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)  =  x2
cons(x1, x2)  =  cons(x1, x2)
delete(x1, x2)  =  delete(x2)
or(x1, x2)  =  or
T  =  T
F  =  F
and(x1, x2)  =  and(x1, x2)
imp(x1, x2)  =  imp(x2)
not(x1)  =  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)  =  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
0  =  0
record_new(x1)  =  record_new
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, x2, x3)
locker2_claim_lock(x1, x2, x3)  =  locker2_claim_lock(x1, x2)
locker2_map_add_pending(x1, x2, x3)  =  locker2_map_add_pending(x1, x2, x3)
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)  =  append(x1, x2)
locker2_release_lock(x1, x2)  =  locker2_release_lock(x1, x2)
case2(x1, x2, x3)  =  case2(x2)
gen_modtageq(x1, x2)  =  gen_modtageq
excllock  =  excllock
case4(x1, x2, x3)  =  case4(x2)
locker2_obtainables(x1, x2)  =  locker2_obtainables
case5(x1, x2, x3, x4)  =  x4
andt(x1, x2)  =  x2
locker2_obtainable(x1, x2)  =  x2
locker2_check_available(x1, x2)  =  locker2_check_available
case6(x1, x2, x3, x4)  =  x4
equal(x1, x2)  =  equal
locker2_check_availables(x1, x2)  =  locker2_check_availables
locker2_adduniq(x1, x2)  =  locker2_adduniq(x1, x2)
case8(x1, x2, x3, x4)  =  case8(x1, x2)
gen_tag(x1)  =  gen_tag(x1)
case9(x1, x2, x3, x4)  =  case9
eqs(x1, x2)  =  x2
empty  =  empty
stack(x1, x2)  =  stack(x1, x2)
pushs(x1, x2)  =  pushs(x1, x2)
pops(x1)  =  x1
tops(x1)  =  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:

imp₁ > [or, T, F, eq, nil, pid₁, excl, locker2_{mapaddpending3}]
if₂ > [or, T, F, eq, nil, pid₁, excl, locker2_{mapaddpending3}]
a > [or, T, F, eq, nil, pid₁, excl, locker2_{mapaddpending3}]
locker > [or, T, F, eq, nil, pid₁, excl, locker2_{mapaddpending3}]
ok > [or, T, F, eq, nil, pid₁, excl, locker2_{mapaddpending3}]
release > [or, T, F, eq, nil, pid₁, excl, locker2_{mapaddpending3}]
request > [or, T, F, eq, nil, pid₁, excl, locker2_{mapaddpending3}]
[tag, gen_tag1] > tuple₂ > and₂ > [or, T, F, eq, nil, pid₁, excl, locker2_{mapaddpending3}]
[element₁, s] > [or, T, F, eq, nil, pid₁, excl, locker2_{mapaddpending3}]
0 > [or, T, F, eq, nil, pid₁, excl, locker2_{mapaddpending3}]
record_new > [lock, locker2_addpending3, case1₃] > undefined > [or, T, F, eq, nil, pid₁, excl, locker2_{mapaddpending3}]
record_new > [lock, locker2_addpending3, case1₃] > mcrlrecord > tuple₂ > and₂ > [or, T, F, eq, nil, pid₁, excl, locker2_{mapaddpending3}]
record_new > [lock, locker2_addpending3, case1₃] > resource > tuple₂ > and₂ > [or, T, F, eq, nil, pid₁, excl, locker2_{mapaddpending3}]
record_new > [lock, locker2_addpending3, case1₃] > record_extract3 > tuple₂ > and₂ > [or, T, F, eq, nil, pid₁, excl, locker2_{mapaddpending3}]
record_new > [lock, locker2_addpending3, case1₃] > append₂ > cons₂ > record_updates2 > record_update3 > tuple₂ > and₂ > [or, T, F, eq, nil, pid₁, excl, locker2_{mapaddpending3}]
record_new > [lock, locker2_addpending3, case1₃] > append₂ > cons₂ > locker2_{checkavailables} > [false, true, member, gen_modtageq, locker2_obtainables, locker2_{checkavailable}, equal, case9] > tuple₂ > and₂ > [or, T, F, eq, nil, pid₁, excl, locker2_{mapaddpending3}]
record_new > [lock, locker2_addpending3, case1₃] > append₂ > cons₂ > locker2_{checkavailables} > [false, true, member, gen_modtageq, locker2_obtainables, locker2_{checkavailable}, equal, case9] > pending > [or, T, F, eq, nil, pid₁, excl, locker2_{mapaddpending3}]
record_new > [lock, locker2_addpending3, case1₃] > append₂ > cons₂ > locker2_{checkavailables} > [false, true, member, gen_modtageq, locker2_obtainables, locker2_{checkavailable}, equal, case9] > excllock > [or, T, F, eq, nil, pid₁, excl, locker2_{mapaddpending3}]
[locker2_{mappromotepending2}, locker2_{promotepending2}] > [lock, locker2_addpending3, case1₃] > undefined > [or, T, F, eq, nil, pid₁, excl, locker2_{mapaddpending3}]
[locker2_{mappromotepending2}, locker2_{promotepending2}] > [lock, locker2_addpending3, case1₃] > mcrlrecord > tuple₂ > and₂ > [or, T, F, eq, nil, pid₁, excl, locker2_{mapaddpending3}]
