Termination Proof using AProVE

Term Rewriting System R:
[B, B1, B2, N2, H2, T2, N1, H1, T1, F0, F1, F2, NewF, Record, Name, Field, Fields, Pending, Lock, Locks, Resources, Client, Pendings, MCRLFree0, MCRLFree1, Resource, List, Head, Tail, E, Pid, Client1, Client2, E2, S2, E1, S1, CS2, CS1, E3]
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)

Innermost Termination of R to be shown.

     ↳Dependency Pair Analysis

R contains the following Dependency Pairs:

EQT(pid(N1), pid(N2)) -> EQT(N1, N2)
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(T1, T2)
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(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_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)
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_{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))
LOCKER2_{PROMOTE_PENDING}(Lock, Client) -> 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_UPDATES(Lock, lock, cons(tuple(pending, tuplenil(subtract(record_extract(Lock, lock, pending), cons(Client, nil)))), nil))
LOCKER2_{REMOVE_PENDING}(Lock, Client) -> SUBTRACT(record_extract(Lock, lock, pending), cons(Client, nil))
LOCKER2_{REMOVE_PENDING}(Lock, Client) -> RECORD_EXTRACT(Lock, lock, pending)
LOCKER2_{ADD_PENDING}(Lock, Resources, Client) -> CASE1(Client, Resources, Lock, member(record_extract(Lock, lock, resource), Resources))
LOCKER2_{ADD_PENDING}(Lock, Resources, Client) -> MEMBER(record_extract(Lock, lock, resource), Resources)
LOCKER2_{ADD_PENDING}(Lock, Resources, Client) -> RECORD_EXTRACT(Lock, lock, resource)
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, true) -> APPEND(record_extract(Lock, lock, pending), cons(Client, nil))
CASE1(Client, Resources, Lock, true) -> RECORD_EXTRACT(Lock, lock, pending)
LOCKER2_{RELEASE_LOCK}(Lock, Client) -> CASE2(Client, Lock, gen_modtageq(Client, record_extract(Lock, lock, excl)))
LOCKER2_{RELEASE_LOCK}(Lock, Client) -> GEN_MODTAGEQ(Client, record_extract(Lock, lock, excl))
LOCKER2_{RELEASE_LOCK}(Lock, 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) -> CASE5(Client, Locks, Lock, member(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) -> 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)) -> CASE6(Locks, Lock, Resource, equal(Resource, record_extract(Lock, lock, resource)))
LOCKER2_{CHECK_AVAILABLE}(Resource, cons(Lock, Locks)) -> RECORD_EXTRACT(Lock, lock, resource)
CASE6(Locks, Lock, Resource, true) -> RECORD_EXTRACT(Lock, lock, excl)
CASE6(Locks, Lock, Resource, true) -> RECORD_EXTRACT(Lock, lock, pending)
CASE6(Locks, Lock, Resource, false) -> LOCKER2_{CHECK_AVAILABLE}(Resource, 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)
APPEND(cons(Head, Tail), List) -> APPEND(Tail, List)
SUBTRACT(List, cons(Head, Tail)) -> SUBTRACT(delete(Head, List), Tail)
SUBTRACT(List, cons(Head, Tail)) -> DELETE(Head, List)
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)) -> AND(eqt(E1, E2), eqs(S1, S2))
EQS(stack(E1, S1), stack(E2, S2)) -> EQT(E1, E2)
EQS(stack(E1, S1), stack(E2, S2)) -> EQS(S1, S2)
ISTOPS(E1, stack(E2, S1)) -> EQT(E1, E2)
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)) -> EQT(E1, E2)
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)) -> EQS(S1, S2)
EQC(calls(E1, S1, CS1), calls(E2, S2, CS2)) -> EQC(CS1, CS2)
PUSH(E1, E2, calls(E3, S1, CS1)) -> PUSH1(E1, E2, E3, S1, CS1, eqt(E1, E3))
PUSH(E1, E2, calls(E3, S1, CS1)) -> EQT(E1, E3)
PUSH1(E1, E2, E3, S1, CS1, T) -> PUSHS(E2, S1)

Furthermore, R contains 11 SCCs.

