Termination w.r.t. Q of the given QTRS could be proven:

(0) Obligation:

Q restricted rewrite system:
The TRS R consists of the following 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)

Q is empty.

(1) DependencyPairsProof (EQUIVALENT transformation)

Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.

(2) Obligation:

Q DP problem:
The TRS P consists of the following rules:

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)

The TRS R consists of the following 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)

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(3) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 10 SCCs with 46 less nodes.

(4) Complex Obligation (AND)

(5) Obligation:

Q DP problem:
The TRS P consists of the following rules:

SUBTRACT(List, cons(Head, Tail)) → SUBTRACT(delete(Head, List), Tail)

The TRS R consists of the following 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)

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(6) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

SUBTRACT(List, cons(Head, Tail)) → SUBTRACT(delete(Head, List), Tail)

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
SUBTRACT(x1, x2)  =  SUBTRACT(x2)
cons(x1, x2)  =  cons(x1, x2)
delete(x1, x2)  =  x2
or(x1, x2)  =  or(x1, x2)
T  =  T
F  =  F
and(x1, x2)  =  and(x1, x2)
imp(x1, x2)  =  imp(x2)
not(x1)  =  not(x1)
if(x1, x2, x3)  =  if(x2, x3)
eq(x1, x2)  =  eq
eqt(x1, x2)  =  eqt(x2)
nil  =  nil
undefined  =  undefined
pid(x1)  =  pid(x1)
int(x1)  =  int(x1)
tuple(x1, x2)  =  tuple(x1, x2)
tuplenil(x1)  =  x1
a  =  a
excl  =  excl
false  =  false
lock  =  lock
locker  =  locker
mcrlrecord  =  mcrlrecord
ok  =  ok
pending  =  pending
release  =  release
request  =  request
resource  =  resource
tag  =  tag
true  =  true
element(x1, x2)  =  element(x1, x2)
s(x1)  =  s(x1)
0  =  0
record_new(x1)  =  record_new(x1)
record_extract(x1, x2, x3)  =  x1
record_update(x1, x2, x3, x4)  =  record_update(x1, x2, x3, x4)
record_updates(x1, x2, x3)  =  record_updates(x1, x2, x3)
locker2_map_promote_pending(x1, x2)  =  locker2_map_promote_pending(x1)
locker2_promote_pending(x1, x2)  =  locker2_promote_pending(x1)
locker2_map_claim_lock(x1, x2, x3)  =  locker2_map_claim_lock(x1, x2, x3)
locker2_claim_lock(x1, x2, x3)  =  x3
locker2_map_add_pending(x1, x2, x3)  =  locker2_map_add_pending(x1, x2)
case0(x1, x2, x3)  =  case0(x2, x3)
locker2_remove_pending(x1, x2)  =  locker2_remove_pending(x1, x2)
subtract(x1, x2)  =  subtract(x1, x2)
locker2_add_pending(x1, x2, x3)  =  locker2_add_pending(x1)
case1(x1, x2, x3, x4)  =  case1(x3, x4)
member(x1, x2)  =  x1
append(x1, x2)  =  x1
locker2_release_lock(x1, x2)  =  locker2_release_lock(x1, x2)
case2(x1, x2, x3)  =  case2(x1, x2)
gen_modtageq(x1, x2)  =  x2
excllock  =  excllock
case4(x1, x2, x3)  =  case4
locker2_obtainables(x1, x2)  =  locker2_obtainables(x1, x2)
case5(x1, x2, x3, x4)  =  case5(x1, x2)
andt(x1, x2)  =  x1
locker2_obtainable(x1, x2)  =  locker2_obtainable(x2)
locker2_check_available(x1, x2)  =  locker2_check_available(x2)
case6(x1, x2, x3, x4)  =  case6(x1, x2, x4)
equal(x1, x2)  =  equal
locker2_check_availables(x1, x2)  =  locker2_check_availables(x2)
locker2_adduniq(x1, x2)  =  locker2_adduniq(x2)
case8(x1, x2, x3, x4)  =  case8(x1, x2)
gen_tag(x1)  =  gen_tag(x1)
case9(x1, x2, x3, x4)  =  x3
eqs(x1, x2)  =  eqs(x2)
empty  =  empty
stack(x1, x2)  =  stack(x1, x2)
pushs(x1, x2)  =  pushs(x1, x2)
pops(x1)  =  pops(x1)
tops(x1)  =  tops(x1)
istops(x1, x2)  =  istops(x1, x2)
eqc(x1, x2)  =  eqc(x2)
nocalls  =  nocalls
calls(x1, x2, x3)  =  calls(x1, x2, x3)
push(x1, x2, x3)  =  push(x1, x2, x3)
push1(x1, x2, x3, x4, x5, x6)  =  push1(x2, x3, x4, x5)

Lexicographic path order with status [LPO].
Quasi-Precedence:

or₂ > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
imp₁ > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
not₁ > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
if₂ > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
eq > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
pid₁ > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
a > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
locker > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
ok > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
release > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
request > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
element₂ > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
0 > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
record_new1 > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
[locker2_{mappromotepending1}, locker2_{promotepending1}] > [record_updates3, case0₂] > [cons₂, case8₂] > SUBTRACT₁ > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
[locker2_{mappromotepending1}, locker2_{promotepending1}] > [record_updates3, case0₂] > [cons₂, case8₂] > record_update4 > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
[locker2_{mappromotepending1}, locker2_{promotepending1}] > [record_updates3, case0₂] > [cons₂, case8₂] > [locker2_obtainables2, case5₂] > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
[locker2_{mappromotepending1}, locker2_{promotepending1}] > [record_updates3, case0₂] > [cons₂, case8₂] > case6₃ > locker2_{checkavailable1} > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
locker2_{mapclaimlock3} > [cons₂, case8₂] > SUBTRACT₁ > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
locker2_{mapclaimlock3} > [cons₂, case8₂] > record_update4 > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
locker2_{mapclaimlock3} > [cons₂, case8₂] > [locker2_obtainables2, case5₂] > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
locker2_{mapclaimlock3} > [cons₂, case8₂] > case6₃ > locker2_{checkavailable1} > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
locker2_{mapaddpending2} > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
locker2_{removepending2} > [record_updates3, case0₂] > [cons₂, case8₂] > SUBTRACT₁ > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
locker2_{removepending2} > [record_updates3, case0₂] > [cons₂, case8₂] > record_update4 > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
locker2_{removepending2} > [record_updates3, case0₂] > [cons₂, case8₂] > [locker2_obtainables2, case5₂] > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
locker2_{removepending2} > [record_updates3, case0₂] > [cons₂, case8₂] > case6₃ > locker2_{checkavailable1} > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
locker2_addpending1 > case1₂ > [record_updates3, case0₂] > [cons₂, case8₂] > SUBTRACT₁ > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
locker2_addpending1 > case1₂ > [record_updates3, case0₂] > [cons₂, case8₂] > record_update4 > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
locker2_addpending1 > case1₂ > [record_updates3, case0₂] > [cons₂, case8₂] > [locker2_obtainables2, case5₂] > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
locker2_addpending1 > case1₂ > [record_updates3, case0₂] > [cons₂, case8₂] > case6₃ > locker2_{checkavailable1} > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
[locker2_releaselock2, case2₂] > [record_updates3, case0₂] > [cons₂, case8₂] > SUBTRACT₁ > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
[locker2_releaselock2, case2₂] > [record_updates3, case0₂] > [cons₂, case8₂] > record_update4 > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
[locker2_releaselock2, case2₂] > [record_updates3, case0₂] > [cons₂, case8₂] > [locker2_obtainables2, case5₂] > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
[locker2_releaselock2, case2₂] > [record_updates3, case0₂] > [cons₂, case8₂] > case6₃ > locker2_{checkavailable1} > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
case4 > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
locker2_{checkavailables1} > locker2_{checkavailable1} > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
locker2_adduniq1 > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
gen_tag1 > tag > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
pops₁ > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
tops₁ > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
istops₂ > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
push₃ > [pushs₂, push1₄] > [eqs₁, stack₂, eqc₁, nocalls] > calls₃ > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]

Status:

SUBTRACT₁: [1]
cons₂: [2,1]
or₂: [2,1]
T: []
F: []
and₂: [2,1]
imp₁: [1]
not₁: [1]
if₂: [1,2]
eq: []
eqt₁: [1]
nil: []
undefined: []
pid₁: [1]
int₁: [1]
tuple₂: [2,1]
a: []
excl: []
false: []
lock: []
locker: []
mcrlrecord: []
ok: []
pending: []
release: []
request: []
resource: []
tag: []
true: []
element₂: [2,1]
s₁: [1]
0: []
record_new1: [1]
record_update4: [3,4,2,1]
record_updates3: [2,3,1]
locker2_{mappromotepending1}: [1]
locker2_{promotepending1}: [1]
locker2_{mapclaimlock3}: [1,3,2]
locker2_{mapaddpending2}: [1,2]
case0₂: [2,1]
locker2_{removepending2}: [1,2]
subtract₂: [2,1]
locker2_addpending1: [1]
case1₂: [2,1]
locker2_releaselock2: [2,1]
case2₂: [1,2]
excllock: []
case4: []
locker2_obtainables2: [1,2]
case5₂: [2,1]
locker2_obtainable1: [1]
locker2_{checkavailable1}: [1]
case6₃: [3,2,1]
equal: []
locker2_{checkavailables1}: [1]
locker2_adduniq1: [1]
case8₂: [1,2]
gen_tag1: [1]
eqs₁: [1]
empty: []
stack₂: [1,2]
pushs₂: [2,1]
pops₁: [1]
tops₁: [1]
istops₂: [1,2]
eqc₁: [1]
nocalls: []
calls₃: [1,2,3]
push₃: [1,2,3]
push1₄: [3,1,4,2]

The following usable rules [FROCOS05] were oriented:

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)

(7) Obligation:

Q DP problem:
P is empty.
The TRS R consists of the following 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)

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(8) PisEmptyProof (EQUIVALENT transformation)

The TRS P is empty. Hence, there is no (P,Q,R) chain.

(9) TRUE

(10) Obligation:

Q DP problem:
The TRS P consists of the following rules:

APPEND(cons(Head, Tail), List) → APPEND(Tail, List)

The TRS R consists of the following 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)

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(11) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

APPEND(cons(Head, Tail), List) → APPEND(Tail, List)

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
APPEND(x1, x2)  =  APPEND(x1)
cons(x1, x2)  =  cons(x1, x2)
or(x1, x2)  =  or(x1, x2)
T  =  T
F  =  F
and(x1, x2)  =  and(x1, x2)
imp(x1, x2)  =  imp(x2)
not(x1)  =  not(x1)
if(x1, x2, x3)  =  if(x2, x3)
eq(x1, x2)  =  eq
eqt(x1, x2)  =  eqt(x2)
nil  =  nil
undefined  =  undefined
pid(x1)  =  pid(x1)
int(x1)  =  int(x1)
tuple(x1, x2)  =  tuple(x1, x2)
tuplenil(x1)  =  x1
a  =  a
excl  =  excl
false  =  false
lock  =  lock
locker  =  locker
mcrlrecord  =  mcrlrecord
ok  =  ok
pending  =  pending
release  =  release
request  =  request
resource  =  resource
tag  =  tag
true  =  true
element(x1, x2)  =  element(x1, x2)
s(x1)  =  s(x1)
0  =  0
record_new(x1)  =  record_new(x1)
record_extract(x1, x2, x3)  =  x1
record_update(x1, x2, x3, x4)  =  record_update(x1, x2, x3, x4)
record_updates(x1, x2, x3)  =  record_updates(x1, x2, x3)
locker2_map_promote_pending(x1, x2)  =  locker2_map_promote_pending(x1)
locker2_promote_pending(x1, x2)  =  locker2_promote_pending(x1)
locker2_map_claim_lock(x1, x2, x3)  =  locker2_map_claim_lock(x1, x2, x3)
locker2_claim_lock(x1, x2, x3)  =  x3
locker2_map_add_pending(x1, x2, x3)  =  locker2_map_add_pending
case0(x1, x2, x3)  =  case0(x2, x3)
locker2_remove_pending(x1, x2)  =  locker2_remove_pending(x1, x2)
subtract(x1, x2)  =  subtract(x1, x2)
locker2_add_pending(x1, x2, x3)  =  locker2_add_pending(x1)
case1(x1, x2, x3, x4)  =  case1(x3, x4)
member(x1, x2)  =  x1
append(x1, x2)  =  x1
locker2_release_lock(x1, x2)  =  locker2_release_lock(x1, x2)
case2(x1, x2, x3)  =  case2(x1, x2)
gen_modtageq(x1, x2)  =  x2
excllock  =  excllock
case4(x1, x2, x3)  =  case4
locker2_obtainables(x1, x2)  =  locker2_obtainables(x1, x2)
case5(x1, x2, x3, x4)  =  case5(x1, x2)
andt(x1, x2)  =  x1
locker2_obtainable(x1, x2)  =  locker2_obtainable(x2)
locker2_check_available(x1, x2)  =  locker2_check_available(x2)
case6(x1, x2, x3, x4)  =  case6(x1, x2, x4)
equal(x1, x2)  =  equal
locker2_check_availables(x1, x2)  =  locker2_check_availables(x2)
locker2_adduniq(x1, x2)  =  locker2_adduniq(x2)
delete(x1, x2)  =  x2
case8(x1, x2, x3, x4)  =  case8(x1, x2)
gen_tag(x1)  =  gen_tag(x1)
case9(x1, x2, x3, x4)  =  x3
eqs(x1, x2)  =  eqs(x2)
empty  =  empty
stack(x1, x2)  =  stack(x1, x2)
pushs(x1, x2)  =  pushs(x1, x2)
pops(x1)  =  pops(x1)
tops(x1)  =  tops(x1)
istops(x1, x2)  =  istops(x1, x2)
eqc(x1, x2)  =  eqc(x2)
nocalls  =  nocalls
calls(x1, x2, x3)  =  calls(x1, x2, x3)
push(x1, x2, x3)  =  push(x1, x2, x3)
push1(x1, x2, x3, x4, x5, x6)  =  push1(x2, x3, x4, x5)

Lexicographic path order with status [LPO].
Quasi-Precedence:

