/export/starexec/sandbox/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES Problem: or(T(),T()) -> T() or(F(),T()) -> T() or(T(),F()) -> T() or(F(),F()) -> F() and(T(),B) -> B and(B,T()) -> B and(F(),B) -> F() and(B,F()) -> F() imp(T(),B) -> B imp(F(),B) -> T() not(T()) -> F() not(F()) -> T() if(T(),B1,B2) -> B1 if(F(),B1,B2) -> B2 eq(T(),T()) -> T() eq(F(),F()) -> T() eq(T(),F()) -> F() eq(F(),T()) -> F() eqt(nil(),undefined()) -> F() eqt(nil(),pid(N2)) -> F() eqt(nil(),int(N2)) -> F() eqt(nil(),cons(H2,T2)) -> F() eqt(nil(),tuple(H2,T2)) -> F() eqt(nil(),tuplenil(H2)) -> F() eqt(a(),nil()) -> F() eqt(a(),a()) -> T() eqt(a(),excl()) -> F() eqt(a(),false()) -> F() eqt(a(),lock()) -> F() eqt(a(),locker()) -> F() eqt(a(),mcrlrecord()) -> F() eqt(a(),ok()) -> F() eqt(a(),pending()) -> F() eqt(a(),release()) -> F() eqt(a(),request()) -> F() eqt(a(),resource()) -> F() eqt(a(),tag()) -> F() eqt(a(),true()) -> F() eqt(a(),undefined()) -> F() eqt(a(),pid(N2)) -> F() eqt(a(),int(N2)) -> F() eqt(a(),cons(H2,T2)) -> F() eqt(a(),tuple(H2,T2)) -> F() eqt(a(),tuplenil(H2)) -> F() eqt(excl(),nil()) -> F() eqt(excl(),a()) -> F() eqt(excl(),excl()) -> T() eqt(excl(),false()) -> F() eqt(excl(),lock()) -> F() eqt(excl(),locker()) -> F() eqt(excl(),mcrlrecord()) -> F() eqt(excl(),ok()) -> F() eqt(excl(),pending()) -> F() eqt(excl(),release()) -> F() eqt(excl(),request()) -> F() eqt(excl(),resource()) -> F() eqt(excl(),tag()) -> F() eqt(excl(),true()) -> F() eqt(excl(),undefined()) -> F() eqt(excl(),pid(N2)) -> F() eqt(excl(),eqt(false(),int(N2))) -> F() eqt(false(),cons(H2,T2)) -> F() eqt(false(),tuple(H2,T2)) -> F() eqt(false(),tuplenil(H2)) -> F() eqt(lock(),nil()) -> F() eqt(lock(),a()) -> F() eqt(lock(),excl()) -> F() eqt(lock(),false()) -> F() eqt(lock(),lock()) -> T() eqt(lock(),locker()) -> F() eqt(lock(),mcrlrecord()) -> F() eqt(lock(),ok()) -> F() eqt(lock(),pending()) -> F() eqt(lock(),release()) -> F() eqt(lock(),request()) -> F() eqt(lock(),resource()) -> F() eqt(lock(),tag()) -> F() eqt(lock(),true()) -> F() eqt(lock(),undefined()) -> F() eqt(lock(),pid(N2)) -> F() eqt(lock(),int(N2)) -> F() eqt(lock(),cons(H2,T2)) -> F() eqt(lock(),tuple(H2,T2)) -> F() eqt(lock(),tuplenil(H2)) -> F() eqt(locker(),nil()) -> F() eqt(locker(),a()) -> F() eqt(locker(),excl()) -> F() eqt(locker(),false()) -> F() eqt(locker(),lock()) -> F() eqt(locker(),locker()) -> T() eqt(locker(),mcrlrecord()) -> F() eqt(locker(),ok()) -> F() eqt(locker(),pending()) -> F() eqt(locker(),release()) -> F() eqt(locker(),request()) -> F() eqt(locker(),resource()) -> F() eqt(locker(),tag()) -> F() eqt(locker(),true()) -> F() eqt(locker(),undefined()) -> F() eqt(locker(),pid(N2)) -> F() eqt(locker(),int(N2)) -> F() eqt(locker(),cons(H2,T2)) -> F() eqt(locker(),tuple(H2,T2)) -> F() eqt(locker(),tuplenil(H2)) -> F() eqt(mcrlrecord(),nil()) -> F() eqt(mcrlrecord(),a()) -> F() eqt(mcrlrecord(),excl()) -> F() eqt(mcrlrecord(),false()) -> F() eqt(mcrlrecord(),lock()) -> F() eqt(mcrlrecord(),locker()) -> F() eqt(mcrlrecord(),mcrlrecord()) -> T() eqt(mcrlrecord(),ok()) -> F() eqt(mcrlrecord(),pending()) -> F() eqt(mcrlrecord(),release()) -> F() eqt(mcrlrecord(),request()) -> F() eqt(mcrlrecord(),resource()) -> F() eqt(ok(),resource()) -> F() eqt(ok(),tag()) -> F() eqt(ok(),true()) -> F() eqt(ok(),undefined()) -> F() eqt(ok(),pid(N2)) -> F() eqt(ok(),int(N2)) -> F() eqt(ok(),cons(H2,T2)) -> F() eqt(ok(),tuple(H2,T2)) -> F() eqt(ok(),tuplenil(H2)) -> F() eqt(pending(),nil()) -> F() eqt(pending(),a()) -> F() eqt(pending(),excl()) -> F() eqt(pending(),false()) -> F() eqt(pending(),lock()) -> F() eqt(pending(),locker()) -> F() eqt(pending(),mcrlrecord()) -> F() eqt(pending(),ok()) -> F() eqt(pending(),pending()) -> T() eqt(pending(),release()) -> F() eqt(pending(),request()) -> F() eqt(pending(),resource()) -> F() eqt(pending(),tag()) -> F() eqt(pending(),true()) -> F() eqt(pending(),undefined()) -> F() eqt(pending(),pid(N2)) -> F() eqt(pending(),int(N2)) -> F() eqt(pending(),cons(H2,T2)) -> F() eqt(pending(),tuple(H2,T2)) -> F() eqt(pending(),tuplenil(H2)) -> F() eqt(release(),nil()) -> F() eqt(release(),a()) -> F() eqt(release(),excl()) -> F() eqt(release(),false()) -> F() eqt(release(),lock()) -> F() eqt(release(),locker()) -> F() eqt(release(),mcrlrecord()) -> F() eqt(release(),ok()) -> F() eqt(request(),mcrlrecord()) -> F() eqt(request(),ok()) -> F() eqt(request(),pending()) -> F() eqt(request(),release()) -> F() eqt(request(),request()) -> T() eqt(request(),resource()) -> F() eqt(request(),tag()) -> F() eqt(request(),true()) -> F() eqt(request(),undefined()) -> F() eqt(request(),pid(N2)) -> F() eqt(request(),int(N2)) -> F() eqt(request(),cons(H2,T2)) -> F() eqt(request(),tuple(H2,T2)) -> F() eqt(request(),tuplenil(H2)) -> F() eqt(resource(),nil()) -> F() eqt(resource(),a()) -> F() eqt(resource(),excl()) -> F() eqt(resource(),false()) -> F() eqt(resource(),lock()) -> F() eqt(resource(),locker()) -> F() eqt(resource(),mcrlrecord()) -> F() eqt(resource(),ok()) -> F() eqt(resource(),pending()) -> F() eqt(resource(),release()) -> F() eqt(resource(),request()) -> F() eqt(resource(),resource()) -> T() eqt(resource(),tag()) -> F() eqt(resource(),true()) -> F() eqt(resource(),undefined()) -> F() eqt(resource(),pid(N2)) -> F() eqt(resource(),int(N2)) -> F() eqt(resource(),cons(H2,T2)) -> F() eqt(resource(),tuple(H2,T2)) -> F() eqt(resource(),tuplenil(H2)) -> F() eqt(tag(),nil()) -> F() eqt(tag(),a()) -> F() eqt(tag(),excl()) -> F() eqt(tag(),false()) -> F() eqt(tag(),lock()) -> F() eqt(tag(),locker()) -> F() eqt(tag(),mcrlrecord()) -> F() eqt(tag(),ok()) -> F() eqt(tag(),pending()) -> F() eqt(tag(),release()) -> F() eqt(tag(),request()) -> F() eqt(tag(),resource()) -> F() eqt(tag(),tag()) -> T() eqt(tag(),true()) -> F() eqt(tag(),undefined()) -> F() eqt(tag(),pid(N2)) -> F() eqt(tag(),int(N2)) -> F() eqt(tag(),cons(H2,T2)) -> F() eqt(tag(),tuple(H2,T2)) -> F() eqt(tag(),tuplenil(H2)) -> F() eqt(true(),nil()) -> F() eqt(true(),a()) -> F() eqt(true(),excl()) -> F() eqt(true(),false()) -> F() eqt(true(),lock()) -> F() eqt(true(),locker()) -> F() eqt(true(),mcrlrecord()) -> F() eqt(true(),ok()) -> F() eqt(true(),pending()) -> F() eqt(true(),release()) -> F() eqt(true(),request()) -> F() eqt(true(),resource()) -> F() eqt(true(),tag()) -> F() eqt(true(),true()) -> T() eqt(true(),undefined()) -> F() eqt(true(),pid(N2)) -> F() eqt(true(),int(N2)) -> F() eqt(true(),cons(H2,T2)) -> F() eqt(true(),tuple(H2,T2)) -> F() eqt(true(),tuplenil(H2)) -> F() eqt(undefined(),nil()) -> F() eqt(undefined(),a()) -> F() eqt(undefined(),tuplenil(H2)) -> F() eqt(pid(N1),nil()) -> F() eqt(pid(N1),a()) -> F() eqt(pid(N1),excl()) -> F() eqt(pid(N1),false()) -> F() eqt(pid(N1),lock()) -> F() eqt(pid(N1),locker()) -> F() eqt(pid(N1),mcrlrecord()) -> F() eqt(pid(N1),ok()) -> F() eqt(pid(N1),pending()) -> F() eqt(pid(N1),release()) -> F() eqt(pid(N1),request()) -> F() eqt(pid(N1),resource()) -> F() eqt(pid(N1),tag()) -> F() eqt(pid(N1),true()) -> F() eqt(pid(N1),undefined()) -> F() eqt(pid(N1),pid(N2)) -> eqt(N1,N2) eqt(pid(N1),int(N2)) -> F() eqt(pid(N1),cons(H2,T2)) -> F() eqt(pid(N1),tuple(H2,T2)) -> F() eqt(pid(N1),tuplenil(H2)) -> F() eqt(int(N1),nil()) -> F() eqt(int(N1),a()) -> F() eqt(int(N1),excl()) -> F() eqt(int(N1),false()) -> F() eqt(int(N1),lock()) -> F() eqt(int(N1),locker()) -> F() eqt(int(N1),mcrlrecord()) -> F() eqt(int(N1),ok()) -> F() eqt(int(N1),pending()) -> F() eqt(int(N1),release()) -> F() eqt(int(N1),request()) -> F() eqt(int(N1),resource()) -> F() eqt(int(N1),tag()) -> F() eqt(int(N1),true()) -> F() eqt(int(N1),undefined()) -> F() eqt(cons(H1,T1),resource()) -> F() eqt(cons(H1,T1),tag()) -> F() eqt(cons(H1,T1),true()) -> F() eqt(cons(H1,T1),undefined()) -> F() eqt(cons(H1,T1),pid(N2)) -> F() eqt(cons(H1,T1),int(N2)) -> F() eqt(cons(H1,T1),cons(H2,T2)) -> and(eqt(H1,H2),eqt(T1,T2)) eqt(cons(H1,T1),tuple(H2,T2)) -> F() eqt(cons(H1,T1),tuplenil(H2)) -> F() eqt(tuple(H1,T1),nil()) -> F() eqt(tuple(H1,T1),a()) -> F() eqt(tuple(H1,T1),excl()) -> F() eqt(tuple(H1,T1),false()) -> F() eqt(tuple(H1,T1),lock()) -> F() eqt(tuple(H1,T1),locker()) -> F() eqt(tuple(H1,T1),mcrlrecord()) -> F() eqt(tuple(H1,T1),ok()) -> F() eqt(tuple(H1,T1),pending()) -> F() eqt(tuple(H1,T1),release()) -> F() eqt(tuple(H1,T1),request()) -> F() eqt(tuple(H1,T1),resource()) -> F() eqt(tuple(H1,T1),tag()) -> F() eqt(tuple(H1,T1),true()) -> F() eqt(tuple(H1,T1),undefined()) -> F() eqt(tuple(H1,T1),pid(N2)) -> F() eqt(tuple(H1,T1),int(N2)) -> F() eqt(tuple(H1,T1),cons(H2,T2)) -> F() eqt(tuple(H1,T1),tuple(H2,T2)) -> and(eqt(H1,H2),eqt(T1,T2)) eqt(tuple(H1,T1),tuplenil(H2)) -> F() eqt(tuplenil(H1),nil()) -> F() eqt(tuplenil(H1),a()) -> F() eqt(tuplenil(H1),excl()) -> F() eqt(tuplenil(H1),false()) -> F() eqt(tuplenil(H1),lock()) -> F() eqt(tuplenil(H1),locker()) -> F() eqt(tuplenil(H1),mcrlrecord()) -> F() eqt(tuplenil(H1),ok()) -> F() eqt(tuplenil(H1),pending()) -> F() eqt(tuplenil(H1),release()) -> F() eqt(tuplenil(H1),request()) -> F() eqt(tuplenil(H1),resource()) -> F() eqt(tuplenil(H1),tag()) -> F() eqt(tuplenil(H1),true()) -> F() eqt(tuplenil(H1),undefined()) -> F() eqt(tuplenil(H1),pid(N2)) -> F() eqt(tuplenil(H1),int(N2)) -> F() eqt(tuplenil(H1),cons(H2,T2)) -> F() eqt(tuplenil(H1),tuple(H2,T2)) -> F() eqt(tuplenil(H1),tuplenil(H2)) -> eqt(H1,H2) element(int(s(0())),tuplenil(T1)) -> T1 element(int(s(0())),tuple(T1,T2)) -> T1 element(int(s(s(N1))),tuple(T1,T2)) -> element(int(s(N1)),T2) record_new(lock()) -> tuple(mcrlrecord(),tuple(lock(),tuple(undefined(),tuple(nil(),tuplenil(nil()))))) record_extract(tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))), lock(),resource()) -> tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))) record_update(tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))), lock(),pending(),NewF) -> tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(NewF))))) record_updates(Record,Name,nil()) -> Record record_updates(Record,Name,cons(tuple(Field,tuplenil(NewF)),Fields)) -> record_updates(record_update(Record,Name,Field,NewF),Name,Fields) locker2_map_promote_pending(nil(),Pending) -> nil() locker2_map_promote_pending(cons(Lock,Locks),Pending) -> cons(locker2_promote_pending(Lock,Pending),locker2_map_promote_pending(Locks,Pending)) locker2_map_claim_lock(nil(),Resources,Client) -> nil() locker2_map_claim_lock(cons(Lock,Locks),Resources,Client) -> cons(locker2_claim_lock(Lock,Resources,Client),locker2_map_claim_lock(Locks,Resources,Client)) locker2_map_add_pending(nil(),Resources,Client) -> nil() locker2_promote_pending(Lock,Client) -> case0(Client,Lock,record_extract(Lock,lock(),pending())) case0(Client,Lock,cons(Client,Pendings)) -> record_updates(Lock,lock(),cons(tuple(excl(),tuplenil(Client)),cons( tuple ( pending(),tuplenil(Pendings)), nil ()))) case0(Client,Lock,MCRLFree0) -> Lock locker2_remove_pending(Lock,Client) -> record_updates(Lock,lock(),cons(tuple(pending(),tuplenil(subtract(record_extract (Lock,lock(),pending()), cons (Client,nil())))), nil())) locker2_add_pending(Lock,Resources,Client) -> case1(Client,Resources,Lock,member(record_extract(Lock,lock(),resource()),Resources)) case1(Client,Resources,Lock,true()) -> record_updates(Lock,lock(),cons(tuple(pending(),tuplenil(append(record_extract (Lock,lock(),pending()), cons (Client,nil())))), nil())) case1(Client,Resources,Lock,false()) -> Lock locker2_release_lock(Lock,Client) -> case2(Client,Lock,gen_modtageq(Client,record_extract(Lock,lock(),excl()))) case2(Client,Lock,true()) -> record_updates(Lock,lock(),cons(tuple(excllock(),excl()),nil())) case4(Client,Lock,MCRLFree1) -> false() locker2_obtainables(nil(),Client) -> true() locker2_obtainables(cons(Lock,Locks),Client) -> case5(Client,Locks,Lock,member(Client,record_extract(Lock,lock(),pending()))) case5(Client,Locks,Lock,true()) -> andt(locker2_obtainable(Lock,Client),locker2_obtainables(Locks,Client)) case5(Client,Locks,Lock,false()) -> locker2_obtainables(Locks,Client) locker2_check_available(Resource,nil()) -> false() locker2_check_available(Resource,cons(Lock,Locks)) -> case6(Locks,Lock,Resource,equal(Resource,record_extract(Lock,lock(),resource()))) case6(Locks,Lock,Resource,true()) -> andt(equal(record_extract(Lock,lock(),excl()),nil()),equal(record_extract(Lock,lock(),pending()), nil())) case6(Locks,Lock,Resource,false()) -> locker2_check_available(Resource,Locks) locker2_check_availables(nil(),Locks) -> true() locker2_check_availables(cons(Resource,Resources),Locks) -> andt(locker2_check_available(Resource,Locks),locker2_check_availables(Resources,Locks)) locker2_adduniq(nil(),List) -> List append(cons(Head,Tail),List) -> cons(Head,append(Tail,List)) subtract(List,nil()) -> List subtract(List,cons(Head,Tail)) -> subtract(delete(Head,List),Tail) delete(E,nil()) -> nil() delete(E,cons(Head,Tail)) -> case8(Tail,Head,E,equal(E,Head)) case8(Tail,Head,E,true()) -> Tail case8(Tail,Head,E,false()) -> cons(Head,delete(E,Tail)) gen_tag(Pid) -> tuple(Pid,tuplenil(tag())) gen_modtageq(Client1,Client2) -> equal(Client1,Client2) member(E,nil()) -> false() member(E,cons(Head,Tail)) -> case9(Tail,Head,E,equal(E,Head)) case9(Tail,Head,E,true()) -> true() case9(Tail,Head,E,false()) -> member(E,Tail) eqs(empty(),empty()) -> T() eqs(empty(),stack(E2,S2)) -> F() eqs(stack(E1,S1),empty()) -> F() eqs(stack(E1,S1),stack(E2,S2)) -> and(eqt(E1,E2),eqs(S1,S2)) pushs(E1,S1) -> stack(E1,S1) pops(stack(E1,S1)) -> S1 tops(stack(E1,S1)) -> E1 istops(E1,empty()) -> F() istops(E1,stack(E2,S1)) -> eqt(E1,E2) eqc(nocalls(),nocalls()) -> T() eqc(nocalls(),calls(E2,S2,CS2)) -> F() eqc(calls(E1,S1,CS1),nocalls()) -> F() eqc(calls(E1,S1,CS1),calls(E2,S2,CS2)) -> and(eqt(E1,E2),and(eqs(S1,S2),eqc(CS1,CS2))) push(E1,E2,nocalls()) -> calls(E1,stack(E2,empty()),nocalls()) push(E1,E2,calls(E3,S1,CS1)) -> push1(E1,E2,E3,S1,CS1,eqt(E1,E3)) push1(E1,E2,E3,S1,CS1,T()) -> calls(E3,pushs(E2,S1),CS1) Proof: DP Processor: DPs: eqt#(pid(N1),pid(N2)) -> eqt#(N1,N2) eqt#(cons(H1,T1),cons(H2,T2)) -> eqt#(T1,T2) eqt#(cons(H1,T1),cons(H2,T2)) -> eqt#(H1,H2) eqt#(cons(H1,T1),cons(H2,T2)) -> and#(eqt(H1,H2),eqt(T1,T2)) eqt#(tuple(H1,T1),tuple(H2,T2)) -> eqt#(T1,T2) eqt#(tuple(H1,T1),tuple(H2,T2)) -> eqt#(H1,H2) eqt#(tuple(H1,T1),tuple(H2,T2)) -> and#(eqt(H1,H2),eqt(T1,T2)) eqt#(tuplenil(H1),tuplenil(H2)) -> eqt#(H1,H2) element#(int(s(s(N1))),tuple(T1,T2)) -> element#(int(s(N1)),T2) record_updates#(Record,Name,cons(tuple(Field,tuplenil(NewF)),Fields)) -> record_update#(Record,Name,Field,NewF) record_updates#(Record,Name,cons(tuple(Field,tuplenil(NewF)),Fields)) -> record_updates#(record_update(Record,Name,Field,NewF),Name,Fields) locker2_map_promote_pending#(cons(Lock,Locks),Pending) -> locker2_map_promote_pending#(Locks,Pending) locker2_map_promote_pending#(cons(Lock,Locks),Pending) -> locker2_promote_pending#(Lock,Pending) locker2_map_claim_lock#(cons(Lock,Locks),Resources,Client) -> locker2_map_claim_lock#(Locks,Resources,Client) locker2_promote_pending#(Lock,Client) -> record_extract#(Lock,lock(),pending()) locker2_promote_pending#(Lock,Client) -> case0#(Client,Lock,record_extract(Lock,lock(),pending())) case0#(Client,Lock,cons(Client,Pendings)) -> record_updates#(Lock,lock(),cons(tuple(excl(),tuplenil(Client)),cons (tuple ( pending(),tuplenil(Pendings)), nil ()))) locker2_remove_pending#(Lock,Client) -> record_extract#(Lock,lock(),pending()) locker2_remove_pending#(Lock,Client) -> subtract#(record_extract(Lock,lock(),pending()),cons(Client,nil())) locker2_remove_pending#(Lock,Client) -> record_updates#(Lock,lock(),cons(tuple(pending(),tuplenil(subtract (record_extract(Lock,lock(),pending()), cons(Client,nil())))), nil())) locker2_add_pending#(Lock,Resources,Client) -> record_extract#(Lock,lock(),resource()) locker2_add_pending#(Lock,Resources,Client) -> member#(record_extract(Lock,lock(),resource()),Resources) locker2_add_pending#(Lock,Resources,Client) -> case1#(Client,Resources,Lock,member(record_extract(Lock,lock(),resource()),Resources)) case1#(Client,Resources,Lock,true()) -> record_extract#(Lock,lock(),pending()) case1#(Client,Resources,Lock,true()) -> append#(record_extract(Lock,lock(),pending()),cons(Client,nil())) case1#(Client,Resources,Lock,true()) -> record_updates#(Lock,lock(),cons(tuple(pending(),tuplenil(append(record_extract ( Lock,lock(),pending()), cons (Client,nil())))), nil())) locker2_release_lock#(Lock,Client) -> record_extract#(Lock,lock(),excl()) locker2_release_lock#(Lock,Client) -> gen_modtageq#(Client,record_extract(Lock,lock(),excl())) locker2_release_lock#(Lock,Client) -> case2#(Client,Lock,gen_modtageq(Client,record_extract(Lock,lock(),excl()))) case2#(Client,Lock,true()) -> record_updates#(Lock,lock(),cons(tuple(excllock(),excl()),nil())) locker2_obtainables#(cons(Lock,Locks),Client) -> record_extract#(Lock,lock(),pending()) locker2_obtainables#(cons(Lock,Locks),Client) -> member#(Client,record_extract(Lock,lock(),pending())) locker2_obtainables#(cons(Lock,Locks),Client) -> case5#(Client,Locks,Lock,member(Client,record_extract(Lock,lock(),pending()))) case5#(Client,Locks,Lock,true()) -> locker2_obtainables#(Locks,Client) case5#(Client,Locks,Lock,false()) -> locker2_obtainables#(Locks,Client) locker2_check_available#(Resource,cons(Lock,Locks)) -> record_extract#(Lock,lock(),resource()) locker2_check_available#(Resource,cons(Lock,Locks)) -> case6#(Locks,Lock,Resource,equal(Resource,record_extract(Lock,lock(),resource()))) case6#(Locks,Lock,Resource,true()) -> record_extract#(Lock,lock(),pending()) case6#(Locks,Lock,Resource,true()) -> record_extract#(Lock,lock(),excl()) case6#(Locks,Lock,Resource,false()) -> locker2_check_available#(Resource,Locks) locker2_check_availables#(cons(Resource,Resources),Locks) -> locker2_check_availables#(Resources,Locks) locker2_check_availables#(cons(Resource,Resources),Locks) -> locker2_check_available#(Resource,Locks) append#(cons(Head,Tail),List) -> append#(Tail,List) subtract#(List,cons(Head,Tail)) -> delete#(Head,List) subtract#(List,cons(Head,Tail)) -> subtract#(delete(Head,List),Tail) delete#(E,cons(Head,Tail)) -> case8#(Tail,Head,E,equal(E,Head)) case8#(Tail,Head,E,false()) -> delete#(E,Tail) member#(E,cons(Head,Tail)) -> case9#(Tail,Head,E,equal(E,Head)) case9#(Tail,Head,E,false()) -> member#(E,Tail) eqs#(stack(E1,S1),stack(E2,S2)) -> eqs#(S1,S2) eqs#(stack(E1,S1),stack(E2,S2)) -> eqt#(E1,E2) eqs#(stack(E1,S1),stack(E2,S2)) -> and#(eqt(E1,E2),eqs(S1,S2)) istops#(E1,stack(E2,S1)) -> eqt#(E1,E2) eqc#(calls(E1,S1,CS1),calls(E2,S2,CS2)) -> eqc#(CS1,CS2) eqc#(calls(E1,S1,CS1),calls(E2,S2,CS2)) -> eqs#(S1,S2) eqc#(calls(E1,S1,CS1),calls(E2,S2,CS2)) -> and#(eqs(S1,S2),eqc(CS1,CS2)) eqc#(calls(E1,S1,CS1),calls(E2,S2,CS2)) -> eqt#(E1,E2) eqc#(calls(E1,S1,CS1),calls(E2,S2,CS2)) -> and#(eqt(E1,E2),and(eqs(S1,S2),eqc(CS1,CS2))) push#(E1,E2,calls(E3,S1,CS1)) -> eqt#(E1,E3) push#(E1,E2,calls(E3,S1,CS1)) -> push1#(E1,E2,E3,S1,CS1,eqt(E1,E3)) push1#(E1,E2,E3,S1,CS1,T()) -> pushs#(E2,S1) TRS: or(T(),T()) -> T() or(F(),T()) -> T() or(T(),F()) -> T() or(F(),F()) -> F() and(T(),B) -> B and(B,T()) -> B and(F(),B) -> F() and(B,F()) -> F() imp(T(),B) -> B imp(F(),B) -> T() not(T()) -> F() not(F()) -> T() if(T(),B1,B2) -> B1 if(F(),B1,B2) -> B2 eq(T(),T()) -> T() eq(F(),F()) -> T() eq(T(),F()) -> F() eq(F(),T()) -> F() eqt(nil(),undefined()) -> F() eqt(nil(),pid(N2)) -> F() eqt(nil(),int(N2)) -> F() eqt(nil(),cons(H2,T2)) -> F() eqt(nil(),tuple(H2,T2)) -> F() eqt(nil(),tuplenil(H2)) -> F() eqt(a(),nil()) -> F() eqt(a(),a()) -> T() eqt(a(),excl()) -> F() eqt(a(),false()) -> F() eqt(a(),lock()) -> F() eqt(a(),locker()) -> F() eqt(a(),mcrlrecord()) -> F() eqt(a(),ok()) -> F() eqt(a(),pending()) -> F() eqt(a(),release()) -> F() eqt(a(),request()) -> F() eqt(a(),resource()) -> F() eqt(a(),tag()) -> F() eqt(a(),true()) -> F() eqt(a(),undefined()) -> F() eqt(a(),pid(N2)) -> F() eqt(a(),int(N2)) -> F() eqt(a(),cons(H2,T2)) -> F() eqt(a(),tuple(H2,T2)) -> F() eqt(a(),tuplenil(H2)) -> F() eqt(excl(),nil()) -> F() eqt(excl(),a()) -> F() eqt(excl(),excl()) -> T() eqt(excl(),false()) -> F() eqt(excl(),lock()) -> F() eqt(excl(),locker()) -> F() eqt(excl(),mcrlrecord()) -> F() eqt(excl(),ok()) -> F() eqt(excl(),pending()) -> F() eqt(excl(),release()) -> F() eqt(excl(),request()) -> F() eqt(excl(),resource()) -> F() eqt(excl(),tag()) -> F() eqt(excl(),true()) -> F() eqt(excl(),undefined()) -> F() eqt(excl(),pid(N2)) -> F() eqt(excl(),eqt(false(),int(N2))) -> F() eqt(false(),cons(H2,T2)) -> F() eqt(false(),tuple(H2,T2)) -> F() eqt(false(),tuplenil(H2)) -> F() eqt(lock(),nil()) -> F() eqt(lock(),a()) -> F() eqt(lock(),excl()) -> F() eqt(lock(),false()) -> F() eqt(lock(),lock()) -> T() eqt(lock(),locker()) -> F() eqt(lock(),mcrlrecord()) -> F() eqt(lock(),ok()) -> F() eqt(lock(),pending()) -> F() eqt(lock(),release()) -> F() eqt(lock(),request()) -> F() eqt(lock(),resource()) -> F() eqt(lock(),tag()) -> F() eqt(lock(),true()) -> F() eqt(lock(),undefined()) -> F() eqt(lock(),pid(N2)) -> F() eqt(lock(),int(N2)) -> F() eqt(lock(),cons(H2,T2)) -> F() eqt(lock(),tuple(H2,T2)) -> F() eqt(lock(),tuplenil(H2)) -> F() eqt(locker(),nil()) -> F() eqt(locker(),a()) -> F() eqt(locker(),excl()) -> F() eqt(locker(),false()) -> F() eqt(locker(),lock()) -> F() eqt(locker(),locker()) -> T() eqt(locker(),mcrlrecord()) -> F() eqt(locker(),ok()) -> F() eqt(locker(),pending()) -> F() eqt(locker(),release()) -> F() eqt(locker(),request()) -> F() eqt(locker(),resource()) -> F() eqt(locker(),tag()) -> F() eqt(locker(),true()) -> F() eqt(locker(),undefined()) -> F() eqt(locker(),pid(N2)) -> F() eqt(locker(),int(N2)) -> F() eqt(locker(),cons(H2,T2)) -> F() eqt(locker(),tuple(H2,T2)) -> F() eqt(locker(),tuplenil(H2)) -> F() eqt(mcrlrecord(),nil()) -> F() eqt(mcrlrecord(),a()) -> F() eqt(mcrlrecord(),excl()) -> F() eqt(mcrlrecord(),false()) -> F() eqt(mcrlrecord(),lock()) -> F() eqt(mcrlrecord(),locker()) -> F() eqt(mcrlrecord(),mcrlrecord()) -> T() eqt(mcrlrecord(),ok()) -> F() eqt(mcrlrecord(),pending()) -> F() eqt(mcrlrecord(),release()) -> F() eqt(mcrlrecord(),request()) -> F() eqt(mcrlrecord(),resource()) -> F() eqt(ok(),resource()) -> F() eqt(ok(),tag()) -> F() eqt(ok(),true()) -> F() eqt(ok(),undefined()) -> F() eqt(ok(),pid(N2)) -> F() eqt(ok(),int(N2)) -> F() eqt(ok(),cons(H2,T2)) -> F() eqt(ok(),tuple(H2,T2)) -> F() eqt(ok(),tuplenil(H2)) -> F() eqt(pending(),nil()) -> F() eqt(pending(),a()) -> F() eqt(pending(),excl()) -> F() eqt(pending(),false()) -> F() eqt(pending(),lock()) -> F() eqt(pending(),locker()) -> F() eqt(pending(),mcrlrecord()) -> F() eqt(pending(),ok()) -> F() eqt(pending(),pending()) -> T() eqt(pending(),release()) -> F() eqt(pending(),request()) -> F() eqt(pending(),resource()) -> F() eqt(pending(),tag()) -> F() eqt(pending(),true()) -> F() eqt(pending(),undefined()) -> F() eqt(pending(),pid(N2)) -> F() eqt(pending(),int(N2)) -> F() eqt(pending(),cons(H2,T2)) -> F() eqt(pending(),tuple(H2,T2)) -> F() eqt(pending(),tuplenil(H2)) -> F() eqt(release(),nil()) -> F() eqt(release(),a()) -> F() eqt(release(),excl()) -> F() eqt(release(),false()) -> F() eqt(release(),lock()) -> F() eqt(release(),locker()) -> F() eqt(release(),mcrlrecord()) -> F() eqt(release(),ok()) -> F() eqt(request(),mcrlrecord()) -> F() eqt(request(),ok()) -> F() eqt(request(),pending()) -> F() eqt(request(),release()) -> F() eqt(request(),request()) -> T() eqt(request(),resource()) -> F() eqt(request(),tag()) -> F() eqt(request(),true()) -> F() eqt(request(),undefined()) -> F() eqt(request(),pid(N2)) -> F() eqt(request(),int(N2)) -> F() eqt(request(),cons(H2,T2)) -> F() eqt(request(),tuple(H2,T2)) -> F() eqt(request(),tuplenil(H2)) -> F() eqt(resource(),nil()) -> F() eqt(resource(),a()) -> F() eqt(resource(),excl()) -> F() eqt(resource(),false()) -> F() eqt(resource(),lock()) -> F() eqt(resource(),locker()) -> F() eqt(resource(),mcrlrecord()) -> F() eqt(resource(),ok()) -> F() eqt(resource(),pending()) -> F() eqt(resource(),release()) -> F() eqt(resource(),request()) -> F() eqt(resource(),resource()) -> T() eqt(resource(),tag()) -> F() eqt(resource(),true()) -> F() eqt(resource(),undefined()) -> F() eqt(resource(),pid(N2)) -> F() eqt(resource(),int(N2)) -> F() eqt(resource(),cons(H2,T2)) -> F() eqt(resource(),tuple(H2,T2)) -> F() eqt(resource(),tuplenil(H2)) -> F() eqt(tag(),nil()) -> F() eqt(tag(),a()) -> F() eqt(tag(),excl()) -> F() eqt(tag(),false()) -> F() eqt(tag(),lock()) -> F() eqt(tag(),locker()) -> F() eqt(tag(),mcrlrecord()) -> F() eqt(tag(),ok()) -> F() eqt(tag(),pending()) -> F() eqt(tag(),release()) -> F() eqt(tag(),request()) -> F() eqt(tag(),resource()) -> F() eqt(tag(),tag()) -> T() eqt(tag(),true()) -> F() eqt(tag(),undefined()) -> F() eqt(tag(),pid(N2)) -> F() eqt(tag(),int(N2)) -> F() eqt(tag(),cons(H2,T2)) -> F() eqt(tag(),tuple(H2,T2)) -> F() eqt(tag(),tuplenil(H2)) -> F() eqt(true(),nil()) -> F() eqt(true(),a()) -> F() eqt(true(),excl()) -> F() eqt(true(),false()) -> F() eqt(true(),lock()) -> F() eqt(true(),locker()) -> F() eqt(true(),mcrlrecord()) -> F() eqt(true(),ok()) -> F() eqt(true(),pending()) -> F() eqt(true(),release()) -> F() eqt(true(),request()) -> F() eqt(true(),resource()) -> F() eqt(true(),tag()) -> F() eqt(true(),true()) -> T() eqt(true(),undefined()) -> F() eqt(true(),pid(N2)) -> F() eqt(true(),int(N2)) -> F() eqt(true(),cons(H2,T2)) -> F() eqt(true(),tuple(H2,T2)) -> F() eqt(true(),tuplenil(H2)) -> F() eqt(undefined(),nil()) -> F() eqt(undefined(),a()) -> F() eqt(undefined(),tuplenil(H2)) -> F() eqt(pid(N1),nil()) -> F() eqt(pid(N1),a()) -> F() eqt(pid(N1),excl()) -> F() eqt(pid(N1),false()) -> F() eqt(pid(N1),lock()) -> F() eqt(pid(N1),locker()) -> F() eqt(pid(N1),mcrlrecord()) -> F() eqt(pid(N1),ok()) -> F() eqt(pid(N1),pending()) -> F() eqt(pid(N1),release()) -> F() eqt(pid(N1),request()) -> F() eqt(pid(N1),resource()) -> F() eqt(pid(N1),tag()) -> F() eqt(pid(N1),true()) -> F() eqt(pid(N1),undefined()) -> F() eqt(pid(N1),pid(N2)) -> eqt(N1,N2) eqt(pid(N1),int(N2)) -> F() eqt(pid(N1),cons(H2,T2)) -> F() eqt(pid(N1),tuple(H2,T2)) -> F() eqt(pid(N1),tuplenil(H2)) -> F() eqt(int(N1),nil()) -> F() eqt(int(N1),a()) -> F() eqt(int(N1),excl()) -> F() eqt(int(N1),false()) -> F() eqt(int(N1),lock()) -> F() eqt(int(N1),locker()) -> F() eqt(int(N1),mcrlrecord()) -> F() eqt(int(N1),ok()) -> F() eqt(int(N1),pending()) -> F() eqt(int(N1),release()) -> F() eqt(int(N1),request()) -> F() eqt(int(N1),resource()) -> F() eqt(int(N1),tag()) -> F() eqt(int(N1),true()) -> F() eqt(int(N1),undefined()) -> F() eqt(cons(H1,T1),resource()) -> F() eqt(cons(H1,T1),tag()) -> F() eqt(cons(H1,T1),true()) -> F() eqt(cons(H1,T1),undefined()) -> F() eqt(cons(H1,T1),pid(N2)) -> F() eqt(cons(H1,T1),int(N2)) -> F() eqt(cons(H1,T1),cons(H2,T2)) -> and(eqt(H1,H2),eqt(T1,T2)) eqt(cons(H1,T1),tuple(H2,T2)) -> F() eqt(cons(H1,T1),tuplenil(H2)) -> F() eqt(tuple(H1,T1),nil()) -> F() eqt(tuple(H1,T1),a()) -> F() eqt(tuple(H1,T1),excl()) -> F() eqt(tuple(H1,T1),false()) -> F() eqt(tuple(H1,T1),lock()) -> F() eqt(tuple(H1,T1),locker()) -> F() eqt(tuple(H1,T1),mcrlrecord()) -> F() eqt(tuple(H1,T1),ok()) -> F() eqt(tuple(H1,T1),pending()) -> F() eqt(tuple(H1,T1),release()) -> F() eqt(tuple(H1,T1),request()) -> F() eqt(tuple(H1,T1),resource()) -> F() eqt(tuple(H1,T1),tag()) -> F() eqt(tuple(H1,T1),true()) -> F() eqt(tuple(H1,T1),undefined()) -> F() eqt(tuple(H1,T1),pid(N2)) -> F() eqt(tuple(H1,T1),int(N2)) -> F() eqt(tuple(H1,T1),cons(H2,T2)) -> F() eqt(tuple(H1,T1),tuple(H2,T2)) -> and(eqt(H1,H2),eqt(T1,T2)) eqt(tuple(H1,T1),tuplenil(H2)) -> F() eqt(tuplenil(H1),nil()) -> F() eqt(tuplenil(H1),a()) -> F() eqt(tuplenil(H1),excl()) -> F() eqt(tuplenil(H1),false()) -> F() eqt(tuplenil(H1),lock()) -> F() eqt(tuplenil(H1),locker()) -> F() eqt(tuplenil(H1),mcrlrecord()) -> F() eqt(tuplenil(H1),ok()) -> F() eqt(tuplenil(H1),pending()) -> F() eqt(tuplenil(H1),release()) -> F() eqt(tuplenil(H1),request()) -> F() eqt(tuplenil(H1),resource()) -> F() eqt(tuplenil(H1),tag()) -> F() eqt(tuplenil(H1),true()) -> F() eqt(tuplenil(H1),undefined()) -> F() eqt(tuplenil(H1),pid(N2)) -> F() eqt(tuplenil(H1),int(N2)) -> F() eqt(tuplenil(H1),cons(H2,T2)) -> F() eqt(tuplenil(H1),tuple(H2,T2)) -> F() eqt(tuplenil(H1),tuplenil(H2)) -> eqt(H1,H2) element(int(s(0())),tuplenil(T1)) -> T1 element(int(s(0())),tuple(T1,T2)) -> T1 element(int(s(s(N1))),tuple(T1,T2)) -> element(int(s(N1)),T2) record_new(lock()) -> tuple(mcrlrecord(),tuple(lock(),tuple(undefined(),tuple(nil(),tuplenil(nil()))))) record_extract(tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))), lock(),resource()) -> tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))) record_update(tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))), lock(),pending(),NewF) -> tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(NewF))))) record_updates(Record,Name,nil()) -> Record record_updates(Record,Name,cons(tuple(Field,tuplenil(NewF)),Fields)) -> record_updates(record_update(Record,Name,Field,NewF),Name,Fields) locker2_map_promote_pending(nil(),Pending) -> nil() locker2_map_promote_pending(cons(Lock,Locks),Pending) -> cons(locker2_promote_pending(Lock,Pending),locker2_map_promote_pending(Locks,Pending)) locker2_map_claim_lock(nil(),Resources,Client) -> nil() locker2_map_claim_lock(cons(Lock,Locks),Resources,Client) -> cons(locker2_claim_lock(Lock,Resources,Client),locker2_map_claim_lock(Locks,Resources,Client)) locker2_map_add_pending(nil(),Resources,Client) -> nil() locker2_promote_pending(Lock,Client) -> case0(Client,Lock,record_extract(Lock,lock(),pending())) case0(Client,Lock,cons(Client,Pendings)) -> record_updates(Lock,lock(),cons(tuple(excl(),tuplenil(Client)),cons (tuple (pending(),tuplenil(Pendings)), nil ()))) case0(Client,Lock,MCRLFree0) -> Lock locker2_remove_pending(Lock,Client) -> record_updates(Lock,lock(),cons(tuple(pending(),tuplenil(subtract( record_extract ( Lock,lock(),pending()), cons (Client,nil())))), nil())) locker2_add_pending(Lock,Resources,Client) -> case1(Client,Resources,Lock,member(record_extract(Lock,lock(),resource()),Resources)) case1(Client,Resources,Lock,true()) -> record_updates(Lock,lock(),cons(tuple(pending(),tuplenil(append(record_extract (Lock,lock(),pending()), cons (Client,nil())))), nil())) case1(Client,Resources,Lock,false()) -> Lock locker2_release_lock(Lock,Client) -> case2(Client,Lock,gen_modtageq(Client,record_extract(Lock,lock(),excl()))) case2(Client,Lock,true()) -> record_updates(Lock,lock(),cons(tuple(excllock(),excl()),nil())) case4(Client,Lock,MCRLFree1) -> false() locker2_obtainables(nil(),Client) -> true() locker2_obtainables(cons(Lock,Locks),Client) -> case5(Client,Locks,Lock,member(Client,record_extract(Lock,lock(),pending()))) case5(Client,Locks,Lock,true()) -> andt(locker2_obtainable(Lock,Client),locker2_obtainables(Locks,Client)) case5(Client,Locks,Lock,false()) -> locker2_obtainables(Locks,Client) locker2_check_available(Resource,nil()) -> false() locker2_check_available(Resource,cons(Lock,Locks)) -> case6(Locks,Lock,Resource,equal(Resource,record_extract(Lock,lock(),resource()))) case6(Locks,Lock,Resource,true()) -> andt(equal(record_extract(Lock,lock(),excl()),nil()),equal(record_extract(Lock,lock(),pending()), nil())) case6(Locks,Lock,Resource,false()) -> locker2_check_available(Resource,Locks) locker2_check_availables(nil(),Locks) -> true() locker2_check_availables(cons(Resource,Resources),Locks) -> andt(locker2_check_available(Resource,Locks),locker2_check_availables(Resources,Locks)) locker2_adduniq(nil(),List) -> List append(cons(Head,Tail),List) -> cons(Head,append(Tail,List)) subtract(List,nil()) -> List subtract(List,cons(Head,Tail)) -> subtract(delete(Head,List),Tail) delete(E,nil()) -> nil() delete(E,cons(Head,Tail)) -> case8(Tail,Head,E,equal(E,Head)) case8(Tail,Head,E,true()) -> Tail case8(Tail,Head,E,false()) -> cons(Head,delete(E,Tail)) gen_tag(Pid) -> tuple(Pid,tuplenil(tag())) gen_modtageq(Client1,Client2) -> equal(Client1,Client2) member(E,nil()) -> false() member(E,cons(Head,Tail)) -> case9(Tail,Head,E,equal(E,Head)) case9(Tail,Head,E,true()) -> true() case9(Tail,Head,E,false()) -> member(E,Tail) eqs(empty(),empty()) -> T() eqs(empty(),stack(E2,S2)) -> F() eqs(stack(E1,S1),empty()) -> F() eqs(stack(E1,S1),stack(E2,S2)) -> and(eqt(E1,E2),eqs(S1,S2)) pushs(E1,S1) -> stack(E1,S1) pops(stack(E1,S1)) -> S1 tops(stack(E1,S1)) -> E1 istops(E1,empty()) -> F() istops(E1,stack(E2,S1)) -> eqt(E1,E2) eqc(nocalls(),nocalls()) -> T() eqc(nocalls(),calls(E2,S2,CS2)) -> F() eqc(calls(E1,S1,CS1),nocalls()) -> F() eqc(calls(E1,S1,CS1),calls(E2,S2,CS2)) -> and(eqt(E1,E2),and(eqs(S1,S2),eqc(CS1,CS2))) push(E1,E2,nocalls()) -> calls(E1,stack(E2,empty()),nocalls()) push(E1,E2,calls(E3,S1,CS1)) -> push1(E1,E2,E3,S1,CS1,eqt(E1,E3)) push1(E1,E2,E3,S1,CS1,T()) -> calls(E3,pushs(E2,S1),CS1) TDG Processor: DPs: eqt#(pid(N1),pid(N2)) -> eqt#(N1,N2) eqt#(cons(H1,T1),cons(H2,T2)) -> eqt#(T1,T2) eqt#(cons(H1,T1),cons(H2,T2)) -> eqt#(H1,H2) eqt#(cons(H1,T1),cons(H2,T2)) -> and#(eqt(H1,H2),eqt(T1,T2)) eqt#(tuple(H1,T1),tuple(H2,T2)) -> eqt#(T1,T2) eqt#(tuple(H1,T1),tuple(H2,T2)) -> eqt#(H1,H2) eqt#(tuple(H1,T1),tuple(H2,T2)) -> and#(eqt(H1,H2),eqt(T1,T2)) eqt#(tuplenil(H1),tuplenil(H2)) -> eqt#(H1,H2) element#(int(s(s(N1))),tuple(T1,T2)) -> element#(int(s(N1)),T2) record_updates#(Record,Name,cons(tuple(Field,tuplenil(NewF)),Fields)) -> record_update#(Record,Name,Field,NewF) record_updates#(Record,Name,cons(tuple(Field,tuplenil(NewF)),Fields)) -> record_updates#(record_update(Record,Name,Field,NewF),Name,Fields) locker2_map_promote_pending#(cons(Lock,Locks),Pending) -> locker2_map_promote_pending#(Locks,Pending) locker2_map_promote_pending#(cons(Lock,Locks),Pending) -> locker2_promote_pending#(Lock,Pending) locker2_map_claim_lock#(cons(Lock,Locks),Resources,Client) -> locker2_map_claim_lock#(Locks,Resources,Client) locker2_promote_pending#(Lock,Client) -> record_extract#(Lock,lock(),pending()) locker2_promote_pending#(Lock,Client) -> case0#(Client,Lock,record_extract(Lock,lock(),pending())) case0#(Client,Lock,cons(Client,Pendings)) -> record_updates#(Lock,lock(),cons(tuple(excl(),tuplenil(Client)),cons ( tuple ( pending(),tuplenil(Pendings)), nil ()))) locker2_remove_pending#(Lock,Client) -> record_extract#(Lock,lock(),pending()) locker2_remove_pending#(Lock,Client) -> subtract#(record_extract(Lock,lock(),pending()),cons(Client,nil())) locker2_remove_pending#(Lock,Client) -> record_updates#(Lock,lock(),cons(tuple(pending(),tuplenil(subtract (record_extract (Lock,lock(),pending()), cons(Client,nil())))), nil())) locker2_add_pending#(Lock,Resources,Client) -> record_extract#(Lock,lock(),resource()) locker2_add_pending#(Lock,Resources,Client) -> member#(record_extract(Lock,lock(),resource()),Resources) locker2_add_pending#(Lock,Resources,Client) -> case1#(Client,Resources,Lock,member(record_extract(Lock,lock(),resource()),Resources)) case1#(Client,Resources,Lock,true()) -> record_extract#(Lock,lock(),pending()) case1#(Client,Resources,Lock,true()) -> append#(record_extract(Lock,lock(),pending()),cons(Client,nil())) case1#(Client,Resources,Lock,true()) -> record_updates#(Lock,lock(),cons(tuple(pending(),tuplenil(append( record_extract ( Lock,lock(),pending()), cons (Client,nil())))), nil())) locker2_release_lock#(Lock,Client) -> record_extract#(Lock,lock(),excl()) locker2_release_lock#(Lock,Client) -> gen_modtageq#(Client,record_extract(Lock,lock(),excl())) locker2_release_lock#(Lock,Client) -> case2#(Client,Lock,gen_modtageq(Client,record_extract(Lock,lock(),excl()))) case2#(Client,Lock,true()) -> record_updates#(Lock,lock(),cons(tuple(excllock(),excl()),nil())) locker2_obtainables#(cons(Lock,Locks),Client) -> record_extract#(Lock,lock(),pending()) locker2_obtainables#(cons(Lock,Locks),Client) -> member#(Client,record_extract(Lock,lock(),pending())) locker2_obtainables#(cons(Lock,Locks),Client) -> case5#(Client,Locks,Lock,member(Client,record_extract(Lock,lock(),pending()))) case5#(Client,Locks,Lock,true()) -> locker2_obtainables#(Locks,Client) case5#(Client,Locks,Lock,false()) -> locker2_obtainables#(Locks,Client) locker2_check_available#(Resource,cons(Lock,Locks)) -> record_extract#(Lock,lock(),resource()) locker2_check_available#(Resource,cons(Lock,Locks)) -> case6#(Locks,Lock,Resource,equal(Resource,record_extract(Lock,lock(),resource()))) case6#(Locks,Lock,Resource,true()) -> record_extract#(Lock,lock(),pending()) case6#(Locks,Lock,Resource,true()) -> record_extract#(Lock,lock(),excl()) case6#(Locks,Lock,Resource,false()) -> locker2_check_available#(Resource,Locks) locker2_check_availables#(cons(Resource,Resources),Locks) -> locker2_check_availables#(Resources,Locks) locker2_check_availables#(cons(Resource,Resources),Locks) -> locker2_check_available#(Resource,Locks) append#(cons(Head,Tail),List) -> append#(Tail,List) subtract#(List,cons(Head,Tail)) -> delete#(Head,List) subtract#(List,cons(Head,Tail)) -> subtract#(delete(Head,List),Tail) delete#(E,cons(Head,Tail)) -> case8#(Tail,Head,E,equal(E,Head)) case8#(Tail,Head,E,false()) -> delete#(E,Tail) member#(E,cons(Head,Tail)) -> case9#(Tail,Head,E,equal(E,Head)) case9#(Tail,Head,E,false()) -> member#(E,Tail) eqs#(stack(E1,S1),stack(E2,S2)) -> eqs#(S1,S2) eqs#(stack(E1,S1),stack(E2,S2)) -> eqt#(E1,E2) eqs#(stack(E1,S1),stack(E2,S2)) -> and#(eqt(E1,E2),eqs(S1,S2)) istops#(E1,stack(E2,S1)) -> eqt#(E1,E2) eqc#(calls(E1,S1,CS1),calls(E2,S2,CS2)) -> eqc#(CS1,CS2) eqc#(calls(E1,S1,CS1),calls(E2,S2,CS2)) -> eqs#(S1,S2) eqc#(calls(E1,S1,CS1),calls(E2,S2,CS2)) -> and#(eqs(S1,S2),eqc(CS1,CS2)) eqc#(calls(E1,S1,CS1),calls(E2,S2,CS2)) -> eqt#(E1,E2) eqc#(calls(E1,S1,CS1),calls(E2,S2,CS2)) -> and#(eqt(E1,E2),and(eqs(S1,S2),eqc(CS1,CS2))) push#(E1,E2,calls(E3,S1,CS1)) -> eqt#(E1,E3) push#(E1,E2,calls(E3,S1,CS1)) -> push1#(E1,E2,E3,S1,CS1,eqt(E1,E3)) push1#(E1,E2,E3,S1,CS1,T()) -> pushs#(E2,S1) TRS: or(T(),T()) -> T() or(F(),T()) -> T() or(T(),F()) -> T() or(F(),F()) -> F() and(T(),B) -> B and(B,T()) -> B and(F(),B) -> F() and(B,F()) -> F() imp(T(),B) -> B imp(F(),B) -> T() not(T()) -> F() not(F()) -> T() if(T(),B1,B2) -> B1 if(F(),B1,B2) -> B2 eq(T(),T()) -> T() eq(F(),F()) -> T() eq(T(),F()) -> F() eq(F(),T()) -> F() eqt(nil(),undefined()) -> F() eqt(nil(),pid(N2)) -> F() eqt(nil(),int(N2)) -> F() eqt(nil(),cons(H2,T2)) -> F() eqt(nil(),tuple(H2,T2)) -> F() eqt(nil(),tuplenil(H2)) -> F() eqt(a(),nil()) -> F() eqt(a(),a()) -> T() eqt(a(),excl()) -> F() eqt(a(),false()) -> F() eqt(a(),lock()) -> F() eqt(a(),locker()) -> F() eqt(a(),mcrlrecord()) -> F() eqt(a(),ok()) -> F() eqt(a(),pending()) -> F() eqt(a(),release()) -> F() eqt(a(),request()) -> F() eqt(a(),resource()) -> F() eqt(a(),tag()) -> F() eqt(a(),true()) -> F() eqt(a(),undefined()) -> F() eqt(a(),pid(N2)) -> F() eqt(a(),int(N2)) -> F() eqt(a(),cons(H2,T2)) -> F() eqt(a(),tuple(H2,T2)) -> F() eqt(a(),tuplenil(H2)) -> F() eqt(excl(),nil()) -> F() eqt(excl(),a()) -> F() eqt(excl(),excl()) -> T() eqt(excl(),false()) -> F() eqt(excl(),lock()) -> F() eqt(excl(),locker()) -> F() eqt(excl(),mcrlrecord()) -> F() eqt(excl(),ok()) -> F() eqt(excl(),pending()) -> F() eqt(excl(),release()) -> F() eqt(excl(),request()) -> F() eqt(excl(),resource()) -> F() eqt(excl(),tag()) -> F() eqt(excl(),true()) -> F() eqt(excl(),undefined()) -> F() eqt(excl(),pid(N2)) -> F() eqt(excl(),eqt(false(),int(N2))) -> F() eqt(false(),cons(H2,T2)) -> F() eqt(false(),tuple(H2,T2)) -> F() eqt(false(),tuplenil(H2)) -> F() eqt(lock(),nil()) -> F() eqt(lock(),a()) -> F() eqt(lock(),excl()) -> F() eqt(lock(),false()) -> F() eqt(lock(),lock()) -> T() eqt(lock(),locker()) -> F() eqt(lock(),mcrlrecord()) -> F() eqt(lock(),ok()) -> F() eqt(lock(),pending()) -> F() eqt(lock(),release()) -> F() eqt(lock(),request()) -> F() eqt(lock(),resource()) -> F() eqt(lock(),tag()) -> F() eqt(lock(),true()) -> F() eqt(lock(),undefined()) -> F() eqt(lock(),pid(N2)) -> F() eqt(lock(),int(N2)) -> F() eqt(lock(),cons(H2,T2)) -> F() eqt(lock(),tuple(H2,T2)) -> F() eqt(lock(),tuplenil(H2)) -> F() eqt(locker(),nil()) -> F() eqt(locker(),a()) -> F() eqt(locker(),excl()) -> F() eqt(locker(),false()) -> F() eqt(locker(),lock()) -> F() eqt(locker(),locker()) -> T() eqt(locker(),mcrlrecord()) -> F() eqt(locker(),ok()) -> F() eqt(locker(),pending()) -> F() eqt(locker(),release()) -> F() eqt(locker(),request()) -> F() eqt(locker(),resource()) -> F() eqt(locker(),tag()) -> F() eqt(locker(),true()) -> F() eqt(locker(),undefined()) -> F() eqt(locker(),pid(N2)) -> F() eqt(locker(),int(N2)) -> F() eqt(locker(),cons(H2,T2)) -> F() eqt(locker(),tuple(H2,T2)) -> F() eqt(locker(),tuplenil(H2)) -> F() eqt(mcrlrecord(),nil()) -> F() eqt(mcrlrecord(),a()) -> F() eqt(mcrlrecord(),excl()) -> F() eqt(mcrlrecord(),false()) -> F() eqt(mcrlrecord(),lock()) -> F() eqt(mcrlrecord(),locker()) -> F() eqt(mcrlrecord(),mcrlrecord()) -> T() eqt(mcrlrecord(),ok()) -> F() eqt(mcrlrecord(),pending()) -> F() eqt(mcrlrecord(),release()) -> F() eqt(mcrlrecord(),request()) -> F() eqt(mcrlrecord(),resource()) -> F() eqt(ok(),resource()) -> F() eqt(ok(),tag()) -> F() eqt(ok(),true()) -> F() eqt(ok(),undefined()) -> F() eqt(ok(),pid(N2)) -> F() eqt(ok(),int(N2)) -> F() eqt(ok(),cons(H2,T2)) -> F() eqt(ok(),tuple(H2,T2)) -> F() eqt(ok(),tuplenil(H2)) -> F() eqt(pending(),nil()) -> F() eqt(pending(),a()) -> F() eqt(pending(),excl()) -> F() eqt(pending(),false()) -> F() eqt(pending(),lock()) -> F() eqt(pending(),locker()) -> F() eqt(pending(),mcrlrecord()) -> F() eqt(pending(),ok()) -> F() eqt(pending(),pending()) -> T() eqt(pending(),release()) -> F() eqt(pending(),request()) -> F() eqt(pending(),resource()) -> F() eqt(pending(),tag()) -> F() eqt(pending(),true()) -> F() eqt(pending(),undefined()) -> F() eqt(pending(),pid(N2)) -> F() eqt(pending(),int(N2)) -> F() eqt(pending(),cons(H2,T2)) -> F() eqt(pending(),tuple(H2,T2)) -> F() eqt(pending(),tuplenil(H2)) -> F() eqt(release(),nil()) -> F() eqt(release(),a()) -> F() eqt(release(),excl()) -> F() eqt(release(),false()) -> F() eqt(release(),lock()) -> F() eqt(release(),locker()) -> F() eqt(release(),mcrlrecord()) -> F() eqt(release(),ok()) -> F() eqt(request(),mcrlrecord()) -> F() eqt(request(),ok()) -> F() eqt(request(),pending()) -> F() eqt(request(),release()) -> F() eqt(request(),request()) -> T() eqt(request(),resource()) -> F() eqt(request(),tag()) -> F() eqt(request(),true()) -> F() eqt(request(),undefined()) -> F() eqt(request(),pid(N2)) -> F() eqt(request(),int(N2)) -> F() eqt(request(),cons(H2,T2)) -> F() eqt(request(),tuple(H2,T2)) -> F() eqt(request(),tuplenil(H2)) -> F() eqt(resource(),nil()) -> F() eqt(resource(),a()) -> F() eqt(resource(),excl()) -> F() eqt(resource(),false()) -> F() eqt(resource(),lock()) -> F() eqt(resource(),locker()) -> F() eqt(resource(),mcrlrecord()) -> F() eqt(resource(),ok()) -> F() eqt(resource(),pending()) -> F() eqt(resource(),release()) -> F() eqt(resource(),request()) -> F() eqt(resource(),resource()) -> T() eqt(resource(),tag()) -> F() eqt(resource(),true()) -> F() eqt(resource(),undefined()) -> F() eqt(resource(),pid(N2)) -> F() eqt(resource(),int(N2)) -> F() eqt(resource(),cons(H2,T2)) -> F() eqt(resource(),tuple(H2,T2)) -> F() eqt(resource(),tuplenil(H2)) -> F() eqt(tag(),nil()) -> F() eqt(tag(),a()) -> F() eqt(tag(),excl()) -> F() eqt(tag(),false()) -> F() eqt(tag(),lock()) -> F() eqt(tag(),locker()) -> F() eqt(tag(),mcrlrecord()) -> F() eqt(tag(),ok()) -> F() eqt(tag(),pending()) -> F() eqt(tag(),release()) -> F() eqt(tag(),request()) -> F() eqt(tag(),resource()) -> F() eqt(tag(),tag()) -> T() eqt(tag(),true()) -> F() eqt(tag(),undefined()) -> F() eqt(tag(),pid(N2)) -> F() eqt(tag(),int(N2)) -> F() eqt(tag(),cons(H2,T2)) -> F() eqt(tag(),tuple(H2,T2)) -> F() eqt(tag(),tuplenil(H2)) -> F() eqt(true(),nil()) -> F() eqt(true(),a()) -> F() eqt(true(),excl()) -> F() eqt(true(),false()) -> F() eqt(true(),lock()) -> F() eqt(true(),locker()) -> F() eqt(true(),mcrlrecord()) -> F() eqt(true(),ok()) -> F() eqt(true(),pending()) -> F() eqt(true(),release()) -> F() eqt(true(),request()) -> F() eqt(true(),resource()) -> F() eqt(true(),tag()) -> F() eqt(true(),true()) -> T() eqt(true(),undefined()) -> F() eqt(true(),pid(N2)) -> F() eqt(true(),int(N2)) -> F() eqt(true(),cons(H2,T2)) -> F() eqt(true(),tuple(H2,T2)) -> F() eqt(true(),tuplenil(H2)) -> F() eqt(undefined(),nil()) -> F() eqt(undefined(),a()) -> F() eqt(undefined(),tuplenil(H2)) -> F() eqt(pid(N1),nil()) -> F() eqt(pid(N1),a()) -> F() eqt(pid(N1),excl()) -> F() eqt(pid(N1),false()) -> F() eqt(pid(N1),lock()) -> F() eqt(pid(N1),locker()) -> F() eqt(pid(N1),mcrlrecord()) -> F() eqt(pid(N1),ok()) -> F() eqt(pid(N1),pending()) -> F() eqt(pid(N1),release()) -> F() eqt(pid(N1),request()) -> F() eqt(pid(N1),resource()) -> F() eqt(pid(N1),tag()) -> F() eqt(pid(N1),true()) -> F() eqt(pid(N1),undefined()) -> F() eqt(pid(N1),pid(N2)) -> eqt(N1,N2) eqt(pid(N1),int(N2)) -> F() eqt(pid(N1),cons(H2,T2)) -> F() eqt(pid(N1),tuple(H2,T2)) -> F() eqt(pid(N1),tuplenil(H2)) -> F() eqt(int(N1),nil()) -> F() eqt(int(N1),a()) -> F() eqt(int(N1),excl()) -> F() eqt(int(N1),false()) -> F() eqt(int(N1),lock()) -> F() eqt(int(N1),locker()) -> F() eqt(int(N1),mcrlrecord()) -> F() eqt(int(N1),ok()) -> F() eqt(int(N1),pending()) -> F() eqt(int(N1),release()) -> F() eqt(int(N1),request()) -> F() eqt(int(N1),resource()) -> F() eqt(int(N1),tag()) -> F() eqt(int(N1),true()) -> F() eqt(int(N1),undefined()) -> F() eqt(cons(H1,T1),resource()) -> F() eqt(cons(H1,T1),tag()) -> F() eqt(cons(H1,T1),true()) -> F() eqt(cons(H1,T1),undefined()) -> F() eqt(cons(H1,T1),pid(N2)) -> F() eqt(cons(H1,T1),int(N2)) -> F() eqt(cons(H1,T1),cons(H2,T2)) -> and(eqt(H1,H2),eqt(T1,T2)) eqt(cons(H1,T1),tuple(H2,T2)) -> F() eqt(cons(H1,T1),tuplenil(H2)) -> F() eqt(tuple(H1,T1),nil()) -> F() eqt(tuple(H1,T1),a()) -> F() eqt(tuple(H1,T1),excl()) -> F() eqt(tuple(H1,T1),false()) -> F() eqt(tuple(H1,T1),lock()) -> F() eqt(tuple(H1,T1),locker()) -> F() eqt(tuple(H1,T1),mcrlrecord()) -> F() eqt(tuple(H1,T1),ok()) -> F() eqt(tuple(H1,T1),pending()) -> F() eqt(tuple(H1,T1),release()) -> F() eqt(tuple(H1,T1),request()) -> F() eqt(tuple(H1,T1),resource()) -> F() eqt(tuple(H1,T1),tag()) -> F() eqt(tuple(H1,T1),true()) -> F() eqt(tuple(H1,T1),undefined()) -> F() eqt(tuple(H1,T1),pid(N2)) -> F() eqt(tuple(H1,T1),int(N2)) -> F() eqt(tuple(H1,T1),cons(H2,T2)) -> F() eqt(tuple(H1,T1),tuple(H2,T2)) -> and(eqt(H1,H2),eqt(T1,T2)) eqt(tuple(H1,T1),tuplenil(H2)) -> F() eqt(tuplenil(H1),nil()) -> F() eqt(tuplenil(H1),a()) -> F() eqt(tuplenil(H1),excl()) -> F() eqt(tuplenil(H1),false()) -> F() eqt(tuplenil(H1),lock()) -> F() eqt(tuplenil(H1),locker()) -> F() eqt(tuplenil(H1),mcrlrecord()) -> F() eqt(tuplenil(H1),ok()) -> F() eqt(tuplenil(H1),pending()) -> F() eqt(tuplenil(H1),release()) -> F() eqt(tuplenil(H1),request()) -> F() eqt(tuplenil(H1),resource()) -> F() eqt(tuplenil(H1),tag()) -> F() eqt(tuplenil(H1),true()) -> F() eqt(tuplenil(H1),undefined()) -> F() eqt(tuplenil(H1),pid(N2)) -> F() eqt(tuplenil(H1),int(N2)) -> F() eqt(tuplenil(H1),cons(H2,T2)) -> F() eqt(tuplenil(H1),tuple(H2,T2)) -> F() eqt(tuplenil(H1),tuplenil(H2)) -> eqt(H1,H2) element(int(s(0())),tuplenil(T1)) -> T1 element(int(s(0())),tuple(T1,T2)) -> T1 element(int(s(s(N1))),tuple(T1,T2)) -> element(int(s(N1)),T2) record_new(lock()) -> tuple(mcrlrecord(),tuple(lock(),tuple(undefined(),tuple(nil(),tuplenil(nil()))))) record_extract(tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))), lock(),resource()) -> tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))) record_update(tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))), lock(),pending(),NewF) -> tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(NewF))))) record_updates(Record,Name,nil()) -> Record record_updates(Record,Name,cons(tuple(Field,tuplenil(NewF)),Fields)) -> record_updates(record_update(Record,Name,Field,NewF),Name,Fields) locker2_map_promote_pending(nil(),Pending) -> nil() locker2_map_promote_pending(cons(Lock,Locks),Pending) -> cons(locker2_promote_pending(Lock,Pending),locker2_map_promote_pending(Locks,Pending)) locker2_map_claim_lock(nil(),Resources,Client) -> nil() locker2_map_claim_lock(cons(Lock,Locks),Resources,Client) -> cons(locker2_claim_lock(Lock,Resources,Client),locker2_map_claim_lock(Locks,Resources,Client)) locker2_map_add_pending(nil(),Resources,Client) -> nil() locker2_promote_pending(Lock,Client) -> case0(Client,Lock,record_extract(Lock,lock(),pending())) case0(Client,Lock,cons(Client,Pendings)) -> record_updates(Lock,lock(),cons(tuple(excl(),tuplenil(Client)),cons (tuple ( pending(),tuplenil(Pendings)), nil ()))) case0(Client,Lock,MCRLFree0) -> Lock locker2_remove_pending(Lock,Client) -> record_updates(Lock,lock(),cons(tuple(pending(),tuplenil(subtract (record_extract(Lock,lock(),pending()), cons(Client,nil())))), nil())) locker2_add_pending(Lock,Resources,Client) -> case1(Client,Resources,Lock,member(record_extract(Lock,lock(),resource()),Resources)) case1(Client,Resources,Lock,true()) -> record_updates(Lock,lock(),cons(tuple(pending(),tuplenil(append(record_extract ( Lock,lock(),pending()), cons (Client,nil())))), nil())) case1(Client,Resources,Lock,false()) -> Lock locker2_release_lock(Lock,Client) -> case2(Client,Lock,gen_modtageq(Client,record_extract(Lock,lock(),excl()))) case2(Client,Lock,true()) -> record_updates(Lock,lock(),cons(tuple(excllock(),excl()),nil())) case4(Client,Lock,MCRLFree1) -> false() locker2_obtainables(nil(),Client) -> true() locker2_obtainables(cons(Lock,Locks),Client) -> case5(Client,Locks,Lock,member(Client,record_extract(Lock,lock(),pending()))) case5(Client,Locks,Lock,true()) -> andt(locker2_obtainable(Lock,Client),locker2_obtainables(Locks,Client)) case5(Client,Locks,Lock,false()) -> locker2_obtainables(Locks,Client) locker2_check_available(Resource,nil()) -> false() locker2_check_available(Resource,cons(Lock,Locks)) -> case6(Locks,Lock,Resource,equal(Resource,record_extract(Lock,lock(),resource()))) case6(Locks,Lock,Resource,true()) -> andt(equal(record_extract(Lock,lock(),excl()),nil()),equal(record_extract (Lock,lock(),pending()), nil())) case6(Locks,Lock,Resource,false()) -> locker2_check_available(Resource,Locks) locker2_check_availables(nil(),Locks) -> true() locker2_check_availables(cons(Resource,Resources),Locks) -> andt(locker2_check_available(Resource,Locks),locker2_check_availables(Resources,Locks)) locker2_adduniq(nil(),List) -> List append(cons(Head,Tail),List) -> cons(Head,append(Tail,List)) subtract(List,nil()) -> List subtract(List,cons(Head,Tail)) -> subtract(delete(Head,List),Tail) delete(E,nil()) -> nil() delete(E,cons(Head,Tail)) -> case8(Tail,Head,E,equal(E,Head)) case8(Tail,Head,E,true()) -> Tail case8(Tail,Head,E,false()) -> cons(Head,delete(E,Tail)) gen_tag(Pid) -> tuple(Pid,tuplenil(tag())) gen_modtageq(Client1,Client2) -> equal(Client1,Client2) member(E,nil()) -> false() member(E,cons(Head,Tail)) -> case9(Tail,Head,E,equal(E,Head)) case9(Tail,Head,E,true()) -> true() case9(Tail,Head,E,false()) -> member(E,Tail) eqs(empty(),empty()) -> T() eqs(empty(),stack(E2,S2)) -> F() eqs(stack(E1,S1),empty()) -> F() eqs(stack(E1,S1),stack(E2,S2)) -> and(eqt(E1,E2),eqs(S1,S2)) pushs(E1,S1) -> stack(E1,S1) pops(stack(E1,S1)) -> S1 tops(stack(E1,S1)) -> E1 istops(E1,empty()) -> F() istops(E1,stack(E2,S1)) -> eqt(E1,E2) eqc(nocalls(),nocalls()) -> T() eqc(nocalls(),calls(E2,S2,CS2)) -> F() eqc(calls(E1,S1,CS1),nocalls()) -> F() eqc(calls(E1,S1,CS1),calls(E2,S2,CS2)) -> and(eqt(E1,E2),and(eqs(S1,S2),eqc(CS1,CS2))) push(E1,E2,nocalls()) -> calls(E1,stack(E2,empty()),nocalls()) push(E1,E2,calls(E3,S1,CS1)) -> push1(E1,E2,E3,S1,CS1,eqt(E1,E3)) push1(E1,E2,E3,S1,CS1,T()) -> calls(E3,pushs(E2,S1),CS1) graph: push#(E1,E2,calls(E3,S1,CS1)) -> push1#(E1,E2,E3,S1,CS1,eqt(E1,E3)) -> push1#(E1,E2,E3,S1,CS1,T()) -> pushs#(E2,S1) push#(E1,E2,calls(E3,S1,CS1)) -> eqt#(E1,E3) -> eqt#(tuplenil(H1),tuplenil(H2)) -> eqt#(H1,H2) push#(E1,E2,calls(E3,S1,CS1)) -> eqt#(E1,E3) -> eqt#(tuple(H1,T1),tuple(H2,T2)) -> and#(eqt(H1,H2),eqt(T1,T2)) push#(E1,E2,calls(E3,S1,CS1)) -> eqt#(E1,E3) -> eqt#(tuple(H1,T1),tuple(H2,T2)) -> eqt#(H1,H2) push#(E1,E2,calls(E3,S1,CS1)) -> eqt#(E1,E3) -> eqt#(tuple(H1,T1),tuple(H2,T2)) -> eqt#(T1,T2) push#(E1,E2,calls(E3,S1,CS1)) -> eqt#(E1,E3) -> eqt#(cons(H1,T1),cons(H2,T2)) -> and#(eqt(H1,H2),eqt(T1,T2)) push#(E1,E2,calls(E3,S1,CS1)) -> eqt#(E1,E3) -> eqt#(cons(H1,T1),cons(H2,T2)) -> eqt#(H1,H2) push#(E1,E2,calls(E3,S1,CS1)) -> eqt#(E1,E3) -> eqt#(cons(H1,T1),cons(H2,T2)) -> eqt#(T1,T2) push#(E1,E2,calls(E3,S1,CS1)) -> eqt#(E1,E3) -> eqt#(pid(N1),pid(N2)) -> eqt#(N1,N2) eqc#(calls(E1,S1,CS1),calls(E2,S2,CS2)) -> eqc#(CS1,CS2) -> eqc#(calls(E1,S1,CS1),calls(E2,S2,CS2)) -> and#(eqt(E1,E2),and(eqs(S1,S2),eqc(CS1,CS2))) eqc#(calls(E1,S1,CS1),calls(E2,S2,CS2)) -> eqc#(CS1,CS2) -> eqc#(calls(E1,S1,CS1),calls(E2,S2,CS2)) -> eqt#(E1,E2) eqc#(calls(E1,S1,CS1),calls(E2,S2,CS2)) -> eqc#(CS1,CS2) -> eqc#(calls(E1,S1,CS1),calls(E2,S2,CS2)) -> and#(eqs(S1,S2),eqc(CS1,CS2)) eqc#(calls(E1,S1,CS1),calls(E2,S2,CS2)) -> eqc#(CS1,CS2) -> eqc#(calls(E1,S1,CS1),calls(E2,S2,CS2)) -> eqs#(S1,S2) eqc#(calls(E1,S1,CS1),calls(E2,S2,CS2)) -> eqc#(CS1,CS2) -> eqc#(calls(E1,S1,CS1),calls(E2,S2,CS2)) -> eqc#(CS1,CS2) eqc#(calls(E1,S1,CS1),calls(E2,S2,CS2)) -> eqs#(S1,S2) -> eqs#(stack(E1,S1),stack(E2,S2)) -> and#(eqt(E1,E2),eqs(S1,S2)) eqc#(calls(E1,S1,CS1),calls(E2,S2,CS2)) -> eqs#(S1,S2) -> eqs#(stack(E1,S1),stack(E2,S2)) -> eqt#(E1,E2) eqc#(calls(E1,S1,CS1),calls(E2,S2,CS2)) -> eqs#(S1,S2) -> eqs#(stack(E1,S1),stack(E2,S2)) -> eqs#(S1,S2) eqc#(calls(E1,S1,CS1),calls(E2,S2,CS2)) -> eqt#(E1,E2) -> eqt#(tuplenil(H1),tuplenil(H2)) -> eqt#(H1,H2) eqc#(calls(E1,S1,CS1),calls(E2,S2,CS2)) -> eqt#(E1,E2) -> eqt#(tuple(H1,T1),tuple(H2,T2)) -> and#(eqt(H1,H2),eqt(T1,T2)) eqc#(calls(E1,S1,CS1),calls(E2,S2,CS2)) -> eqt#(E1,E2) -> eqt#(tuple(H1,T1),tuple(H2,T2)) -> eqt#(H1,H2) eqc#(calls(E1,S1,CS1),calls(E2,S2,CS2)) -> eqt#(E1,E2) -> eqt#(tuple(H1,T1),tuple(H2,T2)) -> eqt#(T1,T2) eqc#(calls(E1,S1,CS1),calls(E2,S2,CS2)) -> eqt#(E1,E2) -> eqt#(cons(H1,T1),cons(H2,T2)) -> and#(eqt(H1,H2),eqt(T1,T2)) eqc#(calls(E1,S1,CS1),calls(E2,S2,CS2)) -> eqt#(E1,E2) -> eqt#(cons(H1,T1),cons(H2,T2)) -> eqt#(H1,H2) eqc#(calls(E1,S1,CS1),calls(E2,S2,CS2)) -> eqt#(E1,E2) -> eqt#(cons(H1,T1),cons(H2,T2)) -> eqt#(T1,T2) eqc#(calls(E1,S1,CS1),calls(E2,S2,CS2)) -> eqt#(E1,E2) -> eqt#(pid(N1),pid(N2)) -> eqt#(N1,N2) istops#(E1,stack(E2,S1)) -> eqt#(E1,E2) -> eqt#(tuplenil(H1),tuplenil(H2)) -> eqt#(H1,H2) istops#(E1,stack(E2,S1)) -> eqt#(E1,E2) -> eqt#(tuple(H1,T1),tuple(H2,T2)) -> and#(eqt(H1,H2),eqt(T1,T2)) istops#(E1,stack(E2,S1)) -> eqt#(E1,E2) -> eqt#(tuple(H1,T1),tuple(H2,T2)) -> eqt#(H1,H2) istops#(E1,stack(E2,S1)) -> eqt#(E1,E2) -> eqt#(tuple(H1,T1),tuple(H2,T2)) -> eqt#(T1,T2) istops#(E1,stack(E2,S1)) -> eqt#(E1,E2) -> eqt#(cons(H1,T1),cons(H2,T2)) -> and#(eqt(H1,H2),eqt(T1,T2)) istops#(E1,stack(E2,S1)) -> eqt#(E1,E2) -> eqt#(cons(H1,T1),cons(H2,T2)) -> eqt#(H1,H2) istops#(E1,stack(E2,S1)) -> eqt#(E1,E2) -> eqt#(cons(H1,T1),cons(H2,T2)) -> eqt#(T1,T2) istops#(E1,stack(E2,S1)) -> eqt#(E1,E2) -> eqt#(pid(N1),pid(N2)) -> eqt#(N1,N2) eqs#(stack(E1,S1),stack(E2,S2)) -> eqs#(S1,S2) -> eqs#(stack(E1,S1),stack(E2,S2)) -> and#(eqt(E1,E2),eqs(S1,S2)) eqs#(stack(E1,S1),stack(E2,S2)) -> eqs#(S1,S2) -> eqs#(stack(E1,S1),stack(E2,S2)) -> eqt#(E1,E2) eqs#(stack(E1,S1),stack(E2,S2)) -> eqs#(S1,S2) -> eqs#(stack(E1,S1),stack(E2,S2)) -> eqs#(S1,S2) eqs#(stack(E1,S1),stack(E2,S2)) -> eqt#(E1,E2) -> eqt#(tuplenil(H1),tuplenil(H2)) -> eqt#(H1,H2) eqs#(stack(E1,S1),stack(E2,S2)) -> eqt#(E1,E2) -> eqt#(tuple(H1,T1),tuple(H2,T2)) -> and#(eqt(H1,H2),eqt(T1,T2)) eqs#(stack(E1,S1),stack(E2,S2)) -> eqt#(E1,E2) -> eqt#(tuple(H1,T1),tuple(H2,T2)) -> eqt#(H1,H2) eqs#(stack(E1,S1),stack(E2,S2)) -> eqt#(E1,E2) -> eqt#(tuple(H1,T1),tuple(H2,T2)) -> eqt#(T1,T2) eqs#(stack(E1,S1),stack(E2,S2)) -> eqt#(E1,E2) -> eqt#(cons(H1,T1),cons(H2,T2)) -> and#(eqt(H1,H2),eqt(T1,T2)) eqs#(stack(E1,S1),stack(E2,S2)) -> eqt#(E1,E2) -> eqt#(cons(H1,T1),cons(H2,T2)) -> eqt#(H1,H2) eqs#(stack(E1,S1),stack(E2,S2)) -> eqt#(E1,E2) -> eqt#(cons(H1,T1),cons(H2,T2)) -> eqt#(T1,T2) eqs#(stack(E1,S1),stack(E2,S2)) -> eqt#(E1,E2) -> eqt#(pid(N1),pid(N2)) -> eqt#(N1,N2) case9#(Tail,Head,E,false()) -> member#(E,Tail) -> member#(E,cons(Head,Tail)) -> case9#(Tail,Head,E,equal(E,Head)) case8#(Tail,Head,E,false()) -> delete#(E,Tail) -> delete#(E,cons(Head,Tail)) -> case8#(Tail,Head,E,equal(E,Head)) delete#(E,cons(Head,Tail)) -> case8#(Tail,Head,E,equal(E,Head)) -> case8#(Tail,Head,E,false()) -> delete#(E,Tail) locker2_check_availables#(cons(Resource,Resources),Locks) -> locker2_check_availables#(Resources,Locks) -> locker2_check_availables#(cons(Resource,Resources),Locks) -> locker2_check_available#(Resource,Locks) locker2_check_availables#(cons(Resource,Resources),Locks) -> locker2_check_availables#(Resources,Locks) -> locker2_check_availables#(cons(Resource,Resources),Locks) -> locker2_check_availables#(Resources,Locks) locker2_check_availables#(cons(Resource,Resources),Locks) -> locker2_check_available#(Resource,Locks) -> locker2_check_available#(Resource,cons(Lock,Locks)) -> case6#(Locks,Lock,Resource,equal(Resource,record_extract(Lock,lock(),resource()))) locker2_check_availables#(cons(Resource,Resources),Locks) -> locker2_check_available#(Resource,Locks) -> locker2_check_available#(Resource,cons(Lock,Locks)) -> record_extract#(Lock,lock(),resource()) case6#(Locks,Lock,Resource,false()) -> locker2_check_available#(Resource,Locks) -> locker2_check_available#(Resource,cons(Lock,Locks)) -> case6#(Locks,Lock,Resource,equal(Resource,record_extract(Lock,lock(),resource()))) case6#(Locks,Lock,Resource,false()) -> locker2_check_available#(Resource,Locks) -> locker2_check_available#(Resource,cons(Lock,Locks)) -> record_extract#(Lock,lock(),resource()) locker2_check_available#(Resource,cons(Lock,Locks)) -> case6#(Locks,Lock,Resource,equal(Resource,record_extract(Lock,lock(),resource()))) -> case6#(Locks,Lock,Resource,false()) -> locker2_check_available#(Resource,Locks) locker2_check_available#(Resource,cons(Lock,Locks)) -> case6#(Locks,Lock,Resource,equal(Resource,record_extract(Lock,lock(),resource()))) -> case6#(Locks,Lock,Resource,true()) -> record_extract#(Lock,lock(),excl()) locker2_check_available#(Resource,cons(Lock,Locks)) -> case6#(Locks,Lock,Resource,equal(Resource,record_extract(Lock,lock(),resource()))) -> case6#(Locks,Lock,Resource,true()) -> record_extract#(Lock,lock(),pending()) case5#(Client,Locks,Lock,true()) -> locker2_obtainables#(Locks,Client) -> locker2_obtainables#(cons(Lock,Locks),Client) -> case5#(Client,Locks,Lock,member(Client,record_extract(Lock,lock(),pending()))) case5#(Client,Locks,Lock,true()) -> locker2_obtainables#(Locks,Client) -> locker2_obtainables#(cons(Lock,Locks),Client) -> member#(Client,record_extract(Lock,lock(),pending())) case5#(Client,Locks,Lock,true()) -> locker2_obtainables#(Locks,Client) -> locker2_obtainables#(cons(Lock,Locks),Client) -> record_extract#(Lock,lock(),pending()) case5#(Client,Locks,Lock,false()) -> locker2_obtainables#(Locks,Client) -> locker2_obtainables#(cons(Lock,Locks),Client) -> case5#(Client,Locks,Lock,member(Client,record_extract(Lock,lock(),pending()))) case5#(Client,Locks,Lock,false()) -> locker2_obtainables#(Locks,Client) -> locker2_obtainables#(cons(Lock,Locks),Client) -> member#(Client,record_extract(Lock,lock(),pending())) case5#(Client,Locks,Lock,false()) -> locker2_obtainables#(Locks,Client) -> locker2_obtainables#(cons(Lock,Locks),Client) -> record_extract#(Lock,lock(),pending()) locker2_obtainables#(cons(Lock,Locks),Client) -> case5#(Client,Locks,Lock,member(Client,record_extract(Lock,lock(),pending()))) -> case5#(Client,Locks,Lock,false()) -> locker2_obtainables#(Locks,Client) locker2_obtainables#(cons(Lock,Locks),Client) -> case5#(Client,Locks,Lock,member(Client,record_extract(Lock,lock(),pending()))) -> case5#(Client,Locks,Lock,true()) -> locker2_obtainables#(Locks,Client) locker2_obtainables#(cons(Lock,Locks),Client) -> member#(Client,record_extract(Lock,lock(),pending())) -> member#(E,cons(Head,Tail)) -> case9#(Tail,Head,E,equal(E,Head)) case2#(Client,Lock,true()) -> record_updates#(Lock,lock(),cons(tuple(excllock(),excl()),nil())) -> record_updates#(Record,Name,cons(tuple(Field,tuplenil(NewF)),Fields)) -> record_updates#(record_update(Record,Name,Field,NewF),Name,Fields) case2#(Client,Lock,true()) -> record_updates#(Lock,lock(),cons(tuple(excllock(),excl()),nil())) -> record_updates#(Record,Name,cons(tuple(Field,tuplenil(NewF)),Fields)) -> record_update#(Record,Name,Field,NewF) locker2_release_lock#(Lock,Client) -> case2#(Client,Lock,gen_modtageq(Client,record_extract(Lock,lock(),excl()))) -> case2#(Client,Lock,true()) -> record_updates#(Lock,lock(),cons(tuple(excllock(),excl()),nil())) append#(cons(Head,Tail),List) -> append#(Tail,List) -> append#(cons(Head,Tail),List) -> append#(Tail,List) case1#(Client,Resources,Lock,true()) -> append#(record_extract(Lock,lock(),pending()),cons(Client,nil())) -> append#(cons(Head,Tail),List) -> append#(Tail,List) case1#(Client,Resources,Lock,true()) -> record_updates#(Lock,lock(),cons(tuple(pending(),tuplenil(append( record_extract ( Lock,lock(),pending()), cons (Client,nil())))), nil())) -> record_updates#(Record,Name,cons(tuple(Field,tuplenil(NewF)),Fields)) -> record_updates#(record_update(Record,Name,Field,NewF),Name,Fields) case1#(Client,Resources,Lock,true()) -> record_updates#(Lock,lock(),cons(tuple(pending(),tuplenil(append( record_extract ( Lock,lock(),pending()), cons (Client,nil())))), nil())) -> record_updates#(Record,Name,cons(tuple(Field,tuplenil(NewF)),Fields)) -> record_update#(Record,Name,Field,NewF) member#(E,cons(Head,Tail)) -> case9#(Tail,Head,E,equal(E,Head)) -> case9#(Tail,Head,E,false()) -> member#(E,Tail) locker2_add_pending#(Lock,Resources,Client) -> case1#(Client,Resources,Lock,member(record_extract(Lock,lock(),resource()),Resources)) -> case1#(Client,Resources,Lock,true()) -> record_updates#(Lock,lock(),cons(tuple(pending(),tuplenil(append( record_extract ( Lock,lock(),pending()), cons (Client,nil())))), nil())) locker2_add_pending#(Lock,Resources,Client) -> case1#(Client,Resources,Lock,member(record_extract(Lock,lock(),resource()),Resources)) -> case1#(Client,Resources,Lock,true()) -> append#(record_extract(Lock,lock(),pending()),cons(Client,nil())) locker2_add_pending#(Lock,Resources,Client) -> case1#(Client,Resources,Lock,member(record_extract(Lock,lock(),resource()),Resources)) -> case1#(Client,Resources,Lock,true()) -> record_extract#(Lock,lock(),pending()) locker2_add_pending#(Lock,Resources,Client) -> member#(record_extract(Lock,lock(),resource()),Resources) -> member#(E,cons(Head,Tail)) -> case9#(Tail,Head,E,equal(E,Head)) subtract#(List,cons(Head,Tail)) -> delete#(Head,List) -> delete#(E,cons(Head,Tail)) -> case8#(Tail,Head,E,equal(E,Head)) subtract#(List,cons(Head,Tail)) -> subtract#(delete(Head,List),Tail) -> subtract#(List,cons(Head,Tail)) -> subtract#(delete(Head,List),Tail) subtract#(List,cons(Head,Tail)) -> subtract#(delete(Head,List),Tail) -> subtract#(List,cons(Head,Tail)) -> delete#(Head,List) locker2_remove_pending#(Lock,Client) -> subtract#(record_extract(Lock,lock(),pending()),cons(Client,nil())) -> subtract#(List,cons(Head,Tail)) -> subtract#(delete(Head,List),Tail) locker2_remove_pending#(Lock,Client) -> subtract#(record_extract(Lock,lock(),pending()),cons(Client,nil())) -> subtract#(List,cons(Head,Tail)) -> delete#(Head,List) locker2_remove_pending#(Lock,Client) -> record_updates#(Lock,lock(),cons(tuple(pending(),tuplenil(subtract (record_extract (Lock,lock(),pending()), cons(Client,nil())))), nil())) -> record_updates#(Record,Name,cons(tuple(Field,tuplenil(NewF)),Fields)) -> record_updates#(record_update(Record,Name,Field,NewF),Name,Fields) locker2_remove_pending#(Lock,Client) -> record_updates#(Lock,lock(),cons(tuple(pending(),tuplenil(subtract (record_extract (Lock,lock(),pending()), cons(Client,nil())))), nil())) -> record_updates#(Record,Name,cons(tuple(Field,tuplenil(NewF)),Fields)) -> record_update#(Record,Name,Field,NewF) case0#(Client,Lock,cons(Client,Pendings)) -> record_updates#(Lock,lock(),cons(tuple(excl(),tuplenil(Client)),cons ( tuple ( pending(),tuplenil(Pendings)), nil ()))) -> record_updates#(Record,Name,cons(tuple(Field,tuplenil(NewF)),Fields)) -> record_updates#(record_update(Record,Name,Field,NewF),Name,Fields) case0#(Client,Lock,cons(Client,Pendings)) -> record_updates#(Lock,lock(),cons(tuple(excl(),tuplenil(Client)),cons ( tuple ( pending(),tuplenil(Pendings)), nil ()))) -> record_updates#(Record,Name,cons(tuple(Field,tuplenil(NewF)),Fields)) -> record_update#(Record,Name,Field,NewF) locker2_map_claim_lock#(cons(Lock,Locks),Resources,Client) -> locker2_map_claim_lock#(Locks,Resources,Client) -> locker2_map_claim_lock#(cons(Lock,Locks),Resources,Client) -> locker2_map_claim_lock#(Locks,Resources,Client) locker2_promote_pending#(Lock,Client) -> case0#(Client,Lock,record_extract(Lock,lock(),pending())) -> case0#(Client,Lock,cons(Client,Pendings)) -> record_updates#(Lock,lock(),cons(tuple(excl(),tuplenil(Client)),cons ( tuple ( pending(),tuplenil(Pendings)), nil ()))) locker2_map_promote_pending#(cons(Lock,Locks),Pending) -> locker2_promote_pending#(Lock,Pending) -> locker2_promote_pending#(Lock,Client) -> case0#(Client,Lock,record_extract(Lock,lock(),pending())) locker2_map_promote_pending#(cons(Lock,Locks),Pending) -> locker2_promote_pending#(Lock,Pending) -> locker2_promote_pending#(Lock,Client) -> record_extract#(Lock,lock(),pending()) locker2_map_promote_pending#(cons(Lock,Locks),Pending) -> locker2_map_promote_pending#(Locks,Pending) -> locker2_map_promote_pending#(cons(Lock,Locks),Pending) -> locker2_promote_pending#(Lock,Pending) locker2_map_promote_pending#(cons(Lock,Locks),Pending) -> locker2_map_promote_pending#(Locks,Pending) -> locker2_map_promote_pending#(cons(Lock,Locks),Pending) -> locker2_map_promote_pending#(Locks,Pending) record_updates#(Record,Name,cons(tuple(Field,tuplenil(NewF)),Fields)) -> record_updates#(record_update(Record,Name,Field,NewF),Name,Fields) -> record_updates#(Record,Name,cons(tuple(Field,tuplenil(NewF)),Fields)) -> record_updates#(record_update(Record,Name,Field,NewF),Name,Fields) record_updates#(Record,Name,cons(tuple(Field,tuplenil(NewF)),Fields)) -> record_updates#(record_update(Record,Name,Field,NewF),Name,Fields) -> record_updates#(Record,Name,cons(tuple(Field,tuplenil(NewF)),Fields)) -> record_update#(Record,Name,Field,NewF) element#(int(s(s(N1))),tuple(T1,T2)) -> element#(int(s(N1)),T2) -> element#(int(s(s(N1))),tuple(T1,T2)) -> element#(int(s(N1)),T2) eqt#(tuplenil(H1),tuplenil(H2)) -> eqt#(H1,H2) -> eqt#(tuplenil(H1),tuplenil(H2)) -> eqt#(H1,H2) eqt#(tuplenil(H1),tuplenil(H2)) -> eqt#(H1,H2) -> eqt#(tuple(H1,T1),tuple(H2,T2)) -> and#(eqt(H1,H2),eqt(T1,T2)) eqt#(tuplenil(H1),tuplenil(H2)) -> eqt#(H1,H2) -> eqt#(tuple(H1,T1),tuple(H2,T2)) -> eqt#(H1,H2) eqt#(tuplenil(H1),tuplenil(H2)) -> eqt#(H1,H2) -> eqt#(tuple(H1,T1),tuple(H2,T2)) -> eqt#(T1,T2) eqt#(tuplenil(H1),tuplenil(H2)) -> eqt#(H1,H2) -> eqt#(cons(H1,T1),cons(H2,T2)) -> and#(eqt(H1,H2),eqt(T1,T2)) eqt#(tuplenil(H1),tuplenil(H2)) -> eqt#(H1,H2) -> eqt#(cons(H1,T1),cons(H2,T2)) -> eqt#(H1,H2) eqt#(tuplenil(H1),tuplenil(H2)) -> eqt#(H1,H2) -> eqt#(cons(H1,T1),cons(H2,T2)) -> eqt#(T1,T2) eqt#(tuplenil(H1),tuplenil(H2)) -> eqt#(H1,H2) -> eqt#(pid(N1),pid(N2)) -> eqt#(N1,N2) eqt#(tuple(H1,T1),tuple(H2,T2)) -> eqt#(T1,T2) -> eqt#(tuplenil(H1),tuplenil(H2)) -> eqt#(H1,H2) eqt#(tuple(H1,T1),tuple(H2,T2)) -> eqt#(T1,T2) -> eqt#(tuple(H1,T1),tuple(H2,T2)) -> and#(eqt(H1,H2),eqt(T1,T2)) eqt#(tuple(H1,T1),tuple(H2,T2)) -> eqt#(T1,T2) -> eqt#(tuple(H1,T1),tuple(H2,T2)) -> eqt#(H1,H2) eqt#(tuple(H1,T1),tuple(H2,T2)) -> eqt#(T1,T2) -> eqt#(tuple(H1,T1),tuple(H2,T2)) -> eqt#(T1,T2) eqt#(tuple(H1,T1),tuple(H2,T2)) -> eqt#(T1,T2) -> eqt#(cons(H1,T1),cons(H2,T2)) -> and#(eqt(H1,H2),eqt(T1,T2)) eqt#(tuple(H1,T1),tuple(H2,T2)) -> eqt#(T1,T2) -> eqt#(cons(H1,T1),cons(H2,T2)) -> eqt#(H1,H2) eqt#(tuple(H1,T1),tuple(H2,T2)) -> eqt#(T1,T2) -> eqt#(cons(H1,T1),cons(H2,T2)) -> eqt#(T1,T2) eqt#(tuple(H1,T1),tuple(H2,T2)) -> eqt#(T1,T2) -> eqt#(pid(N1),pid(N2)) -> eqt#(N1,N2) eqt#(tuple(H1,T1),tuple(H2,T2)) -> eqt#(H1,H2) -> eqt#(tuplenil(H1),tuplenil(H2)) -> eqt#(H1,H2) eqt#(tuple(H1,T1),tuple(H2,T2)) -> eqt#(H1,H2) -> eqt#(tuple(H1,T1),tuple(H2,T2)) -> and#(eqt(H1,H2),eqt(T1,T2)) eqt#(tuple(H1,T1),tuple(H2,T2)) -> eqt#(H1,H2) -> eqt#(tuple(H1,T1),tuple(H2,T2)) -> eqt#(H1,H2) eqt#(tuple(H1,T1),tuple(H2,T2)) -> eqt#(H1,H2) -> eqt#(tuple(H1,T1),tuple(H2,T2)) -> eqt#(T1,T2) eqt#(tuple(H1,T1),tuple(H2,T2)) -> eqt#(H1,H2) -> eqt#(cons(H1,T1),cons(H2,T2)) -> and#(eqt(H1,H2),eqt(T1,T2)) eqt#(tuple(H1,T1),tuple(H2,T2)) -> eqt#(H1,H2) -> eqt#(cons(H1,T1),cons(H2,T2)) -> eqt#(H1,H2) eqt#(tuple(H1,T1),tuple(H2,T2)) -> eqt#(H1,H2) -> eqt#(cons(H1,T1),cons(H2,T2)) -> eqt#(T1,T2) eqt#(tuple(H1,T1),tuple(H2,T2)) -> eqt#(H1,H2) -> eqt#(pid(N1),pid(N2)) -> eqt#(N1,N2) eqt#(cons(H1,T1),cons(H2,T2)) -> eqt#(T1,T2) -> eqt#(tuplenil(H1),tuplenil(H2)) -> eqt#(H1,H2) eqt#(cons(H1,T1),cons(H2,T2)) -> eqt#(T1,T2) -> eqt#(tuple(H1,T1),tuple(H2,T2)) -> and#(eqt(H1,H2),eqt(T1,T2)) eqt#(cons(H1,T1),cons(H2,T2)) -> eqt#(T1,T2) -> eqt#(tuple(H1,T1),tuple(H2,T2)) -> eqt#(H1,H2) eqt#(cons(H1,T1),cons(H2,T2)) -> eqt#(T1,T2) -> eqt#(tuple(H1,T1),tuple(H2,T2)) -> eqt#(T1,T2) eqt#(cons(H1,T1),cons(H2,T2)) -> eqt#(T1,T2) -> eqt#(cons(H1,T1),cons(H2,T2)) -> and#(eqt(H1,H2),eqt(T1,T2)) eqt#(cons(H1,T1),cons(H2,T2)) -> eqt#(T1,T2) -> eqt#(cons(H1,T1),cons(H2,T2)) -> eqt#(H1,H2) eqt#(cons(H1,T1),cons(H2,T2)) -> eqt#(T1,T2) -> eqt#(cons(H1,T1),cons(H2,T2)) -> eqt#(T1,T2) eqt#(cons(H1,T1),cons(H2,T2)) -> eqt#(T1,T2) -> eqt#(pid(N1),pid(N2)) -> eqt#(N1,N2) eqt#(cons(H1,T1),cons(H2,T2)) -> eqt#(H1,H2) -> eqt#(tuplenil(H1),tuplenil(H2)) -> eqt#(H1,H2) eqt#(cons(H1,T1),cons(H2,T2)) -> eqt#(H1,H2) -> eqt#(tuple(H1,T1),tuple(H2,T2)) -> and#(eqt(H1,H2),eqt(T1,T2)) eqt#(cons(H1,T1),cons(H2,T2)) -> eqt#(H1,H2) -> eqt#(tuple(H1,T1),tuple(H2,T2)) -> eqt#(H1,H2) eqt#(cons(H1,T1),cons(H2,T2)) -> eqt#(H1,H2) -> eqt#(tuple(H1,T1),tuple(H2,T2)) -> eqt#(T1,T2) eqt#(cons(H1,T1),cons(H2,T2)) -> eqt#(H1,H2) -> eqt#(cons(H1,T1),cons(H2,T2)) -> and#(eqt(H1,H2),eqt(T1,T2)) eqt#(cons(H1,T1),cons(H2,T2)) -> eqt#(H1,H2) -> eqt#(cons(H1,T1),cons(H2,T2)) -> eqt#(H1,H2) eqt#(cons(H1,T1),cons(H2,T2)) -> eqt#(H1,H2) -> eqt#(cons(H1,T1),cons(H2,T2)) -> eqt#(T1,T2) eqt#(cons(H1,T1),cons(H2,T2)) -> eqt#(H1,H2) -> eqt#(pid(N1),pid(N2)) -> eqt#(N1,N2) eqt#(pid(N1),pid(N2)) -> eqt#(N1,N2) -> eqt#(tuplenil(H1),tuplenil(H2)) -> eqt#(H1,H2) eqt#(pid(N1),pid(N2)) -> eqt#(N1,N2) -> eqt#(tuple(H1,T1),tuple(H2,T2)) -> and#(eqt(H1,H2),eqt(T1,T2)) eqt#(pid(N1),pid(N2)) -> eqt#(N1,N2) -> eqt#(tuple(H1,T1),tuple(H2,T2)) -> eqt#(H1,H2) eqt#(pid(N1),pid(N2)) -> eqt#(N1,N2) -> eqt#(tuple(H1,T1),tuple(H2,T2)) -> eqt#(T1,T2) eqt#(pid(N1),pid(N2)) -> eqt#(N1,N2) -> eqt#(cons(H1,T1),cons(H2,T2)) -> and#(eqt(H1,H2),eqt(T1,T2)) eqt#(pid(N1),pid(N2)) -> eqt#(N1,N2) -> eqt#(cons(H1,T1),cons(H2,T2)) -> eqt#(H1,H2) eqt#(pid(N1),pid(N2)) -> eqt#(N1,N2) -> eqt#(cons(H1,T1),cons(H2,T2)) -> eqt#(T1,T2) eqt#(pid(N1),pid(N2)) -> eqt#(N1,N2) -> eqt#(pid(N1),pid(N2)) -> eqt#(N1,N2) SCC Processor: #sccs: 14 #rules: 24 #arcs: 143/3721 DPs: element#(int(s(s(N1))),tuple(T1,T2)) -> element#(int(s(N1)),T2) TRS: or(T(),T()) -> T() or(F(),T()) -> T() or(T(),F()) -> T() or(F(),F()) -> F() and(T(),B) -> B and(B,T()) -> B and(F(),B) -> F() and(B,F()) -> F() imp(T(),B) -> B imp(F(),B) -> T() not(T()) -> F() not(F()) -> T() if(T(),B1,B2) -> B1 if(F(),B1,B2) -> B2 eq(T(),T()) -> T() eq(F(),F()) -> T() eq(T(),F()) -> F() eq(F(),T()) -> F() eqt(nil(),undefined()) -> F() eqt(nil(),pid(N2)) -> F() eqt(nil(),int(N2)) -> F() eqt(nil(),cons(H2,T2)) -> F() eqt(nil(),tuple(H2,T2)) -> F() eqt(nil(),tuplenil(H2)) -> F() eqt(a(),nil()) -> F() eqt(a(),a()) -> T() eqt(a(),excl()) -> F() eqt(a(),false()) -> F() eqt(a(),lock()) -> F() eqt(a(),locker()) -> F() eqt(a(),mcrlrecord()) -> F() eqt(a(),ok()) -> F() eqt(a(),pending()) -> F() eqt(a(),release()) -> F() eqt(a(),request()) -> F() eqt(a(),resource()) -> F() eqt(a(),tag()) -> F() eqt(a(),true()) -> F() eqt(a(),undefined()) -> F() eqt(a(),pid(N2)) -> F() eqt(a(),int(N2)) -> F() eqt(a(),cons(H2,T2)) -> F() eqt(a(),tuple(H2,T2)) -> F() eqt(a(),tuplenil(H2)) -> F() eqt(excl(),nil()) -> F() eqt(excl(),a()) -> F() eqt(excl(),excl()) -> T() eqt(excl(),false()) -> F() eqt(excl(),lock()) -> F() eqt(excl(),locker()) -> F() eqt(excl(),mcrlrecord()) -> F() eqt(excl(),ok()) -> F() eqt(excl(),pending()) -> F() eqt(excl(),release()) -> F() eqt(excl(),request()) -> F() eqt(excl(),resource()) -> F() eqt(excl(),tag()) -> F() eqt(excl(),true()) -> F() eqt(excl(),undefined()) -> F() eqt(excl(),pid(N2)) -> F() eqt(excl(),eqt(false(),int(N2))) -> F() eqt(false(),cons(H2,T2)) -> F() eqt(false(),tuple(H2,T2)) -> F() eqt(false(),tuplenil(H2)) -> F() eqt(lock(),nil()) -> F() eqt(lock(),a()) -> F() eqt(lock(),excl()) -> F() eqt(lock(),false()) -> F() eqt(lock(),lock()) -> T() eqt(lock(),locker()) -> F() eqt(lock(),mcrlrecord()) -> F() eqt(lock(),ok()) -> F() eqt(lock(),pending()) -> F() eqt(lock(),release()) -> F() eqt(lock(),request()) -> F() eqt(lock(),resource()) -> F() eqt(lock(),tag()) -> F() eqt(lock(),true()) -> F() eqt(lock(),undefined()) -> F() eqt(lock(),pid(N2)) -> F() eqt(lock(),int(N2)) -> F() eqt(lock(),cons(H2,T2)) -> F() eqt(lock(),tuple(H2,T2)) -> F() eqt(lock(),tuplenil(H2)) -> F() eqt(locker(),nil()) -> F() eqt(locker(),a()) -> F() eqt(locker(),excl()) -> F() eqt(locker(),false()) -> F() eqt(locker(),lock()) -> F() eqt(locker(),locker()) -> T() eqt(locker(),mcrlrecord()) -> F() eqt(locker(),ok()) -> F() eqt(locker(),pending()) -> F() eqt(locker(),release()) -> F() eqt(locker(),request()) -> F() eqt(locker(),resource()) -> F() eqt(locker(),tag()) -> F() eqt(locker(),true()) -> F() eqt(locker(),undefined()) -> F() eqt(locker(),pid(N2)) -> F() eqt(locker(),int(N2)) -> F() eqt(locker(),cons(H2,T2)) -> F() eqt(locker(),tuple(H2,T2)) -> F() eqt(locker(),tuplenil(H2)) -> F() eqt(mcrlrecord(),nil()) -> F() eqt(mcrlrecord(),a()) -> F() eqt(mcrlrecord(),excl()) -> F() eqt(mcrlrecord(),false()) -> F() eqt(mcrlrecord(),lock()) -> F() eqt(mcrlrecord(),locker()) -> F() eqt(mcrlrecord(),mcrlrecord()) -> T() eqt(mcrlrecord(),ok()) -> F() eqt(mcrlrecord(),pending()) -> F() eqt(mcrlrecord(),release()) -> F() eqt(mcrlrecord(),request()) -> F() eqt(mcrlrecord(),resource()) -> F() eqt(ok(),resource()) -> F() eqt(ok(),tag()) -> F() eqt(ok(),true()) -> F() eqt(ok(),undefined()) -> F() eqt(ok(),pid(N2)) -> F() eqt(ok(),int(N2)) -> F() eqt(ok(),cons(H2,T2)) -> F() eqt(ok(),tuple(H2,T2)) -> F() eqt(ok(),tuplenil(H2)) -> F() eqt(pending(),nil()) -> F() eqt(pending(),a()) -> F() eqt(pending(),excl()) -> F() eqt(pending(),false()) -> F() eqt(pending(),lock()) -> F() eqt(pending(),locker()) -> F() eqt(pending(),mcrlrecord()) -> F() eqt(pending(),ok()) -> F() eqt(pending(),pending()) -> T() eqt(pending(),release()) -> F() eqt(pending(),request()) -> F() eqt(pending(),resource()) -> F() eqt(pending(),tag()) -> F() eqt(pending(),true()) -> F() eqt(pending(),undefined()) -> F() eqt(pending(),pid(N2)) -> F() eqt(pending(),int(N2)) -> F() eqt(pending(),cons(H2,T2)) -> F() eqt(pending(),tuple(H2,T2)) -> F() eqt(pending(),tuplenil(H2)) -> F() eqt(release(),nil()) -> F() eqt(release(),a()) -> F() eqt(release(),excl()) -> F() eqt(release(),false()) -> F() eqt(release(),lock()) -> F() eqt(release(),locker()) -> F() eqt(release(),mcrlrecord()) -> F() eqt(release(),ok()) -> F() eqt(request(),mcrlrecord()) -> F() eqt(request(),ok()) -> F() eqt(request(),pending()) -> F() eqt(request(),release()) -> F() eqt(request(),request()) -> T() eqt(request(),resource()) -> F() eqt(request(),tag()) -> F() eqt(request(),true()) -> F() eqt(request(),undefined()) -> F() eqt(request(),pid(N2)) -> F() eqt(request(),int(N2)) -> F() eqt(request(),cons(H2,T2)) -> F() eqt(request(),tuple(H2,T2)) -> F() eqt(request(),tuplenil(H2)) -> F() eqt(resource(),nil()) -> F() eqt(resource(),a()) -> F() eqt(resource(),excl()) -> F() eqt(resource(),false()) -> F() eqt(resource(),lock()) -> F() eqt(resource(),locker()) -> F() eqt(resource(),mcrlrecord()) -> F() eqt(resource(),ok()) -> F() eqt(resource(),pending()) -> F() eqt(resource(),release()) -> F() eqt(resource(),request()) -> F() eqt(resource(),resource()) -> T() eqt(resource(),tag()) -> F() eqt(resource(),true()) -> F() eqt(resource(),undefined()) -> F() eqt(resource(),pid(N2)) -> F() eqt(resource(),int(N2)) -> F() eqt(resource(),cons(H2,T2)) -> F() eqt(resource(),tuple(H2,T2)) -> F() eqt(resource(),tuplenil(H2)) -> F() eqt(tag(),nil()) -> F() eqt(tag(),a()) -> F() eqt(tag(),excl()) -> F() eqt(tag(),false()) -> F() eqt(tag(),lock()) -> F() eqt(tag(),locker()) -> F() eqt(tag(),mcrlrecord()) -> F() eqt(tag(),ok()) -> F() eqt(tag(),pending()) -> F() eqt(tag(),release()) -> F() eqt(tag(),request()) -> F() eqt(tag(),resource()) -> F() eqt(tag(),tag()) -> T() eqt(tag(),true()) -> F() eqt(tag(),undefined()) -> F() eqt(tag(),pid(N2)) -> F() eqt(tag(),int(N2)) -> F() eqt(tag(),cons(H2,T2)) -> F() eqt(tag(),tuple(H2,T2)) -> F() eqt(tag(),tuplenil(H2)) -> F() eqt(true(),nil()) -> F() eqt(true(),a()) -> F() eqt(true(),excl()) -> F() eqt(true(),false()) -> F() eqt(true(),lock()) -> F() eqt(true(),locker()) -> F() eqt(true(),mcrlrecord()) -> F() eqt(true(),ok()) -> F() eqt(true(),pending()) -> F() eqt(true(),release()) -> F() eqt(true(),request()) -> F() eqt(true(),resource()) -> F() eqt(true(),tag()) -> F() eqt(true(),true()) -> T() eqt(true(),undefined()) -> F() eqt(true(),pid(N2)) -> F() eqt(true(),int(N2)) -> F() eqt(true(),cons(H2,T2)) -> F() eqt(true(),tuple(H2,T2)) -> F() eqt(true(),tuplenil(H2)) -> F() eqt(undefined(),nil()) -> F() eqt(undefined(),a()) -> F() eqt(undefined(),tuplenil(H2)) -> F() eqt(pid(N1),nil()) -> F() eqt(pid(N1),a()) -> F() eqt(pid(N1),excl()) -> F() eqt(pid(N1),false()) -> F() eqt(pid(N1),lock()) -> F() eqt(pid(N1),locker()) -> F() eqt(pid(N1),mcrlrecord()) -> F() eqt(pid(N1),ok()) -> F() eqt(pid(N1),pending()) -> F() eqt(pid(N1),release()) -> F() eqt(pid(N1),request()) -> F() eqt(pid(N1),resource()) -> F() eqt(pid(N1),tag()) -> F() eqt(pid(N1),true()) -> F() eqt(pid(N1),undefined()) -> F() eqt(pid(N1),pid(N2)) -> eqt(N1,N2) eqt(pid(N1),int(N2)) -> F() eqt(pid(N1),cons(H2,T2)) -> F() eqt(pid(N1),tuple(H2,T2)) -> F() eqt(pid(N1),tuplenil(H2)) -> F() eqt(int(N1),nil()) -> F() eqt(int(N1),a()) -> F() eqt(int(N1),excl()) -> F() eqt(int(N1),false()) -> F() eqt(int(N1),lock()) -> F() eqt(int(N1),locker()) -> F() eqt(int(N1),mcrlrecord()) -> F() eqt(int(N1),ok()) -> F() eqt(int(N1),pending()) -> F() eqt(int(N1),release()) -> F() eqt(int(N1),request()) -> F() eqt(int(N1),resource()) -> F() eqt(int(N1),tag()) -> F() eqt(int(N1),true()) -> F() eqt(int(N1),undefined()) -> F() eqt(cons(H1,T1),resource()) -> F() eqt(cons(H1,T1),tag()) -> F() eqt(cons(H1,T1),true()) -> F() eqt(cons(H1,T1),undefined()) -> F() eqt(cons(H1,T1),pid(N2)) -> F() eqt(cons(H1,T1),int(N2)) -> F() eqt(cons(H1,T1),cons(H2,T2)) -> and(eqt(H1,H2),eqt(T1,T2)) eqt(cons(H1,T1),tuple(H2,T2)) -> F() eqt(cons(H1,T1),tuplenil(H2)) -> F() eqt(tuple(H1,T1),nil()) -> F() eqt(tuple(H1,T1),a()) -> F() eqt(tuple(H1,T1),excl()) -> F() eqt(tuple(H1,T1),false()) -> F() eqt(tuple(H1,T1),lock()) -> F() eqt(tuple(H1,T1),locker()) -> F() eqt(tuple(H1,T1),mcrlrecord()) -> F() eqt(tuple(H1,T1),ok()) -> F() eqt(tuple(H1,T1),pending()) -> F() eqt(tuple(H1,T1),release()) -> F() eqt(tuple(H1,T1),request()) -> F() eqt(tuple(H1,T1),resource()) -> F() eqt(tuple(H1,T1),tag()) -> F() eqt(tuple(H1,T1),true()) -> F() eqt(tuple(H1,T1),undefined()) -> F() eqt(tuple(H1,T1),pid(N2)) -> F() eqt(tuple(H1,T1),int(N2)) -> F() eqt(tuple(H1,T1),cons(H2,T2)) -> F() eqt(tuple(H1,T1),tuple(H2,T2)) -> and(eqt(H1,H2),eqt(T1,T2)) eqt(tuple(H1,T1),tuplenil(H2)) -> F() eqt(tuplenil(H1),nil()) -> F() eqt(tuplenil(H1),a()) -> F() eqt(tuplenil(H1),excl()) -> F() eqt(tuplenil(H1),false()) -> F() eqt(tuplenil(H1),lock()) -> F() eqt(tuplenil(H1),locker()) -> F() eqt(tuplenil(H1),mcrlrecord()) -> F() eqt(tuplenil(H1),ok()) -> F() eqt(tuplenil(H1),pending()) -> F() eqt(tuplenil(H1),release()) -> F() eqt(tuplenil(H1),request()) -> F() eqt(tuplenil(H1),resource()) -> F() eqt(tuplenil(H1),tag()) -> F() eqt(tuplenil(H1),true()) -> F() eqt(tuplenil(H1),undefined()) -> F() eqt(tuplenil(H1),pid(N2)) -> F() eqt(tuplenil(H1),int(N2)) -> F() eqt(tuplenil(H1),cons(H2,T2)) -> F() eqt(tuplenil(H1),tuple(H2,T2)) -> F() eqt(tuplenil(H1),tuplenil(H2)) -> eqt(H1,H2) element(int(s(0())),tuplenil(T1)) -> T1 element(int(s(0())),tuple(T1,T2)) -> T1 element(int(s(s(N1))),tuple(T1,T2)) -> element(int(s(N1)),T2) record_new(lock()) -> tuple(mcrlrecord(),tuple(lock(),tuple(undefined(),tuple(nil(),tuplenil(nil()))))) record_extract(tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))), lock(),resource()) -> tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))) record_update(tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))), lock(),pending(),NewF) -> tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(NewF))))) record_updates(Record,Name,nil()) -> Record record_updates(Record,Name,cons(tuple(Field,tuplenil(NewF)),Fields)) -> record_updates(record_update(Record,Name,Field,NewF),Name,Fields) locker2_map_promote_pending(nil(),Pending) -> nil() locker2_map_promote_pending(cons(Lock,Locks),Pending) -> cons(locker2_promote_pending(Lock,Pending),locker2_map_promote_pending(Locks,Pending)) locker2_map_claim_lock(nil(),Resources,Client) -> nil() locker2_map_claim_lock(cons(Lock,Locks),Resources,Client) -> cons(locker2_claim_lock(Lock,Resources,Client),locker2_map_claim_lock(Locks,Resources,Client)) locker2_map_add_pending(nil(),Resources,Client) -> nil() locker2_promote_pending(Lock,Client) -> case0(Client,Lock,record_extract(Lock,lock(),pending())) case0(Client,Lock,cons(Client,Pendings)) -> record_updates(Lock,lock(),cons(tuple(excl(),tuplenil(Client)),cons ( tuple ( pending(),tuplenil(Pendings)), nil ()))) case0(Client,Lock,MCRLFree0) -> Lock locker2_remove_pending(Lock,Client) -> record_updates(Lock,lock(),cons(tuple(pending(),tuplenil(subtract (record_extract (Lock,lock(),pending()), cons(Client,nil())))), nil())) locker2_add_pending(Lock,Resources,Client) -> case1(Client,Resources,Lock,member(record_extract(Lock,lock(),resource()),Resources)) case1(Client,Resources,Lock,true()) -> record_updates(Lock,lock(),cons(tuple(pending(),tuplenil(append( record_extract ( Lock,lock(),pending()), cons (Client,nil())))), nil())) case1(Client,Resources,Lock,false()) -> Lock locker2_release_lock(Lock,Client) -> case2(Client,Lock,gen_modtageq(Client,record_extract(Lock,lock(),excl()))) case2(Client,Lock,true()) -> record_updates(Lock,lock(),cons(tuple(excllock(),excl()),nil())) case4(Client,Lock,MCRLFree1) -> false() locker2_obtainables(nil(),Client) -> true() locker2_obtainables(cons(Lock,Locks),Client) -> case5(Client,Locks,Lock,member(Client,record_extract(Lock,lock(),pending()))) case5(Client,Locks,Lock,true()) -> andt(locker2_obtainable(Lock,Client),locker2_obtainables(Locks,Client)) case5(Client,Locks,Lock,false()) -> locker2_obtainables(Locks,Client) locker2_check_available(Resource,nil()) -> false() locker2_check_available(Resource,cons(Lock,Locks)) -> case6(Locks,Lock,Resource,equal(Resource,record_extract(Lock,lock(),resource()))) case6(Locks,Lock,Resource,true()) -> andt(equal(record_extract(Lock,lock(),excl()),nil()),equal(record_extract (Lock,lock(),pending()), nil())) case6(Locks,Lock,Resource,false()) -> locker2_check_available(Resource,Locks) locker2_check_availables(nil(),Locks) -> true() locker2_check_availables(cons(Resource,Resources),Locks) -> andt(locker2_check_available(Resource,Locks),locker2_check_availables(Resources,Locks)) locker2_adduniq(nil(),List) -> List append(cons(Head,Tail),List) -> cons(Head,append(Tail,List)) subtract(List,nil()) -> List subtract(List,cons(Head,Tail)) -> subtract(delete(Head,List),Tail) delete(E,nil()) -> nil() delete(E,cons(Head,Tail)) -> case8(Tail,Head,E,equal(E,Head)) case8(Tail,Head,E,true()) -> Tail case8(Tail,Head,E,false()) -> cons(Head,delete(E,Tail)) gen_tag(Pid) -> tuple(Pid,tuplenil(tag())) gen_modtageq(Client1,Client2) -> equal(Client1,Client2) member(E,nil()) -> false() member(E,cons(Head,Tail)) -> case9(Tail,Head,E,equal(E,Head)) case9(Tail,Head,E,true()) -> true() case9(Tail,Head,E,false()) -> member(E,Tail) eqs(empty(),empty()) -> T() eqs(empty(),stack(E2,S2)) -> F() eqs(stack(E1,S1),empty()) -> F() eqs(stack(E1,S1),stack(E2,S2)) -> and(eqt(E1,E2),eqs(S1,S2)) pushs(E1,S1) -> stack(E1,S1) pops(stack(E1,S1)) -> S1 tops(stack(E1,S1)) -> E1 istops(E1,empty()) -> F() istops(E1,stack(E2,S1)) -> eqt(E1,E2) eqc(nocalls(),nocalls()) -> T() eqc(nocalls(),calls(E2,S2,CS2)) -> F() eqc(calls(E1,S1,CS1),nocalls()) -> F() eqc(calls(E1,S1,CS1),calls(E2,S2,CS2)) -> and(eqt(E1,E2),and(eqs(S1,S2),eqc(CS1,CS2))) push(E1,E2,nocalls()) -> calls(E1,stack(E2,empty()),nocalls()) push(E1,E2,calls(E3,S1,CS1)) -> push1(E1,E2,E3,S1,CS1,eqt(E1,E3)) push1(E1,E2,E3,S1,CS1,T()) -> calls(E3,pushs(E2,S1),CS1) Subterm Criterion Processor: simple projection: pi(element#) = 1 problem: DPs: TRS: or(T(),T()) -> T() or(F(),T()) -> T() or(T(),F()) -> T() or(F(),F()) -> F() and(T(),B) -> B and(B,T()) -> B and(F(),B) -> F() and(B,F()) -> F() imp(T(),B) -> B imp(F(),B) -> T() not(T()) -> F() not(F()) -> T() if(T(),B1,B2) -> B1 if(F(),B1,B2) -> B2 eq(T(),T()) -> T() eq(F(),F()) -> T() eq(T(),F()) -> F() eq(F(),T()) -> F() eqt(nil(),undefined()) -> F() eqt(nil(),pid(N2)) -> F() eqt(nil(),int(N2)) -> F() eqt(nil(),cons(H2,T2)) -> F() eqt(nil(),tuple(H2,T2)) -> F() eqt(nil(),tuplenil(H2)) -> F() eqt(a(),nil()) -> F() eqt(a(),a()) -> T() eqt(a(),excl()) -> F() eqt(a(),false()) -> F() eqt(a(),lock()) -> F() eqt(a(),locker()) -> F() eqt(a(),mcrlrecord()) -> F() eqt(a(),ok()) -> F() eqt(a(),pending()) -> F() eqt(a(),release()) -> F() eqt(a(),request()) -> F() eqt(a(),resource()) -> F() eqt(a(),tag()) -> F() eqt(a(),true()) -> F() eqt(a(),undefined()) -> F() eqt(a(),pid(N2)) -> F() eqt(a(),int(N2)) -> F() eqt(a(),cons(H2,T2)) -> F() eqt(a(),tuple(H2,T2)) -> F() eqt(a(),tuplenil(H2)) -> F() eqt(excl(),nil()) -> F() eqt(excl(),a()) -> F() eqt(excl(),excl()) -> T() eqt(excl(),false()) -> F() eqt(excl(),lock()) -> F() eqt(excl(),locker()) -> F() eqt(excl(),mcrlrecord()) -> F() eqt(excl(),ok()) -> F() eqt(excl(),pending()) -> F() eqt(excl(),release()) -> F() eqt(excl(),request()) -> F() eqt(excl(),resource()) -> F() eqt(excl(),tag()) -> F() eqt(excl(),true()) -> F() eqt(excl(),undefined()) -> F() eqt(excl(),pid(N2)) -> F() eqt(excl(),eqt(false(),int(N2))) -> F() eqt(false(),cons(H2,T2)) -> F() eqt(false(),tuple(H2,T2)) -> F() eqt(false(),tuplenil(H2)) -> F() eqt(lock(),nil()) -> F() eqt(lock(),a()) -> F() eqt(lock(),excl()) -> F() eqt(lock(),false()) -> F() eqt(lock(),lock()) -> T() eqt(lock(),locker()) -> F() eqt(lock(),mcrlrecord()) -> F() eqt(lock(),ok()) -> F() eqt(lock(),pending()) -> F() eqt(lock(),release()) -> F() eqt(lock(),request()) -> F() eqt(lock(),resource()) -> F() eqt(lock(),tag()) -> F() eqt(lock(),true()) -> F() eqt(lock(),undefined()) -> F() eqt(lock(),pid(N2)) -> F() eqt(lock(),int(N2)) -> F() eqt(lock(),cons(H2,T2)) -> F() eqt(lock(),tuple(H2,T2)) -> F() eqt(lock(),tuplenil(H2)) -> F() eqt(locker(),nil()) -> F() eqt(locker(),a()) -> F() eqt(locker(),excl()) -> F() eqt(locker(),false()) -> F() eqt(locker(),lock()) -> F() eqt(locker(),locker()) -> T() eqt(locker(),mcrlrecord()) -> F() eqt(locker(),ok()) -> F() eqt(locker(),pending()) -> F() eqt(locker(),release()) -> F() eqt(locker(),request()) -> F() eqt(locker(),resource()) -> F() eqt(locker(),tag()) -> F() eqt(locker(),true()) -> F() eqt(locker(),undefined()) -> F() eqt(locker(),pid(N2)) -> F() eqt(locker(),int(N2)) -> F() eqt(locker(),cons(H2,T2)) -> F() eqt(locker(),tuple(H2,T2)) -> F() eqt(locker(),tuplenil(H2)) -> F() eqt(mcrlrecord(),nil()) -> F() eqt(mcrlrecord(),a()) -> F() eqt(mcrlrecord(),excl()) -> F() eqt(mcrlrecord(),false()) -> F() eqt(mcrlrecord(),lock()) -> F() eqt(mcrlrecord(),locker()) -> F() eqt(mcrlrecord(),mcrlrecord()) -> T() eqt(mcrlrecord(),ok()) -> F() eqt(mcrlrecord(),pending()) -> F() eqt(mcrlrecord(),release()) -> F() eqt(mcrlrecord(),request()) -> F() eqt(mcrlrecord(),resource()) -> F() eqt(ok(),resource()) -> F() eqt(ok(),tag()) -> F() eqt(ok(),true()) -> F() eqt(ok(),undefined()) -> F() eqt(ok(),pid(N2)) -> F() eqt(ok(),int(N2)) -> F() eqt(ok(),cons(H2,T2)) -> F() eqt(ok(),tuple(H2,T2)) -> F() eqt(ok(),tuplenil(H2)) -> F() eqt(pending(),nil()) -> F() eqt(pending(),a()) -> F() eqt(pending(),excl()) -> F() eqt(pending(),false()) -> F() eqt(pending(),lock()) -> F() eqt(pending(),locker()) -> F() eqt(pending(),mcrlrecord()) -> F() eqt(pending(),ok()) -> F() eqt(pending(),pending()) -> T() eqt(pending(),release()) -> F() eqt(pending(),request()) -> F() eqt(pending(),resource()) -> F() eqt(pending(),tag()) -> F() eqt(pending(),true()) -> F() eqt(pending(),undefined()) -> F() eqt(pending(),pid(N2)) -> F() eqt(pending(),int(N2)) -> F() eqt(pending(),cons(H2,T2)) -> F() eqt(pending(),tuple(H2,T2)) -> F() eqt(pending(),tuplenil(H2)) -> F() eqt(release(),nil()) -> F() eqt(release(),a()) -> F() eqt(release(),excl()) -> F() eqt(release(),false()) -> F() eqt(release(),lock()) -> F() eqt(release(),locker()) -> F() eqt(release(),mcrlrecord()) -> F() eqt(release(),ok()) -> F() eqt(request(),mcrlrecord()) -> F() eqt(request(),ok()) -> F() eqt(request(),pending()) -> F() eqt(request(),release()) -> F() eqt(request(),request()) -> T() eqt(request(),resource()) -> F() eqt(request(),tag()) -> F() eqt(request(),true()) -> F() eqt(request(),undefined()) -> F() eqt(request(),pid(N2)) -> F() eqt(request(),int(N2)) -> F() eqt(request(),cons(H2,T2)) -> F() eqt(request(),tuple(H2,T2)) -> F() eqt(request(),tuplenil(H2)) -> F() eqt(resource(),nil()) -> F() eqt(resource(),a()) -> F() eqt(resource(),excl()) -> F() eqt(resource(),false()) -> F() eqt(resource(),lock()) -> F() eqt(resource(),locker()) -> F() eqt(resource(),mcrlrecord()) -> F() eqt(resource(),ok()) -> F() eqt(resource(),pending()) -> F() eqt(resource(),release()) -> F() eqt(resource(),request()) -> F() eqt(resource(),resource()) -> T() eqt(resource(),tag()) -> F() eqt(resource(),true()) -> F() eqt(resource(),undefined()) -> F() eqt(resource(),pid(N2)) -> F() eqt(resource(),int(N2)) -> F() eqt(resource(),cons(H2,T2)) -> F() eqt(resource(),tuple(H2,T2)) -> F() eqt(resource(),tuplenil(H2)) -> F() eqt(tag(),nil()) -> F() eqt(tag(),a()) -> F() eqt(tag(),excl()) -> F() eqt(tag(),false()) -> F() eqt(tag(),lock()) -> F() eqt(tag(),locker()) -> F() eqt(tag(),mcrlrecord()) -> F() eqt(tag(),ok()) -> F() eqt(tag(),pending()) -> F() eqt(tag(),release()) -> F() eqt(tag(),request()) -> F() eqt(tag(),resource()) -> F() eqt(tag(),tag()) -> T() eqt(tag(),true()) -> F() eqt(tag(),undefined()) -> F() eqt(tag(),pid(N2)) -> F() eqt(tag(),int(N2)) -> F() eqt(tag(),cons(H2,T2)) -> F() eqt(tag(),tuple(H2,T2)) -> F() eqt(tag(),tuplenil(H2)) -> F() eqt(true(),nil()) -> F() eqt(true(),a()) -> F() eqt(true(),excl()) -> F() eqt(true(),false()) -> F() eqt(true(),lock()) -> F() eqt(true(),locker()) -> F() eqt(true(),mcrlrecord()) -> F() eqt(true(),ok()) -> F() eqt(true(),pending()) -> F() eqt(true(),release()) -> F() eqt(true(),request()) -> F() eqt(true(),resource()) -> F() eqt(true(),tag()) -> F() eqt(true(),true()) -> T() eqt(true(),undefined()) -> F() eqt(true(),pid(N2)) -> F() eqt(true(),int(N2)) -> F() eqt(true(),cons(H2,T2)) -> F() eqt(true(),tuple(H2,T2)) -> F() eqt(true(),tuplenil(H2)) -> F() eqt(undefined(),nil()) -> F() eqt(undefined(),a()) -> F() eqt(undefined(),tuplenil(H2)) -> F() eqt(pid(N1),nil()) -> F() eqt(pid(N1),a()) -> F() eqt(pid(N1),excl()) -> F() eqt(pid(N1),false()) -> F() eqt(pid(N1),lock()) -> F() eqt(pid(N1),locker()) -> F() eqt(pid(N1),mcrlrecord()) -> F() eqt(pid(N1),ok()) -> F() eqt(pid(N1),pending()) -> F() eqt(pid(N1),release()) -> F() eqt(pid(N1),request()) -> F() eqt(pid(N1),resource()) -> F() eqt(pid(N1),tag()) -> F() eqt(pid(N1),true()) -> F() eqt(pid(N1),undefined()) -> F() eqt(pid(N1),pid(N2)) -> eqt(N1,N2) eqt(pid(N1),int(N2)) -> F() eqt(pid(N1),cons(H2,T2)) -> F() eqt(pid(N1),tuple(H2,T2)) -> F() eqt(pid(N1),tuplenil(H2)) -> F() eqt(int(N1),nil()) -> F() eqt(int(N1),a()) -> F() eqt(int(N1),excl()) -> F() eqt(int(N1),false()) -> F() eqt(int(N1),lock()) -> F() eqt(int(N1),locker()) -> F() eqt(int(N1),mcrlrecord()) -> F() eqt(int(N1),ok()) -> F() eqt(int(N1),pending()) -> F() eqt(int(N1),release()) -> F() eqt(int(N1),request()) -> F() eqt(int(N1),resource()) -> F() eqt(int(N1),tag()) -> F() eqt(int(N1),true()) -> F() eqt(int(N1),undefined()) -> F() eqt(cons(H1,T1),resource()) -> F() eqt(cons(H1,T1),tag()) -> F() eqt(cons(H1,T1),true()) -> F() eqt(cons(H1,T1),undefined()) -> F() eqt(cons(H1,T1),pid(N2)) -> F() eqt(cons(H1,T1),int(N2)) -> F() eqt(cons(H1,T1),cons(H2,T2)) -> and(eqt(H1,H2),eqt(T1,T2)) eqt(cons(H1,T1),tuple(H2,T2)) -> F() eqt(cons(H1,T1),tuplenil(H2)) -> F() eqt(tuple(H1,T1),nil()) -> F() eqt(tuple(H1,T1),a()) -> F() eqt(tuple(H1,T1),excl()) -> F() eqt(tuple(H1,T1),false()) -> F() eqt(tuple(H1,T1),lock()) -> F() eqt(tuple(H1,T1),locker()) -> F() eqt(tuple(H1,T1),mcrlrecord()) -> F() eqt(tuple(H1,T1),ok()) -> F() eqt(tuple(H1,T1),pending()) -> F() eqt(tuple(H1,T1),release()) -> F() eqt(tuple(H1,T1),request()) -> F() eqt(tuple(H1,T1),resource()) -> F() eqt(tuple(H1,T1),tag()) -> F() eqt(tuple(H1,T1),true()) -> F() eqt(tuple(H1,T1),undefined()) -> F() eqt(tuple(H1,T1),pid(N2)) -> F() eqt(tuple(H1,T1),int(N2)) -> F() eqt(tuple(H1,T1),cons(H2,T2)) -> F() eqt(tuple(H1,T1),tuple(H2,T2)) -> and(eqt(H1,H2),eqt(T1,T2)) eqt(tuple(H1,T1),tuplenil(H2)) -> F() eqt(tuplenil(H1),nil()) -> F() eqt(tuplenil(H1),a()) -> F() eqt(tuplenil(H1),excl()) -> F() eqt(tuplenil(H1),false()) -> F() eqt(tuplenil(H1),lock()) -> F() eqt(tuplenil(H1),locker()) -> F() eqt(tuplenil(H1),mcrlrecord()) -> F() eqt(tuplenil(H1),ok()) -> F() eqt(tuplenil(H1),pending()) -> F() eqt(tuplenil(H1),release()) -> F() eqt(tuplenil(H1),request()) -> F() eqt(tuplenil(H1),resource()) -> F() eqt(tuplenil(H1),tag()) -> F() eqt(tuplenil(H1),true()) -> F() eqt(tuplenil(H1),undefined()) -> F() eqt(tuplenil(H1),pid(N2)) -> F() eqt(tuplenil(H1),int(N2)) -> F() eqt(tuplenil(H1),cons(H2,T2)) -> F() eqt(tuplenil(H1),tuple(H2,T2)) -> F() eqt(tuplenil(H1),tuplenil(H2)) -> eqt(H1,H2) element(int(s(0())),tuplenil(T1)) -> T1 element(int(s(0())),tuple(T1,T2)) -> T1 element(int(s(s(N1))),tuple(T1,T2)) -> element(int(s(N1)),T2) record_new(lock()) -> tuple(mcrlrecord(),tuple(lock(),tuple(undefined(),tuple(nil(),tuplenil(nil()))))) record_extract(tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))), lock(),resource()) -> tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))) record_update(tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))), lock(),pending(),NewF) -> tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(NewF))))) record_updates(Record,Name,nil()) -> Record record_updates(Record,Name,cons(tuple(Field,tuplenil(NewF)),Fields)) -> record_updates(record_update(Record,Name,Field,NewF),Name,Fields) locker2_map_promote_pending(nil(),Pending) -> nil() locker2_map_promote_pending(cons(Lock,Locks),Pending) -> cons(locker2_promote_pending(Lock,Pending),locker2_map_promote_pending(Locks,Pending)) locker2_map_claim_lock(nil(),Resources,Client) -> nil() locker2_map_claim_lock(cons(Lock,Locks),Resources,Client) -> cons(locker2_claim_lock(Lock,Resources,Client),locker2_map_claim_lock (Locks,Resources,Client)) locker2_map_add_pending(nil(),Resources,Client) -> nil() locker2_promote_pending(Lock,Client) -> case0(Client,Lock,record_extract(Lock,lock(),pending())) case0(Client,Lock,cons(Client,Pendings)) -> record_updates(Lock,lock(),cons(tuple(excl(),tuplenil(Client)), cons(tuple(pending(),tuplenil(Pendings)),nil()))) case0(Client,Lock,MCRLFree0) -> Lock locker2_remove_pending(Lock,Client) -> record_updates(Lock,lock(),cons(tuple(pending(),tuplenil(subtract (record_extract (Lock,lock(),pending()), cons (Client,nil())))), nil())) locker2_add_pending(Lock,Resources,Client) -> case1(Client,Resources,Lock,member(record_extract(Lock,lock(),resource()),Resources)) case1(Client,Resources,Lock,true()) -> record_updates(Lock,lock(),cons(tuple(pending(),tuplenil(append (record_extract (Lock,lock(),pending()), cons (Client,nil())))), nil())) case1(Client,Resources,Lock,false()) -> Lock locker2_release_lock(Lock,Client) -> case2(Client,Lock,gen_modtageq(Client,record_extract(Lock,lock(),excl()))) case2(Client,Lock,true()) -> record_updates(Lock,lock(),cons(tuple(excllock(),excl()),nil())) case4(Client,Lock,MCRLFree1) -> false() locker2_obtainables(nil(),Client) -> true() locker2_obtainables(cons(Lock,Locks),Client) -> case5(Client,Locks,Lock,member(Client,record_extract(Lock,lock(),pending()))) case5(Client,Locks,Lock,true()) -> andt(locker2_obtainable(Lock,Client),locker2_obtainables(Locks,Client)) case5(Client,Locks,Lock,false()) -> locker2_obtainables(Locks,Client) locker2_check_available(Resource,nil()) -> false() locker2_check_available(Resource,cons(Lock,Locks)) -> case6(Locks,Lock,Resource,equal(Resource,record_extract(Lock,lock(),resource()))) case6(Locks,Lock,Resource,true()) -> andt(equal(record_extract(Lock,lock(),excl()),nil()),equal(record_extract (Lock,lock(),pending()), nil())) case6(Locks,Lock,Resource,false()) -> locker2_check_available(Resource,Locks) locker2_check_availables(nil(),Locks) -> true() locker2_check_availables(cons(Resource,Resources),Locks) -> andt(locker2_check_available(Resource,Locks),locker2_check_availables(Resources,Locks)) locker2_adduniq(nil(),List) -> List append(cons(Head,Tail),List) -> cons(Head,append(Tail,List)) subtract(List,nil()) -> List subtract(List,cons(Head,Tail)) -> subtract(delete(Head,List),Tail) delete(E,nil()) -> nil() delete(E,cons(Head,Tail)) -> case8(Tail,Head,E,equal(E,Head)) case8(Tail,Head,E,true()) -> Tail case8(Tail,Head,E,false()) -> cons(Head,delete(E,Tail)) gen_tag(Pid) -> tuple(Pid,tuplenil(tag())) gen_modtageq(Client1,Client2) -> equal(Client1,Client2) member(E,nil()) -> false() member(E,cons(Head,Tail)) -> case9(Tail,Head,E,equal(E,Head)) case9(Tail,Head,E,true()) -> true() case9(Tail,Head,E,false()) -> member(E,Tail) eqs(empty(),empty()) -> T() eqs(empty(),stack(E2,S2)) -> F() eqs(stack(E1,S1),empty()) -> F() eqs(stack(E1,S1),stack(E2,S2)) -> and(eqt(E1,E2),eqs(S1,S2)) pushs(E1,S1) -> stack(E1,S1) pops(stack(E1,S1)) -> S1 tops(stack(E1,S1)) -> E1 istops(E1,empty()) -> F() istops(E1,stack(E2,S1)) -> eqt(E1,E2) eqc(nocalls(),nocalls()) -> T() eqc(nocalls(),calls(E2,S2,CS2)) -> F() eqc(calls(E1,S1,CS1),nocalls()) -> F() eqc(calls(E1,S1,CS1),calls(E2,S2,CS2)) -> and(eqt(E1,E2),and(eqs(S1,S2),eqc(CS1,CS2))) push(E1,E2,nocalls()) -> calls(E1,stack(E2,empty()),nocalls()) push(E1,E2,calls(E3,S1,CS1)) -> push1(E1,E2,E3,S1,CS1,eqt(E1,E3)) push1(E1,E2,E3,S1,CS1,T()) -> calls(E3,pushs(E2,S1),CS1) Qed DPs: locker2_map_promote_pending#(cons(Lock,Locks),Pending) -> locker2_map_promote_pending#(Locks,Pending) TRS: or(T(),T()) -> T() or(F(),T()) -> T() or(T(),F()) -> T() or(F(),F()) -> F() and(T(),B) -> B and(B,T()) -> B and(F(),B) -> F() and(B,F()) -> F() imp(T(),B) -> B imp(F(),B) -> T() not(T()) -> F() not(F()) -> T() if(T(),B1,B2) -> B1 if(F(),B1,B2) -> B2 eq(T(),T()) -> T() eq(F(),F()) -> T() eq(T(),F()) -> F() eq(F(),T()) -> F() eqt(nil(),undefined()) -> F() eqt(nil(),pid(N2)) -> F() eqt(nil(),int(N2)) -> F() eqt(nil(),cons(H2,T2)) -> F() eqt(nil(),tuple(H2,T2)) -> F() eqt(nil(),tuplenil(H2)) -> F() eqt(a(),nil()) -> F() eqt(a(),a()) -> T() eqt(a(),excl()) -> F() eqt(a(),false()) -> F() eqt(a(),lock()) -> F() eqt(a(),locker()) -> F() eqt(a(),mcrlrecord()) -> F() eqt(a(),ok()) -> F() eqt(a(),pending()) -> F() eqt(a(),release()) -> F() eqt(a(),request()) -> F() eqt(a(),resource()) -> F() eqt(a(),tag()) -> F() eqt(a(),true()) -> F() eqt(a(),undefined()) -> F() eqt(a(),pid(N2)) -> F() eqt(a(),int(N2)) -> F() eqt(a(),cons(H2,T2)) -> F() eqt(a(),tuple(H2,T2)) -> F() eqt(a(),tuplenil(H2)) -> F() eqt(excl(),nil()) -> F() eqt(excl(),a()) -> F() eqt(excl(),excl()) -> T() eqt(excl(),false()) -> F() eqt(excl(),lock()) -> F() eqt(excl(),locker()) -> F() eqt(excl(),mcrlrecord()) -> F() eqt(excl(),ok()) -> F() eqt(excl(),pending()) -> F() eqt(excl(),release()) -> F() eqt(excl(),request()) -> F() eqt(excl(),resource()) -> F() eqt(excl(),tag()) -> F() eqt(excl(),true()) -> F() eqt(excl(),undefined()) -> F() eqt(excl(),pid(N2)) -> F() eqt(excl(),eqt(false(),int(N2))) -> F() eqt(false(),cons(H2,T2)) -> F() eqt(false(),tuple(H2,T2)) -> F() eqt(false(),tuplenil(H2)) -> F() eqt(lock(),nil()) -> F() eqt(lock(),a()) -> F() eqt(lock(),excl()) -> F() eqt(lock(),false()) -> F() eqt(lock(),lock()) -> T() eqt(lock(),locker()) -> F() eqt(lock(),mcrlrecord()) -> F() eqt(lock(),ok()) -> F() eqt(lock(),pending()) -> F() eqt(lock(),release()) -> F() eqt(lock(),request()) -> F() eqt(lock(),resource()) -> F() eqt(lock(),tag()) -> F() eqt(lock(),true()) -> F() eqt(lock(),undefined()) -> F() eqt(lock(),pid(N2)) -> F() eqt(lock(),int(N2)) -> F() eqt(lock(),cons(H2,T2)) -> F() eqt(lock(),tuple(H2,T2)) -> F() eqt(lock(),tuplenil(H2)) -> F() eqt(locker(),nil()) -> F() eqt(locker(),a()) -> F() eqt(locker(),excl()) -> F() eqt(locker(),false()) -> F() eqt(locker(),lock()) -> F() eqt(locker(),locker()) -> T() eqt(locker(),mcrlrecord()) -> F() eqt(locker(),ok()) -> F() eqt(locker(),pending()) -> F() eqt(locker(),release()) -> F() eqt(locker(),request()) -> F() eqt(locker(),resource()) -> F() eqt(locker(),tag()) -> F() eqt(locker(),true()) -> F() eqt(locker(),undefined()) -> F() eqt(locker(),pid(N2)) -> F() eqt(locker(),int(N2)) -> F() eqt(locker(),cons(H2,T2)) -> F() eqt(locker(),tuple(H2,T2)) -> F() eqt(locker(),tuplenil(H2)) -> F() eqt(mcrlrecord(),nil()) -> F() eqt(mcrlrecord(),a()) -> F() eqt(mcrlrecord(),excl()) -> F() eqt(mcrlrecord(),false()) -> F() eqt(mcrlrecord(),lock()) -> F() eqt(mcrlrecord(),locker()) -> F() eqt(mcrlrecord(),mcrlrecord()) -> T() eqt(mcrlrecord(),ok()) -> F() eqt(mcrlrecord(),pending()) -> F() eqt(mcrlrecord(),release()) -> F() eqt(mcrlrecord(),request()) -> F() eqt(mcrlrecord(),resource()) -> F() eqt(ok(),resource()) -> F() eqt(ok(),tag()) -> F() eqt(ok(),true()) -> F() eqt(ok(),undefined()) -> F() eqt(ok(),pid(N2)) -> F() eqt(ok(),int(N2)) -> F() eqt(ok(),cons(H2,T2)) -> F() eqt(ok(),tuple(H2,T2)) -> F() eqt(ok(),tuplenil(H2)) -> F() eqt(pending(),nil()) -> F() eqt(pending(),a()) -> F() eqt(pending(),excl()) -> F() eqt(pending(),false()) -> F() eqt(pending(),lock()) -> F() eqt(pending(),locker()) -> F() eqt(pending(),mcrlrecord()) -> F() eqt(pending(),ok()) -> F() eqt(pending(),pending()) -> T() eqt(pending(),release()) -> F() eqt(pending(),request()) -> F() eqt(pending(),resource()) -> F() eqt(pending(),tag()) -> F() eqt(pending(),true()) -> F() eqt(pending(),undefined()) -> F() eqt(pending(),pid(N2)) -> F() eqt(pending(),int(N2)) -> F() eqt(pending(),cons(H2,T2)) -> F() eqt(pending(),tuple(H2,T2)) -> F() eqt(pending(),tuplenil(H2)) -> F() eqt(release(),nil()) -> F() eqt(release(),a()) -> F() eqt(release(),excl()) -> F() eqt(release(),false()) -> F() eqt(release(),lock()) -> F() eqt(release(),locker()) -> F() eqt(release(),mcrlrecord()) -> F() eqt(release(),ok()) -> F() eqt(request(),mcrlrecord()) -> F() eqt(request(),ok()) -> F() eqt(request(),pending()) -> F() eqt(request(),release()) -> F() eqt(request(),request()) -> T() eqt(request(),resource()) -> F() eqt(request(),tag()) -> F() eqt(request(),true()) -> F() eqt(request(),undefined()) -> F() eqt(request(),pid(N2)) -> F() eqt(request(),int(N2)) -> F() eqt(request(),cons(H2,T2)) -> F() eqt(request(),tuple(H2,T2)) -> F() eqt(request(),tuplenil(H2)) -> F() eqt(resource(),nil()) -> F() eqt(resource(),a()) -> F() eqt(resource(),excl()) -> F() eqt(resource(),false()) -> F() eqt(resource(),lock()) -> F() eqt(resource(),locker()) -> F() eqt(resource(),mcrlrecord()) -> F() eqt(resource(),ok()) -> F() eqt(resource(),pending()) -> F() eqt(resource(),release()) -> F() eqt(resource(),request()) -> F() eqt(resource(),resource()) -> T() eqt(resource(),tag()) -> F() eqt(resource(),true()) -> F() eqt(resource(),undefined()) -> F() eqt(resource(),pid(N2)) -> F() eqt(resource(),int(N2)) -> F() eqt(resource(),cons(H2,T2)) -> F() eqt(resource(),tuple(H2,T2)) -> F() eqt(resource(),tuplenil(H2)) -> F() eqt(tag(),nil()) -> F() eqt(tag(),a()) -> F() eqt(tag(),excl()) -> F() eqt(tag(),false()) -> F() eqt(tag(),lock()) -> F() eqt(tag(),locker()) -> F() eqt(tag(),mcrlrecord()) -> F() eqt(tag(),ok()) -> F() eqt(tag(),pending()) -> F() eqt(tag(),release()) -> F() eqt(tag(),request()) -> F() eqt(tag(),resource()) -> F() eqt(tag(),tag()) -> T() eqt(tag(),true()) -> F() eqt(tag(),undefined()) -> F() eqt(tag(),pid(N2)) -> F() eqt(tag(),int(N2)) -> F() eqt(tag(),cons(H2,T2)) -> F() eqt(tag(),tuple(H2,T2)) -> F() eqt(tag(),tuplenil(H2)) -> F() eqt(true(),nil()) -> F() eqt(true(),a()) -> F() eqt(true(),excl()) -> F() eqt(true(),false()) -> F() eqt(true(),lock()) -> F() eqt(true(),locker()) -> F() eqt(true(),mcrlrecord()) -> F() eqt(true(),ok()) -> F() eqt(true(),pending()) -> F() eqt(true(),release()) -> F() eqt(true(),request()) -> F() eqt(true(),resource()) -> F() eqt(true(),tag()) -> F() eqt(true(),true()) -> T() eqt(true(),undefined()) -> F() eqt(true(),pid(N2)) -> F() eqt(true(),int(N2)) -> F() eqt(true(),cons(H2,T2)) -> F() eqt(true(),tuple(H2,T2)) -> F() eqt(true(),tuplenil(H2)) -> F() eqt(undefined(),nil()) -> F() eqt(undefined(),a()) -> F() eqt(undefined(),tuplenil(H2)) -> F() eqt(pid(N1),nil()) -> F() eqt(pid(N1),a()) -> F() eqt(pid(N1),excl()) -> F() eqt(pid(N1),false()) -> F() eqt(pid(N1),lock()) -> F() eqt(pid(N1),locker()) -> F() eqt(pid(N1),mcrlrecord()) -> F() eqt(pid(N1),ok()) -> F() eqt(pid(N1),pending()) -> F() eqt(pid(N1),release()) -> F() eqt(pid(N1),request()) -> F() eqt(pid(N1),resource()) -> F() eqt(pid(N1),tag()) -> F() eqt(pid(N1),true()) -> F() eqt(pid(N1),undefined()) -> F() eqt(pid(N1),pid(N2)) -> eqt(N1,N2) eqt(pid(N1),int(N2)) -> F() eqt(pid(N1),cons(H2,T2)) -> F() eqt(pid(N1),tuple(H2,T2)) -> F() eqt(pid(N1),tuplenil(H2)) -> F() eqt(int(N1),nil()) -> F() eqt(int(N1),a()) -> F() eqt(int(N1),excl()) -> F() eqt(int(N1),false()) -> F() eqt(int(N1),lock()) -> F() eqt(int(N1),locker()) -> F() eqt(int(N1),mcrlrecord()) -> F() eqt(int(N1),ok()) -> F() eqt(int(N1),pending()) -> F() eqt(int(N1),release()) -> F() eqt(int(N1),request()) -> F() eqt(int(N1),resource()) -> F() eqt(int(N1),tag()) -> F() eqt(int(N1),true()) -> F() eqt(int(N1),undefined()) -> F() eqt(cons(H1,T1),resource()) -> F() eqt(cons(H1,T1),tag()) -> F() eqt(cons(H1,T1),true()) -> F() eqt(cons(H1,T1),undefined()) -> F() eqt(cons(H1,T1),pid(N2)) -> F() eqt(cons(H1,T1),int(N2)) -> F() eqt(cons(H1,T1),cons(H2,T2)) -> and(eqt(H1,H2),eqt(T1,T2)) eqt(cons(H1,T1),tuple(H2,T2)) -> F() eqt(cons(H1,T1),tuplenil(H2)) -> F() eqt(tuple(H1,T1),nil()) -> F() eqt(tuple(H1,T1),a()) -> F() eqt(tuple(H1,T1),excl()) -> F() eqt(tuple(H1,T1),false()) -> F() eqt(tuple(H1,T1),lock()) -> F() eqt(tuple(H1,T1),locker()) -> F() eqt(tuple(H1,T1),mcrlrecord()) -> F() eqt(tuple(H1,T1),ok()) -> F() eqt(tuple(H1,T1),pending()) -> F() eqt(tuple(H1,T1),release()) -> F() eqt(tuple(H1,T1),request()) -> F() eqt(tuple(H1,T1),resource()) -> F() eqt(tuple(H1,T1),tag()) -> F() eqt(tuple(H1,T1),true()) -> F() eqt(tuple(H1,T1),undefined()) -> F() eqt(tuple(H1,T1),pid(N2)) -> F() eqt(tuple(H1,T1),int(N2)) -> F() eqt(tuple(H1,T1),cons(H2,T2)) -> F() eqt(tuple(H1,T1),tuple(H2,T2)) -> and(eqt(H1,H2),eqt(T1,T2)) eqt(tuple(H1,T1),tuplenil(H2)) -> F() eqt(tuplenil(H1),nil()) -> F() eqt(tuplenil(H1),a()) -> F() eqt(tuplenil(H1),excl()) -> F() eqt(tuplenil(H1),false()) -> F() eqt(tuplenil(H1),lock()) -> F() eqt(tuplenil(H1),locker()) -> F() eqt(tuplenil(H1),mcrlrecord()) -> F() eqt(tuplenil(H1),ok()) -> F() eqt(tuplenil(H1),pending()) -> F() eqt(tuplenil(H1),release()) -> F() eqt(tuplenil(H1),request()) -> F() eqt(tuplenil(H1),resource()) -> F() eqt(tuplenil(H1),tag()) -> F() eqt(tuplenil(H1),true()) -> F() eqt(tuplenil(H1),undefined()) -> F() eqt(tuplenil(H1),pid(N2)) -> F() eqt(tuplenil(H1),int(N2)) -> F() eqt(tuplenil(H1),cons(H2,T2)) -> F() eqt(tuplenil(H1),tuple(H2,T2)) -> F() eqt(tuplenil(H1),tuplenil(H2)) -> eqt(H1,H2) element(int(s(0())),tuplenil(T1)) -> T1 element(int(s(0())),tuple(T1,T2)) -> T1 element(int(s(s(N1))),tuple(T1,T2)) -> element(int(s(N1)),T2) record_new(lock()) -> tuple(mcrlrecord(),tuple(lock(),tuple(undefined(),tuple(nil(),tuplenil(nil()))))) record_extract(tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))), lock(),resource()) -> tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))) record_update(tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))), lock(),pending(),NewF) -> tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(NewF))))) record_updates(Record,Name,nil()) -> Record record_updates(Record,Name,cons(tuple(Field,tuplenil(NewF)),Fields)) -> record_updates(record_update(Record,Name,Field,NewF),Name,Fields) locker2_map_promote_pending(nil(),Pending) -> nil() locker2_map_promote_pending(cons(Lock,Locks),Pending) -> cons(locker2_promote_pending(Lock,Pending),locker2_map_promote_pending(Locks,Pending)) locker2_map_claim_lock(nil(),Resources,Client) -> nil() locker2_map_claim_lock(cons(Lock,Locks),Resources,Client) -> cons(locker2_claim_lock(Lock,Resources,Client),locker2_map_claim_lock(Locks,Resources,Client)) locker2_map_add_pending(nil(),Resources,Client) -> nil() locker2_promote_pending(Lock,Client) -> case0(Client,Lock,record_extract(Lock,lock(),pending())) case0(Client,Lock,cons(Client,Pendings)) -> record_updates(Lock,lock(),cons(tuple(excl(),tuplenil(Client)),cons ( tuple ( pending(),tuplenil(Pendings)), nil ()))) case0(Client,Lock,MCRLFree0) -> Lock locker2_remove_pending(Lock,Client) -> record_updates(Lock,lock(),cons(tuple(pending(),tuplenil(subtract (record_extract (Lock,lock(),pending()), cons(Client,nil())))), nil())) locker2_add_pending(Lock,Resources,Client) -> case1(Client,Resources,Lock,member(record_extract(Lock,lock(),resource()),Resources)) case1(Client,Resources,Lock,true()) -> record_updates(Lock,lock(),cons(tuple(pending(),tuplenil(append( record_extract ( Lock,lock(),pending()), cons (Client,nil())))), nil())) case1(Client,Resources,Lock,false()) -> Lock locker2_release_lock(Lock,Client) -> case2(Client,Lock,gen_modtageq(Client,record_extract(Lock,lock(),excl()))) case2(Client,Lock,true()) -> record_updates(Lock,lock(),cons(tuple(excllock(),excl()),nil())) case4(Client,Lock,MCRLFree1) -> false() locker2_obtainables(nil(),Client) -> true() locker2_obtainables(cons(Lock,Locks),Client) -> case5(Client,Locks,Lock,member(Client,record_extract(Lock,lock(),pending()))) case5(Client,Locks,Lock,true()) -> andt(locker2_obtainable(Lock,Client),locker2_obtainables(Locks,Client)) case5(Client,Locks,Lock,false()) -> locker2_obtainables(Locks,Client) locker2_check_available(Resource,nil()) -> false() locker2_check_available(Resource,cons(Lock,Locks)) -> case6(Locks,Lock,Resource,equal(Resource,record_extract(Lock,lock(),resource()))) case6(Locks,Lock,Resource,true()) -> andt(equal(record_extract(Lock,lock(),excl()),nil()),equal(record_extract (Lock,lock(),pending()), nil())) case6(Locks,Lock,Resource,false()) -> locker2_check_available(Resource,Locks) locker2_check_availables(nil(),Locks) -> true() locker2_check_availables(cons(Resource,Resources),Locks) -> andt(locker2_check_available(Resource,Locks),locker2_check_availables(Resources,Locks)) locker2_adduniq(nil(),List) -> List append(cons(Head,Tail),List) -> cons(Head,append(Tail,List)) subtract(List,nil()) -> List subtract(List,cons(Head,Tail)) -> subtract(delete(Head,List),Tail) delete(E,nil()) -> nil() delete(E,cons(Head,Tail)) -> case8(Tail,Head,E,equal(E,Head)) case8(Tail,Head,E,true()) -> Tail case8(Tail,Head,E,false()) -> cons(Head,delete(E,Tail)) gen_tag(Pid) -> tuple(Pid,tuplenil(tag())) gen_modtageq(Client1,Client2) -> equal(Client1,Client2) member(E,nil()) -> false() member(E,cons(Head,Tail)) -> case9(Tail,Head,E,equal(E,Head)) case9(Tail,Head,E,true()) -> true() case9(Tail,Head,E,false()) -> member(E,Tail) eqs(empty(),empty()) -> T() eqs(empty(),stack(E2,S2)) -> F() eqs(stack(E1,S1),empty()) -> F() eqs(stack(E1,S1),stack(E2,S2)) -> and(eqt(E1,E2),eqs(S1,S2)) pushs(E1,S1) -> stack(E1,S1) pops(stack(E1,S1)) -> S1 tops(stack(E1,S1)) -> E1 istops(E1,empty()) -> F() istops(E1,stack(E2,S1)) -> eqt(E1,E2) eqc(nocalls(),nocalls()) -> T() eqc(nocalls(),calls(E2,S2,CS2)) -> F() eqc(calls(E1,S1,CS1),nocalls()) -> F() eqc(calls(E1,S1,CS1),calls(E2,S2,CS2)) -> and(eqt(E1,E2),and(eqs(S1,S2),eqc(CS1,CS2))) push(E1,E2,nocalls()) -> calls(E1,stack(E2,empty()),nocalls()) push(E1,E2,calls(E3,S1,CS1)) -> push1(E1,E2,E3,S1,CS1,eqt(E1,E3)) push1(E1,E2,E3,S1,CS1,T()) -> calls(E3,pushs(E2,S1),CS1) Subterm Criterion Processor: simple projection: pi(locker2_map_promote_pending#) = 0 problem: DPs: TRS: or(T(),T()) -> T() or(F(),T()) -> T() or(T(),F()) -> T() or(F(),F()) -> F() and(T(),B) -> B and(B,T()) -> B and(F(),B) -> F() and(B,F()) -> F() imp(T(),B) -> B imp(F(),B) -> T() not(T()) -> F() not(F()) -> T() if(T(),B1,B2) -> B1 if(F(),B1,B2) -> B2 