     ↳DPs

       →DP Problem 1

         ↳Polynomial Ordering

       →DP Problem 2

         ↳Polo

       →DP Problem 3

         ↳Polo

       →DP Problem 4

         ↳Polo

       →DP Problem 5

         ↳Polo

       →DP Problem 6

         ↳Polo

       →DP Problem 7

         ↳Polo

       →DP Problem 8

         ↳Polo

       →DP Problem 9

         ↳Polo

       →DP Problem 10

         ↳Polo

       →DP Problem 11

         ↳Polo

Dependency Pairs:

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)) -> 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)

Rules:

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)

Strategy:

innermost

The following dependency pair can be strictly oriented:

EQT(pid(N1), pid(N2)) -> EQT(N1, N2)

There are no usable rules for innermost that need to be oriented.

Used ordering: Polynomial ordering with Polynomial interpretation:

POL(EQT(x₁, x₂)) = x₁

POL(cons(x₁, x₂)) = x₁ + x₂

POL(pid(x₁)) = 1 + x₁

POL(tuplenil(x₁)) = x₁

POL(tuple(x₁, x₂)) = x₁ + x₂

resulting in one new DP problem.

     ↳DPs

       →DP Problem 1

         ↳Polo

           →DP Problem 12

             ↳Polynomial Ordering

       →DP Problem 2

         ↳Polo

       →DP Problem 3

         ↳Polo

       →DP Problem 4

         ↳Polo

       →DP Problem 5

         ↳Polo

       →DP Problem 6

         ↳Polo

       →DP Problem 7

         ↳Polo

       →DP Problem 8

         ↳Polo

       →DP Problem 9

         ↳Polo

       →DP Problem 10

         ↳Polo

       →DP Problem 11

         ↳Polo

Dependency Pairs:

Rules:

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)

Strategy:

innermost

The following dependency pair can be strictly oriented:

EQT(tuplenil(H1), tuplenil(H2)) -> EQT(H1, H2)

There are no usable rules for innermost that need to be oriented.

Used ordering: Polynomial ordering with Polynomial interpretation:

POL(EQT(x₁, x₂)) = x₁

POL(cons(x₁, x₂)) = x₁ + x₂

POL(tuplenil(x₁)) = 1 + x₁

POL(tuple(x₁, x₂)) = x₁ + x₂

resulting in one new DP problem.

     ↳DPs

       →DP Problem 1

         ↳Polo

           →DP Problem 12

             ↳Polo

...

               →DP Problem 13

                 ↳Polynomial Ordering

       →DP Problem 2

         ↳Polo

       →DP Problem 3

         ↳Polo

       →DP Problem 4

         ↳Polo

       →DP Problem 5

         ↳Polo

       →DP Problem 6

         ↳Polo

       →DP Problem 7

         ↳Polo

       →DP Problem 8

         ↳Polo

       →DP Problem 9

         ↳Polo

       →DP Problem 10

         ↳Polo

       →DP Problem 11

         ↳Polo

Dependency Pairs:

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)) -> EQT(T1, T2)
EQT(cons(H1, T1), cons(H2, T2)) -> EQT(H1, H2)

Rules:

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)

Strategy:

innermost

The following dependency pairs can be strictly oriented:

EQT(tuple(H1, T1), tuple(H2, T2)) -> EQT(T1, T2)
EQT(tuple(H1, T1), tuple(H2, T2)) -> EQT(H1, H2)

There are no usable rules for innermost that need to be oriented.

Used ordering: Polynomial ordering with Polynomial interpretation:

POL(EQT(x₁, x₂)) = x₁

POL(cons(x₁, x₂)) = x₁ + x₂

POL(tuple(x₁, x₂)) = 1 + x₁ + x₂

resulting in one new DP problem.

     ↳DPs

       →DP Problem 1

         ↳Polo

           →DP Problem 12

             ↳Polo

...