APPEND₁ > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
or₂ > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
imp₁ > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
not₁ > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
if₂ > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
eq > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
pid₁ > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
a > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
locker > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
ok > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
release > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
request > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
element₂ > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
0 > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
record_new1 > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
[locker2_{mappromotepending1}, locker2_{promotepending1}] > [record_updates3, case0₂] > [cons₂, case8₂] > record_update4 > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
[locker2_{mappromotepending1}, locker2_{promotepending1}] > [record_updates3, case0₂] > [cons₂, case8₂] > [locker2_obtainables2, case5₂] > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
[locker2_{mappromotepending1}, locker2_{promotepending1}] > [record_updates3, case0₂] > [cons₂, case8₂] > case6₃ > locker2_{checkavailable1} > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
locker2_{mapclaimlock3} > [cons₂, case8₂] > record_update4 > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
locker2_{mapclaimlock3} > [cons₂, case8₂] > [locker2_obtainables2, case5₂] > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
locker2_{mapclaimlock3} > [cons₂, case8₂] > case6₃ > locker2_{checkavailable1} > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
locker2_{mapaddpending} > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
locker2_{removepending2} > [record_updates3, case0₂] > [cons₂, case8₂] > record_update4 > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
locker2_{removepending2} > [record_updates3, case0₂] > [cons₂, case8₂] > [locker2_obtainables2, case5₂] > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
locker2_{removepending2} > [record_updates3, case0₂] > [cons₂, case8₂] > case6₃ > locker2_{checkavailable1} > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
locker2_addpending1 > case1₂ > [record_updates3, case0₂] > [cons₂, case8₂] > record_update4 > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
locker2_addpending1 > case1₂ > [record_updates3, case0₂] > [cons₂, case8₂] > [locker2_obtainables2, case5₂] > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
locker2_addpending1 > case1₂ > [record_updates3, case0₂] > [cons₂, case8₂] > case6₃ > locker2_{checkavailable1} > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
[locker2_releaselock2, case2₂] > [record_updates3, case0₂] > [cons₂, case8₂] > record_update4 > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
[locker2_releaselock2, case2₂] > [record_updates3, case0₂] > [cons₂, case8₂] > [locker2_obtainables2, case5₂] > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
[locker2_releaselock2, case2₂] > [record_updates3, case0₂] > [cons₂, case8₂] > case6₃ > locker2_{checkavailable1} > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
case4 > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
locker2_{checkavailables1} > locker2_{checkavailable1} > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
locker2_adduniq1 > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
gen_tag1 > tag > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
pops₁ > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
tops₁ > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
istops₂ > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
push₃ > [pushs₂, push1₄] > [eqs₁, stack₂, eqc₁, nocalls] > calls₃ > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]

Status:

APPEND₁: [1]
cons₂: [2,1]
or₂: [2,1]
T: []
F: []
and₂: [2,1]
imp₁: [1]
not₁: [1]
if₂: [1,2]
eq: []
eqt₁: [1]
nil: []
undefined: []
pid₁: [1]
int₁: [1]
tuple₂: [2,1]
a: []
excl: []
false: []
lock: []
locker: []
mcrlrecord: []
ok: []
pending: []
release: []
request: []
resource: []
tag: []
true: []
element₂: [2,1]
s₁: [1]
0: []
record_new1: [1]
record_update4: [4,3,2,1]
record_updates3: [2,3,1]
locker2_{mappromotepending1}: [1]
locker2_{promotepending1}: [1]
locker2_{mapclaimlock3}: [1,3,2]
locker2_{mapaddpending}: []
case0₂: [2,1]
locker2_{removepending2}: [1,2]
subtract₂: [2,1]
locker2_addpending1: [1]
case1₂: [2,1]
locker2_releaselock2: [2,1]
case2₂: [1,2]
excllock: []
case4: []
locker2_obtainables2: [1,2]
case5₂: [2,1]
locker2_obtainable1: [1]
locker2_{checkavailable1}: [1]
case6₃: [1,2,3]
equal: []
locker2_{checkavailables1}: [1]
locker2_adduniq1: [1]
case8₂: [1,2]
gen_tag1: [1]
eqs₁: [1]
empty: []
stack₂: [1,2]
pushs₂: [2,1]
pops₁: [1]
tops₁: [1]
istops₂: [1,2]
eqc₁: [1]
nocalls: []
calls₃: [1,2,3]
push₃: [1,2,3]
push1₄: [3,1,4,2]

The following usable rules [FROCOS05] were oriented:

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)

(12) Obligation:

Q DP problem:
P is empty.
The TRS R consists of the following 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)

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(13) PisEmptyProof (EQUIVALENT transformation)

The TRS P is empty. Hence, there is no (P,Q,R) chain.

(14) TRUE

(15) Obligation:

Q DP problem:
The TRS P consists of the following rules:

LOCKER2_CHECK_AVAILABLES(cons(Resource, Resources), Locks) → LOCKER2_CHECK_AVAILABLES(Resources, Locks)

The TRS R consists of the following 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)

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(16) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

LOCKER2_CHECK_AVAILABLES(cons(Resource, Resources), Locks) → LOCKER2_CHECK_AVAILABLES(Resources, Locks)

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
LOCKER2_CHECK_AVAILABLES(x1, x2)  =  LOCKER2_CHECK_AVAILABLES(x1)
cons(x1, x2)  =  cons(x1, x2)
or(x1, x2)  =  or(x1, x2)
T  =  T
F  =  F
and(x1, x2)  =  and(x1, x2)
imp(x1, x2)  =  imp(x2)
not(x1)  =  not(x1)
if(x1, x2, x3)  =  if(x2, x3)
eq(x1, x2)  =  eq
eqt(x1, x2)  =  eqt(x2)
nil  =  nil
undefined  =  undefined
pid(x1)  =  pid(x1)
int(x1)  =  int(x1)
tuple(x1, x2)  =  tuple(x1, x2)
tuplenil(x1)  =  x1
a  =  a
excl  =  excl
false  =  false
lock  =  lock
locker  =  locker
mcrlrecord  =  mcrlrecord
ok  =  ok
pending  =  pending
release  =  release
request  =  request
resource  =  resource
tag  =  tag
true  =  true
element(x1, x2)  =  element(x1, x2)
s(x1)  =  s(x1)
0  =  0
record_new(x1)  =  record_new(x1)
record_extract(x1, x2, x3)  =  x1
record_update(x1, x2, x3, x4)  =  record_update(x1, x2, x3, x4)
record_updates(x1, x2, x3)  =  record_updates(x1, x2, x3)
locker2_map_promote_pending(x1, x2)  =  locker2_map_promote_pending(x1)
locker2_promote_pending(x1, x2)  =  locker2_promote_pending(x1)
locker2_map_claim_lock(x1, x2, x3)  =  locker2_map_claim_lock(x1, x2, x3)
locker2_claim_lock(x1, x2, x3)  =  x3
locker2_map_add_pending(x1, x2, x3)  =  locker2_map_add_pending
case0(x1, x2, x3)  =  case0(x2, x3)
locker2_remove_pending(x1, x2)  =  locker2_remove_pending(x1, x2)
subtract(x1, x2)  =  subtract(x1, x2)
locker2_add_pending(x1, x2, x3)  =  locker2_add_pending(x1)
case1(x1, x2, x3, x4)  =  case1(x3, x4)
member(x1, x2)  =  x1
append(x1, x2)  =  x1
locker2_release_lock(x1, x2)  =  locker2_release_lock(x1, x2)
case2(x1, x2, x3)  =  case2(x1, x2)
gen_modtageq(x1, x2)  =  x2
excllock  =  excllock
case4(x1, x2, x3)  =  case4
locker2_obtainables(x1, x2)  =  locker2_obtainables(x1, x2)
case5(x1, x2, x3, x4)  =  case5(x1, x2)
andt(x1, x2)  =  x1
locker2_obtainable(x1, x2)  =  locker2_obtainable(x2)
locker2_check_available(x1, x2)  =  locker2_check_available(x2)
case6(x1, x2, x3, x4)  =  case6(x1, x2, x4)
equal(x1, x2)  =  equal
locker2_check_availables(x1, x2)  =  locker2_check_availables(x2)
locker2_adduniq(x1, x2)  =  locker2_adduniq(x2)
delete(x1, x2)  =  x2
case8(x1, x2, x3, x4)  =  case8(x1, x2)
gen_tag(x1)  =  gen_tag(x1)
case9(x1, x2, x3, x4)  =  x3
eqs(x1, x2)  =  eqs(x2)
empty  =  empty
stack(x1, x2)  =  stack(x1, x2)
pushs(x1, x2)  =  pushs(x1, x2)
pops(x1)  =  pops(x1)
tops(x1)  =  tops(x1)
istops(x1, x2)  =  istops(x1, x2)
eqc(x1, x2)  =  eqc(x2)
nocalls  =  nocalls
calls(x1, x2, x3)  =  calls(x1, x2, x3)
push(x1, x2, x3)  =  push(x1, x2, x3)
push1(x1, x2, x3, x4, x5, x6)  =  push1(x2, x3, x4, x5)

Lexicographic path order with status [LPO].
Quasi-Precedence:

LOCKER2_{CHECKAVAILABLES1} > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
or₂ > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
imp₁ > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
not₁ > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
if₂ > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
eq > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
pid₁ > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
a > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
locker > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
ok > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
release > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
request > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
element₂ > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
0 > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
record_new1 > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
[locker2_{mappromotepending1}, locker2_{promotepending1}] > [record_updates3, case0₂] > [cons₂, case8₂] > record_update4 > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
[locker2_{mappromotepending1}, locker2_{promotepending1}] > [record_updates3, case0₂] > [cons₂, case8₂] > [locker2_obtainables2, case5₂] > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
[locker2_{mappromotepending1}, locker2_{promotepending1}] > [record_updates3, case0₂] > [cons₂, case8₂] > case6₃ > locker2_{checkavailable1} > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
locker2_{mapclaimlock3} > [cons₂, case8₂] > record_update4 > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
locker2_{mapclaimlock3} > [cons₂, case8₂] > [locker2_obtainables2, case5₂] > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
locker2_{mapclaimlock3} > [cons₂, case8₂] > case6₃ > locker2_{checkavailable1} > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
locker2_{mapaddpending} > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
locker2_{removepending2} > [record_updates3, case0₂] > [cons₂, case8₂] > record_update4 > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
locker2_{removepending2} > [record_updates3, case0₂] > [cons₂, case8₂] > [locker2_obtainables2, case5₂] > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
locker2_{removepending2} > [record_updates3, case0₂] > [cons₂, case8₂] > case6₃ > locker2_{checkavailable1} > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
locker2_addpending1 > case1₂ > [record_updates3, case0₂] > [cons₂, case8₂] > record_update4 > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
locker2_addpending1 > case1₂ > [record_updates3, case0₂] > [cons₂, case8₂] > [locker2_obtainables2, case5₂] > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
locker2_addpending1 > case1₂ > [record_updates3, case0₂] > [cons₂, case8₂] > case6₃ > locker2_{checkavailable1} > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
[locker2_releaselock2, case2₂] > [record_updates3, case0₂] > [cons₂, case8₂] > record_update4 > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
[locker2_releaselock2, case2₂] > [record_updates3, case0₂] > [cons₂, case8₂] > [locker2_obtainables2, case5₂] > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
[locker2_releaselock2, case2₂] > [record_updates3, case0₂] > [cons₂, case8₂] > case6₃ > locker2_{checkavailable1} > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
case4 > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
locker2_{checkavailables1} > locker2_{checkavailable1} > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
locker2_adduniq1 > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
gen_tag1 > tag > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
pops₁ > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
tops₁ > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
istops₂ > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
push₃ > [pushs₂, push1₄] > [eqs₁, stack₂, eqc₁, nocalls] > calls₃ > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]

Status:

LOCKER2_{CHECKAVAILABLES1}: [1]
cons₂: [2,1]
or₂: [2,1]
T: []
F: []
and₂: [2,1]
imp₁: [1]
not₁: [1]
if₂: [1,2]
eq: []
eqt₁: [1]
nil: []
undefined: []
pid₁: [1]
int₁: [1]
tuple₂: [2,1]
a: []
excl: []
false: []
lock: []
locker: []
mcrlrecord: []
ok: []
pending: []
release: []
request: []
resource: []
tag: []
true: []
element₂: [2,1]
s₁: [1]
0: []
record_new1: [1]
record_update4: [2,4,3,1]
record_updates3: [2,3,1]
locker2_{mappromotepending1}: [1]
locker2_{promotepending1}: [1]
locker2_{mapclaimlock3}: [1,3,2]
locker2_{mapaddpending}: []
case0₂: [2,1]
locker2_{removepending2}: [1,2]
subtract₂: [2,1]
locker2_addpending1: [1]
case1₂: [2,1]
locker2_releaselock2: [2,1]
case2₂: [1,2]
excllock: []
case4: []
locker2_obtainables2: [1,2]
case5₂: [2,1]
locker2_obtainable1: [1]
locker2_{checkavailable1}: [1]
case6₃: [1,2,3]
equal: []
locker2_{checkavailables1}: [1]
locker2_adduniq1: [1]
case8₂: [1,2]
gen_tag1: [1]
eqs₁: [1]
empty: []
stack₂: [1,2]
pushs₂: [2,1]
pops₁: [1]
tops₁: [1]
istops₂: [1,2]
eqc₁: [1]
nocalls: []
calls₃: [1,2,3]
push₃: [1,2,3]
push1₄: [3,1,4,2]

The following usable rules [FROCOS05] were oriented:

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)

(17) Obligation:

Q DP problem:
P is empty.
The TRS R consists of the following 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)

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(18) PisEmptyProof (EQUIVALENT transformation)

The TRS P is empty. Hence, there is no (P,Q,R) chain.

(19) TRUE

(20) Obligation:

Q DP problem:
The TRS P consists of the following rules:

LOCKER2_MAP_CLAIM_LOCK(cons(Lock, Locks), Resources, Client) → LOCKER2_MAP_CLAIM_LOCK(Locks, Resources, Client)

The TRS R consists of the following 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)

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(21) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

LOCKER2_MAP_CLAIM_LOCK(cons(Lock, Locks), Resources, Client) → LOCKER2_MAP_CLAIM_LOCK(Locks, Resources, Client)

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
LOCKER2_MAP_CLAIM_LOCK(x1, x2, x3)  =  LOCKER2_MAP_CLAIM_LOCK(x1, x2, x3)
cons(x1, x2)  =  cons(x1, x2)
or(x1, x2)  =  or(x1, x2)
T  =  T
F  =  F
and(x1, x2)  =  and(x1, x2)
imp(x1, x2)  =  imp(x2)
not(x1)  =  not(x1)
if(x1, x2, x3)  =  if(x2, x3)
eq(x1, x2)  =  eq
eqt(x1, x2)  =  eqt(x2)
nil  =  nil
undefined  =  undefined
pid(x1)  =  pid(x1)
int(x1)  =  int(x1)
tuple(x1, x2)  =  tuple(x1, x2)
tuplenil(x1)  =  x1
a  =  a
excl  =  excl
false  =  false
lock  =  lock
locker  =  locker
mcrlrecord  =  mcrlrecord
ok  =  ok
pending  =  pending
release  =  release
request  =  request
resource  =  resource
tag  =  tag
true  =  true
element(x1, x2)  =  element(x2)
s(x1)  =  s(x1)
0  =  0
record_new(x1)  =  record_new(x1)
record_extract(x1, x2, x3)  =  x1
record_update(x1, x2, x3, x4)  =  record_update(x1, x2, x3, x4)
record_updates(x1, x2, x3)  =  record_updates(x1, x2, x3)
locker2_map_promote_pending(x1, x2)  =  locker2_map_promote_pending(x1, x2)
locker2_promote_pending(x1, x2)  =  locker2_promote_pending(x1, x2)
locker2_map_claim_lock(x1, x2, x3)  =  locker2_map_claim_lock(x1)
locker2_claim_lock(x1, x2, x3)  =  x1
locker2_map_add_pending(x1, x2, x3)  =  locker2_map_add_pending(x1, x2)
case0(x1, x2, x3)  =  case0(x1, x2, x3)
locker2_remove_pending(x1, x2)  =  locker2_remove_pending(x1, x2)
subtract(x1, x2)  =  subtract(x1, x2)
locker2_add_pending(x1, x2, x3)  =  locker2_add_pending(x1, x2, x3)
case1(x1, x2, x3, x4)  =  case1(x1, x2, x3)
member(x1, x2)  =  member
append(x1, x2)  =  x1
locker2_release_lock(x1, x2)  =  locker2_release_lock(x1, x2)
case2(x1, x2, x3)  =  case2(x1, x2)
gen_modtageq(x1, x2)  =  x2
excllock  =  excllock
case4(x1, x2, x3)  =  case4
locker2_obtainables(x1, x2)  =  locker2_obtainables(x1, x2)
case5(x1, x2, x3, x4)  =  case5(x1, x2, x4)
andt(x1, x2)  =  x1
locker2_obtainable(x1, x2)  =  locker2_obtainable(x2)
locker2_check_available(x1, x2)  =  locker2_check_available(x2)
case6(x1, x2, x3, x4)  =  case6(x1, x2, x4)
equal(x1, x2)  =  equal
locker2_check_availables(x1, x2)  =  locker2_check_availables(x2)
locker2_adduniq(x1, x2)  =  locker2_adduniq(x2)
delete(x1, x2)  =  x2
case8(x1, x2, x3, x4)  =  case8(x1, x2)
gen_tag(x1)  =  gen_tag(x1)
case9(x1, x2, x3, x4)  =  x4
eqs(x1, x2)  =  eqs(x2)
empty  =  empty
stack(x1, x2)  =  stack(x1, x2)
pushs(x1, x2)  =  pushs(x1, x2)
pops(x1)  =  pops(x1)
tops(x1)  =  tops(x1)
istops(x1, x2)  =  istops(x1, x2)
eqc(x1, x2)  =  eqc(x2)
nocalls  =  nocalls
calls(x1, x2, x3)  =  calls(x1, x2, x3)
push(x1, x2, x3)  =  push(x1, x2, x3)
push1(x1, x2, x3, x4, x5, x6)  =  push1(x2, x3, x4, x5)

