 17 tt_0() -> 18 tt_1() -> 27 u_0() -> 19 u_1() -> 27 ** Step 1.b:2: EmptyProcessor. WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: __(X1,mark(X2)) -> mark(__(X1,X2)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) active(__(X,nil())) -> mark(X) active(__(X1,X2)) -> __(X1,active(X2)) active(__(X1,X2)) -> __(active(X1),X2) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil(),X)) -> mark(X) active(and(X1,X2)) -> and(active(X1),X2) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(isNeList(V)) active(isList(__(V1,V2))) -> mark(and(isList(V1),isList(V2))) active(isList(nil())) -> mark(tt()) active(isNeList(V)) -> mark(isQid(V)) active(isNeList(__(V1,V2))) -> mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) -> mark(and(isNeList(V1),isList(V2))) active(isNePal(V)) -> mark(isQid(V)) active(isNePal(__(I,__(P,I)))) -> mark(and(isQid(I),isPal(P))) active(isPal(V)) -> mark(isNePal(V)) active(isPal(nil())) -> mark(tt()) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) and(mark(X1),X2) -> mark(and(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(a()) -> ok(a()) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(nil()) -> ok(nil()) proper(o()) -> ok(o()) proper(tt()) -> ok(tt()) proper(u()) -> ok(u()) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {__/2,active/1,and/2,isList/1,isNeList/1,isNePal/1,isPal/1,isQid/1,proper/1,top/1} / {a/0,e/0,i/0,mark/1 ,nil/0,o/0,ok/1,tt/0,u/0} - Obligation: runtime complexity wrt. defined symbols {__,active,and,isList,isNeList,isNePal,isPal,isQid,proper ,top} and constructors {a,e,i,mark,nil,o,ok,tt,u} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(Omega(n^1),O(n^1))