[locker2_{mappromotepending2}, locker2_{promotepending2}] > [lock, locker2_addpending3, case1₃] > resource > tuple₂ > and₂ > [or, T, F, eq, nil, pid₁, excl, locker2_{mapaddpending3}]
[locker2_{mappromotepending2}, locker2_{promotepending2}] > [lock, locker2_addpending3, case1₃] > record_extract3 > tuple₂ > and₂ > [or, T, F, eq, nil, pid₁, excl, locker2_{mapaddpending3}]
[locker2_{mappromotepending2}, locker2_{promotepending2}] > [lock, locker2_addpending3, case1₃] > append₂ > cons₂ > record_updates2 > record_update3 > tuple₂ > and₂ > [or, T, F, eq, nil, pid₁, excl, locker2_{mapaddpending3}]
[locker2_{mappromotepending2}, locker2_{promotepending2}] > [lock, locker2_addpending3, case1₃] > append₂ > cons₂ > locker2_{checkavailables} > [false, true, member, gen_modtageq, locker2_obtainables, locker2_{checkavailable}, equal, case9] > tuple₂ > and₂ > [or, T, F, eq, nil, pid₁, excl, locker2_{mapaddpending3}]
[locker2_{mappromotepending2}, locker2_{promotepending2}] > [lock, locker2_addpending3, case1₃] > append₂ > cons₂ > locker2_{checkavailables} > [false, true, member, gen_modtageq, locker2_obtainables, locker2_{checkavailable}, equal, case9] > pending > [or, T, F, eq, nil, pid₁, excl, locker2_{mapaddpending3}]
[locker2_{mappromotepending2}, locker2_{promotepending2}] > [lock, locker2_addpending3, case1₃] > append₂ > cons₂ > locker2_{checkavailables} > [false, true, member, gen_modtageq, locker2_obtainables, locker2_{checkavailable}, equal, case9] > excllock > [or, T, F, eq, nil, pid₁, excl, locker2_{mapaddpending3}]
[locker2_{mappromotepending2}, locker2_{promotepending2}] > case0₂ > cons₂ > record_updates2 > record_update3 > tuple₂ > and₂ > [or, T, F, eq, nil, pid₁, excl, locker2_{mapaddpending3}]
[locker2_{mappromotepending2}, locker2_{promotepending2}] > case0₂ > cons₂ > locker2_{checkavailables} > [false, true, member, gen_modtageq, locker2_obtainables, locker2_{checkavailable}, equal, case9] > tuple₂ > and₂ > [or, T, F, eq, nil, pid₁, excl, locker2_{mapaddpending3}]
[locker2_{mappromotepending2}, locker2_{promotepending2}] > case0₂ > cons₂ > locker2_{checkavailables} > [false, true, member, gen_modtageq, locker2_obtainables, locker2_{checkavailable}, equal, case9] > pending > [or, T, F, eq, nil, pid₁, excl, locker2_{mapaddpending3}]
[locker2_{mappromotepending2}, locker2_{promotepending2}] > case0₂ > cons₂ > locker2_{checkavailables} > [false, true, member, gen_modtageq, locker2_obtainables, locker2_{checkavailable}, equal, case9] > excllock > [or, T, F, eq, nil, pid₁, excl, locker2_{mapaddpending3}]
locker2_{mapclaimlock3} > cons₂ > record_updates2 > record_update3 > tuple₂ > and₂ > [or, T, F, eq, nil, pid₁, excl, locker2_{mapaddpending3}]
locker2_{mapclaimlock3} > cons₂ > locker2_{checkavailables} > [false, true, member, gen_modtageq, locker2_obtainables, locker2_{checkavailable}, equal, case9] > tuple₂ > and₂ > [or, T, F, eq, nil, pid₁, excl, locker2_{mapaddpending3}]
locker2_{mapclaimlock3} > cons₂ > locker2_{checkavailables} > [false, true, member, gen_modtageq, locker2_obtainables, locker2_{checkavailable}, equal, case9] > pending > [or, T, F, eq, nil, pid₁, excl, locker2_{mapaddpending3}]
locker2_{mapclaimlock3} > cons₂ > locker2_{checkavailables} > [false, true, member, gen_modtageq, locker2_obtainables, locker2_{checkavailable}, equal, case9] > excllock > [or, T, F, eq, nil, pid₁, excl, locker2_{mapaddpending3}]
locker2_{mapclaimlock3} > locker2_claimlock2 > [or, T, F, eq, nil, pid₁, excl, locker2_{mapaddpending3}]
locker2_{removepending2} > [lock, locker2_addpending3, case1₃] > undefined > [or, T, F, eq, nil, pid₁, excl, locker2_{mapaddpending3}]
locker2_{removepending2} > [lock, locker2_addpending3, case1₃] > mcrlrecord > tuple₂ > and₂ > [or, T, F, eq, nil, pid₁, excl, locker2_{mapaddpending3}]
locker2_{removepending2} > [lock, locker2_addpending3, case1₃] > resource > tuple₂ > and₂ > [or, T, F, eq, nil, pid₁, excl, locker2_{mapaddpending3}]
locker2_{removepending2} > [lock, locker2_addpending3, case1₃] > record_extract3 > tuple₂ > and₂ > [or, T, F, eq, nil, pid₁, excl, locker2_{mapaddpending3}]