Lexicographic path order with status [LPO].
Quasi-Precedence:

or₂ > [LOCKER2_{MAPCLAIMLOCK3}, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, subtract₂, member, excllock, locker2_obtainable1, equal, empty]
imp₁ > [LOCKER2_{MAPCLAIMLOCK3}, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, subtract₂, member, excllock, locker2_obtainable1, equal, empty]
not₁ > [LOCKER2_{MAPCLAIMLOCK3}, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, subtract₂, member, excllock, locker2_obtainable1, equal, empty]
if₂ > [LOCKER2_{MAPCLAIMLOCK3}, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, subtract₂, member, excllock, locker2_obtainable1, equal, empty]
eq > [LOCKER2_{MAPCLAIMLOCK3}, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, subtract₂, member, excllock, locker2_obtainable1, equal, empty]
pid₁ > [LOCKER2_{MAPCLAIMLOCK3}, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, subtract₂, member, excllock, locker2_obtainable1, equal, empty]
a > [LOCKER2_{MAPCLAIMLOCK3}, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, subtract₂, member, excllock, locker2_obtainable1, equal, empty]
locker > [LOCKER2_{MAPCLAIMLOCK3}, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, subtract₂, member, excllock, locker2_obtainable1, equal, empty]
ok > [LOCKER2_{MAPCLAIMLOCK3}, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, subtract₂, member, excllock, locker2_obtainable1, equal, empty]
release > [LOCKER2_{MAPCLAIMLOCK3}, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, subtract₂, member, excllock, locker2_obtainable1, equal, empty]
request > [LOCKER2_{MAPCLAIMLOCK3}, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, subtract₂, member, excllock, locker2_obtainable1, equal, empty]
element₁ > [LOCKER2_{MAPCLAIMLOCK3}, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, subtract₂, member, excllock, locker2_obtainable1, equal, empty]
0 > [LOCKER2_{MAPCLAIMLOCK3}, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, subtract₂, member, excllock, locker2_obtainable1, equal, empty]
record_new1 > [LOCKER2_{MAPCLAIMLOCK3}, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, subtract₂, member, excllock, locker2_obtainable1, equal, empty]
[locker2_{mappromotepending2}, locker2_{promotepending2}] > case0₃ > [cons₂, locker2_{mapclaimlock1}, case8₂] > [true, locker2_obtainables2, case5₃] > [LOCKER2_{MAPCLAIMLOCK3}, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, subtract₂, member, excllock, locker2_obtainable1, equal, empty]
[locker2_{mappromotepending2}, locker2_{promotepending2}] > case0₃ > [cons₂, locker2_{mapclaimlock1}, case8₂] > record_updates3 > record_update4 > [LOCKER2_{MAPCLAIMLOCK3}, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, subtract₂, member, excllock, locker2_obtainable1, equal, empty]
[locker2_{mappromotepending2}, locker2_{promotepending2}] > case0₃ > [cons₂, locker2_{mapclaimlock1}, case8₂] > case6₃ > locker2_{checkavailable1} > [LOCKER2_{MAPCLAIMLOCK3}, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, subtract₂, member, excllock, locker2_obtainable1, equal, empty]
locker2_{mapaddpending2} > [LOCKER2_{MAPCLAIMLOCK3}, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, subtract₂, member, excllock, locker2_obtainable1, equal, empty]
locker2_{removepending2} > [cons₂, locker2_{mapclaimlock1}, case8₂] > [true, locker2_obtainables2, case5₃] > [LOCKER2_{MAPCLAIMLOCK3}, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, subtract₂, member, excllock, locker2_obtainable1, equal, empty]
locker2_{removepending2} > [cons₂, locker2_{mapclaimlock1}, case8₂] > record_updates3 > record_update4 > [LOCKER2_{MAPCLAIMLOCK3}, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, subtract₂, member, excllock, locker2_obtainable1, equal, empty]
locker2_{removepending2} > [cons₂, locker2_{mapclaimlock1}, case8₂] > case6₃ > locker2_{checkavailable1} > [LOCKER2_{MAPCLAIMLOCK3}, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, subtract₂, member, excllock, locker2_obtainable1, equal, empty]
[locker2_addpending3, case1₃] > [cons₂, locker2_{mapclaimlock1}, case8₂] > [true, locker2_obtainables2, case5₃] > [LOCKER2_{MAPCLAIMLOCK3}, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, subtract₂, member, excllock, locker2_obtainable1, equal, empty]
[locker2_addpending3, case1₃] > [cons₂, locker2_{mapclaimlock1}, case8₂] > record_updates3 > record_update4 > [LOCKER2_{MAPCLAIMLOCK3}, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, subtract₂, member, excllock, locker2_obtainable1, equal, empty]
[locker2_addpending3, case1₃] > [cons₂, locker2_{mapclaimlock1}, case8₂] > case6₃ > locker2_{checkavailable1} > [LOCKER2_{MAPCLAIMLOCK3}, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, subtract₂, member, excllock, locker2_obtainable1, equal, empty]
[locker2_releaselock2, case2₂] > [cons₂, locker2_{mapclaimlock1}, case8₂] > [true, locker2_obtainables2, case5₃] > [LOCKER2_{MAPCLAIMLOCK3}, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, subtract₂, member, excllock, locker2_obtainable1, equal, empty]
[locker2_releaselock2, case2₂] > [cons₂, locker2_{mapclaimlock1}, case8₂] > record_updates3 > record_update4 > [LOCKER2_{MAPCLAIMLOCK3}, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, subtract₂, member, excllock, locker2_obtainable1, equal, empty]
[locker2_releaselock2, case2₂] > [cons₂, locker2_{mapclaimlock1}, case8₂] > case6₃ > locker2_{checkavailable1} > [LOCKER2_{MAPCLAIMLOCK3}, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, subtract₂, member, excllock, locker2_obtainable1, equal, empty]
case4 > [LOCKER2_{MAPCLAIMLOCK3}, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, subtract₂, member, excllock, locker2_obtainable1, equal, empty]
locker2_{checkavailables1} > [true, locker2_obtainables2, case5₃] > [LOCKER2_{MAPCLAIMLOCK3}, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, subtract₂, member, excllock, locker2_obtainable1, equal, empty]
locker2_{checkavailables1} > locker2_{checkavailable1} > [LOCKER2_{MAPCLAIMLOCK3}, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, subtract₂, member, excllock, locker2_obtainable1, equal, empty]
locker2_adduniq1 > [LOCKER2_{MAPCLAIMLOCK3}, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, subtract₂, member, excllock, locker2_obtainable1, equal, empty]
gen_tag1 > tag > [LOCKER2_{MAPCLAIMLOCK3}, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, subtract₂, member, excllock, locker2_obtainable1, equal, empty]
pops₁ > [LOCKER2_{MAPCLAIMLOCK3}, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, subtract₂, member, excllock, locker2_obtainable1, equal, empty]
tops₁ > [LOCKER2_{MAPCLAIMLOCK3}, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, subtract₂, member, excllock, locker2_obtainable1, equal, empty]
istops₂ > [LOCKER2_{MAPCLAIMLOCK3}, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, subtract₂, member, excllock, locker2_obtainable1, equal, empty]
push₃ > [pushs₂, push1₄] > [eqs₁, stack₂, eqc₁, nocalls] > calls₃ > [LOCKER2_{MAPCLAIMLOCK3}, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, subtract₂, member, excllock, locker2_obtainable1, equal, empty]

Status:

LOCKER2_{MAPCLAIMLOCK3}: [3,2,1]
cons₂: [2,1]
or₂: [2,1]
T: []
F: []
and₂: [2,1]
imp₁: [1]
not₁: [1]
if₂: [1,2]
eq: []
eqt₁: [1]
nil: []
undefined: []
pid₁: [1]
int₁: [1]
tuple₂: [2,1]
a: []
excl: []
false: []
lock: []
locker: []
mcrlrecord: []
ok: []
pending: []
release: []
request: []
resource: []
tag: []
true: []
element₁: [1]
s₁: [1]
0: []
record_new1: [1]
record_update4: [4,3,2,1]
record_updates3: [2,3,1]
locker2_{mappromotepending2}: [2,1]
locker2_{promotepending2}: [2,1]
locker2_{mapclaimlock1}: [1]
locker2_{mapaddpending2}: [1,2]
case0₃: [1,3,2]
locker2_{removepending2}: [1,2]
subtract₂: [2,1]
locker2_addpending3: [1,3,2]
case1₃: [3,1,2]
member: []
locker2_releaselock2: [2,1]
case2₂: [1,2]
excllock: []
case4: []
locker2_obtainables2: [2,1]
case5₃: [1,2,3]
locker2_obtainable1: [1]
locker2_{checkavailable1}: [1]
case6₃: [1,2,3]
equal: []
locker2_{checkavailables1}: [1]
locker2_adduniq1: [1]
case8₂: [1,2]
gen_tag1: [1]
eqs₁: [1]
empty: []
stack₂: [1,2]
pushs₂: [2,1]
pops₁: [1]
tops₁: [1]
istops₂: [1,2]
eqc₁: [1]
nocalls: []
calls₃: [1,2,3]
push₃: [1,2,3]
push1₄: [3,1,4,2]

The following usable rules [FROCOS05] were oriented:

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)

(22) Obligation:

Q DP problem:
P is empty.
The TRS R consists of the following 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)

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(23) PisEmptyProof (EQUIVALENT transformation)

The TRS P is empty. Hence, there is no (P,Q,R) chain.

(24) TRUE

(25) Obligation:

Q DP problem:
The TRS P consists of the following rules:

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

The TRS R consists of the following 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)

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(26) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

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

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
RECORD_UPDATES(x1, x2, x3)  =  RECORD_UPDATES(x1, x2, x3)
cons(x1, x2)  =  cons(x1, x2)
tuple(x1, x2)  =  tuple(x1, x2)
tuplenil(x1)  =  x1
record_update(x1, x2, x3, x4)  =  record_update(x1, x4)
or(x1, x2)  =  or(x1, x2)
T  =  T
F  =  F
and(x1, x2)  =  and(x1, x2)
imp(x1, x2)  =  imp(x2)
not(x1)  =  not(x1)
if(x1, x2, x3)  =  if(x2, x3)
eq(x1, x2)  =  eq
eqt(x1, x2)  =  eqt(x2)
nil  =  nil
undefined  =  undefined
pid(x1)  =  pid(x1)
int(x1)  =  int(x1)
a  =  a
excl  =  excl
false  =  false
lock  =  lock
locker  =  locker
mcrlrecord  =  mcrlrecord
ok  =  ok
pending  =  pending
release  =  release
request  =  request
resource  =  resource
tag  =  tag
true  =  true
element(x1, x2)  =  element(x1, x2)
s(x1)  =  s(x1)
0  =  0
record_new(x1)  =  record_new(x1)
record_extract(x1, x2, x3)  =  record_extract(x1, x2, x3)
record_updates(x1, x2, x3)  =  record_updates(x1, x2, x3)
locker2_map_promote_pending(x1, x2)  =  locker2_map_promote_pending(x1, x2)
locker2_promote_pending(x1, x2)  =  locker2_promote_pending(x1)
locker2_map_claim_lock(x1, x2, x3)  =  locker2_map_claim_lock(x1)
locker2_claim_lock(x1, x2, x3)  =  x1
locker2_map_add_pending(x1, x2, x3)  =  locker2_map_add_pending(x1)
case0(x1, x2, x3)  =  case0(x2, x3)
locker2_remove_pending(x1, x2)  =  locker2_remove_pending(x1, x2)
subtract(x1, x2)  =  subtract(x1, x2)
locker2_add_pending(x1, x2, x3)  =  locker2_add_pending(x1, x2, x3)
case1(x1, x2, x3, x4)  =  case1(x3, x4)
member(x1, x2)  =  member
append(x1, x2)  =  x1
locker2_release_lock(x1, x2)  =  locker2_release_lock(x1, x2)
case2(x1, x2, x3)  =  case2(x1, x2)
gen_modtageq(x1, x2)  =  x2
excllock  =  excllock
case4(x1, x2, x3)  =  case4
locker2_obtainables(x1, x2)  =  locker2_obtainables(x1, x2)
case5(x1, x2, x3, x4)  =  case5(x1, x2, x4)
andt(x1, x2)  =  x1
locker2_obtainable(x1, x2)  =  locker2_obtainable(x2)
locker2_check_available(x1, x2)  =  locker2_check_available(x2)
case6(x1, x2, x3, x4)  =  case6(x1, x2)
equal(x1, x2)  =  equal
locker2_check_availables(x1, x2)  =  locker2_check_availables(x2)
locker2_adduniq(x1, x2)  =  locker2_adduniq(x2)
delete(x1, x2)  =  delete(x1, x2)
case8(x1, x2, x3, x4)  =  case8(x1, x2, x3)
gen_tag(x1)  =  gen_tag(x1)
case9(x1, x2, x3, x4)  =  x4
eqs(x1, x2)  =  eqs(x2)
empty  =  empty
stack(x1, x2)  =  stack(x1, x2)
pushs(x1, x2)  =  pushs(x1, x2)
pops(x1)  =  pops(x1)
tops(x1)  =  tops(x1)
istops(x1, x2)  =  istops(x1, x2)
eqc(x1, x2)  =  eqc(x2)
nocalls  =  nocalls
calls(x1, x2, x3)  =  calls(x1, x2, x3)
push(x1, x2, x3)  =  push(x1, x2, x3)
push1(x1, x2, x3, x4, x5, x6)  =  push1(x2, x3, x4, x5)