               →DP Problem 14

                 ↳Polynomial Ordering

       →DP Problem 2

         ↳Polo

       →DP Problem 3

         ↳Polo

       →DP Problem 4

         ↳Polo

       →DP Problem 5

         ↳Polo

       →DP Problem 6

         ↳Polo

       →DP Problem 7

         ↳Polo

       →DP Problem 8

         ↳Polo

       →DP Problem 9

         ↳Polo

       →DP Problem 10

         ↳Polo

       →DP Problem 11

         ↳Polo

Dependency Pairs:

EQT(cons(H1, T1), cons(H2, T2)) -> EQT(T1, T2)
EQT(cons(H1, T1), cons(H2, T2)) -> EQT(H1, H2)

Rules:

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)

Strategy:

innermost

The following dependency pairs can be strictly oriented:

EQT(cons(H1, T1), cons(H2, T2)) -> EQT(T1, T2)
EQT(cons(H1, T1), cons(H2, T2)) -> EQT(H1, H2)

There are no usable rules for innermost that need to be oriented.

Used ordering: Polynomial ordering with Polynomial interpretation:

POL(EQT(x₁, x₂)) = x₁

POL(cons(x₁, x₂)) = 1 + x₁ + x₂

resulting in one new DP problem.

     ↳DPs

       →DP Problem 1

         ↳Polo

           →DP Problem 12

             ↳Polo

...

               →DP Problem 15

                 ↳Dependency Graph

       →DP Problem 2

         ↳Polo

       →DP Problem 3

         ↳Polo

       →DP Problem 4

         ↳Polo

       →DP Problem 5

         ↳Polo

       →DP Problem 6

         ↳Polo

       →DP Problem 7

         ↳Polo

       →DP Problem 8

         ↳Polo

       →DP Problem 9

         ↳Polo

       →DP Problem 10

         ↳Polo

       →DP Problem 11

         ↳Polo

Dependency Pair:

Rules:

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)

Strategy:

innermost

Using the Dependency Graph resulted in no new DP problems.

     ↳DPs

       →DP Problem 1

         ↳Polo

       →DP Problem 2

         ↳Polynomial Ordering

       →DP Problem 3

         ↳Polo

       →DP Problem 4

         ↳Polo

       →DP Problem 5

         ↳Polo

       →DP Problem 6

         ↳Polo

       →DP Problem 7

         ↳Polo

       →DP Problem 8

         ↳Polo

       →DP Problem 9

         ↳Polo

       →DP Problem 10

         ↳Polo

       →DP Problem 11

         ↳Polo

Dependency Pair:

ELEMENT(int(s(s(N1))), tuple(T1, T2)) -> ELEMENT(int(s(N1)), T2)

Rules:

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)

Strategy:

innermost

The following dependency pair can be strictly oriented:

ELEMENT(int(s(s(N1))), tuple(T1, T2)) -> ELEMENT(int(s(N1)), T2)

There are no usable rules for innermost that need to be oriented.

Used ordering: Polynomial ordering with Polynomial interpretation:

POL(int(x₁)) = 0

POL(s(x₁)) = 0

POL(tuple(x₁, x₂)) = 1 + x₂

POL(ELEMENT(x₁, x₂)) = x₂

resulting in one new DP problem.

     ↳DPs

       →DP Problem 1

         ↳Polo

       →DP Problem 2

         ↳Polo

           →DP Problem 16

             ↳Dependency Graph

       →DP Problem 3

         ↳Polo

       →DP Problem 4

         ↳Polo

       →DP Problem 5

         ↳Polo

       →DP Problem 6

         ↳Polo

       →DP Problem 7

         ↳Polo

       →DP Problem 8

         ↳Polo

       →DP Problem 9

         ↳Polo

       →DP Problem 10

         ↳Polo

       →DP Problem 11

         ↳Polo

Dependency Pair:

Rules:

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)

Strategy:

innermost

Using the Dependency Graph resulted in no new DP problems.

     ↳DPs

       →DP Problem 1

         ↳Polo

       →DP Problem 2

         ↳Polo

       →DP Problem 3

         ↳Polynomial Ordering

       →DP Problem 4

         ↳Polo

       →DP Problem 5

         ↳Polo

       →DP Problem 6

         ↳Polo

       →DP Problem 7

         ↳Polo

       →DP Problem 8

         ↳Polo

       →DP Problem 9

         ↳Polo

       →DP Problem 10

         ↳Polo

       →DP Problem 11

         ↳Polo

Dependency Pair:

RECORD_UPDATES(Record, Name, cons(tuple(Field, tuplenil(NewF)), Fields)) -> RECORD_UPDATES(record_update(Record, Name, Field, NewF), Name, Fields)