eq(T(),T()) -> T() eq(F(),F()) -> T() eq(T(),F()) -> F() eq(F(),T()) -> F() eqt(nil(),undefined()) -> F() eqt(nil(),pid(N2)) -> F() eqt(nil(),int(N2)) -> F() eqt(nil(),cons(H2,T2)) -> F() eqt(nil(),tuple(H2,T2)) -> F() eqt(nil(),tuplenil(H2)) -> F() eqt(a(),nil()) -> F() eqt(a(),a()) -> T() eqt(a(),excl()) -> F() eqt(a(),false()) -> F() eqt(a(),lock()) -> F() eqt(a(),locker()) -> F() eqt(a(),mcrlrecord()) -> F() eqt(a(),ok()) -> F() eqt(a(),pending()) -> F() eqt(a(),release()) -> F() eqt(a(),request()) -> F() eqt(a(),resource()) -> F() eqt(a(),tag()) -> F() eqt(a(),true()) -> F() eqt(a(),undefined()) -> F() eqt(a(),pid(N2)) -> F() eqt(a(),int(N2)) -> F() eqt(a(),cons(H2,T2)) -> F() eqt(a(),tuple(H2,T2)) -> F() eqt(a(),tuplenil(H2)) -> F() eqt(excl(),nil()) -> F() eqt(excl(),a()) -> F() eqt(excl(),excl()) -> T() eqt(excl(),false()) -> F() eqt(excl(),lock()) -> F() eqt(excl(),locker()) -> F() eqt(excl(),mcrlrecord()) -> F() eqt(excl(),ok()) -> F() eqt(excl(),pending()) -> F() eqt(excl(),release()) -> F() eqt(excl(),request()) -> F() eqt(excl(),resource()) -> F() eqt(excl(),tag()) -> F() eqt(excl(),true()) -> F() eqt(excl(),undefined()) -> F() eqt(excl(),pid(N2)) -> F() eqt(excl(),eqt(false(),int(N2))) -> F() eqt(false(),cons(H2,T2)) -> F() eqt(false(),tuple(H2,T2)) -> F() eqt(false(),tuplenil(H2)) -> F() eqt(lock(),nil()) -> F() eqt(lock(),a()) -> F() eqt(lock(),excl()) -> F() eqt(lock(),false()) -> F() eqt(lock(),lock()) -> T() eqt(lock(),locker()) -> F() eqt(lock(),mcrlrecord()) -> F() eqt(lock(),ok()) -> F() eqt(lock(),pending()) -> F() eqt(lock(),release()) -> F() eqt(lock(),request()) -> F() eqt(lock(),resource()) -> F() eqt(lock(),tag()) -> F() eqt(lock(),true()) -> F() eqt(lock(),undefined()) -> F() eqt(lock(),pid(N2)) -> F() eqt(lock(),int(N2)) -> F() eqt(lock(),cons(H2,T2)) -> F() eqt(lock(),tuple(H2,T2)) -> F() eqt(lock(),tuplenil(H2)) -> F() eqt(locker(),nil()) -> F() eqt(locker(),a()) -> F() eqt(locker(),excl()) -> F() eqt(locker(),false()) -> F() eqt(locker(),lock()) -> F() eqt(locker(),locker()) -> T() eqt(locker(),mcrlrecord()) -> F() eqt(locker(),ok()) -> F() eqt(locker(),pending()) -> F() eqt(locker(),release()) -> F() eqt(locker(),request()) -> F() eqt(locker(),resource()) -> F() eqt(locker(),tag()) -> F() eqt(locker(),true()) -> F() eqt(locker(),undefined()) -> F() eqt(locker(),pid(N2)) -> F() eqt(locker(),int(N2)) -> F() eqt(locker(),cons(H2,T2)) -> F() eqt(locker(),tuple(H2,T2)) -> F() eqt(locker(),tuplenil(H2)) -> F() eqt(mcrlrecord(),nil()) -> F() eqt(mcrlrecord(),a()) -> F() eqt(mcrlrecord(),excl()) -> F() eqt(mcrlrecord(),false()) -> F() eqt(mcrlrecord(),lock()) -> F() eqt(mcrlrecord(),locker()) -> F() eqt(mcrlrecord(),mcrlrecord()) -> T() eqt(mcrlrecord(),ok()) -> F() eqt(mcrlrecord(),pending()) -> F() eqt(mcrlrecord(),release()) -> F() eqt(mcrlrecord(),request()) -> F() eqt(mcrlrecord(),resource()) -> F() eqt(ok(),resource()) -> F() eqt(ok(),tag()) -> F() eqt(ok(),true()) -> F() eqt(ok(),undefined()) -> F() eqt(ok(),pid(N2)) -> F() eqt(ok(),int(N2)) -> F() eqt(ok(),cons(H2,T2)) -> F() eqt(ok(),tuple(H2,T2)) -> F() eqt(ok(),tuplenil(H2)) -> F() eqt(pending(),nil()) -> F() eqt(pending(),a()) -> F() eqt(pending(),excl()) -> F() eqt(pending(),false()) -> F() eqt(pending(),lock()) -> F() eqt(pending(),locker()) -> F() eqt(pending(),mcrlrecord()) -> F() eqt(pending(),ok()) -> F() eqt(pending(),pending()) -> T() eqt(pending(),release()) -> F() eqt(pending(),request()) -> F() eqt(pending(),resource()) -> F() eqt(pending(),tag()) -> F() eqt(pending(),true()) -> F() eqt(pending(),undefined()) -> F() eqt(pending(),pid(N2)) -> F() eqt(pending(),int(N2)) -> F() eqt(pending(),cons(H2,T2)) -> F() eqt(pending(),tuple(H2,T2)) -> F() eqt(pending(),tuplenil(H2)) -> F() eqt(release(),nil()) -> F() eqt(release(),a()) -> F() eqt(release(),excl()) -> F() eqt(release(),false()) -> F() eqt(release(),lock()) -> F() eqt(release(),locker()) -> F() eqt(release(),mcrlrecord()) -> F() eqt(release(),ok()) -> F() eqt(request(),mcrlrecord()) -> F() eqt(request(),ok()) -> F() eqt(request(),pending()) -> F() eqt(request(),release()) -> F() eqt(request(),request()) -> T() eqt(request(),resource()) -> F() eqt(request(),tag()) -> F() eqt(request(),true()) -> F() eqt(request(),undefined()) -> F() eqt(request(),pid(N2)) -> F() eqt(request(),int(N2)) -> F() eqt(request(),cons(H2,T2)) -> F() eqt(request(),tuple(H2,T2)) -> F() eqt(request(),tuplenil(H2)) -> F() eqt(resource(),nil()) -> F() eqt(resource(),a()) -> F() eqt(resource(),excl()) -> F() eqt(resource(),false()) -> F() eqt(resource(),lock()) -> F() eqt(resource(),locker()) -> F() eqt(resource(),mcrlrecord()) -> F() eqt(resource(),ok()) -> F() eqt(resource(),pending()) -> F() eqt(resource(),release()) -> F() eqt(resource(),request()) -> F() eqt(resource(),resource()) -> T() eqt(resource(),tag()) -> F() eqt(resource(),true()) -> F() eqt(resource(),undefined()) -> F() eqt(resource(),pid(N2)) -> F() eqt(resource(),int(N2)) -> F() eqt(resource(),cons(H2,T2)) -> F() eqt(resource(),tuple(H2,T2)) -> F() eqt(resource(),tuplenil(H2)) -> F() eqt(tag(),nil()) -> F() eqt(tag(),a()) -> F() eqt(tag(),excl()) -> F() eqt(tag(),false()) -> F() eqt(tag(),lock()) -> F() eqt(tag(),locker()) -> F() eqt(tag(),mcrlrecord()) -> F() eqt(tag(),ok()) -> F() eqt(tag(),pending()) -> F() eqt(tag(),release()) -> F() eqt(tag(),request()) -> F() eqt(tag(),resource()) -> F() eqt(tag(),tag()) -> T() eqt(tag(),true()) -> F() eqt(tag(),undefined()) -> F() eqt(tag(),pid(N2)) -> F() eqt(tag(),int(N2)) -> F() eqt(tag(),cons(H2,T2)) -> F() eqt(tag(),tuple(H2,T2)) -> F() eqt(tag(),tuplenil(H2)) -> F() eqt(true(),nil()) -> F() eqt(true(),a()) -> F() eqt(true(),excl()) -> F() eqt(true(),false()) -> F() eqt(true(),lock()) -> F() eqt(true(),locker()) -> F() eqt(true(),mcrlrecord()) -> F() eqt(true(),ok()) -> F() eqt(true(),pending()) -> F() eqt(true(),release()) -> F() eqt(true(),request()) -> F() eqt(true(),resource()) -> F() eqt(true(),tag()) -> F() eqt(true(),true()) -> T() eqt(true(),undefined()) -> F() eqt(true(),pid(N2)) -> F() eqt(true(),int(N2)) -> F() eqt(true(),cons(H2,T2)) -> F() eqt(true(),tuple(H2,T2)) -> F() eqt(true(),tuplenil(H2)) -> F() eqt(undefined(),nil()) -> F() eqt(undefined(),a()) -> F() eqt(undefined(),tuplenil(H2)) -> F() eqt(pid(N1),nil()) -> F() eqt(pid(N1),a()) -> F() eqt(pid(N1),excl()) -> F() eqt(pid(N1),false()) -> F() eqt(pid(N1),lock()) -> F() eqt(pid(N1),locker()) -> F() eqt(pid(N1),mcrlrecord()) -> F() eqt(pid(N1),ok()) -> F() eqt(pid(N1),pending()) -> F() eqt(pid(N1),release()) -> F() eqt(pid(N1),request()) -> F() eqt(pid(N1),resource()) -> F() eqt(pid(N1),tag()) -> F() eqt(pid(N1),true()) -> F() eqt(pid(N1),undefined()) -> F() eqt(pid(N1),pid(N2)) -> eqt(N1,N2) eqt(pid(N1),int(N2)) -> F() eqt(pid(N1),cons(H2,T2)) -> F() eqt(pid(N1),tuple(H2,T2)) -> F() eqt(pid(N1),tuplenil(H2)) -> F() eqt(int(N1),nil()) -> F() eqt(int(N1),a()) -> F() eqt(int(N1),excl()) -> F() eqt(int(N1),false()) -> F() eqt(int(N1),lock()) -> F() eqt(int(N1),locker()) -> F() eqt(int(N1),mcrlrecord()) -> F() eqt(int(N1),ok()) -> F() eqt(int(N1),pending()) -> F() eqt(int(N1),release()) -> F() eqt(int(N1),request()) -> F() eqt(int(N1),resource()) -> F() eqt(int(N1),tag()) -> F() eqt(int(N1),true()) -> F() eqt(int(N1),undefined()) -> F() eqt(cons(H1,T1),resource()) -> F() eqt(cons(H1,T1),tag()) -> F() eqt(cons(H1,T1),true()) -> F() eqt(cons(H1,T1),undefined()) -> F() eqt(cons(H1,T1),pid(N2)) -> F() eqt(cons(H1,T1),int(N2)) -> F() eqt(cons(H1,T1),cons(H2,T2)) -> and(eqt(H1,H2),eqt(T1,T2)) eqt(cons(H1,T1),tuple(H2,T2)) -> F() eqt(cons(H1,T1),tuplenil(H2)) -> F() eqt(tuple(H1,T1),nil()) -> F() eqt(tuple(H1,T1),a()) -> F() eqt(tuple(H1,T1),excl()) -> F() eqt(tuple(H1,T1),false()) -> F() eqt(tuple(H1,T1),lock()) -> F() eqt(tuple(H1,T1),locker()) -> F() eqt(tuple(H1,T1),mcrlrecord()) -> F() eqt(tuple(H1,T1),ok()) -> F() eqt(tuple(H1,T1),pending()) -> F() eqt(tuple(H1,T1),release()) -> F() eqt(tuple(H1,T1),request()) -> F() eqt(tuple(H1,T1),resource()) -> F() eqt(tuple(H1,T1),tag()) -> F() eqt(tuple(H1,T1),true()) -> F() eqt(tuple(H1,T1),undefined()) -> F() eqt(tuple(H1,T1),pid(N2)) -> F() eqt(tuple(H1,T1),int(N2)) -> F() eqt(tuple(H1,T1),cons(H2,T2)) -> F() eqt(tuple(H1,T1),tuple(H2,T2)) -> and(eqt(H1,H2),eqt(T1,T2)) eqt(tuple(H1,T1),tuplenil(H2)) -> F() eqt(tuplenil(H1),nil()) -> F() eqt(tuplenil(H1),a()) -> F() eqt(tuplenil(H1),excl()) -> F() eqt(tuplenil(H1),false()) -> F() eqt(tuplenil(H1),lock()) -> F() eqt(tuplenil(H1),locker()) -> F() eqt(tuplenil(H1),mcrlrecord()) -> F() eqt(tuplenil(H1),ok()) -> F() eqt(tuplenil(H1),pending()) -> F() eqt(tuplenil(H1),release()) -> F() eqt(tuplenil(H1),request()) -> F() eqt(tuplenil(H1),resource()) -> F() eqt(tuplenil(H1),tag()) -> F() eqt(tuplenil(H1),true()) -> F() eqt(tuplenil(H1),undefined()) -> F() eqt(tuplenil(H1),pid(N2)) -> F() eqt(tuplenil(H1),int(N2)) -> F() eqt(tuplenil(H1),cons(H2,T2)) -> F() eqt(tuplenil(H1),tuple(H2,T2)) -> F() eqt(tuplenil(H1),tuplenil(H2)) -> eqt(H1,H2) element(int(s(0())),tuplenil(T1)) -> T1 element(int(s(0())),tuple(T1,T2)) -> T1 element(int(s(s(N1))),tuple(T1,T2)) -> element(int(s(N1)),T2) record_new(lock()) -> tuple(mcrlrecord(),tuple(lock(),tuple(undefined(),tuple(nil(),tuplenil(nil()))))) record_extract(tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))), lock(),resource()) -> tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))) record_update(tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))), lock(),pending(),NewF) -> tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(NewF))))) record_updates(Record,Name,nil()) -> Record record_updates(Record,Name,cons(tuple(Field,tuplenil(NewF)),Fields)) -> record_updates(record_update(Record,Name,Field,NewF),Name,Fields) locker2_map_promote_pending(nil(),Pending) -> nil() locker2_map_promote_pending(cons(Lock,Locks),Pending) -> cons(locker2_promote_pending(Lock,Pending),locker2_map_promote_pending(Locks,Pending)) locker2_map_claim_lock(nil(),Resources,Client) -> nil() locker2_map_claim_lock(cons(Lock,Locks),Resources,Client) -> cons(locker2_claim_lock(Lock,Resources,Client),locker2_map_claim_lock (Locks,Resources,Client)) locker2_map_add_pending(nil(),Resources,Client) -> nil() locker2_promote_pending(Lock,Client) -> case0(Client,Lock,record_extract(Lock,lock(),pending())) case0(Client,Lock,cons(Client,Pendings)) -> record_updates(Lock,lock(),cons(tuple(excl(),tuplenil(Client)), cons(tuple(pending(),tuplenil(Pendings)),nil()))) case0(Client,Lock,MCRLFree0) -> Lock locker2_remove_pending(Lock,Client) -> record_updates(Lock,lock(),cons(tuple(pending(),tuplenil(subtract (record_extract (Lock,lock(),pending()), cons (Client,nil())))), nil())) locker2_add_pending(Lock,Resources,Client) -> case1(Client,Resources,Lock,member(record_extract(Lock,lock(),resource()),Resources)) case1(Client,Resources,Lock,true()) -> record_updates(Lock,lock(),cons(tuple(pending(),tuplenil(append (record_extract (Lock,lock(),pending()), cons (Client,nil())))), nil())) case1(Client,Resources,Lock,false()) -> Lock locker2_release_lock(Lock,Client) -> case2(Client,Lock,gen_modtageq(Client,record_extract(Lock,lock(),excl()))) case2(Client,Lock,true()) -> record_updates(Lock,lock(),cons(tuple(excllock(),excl()),nil())) case4(Client,Lock,MCRLFree1) -> false() locker2_obtainables(nil(),Client) -> true() locker2_obtainables(cons(Lock,Locks),Client) -> case5(Client,Locks,Lock,member(Client,record_extract(Lock,lock(),pending()))) case5(Client,Locks,Lock,true()) -> andt(locker2_obtainable(Lock,Client),locker2_obtainables(Locks,Client)) case5(Client,Locks,Lock,false()) -> locker2_obtainables(Locks,Client) locker2_check_available(Resource,nil()) -> false() locker2_check_available(Resource,cons(Lock,Locks)) -> case6(Locks,Lock,Resource,equal(Resource,record_extract(Lock,lock(),resource()))) case6(Locks,Lock,Resource,true()) -> andt(equal(record_extract(Lock,lock(),excl()),nil()),equal(record_extract (Lock,lock(),pending()), nil())) case6(Locks,Lock,Resource,false()) -> locker2_check_available(Resource,Locks) locker2_check_availables(nil(),Locks) -> true() locker2_check_availables(cons(Resource,Resources),Locks) -> andt(locker2_check_available(Resource,Locks),locker2_check_availables(Resources,Locks)) locker2_adduniq(nil(),List) -> List append(cons(Head,Tail),List) -> cons(Head,append(Tail,List)) subtract(List,nil()) -> List subtract(List,cons(Head,Tail)) -> subtract(delete(Head,List),Tail) delete(E,nil()) -> nil() delete(E,cons(Head,Tail)) -> case8(Tail,Head,E,equal(E,Head)) case8(Tail,Head,E,true()) -> Tail case8(Tail,Head,E,false()) -> cons(Head,delete(E,Tail)) gen_tag(Pid) -> tuple(Pid,tuplenil(tag())) gen_modtageq(Client1,Client2) -> equal(Client1,Client2) member(E,nil()) -> false() member(E,cons(Head,Tail)) -> case9(Tail,Head,E,equal(E,Head)) case9(Tail,Head,E,true()) -> true() case9(Tail,Head,E,false()) -> member(E,Tail) eqs(empty(),empty()) -> T() eqs(empty(),stack(E2,S2)) -> F() eqs(stack(E1,S1),empty()) -> F() eqs(stack(E1,S1),stack(E2,S2)) -> and(eqt(E1,E2),eqs(S1,S2)) pushs(E1,S1) -> stack(E1,S1) pops(stack(E1,S1)) -> S1 tops(stack(E1,S1)) -> E1 istops(E1,empty()) -> F() istops(E1,stack(E2,S1)) -> eqt(E1,E2) eqc(nocalls(),nocalls()) -> T() eqc(nocalls(),calls(E2,S2,CS2)) -> F() eqc(calls(E1,S1,CS1),nocalls()) -> F() eqc(calls(E1,S1,CS1),calls(E2,S2,CS2)) -> and(eqt(E1,E2),and(eqs(S1,S2),eqc(CS1,CS2))) push(E1,E2,nocalls()) -> calls(E1,stack(E2,empty()),nocalls()) push(E1,E2,calls(E3,S1,CS1)) -> push1(E1,E2,E3,S1,CS1,eqt(E1,E3)) push1(E1,E2,E3,S1,CS1,T()) -> calls(E3,pushs(E2,S1),CS1) Qed DPs: locker2_map_claim_lock#(cons(Lock,Locks),Resources,Client) -> locker2_map_claim_lock#(Locks,Resources,Client) TRS: or(T(),T()) -> T() or(F(),T()) -> T() or(T(),F()) -> T() or(F(),F()) -> F() and(T(),B) -> B and(B,T()) -> B and(F(),B) -> F() and(B,F()) -> F() imp(T(),B) -> B imp(F(),B) -> T() not(T()) -> F() not(F()) -> T() if(T(),B1,B2) -> B1 if(F(),B1,B2) -> B2 eq(T(),T()) -> T() eq(F(),F()) -> T() eq(T(),F()) -> F() eq(F(),T()) -> F() eqt(nil(),undefined()) -> F() eqt(nil(),pid(N2)) -> F() eqt(nil(),int(N2)) -> F() eqt(nil(),cons(H2,T2)) -> F() eqt(nil(),tuple(H2,T2)) -> F() eqt(nil(),tuplenil(H2)) -> F() eqt(a(),nil()) -> F() eqt(a(),a()) -> T() eqt(a(),excl()) -> F() eqt(a(),false()) -> F() eqt(a(),lock()) -> F() eqt(a(),locker()) -> F() eqt(a(),mcrlrecord()) -> F() eqt(a(),ok()) -> F() eqt(a(),pending()) -> F() eqt(a(),release()) -> F() eqt(a(),request()) -> F() eqt(a(),resource()) -> F() eqt(a(),tag()) -> F() eqt(a(),true()) -> F() eqt(a(),undefined()) -> F() eqt(a(),pid(N2)) -> F() eqt(a(),int(N2)) -> F() eqt(a(),cons(H2,T2)) -> F() eqt(a(),tuple(H2,T2)) -> F() eqt(a(),tuplenil(H2)) -> F() eqt(excl(),nil()) -> F() eqt(excl(),a()) -> F() eqt(excl(),excl()) -> T() eqt(excl(),false()) -> F() eqt(excl(),lock()) -> F() eqt(excl(),locker()) -> F() eqt(excl(),mcrlrecord()) -> F() eqt(excl(),ok()) -> F() eqt(excl(),pending()) -> F() eqt(excl(),release()) -> F() eqt(excl(),request()) -> F() eqt(excl(),resource()) -> F() eqt(excl(),tag()) -> F() eqt(excl(),true()) -> F() eqt(excl(),undefined()) -> F() eqt(excl(),pid(N2)) -> F() eqt(excl(),eqt(false(),int(N2))) -> F() eqt(false(),cons(H2,T2)) -> F() eqt(false(),tuple(H2,T2)) -> F() eqt(false(),tuplenil(H2)) -> F() eqt(lock(),nil()) -> F() eqt(lock(),a()) -> F() eqt(lock(),excl()) -> F() eqt(lock(),false()) -> F() eqt(lock(),lock()) -> T() eqt(lock(),locker()) -> F() eqt(lock(),mcrlrecord()) -> F() eqt(lock(),ok()) -> F() eqt(lock(),pending()) -> F() eqt(lock(),release()) -> F() eqt(lock(),request()) -> F() eqt(lock(),resource()) -> F() eqt(lock(),tag()) -> F() eqt(lock(),true()) -> F() eqt(lock(),undefined()) -> F() eqt(lock(),pid(N2)) -> F() eqt(lock(),int(N2)) -> F() eqt(lock(),cons(H2,T2)) -> F() eqt(lock(),tuple(H2,T2)) -> F() eqt(lock(),tuplenil(H2)) -> F() eqt(locker(),nil()) -> F() eqt(locker(),a()) -> F() eqt(locker(),excl()) -> F() eqt(locker(),false()) -> F() eqt(locker(),lock()) -> F() eqt(locker(),locker()) -> T() eqt(locker(),mcrlrecord()) -> F() eqt(locker(),ok()) -> F() eqt(locker(),pending()) -> F() eqt(locker(),release()) -> F() eqt(locker(),request()) -> F() eqt(locker(),resource()) -> F() eqt(locker(),tag()) -> F() eqt(locker(),true()) -> F() eqt(locker(),undefined()) -> F() eqt(locker(),pid(N2)) -> F() eqt(locker(),int(N2)) -> F() eqt(locker(),cons(H2,T2)) -> F() eqt(locker(),tuple(H2,T2)) -> F() eqt(locker(),tuplenil(H2)) -> F() eqt(mcrlrecord(),nil()) -> F() eqt(mcrlrecord(),a()) -> F() eqt(mcrlrecord(),excl()) -> F() eqt(mcrlrecord(),false()) -> F() eqt(mcrlrecord(),lock()) -> F() eqt(mcrlrecord(),locker()) -> F() eqt(mcrlrecord(),mcrlrecord()) -> T() eqt(mcrlrecord(),ok()) -> F() eqt(mcrlrecord(),pending()) -> F() eqt(mcrlrecord(),release()) -> F() eqt(mcrlrecord(),request()) -> F() eqt(mcrlrecord(),resource()) -> F() eqt(ok(),resource()) -> F() eqt(ok(),tag()) -> F() eqt(ok(),true()) -> F() eqt(ok(),undefined()) -> F() eqt(ok(),pid(N2)) -> F() eqt(ok(),int(N2)) -> F() eqt(ok(),cons(H2,T2)) -> F() eqt(ok(),tuple(H2,T2)) -> F() eqt(ok(),tuplenil(H2)) -> F() eqt(pending(),nil()) -> F() eqt(pending(),a()) -> F() eqt(pending(),excl()) -> F() eqt(pending(),false()) -> F() eqt(pending(),lock()) -> F() eqt(pending(),locker()) -> F() eqt(pending(),mcrlrecord()) -> F() eqt(pending(),ok()) -> F() eqt(pending(),pending()) -> T() eqt(pending(),release()) -> F() eqt(pending(),request()) -> F() eqt(pending(),resource()) -> F() eqt(pending(),tag()) -> F() eqt(pending(),true()) -> F() eqt(pending(),undefined()) -> F() eqt(pending(),pid(N2)) -> F() eqt(pending(),int(N2)) -> F() eqt(pending(),cons(H2,T2)) -> F() eqt(pending(),tuple(H2,T2)) -> F() eqt(pending(),tuplenil(H2)) -> F() eqt(release(),nil()) -> F() eqt(release(),a()) -> F() eqt(release(),excl()) -> F() eqt(release(),false()) -> F() eqt(release(),lock()) -> F() eqt(release(),locker()) -> F() eqt(release(),mcrlrecord()) -> F() eqt(release(),ok()) -> F() eqt(request(),mcrlrecord()) -> F() eqt(request(),ok()) -> F() eqt(request(),pending()) -> F() eqt(request(),release()) -> F() eqt(request(),request()) -> T() eqt(request(),resource()) -> F() eqt(request(),tag()) -> F() eqt(request(),true()) -> F() eqt(request(),undefined()) -> F() eqt(request(),pid(N2)) -> F() eqt(request(),int(N2)) -> F() eqt(request(),cons(H2,T2)) -> F() eqt(request(),tuple(H2,T2)) -> F() eqt(request(),tuplenil(H2)) -> F() eqt(resource(),nil()) -> F() eqt(resource(),a()) -> F() eqt(resource(),excl()) -> F() eqt(resource(),false()) -> F() eqt(resource(),lock()) -> F() eqt(resource(),locker()) -> F() eqt(resource(),mcrlrecord()) -> F() eqt(resource(),ok()) -> F() eqt(resource(),pending()) -> F() eqt(resource(),release()) -> F() eqt(resource(),request()) -> F() eqt(resource(),resource()) -> T() eqt(resource(),tag()) -> F() eqt(resource(),true()) -> F() eqt(resource(),undefined()) -> F() eqt(resource(),pid(N2)) -> F() eqt(resource(),int(N2)) -> F() eqt(resource(),cons(H2,T2)) -> F() eqt(resource(),tuple(H2,T2)) -> F() eqt(resource(),tuplenil(H2)) -> F() eqt(tag(),nil()) -> F() eqt(tag(),a()) -> F() eqt(tag(),excl()) -> F() eqt(tag(),false()) -> F() eqt(tag(),lock()) -> F() eqt(tag(),locker()) -> F() eqt(tag(),mcrlrecord()) -> F() eqt(tag(),ok()) -> F() eqt(tag(),pending()) -> F() eqt(tag(),release()) -> F() eqt(tag(),request()) -> F() eqt(tag(),resource()) -> F() eqt(tag(),tag()) -> T() eqt(tag(),true()) -> F() eqt(tag(),undefined()) -> F() eqt(tag(),pid(N2)) -> F() eqt(tag(),int(N2)) -> F() eqt(tag(),cons(H2,T2)) -> F() eqt(tag(),tuple(H2,T2)) -> F() eqt(tag(),tuplenil(H2)) -> F() eqt(true(),nil()) -> F() eqt(true(),a()) -> F() eqt(true(),excl()) -> F() eqt(true(),false()) -> F() eqt(true(),lock()) -> F() eqt(true(),locker()) -> F() eqt(true(),mcrlrecord()) -> F() eqt(true(),ok()) -> F() eqt(true(),pending()) -> F() eqt(true(),release()) -> F() eqt(true(),request()) -> F() eqt(true(),resource()) -> F() eqt(true(),tag()) -> F() eqt(true(),true()) -> T() eqt(true(),undefined()) -> F() eqt(true(),pid(N2)) -> F() eqt(true(),int(N2)) -> F() eqt(true(),cons(H2,T2)) -> F() eqt(true(),tuple(H2,T2)) -> F() eqt(true(),tuplenil(H2)) -> F() eqt(undefined(),nil()) -> F() eqt(undefined(),a()) -> F() eqt(undefined(),tuplenil(H2)) -> F() eqt(pid(N1),nil()) -> F() eqt(pid(N1),a()) -> F() eqt(pid(N1),excl()) -> F() eqt(pid(N1),false()) -> F() eqt(pid(N1),lock()) -> F() eqt(pid(N1),locker()) -> F() eqt(pid(N1),mcrlrecord()) -> F() eqt(pid(N1),ok()) -> F() eqt(pid(N1),pending()) -> F() eqt(pid(N1),release()) -> F() eqt(pid(N1),request()) -> F() eqt(pid(N1),resource()) -> F() eqt(pid(N1),tag()) -> F() eqt(pid(N1),true()) -> F() eqt(pid(N1),undefined()) -> F() eqt(pid(N1),pid(N2)) -> eqt(N1,N2) eqt(pid(N1),int(N2)) -> F() eqt(pid(N1),cons(H2,T2)) -> F() eqt(pid(N1),tuple(H2,T2)) -> F() eqt(pid(N1),tuplenil(H2)) -> F() eqt(int(N1),nil()) -> F() eqt(int(N1),a()) -> F() eqt(int(N1),excl()) -> F() eqt(int(N1),false()) -> F() eqt(int(N1),lock()) -> F() eqt(int(N1),locker()) -> F() eqt(int(N1),mcrlrecord()) -> F() eqt(int(N1),ok()) -> F() eqt(int(N1),pending()) -> F() eqt(int(N1),release()) -> F() eqt(int(N1),request()) -> F() eqt(int(N1),resource()) -> F() eqt(int(N1),tag()) -> F() eqt(int(N1),true()) -> F() eqt(int(N1),undefined()) -> F() eqt(cons(H1,T1),resource()) -> F() eqt(cons(H1,T1),tag()) -> F() eqt(cons(H1,T1),true()) -> F() eqt(cons(H1,T1),undefined()) -> F() eqt(cons(H1,T1),pid(N2)) -> F() eqt(cons(H1,T1),int(N2)) -> F() eqt(cons(H1,T1),cons(H2,T2)) -> and(eqt(H1,H2),eqt(T1,T2)) eqt(cons(H1,T1),tuple(H2,T2)) -> F() eqt(cons(H1,T1),tuplenil(H2)) -> F() eqt(tuple(H1,T1),nil()) -> F() eqt(tuple(H1,T1),a()) -> F() eqt(tuple(H1,T1),excl()) -> F() eqt(tuple(H1,T1),false()) -> F() eqt(tuple(H1,T1),lock()) -> F() eqt(tuple(H1,T1),locker()) -> F() eqt(tuple(H1,T1),mcrlrecord()) -> F() eqt(tuple(H1,T1),ok()) -> F() eqt(tuple(H1,T1),pending()) -> F() eqt(tuple(H1,T1),release()) -> F() eqt(tuple(H1,T1),request()) -> F() eqt(tuple(H1,T1),resource()) -> F() eqt(tuple(H1,T1),tag()) -> F() eqt(tuple(H1,T1),true()) -> F() eqt(tuple(H1,T1),undefined()) -> F() eqt(tuple(H1,T1),pid(N2)) -> F() eqt(tuple(H1,T1),int(N2)) -> F() eqt(tuple(H1,T1),cons(H2,T2)) -> F() eqt(tuple(H1,T1),tuple(H2,T2)) -> and(eqt(H1,H2),eqt(T1,T2)) eqt(tuple(H1,T1),tuplenil(H2)) -> F() eqt(tuplenil(H1),nil()) -> F() eqt(tuplenil(H1),a()) -> F() eqt(tuplenil(H1),excl()) -> F() eqt(tuplenil(H1),false()) -> F() eqt(tuplenil(H1),lock()) -> F() eqt(tuplenil(H1),locker()) -> F() eqt(tuplenil(H1),mcrlrecord()) -> F() eqt(tuplenil(H1),ok()) -> F() eqt(tuplenil(H1),pending()) -> F() eqt(tuplenil(H1),release()) -> F() eqt(tuplenil(H1),request()) -> F() eqt(tuplenil(H1),resource()) -> F() eqt(tuplenil(H1),tag()) -> F() eqt(tuplenil(H1),true()) -> F() eqt(tuplenil(H1),undefined()) -> F() eqt(tuplenil(H1),pid(N2)) -> F() eqt(tuplenil(H1),int(N2)) -> F() eqt(tuplenil(H1),cons(H2,T2)) -> F() eqt(tuplenil(H1),tuple(H2,T2)) -> F() eqt(tuplenil(H1),tuplenil(H2)) -> eqt(H1,H2) element(int(s(0())),tuplenil(T1)) -> T1 element(int(s(0())),tuple(T1,T2)) -> T1 element(int(s(s(N1))),tuple(T1,T2)) -> element(int(s(N1)),T2) record_new(lock()) -> tuple(mcrlrecord(),tuple(lock(),tuple(undefined(),tuple(nil(),tuplenil(nil()))))) record_extract(tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))), lock(),resource()) -> tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))) record_update(tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))), lock(),pending(),NewF) -> tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(NewF))))) record_updates(Record,Name,nil()) -> Record record_updates(Record,Name,cons(tuple(Field,tuplenil(NewF)),Fields)) -> record_updates(record_update(Record,Name,Field,NewF),Name,Fields) locker2_map_promote_pending(nil(),Pending) -> nil() locker2_map_promote_pending(cons(Lock,Locks),Pending) -> cons(locker2_promote_pending(Lock,Pending),locker2_map_promote_pending(Locks,Pending)) locker2_map_claim_lock(nil(),Resources,Client) -> nil() locker2_map_claim_lock(cons(Lock,Locks),Resources,Client) -> cons(locker2_claim_lock(Lock,Resources,Client),locker2_map_claim_lock(Locks,Resources,Client)) locker2_map_add_pending(nil(),Resources,Client) -> nil() locker2_promote_pending(Lock,Client) -> case0(Client,Lock,record_extract(Lock,lock(),pending())) case0(Client,Lock,cons(Client,Pendings)) -> record_updates(Lock,lock(),cons(tuple(excl(),tuplenil(Client)),cons ( tuple ( pending(),tuplenil(Pendings)), nil ()))) case0(Client,Lock,MCRLFree0) -> Lock locker2_remove_pending(Lock,Client) -> record_updates(Lock,lock(),cons(tuple(pending(),tuplenil(subtract (record_extract (Lock,lock(),pending()), cons(Client,nil())))), nil())) locker2_add_pending(Lock,Resources,Client) -> case1(Client,Resources,Lock,member(record_extract(Lock,lock(),resource()),Resources)) case1(Client,Resources,Lock,true()) -> record_updates(Lock,lock(),cons(tuple(pending(),tuplenil(append( record_extract ( Lock,lock(),pending()), cons (Client,nil())))), nil())) case1(Client,Resources,Lock,false()) -> Lock locker2_release_lock(Lock,Client) -> case2(Client,Lock,gen_modtageq(Client,record_extract(Lock,lock(),excl()))) case2(Client,Lock,true()) -> record_updates(Lock,lock(),cons(tuple(excllock(),excl()),nil())) case4(Client,Lock,MCRLFree1) -> false() locker2_obtainables(nil(),Client) -> true() locker2_obtainables(cons(Lock,Locks),Client) -> case5(Client,Locks,Lock,member(Client,record_extract(Lock,lock(),pending()))) case5(Client,Locks,Lock,true()) -> andt(locker2_obtainable(Lock,Client),locker2_obtainables(Locks,Client)) case5(Client,Locks,Lock,false()) -> locker2_obtainables(Locks,Client) locker2_check_available(Resource,nil()) -> false() locker2_check_available(Resource,cons(Lock,Locks)) -> case6(Locks,Lock,Resource,equal(Resource,record_extract(Lock,lock(),resource()))) case6(Locks,Lock,Resource,true()) -> andt(equal(record_extract(Lock,lock(),excl()),nil()),equal(record_extract (Lock,lock(),pending()), nil())) case6(Locks,Lock,Resource,false()) -> locker2_check_available(Resource,Locks) locker2_check_availables(nil(),Locks) -> true() locker2_check_availables(cons(Resource,Resources),Locks) -> andt(locker2_check_available(Resource,Locks),locker2_check_availables(Resources,Locks)) locker2_adduniq(nil(),List) -> List append(cons(Head,Tail),List) -> cons(Head,append(Tail,List)) subtract(List,nil()) -> List subtract(List,cons(Head,Tail)) -> subtract(delete(Head,List),Tail) delete(E,nil()) -> nil() delete(E,cons(Head,Tail)) -> case8(Tail,Head,E,equal(E,Head)) case8(Tail,Head,E,true()) -> Tail case8(Tail,Head,E,false()) -> cons(Head,delete(E,Tail)) gen_tag(Pid) -> tuple(Pid,tuplenil(tag())) gen_modtageq(Client1,Client2) -> equal(Client1,Client2) member(E,nil()) -> false() member(E,cons(Head,Tail)) -> case9(Tail,Head,E,equal(E,Head)) case9(Tail,Head,E,true()) -> true() case9(Tail,Head,E,false()) -> member(E,Tail) eqs(empty(),empty()) -> T() eqs(empty(),stack(E2,S2)) -> F() eqs(stack(E1,S1),empty()) -> F() eqs(stack(E1,S1),stack(E2,S2)) -> and(eqt(E1,E2),eqs(S1,S2)) pushs(E1,S1) -> stack(E1,S1) pops(stack(E1,S1)) -> S1 tops(stack(E1,S1)) -> E1 istops(E1,empty()) -> F() istops(E1,stack(E2,S1)) -> eqt(E1,E2) eqc(nocalls(),nocalls()) -> T() eqc(nocalls(),calls(E2,S2,CS2)) -> F() eqc(calls(E1,S1,CS1),nocalls()) -> F() eqc(calls(E1,S1,CS1),calls(E2,S2,CS2)) -> and(eqt(E1,E2),and(eqs(S1,S2),eqc(CS1,CS2))) push(E1,E2,nocalls()) -> calls(E1,stack(E2,empty()),nocalls()) push(E1,E2,calls(E3,S1,CS1)) -> push1(E1,E2,E3,S1,CS1,eqt(E1,E3)) push1(E1,E2,E3,S1,CS1,T()) -> calls(E3,pushs(E2,S1),CS1) Subterm Criterion Processor: simple projection: pi(locker2_map_claim_lock#) = 0 problem: DPs: TRS: or(T(),T()) -> T() or(F(),T()) -> T() or(T(),F()) -> T() or(F(),F()) -> F() and(T(),B) -> B and(B,T()) -> B and(F(),B) -> F() and(B,F()) -> F() imp(T(),B) -> B imp(F(),B) -> T() not(T()) -> F() not(F()) -> T() if(T(),B1,B2) -> B1 if(F(),B1,B2) -> B2 eq(T(),T()) -> T() eq(F(),F()) -> T() eq(T(),F()) -> F() eq(F(),T()) -> F() eqt(nil(),undefined()) -> F() eqt(nil(),pid(N2)) -> F() eqt(nil(),int(N2)) -> F() eqt(nil(),cons(H2,T2)) -> F() eqt(nil(),tuple(H2,T2)) -> F() eqt(nil(),tuplenil(H2)) -> F() eqt(a(),nil()) -> F() eqt(a(),a()) -> T() eqt(a(),excl()) -> F() eqt(a(),false()) -> F() eqt(a(),lock()) -> F() eqt(a(),locker()) -> F() eqt(a(),mcrlrecord()) -> F() eqt(a(),ok()) -> F() eqt(a(),pending()) -> F() eqt(a(),release()) -> F() eqt(a(),request()) -> F() eqt(a(),resource()) -> F() eqt(a(),tag()) -> F() eqt(a(),true()) -> F() eqt(a(),undefined()) -> F() eqt(a(),pid(N2)) -> F() eqt(a(),int(N2)) -> F() eqt(a(),cons(H2,T2)) -> F() eqt(a(),tuple(H2,T2)) -> F() eqt(a(),tuplenil(H2)) -> F() eqt(excl(),nil()) -> F() eqt(excl(),a()) -> F() eqt(excl(),excl()) -> T() eqt(excl(),false()) -> F() eqt(excl(),lock()) -> F() eqt(excl(),locker()) -> F() eqt(excl(),mcrlrecord()) -> F() eqt(excl(),ok()) -> F() eqt(excl(),pending()) -> F() eqt(excl(),release()) -> F() eqt(excl(),request()) -> F() eqt(excl(),resource()) -> F() eqt(excl(),tag()) -> F() eqt(excl(),true()) -> F() eqt(excl(),undefined()) -> F() eqt(excl(),pid(N2)) -> F() eqt(excl(),eqt(false(),int(N2))) -> F() eqt(false(),cons(H2,T2)) -> F() eqt(false(),tuple(H2,T2)) -> F() eqt(false(),tuplenil(H2)) -> F() eqt(lock(),nil()) -> F() eqt(lock(),a()) -> F() eqt(lock(),excl()) -> F() eqt(lock(),false()) -> F() eqt(lock(),lock()) -> T() eqt(lock(),locker()) -> F() eqt(lock(),mcrlrecord()) -> F() eqt(lock(),ok()) -> F() eqt(lock(),pending()) -> F() eqt(lock(),release()) -> F() eqt(lock(),request()) -> F() eqt(lock(),resource()) -> F() eqt(lock(),tag()) -> F() eqt(lock(),true()) -> F() eqt(lock(),undefined()) -> F() eqt(lock(),pid(N2)) -> F() eqt(lock(),int(N2)) -> F() eqt(lock(),cons(H2,T2)) -> F() eqt(lock(),tuple(H2,T2)) -> F() eqt(lock(),tuplenil(H2)) -> F() eqt(locker(),nil()) -> F() eqt(locker(),a()) -> F() eqt(locker(),excl()) -> F() eqt(locker(),false()) -> F() eqt(locker(),lock()) -> F() eqt(locker(),locker()) -> T() eqt(locker(),mcrlrecord()) -> F() eqt(locker(),ok()) -> F() eqt(locker(),pending()) -> F() eqt(locker(),release()) -> F() eqt(locker(),request()) -> F() eqt(locker(),resource()) -> F() eqt(locker(),tag()) -> F() eqt(locker(),true()) -> F() eqt(locker(),undefined()) -> F() eqt(locker(),pid(N2)) -> F() eqt(locker(),int(N2)) -> F() eqt(locker(),cons(H2,T2)) -> F() eqt(locker(),tuple(H2,T2)) -> F() eqt(locker(),tuplenil(H2)) -> F() eqt(mcrlrecord(),nil()) -> F() eqt(mcrlrecord(),a()) -> F() eqt(mcrlrecord(),excl()) -> F() eqt(mcrlrecord(),false()) -> F() eqt(mcrlrecord(),lock()) -> F() eqt(mcrlrecord(),locker()) -> F() eqt(mcrlrecord(),mcrlrecord()) -> T() eqt(mcrlrecord(),ok()) -> F() eqt(mcrlrecord(),pending()) -> F() eqt(mcrlrecord(),release()) -> F() eqt(mcrlrecord(),request()) -> F() eqt(mcrlrecord(),resource()) -> F() eqt(ok(),resource()) -> F() eqt(ok(),tag()) -> F() eqt(ok(),true()) -> F() eqt(ok(),undefined()) -> F() eqt(ok(),pid(N2)) -> F() eqt(ok(),int(N2)) -> F() eqt(ok(),cons(H2,T2)) -> F() eqt(ok(),tuple(H2,T2)) -> F() eqt(ok(),tuplenil(H2)) -> F() eqt(pending(),nil()) -> F() eqt(pending(),a()) -> F() eqt(pending(),excl()) -> F() eqt(pending(),false()) -> F() eqt(pending(),lock()) -> F() eqt(pending(),locker()) -> F() eqt(pending(),mcrlrecord()) -> F() eqt(pending(),ok()) -> F() eqt(pending(),pending()) -> T() eqt(pending(),release()) -> F() eqt(pending(),request()) -> F() eqt(pending(),resource()) -> F() eqt(pending(),tag()) -> F() eqt(pending(),true()) -> F() eqt(pending(),undefined()) -> F() eqt(pending(),pid(N2)) -> F() eqt(pending(),int(N2)) -> F() eqt(pending(),cons(H2,T2)) -> F() eqt(pending(),tuple(H2,T2)) -> F() eqt(pending(),tuplenil(H2)) -> F() eqt(release(),nil()) -> F() eqt(release(),a()) -> F() eqt(release(),excl()) -> F() eqt(release(),false()) -> F() eqt(release(),lock()) -> F() eqt(release(),locker()) -> F() eqt(release(),mcrlrecord()) -> F() eqt(release(),ok()) -> F() eqt(request(),mcrlrecord()) -> F() eqt(request(),ok()) -> F() eqt(request(),pending()) -> F() eqt(request(),release()) -> F() eqt(request(),request()) -> T() eqt(request(),resource()) -> F() eqt(request(),tag()) -> F() eqt(request(),true()) -> F() eqt(request(),undefined()) -> F() eqt(request(),pid(N2)) -> F() eqt(request(),int(N2)) -> F() eqt(request(),cons(H2,T2)) -> F() eqt(request(),tuple(H2,T2)) -> F() eqt(request(),tuplenil(H2)) -> F() eqt(resource(),nil()) -> F() eqt(resource(),a()) -> F() eqt(resource(),excl()) -> F() eqt(resource(),false()) -> F() eqt(resource(),lock()) -> F() eqt(resource(),locker()) -> F() eqt(resource(),mcrlrecord()) -> F() eqt(resource(),ok()) -> F() eqt(resource(),pending()) -> F() eqt(resource(),release()) -> F() eqt(resource(),request()) -> F() eqt(resource(),resource()) -> T() eqt(resource(),tag()) -> F() eqt(resource(),true()) -> F() eqt(resource(),undefined()) -> F() eqt(resource(),pid(N2)) -> F() eqt(resource(),int(N2)) -> F() eqt(resource(),cons(H2,T2)) -> F() eqt(resource(),tuple(H2,T2)) -> F() eqt(resource(),tuplenil(H2)) -> F() eqt(tag(),nil()) -> F() eqt(tag(),a()) -> F() eqt(tag(),excl()) -> F() eqt(tag(),false()) -> F() eqt(tag(),lock()) -> F() eqt(tag(),locker()) -> F() eqt(tag(),mcrlrecord()) -> F() eqt(tag(),ok()) -> F() eqt(tag(),pending()) -> F() eqt(tag(),release()) -> F() eqt(tag(),request()) -> F() eqt(tag(),resource()) -> F() eqt(tag(),tag()) -> T() eqt(tag(),true()) -> F() eqt(tag(),undefined()) -> F() eqt(tag(),pid(N2)) -> F() eqt(tag(),int(N2)) -> F() eqt(tag(),cons(H2,T2)) -> F() eqt(tag(),tuple(H2,T2)) -> F() eqt(tag(),tuplenil(H2)) -> F() eqt(true(),nil()) -> F() eqt(true(),a()) -> F() eqt(true(),excl()) -> F() eqt(true(),false()) -> F() eqt(true(),lock()) -> F() eqt(true(),locker()) -> F() eqt(true(),mcrlrecord()) -> F() eqt(true(),ok()) -> F() eqt(true(),pending()) -> F() eqt(true(),release()) -> F() eqt(true(),request()) -> F() eqt(true(),resource()) -> F() eqt(true(),tag()) -> F() eqt(true(),true()) -> T() eqt(true(),undefined()) -> F() eqt(true(),pid(N2)) -> F() eqt(true(),int(N2)) -> F() eqt(true(),cons(H2,T2)) -> F() eqt(true(),tuple(H2,T2)) -> F() eqt(true(),tuplenil(H2)) -> F() eqt(undefined(),nil()) -> F() eqt(undefined(),a()) -> F() eqt(undefined(),tuplenil(H2)) -> F() eqt(pid(N1),nil()) -> F() eqt(pid(N1),a()) -> F() eqt(pid(N1),excl()) -> F() eqt(pid(N1),false()) -> F() eqt(pid(N1),lock()) -> F() eqt(pid(N1),locker()) -> F() eqt(pid(N1),mcrlrecord()) -> F() eqt(pid(N1),ok()) -> F() eqt(pid(N1),pending()) -> F() eqt(pid(N1),release()) -> F() eqt(pid(N1),request()) -> F() eqt(pid(N1),resource()) -> F() eqt(pid(N1),tag()) -> F() eqt(pid(N1),true()) -> F() eqt(pid(N1),undefined()) -> F() eqt(pid(N1),pid(N2)) -> eqt(N1,N2) eqt(pid(N1),int(N2)) -> F() eqt(pid(N1),cons(H2,T2)) -> F() eqt(pid(N1),tuple(H2,T2)) -> F() eqt(pid(N1),tuplenil(H2)) -> F() eqt(int(N1),nil()) -> F() eqt(int(N1),a()) -> F() eqt(int(N1),excl()) -> F() eqt(int(N1),false()) -> F() eqt(int(N1),lock()) -> F() eqt(int(N1),locker()) -> F() eqt(int(N1),mcrlrecord()) -> F() eqt(int(N1),ok()) -> F() eqt(int(N1),pending()) -> F() eqt(int(N1),release()) -> F() eqt(int(N1),request()) -> F() eqt(int(N1),resource()) -> F() eqt(int(N1),tag()) -> F() eqt(int(N1),true()) -> F() eqt(int(N1),undefined()) -> F() eqt(cons(H1,T1),resource()) -> F() eqt(cons(H1,T1),tag()) -> F() eqt(cons(H1,T1),true()) -> F() eqt(cons(H1,T1),undefined()) -> F() eqt(cons(H1,T1),pid(N2)) -> F() eqt(cons(H1,T1),int(N2)) -> F() eqt(cons(H1,T1),cons(H2,T2)) -> and(eqt(H1,H2),eqt(T1,T2)) eqt(cons(H1,T1),tuple(H2,T2)) -> F() eqt(cons(H1,T1),tuplenil(H2)) -> F() eqt(tuple(H1,T1),nil()) -> F() eqt(tuple(H1,T1),a()) -> F() eqt(tuple(H1,T1),excl()) -> F() eqt(tuple(H1,T1),false()) -> F() eqt(tuple(H1,T1),lock()) -> F() eqt(tuple(H1,T1),locker()) -> F() eqt(tuple(H1,T1),mcrlrecord()) -> F() eqt(tuple(H1,T1),ok()) -> F() eqt(tuple(H1,T1),pending()) -> F() eqt(tuple(H1,T1),release()) -> F() eqt(tuple(H1,T1),request()) -> F() eqt(tuple(H1,T1),resource()) -> F() eqt(tuple(H1,T1),tag()) -> F() eqt(tuple(H1,T1),true()) -> F() eqt(tuple(H1,T1),undefined()) -> F() eqt(tuple(H1,T1),pid(N2)) -> F() eqt(tuple(H1,T1),int(N2)) -> F() eqt(tuple(H1,T1),cons(H2,T2)) -> F() eqt(tuple(H1,T1),tuple(H2,T2)) -> and(eqt(H1,H2),eqt(T1,T2)) eqt(tuple(H1,T1),tuplenil(H2)) -> F() eqt(tuplenil(H1),nil()) -> F() eqt(tuplenil(H1),a()) -> F() eqt(tuplenil(H1),excl()) -> F() eqt(tuplenil(H1),false()) -> F() eqt(tuplenil(H1),lock()) -> F() eqt(tuplenil(H1),locker()) -> F() eqt(tuplenil(H1),mcrlrecord()) -> F() eqt(tuplenil(H1),ok()) -> F() eqt(tuplenil(H1),pending()) -> F() eqt(tuplenil(H1),release()) -> F() eqt(tuplenil(H1),request()) -> F() eqt(tuplenil(H1),resource()) -> F() eqt(tuplenil(H1),tag()) -> F() eqt(tuplenil(H1),true()) -> F() eqt(tuplenil(H1),undefined()) -> F() eqt(tuplenil(H1),pid(N2)) -> F() eqt(tuplenil(H1),int(N2)) -> F() eqt(tuplenil(H1),cons(H2,T2)) -> F() eqt(tuplenil(H1),tuple(H2,T2)) -> F() eqt(tuplenil(H1),tuplenil(H2)) -> eqt(H1,H2) element(int(s(0())),tuplenil(T1)) -> T1 element(int(s(0())),tuple(T1,T2)) -> T1 element(int(s(s(N1))),tuple(T1,T2)) -> element(int(s(N1)),T2) record_new(lock()) -> tuple(mcrlrecord(),tuple(lock(),tuple(undefined(),tuple(nil(),tuplenil(nil()))))) record_extract(tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))), lock(),resource()) -> tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))) record_update(tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))), lock(),pending(),NewF) -> tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(NewF))))) record_updates(Record,Name,nil()) -> Record record_updates(Record,Name,cons(tuple(Field,tuplenil(NewF)),Fields)) -> record_updates(record_update(Record,Name,Field,NewF),Name,Fields) locker2_map_promote_pending(nil(),Pending) -> nil() locker2_map_promote_pending(cons(Lock,Locks),Pending) -> cons(locker2_promote_pending(Lock,Pending),locker2_map_promote_pending(Locks,Pending)) locker2_map_claim_lock(nil(),Resources,Client) -> nil() locker2_map_claim_lock(cons(Lock,Locks),Resources,Client) -> cons(locker2_claim_lock(Lock,Resources,Client),locker2_map_claim_lock (Locks,Resources,Client)) locker2_map_add_pending(nil(),Resources,Client) -> nil() locker2_promote_pending(Lock,Client) -> case0(Client,Lock,record_extract(Lock,lock(),pending())) case0(Client,Lock,cons(Client,Pendings)) -> record_updates(Lock,lock(),cons(tuple(excl(),tuplenil(Client)), cons(tuple(pending(),tuplenil(Pendings)),nil()))) case0(Client,Lock,MCRLFree0) -> Lock locker2_remove_pending(Lock,Client) -> record_updates(Lock,lock(),cons(tuple(pending(),tuplenil(subtract (record_extract (Lock,lock(),pending()), cons (Client,nil())))), nil())) locker2_add_pending(Lock,Resources,Client) -> case1(Client,Resources,Lock,member(record_extract(Lock,lock(),resource()),Resources)) case1(Client,Resources,Lock,true()) -> record_updates(Lock,lock(),cons(tuple(pending(),tuplenil(append (record_extract (Lock,lock(),pending()), cons (Client,nil())))), nil())) case1(Client,Resources,Lock,false()) -> Lock locker2_release_lock(Lock,Client) -> case2(Client,Lock,gen_modtageq(Client,record_extract(Lock,lock(),excl()))) case2(Client,Lock,true()) -> record_updates(Lock,lock(),cons(tuple(excllock(),excl()),nil())) case4(Client,Lock,MCRLFree1) -> false() locker2_obtainables(nil(),Client) -> true() locker2_obtainables(cons(Lock,Locks),Client) -> case5(Client,Locks,Lock,member(Client,record_extract(Lock,lock(),pending()))) case5(Client,Locks,Lock,true()) -> andt(locker2_obtainable(Lock,Client),locker2_obtainables(Locks,Client)) case5(Client,Locks,Lock,false()) -> locker2_obtainables(Locks,Client) locker2_check_available(Resource,nil()) -> false() locker2_check_available(Resource,cons(Lock,Locks)) -> case6(Locks,Lock,Resource,equal(Resource,record_extract(Lock,lock(),resource()))) case6(Locks,Lock,Resource,true()) -> andt(equal(record_extract(Lock,lock(),excl()),nil()),equal(record_extract (Lock,lock(),pending()), nil())) case6(Locks,Lock,Resource,false()) -> locker2_check_available(Resource,Locks) locker2_check_availables(nil(),Locks) -> true() locker2_check_availables(cons(Resource,Resources),Locks) -> andt(locker2_check_available(Resource,Locks),locker2_check_availables(Resources,Locks)) locker2_adduniq(nil(),List) -> List append(cons(Head,Tail),List) -> cons(Head,append(Tail,List)) subtract(List,nil()) -> List subtract(List,cons(Head,Tail)) -> subtract(delete(Head,List),Tail) delete(E,nil()) -> nil() delete(E,cons(Head,Tail)) -> case8(Tail,Head,E,equal(E,Head)) case8(Tail,Head,E,true()) -> Tail case8(Tail,Head,E,false()) -> cons(Head,delete(E,Tail)) gen_tag(Pid) -> tuple(Pid,tuplenil(tag())) gen_modtageq(Client1,Client2) -> equal(Client1,Client2) member(E,nil()) -> false() member(E,cons(Head,Tail)) -> case9(Tail,Head,E,equal(E,Head)) case9(Tail,Head,E,true()) -> true() case9(Tail,Head,E,false()) -> member(E,Tail) eqs(empty(),empty()) -> T() eqs(empty(),stack(E2,S2)) -> F() eqs(stack(E1,S1),empty()) -> F() eqs(stack(E1,S1),stack(E2,S2)) -> and(eqt(E1,E2),eqs(S1,S2)) pushs(E1,S1) -> stack(E1,S1) pops(stack(E1,S1)) -> S1 tops(stack(E1,S1)) -> E1 istops(E1,empty()) -> F() istops(E1,stack(E2,S1)) -> eqt(E1,E2) eqc(nocalls(),nocalls()) -> T() eqc(nocalls(),calls(E2,S2,CS2)) -> F() eqc(calls(E1,S1,CS1),nocalls()) -> F() eqc(calls(E1,S1,CS1),calls(E2,S2,CS2)) -> and(eqt(E1,E2),and(eqs(S1,S2),eqc(CS1,CS2))) push(E1,E2,nocalls()) -> calls(E1,stack(E2,empty()),nocalls()) push(E1,E2,calls(E3,S1,CS1)) -> push1(E1,E2,E3,S1,CS1,eqt(E1,E3)) push1(E1,E2,E3,S1,CS1,T()) -> calls(E3,pushs(E2,S1),CS1) Qed DPs: subtract#(List,cons(Head,Tail)) -> subtract#(delete(Head,List),Tail) TRS: or(T(),T()) -> T() or(F(),T()) -> T() or(T(),F()) -> T() or(F(),F()) -> F() and(T(),B) -> B and(B,T()) -> B and(F(),B) -> F() and(B,F()) -> F() imp(T(),B) -> B imp(F(),B) -> T() not(T()) -> F() not(F()) -> T() if(T(),B1,B2) -> B1 if(F(),B1,B2) -> B2 eq(T(),T()) -> T() eq(F(),F()) -> T() eq(T(),F()) -> F() eq(F(),T()) -> F() eqt(nil(),undefined()) -> F() eqt(nil(),pid(N2)) -> F() eqt(nil(),int(N2)) -> F() eqt(nil(),cons(H2,T2)) -> F() eqt(nil(),tuple(H2,T2)) -> F() eqt(nil(),tuplenil(H2)) -> F() eqt(a(),nil()) -> F() eqt(a(),a()) -> T() eqt(a(),excl()) -> F() eqt(a(),false()) -> F() eqt(a(),lock()) -> F() eqt(a(),locker()) -> F() eqt(a(),mcrlrecord()) -> F() eqt(a(),ok()) -> F() eqt(a(),pending()) -> F() eqt(a(),release()) -> F() eqt(a(),request()) -> F() eqt(a(),resource()) -> F() eqt(a(),tag()) -> F() eqt(a(),true()) -> F() eqt(a(),undefined()) -> F() eqt(a(),pid(N2)) -> F() eqt(a(),int(N2)) -> F() eqt(a(),cons(H2,T2)) -> F() eqt(a(),tuple(H2,T2)) -> F() eqt(a(),tuplenil(H2)) -> F() eqt(excl(),nil()) -> F() eqt(excl(),a()) -> F() eqt(excl(),excl()) -> T() eqt(excl(),false()) -> F() eqt(excl(),lock()) -> F() eqt(excl(),locker()) -> F() eqt(excl(),mcrlrecord()) -> F() eqt(excl(),ok()) -> F() eqt(excl(),pending()) -> F() eqt(excl(),release()) -> F() eqt(excl(),request()) -> F() eqt(excl(),resource()) -> F() eqt(excl(),tag()) -> F() eqt(excl(),true()) -> F() eqt(excl(),undefined()) -> F() eqt(excl(),pid(N2)) -> F() eqt(excl(),eqt(false(),int(N2))) -> F() eqt(false(),cons(H2,T2)) -> F() eqt(false(),tuple(H2,T2)) -> F() eqt(false(),tuplenil(H2)) -> F() eqt(lock(),nil()) -> F() eqt(lock(),a()) -> F() eqt(lock(),excl()) -> F() eqt(lock(),false()) -> F() eqt(lock(),lock()) -> T() eqt(lock(),locker()) -> F() eqt(lock(),mcrlrecord()) -> F() eqt(lock(),ok()) -> F() eqt(lock(),pending()) -> F() eqt(lock(),release()) -> F() eqt(lock(),request()) -> F() eqt(lock(),resource()) -> F() eqt(lock(),tag()) -> F() eqt(lock(),true()) -> F() eqt(lock(),undefined()) -> F() eqt(lock(),pid(N2)) -> F() eqt(lock(),int(N2)) -> F() eqt(lock(),cons(H2,T2)) -> F() eqt(lock(),tuple(H2,T2)) -> F() eqt(lock(),tuplenil(H2)) -> F() eqt(locker(),nil()) -> F() eqt(locker(),a()) -> F() eqt(locker(),excl()) -> F() eqt(locker(),false()) -> F() eqt(locker(),lock()) -> F() eqt(locker(),locker()) -> T() eqt(locker(),mcrlrecord()) -> F() eqt(locker(),ok()) -> F() eqt(locker(),pending()) -> F() eqt(locker(),release()) -> F() eqt(locker(),request()) -> F() eqt(locker(),resource()) -> F() eqt(locker(),tag()) -> F() eqt(locker(),true()) -> F() eqt(locker(),undefined()) -> F() eqt(locker(),pid(N2)) -> F() eqt(locker(),int(N2)) -> F() eqt(locker(),cons(H2,T2)) -> F() eqt(locker(),tuple(H2,T2)) -> F() eqt(locker(),tuplenil(H2)) -> F() eqt(mcrlrecord(),nil()) -> F() eqt(mcrlrecord(),a()) -> F() eqt(mcrlrecord(),excl()) -> F() eqt(mcrlrecord(),false()) -> F() eqt(mcrlrecord(),lock()) -> F() eqt(mcrlrecord(),locker()) -> F() eqt(mcrlrecord(),mcrlrecord()) -> T() eqt(mcrlrecord(),ok()) -> F() eqt(mcrlrecord(),pending()) -> F() eqt(mcrlrecord(),release()) -> F() eqt(mcrlrecord(),request()) -> F() eqt(mcrlrecord(),resource()) -> F() eqt(ok(),resource()) -> F() eqt(ok(),tag()) -> F() eqt(ok(),true()) -> F() eqt(ok(),undefined()) -> F() eqt(ok(),pid(N2)) -> F() eqt(ok(),int(N2)) -> F() eqt(ok(),cons(H2,T2)) -> F() eqt(ok(),tuple(H2,T2)) -> F() eqt(ok(),tuplenil(H2)) -> F() eqt(pending(),nil()) -> F() eqt(pending(),a()) -> F() eqt(pending(),excl()) -> F() eqt(pending(),false()) -> F() eqt(pending(),lock()) -> F() eqt(pending(),locker()) -> F() eqt(pending(),mcrlrecord()) -> F() eqt(pending(),ok()) -> F() eqt(pending(),pending()) -> T() eqt(pending(),release()) -> F() eqt(pending(),request()) -> F() eqt(pending(),resource()) -> F() eqt(pending(),tag()) -> F() eqt(pending(),true()) -> F() eqt(pending(),undefined()) -> F() eqt(pending(),pid(N2)) -> F() eqt(pending(),int(N2)) -> F() eqt(pending(),cons(H2,T2)) -> F() eqt(pending(),tuple(H2,T2)) -> F() eqt(pending(),tuplenil(H2)) -> F() eqt(release(),nil()) -> F() eqt(release(),a()) -> F() eqt(release(),excl()) -> F() eqt(release(),false()) -> F() eqt(release(),lock()) -> F() eqt(release(),locker()) -> F() eqt(release(),mcrlrecord()) -> F() eqt(release(),ok()) -> F() eqt(request(),mcrlrecord()) -> F() eqt(request(),ok()) -> F() eqt(request(),pending()) -> F() eqt(request(),release()) -> F() eqt(request(),request()) -> T() eqt(request(),resource()) -> F() eqt(request(),tag()) -> F() eqt(request(),true()) -> F() eqt(request(),undefined()) -> F() eqt(request(),pid(N2)) -> F() eqt(request(),int(N2)) -> F() eqt(request(),cons(H2,T2)) -> F() eqt(request(),tuple(H2,T2)) -> F() eqt(request(),tuplenil(H2)) -> F() eqt(resource(),nil()) -> F() eqt(resource(),a()) -> F() eqt(resource(),excl()) -> F() eqt(resource(),false()) -> F() eqt(resource(),lock()) -> F() eqt(resource(),locker()) -> F() eqt(resource(),mcrlrecord()) -> F() eqt(resource(),ok()) -> F() eqt(resource(),pending()) -> F() eqt(resource(),release()) -> F() eqt(resource(),request()) -> F() eqt(resource(),resource()) -> T() eqt(resource(),tag()) -> F() eqt(resource(),true()) -> F() eqt(resource(),undefined()) -> F() eqt(resource(),pid(N2)) -> F() eqt(resource(),int(N2)) -> F() eqt(resource(),cons(H2,T2)) -> F() eqt(resource(),tuple(H2,T2)) -> F() eqt(resource(),tuplenil(H2)) -> F() eqt(tag(),nil()) -> F() eqt(tag(),a()) -> F() eqt(tag(),excl()) -> F() eqt(tag(),false()) -> F() eqt(tag(),lock()) -> F() eqt(tag(),locker()) -> F() eqt(tag(),mcrlrecord()) -> F() eqt(tag(),ok()) -> F() eqt(tag(),pending()) -> F() eqt(tag(),release()) -> F() eqt(tag(),request()) -> F() eqt(tag(),resource()) -> F() eqt(tag(),tag()) -> T() eqt(tag(),true()) -> F() eqt(tag(),undefined()) -> F() eqt(tag(),pid(N2)) -> F() eqt(tag(),int(N2)) -> F() eqt(tag(),cons(H2,T2)) -> F() eqt(tag(),tuple(H2,T2)) -> F() eqt(tag(),tuplenil(H2)) -> F() eqt(true(),nil()) -> F() eqt(true(),a()) -> F() eqt(true(),excl()) -> F() eqt(true(),false()) -> F() eqt(true(),lock()) -> F() eqt(true(),locker()) -> F() eqt(true(),mcrlrecord()) -> F() eqt(true(),ok()) -> F() eqt(true(),pending()) -> F() eqt(true(),release()) -> F() eqt(true(),request()) -> F() eqt(true(),resource()) -> F() eqt(true(),tag()) -> F() eqt(true(),true()) -> T() eqt(true(),undefined()) -> F() eqt(true(),pid(N2)) -> F() eqt(true(),int(N2)) -> F() eqt(true(),cons(H2,T2)) -> F() eqt(true(),tuple(H2,T2)) -> F() eqt(true(),tuplenil(H2)) -> F() eqt(undefined(),nil()) -> F() eqt(undefined(),a()) -> F() eqt(undefined(),tuplenil(H2)) -> F() eqt(pid(N1),nil()) -> F() eqt(pid(N1),a()) -> F() eqt(pid(N1),excl()) -> F() eqt(pid(N1),false()) -> F() eqt(pid(N1),lock()) -> F() eqt(pid(N1),locker()) -> F() eqt(pid(N1),mcrlrecord()) -> F() eqt(pid(N1),ok()) -> F() eqt(pid(N1),pending()) -> F() eqt(pid(N1),release()) -> F() eqt(pid(N1),request()) -> F() eqt(pid(N1),resource()) -> F() eqt(pid(N1),tag()) -> F() eqt(pid(N1),true()) -> F() eqt(pid(N1),undefined()) -> F() eqt(pid(N1),pid(N2)) -> eqt(N1,N2) eqt(pid(N1),int(N2)) -> F() eqt(pid(N1),cons(H2,T2)) -> F() eqt(pid(N1),tuple(H2,T2)) -> F() eqt(pid(N1),tuplenil(H2)) -> F() eqt(int(N1),nil()) -> F() eqt(int(N1),a()) -> F() eqt(int(N1),excl()) -> F() eqt(int(N1),false()) -> F() eqt(int(N1),lock()) -> F() eqt(int(N1),locker()) -> F() eqt(int(N1),mcrlrecord()) -> F() eqt(int(N1),ok()) -> F() eqt(int(N1),pending()) -> F() eqt(int(N1),release()) -> F() eqt(int(N1),request()) -> F() eqt(int(N1),resource()) -> F() eqt(int(N1),tag()) -> F() eqt(int(N1),true()) -> F() eqt(int(N1),undefined()) -> F() eqt(cons(H1,T1),resource()) -> F() eqt(cons(H1,T1),tag()) -> F() eqt(cons(H1,T1),true()) -> F() eqt(cons(H1,T1),undefined()) -> F() eqt(cons(H1,T1),pid(N2)) -> F() eqt(cons(H1,T1),int(N2)) -> F() eqt(cons(H1,T1),cons(H2,T2)) -> and(eqt(H1,H2),eqt(T1,T2)) eqt(cons(H1,T1),tuple(H2,T2)) -> F() eqt(cons(H1,T1),tuplenil(H2)) -> F() eqt(tuple(H1,T1),nil()) -> F() eqt(tuple(H1,T1),a()) -> F() eqt(tuple(H1,T1),excl()) -> F() eqt(tuple(H1,T1),false()) -> F() eqt(tuple(H1,T1),lock()) -> F() eqt(tuple(H1,T1),locker()) -> F() eqt(tuple(H1,T1),mcrlrecord()) -> F() eqt(tuple(H1,T1),ok()) -> F() eqt(tuple(H1,T1),pending()) -> F() eqt(tuple(H1,T1),release()) -> F() eqt(tuple(H1,T1),request()) -> F() eqt(tuple(H1,T1),resource()) -> F() eqt(tuple(H1,T1),tag()) -> F() eqt(tuple(H1,T1),true()) -> F() eqt(tuple(H1,T1),undefined()) -> F() eqt(tuple(H1,T1),pid(N2)) -> F() eqt(tuple(H1,T1),int(N2)) -> F() eqt(tuple(H1,T1),cons(H2,T2)) -> F() eqt(tuple(H1,T1),tuple(H2,T2)) -> and(eqt(H1,H2),eqt(T1,T2)) eqt(tuple(H1,T1),tuplenil(H2)) -> F() eqt(tuplenil(H1),nil()) -> F() eqt(tuplenil(H1),a()) -> F() eqt(tuplenil(H1),excl()) -> F() eqt(tuplenil(H1),false()) -> F() eqt(tuplenil(H1),lock()) -> F() eqt(tuplenil(H1),locker()) -> F() eqt(tuplenil(H1),mcrlrecord()) -> F() eqt(tuplenil(H1),ok()) -> F() eqt(tuplenil(H1),pending()) -> F() eqt(tuplenil(H1),release()) -> F() eqt(tuplenil(H1),request()) -> F() eqt(tuplenil(H1),resource()) -> F() eqt(tuplenil(H1),tag()) -> F() eqt(tuplenil(H1),true()) -> F() eqt(tuplenil(H1),undefined()) -> F() eqt(tuplenil(H1),pid(N2)) -> F() eqt(tuplenil(H1),int(N2)) -> F() eqt(tuplenil(H1),cons(H2,T2)) -> F() eqt(tuplenil(H1),tuple(H2,T2)) -> F() eqt(tuplenil(H1),tuplenil(H2)) -> eqt(H1,H2) element(int(s(0())),tuplenil(T1)) -> T1 element(int(s(0())),tuple(T1,T2)) -> T1 element(int(s(s(N1))),tuple(T1,T2)) -> element(int(s(N1)),T2) record_new(lock()) -> tuple(mcrlrecord(),tuple(lock(),tuple(undefined(),tuple(nil(),tuplenil(nil()))))) record_extract(tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))), lock(),resource()) -> tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))) record_update(tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))), lock(),pending(),NewF) -> tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(NewF))))) record_updates(Record,Name,nil()) -> Record record_updates(Record,Name,cons(tuple(Field,tuplenil(NewF)),Fields)) -> record_updates(record_update(Record,Name,Field,NewF),Name,Fields) locker2_map_promote_pending(nil(),Pending) -> nil() locker2_map_promote_pending(cons(Lock,Locks),Pending) -> cons(locker2_promote_pending(Lock,Pending),locker2_map_promote_pending(Locks,Pending)) locker2_map_claim_lock(nil(),Resources,Client) -> nil() locker2_map_claim_lock(cons(Lock,Locks),Resources,Client) -> cons(locker2_claim_lock(Lock,Resources,Client),locker2_map_claim_lock(Locks,Resources,Client)) locker2_map_add_pending(nil(),Resources,Client) -> nil() locker2_promote_pending(Lock,Client) -> case0(Client,Lock,record_extract(Lock,lock(),pending())) case0(Client,Lock,cons(Client,Pendings)) -> record_updates(Lock,lock(),cons(tuple(excl(),tuplenil(Client)),cons ( tuple ( pending(),tuplenil(Pendings)), nil ()))) case0(Client,Lock,MCRLFree0) -> Lock locker2_remove_pending(Lock,Client) -> record_updates(Lock,lock(),cons(tuple(pending(),tuplenil(subtract (record_extract (Lock,lock(),pending()), cons(Client,nil())))), nil())) locker2_add_pending(Lock,Resources,Client) -> case1(Client,Resources,Lock,member(record_extract(Lock,lock(),resource()),Resources)) case1(Client,Resources,Lock,true()) -> record_updates(Lock,lock(),cons(tuple(pending(),tuplenil(append( record_extract ( Lock,lock(),pending()), cons (Client,nil())))), nil())) case1(Client,Resources,Lock,false()) -> Lock locker2_release_lock(Lock,Client) -> case2(Client,Lock,gen_modtageq(Client,record_extract(Lock,lock(),excl()))) case2(Client,Lock,true()) -> record_updates(Lock,lock(),cons(tuple(excllock(),excl()),nil())) case4(Client,Lock,MCRLFree1) -> false() locker2_obtainables(nil(),Client) -> true() locker2_obtainables(cons(Lock,Locks),Client) -> case5(Client,Locks,Lock,member(Client,record_extract(Lock,lock(),pending()))) case5(Client,Locks,Lock,true()) -> andt(locker2_obtainable(Lock,Client),locker2_obtainables(Locks,Client)) case5(Client,Locks,Lock,false()) -> locker2_obtainables(Locks,Client) locker2_check_available(Resource,nil()) -> false() locker2_check_available(Resource,cons(Lock,Locks)) -> case6(Locks,Lock,Resource,equal(Resource,record_extract(Lock,lock(),resource()))) case6(Locks,Lock,Resource,true()) -> andt(equal(record_extract(Lock,lock(),excl()),nil()),equal(record_extract (Lock,lock(),pending()), nil())) case6(Locks,Lock,Resource,false()) -> locker2_check_available(Resource,Locks) locker2_check_availables(nil(),Locks) -> true() locker2_check_availables(cons(Resource,Resources),Locks) -> andt(locker2_check_available(Resource,Locks),locker2_check_availables(Resources,Locks)) locker2_adduniq(nil(),List) -> List append(cons(Head,Tail),List) -> cons(Head,append(Tail,List)) subtract(List,nil()) -> List subtract(List,cons(Head,Tail)) -> subtract(delete(Head,List),Tail) delete(E,nil()) -> nil() delete(E,cons(Head,Tail)) -> case8(Tail,Head,E,equal(E,Head)) case8(Tail,Head,E,true()) -> Tail case8(Tail,Head,E,false()) -> cons(Head,delete(E,Tail)) gen_tag(Pid) -> tuple(Pid,tuplenil(tag())) gen_modtageq(Client1,Client2) -> equal(Client1,Client2) member(E,nil()) -> false() member(E,cons(Head,Tail)) -> case9(Tail,Head,E,equal(E,Head)) case9(Tail,Head,E,true()) -> true() case9(Tail,Head,E,false()) -> member(E,Tail) eqs(empty(),empty()) -> T() eqs(empty(),stack(E2,S2)) -> F() eqs(stack(E1,S1),empty()) -> F() eqs(stack(E1,S1),stack(E2,S2)) -> and(eqt(E1,E2),eqs(S1,S2)) pushs(E1,S1) -> stack(E1,S1) pops(stack(E1,S1)) -> S1 tops(stack(E1,S1)) -> E1 istops(E1,empty()) -> F() istops(E1,stack(E2,S1)) -> eqt(E1,E2) eqc(nocalls(),nocalls()) -> T() eqc(nocalls(),calls(E2,S2,CS2)) -> F() eqc(calls(E1,S1,CS1),nocalls()) -> F() eqc(calls(E1,S1,CS1),calls(E2,S2,CS2)) -> and(eqt(E1,E2),and(eqs(S1,S2),eqc(CS1,CS2))) push(E1,E2,nocalls()) -> calls(E1,stack(E2,empty()),nocalls()) push(E1,E2,calls(E3,S1,CS1)) -> push1(E1,E2,E3,S1,CS1,eqt(E1,E3)) push1(E1,E2,E3,S1,CS1,T()) -> calls(E3,pushs(E2,S1),CS1) Subterm Criterion Processor: simple projection: pi(subtract#) = 1 problem: DPs: TRS: or(T(),T()) -> T() or(F(),T()) -> T() or(T(),F()) -> T() or(F(),F()) -> F() and(T(),B) -> B and(B,T()) -> B and(F(),B) -> F() and(B,F()) -> F() imp(T(),B) -> B imp(F(),B) -> T() not(T()) -> F() not(F()) -> T() if(T(),B1,B2) -> B1 if(F(),B1,B2) -> B2 