Lexicographic path order with status [LPO].
Quasi-Precedence:

or₂ > [tuple₂, record_update2, T, F, and₂, eqt₁, nil, undefined, int₁, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
imp₁ > [tuple₂, record_update2, T, F, and₂, eqt₁, nil, undefined, int₁, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
not₁ > [tuple₂, record_update2, T, F, and₂, eqt₁, nil, undefined, int₁, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
if₂ > [tuple₂, record_update2, T, F, and₂, eqt₁, nil, undefined, int₁, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
eq > [tuple₂, record_update2, T, F, and₂, eqt₁, nil, undefined, int₁, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
pid₁ > [tuple₂, record_update2, T, F, and₂, eqt₁, nil, undefined, int₁, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
a > [tuple₂, record_update2, T, F, and₂, eqt₁, nil, undefined, int₁, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
locker > [tuple₂, record_update2, T, F, and₂, eqt₁, nil, undefined, int₁, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
ok > [tuple₂, record_update2, T, F, and₂, eqt₁, nil, undefined, int₁, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
release > [tuple₂, record_update2, T, F, and₂, eqt₁, nil, undefined, int₁, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
request > [tuple₂, record_update2, T, F, and₂, eqt₁, nil, undefined, int₁, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
element₂ > [tuple₂, record_update2, T, F, and₂, eqt₁, nil, undefined, int₁, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
0 > [tuple₂, record_update2, T, F, and₂, eqt₁, nil, undefined, int₁, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
record_new1 > [tuple₂, record_update2, T, F, and₂, eqt₁, nil, undefined, int₁, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
locker2_{mappromotepending2} > locker2_{promotepending1} > case0₂ > [RECORD_UPDATES3, cons₂, true, locker2_{mapclaimlock1}, locker2_obtainables2, case5₃, case6₂] > locker2_{checkavailable1} > [tuple₂, record_update2, T, F, and₂, eqt₁, nil, undefined, int₁, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
locker2_{mappromotepending2} > locker2_{promotepending1} > case0₂ > record_updates3 > [tuple₂, record_update2, T, F, and₂, eqt₁, nil, undefined, int₁, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
locker2_{mapaddpending1} > [tuple₂, record_update2, T, F, and₂, eqt₁, nil, undefined, int₁, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
locker2_{removepending2} > record_updates3 > [tuple₂, record_update2, T, F, and₂, eqt₁, nil, undefined, int₁, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
locker2_{removepending2} > subtract₂ > [delete₂, case8₃] > [RECORD_UPDATES3, cons₂, true, locker2_{mapclaimlock1}, locker2_obtainables2, case5₃, case6₂] > locker2_{checkavailable1} > [tuple₂, record_update2, T, F, and₂, eqt₁, nil, undefined, int₁, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
[locker2_addpending3, case1₂] > [RECORD_UPDATES3, cons₂, true, locker2_{mapclaimlock1}, locker2_obtainables2, case5₃, case6₂] > locker2_{checkavailable1} > [tuple₂, record_update2, T, F, and₂, eqt₁, nil, undefined, int₁, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
[locker2_addpending3, case1₂] > record_updates3 > [tuple₂, record_update2, T, F, and₂, eqt₁, nil, undefined, int₁, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
[locker2_releaselock2, case2₂] > [RECORD_UPDATES3, cons₂, true, locker2_{mapclaimlock1}, locker2_obtainables2, case5₃, case6₂] > locker2_{checkavailable1} > [tuple₂, record_update2, T, F, and₂, eqt₁, nil, undefined, int₁, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
[locker2_releaselock2, case2₂] > record_updates3 > [tuple₂, record_update2, T, F, and₂, eqt₁, nil, undefined, int₁, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
case4 > [tuple₂, record_update2, T, F, and₂, eqt₁, nil, undefined, int₁, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
locker2_{checkavailables1} > [RECORD_UPDATES3, cons₂, true, locker2_{mapclaimlock1}, locker2_obtainables2, case5₃, case6₂] > locker2_{checkavailable1} > [tuple₂, record_update2, T, F, and₂, eqt₁, nil, undefined, int₁, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
locker2_adduniq1 > [tuple₂, record_update2, T, F, and₂, eqt₁, nil, undefined, int₁, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
gen_tag1 > tag > [tuple₂, record_update2, T, F, and₂, eqt₁, nil, undefined, int₁, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
pops₁ > [tuple₂, record_update2, T, F, and₂, eqt₁, nil, undefined, int₁, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
tops₁ > [tuple₂, record_update2, T, F, and₂, eqt₁, nil, undefined, int₁, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
istops₂ > [tuple₂, record_update2, T, F, and₂, eqt₁, nil, undefined, int₁, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
push₃ > [pushs₂, push1₄] > [eqs₁, stack₂, eqc₁, nocalls] > calls₃ > [tuple₂, record_update2, T, F, and₂, eqt₁, nil, undefined, int₁, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]

Status:

RECORD_UPDATES3: [3,1,2]
cons₂: [2,1]
tuple₂: [1,2]
record_update2: [1,2]
or₂: [2,1]
T: []
F: []
and₂: [1,2]
imp₁: [1]
not₁: [1]
if₂: [1,2]
eq: []
eqt₁: [1]
nil: []
undefined: []
pid₁: [1]
int₁: [1]
a: []
excl: []
false: []
lock: []
locker: []
mcrlrecord: []
ok: []
pending: []
release: []
request: []
resource: []
tag: []
true: []
element₂: [2,1]
s₁: [1]
0: []
record_new1: [1]
record_extract3: [2,3,1]
record_updates3: [3,1,2]
locker2_{mappromotepending2}: [2,1]
locker2_{promotepending1}: [1]
locker2_{mapclaimlock1}: [1]
locker2_{mapaddpending1}: [1]
case0₂: [1,2]
locker2_{removepending2}: [1,2]
subtract₂: [2,1]
locker2_addpending3: [3,1,2]
case1₂: [2,1]
member: []
locker2_releaselock2: [2,1]
case2₂: [1,2]
excllock: []
case4: []
locker2_obtainables2: [2,1]
case5₃: [1,2,3]
locker2_obtainable1: [1]
locker2_{checkavailable1}: [1]
case6₂: [1,2]
equal: []
locker2_{checkavailables1}: [1]
locker2_adduniq1: [1]
delete₂: [2,1]
case8₃: [1,3,2]
gen_tag1: [1]
eqs₁: [1]
empty: []
stack₂: [1,2]
pushs₂: [2,1]
pops₁: [1]
tops₁: [1]
istops₂: [1,2]
eqc₁: [1]
nocalls: []
calls₃: [1,2,3]
push₃: [1,2,3]
push1₄: [3,1,4,2]

The following usable rules [FROCOS05] were oriented:

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)

(27) Obligation:

Q DP problem:
P is empty.
The TRS R consists of the following 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)

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(28) PisEmptyProof (EQUIVALENT transformation)

The TRS P is empty. Hence, there is no (P,Q,R) chain.

(29) TRUE

(30) Obligation:

Q DP problem:
The TRS P consists of the following rules:

LOCKER2_MAP_PROMOTE_PENDING(cons(Lock, Locks), Pending) → LOCKER2_MAP_PROMOTE_PENDING(Locks, Pending)

The TRS R consists of the following 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)

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(31) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

LOCKER2_MAP_PROMOTE_PENDING(cons(Lock, Locks), Pending) → LOCKER2_MAP_PROMOTE_PENDING(Locks, Pending)

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
LOCKER2_MAP_PROMOTE_PENDING(x1, x2)  =  LOCKER2_MAP_PROMOTE_PENDING(x1)
cons(x1, x2)  =  cons(x1, x2)
or(x1, x2)  =  or(x1, x2)
T  =  T
F  =  F
and(x1, x2)  =  and(x1, x2)
imp(x1, x2)  =  imp(x2)
not(x1)  =  not(x1)
if(x1, x2, x3)  =  if(x2, x3)
eq(x1, x2)  =  eq
eqt(x1, x2)  =  eqt(x2)
nil  =  nil
undefined  =  undefined
pid(x1)  =  pid(x1)
int(x1)  =  int(x1)
tuple(x1, x2)  =  tuple(x1, x2)
tuplenil(x1)  =  x1
a  =  a
excl  =  excl
false  =  false
lock  =  lock
locker  =  locker
mcrlrecord  =  mcrlrecord
ok  =  ok
pending  =  pending
release  =  release
request  =  request
resource  =  resource
tag  =  tag
true  =  true
element(x1, x2)  =  element(x1, x2)
s(x1)  =  s(x1)
0  =  0
record_new(x1)  =  record_new(x1)
record_extract(x1, x2, x3)  =  x1
record_update(x1, x2, x3, x4)  =  record_update(x1, x2, x3, x4)
record_updates(x1, x2, x3)  =  record_updates(x1, x2, x3)
locker2_map_promote_pending(x1, x2)  =  locker2_map_promote_pending(x1)
locker2_promote_pending(x1, x2)  =  locker2_promote_pending(x1)
locker2_map_claim_lock(x1, x2, x3)  =  locker2_map_claim_lock(x1, x2, x3)
locker2_claim_lock(x1, x2, x3)  =  x3
locker2_map_add_pending(x1, x2, x3)  =  locker2_map_add_pending
case0(x1, x2, x3)  =  case0(x2, x3)
locker2_remove_pending(x1, x2)  =  locker2_remove_pending(x1, x2)
subtract(x1, x2)  =  subtract(x1, x2)
locker2_add_pending(x1, x2, x3)  =  locker2_add_pending(x1)
case1(x1, x2, x3, x4)  =  case1(x3, x4)
member(x1, x2)  =  x1
append(x1, x2)  =  x1
locker2_release_lock(x1, x2)  =  locker2_release_lock(x1, x2)
case2(x1, x2, x3)  =  case2(x1, x2)
gen_modtageq(x1, x2)  =  x2
excllock  =  excllock
case4(x1, x2, x3)  =  case4
locker2_obtainables(x1, x2)  =  locker2_obtainables(x1, x2)
case5(x1, x2, x3, x4)  =  case5(x1, x2)
andt(x1, x2)  =  x1
locker2_obtainable(x1, x2)  =  locker2_obtainable(x2)
locker2_check_available(x1, x2)  =  locker2_check_available(x2)
case6(x1, x2, x3, x4)  =  case6(x1, x2, x4)
equal(x1, x2)  =  equal
locker2_check_availables(x1, x2)  =  locker2_check_availables(x2)
locker2_adduniq(x1, x2)  =  locker2_adduniq(x2)
delete(x1, x2)  =  x2
case8(x1, x2, x3, x4)  =  case8(x1, x2)
gen_tag(x1)  =  gen_tag(x1)
case9(x1, x2, x3, x4)  =  x3
eqs(x1, x2)  =  eqs(x2)
empty  =  empty
stack(x1, x2)  =  stack(x1, x2)
pushs(x1, x2)  =  pushs(x1, x2)
pops(x1)  =  pops(x1)
tops(x1)  =  tops(x1)
istops(x1, x2)  =  istops(x1, x2)
eqc(x1, x2)  =  eqc(x2)
nocalls  =  nocalls
calls(x1, x2, x3)  =  calls(x1, x2, x3)
push(x1, x2, x3)  =  push(x1, x2, x3)
push1(x1, x2, x3, x4, x5, x6)  =  push1(x2, x3, x4, x5)

Lexicographic path order with status [LPO].
Quasi-Precedence:

LOCKER2_{MAPPROMOTEPENDING1} > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
or₂ > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
imp₁ > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
not₁ > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
if₂ > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
eq > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
pid₁ > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
a > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
locker > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
ok > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
release > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
request > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
element₂ > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
0 > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
record_new1 > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
[locker2_{mappromotepending1}, locker2_{promotepending1}] > [record_updates3, case0₂] > [cons₂, case8₂] > record_update4 > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
[locker2_{mappromotepending1}, locker2_{promotepending1}] > [record_updates3, case0₂] > [cons₂, case8₂] > [locker2_obtainables2, case5₂] > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
[locker2_{mappromotepending1}, locker2_{promotepending1}] > [record_updates3, case0₂] > [cons₂, case8₂] > case6₃ > locker2_{checkavailable1} > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
locker2_{mapclaimlock3} > [cons₂, case8₂] > record_update4 > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
locker2_{mapclaimlock3} > [cons₂, case8₂] > [locker2_obtainables2, case5₂] > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
locker2_{mapclaimlock3} > [cons₂, case8₂] > case6₃ > locker2_{checkavailable1} > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
locker2_{mapaddpending} > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
locker2_{removepending2} > [record_updates3, case0₂] > [cons₂, case8₂] > record_update4 > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
locker2_{removepending2} > [record_updates3, case0₂] > [cons₂, case8₂] > [locker2_obtainables2, case5₂] > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
locker2_{removepending2} > [record_updates3, case0₂] > [cons₂, case8₂] > case6₃ > locker2_{checkavailable1} > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
locker2_addpending1 > case1₂ > [record_updates3, case0₂] > [cons₂, case8₂] > record_update4 > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
locker2_addpending1 > case1₂ > [record_updates3, case0₂] > [cons₂, case8₂] > [locker2_obtainables2, case5₂] > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
locker2_addpending1 > case1₂ > [record_updates3, case0₂] > [cons₂, case8₂] > case6₃ > locker2_{checkavailable1} > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
[locker2_releaselock2, case2₂] > [record_updates3, case0₂] > [cons₂, case8₂] > record_update4 > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
[locker2_releaselock2, case2₂] > [record_updates3, case0₂] > [cons₂, case8₂] > [locker2_obtainables2, case5₂] > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
[locker2_releaselock2, case2₂] > [record_updates3, case0₂] > [cons₂, case8₂] > case6₃ > locker2_{checkavailable1} > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
case4 > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
locker2_{checkavailables1} > locker2_{checkavailable1} > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
locker2_adduniq1 > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
gen_tag1 > tag > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
pops₁ > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
tops₁ > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
istops₂ > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]
push₃ > [pushs₂, push1₄] > [eqs₁, stack₂, eqc₁, nocalls] > calls₃ > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, true, s₁, subtract₂, excllock, locker2_obtainable1, equal, empty]

Status:

LOCKER2_{MAPPROMOTEPENDING1}: [1]
cons₂: [2,1]
or₂: [2,1]
T: []
F: []
and₂: [2,1]
imp₁: [1]
not₁: [1]
if₂: [1,2]
eq: []
eqt₁: [1]
nil: []
undefined: []
pid₁: [1]
int₁: [1]
tuple₂: [2,1]
a: []
excl: []
false: []
lock: []
locker: []
mcrlrecord: []
ok: []
pending: []
release: []
request: []
resource: []
tag: []
true: []
element₂: [2,1]
s₁: [1]
0: []
record_new1: [1]
record_update4: [4,3,2,1]
record_updates3: [2,3,1]
locker2_{mappromotepending1}: [1]
locker2_{promotepending1}: [1]
locker2_{mapclaimlock3}: [1,3,2]
locker2_{mapaddpending}: []
case0₂: [2,1]
locker2_{removepending2}: [1,2]
subtract₂: [2,1]
locker2_addpending1: [1]
case1₂: [2,1]
locker2_releaselock2: [2,1]
case2₂: [1,2]
excllock: []
case4: []
locker2_obtainables2: [1,2]
case5₂: [2,1]
locker2_obtainable1: [1]
locker2_{checkavailable1}: [1]
case6₃: [1,2,3]
equal: []
locker2_{checkavailables1}: [1]
locker2_adduniq1: [1]
case8₂: [1,2]
gen_tag1: [1]
eqs₁: [1]
empty: []
stack₂: [1,2]
pushs₂: [2,1]
pops₁: [1]
tops₁: [1]
istops₂: [1,2]
eqc₁: [1]
nocalls: []
calls₃: [1,2,3]
push₃: [1,2,3]
push1₄: [3,1,4,2]

The following usable rules [FROCOS05] were oriented:

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)

(32) Obligation:

Q DP problem:
P is empty.
The TRS R consists of the following 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)

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(33) PisEmptyProof (EQUIVALENT transformation)

The TRS P is empty. Hence, there is no (P,Q,R) chain.