Rules:

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)

Strategy:

innermost

The following dependency pair can be strictly oriented:

RECORD_UPDATES(Record, Name, cons(tuple(Field, tuplenil(NewF)), Fields)) -> RECORD_UPDATES(record_update(Record, Name, Field, NewF), Name, Fields)

Additionally, the following usable rule for innermost can be oriented:

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)))))

Used ordering: Polynomial ordering with Polynomial interpretation:

POL(pending) = 0

POL(RECORD_UPDATES(x₁, x₂, x₃)) = x₃

POL(cons(x₁, x₂)) = 1 + x₂

POL(lock) = 0

POL(tuplenil(x₁)) = 0

POL(mcrlrecord) = 0

POL(record_update(x₁, x₂, x₃, x₄)) = 0

POL(tuple(x₁, x₂)) = 0

resulting in one new DP problem.

     ↳DPs

       →DP Problem 1

         ↳Polo

       →DP Problem 2

         ↳Polo

       →DP Problem 3

         ↳Polo

           →DP Problem 17

             ↳Dependency Graph

       →DP Problem 4

         ↳Polo

       →DP Problem 5

         ↳Polo

       →DP Problem 6

         ↳Polo

       →DP Problem 7

         ↳Polo

       →DP Problem 8

         ↳Polo

       →DP Problem 9

         ↳Polo

       →DP Problem 10

         ↳Polo

       →DP Problem 11

         ↳Polo

Dependency Pair:

Rules:

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)

Strategy:

innermost

Using the Dependency Graph resulted in no new DP problems.

     ↳DPs

       →DP Problem 1

         ↳Polo

       →DP Problem 2

         ↳Polo

       →DP Problem 3

         ↳Polo

       →DP Problem 4

         ↳Polynomial Ordering

       →DP Problem 5

         ↳Polo

       →DP Problem 6

         ↳Polo

       →DP Problem 7

         ↳Polo

       →DP Problem 8

         ↳Polo

       →DP Problem 9

         ↳Polo

       →DP Problem 10

         ↳Polo

       →DP Problem 11

         ↳Polo

Dependency Pair:

LOCKER2_{MAP_{PROMOTE_PENDING}}(cons(Lock, Locks), Pending) -> LOCKER2_{MAP_{PROMOTE_PENDING}}(Locks, Pending)

Rules:

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)

Strategy:

innermost

The following dependency pair can be strictly oriented:

LOCKER2_{MAP_{PROMOTE_PENDING}}(cons(Lock, Locks), Pending) -> LOCKER2_{MAP_{PROMOTE_PENDING}}(Locks, Pending)

There are no usable rules for innermost that need to be oriented.

Used ordering: Polynomial ordering with Polynomial interpretation:

POL(LOCKER2_MAP_PROMOTE_PENDING(x₁, x₂)) = x₁

POL(cons(x₁, x₂)) = 1 + x₂

resulting in one new DP problem.

     ↳DPs

       →DP Problem 1

         ↳Polo

       →DP Problem 2

         ↳Polo

       →DP Problem 3

         ↳Polo

       →DP Problem 4

         ↳Polo

           →DP Problem 18

             ↳Dependency Graph

       →DP Problem 5

         ↳Polo

       →DP Problem 6

         ↳Polo

       →DP Problem 7

         ↳Polo

       →DP Problem 8

         ↳Polo

       →DP Problem 9

         ↳Polo

       →DP Problem 10

         ↳Polo

       →DP Problem 11

         ↳Polo

Dependency Pair:

Rules:

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)

Strategy:

innermost

Using the Dependency Graph resulted in no new DP problems.

     ↳DPs

       →DP Problem 1

         ↳Polo

       →DP Problem 2

         ↳Polo

       →DP Problem 3

         ↳Polo

       →DP Problem 4

         ↳Polo

       →DP Problem 5

         ↳Polynomial Ordering

       →DP Problem 6

         ↳Polo

       →DP Problem 7

         ↳Polo

       →DP Problem 8

         ↳Polo

       →DP Problem 9

         ↳Polo

       →DP Problem 10

         ↳Polo

       →DP Problem 11

         ↳Polo

Dependency Pair:

LOCKER2_{MAP_{CLAIM_LOCK}}(cons(Lock, Locks), Resources, Client) -> LOCKER2_{MAP_{CLAIM_LOCK}}(Locks, Resources, Client)

Rules:

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)

Strategy:

innermost

The following dependency pair can be strictly oriented:

LOCKER2_{MAP_{CLAIM_LOCK}}(cons(Lock, Locks), Resources, Client) -> LOCKER2_{MAP_{CLAIM_LOCK}}(Locks, Resources, Client)

There are no usable rules for innermost that need to be oriented.