locker2_{removepending2} > [lock, locker2_addpending3, case1₃] > append₂ > cons₂ > record_updates2 > record_update3 > tuple₂ > and₂ > [or, T, F, eq, nil, pid₁, excl, locker2_{mapaddpending3}]
locker2_{removepending2} > [lock, locker2_addpending3, case1₃] > append₂ > cons₂ > locker2_{checkavailables} > [false, true, member, gen_modtageq, locker2_obtainables, locker2_{checkavailable}, equal, case9] > tuple₂ > and₂ > [or, T, F, eq, nil, pid₁, excl, locker2_{mapaddpending3}]
locker2_{removepending2} > [lock, locker2_addpending3, case1₃] > append₂ > cons₂ > locker2_{checkavailables} > [false, true, member, gen_modtageq, locker2_obtainables, locker2_{checkavailable}, equal, case9] > pending > [or, T, F, eq, nil, pid₁, excl, locker2_{mapaddpending3}]
locker2_{removepending2} > [lock, locker2_addpending3, case1₃] > append₂ > cons₂ > locker2_{checkavailables} > [false, true, member, gen_modtageq, locker2_obtainables, locker2_{checkavailable}, equal, case9] > excllock > [or, T, F, eq, nil, pid₁, excl, locker2_{mapaddpending3}]
locker2_{removepending2} > subtract₂ > [delete₁, case8₂] > cons₂ > record_updates2 > record_update3 > tuple₂ > and₂ > [or, T, F, eq, nil, pid₁, excl, locker2_{mapaddpending3}]
locker2_{removepending2} > subtract₂ > [delete₁, case8₂] > cons₂ > locker2_{checkavailables} > [false, true, member, gen_modtageq, locker2_obtainables, locker2_{checkavailable}, equal, case9] > tuple₂ > and₂ > [or, T, F, eq, nil, pid₁, excl, locker2_{mapaddpending3}]
locker2_{removepending2} > subtract₂ > [delete₁, case8₂] > cons₂ > locker2_{checkavailables} > [false, true, member, gen_modtageq, locker2_obtainables, locker2_{checkavailable}, equal, case9] > pending > [or, T, F, eq, nil, pid₁, excl, locker2_{mapaddpending3}]
locker2_{removepending2} > subtract₂ > [delete₁, case8₂] > cons₂ > locker2_{checkavailables} > [false, true, member, gen_modtageq, locker2_obtainables, locker2_{checkavailable}, equal, case9] > excllock > [or, T, F, eq, nil, pid₁, excl, locker2_{mapaddpending3}]
locker2_releaselock2 > [lock, locker2_addpending3, case1₃] > undefined > [or, T, F, eq, nil, pid₁, excl, locker2_{mapaddpending3}]
locker2_releaselock2 > [lock, locker2_addpending3, case1₃] > mcrlrecord > tuple₂ > and₂ > [or, T, F, eq, nil, pid₁, excl, locker2_{mapaddpending3}]
locker2_releaselock2 > [lock, locker2_addpending3, case1₃] > resource > tuple₂ > and₂ > [or, T, F, eq, nil, pid₁, excl, locker2_{mapaddpending3}]
locker2_releaselock2 > [lock, locker2_addpending3, case1₃] > record_extract3 > tuple₂ > and₂ > [or, T, F, eq, nil, pid₁, excl, locker2_{mapaddpending3}]
locker2_releaselock2 > [lock, locker2_addpending3, case1₃] > append₂ > cons₂ > record_updates2 > record_update3 > tuple₂ > and₂ > [or, T, F, eq, nil, pid₁, excl, locker2_{mapaddpending3}]
locker2_releaselock2 > [lock, locker2_addpending3, case1₃] > append₂ > cons₂ > locker2_{checkavailables} > [false, true, member, gen_modtageq, locker2_obtainables, locker2_{checkavailable}, equal, case9] > tuple₂ > and₂ > [or, T, F, eq, nil, pid₁, excl, locker2_{mapaddpending3}]
locker2_releaselock2 > [lock, locker2_addpending3, case1₃] > append₂ > cons₂ > locker2_{checkavailables} > [false, true, member, gen_modtageq, locker2_obtainables, locker2_{checkavailable}, equal, case9] > pending > [or, T, F, eq, nil, pid₁, excl, locker2_{mapaddpending3}]
locker2_releaselock2 > [lock, locker2_addpending3, case1₃] > append₂ > cons₂ > locker2_{checkavailables} > [false, true, member, gen_modtageq, locker2_obtainables, locker2_{checkavailable}, equal, case9] > excllock > [or, T, F, eq, nil, pid₁, excl, locker2_{mapaddpending3}]
locker2_releaselock2 > case2₁ > cons₂ > record_updates2 > record_update3 > tuple₂ > and₂ > [or, T, F, eq, nil, pid₁, excl, locker2_{mapaddpending3}]
locker2_releaselock2 > case2₁ > cons₂ > locker2_{checkavailables} > [false, true, member, gen_modtageq, locker2_obtainables, locker2_{checkavailable}, equal, case9] > tuple₂ > and₂ > [or, T, F, eq, nil, pid₁, excl, locker2_{mapaddpending3}]