(34) TRUE

(35) Obligation:

Q DP problem:
The TRS P consists of the following rules:

ELEMENT(int(s(s(N1))), tuple(T1, T2)) → ELEMENT(int(s(N1)), T2)

The TRS R consists of the following 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)

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(36) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

ELEMENT(int(s(s(N1))), tuple(T1, T2)) → ELEMENT(int(s(N1)), T2)

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
ELEMENT(x1, x2)  =  ELEMENT(x1, x2)
int(x1)  =  int(x1)
s(x1)  =  s(x1)
tuple(x1, x2)  =  tuple(x1, x2)
or(x1, x2)  =  or(x1, x2)
T  =  T
F  =  F
and(x1, x2)  =  and(x1, x2)
imp(x1, x2)  =  imp(x2)
not(x1)  =  not(x1)
if(x1, x2, x3)  =  if(x2, x3)
eq(x1, x2)  =  eq
eqt(x1, x2)  =  eqt(x2)
nil  =  nil
undefined  =  undefined
pid(x1)  =  pid(x1)
cons(x1, x2)  =  cons(x1, x2)
tuplenil(x1)  =  x1
a  =  a
excl  =  excl
false  =  false
lock  =  lock
locker  =  locker
mcrlrecord  =  mcrlrecord
ok  =  ok
pending  =  pending
release  =  release
request  =  request
resource  =  resource
tag  =  tag
true  =  true
element(x1, x2)  =  element(x1, x2)
0  =  0
record_new(x1)  =  record_new(x1)
record_extract(x1, x2, x3)  =  record_extract(x1, x2, x3)
record_update(x1, x2, x3, x4)  =  record_update(x1, x2, x3, x4)
record_updates(x1, x2, x3)  =  record_updates(x1, x2, x3)
locker2_map_promote_pending(x1, x2)  =  locker2_map_promote_pending(x1, x2)
locker2_promote_pending(x1, x2)  =  locker2_promote_pending(x1, x2)
locker2_map_claim_lock(x1, x2, x3)  =  locker2_map_claim_lock(x1)
locker2_claim_lock(x1, x2, x3)  =  x1
locker2_map_add_pending(x1, x2, x3)  =  locker2_map_add_pending(x1)
case0(x1, x2, x3)  =  case0(x1, x2, x3)
locker2_remove_pending(x1, x2)  =  locker2_remove_pending(x1, x2)
subtract(x1, x2)  =  subtract(x1, x2)
locker2_add_pending(x1, x2, x3)  =  locker2_add_pending(x1, x2, x3)
case1(x1, x2, x3, x4)  =  case1(x1, x2, x3)
member(x1, x2)  =  member
append(x1, x2)  =  x1
locker2_release_lock(x1, x2)  =  locker2_release_lock(x1, x2)
case2(x1, x2, x3)  =  case2(x1, x2)
gen_modtageq(x1, x2)  =  x2
excllock  =  excllock
case4(x1, x2, x3)  =  case4
locker2_obtainables(x1, x2)  =  locker2_obtainables(x1, x2)
case5(x1, x2, x3, x4)  =  case5(x1, x2)
andt(x1, x2)  =  x1
locker2_obtainable(x1, x2)  =  locker2_obtainable(x2)
locker2_check_available(x1, x2)  =  locker2_check_available(x2)
case6(x1, x2, x3, x4)  =  case6(x1, x2, x4)
equal(x1, x2)  =  equal
locker2_check_availables(x1, x2)  =  locker2_check_availables(x2)
locker2_adduniq(x1, x2)  =  locker2_adduniq(x2)
delete(x1, x2)  =  delete(x1, x2)
case8(x1, x2, x3, x4)  =  case8(x1, x2, x3, x4)
gen_tag(x1)  =  gen_tag(x1)
case9(x1, x2, x3, x4)  =  x4
eqs(x1, x2)  =  eqs(x2)
empty  =  empty
stack(x1, x2)  =  stack(x1, x2)
pushs(x1, x2)  =  pushs(x1, x2)
pops(x1)  =  pops(x1)
tops(x1)  =  tops(x1)
istops(x1, x2)  =  istops(x1, x2)
eqc(x1, x2)  =  eqc(x2)
nocalls  =  nocalls
calls(x1, x2, x3)  =  calls(x1, x2, x3)
push(x1, x2, x3)  =  push(x1, x2, x3)
push1(x1, x2, x3, x4, x5, x6)  =  push1(x2, x3, x4, x5)

Lexicographic path order with status [LPO].
Quasi-Precedence:

or₂ > [ELEMENT₂, int₁, s₁, tuple₂, T, F, and₂, eqt₁, nil, undefined, excl, false, lock, mcrlrecord, pending, resource, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
imp₁ > [ELEMENT₂, int₁, s₁, tuple₂, T, F, and₂, eqt₁, nil, undefined, excl, false, lock, mcrlrecord, pending, resource, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
not₁ > [ELEMENT₂, int₁, s₁, tuple₂, T, F, and₂, eqt₁, nil, undefined, excl, false, lock, mcrlrecord, pending, resource, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
if₂ > [ELEMENT₂, int₁, s₁, tuple₂, T, F, and₂, eqt₁, nil, undefined, excl, false, lock, mcrlrecord, pending, resource, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
eq > [ELEMENT₂, int₁, s₁, tuple₂, T, F, and₂, eqt₁, nil, undefined, excl, false, lock, mcrlrecord, pending, resource, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
pid₁ > [ELEMENT₂, int₁, s₁, tuple₂, T, F, and₂, eqt₁, nil, undefined, excl, false, lock, mcrlrecord, pending, resource, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
a > [ELEMENT₂, int₁, s₁, tuple₂, T, F, and₂, eqt₁, nil, undefined, excl, false, lock, mcrlrecord, pending, resource, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
locker > [ELEMENT₂, int₁, s₁, tuple₂, T, F, and₂, eqt₁, nil, undefined, excl, false, lock, mcrlrecord, pending, resource, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
ok > [ELEMENT₂, int₁, s₁, tuple₂, T, F, and₂, eqt₁, nil, undefined, excl, false, lock, mcrlrecord, pending, resource, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
release > [ELEMENT₂, int₁, s₁, tuple₂, T, F, and₂, eqt₁, nil, undefined, excl, false, lock, mcrlrecord, pending, resource, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
request > [ELEMENT₂, int₁, s₁, tuple₂, T, F, and₂, eqt₁, nil, undefined, excl, false, lock, mcrlrecord, pending, resource, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
element₂ > [ELEMENT₂, int₁, s₁, tuple₂, T, F, and₂, eqt₁, nil, undefined, excl, false, lock, mcrlrecord, pending, resource, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
0 > [ELEMENT₂, int₁, s₁, tuple₂, T, F, and₂, eqt₁, nil, undefined, excl, false, lock, mcrlrecord, pending, resource, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
record_new1 > [ELEMENT₂, int₁, s₁, tuple₂, T, F, and₂, eqt₁, nil, undefined, excl, false, lock, mcrlrecord, pending, resource, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
locker2_{mappromotepending2} > locker2_{promotepending2} > case0₃ > cons₂ > [true, locker2_obtainables2, case5₂] > [ELEMENT₂, int₁, s₁, tuple₂, T, F, and₂, eqt₁, nil, undefined, excl, false, lock, mcrlrecord, pending, resource, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
locker2_{mappromotepending2} > locker2_{promotepending2} > case0₃ > cons₂ > record_updates3 > record_update4 > [ELEMENT₂, int₁, s₁, tuple₂, T, F, and₂, eqt₁, nil, undefined, excl, false, lock, mcrlrecord, pending, resource, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
locker2_{mappromotepending2} > locker2_{promotepending2} > case0₃ > cons₂ > case6₃ > locker2_{checkavailable1} > [ELEMENT₂, int₁, s₁, tuple₂, T, F, and₂, eqt₁, nil, undefined, excl, false, lock, mcrlrecord, pending, resource, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
locker2_{mapclaimlock1} > cons₂ > [true, locker2_obtainables2, case5₂] > [ELEMENT₂, int₁, s₁, tuple₂, T, F, and₂, eqt₁, nil, undefined, excl, false, lock, mcrlrecord, pending, resource, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
locker2_{mapclaimlock1} > cons₂ > record_updates3 > record_update4 > [ELEMENT₂, int₁, s₁, tuple₂, T, F, and₂, eqt₁, nil, undefined, excl, false, lock, mcrlrecord, pending, resource, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
locker2_{mapclaimlock1} > cons₂ > case6₃ > locker2_{checkavailable1} > [ELEMENT₂, int₁, s₁, tuple₂, T, F, and₂, eqt₁, nil, undefined, excl, false, lock, mcrlrecord, pending, resource, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
locker2_{mapaddpending1} > [ELEMENT₂, int₁, s₁, tuple₂, T, F, and₂, eqt₁, nil, undefined, excl, false, lock, mcrlrecord, pending, resource, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
locker2_{removepending2} > [subtract₂, delete₂, case8₄] > cons₂ > [true, locker2_obtainables2, case5₂] > [ELEMENT₂, int₁, s₁, tuple₂, T, F, and₂, eqt₁, nil, undefined, excl, false, lock, mcrlrecord, pending, resource, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
locker2_{removepending2} > [subtract₂, delete₂, case8₄] > cons₂ > record_updates3 > record_update4 > [ELEMENT₂, int₁, s₁, tuple₂, T, F, and₂, eqt₁, nil, undefined, excl, false, lock, mcrlrecord, pending, resource, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
locker2_{removepending2} > [subtract₂, delete₂, case8₄] > cons₂ > case6₃ > locker2_{checkavailable1} > [ELEMENT₂, int₁, s₁, tuple₂, T, F, and₂, eqt₁, nil, undefined, excl, false, lock, mcrlrecord, pending, resource, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
[locker2_addpending3, case1₃] > cons₂ > [true, locker2_obtainables2, case5₂] > [ELEMENT₂, int₁, s₁, tuple₂, T, F, and₂, eqt₁, nil, undefined, excl, false, lock, mcrlrecord, pending, resource, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
[locker2_addpending3, case1₃] > cons₂ > record_updates3 > record_update4 > [ELEMENT₂, int₁, s₁, tuple₂, T, F, and₂, eqt₁, nil, undefined, excl, false, lock, mcrlrecord, pending, resource, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
[locker2_addpending3, case1₃] > cons₂ > case6₃ > locker2_{checkavailable1} > [ELEMENT₂, int₁, s₁, tuple₂, T, F, and₂, eqt₁, nil, undefined, excl, false, lock, mcrlrecord, pending, resource, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
[locker2_releaselock2, case2₂] > cons₂ > [true, locker2_obtainables2, case5₂] > [ELEMENT₂, int₁, s₁, tuple₂, T, F, and₂, eqt₁, nil, undefined, excl, false, lock, mcrlrecord, pending, resource, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
[locker2_releaselock2, case2₂] > cons₂ > record_updates3 > record_update4 > [ELEMENT₂, int₁, s₁, tuple₂, T, F, and₂, eqt₁, nil, undefined, excl, false, lock, mcrlrecord, pending, resource, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
[locker2_releaselock2, case2₂] > cons₂ > case6₃ > locker2_{checkavailable1} > [ELEMENT₂, int₁, s₁, tuple₂, T, F, and₂, eqt₁, nil, undefined, excl, false, lock, mcrlrecord, pending, resource, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
case4 > [ELEMENT₂, int₁, s₁, tuple₂, T, F, and₂, eqt₁, nil, undefined, excl, false, lock, mcrlrecord, pending, resource, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
locker2_{checkavailables1} > [true, locker2_obtainables2, case5₂] > [ELEMENT₂, int₁, s₁, tuple₂, T, F, and₂, eqt₁, nil, undefined, excl, false, lock, mcrlrecord, pending, resource, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
locker2_{checkavailables1} > locker2_{checkavailable1} > [ELEMENT₂, int₁, s₁, tuple₂, T, F, and₂, eqt₁, nil, undefined, excl, false, lock, mcrlrecord, pending, resource, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
locker2_adduniq1 > [ELEMENT₂, int₁, s₁, tuple₂, T, F, and₂, eqt₁, nil, undefined, excl, false, lock, mcrlrecord, pending, resource, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
gen_tag1 > tag > [ELEMENT₂, int₁, s₁, tuple₂, T, F, and₂, eqt₁, nil, undefined, excl, false, lock, mcrlrecord, pending, resource, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
pops₁ > [ELEMENT₂, int₁, s₁, tuple₂, T, F, and₂, eqt₁, nil, undefined, excl, false, lock, mcrlrecord, pending, resource, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
tops₁ > [ELEMENT₂, int₁, s₁, tuple₂, T, F, and₂, eqt₁, nil, undefined, excl, false, lock, mcrlrecord, pending, resource, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
istops₂ > [ELEMENT₂, int₁, s₁, tuple₂, T, F, and₂, eqt₁, nil, undefined, excl, false, lock, mcrlrecord, pending, resource, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
push₃ > [pushs₂, push1₄] > [eqs₁, stack₂, eqc₁, nocalls] > calls₃ > [ELEMENT₂, int₁, s₁, tuple₂, T, F, and₂, eqt₁, nil, undefined, excl, false, lock, mcrlrecord, pending, resource, record_extract3, member, excllock, locker2_obtainable1, equal, empty]

Status:

ELEMENT₂: [2,1]
int₁: [1]
s₁: [1]
tuple₂: [1,2]
or₂: [2,1]
T: []
F: []
and₂: [1,2]
imp₁: [1]
not₁: [1]
if₂: [1,2]
eq: []
eqt₁: [1]
nil: []
undefined: []
pid₁: [1]
cons₂: [2,1]
a: []
excl: []
false: []
lock: []
locker: []
mcrlrecord: []
ok: []
pending: []
release: []
request: []
resource: []
tag: []
true: []
element₂: [2,1]
0: []
record_new1: [1]
record_extract3: [2,3,1]
record_update4: [2,4,3,1]
record_updates3: [3,1,2]
locker2_{mappromotepending2}: [2,1]
locker2_{promotepending2}: [2,1]
locker2_{mapclaimlock1}: [1]
locker2_{mapaddpending1}: [1]
case0₃: [3,1,2]
locker2_{removepending2}: [2,1]
subtract₂: [2,1]
locker2_addpending3: [2,1,3]
case1₃: [2,3,1]
member: []
locker2_releaselock2: [2,1]
case2₂: [1,2]
excllock: []
case4: []
locker2_obtainables2: [1,2]
case5₂: [2,1]
locker2_obtainable1: [1]
locker2_{checkavailable1}: [1]
case6₃: [1,2,3]
equal: []
locker2_{checkavailables1}: [1]
locker2_adduniq1: [1]
delete₂: [1,2]
case8₄: [3,1,4,2]
gen_tag1: [1]
eqs₁: [1]
empty: []
stack₂: [1,2]
pushs₂: [2,1]
pops₁: [1]
tops₁: [1]
istops₂: [1,2]
eqc₁: [1]
nocalls: []
calls₃: [1,2,3]
push₃: [1,2,3]
push1₄: [3,1,4,2]

The following usable rules [FROCOS05] were oriented:

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)

(37) Obligation:

Q DP problem:
P is empty.
The TRS R consists of the following 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)

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(38) PisEmptyProof (EQUIVALENT transformation)

The TRS P is empty. Hence, there is no (P,Q,R) chain.