eq(T(),T()) -> T() eq(F(),F()) -> T() eq(T(),F()) -> F() eq(F(),T()) -> F() eqt(nil(),undefined()) -> F() eqt(nil(),pid(N2)) -> F() eqt(nil(),int(N2)) -> F() eqt(nil(),cons(H2,T2)) -> F() eqt(nil(),tuple(H2,T2)) -> F() eqt(nil(),tuplenil(H2)) -> F() eqt(a(),nil()) -> F() eqt(a(),a()) -> T() eqt(a(),excl()) -> F() eqt(a(),false()) -> F() eqt(a(),lock()) -> F() eqt(a(),locker()) -> F() eqt(a(),mcrlrecord()) -> F() eqt(a(),ok()) -> F() eqt(a(),pending()) -> F() eqt(a(),release()) -> F() eqt(a(),request()) -> F() eqt(a(),resource()) -> F() eqt(a(),tag()) -> F() eqt(a(),true()) -> F() eqt(a(),undefined()) -> F() eqt(a(),pid(N2)) -> F() eqt(a(),int(N2)) -> F() eqt(a(),cons(H2,T2)) -> F() eqt(a(),tuple(H2,T2)) -> F() eqt(a(),tuplenil(H2)) -> F() eqt(excl(),nil()) -> F() eqt(excl(),a()) -> F() eqt(excl(),excl()) -> T() eqt(excl(),false()) -> F() eqt(excl(),lock()) -> F() eqt(excl(),locker()) -> F() eqt(excl(),mcrlrecord()) -> F() eqt(excl(),ok()) -> F() eqt(excl(),pending()) -> F() eqt(excl(),release()) -> F() eqt(excl(),request()) -> F() eqt(excl(),resource()) -> F() eqt(excl(),tag()) -> F() eqt(excl(),true()) -> F() eqt(excl(),undefined()) -> F() eqt(excl(),pid(N2)) -> F() eqt(excl(),eqt(false(),int(N2))) -> F() eqt(false(),cons(H2,T2)) -> F() eqt(false(),tuple(H2,T2)) -> F() eqt(false(),tuplenil(H2)) -> F() eqt(lock(),nil()) -> F() eqt(lock(),a()) -> F() eqt(lock(),excl()) -> F() eqt(lock(),false()) -> F() eqt(lock(),lock()) -> T() eqt(lock(),locker()) -> F() eqt(lock(),mcrlrecord()) -> F() eqt(lock(),ok()) -> F() eqt(lock(),pending()) -> F() eqt(lock(),release()) -> F() eqt(lock(),request()) -> F() eqt(lock(),resource()) -> F() eqt(lock(),tag()) -> F() eqt(lock(),true()) -> F() eqt(lock(),undefined()) -> F() eqt(lock(),pid(N2)) -> F() eqt(lock(),int(N2)) -> F() eqt(lock(),cons(H2,T2)) -> F() eqt(lock(),tuple(H2,T2)) -> F() eqt(lock(),tuplenil(H2)) -> F() eqt(locker(),nil()) -> F() eqt(locker(),a()) -> F() eqt(locker(),excl()) -> F() eqt(locker(),false()) -> F() eqt(locker(),lock()) -> F() eqt(locker(),locker()) -> T() eqt(locker(),mcrlrecord()) -> F() eqt(locker(),ok()) -> F() eqt(locker(),pending()) -> F() eqt(locker(),release()) -> F() eqt(locker(),request()) -> F() eqt(locker(),resource()) -> F() eqt(locker(),tag()) -> F() eqt(locker(),true()) -> F() eqt(locker(),undefined()) -> F() eqt(locker(),pid(N2)) -> F() eqt(locker(),int(N2)) -> F() eqt(locker(),cons(H2,T2)) -> F() eqt(locker(),tuple(H2,T2)) -> F() eqt(locker(),tuplenil(H2)) -> F() eqt(mcrlrecord(),nil()) -> F() eqt(mcrlrecord(),a()) -> F() eqt(mcrlrecord(),excl()) -> F() eqt(mcrlrecord(),false()) -> F() eqt(mcrlrecord(),lock()) -> F() eqt(mcrlrecord(),locker()) -> F() eqt(mcrlrecord(),mcrlrecord()) -> T() eqt(mcrlrecord(),ok()) -> F() eqt(mcrlrecord(),pending()) -> F() eqt(mcrlrecord(),release()) -> F() eqt(mcrlrecord(),request()) -> F() eqt(mcrlrecord(),resource()) -> F() eqt(ok(),resource()) -> F() eqt(ok(),tag()) -> F() eqt(ok(),true()) -> F() eqt(ok(),undefined()) -> F() eqt(ok(),pid(N2)) -> F() eqt(ok(),int(N2)) -> F() eqt(ok(),cons(H2,T2)) -> F() eqt(ok(),tuple(H2,T2)) -> F() eqt(ok(),tuplenil(H2)) -> F() eqt(pending(),nil()) -> F() eqt(pending(),a()) -> F() eqt(pending(),excl()) -> F() eqt(pending(),false()) -> F() eqt(pending(),lock()) -> F() eqt(pending(),locker()) -> F() eqt(pending(),mcrlrecord()) -> F() eqt(pending(),ok()) -> F() eqt(pending(),pending()) -> T() eqt(pending(),release()) -> F() eqt(pending(),request()) -> F() eqt(pending(),resource()) -> F() eqt(pending(),tag()) -> F() eqt(pending(),true()) -> F() eqt(pending(),undefined()) -> F() eqt(pending(),pid(N2)) -> F() eqt(pending(),int(N2)) -> F() eqt(pending(),cons(H2,T2)) -> F() eqt(pending(),tuple(H2,T2)) -> F() eqt(pending(),tuplenil(H2)) -> F() eqt(release(),nil()) -> F() eqt(release(),a()) -> F() eqt(release(),excl()) -> F() eqt(release(),false()) -> F() eqt(release(),lock()) -> F() eqt(release(),locker()) -> F() eqt(release(),mcrlrecord()) -> F() eqt(release(),ok()) -> F() eqt(request(),mcrlrecord()) -> F() eqt(request(),ok()) -> F() eqt(request(),pending()) -> F() eqt(request(),release()) -> F() eqt(request(),request()) -> T() eqt(request(),resource()) -> F() eqt(request(),tag()) -> F() eqt(request(),true()) -> F() eqt(request(),undefined()) -> F() eqt(request(),pid(N2)) -> F() eqt(request(),int(N2)) -> F() eqt(request(),cons(H2,T2)) -> F() eqt(request(),tuple(H2,T2)) -> F() eqt(request(),tuplenil(H2)) -> F() eqt(resource(),nil()) -> F() eqt(resource(),a()) -> F() eqt(resource(),excl()) -> F() eqt(resource(),false()) -> F() eqt(resource(),lock()) -> F() eqt(resource(),locker()) -> F() eqt(resource(),mcrlrecord()) -> F() eqt(resource(),ok()) -> F() eqt(resource(),pending()) -> F() eqt(resource(),release()) -> F() eqt(resource(),request()) -> F() eqt(resource(),resource()) -> T() eqt(resource(),tag()) -> F() eqt(resource(),true()) -> F() eqt(resource(),undefined()) -> F() eqt(resource(),pid(N2)) -> F() eqt(resource(),int(N2)) -> F() eqt(resource(),cons(H2,T2)) -> F() eqt(resource(),tuple(H2,T2)) -> F() eqt(resource(),tuplenil(H2)) -> F() eqt(tag(),nil()) -> F() eqt(tag(),a()) -> F() eqt(tag(),excl()) -> F() eqt(tag(),false()) -> F() eqt(tag(),lock()) -> F() eqt(tag(),locker()) -> F() eqt(tag(),mcrlrecord()) -> F() eqt(tag(),ok()) -> F() eqt(tag(),pending()) -> F() eqt(tag(),release()) -> F() eqt(tag(),request()) -> F() eqt(tag(),resource()) -> F() eqt(tag(),tag()) -> T() eqt(tag(),true()) -> F() eqt(tag(),undefined()) -> F() eqt(tag(),pid(N2)) -> F() eqt(tag(),int(N2)) -> F() eqt(tag(),cons(H2,T2)) -> F() eqt(tag(),tuple(H2,T2)) -> F() eqt(tag(),tuplenil(H2)) -> F() eqt(true(),nil()) -> F() eqt(true(),a()) -> F() eqt(true(),excl()) -> F() eqt(true(),false()) -> F() eqt(true(),lock()) -> F() eqt(true(),locker()) -> F() eqt(true(),mcrlrecord()) -> F() eqt(true(),ok()) -> F() eqt(true(),pending()) -> F() eqt(true(),release()) -> F() eqt(true(),request()) -> F() eqt(true(),resource()) -> F() eqt(true(),tag()) -> F() eqt(true(),true()) -> T() eqt(true(),undefined()) -> F() eqt(true(),pid(N2)) -> F() eqt(true(),int(N2)) -> F() eqt(true(),cons(H2,T2)) -> F() eqt(true(),tuple(H2,T2)) -> F() eqt(true(),tuplenil(H2)) -> F() eqt(undefined(),nil()) -> F() eqt(undefined(),a()) -> F() eqt(undefined(),tuplenil(H2)) -> F() eqt(pid(N1),nil()) -> F() eqt(pid(N1),a()) -> F() eqt(pid(N1),excl()) -> F() eqt(pid(N1),false()) -> F() eqt(pid(N1),lock()) -> F() eqt(pid(N1),locker()) -> F() eqt(pid(N1),mcrlrecord()) -> F() eqt(pid(N1),ok()) -> F() eqt(pid(N1),pending()) -> F() eqt(pid(N1),release()) -> F() eqt(pid(N1),request()) -> F() eqt(pid(N1),resource()) -> F() eqt(pid(N1),tag()) -> F() eqt(pid(N1),true()) -> F() eqt(pid(N1),undefined()) -> F() eqt(pid(N1),pid(N2)) -> eqt(N1,N2) eqt(pid(N1),int(N2)) -> F() eqt(pid(N1),cons(H2,T2)) -> F() eqt(pid(N1),tuple(H2,T2)) -> F() eqt(pid(N1),tuplenil(H2)) -> F() eqt(int(N1),nil()) -> F() eqt(int(N1),a()) -> F() eqt(int(N1),excl()) -> F() eqt(int(N1),false()) -> F() eqt(int(N1),lock()) -> F() eqt(int(N1),locker()) -> F() eqt(int(N1),mcrlrecord()) -> F() eqt(int(N1),ok()) -> F() eqt(int(N1),pending()) -> F() eqt(int(N1),release()) -> F() eqt(int(N1),request()) -> F() eqt(int(N1),resource()) -> F() eqt(int(N1),tag()) -> F() eqt(int(N1),true()) -> F() eqt(int(N1),undefined()) -> F() eqt(cons(H1,T1),resource()) -> F() eqt(cons(H1,T1),tag()) -> F() eqt(cons(H1,T1),true()) -> F() eqt(cons(H1,T1),undefined()) -> F() eqt(cons(H1,T1),pid(N2)) -> F() eqt(cons(H1,T1),int(N2)) -> F() eqt(cons(H1,T1),cons(H2,T2)) -> and(eqt(H1,H2),eqt(T1,T2)) eqt(cons(H1,T1),tuple(H2,T2)) -> F() eqt(cons(H1,T1),tuplenil(H2)) -> F() eqt(tuple(H1,T1),nil()) -> F() eqt(tuple(H1,T1),a()) -> F() eqt(tuple(H1,T1),excl()) -> F() eqt(tuple(H1,T1),false()) -> F() eqt(tuple(H1,T1),lock()) -> F() eqt(tuple(H1,T1),locker()) -> F() eqt(tuple(H1,T1),mcrlrecord()) -> F() eqt(tuple(H1,T1),ok()) -> F() eqt(tuple(H1,T1),pending()) -> F() eqt(tuple(H1,T1),release()) -> F() eqt(tuple(H1,T1),request()) -> F() eqt(tuple(H1,T1),resource()) -> F() eqt(tuple(H1,T1),tag()) -> F() eqt(tuple(H1,T1),true()) -> F() eqt(tuple(H1,T1),undefined()) -> F() eqt(tuple(H1,T1),pid(N2)) -> F() eqt(tuple(H1,T1),int(N2)) -> F() eqt(tuple(H1,T1),cons(H2,T2)) -> F() eqt(tuple(H1,T1),tuple(H2,T2)) -> and(eqt(H1,H2),eqt(T1,T2)) eqt(tuple(H1,T1),tuplenil(H2)) -> F() eqt(tuplenil(H1),nil()) -> F() eqt(tuplenil(H1),a()) -> F() eqt(tuplenil(H1),excl()) -> F() eqt(tuplenil(H1),false()) -> F() eqt(tuplenil(H1),lock()) -> F() eqt(tuplenil(H1),locker()) -> F() eqt(tuplenil(H1),mcrlrecord()) -> F() eqt(tuplenil(H1),ok()) -> F() eqt(tuplenil(H1),pending()) -> F() eqt(tuplenil(H1),release()) -> F() eqt(tuplenil(H1),request()) -> F() eqt(tuplenil(H1),resource()) -> F() eqt(tuplenil(H1),tag()) -> F() eqt(tuplenil(H1),true()) -> F() eqt(tuplenil(H1),undefined()) -> F() eqt(tuplenil(H1),pid(N2)) -> F() eqt(tuplenil(H1),int(N2)) -> F() eqt(tuplenil(H1),cons(H2,T2)) -> F() eqt(tuplenil(H1),tuple(H2,T2)) -> F() eqt(tuplenil(H1),tuplenil(H2)) -> eqt(H1,H2) element(int(s(0())),tuplenil(T1)) -> T1 element(int(s(0())),tuple(T1,T2)) -> T1 element(int(s(s(N1))),tuple(T1,T2)) -> element(int(s(N1)),T2) record_new(lock()) -> tuple(mcrlrecord(),tuple(lock(),tuple(undefined(),tuple(nil(),tuplenil(nil()))))) record_extract(tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))), lock(),resource()) -> tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))) record_update(tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))), lock(),pending(),NewF) -> tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(NewF))))) record_updates(Record,Name,nil()) -> Record record_updates(Record,Name,cons(tuple(Field,tuplenil(NewF)),Fields)) -> record_updates(record_update(Record,Name,Field,NewF),Name,Fields) locker2_map_promote_pending(nil(),Pending) -> nil() locker2_map_promote_pending(cons(Lock,Locks),Pending) -> cons(locker2_promote_pending(Lock,Pending),locker2_map_promote_pending(Locks,Pending)) locker2_map_claim_lock(nil(),Resources,Client) -> nil() locker2_map_claim_lock(cons(Lock,Locks),Resources,Client) -> cons(locker2_claim_lock(Lock,Resources,Client),locker2_map_claim_lock (Locks,Resources,Client)) locker2_map_add_pending(nil(),Resources,Client) -> nil() locker2_promote_pending(Lock,Client) -> case0(Client,Lock,record_extract(Lock,lock(),pending())) case0(Client,Lock,cons(Client,Pendings)) -> record_updates(Lock,lock(),cons(tuple(excl(),tuplenil(Client)), cons(tuple(pending(),tuplenil(Pendings)),nil()))) case0(Client,Lock,MCRLFree0) -> Lock locker2_remove_pending(Lock,Client) -> record_updates(Lock,lock(),cons(tuple(pending(),tuplenil(subtract (record_extract (Lock,lock(),pending()), cons (Client,nil())))), nil())) locker2_add_pending(Lock,Resources,Client) -> case1(Client,Resources,Lock,member(record_extract(Lock,lock(),resource()),Resources)) case1(Client,Resources,Lock,true()) -> record_updates(Lock,lock(),cons(tuple(pending(),tuplenil(append (record_extract (Lock,lock(),pending()), cons (Client,nil())))), nil())) case1(Client,Resources,Lock,false()) -> Lock locker2_release_lock(Lock,Client) -> case2(Client,Lock,gen_modtageq(Client,record_extract(Lock,lock(),excl()))) case2(Client,Lock,true()) -> record_updates(Lock,lock(),cons(tuple(excllock(),excl()),nil())) case4(Client,Lock,MCRLFree1) -> false() locker2_obtainables(nil(),Client) -> true() locker2_obtainables(cons(Lock,Locks),Client) -> case5(Client,Locks,Lock,member(Client,record_extract(Lock,lock(),pending()))) case5(Client,Locks,Lock,true()) -> andt(locker2_obtainable(Lock,Client),locker2_obtainables(Locks,Client)) case5(Client,Locks,Lock,false()) -> locker2_obtainables(Locks,Client) locker2_check_available(Resource,nil()) -> false() locker2_check_available(Resource,cons(Lock,Locks)) -> case6(Locks,Lock,Resource,equal(Resource,record_extract(Lock,lock(),resource()))) case6(Locks,Lock,Resource,true()) -> andt(equal(record_extract(Lock,lock(),excl()),nil()),equal(record_extract (Lock,lock(),pending()), nil())) case6(Locks,Lock,Resource,false()) -> locker2_check_available(Resource,Locks) locker2_check_availables(nil(),Locks) -> true() locker2_check_availables(cons(Resource,Resources),Locks) -> andt(locker2_check_available(Resource,Locks),locker2_check_availables(Resources,Locks)) locker2_adduniq(nil(),List) -> List append(cons(Head,Tail),List) -> cons(Head,append(Tail,List)) subtract(List,nil()) -> List subtract(List,cons(Head,Tail)) -> subtract(delete(Head,List),Tail) delete(E,nil()) -> nil() delete(E,cons(Head,Tail)) -> case8(Tail,Head,E,equal(E,Head)) case8(Tail,Head,E,true()) -> Tail case8(Tail,Head,E,false()) -> cons(Head,delete(E,Tail)) gen_tag(Pid) -> tuple(Pid,tuplenil(tag())) gen_modtageq(Client1,Client2) -> equal(Client1,Client2) member(E,nil()) -> false() member(E,cons(Head,Tail)) -> case9(Tail,Head,E,equal(E,Head)) case9(Tail,Head,E,true()) -> true() case9(Tail,Head,E,false()) -> member(E,Tail) eqs(empty(),empty()) -> T() eqs(empty(),stack(E2,S2)) -> F() eqs(stack(E1,S1),empty()) -> F() eqs(stack(E1,S1),stack(E2,S2)) -> and(eqt(E1,E2),eqs(S1,S2)) pushs(E1,S1) -> stack(E1,S1) pops(stack(E1,S1)) -> S1 tops(stack(E1,S1)) -> E1 istops(E1,empty()) -> F() istops(E1,stack(E2,S1)) -> eqt(E1,E2) eqc(nocalls(),nocalls()) -> T() eqc(nocalls(),calls(E2,S2,CS2)) -> F() eqc(calls(E1,S1,CS1),nocalls()) -> F() eqc(calls(E1,S1,CS1),calls(E2,S2,CS2)) -> and(eqt(E1,E2),and(eqs(S1,S2),eqc(CS1,CS2))) push(E1,E2,nocalls()) -> calls(E1,stack(E2,empty()),nocalls()) push(E1,E2,calls(E3,S1,CS1)) -> push1(E1,E2,E3,S1,CS1,eqt(E1,E3)) push1(E1,E2,E3,S1,CS1,T()) -> calls(E3,pushs(E2,S1),CS1) Qed DPs: append#(cons(Head,Tail),List) -> append#(Tail,List) TRS: or(T(),T()) -> T() or(F(),T()) -> T() or(T(),F()) -> T() or(F(),F()) -> F() and(T(),B) -> B and(B,T()) -> B and(F(),B) -> F() and(B,F()) -> F() imp(T(),B) -> B imp(F(),B) -> T() not(T()) -> F() not(F()) -> T() if(T(),B1,B2) -> B1 if(F(),B1,B2) -> B2 eq(T(),T()) -> T() eq(F(),F()) -> T() eq(T(),F()) -> F() eq(F(),T()) -> F() eqt(nil(),undefined()) -> F() eqt(nil(),pid(N2)) -> F() eqt(nil(),int(N2)) -> F() eqt(nil(),cons(H2,T2)) -> F() eqt(nil(),tuple(H2,T2)) -> F() eqt(nil(),tuplenil(H2)) -> F() eqt(a(),nil()) -> F() eqt(a(),a()) -> T() eqt(a(),excl()) -> F() eqt(a(),false()) -> F() eqt(a(),lock()) -> F() eqt(a(),locker()) -> F() eqt(a(),mcrlrecord()) -> F() eqt(a(),ok()) -> F() eqt(a(),pending()) -> F() eqt(a(),release()) -> F() eqt(a(),request()) -> F() eqt(a(),resource()) -> F() eqt(a(),tag()) -> F() eqt(a(),true()) -> F() eqt(a(),undefined()) -> F() eqt(a(),pid(N2)) -> F() eqt(a(),int(N2)) -> F() eqt(a(),cons(H2,T2)) -> F() eqt(a(),tuple(H2,T2)) -> F() eqt(a(),tuplenil(H2)) -> F() eqt(excl(),nil()) -> F() eqt(excl(),a()) -> F() eqt(excl(),excl()) -> T() eqt(excl(),false()) -> F() eqt(excl(),lock()) -> F() eqt(excl(),locker()) -> F() eqt(excl(),mcrlrecord()) -> F() eqt(excl(),ok()) -> F() eqt(excl(),pending()) -> F() eqt(excl(),release()) -> F() eqt(excl(),request()) -> F() eqt(excl(),resource()) -> F() eqt(excl(),tag()) -> F() eqt(excl(),true()) -> F() eqt(excl(),undefined()) -> F() eqt(excl(),pid(N2)) -> F() eqt(excl(),eqt(false(),int(N2))) -> F() eqt(false(),cons(H2,T2)) -> F() eqt(false(),tuple(H2,T2)) -> F() eqt(false(),tuplenil(H2)) -> F() eqt(lock(),nil()) -> F() eqt(lock(),a()) -> F() eqt(lock(),excl()) -> F() eqt(lock(),false()) -> F() eqt(lock(),lock()) -> T() eqt(lock(),locker()) -> F() eqt(lock(),mcrlrecord()) -> F() eqt(lock(),ok()) -> F() eqt(lock(),pending()) -> F() eqt(lock(),release()) -> F() eqt(lock(),request()) -> F() eqt(lock(),resource()) -> F() eqt(lock(),tag()) -> F() eqt(lock(),true()) -> F() eqt(lock(),undefined()) -> F() eqt(lock(),pid(N2)) -> F() eqt(lock(),int(N2)) -> F() eqt(lock(),cons(H2,T2)) -> F() eqt(lock(),tuple(H2,T2)) -> F() eqt(lock(),tuplenil(H2)) -> F() eqt(locker(),nil()) -> F() eqt(locker(),a()) -> F() eqt(locker(),excl()) -> F() eqt(locker(),false()) -> F() eqt(locker(),lock()) -> F() eqt(locker(),locker()) -> T() eqt(locker(),mcrlrecord()) -> F() eqt(locker(),ok()) -> F() eqt(locker(),pending()) -> F() eqt(locker(),release()) -> F() eqt(locker(),request()) -> F() eqt(locker(),resource()) -> F() eqt(locker(),tag()) -> F() eqt(locker(),true()) -> F() eqt(locker(),undefined()) -> F() eqt(locker(),pid(N2)) -> F() eqt(locker(),int(N2)) -> F() eqt(locker(),cons(H2,T2)) -> F() eqt(locker(),tuple(H2,T2)) -> F() eqt(locker(),tuplenil(H2)) -> F() eqt(mcrlrecord(),nil()) -> F() eqt(mcrlrecord(),a()) -> F() eqt(mcrlrecord(),excl()) -> F() eqt(mcrlrecord(),false()) -> F() eqt(mcrlrecord(),lock()) -> F() eqt(mcrlrecord(),locker()) -> F() eqt(mcrlrecord(),mcrlrecord()) -> T() eqt(mcrlrecord(),ok()) -> F() eqt(mcrlrecord(),pending()) -> F() eqt(mcrlrecord(),release()) -> F() eqt(mcrlrecord(),request()) -> F() eqt(mcrlrecord(),resource()) -> F() eqt(ok(),resource()) -> F() eqt(ok(),tag()) -> F() eqt(ok(),true()) -> F() eqt(ok(),undefined()) -> F() eqt(ok(),pid(N2)) -> F() eqt(ok(),int(N2)) -> F() eqt(ok(),cons(H2,T2)) -> F() eqt(ok(),tuple(H2,T2)) -> F() eqt(ok(),tuplenil(H2)) -> F() eqt(pending(),nil()) -> F() eqt(pending(),a()) -> F() eqt(pending(),excl()) -> F() eqt(pending(),false()) -> F() eqt(pending(),lock()) -> F() eqt(pending(),locker()) -> F() eqt(pending(),mcrlrecord()) -> F() eqt(pending(),ok()) -> F() eqt(pending(),pending()) -> T() eqt(pending(),release()) -> F() eqt(pending(),request()) -> F() eqt(pending(),resource()) -> F() eqt(pending(),tag()) -> F() eqt(pending(),true()) -> F() eqt(pending(),undefined()) -> F() eqt(pending(),pid(N2)) -> F() eqt(pending(),int(N2)) -> F() eqt(pending(),cons(H2,T2)) -> F() eqt(pending(),tuple(H2,T2)) -> F() eqt(pending(),tuplenil(H2)) -> F() eqt(release(),nil()) -> F() eqt(release(),a()) -> F() eqt(release(),excl()) -> F() eqt(release(),false()) -> F() eqt(release(),lock()) -> F() eqt(release(),locker()) -> F() eqt(release(),mcrlrecord()) -> F() eqt(release(),ok()) -> F() eqt(request(),mcrlrecord()) -> F() eqt(request(),ok()) -> F() eqt(request(),pending()) -> F() eqt(request(),release()) -> F() eqt(request(),request()) -> T() eqt(request(),resource()) -> F() eqt(request(),tag()) -> F() eqt(request(),true()) -> F() eqt(request(),undefined()) -> F() eqt(request(),pid(N2)) -> F() eqt(request(),int(N2)) -> F() eqt(request(),cons(H2,T2)) -> F() eqt(request(),tuple(H2,T2)) -> F() eqt(request(),tuplenil(H2)) -> F() eqt(resource(),nil()) -> F() eqt(resource(),a()) -> F() eqt(resource(),excl()) -> F() eqt(resource(),false()) -> F() eqt(resource(),lock()) -> F() eqt(resource(),locker()) -> F() eqt(resource(),mcrlrecord()) -> F() eqt(resource(),ok()) -> F() eqt(resource(),pending()) -> F() eqt(resource(),release()) -> F() eqt(resource(),request()) -> F() eqt(resource(),resource()) -> T() eqt(resource(),tag()) -> F() eqt(resource(),true()) -> F() eqt(resource(),undefined()) -> F() eqt(resource(),pid(N2)) -> F() eqt(resource(),int(N2)) -> F() eqt(resource(),cons(H2,T2)) -> F() eqt(resource(),tuple(H2,T2)) -> F() eqt(resource(),tuplenil(H2)) -> F() eqt(tag(),nil()) -> F() eqt(tag(),a()) -> F() eqt(tag(),excl()) -> F() eqt(tag(),false()) -> F() eqt(tag(),lock()) -> F() eqt(tag(),locker()) -> F() eqt(tag(),mcrlrecord()) -> F() eqt(tag(),ok()) -> F() eqt(tag(),pending()) -> F() eqt(tag(),release()) -> F() eqt(tag(),request()) -> F() eqt(tag(),resource()) -> F() eqt(tag(),tag()) -> T() eqt(tag(),true()) -> F() eqt(tag(),undefined()) -> F() eqt(tag(),pid(N2)) -> F() eqt(tag(),int(N2)) -> F() eqt(tag(),cons(H2,T2)) -> F() eqt(tag(),tuple(H2,T2)) -> F() eqt(tag(),tuplenil(H2)) -> F() eqt(true(),nil()) -> F() eqt(true(),a()) -> F() eqt(true(),excl()) -> F() eqt(true(),false()) -> F() eqt(true(),lock()) -> F() eqt(true(),locker()) -> F() eqt(true(),mcrlrecord()) -> F() eqt(true(),ok()) -> F() eqt(true(),pending()) -> F() eqt(true(),release()) -> F() eqt(true(),request()) -> F() eqt(true(),resource()) -> F() eqt(true(),tag()) -> F() eqt(true(),true()) -> T() eqt(true(),undefined()) -> F() eqt(true(),pid(N2)) -> F() eqt(true(),int(N2)) -> F() eqt(true(),cons(H2,T2)) -> F() eqt(true(),tuple(H2,T2)) -> F() eqt(true(),tuplenil(H2)) -> F() eqt(undefined(),nil()) -> F() eqt(undefined(),a()) -> F() eqt(undefined(),tuplenil(H2)) -> F() eqt(pid(N1),nil()) -> F() eqt(pid(N1),a()) -> F() eqt(pid(N1),excl()) -> F() eqt(pid(N1),false()) -> F() eqt(pid(N1),lock()) -> F() eqt(pid(N1),locker()) -> F() eqt(pid(N1),mcrlrecord()) -> F() eqt(pid(N1),ok()) -> F() eqt(pid(N1),pending()) -> F() eqt(pid(N1),release()) -> F() eqt(pid(N1),request()) -> F() eqt(pid(N1),resource()) -> F() eqt(pid(N1),tag()) -> F() eqt(pid(N1),true()) -> F() eqt(pid(N1),undefined()) -> F() eqt(pid(N1),pid(N2)) -> eqt(N1,N2) eqt(pid(N1),int(N2)) -> F() eqt(pid(N1),cons(H2,T2)) -> F() eqt(pid(N1),tuple(H2,T2)) -> F() eqt(pid(N1),tuplenil(H2)) -> F() eqt(int(N1),nil()) -> F() eqt(int(N1),a()) -> F() eqt(int(N1),excl()) -> F() eqt(int(N1),false()) -> F() eqt(int(N1),lock()) -> F() eqt(int(N1),locker()) -> F() eqt(int(N1),mcrlrecord()) -> F() eqt(int(N1),ok()) -> F() eqt(int(N1),pending()) -> F() eqt(int(N1),release()) -> F() eqt(int(N1),request()) -> F() eqt(int(N1),resource()) -> F() eqt(int(N1),tag()) -> F() eqt(int(N1),true()) -> F() eqt(int(N1),undefined()) -> F() eqt(cons(H1,T1),resource()) -> F() eqt(cons(H1,T1),tag()) -> F() eqt(cons(H1,T1),true()) -> F() eqt(cons(H1,T1),undefined()) -> F() eqt(cons(H1,T1),pid(N2)) -> F() eqt(cons(H1,T1),int(N2)) -> F() eqt(cons(H1,T1),cons(H2,T2)) -> and(eqt(H1,H2),eqt(T1,T2)) eqt(cons(H1,T1),tuple(H2,T2)) -> F() eqt(cons(H1,T1),tuplenil(H2)) -> F() eqt(tuple(H1,T1),nil()) -> F() eqt(tuple(H1,T1),a()) -> F() eqt(tuple(H1,T1),excl()) -> F() eqt(tuple(H1,T1),false()) -> F() eqt(tuple(H1,T1),lock()) -> F() eqt(tuple(H1,T1),locker()) -> F() eqt(tuple(H1,T1),mcrlrecord()) -> F() eqt(tuple(H1,T1),ok()) -> F() eqt(tuple(H1,T1),pending()) -> F() eqt(tuple(H1,T1),release()) -> F() eqt(tuple(H1,T1),request()) -> F() eqt(tuple(H1,T1),resource()) -> F() eqt(tuple(H1,T1),tag()) -> F() eqt(tuple(H1,T1),true()) -> F() eqt(tuple(H1,T1),undefined()) -> F() eqt(tuple(H1,T1),pid(N2)) -> F() eqt(tuple(H1,T1),int(N2)) -> F() eqt(tuple(H1,T1),cons(H2,T2)) -> F() eqt(tuple(H1,T1),tuple(H2,T2)) -> and(eqt(H1,H2),eqt(T1,T2)) eqt(tuple(H1,T1),tuplenil(H2)) -> F() eqt(tuplenil(H1),nil()) -> F() eqt(tuplenil(H1),a()) -> F() eqt(tuplenil(H1),excl()) -> F() eqt(tuplenil(H1),false()) -> F() eqt(tuplenil(H1),lock()) -> F() eqt(tuplenil(H1),locker()) -> F() eqt(tuplenil(H1),mcrlrecord()) -> F() eqt(tuplenil(H1),ok()) -> F() eqt(tuplenil(H1),pending()) -> F() eqt(tuplenil(H1),release()) -> F() eqt(tuplenil(H1),request()) -> F() eqt(tuplenil(H1),resource()) -> F() eqt(tuplenil(H1),tag()) -> F() eqt(tuplenil(H1),true()) -> F() eqt(tuplenil(H1),undefined()) -> F() eqt(tuplenil(H1),pid(N2)) -> F() eqt(tuplenil(H1),int(N2)) -> F() eqt(tuplenil(H1),cons(H2,T2)) -> F() eqt(tuplenil(H1),tuple(H2,T2)) -> F() eqt(tuplenil(H1),tuplenil(H2)) -> eqt(H1,H2) element(int(s(0())),tuplenil(T1)) -> T1 element(int(s(0())),tuple(T1,T2)) -> T1 element(int(s(s(N1))),tuple(T1,T2)) -> element(int(s(N1)),T2) record_new(lock()) -> tuple(mcrlrecord(),tuple(lock(),tuple(undefined(),tuple(nil(),tuplenil(nil()))))) record_extract(tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))), lock(),resource()) -> tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))) record_update(tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))), lock(),pending(),NewF) -> tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(NewF))))) record_updates(Record,Name,nil()) -> Record record_updates(Record,Name,cons(tuple(Field,tuplenil(NewF)),Fields)) -> record_updates(record_update(Record,Name,Field,NewF),Name,Fields) locker2_map_promote_pending(nil(),Pending) -> nil() locker2_map_promote_pending(cons(Lock,Locks),Pending) -> cons(locker2_promote_pending(Lock,Pending),locker2_map_promote_pending(Locks,Pending)) locker2_map_claim_lock(nil(),Resources,Client) -> nil() locker2_map_claim_lock(cons(Lock,Locks),Resources,Client) -> cons(locker2_claim_lock(Lock,Resources,Client),locker2_map_claim_lock(Locks,Resources,Client)) locker2_map_add_pending(nil(),Resources,Client) -> nil() locker2_promote_pending(Lock,Client) -> case0(Client,Lock,record_extract(Lock,lock(),pending())) case0(Client,Lock,cons(Client,Pendings)) -> record_updates(Lock,lock(),cons(tuple(excl(),tuplenil(Client)),cons ( tuple ( pending(),tuplenil(Pendings)), nil ()))) case0(Client,Lock,MCRLFree0) -> Lock locker2_remove_pending(Lock,Client) -> record_updates(Lock,lock(),cons(tuple(pending(),tuplenil(subtract (record_extract (Lock,lock(),pending()), cons(Client,nil())))), nil())) locker2_add_pending(Lock,Resources,Client) -> case1(Client,Resources,Lock,member(record_extract(Lock,lock(),resource()),Resources)) case1(Client,Resources,Lock,true()) -> record_updates(Lock,lock(),cons(tuple(pending(),tuplenil(append( record_extract ( Lock,lock(),pending()), cons (Client,nil())))), nil())) case1(Client,Resources,Lock,false()) -> Lock locker2_release_lock(Lock,Client) -> case2(Client,Lock,gen_modtageq(Client,record_extract(Lock,lock(),excl()))) case2(Client,Lock,true()) -> record_updates(Lock,lock(),cons(tuple(excllock(),excl()),nil())) case4(Client,Lock,MCRLFree1) -> false() locker2_obtainables(nil(),Client) -> true() locker2_obtainables(cons(Lock,Locks),Client) -> case5(Client,Locks,Lock,member(Client,record_extract(Lock,lock(),pending()))) case5(Client,Locks,Lock,true()) -> andt(locker2_obtainable(Lock,Client),locker2_obtainables(Locks,Client)) case5(Client,Locks,Lock,false()) -> locker2_obtainables(Locks,Client) locker2_check_available(Resource,nil()) -> false() locker2_check_available(Resource,cons(Lock,Locks)) -> case6(Locks,Lock,Resource,equal(Resource,record_extract(Lock,lock(),resource()))) case6(Locks,Lock,Resource,true()) -> andt(equal(record_extract(Lock,lock(),excl()),nil()),equal(record_extract (Lock,lock(),pending()), nil())) case6(Locks,Lock,Resource,false()) -> locker2_check_available(Resource,Locks) locker2_check_availables(nil(),Locks) -> true() locker2_check_availables(cons(Resource,Resources),Locks) -> andt(locker2_check_available(Resource,Locks),locker2_check_availables(Resources,Locks)) locker2_adduniq(nil(),List) -> List append(cons(Head,Tail),List) -> cons(Head,append(Tail,List)) subtract(List,nil()) -> List subtract(List,cons(Head,Tail)) -> subtract(delete(Head,List),Tail) delete(E,nil()) -> nil() delete(E,cons(Head,Tail)) -> case8(Tail,Head,E,equal(E,Head)) case8(Tail,Head,E,true()) -> Tail case8(Tail,Head,E,false()) -> cons(Head,delete(E,Tail)) gen_tag(Pid) -> tuple(Pid,tuplenil(tag())) gen_modtageq(Client1,Client2) -> equal(Client1,Client2) member(E,nil()) -> false() member(E,cons(Head,Tail)) -> case9(Tail,Head,E,equal(E,Head)) case9(Tail,Head,E,true()) -> true() case9(Tail,Head,E,false()) -> member(E,Tail) eqs(empty(),empty()) -> T() eqs(empty(),stack(E2,S2)) -> F() eqs(stack(E1,S1),empty()) -> F() eqs(stack(E1,S1),stack(E2,S2)) -> and(eqt(E1,E2),eqs(S1,S2)) pushs(E1,S1) -> stack(E1,S1) pops(stack(E1,S1)) -> S1 tops(stack(E1,S1)) -> E1 istops(E1,empty()) -> F() istops(E1,stack(E2,S1)) -> eqt(E1,E2) eqc(nocalls(),nocalls()) -> T() eqc(nocalls(),calls(E2,S2,CS2)) -> F() eqc(calls(E1,S1,CS1),nocalls()) -> F() eqc(calls(E1,S1,CS1),calls(E2,S2,CS2)) -> and(eqt(E1,E2),and(eqs(S1,S2),eqc(CS1,CS2))) push(E1,E2,nocalls()) -> calls(E1,stack(E2,empty()),nocalls()) push(E1,E2,calls(E3,S1,CS1)) -> push1(E1,E2,E3,S1,CS1,eqt(E1,E3)) push1(E1,E2,E3,S1,CS1,T()) -> calls(E3,pushs(E2,S1),CS1) Subterm Criterion Processor: simple projection: pi(append#) = 0 problem: DPs: TRS: or(T(),T()) -> T() or(F(),T()) -> T() or(T(),F()) -> T() or(F(),F()) -> F() and(T(),B) -> B and(B,T()) -> B and(F(),B) -> F() and(B,F()) -> F() imp(T(),B) -> B imp(F(),B) -> T() not(T()) -> F() not(F()) -> T() if(T(),B1,B2) -> B1 if(F(),B1,B2) -> B2 eq(T(),T()) -> T() eq(F(),F()) -> T() eq(T(),F()) -> F() eq(F(),T()) -> F() eqt(nil(),undefined()) -> F() eqt(nil(),pid(N2)) -> F() eqt(nil(),int(N2)) -> F() eqt(nil(),cons(H2,T2)) -> F() eqt(nil(),tuple(H2,T2)) -> F() eqt(nil(),tuplenil(H2)) -> F() eqt(a(),nil()) -> F() eqt(a(),a()) -> T() eqt(a(),excl()) -> F() eqt(a(),false()) -> F() eqt(a(),lock()) -> F() eqt(a(),locker()) -> F() eqt(a(),mcrlrecord()) -> F() eqt(a(),ok()) -> F() eqt(a(),pending()) -> F() eqt(a(),release()) -> F() eqt(a(),request()) -> F() eqt(a(),resource()) -> F() eqt(a(),tag()) -> F() eqt(a(),true()) -> F() eqt(a(),undefined()) -> F() eqt(a(),pid(N2)) -> F() eqt(a(),int(N2)) -> F() eqt(a(),cons(H2,T2)) -> F() eqt(a(),tuple(H2,T2)) -> F() eqt(a(),tuplenil(H2)) -> F() eqt(excl(),nil()) -> F() eqt(excl(),a()) -> F() eqt(excl(),excl()) -> T() eqt(excl(),false()) -> F() eqt(excl(),lock()) -> F() eqt(excl(),locker()) -> F() eqt(excl(),mcrlrecord()) -> F() eqt(excl(),ok()) -> F() eqt(excl(),pending()) -> F() eqt(excl(),release()) -> F() eqt(excl(),request()) -> F() eqt(excl(),resource()) -> F() eqt(excl(),tag()) -> F() eqt(excl(),true()) -> F() eqt(excl(),undefined()) -> F() eqt(excl(),pid(N2)) -> F() eqt(excl(),eqt(false(),int(N2))) -> F() eqt(false(),cons(H2,T2)) -> F() eqt(false(),tuple(H2,T2)) -> F() eqt(false(),tuplenil(H2)) -> F() eqt(lock(),nil()) -> F() eqt(lock(),a()) -> F() eqt(lock(),excl()) -> F() eqt(lock(),false()) -> F() eqt(lock(),lock()) -> T() eqt(lock(),locker()) -> F() eqt(lock(),mcrlrecord()) -> F() eqt(lock(),ok()) -> F() eqt(lock(),pending()) -> F() eqt(lock(),release()) -> F() eqt(lock(),request()) -> F() eqt(lock(),resource()) -> F() eqt(lock(),tag()) -> F() eqt(lock(),true()) -> F() eqt(lock(),undefined()) -> F() eqt(lock(),pid(N2)) -> F() eqt(lock(),int(N2)) -> F() eqt(lock(),cons(H2,T2)) -> F() eqt(lock(),tuple(H2,T2)) -> F() eqt(lock(),tuplenil(H2)) -> F() eqt(locker(),nil()) -> F() eqt(locker(),a()) -> F() eqt(locker(),excl()) -> F() eqt(locker(),false()) -> F() eqt(locker(),lock()) -> F() eqt(locker(),locker()) -> T() eqt(locker(),mcrlrecord()) -> F() eqt(locker(),ok()) -> F() eqt(locker(),pending()) -> F() eqt(locker(),release()) -> F() eqt(locker(),request()) -> F() eqt(locker(),resource()) -> F() eqt(locker(),tag()) -> F() eqt(locker(),true()) -> F() eqt(locker(),undefined()) -> F() eqt(locker(),pid(N2)) -> F() eqt(locker(),int(N2)) -> F() eqt(locker(),cons(H2,T2)) -> F() eqt(locker(),tuple(H2,T2)) -> F() eqt(locker(),tuplenil(H2)) -> F() eqt(mcrlrecord(),nil()) -> F() eqt(mcrlrecord(),a()) -> F() eqt(mcrlrecord(),excl()) -> F() eqt(mcrlrecord(),false()) -> F() eqt(mcrlrecord(),lock()) -> F() eqt(mcrlrecord(),locker()) -> F() eqt(mcrlrecord(),mcrlrecord()) -> T() eqt(mcrlrecord(),ok()) -> F() eqt(mcrlrecord(),pending()) -> F() eqt(mcrlrecord(),release()) -> F() eqt(mcrlrecord(),request()) -> F() eqt(mcrlrecord(),resource()) -> F() eqt(ok(),resource()) -> F() eqt(ok(),tag()) -> F() eqt(ok(),true()) -> F() eqt(ok(),undefined()) -> F() eqt(ok(),pid(N2)) -> F() eqt(ok(),int(N2)) -> F() eqt(ok(),cons(H2,T2)) -> F() eqt(ok(),tuple(H2,T2)) -> F() eqt(ok(),tuplenil(H2)) -> F() eqt(pending(),nil()) -> F() eqt(pending(),a()) -> F() eqt(pending(),excl()) -> F() eqt(pending(),false()) -> F() eqt(pending(),lock()) -> F() eqt(pending(),locker()) -> F() eqt(pending(),mcrlrecord()) -> F() eqt(pending(),ok()) -> F() eqt(pending(),pending()) -> T() eqt(pending(),release()) -> F() eqt(pending(),request()) -> F() eqt(pending(),resource()) -> F() eqt(pending(),tag()) -> F() eqt(pending(),true()) -> F() eqt(pending(),undefined()) -> F() eqt(pending(),pid(N2)) -> F() eqt(pending(),int(N2)) -> F() eqt(pending(),cons(H2,T2)) -> F() eqt(pending(),tuple(H2,T2)) -> F() eqt(pending(),tuplenil(H2)) -> F() eqt(release(),nil()) -> F() eqt(release(),a()) -> F() eqt(release(),excl()) -> F() eqt(release(),false()) -> F() eqt(release(),lock()) -> F() eqt(release(),locker()) -> F() eqt(release(),mcrlrecord()) -> F() eqt(release(),ok()) -> F() eqt(request(),mcrlrecord()) -> F() eqt(request(),ok()) -> F() eqt(request(),pending()) -> F() eqt(request(),release()) -> F() eqt(request(),request()) -> T() eqt(request(),resource()) -> F() eqt(request(),tag()) -> F() eqt(request(),true()) -> F() eqt(request(),undefined()) -> F() eqt(request(),pid(N2)) -> F() eqt(request(),int(N2)) -> F() eqt(request(),cons(H2,T2)) -> F() eqt(request(),tuple(H2,T2)) -> F() eqt(request(),tuplenil(H2)) -> F() eqt(resource(),nil()) -> F() eqt(resource(),a()) -> F() eqt(resource(),excl()) -> F() eqt(resource(),false()) -> F() eqt(resource(),lock()) -> F() eqt(resource(),locker()) -> F() eqt(resource(),mcrlrecord()) -> F() eqt(resource(),ok()) -> F() eqt(resource(),pending()) -> F() eqt(resource(),release()) -> F() eqt(resource(),request()) -> F() eqt(resource(),resource()) -> T() eqt(resource(),tag()) -> F() eqt(resource(),true()) -> F() eqt(resource(),undefined()) -> F() eqt(resource(),pid(N2)) -> F() eqt(resource(),int(N2)) -> F() eqt(resource(),cons(H2,T2)) -> F() eqt(resource(),tuple(H2,T2)) -> F() eqt(resource(),tuplenil(H2)) -> F() eqt(tag(),nil()) -> F() eqt(tag(),a()) -> F() eqt(tag(),excl()) -> F() eqt(tag(),false()) -> F() eqt(tag(),lock()) -> F() eqt(tag(),locker()) -> F() eqt(tag(),mcrlrecord()) -> F() eqt(tag(),ok()) -> F() eqt(tag(),pending()) -> F() eqt(tag(),release()) -> F() eqt(tag(),request()) -> F() eqt(tag(),resource()) -> F() eqt(tag(),tag()) -> T() eqt(tag(),true()) -> F() eqt(tag(),undefined()) -> F() eqt(tag(),pid(N2)) -> F() eqt(tag(),int(N2)) -> F() eqt(tag(),cons(H2,T2)) -> F() eqt(tag(),tuple(H2,T2)) -> F() eqt(tag(),tuplenil(H2)) -> F() eqt(true(),nil()) -> F() eqt(true(),a()) -> F() eqt(true(),excl()) -> F() eqt(true(),false()) -> F() eqt(true(),lock()) -> F() eqt(true(),locker()) -> F() eqt(true(),mcrlrecord()) -> F() eqt(true(),ok()) -> F() eqt(true(),pending()) -> F() eqt(true(),release()) -> F() eqt(true(),request()) -> F() eqt(true(),resource()) -> F() eqt(true(),tag()) -> F() eqt(true(),true()) -> T() eqt(true(),undefined()) -> F() eqt(true(),pid(N2)) -> F() eqt(true(),int(N2)) -> F() eqt(true(),cons(H2,T2)) -> F() eqt(true(),tuple(H2,T2)) -> F() eqt(true(),tuplenil(H2)) -> F() eqt(undefined(),nil()) -> F() eqt(undefined(),a()) -> F() eqt(undefined(),tuplenil(H2)) -> F() eqt(pid(N1),nil()) -> F() eqt(pid(N1),a()) -> F() eqt(pid(N1),excl()) -> F() eqt(pid(N1),false()) -> F() eqt(pid(N1),lock()) -> F() eqt(pid(N1),locker()) -> F() eqt(pid(N1),mcrlrecord()) -> F() eqt(pid(N1),ok()) -> F() eqt(pid(N1),pending()) -> F() eqt(pid(N1),release()) -> F() eqt(pid(N1),request()) -> F() eqt(pid(N1),resource()) -> F() eqt(pid(N1),tag()) -> F() eqt(pid(N1),true()) -> F() eqt(pid(N1),undefined()) -> F() eqt(pid(N1),pid(N2)) -> eqt(N1,N2) eqt(pid(N1),int(N2)) -> F() eqt(pid(N1),cons(H2,T2)) -> F() eqt(pid(N1),tuple(H2,T2)) -> F() eqt(pid(N1),tuplenil(H2)) -> F() eqt(int(N1),nil()) -> F() eqt(int(N1),a()) -> F() eqt(int(N1),excl()) -> F() eqt(int(N1),false()) -> F() eqt(int(N1),lock()) -> F() eqt(int(N1),locker()) -> F() eqt(int(N1),mcrlrecord()) -> F() eqt(int(N1),ok()) -> F() eqt(int(N1),pending()) -> F() eqt(int(N1),release()) -> F() eqt(int(N1),request()) -> F() eqt(int(N1),resource()) -> F() eqt(int(N1),tag()) -> F() eqt(int(N1),true()) -> F() eqt(int(N1),undefined()) -> F() eqt(cons(H1,T1),resource()) -> F() eqt(cons(H1,T1),tag()) -> F() eqt(cons(H1,T1),true()) -> F() eqt(cons(H1,T1),undefined()) -> F() eqt(cons(H1,T1),pid(N2)) -> F() eqt(cons(H1,T1),int(N2)) -> F() eqt(cons(H1,T1),cons(H2,T2)) -> and(eqt(H1,H2),eqt(T1,T2)) eqt(cons(H1,T1),tuple(H2,T2)) -> F() eqt(cons(H1,T1),tuplenil(H2)) -> F() eqt(tuple(H1,T1),nil()) -> F() eqt(tuple(H1,T1),a()) -> F() eqt(tuple(H1,T1),excl()) -> F() eqt(tuple(H1,T1),false()) -> F() eqt(tuple(H1,T1),lock()) -> F() eqt(tuple(H1,T1),locker()) -> F() eqt(tuple(H1,T1),mcrlrecord()) -> F() eqt(tuple(H1,T1),ok()) -> F() eqt(tuple(H1,T1),pending()) -> F() eqt(tuple(H1,T1),release()) -> F() eqt(tuple(H1,T1),request()) -> F() eqt(tuple(H1,T1),resource()) -> F() eqt(tuple(H1,T1),tag()) -> F() eqt(tuple(H1,T1),true()) -> F() eqt(tuple(H1,T1),undefined()) -> F() eqt(tuple(H1,T1),pid(N2)) -> F() eqt(tuple(H1,T1),int(N2)) -> F() eqt(tuple(H1,T1),cons(H2,T2)) -> F() eqt(tuple(H1,T1),tuple(H2,T2)) -> and(eqt(H1,H2),eqt(T1,T2)) eqt(tuple(H1,T1),tuplenil(H2)) -> F() eqt(tuplenil(H1),nil()) -> F() eqt(tuplenil(H1),a()) -> F() eqt(tuplenil(H1),excl()) -> F() eqt(tuplenil(H1),false()) -> F() eqt(tuplenil(H1),lock()) -> F() eqt(tuplenil(H1),locker()) -> F() eqt(tuplenil(H1),mcrlrecord()) -> F() eqt(tuplenil(H1),ok()) -> F() eqt(tuplenil(H1),pending()) -> F() eqt(tuplenil(H1),release()) -> F() eqt(tuplenil(H1),request()) -> F() eqt(tuplenil(H1),resource()) -> F() eqt(tuplenil(H1),tag()) -> F() eqt(tuplenil(H1),true()) -> F() eqt(tuplenil(H1),undefined()) -> F() eqt(tuplenil(H1),pid(N2)) -> F() eqt(tuplenil(H1),int(N2)) -> F() eqt(tuplenil(H1),cons(H2,T2)) -> F() eqt(tuplenil(H1),tuple(H2,T2)) -> F() eqt(tuplenil(H1),tuplenil(H2)) -> eqt(H1,H2) element(int(s(0())),tuplenil(T1)) -> T1 element(int(s(0())),tuple(T1,T2)) -> T1 element(int(s(s(N1))),tuple(T1,T2)) -> element(int(s(N1)),T2) record_new(lock()) -> tuple(mcrlrecord(),tuple(lock(),tuple(undefined(),tuple(nil(),tuplenil(nil()))))) record_extract(tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))), lock(),resource()) -> tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))) record_update(tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))), lock(),pending(),NewF) -> tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(NewF))))) record_updates(Record,Name,nil()) -> Record record_updates(Record,Name,cons(tuple(Field,tuplenil(NewF)),Fields)) -> record_updates(record_update(Record,Name,Field,NewF),Name,Fields) locker2_map_promote_pending(nil(),Pending) -> nil() locker2_map_promote_pending(cons(Lock,Locks),Pending) -> cons(locker2_promote_pending(Lock,Pending),locker2_map_promote_pending(Locks,Pending)) locker2_map_claim_lock(nil(),Resources,Client) -> nil() locker2_map_claim_lock(cons(Lock,Locks),Resources,Client) -> cons(locker2_claim_lock(Lock,Resources,Client),locker2_map_claim_lock (Locks,Resources,Client)) locker2_map_add_pending(nil(),Resources,Client) -> nil() locker2_promote_pending(Lock,Client) -> case0(Client,Lock,record_extract(Lock,lock(),pending())) case0(Client,Lock,cons(Client,Pendings)) -> record_updates(Lock,lock(),cons(tuple(excl(),tuplenil(Client)), cons(tuple(pending(),tuplenil(Pendings)),nil()))) case0(Client,Lock,MCRLFree0) -> Lock locker2_remove_pending(Lock,Client) -> record_updates(Lock,lock(),cons(tuple(pending(),tuplenil(subtract (record_extract (Lock,lock(),pending()), cons (Client,nil())))), nil())) locker2_add_pending(Lock,Resources,Client) -> case1(Client,Resources,Lock,member(record_extract(Lock,lock(),resource()),Resources)) case1(Client,Resources,Lock,true()) -> record_updates(Lock,lock(),cons(tuple(pending(),tuplenil(append (record_extract (Lock,lock(),pending()), cons (Client,nil())))), nil())) case1(Client,Resources,Lock,false()) -> Lock locker2_release_lock(Lock,Client) -> case2(Client,Lock,gen_modtageq(Client,record_extract(Lock,lock(),excl()))) case2(Client,Lock,true()) -> record_updates(Lock,lock(),cons(tuple(excllock(),excl()),nil())) case4(Client,Lock,MCRLFree1) -> false() locker2_obtainables(nil(),Client) -> true() locker2_obtainables(cons(Lock,Locks),Client) -> case5(Client,Locks,Lock,member(Client,record_extract(Lock,lock(),pending()))) case5(Client,Locks,Lock,true()) -> andt(locker2_obtainable(Lock,Client),locker2_obtainables(Locks,Client)) case5(Client,Locks,Lock,false()) -> locker2_obtainables(Locks,Client) locker2_check_available(Resource,nil()) -> false() locker2_check_available(Resource,cons(Lock,Locks)) -> case6(Locks,Lock,Resource,equal(Resource,record_extract(Lock,lock(),resource()))) case6(Locks,Lock,Resource,true()) -> andt(equal(record_extract(Lock,lock(),excl()),nil()),equal(record_extract (Lock,lock(),pending()), nil())) case6(Locks,Lock,Resource,false()) -> locker2_check_available(Resource,Locks) locker2_check_availables(nil(),Locks) -> true() locker2_check_availables(cons(Resource,Resources),Locks) -> andt(locker2_check_available(Resource,Locks),locker2_check_availables(Resources,Locks)) locker2_adduniq(nil(),List) -> List append(cons(Head,Tail),List) -> cons(Head,append(Tail,List)) subtract(List,nil()) -> List subtract(List,cons(Head,Tail)) -> subtract(delete(Head,List),Tail) delete(E,nil()) -> nil() delete(E,cons(Head,Tail)) -> case8(Tail,Head,E,equal(E,Head)) case8(Tail,Head,E,true()) -> Tail case8(Tail,Head,E,false()) -> cons(Head,delete(E,Tail)) gen_tag(Pid) -> tuple(Pid,tuplenil(tag())) gen_modtageq(Client1,Client2) -> equal(Client1,Client2) member(E,nil()) -> false() member(E,cons(Head,Tail)) -> case9(Tail,Head,E,equal(E,Head)) case9(Tail,Head,E,true()) -> true() case9(Tail,Head,E,false()) -> member(E,Tail) eqs(empty(),empty()) -> T() eqs(empty(),stack(E2,S2)) -> F() eqs(stack(E1,S1),empty()) -> F() eqs(stack(E1,S1),stack(E2,S2)) -> and(eqt(E1,E2),eqs(S1,S2)) pushs(E1,S1) -> stack(E1,S1) pops(stack(E1,S1)) -> S1 tops(stack(E1,S1)) -> E1 istops(E1,empty()) -> F() istops(E1,stack(E2,S1)) -> eqt(E1,E2) eqc(nocalls(),nocalls()) -> T() eqc(nocalls(),calls(E2,S2,CS2)) -> F() eqc(calls(E1,S1,CS1),nocalls()) -> F() eqc(calls(E1,S1,CS1),calls(E2,S2,CS2)) -> and(eqt(E1,E2),and(eqs(S1,S2),eqc(CS1,CS2))) push(E1,E2,nocalls()) -> calls(E1,stack(E2,empty()),nocalls()) push(E1,E2,calls(E3,S1,CS1)) -> push1(E1,E2,E3,S1,CS1,eqt(E1,E3)) push1(E1,E2,E3,S1,CS1,T()) -> calls(E3,pushs(E2,S1),CS1) Qed DPs: record_updates#(Record,Name,cons(tuple(Field,tuplenil(NewF)),Fields)) -> record_updates#(record_update(Record,Name,Field,NewF),Name,Fields) TRS: or(T(),T()) -> T() or(F(),T()) -> T() or(T(),F()) -> T() or(F(),F()) -> F() and(T(),B) -> B and(B,T()) -> B and(F(),B) -> F() and(B,F()) -> F() imp(T(),B) -> B imp(F(),B) -> T() not(T()) -> F() not(F()) -> T() if(T(),B1,B2) -> B1 if(F(),B1,B2) -> B2 eq(T(),T()) -> T() eq(F(),F()) -> T() eq(T(),F()) -> F() eq(F(),T()) -> F() eqt(nil(),undefined()) -> F() eqt(nil(),pid(N2)) -> F() eqt(nil(),int(N2)) -> F() eqt(nil(),cons(H2,T2)) -> F() eqt(nil(),tuple(H2,T2)) -> F() eqt(nil(),tuplenil(H2)) -> F() eqt(a(),nil()) -> F() eqt(a(),a()) -> T() eqt(a(),excl()) -> F() eqt(a(),false()) -> F() eqt(a(),lock()) -> F() eqt(a(),locker()) -> F() eqt(a(),mcrlrecord()) -> F() eqt(a(),ok()) -> F() eqt(a(),pending()) -> F() eqt(a(),release()) -> F() eqt(a(),request()) -> F() eqt(a(),resource()) -> F() eqt(a(),tag()) -> F() eqt(a(),true()) -> F() eqt(a(),undefined()) -> F() eqt(a(),pid(N2)) -> F() eqt(a(),int(N2)) -> F() eqt(a(),cons(H2,T2)) -> F() eqt(a(),tuple(H2,T2)) -> F() eqt(a(),tuplenil(H2)) -> F() eqt(excl(),nil()) -> F() eqt(excl(),a()) -> F() eqt(excl(),excl()) -> T() eqt(excl(),false()) -> F() eqt(excl(),lock()) -> F() eqt(excl(),locker()) -> F() eqt(excl(),mcrlrecord()) -> F() eqt(excl(),ok()) -> F() eqt(excl(),pending()) -> F() eqt(excl(),release()) -> F() eqt(excl(),request()) -> F() eqt(excl(),resource()) -> F() eqt(excl(),tag()) -> F() eqt(excl(),true()) -> F() eqt(excl(),undefined()) -> F() eqt(excl(),pid(N2)) -> F() eqt(excl(),eqt(false(),int(N2))) -> F() eqt(false(),cons(H2,T2)) -> F() eqt(false(),tuple(H2,T2)) -> F() eqt(false(),tuplenil(H2)) -> F() eqt(lock(),nil()) -> F() eqt(lock(),a()) -> F() eqt(lock(),excl()) -> F() eqt(lock(),false()) -> F() eqt(lock(),lock()) -> T() eqt(lock(),locker()) -> F() eqt(lock(),mcrlrecord()) -> F() eqt(lock(),ok()) -> F() eqt(lock(),pending()) -> F() eqt(lock(),release()) -> F() eqt(lock(),request()) -> F() eqt(lock(),resource()) -> F() eqt(lock(),tag()) -> F() eqt(lock(),true()) -> F() eqt(lock(),undefined()) -> F() eqt(lock(),pid(N2)) -> F() eqt(lock(),int(N2)) -> F() eqt(lock(),cons(H2,T2)) -> F() eqt(lock(),tuple(H2,T2)) -> F() eqt(lock(),tuplenil(H2)) -> F() eqt(locker(),nil()) -> F() eqt(locker(),a()) -> F() eqt(locker(),excl()) -> F() eqt(locker(),false()) -> F() eqt(locker(),lock()) -> F() eqt(locker(),locker()) -> T() eqt(locker(),mcrlrecord()) -> F() eqt(locker(),ok()) -> F() eqt(locker(),pending()) -> F() eqt(locker(),release()) -> F() eqt(locker(),request()) -> F() eqt(locker(),resource()) -> F() eqt(locker(),tag()) -> F() eqt(locker(),true()) -> F() eqt(locker(),undefined()) -> F() eqt(locker(),pid(N2)) -> F() eqt(locker(),int(N2)) -> F() eqt(locker(),cons(H2,T2)) -> F() eqt(locker(),tuple(H2,T2)) -> F() eqt(locker(),tuplenil(H2)) -> F() eqt(mcrlrecord(),nil()) -> F() eqt(mcrlrecord(),a()) -> F() eqt(mcrlrecord(),excl()) -> F() eqt(mcrlrecord(),false()) -> F() eqt(mcrlrecord(),lock()) -> F() eqt(mcrlrecord(),locker()) -> F() eqt(mcrlrecord(),mcrlrecord()) -> T() eqt(mcrlrecord(),ok()) -> F() eqt(mcrlrecord(),pending()) -> F() eqt(mcrlrecord(),release()) -> F() eqt(mcrlrecord(),request()) -> F() eqt(mcrlrecord(),resource()) -> F() eqt(ok(),resource()) -> F() eqt(ok(),tag()) -> F() eqt(ok(),true()) -> F() eqt(ok(),undefined()) -> F() eqt(ok(),pid(N2)) -> F() eqt(ok(),int(N2)) -> F() eqt(ok(),cons(H2,T2)) -> F() eqt(ok(),tuple(H2,T2)) -> F() eqt(ok(),tuplenil(H2)) -> F() eqt(pending(),nil()) -> F() eqt(pending(),a()) -> F() eqt(pending(),excl()) -> F() eqt(pending(),false()) -> F() eqt(pending(),lock()) -> F() eqt(pending(),locker()) -> F() eqt(pending(),mcrlrecord()) -> F() eqt(pending(),ok()) -> F() eqt(pending(),pending()) -> T() eqt(pending(),release()) -> F() eqt(pending(),request()) -> F() eqt(pending(),resource()) -> F() eqt(pending(),tag()) -> F() eqt(pending(),true()) -> F() eqt(pending(),undefined()) -> F() eqt(pending(),pid(N2)) -> F() eqt(pending(),int(N2)) -> F() eqt(pending(),cons(H2,T2)) -> F() eqt(pending(),tuple(H2,T2)) -> F() eqt(pending(),tuplenil(H2)) -> F() eqt(release(),nil()) -> F() eqt(release(),a()) -> F() eqt(release(),excl()) -> F() eqt(release(),false()) -> F() eqt(release(),lock()) -> F() eqt(release(),locker()) -> F() eqt(release(),mcrlrecord()) -> F() eqt(release(),ok()) -> F() eqt(request(),mcrlrecord()) -> F() eqt(request(),ok()) -> F() eqt(request(),pending()) -> F() eqt(request(),release()) -> F() eqt(request(),request()) -> T() eqt(request(),resource()) -> F() eqt(request(),tag()) -> F() eqt(request(),true()) -> F() eqt(request(),undefined()) -> F() eqt(request(),pid(N2)) -> F() eqt(request(),int(N2)) -> F() eqt(request(),cons(H2,T2)) -> F() eqt(request(),tuple(H2,T2)) -> F() eqt(request(),tuplenil(H2)) -> F() eqt(resource(),nil()) -> F() eqt(resource(),a()) -> F() eqt(resource(),excl()) -> F() eqt(resource(),false()) -> F() eqt(resource(),lock()) -> F() eqt(resource(),locker()) -> F() eqt(resource(),mcrlrecord()) -> F() eqt(resource(),ok()) -> F() eqt(resource(),pending()) -> F() eqt(resource(),release()) -> F() eqt(resource(),request()) -> F() eqt(resource(),resource()) -> T() eqt(resource(),tag()) -> F() eqt(resource(),true()) -> F() eqt(resource(),undefined()) -> F() eqt(resource(),pid(N2)) -> F() eqt(resource(),int(N2)) -> F() eqt(resource(),cons(H2,T2)) -> F() eqt(resource(),tuple(H2,T2)) -> F() eqt(resource(),tuplenil(H2)) -> F() eqt(tag(),nil()) -> F() eqt(tag(),a()) -> F() eqt(tag(),excl()) -> F() eqt(tag(),false()) -> F() eqt(tag(),lock()) -> F() eqt(tag(),locker()) -> F() eqt(tag(),mcrlrecord()) -> F() eqt(tag(),ok()) -> F() eqt(tag(),pending()) -> F() eqt(tag(),release()) -> F() eqt(tag(),request()) -> F() eqt(tag(),resource()) -> F() eqt(tag(),tag()) -> T() eqt(tag(),true()) -> F() eqt(tag(),undefined()) -> F() eqt(tag(),pid(N2)) -> F() eqt(tag(),int(N2)) -> F() eqt(tag(),cons(H2,T2)) -> F() eqt(tag(),tuple(H2,T2)) -> F() eqt(tag(),tuplenil(H2)) -> F() eqt(true(),nil()) -> F() eqt(true(),a()) -> F() eqt(true(),excl()) -> F() eqt(true(),false()) -> F() eqt(true(),lock()) -> F() eqt(true(),locker()) -> F() eqt(true(),mcrlrecord()) -> F() eqt(true(),ok()) -> F() eqt(true(),pending()) -> F() eqt(true(),release()) -> F() eqt(true(),request()) -> F() eqt(true(),resource()) -> F() eqt(true(),tag()) -> F() eqt(true(),true()) -> T() eqt(true(),undefined()) -> F() eqt(true(),pid(N2)) -> F() eqt(true(),int(N2)) -> F() eqt(true(),cons(H2,T2)) -> F() eqt(true(),tuple(H2,T2)) -> F() eqt(true(),tuplenil(H2)) -> F() eqt(undefined(),nil()) -> F() eqt(undefined(),a()) -> F() eqt(undefined(),tuplenil(H2)) -> F() eqt(pid(N1),nil()) -> F() eqt(pid(N1),a()) -> F() eqt(pid(N1),excl()) -> F() eqt(pid(N1),false()) -> F() eqt(pid(N1),lock()) -> F() eqt(pid(N1),locker()) -> F() eqt(pid(N1),mcrlrecord()) -> F() eqt(pid(N1),ok()) -> F() eqt(pid(N1),pending()) -> F() eqt(pid(N1),release()) -> F() eqt(pid(N1),request()) -> F() eqt(pid(N1),resource()) -> F() eqt(pid(N1),tag()) -> F() eqt(pid(N1),true()) -> F() eqt(pid(N1),undefined()) -> F() eqt(pid(N1),pid(N2)) -> eqt(N1,N2) eqt(pid(N1),int(N2)) -> F() eqt(pid(N1),cons(H2,T2)) -> F() eqt(pid(N1),tuple(H2,T2)) -> F() eqt(pid(N1),tuplenil(H2)) -> F() eqt(int(N1),nil()) -> F() eqt(int(N1),a()) -> F() eqt(int(N1),excl()) -> F() eqt(int(N1),false()) -> F() eqt(int(N1),lock()) -> F() eqt(int(N1),locker()) -> F() eqt(int(N1),mcrlrecord()) -> F() eqt(int(N1),ok()) -> F() eqt(int(N1),pending()) -> F() eqt(int(N1),release()) -> F() eqt(int(N1),request()) -> F() eqt(int(N1),resource()) -> F() eqt(int(N1),tag()) -> F() eqt(int(N1),true()) -> F() eqt(int(N1),undefined()) -> F() eqt(cons(H1,T1),resource()) -> F() eqt(cons(H1,T1),tag()) -> F() eqt(cons(H1,T1),true()) -> F() eqt(cons(H1,T1),undefined()) -> F() eqt(cons(H1,T1),pid(N2)) -> F() eqt(cons(H1,T1),int(N2)) -> F() eqt(cons(H1,T1),cons(H2,T2)) -> and(eqt(H1,H2),eqt(T1,T2)) eqt(cons(H1,T1),tuple(H2,T2)) -> F() eqt(cons(H1,T1),tuplenil(H2)) -> F() eqt(tuple(H1,T1),nil()) -> F() eqt(tuple(H1,T1),a()) -> F() eqt(tuple(H1,T1),excl()) -> F() eqt(tuple(H1,T1),false()) -> F() eqt(tuple(H1,T1),lock()) -> F() eqt(tuple(H1,T1),locker()) -> F() eqt(tuple(H1,T1),mcrlrecord()) -> F() eqt(tuple(H1,T1),ok()) -> F() eqt(tuple(H1,T1),pending()) -> F() eqt(tuple(H1,T1),release()) -> F() eqt(tuple(H1,T1),request()) -> F() eqt(tuple(H1,T1),resource()) -> F() eqt(tuple(H1,T1),tag()) -> F() eqt(tuple(H1,T1),true()) -> F() eqt(tuple(H1,T1),undefined()) -> F() eqt(tuple(H1,T1),pid(N2)) -> F() eqt(tuple(H1,T1),int(N2)) -> F() eqt(tuple(H1,T1),cons(H2,T2)) -> F() eqt(tuple(H1,T1),tuple(H2,T2)) -> and(eqt(H1,H2),eqt(T1,T2)) eqt(tuple(H1,T1),tuplenil(H2)) -> F() eqt(tuplenil(H1),nil()) -> F() eqt(tuplenil(H1),a()) -> F() eqt(tuplenil(H1),excl()) -> F() eqt(tuplenil(H1),false()) -> F() eqt(tuplenil(H1),lock()) -> F() eqt(tuplenil(H1),locker()) -> F() eqt(tuplenil(H1),mcrlrecord()) -> F() eqt(tuplenil(H1),ok()) -> F() eqt(tuplenil(H1),pending()) -> F() eqt(tuplenil(H1),release()) -> F() eqt(tuplenil(H1),request()) -> F() eqt(tuplenil(H1),resource()) -> F() eqt(tuplenil(H1),tag()) -> F() eqt(tuplenil(H1),true()) -> F() eqt(tuplenil(H1),undefined()) -> F() eqt(tuplenil(H1),pid(N2)) -> F() eqt(tuplenil(H1),int(N2)) -> F() eqt(tuplenil(H1),cons(H2,T2)) -> F() eqt(tuplenil(H1),tuple(H2,T2)) -> F() eqt(tuplenil(H1),tuplenil(H2)) -> eqt(H1,H2) element(int(s(0())),tuplenil(T1)) -> T1 element(int(s(0())),tuple(T1,T2)) -> T1 element(int(s(s(N1))),tuple(T1,T2)) -> element(int(s(N1)),T2) record_new(lock()) -> tuple(mcrlrecord(),tuple(lock(),tuple(undefined(),tuple(nil(),tuplenil(nil()))))) record_extract(tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))), lock(),resource()) -> tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))) record_update(tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))), lock(),pending(),NewF) -> tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(NewF))))) record_updates(Record,Name,nil()) -> Record record_updates(Record,Name,cons(tuple(Field,tuplenil(NewF)),Fields)) -> record_updates(record_update(Record,Name,Field,NewF),Name,Fields) locker2_map_promote_pending(nil(),Pending) -> nil() locker2_map_promote_pending(cons(Lock,Locks),Pending) -> cons(locker2_promote_pending(Lock,Pending),locker2_map_promote_pending(Locks,Pending)) locker2_map_claim_lock(nil(),Resources,Client) -> nil() locker2_map_claim_lock(cons(Lock,Locks),Resources,Client) -> cons(locker2_claim_lock(Lock,Resources,Client),locker2_map_claim_lock(Locks,Resources,Client)) locker2_map_add_pending(nil(),Resources,Client) -> nil() locker2_promote_pending(Lock,Client) -> case0(Client,Lock,record_extract(Lock,lock(),pending())) case0(Client,Lock,cons(Client,Pendings)) -> record_updates(Lock,lock(),cons(tuple(excl(),tuplenil(Client)),cons ( tuple ( pending(),tuplenil(Pendings)), nil ()))) case0(Client,Lock,MCRLFree0) -> Lock locker2_remove_pending(Lock,Client) -> record_updates(Lock,lock(),cons(tuple(pending(),tuplenil(subtract (record_extract (Lock,lock(),pending()), cons(Client,nil())))), nil())) locker2_add_pending(Lock,Resources,Client) -> case1(Client,Resources,Lock,member(record_extract(Lock,lock(),resource()),Resources)) case1(Client,Resources,Lock,true()) -> record_updates(Lock,lock(),cons(tuple(pending(),tuplenil(append( record_extract ( Lock,lock(),pending()), cons (Client,nil())))), nil())) case1(Client,Resources,Lock,false()) -> Lock locker2_release_lock(Lock,Client) -> case2(Client,Lock,gen_modtageq(Client,record_extract(Lock,lock(),excl()))) case2(Client,Lock,true()) -> record_updates(Lock,lock(),cons(tuple(excllock(),excl()),nil())) case4(Client,Lock,MCRLFree1) -> false() locker2_obtainables(nil(),Client) -> true() locker2_obtainables(cons(Lock,Locks),Client) -> case5(Client,Locks,Lock,member(Client,record_extract(Lock,lock(),pending()))) case5(Client,Locks,Lock,true()) -> andt(locker2_obtainable(Lock,Client),locker2_obtainables(Locks,Client)) case5(Client,Locks,Lock,false()) -> locker2_obtainables(Locks,Client) locker2_check_available(Resource,nil()) -> false() locker2_check_available(Resource,cons(Lock,Locks)) -> case6(Locks,Lock,Resource,equal(Resource,record_extract(Lock,lock(),resource()))) case6(Locks,Lock,Resource,true()) -> andt(equal(record_extract(Lock,lock(),excl()),nil()),equal(record_extract (Lock,lock(),pending()), nil())) case6(Locks,Lock,Resource,false()) -> locker2_check_available(Resource,Locks) locker2_check_availables(nil(),Locks) -> true() locker2_check_availables(cons(Resource,Resources),Locks) -> andt(locker2_check_available(Resource,Locks),locker2_check_availables(Resources,Locks)) locker2_adduniq(nil(),List) -> List append(cons(Head,Tail),List) -> cons(Head,append(Tail,List)) subtract(List,nil()) -> List subtract(List,cons(Head,Tail)) -> subtract(delete(Head,List),Tail) delete(E,nil()) -> nil() delete(E,cons(Head,Tail)) -> case8(Tail,Head,E,equal(E,Head)) case8(Tail,Head,E,true()) -> Tail case8(Tail,Head,E,false()) -> cons(Head,delete(E,Tail)) gen_tag(Pid) -> tuple(Pid,tuplenil(tag())) gen_modtageq(Client1,Client2) -> equal(Client1,Client2) member(E,nil()) -> false() member(E,cons(Head,Tail)) -> case9(Tail,Head,E,equal(E,Head)) case9(Tail,Head,E,true()) -> true() case9(Tail,Head,E,false()) -> member(E,Tail) eqs(empty(),empty()) -> T() eqs(empty(),stack(E2,S2)) -> F() eqs(stack(E1,S1),empty()) -> F() eqs(stack(E1,S1),stack(E2,S2)) -> and(eqt(E1,E2),eqs(S1,S2)) pushs(E1,S1) -> stack(E1,S1) pops(stack(E1,S1)) -> S1 tops(stack(E1,S1)) -> E1 istops(E1,empty()) -> F() istops(E1,stack(E2,S1)) -> eqt(E1,E2) eqc(nocalls(),nocalls()) -> T() eqc(nocalls(),calls(E2,S2,CS2)) -> F() eqc(calls(E1,S1,CS1),nocalls()) -> F() eqc(calls(E1,S1,CS1),calls(E2,S2,CS2)) -> and(eqt(E1,E2),and(eqs(S1,S2),eqc(CS1,CS2))) push(E1,E2,nocalls()) -> calls(E1,stack(E2,empty()),nocalls()) push(E1,E2,calls(E3,S1,CS1)) -> push1(E1,E2,E3,S1,CS1,eqt(E1,E3)) push1(E1,E2,E3,S1,CS1,T()) -> calls(E3,pushs(E2,S1),CS1) Subterm Criterion Processor: simple projection: pi(record_updates#) = 2 problem: DPs: TRS: or(T(),T()) -> T() or(F(),T()) -> T() or(T(),F()) -> T() or(F(),F()) -> F() and(T(),B) -> B and(B,T()) -> B and(F(),B) -> F() and(B,F()) -> F() imp(T(),B) -> B imp(F(),B) -> T() not(T()) -> F() not(F()) -> T() if(T(),B1,B2) -> B1 if(F(),B1,B2) -> B2 eq(T(),T()) -> T() eq(F(),F()) -> T() eq(T(),F()) -> F() eq(F(),T()) -> F() eqt(nil(),undefined()) -> F() eqt(nil(),pid(N2)) -> F() eqt(nil(),int(N2)) -> F() eqt(nil(),cons(H2,T2)) -> F() eqt(nil(),tuple(H2,T2)) -> F() eqt(nil(),tuplenil(H2)) -> F() eqt(a(),nil()) -> F() eqt(a(),a()) -> T() eqt(a(),excl()) -> F() eqt(a(),false()) -> F() eqt(a(),lock()) -> F() eqt(a(),locker()) -> F() eqt(a(),mcrlrecord()) -> F() eqt(a(),ok()) -> F() eqt(a(),pending()) -> F() eqt(a(),release()) -> F() eqt(a(),request()) -> F() eqt(a(),resource()) -> F() eqt(a(),tag()) -> F() eqt(a(),true()) -> F() eqt(a(),undefined()) -> F() eqt(a(),pid(N2)) -> F() eqt(a(),int(N2)) -> F() eqt(a(),cons(H2,T2)) -> F() eqt(a(),tuple(H2,T2)) -> F() eqt(a(),tuplenil(H2)) -> F() eqt(excl(),nil()) -> F() eqt(excl(),a()) -> F() eqt(excl(),excl()) -> T() eqt(excl(),false()) -> F() eqt(excl(),lock()) -> F() eqt(excl(),locker()) -> F() eqt(excl(),mcrlrecord()) -> F() eqt(excl(),ok()) -> F() eqt(excl(),pending()) -> F() eqt(excl(),release()) -> F() eqt(excl(),request()) -> F() eqt(excl(),resource()) -> F() eqt(excl(),tag()) -> F() eqt(excl(),true()) -> F() eqt(excl(),undefined()) -> F() eqt(excl(),pid(N2)) -> F() eqt(excl(),eqt(false(),int(N2))) -> F() eqt(false(),cons(H2,T2)) -> F() eqt(false(),tuple(H2,T2)) -> F() eqt(false(),tuplenil(H2)) -> F() eqt(lock(),nil()) -> F() eqt(lock(),a()) -> F() eqt(lock(),excl()) -> F() eqt(lock(),false()) -> F() eqt(lock(),lock()) -> T() eqt(lock(),locker()) -> F() eqt(lock(),mcrlrecord()) -> F() eqt(lock(),ok()) -> F() eqt(lock(),pending()) -> F() eqt(lock(),release()) -> F() eqt(lock(),request()) -> F() eqt(lock(),resource()) -> F() eqt(lock(),tag()) -> F() eqt(lock(),true()) -> F() eqt(lock(),undefined()) -> F() eqt(lock(),pid(N2)) -> F() eqt(lock(),int(N2)) -> F() eqt(lock(),cons(H2,T2)) -> F() eqt(lock(),tuple(H2,T2)) -> F() eqt(lock(),tuplenil(H2)) -> F() eqt(locker(),nil()) -> F() eqt(locker(),a()) -> F() eqt(locker(),excl()) -> F() eqt(locker(),false()) -> F() eqt(locker(),lock()) -> F() eqt(locker(),locker()) -> T() eqt(locker(),mcrlrecord()) -> F() eqt(locker(),ok()) -> F() eqt(locker(),pending()) -> F() eqt(locker(),release()) -> F() eqt(locker(),request()) -> F() eqt(locker(),resource()) -> F() eqt(locker(),tag()) -> F() eqt(locker(),true()) -> F() eqt(locker(),undefined()) -> F() eqt(locker(),pid(N2)) -> F() eqt(locker(),int(N2)) -> F() eqt(locker(),cons(H2,T2)) -> F() eqt(locker(),tuple(H2,T2)) -> F() eqt(locker(),tuplenil(H2)) -> F() eqt(mcrlrecord(),nil()) -> F() eqt(mcrlrecord(),a()) -> F() eqt(mcrlrecord(),excl()) -> F() eqt(mcrlrecord(),false()) -> F() eqt(mcrlrecord(),lock()) -> F() eqt(mcrlrecord(),locker()) -> F() eqt(mcrlrecord(),mcrlrecord()) -> T() eqt(mcrlrecord(),ok()) -> F() eqt(mcrlrecord(),pending()) -> F() eqt(mcrlrecord(),release()) -> F() eqt(mcrlrecord(),request()) -> F() eqt(mcrlrecord(),resource()) -> F() eqt(ok(),resource()) -> F() eqt(ok(),tag()) -> F() eqt(ok(),true()) -> F() eqt(ok(),undefined()) -> F() eqt(ok(),pid(N2)) -> F() eqt(ok(),int(N2)) -> F() eqt(ok(),cons(H2,T2)) -> F() eqt(ok(),tuple(H2,T2)) -> F() eqt(ok(),tuplenil(H2)) -> F() eqt(pending(),nil()) -> F() eqt(pending(),a()) -> F() eqt(pending(),excl()) -> F() eqt(pending(),false()) -> F() eqt(pending(),lock()) -> F() eqt(pending(),locker()) -> F() eqt(pending(),mcrlrecord()) -> F() eqt(pending(),ok()) -> F() eqt(pending(),pending()) -> T() eqt(pending(),release()) -> F() eqt(pending(),request()) -> F() eqt(pending(),resource()) -> F() eqt(pending(),tag()) -> F() eqt(pending(),true()) -> F() eqt(pending(),undefined()) -> F() eqt(pending(),pid(N2)) -> F() eqt(pending(),int(N2)) -> F() eqt(pending(),cons(H2,T2)) -> F() eqt(pending(),tuple(H2,T2)) -> F() eqt(pending(),tuplenil(H2)) -> F() eqt(release(),nil()) -> F() eqt(release(),a()) -> F() eqt(release(),excl()) -> F() eqt(release(),false()) -> F() eqt(release(),lock()) -> F() eqt(release(),locker()) -> F() eqt(release(),mcrlrecord()) -> F() eqt(release(),ok()) -> F() eqt(request(),mcrlrecord()) -> F() eqt(request(),ok()) -> F() eqt(request(),pending()) -> F() eqt(request(),release()) -> F() eqt(request(),request()) -> T() eqt(request(),resource()) -> F() eqt(request(),tag()) -> F() eqt(request(),true()) -> F() eqt(request(),undefined()) -> F() eqt(request(),pid(N2)) -> F() eqt(request(),int(N2)) -> F() eqt(request(),cons(H2,T2)) -> F() eqt(request(),tuple(H2,T2)) -> F() eqt(request(),tuplenil(H2)) -> F() eqt(resource(),nil()) -> F() eqt(resource(),a()) -> F() eqt(resource(),excl()) -> F() eqt(resource(),false()) -> F() eqt(resource(),lock()) -> F() eqt(resource(),locker()) -> F() eqt(resource(),mcrlrecord()) -> F() eqt(resource(),ok()) -> F() eqt(resource(),pending()) -> F() eqt(resource(),release()) -> F() eqt(resource(),request()) -> F() eqt(resource(),resource()) -> T() eqt(resource(),tag()) -> F() eqt(resource(),true()) -> F() eqt(resource(),undefined()) -> F() eqt(resource(),pid(N2)) -> F() eqt(resource(),int(N2)) -> F() eqt(resource(),cons(H2,T2)) -> F() eqt(resource(),tuple(H2,T2)) -> F() eqt(resource(),tuplenil(H2)) -> F() eqt(tag(),nil()) -> F() eqt(tag(),a()) -> F() eqt(tag(),excl()) -> F() eqt(tag(),false()) -> F() eqt(tag(),lock()) -> F() eqt(tag(),locker()) -> F() eqt(tag(),mcrlrecord()) -> F() eqt(tag(),ok()) -> F() eqt(tag(),pending()) -> F() eqt(tag(),release()) -> F() eqt(tag(),request()) -> F() eqt(tag(),resource()) -> F() eqt(tag(),tag()) -> T() eqt(tag(),true()) -> F() eqt(tag(),undefined()) -> F() eqt(tag(),pid(N2)) -> F() eqt(tag(),int(N2)) -> F() eqt(tag(),cons(H2,T2)) -> F() eqt(tag(),tuple(H2,T2)) -> F() eqt(tag(),tuplenil(H2)) -> F() eqt(true(),nil()) -> F() eqt(true(),a()) -> F() eqt(true(),excl()) -> F() eqt(true(),false()) -> F() eqt(true(),lock()) -> F() eqt(true(),locker()) -> F() eqt(true(),mcrlrecord()) -> F() eqt(true(),ok()) -> F() eqt(true(),pending()) -> F() eqt(true(),release()) -> F() eqt(true(),request()) -> F() eqt(true(),resource()) -> F() eqt(true(),tag()) -> F() eqt(true(),true()) -> T() eqt(true(),undefined()) -> F() eqt(true(),pid(N2)) -> F() eqt(true(),int(N2)) -> F() eqt(true(),cons(H2,T2)) -> F() eqt(true(),tuple(H2,T2)) -> F() eqt(true(),tuplenil(H2)) -> F() eqt(undefined(),nil()) -> F() eqt(undefined(),a()) -> F() eqt(undefined(),tuplenil(H2)) -> F() eqt(pid(N1),nil()) -> F() eqt(pid(N1),a()) -> F() eqt(pid(N1),excl()) -> F() eqt(pid(N1),false()) -> F() eqt(pid(N1),lock()) -> F() eqt(pid(N1),locker()) -> F() eqt(pid(N1),mcrlrecord()) -> F() eqt(pid(N1),ok()) -> F() eqt(pid(N1),pending()) -> F() eqt(pid(N1),release()) -> F() eqt(pid(N1),request()) -> F() eqt(pid(N1),resource()) -> F() eqt(pid(N1),tag()) -> F() eqt(pid(N1),true()) -> F() eqt(pid(N1),undefined()) -> F() eqt(pid(N1),pid(N2)) -> eqt(N1,N2) eqt(pid(N1),int(N2)) -> F() eqt(pid(N1),cons(H2,T2)) -> F() eqt(pid(N1),tuple(H2,T2)) -> F() eqt(pid(N1),tuplenil(H2)) -> F() eqt(int(N1),nil()) -> F() eqt(int(N1),a()) -> F() eqt(int(N1),excl()) -> F() eqt(int(N1),false()) -> F() eqt(int(N1),lock()) -> F() eqt(int(N1),locker()) -> F() eqt(int(N1),mcrlrecord()) -> F() eqt(int(N1),ok()) -> F() eqt(int(N1),pending()) -> F() eqt(int(N1),release()) -> F() eqt(int(N1),request()) -> F() eqt(int(N1),resource()) -> F() eqt(int(N1),tag()) -> F() eqt(int(N1),true()) -> F() eqt(int(N1),undefined()) -> F() eqt(cons(H1,T1),resource()) -> F() eqt(cons(H1,T1),tag()) -> F() eqt(cons(H1,T1),true()) -> F() eqt(cons(H1,T1),undefined()) -> F() eqt(cons(H1,T1),pid(N2)) -> F() eqt(cons(H1,T1),int(N2)) -> F() eqt(cons(H1,T1),cons(H2,T2)) -> and(eqt(H1,H2),eqt(T1,T2)) eqt(cons(H1,T1),tuple(H2,T2)) -> F() eqt(cons(H1,T1),tuplenil(H2)) -> F() eqt(tuple(H1,T1),nil()) -> F() eqt(tuple(H1,T1),a()) -> F() eqt(tuple(H1,T1),excl()) -> F() eqt(tuple(H1,T1),false()) -> F() eqt(tuple(H1,T1),lock()) -> F() eqt(tuple(H1,T1),locker()) -> F() eqt(tuple(H1,T1),mcrlrecord()) -> F() eqt(tuple(H1,T1),ok()) -> F() eqt(tuple(H1,T1),pending()) -> F() eqt(tuple(H1,T1),release()) -> F() eqt(tuple(H1,T1),request()) -> F() eqt(tuple(H1,T1),resource()) -> F() eqt(tuple(H1,T1),tag()) -> F() eqt(tuple(H1,T1),true()) -> F() eqt(tuple(H1,T1),undefined()) -> F() eqt(tuple(H1,T1),pid(N2)) -> F() eqt(tuple(H1,T1),int(N2)) -> F() eqt(tuple(H1,T1),cons(H2,T2)) -> F() eqt(tuple(H1,T1),tuple(H2,T2)) -> and(eqt(H1,H2),eqt(T1,T2)) eqt(tuple(H1,T1),tuplenil(H2)) -> F() eqt(tuplenil(H1),nil()) -> F() eqt(tuplenil(H1),a()) -> F() eqt(tuplenil(H1),excl()) -> F() eqt(tuplenil(H1),false()) -> F() eqt(tuplenil(H1),lock()) -> F() eqt(tuplenil(H1),locker()) -> F() eqt(tuplenil(H1),mcrlrecord()) -> F() eqt(tuplenil(H1),ok()) -> F() eqt(tuplenil(H1),pending()) -> F() eqt(tuplenil(H1),release()) -> F() eqt(tuplenil(H1),request()) -> F() eqt(tuplenil(H1),resource()) -> F() eqt(tuplenil(H1),tag()) -> F() eqt(tuplenil(H1),true()) -> F() eqt(tuplenil(H1),undefined()) -> F() eqt(tuplenil(H1),pid(N2)) -> F() eqt(tuplenil(H1),int(N2)) -> F() eqt(tuplenil(H1),cons(H2,T2)) -> F() eqt(tuplenil(H1),tuple(H2,T2)) -> F() eqt(tuplenil(H1),tuplenil(H2)) -> eqt(H1,H2) element(int(s(0())),tuplenil(T1)) -> T1 