Used ordering: Polynomial ordering with Polynomial interpretation:

POL(cons(x₁, x₂)) = 1 + x₂

POL(LOCKER2_MAP_CLAIM_LOCK(x₁, x₂, x₃)) = x₁

resulting in one new DP problem.

     ↳DPs

       →DP Problem 1

         ↳Polo

       →DP Problem 2

         ↳Polo

       →DP Problem 3

         ↳Polo

       →DP Problem 4

         ↳Polo

       →DP Problem 5

         ↳Polo

           →DP Problem 19

             ↳Dependency Graph

       →DP Problem 6

         ↳Polo

       →DP Problem 7

         ↳Polo

       →DP Problem 8

         ↳Polo

       →DP Problem 9

         ↳Polo

       →DP Problem 10

         ↳Polo

       →DP Problem 11

         ↳Polo

Dependency Pair:

Rules:

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)

Strategy:

innermost

Using the Dependency Graph resulted in no new DP problems.

     ↳DPs

       →DP Problem 1

         ↳Polo

       →DP Problem 2

         ↳Polo

       →DP Problem 3

         ↳Polo

       →DP Problem 4

         ↳Polo

       →DP Problem 5

         ↳Polo

       →DP Problem 6

         ↳Polynomial Ordering

       →DP Problem 7

         ↳Polo

       →DP Problem 8

         ↳Polo

       →DP Problem 9

         ↳Polo

       →DP Problem 10

         ↳Polo

       →DP Problem 11

         ↳Polo

Dependency Pair:

SUBTRACT(List, cons(Head, Tail)) -> SUBTRACT(delete(Head, List), Tail)

Rules:

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)

Strategy:

innermost

The following dependency pair can be strictly oriented:

SUBTRACT(List, cons(Head, Tail)) -> SUBTRACT(delete(Head, List), Tail)

Additionally, the following usable rules for innermost can be oriented:

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))

Used ordering: Polynomial ordering with Polynomial interpretation:

POL(case8(x₁, x₂, x₃, x₄)) = 1 + x₁

POL(SUBTRACT(x₁, x₂)) = x₂

POL(equal(x₁, x₂)) = 0

POL(cons(x₁, x₂)) = 1 + x₂

POL(false) = 0

POL(nil) = 0

POL(true) = 1

POL(delete(x₁, x₂)) = x₂

resulting in one new DP problem.

     ↳DPs

       →DP Problem 1

         ↳Polo

       →DP Problem 2

         ↳Polo

       →DP Problem 3

         ↳Polo

       →DP Problem 4

         ↳Polo

       →DP Problem 5

         ↳Polo

       →DP Problem 6

         ↳Polo

           →DP Problem 20

             ↳Dependency Graph

       →DP Problem 7

         ↳Polo

       →DP Problem 8

         ↳Polo

       →DP Problem 9

         ↳Polo

       →DP Problem 10

         ↳Polo

       →DP Problem 11

         ↳Polo

Dependency Pair:

Rules:

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)

Strategy:

innermost

Using the Dependency Graph resulted in no new DP problems.

     ↳DPs

       →DP Problem 1

         ↳Polo

       →DP Problem 2

         ↳Polo

       →DP Problem 3

         ↳Polo

       →DP Problem 4

         ↳Polo

       →DP Problem 5

         ↳Polo

       →DP Problem 6

         ↳Polo

       →DP Problem 7

         ↳Polynomial Ordering

       →DP Problem 8

         ↳Polo

       →DP Problem 9

         ↳Polo

       →DP Problem 10

         ↳Polo

       →DP Problem 11

         ↳Polo

Dependency Pair:

APPEND(cons(Head, Tail), List) -> APPEND(Tail, List)

Rules:

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)

Strategy:

innermost

The following dependency pair can be strictly oriented:

APPEND(cons(Head, Tail), List) -> APPEND(Tail, List)

There are no usable rules for innermost that need to be oriented.