(39) TRUE

(40) Obligation:

Q DP problem:
The TRS P consists of the following rules:

EQT(cons(H1, T1), cons(H2, T2)) → EQT(H1, H2)
EQT(pid(N1), pid(N2)) → EQT(N1, N2)
EQT(cons(H1, T1), cons(H2, T2)) → EQT(T1, T2)
EQT(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)

The TRS R consists of the following 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)

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(41) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

EQT(cons(H1, T1), cons(H2, T2)) → EQT(H1, H2)
EQT(pid(N1), pid(N2)) → EQT(N1, N2)
EQT(cons(H1, T1), cons(H2, T2)) → EQT(T1, T2)
EQT(tuple(H1, T1), tuple(H2, T2)) → EQT(H1, H2)
EQT(tuple(H1, T1), tuple(H2, T2)) → EQT(T1, T2)

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
EQT(x1, x2)  =  EQT(x1, x2)
cons(x1, x2)  =  cons(x1, x2)
pid(x1)  =  pid(x1)
tuple(x1, x2)  =  tuple(x1, x2)
tuplenil(x1)  =  x1
or(x1, x2)  =  or(x1, x2)
T  =  T
F  =  F
and(x1, x2)  =  and(x1, x2)
imp(x1, x2)  =  imp(x2)
not(x1)  =  not(x1)
if(x1, x2, x3)  =  if(x2, x3)
eq(x1, x2)  =  eq
eqt(x1, x2)  =  eqt(x2)
nil  =  nil
undefined  =  undefined
int(x1)  =  int(x1)
a  =  a
excl  =  excl
false  =  false
lock  =  lock
locker  =  locker
mcrlrecord  =  mcrlrecord
ok  =  ok
pending  =  pending
release  =  release
request  =  request
resource  =  resource
tag  =  tag
true  =  true
element(x1, x2)  =  element(x2)
s(x1)  =  s(x1)
0  =  0
record_new(x1)  =  record_new(x1)
record_extract(x1, x2, x3)  =  record_extract(x1, x2, x3)
record_update(x1, x2, x3, x4)  =  record_update(x1, x3, x4)
record_updates(x1, x2, x3)  =  record_updates(x1, x3)
locker2_map_promote_pending(x1, x2)  =  locker2_map_promote_pending(x1, x2)
locker2_promote_pending(x1, x2)  =  locker2_promote_pending(x1, x2)
locker2_map_claim_lock(x1, x2, x3)  =  locker2_map_claim_lock(x1)
locker2_claim_lock(x1, x2, x3)  =  x1
locker2_map_add_pending(x1, x2, x3)  =  locker2_map_add_pending
case0(x1, x2, x3)  =  case0(x1, x2, x3)
locker2_remove_pending(x1, x2)  =  locker2_remove_pending(x1, x2)
subtract(x1, x2)  =  subtract(x1)
locker2_add_pending(x1, x2, x3)  =  locker2_add_pending(x1, x2, x3)
case1(x1, x2, x3, x4)  =  case1(x1, x2, x3, x4)
member(x1, x2)  =  member
append(x1, x2)  =  x1
locker2_release_lock(x1, x2)  =  locker2_release_lock(x1, x2)
case2(x1, x2, x3)  =  case2(x1, x2)
gen_modtageq(x1, x2)  =  x2
excllock  =  excllock
case4(x1, x2, x3)  =  case4
locker2_obtainables(x1, x2)  =  locker2_obtainables(x1, x2)
case5(x1, x2, x3, x4)  =  case5(x1, x2)
andt(x1, x2)  =  x1
locker2_obtainable(x1, x2)  =  locker2_obtainable(x2)
locker2_check_available(x1, x2)  =  locker2_check_available(x2)
case6(x1, x2, x3, x4)  =  case6(x1, x2)
equal(x1, x2)  =  equal
locker2_check_availables(x1, x2)  =  locker2_check_availables(x2)
locker2_adduniq(x1, x2)  =  locker2_adduniq(x2)
delete(x1, x2)  =  x2
case8(x1, x2, x3, x4)  =  case8(x1, x2)
gen_tag(x1)  =  gen_tag(x1)
case9(x1, x2, x3, x4)  =  x4
eqs(x1, x2)  =  eqs(x2)
empty  =  empty
stack(x1, x2)  =  stack(x1, x2)
pushs(x1, x2)  =  pushs(x1, x2)
pops(x1)  =  pops(x1)
tops(x1)  =  tops(x1)
istops(x1, x2)  =  istops(x1, x2)
eqc(x1, x2)  =  eqc(x2)
nocalls  =  nocalls
calls(x1, x2, x3)  =  calls(x1, x2, x3)
push(x1, x2, x3)  =  push(x1, x2, x3)
push1(x1, x2, x3, x4, x5, x6)  =  push1(x2, x3, x4, x5)

Lexicographic path order with status [LPO].
Quasi-Precedence:

pid₁ > [EQT₂, tuple₂, T, F, and₂, eqt₁, nil, undefined, int₁, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, subtract₁, member, excllock, locker2_obtainable1, equal, empty]
or₂ > [EQT₂, tuple₂, T, F, and₂, eqt₁, nil, undefined, int₁, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, subtract₁, member, excllock, locker2_obtainable1, equal, empty]
imp₁ > [EQT₂, tuple₂, T, F, and₂, eqt₁, nil, undefined, int₁, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, subtract₁, member, excllock, locker2_obtainable1, equal, empty]
not₁ > [EQT₂, tuple₂, T, F, and₂, eqt₁, nil, undefined, int₁, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, subtract₁, member, excllock, locker2_obtainable1, equal, empty]
if₂ > [EQT₂, tuple₂, T, F, and₂, eqt₁, nil, undefined, int₁, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, subtract₁, member, excllock, locker2_obtainable1, equal, empty]
eq > [EQT₂, tuple₂, T, F, and₂, eqt₁, nil, undefined, int₁, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, subtract₁, member, excllock, locker2_obtainable1, equal, empty]
a > [EQT₂, tuple₂, T, F, and₂, eqt₁, nil, undefined, int₁, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, subtract₁, member, excllock, locker2_obtainable1, equal, empty]
locker > [EQT₂, tuple₂, T, F, and₂, eqt₁, nil, undefined, int₁, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, subtract₁, member, excllock, locker2_obtainable1, equal, empty]
ok > [EQT₂, tuple₂, T, F, and₂, eqt₁, nil, undefined, int₁, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, subtract₁, member, excllock, locker2_obtainable1, equal, empty]
release > [EQT₂, tuple₂, T, F, and₂, eqt₁, nil, undefined, int₁, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, subtract₁, member, excllock, locker2_obtainable1, equal, empty]
request > [EQT₂, tuple₂, T, F, and₂, eqt₁, nil, undefined, int₁, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, subtract₁, member, excllock, locker2_obtainable1, equal, empty]
element₁ > [EQT₂, tuple₂, T, F, and₂, eqt₁, nil, undefined, int₁, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, subtract₁, member, excllock, locker2_obtainable1, equal, empty]
0 > [EQT₂, tuple₂, T, F, and₂, eqt₁, nil, undefined, int₁, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, subtract₁, member, excllock, locker2_obtainable1, equal, empty]
record_new1 > [EQT₂, tuple₂, T, F, and₂, eqt₁, nil, undefined, int₁, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, subtract₁, member, excllock, locker2_obtainable1, equal, empty]
[locker2_{mappromotepending2}, locker2_{promotepending2}] > case0₃ > record_updates2 > [cons₂, true, record_update3, locker2_{mapclaimlock1}, locker2_obtainables2, case5₂, case6₂, case8₂] > locker2_{checkavailable1} > [EQT₂, tuple₂, T, F, and₂, eqt₁, nil, undefined, int₁, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, subtract₁, member, excllock, locker2_obtainable1, equal, empty]
locker2_{mapaddpending} > [EQT₂, tuple₂, T, F, and₂, eqt₁, nil, undefined, int₁, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, subtract₁, member, excllock, locker2_obtainable1, equal, empty]
locker2_{removepending2} > record_updates2 > [cons₂, true, record_update3, locker2_{mapclaimlock1}, locker2_obtainables2, case5₂, case6₂, case8₂] > locker2_{checkavailable1} > [EQT₂, tuple₂, T, F, and₂, eqt₁, nil, undefined, int₁, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, subtract₁, member, excllock, locker2_obtainable1, equal, empty]
locker2_addpending3 > case1₄ > record_updates2 > [cons₂, true, record_update3, locker2_{mapclaimlock1}, locker2_obtainables2, case5₂, case6₂, case8₂] > locker2_{checkavailable1} > [EQT₂, tuple₂, T, F, and₂, eqt₁, nil, undefined, int₁, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, subtract₁, member, excllock, locker2_obtainable1, equal, empty]
[locker2_releaselock2, case2₂] > record_updates2 > [cons₂, true, record_update3, locker2_{mapclaimlock1}, locker2_obtainables2, case5₂, case6₂, case8₂] > locker2_{checkavailable1} > [EQT₂, tuple₂, T, F, and₂, eqt₁, nil, undefined, int₁, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, subtract₁, member, excllock, locker2_obtainable1, equal, empty]
case4 > [EQT₂, tuple₂, T, F, and₂, eqt₁, nil, undefined, int₁, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, subtract₁, member, excllock, locker2_obtainable1, equal, empty]
locker2_{checkavailables1} > [cons₂, true, record_update3, locker2_{mapclaimlock1}, locker2_obtainables2, case5₂, case6₂, case8₂] > locker2_{checkavailable1} > [EQT₂, tuple₂, T, F, and₂, eqt₁, nil, undefined, int₁, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, subtract₁, member, excllock, locker2_obtainable1, equal, empty]
locker2_adduniq1 > [EQT₂, tuple₂, T, F, and₂, eqt₁, nil, undefined, int₁, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, subtract₁, member, excllock, locker2_obtainable1, equal, empty]
gen_tag1 > tag > [EQT₂, tuple₂, T, F, and₂, eqt₁, nil, undefined, int₁, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, subtract₁, member, excllock, locker2_obtainable1, equal, empty]
pops₁ > [EQT₂, tuple₂, T, F, and₂, eqt₁, nil, undefined, int₁, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, subtract₁, member, excllock, locker2_obtainable1, equal, empty]
tops₁ > [EQT₂, tuple₂, T, F, and₂, eqt₁, nil, undefined, int₁, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, subtract₁, member, excllock, locker2_obtainable1, equal, empty]
istops₂ > [EQT₂, tuple₂, T, F, and₂, eqt₁, nil, undefined, int₁, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, subtract₁, member, excllock, locker2_obtainable1, equal, empty]
push₃ > [pushs₂, push1₄] > [eqs₁, stack₂, eqc₁, nocalls] > calls₃ > [EQT₂, tuple₂, T, F, and₂, eqt₁, nil, undefined, int₁, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, subtract₁, member, excllock, locker2_obtainable1, equal, empty]

Status:

EQT₂: [1,2]
cons₂: [2,1]
pid₁: [1]
tuple₂: [2,1]
or₂: [2,1]
T: []
F: []
and₂: [2,1]
imp₁: [1]
not₁: [1]
if₂: [1,2]
eq: []
eqt₁: [1]
nil: []
undefined: []
int₁: [1]
a: []
excl: []
false: []
lock: []
locker: []
mcrlrecord: []
ok: []
pending: []
release: []
request: []
resource: []
tag: []
true: []
element₁: [1]
s₁: [1]
0: []
record_new1: [1]
record_extract3: [2,3,1]
record_update3: [2,3,1]
record_updates2: [2,1]
locker2_{mappromotepending2}: [2,1]
locker2_{promotepending2}: [2,1]
locker2_{mapclaimlock1}: [1]
locker2_{mapaddpending}: []
case0₃: [1,2,3]
locker2_{removepending2}: [2,1]
subtract₁: [1]
locker2_addpending3: [2,3,1]
case1₄: [4,3,1,2]
member: []
locker2_releaselock2: [2,1]
case2₂: [1,2]
excllock: []
case4: []
locker2_obtainables2: [1,2]
case5₂: [2,1]
locker2_obtainable1: [1]
locker2_{checkavailable1}: [1]
case6₂: [1,2]
equal: []
locker2_{checkavailables1}: [1]
locker2_adduniq1: [1]
case8₂: [1,2]
gen_tag1: [1]
eqs₁: [1]
empty: []
stack₂: [1,2]
pushs₂: [2,1]
pops₁: [1]
tops₁: [1]
istops₂: [1,2]
eqc₁: [1]
nocalls: []
calls₃: [1,2,3]
push₃: [1,2,3]
push1₄: [3,1,4,2]

The following usable rules [FROCOS05] were oriented:

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)

(42) Obligation:

Q DP problem:
The TRS P consists of the following rules:

EQT(tuplenil(H1), tuplenil(H2)) → EQT(H1, H2)

The TRS R consists of the following 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)

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(43) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

EQT(tuplenil(H1), tuplenil(H2)) → EQT(H1, H2)