locker2_releaselock2 > case2₁ > cons₂ > locker2_{checkavailables} > [false, true, member, gen_modtageq, locker2_obtainables, locker2_{checkavailable}, equal, case9] > pending > [or, T, F, eq, nil, pid₁, excl, locker2_{mapaddpending3}]
locker2_releaselock2 > case2₁ > cons₂ > locker2_{checkavailables} > [false, true, member, gen_modtageq, locker2_obtainables, locker2_{checkavailable}, equal, case9] > excllock > [or, T, F, eq, nil, pid₁, excl, locker2_{mapaddpending3}]
case4₁ > [false, true, member, gen_modtageq, locker2_obtainables, locker2_{checkavailable}, equal, case9] > tuple₂ > and₂ > [or, T, F, eq, nil, pid₁, excl, locker2_{mapaddpending3}]
case4₁ > [false, true, member, gen_modtageq, locker2_obtainables, locker2_{checkavailable}, equal, case9] > pending > [or, T, F, eq, nil, pid₁, excl, locker2_{mapaddpending3}]
case4₁ > [false, true, member, gen_modtageq, locker2_obtainables, locker2_{checkavailable}, equal, case9] > excllock > [or, T, F, eq, nil, pid₁, excl, locker2_{mapaddpending3}]
locker2_adduniq2 > [or, T, F, eq, nil, pid₁, excl, locker2_{mapaddpending3}]
istops₂ > [or, T, F, eq, nil, pid₁, excl, locker2_{mapaddpending3}]
nocalls > empty > [or, T, F, eq, nil, pid₁, excl, locker2_{mapaddpending3}]
nocalls > stack₂ > and₂ > [or, T, F, eq, nil, pid₁, excl, locker2_{mapaddpending3}]
nocalls > calls₃ > eqc₂ > and₂ > [or, T, F, eq, nil, pid₁, excl, locker2_{mapaddpending3}]
push₃ > empty > [or, T, F, eq, nil, pid₁, excl, locker2_{mapaddpending3}]
push₃ > [pushs₂, push1₆] > stack₂ > and₂ > [or, T, F, eq, nil, pid₁, excl, locker2_{mapaddpending3}]
push₃ > [pushs₂, push1₆] > calls₃ > eqc₂ > and₂ > [or, T, F, eq, nil, pid₁, excl, locker2_{mapaddpending3}]

Status:

push₃: [2,1,3]
locker2_{removepending2}: [1,2]
locker2_{mappromotepending2}: [1,2]
gen_tag1: [1]
pushs₂: [1,2]
locker2_{checkavailables}: []
excllock: []
delete₁: [1]
nil: []
locker2_releaselock2: [2,1]
T: []
locker2_addpending3: [1,2,3]
or: []
resource: []
locker: []
true: []
record_new: []
empty: []
eqc₂: [1,2]
push1₆: [2,4,5,6,1,3]
member: []
gen_modtageq: []
imp₁: [1]
element₁: [1]
pid₁: [1]
ok: []
case9: []
F: []
lock: []
case8₂: [1,2]
equal: []
case0₂: [1,2]
calls₃: [3,1,2]
and₂: [1,2]
append₂: [2,1]
case4₁: [1]
stack₂: [1,2]
pending: []
case2₁: [1]
istops₂: [1,2]
record_updates2: [2,1]
locker2_{mapclaimlock3}: [1,3,2]
case1₃: [3,2,1]
undefined: []
tag: []
eq: []
mcrlrecord: []
a: []
request: []
if₂: [1,2]
locker2_claimlock2: [2,1]
excl: []
subtract₂: [2,1]
locker2_{promotepending2}: [1,2]
nocalls: []
s: []
record_update3: [1,2,3]
0: []
cons₂: [2,1]
locker2_{mapaddpending3}: [3,1,2]
locker2_{checkavailable}: []
record_extract3: [3,1,2]
release: []
false: []
tuple₂: [1,2]
locker2_obtainables: []
locker2_adduniq2: [1,2]

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, x2)
cons(x1, x2)  =  cons(x1, x2)
or(x1, x2)  =  x2
T  =  T
F  =  F
and(x1, x2)  =  and(x1, x2)
imp(x1, x2)  =  imp(x1, x2)
not(x1)  =  x1
if(x1, x2, x3)  =  if(x1, x2, x3)
eq(x1, x2)  =  x2
eqt(x1, x2)  =  eqt(x1)
nil  =  nil
undefined  =  undefined
pid(x1)  =  x1
int(x1)  =  int(x1)
tuple(x1, x2)  =  tuple(x1, x2)
tuplenil(x1)  =  tuplenil(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
0  =  0
record_new(x1)  =  record_new(x1)
record_extract(x1, x2, x3)  =  record_extract(x1, x3)
record_update(x1, x2, x3, x4)  =  record_update(x1, 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, x3)
locker2_claim_lock(x1, x2, x3)  =  locker2_claim_lock
locker2_map_add_pending(x1, x2, x3)  =  x1
case0(x1, x2, x3)  =  case0(x2, x3)
locker2_remove_pending(x1, x2)  =  locker2_remove_pending(x1)
subtract(x1, x2)  =  subtract(x1)
locker2_add_pending(x1, x2, x3)  =  locker2_add_pending(x1, x2)
case1(x1, x2, x3, x4)  =  case1(x2, x3, x4)
member(x1, x2)  =  member
append(x1, x2)  =  append(x1)
locker2_release_lock(x1, x2)  =  locker2_release_lock(x1, x2)
case2(x1, x2, x3)  =  case2(x1, x2)
gen_modtageq(x1, x2)  =  gen_modtageq(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, x4)
equal(x1, x2)  =  x2
locker2_check_availables(x1, x2)  =  locker2_check_availables(x1, x2)
locker2_adduniq(x1, x2)  =  x2
delete(x1, x2)  =  x2
case8(x1, x2, x3, x4)  =  case8(x1, x2)