Used ordering: Polynomial ordering with Polynomial interpretation:

POL(cons(x₁, x₂)) = 1 + x₂

POL(APPEND(x₁, x₂)) = x₁

resulting in one new DP problem.

     ↳DPs

       →DP Problem 1

         ↳Polo

       →DP Problem 2

         ↳Polo

       →DP Problem 3

         ↳Polo

       →DP Problem 4

         ↳Polo

       →DP Problem 5

         ↳Polo

       →DP Problem 6

         ↳Polo

       →DP Problem 7

         ↳Polo

           →DP Problem 21

             ↳Dependency Graph

       →DP Problem 8

         ↳Polo

       →DP Problem 9

         ↳Polo

       →DP Problem 10

         ↳Polo

       →DP Problem 11

         ↳Polo

Dependency Pair:

Rules:

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)

Strategy:

innermost

Using the Dependency Graph resulted in no new DP problems.

     ↳DPs

       →DP Problem 1

         ↳Polo

       →DP Problem 2

         ↳Polo

       →DP Problem 3

         ↳Polo

       →DP Problem 4

         ↳Polo

       →DP Problem 5

         ↳Polo

       →DP Problem 6

         ↳Polo

       →DP Problem 7

         ↳Polo

       →DP Problem 8

         ↳Polynomial Ordering

       →DP Problem 9

         ↳Polo

       →DP Problem 10

         ↳Polo

       →DP Problem 11

         ↳Polo

Dependency Pairs:

CASE5(Client, Locks, Lock, false) -> LOCKER2_OBTAINABLES(Locks, Client)
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)))

Rules:

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)

Strategy:

innermost

The following dependency pair can be strictly oriented:

LOCKER2_OBTAINABLES(cons(Lock, Locks), Client) -> CASE5(Client, Locks, Lock, member(Client, record_extract(Lock, lock, pending)))

Additionally, the following usable rules for innermost can be oriented:

member(E, nil) -> false
member(E, cons(Head, Tail)) -> case9(Tail, Head, E, equal(E, Head))
record_extract(tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))), lock, resource) -> tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2)))))
case9(Tail, Head, E, true) -> true
case9(Tail, Head, E, false) -> member(E, Tail)

Used ordering: Polynomial ordering with Polynomial interpretation:

POL(equal(x₁, x₂)) = 0

POL(CASE5(x₁, x₂, x₃, x₄)) = x₂

POL(false) = 0

POL(lock) = 0

POL(tuplenil(x₁)) = 0

POL(true) = 0

POL(tuple(x₁, x₂)) = 0

POL(record_extract(x₁, x₂, x₃)) = 0

POL(pending) = 0

POL(cons(x₁, x₂)) = 1 + x₂

POL(case9(x₁, x₂, x₃, x₄)) = 0

POL(member(x₁, x₂)) = 0

POL(mcrlrecord) = 0

POL(nil) = 0

POL(LOCKER2_OBTAINABLES(x₁, x₂)) = x₁

POL(resource) = 0

resulting in one new DP problem.

     ↳DPs

       →DP Problem 1

         ↳Polo

       →DP Problem 2

         ↳Polo

       →DP Problem 3

         ↳Polo

       →DP Problem 4

         ↳Polo

       →DP Problem 5

         ↳Polo

       →DP Problem 6

         ↳Polo

       →DP Problem 7

         ↳Polo

       →DP Problem 8

         ↳Polo

           →DP Problem 22

             ↳Dependency Graph

       →DP Problem 9

         ↳Polo

       →DP Problem 10

         ↳Polo

       →DP Problem 11

         ↳Polo

Dependency Pairs:

CASE5(Client, Locks, Lock, false) -> LOCKER2_OBTAINABLES(Locks, Client)
CASE5(Client, Locks, Lock, true) -> LOCKER2_OBTAINABLES(Locks, Client)

Rules:

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)

Strategy:

innermost

Using the Dependency Graph resulted in no new DP problems.