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
EQT(x1, x2)  =  x2
tuplenil(x1)  =  tuplenil(x1)
or(x1, x2)  =  or(x1, x2)
T  =  T
F  =  F
and(x1, x2)  =  and(x1, x2)
imp(x1, x2)  =  imp(x2)
not(x1)  =  not(x1)
if(x1, x2, x3)  =  if(x2, x3)
eq(x1, x2)  =  eq
eqt(x1, x2)  =  eqt(x2)
nil  =  nil
undefined  =  undefined
pid(x1)  =  pid(x1)
int(x1)  =  int(x1)
cons(x1, x2)  =  cons(x1, x2)
tuple(x1, x2)  =  tuple(x1, x2)
a  =  a
excl  =  excl
false  =  false
lock  =  lock
locker  =  locker
mcrlrecord  =  mcrlrecord
ok  =  ok
pending  =  pending
release  =  release
request  =  request
resource  =  resource
tag  =  tag
true  =  true
element(x1, x2)  =  element(x1, x2)
s(x1)  =  s(x1)
0  =  0
record_new(x1)  =  record_new(x1)
record_extract(x1, x2, x3)  =  record_extract(x1, x2, x3)
record_update(x1, x2, x3, x4)  =  record_update(x1, x2, x3, x4)
record_updates(x1, x2, x3)  =  record_updates(x1, x2, x3)
locker2_map_promote_pending(x1, x2)  =  locker2_map_promote_pending(x1, x2)
locker2_promote_pending(x1, x2)  =  locker2_promote_pending(x1, x2)
locker2_map_claim_lock(x1, x2, x3)  =  locker2_map_claim_lock(x1)
locker2_claim_lock(x1, x2, x3)  =  x1
locker2_map_add_pending(x1, x2, x3)  =  locker2_map_add_pending
case0(x1, x2, x3)  =  case0(x1, x2, x3)
locker2_remove_pending(x1, x2)  =  locker2_remove_pending(x1, x2)
subtract(x1, x2)  =  subtract(x1, x2)
locker2_add_pending(x1, x2, x3)  =  locker2_add_pending(x1, x2, x3)
case1(x1, x2, x3, x4)  =  case1(x1, x2, x3)
member(x1, x2)  =  member
append(x1, x2)  =  x1
locker2_release_lock(x1, x2)  =  locker2_release_lock(x1, x2)
case2(x1, x2, x3)  =  case2(x1, x2)
gen_modtageq(x1, x2)  =  x2
excllock  =  excllock
case4(x1, x2, x3)  =  case4
locker2_obtainables(x1, x2)  =  locker2_obtainables(x1, x2)
case5(x1, x2, x3, x4)  =  case5(x1, x2, x4)
andt(x1, x2)  =  x1
locker2_obtainable(x1, x2)  =  locker2_obtainable(x2)
locker2_check_available(x1, x2)  =  locker2_check_available(x2)
case6(x1, x2, x3, x4)  =  case6(x1, x2, x4)
equal(x1, x2)  =  equal
locker2_check_availables(x1, x2)  =  locker2_check_availables(x2)
locker2_adduniq(x1, x2)  =  locker2_adduniq(x2)
delete(x1, x2)  =  delete(x1, x2)
case8(x1, x2, x3, x4)  =  case8(x1, x2, x3, x4)
gen_tag(x1)  =  gen_tag(x1)
case9(x1, x2, x3, x4)  =  x4
eqs(x1, x2)  =  eqs(x2)
empty  =  empty
stack(x1, x2)  =  stack(x1, x2)
pushs(x1, x2)  =  pushs(x1, x2)
pops(x1)  =  pops(x1)
tops(x1)  =  tops(x1)
istops(x1, x2)  =  istops(x1, x2)
eqc(x1, x2)  =  eqc(x2)
nocalls  =  nocalls
calls(x1, x2, x3)  =  calls(x1, x2, x3)
push(x1, x2, x3)  =  push(x1, x2, x3)
push1(x1, x2, x3, x4, x5, x6)  =  push1(x2, x3, x4, x5)

Lexicographic path order with status [LPO].
Quasi-Precedence:

or₂ > [tuplenil₁, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
imp₁ > [tuplenil₁, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
not₁ > [tuplenil₁, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
if₂ > [tuplenil₁, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
eq > [tuplenil₁, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
pid₁ > [tuplenil₁, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
a > [tuplenil₁, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
locker > [tuplenil₁, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
ok > [tuplenil₁, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
release > [tuplenil₁, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
request > [tuplenil₁, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
element₂ > [tuplenil₁, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
0 > [tuplenil₁, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
record_new1 > [tuplenil₁, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
locker2_{mappromotepending2} > locker2_{promotepending2} > [record_updates3, case0₃] > [cons₂, locker2_{mapclaimlock1}] > [true, locker2_obtainables2, case5₃] > [tuplenil₁, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
locker2_{mappromotepending2} > locker2_{promotepending2} > [record_updates3, case0₃] > [cons₂, locker2_{mapclaimlock1}] > record_update4 > [tuplenil₁, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
locker2_{mappromotepending2} > locker2_{promotepending2} > [record_updates3, case0₃] > [cons₂, locker2_{mapclaimlock1}] > case6₃ > locker2_{checkavailable1} > [tuplenil₁, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
locker2_{mapaddpending} > [tuplenil₁, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
locker2_{removepending2} > [record_updates3, case0₃] > [cons₂, locker2_{mapclaimlock1}] > [true, locker2_obtainables2, case5₃] > [tuplenil₁, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
locker2_{removepending2} > [record_updates3, case0₃] > [cons₂, locker2_{mapclaimlock1}] > record_update4 > [tuplenil₁, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
locker2_{removepending2} > [record_updates3, case0₃] > [cons₂, locker2_{mapclaimlock1}] > case6₃ > locker2_{checkavailable1} > [tuplenil₁, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
locker2_{removepending2} > subtract₂ > [delete₂, case8₄] > [cons₂, locker2_{mapclaimlock1}] > [true, locker2_obtainables2, case5₃] > [tuplenil₁, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
locker2_{removepending2} > subtract₂ > [delete₂, case8₄] > [cons₂, locker2_{mapclaimlock1}] > record_update4 > [tuplenil₁, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
locker2_{removepending2} > subtract₂ > [delete₂, case8₄] > [cons₂, locker2_{mapclaimlock1}] > case6₃ > locker2_{checkavailable1} > [tuplenil₁, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
[locker2_addpending3, case1₃] > [record_updates3, case0₃] > [cons₂, locker2_{mapclaimlock1}] > [true, locker2_obtainables2, case5₃] > [tuplenil₁, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
[locker2_addpending3, case1₃] > [record_updates3, case0₃] > [cons₂, locker2_{mapclaimlock1}] > record_update4 > [tuplenil₁, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
[locker2_addpending3, case1₃] > [record_updates3, case0₃] > [cons₂, locker2_{mapclaimlock1}] > case6₃ > locker2_{checkavailable1} > [tuplenil₁, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
[locker2_releaselock2, case2₂] > [record_updates3, case0₃] > [cons₂, locker2_{mapclaimlock1}] > [true, locker2_obtainables2, case5₃] > [tuplenil₁, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
[locker2_releaselock2, case2₂] > [record_updates3, case0₃] > [cons₂, locker2_{mapclaimlock1}] > record_update4 > [tuplenil₁, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
[locker2_releaselock2, case2₂] > [record_updates3, case0₃] > [cons₂, locker2_{mapclaimlock1}] > case6₃ > locker2_{checkavailable1} > [tuplenil₁, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
case4 > [tuplenil₁, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
locker2_{checkavailables1} > [true, locker2_obtainables2, case5₃] > [tuplenil₁, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
locker2_{checkavailables1} > locker2_{checkavailable1} > [tuplenil₁, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
locker2_adduniq1 > [tuplenil₁, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
gen_tag1 > tag > [tuplenil₁, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
pops₁ > [tuplenil₁, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
tops₁ > [tuplenil₁, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
istops₂ > [tuplenil₁, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
push₃ > [pushs₂, push1₄] > [eqs₁, stack₂, eqc₁, nocalls] > calls₃ > [tuplenil₁, T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]

Status:

tuplenil₁: [1]
or₂: [2,1]
T: []
F: []
and₂: [2,1]
imp₁: [1]
not₁: [1]
if₂: [1,2]
eq: []
eqt₁: [1]
nil: []
undefined: []
pid₁: [1]
int₁: [1]
cons₂: [1,2]
tuple₂: [2,1]
a: []
excl: []
false: []
lock: []
locker: []
mcrlrecord: []
ok: []
pending: []
release: []
request: []
resource: []
tag: []
true: []
element₂: [2,1]
s₁: [1]
0: []
record_new1: [1]
record_extract3: [2,3,1]
record_update4: [2,4,3,1]
record_updates3: [2,3,1]
locker2_{mappromotepending2}: [2,1]
locker2_{promotepending2}: [2,1]
locker2_{mapclaimlock1}: [1]
locker2_{mapaddpending}: []
case0₃: [3,1,2]
locker2_{removepending2}: [1,2]
subtract₂: [2,1]
locker2_addpending3: [2,1,3]
case1₃: [2,3,1]
member: []
locker2_releaselock2: [2,1]
case2₂: [1,2]
excllock: []
case4: []
locker2_obtainables2: [2,1]
case5₃: [1,2,3]
locker2_obtainable1: [1]
locker2_{checkavailable1}: [1]
case6₃: [1,2,3]
equal: []
locker2_{checkavailables1}: [1]
locker2_adduniq1: [1]
delete₂: [1,2]
case8₄: [3,1,4,2]
gen_tag1: [1]
eqs₁: [1]
empty: []
stack₂: [1,2]
pushs₂: [2,1]
pops₁: [1]
tops₁: [1]
istops₂: [1,2]
eqc₁: [1]
nocalls: []
calls₃: [1,2,3]
push₃: [1,2,3]
push1₄: [3,1,4,2]

The following usable rules [FROCOS05] were oriented:

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)

(44) Obligation:

Q DP problem:
P is empty.
The TRS R consists of the following 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)

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(45) PisEmptyProof (EQUIVALENT transformation)

The TRS P is empty. Hence, there is no (P,Q,R) chain.

(46) TRUE

(47) Obligation:

Q DP problem:
The TRS P consists of the following rules:

EQS(stack(E1, S1), stack(E2, S2)) → EQS(S1, S2)

The TRS R consists of the following 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)

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(48) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

EQS(stack(E1, S1), stack(E2, S2)) → EQS(S1, S2)

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
EQS(x1, x2)  =  EQS(x1, x2)
stack(x1, x2)  =  stack(x1, x2)
or(x1, x2)  =  or(x1, x2)
T  =  T
F  =  F
and(x1, x2)  =  and(x1, x2)
imp(x1, x2)  =  imp(x2)
not(x1)  =  not(x1)
if(x1, x2, x3)  =  if(x2, x3)
eq(x1, x2)  =  eq
eqt(x1, x2)  =  eqt(x1)
nil  =  nil
undefined  =  undefined
pid(x1)  =  pid(x1)
int(x1)  =  int(x1)
cons(x1, x2)  =  cons(x1, x2)
tuple(x1, x2)  =  tuple(x1, x2)
tuplenil(x1)  =  x1
a  =  a
excl  =  excl
false  =  false
lock  =  lock
locker  =  locker
mcrlrecord  =  mcrlrecord
ok  =  ok
pending  =  pending
release  =  release
request  =  request
resource  =  resource
tag  =  tag
true  =  true
element(x1, x2)  =  element(x1, x2)
s(x1)  =  s(x1)
0  =  0
record_new(x1)  =  record_new(x1)
record_extract(x1, x2, x3)  =  x1
record_update(x1, x2, x3, x4)  =  record_update(x1, x2, x3, x4)
record_updates(x1, x2, x3)  =  record_updates(x1, x2, x3)
locker2_map_promote_pending(x1, x2)  =  locker2_map_promote_pending(x1)
locker2_promote_pending(x1, x2)  =  locker2_promote_pending(x1)
locker2_map_claim_lock(x1, x2, x3)  =  x1
locker2_claim_lock(x1, x2, x3)  =  x1
locker2_map_add_pending(x1, x2, x3)  =  locker2_map_add_pending
case0(x1, x2, x3)  =  case0(x2, x3)
locker2_remove_pending(x1, x2)  =  locker2_remove_pending(x1, x2)
subtract(x1, x2)  =  subtract(x1, x2)
locker2_add_pending(x1, x2, x3)  =  locker2_add_pending(x1, x2, x3)
case1(x1, x2, x3, x4)  =  case1(x1, x2, x3)
member(x1, x2)  =  member
append(x1, x2)  =  x1
locker2_release_lock(x1, x2)  =  locker2_release_lock(x1, x2)
case2(x1, x2, x3)  =  case2(x1, x2)
gen_modtageq(x1, x2)  =  x2
excllock  =  excllock
case4(x1, x2, x3)  =  case4
locker2_obtainables(x1, x2)  =  locker2_obtainables(x1, x2)
case5(x1, x2, x3, x4)  =  case5(x1, x2)
andt(x1, x2)  =  x1
locker2_obtainable(x1, x2)  =  locker2_obtainable(x2)
locker2_check_available(x1, x2)  =  locker2_check_available(x2)
case6(x1, x2, x3, x4)  =  case6(x1, x2, x4)
equal(x1, x2)  =  equal
locker2_check_availables(x1, x2)  =  locker2_check_availables(x2)
locker2_adduniq(x1, x2)  =  locker2_adduniq(x2)
delete(x1, x2)  =  delete(x1, x2)
case8(x1, x2, x3, x4)  =  case8(x1, x2, x3, x4)
gen_tag(x1)  =  gen_tag(x1)
case9(x1, x2, x3, x4)  =  x4
eqs(x1, x2)  =  x1
empty  =  empty
pushs(x1, x2)  =  pushs(x1, x2)
pops(x1)  =  pops(x1)
tops(x1)  =  tops(x1)
istops(x1, x2)  =  istops(x1, x2)
eqc(x1, x2)  =  eqc(x1, x2)
nocalls  =  nocalls
calls(x1, x2, x3)  =  calls(x1, x2, x3)
push(x1, x2, x3)  =  push(x1, x2, x3)
push1(x1, x2, x3, x4, x5, x6)  =  push1(x1, x2, x3, x4, x5, x6)

Lexicographic path order with status [LPO].
Quasi-Precedence:

EQS₂ > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, member, excllock, locker2_obtainable1, equal, empty]
or₂ > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, member, excllock, locker2_obtainable1, equal, empty]
imp₁ > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, member, excllock, locker2_obtainable1, equal, empty]
not₁ > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, member, excllock, locker2_obtainable1, equal, empty]
if₂ > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, member, excllock, locker2_obtainable1, equal, empty]
eq > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, member, excllock, locker2_obtainable1, equal, empty]
pid₁ > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, member, excllock, locker2_obtainable1, equal, empty]
a > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, member, excllock, locker2_obtainable1, equal, empty]
locker > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, member, excllock, locker2_obtainable1, equal, empty]
ok > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, member, excllock, locker2_obtainable1, equal, empty]
release > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, member, excllock, locker2_obtainable1, equal, empty]
request > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, member, excllock, locker2_obtainable1, equal, empty]
element₂ > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, member, excllock, locker2_obtainable1, equal, empty]
0 > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, member, excllock, locker2_obtainable1, equal, empty]
record_new1 > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, member, excllock, locker2_obtainable1, equal, empty]
locker2_{mappromotepending1} > locker2_{promotepending1} > [record_updates3, case0₂] > cons₂ > [true, locker2_obtainables2, case5₂] > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, member, excllock, locker2_obtainable1, equal, empty]
locker2_{mappromotepending1} > locker2_{promotepending1} > [record_updates3, case0₂] > cons₂ > record_update4 > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, member, excllock, locker2_obtainable1, equal, empty]
locker2_{mappromotepending1} > locker2_{promotepending1} > [record_updates3, case0₂] > cons₂ > case6₃ > locker2_{checkavailable1} > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, member, excllock, locker2_obtainable1, equal, empty]
locker2_{mapaddpending} > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, member, excllock, locker2_obtainable1, equal, empty]
locker2_{removepending2} > [record_updates3, case0₂] > cons₂ > [true, locker2_obtainables2, case5₂] > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, member, excllock, locker2_obtainable1, equal, empty]
locker2_{removepending2} > [record_updates3, case0₂] > cons₂ > record_update4 > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, member, excllock, locker2_obtainable1, equal, empty]
locker2_{removepending2} > [record_updates3, case0₂] > cons₂ > case6₃ > locker2_{checkavailable1} > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, member, excllock, locker2_obtainable1, equal, empty]
locker2_{removepending2} > subtract₂ > [delete₂, case8₄] > cons₂ > [true, locker2_obtainables2, case5₂] > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, member, excllock, locker2_obtainable1, equal, empty]
locker2_{removepending2} > subtract₂ > [delete₂, case8₄] > cons₂ > record_update4 > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, member, excllock, locker2_obtainable1, equal, empty]
locker2_{removepending2} > subtract₂ > [delete₂, case8₄] > cons₂ > case6₃ > locker2_{checkavailable1} > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, member, excllock, locker2_obtainable1, equal, empty]
[locker2_addpending3, case1₃] > [record_updates3, case0₂] > cons₂ > [true, locker2_obtainables2, case5₂] > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, member, excllock, locker2_obtainable1, equal, empty]
[locker2_addpending3, case1₃] > [record_updates3, case0₂] > cons₂ > record_update4 > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, member, excllock, locker2_obtainable1, equal, empty]
[locker2_addpending3, case1₃] > [record_updates3, case0₂] > cons₂ > case6₃ > locker2_{checkavailable1} > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, member, excllock, locker2_obtainable1, equal, empty]
[locker2_releaselock2, case2₂] > [record_updates3, case0₂] > cons₂ > [true, locker2_obtainables2, case5₂] > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, member, excllock, locker2_obtainable1, equal, empty]
[locker2_releaselock2, case2₂] > [record_updates3, case0₂] > cons₂ > record_update4 > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, member, excllock, locker2_obtainable1, equal, empty]
[locker2_releaselock2, case2₂] > [record_updates3, case0₂] > cons₂ > case6₃ > locker2_{checkavailable1} > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, member, excllock, locker2_obtainable1, equal, empty]
case4 > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, member, excllock, locker2_obtainable1, equal, empty]
locker2_{checkavailables1} > [true, locker2_obtainables2, case5₂] > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, member, excllock, locker2_obtainable1, equal, empty]
locker2_{checkavailables1} > locker2_{checkavailable1} > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, member, excllock, locker2_obtainable1, equal, empty]
locker2_adduniq1 > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, member, excllock, locker2_obtainable1, equal, empty]
gen_tag1 > tag > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, member, excllock, locker2_obtainable1, equal, empty]
pops₁ > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, member, excllock, locker2_obtainable1, equal, empty]
tops₁ > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, member, excllock, locker2_obtainable1, equal, empty]
istops₂ > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, member, excllock, locker2_obtainable1, equal, empty]
eqc₂ > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, member, excllock, locker2_obtainable1, equal, empty]
push₃ > [pushs₂, push1₆] > [stack₂, nocalls] > calls₃ > [T, F, and₂, eqt₁, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, member, excllock, locker2_obtainable1, equal, empty]