gen_tag(x1)  =  gen_tag(x1)
case9(x1, x2, x3, x4)  =  case9
eqs(x1, x2)  =  x1
empty  =  empty
stack(x1, x2)  =  stack(x1, x2)
pushs(x1, x2)  =  pushs(x1, x2)
pops(x1)  =  x1
tops(x1)  =  tops(x1)
istops(x1, x2)  =  istops(x1, x2)
eqc(x1, x2)  =  x1
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:

APPEND₂ > [tuple₂, tuplenil₁, resource, tag, locker2_obtainables2, case5₂, locker2_obtainable1, locker2_{checkavailable1}, case6₂]
imp₂ > [T, F, ok] > [tuple₂, tuplenil₁, resource, tag, locker2_obtainables2, case5₂, locker2_obtainable1, locker2_{checkavailable1}, case6₂]
if₃ > [tuple₂, tuplenil₁, resource, tag, locker2_obtainables2, case5₂, locker2_obtainable1, locker2_{checkavailable1}, case6₂]
a > [T, F, ok] > [tuple₂, tuplenil₁, resource, tag, locker2_obtainables2, case5₂, locker2_obtainable1, locker2_{checkavailable1}, case6₂]
locker > [T, F, ok] > [tuple₂, tuplenil₁, resource, tag, locker2_obtainables2, case5₂, locker2_obtainable1, locker2_{checkavailable1}, case6₂]
[mcrlrecord, record_new1] > [nil, false, true, case0₂, locker2_{removepending1}, locker2_addpending2, member, case9] > excl > [T, F, ok] > [tuple₂, tuplenil₁, resource, tag, locker2_obtainables2, case5₂, locker2_obtainable1, locker2_{checkavailable1}, case6₂]
[mcrlrecord, record_new1] > [nil, false, true, case0₂, locker2_{removepending1}, locker2_addpending2, member, case9] > lock > [T, F, ok] > [tuple₂, tuplenil₁, resource, tag, locker2_obtainables2, case5₂, locker2_obtainable1, locker2_{checkavailable1}, case6₂]
[mcrlrecord, record_new1] > [nil, false, true, case0₂, locker2_{removepending1}, locker2_addpending2, member, case9] > pending > [tuple₂, tuplenil₁, resource, tag, locker2_obtainables2, case5₂, locker2_obtainable1, locker2_{checkavailable1}, case6₂]
[mcrlrecord, record_new1] > [nil, false, true, case0₂, locker2_{removepending1}, locker2_addpending2, member, case9] > subtract₁ > [tuple₂, tuplenil₁, resource, tag, locker2_obtainables2, case5₂, locker2_obtainable1, locker2_{checkavailable1}, case6₂]
[mcrlrecord, record_new1] > [nil, false, true, case0₂, locker2_{removepending1}, locker2_addpending2, member, case9] > case1₃ > [cons₂, record_extract2, record_updates2, append₁, case8₂] > record_update2 > [tuple₂, tuplenil₁, resource, tag, locker2_obtainables2, case5₂, locker2_obtainable1, locker2_{checkavailable1}, case6₂]
[mcrlrecord, record_new1] > undefined > [T, F, ok] > [tuple₂, tuplenil₁, resource, tag, locker2_obtainables2, case5₂, locker2_obtainable1, locker2_{checkavailable1}, case6₂]
release > [T, F, ok] > [tuple₂, tuplenil₁, resource, tag, locker2_obtainables2, case5₂, locker2_obtainable1, locker2_{checkavailable1}, case6₂]
request > [tuple₂, tuplenil₁, resource, tag, locker2_obtainables2, case5₂, locker2_obtainable1, locker2_{checkavailable1}, case6₂]
s > int₁ > [T, F, ok] > [tuple₂, tuplenil₁, resource, tag, locker2_obtainables2, case5₂, locker2_obtainable1, locker2_{checkavailable1}, case6₂]
s > int₁ > element₂ > [tuple₂, tuplenil₁, resource, tag, locker2_obtainables2, case5₂, locker2_obtainable1, locker2_{checkavailable1}, case6₂]
0 > [tuple₂, tuplenil₁, resource, tag, locker2_obtainables2, case5₂, locker2_obtainable1, locker2_{checkavailable1}, case6₂]
[locker2_{mappromotepending2}, locker2_{promotepending2}] > [nil, false, true, case0₂, locker2_{removepending1}, locker2_addpending2, member, case9] > excl > [T, F, ok] > [tuple₂, tuplenil₁, resource, tag, locker2_obtainables2, case5₂, locker2_obtainable1, locker2_{checkavailable1}, case6₂]
[locker2_{mappromotepending2}, locker2_{promotepending2}] > [nil, false, true, case0₂, locker2_{removepending1}, locker2_addpending2, member, case9] > lock > [T, F, ok] > [tuple₂, tuplenil₁, resource, tag, locker2_obtainables2, case5₂, locker2_obtainable1, locker2_{checkavailable1}, case6₂]
[locker2_{mappromotepending2}, locker2_{promotepending2}] > [nil, false, true, case0₂, locker2_{removepending1}, locker2_addpending2, member, case9] > pending > [tuple₂, tuplenil₁, resource, tag, locker2_obtainables2, case5₂, locker2_obtainable1, locker2_{checkavailable1}, case6₂]