element(int(s(0())),tuple(T1,T2)) -> T1 element(int(s(s(N1))),tuple(T1,T2)) -> element(int(s(N1)),T2) record_new(lock()) -> tuple(mcrlrecord(),tuple(lock(),tuple(undefined(),tuple(nil(),tuplenil(nil()))))) record_extract(tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))), lock(),resource()) -> tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))) record_update(tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))), lock(),pending(),NewF) -> tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(NewF))))) record_updates(Record,Name,nil()) -> Record record_updates(Record,Name,cons(tuple(Field,tuplenil(NewF)),Fields)) -> record_updates(record_update(Record,Name,Field,NewF),Name,Fields) locker2_map_promote_pending(nil(),Pending) -> nil() locker2_map_promote_pending(cons(Lock,Locks),Pending) -> cons(locker2_promote_pending(Lock,Pending),locker2_map_promote_pending(Locks,Pending)) locker2_map_claim_lock(nil(),Resources,Client) -> nil() locker2_map_claim_lock(cons(Lock,Locks),Resources,Client) -> cons(locker2_claim_lock(Lock,Resources,Client),locker2_map_claim_lock (Locks,Resources,Client)) locker2_map_add_pending(nil(),Resources,Client) -> nil() locker2_promote_pending(Lock,Client) -> case0(Client,Lock,record_extract(Lock,lock(),pending())) case0(Client,Lock,cons(Client,Pendings)) -> record_updates(Lock,lock(),cons(tuple(excl(),tuplenil(Client)), cons(tuple(pending(),tuplenil(Pendings)),nil()))) case0(Client,Lock,MCRLFree0) -> Lock locker2_remove_pending(Lock,Client) -> record_updates(Lock,lock(),cons(tuple(pending(),tuplenil(subtract (record_extract (Lock,lock(),pending()), cons (Client,nil())))), nil())) locker2_add_pending(Lock,Resources,Client) -> case1(Client,Resources,Lock,member(record_extract(Lock,lock(),resource()),Resources)) case1(Client,Resources,Lock,true()) -> record_updates(Lock,lock(),cons(tuple(pending(),tuplenil(append (record_extract (Lock,lock(),pending()), cons (Client,nil())))), nil())) case1(Client,Resources,Lock,false()) -> Lock locker2_release_lock(Lock,Client) -> case2(Client,Lock,gen_modtageq(Client,record_extract(Lock,lock(),excl()))) case2(Client,Lock,true()) -> record_updates(Lock,lock(),cons(tuple(excllock(),excl()),nil())) case4(Client,Lock,MCRLFree1) -> false() locker2_obtainables(nil(),Client) -> true() locker2_obtainables(cons(Lock,Locks),Client) -> case5(Client,Locks,Lock,member(Client,record_extract(Lock,lock(),pending()))) case5(Client,Locks,Lock,true()) -> andt(locker2_obtainable(Lock,Client),locker2_obtainables(Locks,Client)) case5(Client,Locks,Lock,false()) -> locker2_obtainables(Locks,Client) locker2_check_available(Resource,nil()) -> false() locker2_check_available(Resource,cons(Lock,Locks)) -> case6(Locks,Lock,Resource,equal(Resource,record_extract(Lock,lock(),resource()))) case6(Locks,Lock,Resource,true()) -> andt(equal(record_extract(Lock,lock(),excl()),nil()),equal(record_extract (Lock,lock(),pending()), nil())) case6(Locks,Lock,Resource,false()) -> locker2_check_available(Resource,Locks) locker2_check_availables(nil(),Locks) -> true() locker2_check_availables(cons(Resource,Resources),Locks) -> andt(locker2_check_available(Resource,Locks),locker2_check_availables(Resources,Locks)) locker2_adduniq(nil(),List) -> List append(cons(Head,Tail),List) -> cons(Head,append(Tail,List)) subtract(List,nil()) -> List subtract(List,cons(Head,Tail)) -> subtract(delete(Head,List),Tail) delete(E,nil()) -> nil() delete(E,cons(Head,Tail)) -> case8(Tail,Head,E,equal(E,Head)) case8(Tail,Head,E,true()) -> Tail case8(Tail,Head,E,false()) -> cons(Head,delete(E,Tail)) gen_tag(Pid) -> tuple(Pid,tuplenil(tag())) gen_modtageq(Client1,Client2) -> equal(Client1,Client2) member(E,nil()) -> false() member(E,cons(Head,Tail)) -> case9(Tail,Head,E,equal(E,Head)) case9(Tail,Head,E,true()) -> true() case9(Tail,Head,E,false()) -> member(E,Tail) eqs(empty(),empty()) -> T() eqs(empty(),stack(E2,S2)) -> F() eqs(stack(E1,S1),empty()) -> F() eqs(stack(E1,S1),stack(E2,S2)) -> and(eqt(E1,E2),eqs(S1,S2)) pushs(E1,S1) -> stack(E1,S1) pops(stack(E1,S1)) -> S1 tops(stack(E1,S1)) -> E1 istops(E1,empty()) -> F() istops(E1,stack(E2,S1)) -> eqt(E1,E2) eqc(nocalls(),nocalls()) -> T() eqc(nocalls(),calls(E2,S2,CS2)) -> F() eqc(calls(E1,S1,CS1),nocalls()) -> F() eqc(calls(E1,S1,CS1),calls(E2,S2,CS2)) -> and(eqt(E1,E2),and(eqs(S1,S2),eqc(CS1,CS2))) push(E1,E2,nocalls()) -> calls(E1,stack(E2,empty()),nocalls()) push(E1,E2,calls(E3,S1,CS1)) -> push1(E1,E2,E3,S1,CS1,eqt(E1,E3)) push1(E1,E2,E3,S1,CS1,T()) -> calls(E3,pushs(E2,S1),CS1) Qed DPs: case5#(Client,Locks,Lock,true()) -> locker2_obtainables#(Locks,Client) locker2_obtainables#(cons(Lock,Locks),Client) -> case5#(Client,Locks,Lock,member(Client,record_extract(Lock,lock(),pending()))) case5#(Client,Locks,Lock,false()) -> locker2_obtainables#(Locks,Client) TRS: or(T(),T()) -> T() or(F(),T()) -> T() or(T(),F()) -> T() or(F(),F()) -> F() and(T(),B) -> B and(B,T()) -> B and(F(),B) -> F() and(B,F()) -> F() imp(T(),B) -> B imp(F(),B) -> T() not(T()) -> F() not(F()) -> T() if(T(),B1,B2) -> B1 if(F(),B1,B2) -> B2 eq(T(),T()) -> T() eq(F(),F()) -> T() eq(T(),F()) -> F() eq(F(),T()) -> F() eqt(nil(),undefined()) -> F() eqt(nil(),pid(N2)) -> F() eqt(nil(),int(N2)) -> F() eqt(nil(),cons(H2,T2)) -> F() eqt(nil(),tuple(H2,T2)) -> F() eqt(nil(),tuplenil(H2)) -> F() eqt(a(),nil()) -> F() eqt(a(),a()) -> T() eqt(a(),excl()) -> F() eqt(a(),false()) -> F() eqt(a(),lock()) -> F() eqt(a(),locker()) -> F() eqt(a(),mcrlrecord()) -> F() eqt(a(),ok()) -> F() eqt(a(),pending()) -> F() eqt(a(),release()) -> F() eqt(a(),request()) -> F() eqt(a(),resource()) -> F() eqt(a(),tag()) -> F() eqt(a(),true()) -> F() eqt(a(),undefined()) -> F() eqt(a(),pid(N2)) -> F() eqt(a(),int(N2)) -> F() eqt(a(),cons(H2,T2)) -> F() eqt(a(),tuple(H2,T2)) -> F() eqt(a(),tuplenil(H2)) -> F() eqt(excl(),nil()) -> F() eqt(excl(),a()) -> F() eqt(excl(),excl()) -> T() eqt(excl(),false()) -> F() eqt(excl(),lock()) -> F() eqt(excl(),locker()) -> F() eqt(excl(),mcrlrecord()) -> F() eqt(excl(),ok()) -> F() eqt(excl(),pending()) -> F() eqt(excl(),release()) -> F() eqt(excl(),request()) -> F() eqt(excl(),resource()) -> F() eqt(excl(),tag()) -> F() eqt(excl(),true()) -> F() eqt(excl(),undefined()) -> F() eqt(excl(),pid(N2)) -> F() eqt(excl(),eqt(false(),int(N2))) -> F() eqt(false(),cons(H2,T2)) -> F() eqt(false(),tuple(H2,T2)) -> F() eqt(false(),tuplenil(H2)) -> F() eqt(lock(),nil()) -> F() eqt(lock(),a()) -> F() eqt(lock(),excl()) -> F() eqt(lock(),false()) -> F() eqt(lock(),lock()) -> T() eqt(lock(),locker()) -> F() eqt(lock(),mcrlrecord()) -> F() eqt(lock(),ok()) -> F() eqt(lock(),pending()) -> F() eqt(lock(),release()) -> F() eqt(lock(),request()) -> F() eqt(lock(),resource()) -> F() eqt(lock(),tag()) -> F() eqt(lock(),true()) -> F() eqt(lock(),undefined()) -> F() eqt(lock(),pid(N2)) -> F() eqt(lock(),int(N2)) -> F() eqt(lock(),cons(H2,T2)) -> F() eqt(lock(),tuple(H2,T2)) -> F() eqt(lock(),tuplenil(H2)) -> F() eqt(locker(),nil()) -> F() eqt(locker(),a()) -> F() eqt(locker(),excl()) -> F() eqt(locker(),false()) -> F() eqt(locker(),lock()) -> F() eqt(locker(),locker()) -> T() eqt(locker(),mcrlrecord()) -> F() eqt(locker(),ok()) -> F() eqt(locker(),pending()) -> F() eqt(locker(),release()) -> F() eqt(locker(),request()) -> F() eqt(locker(),resource()) -> F() eqt(locker(),tag()) -> F() eqt(locker(),true()) -> F() eqt(locker(),undefined()) -> F() eqt(locker(),pid(N2)) -> F() eqt(locker(),int(N2)) -> F() eqt(locker(),cons(H2,T2)) -> F() eqt(locker(),tuple(H2,T2)) -> F() eqt(locker(),tuplenil(H2)) -> F() eqt(mcrlrecord(),nil()) -> F() eqt(mcrlrecord(),a()) -> F() eqt(mcrlrecord(),excl()) -> F() eqt(mcrlrecord(),false()) -> F() eqt(mcrlrecord(),lock()) -> F() eqt(mcrlrecord(),locker()) -> F() eqt(mcrlrecord(),mcrlrecord()) -> T() eqt(mcrlrecord(),ok()) -> F() eqt(mcrlrecord(),pending()) -> F() eqt(mcrlrecord(),release()) -> F() eqt(mcrlrecord(),request()) -> F() eqt(mcrlrecord(),resource()) -> F() eqt(ok(),resource()) -> F() eqt(ok(),tag()) -> F() eqt(ok(),true()) -> F() eqt(ok(),undefined()) -> F() eqt(ok(),pid(N2)) -> F() eqt(ok(),int(N2)) -> F() eqt(ok(),cons(H2,T2)) -> F() eqt(ok(),tuple(H2,T2)) -> F() eqt(ok(),tuplenil(H2)) -> F() eqt(pending(),nil()) -> F() eqt(pending(),a()) -> F() eqt(pending(),excl()) -> F() eqt(pending(),false()) -> F() eqt(pending(),lock()) -> F() eqt(pending(),locker()) -> F() eqt(pending(),mcrlrecord()) -> F() eqt(pending(),ok()) -> F() eqt(pending(),pending()) -> T() eqt(pending(),release()) -> F() eqt(pending(),request()) -> F() eqt(pending(),resource()) -> F() eqt(pending(),tag()) -> F() eqt(pending(),true()) -> F() eqt(pending(),undefined()) -> F() eqt(pending(),pid(N2)) -> F() eqt(pending(),int(N2)) -> F() eqt(pending(),cons(H2,T2)) -> F() eqt(pending(),tuple(H2,T2)) -> F() eqt(pending(),tuplenil(H2)) -> F() eqt(release(),nil()) -> F() eqt(release(),a()) -> F() eqt(release(),excl()) -> F() eqt(release(),false()) -> F() eqt(release(),lock()) -> F() eqt(release(),locker()) -> F() eqt(release(),mcrlrecord()) -> F() eqt(release(),ok()) -> F() eqt(request(),mcrlrecord()) -> F() eqt(request(),ok()) -> F() eqt(request(),pending()) -> F() eqt(request(),release()) -> F() eqt(request(),request()) -> T() eqt(request(),resource()) -> F() eqt(request(),tag()) -> F() eqt(request(),true()) -> F() eqt(request(),undefined()) -> F() eqt(request(),pid(N2)) -> F() eqt(request(),int(N2)) -> F() eqt(request(),cons(H2,T2)) -> F() eqt(request(),tuple(H2,T2)) -> F() eqt(request(),tuplenil(H2)) -> F() eqt(resource(),nil()) -> F() eqt(resource(),a()) -> F() eqt(resource(),excl()) -> F() eqt(resource(),false()) -> F() eqt(resource(),lock()) -> F() eqt(resource(),locker()) -> F() eqt(resource(),mcrlrecord()) -> F() eqt(resource(),ok()) -> F() eqt(resource(),pending()) -> F() eqt(resource(),release()) -> F() eqt(resource(),request()) -> F() eqt(resource(),resource()) -> T() eqt(resource(),tag()) -> F() eqt(resource(),true()) -> F() eqt(resource(),undefined()) -> F() eqt(resource(),pid(N2)) -> F() eqt(resource(),int(N2)) -> F() eqt(resource(),cons(H2,T2)) -> F() eqt(resource(),tuple(H2,T2)) -> F() eqt(resource(),tuplenil(H2)) -> F() eqt(tag(),nil()) -> F() eqt(tag(),a()) -> F() eqt(tag(),excl()) -> F() eqt(tag(),false()) -> F() eqt(tag(),lock()) -> F() eqt(tag(),locker()) -> F() eqt(tag(),mcrlrecord()) -> F() eqt(tag(),ok()) -> F() eqt(tag(),pending()) -> F() eqt(tag(),release()) -> F() eqt(tag(),request()) -> F() eqt(tag(),resource()) -> F() eqt(tag(),tag()) -> T() eqt(tag(),true()) -> F() eqt(tag(),undefined()) -> F() eqt(tag(),pid(N2)) -> F() eqt(tag(),int(N2)) -> F() eqt(tag(),cons(H2,T2)) -> F() eqt(tag(),tuple(H2,T2)) -> F() eqt(tag(),tuplenil(H2)) -> F() eqt(true(),nil()) -> F() eqt(true(),a()) -> F() eqt(true(),excl()) -> F() eqt(true(),false()) -> F() eqt(true(),lock()) -> F() eqt(true(),locker()) -> F() eqt(true(),mcrlrecord()) -> F() eqt(true(),ok()) -> F() eqt(true(),pending()) -> F() eqt(true(),release()) -> F() eqt(true(),request()) -> F() eqt(true(),resource()) -> F() eqt(true(),tag()) -> F() eqt(true(),true()) -> T() eqt(true(),undefined()) -> F() eqt(true(),pid(N2)) -> F() eqt(true(),int(N2)) -> F() eqt(true(),cons(H2,T2)) -> F() eqt(true(),tuple(H2,T2)) -> F() eqt(true(),tuplenil(H2)) -> F() eqt(undefined(),nil()) -> F() eqt(undefined(),a()) -> F() eqt(undefined(),tuplenil(H2)) -> F() eqt(pid(N1),nil()) -> F() eqt(pid(N1),a()) -> F() eqt(pid(N1),excl()) -> F() eqt(pid(N1),false()) -> F() eqt(pid(N1),lock()) -> F() eqt(pid(N1),locker()) -> F() eqt(pid(N1),mcrlrecord()) -> F() eqt(pid(N1),ok()) -> F() eqt(pid(N1),pending()) -> F() eqt(pid(N1),release()) -> F() eqt(pid(N1),request()) -> F() eqt(pid(N1),resource()) -> F() eqt(pid(N1),tag()) -> F() eqt(pid(N1),true()) -> F() eqt(pid(N1),undefined()) -> F() eqt(pid(N1),pid(N2)) -> eqt(N1,N2) eqt(pid(N1),int(N2)) -> F() eqt(pid(N1),cons(H2,T2)) -> F() eqt(pid(N1),tuple(H2,T2)) -> F() eqt(pid(N1),tuplenil(H2)) -> F() eqt(int(N1),nil()) -> F() eqt(int(N1),a()) -> F() eqt(int(N1),excl()) -> F() eqt(int(N1),false()) -> F() eqt(int(N1),lock()) -> F() eqt(int(N1),locker()) -> F() eqt(int(N1),mcrlrecord()) -> F() eqt(int(N1),ok()) -> F() eqt(int(N1),pending()) -> F() eqt(int(N1),release()) -> F() eqt(int(N1),request()) -> F() eqt(int(N1),resource()) -> F() eqt(int(N1),tag()) -> F() eqt(int(N1),true()) -> F() eqt(int(N1),undefined()) -> F() eqt(cons(H1,T1),resource()) -> F() eqt(cons(H1,T1),tag()) -> F() eqt(cons(H1,T1),true()) -> F() eqt(cons(H1,T1),undefined()) -> F() eqt(cons(H1,T1),pid(N2)) -> F() eqt(cons(H1,T1),int(N2)) -> F() eqt(cons(H1,T1),cons(H2,T2)) -> and(eqt(H1,H2),eqt(T1,T2)) eqt(cons(H1,T1),tuple(H2,T2)) -> F() eqt(cons(H1,T1),tuplenil(H2)) -> F() eqt(tuple(H1,T1),nil()) -> F() eqt(tuple(H1,T1),a()) -> F() eqt(tuple(H1,T1),excl()) -> F() eqt(tuple(H1,T1),false()) -> F() eqt(tuple(H1,T1),lock()) -> F() eqt(tuple(H1,T1),locker()) -> F() eqt(tuple(H1,T1),mcrlrecord()) -> F() eqt(tuple(H1,T1),ok()) -> F() eqt(tuple(H1,T1),pending()) -> F() eqt(tuple(H1,T1),release()) -> F() eqt(tuple(H1,T1),request()) -> F() eqt(tuple(H1,T1),resource()) -> F() eqt(tuple(H1,T1),tag()) -> F() eqt(tuple(H1,T1),true()) -> F() eqt(tuple(H1,T1),undefined()) -> F() eqt(tuple(H1,T1),pid(N2)) -> F() eqt(tuple(H1,T1),int(N2)) -> F() eqt(tuple(H1,T1),cons(H2,T2)) -> F() eqt(tuple(H1,T1),tuple(H2,T2)) -> and(eqt(H1,H2),eqt(T1,T2)) eqt(tuple(H1,T1),tuplenil(H2)) -> F() eqt(tuplenil(H1),nil()) -> F() eqt(tuplenil(H1),a()) -> F() eqt(tuplenil(H1),excl()) -> F() eqt(tuplenil(H1),false()) -> F() eqt(tuplenil(H1),lock()) -> F() eqt(tuplenil(H1),locker()) -> F() eqt(tuplenil(H1),mcrlrecord()) -> F() eqt(tuplenil(H1),ok()) -> F() eqt(tuplenil(H1),pending()) -> F() eqt(tuplenil(H1),release()) -> F() eqt(tuplenil(H1),request()) -> F() eqt(tuplenil(H1),resource()) -> F() eqt(tuplenil(H1),tag()) -> F() eqt(tuplenil(H1),true()) -> F() eqt(tuplenil(H1),undefined()) -> F() eqt(tuplenil(H1),pid(N2)) -> F() eqt(tuplenil(H1),int(N2)) -> F() eqt(tuplenil(H1),cons(H2,T2)) -> F() eqt(tuplenil(H1),tuple(H2,T2)) -> F() eqt(tuplenil(H1),tuplenil(H2)) -> eqt(H1,H2) element(int(s(0())),tuplenil(T1)) -> T1 element(int(s(0())),tuple(T1,T2)) -> T1 element(int(s(s(N1))),tuple(T1,T2)) -> element(int(s(N1)),T2) record_new(lock()) -> tuple(mcrlrecord(),tuple(lock(),tuple(undefined(),tuple(nil(),tuplenil(nil()))))) record_extract(tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))), lock(),resource()) -> tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))) record_update(tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))), lock(),pending(),NewF) -> tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(NewF))))) record_updates(Record,Name,nil()) -> Record record_updates(Record,Name,cons(tuple(Field,tuplenil(NewF)),Fields)) -> record_updates(record_update(Record,Name,Field,NewF),Name,Fields) locker2_map_promote_pending(nil(),Pending) -> nil() locker2_map_promote_pending(cons(Lock,Locks),Pending) -> cons(locker2_promote_pending(Lock,Pending),locker2_map_promote_pending(Locks,Pending)) locker2_map_claim_lock(nil(),Resources,Client) -> nil() locker2_map_claim_lock(cons(Lock,Locks),Resources,Client) -> cons(locker2_claim_lock(Lock,Resources,Client),locker2_map_claim_lock(Locks,Resources,Client)) locker2_map_add_pending(nil(),Resources,Client) -> nil() locker2_promote_pending(Lock,Client) -> case0(Client,Lock,record_extract(Lock,lock(),pending())) case0(Client,Lock,cons(Client,Pendings)) -> record_updates(Lock,lock(),cons(tuple(excl(),tuplenil(Client)),cons ( tuple ( pending(),tuplenil(Pendings)), nil ()))) case0(Client,Lock,MCRLFree0) -> Lock locker2_remove_pending(Lock,Client) -> record_updates(Lock,lock(),cons(tuple(pending(),tuplenil(subtract (record_extract (Lock,lock(),pending()), cons(Client,nil())))), nil())) locker2_add_pending(Lock,Resources,Client) -> case1(Client,Resources,Lock,member(record_extract(Lock,lock(),resource()),Resources)) case1(Client,Resources,Lock,true()) -> record_updates(Lock,lock(),cons(tuple(pending(),tuplenil(append( record_extract ( Lock,lock(),pending()), cons (Client,nil())))), nil())) case1(Client,Resources,Lock,false()) -> Lock locker2_release_lock(Lock,Client) -> case2(Client,Lock,gen_modtageq(Client,record_extract(Lock,lock(),excl()))) case2(Client,Lock,true()) -> record_updates(Lock,lock(),cons(tuple(excllock(),excl()),nil())) case4(Client,Lock,MCRLFree1) -> false() locker2_obtainables(nil(),Client) -> true() locker2_obtainables(cons(Lock,Locks),Client) -> case5(Client,Locks,Lock,member(Client,record_extract(Lock,lock(),pending()))) case5(Client,Locks,Lock,true()) -> andt(locker2_obtainable(Lock,Client),locker2_obtainables(Locks,Client)) case5(Client,Locks,Lock,false()) -> locker2_obtainables(Locks,Client) locker2_check_available(Resource,nil()) -> false() locker2_check_available(Resource,cons(Lock,Locks)) -> case6(Locks,Lock,Resource,equal(Resource,record_extract(Lock,lock(),resource()))) case6(Locks,Lock,Resource,true()) -> andt(equal(record_extract(Lock,lock(),excl()),nil()),equal(record_extract (Lock,lock(),pending()), nil())) case6(Locks,Lock,Resource,false()) -> locker2_check_available(Resource,Locks) locker2_check_availables(nil(),Locks) -> true() locker2_check_availables(cons(Resource,Resources),Locks) -> andt(locker2_check_available(Resource,Locks),locker2_check_availables(Resources,Locks)) locker2_adduniq(nil(),List) -> List append(cons(Head,Tail),List) -> cons(Head,append(Tail,List)) subtract(List,nil()) -> List subtract(List,cons(Head,Tail)) -> subtract(delete(Head,List),Tail) delete(E,nil()) -> nil() delete(E,cons(Head,Tail)) -> case8(Tail,Head,E,equal(E,Head)) case8(Tail,Head,E,true()) -> Tail case8(Tail,Head,E,false()) -> cons(Head,delete(E,Tail)) gen_tag(Pid) -> tuple(Pid,tuplenil(tag())) gen_modtageq(Client1,Client2) -> equal(Client1,Client2) member(E,nil()) -> false() member(E,cons(Head,Tail)) -> case9(Tail,Head,E,equal(E,Head)) case9(Tail,Head,E,true()) -> true() case9(Tail,Head,E,false()) -> member(E,Tail) eqs(empty(),empty()) -> T() eqs(empty(),stack(E2,S2)) -> F() eqs(stack(E1,S1),empty()) -> F() eqs(stack(E1,S1),stack(E2,S2)) -> and(eqt(E1,E2),eqs(S1,S2)) pushs(E1,S1) -> stack(E1,S1) pops(stack(E1,S1)) -> S1 tops(stack(E1,S1)) -> E1 istops(E1,empty()) -> F() istops(E1,stack(E2,S1)) -> eqt(E1,E2) eqc(nocalls(),nocalls()) -> T() eqc(nocalls(),calls(E2,S2,CS2)) -> F() eqc(calls(E1,S1,CS1),nocalls()) -> F() eqc(calls(E1,S1,CS1),calls(E2,S2,CS2)) -> and(eqt(E1,E2),and(eqs(S1,S2),eqc(CS1,CS2))) push(E1,E2,nocalls()) -> calls(E1,stack(E2,empty()),nocalls()) push(E1,E2,calls(E3,S1,CS1)) -> push1(E1,E2,E3,S1,CS1,eqt(E1,E3)) push1(E1,E2,E3,S1,CS1,T()) -> calls(E3,pushs(E2,S1),CS1) Subterm Criterion Processor: simple projection: pi(locker2_obtainables#) = 0 pi(case5#) = 1 problem: DPs: case5#(Client,Locks,Lock,true()) -> locker2_obtainables#(Locks,Client) case5#(Client,Locks,Lock,false()) -> locker2_obtainables#(Locks,Client) TRS: or(T(),T()) -> T() or(F(),T()) -> T() or(T(),F()) -> T() or(F(),F()) -> F() and(T(),B) -> B and(B,T()) -> B and(F(),B) -> F() and(B,F()) -> F() imp(T(),B) -> B imp(F(),B) -> T() not(T()) -> F() not(F()) -> T() if(T(),B1,B2) -> B1 if(F(),B1,B2) -> B2 eq(T(),T()) -> T() eq(F(),F()) -> T() eq(T(),F()) -> F() eq(F(),T()) -> F() eqt(nil(),undefined()) -> F() eqt(nil(),pid(N2)) -> F() eqt(nil(),int(N2)) -> F() eqt(nil(),cons(H2,T2)) -> F() eqt(nil(),tuple(H2,T2)) -> F() eqt(nil(),tuplenil(H2)) -> F() eqt(a(),nil()) -> F() eqt(a(),a()) -> T() eqt(a(),excl()) -> F() eqt(a(),false()) -> F() eqt(a(),lock()) -> F() eqt(a(),locker()) -> F() eqt(a(),mcrlrecord()) -> F() eqt(a(),ok()) -> F() eqt(a(),pending()) -> F() eqt(a(),release()) -> F() eqt(a(),request()) -> F() eqt(a(),resource()) -> F() eqt(a(),tag()) -> F() eqt(a(),true()) -> F() eqt(a(),undefined()) -> F() eqt(a(),pid(N2)) -> F() eqt(a(),int(N2)) -> F() eqt(a(),cons(H2,T2)) -> F() eqt(a(),tuple(H2,T2)) -> F() eqt(a(),tuplenil(H2)) -> F() eqt(excl(),nil()) -> F() eqt(excl(),a()) -> F() eqt(excl(),excl()) -> T() eqt(excl(),false()) -> F() eqt(excl(),lock()) -> F() eqt(excl(),locker()) -> F() eqt(excl(),mcrlrecord()) -> F() eqt(excl(),ok()) -> F() eqt(excl(),pending()) -> F() eqt(excl(),release()) -> F() eqt(excl(),request()) -> F() eqt(excl(),resource()) -> F() eqt(excl(),tag()) -> F() eqt(excl(),true()) -> F() eqt(excl(),undefined()) -> F() eqt(excl(),pid(N2)) -> F() eqt(excl(),eqt(false(),int(N2))) -> F() eqt(false(),cons(H2,T2)) -> F() eqt(false(),tuple(H2,T2)) -> F() eqt(false(),tuplenil(H2)) -> F() eqt(lock(),nil()) -> F() eqt(lock(),a()) -> F() eqt(lock(),excl()) -> F() eqt(lock(),false()) -> F() eqt(lock(),lock()) -> T() eqt(lock(),locker()) -> F() eqt(lock(),mcrlrecord()) -> F() eqt(lock(),ok()) -> F() eqt(lock(),pending()) -> F() eqt(lock(),release()) -> F() eqt(lock(),request()) -> F() eqt(lock(),resource()) -> F() eqt(lock(),tag()) -> F() eqt(lock(),true()) -> F() eqt(lock(),undefined()) -> F() eqt(lock(),pid(N2)) -> F() eqt(lock(),int(N2)) -> F() eqt(lock(),cons(H2,T2)) -> F() eqt(lock(),tuple(H2,T2)) -> F() eqt(lock(),tuplenil(H2)) -> F() eqt(locker(),nil()) -> F() eqt(locker(),a()) -> F() eqt(locker(),excl()) -> F() eqt(locker(),false()) -> F() eqt(locker(),lock()) -> F() eqt(locker(),locker()) -> T() eqt(locker(),mcrlrecord()) -> F() eqt(locker(),ok()) -> F() eqt(locker(),pending()) -> F() eqt(locker(),release()) -> F() eqt(locker(),request()) -> F() eqt(locker(),resource()) -> F() eqt(locker(),tag()) -> F() eqt(locker(),true()) -> F() eqt(locker(),undefined()) -> F() eqt(locker(),pid(N2)) -> F() eqt(locker(),int(N2)) -> F() eqt(locker(),cons(H2,T2)) -> F() eqt(locker(),tuple(H2,T2)) -> F() eqt(locker(),tuplenil(H2)) -> F() eqt(mcrlrecord(),nil()) -> F() eqt(mcrlrecord(),a()) -> F() eqt(mcrlrecord(),excl()) -> F() eqt(mcrlrecord(),false()) -> F() eqt(mcrlrecord(),lock()) -> F() eqt(mcrlrecord(),locker()) -> F() eqt(mcrlrecord(),mcrlrecord()) -> T() eqt(mcrlrecord(),ok()) -> F() eqt(mcrlrecord(),pending()) -> F() eqt(mcrlrecord(),release()) -> F() eqt(mcrlrecord(),request()) -> F() eqt(mcrlrecord(),resource()) -> F() eqt(ok(),resource()) -> F() eqt(ok(),tag()) -> F() eqt(ok(),true()) -> F() eqt(ok(),undefined()) -> F() eqt(ok(),pid(N2)) -> F() eqt(ok(),int(N2)) -> F() eqt(ok(),cons(H2,T2)) -> F() eqt(ok(),tuple(H2,T2)) -> F() eqt(ok(),tuplenil(H2)) -> F() eqt(pending(),nil()) -> F() eqt(pending(),a()) -> F() eqt(pending(),excl()) -> F() eqt(pending(),false()) -> F() eqt(pending(),lock()) -> F() eqt(pending(),locker()) -> F() eqt(pending(),mcrlrecord()) -> F() eqt(pending(),ok()) -> F() eqt(pending(),pending()) -> T() eqt(pending(),release()) -> F() eqt(pending(),request()) -> F() eqt(pending(),resource()) -> F() eqt(pending(),tag()) -> F() eqt(pending(),true()) -> F() eqt(pending(),undefined()) -> F() eqt(pending(),pid(N2)) -> F() eqt(pending(),int(N2)) -> F() eqt(pending(),cons(H2,T2)) -> F() eqt(pending(),tuple(H2,T2)) -> F() eqt(pending(),tuplenil(H2)) -> F() eqt(release(),nil()) -> F() eqt(release(),a()) -> F() eqt(release(),excl()) -> F() eqt(release(),false()) -> F() eqt(release(),lock()) -> F() eqt(release(),locker()) -> F() eqt(release(),mcrlrecord()) -> F() eqt(release(),ok()) -> F() eqt(request(),mcrlrecord()) -> F() eqt(request(),ok()) -> F() eqt(request(),pending()) -> F() eqt(request(),release()) -> F() eqt(request(),request()) -> T() eqt(request(),resource()) -> F() eqt(request(),tag()) -> F() eqt(request(),true()) -> F() eqt(request(),undefined()) -> F() eqt(request(),pid(N2)) -> F() eqt(request(),int(N2)) -> F() eqt(request(),cons(H2,T2)) -> F() eqt(request(),tuple(H2,T2)) -> F() eqt(request(),tuplenil(H2)) -> F() eqt(resource(),nil()) -> F() eqt(resource(),a()) -> F() eqt(resource(),excl()) -> F() eqt(resource(),false()) -> F() eqt(resource(),lock()) -> F() eqt(resource(),locker()) -> F() eqt(resource(),mcrlrecord()) -> F() eqt(resource(),ok()) -> F() eqt(resource(),pending()) -> F() eqt(resource(),release()) -> F() eqt(resource(),request()) -> F() eqt(resource(),resource()) -> T() eqt(resource(),tag()) -> F() eqt(resource(),true()) -> F() eqt(resource(),undefined()) -> F() eqt(resource(),pid(N2)) -> F() eqt(resource(),int(N2)) -> F() eqt(resource(),cons(H2,T2)) -> F() eqt(resource(),tuple(H2,T2)) -> F() eqt(resource(),tuplenil(H2)) -> F() eqt(tag(),nil()) -> F() eqt(tag(),a()) -> F() eqt(tag(),excl()) -> F() eqt(tag(),false()) -> F() eqt(tag(),lock()) -> F() eqt(tag(),locker()) -> F() eqt(tag(),mcrlrecord()) -> F() eqt(tag(),ok()) -> F() eqt(tag(),pending()) -> F() eqt(tag(),release()) -> F() eqt(tag(),request()) -> F() eqt(tag(),resource()) -> F() eqt(tag(),tag()) -> T() eqt(tag(),true()) -> F() eqt(tag(),undefined()) -> F() eqt(tag(),pid(N2)) -> F() eqt(tag(),int(N2)) -> F() eqt(tag(),cons(H2,T2)) -> F() eqt(tag(),tuple(H2,T2)) -> F() eqt(tag(),tuplenil(H2)) -> F() eqt(true(),nil()) -> F() eqt(true(),a()) -> F() eqt(true(),excl()) -> F() eqt(true(),false()) -> F() eqt(true(),lock()) -> F() eqt(true(),locker()) -> F() eqt(true(),mcrlrecord()) -> F() eqt(true(),ok()) -> F() eqt(true(),pending()) -> F() eqt(true(),release()) -> F() eqt(true(),request()) -> F() eqt(true(),resource()) -> F() eqt(true(),tag()) -> F() eqt(true(),true()) -> T() eqt(true(),undefined()) -> F() eqt(true(),pid(N2)) -> F() eqt(true(),int(N2)) -> F() eqt(true(),cons(H2,T2)) -> F() eqt(true(),tuple(H2,T2)) -> F() eqt(true(),tuplenil(H2)) -> F() eqt(undefined(),nil()) -> F() eqt(undefined(),a()) -> F() eqt(undefined(),tuplenil(H2)) -> F() eqt(pid(N1),nil()) -> F() eqt(pid(N1),a()) -> F() eqt(pid(N1),excl()) -> F() eqt(pid(N1),false()) -> F() eqt(pid(N1),lock()) -> F() eqt(pid(N1),locker()) -> F() eqt(pid(N1),mcrlrecord()) -> F() eqt(pid(N1),ok()) -> F() eqt(pid(N1),pending()) -> F() eqt(pid(N1),release()) -> F() eqt(pid(N1),request()) -> F() eqt(pid(N1),resource()) -> F() eqt(pid(N1),tag()) -> F() eqt(pid(N1),true()) -> F() eqt(pid(N1),undefined()) -> F() eqt(pid(N1),pid(N2)) -> eqt(N1,N2) eqt(pid(N1),int(N2)) -> F() eqt(pid(N1),cons(H2,T2)) -> F() eqt(pid(N1),tuple(H2,T2)) -> F() eqt(pid(N1),tuplenil(H2)) -> F() eqt(int(N1),nil()) -> F() eqt(int(N1),a()) -> F() eqt(int(N1),excl()) -> F() eqt(int(N1),false()) -> F() eqt(int(N1),lock()) -> F() eqt(int(N1),locker()) -> F() eqt(int(N1),mcrlrecord()) -> F() eqt(int(N1),ok()) -> F() eqt(int(N1),pending()) -> F() eqt(int(N1),release()) -> F() eqt(int(N1),request()) -> F() eqt(int(N1),resource()) -> F() eqt(int(N1),tag()) -> F() eqt(int(N1),true()) -> F() eqt(int(N1),undefined()) -> F() eqt(cons(H1,T1),resource()) -> F() eqt(cons(H1,T1),tag()) -> F() eqt(cons(H1,T1),true()) -> F() eqt(cons(H1,T1),undefined()) -> F() eqt(cons(H1,T1),pid(N2)) -> F() eqt(cons(H1,T1),int(N2)) -> F() eqt(cons(H1,T1),cons(H2,T2)) -> and(eqt(H1,H2),eqt(T1,T2)) eqt(cons(H1,T1),tuple(H2,T2)) -> F() eqt(cons(H1,T1),tuplenil(H2)) -> F() eqt(tuple(H1,T1),nil()) -> F() eqt(tuple(H1,T1),a()) -> F() eqt(tuple(H1,T1),excl()) -> F() eqt(tuple(H1,T1),false()) -> F() eqt(tuple(H1,T1),lock()) -> F() eqt(tuple(H1,T1),locker()) -> F() eqt(tuple(H1,T1),mcrlrecord()) -> F() eqt(tuple(H1,T1),ok()) -> F() eqt(tuple(H1,T1),pending()) -> F() eqt(tuple(H1,T1),release()) -> F() eqt(tuple(H1,T1),request()) -> F() eqt(tuple(H1,T1),resource()) -> F() eqt(tuple(H1,T1),tag()) -> F() eqt(tuple(H1,T1),true()) -> F() eqt(tuple(H1,T1),undefined()) -> F() eqt(tuple(H1,T1),pid(N2)) -> F() eqt(tuple(H1,T1),int(N2)) -> F() eqt(tuple(H1,T1),cons(H2,T2)) -> F() eqt(tuple(H1,T1),tuple(H2,T2)) -> and(eqt(H1,H2),eqt(T1,T2)) eqt(tuple(H1,T1),tuplenil(H2)) -> F() eqt(tuplenil(H1),nil()) -> F() eqt(tuplenil(H1),a()) -> F() eqt(tuplenil(H1),excl()) -> F() eqt(tuplenil(H1),false()) -> F() eqt(tuplenil(H1),lock()) -> F() eqt(tuplenil(H1),locker()) -> F() eqt(tuplenil(H1),mcrlrecord()) -> F() eqt(tuplenil(H1),ok()) -> F() eqt(tuplenil(H1),pending()) -> F() eqt(tuplenil(H1),release()) -> F() eqt(tuplenil(H1),request()) -> F() eqt(tuplenil(H1),resource()) -> F() eqt(tuplenil(H1),tag()) -> F() eqt(tuplenil(H1),true()) -> F() eqt(tuplenil(H1),undefined()) -> F() eqt(tuplenil(H1),pid(N2)) -> F() eqt(tuplenil(H1),int(N2)) -> F() eqt(tuplenil(H1),cons(H2,T2)) -> F() eqt(tuplenil(H1),tuple(H2,T2)) -> F() eqt(tuplenil(H1),tuplenil(H2)) -> eqt(H1,H2) element(int(s(0())),tuplenil(T1)) -> T1 element(int(s(0())),tuple(T1,T2)) -> T1 element(int(s(s(N1))),tuple(T1,T2)) -> element(int(s(N1)),T2) record_new(lock()) -> tuple(mcrlrecord(),tuple(lock(),tuple(undefined(),tuple(nil(),tuplenil(nil()))))) record_extract(tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))), lock(),resource()) -> tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))) record_update(tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))), lock(),pending(),NewF) -> tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(NewF))))) record_updates(Record,Name,nil()) -> Record record_updates(Record,Name,cons(tuple(Field,tuplenil(NewF)),Fields)) -> record_updates(record_update(Record,Name,Field,NewF),Name,Fields) locker2_map_promote_pending(nil(),Pending) -> nil() locker2_map_promote_pending(cons(Lock,Locks),Pending) -> cons(locker2_promote_pending(Lock,Pending),locker2_map_promote_pending(Locks,Pending)) locker2_map_claim_lock(nil(),Resources,Client) -> nil() locker2_map_claim_lock(cons(Lock,Locks),Resources,Client) -> cons(locker2_claim_lock(Lock,Resources,Client),locker2_map_claim_lock (Locks,Resources,Client)) locker2_map_add_pending(nil(),Resources,Client) -> nil() locker2_promote_pending(Lock,Client) -> case0(Client,Lock,record_extract(Lock,lock(),pending())) case0(Client,Lock,cons(Client,Pendings)) -> record_updates(Lock,lock(),cons(tuple(excl(),tuplenil(Client)), cons(tuple(pending(),tuplenil(Pendings)),nil()))) case0(Client,Lock,MCRLFree0) -> Lock locker2_remove_pending(Lock,Client) -> record_updates(Lock,lock(),cons(tuple(pending(),tuplenil(subtract (record_extract (Lock,lock(),pending()), cons (Client,nil())))), nil())) locker2_add_pending(Lock,Resources,Client) -> case1(Client,Resources,Lock,member(record_extract(Lock,lock(),resource()),Resources)) case1(Client,Resources,Lock,true()) -> record_updates(Lock,lock(),cons(tuple(pending(),tuplenil(append (record_extract (Lock,lock(),pending()), cons (Client,nil())))), nil())) case1(Client,Resources,Lock,false()) -> Lock locker2_release_lock(Lock,Client) -> case2(Client,Lock,gen_modtageq(Client,record_extract(Lock,lock(),excl()))) case2(Client,Lock,true()) -> record_updates(Lock,lock(),cons(tuple(excllock(),excl()),nil())) case4(Client,Lock,MCRLFree1) -> false() locker2_obtainables(nil(),Client) -> true() locker2_obtainables(cons(Lock,Locks),Client) -> case5(Client,Locks,Lock,member(Client,record_extract(Lock,lock(),pending()))) case5(Client,Locks,Lock,true()) -> andt(locker2_obtainable(Lock,Client),locker2_obtainables(Locks,Client)) case5(Client,Locks,Lock,false()) -> locker2_obtainables(Locks,Client) locker2_check_available(Resource,nil()) -> false() locker2_check_available(Resource,cons(Lock,Locks)) -> case6(Locks,Lock,Resource,equal(Resource,record_extract(Lock,lock(),resource()))) case6(Locks,Lock,Resource,true()) -> andt(equal(record_extract(Lock,lock(),excl()),nil()),equal(record_extract (Lock,lock(),pending()), nil())) case6(Locks,Lock,Resource,false()) -> locker2_check_available(Resource,Locks) locker2_check_availables(nil(),Locks) -> true() locker2_check_availables(cons(Resource,Resources),Locks) -> andt(locker2_check_available(Resource,Locks),locker2_check_availables(Resources,Locks)) locker2_adduniq(nil(),List) -> List append(cons(Head,Tail),List) -> cons(Head,append(Tail,List)) subtract(List,nil()) -> List subtract(List,cons(Head,Tail)) -> subtract(delete(Head,List),Tail) delete(E,nil()) -> nil() delete(E,cons(Head,Tail)) -> case8(Tail,Head,E,equal(E,Head)) case8(Tail,Head,E,true()) -> Tail case8(Tail,Head,E,false()) -> cons(Head,delete(E,Tail)) gen_tag(Pid) -> tuple(Pid,tuplenil(tag())) gen_modtageq(Client1,Client2) -> equal(Client1,Client2) member(E,nil()) -> false() member(E,cons(Head,Tail)) -> case9(Tail,Head,E,equal(E,Head)) case9(Tail,Head,E,true()) -> true() case9(Tail,Head,E,false()) -> member(E,Tail) eqs(empty(),empty()) -> T() eqs(empty(),stack(E2,S2)) -> F() eqs(stack(E1,S1),empty()) -> F() eqs(stack(E1,S1),stack(E2,S2)) -> and(eqt(E1,E2),eqs(S1,S2)) pushs(E1,S1) -> stack(E1,S1) pops(stack(E1,S1)) -> S1 tops(stack(E1,S1)) -> E1 istops(E1,empty()) -> F() istops(E1,stack(E2,S1)) -> eqt(E1,E2) eqc(nocalls(),nocalls()) -> T() eqc(nocalls(),calls(E2,S2,CS2)) -> F() eqc(calls(E1,S1,CS1),nocalls()) -> F() eqc(calls(E1,S1,CS1),calls(E2,S2,CS2)) -> and(eqt(E1,E2),and(eqs(S1,S2),eqc(CS1,CS2))) push(E1,E2,nocalls()) -> calls(E1,stack(E2,empty()),nocalls()) push(E1,E2,calls(E3,S1,CS1)) -> push1(E1,E2,E3,S1,CS1,eqt(E1,E3)) push1(E1,E2,E3,S1,CS1,T()) -> calls(E3,pushs(E2,S1),CS1) SCC Processor: #sccs: 0 #rules: 0 #arcs: 4/4 DPs: locker2_check_availables#(cons(Resource,Resources),Locks) -> locker2_check_availables#(Resources,Locks) TRS: or(T(),T()) -> T() or(F(),T()) -> T() or(T(),F()) -> T() or(F(),F()) -> F() and(T(),B) -> B and(B,T()) -> B and(F(),B) -> F() and(B,F()) -> F() imp(T(),B) -> B imp(F(),B) -> T() not(T()) -> F() not(F()) -> T() if(T(),B1,B2) -> B1 if(F(),B1,B2) -> B2 eq(T(),T()) -> T() eq(F(),F()) -> T() eq(T(),F()) -> F() eq(F(),T()) -> F() eqt(nil(),undefined()) -> F() eqt(nil(),pid(N2)) -> F() eqt(nil(),int(N2)) -> F() eqt(nil(),cons(H2,T2)) -> F() eqt(nil(),tuple(H2,T2)) -> F() eqt(nil(),tuplenil(H2)) -> F() eqt(a(),nil()) -> F() eqt(a(),a()) -> T() eqt(a(),excl()) -> F() eqt(a(),false()) -> F() eqt(a(),lock()) -> F() eqt(a(),locker()) -> F() eqt(a(),mcrlrecord()) -> F() eqt(a(),ok()) -> F() eqt(a(),pending()) -> F() eqt(a(),release()) -> F() eqt(a(),request()) -> F() eqt(a(),resource()) -> F() eqt(a(),tag()) -> F() eqt(a(),true()) -> F() eqt(a(),undefined()) -> F() eqt(a(),pid(N2)) -> F() eqt(a(),int(N2)) -> F() eqt(a(),cons(H2,T2)) -> F() eqt(a(),tuple(H2,T2)) -> F() eqt(a(),tuplenil(H2)) -> F() eqt(excl(),nil()) -> F() eqt(excl(),a()) -> F() eqt(excl(),excl()) -> T() eqt(excl(),false()) -> F() eqt(excl(),lock()) -> F() eqt(excl(),locker()) -> F() eqt(excl(),mcrlrecord()) -> F() eqt(excl(),ok()) -> F() eqt(excl(),pending()) -> F() eqt(excl(),release()) -> F() eqt(excl(),request()) -> F() eqt(excl(),resource()) -> F() eqt(excl(),tag()) -> F() eqt(excl(),true()) -> F() eqt(excl(),undefined()) -> F() eqt(excl(),pid(N2)) -> F() eqt(excl(),eqt(false(),int(N2))) -> F() eqt(false(),cons(H2,T2)) -> F() eqt(false(),tuple(H2,T2)) -> F() eqt(false(),tuplenil(H2)) -> F() eqt(lock(),nil()) -> F() eqt(lock(),a()) -> F() eqt(lock(),excl()) -> F() eqt(lock(),false()) -> F() eqt(lock(),lock()) -> T() eqt(lock(),locker()) -> F() eqt(lock(),mcrlrecord()) -> F() eqt(lock(),ok()) -> F() eqt(lock(),pending()) -> F() eqt(lock(),release()) -> F() eqt(lock(),request()) -> F() eqt(lock(),resource()) -> F() eqt(lock(),tag()) -> F() eqt(lock(),true()) -> F() eqt(lock(),undefined()) -> F() eqt(lock(),pid(N2)) -> F() eqt(lock(),int(N2)) -> F() eqt(lock(),cons(H2,T2)) -> F() eqt(lock(),tuple(H2,T2)) -> F() eqt(lock(),tuplenil(H2)) -> F() eqt(locker(),nil()) -> F() eqt(locker(),a()) -> F() eqt(locker(),excl()) -> F() eqt(locker(),false()) -> F() eqt(locker(),lock()) -> F() eqt(locker(),locker()) -> T() eqt(locker(),mcrlrecord()) -> F() eqt(locker(),ok()) -> F() eqt(locker(),pending()) -> F() eqt(locker(),release()) -> F() eqt(locker(),request()) -> F() eqt(locker(),resource()) -> F() eqt(locker(),tag()) -> F() eqt(locker(),true()) -> F() eqt(locker(),undefined()) -> F() eqt(locker(),pid(N2)) -> F() eqt(locker(),int(N2)) -> F() eqt(locker(),cons(H2,T2)) -> F() eqt(locker(),tuple(H2,T2)) -> F() eqt(locker(),tuplenil(H2)) -> F() eqt(mcrlrecord(),nil()) -> F() eqt(mcrlrecord(),a()) -> F() eqt(mcrlrecord(),excl()) -> F() eqt(mcrlrecord(),false()) -> F() eqt(mcrlrecord(),lock()) -> F() eqt(mcrlrecord(),locker()) -> F() eqt(mcrlrecord(),mcrlrecord()) -> T() eqt(mcrlrecord(),ok()) -> F() eqt(mcrlrecord(),pending()) -> F() eqt(mcrlrecord(),release()) -> F() eqt(mcrlrecord(),request()) -> F() eqt(mcrlrecord(),resource()) -> F() eqt(ok(),resource()) -> F() eqt(ok(),tag()) -> F() eqt(ok(),true()) -> F() eqt(ok(),undefined()) -> F() eqt(ok(),pid(N2)) -> F() eqt(ok(),int(N2)) -> F() eqt(ok(),cons(H2,T2)) -> F() eqt(ok(),tuple(H2,T2)) -> F() eqt(ok(),tuplenil(H2)) -> F() eqt(pending(),nil()) -> F() eqt(pending(),a()) -> F() eqt(pending(),excl()) -> F() eqt(pending(),false()) -> F() eqt(pending(),lock()) -> F() eqt(pending(),locker()) -> F() eqt(pending(),mcrlrecord()) -> F() eqt(pending(),ok()) -> F() eqt(pending(),pending()) -> T() eqt(pending(),release()) -> F() eqt(pending(),request()) -> F() eqt(pending(),resource()) -> F() eqt(pending(),tag()) -> F() eqt(pending(),true()) -> F() eqt(pending(),undefined()) -> F() eqt(pending(),pid(N2)) -> F() eqt(pending(),int(N2)) -> F() eqt(pending(),cons(H2,T2)) -> F() eqt(pending(),tuple(H2,T2)) -> F() eqt(pending(),tuplenil(H2)) -> F() eqt(release(),nil()) -> F() eqt(release(),a()) -> F() eqt(release(),excl()) -> F() eqt(release(),false()) -> F() eqt(release(),lock()) -> F() eqt(release(),locker()) -> F() eqt(release(),mcrlrecord()) -> F() eqt(release(),ok()) -> F() eqt(request(),mcrlrecord()) -> F() eqt(request(),ok()) -> F() eqt(request(),pending()) -> F() eqt(request(),release()) -> F() eqt(request(),request()) -> T() eqt(request(),resource()) -> F() eqt(request(),tag()) -> F() eqt(request(),true()) -> F() eqt(request(),undefined()) -> F() eqt(request(),pid(N2)) -> F() eqt(request(),int(N2)) -> F() eqt(request(),cons(H2,T2)) -> F() eqt(request(),tuple(H2,T2)) -> F() eqt(request(),tuplenil(H2)) -> F() eqt(resource(),nil()) -> F() eqt(resource(),a()) -> F() eqt(resource(),excl()) -> F() eqt(resource(),false()) -> F() eqt(resource(),lock()) -> F() eqt(resource(),locker()) -> F() eqt(resource(),mcrlrecord()) -> F() eqt(resource(),ok()) -> F() eqt(resource(),pending()) -> F() eqt(resource(),release()) -> F() eqt(resource(),request()) -> F() eqt(resource(),resource()) -> T() eqt(resource(),tag()) -> F() eqt(resource(),true()) -> F() eqt(resource(),undefined()) -> F() eqt(resource(),pid(N2)) -> F() eqt(resource(),int(N2)) -> F() eqt(resource(),cons(H2,T2)) -> F() eqt(resource(),tuple(H2,T2)) -> F() eqt(resource(),tuplenil(H2)) -> F() eqt(tag(),nil()) -> F() eqt(tag(),a()) -> F() eqt(tag(),excl()) -> F() eqt(tag(),false()) -> F() eqt(tag(),lock()) -> F() eqt(tag(),locker()) -> F() eqt(tag(),mcrlrecord()) -> F() eqt(tag(),ok()) -> F() eqt(tag(),pending()) -> F() eqt(tag(),release()) -> F() eqt(tag(),request()) -> F() eqt(tag(),resource()) -> F() eqt(tag(),tag()) -> T() eqt(tag(),true()) -> F() eqt(tag(),undefined()) -> F() eqt(tag(),pid(N2)) -> F() eqt(tag(),int(N2)) -> F() eqt(tag(),cons(H2,T2)) -> F() eqt(tag(),tuple(H2,T2)) -> F() eqt(tag(),tuplenil(H2)) -> F() eqt(true(),nil()) -> F() eqt(true(),a()) -> F() eqt(true(),excl()) -> F() eqt(true(),false()) -> F() eqt(true(),lock()) -> F() eqt(true(),locker()) -> F() eqt(true(),mcrlrecord()) -> F() eqt(true(),ok()) -> F() eqt(true(),pending()) -> F() eqt(true(),release()) -> F() eqt(true(),request()) -> F() eqt(true(),resource()) -> F() eqt(true(),tag()) -> F() eqt(true(),true()) -> T() eqt(true(),undefined()) -> F() eqt(true(),pid(N2)) -> F() eqt(true(),int(N2)) -> F() eqt(true(),cons(H2,T2)) -> F() eqt(true(),tuple(H2,T2)) -> F() eqt(true(),tuplenil(H2)) -> F() eqt(undefined(),nil()) -> F() eqt(undefined(),a()) -> F() eqt(undefined(),tuplenil(H2)) -> F() eqt(pid(N1),nil()) -> F() eqt(pid(N1),a()) -> F() eqt(pid(N1),excl()) -> F() eqt(pid(N1),false()) -> F() eqt(pid(N1),lock()) -> F() eqt(pid(N1),locker()) -> F() eqt(pid(N1),mcrlrecord()) -> F() eqt(pid(N1),ok()) -> F() eqt(pid(N1),pending()) -> F() eqt(pid(N1),release()) -> F() eqt(pid(N1),request()) -> F() eqt(pid(N1),resource()) -> F() eqt(pid(N1),tag()) -> F() eqt(pid(N1),true()) -> F() eqt(pid(N1),undefined()) -> F() eqt(pid(N1),pid(N2)) -> eqt(N1,N2) eqt(pid(N1),int(N2)) -> F() eqt(pid(N1),cons(H2,T2)) -> F() eqt(pid(N1),tuple(H2,T2)) -> F() eqt(pid(N1),tuplenil(H2)) -> F() eqt(int(N1),nil()) -> F() eqt(int(N1),a()) -> F() eqt(int(N1),excl()) -> F() eqt(int(N1),false()) -> F() eqt(int(N1),lock()) -> F() eqt(int(N1),locker()) -> F() eqt(int(N1),mcrlrecord()) -> F() eqt(int(N1),ok()) -> F() eqt(int(N1),pending()) -> F() eqt(int(N1),release()) -> F() eqt(int(N1),request()) -> F() eqt(int(N1),resource()) -> F() eqt(int(N1),tag()) -> F() eqt(int(N1),true()) -> F() eqt(int(N1),undefined()) -> F() eqt(cons(H1,T1),resource()) -> F() eqt(cons(H1,T1),tag()) -> F() eqt(cons(H1,T1),true()) -> F() eqt(cons(H1,T1),undefined()) -> F() eqt(cons(H1,T1),pid(N2)) -> F() eqt(cons(H1,T1),int(N2)) -> F() eqt(cons(H1,T1),cons(H2,T2)) -> and(eqt(H1,H2),eqt(T1,T2)) eqt(cons(H1,T1),tuple(H2,T2)) -> F() eqt(cons(H1,T1),tuplenil(H2)) -> F() eqt(tuple(H1,T1),nil()) -> F() eqt(tuple(H1,T1),a()) -> F() eqt(tuple(H1,T1),excl()) -> F() eqt(tuple(H1,T1),false()) -> F() eqt(tuple(H1,T1),lock()) -> F() eqt(tuple(H1,T1),locker()) -> F() eqt(tuple(H1,T1),mcrlrecord()) -> F() eqt(tuple(H1,T1),ok()) -> F() eqt(tuple(H1,T1),pending()) -> F() eqt(tuple(H1,T1),release()) -> F() eqt(tuple(H1,T1),request()) -> F() eqt(tuple(H1,T1),resource()) -> F() eqt(tuple(H1,T1),tag()) -> F() eqt(tuple(H1,T1),true()) -> F() eqt(tuple(H1,T1),undefined()) -> F() eqt(tuple(H1,T1),pid(N2)) -> F() eqt(tuple(H1,T1),int(N2)) -> F() eqt(tuple(H1,T1),cons(H2,T2)) -> F() eqt(tuple(H1,T1),tuple(H2,T2)) -> and(eqt(H1,H2),eqt(T1,T2)) eqt(tuple(H1,T1),tuplenil(H2)) -> F() eqt(tuplenil(H1),nil()) -> F() eqt(tuplenil(H1),a()) -> F() eqt(tuplenil(H1),excl()) -> F() eqt(tuplenil(H1),false()) -> F() eqt(tuplenil(H1),lock()) -> F() eqt(tuplenil(H1),locker()) -> F() eqt(tuplenil(H1),mcrlrecord()) -> F() eqt(tuplenil(H1),ok()) -> F() eqt(tuplenil(H1),pending()) -> F() eqt(tuplenil(H1),release()) -> F() eqt(tuplenil(H1),request()) -> F() eqt(tuplenil(H1),resource()) -> F() eqt(tuplenil(H1),tag()) -> F() eqt(tuplenil(H1),true()) -> F() eqt(tuplenil(H1),undefined()) -> F() eqt(tuplenil(H1),pid(N2)) -> F() eqt(tuplenil(H1),int(N2)) -> F() eqt(tuplenil(H1),cons(H2,T2)) -> F() eqt(tuplenil(H1),tuple(H2,T2)) -> F() eqt(tuplenil(H1),tuplenil(H2)) -> eqt(H1,H2) element(int(s(0())),tuplenil(T1)) -> T1 element(int(s(0())),tuple(T1,T2)) -> T1 element(int(s(s(N1))),tuple(T1,T2)) -> element(int(s(N1)),T2) record_new(lock()) -> tuple(mcrlrecord(),tuple(lock(),tuple(undefined(),tuple(nil(),tuplenil(nil()))))) record_extract(tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))), lock(),resource()) -> tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))) record_update(tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))), lock(),pending(),NewF) -> tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(NewF))))) record_updates(Record,Name,nil()) -> Record record_updates(Record,Name,cons(tuple(Field,tuplenil(NewF)),Fields)) -> record_updates(record_update(Record,Name,Field,NewF),Name,Fields) locker2_map_promote_pending(nil(),Pending) -> nil() locker2_map_promote_pending(cons(Lock,Locks),Pending) -> cons(locker2_promote_pending(Lock,Pending),locker2_map_promote_pending(Locks,Pending)) locker2_map_claim_lock(nil(),Resources,Client) -> nil() locker2_map_claim_lock(cons(Lock,Locks),Resources,Client) -> cons(locker2_claim_lock(Lock,Resources,Client),locker2_map_claim_lock(Locks,Resources,Client)) locker2_map_add_pending(nil(),Resources,Client) -> nil() locker2_promote_pending(Lock,Client) -> case0(Client,Lock,record_extract(Lock,lock(),pending())) case0(Client,Lock,cons(Client,Pendings)) -> record_updates(Lock,lock(),cons(tuple(excl(),tuplenil(Client)),cons ( tuple ( pending(),tuplenil(Pendings)), nil ()))) case0(Client,Lock,MCRLFree0) -> Lock locker2_remove_pending(Lock,Client) -> record_updates(Lock,lock(),cons(tuple(pending(),tuplenil(subtract (record_extract (Lock,lock(),pending()), cons(Client,nil())))), nil())) locker2_add_pending(Lock,Resources,Client) -> case1(Client,Resources,Lock,member(record_extract(Lock,lock(),resource()),Resources)) case1(Client,Resources,Lock,true()) -> record_updates(Lock,lock(),cons(tuple(pending(),tuplenil(append( record_extract ( Lock,lock(),pending()), cons (Client,nil())))), nil())) case1(Client,Resources,Lock,false()) -> Lock locker2_release_lock(Lock,Client) -> case2(Client,Lock,gen_modtageq(Client,record_extract(Lock,lock(),excl()))) case2(Client,Lock,true()) -> record_updates(Lock,lock(),cons(tuple(excllock(),excl()),nil())) case4(Client,Lock,MCRLFree1) -> false() locker2_obtainables(nil(),Client) -> true() locker2_obtainables(cons(Lock,Locks),Client) -> case5(Client,Locks,Lock,member(Client,record_extract(Lock,lock(),pending()))) case5(Client,Locks,Lock,true()) -> andt(locker2_obtainable(Lock,Client),locker2_obtainables(Locks,Client)) case5(Client,Locks,Lock,false()) -> locker2_obtainables(Locks,Client) locker2_check_available(Resource,nil()) -> false() locker2_check_available(Resource,cons(Lock,Locks)) -> case6(Locks,Lock,Resource,equal(Resource,record_extract(Lock,lock(),resource()))) case6(Locks,Lock,Resource,true()) -> andt(equal(record_extract(Lock,lock(),excl()),nil()),equal(record_extract (Lock,lock(),pending()), nil())) case6(Locks,Lock,Resource,false()) -> locker2_check_available(Resource,Locks) locker2_check_availables(nil(),Locks) -> true() locker2_check_availables(cons(Resource,Resources),Locks) -> andt(locker2_check_available(Resource,Locks),locker2_check_availables(Resources,Locks)) locker2_adduniq(nil(),List) -> List append(cons(Head,Tail),List) -> cons(Head,append(Tail,List)) subtract(List,nil()) -> List subtract(List,cons(Head,Tail)) -> subtract(delete(Head,List),Tail) delete(E,nil()) -> nil() delete(E,cons(Head,Tail)) -> case8(Tail,Head,E,equal(E,Head)) case8(Tail,Head,E,true()) -> Tail case8(Tail,Head,E,false()) -> cons(Head,delete(E,Tail)) gen_tag(Pid) -> tuple(Pid,tuplenil(tag())) gen_modtageq(Client1,Client2) -> equal(Client1,Client2) member(E,nil()) -> false() member(E,cons(Head,Tail)) -> case9(Tail,Head,E,equal(E,Head)) case9(Tail,Head,E,true()) -> true() case9(Tail,Head,E,false()) -> member(E,Tail) eqs(empty(),empty()) -> T() eqs(empty(),stack(E2,S2)) -> F() eqs(stack(E1,S1),empty()) -> F() eqs(stack(E1,S1),stack(E2,S2)) -> and(eqt(E1,E2),eqs(S1,S2)) pushs(E1,S1) -> stack(E1,S1) pops(stack(E1,S1)) -> S1 tops(stack(E1,S1)) -> E1 istops(E1,empty()) -> F() istops(E1,stack(E2,S1)) -> eqt(E1,E2) eqc(nocalls(),nocalls()) -> T() eqc(nocalls(),calls(E2,S2,CS2)) -> F() eqc(calls(E1,S1,CS1),nocalls()) -> F() eqc(calls(E1,S1,CS1),calls(E2,S2,CS2)) -> and(eqt(E1,E2),and(eqs(S1,S2),eqc(CS1,CS2))) push(E1,E2,nocalls()) -> calls(E1,stack(E2,empty()),nocalls()) push(E1,E2,calls(E3,S1,CS1)) -> push1(E1,E2,E3,S1,CS1,eqt(E1,E3)) push1(E1,E2,E3,S1,CS1,T()) -> calls(E3,pushs(E2,S1),CS1) Subterm Criterion Processor: simple projection: pi(locker2_check_availables#) = 0 problem: DPs: TRS: or(T(),T()) -> T() or(F(),T()) -> T() or(T(),F()) -> T() or(F(),F()) -> F() and(T(),B) -> B and(B,T()) -> B and(F(),B) -> F() and(B,F()) -> F() imp(T(),B) -> B imp(F(),B) -> T() not(T()) -> F() not(F()) -> T() if(T(),B1,B2) -> B1 if(F(),B1,B2) -> B2 eq(T(),T()) -> T() eq(F(),F()) -> T() eq(T(),F()) -> F() eq(F(),T()) -> F() eqt(nil(),undefined()) -> F() eqt(nil(),pid(N2)) -> F() eqt(nil(),int(N2)) -> F() eqt(nil(),cons(H2,T2)) -> F() eqt(nil(),tuple(H2,T2)) -> F() eqt(nil(),tuplenil(H2)) -> F() eqt(a(),nil()) -> F() eqt(a(),a()) -> T() eqt(a(),excl()) -> F() eqt(a(),false()) -> F() eqt(a(),lock()) -> F() eqt(a(),locker()) -> F() eqt(a(),mcrlrecord()) -> F() eqt(a(),ok()) -> F() eqt(a(),pending()) -> F() eqt(a(),release()) -> F() eqt(a(),request()) -> F() eqt(a(),resource()) -> F() eqt(a(),tag()) -> F() eqt(a(),true()) -> F() eqt(a(),undefined()) -> F() eqt(a(),pid(N2)) -> F() eqt(a(),int(N2)) -> F() eqt(a(),cons(H2,T2)) -> F() eqt(a(),tuple(H2,T2)) -> F() eqt(a(),tuplenil(H2)) -> F() eqt(excl(),nil()) -> F() eqt(excl(),a()) -> F() eqt(excl(),excl()) -> T() eqt(excl(),false()) -> F() eqt(excl(),lock()) -> F() eqt(excl(),locker()) -> F() eqt(excl(),mcrlrecord()) -> F() eqt(excl(),ok()) -> F() eqt(excl(),pending()) -> F() eqt(excl(),release()) -> F() eqt(excl(),request()) -> F() eqt(excl(),resource()) -> F() eqt(excl(),tag()) -> F() eqt(excl(),true()) -> F() eqt(excl(),undefined()) -> F() eqt(excl(),pid(N2)) -> F() eqt(excl(),eqt(false(),int(N2))) -> F() eqt(false(),cons(H2,T2)) -> F() eqt(false(),tuple(H2,T2)) -> F() eqt(false(),tuplenil(H2)) -> F() eqt(lock(),nil()) -> F() eqt(lock(),a()) -> F() eqt(lock(),excl()) -> F() eqt(lock(),false()) -> F() eqt(lock(),lock()) -> T() eqt(lock(),locker()) -> F() eqt(lock(),mcrlrecord()) -> F() eqt(lock(),ok()) -> F() eqt(lock(),pending()) -> F() eqt(lock(),release()) -> F() eqt(lock(),request()) -> F() eqt(lock(),resource()) -> F() eqt(lock(),tag()) -> F() eqt(lock(),true()) -> F() eqt(lock(),undefined()) -> F() eqt(lock(),pid(N2)) -> F() eqt(lock(),int(N2)) -> F() eqt(lock(),cons(H2,T2)) -> F() eqt(lock(),tuple(H2,T2)) -> F() eqt(lock(),tuplenil(H2)) -> F() eqt(locker(),nil()) -> F() eqt(locker(),a()) -> F() eqt(locker(),excl()) -> F() eqt(locker(),false()) -> F() eqt(locker(),lock()) -> F() eqt(locker(),locker()) -> T() eqt(locker(),mcrlrecord()) -> F() eqt(locker(),ok()) -> F() eqt(locker(),pending()) -> F() eqt(locker(),release()) -> F() eqt(locker(),request()) -> F() eqt(locker(),resource()) -> F() eqt(locker(),tag()) -> F() eqt(locker(),true()) -> F() eqt(locker(),undefined()) -> F() eqt(locker(),pid(N2)) -> F() eqt(locker(),int(N2)) -> F() eqt(locker(),cons(H2,T2)) -> F() eqt(locker(),tuple(H2,T2)) -> F() eqt(locker(),tuplenil(H2)) -> F() eqt(mcrlrecord(),nil()) -> F() eqt(mcrlrecord(),a()) -> F() eqt(mcrlrecord(),excl()) -> F() eqt(mcrlrecord(),false()) -> F() eqt(mcrlrecord(),lock()) -> F() eqt(mcrlrecord(),locker()) -> F() eqt(mcrlrecord(),mcrlrecord()) -> T() eqt(mcrlrecord(),ok()) -> F() eqt(mcrlrecord(),pending()) -> F() eqt(mcrlrecord(),release()) -> F() eqt(mcrlrecord(),request()) -> F() eqt(mcrlrecord(),resource()) -> F() eqt(ok(),resource()) -> F() eqt(ok(),tag()) -> F() eqt(ok(),true()) -> F() eqt(ok(),undefined()) -> F() eqt(ok(),pid(N2)) -> F() eqt(ok(),int(N2)) -> F() eqt(ok(),cons(H2,T2)) -> F() eqt(ok(),tuple(H2,T2)) -> F() eqt(ok(),tuplenil(H2)) -> F() eqt(pending(),nil()) -> F() eqt(pending(),a()) -> F() eqt(pending(),excl()) -> F() eqt(pending(),false()) -> F() eqt(pending(),lock()) -> F() eqt(pending(),locker()) -> F() eqt(pending(),mcrlrecord()) -> F() eqt(pending(),ok()) -> F() eqt(pending(),pending()) -> T() eqt(pending(),release()) -> F() eqt(pending(),request()) -> F() eqt(pending(),resource()) -> F() eqt(pending(),tag()) -> F() eqt(pending(),true()) -> F() eqt(pending(),undefined()) -> F() eqt(pending(),pid(N2)) -> F() eqt(pending(),int(N2)) -> F() eqt(pending(),cons(H2,T2)) -> F() eqt(pending(),tuple(H2,T2)) -> F() eqt(pending(),tuplenil(H2)) -> F() eqt(release(),nil()) -> F() eqt(release(),a()) -> F() eqt(release(),excl()) -> F() eqt(release(),false()) -> F() eqt(release(),lock()) -> F() eqt(release(),locker()) -> F() eqt(release(),mcrlrecord()) -> F() eqt(release(),ok()) -> F() eqt(request(),mcrlrecord()) -> F() eqt(request(),ok()) -> F() eqt(request(),pending()) -> F() eqt(request(),release()) -> F() eqt(request(),request()) -> T() eqt(request(),resource()) -> F() eqt(request(),tag()) -> F() eqt(request(),true()) -> F() eqt(request(),undefined()) -> F() eqt(request(),pid(N2)) -> F() eqt(request(),int(N2)) -> F() eqt(request(),cons(H2,T2)) -> F() eqt(request(),tuple(H2,T2)) -> F() eqt(request(),tuplenil(H2)) -> F() eqt(resource(),nil()) -> F() eqt(resource(),a()) -> F() eqt(resource(),excl()) -> F() eqt(resource(),false()) -> F() eqt(resource(),lock()) -> F() eqt(resource(),locker()) -> F() eqt(resource(),mcrlrecord()) -> F() eqt(resource(),ok()) -> F() eqt(resource(),pending()) -> F() eqt(resource(),release()) -> F() eqt(resource(),request()) -> F() eqt(resource(),resource()) -> T() eqt(resource(),tag()) -> F() eqt(resource(),true()) -> F() eqt(resource(),undefined()) -> F() eqt(resource(),pid(N2)) -> F() eqt(resource(),int(N2)) -> F() eqt(resource(),cons(H2,T2)) -> F() eqt(resource(),tuple(H2,T2)) -> F() eqt(resource(),tuplenil(H2)) -> F() eqt(tag(),nil()) -> F() eqt(tag(),a()) -> F() eqt(tag(),excl()) -> F() eqt(tag(),false()) -> F() eqt(tag(),lock()) -> F() eqt(tag(),locker()) -> F() eqt(tag(),mcrlrecord()) -> F() eqt(tag(),ok()) -> F() eqt(tag(),pending()) -> F() eqt(tag(),release()) -> F() eqt(tag(),request()) -> F() eqt(tag(),resource()) -> F() eqt(tag(),tag()) -> T() eqt(tag(),true()) -> F() eqt(tag(),undefined()) -> F() eqt(tag(),pid(N2)) -> F() eqt(tag(),int(N2)) -> F() eqt(tag(),cons(H2,T2)) -> F() eqt(tag(),tuple(H2,T2)) -> F() eqt(tag(),tuplenil(H2)) -> F() eqt(true(),nil()) -> F() eqt(true(),a()) -> F() eqt(true(),excl()) -> F() eqt(true(),false()) -> F() eqt(true(),lock()) -> F() eqt(true(),locker()) -> F() eqt(true(),mcrlrecord()) -> F() eqt(true(),ok()) -> F() eqt(true(),pending()) -> F() eqt(true(),release()) -> F() eqt(true(),request()) -> F() eqt(true(),resource()) -> F() eqt(true(),tag()) -> F() eqt(true(),true()) -> T() eqt(true(),undefined()) -> F() eqt(true(),pid(N2)) -> F() eqt(true(),int(N2)) -> F() eqt(true(),cons(H2,T2)) -> F() eqt(true(),tuple(H2,T2)) -> F() eqt(true(),tuplenil(H2)) -> F() eqt(undefined(),nil()) -> F() eqt(undefined(),a()) -> F() eqt(undefined(),tuplenil(H2)) -> F() eqt(pid(N1),nil()) -> F() eqt(pid(N1),a()) -> F() eqt(pid(N1),excl()) -> F() eqt(pid(N1),false()) -> F() eqt(pid(N1),lock()) -> F() eqt(pid(N1),locker()) -> F() eqt(pid(N1),mcrlrecord()) -> F() eqt(pid(N1),ok()) -> F() eqt(pid(N1),pending()) -> F() eqt(pid(N1),release()) -> F() eqt(pid(N1),request()) -> F() eqt(pid(N1),resource()) -> F() eqt(pid(N1),tag()) -> F() eqt(pid(N1),true()) -> F() eqt(pid(N1),undefined()) -> F() eqt(pid(N1),pid(N2)) -> eqt(N1,N2) eqt(pid(N1),int(N2)) -> F() eqt(pid(N1),cons(H2,T2)) -> F() eqt(pid(N1),tuple(H2,T2)) -> F() eqt(pid(N1),tuplenil(H2)) -> F() eqt(int(N1),nil()) -> F() eqt(int(N1),a()) -> F() eqt(int(N1),excl()) -> F() eqt(int(N1),false()) -> F() eqt(int(N1),lock()) -> F() eqt(int(N1),locker()) -> F() eqt(int(N1),mcrlrecord()) -> F() eqt(int(N1),ok()) -> F() eqt(int(N1),pending()) -> F() eqt(int(N1),release()) -> F() eqt(int(N1),request()) -> F() eqt(int(N1),resource()) -> F() eqt(int(N1),tag()) -> F() eqt(int(N1),true()) -> F() eqt(int(N1),undefined()) -> F() eqt(cons(H1,T1),resource()) -> F() eqt(cons(H1,T1),tag()) -> F() eqt(cons(H1,T1),true()) -> F() eqt(cons(H1,T1),undefined()) -> F() eqt(cons(H1,T1),pid(N2)) -> F() eqt(cons(H1,T1),int(N2)) -> F() eqt(cons(H1,T1),cons(H2,T2)) -> and(eqt(H1,H2),eqt(T1,T2)) eqt(cons(H1,T1),tuple(H2,T2)) -> F() eqt(cons(H1,T1),tuplenil(H2)) -> F() eqt(tuple(H1,T1),nil()) -> F() eqt(tuple(H1,T1),a()) -> F() eqt(tuple(H1,T1),excl()) -> F() eqt(tuple(H1,T1),false()) -> F() eqt(tuple(H1,T1),lock()) -> F() eqt(tuple(H1,T1),locker()) -> F() eqt(tuple(H1,T1),mcrlrecord()) -> F() eqt(tuple(H1,T1),ok()) -> F() eqt(tuple(H1,T1),pending()) -> F() eqt(tuple(H1,T1),release()) -> F() eqt(tuple(H1,T1),request()) -> F() eqt(tuple(H1,T1),resource()) -> F() eqt(tuple(H1,T1),tag()) -> F() eqt(tuple(H1,T1),true()) -> F() eqt(tuple(H1,T1),undefined()) -> F() eqt(tuple(H1,T1),pid(N2)) -> F() eqt(tuple(H1,T1),int(N2)) -> F() eqt(tuple(H1,T1),cons(H2,T2)) -> F() eqt(tuple(H1,T1),tuple(H2,T2)) -> and(eqt(H1,H2),eqt(T1,T2)) eqt(tuple(H1,T1),tuplenil(H2)) -> F() eqt(tuplenil(H1),nil()) -> F() eqt(tuplenil(H1),a()) -> F() eqt(tuplenil(H1),excl()) -> F() eqt(tuplenil(H1),false()) -> F() eqt(tuplenil(H1),lock()) -> F() eqt(tuplenil(H1),locker()) -> F() eqt(tuplenil(H1),mcrlrecord()) -> F() eqt(tuplenil(H1),ok()) -> F() eqt(tuplenil(H1),pending()) -> F() eqt(tuplenil(H1),release()) -> F() eqt(tuplenil(H1),request()) -> F() eqt(tuplenil(H1),resource()) -> F() eqt(tuplenil(H1),tag()) -> F() eqt(tuplenil(H1),true()) -> F() eqt(tuplenil(H1),undefined()) -> F() eqt(tuplenil(H1),pid(N2)) -> F() eqt(tuplenil(H1),int(N2)) -> F() eqt(tuplenil(H1),cons(H2,T2)) -> F() eqt(tuplenil(H1),tuple(H2,T2)) -> F() eqt(tuplenil(H1),tuplenil(H2)) -> eqt(H1,H2) element(int(s(0())),tuplenil(T1)) -> T1 