/export/starexec/sandbox/solver/bin/starexec_run_tct_rci /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/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: deeprev(C(x1,x2)) -> deeprevapp(C(x1,x2),N()) deeprev(N()) -> N() deeprev(V(n)) -> V(n) deeprevapp(C(x1,x2),rest) -> deeprevapp(x2,C(x1,rest)) deeprevapp(N(),rest) -> rest deeprevapp(V(n),rest) -> revconsapp(rest,V(n)) first(C(x1,x2)) -> x1 first(V(n)) -> N() goal(x) -> deeprev(x) isEmptyT(C(x1,x2)) -> False() isEmptyT(N()) -> True() isEmptyT(V(n)) -> False() isNotEmptyT(C(x1,x2)) -> True() isNotEmptyT(N()) -> False() isNotEmptyT(V(n)) -> False() isVal(C(x1,x2)) -> False() isVal(N()) -> False() isVal(V(n)) -> True() revconsapp(C(x1,x2),r) -> revconsapp(x2,C(x1,r)) revconsapp(N(),r) -> r revconsapp(V(n),r) -> r second(C(x1,x2)) -> x2 second(V(n)) -> N() - Signature: {deeprev/1,deeprevapp/2,first/1,goal/1,isEmptyT/1,isNotEmptyT/1,isVal/1,revconsapp/2,second/1} / {C/2 ,False/0,N/0,True/0,V/1} - Obligation: innermost runtime complexity wrt. defined symbols {deeprev,deeprevapp,first,goal,isEmptyT,isNotEmptyT,isVal ,revconsapp,second} and constructors {C,False,N,True,V} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () ** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: deeprev(C(x1,x2)) -> deeprevapp(C(x1,x2),N()) deeprev(N()) -> N() deeprev(V(n)) -> V(n) deeprevapp(C(x1,x2),rest) -> deeprevapp(x2,C(x1,rest)) deeprevapp(N(),rest) -> rest deeprevapp(V(n),rest) -> revconsapp(rest,V(n)) first(C(x1,x2)) -> x1 first(V(n)) -> N() goal(x) -> deeprev(x) isEmptyT(C(x1,x2)) -> False() isEmptyT(N()) -> True() isEmptyT(V(n)) -> False() isNotEmptyT(C(x1,x2)) -> True() isNotEmptyT(N()) -> False() isNotEmptyT(V(n)) -> False() isVal(C(x1,x2)) -> False() isVal(N()) -> False() isVal(V(n)) -> True() revconsapp(C(x1,x2),r) -> revconsapp(x2,C(x1,r)) revconsapp(N(),r) -> r revconsapp(V(n),r) -> r second(C(x1,x2)) -> x2 second(V(n)) -> N() - Signature: {deeprev/1,deeprevapp/2,first/1,goal/1,isEmptyT/1,isNotEmptyT/1,isVal/1,revconsapp/2,second/1} / {C/2 ,False/0,N/0,True/0,V/1} - Obligation: innermost runtime complexity wrt. defined symbols {deeprev,deeprevapp,first,goal,isEmptyT,isNotEmptyT,isVal ,revconsapp,second} and constructors {C,False,N,True,V} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: deeprevapp(y,z){y -> C(x,y)} = deeprevapp(C(x,y),z) ->^+ deeprevapp(y,C(x,z)) = C[deeprevapp(y,C(x,z)) = deeprevapp(y,z){z -> C(x,z)}] ** Step 1.b:1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: deeprev(C(x1,x2)) -> deeprevapp(C(x1,x2),N()) deeprev(N()) -> N() deeprev(V(n)) -> V(n) deeprevapp(C(x1,x2),rest) -> deeprevapp(x2,C(x1,rest)) deeprevapp(N(),rest) -> rest deeprevapp(V(n),rest) -> revconsapp(rest,V(n)) first(C(x1,x2)) -> x1 first(V(n)) -> N() goal(x) -> deeprev(x) isEmptyT(C(x1,x2)) -> False() isEmptyT(N()) -> True() isEmptyT(V(n)) -> False() isNotEmptyT(C(x1,x2)) -> True() isNotEmptyT(N()) -> False() isNotEmptyT(V(n)) -> False() isVal(C(x1,x2)) -> False() isVal(N()) -> False() isVal(V(n)) -> True() revconsapp(C(x1,x2),r) -> revconsapp(x2,C(x1,r)) revconsapp(N(),r) -> r revconsapp(V(n),r) -> r second(C(x1,x2)) -> x2 second(V(n)) -> N() - Signature: {deeprev/1,deeprevapp/2,first/1,goal/1,isEmptyT/1,isNotEmptyT/1,isVal/1,revconsapp/2,second/1} / {C/2 ,False/0,N/0,True/0,V/1} - Obligation: innermost runtime complexity wrt. defined symbols {deeprev,deeprevapp,first,goal,isEmptyT,isNotEmptyT,isVal ,revconsapp,second} and constructors {C,False,N,True,V} + Applied Processor: Ara {araHeuristics = NoHeuristics, minDegree = 1, maxDegree = 2, araTimeout = 5, araRuleShifting = Nothing} + Details: Signatures used: ---------------- C :: ["A"(11) x "A"(11)] -(11)-> "A"(11) C :: ["A"(9) x "A"(9)] -(9)-> "A"(9) C :: ["A"(15) x "A"(15)] -(15)-> "A"(15) C :: ["A"(14) x "A"(14)] -(14)-> "A"(14) C :: ["A"(7) x "A"(7)] -(7)-> "A"(7) C :: ["A"(8) x "A"(8)] -(8)-> "A"(8) C :: ["A"(3) x "A"(3)] -(3)-> "A"(3) False :: [] -(0)-> "A"(0) N :: [] -(0)-> "A"(11) N :: [] -(0)-> "A"(9) N :: [] -(0)-> "A"(14) N :: [] -(0)-> "A"(15) N :: [] -(0)-> "A"(7) N :: [] -(0)-> "A"(12) N :: [] -(0)-> "A"(1) N :: [] -(0)-> "A"(0) True :: [] -(0)-> "A"(0) V :: ["A"(0)] -(0)-> "A"(11) V :: ["A"(0)] -(0)-> "A"(9) V :: ["A"(0)] -(0)-> "A"(15) V :: ["A"(0)] -(0)-> "A"(14) V :: ["A"(0)] -(0)-> "A"(7) V :: ["A"(0)] -(0)-> "A"(6) deeprev :: ["A"(11)] -(14)-> "A"(1) deeprevapp :: ["A"(9) x "A"(8)] -(15)-> "A"(2) first :: ["A"(15)] -(8)-> "A"(0) goal :: ["A"(15)] -(16)-> "A"(1) isEmptyT :: ["A"(14)] -(10)-> "A"(0) isNotEmptyT :: ["A"(14)] -(10)-> "A"(0) isVal :: ["A"(15)] -(9)-> "A"(0) revconsapp :: ["A"(7) x "A"(3)] -(5)-> "A"(2) second :: ["A"(15)] -(8)-> "A"(12) Cost-free Signatures used: -------------------------- Base Constructor Signatures used: --------------------------------- "C_A" :: ["A"(1) x "A"(1)] -(1)-> "A"(1) "False_A" :: [] -(0)-> "A"(1) "N_A" :: [] -(0)-> "A"(1) "True_A" :: [] -(0)-> "A"(1) "V_A" :: ["A"(0)] -(0)-> "A"(1) WORST_CASE(Omega(n^1),O(n^1))