[locker2_{mappromotepending2}, locker2_{promotepending2}] > [nil, false, true, case0₂, locker2_{removepending1}, locker2_addpending2, member, case9] > subtract₁ > [tuple₂, tuplenil₁, resource, tag, locker2_obtainables2, case5₂, locker2_obtainable1, locker2_{checkavailable1}, case6₂]
[locker2_{mappromotepending2}, locker2_{promotepending2}] > [nil, false, true, case0₂, locker2_{removepending1}, locker2_addpending2, member, case9] > case1₃ > [cons₂, record_extract2, record_updates2, append₁, case8₂] > record_update2 > [tuple₂, tuplenil₁, resource, tag, locker2_obtainables2, case5₂, locker2_obtainable1, locker2_{checkavailable1}, case6₂]
locker2_{mapclaimlock2} > [cons₂, record_extract2, record_updates2, append₁, case8₂] > record_update2 > [tuple₂, tuplenil₁, resource, tag, locker2_obtainables2, case5₂, locker2_obtainable1, locker2_{checkavailable1}, case6₂]
locker2_{mapclaimlock2} > locker2_claimlock > [tuple₂, tuplenil₁, resource, tag, locker2_obtainables2, case5₂, locker2_obtainable1, locker2_{checkavailable1}, case6₂]
[locker2_releaselock2, case2₂] > [nil, false, true, case0₂, locker2_{removepending1}, locker2_addpending2, member, case9] > excl > [T, F, ok] > [tuple₂, tuplenil₁, resource, tag, locker2_obtainables2, case5₂, locker2_obtainable1, locker2_{checkavailable1}, case6₂]
[locker2_releaselock2, case2₂] > [nil, false, true, case0₂, locker2_{removepending1}, locker2_addpending2, member, case9] > lock > [T, F, ok] > [tuple₂, tuplenil₁, resource, tag, locker2_obtainables2, case5₂, locker2_obtainable1, locker2_{checkavailable1}, case6₂]
[locker2_releaselock2, case2₂] > [nil, false, true, case0₂, locker2_{removepending1}, locker2_addpending2, member, case9] > pending > [tuple₂, tuplenil₁, resource, tag, locker2_obtainables2, case5₂, locker2_obtainable1, locker2_{checkavailable1}, case6₂]
[locker2_releaselock2, case2₂] > [nil, false, true, case0₂, locker2_{removepending1}, locker2_addpending2, member, case9] > subtract₁ > [tuple₂, tuplenil₁, resource, tag, locker2_obtainables2, case5₂, locker2_obtainable1, locker2_{checkavailable1}, case6₂]
[locker2_releaselock2, case2₂] > [nil, false, true, case0₂, locker2_{removepending1}, locker2_addpending2, member, case9] > case1₃ > [cons₂, record_extract2, record_updates2, append₁, case8₂] > record_update2 > [tuple₂, tuplenil₁, resource, tag, locker2_obtainables2, case5₂, locker2_obtainable1, locker2_{checkavailable1}, case6₂]
[locker2_releaselock2, case2₂] > gen_modtageq1 > [tuple₂, tuplenil₁, resource, tag, locker2_obtainables2, case5₂, locker2_obtainable1, locker2_{checkavailable1}, case6₂]
[locker2_releaselock2, case2₂] > excllock > [tuple₂, tuplenil₁, resource, tag, locker2_obtainables2, case5₂, locker2_obtainable1, locker2_{checkavailable1}, case6₂]
case4 > [nil, false, true, case0₂, locker2_{removepending1}, locker2_addpending2, member, case9] > excl > [T, F, ok] > [tuple₂, tuplenil₁, resource, tag, locker2_obtainables2, case5₂, locker2_obtainable1, locker2_{checkavailable1}, case6₂]
case4 > [nil, false, true, case0₂, locker2_{removepending1}, locker2_addpending2, member, case9] > lock > [T, F, ok] > [tuple₂, tuplenil₁, resource, tag, locker2_obtainables2, case5₂, locker2_obtainable1, locker2_{checkavailable1}, case6₂]
case4 > [nil, false, true, case0₂, locker2_{removepending1}, locker2_addpending2, member, case9] > pending > [tuple₂, tuplenil₁, resource, tag, locker2_obtainables2, case5₂, locker2_obtainable1, locker2_{checkavailable1}, case6₂]
case4 > [nil, false, true, case0₂, locker2_{removepending1}, locker2_addpending2, member, case9] > subtract₁ > [tuple₂, tuplenil₁, resource, tag, locker2_obtainables2, case5₂, locker2_obtainable1, locker2_{checkavailable1}, case6₂]
case4 > [nil, false, true, case0₂, locker2_{removepending1}, locker2_addpending2, member, case9] > case1₃ > [cons₂, record_extract2, record_updates2, append₁, case8₂] > record_update2 > [tuple₂, tuplenil₁, resource, tag, locker2_obtainables2, case5₂, locker2_obtainable1, locker2_{checkavailable1}, case6₂]