     ↳DPs

       →DP Problem 1

         ↳Polo

       →DP Problem 2

         ↳Polo

       →DP Problem 3

         ↳Polo

       →DP Problem 4

         ↳Polo

       →DP Problem 5

         ↳Polo

       →DP Problem 6

         ↳Polo

       →DP Problem 7

         ↳Polo

       →DP Problem 8

         ↳Polo

       →DP Problem 9

         ↳Polynomial Ordering

       →DP Problem 10

         ↳Polo

       →DP Problem 11

         ↳Polo

Dependency Pair:

LOCKER2_{CHECK_AVAILABLES}(cons(Resource, Resources), Locks) -> LOCKER2_{CHECK_AVAILABLES}(Resources, Locks)

Rules:

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)

Strategy:

innermost

The following dependency pair can be strictly oriented:

LOCKER2_{CHECK_AVAILABLES}(cons(Resource, Resources), Locks) -> LOCKER2_{CHECK_AVAILABLES}(Resources, Locks)

There are no usable rules for innermost that need to be oriented.

Used ordering: Polynomial ordering with Polynomial interpretation:

POL(cons(x₁, x₂)) = 1 + x₂

POL(LOCKER2_CHECK_AVAILABLES(x₁, x₂)) = x₁

resulting in one new DP problem.

     ↳DPs

       →DP Problem 1

         ↳Polo

       →DP Problem 2

         ↳Polo

       →DP Problem 3

         ↳Polo

       →DP Problem 4

         ↳Polo

       →DP Problem 5

         ↳Polo

       →DP Problem 6

         ↳Polo

       →DP Problem 7

         ↳Polo

       →DP Problem 8

         ↳Polo

       →DP Problem 9

         ↳Polo

           →DP Problem 23

             ↳Dependency Graph

       →DP Problem 10

         ↳Polo

       →DP Problem 11

         ↳Polo

Dependency Pair:

Rules:

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)

Strategy:

innermost

Using the Dependency Graph resulted in no new DP problems.

     ↳DPs

       →DP Problem 1

         ↳Polo

       →DP Problem 2

         ↳Polo

       →DP Problem 3

         ↳Polo

       →DP Problem 4

         ↳Polo

       →DP Problem 5

         ↳Polo

       →DP Problem 6

         ↳Polo

       →DP Problem 7

         ↳Polo

       →DP Problem 8

         ↳Polo

       →DP Problem 9

         ↳Polo

       →DP Problem 10

         ↳Polynomial Ordering

       →DP Problem 11

         ↳Polo

Dependency Pair:

EQS(stack(E1, S1), stack(E2, S2)) -> EQS(S1, S2)

Rules:

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)

Strategy:

innermost

The following dependency pair can be strictly oriented:

EQS(stack(E1, S1), stack(E2, S2)) -> EQS(S1, S2)

There are no usable rules for innermost that need to be oriented.

Used ordering: Polynomial ordering with Polynomial interpretation:

POL(EQS(x₁, x₂)) = x₁

POL(stack(x₁, x₂)) = 1 + x₂

resulting in one new DP problem.

     ↳DPs

       →DP Problem 1

         ↳Polo

       →DP Problem 2

         ↳Polo

       →DP Problem 3

         ↳Polo

       →DP Problem 4

         ↳Polo

       →DP Problem 5

         ↳Polo

       →DP Problem 6

         ↳Polo

       →DP Problem 7

         ↳Polo

       →DP Problem 8

         ↳Polo

       →DP Problem 9

         ↳Polo

       →DP Problem 10

         ↳Polo

           →DP Problem 24

             ↳Dependency Graph

       →DP Problem 11

         ↳Polo

Dependency Pair:

Rules:

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)

Strategy:

innermost

Using the Dependency Graph resulted in no new DP problems.

     ↳DPs

       →DP Problem 1

         ↳Polo

       →DP Problem 2

         ↳Polo

       →DP Problem 3

         ↳Polo

       →DP Problem 4

         ↳Polo

       →DP Problem 5

         ↳Polo

       →DP Problem 6

         ↳Polo

       →DP Problem 7

         ↳Polo

       →DP Problem 8

         ↳Polo

       →DP Problem 9

         ↳Polo

       →DP Problem 10

         ↳Polo

       →DP Problem 11

         ↳Polynomial Ordering

Dependency Pair:

EQC(calls(E1, S1, CS1), calls(E2, S2, CS2)) -> EQC(CS1, CS2)

Rules:

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)

Strategy:

innermost

The following dependency pair can be strictly oriented:

EQC(calls(E1, S1, CS1), calls(E2, S2, CS2)) -> EQC(CS1, CS2)

There are no usable rules for innermost that need to be oriented.