element(int(s(0())),tuple(T1,T2)) -> T1 element(int(s(s(N1))),tuple(T1,T2)) -> element(int(s(N1)),T2) record_new(lock()) -> tuple(mcrlrecord(),tuple(lock(),tuple(undefined(),tuple(nil(),tuplenil(nil()))))) record_extract(tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))), lock(),resource()) -> tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))) record_update(tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))), lock(),pending(),NewF) -> tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(NewF))))) record_updates(Record,Name,nil()) -> Record record_updates(Record,Name,cons(tuple(Field,tuplenil(NewF)),Fields)) -> record_updates(record_update(Record,Name,Field,NewF),Name,Fields) locker2_map_promote_pending(nil(),Pending) -> nil() locker2_map_promote_pending(cons(Lock,Locks),Pending) -> cons(locker2_promote_pending(Lock,Pending),locker2_map_promote_pending(Locks,Pending)) locker2_map_claim_lock(nil(),Resources,Client) -> nil() locker2_map_claim_lock(cons(Lock,Locks),Resources,Client) -> cons(locker2_claim_lock(Lock,Resources,Client),locker2_map_claim_lock (Locks,Resources,Client)) locker2_map_add_pending(nil(),Resources,Client) -> nil() locker2_promote_pending(Lock,Client) -> case0(Client,Lock,record_extract(Lock,lock(),pending())) case0(Client,Lock,cons(Client,Pendings)) -> record_updates(Lock,lock(),cons(tuple(excl(),tuplenil(Client)), cons(tuple(pending(),tuplenil(Pendings)),nil()))) case0(Client,Lock,MCRLFree0) -> Lock locker2_remove_pending(Lock,Client) -> record_updates(Lock,lock(),cons(tuple(pending(),tuplenil(subtract (record_extract (Lock,lock(),pending()), cons (Client,nil())))), nil())) locker2_add_pending(Lock,Resources,Client) -> case1(Client,Resources,Lock,member(record_extract(Lock,lock(),resource()),Resources)) case1(Client,Resources,Lock,true()) -> record_updates(Lock,lock(),cons(tuple(pending(),tuplenil(append (record_extract (Lock,lock(),pending()), cons (Client,nil())))), nil())) case1(Client,Resources,Lock,false()) -> Lock locker2_release_lock(Lock,Client) -> case2(Client,Lock,gen_modtageq(Client,record_extract(Lock,lock(),excl()))) case2(Client,Lock,true()) -> record_updates(Lock,lock(),cons(tuple(excllock(),excl()),nil())) case4(Client,Lock,MCRLFree1) -> false() locker2_obtainables(nil(),Client) -> true() locker2_obtainables(cons(Lock,Locks),Client) -> case5(Client,Locks,Lock,member(Client,record_extract(Lock,lock(),pending()))) case5(Client,Locks,Lock,true()) -> andt(locker2_obtainable(Lock,Client),locker2_obtainables(Locks,Client)) case5(Client,Locks,Lock,false()) -> locker2_obtainables(Locks,Client) locker2_check_available(Resource,nil()) -> false() locker2_check_available(Resource,cons(Lock,Locks)) -> case6(Locks,Lock,Resource,equal(Resource,record_extract(Lock,lock(),resource()))) case6(Locks,Lock,Resource,true()) -> andt(equal(record_extract(Lock,lock(),excl()),nil()),equal(record_extract (Lock,lock(),pending()), nil())) case6(Locks,Lock,Resource,false()) -> locker2_check_available(Resource,Locks) locker2_check_availables(nil(),Locks) -> true() locker2_check_availables(cons(Resource,Resources),Locks) -> andt(locker2_check_available(Resource,Locks),locker2_check_availables(Resources,Locks)) locker2_adduniq(nil(),List) -> List append(cons(Head,Tail),List) -> cons(Head,append(Tail,List)) subtract(List,nil()) -> List subtract(List,cons(Head,Tail)) -> subtract(delete(Head,List),Tail) delete(E,nil()) -> nil() delete(E,cons(Head,Tail)) -> case8(Tail,Head,E,equal(E,Head)) case8(Tail,Head,E,true()) -> Tail case8(Tail,Head,E,false()) -> cons(Head,delete(E,Tail)) gen_tag(Pid) -> tuple(Pid,tuplenil(tag())) gen_modtageq(Client1,Client2) -> equal(Client1,Client2) member(E,nil()) -> false() member(E,cons(Head,Tail)) -> case9(Tail,Head,E,equal(E,Head)) case9(Tail,Head,E,true()) -> true() case9(Tail,Head,E,false()) -> member(E,Tail) eqs(empty(),empty()) -> T() eqs(empty(),stack(E2,S2)) -> F() eqs(stack(E1,S1),empty()) -> F() eqs(stack(E1,S1),stack(E2,S2)) -> and(eqt(E1,E2),eqs(S1,S2)) pushs(E1,S1) -> stack(E1,S1) pops(stack(E1,S1)) -> S1 tops(stack(E1,S1)) -> E1 istops(E1,empty()) -> F() istops(E1,stack(E2,S1)) -> eqt(E1,E2) eqc(nocalls(),nocalls()) -> T() eqc(nocalls(),calls(E2,S2,CS2)) -> F() eqc(calls(E1,S1,CS1),nocalls()) -> F() eqc(calls(E1,S1,CS1),calls(E2,S2,CS2)) -> and(eqt(E1,E2),and(eqs(S1,S2),eqc(CS1,CS2))) push(E1,E2,nocalls()) -> calls(E1,stack(E2,empty()),nocalls()) push(E1,E2,calls(E3,S1,CS1)) -> push1(E1,E2,E3,S1,CS1,eqt(E1,E3)) push1(E1,E2,E3,S1,CS1,T()) -> calls(E3,pushs(E2,S1),CS1) Qed DPs: locker2_check_available#(Resource,cons(Lock,Locks)) -> case6#(Locks,Lock,Resource,equal(Resource,record_extract(Lock,lock(),resource()))) case6#(Locks,Lock,Resource,false()) -> locker2_check_available#(Resource,Locks) TRS: or(T(),T()) -> T() or(F(),T()) -> T() or(T(),F()) -> T() or(F(),F()) -> F() and(T(),B) -> B and(B,T()) -> B and(F(),B) -> F() and(B,F()) -> F() imp(T(),B) -> B imp(F(),B) -> T() not(T()) -> F() not(F()) -> T() if(T(),B1,B2) -> B1 if(F(),B1,B2) -> B2 eq(T(),T()) -> T() eq(F(),F()) -> T() eq(T(),F()) -> F() eq(F(),T()) -> F() eqt(nil(),undefined()) -> F() eqt(nil(),pid(N2)) -> F() eqt(nil(),int(N2)) -> F() eqt(nil(),cons(H2,T2)) -> F() eqt(nil(),tuple(H2,T2)) -> F() eqt(nil(),tuplenil(H2)) -> F() eqt(a(),nil()) -> F() eqt(a(),a()) -> T() eqt(a(),excl()) -> F() eqt(a(),false()) -> F() eqt(a(),lock()) -> F() eqt(a(),locker()) -> F() eqt(a(),mcrlrecord()) -> F() eqt(a(),ok()) -> F() eqt(a(),pending()) -> F() eqt(a(),release()) -> F() eqt(a(),request()) -> F() eqt(a(),resource()) -> F() eqt(a(),tag()) -> F() eqt(a(),true()) -> F() eqt(a(),undefined()) -> F() eqt(a(),pid(N2)) -> F() eqt(a(),int(N2)) -> F() eqt(a(),cons(H2,T2)) -> F() eqt(a(),tuple(H2,T2)) -> F() eqt(a(),tuplenil(H2)) -> F() eqt(excl(),nil()) -> F() eqt(excl(),a()) -> F() eqt(excl(),excl()) -> T() eqt(excl(),false()) -> F() eqt(excl(),lock()) -> F() eqt(excl(),locker()) -> F() eqt(excl(),mcrlrecord()) -> F() eqt(excl(),ok()) -> F() eqt(excl(),pending()) -> F() eqt(excl(),release()) -> F() eqt(excl(),request()) -> F() eqt(excl(),resource()) -> F() eqt(excl(),tag()) -> F() eqt(excl(),true()) -> F() eqt(excl(),undefined()) -> F() eqt(excl(),pid(N2)) -> F() eqt(excl(),eqt(false(),int(N2))) -> F() eqt(false(),cons(H2,T2)) -> F() eqt(false(),tuple(H2,T2)) -> F() eqt(false(),tuplenil(H2)) -> F() eqt(lock(),nil()) -> F() eqt(lock(),a()) -> F() eqt(lock(),excl()) -> F() eqt(lock(),false()) -> F() eqt(lock(),lock()) -> T() eqt(lock(),locker()) -> F() eqt(lock(),mcrlrecord()) -> F() eqt(lock(),ok()) -> F() eqt(lock(),pending()) -> F() eqt(lock(),release()) -> F() eqt(lock(),request()) -> F() eqt(lock(),resource()) -> F() eqt(lock(),tag()) -> F() eqt(lock(),true()) -> F() eqt(lock(),undefined()) -> F() eqt(lock(),pid(N2)) -> F() eqt(lock(),int(N2)) -> F() eqt(lock(),cons(H2,T2)) -> F() eqt(lock(),tuple(H2,T2)) -> F() eqt(lock(),tuplenil(H2)) -> F() eqt(locker(),nil()) -> F() eqt(locker(),a()) -> F() eqt(locker(),excl()) -> F() eqt(locker(),false()) -> F() eqt(locker(),lock()) -> F() eqt(locker(),locker()) -> T() eqt(locker(),mcrlrecord()) -> F() eqt(locker(),ok()) -> F() eqt(locker(),pending()) -> F() eqt(locker(),release()) -> F() eqt(locker(),request()) -> F() eqt(locker(),resource()) -> F() eqt(locker(),tag()) -> F() eqt(locker(),true()) -> F() eqt(locker(),undefined()) -> F() eqt(locker(),pid(N2)) -> F() eqt(locker(),int(N2)) -> F() eqt(locker(),cons(H2,T2)) -> F() eqt(locker(),tuple(H2,T2)) -> F() eqt(locker(),tuplenil(H2)) -> F() eqt(mcrlrecord(),nil()) -> F() eqt(mcrlrecord(),a()) -> F() eqt(mcrlrecord(),excl()) -> F() eqt(mcrlrecord(),false()) -> F() eqt(mcrlrecord(),lock()) -> F() eqt(mcrlrecord(),locker()) -> F() eqt(mcrlrecord(),mcrlrecord()) -> T() eqt(mcrlrecord(),ok()) -> F() eqt(mcrlrecord(),pending()) -> F() eqt(mcrlrecord(),release()) -> F() eqt(mcrlrecord(),request()) -> F() eqt(mcrlrecord(),resource()) -> F() eqt(ok(),resource()) -> F() eqt(ok(),tag()) -> F() eqt(ok(),true()) -> F() eqt(ok(),undefined()) -> F() eqt(ok(),pid(N2)) -> F() eqt(ok(),int(N2)) -> F() eqt(ok(),cons(H2,T2)) -> F() eqt(ok(),tuple(H2,T2)) -> F() eqt(ok(),tuplenil(H2)) -> F() eqt(pending(),nil()) -> F() eqt(pending(),a()) -> F() eqt(pending(),excl()) -> F() eqt(pending(),false()) -> F() eqt(pending(),lock()) -> F() eqt(pending(),locker()) -> F() eqt(pending(),mcrlrecord()) -> F() eqt(pending(),ok()) -> F() eqt(pending(),pending()) -> T() eqt(pending(),release()) -> F() eqt(pending(),request()) -> F() eqt(pending(),resource()) -> F() eqt(pending(),tag()) -> F() eqt(pending(),true()) -> F() eqt(pending(),undefined()) -> F() eqt(pending(),pid(N2)) -> F() eqt(pending(),int(N2)) -> F() eqt(pending(),cons(H2,T2)) -> F() eqt(pending(),tuple(H2,T2)) -> F() eqt(pending(),tuplenil(H2)) -> F() eqt(release(),nil()) -> F() eqt(release(),a()) -> F() eqt(release(),excl()) -> F() eqt(release(),false()) -> F() eqt(release(),lock()) -> F() eqt(release(),locker()) -> F() eqt(release(),mcrlrecord()) -> F() eqt(release(),ok()) -> F() eqt(request(),mcrlrecord()) -> F() eqt(request(),ok()) -> F() eqt(request(),pending()) -> F() eqt(request(),release()) -> F() eqt(request(),request()) -> T() eqt(request(),resource()) -> F() eqt(request(),tag()) -> F() eqt(request(),true()) -> F() eqt(request(),undefined()) -> F() eqt(request(),pid(N2)) -> F() eqt(request(),int(N2)) -> F() eqt(request(),cons(H2,T2)) -> F() eqt(request(),tuple(H2,T2)) -> F() eqt(request(),tuplenil(H2)) -> F() eqt(resource(),nil()) -> F() eqt(resource(),a()) -> F() eqt(resource(),excl()) -> F() eqt(resource(),false()) -> F() eqt(resource(),lock()) -> F() eqt(resource(),locker()) -> F() eqt(resource(),mcrlrecord()) -> F() eqt(resource(),ok()) -> F() eqt(resource(),pending()) -> F() eqt(resource(),release()) -> F() eqt(resource(),request()) -> F() eqt(resource(),resource()) -> T() eqt(resource(),tag()) -> F() eqt(resource(),true()) -> F() eqt(resource(),undefined()) -> F() eqt(resource(),pid(N2)) -> F() eqt(resource(),int(N2)) -> F() eqt(resource(),cons(H2,T2)) -> F() eqt(resource(),tuple(H2,T2)) -> F() eqt(resource(),tuplenil(H2)) -> F() eqt(tag(),nil()) -> F() eqt(tag(),a()) -> F() eqt(tag(),excl()) -> F() eqt(tag(),false()) -> F() eqt(tag(),lock()) -> F() eqt(tag(),locker()) -> F() eqt(tag(),mcrlrecord()) -> F() eqt(tag(),ok()) -> F() eqt(tag(),pending()) -> F() eqt(tag(),release()) -> F() eqt(tag(),request()) -> F() eqt(tag(),resource()) -> F() eqt(tag(),tag()) -> T() eqt(tag(),true()) -> F() eqt(tag(),undefined()) -> F() eqt(tag(),pid(N2)) -> F() eqt(tag(),int(N2)) -> F() eqt(tag(),cons(H2,T2)) -> F() eqt(tag(),tuple(H2,T2)) -> F() eqt(tag(),tuplenil(H2)) -> F() eqt(true(),nil()) -> F() eqt(true(),a()) -> F() eqt(true(),excl()) -> F() eqt(true(),false()) -> F() eqt(true(),lock()) -> F() eqt(true(),locker()) -> F() eqt(true(),mcrlrecord()) -> F() eqt(true(),ok()) -> F() eqt(true(),pending()) -> F() eqt(true(),release()) -> F() eqt(true(),request()) -> F() eqt(true(),resource()) -> F() eqt(true(),tag()) -> F() eqt(true(),true()) -> T() eqt(true(),undefined()) -> F() eqt(true(),pid(N2)) -> F() eqt(true(),int(N2)) -> F() eqt(true(),cons(H2,T2)) -> F() eqt(true(),tuple(H2,T2)) -> F() eqt(true(),tuplenil(H2)) -> F() eqt(undefined(),nil()) -> F() eqt(undefined(),a()) -> F() eqt(undefined(),tuplenil(H2)) -> F() eqt(pid(N1),nil()) -> F() eqt(pid(N1),a()) -> F() eqt(pid(N1),excl()) -> F() eqt(pid(N1),false()) -> F() eqt(pid(N1),lock()) -> F() eqt(pid(N1),locker()) -> F() eqt(pid(N1),mcrlrecord()) -> F() eqt(pid(N1),ok()) -> F() eqt(pid(N1),pending()) -> F() eqt(pid(N1),release()) -> F() eqt(pid(N1),request()) -> F() eqt(pid(N1),resource()) -> F() eqt(pid(N1),tag()) -> F() eqt(pid(N1),true()) -> F() eqt(pid(N1),undefined()) -> F() eqt(pid(N1),pid(N2)) -> eqt(N1,N2) eqt(pid(N1),int(N2)) -> F() eqt(pid(N1),cons(H2,T2)) -> F() eqt(pid(N1),tuple(H2,T2)) -> F() eqt(pid(N1),tuplenil(H2)) -> F() eqt(int(N1),nil()) -> F() eqt(int(N1),a()) -> F() eqt(int(N1),excl()) -> F() eqt(int(N1),false()) -> F() eqt(int(N1),lock()) -> F() eqt(int(N1),locker()) -> F() eqt(int(N1),mcrlrecord()) -> F() eqt(int(N1),ok()) -> F() eqt(int(N1),pending()) -> F() eqt(int(N1),release()) -> F() eqt(int(N1),request()) -> F() eqt(int(N1),resource()) -> F() eqt(int(N1),tag()) -> F() eqt(int(N1),true()) -> F() eqt(int(N1),undefined()) -> F() eqt(cons(H1,T1),resource()) -> F() eqt(cons(H1,T1),tag()) -> F() eqt(cons(H1,T1),true()) -> F() eqt(cons(H1,T1),undefined()) -> F() eqt(cons(H1,T1),pid(N2)) -> F() eqt(cons(H1,T1),int(N2)) -> F() eqt(cons(H1,T1),cons(H2,T2)) -> and(eqt(H1,H2),eqt(T1,T2)) eqt(cons(H1,T1),tuple(H2,T2)) -> F() eqt(cons(H1,T1),tuplenil(H2)) -> F() eqt(tuple(H1,T1),nil()) -> F() eqt(tuple(H1,T1),a()) -> F() eqt(tuple(H1,T1),excl()) -> F() eqt(tuple(H1,T1),false()) -> F() eqt(tuple(H1,T1),lock()) -> F() eqt(tuple(H1,T1),locker()) -> F() eqt(tuple(H1,T1),mcrlrecord()) -> F() eqt(tuple(H1,T1),ok()) -> F() eqt(tuple(H1,T1),pending()) -> F() eqt(tuple(H1,T1),release()) -> F() eqt(tuple(H1,T1),request()) -> F() eqt(tuple(H1,T1),resource()) -> F() eqt(tuple(H1,T1),tag()) -> F() eqt(tuple(H1,T1),true()) -> F() eqt(tuple(H1,T1),undefined()) -> F() eqt(tuple(H1,T1),pid(N2)) -> F() eqt(tuple(H1,T1),int(N2)) -> F() eqt(tuple(H1,T1),cons(H2,T2)) -> F() eqt(tuple(H1,T1),tuple(H2,T2)) -> and(eqt(H1,H2),eqt(T1,T2)) eqt(tuple(H1,T1),tuplenil(H2)) -> F() eqt(tuplenil(H1),nil()) -> F() eqt(tuplenil(H1),a()) -> F() eqt(tuplenil(H1),excl()) -> F() eqt(tuplenil(H1),false()) -> F() eqt(tuplenil(H1),lock()) -> F() eqt(tuplenil(H1),locker()) -> F() eqt(tuplenil(H1),mcrlrecord()) -> F() eqt(tuplenil(H1),ok()) -> F() eqt(tuplenil(H1),pending()) -> F() eqt(tuplenil(H1),release()) -> F() eqt(tuplenil(H1),request()) -> F() eqt(tuplenil(H1),resource()) -> F() eqt(tuplenil(H1),tag()) -> F() eqt(tuplenil(H1),true()) -> F() eqt(tuplenil(H1),undefined()) -> F() eqt(tuplenil(H1),pid(N2)) -> F() eqt(tuplenil(H1),int(N2)) -> F() eqt(tuplenil(H1),cons(H2,T2)) -> F() eqt(tuplenil(H1),tuple(H2,T2)) -> F() eqt(tuplenil(H1),tuplenil(H2)) -> eqt(H1,H2) element(int(s(0())),tuplenil(T1)) -> T1 element(int(s(0())),tuple(T1,T2)) -> T1 element(int(s(s(N1))),tuple(T1,T2)) -> element(int(s(N1)),T2) record_new(lock()) -> tuple(mcrlrecord(),tuple(lock(),tuple(undefined(),tuple(nil(),tuplenil(nil()))))) record_extract(tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))), lock(),resource()) -> tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))) record_update(tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))), lock(),pending(),NewF) -> tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(NewF))))) record_updates(Record,Name,nil()) -> Record record_updates(Record,Name,cons(tuple(Field,tuplenil(NewF)),Fields)) -> record_updates(record_update(Record,Name,Field,NewF),Name,Fields) locker2_map_promote_pending(nil(),Pending) -> nil() locker2_map_promote_pending(cons(Lock,Locks),Pending) -> cons(locker2_promote_pending(Lock,Pending),locker2_map_promote_pending(Locks,Pending)) locker2_map_claim_lock(nil(),Resources,Client) -> nil() locker2_map_claim_lock(cons(Lock,Locks),Resources,Client) -> cons(locker2_claim_lock(Lock,Resources,Client),locker2_map_claim_lock(Locks,Resources,Client)) locker2_map_add_pending(nil(),Resources,Client) -> nil() locker2_promote_pending(Lock,Client) -> case0(Client,Lock,record_extract(Lock,lock(),pending())) case0(Client,Lock,cons(Client,Pendings)) -> record_updates(Lock,lock(),cons(tuple(excl(),tuplenil(Client)),cons ( tuple ( pending(),tuplenil(Pendings)), nil ()))) case0(Client,Lock,MCRLFree0) -> Lock locker2_remove_pending(Lock,Client) -> record_updates(Lock,lock(),cons(tuple(pending(),tuplenil(subtract (record_extract (Lock,lock(),pending()), cons(Client,nil())))), nil())) locker2_add_pending(Lock,Resources,Client) -> case1(Client,Resources,Lock,member(record_extract(Lock,lock(),resource()),Resources)) case1(Client,Resources,Lock,true()) -> record_updates(Lock,lock(),cons(tuple(pending(),tuplenil(append( record_extract ( Lock,lock(),pending()), cons (Client,nil())))), nil())) case1(Client,Resources,Lock,false()) -> Lock locker2_release_lock(Lock,Client) -> case2(Client,Lock,gen_modtageq(Client,record_extract(Lock,lock(),excl()))) case2(Client,Lock,true()) -> record_updates(Lock,lock(),cons(tuple(excllock(),excl()),nil())) case4(Client,Lock,MCRLFree1) -> false() locker2_obtainables(nil(),Client) -> true() locker2_obtainables(cons(Lock,Locks),Client) -> case5(Client,Locks,Lock,member(Client,record_extract(Lock,lock(),pending()))) case5(Client,Locks,Lock,true()) -> andt(locker2_obtainable(Lock,Client),locker2_obtainables(Locks,Client)) case5(Client,Locks,Lock,false()) -> locker2_obtainables(Locks,Client) locker2_check_available(Resource,nil()) -> false() locker2_check_available(Resource,cons(Lock,Locks)) -> case6(Locks,Lock,Resource,equal(Resource,record_extract(Lock,lock(),resource()))) case6(Locks,Lock,Resource,true()) -> andt(equal(record_extract(Lock,lock(),excl()),nil()),equal(record_extract (Lock,lock(),pending()), nil())) case6(Locks,Lock,Resource,false()) -> locker2_check_available(Resource,Locks) locker2_check_availables(nil(),Locks) -> true() locker2_check_availables(cons(Resource,Resources),Locks) -> andt(locker2_check_available(Resource,Locks),locker2_check_availables(Resources,Locks)) locker2_adduniq(nil(),List) -> List append(cons(Head,Tail),List) -> cons(Head,append(Tail,List)) subtract(List,nil()) -> List subtract(List,cons(Head,Tail)) -> subtract(delete(Head,List),Tail) delete(E,nil()) -> nil() delete(E,cons(Head,Tail)) -> case8(Tail,Head,E,equal(E,Head)) case8(Tail,Head,E,true()) -> Tail case8(Tail,Head,E,false()) -> cons(Head,delete(E,Tail)) gen_tag(Pid) -> tuple(Pid,tuplenil(tag())) gen_modtageq(Client1,Client2) -> equal(Client1,Client2) member(E,nil()) -> false() member(E,cons(Head,Tail)) -> case9(Tail,Head,E,equal(E,Head)) case9(Tail,Head,E,true()) -> true() case9(Tail,Head,E,false()) -> member(E,Tail) eqs(empty(),empty()) -> T() eqs(empty(),stack(E2,S2)) -> F() eqs(stack(E1,S1),empty()) -> F() eqs(stack(E1,S1),stack(E2,S2)) -> and(eqt(E1,E2),eqs(S1,S2)) pushs(E1,S1) -> stack(E1,S1) pops(stack(E1,S1)) -> S1 tops(stack(E1,S1)) -> E1 istops(E1,empty()) -> F() istops(E1,stack(E2,S1)) -> eqt(E1,E2) eqc(nocalls(),nocalls()) -> T() eqc(nocalls(),calls(E2,S2,CS2)) -> F() eqc(calls(E1,S1,CS1),nocalls()) -> F() eqc(calls(E1,S1,CS1),calls(E2,S2,CS2)) -> and(eqt(E1,E2),and(eqs(S1,S2),eqc(CS1,CS2))) push(E1,E2,nocalls()) -> calls(E1,stack(E2,empty()),nocalls()) push(E1,E2,calls(E3,S1,CS1)) -> push1(E1,E2,E3,S1,CS1,eqt(E1,E3)) push1(E1,E2,E3,S1,CS1,T()) -> calls(E3,pushs(E2,S1),CS1) Subterm Criterion Processor: simple projection: pi(locker2_check_available#) = 1 pi(case6#) = 0 problem: DPs: case6#(Locks,Lock,Resource,false()) -> locker2_check_available#(Resource,Locks) TRS: or(T(),T()) -> T() or(F(),T()) -> T() or(T(),F()) -> T() or(F(),F()) -> F() and(T(),B) -> B and(B,T()) -> B and(F(),B) -> F() and(B,F()) -> F() imp(T(),B) -> B imp(F(),B) -> T() not(T()) -> F() not(F()) -> T() if(T(),B1,B2) -> B1 if(F(),B1,B2) -> B2 eq(T(),T()) -> T() eq(F(),F()) -> T() eq(T(),F()) -> F() eq(F(),T()) -> F() eqt(nil(),undefined()) -> F() eqt(nil(),pid(N2)) -> F() eqt(nil(),int(N2)) -> F() eqt(nil(),cons(H2,T2)) -> F() eqt(nil(),tuple(H2,T2)) -> F() eqt(nil(),tuplenil(H2)) -> F() eqt(a(),nil()) -> F() eqt(a(),a()) -> T() eqt(a(),excl()) -> F() eqt(a(),false()) -> F() eqt(a(),lock()) -> F() eqt(a(),locker()) -> F() eqt(a(),mcrlrecord()) -> F() eqt(a(),ok()) -> F() eqt(a(),pending()) -> F() eqt(a(),release()) -> F() eqt(a(),request()) -> F() eqt(a(),resource()) -> F() eqt(a(),tag()) -> F() eqt(a(),true()) -> F() eqt(a(),undefined()) -> F() eqt(a(),pid(N2)) -> F() eqt(a(),int(N2)) -> F() eqt(a(),cons(H2,T2)) -> F() eqt(a(),tuple(H2,T2)) -> F() eqt(a(),tuplenil(H2)) -> F() eqt(excl(),nil()) -> F() eqt(excl(),a()) -> F() eqt(excl(),excl()) -> T() eqt(excl(),false()) -> F() eqt(excl(),lock()) -> F() eqt(excl(),locker()) -> F() eqt(excl(),mcrlrecord()) -> F() eqt(excl(),ok()) -> F() eqt(excl(),pending()) -> F() eqt(excl(),release()) -> F() eqt(excl(),request()) -> F() eqt(excl(),resource()) -> F() eqt(excl(),tag()) -> F() eqt(excl(),true()) -> F() eqt(excl(),undefined()) -> F() eqt(excl(),pid(N2)) -> F() eqt(excl(),eqt(false(),int(N2))) -> F() eqt(false(),cons(H2,T2)) -> F() eqt(false(),tuple(H2,T2)) -> F() eqt(false(),tuplenil(H2)) -> F() eqt(lock(),nil()) -> F() eqt(lock(),a()) -> F() eqt(lock(),excl()) -> F() eqt(lock(),false()) -> F() eqt(lock(),lock()) -> T() eqt(lock(),locker()) -> F() eqt(lock(),mcrlrecord()) -> F() eqt(lock(),ok()) -> F() eqt(lock(),pending()) -> F() eqt(lock(),release()) -> F() eqt(lock(),request()) -> F() eqt(lock(),resource()) -> F() eqt(lock(),tag()) -> F() eqt(lock(),true()) -> F() eqt(lock(),undefined()) -> F() eqt(lock(),pid(N2)) -> F() eqt(lock(),int(N2)) -> F() eqt(lock(),cons(H2,T2)) -> F() eqt(lock(),tuple(H2,T2)) -> F() eqt(lock(),tuplenil(H2)) -> F() eqt(locker(),nil()) -> F() eqt(locker(),a()) -> F() eqt(locker(),excl()) -> F() eqt(locker(),false()) -> F() eqt(locker(),lock()) -> F() eqt(locker(),locker()) -> T() eqt(locker(),mcrlrecord()) -> F() eqt(locker(),ok()) -> F() eqt(locker(),pending()) -> F() eqt(locker(),release()) -> F() eqt(locker(),request()) -> F() eqt(locker(),resource()) -> F() eqt(locker(),tag()) -> F() eqt(locker(),true()) -> F() eqt(locker(),undefined()) -> F() eqt(locker(),pid(N2)) -> F() eqt(locker(),int(N2)) -> F() eqt(locker(),cons(H2,T2)) -> F() eqt(locker(),tuple(H2,T2)) -> F() eqt(locker(),tuplenil(H2)) -> F() eqt(mcrlrecord(),nil()) -> F() eqt(mcrlrecord(),a()) -> F() eqt(mcrlrecord(),excl()) -> F() eqt(mcrlrecord(),false()) -> F() eqt(mcrlrecord(),lock()) -> F() eqt(mcrlrecord(),locker()) -> F() eqt(mcrlrecord(),mcrlrecord()) -> T() eqt(mcrlrecord(),ok()) -> F() eqt(mcrlrecord(),pending()) -> F() eqt(mcrlrecord(),release()) -> F() eqt(mcrlrecord(),request()) -> F() eqt(mcrlrecord(),resource()) -> F() eqt(ok(),resource()) -> F() eqt(ok(),tag()) -> F() eqt(ok(),true()) -> F() eqt(ok(),undefined()) -> F() eqt(ok(),pid(N2)) -> F() eqt(ok(),int(N2)) -> F() eqt(ok(),cons(H2,T2)) -> F() eqt(ok(),tuple(H2,T2)) -> F() eqt(ok(),tuplenil(H2)) -> F() eqt(pending(),nil()) -> F() eqt(pending(),a()) -> F() eqt(pending(),excl()) -> F() eqt(pending(),false()) -> F() eqt(pending(),lock()) -> F() eqt(pending(),locker()) -> F() eqt(pending(),mcrlrecord()) -> F() eqt(pending(),ok()) -> F() eqt(pending(),pending()) -> T() eqt(pending(),release()) -> F() eqt(pending(),request()) -> F() eqt(pending(),resource()) -> F() eqt(pending(),tag()) -> F() eqt(pending(),true()) -> F() eqt(pending(),undefined()) -> F() eqt(pending(),pid(N2)) -> F() eqt(pending(),int(N2)) -> F() eqt(pending(),cons(H2,T2)) -> F() eqt(pending(),tuple(H2,T2)) -> F() eqt(pending(),tuplenil(H2)) -> F() eqt(release(),nil()) -> F() eqt(release(),a()) -> F() eqt(release(),excl()) -> F() eqt(release(),false()) -> F() eqt(release(),lock()) -> F() eqt(release(),locker()) -> F() eqt(release(),mcrlrecord()) -> F() eqt(release(),ok()) -> F() eqt(request(),mcrlrecord()) -> F() eqt(request(),ok()) -> F() eqt(request(),pending()) -> F() eqt(request(),release()) -> F() eqt(request(),request()) -> T() eqt(request(),resource()) -> F() eqt(request(),tag()) -> F() eqt(request(),true()) -> F() eqt(request(),undefined()) -> F() eqt(request(),pid(N2)) -> F() eqt(request(),int(N2)) -> F() eqt(request(),cons(H2,T2)) -> F() eqt(request(),tuple(H2,T2)) -> F() eqt(request(),tuplenil(H2)) -> F() eqt(resource(),nil()) -> F() eqt(resource(),a()) -> F() eqt(resource(),excl()) -> F() eqt(resource(),false()) -> F() eqt(resource(),lock()) -> F() eqt(resource(),locker()) -> F() eqt(resource(),mcrlrecord()) -> F() eqt(resource(),ok()) -> F() eqt(resource(),pending()) -> F() eqt(resource(),release()) -> F() eqt(resource(),request()) -> F() eqt(resource(),resource()) -> T() eqt(resource(),tag()) -> F() eqt(resource(),true()) -> F() eqt(resource(),undefined()) -> F() eqt(resource(),pid(N2)) -> F() eqt(resource(),int(N2)) -> F() eqt(resource(),cons(H2,T2)) -> F() eqt(resource(),tuple(H2,T2)) -> F() eqt(resource(),tuplenil(H2)) -> F() eqt(tag(),nil()) -> F() eqt(tag(),a()) -> F() eqt(tag(),excl()) -> F() eqt(tag(),false()) -> F() eqt(tag(),lock()) -> F() eqt(tag(),locker()) -> F() eqt(tag(),mcrlrecord()) -> F() eqt(tag(),ok()) -> F() eqt(tag(),pending()) -> F() eqt(tag(),release()) -> F() eqt(tag(),request()) -> F() eqt(tag(),resource()) -> F() eqt(tag(),tag()) -> T() eqt(tag(),true()) -> F() eqt(tag(),undefined()) -> F() eqt(tag(),pid(N2)) -> F() eqt(tag(),int(N2)) -> F() eqt(tag(),cons(H2,T2)) -> F() eqt(tag(),tuple(H2,T2)) -> F() eqt(tag(),tuplenil(H2)) -> F() eqt(true(),nil()) -> F() eqt(true(),a()) -> F() eqt(true(),excl()) -> F() eqt(true(),false()) -> F() eqt(true(),lock()) -> F() eqt(true(),locker()) -> F() eqt(true(),mcrlrecord()) -> F() eqt(true(),ok()) -> F() eqt(true(),pending()) -> F() eqt(true(),release()) -> F() eqt(true(),request()) -> F() eqt(true(),resource()) -> F() eqt(true(),tag()) -> F() eqt(true(),true()) -> T() eqt(true(),undefined()) -> F() eqt(true(),pid(N2)) -> F() eqt(true(),int(N2)) -> F() eqt(true(),cons(H2,T2)) -> F() eqt(true(),tuple(H2,T2)) -> F() eqt(true(),tuplenil(H2)) -> F() eqt(undefined(),nil()) -> F() eqt(undefined(),a()) -> F() eqt(undefined(),tuplenil(H2)) -> F() eqt(pid(N1),nil()) -> F() eqt(pid(N1),a()) -> F() eqt(pid(N1),excl()) -> F() eqt(pid(N1),false()) -> F() eqt(pid(N1),lock()) -> F() eqt(pid(N1),locker()) -> F() eqt(pid(N1),mcrlrecord()) -> F() eqt(pid(N1),ok()) -> F() eqt(pid(N1),pending()) -> F() eqt(pid(N1),release()) -> F() eqt(pid(N1),request()) -> F() eqt(pid(N1),resource()) -> F() eqt(pid(N1),tag()) -> F() eqt(pid(N1),true()) -> F() eqt(pid(N1),undefined()) -> F() eqt(pid(N1),pid(N2)) -> eqt(N1,N2) eqt(pid(N1),int(N2)) -> F() eqt(pid(N1),cons(H2,T2)) -> F() eqt(pid(N1),tuple(H2,T2)) -> F() eqt(pid(N1),tuplenil(H2)) -> F() eqt(int(N1),nil()) -> F() eqt(int(N1),a()) -> F() eqt(int(N1),excl()) -> F() eqt(int(N1),false()) -> F() eqt(int(N1),lock()) -> F() eqt(int(N1),locker()) -> F() eqt(int(N1),mcrlrecord()) -> F() eqt(int(N1),ok()) -> F() eqt(int(N1),pending()) -> F() eqt(int(N1),release()) -> F() eqt(int(N1),request()) -> F() eqt(int(N1),resource()) -> F() eqt(int(N1),tag()) -> F() eqt(int(N1),true()) -> F() eqt(int(N1),undefined()) -> F() eqt(cons(H1,T1),resource()) -> F() eqt(cons(H1,T1),tag()) -> F() eqt(cons(H1,T1),true()) -> F() eqt(cons(H1,T1),undefined()) -> F() eqt(cons(H1,T1),pid(N2)) -> F() eqt(cons(H1,T1),int(N2)) -> F() eqt(cons(H1,T1),cons(H2,T2)) -> and(eqt(H1,H2),eqt(T1,T2)) eqt(cons(H1,T1),tuple(H2,T2)) -> F() eqt(cons(H1,T1),tuplenil(H2)) -> F() eqt(tuple(H1,T1),nil()) -> F() eqt(tuple(H1,T1),a()) -> F() eqt(tuple(H1,T1),excl()) -> F() eqt(tuple(H1,T1),false()) -> F() eqt(tuple(H1,T1),lock()) -> F() eqt(tuple(H1,T1),locker()) -> F() eqt(tuple(H1,T1),mcrlrecord()) -> F() eqt(tuple(H1,T1),ok()) -> F() eqt(tuple(H1,T1),pending()) -> F() eqt(tuple(H1,T1),release()) -> F() eqt(tuple(H1,T1),request()) -> F() eqt(tuple(H1,T1),resource()) -> F() eqt(tuple(H1,T1),tag()) -> F() eqt(tuple(H1,T1),true()) -> F() eqt(tuple(H1,T1),undefined()) -> F() eqt(tuple(H1,T1),pid(N2)) -> F() eqt(tuple(H1,T1),int(N2)) -> F() eqt(tuple(H1,T1),cons(H2,T2)) -> F() eqt(tuple(H1,T1),tuple(H2,T2)) -> and(eqt(H1,H2),eqt(T1,T2)) eqt(tuple(H1,T1),tuplenil(H2)) -> F() eqt(tuplenil(H1),nil()) -> F() eqt(tuplenil(H1),a()) -> F() eqt(tuplenil(H1),excl()) -> F() eqt(tuplenil(H1),false()) -> F() eqt(tuplenil(H1),lock()) -> F() eqt(tuplenil(H1),locker()) -> F() eqt(tuplenil(H1),mcrlrecord()) -> F() eqt(tuplenil(H1),ok()) -> F() eqt(tuplenil(H1),pending()) -> F() eqt(tuplenil(H1),release()) -> F() eqt(tuplenil(H1),request()) -> F() eqt(tuplenil(H1),resource()) -> F() eqt(tuplenil(H1),tag()) -> F() eqt(tuplenil(H1),true()) -> F() eqt(tuplenil(H1),undefined()) -> F() eqt(tuplenil(H1),pid(N2)) -> F() eqt(tuplenil(H1),int(N2)) -> F() eqt(tuplenil(H1),cons(H2,T2)) -> F() eqt(tuplenil(H1),tuple(H2,T2)) -> F() eqt(tuplenil(H1),tuplenil(H2)) -> eqt(H1,H2) element(int(s(0())),tuplenil(T1)) -> T1 element(int(s(0())),tuple(T1,T2)) -> T1 element(int(s(s(N1))),tuple(T1,T2)) -> element(int(s(N1)),T2) record_new(lock()) -> tuple(mcrlrecord(),tuple(lock(),tuple(undefined(),tuple(nil(),tuplenil(nil()))))) record_extract(tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))), lock(),resource()) -> tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))) record_update(tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))), lock(),pending(),NewF) -> tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(NewF))))) record_updates(Record,Name,nil()) -> Record record_updates(Record,Name,cons(tuple(Field,tuplenil(NewF)),Fields)) -> record_updates(record_update(Record,Name,Field,NewF),Name,Fields) locker2_map_promote_pending(nil(),Pending) -> nil() locker2_map_promote_pending(cons(Lock,Locks),Pending) -> cons(locker2_promote_pending(Lock,Pending),locker2_map_promote_pending(Locks,Pending)) locker2_map_claim_lock(nil(),Resources,Client) -> nil() locker2_map_claim_lock(cons(Lock,Locks),Resources,Client) -> cons(locker2_claim_lock(Lock,Resources,Client),locker2_map_claim_lock (Locks,Resources,Client)) locker2_map_add_pending(nil(),Resources,Client) -> nil() locker2_promote_pending(Lock,Client) -> case0(Client,Lock,record_extract(Lock,lock(),pending())) case0(Client,Lock,cons(Client,Pendings)) -> record_updates(Lock,lock(),cons(tuple(excl(),tuplenil(Client)), cons(tuple(pending(),tuplenil(Pendings)),nil()))) case0(Client,Lock,MCRLFree0) -> Lock locker2_remove_pending(Lock,Client) -> record_updates(Lock,lock(),cons(tuple(pending(),tuplenil(subtract (record_extract (Lock,lock(),pending()), cons (Client,nil())))), nil())) locker2_add_pending(Lock,Resources,Client) -> case1(Client,Resources,Lock,member(record_extract(Lock,lock(),resource()),Resources)) case1(Client,Resources,Lock,true()) -> record_updates(Lock,lock(),cons(tuple(pending(),tuplenil(append (record_extract (Lock,lock(),pending()), cons (Client,nil())))), nil())) case1(Client,Resources,Lock,false()) -> Lock locker2_release_lock(Lock,Client) -> case2(Client,Lock,gen_modtageq(Client,record_extract(Lock,lock(),excl()))) case2(Client,Lock,true()) -> record_updates(Lock,lock(),cons(tuple(excllock(),excl()),nil())) case4(Client,Lock,MCRLFree1) -> false() locker2_obtainables(nil(),Client) -> true() locker2_obtainables(cons(Lock,Locks),Client) -> case5(Client,Locks,Lock,member(Client,record_extract(Lock,lock(),pending()))) case5(Client,Locks,Lock,true()) -> andt(locker2_obtainable(Lock,Client),locker2_obtainables(Locks,Client)) case5(Client,Locks,Lock,false()) -> locker2_obtainables(Locks,Client) locker2_check_available(Resource,nil()) -> false() locker2_check_available(Resource,cons(Lock,Locks)) -> case6(Locks,Lock,Resource,equal(Resource,record_extract(Lock,lock(),resource()))) case6(Locks,Lock,Resource,true()) -> andt(equal(record_extract(Lock,lock(),excl()),nil()),equal(record_extract (Lock,lock(),pending()), nil())) case6(Locks,Lock,Resource,false()) -> locker2_check_available(Resource,Locks) locker2_check_availables(nil(),Locks) -> true() locker2_check_availables(cons(Resource,Resources),Locks) -> andt(locker2_check_available(Resource,Locks),locker2_check_availables(Resources,Locks)) locker2_adduniq(nil(),List) -> List append(cons(Head,Tail),List) -> cons(Head,append(Tail,List)) subtract(List,nil()) -> List subtract(List,cons(Head,Tail)) -> subtract(delete(Head,List),Tail) delete(E,nil()) -> nil() delete(E,cons(Head,Tail)) -> case8(Tail,Head,E,equal(E,Head)) case8(Tail,Head,E,true()) -> Tail case8(Tail,Head,E,false()) -> cons(Head,delete(E,Tail)) gen_tag(Pid) -> tuple(Pid,tuplenil(tag())) gen_modtageq(Client1,Client2) -> equal(Client1,Client2) member(E,nil()) -> false() member(E,cons(Head,Tail)) -> case9(Tail,Head,E,equal(E,Head)) case9(Tail,Head,E,true()) -> true() case9(Tail,Head,E,false()) -> member(E,Tail) eqs(empty(),empty()) -> T() eqs(empty(),stack(E2,S2)) -> F() eqs(stack(E1,S1),empty()) -> F() eqs(stack(E1,S1),stack(E2,S2)) -> and(eqt(E1,E2),eqs(S1,S2)) pushs(E1,S1) -> stack(E1,S1) pops(stack(E1,S1)) -> S1 tops(stack(E1,S1)) -> E1 istops(E1,empty()) -> F() istops(E1,stack(E2,S1)) -> eqt(E1,E2) eqc(nocalls(),nocalls()) -> T() eqc(nocalls(),calls(E2,S2,CS2)) -> F() eqc(calls(E1,S1,CS1),nocalls()) -> F() eqc(calls(E1,S1,CS1),calls(E2,S2,CS2)) -> and(eqt(E1,E2),and(eqs(S1,S2),eqc(CS1,CS2))) push(E1,E2,nocalls()) -> calls(E1,stack(E2,empty()),nocalls()) push(E1,E2,calls(E3,S1,CS1)) -> push1(E1,E2,E3,S1,CS1,eqt(E1,E3)) push1(E1,E2,E3,S1,CS1,T()) -> calls(E3,pushs(E2,S1),CS1) SCC Processor: #sccs: 0 #rules: 0 #arcs: 2/1 DPs: case8#(Tail,Head,E,false()) -> delete#(E,Tail) delete#(E,cons(Head,Tail)) -> case8#(Tail,Head,E,equal(E,Head)) TRS: or(T(),T()) -> T() or(F(),T()) -> T() or(T(),F()) -> T() or(F(),F()) -> F() and(T(),B) -> B and(B,T()) -> B and(F(),B) -> F() and(B,F()) -> F() imp(T(),B) -> B imp(F(),B) -> T() not(T()) -> F() not(F()) -> T() if(T(),B1,B2) -> B1 if(F(),B1,B2) -> B2 eq(T(),T()) -> T() eq(F(),F()) -> T() eq(T(),F()) -> F() eq(F(),T()) -> F() eqt(nil(),undefined()) -> F() eqt(nil(),pid(N2)) -> F() eqt(nil(),int(N2)) -> F() eqt(nil(),cons(H2,T2)) -> F() eqt(nil(),tuple(H2,T2)) -> F() eqt(nil(),tuplenil(H2)) -> F() eqt(a(),nil()) -> F() eqt(a(),a()) -> T() eqt(a(),excl()) -> F() eqt(a(),false()) -> F() eqt(a(),lock()) -> F() eqt(a(),locker()) -> F() eqt(a(),mcrlrecord()) -> F() eqt(a(),ok()) -> F() eqt(a(),pending()) -> F() eqt(a(),release()) -> F() eqt(a(),request()) -> F() eqt(a(),resource()) -> F() eqt(a(),tag()) -> F() eqt(a(),true()) -> F() eqt(a(),undefined()) -> F() eqt(a(),pid(N2)) -> F() eqt(a(),int(N2)) -> F() eqt(a(),cons(H2,T2)) -> F() eqt(a(),tuple(H2,T2)) -> F() eqt(a(),tuplenil(H2)) -> F() eqt(excl(),nil()) -> F() eqt(excl(),a()) -> F() eqt(excl(),excl()) -> T() eqt(excl(),false()) -> F() eqt(excl(),lock()) -> F() eqt(excl(),locker()) -> F() eqt(excl(),mcrlrecord()) -> F() eqt(excl(),ok()) -> F() eqt(excl(),pending()) -> F() eqt(excl(),release()) -> F() eqt(excl(),request()) -> F() eqt(excl(),resource()) -> F() eqt(excl(),tag()) -> F() eqt(excl(),true()) -> F() eqt(excl(),undefined()) -> F() eqt(excl(),pid(N2)) -> F() eqt(excl(),eqt(false(),int(N2))) -> F() eqt(false(),cons(H2,T2)) -> F() eqt(false(),tuple(H2,T2)) -> F() eqt(false(),tuplenil(H2)) -> F() eqt(lock(),nil()) -> F() eqt(lock(),a()) -> F() eqt(lock(),excl()) -> F() eqt(lock(),false()) -> F() eqt(lock(),lock()) -> T() eqt(lock(),locker()) -> F() eqt(lock(),mcrlrecord()) -> F() eqt(lock(),ok()) -> F() eqt(lock(),pending()) -> F() eqt(lock(),release()) -> F() eqt(lock(),request()) -> F() eqt(lock(),resource()) -> F() eqt(lock(),tag()) -> F() eqt(lock(),true()) -> F() eqt(lock(),undefined()) -> F() eqt(lock(),pid(N2)) -> F() eqt(lock(),int(N2)) -> F() eqt(lock(),cons(H2,T2)) -> F() eqt(lock(),tuple(H2,T2)) -> F() eqt(lock(),tuplenil(H2)) -> F() eqt(locker(),nil()) -> F() eqt(locker(),a()) -> F() eqt(locker(),excl()) -> F() eqt(locker(),false()) -> F() eqt(locker(),lock()) -> F() eqt(locker(),locker()) -> T() eqt(locker(),mcrlrecord()) -> F() eqt(locker(),ok()) -> F() eqt(locker(),pending()) -> F() eqt(locker(),release()) -> F() eqt(locker(),request()) -> F() eqt(locker(),resource()) -> F() eqt(locker(),tag()) -> F() eqt(locker(),true()) -> F() eqt(locker(),undefined()) -> F() eqt(locker(),pid(N2)) -> F() eqt(locker(),int(N2)) -> F() eqt(locker(),cons(H2,T2)) -> F() eqt(locker(),tuple(H2,T2)) -> F() eqt(locker(),tuplenil(H2)) -> F() eqt(mcrlrecord(),nil()) -> F() eqt(mcrlrecord(),a()) -> F() eqt(mcrlrecord(),excl()) -> F() eqt(mcrlrecord(),false()) -> F() eqt(mcrlrecord(),lock()) -> F() eqt(mcrlrecord(),locker()) -> F() eqt(mcrlrecord(),mcrlrecord()) -> T() eqt(mcrlrecord(),ok()) -> F() eqt(mcrlrecord(),pending()) -> F() eqt(mcrlrecord(),release()) -> F() eqt(mcrlrecord(),request()) -> F() eqt(mcrlrecord(),resource()) -> F() eqt(ok(),resource()) -> F() eqt(ok(),tag()) -> F() eqt(ok(),true()) -> F() eqt(ok(),undefined()) -> F() eqt(ok(),pid(N2)) -> F() eqt(ok(),int(N2)) -> F() eqt(ok(),cons(H2,T2)) -> F() eqt(ok(),tuple(H2,T2)) -> F() eqt(ok(),tuplenil(H2)) -> F() eqt(pending(),nil()) -> F() eqt(pending(),a()) -> F() eqt(pending(),excl()) -> F() eqt(pending(),false()) -> F() eqt(pending(),lock()) -> F() eqt(pending(),locker()) -> F() eqt(pending(),mcrlrecord()) -> F() eqt(pending(),ok()) -> F() eqt(pending(),pending()) -> T() eqt(pending(),release()) -> F() eqt(pending(),request()) -> F() eqt(pending(),resource()) -> F() eqt(pending(),tag()) -> F() eqt(pending(),true()) -> F() eqt(pending(),undefined()) -> F() eqt(pending(),pid(N2)) -> F() eqt(pending(),int(N2)) -> F() eqt(pending(),cons(H2,T2)) -> F() eqt(pending(),tuple(H2,T2)) -> F() eqt(pending(),tuplenil(H2)) -> F() eqt(release(),nil()) -> F() eqt(release(),a()) -> F() eqt(release(),excl()) -> F() eqt(release(),false()) -> F() eqt(release(),lock()) -> F() eqt(release(),locker()) -> F() eqt(release(),mcrlrecord()) -> F() eqt(release(),ok()) -> F() eqt(request(),mcrlrecord()) -> F() eqt(request(),ok()) -> F() eqt(request(),pending()) -> F() eqt(request(),release()) -> F() eqt(request(),request()) -> T() eqt(request(),resource()) -> F() eqt(request(),tag()) -> F() eqt(request(),true()) -> F() eqt(request(),undefined()) -> F() eqt(request(),pid(N2)) -> F() eqt(request(),int(N2)) -> F() eqt(request(),cons(H2,T2)) -> F() eqt(request(),tuple(H2,T2)) -> F() eqt(request(),tuplenil(H2)) -> F() eqt(resource(),nil()) -> F() eqt(resource(),a()) -> F() eqt(resource(),excl()) -> F() eqt(resource(),false()) -> F() eqt(resource(),lock()) -> F() eqt(resource(),locker()) -> F() eqt(resource(),mcrlrecord()) -> F() eqt(resource(),ok()) -> F() eqt(resource(),pending()) -> F() eqt(resource(),release()) -> F() eqt(resource(),request()) -> F() eqt(resource(),resource()) -> T() eqt(resource(),tag()) -> F() eqt(resource(),true()) -> F() eqt(resource(),undefined()) -> F() eqt(resource(),pid(N2)) -> F() eqt(resource(),int(N2)) -> F() eqt(resource(),cons(H2,T2)) -> F() eqt(resource(),tuple(H2,T2)) -> F() eqt(resource(),tuplenil(H2)) -> F() eqt(tag(),nil()) -> F() eqt(tag(),a()) -> F() eqt(tag(),excl()) -> F() eqt(tag(),false()) -> F() eqt(tag(),lock()) -> F() eqt(tag(),locker()) -> F() eqt(tag(),mcrlrecord()) -> F() eqt(tag(),ok()) -> F() eqt(tag(),pending()) -> F() eqt(tag(),release()) -> F() eqt(tag(),request()) -> F() eqt(tag(),resource()) -> F() eqt(tag(),tag()) -> T() eqt(tag(),true()) -> F() eqt(tag(),undefined()) -> F() eqt(tag(),pid(N2)) -> F() eqt(tag(),int(N2)) -> F() eqt(tag(),cons(H2,T2)) -> F() eqt(tag(),tuple(H2,T2)) -> F() eqt(tag(),tuplenil(H2)) -> F() eqt(true(),nil()) -> F() eqt(true(),a()) -> F() eqt(true(),excl()) -> F() eqt(true(),false()) -> F() eqt(true(),lock()) -> F() eqt(true(),locker()) -> F() eqt(true(),mcrlrecord()) -> F() eqt(true(),ok()) -> F() eqt(true(),pending()) -> F() eqt(true(),release()) -> F() eqt(true(),request()) -> F() eqt(true(),resource()) -> F() eqt(true(),tag()) -> F() eqt(true(),true()) -> T() eqt(true(),undefined()) -> F() eqt(true(),pid(N2)) -> F() eqt(true(),int(N2)) -> F() eqt(true(),cons(H2,T2)) -> F() eqt(true(),tuple(H2,T2)) -> F() eqt(true(),tuplenil(H2)) -> F() eqt(undefined(),nil()) -> F() eqt(undefined(),a()) -> F() eqt(undefined(),tuplenil(H2)) -> F() eqt(pid(N1),nil()) -> F() eqt(pid(N1),a()) -> F() eqt(pid(N1),excl()) -> F() eqt(pid(N1),false()) -> F() eqt(pid(N1),lock()) -> F() eqt(pid(N1),locker()) -> F() eqt(pid(N1),mcrlrecord()) -> F() eqt(pid(N1),ok()) -> F() eqt(pid(N1),pending()) -> F() eqt(pid(N1),release()) -> F() eqt(pid(N1),request()) -> F() eqt(pid(N1),resource()) -> F() eqt(pid(N1),tag()) -> F() eqt(pid(N1),true()) -> F() eqt(pid(N1),undefined()) -> F() eqt(pid(N1),pid(N2)) -> eqt(N1,N2) eqt(pid(N1),int(N2)) -> F() eqt(pid(N1),cons(H2,T2)) -> F() eqt(pid(N1),tuple(H2,T2)) -> F() eqt(pid(N1),tuplenil(H2)) -> F() eqt(int(N1),nil()) -> F() eqt(int(N1),a()) -> F() eqt(int(N1),excl()) -> F() eqt(int(N1),false()) -> F() eqt(int(N1),lock()) -> F() eqt(int(N1),locker()) -> F() eqt(int(N1),mcrlrecord()) -> F() eqt(int(N1),ok()) -> F() eqt(int(N1),pending()) -> F() eqt(int(N1),release()) -> F() eqt(int(N1),request()) -> F() eqt(int(N1),resource()) -> F() eqt(int(N1),tag()) -> F() eqt(int(N1),true()) -> F() eqt(int(N1),undefined()) -> F() eqt(cons(H1,T1),resource()) -> F() eqt(cons(H1,T1),tag()) -> F() eqt(cons(H1,T1),true()) -> F() eqt(cons(H1,T1),undefined()) -> F() eqt(cons(H1,T1),pid(N2)) -> F() eqt(cons(H1,T1),int(N2)) -> F() eqt(cons(H1,T1),cons(H2,T2)) -> and(eqt(H1,H2),eqt(T1,T2)) eqt(cons(H1,T1),tuple(H2,T2)) -> F() eqt(cons(H1,T1),tuplenil(H2)) -> F() eqt(tuple(H1,T1),nil()) -> F() eqt(tuple(H1,T1),a()) -> F() eqt(tuple(H1,T1),excl()) -> F() eqt(tuple(H1,T1),false()) -> F() eqt(tuple(H1,T1),lock()) -> F() eqt(tuple(H1,T1),locker()) -> F() eqt(tuple(H1,T1),mcrlrecord()) -> F() eqt(tuple(H1,T1),ok()) -> F() eqt(tuple(H1,T1),pending()) -> F() eqt(tuple(H1,T1),release()) -> F() eqt(tuple(H1,T1),request()) -> F() eqt(tuple(H1,T1),resource()) -> F() eqt(tuple(H1,T1),tag()) -> F() eqt(tuple(H1,T1),true()) -> F() eqt(tuple(H1,T1),undefined()) -> F() eqt(tuple(H1,T1),pid(N2)) -> F() eqt(tuple(H1,T1),int(N2)) -> F() eqt(tuple(H1,T1),cons(H2,T2)) -> F() eqt(tuple(H1,T1),tuple(H2,T2)) -> and(eqt(H1,H2),eqt(T1,T2)) eqt(tuple(H1,T1),tuplenil(H2)) -> F() eqt(tuplenil(H1),nil()) -> F() eqt(tuplenil(H1),a()) -> F() eqt(tuplenil(H1),excl()) -> F() eqt(tuplenil(H1),false()) -> F() eqt(tuplenil(H1),lock()) -> F() eqt(tuplenil(H1),locker()) -> F() eqt(tuplenil(H1),mcrlrecord()) -> F() eqt(tuplenil(H1),ok()) -> F() eqt(tuplenil(H1),pending()) -> F() eqt(tuplenil(H1),release()) -> F() eqt(tuplenil(H1),request()) -> F() eqt(tuplenil(H1),resource()) -> F() eqt(tuplenil(H1),tag()) -> F() eqt(tuplenil(H1),true()) -> F() eqt(tuplenil(H1),undefined()) -> F() eqt(tuplenil(H1),pid(N2)) -> F() eqt(tuplenil(H1),int(N2)) -> F() eqt(tuplenil(H1),cons(H2,T2)) -> F() eqt(tuplenil(H1),tuple(H2,T2)) -> F() eqt(tuplenil(H1),tuplenil(H2)) -> eqt(H1,H2) element(int(s(0())),tuplenil(T1)) -> T1 element(int(s(0())),tuple(T1,T2)) -> T1 element(int(s(s(N1))),tuple(T1,T2)) -> element(int(s(N1)),T2) record_new(lock()) -> tuple(mcrlrecord(),tuple(lock(),tuple(undefined(),tuple(nil(),tuplenil(nil()))))) record_extract(tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))), lock(),resource()) -> tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))) record_update(tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))), lock(),pending(),NewF) -> tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(NewF))))) record_updates(Record,Name,nil()) -> Record record_updates(Record,Name,cons(tuple(Field,tuplenil(NewF)),Fields)) -> record_updates(record_update(Record,Name,Field,NewF),Name,Fields) locker2_map_promote_pending(nil(),Pending) -> nil() locker2_map_promote_pending(cons(Lock,Locks),Pending) -> cons(locker2_promote_pending(Lock,Pending),locker2_map_promote_pending(Locks,Pending)) locker2_map_claim_lock(nil(),Resources,Client) -> nil() locker2_map_claim_lock(cons(Lock,Locks),Resources,Client) -> cons(locker2_claim_lock(Lock,Resources,Client),locker2_map_claim_lock(Locks,Resources,Client)) locker2_map_add_pending(nil(),Resources,Client) -> nil() locker2_promote_pending(Lock,Client) -> case0(Client,Lock,record_extract(Lock,lock(),pending())) case0(Client,Lock,cons(Client,Pendings)) -> record_updates(Lock,lock(),cons(tuple(excl(),tuplenil(Client)),cons ( tuple ( pending(),tuplenil(Pendings)), nil ()))) case0(Client,Lock,MCRLFree0) -> Lock locker2_remove_pending(Lock,Client) -> record_updates(Lock,lock(),cons(tuple(pending(),tuplenil(subtract (record_extract (Lock,lock(),pending()), cons(Client,nil())))), nil())) locker2_add_pending(Lock,Resources,Client) -> case1(Client,Resources,Lock,member(record_extract(Lock,lock(),resource()),Resources)) case1(Client,Resources,Lock,true()) -> record_updates(Lock,lock(),cons(tuple(pending(),tuplenil(append( record_extract ( Lock,lock(),pending()), cons (Client,nil())))), nil())) case1(Client,Resources,Lock,false()) -> Lock locker2_release_lock(Lock,Client) -> case2(Client,Lock,gen_modtageq(Client,record_extract(Lock,lock(),excl()))) case2(Client,Lock,true()) -> record_updates(Lock,lock(),cons(tuple(excllock(),excl()),nil())) case4(Client,Lock,MCRLFree1) -> false() locker2_obtainables(nil(),Client) -> true() locker2_obtainables(cons(Lock,Locks),Client) -> case5(Client,Locks,Lock,member(Client,record_extract(Lock,lock(),pending()))) case5(Client,Locks,Lock,true()) -> andt(locker2_obtainable(Lock,Client),locker2_obtainables(Locks,Client)) case5(Client,Locks,Lock,false()) -> locker2_obtainables(Locks,Client) locker2_check_available(Resource,nil()) -> false() locker2_check_available(Resource,cons(Lock,Locks)) -> case6(Locks,Lock,Resource,equal(Resource,record_extract(Lock,lock(),resource()))) case6(Locks,Lock,Resource,true()) -> andt(equal(record_extract(Lock,lock(),excl()),nil()),equal(record_extract (Lock,lock(),pending()), nil())) case6(Locks,Lock,Resource,false()) -> locker2_check_available(Resource,Locks) locker2_check_availables(nil(),Locks) -> true() locker2_check_availables(cons(Resource,Resources),Locks) -> andt(locker2_check_available(Resource,Locks),locker2_check_availables(Resources,Locks)) locker2_adduniq(nil(),List) -> List append(cons(Head,Tail),List) -> cons(Head,append(Tail,List)) subtract(List,nil()) -> List subtract(List,cons(Head,Tail)) -> subtract(delete(Head,List),Tail) delete(E,nil()) -> nil() delete(E,cons(Head,Tail)) -> case8(Tail,Head,E,equal(E,Head)) case8(Tail,Head,E,true()) -> Tail case8(Tail,Head,E,false()) -> cons(Head,delete(E,Tail)) gen_tag(Pid) -> tuple(Pid,tuplenil(tag())) gen_modtageq(Client1,Client2) -> equal(Client1,Client2) member(E,nil()) -> false() member(E,cons(Head,Tail)) -> case9(Tail,Head,E,equal(E,Head)) case9(Tail,Head,E,true()) -> true() case9(Tail,Head,E,false()) -> member(E,Tail) eqs(empty(),empty()) -> T() eqs(empty(),stack(E2,S2)) -> F() eqs(stack(E1,S1),empty()) -> F() eqs(stack(E1,S1),stack(E2,S2)) -> and(eqt(E1,E2),eqs(S1,S2)) pushs(E1,S1) -> stack(E1,S1) pops(stack(E1,S1)) -> S1 tops(stack(E1,S1)) -> E1 istops(E1,empty()) -> F() istops(E1,stack(E2,S1)) -> eqt(E1,E2) eqc(nocalls(),nocalls()) -> T() eqc(nocalls(),calls(E2,S2,CS2)) -> F() eqc(calls(E1,S1,CS1),nocalls()) -> F() eqc(calls(E1,S1,CS1),calls(E2,S2,CS2)) -> and(eqt(E1,E2),and(eqs(S1,S2),eqc(CS1,CS2))) push(E1,E2,nocalls()) -> calls(E1,stack(E2,empty()),nocalls()) push(E1,E2,calls(E3,S1,CS1)) -> push1(E1,E2,E3,S1,CS1,eqt(E1,E3)) push1(E1,E2,E3,S1,CS1,T()) -> calls(E3,pushs(E2,S1),CS1) Subterm Criterion Processor: simple projection: pi(delete#) = 1 pi(case8#) = 0 problem: DPs: case8#(Tail,Head,E,false()) -> delete#(E,Tail) TRS: or(T(),T()) -> T() or(F(),T()) -> T() or(T(),F()) -> T() or(F(),F()) -> F() and(T(),B) -> B and(B,T()) -> B and(F(),B) -> F() and(B,F()) -> F() imp(T(),B) -> B imp(F(),B) -> T() not(T()) -> F() not(F()) -> T() if(T(),B1,B2) -> B1 if(F(),B1,B2) -> B2 eq(T(),T()) -> T() eq(F(),F()) -> T() eq(T(),F()) -> F() eq(F(),T()) -> F() eqt(nil(),undefined()) -> F() eqt(nil(),pid(N2)) -> F() eqt(nil(),int(N2)) -> F() eqt(nil(),cons(H2,T2)) -> F() eqt(nil(),tuple(H2,T2)) -> F() eqt(nil(),tuplenil(H2)) -> F() eqt(a(),nil()) -> F() eqt(a(),a()) -> T() eqt(a(),excl()) -> F() eqt(a(),false()) -> F() eqt(a(),lock()) -> F() eqt(a(),locker()) -> F() eqt(a(),mcrlrecord()) -> F() eqt(a(),ok()) -> F() eqt(a(),pending()) -> F() eqt(a(),release()) -> F() eqt(a(),request()) -> F() eqt(a(),resource()) -> F() eqt(a(),tag()) -> F() eqt(a(),true()) -> F() eqt(a(),undefined()) -> F() eqt(a(),pid(N2)) -> F() eqt(a(),int(N2)) -> F() eqt(a(),cons(H2,T2)) -> F() eqt(a(),tuple(H2,T2)) -> F() eqt(a(),tuplenil(H2)) -> F() eqt(excl(),nil()) -> F() eqt(excl(),a()) -> F() eqt(excl(),excl()) -> T() eqt(excl(),false()) -> F() eqt(excl(),lock()) -> F() eqt(excl(),locker()) -> F() eqt(excl(),mcrlrecord()) -> F() eqt(excl(),ok()) -> F() eqt(excl(),pending()) -> F() eqt(excl(),release()) -> F() eqt(excl(),request()) -> F() eqt(excl(),resource()) -> F() eqt(excl(),tag()) -> F() eqt(excl(),true()) -> F() eqt(excl(),undefined()) -> F() eqt(excl(),pid(N2)) -> F() eqt(excl(),eqt(false(),int(N2))) -> F() eqt(false(),cons(H2,T2)) -> F() eqt(false(),tuple(H2,T2)) -> F() eqt(false(),tuplenil(H2)) -> F() eqt(lock(),nil()) -> F() eqt(lock(),a()) -> F() eqt(lock(),excl()) -> F() eqt(lock(),false()) -> F() eqt(lock(),lock()) -> T() eqt(lock(),locker()) -> F() eqt(lock(),mcrlrecord()) -> F() eqt(lock(),ok()) -> F() eqt(lock(),pending()) -> F() eqt(lock(),release()) -> F() eqt(lock(),request()) -> F() eqt(lock(),resource()) -> F() eqt(lock(),tag()) -> F() eqt(lock(),true()) -> F() eqt(lock(),undefined()) -> F() eqt(lock(),pid(N2)) -> F() eqt(lock(),int(N2)) -> F() eqt(lock(),cons(H2,T2)) -> F() eqt(lock(),tuple(H2,T2)) -> F() eqt(lock(),tuplenil(H2)) -> F() eqt(locker(),nil()) -> F() eqt(locker(),a()) -> F() eqt(locker(),excl()) -> F() eqt(locker(),false()) -> F() eqt(locker(),lock()) -> F() eqt(locker(),locker()) -> T() eqt(locker(),mcrlrecord()) -> F() eqt(locker(),ok()) -> F() eqt(locker(),pending()) -> F() eqt(locker(),release()) -> F() eqt(locker(),request()) -> F() eqt(locker(),resource()) -> F() eqt(locker(),tag()) -> F() eqt(locker(),true()) -> F() eqt(locker(),undefined()) -> F() eqt(locker(),pid(N2)) -> F() eqt(locker(),int(N2)) -> F() eqt(locker(),cons(H2,T2)) -> F() eqt(locker(),tuple(H2,T2)) -> F() eqt(locker(),tuplenil(H2)) -> F() eqt(mcrlrecord(),nil()) -> F() eqt(mcrlrecord(),a()) -> F() eqt(mcrlrecord(),excl()) -> F() eqt(mcrlrecord(),false()) -> F() eqt(mcrlrecord(),lock()) -> F() eqt(mcrlrecord(),locker()) -> F() eqt(mcrlrecord(),mcrlrecord()) -> T() eqt(mcrlrecord(),ok()) -> F() eqt(mcrlrecord(),pending()) -> F() eqt(mcrlrecord(),release()) -> F() eqt(mcrlrecord(),request()) -> F() eqt(mcrlrecord(),resource()) -> F() eqt(ok(),resource()) -> F() eqt(ok(),tag()) -> F() eqt(ok(),true()) -> F() eqt(ok(),undefined()) -> F() eqt(ok(),pid(N2)) -> F() eqt(ok(),int(N2)) -> F() eqt(ok(),cons(H2,T2)) -> F() eqt(ok(),tuple(H2,T2)) -> F() eqt(ok(),tuplenil(H2)) -> F() eqt(pending(),nil()) -> F() eqt(pending(),a()) -> F() eqt(pending(),excl()) -> F() eqt(pending(),false()) -> F() eqt(pending(),lock()) -> F() eqt(pending(),locker()) -> F() eqt(pending(),mcrlrecord()) -> F() eqt(pending(),ok()) -> F() eqt(pending(),pending()) -> T() eqt(pending(),release()) -> F() eqt(pending(),request()) -> F() eqt(pending(),resource()) -> F() eqt(pending(),tag()) -> F() eqt(pending(),true()) -> F() eqt(pending(),undefined()) -> F() eqt(pending(),pid(N2)) -> F() eqt(pending(),int(N2)) -> F() eqt(pending(),cons(H2,T2)) -> F() eqt(pending(),tuple(H2,T2)) -> F() eqt(pending(),tuplenil(H2)) -> F() eqt(release(),nil()) -> F() eqt(release(),a()) -> F() eqt(release(),excl()) -> F() eqt(release(),false()) -> F() eqt(release(),lock()) -> F() eqt(release(),locker()) -> F() eqt(release(),mcrlrecord()) -> F() eqt(release(),ok()) -> F() eqt(request(),mcrlrecord()) -> F() eqt(request(),ok()) -> F() eqt(request(),pending()) -> F() eqt(request(),release()) -> F() eqt(request(),request()) -> T() eqt(request(),resource()) -> F() eqt(request(),tag()) -> F() eqt(request(),true()) -> F() eqt(request(),undefined()) -> F() eqt(request(),pid(N2)) -> F() eqt(request(),int(N2)) -> F() eqt(request(),cons(H2,T2)) -> F() eqt(request(),tuple(H2,T2)) -> F() eqt(request(),tuplenil(H2)) -> F() eqt(resource(),nil()) -> F() eqt(resource(),a()) -> F() eqt(resource(),excl()) -> F() eqt(resource(),false()) -> F() eqt(resource(),lock()) -> F() eqt(resource(),locker()) -> F() eqt(resource(),mcrlrecord()) -> F() eqt(resource(),ok()) -> F() eqt(resource(),pending()) -> F() eqt(resource(),release()) -> F() eqt(resource(),request()) -> F() eqt(resource(),resource()) -> T() eqt(resource(),tag()) -> F() eqt(resource(),true()) -> F() eqt(resource(),undefined()) -> F() eqt(resource(),pid(N2)) -> F() eqt(resource(),int(N2)) -> F() eqt(resource(),cons(H2,T2)) -> F() eqt(resource(),tuple(H2,T2)) -> F() eqt(resource(),tuplenil(H2)) -> F() eqt(tag(),nil()) -> F() eqt(tag(),a()) -> F() eqt(tag(),excl()) -> F() eqt(tag(),false()) -> F() eqt(tag(),lock()) -> F() eqt(tag(),locker()) -> F() eqt(tag(),mcrlrecord()) -> F() eqt(tag(),ok()) -> F() eqt(tag(),pending()) -> F() eqt(tag(),release()) -> F() eqt(tag(),request()) -> F() eqt(tag(),resource()) -> F() eqt(tag(),tag()) -> T() eqt(tag(),true()) -> F() eqt(tag(),undefined()) -> F() eqt(tag(),pid(N2)) -> F() eqt(tag(),int(N2)) -> F() eqt(tag(),cons(H2,T2)) -> F() eqt(tag(),tuple(H2,T2)) -> F() eqt(tag(),tuplenil(H2)) -> F() eqt(true(),nil()) -> F() eqt(true(),a()) -> F() eqt(true(),excl()) -> F() eqt(true(),false()) -> F() eqt(true(),lock()) -> F() eqt(true(),locker()) -> F() eqt(true(),mcrlrecord()) -> F() eqt(true(),ok()) -> F() eqt(true(),pending()) -> F() eqt(true(),release()) -> F() eqt(true(),request()) -> F() eqt(true(),resource()) -> F() eqt(true(),tag()) -> F() eqt(true(),true()) -> T() eqt(true(),undefined()) -> F() eqt(true(),pid(N2)) -> F() eqt(true(),int(N2)) -> F() eqt(true(),cons(H2,T2)) -> F() eqt(true(),tuple(H2,T2)) -> F() eqt(true(),tuplenil(H2)) -> F() eqt(undefined(),nil()) -> F() eqt(undefined(),a()) -> F() eqt(undefined(),tuplenil(H2)) -> F() eqt(pid(N1),nil()) -> F() eqt(pid(N1),a()) -> F() eqt(pid(N1),excl()) -> F() eqt(pid(N1),false()) -> F() eqt(pid(N1),lock()) -> F() eqt(pid(N1),locker()) -> F() eqt(pid(N1),mcrlrecord()) -> F() eqt(pid(N1),ok()) -> F() eqt(pid(N1),pending()) -> F() eqt(pid(N1),release()) -> F() eqt(pid(N1),request()) -> F() eqt(pid(N1),resource()) -> F() eqt(pid(N1),tag()) -> F() eqt(pid(N1),true()) -> F() eqt(pid(N1),undefined()) -> F() eqt(pid(N1),pid(N2)) -> eqt(N1,N2) eqt(pid(N1),int(N2)) -> F() eqt(pid(N1),cons(H2,T2)) -> F() eqt(pid(N1),tuple(H2,T2)) -> F() eqt(pid(N1),tuplenil(H2)) -> F() eqt(int(N1),nil()) -> F() eqt(int(N1),a()) -> F() eqt(int(N1),excl()) -> F() eqt(int(N1),false()) -> F() eqt(int(N1),lock()) -> F() eqt(int(N1),locker()) -> F() eqt(int(N1),mcrlrecord()) -> F() eqt(int(N1),ok()) -> F() eqt(int(N1),pending()) -> F() eqt(int(N1),release()) -> F() eqt(int(N1),request()) -> F() eqt(int(N1),resource()) -> F() eqt(int(N1),tag()) -> F() eqt(int(N1),true()) -> F() eqt(int(N1),undefined()) -> F() eqt(cons(H1,T1),resource()) -> F() eqt(cons(H1,T1),tag()) -> F() eqt(cons(H1,T1),true()) -> F() eqt(cons(H1,T1),undefined()) -> F() eqt(cons(H1,T1),pid(N2)) -> F() eqt(cons(H1,T1),int(N2)) -> F() eqt(cons(H1,T1),cons(H2,T2)) -> and(eqt(H1,H2),eqt(T1,T2)) eqt(cons(H1,T1),tuple(H2,T2)) -> F() eqt(cons(H1,T1),tuplenil(H2)) -> F() eqt(tuple(H1,T1),nil()) -> F() eqt(tuple(H1,T1),a()) -> F() eqt(tuple(H1,T1),excl()) -> F() eqt(tuple(H1,T1),false()) -> F() eqt(tuple(H1,T1),lock()) -> F() eqt(tuple(H1,T1),locker()) -> F() eqt(tuple(H1,T1),mcrlrecord()) -> F() eqt(tuple(H1,T1),ok()) -> F() eqt(tuple(H1,T1),pending()) -> F() eqt(tuple(H1,T1),release()) -> F() eqt(tuple(H1,T1),request()) -> F() eqt(tuple(H1,T1),resource()) -> F() eqt(tuple(H1,T1),tag()) -> F() eqt(tuple(H1,T1),true()) -> F() eqt(tuple(H1,T1),undefined()) -> F() eqt(tuple(H1,T1),pid(N2)) -> F() eqt(tuple(H1,T1),int(N2)) -> F() eqt(tuple(H1,T1),cons(H2,T2)) -> F() eqt(tuple(H1,T1),tuple(H2,T2)) -> and(eqt(H1,H2),eqt(T1,T2)) eqt(tuple(H1,T1),tuplenil(H2)) -> F() eqt(tuplenil(H1),nil()) -> F() eqt(tuplenil(H1),a()) -> F() eqt(tuplenil(H1),excl()) -> F() eqt(tuplenil(H1),false()) -> F() eqt(tuplenil(H1),lock()) -> F() eqt(tuplenil(H1),locker()) -> F() eqt(tuplenil(H1),mcrlrecord()) -> F() eqt(tuplenil(H1),ok()) -> F() eqt(tuplenil(H1),pending()) -> F() eqt(tuplenil(H1),release()) -> F() eqt(tuplenil(H1),request()) -> F() eqt(tuplenil(H1),resource()) -> F() eqt(tuplenil(H1),tag()) -> F() eqt(tuplenil(H1),true()) -> F() eqt(tuplenil(H1),undefined()) -> F() eqt(tuplenil(H1),pid(N2)) -> F() eqt(tuplenil(H1),int(N2)) -> F() eqt(tuplenil(H1),cons(H2,T2)) -> F() eqt(tuplenil(H1),tuple(H2,T2)) -> F() eqt(tuplenil(H1),tuplenil(H2)) -> eqt(H1,H2) element(int(s(0())),tuplenil(T1)) -> T1 element(int(s(0())),tuple(T1,T2)) -> T1 element(int(s(s(N1))),tuple(T1,T2)) -> element(int(s(N1)),T2) record_new(lock()) -> tuple(mcrlrecord(),tuple(lock(),tuple(undefined(),tuple(nil(),tuplenil(nil()))))) record_extract(tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))), lock(),resource()) -> tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))) record_update(tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))), lock(),pending(),NewF) -> tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(NewF))))) record_updates(Record,Name,nil()) -> Record