locker2_{checkavailables2} > [nil, false, true, case0₂, locker2_{removepending1}, locker2_addpending2, member, case9] > excl > [T, F, ok] > [tuple₂, tuplenil₁, resource, tag, locker2_obtainables2, case5₂, locker2_obtainable1, locker2_{checkavailable1}, case6₂]
locker2_{checkavailables2} > [nil, false, true, case0₂, locker2_{removepending1}, locker2_addpending2, member, case9] > lock > [T, F, ok] > [tuple₂, tuplenil₁, resource, tag, locker2_obtainables2, case5₂, locker2_obtainable1, locker2_{checkavailable1}, case6₂]
locker2_{checkavailables2} > [nil, false, true, case0₂, locker2_{removepending1}, locker2_addpending2, member, case9] > pending > [tuple₂, tuplenil₁, resource, tag, locker2_obtainables2, case5₂, locker2_obtainable1, locker2_{checkavailable1}, case6₂]
locker2_{checkavailables2} > [nil, false, true, case0₂, locker2_{removepending1}, locker2_addpending2, member, case9] > subtract₁ > [tuple₂, tuplenil₁, resource, tag, locker2_obtainables2, case5₂, locker2_obtainable1, locker2_{checkavailable1}, case6₂]
locker2_{checkavailables2} > [nil, false, true, case0₂, locker2_{removepending1}, locker2_addpending2, member, case9] > case1₃ > [cons₂, record_extract2, record_updates2, append₁, case8₂] > record_update2 > [tuple₂, tuplenil₁, resource, tag, locker2_obtainables2, case5₂, locker2_obtainable1, locker2_{checkavailable1}, case6₂]
gen_tag1 > [tuple₂, tuplenil₁, resource, tag, locker2_obtainables2, case5₂, locker2_obtainable1, locker2_{checkavailable1}, case6₂]
[empty, push₃, push1₆] > nocalls > [stack₂, pushs₂] > eqt₁ > and₂ > [T, F, ok] > [tuple₂, tuplenil₁, resource, tag, locker2_obtainables2, case5₂, locker2_obtainable1, locker2_{checkavailable1}, case6₂]
[empty, push₃, push1₆] > calls₃ > eqt₁ > and₂ > [T, F, ok] > [tuple₂, tuplenil₁, resource, tag, locker2_obtainables2, case5₂, locker2_obtainable1, locker2_{checkavailable1}, case6₂]
tops₁ > [tuple₂, tuplenil₁, resource, tag, locker2_obtainables2, case5₂, locker2_obtainable1, locker2_{checkavailable1}, case6₂]
istops₂ > eqt₁ > and₂ > [T, F, ok] > [tuple₂, tuplenil₁, resource, tag, locker2_obtainables2, case5₂, locker2_obtainable1, locker2_{checkavailable1}, case6₂]

Status:

locker2_claimlock: []
case2₂: [1,2]
push₃: [2,1,3]
locker2_{mappromotepending2}: [2,1]
gen_tag1: [1]
pushs₂: [1,2]
record_new1: [1]
excllock: []
nil: []
element₂: [1,2]
locker2_releaselock2: [2,1]
locker2_obtainable1: [1]
locker2_obtainables2: [2,1]
gen_modtageq1: [1]
T: []
resource: []
locker2_{checkavailable1}: [1]
locker: []
true: []
empty: []
push1₆: [2,1,4,3,6,5]
member: []
locker2_{checkavailables2}: [1,2]
ok: []
case9: []
F: []
lock: []
locker2_{removepending1}: [1]
tops₁: [1]
append₁: [1]
case8₂: [2,1]
APPEND₂: [2,1]
case0₂: [1,2]
record_extract2: [1,2]
calls₃: [3,2,1]
tuplenil₁: [1]
eqt₁: [1]
and₂: [1,2]
stack₂: [1,2]
if₃: [1,2,3]
pending: []
subtract₁: [1]
int₁: [1]
istops₂: [1,2]
record_updates2: [2,1]
case5₂: [1,2]
case1₃: [3,1,2]
undefined: []
tag: []
mcrlrecord: []
a: []
request: []
excl: []
record_update2: [1,2]
locker2_{promotepending2}: [2,1]
locker2_{mapclaimlock2}: [2,1]
nocalls: []
s: []
0: []
locker2_addpending2: [2,1]
cons₂: [1,2]
case6₂: [1,2]
release: []
false: []
imp₂: [1,2]
tuple₂: [2,1]
case4: []

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, x2)
cons(x1, x2)  =  cons(x1, x2)
or(x1, x2)  =  or
T  =  T
F  =  F
and(x1, x2)  =  and(x1, x2)
imp(x1, x2)  =  imp(x1, x2)
not(x1)  =  x1
if(x1, x2, x3)  =  if(x1, x2, x3)
eq(x1, x2)  =  x1
eqt(x1, x2)  =  eqt(x2)
nil  =  nil
undefined  =  undefined
pid(x1)  =  pid(x1)
int(x1)  =  int
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
0  =  0
record_new(x1)  =  record_new
record_extract(x1, x2, x3)  =  record_extract(x1, x2, x3)
record_update(x1, x2, x3, x4)  =  record_update(x1, 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, x2, x3)
locker2_claim_lock(x1, x2, x3)  =  locker2_claim_lock(x1, x2, x3)
locker2_map_add_pending(x1, x2, x3)  =  locker2_map_add_pending(x1, x2, x3)
case0(x1, x2, x3)  =  case0(x2, x3)
locker2_remove_pending(x1, x2)  =  locker2_remove_pending(x1, x2)
subtract(x1, x2)  =  x1
locker2_add_pending(x1, x2, x3)  =  locker2_add_pending(x1, x2)