Used ordering: Polynomial ordering with Polynomial interpretation:

POL(calls(x₁, x₂, x₃)) = 1 + x₃

POL(EQC(x₁, x₂)) = x₁

resulting in one new DP problem.

     ↳DPs

       →DP Problem 1

         ↳Polo

       →DP Problem 2

         ↳Polo

       →DP Problem 3

         ↳Polo

       →DP Problem 4

         ↳Polo

       →DP Problem 5

         ↳Polo

       →DP Problem 6

         ↳Polo

       →DP Problem 7

         ↳Polo

       →DP Problem 8

         ↳Polo

       →DP Problem 9

         ↳Polo

       →DP Problem 10

         ↳Polo

       →DP Problem 11

         ↳Polo

           →DP Problem 25

             ↳Dependency Graph

Dependency Pair:

Rules:

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)

Strategy:

innermost

Using the Dependency Graph resulted in no new DP problems.

Innermost Termination of R successfully shown.
Duration:
0:22 minutes

POL(EQT(x₁, x₂))	= x₁
POL(cons(x₁, x₂))	= x₁ + x₂
POL(pid(x₁))	= 1 + x₁
POL(tuplenil(x₁))	= x₁
POL(tuple(x₁, x₂))	= x₁ + x₂

POL(int(x₁))	= 0
POL(s(x₁))	= 0
POL(tuple(x₁, x₂))	= 1 + x₂
POL(ELEMENT(x₁, x₂))	= x₂

POL(pending)	= 0
POL(RECORD_UPDATES(x₁, x₂, x₃))	= x₃
POL(cons(x₁, x₂))	= 1 + x₂
POL(lock)	= 0
POL(tuplenil(x₁))	= 0
POL(mcrlrecord)	= 0
POL(record_update(x₁, x₂, x₃, x₄))	= 0
POL(tuple(x₁, x₂))	= 0

POL(LOCKER2_MAP_PROMOTE_PENDING(x₁, x₂))	= x₁
POL(cons(x₁, x₂))	= 1 + x₂

POL(cons(x₁, x₂))	= 1 + x₂
POL(LOCKER2_MAP_CLAIM_LOCK(x₁, x₂, x₃))	= x₁

POL(case8(x₁, x₂, x₃, x₄))	= 1 + x₁
POL(SUBTRACT(x₁, x₂))	= x₂
POL(equal(x₁, x₂))	= 0
POL(cons(x₁, x₂))	= 1 + x₂
POL(false)	= 0
POL(nil)	= 0
POL(true)	= 1
POL(delete(x₁, x₂))	= x₂

POL(cons(x₁, x₂))	= 1 + x₂
POL(APPEND(x₁, x₂))	= x₁

POL(equal(x₁, x₂))	= 0
POL(CASE5(x₁, x₂, x₃, x₄))	= x₂
POL(false)	= 0
POL(lock)	= 0
POL(tuplenil(x₁))	= 0
POL(true)	= 0
POL(tuple(x₁, x₂))	= 0
POL(record_extract(x₁, x₂, x₃))	= 0
POL(pending)	= 0
POL(cons(x₁, x₂))	= 1 + x₂
POL(case9(x₁, x₂, x₃, x₄))	= 0
POL(member(x₁, x₂))	= 0
POL(mcrlrecord)	= 0
POL(nil)	= 0
POL(LOCKER2_OBTAINABLES(x₁, x₂))	= x₁
POL(resource)	= 0

POL(cons(x₁, x₂))	= 1 + x₂
POL(LOCKER2_CHECK_AVAILABLES(x₁, x₂))	= x₁

POL(EQS(x₁, x₂))	= x₁
POL(stack(x₁, x₂))	= 1 + x₂

POL(calls(x₁, x₂, x₃))	= 1 + x₃
POL(EQC(x₁, x₂))	= x₁