record_updates(Record,Name,cons(tuple(Field,tuplenil(NewF)),Fields)) -> record_updates(record_update(Record,Name,Field,NewF),Name,Fields) locker2_map_promote_pending(nil(),Pending) -> nil() locker2_map_promote_pending(cons(Lock,Locks),Pending) -> cons(locker2_promote_pending(Lock,Pending),locker2_map_promote_pending(Locks,Pending)) locker2_map_claim_lock(nil(),Resources,Client) -> nil() locker2_map_claim_lock(cons(Lock,Locks),Resources,Client) -> cons(locker2_claim_lock(Lock,Resources,Client),locker2_map_claim_lock (Locks,Resources,Client)) locker2_map_add_pending(nil(),Resources,Client) -> nil() locker2_promote_pending(Lock,Client) -> case0(Client,Lock,record_extract(Lock,lock(),pending())) case0(Client,Lock,cons(Client,Pendings)) -> record_updates(Lock,lock(),cons(tuple(excl(),tuplenil(Client)), cons(tuple(pending(),tuplenil(Pendings)),nil()))) case0(Client,Lock,MCRLFree0) -> Lock locker2_remove_pending(Lock,Client) -> record_updates(Lock,lock(),cons(tuple(pending(),tuplenil(subtract (record_extract (Lock,lock(),pending()), cons (Client,nil())))), nil())) locker2_add_pending(Lock,Resources,Client) -> case1(Client,Resources,Lock,member(record_extract(Lock,lock(),resource()),Resources)) case1(Client,Resources,Lock,true()) -> record_updates(Lock,lock(),cons(tuple(pending(),tuplenil(append (record_extract (Lock,lock(),pending()), cons (Client,nil())))), nil())) case1(Client,Resources,Lock,false()) -> Lock locker2_release_lock(Lock,Client) -> case2(Client,Lock,gen_modtageq(Client,record_extract(Lock,lock(),excl()))) case2(Client,Lock,true()) -> record_updates(Lock,lock(),cons(tuple(excllock(),excl()),nil())) case4(Client,Lock,MCRLFree1) -> false() locker2_obtainables(nil(),Client) -> true() locker2_obtainables(cons(Lock,Locks),Client) -> case5(Client,Locks,Lock,member(Client,record_extract(Lock,lock(),pending()))) case5(Client,Locks,Lock,true()) -> andt(locker2_obtainable(Lock,Client),locker2_obtainables(Locks,Client)) case5(Client,Locks,Lock,false()) -> locker2_obtainables(Locks,Client) locker2_check_available(Resource,nil()) -> false() locker2_check_available(Resource,cons(Lock,Locks)) -> case6(Locks,Lock,Resource,equal(Resource,record_extract(Lock,lock(),resource()))) case6(Locks,Lock,Resource,true()) -> andt(equal(record_extract(Lock,lock(),excl()),nil()),equal(record_extract (Lock,lock(),pending()), nil())) case6(Locks,Lock,Resource,false()) -> locker2_check_available(Resource,Locks) locker2_check_availables(nil(),Locks) -> true() locker2_check_availables(cons(Resource,Resources),Locks) -> andt(locker2_check_available(Resource,Locks),locker2_check_availables(Resources,Locks)) locker2_adduniq(nil(),List) -> List append(cons(Head,Tail),List) -> cons(Head,append(Tail,List)) subtract(List,nil()) -> List subtract(List,cons(Head,Tail)) -> subtract(delete(Head,List),Tail) delete(E,nil()) -> nil() delete(E,cons(Head,Tail)) -> case8(Tail,Head,E,equal(E,Head)) case8(Tail,Head,E,true()) -> Tail case8(Tail,Head,E,false()) -> cons(Head,delete(E,Tail)) gen_tag(Pid) -> tuple(Pid,tuplenil(tag())) gen_modtageq(Client1,Client2) -> equal(Client1,Client2) member(E,nil()) -> false() member(E,cons(Head,Tail)) -> case9(Tail,Head,E,equal(E,Head)) case9(Tail,Head,E,true()) -> true() case9(Tail,Head,E,false()) -> member(E,Tail) eqs(empty(),empty()) -> T() eqs(empty(),stack(E2,S2)) -> F() eqs(stack(E1,S1),empty()) -> F() eqs(stack(E1,S1),stack(E2,S2)) -> and(eqt(E1,E2),eqs(S1,S2)) pushs(E1,S1) -> stack(E1,S1) pops(stack(E1,S1)) -> S1 tops(stack(E1,S1)) -> E1 istops(E1,empty()) -> F() istops(E1,stack(E2,S1)) -> eqt(E1,E2) eqc(nocalls(),nocalls()) -> T() eqc(nocalls(),calls(E2,S2,CS2)) -> F() eqc(calls(E1,S1,CS1),nocalls()) -> F() eqc(calls(E1,S1,CS1),calls(E2,S2,CS2)) -> and(eqt(E1,E2),and(eqs(S1,S2),eqc(CS1,CS2))) push(E1,E2,nocalls()) -> calls(E1,stack(E2,empty()),nocalls()) push(E1,E2,calls(E3,S1,CS1)) -> push1(E1,E2,E3,S1,CS1,eqt(E1,E3)) push1(E1,E2,E3,S1,CS1,T()) -> calls(E3,pushs(E2,S1),CS1) SCC Processor: #sccs: 0 #rules: 0 #arcs: 2/1 DPs: case9#(Tail,Head,E,false()) -> member#(E,Tail) member#(E,cons(Head,Tail)) -> case9#(Tail,Head,E,equal(E,Head)) TRS: or(T(),T()) -> T() or(F(),T()) -> T() or(T(),F()) -> T() or(F(),F()) -> F() and(T(),B) -> B and(B,T()) -> B and(F(),B) -> F() and(B,F()) -> F() imp(T(),B) -> B imp(F(),B) -> T() not(T()) -> F() not(F()) -> T() if(T(),B1,B2) -> B1 if(F(),B1,B2) -> B2 eq(T(),T()) -> T() eq(F(),F()) -> T() eq(T(),F()) -> F() eq(F(),T()) -> F() eqt(nil(),undefined()) -> F() eqt(nil(),pid(N2)) -> F() eqt(nil(),int(N2)) -> F() eqt(nil(),cons(H2,T2)) -> F() eqt(nil(),tuple(H2,T2)) -> F() eqt(nil(),tuplenil(H2)) -> F() eqt(a(),nil()) -> F() eqt(a(),a()) -> T() eqt(a(),excl()) -> F() eqt(a(),false()) -> F() eqt(a(),lock()) -> F() eqt(a(),locker()) -> F() eqt(a(),mcrlrecord()) -> F() eqt(a(),ok()) -> F() eqt(a(),pending()) -> F() eqt(a(),release()) -> F() eqt(a(),request()) -> F() eqt(a(),resource()) -> F() eqt(a(),tag()) -> F() eqt(a(),true()) -> F() eqt(a(),undefined()) -> F() eqt(a(),pid(N2)) -> F() eqt(a(),int(N2)) -> F() eqt(a(),cons(H2,T2)) -> F() eqt(a(),tuple(H2,T2)) -> F() eqt(a(),tuplenil(H2)) -> F() eqt(excl(),nil()) -> F() eqt(excl(),a()) -> F() eqt(excl(),excl()) -> T() eqt(excl(),false()) -> F() eqt(excl(),lock()) -> F() eqt(excl(),locker()) -> F() eqt(excl(),mcrlrecord()) -> F() eqt(excl(),ok()) -> F() eqt(excl(),pending()) -> F() eqt(excl(),release()) -> F() eqt(excl(),request()) -> F() eqt(excl(),resource()) -> F() eqt(excl(),tag()) -> F() eqt(excl(),true()) -> F() eqt(excl(),undefined()) -> F() eqt(excl(),pid(N2)) -> F() eqt(excl(),eqt(false(),int(N2))) -> F() eqt(false(),cons(H2,T2)) -> F() eqt(false(),tuple(H2,T2)) -> F() eqt(false(),tuplenil(H2)) -> F() eqt(lock(),nil()) -> F() eqt(lock(),a()) -> F() eqt(lock(),excl()) -> F() eqt(lock(),false()) -> F() eqt(lock(),lock()) -> T() eqt(lock(),locker()) -> F() eqt(lock(),mcrlrecord()) -> F() eqt(lock(),ok()) -> F() eqt(lock(),pending()) -> F() eqt(lock(),release()) -> F() eqt(lock(),request()) -> F() eqt(lock(),resource()) -> F() eqt(lock(),tag()) -> F() eqt(lock(),true()) -> F() eqt(lock(),undefined()) -> F() eqt(lock(),pid(N2)) -> F() eqt(lock(),int(N2)) -> F() eqt(lock(),cons(H2,T2)) -> F() eqt(lock(),tuple(H2,T2)) -> F() eqt(lock(),tuplenil(H2)) -> F() eqt(locker(),nil()) -> F() eqt(locker(),a()) -> F() eqt(locker(),excl()) -> F() eqt(locker(),false()) -> F() eqt(locker(),lock()) -> F() eqt(locker(),locker()) -> T() eqt(locker(),mcrlrecord()) -> F() eqt(locker(),ok()) -> F() eqt(locker(),pending()) -> F() eqt(locker(),release()) -> F() eqt(locker(),request()) -> F() eqt(locker(),resource()) -> F() eqt(locker(),tag()) -> F() eqt(locker(),true()) -> F() eqt(locker(),undefined()) -> F() eqt(locker(),pid(N2)) -> F() eqt(locker(),int(N2)) -> F() eqt(locker(),cons(H2,T2)) -> F() eqt(locker(),tuple(H2,T2)) -> F() eqt(locker(),tuplenil(H2)) -> F() eqt(mcrlrecord(),nil()) -> F() eqt(mcrlrecord(),a()) -> F() eqt(mcrlrecord(),excl()) -> F() eqt(mcrlrecord(),false()) -> F() eqt(mcrlrecord(),lock()) -> F() eqt(mcrlrecord(),locker()) -> F() eqt(mcrlrecord(),mcrlrecord()) -> T() eqt(mcrlrecord(),ok()) -> F() eqt(mcrlrecord(),pending()) -> F() eqt(mcrlrecord(),release()) -> F() eqt(mcrlrecord(),request()) -> F() eqt(mcrlrecord(),resource()) -> F() eqt(ok(),resource()) -> F() eqt(ok(),tag()) -> F() eqt(ok(),true()) -> F() eqt(ok(),undefined()) -> F() eqt(ok(),pid(N2)) -> F() eqt(ok(),int(N2)) -> F() eqt(ok(),cons(H2,T2)) -> F() eqt(ok(),tuple(H2,T2)) -> F() eqt(ok(),tuplenil(H2)) -> F() eqt(pending(),nil()) -> F() eqt(pending(),a()) -> F() eqt(pending(),excl()) -> F() eqt(pending(),false()) -> F() eqt(pending(),lock()) -> F() eqt(pending(),locker()) -> F() eqt(pending(),mcrlrecord()) -> F() eqt(pending(),ok()) -> F() eqt(pending(),pending()) -> T() eqt(pending(),release()) -> F() eqt(pending(),request()) -> F() eqt(pending(),resource()) -> F() eqt(pending(),tag()) -> F() eqt(pending(),true()) -> F() eqt(pending(),undefined()) -> F() eqt(pending(),pid(N2)) -> F() eqt(pending(),int(N2)) -> F() eqt(pending(),cons(H2,T2)) -> F() eqt(pending(),tuple(H2,T2)) -> F() eqt(pending(),tuplenil(H2)) -> F() eqt(release(),nil()) -> F() eqt(release(),a()) -> F() eqt(release(),excl()) -> F() eqt(release(),false()) -> F() eqt(release(),lock()) -> F() eqt(release(),locker()) -> F() eqt(release(),mcrlrecord()) -> F() eqt(release(),ok()) -> F() eqt(request(),mcrlrecord()) -> F() eqt(request(),ok()) -> F() eqt(request(),pending()) -> F() eqt(request(),release()) -> F() eqt(request(),request()) -> T() eqt(request(),resource()) -> F() eqt(request(),tag()) -> F() eqt(request(),true()) -> F() eqt(request(),undefined()) -> F() eqt(request(),pid(N2)) -> F() eqt(request(),int(N2)) -> F() eqt(request(),cons(H2,T2)) -> F() eqt(request(),tuple(H2,T2)) -> F() eqt(request(),tuplenil(H2)) -> F() eqt(resource(),nil()) -> F() eqt(resource(),a()) -> F() eqt(resource(),excl()) -> F() eqt(resource(),false()) -> F() eqt(resource(),lock()) -> F() eqt(resource(),locker()) -> F() eqt(resource(),mcrlrecord()) -> F() eqt(resource(),ok()) -> F() eqt(resource(),pending()) -> F() eqt(resource(),release()) -> F() eqt(resource(),request()) -> F() eqt(resource(),resource()) -> T() eqt(resource(),tag()) -> F() eqt(resource(),true()) -> F() eqt(resource(),undefined()) -> F() eqt(resource(),pid(N2)) -> F() eqt(resource(),int(N2)) -> F() eqt(resource(),cons(H2,T2)) -> F() eqt(resource(),tuple(H2,T2)) -> F() eqt(resource(),tuplenil(H2)) -> F() eqt(tag(),nil()) -> F() eqt(tag(),a()) -> F() eqt(tag(),excl()) -> F() eqt(tag(),false()) -> F() eqt(tag(),lock()) -> F() eqt(tag(),locker()) -> F() eqt(tag(),mcrlrecord()) -> F() eqt(tag(),ok()) -> F() eqt(tag(),pending()) -> F() eqt(tag(),release()) -> F() eqt(tag(),request()) -> F() eqt(tag(),resource()) -> F() eqt(tag(),tag()) -> T() eqt(tag(),true()) -> F() eqt(tag(),undefined()) -> F() eqt(tag(),pid(N2)) -> F() eqt(tag(),int(N2)) -> F() eqt(tag(),cons(H2,T2)) -> F() eqt(tag(),tuple(H2,T2)) -> F() eqt(tag(),tuplenil(H2)) -> F() eqt(true(),nil()) -> F() eqt(true(),a()) -> F() eqt(true(),excl()) -> F() eqt(true(),false()) -> F() eqt(true(),lock()) -> F() eqt(true(),locker()) -> F() eqt(true(),mcrlrecord()) -> F() eqt(true(),ok()) -> F() eqt(true(),pending()) -> F() eqt(true(),release()) -> F() eqt(true(),request()) -> F() eqt(true(),resource()) -> F() eqt(true(),tag()) -> F() eqt(true(),true()) -> T() eqt(true(),undefined()) -> F() eqt(true(),pid(N2)) -> F() eqt(true(),int(N2)) -> F() eqt(true(),cons(H2,T2)) -> F() eqt(true(),tuple(H2,T2)) -> F() eqt(true(),tuplenil(H2)) -> F() eqt(undefined(),nil()) -> F() eqt(undefined(),a()) -> F() eqt(undefined(),tuplenil(H2)) -> F() eqt(pid(N1),nil()) -> F() eqt(pid(N1),a()) -> F() eqt(pid(N1),excl()) -> F() eqt(pid(N1),false()) -> F() eqt(pid(N1),lock()) -> F() eqt(pid(N1),locker()) -> F() eqt(pid(N1),mcrlrecord()) -> F() eqt(pid(N1),ok()) -> F() eqt(pid(N1),pending()) -> F() eqt(pid(N1),release()) -> F() eqt(pid(N1),request()) -> F() eqt(pid(N1),resource()) -> F() eqt(pid(N1),tag()) -> F() eqt(pid(N1),true()) -> F() eqt(pid(N1),undefined()) -> F() eqt(pid(N1),pid(N2)) -> eqt(N1,N2) eqt(pid(N1),int(N2)) -> F() eqt(pid(N1),cons(H2,T2)) -> F() eqt(pid(N1),tuple(H2,T2)) -> F() eqt(pid(N1),tuplenil(H2)) -> F() eqt(int(N1),nil()) -> F() eqt(int(N1),a()) -> F() eqt(int(N1),excl()) -> F() eqt(int(N1),false()) -> F() eqt(int(N1),lock()) -> F() eqt(int(N1),locker()) -> F() eqt(int(N1),mcrlrecord()) -> F() eqt(int(N1),ok()) -> F() eqt(int(N1),pending()) -> F() eqt(int(N1),release()) -> F() eqt(int(N1),request()) -> F() eqt(int(N1),resource()) -> F() eqt(int(N1),tag()) -> F() eqt(int(N1),true()) -> F() eqt(int(N1),undefined()) -> F() eqt(cons(H1,T1),resource()) -> F() eqt(cons(H1,T1),tag()) -> F() eqt(cons(H1,T1),true()) -> F() eqt(cons(H1,T1),undefined()) -> F() eqt(cons(H1,T1),pid(N2)) -> F() eqt(cons(H1,T1),int(N2)) -> F() eqt(cons(H1,T1),cons(H2,T2)) -> and(eqt(H1,H2),eqt(T1,T2)) eqt(cons(H1,T1),tuple(H2,T2)) -> F() eqt(cons(H1,T1),tuplenil(H2)) -> F() eqt(tuple(H1,T1),nil()) -> F() eqt(tuple(H1,T1),a()) -> F() eqt(tuple(H1,T1),excl()) -> F() eqt(tuple(H1,T1),false()) -> F() eqt(tuple(H1,T1),lock()) -> F() eqt(tuple(H1,T1),locker()) -> F() eqt(tuple(H1,T1),mcrlrecord()) -> F() eqt(tuple(H1,T1),ok()) -> F() eqt(tuple(H1,T1),pending()) -> F() eqt(tuple(H1,T1),release()) -> F() eqt(tuple(H1,T1),request()) -> F() eqt(tuple(H1,T1),resource()) -> F() eqt(tuple(H1,T1),tag()) -> F() eqt(tuple(H1,T1),true()) -> F() eqt(tuple(H1,T1),undefined()) -> F() eqt(tuple(H1,T1),pid(N2)) -> F() eqt(tuple(H1,T1),int(N2)) -> F() eqt(tuple(H1,T1),cons(H2,T2)) -> F() eqt(tuple(H1,T1),tuple(H2,T2)) -> and(eqt(H1,H2),eqt(T1,T2)) eqt(tuple(H1,T1),tuplenil(H2)) -> F() eqt(tuplenil(H1),nil()) -> F() eqt(tuplenil(H1),a()) -> F() eqt(tuplenil(H1),excl()) -> F() eqt(tuplenil(H1),false()) -> F() eqt(tuplenil(H1),lock()) -> F() eqt(tuplenil(H1),locker()) -> F() eqt(tuplenil(H1),mcrlrecord()) -> F() eqt(tuplenil(H1),ok()) -> F() eqt(tuplenil(H1),pending()) -> F() eqt(tuplenil(H1),release()) -> F() eqt(tuplenil(H1),request()) -> F() eqt(tuplenil(H1),resource()) -> F() eqt(tuplenil(H1),tag()) -> F() eqt(tuplenil(H1),true()) -> F() eqt(tuplenil(H1),undefined()) -> F() eqt(tuplenil(H1),pid(N2)) -> F() eqt(tuplenil(H1),int(N2)) -> F() eqt(tuplenil(H1),cons(H2,T2)) -> F() eqt(tuplenil(H1),tuple(H2,T2)) -> F() eqt(tuplenil(H1),tuplenil(H2)) -> eqt(H1,H2) element(int(s(0())),tuplenil(T1)) -> T1 element(int(s(0())),tuple(T1,T2)) -> T1 element(int(s(s(N1))),tuple(T1,T2)) -> element(int(s(N1)),T2) record_new(lock()) -> tuple(mcrlrecord(),tuple(lock(),tuple(undefined(),tuple(nil(),tuplenil(nil()))))) record_extract(tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))), lock(),resource()) -> tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))) record_update(tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))), lock(),pending(),NewF) -> tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(NewF))))) record_updates(Record,Name,nil()) -> Record record_updates(Record,Name,cons(tuple(Field,tuplenil(NewF)),Fields)) -> record_updates(record_update(Record,Name,Field,NewF),Name,Fields) locker2_map_promote_pending(nil(),Pending) -> nil() locker2_map_promote_pending(cons(Lock,Locks),Pending) -> cons(locker2_promote_pending(Lock,Pending),locker2_map_promote_pending(Locks,Pending)) locker2_map_claim_lock(nil(),Resources,Client) -> nil() locker2_map_claim_lock(cons(Lock,Locks),Resources,Client) -> cons(locker2_claim_lock(Lock,Resources,Client),locker2_map_claim_lock(Locks,Resources,Client)) locker2_map_add_pending(nil(),Resources,Client) -> nil() locker2_promote_pending(Lock,Client) -> case0(Client,Lock,record_extract(Lock,lock(),pending())) case0(Client,Lock,cons(Client,Pendings)) -> record_updates(Lock,lock(),cons(tuple(excl(),tuplenil(Client)),cons ( tuple ( pending(),tuplenil(Pendings)), nil ()))) case0(Client,Lock,MCRLFree0) -> Lock locker2_remove_pending(Lock,Client) -> record_updates(Lock,lock(),cons(tuple(pending(),tuplenil(subtract (record_extract (Lock,lock(),pending()), cons(Client,nil())))), nil())) locker2_add_pending(Lock,Resources,Client) -> case1(Client,Resources,Lock,member(record_extract(Lock,lock(),resource()),Resources)) case1(Client,Resources,Lock,true()) -> record_updates(Lock,lock(),cons(tuple(pending(),tuplenil(append( record_extract ( Lock,lock(),pending()), cons (Client,nil())))), nil())) case1(Client,Resources,Lock,false()) -> Lock locker2_release_lock(Lock,Client) -> case2(Client,Lock,gen_modtageq(Client,record_extract(Lock,lock(),excl()))) case2(Client,Lock,true()) -> record_updates(Lock,lock(),cons(tuple(excllock(),excl()),nil())) case4(Client,Lock,MCRLFree1) -> false() locker2_obtainables(nil(),Client) -> true() locker2_obtainables(cons(Lock,Locks),Client) -> case5(Client,Locks,Lock,member(Client,record_extract(Lock,lock(),pending()))) case5(Client,Locks,Lock,true()) -> andt(locker2_obtainable(Lock,Client),locker2_obtainables(Locks,Client)) case5(Client,Locks,Lock,false()) -> locker2_obtainables(Locks,Client) locker2_check_available(Resource,nil()) -> false() locker2_check_available(Resource,cons(Lock,Locks)) -> case6(Locks,Lock,Resource,equal(Resource,record_extract(Lock,lock(),resource()))) case6(Locks,Lock,Resource,true()) -> andt(equal(record_extract(Lock,lock(),excl()),nil()),equal(record_extract (Lock,lock(),pending()), nil())) case6(Locks,Lock,Resource,false()) -> locker2_check_available(Resource,Locks) locker2_check_availables(nil(),Locks) -> true() locker2_check_availables(cons(Resource,Resources),Locks) -> andt(locker2_check_available(Resource,Locks),locker2_check_availables(Resources,Locks)) locker2_adduniq(nil(),List) -> List append(cons(Head,Tail),List) -> cons(Head,append(Tail,List)) subtract(List,nil()) -> List subtract(List,cons(Head,Tail)) -> subtract(delete(Head,List),Tail) delete(E,nil()) -> nil() delete(E,cons(Head,Tail)) -> case8(Tail,Head,E,equal(E,Head)) case8(Tail,Head,E,true()) -> Tail case8(Tail,Head,E,false()) -> cons(Head,delete(E,Tail)) gen_tag(Pid) -> tuple(Pid,tuplenil(tag())) gen_modtageq(Client1,Client2) -> equal(Client1,Client2) member(E,nil()) -> false() member(E,cons(Head,Tail)) -> case9(Tail,Head,E,equal(E,Head)) case9(Tail,Head,E,true()) -> true() case9(Tail,Head,E,false()) -> member(E,Tail) eqs(empty(),empty()) -> T() eqs(empty(),stack(E2,S2)) -> F() eqs(stack(E1,S1),empty()) -> F() eqs(stack(E1,S1),stack(E2,S2)) -> and(eqt(E1,E2),eqs(S1,S2)) pushs(E1,S1) -> stack(E1,S1) pops(stack(E1,S1)) -> S1 tops(stack(E1,S1)) -> E1 istops(E1,empty()) -> F() istops(E1,stack(E2,S1)) -> eqt(E1,E2) eqc(nocalls(),nocalls()) -> T() eqc(nocalls(),calls(E2,S2,CS2)) -> F() eqc(calls(E1,S1,CS1),nocalls()) -> F() eqc(calls(E1,S1,CS1),calls(E2,S2,CS2)) -> and(eqt(E1,E2),and(eqs(S1,S2),eqc(CS1,CS2))) push(E1,E2,nocalls()) -> calls(E1,stack(E2,empty()),nocalls()) push(E1,E2,calls(E3,S1,CS1)) -> push1(E1,E2,E3,S1,CS1,eqt(E1,E3)) push1(E1,E2,E3,S1,CS1,T()) -> calls(E3,pushs(E2,S1),CS1) Subterm Criterion Processor: simple projection: pi(member#) = 1 pi(case9#) = 0 problem: DPs: case9#(Tail,Head,E,false()) -> member#(E,Tail) TRS: or(T(),T()) -> T() or(F(),T()) -> T() or(T(),F()) -> T() or(F(),F()) -> F() and(T(),B) -> B and(B,T()) -> B and(F(),B) -> F() and(B,F()) -> F() imp(T(),B) -> B imp(F(),B) -> T() not(T()) -> F() not(F()) -> T() if(T(),B1,B2) -> B1 if(F(),B1,B2) -> B2 eq(T(),T()) -> T() eq(F(),F()) -> T() eq(T(),F()) -> F() eq(F(),T()) -> F() eqt(nil(),undefined()) -> F() eqt(nil(),pid(N2)) -> F() eqt(nil(),int(N2)) -> F() eqt(nil(),cons(H2,T2)) -> F() eqt(nil(),tuple(H2,T2)) -> F() eqt(nil(),tuplenil(H2)) -> F() eqt(a(),nil()) -> F() eqt(a(),a()) -> T() eqt(a(),excl()) -> F() eqt(a(),false()) -> F() eqt(a(),lock()) -> F() eqt(a(),locker()) -> F() eqt(a(),mcrlrecord()) -> F() eqt(a(),ok()) -> F() eqt(a(),pending()) -> F() eqt(a(),release()) -> F() eqt(a(),request()) -> F() eqt(a(),resource()) -> F() eqt(a(),tag()) -> F() eqt(a(),true()) -> F() eqt(a(),undefined()) -> F() eqt(a(),pid(N2)) -> F() eqt(a(),int(N2)) -> F() eqt(a(),cons(H2,T2)) -> F() eqt(a(),tuple(H2,T2)) -> F() eqt(a(),tuplenil(H2)) -> F() eqt(excl(),nil()) -> F() eqt(excl(),a()) -> F() eqt(excl(),excl()) -> T() eqt(excl(),false()) -> F() eqt(excl(),lock()) -> F() eqt(excl(),locker()) -> F() eqt(excl(),mcrlrecord()) -> F() eqt(excl(),ok()) -> F() eqt(excl(),pending()) -> F() eqt(excl(),release()) -> F() eqt(excl(),request()) -> F() eqt(excl(),resource()) -> F() eqt(excl(),tag()) -> F() eqt(excl(),true()) -> F() eqt(excl(),undefined()) -> F() eqt(excl(),pid(N2)) -> F() eqt(excl(),eqt(false(),int(N2))) -> F() eqt(false(),cons(H2,T2)) -> F() eqt(false(),tuple(H2,T2)) -> F() eqt(false(),tuplenil(H2)) -> F() eqt(lock(),nil()) -> F() eqt(lock(),a()) -> F() eqt(lock(),excl()) -> F() eqt(lock(),false()) -> F() eqt(lock(),lock()) -> T() eqt(lock(),locker()) -> F() eqt(lock(),mcrlrecord()) -> F() eqt(lock(),ok()) -> F() eqt(lock(),pending()) -> F() eqt(lock(),release()) -> F() eqt(lock(),request()) -> F() eqt(lock(),resource()) -> F() eqt(lock(),tag()) -> F() eqt(lock(),true()) -> F() eqt(lock(),undefined()) -> F() eqt(lock(),pid(N2)) -> F() eqt(lock(),int(N2)) -> F() eqt(lock(),cons(H2,T2)) -> F() eqt(lock(),tuple(H2,T2)) -> F() eqt(lock(),tuplenil(H2)) -> F() eqt(locker(),nil()) -> F() eqt(locker(),a()) -> F() eqt(locker(),excl()) -> F() eqt(locker(),false()) -> F() eqt(locker(),lock()) -> F() eqt(locker(),locker()) -> T() eqt(locker(),mcrlrecord()) -> F() eqt(locker(),ok()) -> F() eqt(locker(),pending()) -> F() eqt(locker(),release()) -> F() eqt(locker(),request()) -> F() eqt(locker(),resource()) -> F() eqt(locker(),tag()) -> F() eqt(locker(),true()) -> F() eqt(locker(),undefined()) -> F() eqt(locker(),pid(N2)) -> F() eqt(locker(),int(N2)) -> F() eqt(locker(),cons(H2,T2)) -> F() eqt(locker(),tuple(H2,T2)) -> F() eqt(locker(),tuplenil(H2)) -> F() eqt(mcrlrecord(),nil()) -> F() eqt(mcrlrecord(),a()) -> F() eqt(mcrlrecord(),excl()) -> F() eqt(mcrlrecord(),false()) -> F() eqt(mcrlrecord(),lock()) -> F() eqt(mcrlrecord(),locker()) -> F() eqt(mcrlrecord(),mcrlrecord()) -> T() eqt(mcrlrecord(),ok()) -> F() eqt(mcrlrecord(),pending()) -> F() eqt(mcrlrecord(),release()) -> F() eqt(mcrlrecord(),request()) -> F() eqt(mcrlrecord(),resource()) -> F() eqt(ok(),resource()) -> F() eqt(ok(),tag()) -> F() eqt(ok(),true()) -> F() eqt(ok(),undefined()) -> F() eqt(ok(),pid(N2)) -> F() eqt(ok(),int(N2)) -> F() eqt(ok(),cons(H2,T2)) -> F() eqt(ok(),tuple(H2,T2)) -> F() eqt(ok(),tuplenil(H2)) -> F() eqt(pending(),nil()) -> F() eqt(pending(),a()) -> F() eqt(pending(),excl()) -> F() eqt(pending(),false()) -> F() eqt(pending(),lock()) -> F() eqt(pending(),locker()) -> F() eqt(pending(),mcrlrecord()) -> F() eqt(pending(),ok()) -> F() eqt(pending(),pending()) -> T() eqt(pending(),release()) -> F() eqt(pending(),request()) -> F() eqt(pending(),resource()) -> F() eqt(pending(),tag()) -> F() eqt(pending(),true()) -> F() eqt(pending(),undefined()) -> F() eqt(pending(),pid(N2)) -> F() eqt(pending(),int(N2)) -> F() eqt(pending(),cons(H2,T2)) -> F() eqt(pending(),tuple(H2,T2)) -> F() eqt(pending(),tuplenil(H2)) -> F() eqt(release(),nil()) -> F() eqt(release(),a()) -> F() eqt(release(),excl()) -> F() eqt(release(),false()) -> F() eqt(release(),lock()) -> F() eqt(release(),locker()) -> F() eqt(release(),mcrlrecord()) -> F() eqt(release(),ok()) -> F() eqt(request(),mcrlrecord()) -> F() eqt(request(),ok()) -> F() eqt(request(),pending()) -> F() eqt(request(),release()) -> F() eqt(request(),request()) -> T() eqt(request(),resource()) -> F() eqt(request(),tag()) -> F() eqt(request(),true()) -> F() eqt(request(),undefined()) -> F() eqt(request(),pid(N2)) -> F() eqt(request(),int(N2)) -> F() eqt(request(),cons(H2,T2)) -> F() eqt(request(),tuple(H2,T2)) -> F() eqt(request(),tuplenil(H2)) -> F() eqt(resource(),nil()) -> F() eqt(resource(),a()) -> F() eqt(resource(),excl()) -> F() eqt(resource(),false()) -> F() eqt(resource(),lock()) -> F() eqt(resource(),locker()) -> F() eqt(resource(),mcrlrecord()) -> F() eqt(resource(),ok()) -> F() eqt(resource(),pending()) -> F() eqt(resource(),release()) -> F() eqt(resource(),request()) -> F() eqt(resource(),resource()) -> T() eqt(resource(),tag()) -> F() eqt(resource(),true()) -> F() eqt(resource(),undefined()) -> F() eqt(resource(),pid(N2)) -> F() eqt(resource(),int(N2)) -> F() eqt(resource(),cons(H2,T2)) -> F() eqt(resource(),tuple(H2,T2)) -> F() eqt(resource(),tuplenil(H2)) -> F() eqt(tag(),nil()) -> F() eqt(tag(),a()) -> F() eqt(tag(),excl()) -> F() eqt(tag(),false()) -> F() eqt(tag(),lock()) -> F() eqt(tag(),locker()) -> F() eqt(tag(),mcrlrecord()) -> F() eqt(tag(),ok()) -> F() eqt(tag(),pending()) -> F() eqt(tag(),release()) -> F() eqt(tag(),request()) -> F() eqt(tag(),resource()) -> F() eqt(tag(),tag()) -> T() eqt(tag(),true()) -> F() eqt(tag(),undefined()) -> F() eqt(tag(),pid(N2)) -> F() eqt(tag(),int(N2)) -> F() eqt(tag(),cons(H2,T2)) -> F() eqt(tag(),tuple(H2,T2)) -> F() eqt(tag(),tuplenil(H2)) -> F() eqt(true(),nil()) -> F() eqt(true(),a()) -> F() eqt(true(),excl()) -> F() eqt(true(),false()) -> F() eqt(true(),lock()) -> F() eqt(true(),locker()) -> F() eqt(true(),mcrlrecord()) -> F() eqt(true(),ok()) -> F() eqt(true(),pending()) -> F() eqt(true(),release()) -> F() eqt(true(),request()) -> F() eqt(true(),resource()) -> F() eqt(true(),tag()) -> F() eqt(true(),true()) -> T() eqt(true(),undefined()) -> F() eqt(true(),pid(N2)) -> F() eqt(true(),int(N2)) -> F() eqt(true(),cons(H2,T2)) -> F() eqt(true(),tuple(H2,T2)) -> F() eqt(true(),tuplenil(H2)) -> F() eqt(undefined(),nil()) -> F() eqt(undefined(),a()) -> F() eqt(undefined(),tuplenil(H2)) -> F() eqt(pid(N1),nil()) -> F() eqt(pid(N1),a()) -> F() eqt(pid(N1),excl()) -> F() eqt(pid(N1),false()) -> F() eqt(pid(N1),lock()) -> F() eqt(pid(N1),locker()) -> F() eqt(pid(N1),mcrlrecord()) -> F() eqt(pid(N1),ok()) -> F() eqt(pid(N1),pending()) -> F() eqt(pid(N1),release()) -> F() eqt(pid(N1),request()) -> F() eqt(pid(N1),resource()) -> F() eqt(pid(N1),tag()) -> F() eqt(pid(N1),true()) -> F() eqt(pid(N1),undefined()) -> F() eqt(pid(N1),pid(N2)) -> eqt(N1,N2) eqt(pid(N1),int(N2)) -> F() eqt(pid(N1),cons(H2,T2)) -> F() eqt(pid(N1),tuple(H2,T2)) -> F() eqt(pid(N1),tuplenil(H2)) -> F() eqt(int(N1),nil()) -> F() eqt(int(N1),a()) -> F() eqt(int(N1),excl()) -> F() eqt(int(N1),false()) -> F() eqt(int(N1),lock()) -> F() eqt(int(N1),locker()) -> F() eqt(int(N1),mcrlrecord()) -> F() eqt(int(N1),ok()) -> F() eqt(int(N1),pending()) -> F() eqt(int(N1),release()) -> F() eqt(int(N1),request()) -> F() eqt(int(N1),resource()) -> F() eqt(int(N1),tag()) -> F() eqt(int(N1),true()) -> F() eqt(int(N1),undefined()) -> F() eqt(cons(H1,T1),resource()) -> F() eqt(cons(H1,T1),tag()) -> F() eqt(cons(H1,T1),true()) -> F() eqt(cons(H1,T1),undefined()) -> F() eqt(cons(H1,T1),pid(N2)) -> F() eqt(cons(H1,T1),int(N2)) -> F() eqt(cons(H1,T1),cons(H2,T2)) -> and(eqt(H1,H2),eqt(T1,T2)) eqt(cons(H1,T1),tuple(H2,T2)) -> F() eqt(cons(H1,T1),tuplenil(H2)) -> F() eqt(tuple(H1,T1),nil()) -> F() eqt(tuple(H1,T1),a()) -> F() eqt(tuple(H1,T1),excl()) -> F() eqt(tuple(H1,T1),false()) -> F() eqt(tuple(H1,T1),lock()) -> F() eqt(tuple(H1,T1),locker()) -> F() eqt(tuple(H1,T1),mcrlrecord()) -> F() eqt(tuple(H1,T1),ok()) -> F() eqt(tuple(H1,T1),pending()) -> F() eqt(tuple(H1,T1),release()) -> F() eqt(tuple(H1,T1),request()) -> F() eqt(tuple(H1,T1),resource()) -> F() eqt(tuple(H1,T1),tag()) -> F() eqt(tuple(H1,T1),true()) -> F() eqt(tuple(H1,T1),undefined()) -> F() eqt(tuple(H1,T1),pid(N2)) -> F() eqt(tuple(H1,T1),int(N2)) -> F() eqt(tuple(H1,T1),cons(H2,T2)) -> F() eqt(tuple(H1,T1),tuple(H2,T2)) -> and(eqt(H1,H2),eqt(T1,T2)) eqt(tuple(H1,T1),tuplenil(H2)) -> F() eqt(tuplenil(H1),nil()) -> F() eqt(tuplenil(H1),a()) -> F() eqt(tuplenil(H1),excl()) -> F() eqt(tuplenil(H1),false()) -> F() eqt(tuplenil(H1),lock()) -> F() eqt(tuplenil(H1),locker()) -> F() eqt(tuplenil(H1),mcrlrecord()) -> F() eqt(tuplenil(H1),ok()) -> F() eqt(tuplenil(H1),pending()) -> F() eqt(tuplenil(H1),release()) -> F() eqt(tuplenil(H1),request()) -> F() eqt(tuplenil(H1),resource()) -> F() eqt(tuplenil(H1),tag()) -> F() eqt(tuplenil(H1),true()) -> F() eqt(tuplenil(H1),undefined()) -> F() eqt(tuplenil(H1),pid(N2)) -> F() eqt(tuplenil(H1),int(N2)) -> F() eqt(tuplenil(H1),cons(H2,T2)) -> F() eqt(tuplenil(H1),tuple(H2,T2)) -> F() eqt(tuplenil(H1),tuplenil(H2)) -> eqt(H1,H2) element(int(s(0())),tuplenil(T1)) -> T1 element(int(s(0())),tuple(T1,T2)) -> T1 element(int(s(s(N1))),tuple(T1,T2)) -> element(int(s(N1)),T2) record_new(lock()) -> tuple(mcrlrecord(),tuple(lock(),tuple(undefined(),tuple(nil(),tuplenil(nil()))))) record_extract(tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))), lock(),resource()) -> tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))) record_update(tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))), lock(),pending(),NewF) -> tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(NewF))))) record_updates(Record,Name,nil()) -> Record record_updates(Record,Name,cons(tuple(Field,tuplenil(NewF)),Fields)) -> record_updates(record_update(Record,Name,Field,NewF),Name,Fields) locker2_map_promote_pending(nil(),Pending) -> nil() locker2_map_promote_pending(cons(Lock,Locks),Pending) -> cons(locker2_promote_pending(Lock,Pending),locker2_map_promote_pending(Locks,Pending)) locker2_map_claim_lock(nil(),Resources,Client) -> nil() locker2_map_claim_lock(cons(Lock,Locks),Resources,Client) -> cons(locker2_claim_lock(Lock,Resources,Client),locker2_map_claim_lock (Locks,Resources,Client)) locker2_map_add_pending(nil(),Resources,Client) -> nil() locker2_promote_pending(Lock,Client) -> case0(Client,Lock,record_extract(Lock,lock(),pending())) case0(Client,Lock,cons(Client,Pendings)) -> record_updates(Lock,lock(),cons(tuple(excl(),tuplenil(Client)), cons(tuple(pending(),tuplenil(Pendings)),nil()))) case0(Client,Lock,MCRLFree0) -> Lock locker2_remove_pending(Lock,Client) -> record_updates(Lock,lock(),cons(tuple(pending(),tuplenil(subtract (record_extract (Lock,lock(),pending()), cons (Client,nil())))), nil())) locker2_add_pending(Lock,Resources,Client) -> case1(Client,Resources,Lock,member(record_extract(Lock,lock(),resource()),Resources)) case1(Client,Resources,Lock,true()) -> record_updates(Lock,lock(),cons(tuple(pending(),tuplenil(append (record_extract (Lock,lock(),pending()), cons (Client,nil())))), nil())) case1(Client,Resources,Lock,false()) -> Lock locker2_release_lock(Lock,Client) -> case2(Client,Lock,gen_modtageq(Client,record_extract(Lock,lock(),excl()))) case2(Client,Lock,true()) -> record_updates(Lock,lock(),cons(tuple(excllock(),excl()),nil())) case4(Client,Lock,MCRLFree1) -> false() locker2_obtainables(nil(),Client) -> true() locker2_obtainables(cons(Lock,Locks),Client) -> case5(Client,Locks,Lock,member(Client,record_extract(Lock,lock(),pending()))) case5(Client,Locks,Lock,true()) -> andt(locker2_obtainable(Lock,Client),locker2_obtainables(Locks,Client)) case5(Client,Locks,Lock,false()) -> locker2_obtainables(Locks,Client) locker2_check_available(Resource,nil()) -> false() locker2_check_available(Resource,cons(Lock,Locks)) -> case6(Locks,Lock,Resource,equal(Resource,record_extract(Lock,lock(),resource()))) case6(Locks,Lock,Resource,true()) -> andt(equal(record_extract(Lock,lock(),excl()),nil()),equal(record_extract (Lock,lock(),pending()), nil())) case6(Locks,Lock,Resource,false()) -> locker2_check_available(Resource,Locks) locker2_check_availables(nil(),Locks) -> true() locker2_check_availables(cons(Resource,Resources),Locks) -> andt(locker2_check_available(Resource,Locks),locker2_check_availables(Resources,Locks)) locker2_adduniq(nil(),List) -> List append(cons(Head,Tail),List) -> cons(Head,append(Tail,List)) subtract(List,nil()) -> List subtract(List,cons(Head,Tail)) -> subtract(delete(Head,List),Tail) delete(E,nil()) -> nil() delete(E,cons(Head,Tail)) -> case8(Tail,Head,E,equal(E,Head)) case8(Tail,Head,E,true()) -> Tail case8(Tail,Head,E,false()) -> cons(Head,delete(E,Tail)) gen_tag(Pid) -> tuple(Pid,tuplenil(tag())) gen_modtageq(Client1,Client2) -> equal(Client1,Client2) member(E,nil()) -> false() member(E,cons(Head,Tail)) -> case9(Tail,Head,E,equal(E,Head)) case9(Tail,Head,E,true()) -> true() case9(Tail,Head,E,false()) -> member(E,Tail) eqs(empty(),empty()) -> T() eqs(empty(),stack(E2,S2)) -> F() eqs(stack(E1,S1),empty()) -> F() eqs(stack(E1,S1),stack(E2,S2)) -> and(eqt(E1,E2),eqs(S1,S2)) pushs(E1,S1) -> stack(E1,S1) pops(stack(E1,S1)) -> S1 tops(stack(E1,S1)) -> E1 istops(E1,empty()) -> F() istops(E1,stack(E2,S1)) -> eqt(E1,E2) eqc(nocalls(),nocalls()) -> T() eqc(nocalls(),calls(E2,S2,CS2)) -> F() eqc(calls(E1,S1,CS1),nocalls()) -> F() eqc(calls(E1,S1,CS1),calls(E2,S2,CS2)) -> and(eqt(E1,E2),and(eqs(S1,S2),eqc(CS1,CS2))) push(E1,E2,nocalls()) -> calls(E1,stack(E2,empty()),nocalls()) push(E1,E2,calls(E3,S1,CS1)) -> push1(E1,E2,E3,S1,CS1,eqt(E1,E3)) push1(E1,E2,E3,S1,CS1,T()) -> calls(E3,pushs(E2,S1),CS1) SCC Processor: #sccs: 0 #rules: 0 #arcs: 2/1 DPs: eqc#(calls(E1,S1,CS1),calls(E2,S2,CS2)) -> eqc#(CS1,CS2) TRS: or(T(),T()) -> T() or(F(),T()) -> T() or(T(),F()) -> T() or(F(),F()) -> F() and(T(),B) -> B and(B,T()) -> B and(F(),B) -> F() and(B,F()) -> F() imp(T(),B) -> B imp(F(),B) -> T() not(T()) -> F() not(F()) -> T() if(T(),B1,B2) -> B1 if(F(),B1,B2) -> B2 eq(T(),T()) -> T() eq(F(),F()) -> T() eq(T(),F()) -> F() eq(F(),T()) -> F() eqt(nil(),undefined()) -> F() eqt(nil(),pid(N2)) -> F() eqt(nil(),int(N2)) -> F() eqt(nil(),cons(H2,T2)) -> F() eqt(nil(),tuple(H2,T2)) -> F() eqt(nil(),tuplenil(H2)) -> F() eqt(a(),nil()) -> F() eqt(a(),a()) -> T() eqt(a(),excl()) -> F() eqt(a(),false()) -> F() eqt(a(),lock()) -> F() eqt(a(),locker()) -> F() eqt(a(),mcrlrecord()) -> F() eqt(a(),ok()) -> F() eqt(a(),pending()) -> F() eqt(a(),release()) -> F() eqt(a(),request()) -> F() eqt(a(),resource()) -> F() eqt(a(),tag()) -> F() eqt(a(),true()) -> F() eqt(a(),undefined()) -> F() eqt(a(),pid(N2)) -> F() eqt(a(),int(N2)) -> F() eqt(a(),cons(H2,T2)) -> F() eqt(a(),tuple(H2,T2)) -> F() eqt(a(),tuplenil(H2)) -> F() eqt(excl(),nil()) -> F() eqt(excl(),a()) -> F() eqt(excl(),excl()) -> T() eqt(excl(),false()) -> F() eqt(excl(),lock()) -> F() eqt(excl(),locker()) -> F() eqt(excl(),mcrlrecord()) -> F() eqt(excl(),ok()) -> F() eqt(excl(),pending()) -> F() eqt(excl(),release()) -> F() eqt(excl(),request()) -> F() eqt(excl(),resource()) -> F() eqt(excl(),tag()) -> F() eqt(excl(),true()) -> F() eqt(excl(),undefined()) -> F() eqt(excl(),pid(N2)) -> F() eqt(excl(),eqt(false(),int(N2))) -> F() eqt(false(),cons(H2,T2)) -> F() eqt(false(),tuple(H2,T2)) -> F() eqt(false(),tuplenil(H2)) -> F() eqt(lock(),nil()) -> F() eqt(lock(),a()) -> F() eqt(lock(),excl()) -> F() eqt(lock(),false()) -> F() eqt(lock(),lock()) -> T() eqt(lock(),locker()) -> F() eqt(lock(),mcrlrecord()) -> F() eqt(lock(),ok()) -> F() eqt(lock(),pending()) -> F() eqt(lock(),release()) -> F() eqt(lock(),request()) -> F() eqt(lock(),resource()) -> F() eqt(lock(),tag()) -> F() eqt(lock(),true()) -> F() eqt(lock(),undefined()) -> F() eqt(lock(),pid(N2)) -> F() eqt(lock(),int(N2)) -> F() eqt(lock(),cons(H2,T2)) -> F() eqt(lock(),tuple(H2,T2)) -> F() eqt(lock(),tuplenil(H2)) -> F() eqt(locker(),nil()) -> F() eqt(locker(),a()) -> F() eqt(locker(),excl()) -> F() eqt(locker(),false()) -> F() eqt(locker(),lock()) -> F() eqt(locker(),locker()) -> T() eqt(locker(),mcrlrecord()) -> F() eqt(locker(),ok()) -> F() eqt(locker(),pending()) -> F() eqt(locker(),release()) -> F() eqt(locker(),request()) -> F() eqt(locker(),resource()) -> F() eqt(locker(),tag()) -> F() eqt(locker(),true()) -> F() eqt(locker(),undefined()) -> F() eqt(locker(),pid(N2)) -> F() eqt(locker(),int(N2)) -> F() eqt(locker(),cons(H2,T2)) -> F() eqt(locker(),tuple(H2,T2)) -> F() eqt(locker(),tuplenil(H2)) -> F() eqt(mcrlrecord(),nil()) -> F() eqt(mcrlrecord(),a()) -> F() eqt(mcrlrecord(),excl()) -> F() eqt(mcrlrecord(),false()) -> F() eqt(mcrlrecord(),lock()) -> F() eqt(mcrlrecord(),locker()) -> F() eqt(mcrlrecord(),mcrlrecord()) -> T() eqt(mcrlrecord(),ok()) -> F() eqt(mcrlrecord(),pending()) -> F() eqt(mcrlrecord(),release()) -> F() eqt(mcrlrecord(),request()) -> F() eqt(mcrlrecord(),resource()) -> F() eqt(ok(),resource()) -> F() eqt(ok(),tag()) -> F() eqt(ok(),true()) -> F() eqt(ok(),undefined()) -> F() eqt(ok(),pid(N2)) -> F() eqt(ok(),int(N2)) -> F() eqt(ok(),cons(H2,T2)) -> F() eqt(ok(),tuple(H2,T2)) -> F() eqt(ok(),tuplenil(H2)) -> F() eqt(pending(),nil()) -> F() eqt(pending(),a()) -> F() eqt(pending(),excl()) -> F() eqt(pending(),false()) -> F() eqt(pending(),lock()) -> F() eqt(pending(),locker()) -> F() eqt(pending(),mcrlrecord()) -> F() eqt(pending(),ok()) -> F() eqt(pending(),pending()) -> T() eqt(pending(),release()) -> F() eqt(pending(),request()) -> F() eqt(pending(),resource()) -> F() eqt(pending(),tag()) -> F() eqt(pending(),true()) -> F() eqt(pending(),undefined()) -> F() eqt(pending(),pid(N2)) -> F() eqt(pending(),int(N2)) -> F() eqt(pending(),cons(H2,T2)) -> F() eqt(pending(),tuple(H2,T2)) -> F() eqt(pending(),tuplenil(H2)) -> F() eqt(release(),nil()) -> F() eqt(release(),a()) -> F() eqt(release(),excl()) -> F() eqt(release(),false()) -> F() eqt(release(),lock()) -> F() eqt(release(),locker()) -> F() eqt(release(),mcrlrecord()) -> F() eqt(release(),ok()) -> F() eqt(request(),mcrlrecord()) -> F() eqt(request(),ok()) -> F() eqt(request(),pending()) -> F() eqt(request(),release()) -> F() eqt(request(),request()) -> T() eqt(request(),resource()) -> F() eqt(request(),tag()) -> F() eqt(request(),true()) -> F() eqt(request(),undefined()) -> F() eqt(request(),pid(N2)) -> F() eqt(request(),int(N2)) -> F() eqt(request(),cons(H2,T2)) -> F() eqt(request(),tuple(H2,T2)) -> F() eqt(request(),tuplenil(H2)) -> F() eqt(resource(),nil()) -> F() eqt(resource(),a()) -> F() eqt(resource(),excl()) -> F() eqt(resource(),false()) -> F() eqt(resource(),lock()) -> F() eqt(resource(),locker()) -> F() eqt(resource(),mcrlrecord()) -> F() eqt(resource(),ok()) -> F() eqt(resource(),pending()) -> F() eqt(resource(),release()) -> F() eqt(resource(),request()) -> F() eqt(resource(),resource()) -> T() eqt(resource(),tag()) -> F() eqt(resource(),true()) -> F() eqt(resource(),undefined()) -> F() eqt(resource(),pid(N2)) -> F() eqt(resource(),int(N2)) -> F() eqt(resource(),cons(H2,T2)) -> F() eqt(resource(),tuple(H2,T2)) -> F() eqt(resource(),tuplenil(H2)) -> F() eqt(tag(),nil()) -> F() eqt(tag(),a()) -> F() eqt(tag(),excl()) -> F() eqt(tag(),false()) -> F() eqt(tag(),lock()) -> F() eqt(tag(),locker()) -> F() eqt(tag(),mcrlrecord()) -> F() eqt(tag(),ok()) -> F() eqt(tag(),pending()) -> F() eqt(tag(),release()) -> F() eqt(tag(),request()) -> F() eqt(tag(),resource()) -> F() eqt(tag(),tag()) -> T() eqt(tag(),true()) -> F() eqt(tag(),undefined()) -> F() eqt(tag(),pid(N2)) -> F() eqt(tag(),int(N2)) -> F() eqt(tag(),cons(H2,T2)) -> F() eqt(tag(),tuple(H2,T2)) -> F() eqt(tag(),tuplenil(H2)) -> F() eqt(true(),nil()) -> F() eqt(true(),a()) -> F() eqt(true(),excl()) -> F() eqt(true(),false()) -> F() eqt(true(),lock()) -> F() eqt(true(),locker()) -> F() eqt(true(),mcrlrecord()) -> F() eqt(true(),ok()) -> F() eqt(true(),pending()) -> F() eqt(true(),release()) -> F() eqt(true(),request()) -> F() eqt(true(),resource()) -> F() eqt(true(),tag()) -> F() eqt(true(),true()) -> T() eqt(true(),undefined()) -> F() eqt(true(),pid(N2)) -> F() eqt(true(),int(N2)) -> F() eqt(true(),cons(H2,T2)) -> F() eqt(true(),tuple(H2,T2)) -> F() eqt(true(),tuplenil(H2)) -> F() eqt(undefined(),nil()) -> F() eqt(undefined(),a()) -> F() eqt(undefined(),tuplenil(H2)) -> F() eqt(pid(N1),nil()) -> F() eqt(pid(N1),a()) -> F() eqt(pid(N1),excl()) -> F() eqt(pid(N1),false()) -> F() eqt(pid(N1),lock()) -> F() eqt(pid(N1),locker()) -> F() eqt(pid(N1),mcrlrecord()) -> F() eqt(pid(N1),ok()) -> F() eqt(pid(N1),pending()) -> F() eqt(pid(N1),release()) -> F() eqt(pid(N1),request()) -> F() eqt(pid(N1),resource()) -> F() eqt(pid(N1),tag()) -> F() eqt(pid(N1),true()) -> F() eqt(pid(N1),undefined()) -> F() eqt(pid(N1),pid(N2)) -> eqt(N1,N2) eqt(pid(N1),int(N2)) -> F() eqt(pid(N1),cons(H2,T2)) -> F() eqt(pid(N1),tuple(H2,T2)) -> F() eqt(pid(N1),tuplenil(H2)) -> F() eqt(int(N1),nil()) -> F() eqt(int(N1),a()) -> F() eqt(int(N1),excl()) -> F() eqt(int(N1),false()) -> F() eqt(int(N1),lock()) -> F() eqt(int(N1),locker()) -> F() eqt(int(N1),mcrlrecord()) -> F() eqt(int(N1),ok()) -> F() eqt(int(N1),pending()) -> F() eqt(int(N1),release()) -> F() eqt(int(N1),request()) -> F() eqt(int(N1),resource()) -> F() eqt(int(N1),tag()) -> F() eqt(int(N1),true()) -> F() eqt(int(N1),undefined()) -> F() eqt(cons(H1,T1),resource()) -> F() eqt(cons(H1,T1),tag()) -> F() eqt(cons(H1,T1),true()) -> F() eqt(cons(H1,T1),undefined()) -> F() eqt(cons(H1,T1),pid(N2)) -> F() eqt(cons(H1,T1),int(N2)) -> F() eqt(cons(H1,T1),cons(H2,T2)) -> and(eqt(H1,H2),eqt(T1,T2)) eqt(cons(H1,T1),tuple(H2,T2)) -> F() eqt(cons(H1,T1),tuplenil(H2)) -> F() eqt(tuple(H1,T1),nil()) -> F() eqt(tuple(H1,T1),a()) -> F() eqt(tuple(H1,T1),excl()) -> F() eqt(tuple(H1,T1),false()) -> F() eqt(tuple(H1,T1),lock()) -> F() eqt(tuple(H1,T1),locker()) -> F() eqt(tuple(H1,T1),mcrlrecord()) -> F() eqt(tuple(H1,T1),ok()) -> F() eqt(tuple(H1,T1),pending()) -> F() eqt(tuple(H1,T1),release()) -> F() eqt(tuple(H1,T1),request()) -> F() eqt(tuple(H1,T1),resource()) -> F() eqt(tuple(H1,T1),tag()) -> F() eqt(tuple(H1,T1),true()) -> F() eqt(tuple(H1,T1),undefined()) -> F() eqt(tuple(H1,T1),pid(N2)) -> F() eqt(tuple(H1,T1),int(N2)) -> F() eqt(tuple(H1,T1),cons(H2,T2)) -> F() eqt(tuple(H1,T1),tuple(H2,T2)) -> and(eqt(H1,H2),eqt(T1,T2)) eqt(tuple(H1,T1),tuplenil(H2)) -> F() eqt(tuplenil(H1),nil()) -> F() eqt(tuplenil(H1),a()) -> F() eqt(tuplenil(H1),excl()) -> F() eqt(tuplenil(H1),false()) -> F() eqt(tuplenil(H1),lock()) -> F() eqt(tuplenil(H1),locker()) -> F() eqt(tuplenil(H1),mcrlrecord()) -> F() eqt(tuplenil(H1),ok()) -> F() eqt(tuplenil(H1),pending()) -> F() eqt(tuplenil(H1),release()) -> F() eqt(tuplenil(H1),request()) -> F() eqt(tuplenil(H1),resource()) -> F() eqt(tuplenil(H1),tag()) -> F() eqt(tuplenil(H1),true()) -> F() eqt(tuplenil(H1),undefined()) -> F() eqt(tuplenil(H1),pid(N2)) -> F() eqt(tuplenil(H1),int(N2)) -> F() eqt(tuplenil(H1),cons(H2,T2)) -> F() eqt(tuplenil(H1),tuple(H2,T2)) -> F() eqt(tuplenil(H1),tuplenil(H2)) -> eqt(H1,H2) element(int(s(0())),tuplenil(T1)) -> T1 element(int(s(0())),tuple(T1,T2)) -> T1 element(int(s(s(N1))),tuple(T1,T2)) -> element(int(s(N1)),T2) record_new(lock()) -> tuple(mcrlrecord(),tuple(lock(),tuple(undefined(),tuple(nil(),tuplenil(nil()))))) record_extract(tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))), lock(),resource()) -> tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))) record_update(tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))), lock(),pending(),NewF) -> tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(NewF))))) record_updates(Record,Name,nil()) -> Record record_updates(Record,Name,cons(tuple(Field,tuplenil(NewF)),Fields)) -> record_updates(record_update(Record,Name,Field,NewF),Name,Fields) locker2_map_promote_pending(nil(),Pending) -> nil() locker2_map_promote_pending(cons(Lock,Locks),Pending) -> cons(locker2_promote_pending(Lock,Pending),locker2_map_promote_pending(Locks,Pending)) locker2_map_claim_lock(nil(),Resources,Client) -> nil() locker2_map_claim_lock(cons(Lock,Locks),Resources,Client) -> cons(locker2_claim_lock(Lock,Resources,Client),locker2_map_claim_lock(Locks,Resources,Client)) locker2_map_add_pending(nil(),Resources,Client) -> nil() locker2_promote_pending(Lock,Client) -> case0(Client,Lock,record_extract(Lock,lock(),pending())) case0(Client,Lock,cons(Client,Pendings)) -> record_updates(Lock,lock(),cons(tuple(excl(),tuplenil(Client)),cons ( tuple ( pending(),tuplenil(Pendings)), nil ()))) case0(Client,Lock,MCRLFree0) -> Lock locker2_remove_pending(Lock,Client) -> record_updates(Lock,lock(),cons(tuple(pending(),tuplenil(subtract (record_extract (Lock,lock(),pending()), cons(Client,nil())))), nil())) locker2_add_pending(Lock,Resources,Client) -> case1(Client,Resources,Lock,member(record_extract(Lock,lock(),resource()),Resources)) case1(Client,Resources,Lock,true()) -> record_updates(Lock,lock(),cons(tuple(pending(),tuplenil(append( record_extract ( Lock,lock(),pending()), cons (Client,nil())))), nil())) case1(Client,Resources,Lock,false()) -> Lock locker2_release_lock(Lock,Client) -> case2(Client,Lock,gen_modtageq(Client,record_extract(Lock,lock(),excl()))) case2(Client,Lock,true()) -> record_updates(Lock,lock(),cons(tuple(excllock(),excl()),nil())) case4(Client,Lock,MCRLFree1) -> false() locker2_obtainables(nil(),Client) -> true() locker2_obtainables(cons(Lock,Locks),Client) -> case5(Client,Locks,Lock,member(Client,record_extract(Lock,lock(),pending()))) case5(Client,Locks,Lock,true()) -> andt(locker2_obtainable(Lock,Client),locker2_obtainables(Locks,Client)) case5(Client,Locks,Lock,false()) -> locker2_obtainables(Locks,Client) locker2_check_available(Resource,nil()) -> false() locker2_check_available(Resource,cons(Lock,Locks)) -> case6(Locks,Lock,Resource,equal(Resource,record_extract(Lock,lock(),resource()))) case6(Locks,Lock,Resource,true()) -> andt(equal(record_extract(Lock,lock(),excl()),nil()),equal(record_extract (Lock,lock(),pending()), nil())) case6(Locks,Lock,Resource,false()) -> locker2_check_available(Resource,Locks) locker2_check_availables(nil(),Locks) -> true() locker2_check_availables(cons(Resource,Resources),Locks) -> andt(locker2_check_available(Resource,Locks),locker2_check_availables(Resources,Locks)) locker2_adduniq(nil(),List) -> List append(cons(Head,Tail),List) -> cons(Head,append(Tail,List)) subtract(List,nil()) -> List subtract(List,cons(Head,Tail)) -> subtract(delete(Head,List),Tail) delete(E,nil()) -> nil() delete(E,cons(Head,Tail)) -> case8(Tail,Head,E,equal(E,Head)) case8(Tail,Head,E,true()) -> Tail case8(Tail,Head,E,false()) -> cons(Head,delete(E,Tail)) gen_tag(Pid) -> tuple(Pid,tuplenil(tag())) gen_modtageq(Client1,Client2) -> equal(Client1,Client2) member(E,nil()) -> false() member(E,cons(Head,Tail)) -> case9(Tail,Head,E,equal(E,Head)) case9(Tail,Head,E,true()) -> true() case9(Tail,Head,E,false()) -> member(E,Tail) eqs(empty(),empty()) -> T() eqs(empty(),stack(E2,S2)) -> F() eqs(stack(E1,S1),empty()) -> F() eqs(stack(E1,S1),stack(E2,S2)) -> and(eqt(E1,E2),eqs(S1,S2)) pushs(E1,S1) -> stack(E1,S1) pops(stack(E1,S1)) -> S1 tops(stack(E1,S1)) -> E1 istops(E1,empty()) -> F() istops(E1,stack(E2,S1)) -> eqt(E1,E2) eqc(nocalls(),nocalls()) -> T() eqc(nocalls(),calls(E2,S2,CS2)) -> F() eqc(calls(E1,S1,CS1),nocalls()) -> F() eqc(calls(E1,S1,CS1),calls(E2,S2,CS2)) -> and(eqt(E1,E2),and(eqs(S1,S2),eqc(CS1,CS2))) push(E1,E2,nocalls()) -> calls(E1,stack(E2,empty()),nocalls()) push(E1,E2,calls(E3,S1,CS1)) -> push1(E1,E2,E3,S1,CS1,eqt(E1,E3)) push1(E1,E2,E3,S1,CS1,T()) -> calls(E3,pushs(E2,S1),CS1) Subterm Criterion Processor: simple projection: pi(eqc#) = 0 problem: DPs: TRS: or(T(),T()) -> T() or(F(),T()) -> T() or(T(),F()) -> T() or(F(),F()) -> F() and(T(),B) -> B and(B,T()) -> B and(F(),B) -> F() and(B,F()) -> F() imp(T(),B) -> B imp(F(),B) -> T() not(T()) -> F() not(F()) -> T() if(T(),B1,B2) -> B1 if(F(),B1,B2) -> B2 eq(T(),T()) -> T() eq(F(),F()) -> T() eq(T(),F()) -> F() eq(F(),T()) -> F() eqt(nil(),undefined()) -> F() eqt(nil(),pid(N2)) -> F() eqt(nil(),int(N2)) -> F() eqt(nil(),cons(H2,T2)) -> F() eqt(nil(),tuple(H2,T2)) -> F() eqt(nil(),tuplenil(H2)) -> F() eqt(a(),nil()) -> F() eqt(a(),a()) -> T() eqt(a(),excl()) -> F() eqt(a(),false()) -> F() eqt(a(),lock()) -> F() eqt(a(),locker()) -> F() eqt(a(),mcrlrecord()) -> F() eqt(a(),ok()) -> F() eqt(a(),pending()) -> F() eqt(a(),release()) -> F() eqt(a(),request()) -> F() eqt(a(),resource()) -> F() eqt(a(),tag()) -> F() eqt(a(),true()) -> F() eqt(a(),undefined()) -> F() eqt(a(),pid(N2)) -> F() eqt(a(),int(N2)) -> F() eqt(a(),cons(H2,T2)) -> F() eqt(a(),tuple(H2,T2)) -> F() eqt(a(),tuplenil(H2)) -> F() eqt(excl(),nil()) -> F() eqt(excl(),a()) -> F() eqt(excl(),excl()) -> T() eqt(excl(),false()) -> F() eqt(excl(),lock()) -> F() eqt(excl(),locker()) -> F() eqt(excl(),mcrlrecord()) -> F() eqt(excl(),ok()) -> F() eqt(excl(),pending()) -> F() eqt(excl(),release()) -> F() eqt(excl(),request()) -> F() eqt(excl(),resource()) -> F() eqt(excl(),tag()) -> F() eqt(excl(),true()) -> F() eqt(excl(),undefined()) -> F() eqt(excl(),pid(N2)) -> F() eqt(excl(),eqt(false(),int(N2))) -> F() eqt(false(),cons(H2,T2)) -> F() eqt(false(),tuple(H2,T2)) -> F() eqt(false(),tuplenil(H2)) -> F() eqt(lock(),nil()) -> F() eqt(lock(),a()) -> F() eqt(lock(),excl()) -> F() eqt(lock(),false()) -> F() eqt(lock(),lock()) -> T() eqt(lock(),locker()) -> F() eqt(lock(),mcrlrecord()) -> F() eqt(lock(),ok()) -> F() eqt(lock(),pending()) -> F() eqt(lock(),release()) -> F() eqt(lock(),request()) -> F() eqt(lock(),resource()) -> F() eqt(lock(),tag()) -> F() eqt(lock(),true()) -> F() eqt(lock(),undefined()) -> F() eqt(lock(),pid(N2)) -> F() eqt(lock(),int(N2)) -> F() eqt(lock(),cons(H2,T2)) -> F() eqt(lock(),tuple(H2,T2)) -> F() eqt(lock(),tuplenil(H2)) -> F() eqt(locker(),nil()) -> F() eqt(locker(),a()) -> F() eqt(locker(),excl()) -> F() eqt(locker(),false()) -> F() eqt(locker(),lock()) -> F() eqt(locker(),locker()) -> T() eqt(locker(),mcrlrecord()) -> F() eqt(locker(),ok()) -> F() eqt(locker(),pending()) -> F() eqt(locker(),release()) -> F() eqt(locker(),request()) -> F() eqt(locker(),resource()) -> F() eqt(locker(),tag()) -> F() eqt(locker(),true()) -> F() eqt(locker(),undefined()) -> F() eqt(locker(),pid(N2)) -> F() eqt(locker(),int(N2)) -> F() eqt(locker(),cons(H2,T2)) -> F() eqt(locker(),tuple(H2,T2)) -> F() eqt(locker(),tuplenil(H2)) -> F() eqt(mcrlrecord(),nil()) -> F() eqt(mcrlrecord(),a()) -> F() eqt(mcrlrecord(),excl()) -> F() eqt(mcrlrecord(),false()) -> F() eqt(mcrlrecord(),lock()) -> F() eqt(mcrlrecord(),locker()) -> F() eqt(mcrlrecord(),mcrlrecord()) -> T() eqt(mcrlrecord(),ok()) -> F() eqt(mcrlrecord(),pending()) -> F() eqt(mcrlrecord(),release()) -> F() eqt(mcrlrecord(),request()) -> F() eqt(mcrlrecord(),resource()) -> F() eqt(ok(),resource()) -> F() eqt(ok(),tag()) -> F() eqt(ok(),true()) -> F() eqt(ok(),undefined()) -> F() eqt(ok(),pid(N2)) -> F() eqt(ok(),int(N2)) -> F() eqt(ok(),cons(H2,T2)) -> F() eqt(ok(),tuple(H2,T2)) -> F() eqt(ok(),tuplenil(H2)) -> F() eqt(pending(),nil()) -> F() eqt(pending(),a()) -> F() eqt(pending(),excl()) -> F() eqt(pending(),false()) -> F() eqt(pending(),lock()) -> F() eqt(pending(),locker()) -> F() eqt(pending(),mcrlrecord()) -> F() eqt(pending(),ok()) -> F() eqt(pending(),pending()) -> T() eqt(pending(),release()) -> F() eqt(pending(),request()) -> F() eqt(pending(),resource()) -> F() eqt(pending(),tag()) -> F() eqt(pending(),true()) -> F() eqt(pending(),undefined()) -> F() eqt(pending(),pid(N2)) -> F() eqt(pending(),int(N2)) -> F() eqt(pending(),cons(H2,T2)) -> F() eqt(pending(),tuple(H2,T2)) -> F() eqt(pending(),tuplenil(H2)) -> F() eqt(release(),nil()) -> F() eqt(release(),a()) -> F() eqt(release(),excl()) -> F() eqt(release(),false()) -> F() eqt(release(),lock()) -> F() eqt(release(),locker()) -> F() eqt(release(),mcrlrecord()) -> F() eqt(release(),ok()) -> F() eqt(request(),mcrlrecord()) -> F() eqt(request(),ok()) -> F() eqt(request(),pending()) -> F() eqt(request(),release()) -> F() eqt(request(),request()) -> T() eqt(request(),resource()) -> F() eqt(request(),tag()) -> F() eqt(request(),true()) -> F() eqt(request(),undefined()) -> F() eqt(request(),pid(N2)) -> F() eqt(request(),int(N2)) -> F() eqt(request(),cons(H2,T2)) -> F() eqt(request(),tuple(H2,T2)) -> F() eqt(request(),tuplenil(H2)) -> F() eqt(resource(),nil()) -> F() eqt(resource(),a()) -> F() eqt(resource(),excl()) -> F() eqt(resource(),false()) -> F() eqt(resource(),lock()) -> F() eqt(resource(),locker()) -> F() eqt(resource(),mcrlrecord()) -> F() eqt(resource(),ok()) -> F() eqt(resource(),pending()) -> F() eqt(resource(),release()) -> F() eqt(resource(),request()) -> F() eqt(resource(),resource()) -> T() eqt(resource(),tag()) -> F() eqt(resource(),true()) -> F() eqt(resource(),undefined()) -> F() eqt(resource(),pid(N2)) -> F() eqt(resource(),int(N2)) -> F() eqt(resource(),cons(H2,T2)) -> F() eqt(resource(),tuple(H2,T2)) -> F() eqt(resource(),tuplenil(H2)) -> F() eqt(tag(),nil()) -> F() eqt(tag(),a()) -> F() eqt(tag(),excl()) -> F() eqt(tag(),false()) -> F() eqt(tag(),lock()) -> F() eqt(tag(),locker()) -> F() eqt(tag(),mcrlrecord()) -> F() eqt(tag(),ok()) -> F() eqt(tag(),pending()) -> F() eqt(tag(),release()) -> F() eqt(tag(),request()) -> F() eqt(tag(),resource()) -> F() eqt(tag(),tag()) -> T() eqt(tag(),true()) -> F() eqt(tag(),undefined()) -> F() eqt(tag(),pid(N2)) -> F() eqt(tag(),int(N2)) -> F() eqt(tag(),cons(H2,T2)) -> F() eqt(tag(),tuple(H2,T2)) -> F() eqt(tag(),tuplenil(H2)) -> F() eqt(true(),nil()) -> F() eqt(true(),a()) -> F() eqt(true(),excl()) -> F() eqt(true(),false()) -> F() eqt(true(),lock()) -> F() eqt(true(),locker()) -> F() eqt(true(),mcrlrecord()) -> F() eqt(true(),ok()) -> F() eqt(true(),pending()) -> F() eqt(true(),release()) -> F() eqt(true(),request()) -> F() eqt(true(),resource()) -> F() eqt(true(),tag()) -> F() eqt(true(),true()) -> T() eqt(true(),undefined()) -> F() eqt(true(),pid(N2)) -> F() eqt(true(),int(N2)) -> F() eqt(true(),cons(H2,T2)) -> F() eqt(true(),tuple(H2,T2)) -> F() eqt(true(),tuplenil(H2)) -> F() eqt(undefined(),nil()) -> F() eqt(undefined(),a()) -> F() eqt(undefined(),tuplenil(H2)) -> F() eqt(pid(N1),nil()) -> F() eqt(pid(N1),a()) -> F() eqt(pid(N1),excl()) -> F() eqt(pid(N1),false()) -> F() eqt(pid(N1),lock()) -> F() eqt(pid(N1),locker()) -> F() eqt(pid(N1),mcrlrecord()) -> F() eqt(pid(N1),ok()) -> F() eqt(pid(N1),pending()) -> F() eqt(pid(N1),release()) -> F() eqt(pid(N1),request()) -> F() eqt(pid(N1),resource()) -> F() eqt(pid(N1),tag()) -> F() eqt(pid(N1),true()) -> F() eqt(pid(N1),undefined()) -> F() eqt(pid(N1),pid(N2)) -> eqt(N1,N2) eqt(pid(N1),int(N2)) -> F() eqt(pid(N1),cons(H2,T2)) -> F() eqt(pid(N1),tuple(H2,T2)) -> F() eqt(pid(N1),tuplenil(H2)) -> F() eqt(int(N1),nil()) -> F() eqt(int(N1),a()) -> F() eqt(int(N1),excl()) -> F() eqt(int(N1),false()) -> F() eqt(int(N1),lock()) -> F() eqt(int(N1),locker()) -> F() eqt(int(N1),mcrlrecord()) -> F() eqt(int(N1),ok()) -> F() eqt(int(N1),pending()) -> F() eqt(int(N1),release()) -> F() eqt(int(N1),request()) -> F() eqt(int(N1),resource()) -> F() eqt(int(N1),tag()) -> F() eqt(int(N1),true()) -> F() eqt(int(N1),undefined()) -> F() eqt(cons(H1,T1),resource()) -> F() eqt(cons(H1,T1),tag()) -> F() eqt(cons(H1,T1),true()) -> F() eqt(cons(H1,T1),undefined()) -> F() eqt(cons(H1,T1),pid(N2)) -> F() eqt(cons(H1,T1),int(N2)) -> F() eqt(cons(H1,T1),cons(H2,T2)) -> and(eqt(H1,H2),eqt(T1,T2)) eqt(cons(H1,T1),tuple(H2,T2)) -> F() eqt(cons(H1,T1),tuplenil(H2)) -> F() eqt(tuple(H1,T1),nil()) -> F() eqt(tuple(H1,T1),a()) -> F() eqt(tuple(H1,T1),excl()) -> F() eqt(tuple(H1,T1),false()) -> F() eqt(tuple(H1,T1),lock()) -> F() eqt(tuple(H1,T1),locker()) -> F() eqt(tuple(H1,T1),mcrlrecord()) -> F() eqt(tuple(H1,T1),ok()) -> F() eqt(tuple(H1,T1),pending()) -> F() eqt(tuple(H1,T1),release()) -> F() eqt(tuple(H1,T1),request()) -> F() eqt(tuple(H1,T1),resource()) -> F() eqt(tuple(H1,T1),tag()) -> F() eqt(tuple(H1,T1),true()) -> F() eqt(tuple(H1,T1),undefined()) -> F() eqt(tuple(H1,T1),pid(N2)) -> F() eqt(tuple(H1,T1),int(N2)) -> F() eqt(tuple(H1,T1),cons(H2,T2)) -> F() eqt(tuple(H1,T1),tuple(H2,T2)) -> and(eqt(H1,H2),eqt(T1,T2)) eqt(tuple(H1,T1),tuplenil(H2)) -> F() eqt(tuplenil(H1),nil()) -> F() eqt(tuplenil(H1),a()) -> F() eqt(tuplenil(H1),excl()) -> F() eqt(tuplenil(H1),false()) -> F() eqt(tuplenil(H1),lock()) -> F() eqt(tuplenil(H1),locker()) -> F() eqt(tuplenil(H1),mcrlrecord()) -> F() eqt(tuplenil(H1),ok()) -> F() eqt(tuplenil(H1),pending()) -> F() eqt(tuplenil(H1),release()) -> F() eqt(tuplenil(H1),request()) -> F() eqt(tuplenil(H1),resource()) -> F() eqt(tuplenil(H1),tag()) -> F() eqt(tuplenil(H1),true()) -> F() eqt(tuplenil(H1),undefined()) -> F() eqt(tuplenil(H1),pid(N2)) -> F() eqt(tuplenil(H1),int(N2)) -> F() eqt(tuplenil(H1),cons(H2,T2)) -> F() eqt(tuplenil(H1),tuple(H2,T2)) -> F() eqt(tuplenil(H1),tuplenil(H2)) -> eqt(H1,H2) element(int(s(0())),tuplenil(T1)) -> T1 element(int(s(0())),tuple(T1,T2)) -> T1 element(int(s(s(N1))),tuple(T1,T2)) -> element(int(s(N1)),T2) record_new(lock()) -> tuple(mcrlrecord(),tuple(lock(),tuple(undefined(),tuple(nil(),tuplenil(nil()))))) record_extract(tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))), lock(),resource()) -> tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))) record_update(tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))), lock(),pending(),NewF) -> tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(NewF))))) record_updates(Record,Name,nil()) -> Record record_updates(Record,Name,cons(tuple(Field,tuplenil(NewF)),Fields)) -> record_updates(record_update(Record,Name,Field,NewF),Name,Fields) locker2_map_promote_pending(nil(),Pending) -> nil() locker2_map_promote_pending(cons(Lock,Locks),Pending) -> cons(locker2_promote_pending(Lock,Pending),locker2_map_promote_pending(Locks,Pending)) locker2_map_claim_lock(nil(),Resources,Client) -> nil() locker2_map_claim_lock(cons(Lock,Locks),Resources,Client) -> cons(locker2_claim_lock(Lock,Resources,Client),locker2_map_claim_lock (Locks,Resources,Client)) locker2_map_add_pending(nil(),Resources,Client) -> nil() locker2_promote_pending(Lock,Client) -> case0(Client,Lock,record_extract(Lock,lock(),pending())) case0(Client,Lock,cons(Client,Pendings)) -> record_updates(Lock,lock(),cons(tuple(excl(),tuplenil(Client)), cons(tuple(pending(),tuplenil(Pendings)),nil()))) case0(Client,Lock,MCRLFree0) -> Lock locker2_remove_pending(Lock,Client) -> record_updates(Lock,lock(),cons(tuple(pending(),tuplenil(subtract (record_extract (Lock,lock(),pending()), cons (Client,nil())))), nil())) locker2_add_pending(Lock,Resources,Client) -> case1(Client,Resources,Lock,member(record_extract(Lock,lock(),resource()),Resources)) case1(Client,Resources,Lock,true()) -> record_updates(Lock,lock(),cons(tuple(pending(),tuplenil(append (record_extract (Lock,lock(),pending()), cons (Client,nil())))), nil())) case1(Client,Resources,Lock,false()) -> Lock locker2_release_lock(Lock,Client) -> case2(Client,Lock,gen_modtageq(Client,record_extract(Lock,lock(),excl()))) case2(Client,Lock,true()) -> record_updates(Lock,lock(),cons(tuple(excllock(),excl()),nil())) case4(Client,Lock,MCRLFree1) -> false() locker2_obtainables(nil(),Client) -> true() locker2_obtainables(cons(Lock,Locks),Client) -> case5(Client,Locks,Lock,member(Client,record_extract(Lock,lock(),pending()))) case5(Client,Locks,Lock,true()) -> andt(locker2_obtainable(Lock,Client),locker2_obtainables(Locks,Client)) case5(Client,Locks,Lock,false()) -> locker2_obtainables(Locks,Client) locker2_check_available(Resource,nil()) -> false() locker2_check_available(Resource,cons(Lock,Locks)) -> case6(Locks,Lock,Resource,equal(Resource,record_extract(Lock,lock(),resource()))) case6(Locks,Lock,Resource,true()) -> andt(equal(record_extract(Lock,lock(),excl()),nil()),equal(record_extract (Lock,lock(),pending()), nil())) case6(Locks,Lock,Resource,false()) -> locker2_check_available(Resource,Locks) locker2_check_availables(nil(),Locks) -> true() locker2_check_availables(cons(Resource,Resources),Locks) -> andt(locker2_check_available(Resource,Locks),locker2_check_availables(Resources,Locks)) locker2_adduniq(nil(),List) -> List append(cons(Head,Tail),List) -> cons(Head,append(Tail,List)) subtract(List,nil()) -> List subtract(List,cons(Head,Tail)) -> subtract(delete(Head,List),Tail) delete(E,nil()) -> nil() delete(E,cons(Head,Tail)) -> case8(Tail,Head,E,equal(E,Head)) case8(Tail,Head,E,true()) -> Tail case8(Tail,Head,E,false()) -> cons(Head,delete(E,Tail)) gen_tag(Pid) -> tuple(Pid,tuplenil(tag())) gen_modtageq(Client1,Client2) -> equal(Client1,Client2) member(E,nil()) -> false() member(E,cons(Head,Tail)) -> case9(Tail,Head,E,equal(E,Head)) case9(Tail,Head,E,true()) -> true() case9(Tail,Head,E,false()) -> member(E,Tail) eqs(empty(),empty()) -> T() eqs(empty(),stack(E2,S2)) -> F() eqs(stack(E1,S1),empty()) -> F() eqs(stack(E1,S1),stack(E2,S2)) -> and(eqt(E1,E2),eqs(S1,S2)) pushs(E1,S1) -> stack(E1,S1) pops(stack(E1,S1)) -> S1 tops(stack(E1,S1)) -> E1 istops(E1,empty()) -> F() istops(E1,stack(E2,S1)) -> eqt(E1,E2) eqc(nocalls(),nocalls()) -> T() eqc(nocalls(),calls(E2,S2,CS2)) -> F() eqc(calls(E1,S1,CS1),nocalls()) -> F() eqc(calls(E1,S1,CS1),calls(E2,S2,CS2)) -> and(eqt(E1,E2),and(eqs(S1,S2),eqc(CS1,CS2))) push(E1,E2,nocalls()) -> calls(E1,stack(E2,empty()),nocalls()) push(E1,E2,calls(E3,S1,CS1)) -> push1(E1,E2,E3,S1,CS1,eqt(E1,E3)) push1(E1,E2,E3,S1,CS1,T()) -> calls(E3,pushs(E2,S1),CS1) Qed DPs: eqs#(stack(E1,S1),stack(E2,S2)) -> eqs#(S1,S2) TRS: or(T(),T()) -> T() or(F(),T()) -> T() or(T(),F()) -> T() or(F(),F()) -> F() and(T(),B) -> B and(B,T()) -> B and(F(),B) -> F() and(B,F()) -> F() imp(T(),B) -> B imp(F(),B) -> T() not(T()) -> F() not(F()) -> T() if(T(),B1,B2) -> B1 if(F(),B1,B2) -> B2 eq(T(),T()) -> T() eq(F(),F()) -> T() eq(T(),F()) -> F() eq(F(),T()) -> F() eqt(nil(),undefined()) -> F() eqt(nil(),pid(N2)) -> F() eqt(nil(),int(N2)) -> F() eqt(nil(),cons(H2,T2)) -> F() eqt(nil(),tuple(H2,T2)) -> F() eqt(nil(),tuplenil(H2)) -> F() eqt(a(),nil()) -> F() eqt(a(),a()) -> T() eqt(a(),excl()) -> F() eqt(a(),false()) -> F() eqt(a(),lock()) -> F() eqt(a(),locker()) -> F() eqt(a(),mcrlrecord()) -> F() eqt(a(),ok()) -> F() eqt(a(),pending()) -> F() eqt(a(),release()) -> F() eqt(a(),request()) -> F() eqt(a(),resource()) -> F() eqt(a(),tag()) -> F() eqt(a(),true()) -> F() eqt(a(),undefined()) -> F() eqt(a(),pid(N2)) -> F() eqt(a(),int(N2)) -> F() eqt(a(),cons(H2,T2)) -> F() eqt(a(),tuple(H2,T2)) -> F() eqt(a(),tuplenil(H2)) -> F() eqt(excl(),nil()) -> F() eqt(excl(),a()) -> F() eqt(excl(),excl()) -> T() eqt(excl(),false()) -> F() eqt(excl(),lock()) -> F() eqt(excl(),locker()) -> F() eqt(excl(),mcrlrecord()) -> F() eqt(excl(),ok()) -> F() eqt(excl(),pending()) -> F() eqt(excl(),release()) -> F() eqt(excl(),request()) -> F() eqt(excl(),resource()) -> F() eqt(excl(),tag()) -> F() eqt(excl(),true()) -> F() eqt(excl(),undefined()) -> F() eqt(excl(),pid(N2)) -> F() eqt(excl(),eqt(false(),int(N2))) -> F() eqt(false(),cons(H2,T2)) -> F() eqt(false(),tuple(H2,T2)) -> F() eqt(false(),tuplenil(H2)) -> F() eqt(lock(),nil()) -> F() eqt(lock(),a()) -> F() eqt(lock(),excl()) -> F() eqt(lock(),false()) -> F() eqt(lock(),lock()) -> T() eqt(lock(),locker()) -> F() eqt(lock(),mcrlrecord()) -> F() eqt(lock(),ok()) -> F() eqt(lock(),pending()) -> F() eqt(lock(),release()) -> F() eqt(lock(),request()) -> F() eqt(lock(),resource()) -> F() eqt(lock(),tag()) -> F() eqt(lock(),true()) -> F() eqt(lock(),undefined()) -> F() eqt(lock(),pid(N2)) -> F() eqt(lock(),int(N2)) -> F() eqt(lock(),cons(H2,T2)) -> F() eqt(lock(),tuple(H2,T2)) -> F() eqt(lock(),tuplenil(H2)) -> F() eqt(locker(),nil()) -> F() eqt(locker(),a()) -> F() eqt(locker(),excl()) -> F() eqt(locker(),false()) -> F() eqt(locker(),lock()) -> F() eqt(locker(),locker()) -> T() eqt(locker(),mcrlrecord()) -> F() eqt(locker(),ok()) -> F() eqt(locker(),pending()) -> F() eqt(locker(),release()) -> F() eqt(locker(),request()) -> F() eqt(locker(),resource()) -> F() eqt(locker(),tag()) -> F() eqt(locker(),true()) -> F() eqt(locker(),undefined()) -> F() eqt(locker(),pid(N2)) -> F() eqt(locker(),int(N2)) -> F() eqt(locker(),cons(H2,T2)) -> F() eqt(locker(),tuple(H2,T2)) -> F() eqt(locker(),tuplenil(H2)) -> F() eqt(mcrlrecord(),nil()) -> F() eqt(mcrlrecord(),a()) -> F() eqt(mcrlrecord(),excl()) -> F() eqt(mcrlrecord(),false()) -> F() eqt(mcrlrecord(),lock()) -> F() eqt(mcrlrecord(),locker()) -> F() eqt(mcrlrecord(),mcrlrecord()) -> T() eqt(mcrlrecord(),ok()) -> F() eqt(mcrlrecord(),pending()) -> F() eqt(mcrlrecord(),release()) -> F() eqt(mcrlrecord(),request()) -> F() eqt(mcrlrecord(),resource()) -> F() eqt(ok(),resource()) -> F() eqt(ok(),tag()) -> F() eqt(ok(),true()) -> F() eqt(ok(),undefined()) -> F() eqt(ok(),pid(N2)) -> F() eqt(ok(),int(N2)) -> F() eqt(ok(),cons(H2,T2)) -> F() eqt(ok(),tuple(H2,T2)) -> F() eqt(ok(),tuplenil(H2)) -> F() eqt(pending(),nil()) -> F() eqt(pending(),a()) -> F() eqt(pending(),excl()) -> F() eqt(pending(),false()) -> F() eqt(pending(),lock()) -> F() eqt(pending(),locker()) -> F() eqt(pending(),mcrlrecord()) -> F() eqt(pending(),ok()) -> F() eqt(pending(),pending()) -> T() eqt(pending(),release()) -> F() eqt(pending(),request()) -> F() eqt(pending(),resource()) -> F() eqt(pending(),tag()) -> F() eqt(pending(),true()) -> F() eqt(pending(),undefined()) -> F() eqt(pending(),pid(N2)) -> F() eqt(pending(),int(N2)) -> F() eqt(pending(),cons(H2,T2)) -> F() eqt(pending(),tuple(H2,T2)) -> F() eqt(pending(),tuplenil(H2)) -> F() eqt(release(),nil()) -> F() eqt(release(),a()) -> F() eqt(release(),excl()) -> F() eqt(release(),false()) -> F() eqt(release(),lock()) -> F() eqt(release(),locker()) -> F() eqt(release(),mcrlrecord()) -> F() eqt(release(),ok()) -> F() eqt(request(),mcrlrecord()) -> F() eqt(request(),ok()) -> F() eqt(request(),pending()) -> F() eqt(request(),release()) -> F() eqt(request(),request()) -> T() eqt(request(),resource()) -> F() eqt(request(),tag()) -> F() eqt(request(),true()) -> F() eqt(request(),undefined()) -> F() eqt(request(),pid(N2)) -> F() eqt(request(),int(N2)) -> F() eqt(request(),cons(H2,T2)) -> F() eqt(request(),tuple(H2,T2)) -> F() eqt(request(),tuplenil(H2)) -> F() eqt(resource(),nil()) -> F() eqt(resource(),a()) -> F() eqt(resource(),excl()) -> F() eqt(resource(),false()) -> F() eqt(resource(),lock()) -> F() eqt(resource(),locker()) -> F() eqt(resource(),mcrlrecord()) -> F() eqt(resource(),ok()) -> F() eqt(resource(),pending()) -> F() eqt(resource(),release()) -> F() eqt(resource(),request()) -> F() eqt(resource(),resource()) -> T() eqt(resource(),tag()) -> F() eqt(resource(),true()) -> F() eqt(resource(),undefined()) -> F() eqt(resource(),pid(N2)) -> F() eqt(resource(),int(N2)) -> F() eqt(resource(),cons(H2,T2)) -> F() eqt(resource(),tuple(H2,T2)) -> F() eqt(resource(),tuplenil(H2)) -> F() eqt(tag(),nil()) -> F() eqt(tag(),a()) -> F() eqt(tag(),excl()) -> F() eqt(tag(),false()) -> F() eqt(tag(),lock()) -> F() eqt(tag(),locker()) -> F() eqt(tag(),mcrlrecord()) -> F() eqt(tag(),ok()) -> F() eqt(tag(),pending()) -> F() eqt(tag(),release()) -> F() eqt(tag(),request()) -> F() eqt(tag(),resource()) -> F() eqt(tag(),tag()) -> T() eqt(tag(),true()) -> F() eqt(tag(),undefined()) -> F() eqt(tag(),pid(N2)) -> F() eqt(tag(),int(N2)) -> F() eqt(tag(),cons(H2,T2)) -> F() eqt(tag(),tuple(H2,T2)) -> F() eqt(tag(),tuplenil(H2)) -> F() eqt(true(),nil()) -> F() eqt(true(),a()) -> F() eqt(true(),excl()) -> F() eqt(true(),false()) -> F() eqt(true(),lock()) -> F() eqt(true(),locker()) -> F() eqt(true(),mcrlrecord()) -> F() eqt(true(),ok()) -> F() eqt(true(),pending()) -> F() eqt(true(),release()) -> F() eqt(true(),request()) -> F() eqt(true(),resource()) -> F() eqt(true(),tag()) -> F() eqt(true(),true()) -> T() eqt(true(),undefined()) -> F() eqt(true(),pid(N2)) -> F() eqt(true(),int(N2)) -> F() eqt(true(),cons(H2,T2)) -> F() eqt(true(),tuple(H2,T2)) -> F() eqt(true(),tuplenil(H2)) -> F() eqt(undefined(),nil()) -> F() eqt(undefined(),a()) -> F() eqt(undefined(),tuplenil(H2)) -> F() eqt(pid(N1),nil()) -> F() eqt(pid(N1),a()) -> F() eqt(pid(N1),excl()) -> F() eqt(pid(N1),false()) -> F() eqt(pid(N1),lock()) -> F() eqt(pid(N1),locker()) -> F() eqt(pid(N1),mcrlrecord()) -> F() eqt(pid(N1),ok()) -> F() eqt(pid(N1),pending()) -> F() eqt(pid(N1),release()) -> F() eqt(pid(N1),request()) -> F() eqt(pid(N1),resource()) -> F() eqt(pid(N1),tag()) -> F() eqt(pid(N1),true()) -> F() eqt(pid(N1),undefined()) -> F() eqt(pid(N1),pid(N2)) -> eqt(N1,N2) eqt(pid(N1),int(N2)) -> F() eqt(pid(N1),cons(H2,T2)) -> F() eqt(pid(N1),tuple(H2,T2)) -> F() eqt(pid(N1),tuplenil(H2)) -> F() eqt(int(N1),nil()) -> F() eqt(int(N1),a()) -> F() eqt(int(N1),excl()) -> F() eqt(int(N1),false()) -> F() eqt(int(N1),lock()) -> F() eqt(int(N1),locker()) -> F() eqt(int(N1),mcrlrecord()) -> F() eqt(int(N1),ok()) -> F() eqt(int(N1),pending()) -> F() eqt(int(N1),release()) -> F() eqt(int(N1),request()) -> F() eqt(int(N1),resource()) -> F() eqt(int(N1),tag()) -> F() eqt(int(N1),true()) -> F() eqt(int(N1),undefined()) -> F() eqt(cons(H1,T1),resource()) -> F() eqt(cons(H1,T1),tag()) -> F() eqt(cons(H1,T1),true()) -> F() eqt(cons(H1,T1),undefined()) -> F() eqt(cons(H1,T1),pid(N2)) -> F() eqt(cons(H1,T1),int(N2)) -> F() eqt(cons(H1,T1),cons(H2,T2)) -> and(eqt(H1,H2),eqt(T1,T2)) eqt(cons(H1,T1),tuple(H2,T2)) -> F() eqt(cons(H1,T1),tuplenil(H2)) -> F() eqt(tuple(H1,T1),nil()) -> F() eqt(tuple(H1,T1),a()) -> F() eqt(tuple(H1,T1),excl()) -> F() eqt(tuple(H1,T1),false()) -> F() eqt(tuple(H1,T1),lock()) -> F() eqt(tuple(H1,T1),locker()) -> F() eqt(tuple(H1,T1),mcrlrecord()) -> F() eqt(tuple(H1,T1),ok()) -> F() eqt(tuple(H1,T1),pending()) -> F() eqt(tuple(H1,T1),release()) -> F() eqt(tuple(H1,T1),request()) -> F() eqt(tuple(H1,T1),resource()) -> F() eqt(tuple(H1,T1),tag()) -> F() eqt(tuple(H1,T1),true()) -> F() eqt(tuple(H1,T1),undefined()) -> F() eqt(tuple(H1,T1),pid(N2)) -> F() eqt(tuple(H1,T1),int(N2)) -> F() eqt(tuple(H1,T1),cons(H2,T2)) -> F() eqt(tuple(H1,T1),tuple(H2,T2)) -> and(eqt(H1,H2),eqt(T1,T2)) eqt(tuple(H1,T1),tuplenil(H2)) -> F() eqt(tuplenil(H1),nil()) -> F() eqt(tuplenil(H1),a()) -> F() eqt(tuplenil(H1),excl()) -> F() eqt(tuplenil(H1),false()) -> F() eqt(tuplenil(H1),lock()) -> F() eqt(tuplenil(H1),locker()) -> F() eqt(tuplenil(H1),mcrlrecord()) -> F() eqt(tuplenil(H1),ok()) -> F() eqt(tuplenil(H1),pending()) -> F() eqt(tuplenil(H1),release()) -> F() eqt(tuplenil(H1),request()) -> F() eqt(tuplenil(H1),resource()) -> F() eqt(tuplenil(H1),tag()) -> F() eqt(tuplenil(H1),true()) -> F() eqt(tuplenil(H1),undefined()) -> F() eqt(tuplenil(H1),pid(N2)) -> F() eqt(tuplenil(H1),int(N2)) -> F() eqt(tuplenil(H1),cons(H2,T2)) -> F() eqt(tuplenil(H1),tuple(H2,T2)) -> F() eqt(tuplenil(H1),tuplenil(H2)) -> eqt(H1,H2) element(int(s(0())),tuplenil(T1)) -> T1 element(int(s(0())),tuple(T1,T2)) -> T1 element(int(s(s(N1))),tuple(T1,T2)) -> element(int(s(N1)),T2) record_new(lock()) -> tuple(mcrlrecord(),tuple(lock(),tuple(undefined(),tuple(nil(),tuplenil(nil()))))) record_extract(tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))), lock(),resource()) -> tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))) record_update(tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))), lock(),pending(),NewF) -> tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(NewF))))) record_updates(Record,Name,nil()) -> Record record_updates(Record,Name,cons(tuple(Field,tuplenil(NewF)),Fields)) -> record_updates(record_update(Record,Name,Field,NewF),Name,Fields) locker2_map_promote_pending(nil(),Pending) -> nil() locker2_map_promote_pending(cons(Lock,Locks),Pending) -> cons(locker2_promote_pending(Lock,Pending),locker2_map_promote_pending(Locks,Pending)) locker2_map_claim_lock(nil(),Resources,Client) -> nil() locker2_map_claim_lock(cons(Lock,Locks),Resources,Client) -> cons(locker2_claim_lock(Lock,Resources,Client),locker2_map_claim_lock(Locks,Resources,Client)) locker2_map_add_pending(nil(),Resources,Client) -> nil() locker2_promote_pending(Lock,Client) -> case0(Client,Lock,record_extract(Lock,lock(),pending())) case0(Client,Lock,cons(Client,Pendings)) -> record_updates(Lock,lock(),cons(tuple(excl(),tuplenil(Client)),cons ( tuple ( pending(),tuplenil(Pendings)), nil ()))) case0(Client,Lock,MCRLFree0) -> Lock locker2_remove_pending(Lock,Client) -> record_updates(Lock,lock(),cons(tuple(pending(),tuplenil(subtract (record_extract (Lock,lock(),pending()), cons(Client,nil())))), nil())) locker2_add_pending(Lock,Resources,Client) -> case1(Client,Resources,Lock,member(record_extract(Lock,lock(),resource()),Resources)) case1(Client,Resources,Lock,true()) -> record_updates(Lock,lock(),cons(tuple(pending(),tuplenil(append( record_extract ( Lock,lock(),pending()), cons (Client,nil())))), nil())) case1(Client,Resources,Lock,false()) -> Lock locker2_release_lock(Lock,Client) -> case2(Client,Lock,gen_modtageq(Client,record_extract(Lock,lock(),excl()))) case2(Client,Lock,true()) -> record_updates(Lock,lock(),cons(tuple(excllock(),excl()),nil())) case4(Client,Lock,MCRLFree1) -> false() locker2_obtainables(nil(),Client) -> true() locker2_obtainables(cons(Lock,Locks),Client) -> case5(Client,Locks,Lock,member(Client,record_extract(Lock,lock(),pending()))) case5(Client,Locks,Lock,true()) -> andt(locker2_obtainable(Lock,Client),locker2_obtainables(Locks,Client)) case5(Client,Locks,Lock,false()) -> locker2_obtainables(Locks,Client) locker2_check_available(Resource,nil()) -> false() locker2_check_available(Resource,cons(Lock,Locks)) -> case6(Locks,Lock,Resource,equal(Resource,record_extract(Lock,lock(),resource()))) case6(Locks,Lock,Resource,true()) -> andt(equal(record_extract(Lock,lock(),excl()),nil()),equal(record_extract (Lock,lock(),pending()), nil())) case6(Locks,Lock,Resource,false()) -> locker2_check_available(Resource,Locks) locker2_check_availables(nil(),Locks) -> true() locker2_check_availables(cons(Resource,Resources),Locks) -> andt(locker2_check_available(Resource,Locks),locker2_check_availables(Resources,Locks)) locker2_adduniq(nil(),List) -> List append(cons(Head,Tail),List) -> cons(Head,append(Tail,List)) subtract(List,nil()) -> List subtract(List,cons(Head,Tail)) -> subtract(delete(Head,List),Tail) delete(E,nil()) -> nil() delete(E,cons(Head,Tail)) -> case8(Tail,Head,E,equal(E,Head)) case8(Tail,Head,E,true()) -> Tail case8(Tail,Head,E,false()) -> cons(Head,delete(E,Tail)) gen_tag(Pid) -> tuple(Pid,tuplenil(tag())) gen_modtageq(Client1,Client2) -> equal(Client1,Client2) member(E,nil()) -> false() member(E,cons(Head,Tail)) -> case9(Tail,Head,E,equal(E,Head)) case9(Tail,Head,E,true()) -> true() case9(Tail,Head,E,false()) -> member(E,Tail) eqs(empty(),empty()) -> T() eqs(empty(),stack(E2,S2)) -> F() eqs(stack(E1,S1),empty()) -> F() eqs(stack(E1,S1),stack(E2,S2)) -> and(eqt(E1,E2),eqs(S1,S2)) pushs(E1,S1) -> stack(E1,S1) pops(stack(E1,S1)) -> S1 tops(stack(E1,S1)) -> E1 istops(E1,empty()) -> F() istops(E1,stack(E2,S1)) -> eqt(E1,E2) eqc(nocalls(),nocalls()) -> T() eqc(nocalls(),calls(E2,S2,CS2)) -> F() eqc(calls(E1,S1,CS1),nocalls()) -> F() eqc(calls(E1,S1,CS1),calls(E2,S2,CS2)) -> and(eqt(E1,E2),and(eqs(S1,S2),eqc(CS1,CS2))) push(E1,E2,nocalls()) -> calls(E1,stack(E2,empty()),nocalls()) push(E1,E2,calls(E3,S1,CS1)) -> push1(E1,E2,E3,S1,CS1,eqt(E1,E3)) push1(E1,E2,E3,S1,CS1,T()) -> calls(E3,pushs(E2,S1),CS1) Subterm Criterion Processor: simple projection: pi(eqs#) = 0 problem: DPs: TRS: or(T(),T()) -> T() or(F(),T()) -> T() or(T(),F()) -> T() or(F(),F()) -> F() and(T(),B) -> B and(B,T()) -> B and(F(),B) -> F() and(B,F()) -> F() imp(T(),B) -> B imp(F(),B) -> T() not(T()) -> F() not(F()) -> T() if(T(),B1,B2) -> B1 if(F(),B1,B2) -> B2 eq(T(),T()) -> T() eq(F(),F()) -> T() eq(T(),F()) -> F() eq(F(),T()) -> F() eqt(nil(),undefined()) -> F() eqt(nil(),pid(N2)) -> F() eqt(nil(),int(N2)) -> F() eqt(nil(),cons(H2,T2)) -> F() eqt(nil(),tuple(H2,T2)) -> F() eqt(nil(),tuplenil(H2)) -> F() eqt(a(),nil()) -> F() eqt(a(),a()) -> T() eqt(a(),excl()) -> F() eqt(a(),false()) -> F() eqt(a(),lock()) -> F() eqt(a(),locker()) -> F() eqt(a(),mcrlrecord()) -> F() eqt(a(),ok()) -> F() eqt(a(),pending()) -> F() eqt(a(),release()) -> F() eqt(a(),request()) -> F() eqt(a(),resource()) -> F() eqt(a(),tag()) -> F() eqt(a(),true()) -> F() eqt(a(),undefined()) -> F() eqt(a(),pid(N2)) -> F() eqt(a(),int(N2)) -> F() eqt(a(),cons(H2,T2)) -> F() eqt(a(),tuple(H2,T2)) -> F() eqt(a(),tuplenil(H2)) -> F() eqt(excl(),nil()) -> F() eqt(excl(),a()) -> F() eqt(excl(),excl()) -> T() eqt(excl(),false()) -> F() eqt(excl(),lock()) -> F() eqt(excl(),locker()) -> F() eqt(excl(),mcrlrecord()) -> F() eqt(excl(),ok()) -> F() eqt(excl(),pending()) -> F() eqt(excl(),release()) -> F() eqt(excl(),request()) -> F() eqt(excl(),resource()) -> F() eqt(excl(),tag()) -> F() eqt(excl(),true()) -> F() eqt(excl(),undefined()) -> F() eqt(excl(),pid(N2)) -> F() eqt(excl(),eqt(false(),int(N2))) -> F() eqt(false(),cons(H2,T2)) -> F() eqt(false(),tuple(H2,T2)) -> F() eqt(false(),tuplenil(H2)) -> F() eqt(lock(),nil()) -> F() eqt(lock(),a()) -> F() eqt(lock(),excl()) -> F() eqt(lock(),false()) -> F() eqt(lock(),lock()) -> T() eqt(lock(),locker()) -> F() eqt(lock(),mcrlrecord()) -> F() eqt(lock(),ok()) -> F() eqt(lock(),pending()) -> F() eqt(lock(),release()) -> F() eqt(lock(),request()) -> F() eqt(lock(),resource()) -> F() eqt(lock(),tag()) -> F() eqt(lock(),true()) -> F() eqt(lock(),undefined()) -> F() eqt(lock(),pid(N2)) -> F() eqt(lock(),int(N2)) -> F() eqt(lock(),cons(H2,T2)) -> F() eqt(lock(),tuple(H2,T2)) -> F() eqt(lock(),tuplenil(H2)) -> F() eqt(locker(),nil()) -> F() eqt(locker(),a()) -> F() eqt(locker(),excl()) -> F() eqt(locker(),false()) -> F() eqt(locker(),lock()) -> F() eqt(locker(),locker()) -> T() eqt(locker(),mcrlrecord()) -> F() eqt(locker(),ok()) -> F() eqt(locker(),pending()) -> F() eqt(locker(),release()) -> F() eqt(locker(),request()) -> F() eqt(locker(),resource()) -> F() eqt(locker(),tag()) -> F() eqt(locker(),true()) -> F() eqt(locker(),undefined()) -> F() eqt(locker(),pid(N2)) -> F() eqt(locker(),int(N2)) -> F() eqt(locker(),cons(H2,T2)) -> F() eqt(locker(),tuple(H2,T2)) -> F() eqt(locker(),tuplenil(H2)) -> F() eqt(mcrlrecord(),nil()) -> F() eqt(mcrlrecord(),a()) -> F() eqt(mcrlrecord(),excl()) -> F() eqt(mcrlrecord(),false()) -> F() eqt(mcrlrecord(),lock()) -> F() eqt(mcrlrecord(),locker()) -> F() eqt(mcrlrecord(),mcrlrecord()) -> T() eqt(mcrlrecord(),ok()) -> F() eqt(mcrlrecord(),pending()) -> F() eqt(mcrlrecord(),release()) -> F() eqt(mcrlrecord(),request()) -> F() eqt(mcrlrecord(),resource()) -> F() eqt(ok(),resource()) -> F() eqt(ok(),tag()) -> F() eqt(ok(),true()) -> F() eqt(ok(),undefined()) -> F() eqt(ok(),pid(N2)) -> F() eqt(ok(),int(N2)) -> F() eqt(ok(),cons(H2,T2)) -> F() eqt(ok(),tuple(H2,T2)) -> F() eqt(ok(),tuplenil(H2)) -> F() eqt(pending(),nil()) -> F() eqt(pending(),a()) -> F() eqt(pending(),excl()) -> F() eqt(pending(),false()) -> F() eqt(pending(),lock()) -> F() eqt(pending(),locker()) -> F() eqt(pending(),mcrlrecord()) -> F() eqt(pending(),ok()) -> F() eqt(pending(),pending()) -> T() eqt(pending(),release()) -> F() eqt(pending(),request()) -> F() eqt(pending(),resource()) -> F() eqt(pending(),tag()) -> F() eqt(pending(),true()) -> F() eqt(pending(),undefined()) -> F() eqt(pending(),pid(N2)) -> F() eqt(pending(),int(N2)) -> F() eqt(pending(),cons(H2,T2)) -> F() eqt(pending(),tuple(H2,T2)) -> F() eqt(pending(),tuplenil(H2)) -> F() eqt(release(),nil()) -> F() eqt(release(),a()) -> F() eqt(release(),excl()) -> F() eqt(release(),false()) -> F() eqt(release(),lock()) -> F() eqt(release(),locker()) -> F() eqt(release(),mcrlrecord()) -> F() eqt(release(),ok()) -> F() eqt(request(),mcrlrecord()) -> F() eqt(request(),ok()) -> F() eqt(request(),pending()) -> F() eqt(request(),release()) -> F() eqt(request(),request()) -> T() eqt(request(),resource()) -> F() eqt(request(),tag()) -> F() eqt(request(),true()) -> F() eqt(request(),undefined()) -> F() eqt(request(),pid(N2)) -> F() eqt(request(),int(N2)) -> F() eqt(request(),cons(H2,T2)) -> F() eqt(request(),tuple(H2,T2)) -> F() eqt(request(),tuplenil(H2)) -> F() eqt(resource(),nil()) -> F() eqt(resource(),a()) -> F() eqt(resource(),excl()) -> F() eqt(resource(),false()) -> F() eqt(resource(),lock()) -> F() eqt(resource(),locker()) -> F() eqt(resource(),mcrlrecord()) -> F() eqt(resource(),ok()) -> F() eqt(resource(),pending()) -> F() eqt(resource(),release()) -> F() eqt(resource(),request()) -> F() eqt(resource(),resource()) -> T() eqt(resource(),tag()) -> F() eqt(resource(),true()) -> F() eqt(resource(),undefined()) -> F() eqt(resource(),pid(N2)) -> F() eqt(resource(),int(N2)) -> F() eqt(resource(),cons(H2,T2)) -> F() eqt(resource(),tuple(H2,T2)) -> F() eqt(resource(),tuplenil(H2)) -> F() eqt(tag(),nil()) -> F() eqt(tag(),a()) -> F() eqt(tag(),excl()) -> F() eqt(tag(),false()) -> F() eqt(tag(),lock()) -> F() eqt(tag(),locker()) -> F() eqt(tag(),mcrlrecord()) -> F() eqt(tag(),ok()) -> F() eqt(tag(),pending()) -> F() eqt(tag(),release()) -> F() eqt(tag(),request()) -> F() eqt(tag(),resource()) -> F() eqt(tag(),tag()) -> T() eqt(tag(),true()) -> F() eqt(tag(),undefined()) -> F() eqt(tag(),pid(N2)) -> F() eqt(tag(),int(N2)) -> F() eqt(tag(),cons(H2,T2)) -> F() eqt(tag(),tuple(H2,T2)) -> F() eqt(tag(),tuplenil(H2)) -> F() eqt(true(),nil()) -> F() eqt(true(),a()) -> F() eqt(true(),excl()) -> F() eqt(true(),false()) -> F() eqt(true(),lock()) -> F() eqt(true(),locker()) -> F() eqt(true(),mcrlrecord()) -> F() eqt(true(),ok()) -> F() eqt(true(),pending()) -> F() eqt(true(),release()) -> F() eqt(true(),request()) -> F() eqt(true(),resource()) -> F() eqt(true(),tag()) -> F() eqt(true(),true()) -> T() eqt(true(),undefined()) -> F() eqt(true(),pid(N2)) -> F() eqt(true(),int(N2)) -> F() eqt(true(),cons(H2,T2)) -> F() eqt(true(),tuple(H2,T2)) -> F() eqt(true(),tuplenil(H2)) -> F() eqt(undefined(),nil()) -> F() eqt(undefined(),a()) -> F() eqt(undefined(),tuplenil(H2)) -> F() eqt(pid(N1),nil()) -> F() eqt(pid(N1),a()) -> F() eqt(pid(N1),excl()) -> F() eqt(pid(N1),false()) -> F() eqt(pid(N1),lock()) -> F() eqt(pid(N1),locker()) -> F() eqt(pid(N1),mcrlrecord()) -> F() eqt(pid(N1),ok()) -> F() eqt(pid(N1),pending()) -> F() eqt(pid(N1),release()) -> F() eqt(pid(N1),request()) -> F() eqt(pid(N1),resource()) -> F() eqt(pid(N1),tag()) -> F() eqt(pid(N1),true()) -> F() eqt(pid(N1),undefined()) -> F() eqt(pid(N1),pid(N2)) -> eqt(N1,N2) eqt(pid(N1),int(N2)) -> F() eqt(pid(N1),cons(H2,T2)) -> F() eqt(pid(N1),tuple(H2,T2)) -> F() eqt(pid(N1),tuplenil(H2)) -> F() eqt(int(N1),nil()) -> F() eqt(int(N1),a()) -> F() eqt(int(N1),excl()) -> F() eqt(int(N1),false()) -> F() eqt(int(N1),lock()) -> F() eqt(int(N1),locker()) -> F() eqt(int(N1),mcrlrecord()) -> F() eqt(int(N1),ok()) -> F() eqt(int(N1),pending()) -> F() eqt(int(N1),release()) -> F() eqt(int(N1),request()) -> F() eqt(int(N1),resource()) -> F() eqt(int(N1),tag()) -> F() eqt(int(N1),true()) -> F() eqt(int(N1),undefined()) -> F() eqt(cons(H1,T1),resource()) -> F() eqt(cons(H1,T1),tag()) -> F() eqt(cons(H1,T1),true()) -> F() eqt(cons(H1,T1),undefined()) -> F() eqt(cons(H1,T1),pid(N2)) -> F() eqt(cons(H1,T1),int(N2)) -> F() eqt(cons(H1,T1),cons(H2,T2)) -> and(eqt(H1,H2),eqt(T1,T2)) eqt(cons(H1,T1),tuple(H2,T2)) -> F() eqt(cons(H1,T1),tuplenil(H2)) -> F() eqt(tuple(H1,T1),nil()) -> F() eqt(tuple(H1,T1),a()) -> F() eqt(tuple(H1,T1),excl()) -> F() eqt(tuple(H1,T1),false()) -> F() eqt(tuple(H1,T1),lock()) -> F() eqt(tuple(H1,T1),locker()) -> F() eqt(tuple(H1,T1),mcrlrecord()) -> F() eqt(tuple(H1,T1),ok()) -> F() eqt(tuple(H1,T1),pending()) -> F() eqt(tuple(H1,T1),release()) -> F() eqt(tuple(H1,T1),request()) -> F() eqt(tuple(H1,T1),resource()) -> F() eqt(tuple(H1,T1),tag()) -> F() eqt(tuple(H1,T1),true()) -> F() eqt(tuple(H1,T1),undefined()) -> F() eqt(tuple(H1,T1),pid(N2)) -> F() eqt(tuple(H1,T1),int(N2)) -> F() eqt(tuple(H1,T1),cons(H2,T2)) -> F() eqt(tuple(H1,T1),tuple(H2,T2)) -> and(eqt(H1,H2),eqt(T1,T2)) eqt(tuple(H1,T1),tuplenil(H2)) -> F() eqt(tuplenil(H1),nil()) -> F() eqt(tuplenil(H1),a()) -> F() eqt(tuplenil(H1),excl()) -> F() eqt(tuplenil(H1),false()) -> F() eqt(tuplenil(H1),lock()) -> F() eqt(tuplenil(H1),locker()) -> F() eqt(tuplenil(H1),mcrlrecord()) -> F() eqt(tuplenil(H1),ok()) -> F() eqt(tuplenil(H1),pending()) -> F() eqt(tuplenil(H1),release()) -> F() eqt(tuplenil(H1),request()) -> F() eqt(tuplenil(H1),resource()) -> F() eqt(tuplenil(H1),tag()) -> F() eqt(tuplenil(H1),true()) -> F() eqt(tuplenil(H1),undefined()) -> F() eqt(tuplenil(H1),pid(N2)) -> F() eqt(tuplenil(H1),int(N2)) -> F() eqt(tuplenil(H1),cons(H2,T2)) -> F() eqt(tuplenil(H1),tuple(H2,T2)) -> F() eqt(tuplenil(H1),tuplenil(H2)) -> eqt(H1,H2) element(int(s(0())),tuplenil(T1)) -> T1 element(int(s(0())),tuple(T1,T2)) -> T1 element(int(s(s(N1))),tuple(T1,T2)) -> element(int(s(N1)),T2) record_new(lock()) -> tuple(mcrlrecord(),tuple(lock(),tuple(undefined(),tuple(nil(),tuplenil(nil()))))) record_extract(tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))), lock(),resource()) -> tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))) record_update(tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))), lock(),pending(),NewF) -> tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(NewF))))) record_updates(Record,Name,nil()) -> Record record_updates(Record,Name,cons(tuple(Field,tuplenil(NewF)),Fields)) -> record_updates(record_update(Record,Name,Field,NewF),Name,Fields) locker2_map_promote_pending(nil(),Pending) -> nil() locker2_map_promote_pending(cons(Lock,Locks),Pending) -> cons(locker2_promote_pending(Lock,Pending),locker2_map_promote_pending(Locks,Pending)) locker2_map_claim_lock(nil(),Resources,Client) -> nil() locker2_map_claim_lock(cons(Lock,Locks),Resources,Client) -> cons(locker2_claim_lock(Lock,Resources,Client),locker2_map_claim_lock (Locks,Resources,Client)) locker2_map_add_pending(nil(),Resources,Client) -> nil() locker2_promote_pending(Lock,Client) -> case0(Client,Lock,record_extract(Lock,lock(),pending())) case0(Client,Lock,cons(Client,Pendings)) -> record_updates(Lock,lock(),cons(tuple(excl(),tuplenil(Client)), cons(tuple(pending(),tuplenil(Pendings)),nil()))) case0(Client,Lock,MCRLFree0) -> Lock locker2_remove_pending(Lock,Client) -> record_updates(Lock,lock(),cons(tuple(pending(),tuplenil(subtract (record_extract (Lock,lock(),pending()), cons (Client,nil())))), nil())) locker2_add_pending(Lock,Resources,Client) -> case1(Client,Resources,Lock,member(record_extract(Lock,lock(),resource()),Resources)) case1(Client,Resources,Lock,true()) -> record_updates(Lock,lock(),cons(tuple(pending(),tuplenil(append (record_extract (Lock,lock(),pending()), cons (Client,nil())))), nil())) case1(Client,Resources,Lock,false()) -> Lock locker2_release_lock(Lock,Client) -> case2(Client,Lock,gen_modtageq(Client,record_extract(Lock,lock(),excl()))) case2(Client,Lock,true()) -> record_updates(Lock,lock(),cons(tuple(excllock(),excl()),nil())) case4(Client,Lock,MCRLFree1) -> false() locker2_obtainables(nil(),Client) -> true() locker2_obtainables(cons(Lock,Locks),Client) -> case5(Client,Locks,Lock,member(Client,record_extract(Lock,lock(),pending()))) case5(Client,Locks,Lock,true()) -> andt(locker2_obtainable(Lock,Client),locker2_obtainables(Locks,Client)) case5(Client,Locks,Lock,false()) -> locker2_obtainables(Locks,Client) locker2_check_available(Resource,nil()) -> false() locker2_check_available(Resource,cons(Lock,Locks)) -> case6(Locks,Lock,Resource,equal(Resource,record_extract(Lock,lock(),resource()))) case6(Locks,Lock,Resource,true()) -> andt(equal(record_extract(Lock,lock(),excl()),nil()),equal(record_extract (Lock,lock(),pending()), nil())) case6(Locks,Lock,Resource,false()) -> locker2_check_available(Resource,Locks) locker2_check_availables(nil(),Locks) -> true() locker2_check_availables(cons(Resource,Resources),Locks) -> andt(locker2_check_available(Resource,Locks),locker2_check_availables(Resources,Locks)) locker2_adduniq(nil(),List) -> List append(cons(Head,Tail),List) -> cons(Head,append(Tail,List)) subtract(List,nil()) -> List subtract(List,cons(Head,Tail)) -> subtract(delete(Head,List),Tail) delete(E,nil()) -> nil() delete(E,cons(Head,Tail)) -> case8(Tail,Head,E,equal(E,Head)) case8(Tail,Head,E,true()) -> Tail case8(Tail,Head,E,false()) -> cons(Head,delete(E,Tail)) gen_tag(Pid) -> tuple(Pid,tuplenil(tag())) gen_modtageq(Client1,Client2) -> equal(Client1,Client2) member(E,nil()) -> false() member(E,cons(Head,Tail)) -> case9(Tail,Head,E,equal(E,Head)) case9(Tail,Head,E,true()) -> true() case9(Tail,Head,E,false()) -> member(E,Tail) eqs(empty(),empty()) -> T() eqs(empty(),stack(E2,S2)) -> F() eqs(stack(E1,S1),empty()) -> F() eqs(stack(E1,S1),stack(E2,S2)) -> and(eqt(E1,E2),eqs(S1,S2)) pushs(E1,S1) -> stack(E1,S1) pops(stack(E1,S1)) -> S1 tops(stack(E1,S1)) -> E1 istops(E1,empty()) -> F() istops(E1,stack(E2,S1)) -> eqt(E1,E2) eqc(nocalls(),nocalls()) -> T() eqc(nocalls(),calls(E2,S2,CS2)) -> F() eqc(calls(E1,S1,CS1),nocalls()) -> F() eqc(calls(E1,S1,CS1),calls(E2,S2,CS2)) -> and(eqt(E1,E2),and(eqs(S1,S2),eqc(CS1,CS2))) push(E1,E2,nocalls()) -> calls(E1,stack(E2,empty()),nocalls()) push(E1,E2,calls(E3,S1,CS1)) -> push1(E1,E2,E3,S1,CS1,eqt(E1,E3)) push1(E1,E2,E3,S1,CS1,T()) -> calls(E3,pushs(E2,S1),CS1) Qed DPs: eqt#(pid(N1),pid(N2)) -> eqt#(N1,N2) eqt#(cons(H1,T1),cons(H2,T2)) -> eqt#(T1,T2) eqt#(cons(H1,T1),cons(H2,T2)) -> eqt#(H1,H2) eqt#(tuple(H1,T1),tuple(H2,T2)) -> eqt#(T1,T2) eqt#(tuple(H1,T1),tuple(H2,T2)) -> eqt#(H1,H2) eqt#(tuplenil(H1),tuplenil(H2)) -> eqt#(H1,H2) TRS: or(T(),T()) -> T() or(F(),T()) -> T() or(T(),F()) -> T() or(F(),F()) -> F() and(T(),B) -> B and(B,T()) -> B and(F(),B) -> F() and(B,F()) -> F() imp(T(),B) -> B imp(F(),B) -> T() not(T()) -> F() not(F()) -> T() if(T(),B1,B2) -> B1 if(F(),B1,B2) -> B2 eq(T(),T()) -> T() eq(F(),F()) -> T() eq(T(),F()) -> F() eq(F(),T()) -> F() eqt(nil(),undefined()) -> F() eqt(nil(),pid(N2)) -> F() eqt(nil(),int(N2)) -> F() eqt(nil(),cons(H2,T2)) -> F() eqt(nil(),tuple(H2,T2)) -> F() eqt(nil(),tuplenil(H2)) -> F() eqt(a(),nil()) -> F() eqt(a(),a()) -> T() eqt(a(),excl()) -> F() eqt(a(),false()) -> F() eqt(a(),lock()) -> F() eqt(a(),locker()) -> F() eqt(a(),mcrlrecord()) -> F() eqt(a(),ok()) -> F() eqt(a(),pending()) -> F() eqt(a(),release()) -> F() eqt(a(),request()) -> F() eqt(a(),resource()) -> F() eqt(a(),tag()) -> F() eqt(a(),true()) -> F() eqt(a(),undefined()) -> F() eqt(a(),pid(N2)) -> F() eqt(a(),int(N2)) -> F() eqt(a(),cons(H2,T2)) -> F() eqt(a(),tuple(H2,T2)) -> F() eqt(a(),tuplenil(H2)) -> F() eqt(excl(),nil()) -> F() eqt(excl(),a()) -> F() eqt(excl(),excl()) -> T() eqt(excl(),false()) -> F() eqt(excl(),lock()) -> F() eqt(excl(),locker()) -> F() eqt(excl(),mcrlrecord()) -> F() eqt(excl(),ok()) -> F() eqt(excl(),pending()) -> F() eqt(excl(),release()) -> F() eqt(excl(),request()) -> F() eqt(excl(),resource()) -> F() eqt(excl(),tag()) -> F() eqt(excl(),true()) -> F() eqt(excl(),undefined()) -> F() eqt(excl(),pid(N2)) -> F() eqt(excl(),eqt(false(),int(N2))) -> F() eqt(false(),cons(H2,T2)) -> F() eqt(false(),tuple(H2,T2)) -> F() eqt(false(),tuplenil(H2)) -> F() eqt(lock(),nil()) -> F() eqt(lock(),a()) -> F() eqt(lock(),excl()) -> F() eqt(lock(),false()) -> F() eqt(lock(),lock()) -> T() eqt(lock(),locker()) -> F() eqt(lock(),mcrlrecord()) -> F() eqt(lock(),ok()) -> F() eqt(lock(),pending()) -> F() eqt(lock(),release()) -> F() eqt(lock(),request()) -> F() eqt(lock(),resource()) -> F() eqt(lock(),tag()) -> F() eqt(lock(),true()) -> F() eqt(lock(),undefined()) -> F() eqt(lock(),pid(N2)) -> F() eqt(lock(),int(N2)) -> F() eqt(lock(),cons(H2,T2)) -> F() eqt(lock(),tuple(H2,T2)) -> F() eqt(lock(),tuplenil(H2)) -> F() eqt(locker(),nil()) -> F() eqt(locker(),a()) -> F() eqt(locker(),excl()) -> F() eqt(locker(),false()) -> F() eqt(locker(),lock()) -> F() eqt(locker(),locker()) -> T() eqt(locker(),mcrlrecord()) -> F() eqt(locker(),ok()) -> F() eqt(locker(),pending()) -> F() eqt(locker(),release()) -> F() eqt(locker(),request()) -> F() eqt(locker(),resource()) -> F() eqt(locker(),tag()) -> F() eqt(locker(),true()) -> F() eqt(locker(),undefined()) -> F() eqt(locker(),pid(N2)) -> F() eqt(locker(),int(N2)) -> F() eqt(locker(),cons(H2,T2)) -> F() eqt(locker(),tuple(H2,T2)) -> F() eqt(locker(),tuplenil(H2)) -> F() eqt(mcrlrecord(),nil()) -> F() eqt(mcrlrecord(),a()) -> F() eqt(mcrlrecord(),excl()) -> F() eqt(mcrlrecord(),false()) -> F() eqt(mcrlrecord(),lock()) -> F() eqt(mcrlrecord(),locker()) -> F() eqt(mcrlrecord(),mcrlrecord()) -> T() eqt(mcrlrecord(),ok()) -> F() eqt(mcrlrecord(),pending()) -> F() eqt(mcrlrecord(),release()) -> F() eqt(mcrlrecord(),request()) -> F() eqt(mcrlrecord(),resource()) -> F() eqt(ok(),resource()) -> F() eqt(ok(),tag()) -> F() eqt(ok(),true()) -> F() eqt(ok(),undefined()) -> F() eqt(ok(),pid(N2)) -> F() eqt(ok(),int(N2)) -> F() eqt(ok(),cons(H2,T2)) -> F() eqt(ok(),tuple(H2,T2)) -> F() eqt(ok(),tuplenil(H2)) -> F() eqt(pending(),nil()) -> F() eqt(pending(),a()) -> F() eqt(pending(),excl()) -> F() eqt(pending(),false()) -> F() eqt(pending(),lock()) -> F() eqt(pending(),locker()) -> F() eqt(pending(),mcrlrecord()) -> F() eqt(pending(),ok()) -> F() eqt(pending(),pending()) -> T() eqt(pending(),release()) -> F() eqt(pending(),request()) -> F() eqt(pending(),resource()) -> F() eqt(pending(),tag()) -> F() eqt(pending(),true()) -> F() eqt(pending(),undefined()) -> F() eqt(pending(),pid(N2)) -> F() eqt(pending(),int(N2)) -> F() eqt(pending(),cons(H2,T2)) -> F() eqt(pending(),tuple(H2,T2)) -> F() eqt(pending(),tuplenil(H2)) -> F() eqt(release(),nil()) -> F() eqt(release(),a()) -> F() eqt(release(),excl()) -> F() eqt(release(),false()) -> F() eqt(release(),lock()) -> F() eqt(release(),locker()) -> F() eqt(release(),mcrlrecord()) -> F() eqt(release(),ok()) -> F() eqt(request(),mcrlrecord()) -> F() eqt(request(),ok()) -> F() eqt(request(),pending()) -> F() eqt(request(),release()) -> F() eqt(request(),request()) -> T() eqt(request(),resource()) -> F() eqt(request(),tag()) -> F() eqt(request(),true()) -> F() eqt(request(),undefined()) -> F() eqt(request(),pid(N2)) -> F() eqt(request(),int(N2)) -> F() eqt(request(),cons(H2,T2)) -> F() eqt(request(),tuple(H2,T2)) -> F() eqt(request(),tuplenil(H2)) -> F() eqt(resource(),nil()) -> F() eqt(resource(),a()) -> F() eqt(resource(),excl()) -> F() eqt(resource(),false()) -> F() eqt(resource(),lock()) -> F() eqt(resource(),locker()) -> F() eqt(resource(),mcrlrecord()) -> F() eqt(resource(),ok()) -> F() eqt(resource(),pending()) -> F() eqt(resource(),release()) -> F() eqt(resource(),request()) -> F() eqt(resource(),resource()) -> T() eqt(resource(),tag()) -> F() eqt(resource(),true()) -> F() eqt(resource(),undefined()) -> F() eqt(resource(),pid(N2)) -> F() eqt(resource(),int(N2)) -> F() eqt(resource(),cons(H2,T2)) -> F() eqt(resource(),tuple(H2,T2)) -> F() eqt(resource(),tuplenil(H2)) -> F() eqt(tag(),nil()) -> F() eqt(tag(),a()) -> F() eqt(tag(),excl()) -> F() eqt(tag(),false()) -> F() eqt(tag(),lock()) -> F() eqt(tag(),locker()) -> F() eqt(tag(),mcrlrecord()) -> F() eqt(tag(),ok()) -> F() eqt(tag(),pending()) -> F() eqt(tag(),release()) -> F() eqt(tag(),request()) -> F() eqt(tag(),resource()) -> F() eqt(tag(),tag()) -> T() eqt(tag(),true()) -> F() eqt(tag(),undefined()) -> F() eqt(tag(),pid(N2)) -> F() eqt(tag(),int(N2)) -> F() eqt(tag(),cons(H2,T2)) -> F() eqt(tag(),tuple(H2,T2)) -> F() eqt(tag(),tuplenil(H2)) -> F() eqt(true(),nil()) -> F() eqt(true(),a()) -> F() eqt(true(),excl()) -> F() eqt(true(),false()) -> F() eqt(true(),lock()) -> F() eqt(true(),locker()) -> F() eqt(true(),mcrlrecord()) -> F() eqt(true(),ok()) -> F() eqt(true(),pending()) -> F() eqt(true(),release()) -> F() eqt(true(),request()) -> F() eqt(true(),resource()) -> F() eqt(true(),tag()) -> F() eqt(true(),true()) -> T() eqt(true(),undefined()) -> F() eqt(true(),pid(N2)) -> F() eqt(true(),int(N2)) -> F() eqt(true(),cons(H2,T2)) -> F() eqt(true(),tuple(H2,T2)) -> F() eqt(true(),tuplenil(H2)) -> F() eqt(undefined(),nil()) -> F() eqt(undefined(),a()) -> F() eqt(undefined(),tuplenil(H2)) -> F() eqt(pid(N1),nil()) -> F() eqt(pid(N1),a()) -> F() eqt(pid(N1),excl()) -> F() eqt(pid(N1),false()) -> F() eqt(pid(N1),lock()) -> F() eqt(pid(N1),locker()) -> F() eqt(pid(N1),mcrlrecord()) -> F() eqt(pid(N1),ok()) -> F() eqt(pid(N1),pending()) -> F() eqt(pid(N1),release()) -> F() eqt(pid(N1),request()) -> F() eqt(pid(N1),resource()) -> F() eqt(pid(N1),tag()) -> F() eqt(pid(N1),true()) -> F() eqt(pid(N1),undefined()) -> F() eqt(pid(N1),pid(N2)) -> eqt(N1,N2) eqt(pid(N1),int(N2)) -> F() eqt(pid(N1),cons(H2,T2)) -> F() eqt(pid(N1),tuple(H2,T2)) -> F() eqt(pid(N1),tuplenil(H2)) -> F() eqt(int(N1),nil()) -> F() eqt(int(N1),a()) -> F() eqt(int(N1),excl()) -> F() eqt(int(N1),false()) -> F() eqt(int(N1),lock()) -> F() eqt(int(N1),locker()) -> F() eqt(int(N1),mcrlrecord()) -> F() eqt(int(N1),ok()) -> F() eqt(int(N1),pending()) -> F() eqt(int(N1),release()) -> F() eqt(int(N1),request()) -> F() eqt(int(N1),resource()) -> F() eqt(int(N1),tag()) -> F() eqt(int(N1),true()) -> F() eqt(int(N1),undefined()) -> F() eqt(cons(H1,T1),resource()) -> F() eqt(cons(H1,T1),tag()) -> F() eqt(cons(H1,T1),true()) -> F() eqt(cons(H1,T1),undefined()) -> F() eqt(cons(H1,T1),pid(N2)) -> F() eqt(cons(H1,T1),int(N2)) -> F() eqt(cons(H1,T1),cons(H2,T2)) -> and(eqt(H1,H2),eqt(T1,T2)) eqt(cons(H1,T1),tuple(H2,T2)) -> F() eqt(cons(H1,T1),tuplenil(H2)) -> F() eqt(tuple(H1,T1),nil()) -> F() eqt(tuple(H1,T1),a()) -> F() eqt(tuple(H1,T1),excl()) -> F() eqt(tuple(H1,T1),false()) -> F() eqt(tuple(H1,T1),lock()) -> F() eqt(tuple(H1,T1),locker()) -> F() eqt(tuple(H1,T1),mcrlrecord()) -> F() eqt(tuple(H1,T1),ok()) -> F() eqt(tuple(H1,T1),pending()) -> F() eqt(tuple(H1,T1),release()) -> F() eqt(tuple(H1,T1),request()) -> F() eqt(tuple(H1,T1),resource()) -> F() eqt(tuple(H1,T1),tag()) -> F() eqt(tuple(H1,T1),true()) -> F() eqt(tuple(H1,T1),undefined()) -> F() eqt(tuple(H1,T1),pid(N2)) -> F() eqt(tuple(H1,T1),int(N2)) -> F() eqt(tuple(H1,T1),cons(H2,T2)) -> F() eqt(tuple(H1,T1),tuple(H2,T2)) -> and(eqt(H1,H2),eqt(T1,T2)) eqt(tuple(H1,T1),tuplenil(H2)) -> F() eqt(tuplenil(H1),nil()) -> F() eqt(tuplenil(H1),a()) -> F() eqt(tuplenil(H1),excl()) -> F() eqt(tuplenil(H1),false()) -> F() eqt(tuplenil(H1),lock()) -> F() eqt(tuplenil(H1),locker()) -> F() eqt(tuplenil(H1),mcrlrecord()) -> F() eqt(tuplenil(H1),ok()) -> F() eqt(tuplenil(H1),pending()) -> F() eqt(tuplenil(H1),release()) -> F() eqt(tuplenil(H1),request()) -> F() eqt(tuplenil(H1),resource()) -> F() eqt(tuplenil(H1),tag()) -> F() eqt(tuplenil(H1),true()) -> F() eqt(tuplenil(H1),undefined()) -> F() eqt(tuplenil(H1),pid(N2)) -> F() eqt(tuplenil(H1),int(N2)) -> F() eqt(tuplenil(H1),cons(H2,T2)) -> F() eqt(tuplenil(H1),tuple(H2,T2)) -> F() eqt(tuplenil(H1),tuplenil(H2)) -> eqt(H1,H2) element(int(s(0())),tuplenil(T1)) -> T1 element(int(s(0())),tuple(T1,T2)) -> T1 element(int(s(s(N1))),tuple(T1,T2)) -> element(int(s(N1)),T2) record_new(lock()) -> tuple(mcrlrecord(),tuple(lock(),tuple(undefined(),tuple(nil(),tuplenil(nil()))))) record_extract(tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))), lock(),resource()) -> tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))) record_update(tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))), lock(),pending(),NewF) -> tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(NewF))))) record_updates(Record,Name,nil()) -> Record record_updates(Record,Name,cons(tuple(Field,tuplenil(NewF)),Fields)) -> record_updates(record_update(Record,Name,Field,NewF),Name,Fields) locker2_map_promote_pending(nil(),Pending) -> nil() locker2_map_promote_pending(cons(Lock,Locks),Pending) -> cons(locker2_promote_pending(Lock,Pending),locker2_map_promote_pending(Locks,Pending)) locker2_map_claim_lock(nil(),Resources,Client) -> nil() locker2_map_claim_lock(cons(Lock,Locks),Resources,Client) -> cons(locker2_claim_lock(Lock,Resources,Client),locker2_map_claim_lock(Locks,Resources,Client)) locker2_map_add_pending(nil(),Resources,Client) -> nil() locker2_promote_pending(Lock,Client) -> case0(Client,Lock,record_extract(Lock,lock(),pending())) case0(Client,Lock,cons(Client,Pendings)) -> record_updates(Lock,lock(),cons(tuple(excl(),tuplenil(Client)),cons ( tuple ( pending(),tuplenil(Pendings)), nil ()))) case0(Client,Lock,MCRLFree0) -> Lock locker2_remove_pending(Lock,Client) -> record_updates(Lock,lock(),cons(tuple(pending(),tuplenil(subtract (record_extract (Lock,lock(),pending()), cons(Client,nil())))), nil())) locker2_add_pending(Lock,Resources,Client) -> case1(Client,Resources,Lock,member(record_extract(Lock,lock(),resource()),Resources)) case1(Client,Resources,Lock,true()) -> record_updates(Lock,lock(),cons(tuple(pending(),tuplenil(append( record_extract ( Lock,lock(),pending()), cons (Client,nil())))), nil())) case1(Client,Resources,Lock,false()) -> Lock locker2_release_lock(Lock,Client) -> case2(Client,Lock,gen_modtageq(Client,record_extract(Lock,lock(),excl()))) case2(Client,Lock,true()) -> record_updates(Lock,lock(),cons(tuple(excllock(),excl()),nil())) case4(Client,Lock,MCRLFree1) -> false() locker2_obtainables(nil(),Client) -> true() locker2_obtainables(cons(Lock,Locks),Client) -> case5(Client,Locks,Lock,member(Client,record_extract(Lock,lock(),pending()))) case5(Client,Locks,Lock,true()) -> andt(locker2_obtainable(Lock,Client),locker2_obtainables(Locks,Client)) case5(Client,Locks,Lock,false()) -> locker2_obtainables(Locks,Client) locker2_check_available(Resource,nil()) -> false() locker2_check_available(Resource,cons(Lock,Locks)) -> case6(Locks,Lock,Resource,equal(Resource,record_extract(Lock,lock(),resource()))) case6(Locks,Lock,Resource,true()) -> andt(equal(record_extract(Lock,lock(),excl()),nil()),equal(record_extract (Lock,lock(),pending()), nil())) case6(Locks,Lock,Resource,false()) -> locker2_check_available(Resource,Locks) locker2_check_availables(nil(),Locks) -> true() locker2_check_availables(cons(Resource,Resources),Locks) -> andt(locker2_check_available(Resource,Locks),locker2_check_availables(Resources,Locks)) locker2_adduniq(nil(),List) -> List append(cons(Head,Tail),List) -> cons(Head,append(Tail,List)) subtract(List,nil()) -> List subtract(List,cons(Head,Tail)) -> subtract(delete(Head,List),Tail) delete(E,nil()) -> nil() delete(E,cons(Head,Tail)) -> case8(Tail,Head,E,equal(E,Head)) case8(Tail,Head,E,true()) -> Tail case8(Tail,Head,E,false()) -> cons(Head,delete(E,Tail)) gen_tag(Pid) -> tuple(Pid,tuplenil(tag())) gen_modtageq(Client1,Client2) -> equal(Client1,Client2) member(E,nil()) -> false() member(E,cons(Head,Tail)) -> case9(Tail,Head,E,equal(E,Head)) case9(Tail,Head,E,true()) -> true() case9(Tail,Head,E,false()) -> member(E,Tail) eqs(empty(),empty()) -> T() eqs(empty(),stack(E2,S2)) -> F() eqs(stack(E1,S1),empty()) -> F() eqs(stack(E1,S1),stack(E2,S2)) -> and(eqt(E1,E2),eqs(S1,S2)) pushs(E1,S1) -> stack(E1,S1) pops(stack(E1,S1)) -> S1 tops(stack(E1,S1)) -> E1 istops(E1,empty()) -> F() istops(E1,stack(E2,S1)) -> eqt(E1,E2) eqc(nocalls(),nocalls()) -> T() eqc(nocalls(),calls(E2,S2,CS2)) -> F() eqc(calls(E1,S1,CS1),nocalls()) -> F() eqc(calls(E1,S1,CS1),calls(E2,S2,CS2)) -> and(eqt(E1,E2),and(eqs(S1,S2),eqc(CS1,CS2))) push(E1,E2,nocalls()) -> calls(E1,stack(E2,empty()),nocalls()) push(E1,E2,calls(E3,S1,CS1)) -> push1(E1,E2,E3,S1,CS1,eqt(E1,E3)) push1(E1,E2,E3,S1,CS1,T()) -> calls(E3,pushs(E2,S1),CS1) Subterm Criterion Processor: simple projection: pi(eqt#) = 0 problem: DPs: TRS: or(T(),T()) -> T() or(F(),T()) -> T() or(T(),F()) -> T() or(F(),F()) -> F() and(T(),B) -> B and(B,T()) -> B and(F(),B) -> F() and(B,F()) -> F() imp(T(),B) -> B imp(F(),B) -> T() not(T()) -> F() not(F()) -> T() if(T(),B1,B2) -> B1 if(F(),B1,B2) -> B2 eq(T(),T()) -> T() eq(F(),F()) -> T() eq(T(),F()) -> F() eq(F(),T()) -> F() eqt(nil(),undefined()) -> F() eqt(nil(),pid(N2)) -> F() eqt(nil(),int(N2)) -> F() eqt(nil(),cons(H2,T2)) -> F() eqt(nil(),tuple(H2,T2)) -> F() eqt(nil(),tuplenil(H2)) -> F() eqt(a(),nil()) -> F() eqt(a(),a()) -> T() eqt(a(),excl()) -> F() eqt(a(),false()) -> F() eqt(a(),lock()) -> F() eqt(a(),locker()) -> F() eqt(a(),mcrlrecord()) -> F() eqt(a(),ok()) -> F() eqt(a(),pending()) -> F() eqt(a(),release()) -> F() eqt(a(),request()) -> F() eqt(a(),resource()) -> F() eqt(a(),tag()) -> F() eqt(a(),true()) -> F() eqt(a(),undefined()) -> F() eqt(a(),pid(N2)) -> F() eqt(a(),int(N2)) -> F() eqt(a(),cons(H2,T2)) -> F() eqt(a(),tuple(H2,T2)) -> F() eqt(a(),tuplenil(H2)) -> F() eqt(excl(),nil()) -> F() eqt(excl(),a()) -> F() eqt(excl(),excl()) -> T() eqt(excl(),false()) -> F() eqt(excl(),lock()) -> F() eqt(excl(),locker()) -> F() eqt(excl(),mcrlrecord()) -> F() eqt(excl(),ok()) -> F() eqt(excl(),pending()) -> F() eqt(excl(),release()) -> F() eqt(excl(),request()) -> F() eqt(excl(),resource()) -> F() eqt(excl(),tag()) -> F() eqt(excl(),true()) -> F() eqt(excl(),undefined()) -> F() eqt(excl(),pid(N2)) -> F() eqt(excl(),eqt(false(),int(N2))) -> F() eqt(false(),cons(H2,T2)) -> F() eqt(false(),tuple(H2,T2)) -> F() eqt(false(),tuplenil(H2)) -> F() eqt(lock(),nil()) -> F() eqt(lock(),a()) -> F() eqt(lock(),excl()) -> F() eqt(lock(),false()) -> F() eqt(lock(),lock()) -> T() eqt(lock(),locker()) -> F() eqt(lock(),mcrlrecord()) -> F() eqt(lock(),ok()) -> F() eqt(lock(),pending()) -> F() eqt(lock(),release()) -> F() eqt(lock(),request()) -> F() eqt(lock(),resource()) -> F() eqt(lock(),tag()) -> F() eqt(lock(),true()) -> F() eqt(lock(),undefined()) -> F() eqt(lock(),pid(N2)) -> F() eqt(lock(),int(N2)) -> F() eqt(lock(),cons(H2,T2)) -> F() eqt(lock(),tuple(H2,T2)) -> F() eqt(lock(),tuplenil(H2)) -> F() eqt(locker(),nil()) -> F() eqt(locker(),a()) -> F() eqt(locker(),excl()) -> F() eqt(locker(),false()) -> F() eqt(locker(),lock()) -> F() eqt(locker(),locker()) -> T() eqt(locker(),mcrlrecord()) -> F() eqt(locker(),ok()) -> F() eqt(locker(),pending()) -> F() eqt(locker(),release()) -> F() eqt(locker(),request()) -> F() eqt(locker(),resource()) -> F() eqt(locker(),tag()) -> F() eqt(locker(),true()) -> F() eqt(locker(),undefined()) -> F() eqt(locker(),pid(N2)) -> F() eqt(locker(),int(N2)) -> F() eqt(locker(),cons(H2,T2)) -> F() eqt(locker(),tuple(H2,T2)) -> F() eqt(locker(),tuplenil(H2)) -> F() eqt(mcrlrecord(),nil()) -> F() eqt(mcrlrecord(),a()) -> F() eqt(mcrlrecord(),excl()) -> F() eqt(mcrlrecord(),false()) -> F() eqt(mcrlrecord(),lock()) -> F() eqt(mcrlrecord(),locker()) -> F() eqt(mcrlrecord(),mcrlrecord()) -> T() eqt(mcrlrecord(),ok()) -> F() eqt(mcrlrecord(),pending()) -> F() eqt(mcrlrecord(),release()) -> F() eqt(mcrlrecord(),request()) -> F() eqt(mcrlrecord(),resource()) -> F() eqt(ok(),resource()) -> F() eqt(ok(),tag()) -> F() eqt(ok(),true()) -> F() eqt(ok(),undefined()) -> F() eqt(ok(),pid(N2)) -> F() eqt(ok(),int(N2)) -> F() eqt(ok(),cons(H2,T2)) -> F() eqt(ok(),tuple(H2,T2)) -> F() eqt(ok(),tuplenil(H2)) -> F() eqt(pending(),nil()) -> F() eqt(pending(),a()) -> F() eqt(pending(),excl()) -> F() eqt(pending(),false()) -> F() eqt(pending(),lock()) -> F() eqt(pending(),locker()) -> F() eqt(pending(),mcrlrecord()) -> F() eqt(pending(),ok()) -> F() eqt(pending(),pending()) -> T() eqt(pending(),release()) -> F() eqt(pending(),request()) -> F() eqt(pending(),resource()) -> F() eqt(pending(),tag()) -> F() eqt(pending(),true()) -> F() eqt(pending(),undefined()) -> F() eqt(pending(),pid(N2)) -> F() eqt(pending(),int(N2)) -> F() eqt(pending(),cons(H2,T2)) -> F() eqt(pending(),tuple(H2,T2)) -> F() eqt(pending(),tuplenil(H2)) -> F() eqt(release(),nil()) -> F() eqt(release(),a()) -> F() eqt(release(),excl()) -> F() eqt(release(),false()) -> F() eqt(release(),lock()) -> F() eqt(release(),locker()) -> F() eqt(release(),mcrlrecord()) -> F() eqt(release(),ok()) -> F() eqt(request(),mcrlrecord()) -> F() eqt(request(),ok()) -> F() eqt(request(),pending()) -> F() eqt(request(),release()) -> F() eqt(request(),request()) -> T() eqt(request(),resource()) -> F() eqt(request(),tag()) -> F() eqt(request(),true()) -> F() eqt(request(),undefined()) -> F() eqt(request(),pid(N2)) -> F() eqt(request(),int(N2)) -> F() eqt(request(),cons(H2,T2)) -> F() eqt(request(),tuple(H2,T2)) -> F() eqt(request(),tuplenil(H2)) -> F() eqt(resource(),nil()) -> F() eqt(resource(),a()) -> F() eqt(resource(),excl()) -> F() eqt(resource(),false()) -> F() eqt(resource(),lock()) -> F() eqt(resource(),locker()) -> F() eqt(resource(),mcrlrecord()) -> F() eqt(resource(),ok()) -> F() eqt(resource(),pending()) -> F() eqt(resource(),release()) -> F() eqt(resource(),request()) -> F() eqt(resource(),resource()) -> T() eqt(resource(),tag()) -> F() eqt(resource(),true()) -> F() eqt(resource(),undefined()) -> F() eqt(resource(),pid(N2)) -> F() eqt(resource(),int(N2)) -> F() eqt(resource(),cons(H2,T2)) -> F() eqt(resource(),tuple(H2,T2)) -> F() eqt(resource(),tuplenil(H2)) -> F() eqt(tag(),nil()) -> F() eqt(tag(),a()) -> F() eqt(tag(),excl()) -> F() eqt(tag(),false()) -> F() eqt(tag(),lock()) -> F() eqt(tag(),locker()) -> F() eqt(tag(),mcrlrecord()) -> F() eqt(tag(),ok()) -> F() eqt(tag(),pending()) -> F() eqt(tag(),release()) -> F() eqt(tag(),request()) -> F() eqt(tag(),resource()) -> F() eqt(tag(),tag()) -> T() eqt(tag(),true()) -> F() eqt(tag(),undefined()) -> F() eqt(tag(),pid(N2)) -> F() eqt(tag(),int(N2)) -> F() eqt(tag(),cons(H2,T2)) -> F() eqt(tag(),tuple(H2,T2)) -> F() eqt(tag(),tuplenil(H2)) -> F() eqt(true(),nil()) -> F() eqt(true(),a()) -> F() eqt(true(),excl()) -> F() eqt(true(),false()) -> F() eqt(true(),lock()) -> F() eqt(true(),locker()) -> F() eqt(true(),mcrlrecord()) -> F() eqt(true(),ok()) -> F() eqt(true(),pending()) -> F() eqt(true(),release()) -> F() eqt(true(),request()) -> F() eqt(true(),resource()) -> F() eqt(true(),tag()) -> F() eqt(true(),true()) -> T() eqt(true(),undefined()) -> F() eqt(true(),pid(N2)) -> F() eqt(true(),int(N2)) -> F() eqt(true(),cons(H2,T2)) -> F() eqt(true(),tuple(H2,T2)) -> F() eqt(true(),tuplenil(H2)) -> F() eqt(undefined(),nil()) -> F() eqt(undefined(),a()) -> F() eqt(undefined(),tuplenil(H2)) -> F() eqt(pid(N1),nil()) -> F() eqt(pid(N1),a()) -> F() eqt(pid(N1),excl()) -> F() eqt(pid(N1),false()) -> F() eqt(pid(N1),lock()) -> F() eqt(pid(N1),locker()) -> F() eqt(pid(N1),mcrlrecord()) -> F() eqt(pid(N1),ok()) -> F() eqt(pid(N1),pending()) -> F() eqt(pid(N1),release()) -> F() eqt(pid(N1),request()) -> F() eqt(pid(N1),resource()) -> F() eqt(pid(N1),tag()) -> F() eqt(pid(N1),true()) -> F() eqt(pid(N1),undefined()) -> F() eqt(pid(N1),pid(N2)) -> eqt(N1,N2) eqt(pid(N1),int(N2)) -> F() eqt(pid(N1),cons(H2,T2)) -> F() eqt(pid(N1),tuple(H2,T2)) -> F() eqt(pid(N1),tuplenil(H2)) -> F() eqt(int(N1),nil()) -> F() eqt(int(N1),a()) -> F() eqt(int(N1),excl()) -> F() eqt(int(N1),false()) -> F() eqt(int(N1),lock()) -> F() eqt(int(N1),locker()) -> F() eqt(int(N1),mcrlrecord()) -> F() eqt(int(N1),ok()) -> F() eqt(int(N1),pending()) -> F() eqt(int(N1),release()) -> F() eqt(int(N1),request()) -> F() eqt(int(N1),resource()) -> F() eqt(int(N1),tag()) -> F() eqt(int(N1),true()) -> F() eqt(int(N1),undefined()) -> F() eqt(cons(H1,T1),resource()) -> F() eqt(cons(H1,T1),tag()) -> F() eqt(cons(H1,T1),true()) -> F() eqt(cons(H1,T1),undefined()) -> F() eqt(cons(H1,T1),pid(N2)) -> F() eqt(cons(H1,T1),int(N2)) -> F() eqt(cons(H1,T1),cons(H2,T2)) -> and(eqt(H1,H2),eqt(T1,T2)) eqt(cons(H1,T1),tuple(H2,T2)) -> F() eqt(cons(H1,T1),tuplenil(H2)) -> F() eqt(tuple(H1,T1),nil()) -> F() eqt(tuple(H1,T1),a()) -> F() eqt(tuple(H1,T1),excl()) -> F() eqt(tuple(H1,T1),false()) -> F() eqt(tuple(H1,T1),lock()) -> F() eqt(tuple(H1,T1),locker()) -> F() eqt(tuple(H1,T1),mcrlrecord()) -> F() eqt(tuple(H1,T1),ok()) -> F() eqt(tuple(H1,T1),pending()) -> F() eqt(tuple(H1,T1),release()) -> F() eqt(tuple(H1,T1),request()) -> F() eqt(tuple(H1,T1),resource()) -> F() eqt(tuple(H1,T1),tag()) -> F() eqt(tuple(H1,T1),true()) -> F() eqt(tuple(H1,T1),undefined()) -> F() eqt(tuple(H1,T1),pid(N2)) -> F() eqt(tuple(H1,T1),int(N2)) -> F() eqt(tuple(H1,T1),cons(H2,T2)) -> F() eqt(tuple(H1,T1),tuple(H2,T2)) -> and(eqt(H1,H2),eqt(T1,T2)) eqt(tuple(H1,T1),tuplenil(H2)) -> F() eqt(tuplenil(H1),nil()) -> F() eqt(tuplenil(H1),a()) -> F() eqt(tuplenil(H1),excl()) -> F() eqt(tuplenil(H1),false()) -> F() eqt(tuplenil(H1),lock()) -> F() eqt(tuplenil(H1),locker()) -> F() eqt(tuplenil(H1),mcrlrecord()) -> F() eqt(tuplenil(H1),ok()) -> F() eqt(tuplenil(H1),pending()) -> F() eqt(tuplenil(H1),release()) -> F() eqt(tuplenil(H1),request()) -> F() eqt(tuplenil(H1),resource()) -> F() eqt(tuplenil(H1),tag()) -> F() eqt(tuplenil(H1),true()) -> F() eqt(tuplenil(H1),undefined()) -> F() eqt(tuplenil(H1),pid(N2)) -> F() eqt(tuplenil(H1),int(N2)) -> F() eqt(tuplenil(H1),cons(H2,T2)) -> F() eqt(tuplenil(H1),tuple(H2,T2)) -> F() eqt(tuplenil(H1),tuplenil(H2)) -> eqt(H1,H2) element(int(s(0())),tuplenil(T1)) -> T1 element(int(s(0())),tuple(T1,T2)) -> T1 element(int(s(s(N1))),tuple(T1,T2)) -> element(int(s(N1)),T2) record_new(lock()) -> tuple(mcrlrecord(),tuple(lock(),tuple(undefined(),tuple(nil(),tuplenil(nil()))))) record_extract(tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))), lock(),resource()) -> tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))) record_update(tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(F2))))), lock(),pending(),NewF) -> tuple(mcrlrecord(),tuple(lock(),tuple(F0,tuple(F1,tuplenil(NewF))))) record_updates(Record,Name,nil()) -> Record record_updates(Record,Name,cons(tuple(Field,tuplenil(NewF)),Fields)) -> record_updates(record_update(Record,Name,Field,NewF),Name,Fields) locker2_map_promote_pending(nil(),Pending) -> nil() locker2_map_promote_pending(cons(Lock,Locks),Pending) -> cons(locker2_promote_pending(Lock,Pending),locker2_map_promote_pending(Locks,Pending)) locker2_map_claim_lock(nil(),Resources,Client) -> nil() locker2_map_claim_lock(cons(Lock,Locks),Resources,Client) -> cons(locker2_claim_lock(Lock,Resources,Client),locker2_map_claim_lock (Locks,Resources,Client)) locker2_map_add_pending(nil(),Resources,Client) -> nil() locker2_promote_pending(Lock,Client) -> case0(Client,Lock,record_extract(Lock,lock(),pending())) case0(Client,Lock,cons(Client,Pendings)) -> record_updates(Lock,lock(),cons(tuple(excl(),tuplenil(Client)), cons(tuple(pending(),tuplenil(Pendings)),nil()))) case0(Client,Lock,MCRLFree0) -> Lock locker2_remove_pending(Lock,Client) -> record_updates(Lock,lock(),cons(tuple(pending(),tuplenil(subtract (record_extract (Lock,lock(),pending()), cons (Client,nil())))), nil())) locker2_add_pending(Lock,Resources,Client) -> case1(Client,Resources,Lock,member(record_extract(Lock,lock(),resource()),Resources)) case1(Client,Resources,Lock,true()) -> record_updates(Lock,lock(),cons(tuple(pending(),tuplenil(append (record_extract (Lock,lock(),pending()), cons (Client,nil())))), nil())) case1(Client,Resources,Lock,false()) -> Lock locker2_release_lock(Lock,Client) -> case2(Client,Lock,gen_modtageq(Client,record_extract(Lock,lock(),excl()))) case2(Client,Lock,true()) -> record_updates(Lock,lock(),cons(tuple(excllock(),excl()),nil())) case4(Client,Lock,MCRLFree1) -> false() locker2_obtainables(nil(),Client) -> true() locker2_obtainables(cons(Lock,Locks),Client) -> case5(Client,Locks,Lock,member(Client,record_extract(Lock,lock(),pending()))) case5(Client,Locks,Lock,true()) -> andt(locker2_obtainable(Lock,Client),locker2_obtainables(Locks,Client)) case5(Client,Locks,Lock,false()) -> locker2_obtainables(Locks,Client) locker2_check_available(Resource,nil()) -> false() locker2_check_available(Resource,cons(Lock,Locks)) -> case6(Locks,Lock,Resource,equal(Resource,record_extract(Lock,lock(),resource()))) case6(Locks,Lock,Resource,true()) -> andt(equal(record_extract(Lock,lock(),excl()),nil()),equal(record_extract (Lock,lock(),pending()), nil())) case6(Locks,Lock,Resource,false()) -> locker2_check_available(Resource,Locks) locker2_check_availables(nil(),Locks) -> true() locker2_check_availables(cons(Resource,Resources),Locks) -> andt(locker2_check_available(Resource,Locks),locker2_check_availables(Resources,Locks)) locker2_adduniq(nil(),List) -> List append(cons(Head,Tail),List) -> cons(Head,append(Tail,List)) subtract(List,nil()) -> List subtract(List,cons(Head,Tail)) -> subtract(delete(Head,List),Tail) delete(E,nil()) -> nil() delete(E,cons(Head,Tail)) -> case8(Tail,Head,E,equal(E,Head)) case8(Tail,Head,E,true()) -> Tail case8(Tail,Head,E,false()) -> cons(Head,delete(E,Tail)) gen_tag(Pid) -> tuple(Pid,tuplenil(tag())) gen_modtageq(Client1,Client2) -> equal(Client1,Client2) member(E,nil()) -> false() member(E,cons(Head,Tail)) -> case9(Tail,Head,E,equal(E,Head)) case9(Tail,Head,E,true()) -> true() case9(Tail,Head,E,false()) -> member(E,Tail) eqs(empty(),empty()) -> T() eqs(empty(),stack(E2,S2)) -> F() eqs(stack(E1,S1),empty()) -> F() eqs(stack(E1,S1),stack(E2,S2)) -> and(eqt(E1,E2),eqs(S1,S2)) pushs(E1,S1) -> stack(E1,S1) pops(stack(E1,S1)) -> S1 tops(stack(E1,S1)) -> E1 istops(E1,empty()) -> F() istops(E1,stack(E2,S1)) -> eqt(E1,E2) eqc(nocalls(),nocalls()) -> T() eqc(nocalls(),calls(E2,S2,CS2)) -> F() eqc(calls(E1,S1,CS1),nocalls()) -> F() eqc(calls(E1,S1,CS1),calls(E2,S2,CS2)) -> and(eqt(E1,E2),and(eqs(S1,S2),eqc(CS1,CS2))) push(E1,E2,nocalls()) -> calls(E1,stack(E2,empty()),nocalls()) push(E1,E2,calls(E3,S1,CS1)) -> push1(E1,E2,E3,S1,CS1,eqt(E1,E3)) push1(E1,E2,E3,S1,CS1,T()) -> calls(E3,pushs(E2,S1),CS1) Qed