Status:

EQS₂: [1,2]
stack₂: [2,1]
or₂: [2,1]
T: []
F: []
and₂: [2,1]
imp₁: [1]
not₁: [1]
if₂: [1,2]
eq: []
eqt₁: [1]
nil: []
undefined: []
pid₁: [1]
int₁: [1]
cons₂: [1,2]
tuple₂: [2,1]
a: []
excl: []
false: []
lock: []
locker: []
mcrlrecord: []
ok: []
pending: []
release: []
request: []
resource: []
tag: []
true: []
element₂: [2,1]
s₁: [1]
0: []
record_new1: [1]
record_update4: [2,4,3,1]
record_updates3: [2,3,1]
locker2_{mappromotepending1}: [1]
locker2_{promotepending1}: [1]
locker2_{mapaddpending}: []
case0₂: [2,1]
locker2_{removepending2}: [1,2]
subtract₂: [2,1]
locker2_addpending3: [2,1,3]
case1₃: [2,3,1]
member: []
locker2_releaselock2: [2,1]
case2₂: [1,2]
excllock: []
case4: []
locker2_obtainables2: [1,2]
case5₂: [2,1]
locker2_obtainable1: [1]
locker2_{checkavailable1}: [1]
case6₃: [1,2,3]
equal: []
locker2_{checkavailables1}: [1]
locker2_adduniq1: [1]
delete₂: [1,2]
case8₄: [3,1,4,2]
gen_tag1: [1]
empty: []
pushs₂: [2,1]
pops₁: [1]
tops₁: [1]
istops₂: [1,2]
eqc₂: [2,1]
nocalls: []
calls₃: [1,2,3]
push₃: [1,2,3]
push1₆: [4,2,6,5,3,1]

The following usable rules [FROCOS05] were oriented:

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)

(49) Obligation:

Q DP problem:
P is empty.
The TRS R consists of the following 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)

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(50) PisEmptyProof (EQUIVALENT transformation)

The TRS P is empty. Hence, there is no (P,Q,R) chain.

(51) TRUE

(52) Obligation:

Q DP problem:
The TRS P consists of the following rules:

EQC(calls(E1, S1, CS1), calls(E2, S2, CS2)) → EQC(CS1, CS2)

The TRS R consists of the following 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)

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(53) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

EQC(calls(E1, S1, CS1), calls(E2, S2, CS2)) → EQC(CS1, CS2)

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
EQC(x1, x2)  =  EQC(x1, x2)
calls(x1, x2, x3)  =  calls(x1, x2, x3)
or(x1, x2)  =  or(x1, x2)
T  =  T
F  =  F
and(x1, x2)  =  and(x1, x2)
imp(x1, x2)  =  imp(x2)
not(x1)  =  not(x1)
if(x1, x2, x3)  =  if(x2, x3)
eq(x1, x2)  =  eq
eqt(x1, x2)  =  x2
nil  =  nil
undefined  =  undefined
pid(x1)  =  pid(x1)
int(x1)  =  int(x1)
cons(x1, x2)  =  cons(x1, x2)
tuple(x1, x2)  =  tuple(x1, x2)
tuplenil(x1)  =  x1
a  =  a
excl  =  excl
false  =  false
lock  =  lock
locker  =  locker
mcrlrecord  =  mcrlrecord
ok  =  ok
pending  =  pending
release  =  release
request  =  request
resource  =  resource
tag  =  tag
true  =  true
element(x1, x2)  =  element(x2)
s(x1)  =  s(x1)
0  =  0
record_new(x1)  =  record_new(x1)
record_extract(x1, x2, x3)  =  record_extract(x1, x2, x3)
record_update(x1, x2, x3, x4)  =  record_update(x1, x2, x3, x4)
record_updates(x1, x2, x3)  =  record_updates(x1, x2, x3)
locker2_map_promote_pending(x1, x2)  =  locker2_map_promote_pending(x1, x2)
locker2_promote_pending(x1, x2)  =  locker2_promote_pending(x1, x2)
locker2_map_claim_lock(x1, x2, x3)  =  locker2_map_claim_lock(x1)
locker2_claim_lock(x1, x2, x3)  =  x1
locker2_map_add_pending(x1, x2, x3)  =  locker2_map_add_pending(x1)
case0(x1, x2, x3)  =  case0(x1, x2, x3)
locker2_remove_pending(x1, x2)  =  locker2_remove_pending(x1, x2)
subtract(x1, x2)  =  subtract(x1, x2)
locker2_add_pending(x1, x2, x3)  =  locker2_add_pending(x1, x2, x3)
case1(x1, x2, x3, x4)  =  case1(x1, x2, x3)
member(x1, x2)  =  member
append(x1, x2)  =  x1
locker2_release_lock(x1, x2)  =  locker2_release_lock(x1, x2)
case2(x1, x2, x3)  =  case2(x1, x2)
gen_modtageq(x1, x2)  =  x2
excllock  =  excllock
case4(x1, x2, x3)  =  case4
locker2_obtainables(x1, x2)  =  locker2_obtainables(x1, x2)
case5(x1, x2, x3, x4)  =  case5(x1, x2, x4)
andt(x1, x2)  =  x1
locker2_obtainable(x1, x2)  =  locker2_obtainable(x2)
locker2_check_available(x1, x2)  =  locker2_check_available(x2)
case6(x1, x2, x3, x4)  =  case6(x1, x2, x4)
equal(x1, x2)  =  equal
locker2_check_availables(x1, x2)  =  locker2_check_availables(x2)
locker2_adduniq(x1, x2)  =  locker2_adduniq(x2)
delete(x1, x2)  =  delete(x1, x2)
case8(x1, x2, x3, x4)  =  case8(x1, x2, x3, x4)
gen_tag(x1)  =  gen_tag(x1)
case9(x1, x2, x3, x4)  =  x4
eqs(x1, x2)  =  eqs(x2)
empty  =  empty
stack(x1, x2)  =  stack(x1, x2)
pushs(x1, x2)  =  pushs(x1, x2)
pops(x1)  =  pops(x1)
tops(x1)  =  tops(x1)
istops(x1, x2)  =  istops(x1, x2)
eqc(x1, x2)  =  eqc(x1, x2)
nocalls  =  nocalls
push(x1, x2, x3)  =  push(x1, x2, x3)
push1(x1, x2, x3, x4, x5, x6)  =  push1(x1, x2, x3, x4, x5, x6)

Lexicographic path order with status [LPO].
Quasi-Precedence:

or₂ > [EQC₂, T, F, and₂, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
imp₁ > [EQC₂, T, F, and₂, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
not₁ > [EQC₂, T, F, and₂, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
if₂ > [EQC₂, T, F, and₂, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
eq > [EQC₂, T, F, and₂, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
pid₁ > [EQC₂, T, F, and₂, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
a > [EQC₂, T, F, and₂, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
locker > [EQC₂, T, F, and₂, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
ok > [EQC₂, T, F, and₂, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
release > [EQC₂, T, F, and₂, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
request > [EQC₂, T, F, and₂, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
element₁ > [EQC₂, T, F, and₂, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
0 > [EQC₂, T, F, and₂, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
record_new1 > [EQC₂, T, F, and₂, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
locker2_{mappromotepending2} > locker2_{promotepending2} > [record_updates3, case0₃] > [cons₂, locker2_{mapclaimlock1}] > [true, locker2_obtainables2, case5₃] > [EQC₂, T, F, and₂, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
locker2_{mappromotepending2} > locker2_{promotepending2} > [record_updates3, case0₃] > [cons₂, locker2_{mapclaimlock1}] > record_update4 > [EQC₂, T, F, and₂, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
locker2_{mappromotepending2} > locker2_{promotepending2} > [record_updates3, case0₃] > [cons₂, locker2_{mapclaimlock1}] > case6₃ > locker2_{checkavailable1} > [EQC₂, T, F, and₂, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
locker2_{mapaddpending1} > [EQC₂, T, F, and₂, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
locker2_{removepending2} > [record_updates3, case0₃] > [cons₂, locker2_{mapclaimlock1}] > [true, locker2_obtainables2, case5₃] > [EQC₂, T, F, and₂, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
locker2_{removepending2} > [record_updates3, case0₃] > [cons₂, locker2_{mapclaimlock1}] > record_update4 > [EQC₂, T, F, and₂, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
locker2_{removepending2} > [record_updates3, case0₃] > [cons₂, locker2_{mapclaimlock1}] > case6₃ > locker2_{checkavailable1} > [EQC₂, T, F, and₂, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
locker2_{removepending2} > subtract₂ > [delete₂, case8₄] > [cons₂, locker2_{mapclaimlock1}] > [true, locker2_obtainables2, case5₃] > [EQC₂, T, F, and₂, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
locker2_{removepending2} > subtract₂ > [delete₂, case8₄] > [cons₂, locker2_{mapclaimlock1}] > record_update4 > [EQC₂, T, F, and₂, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
locker2_{removepending2} > subtract₂ > [delete₂, case8₄] > [cons₂, locker2_{mapclaimlock1}] > case6₃ > locker2_{checkavailable1} > [EQC₂, T, F, and₂, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
[locker2_addpending3, case1₃] > [record_updates3, case0₃] > [cons₂, locker2_{mapclaimlock1}] > [true, locker2_obtainables2, case5₃] > [EQC₂, T, F, and₂, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
[locker2_addpending3, case1₃] > [record_updates3, case0₃] > [cons₂, locker2_{mapclaimlock1}] > record_update4 > [EQC₂, T, F, and₂, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
[locker2_addpending3, case1₃] > [record_updates3, case0₃] > [cons₂, locker2_{mapclaimlock1}] > case6₃ > locker2_{checkavailable1} > [EQC₂, T, F, and₂, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
[locker2_releaselock2, case2₂] > [record_updates3, case0₃] > [cons₂, locker2_{mapclaimlock1}] > [true, locker2_obtainables2, case5₃] > [EQC₂, T, F, and₂, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
[locker2_releaselock2, case2₂] > [record_updates3, case0₃] > [cons₂, locker2_{mapclaimlock1}] > record_update4 > [EQC₂, T, F, and₂, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
[locker2_releaselock2, case2₂] > [record_updates3, case0₃] > [cons₂, locker2_{mapclaimlock1}] > case6₃ > locker2_{checkavailable1} > [EQC₂, T, F, and₂, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
case4 > [EQC₂, T, F, and₂, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
locker2_{checkavailables1} > [true, locker2_obtainables2, case5₃] > [EQC₂, T, F, and₂, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
locker2_{checkavailables1} > locker2_{checkavailable1} > [EQC₂, T, F, and₂, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
locker2_adduniq1 > [EQC₂, T, F, and₂, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
gen_tag1 > tag > [EQC₂, T, F, and₂, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
[pushs₂, push₃, push1₆] > [calls₃, eqs₁, stack₂, eqc₂, nocalls] > [EQC₂, T, F, and₂, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
pops₁ > [EQC₂, T, F, and₂, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
tops₁ > [EQC₂, T, F, and₂, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]
istops₂ > [EQC₂, T, F, and₂, nil, undefined, int₁, tuple₂, excl, false, lock, mcrlrecord, pending, resource, s₁, record_extract3, member, excllock, locker2_obtainable1, equal, empty]

Status:

EQC₂: [1,2]
calls₃: [1,2,3]
or₂: [2,1]
T: []
F: []
and₂: [2,1]
imp₁: [1]
not₁: [1]
if₂: [1,2]
eq: []
nil: []
undefined: []
pid₁: [1]
int₁: [1]
cons₂: [1,2]
tuple₂: [2,1]
a: []
excl: []
false: []
lock: []
locker: []
mcrlrecord: []
ok: []
pending: []
release: []
request: []
resource: []
tag: []
true: []
element₁: [1]
s₁: [1]
0: []
record_new1: [1]
record_extract3: [2,3,1]
record_update4: [4,3,2,1]
record_updates3: [2,3,1]
locker2_{mappromotepending2}: [2,1]
locker2_{promotepending2}: [2,1]
locker2_{mapclaimlock1}: [1]
locker2_{mapaddpending1}: [1]
case0₃: [3,1,2]
locker2_{removepending2}: [1,2]
subtract₂: [2,1]
locker2_addpending3: [2,1,3]
case1₃: [2,3,1]
member: []
locker2_releaselock2: [2,1]
case2₂: [1,2]
excllock: []
case4: []
locker2_obtainables2: [2,1]
case5₃: [1,2,3]
locker2_obtainable1: [1]
locker2_{checkavailable1}: [1]
case6₃: [2,1,3]
equal: []
locker2_{checkavailables1}: [1]
locker2_adduniq1: [1]
delete₂: [1,2]
case8₄: [3,1,4,2]
gen_tag1: [1]
eqs₁: [1]
empty: []
stack₂: [2,1]
pushs₂: [1,2]
pops₁: [1]
tops₁: [1]
istops₂: [1,2]
eqc₂: [2,1]
nocalls: []
push₃: [2,3,1]
push1₆: [2,4,6,5,3,1]

The following usable rules [FROCOS05] were oriented:

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)

(54) Obligation:

Q DP problem:
P is empty.
The TRS R consists of the following 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)

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(55) PisEmptyProof (EQUIVALENT transformation)

The TRS P is empty. Hence, there is no (P,Q,R) chain.

(56) TRUE