case1(x1, x2, x3, x4)  =  case1(x2, x3, x4)
member(x1, x2)  =  member(x1, x2)
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)  =  gen_modtageq(x1)
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)  =  andt
locker2_obtainable(x1, x2)  =  locker2_obtainable(x1)
locker2_check_available(x1, x2)  =  locker2_check_available(x1, x2)
case6(x1, x2, x3, x4)  =  case6(x1, x3, x4)
equal(x1, x2)  =  x1
locker2_check_availables(x1, x2)  =  locker2_check_availables
locker2_adduniq(x1, x2)  =  x2
delete(x1, x2)  =  x2
case8(x1, x2, x3, x4)  =  case8(x1, x2)
gen_tag(x1)  =  gen_tag(x1)
case9(x1, x2, x3, x4)  =  case9(x1, x3)
eqs(x1, x2)  =  eqs(x1, x2)
empty  =  empty
stack(x1, x2)  =  stack(x1, x2)
pushs(x1, x2)  =  pushs(x1, x2)
pops(x1)  =  x1
tops(x1)  =  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(x2, x3, x4, x5)

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

or > [T, F, int] > element₁
or > [T, F, int] > pushs₂ > stack₂
or > [T, F, int] > calls₃
[eqt₁, eqs₂, istops₂, eqc₂] > and₂ > [T, F, int] > element₁
[eqt₁, eqs₂, istops₂, eqc₂] > and₂ > [T, F, int] > pushs₂ > stack₂
[eqt₁, eqs₂, istops₂, eqc₂] > and₂ > [T, F, int] > calls₃
pid₁ > [T, F, int] > element₁
pid₁ > [T, F, int] > pushs₂ > stack₂
pid₁ > [T, F, int] > calls₃
locker > [T, F, int] > element₁
locker > [T, F, int] > pushs₂ > stack₂
locker > [T, F, int] > calls₃
release > [T, F, int] > element₁
release > [T, F, int] > pushs₂ > stack₂
release > [T, F, int] > calls₃
request > [T, F, int] > element₁
request > [T, F, int] > pushs₂ > stack₂
request > [T, F, int] > calls₃
[tag, gen_tag1] > [tuple₂, record_update2]
s > [T, F, int] > element₁
s > [T, F, int] > pushs₂ > stack₂
s > [T, F, int] > calls₃
record_new > nil
record_new > undefined > [T, F, int] > element₁
record_new > undefined > [T, F, int] > pushs₂ > stack₂
record_new > undefined > [T, F, int] > calls₃
record_new > [mcrlrecord, record_extract3] > [cons₂, lock, case8₂] > record_updates3 > [tuple₂, record_update2]
record_new > [mcrlrecord, record_extract3] > [T, F, int] > element₁
record_new > [mcrlrecord, record_extract3] > [T, F, int] > pushs₂ > stack₂
record_new > [mcrlrecord, record_extract3] > [T, F, int] > calls₃
locker2_{mappromotepending2} > locker2_{promotepending2} > [mcrlrecord, record_extract3] > [cons₂, lock, case8₂] > record_updates3 > [tuple₂, record_update2]
locker2_{mappromotepending2} > locker2_{promotepending2} > [mcrlrecord, record_extract3] > [T, F, int] > element₁
locker2_{mappromotepending2} > locker2_{promotepending2} > [mcrlrecord, record_extract3] > [T, F, int] > pushs₂ > stack₂
locker2_{mappromotepending2} > locker2_{promotepending2} > [mcrlrecord, record_extract3] > [T, F, int] > calls₃
locker2_{mappromotepending2} > locker2_{promotepending2} > case0₂ > nil
locker2_{mappromotepending2} > locker2_{promotepending2} > case0₂ > excl
locker2_{mappromotepending2} > locker2_{promotepending2} > case0₂ > pending > [cons₂, lock, case8₂] > record_updates3 > [tuple₂, record_update2]
locker2_{mapclaimlock3} > [cons₂, lock, case8₂] > record_updates3 > [tuple₂, record_update2]
locker2_{mapclaimlock3} > nil
locker2_{mapclaimlock3} > locker2_claimlock3
locker2_{mapaddpending3} > nil
locker2_{removepending2} > nil
locker2_{removepending2} > [mcrlrecord, record_extract3] > [cons₂, lock, case8₂] > record_updates3 > [tuple₂, record_update2]
locker2_{removepending2} > [mcrlrecord, record_extract3] > [T, F, int] > element₁
locker2_{removepending2} > [mcrlrecord, record_extract3] > [T, F, int] > pushs₂ > stack₂
locker2_{removepending2} > [mcrlrecord, record_extract3] > [T, F, int] > calls₃
locker2_{removepending2} > pending > [cons₂, lock, case8₂] > record_updates3 > [tuple₂, record_update2]
locker2_addpending2 > resource > [cons₂, lock, case8₂] > record_updates3 > [tuple₂, record_update2]
locker2_addpending2 > case1₃ > nil
locker2_addpending2 > case1₃ > [mcrlrecord, record_extract3] > [cons₂, lock, case8₂] > record_updates3 > [tuple₂, record_update2]
locker2_addpending2 > case1₃ > [mcrlrecord, record_extract3] > [T, F, int] > element₁
locker2_addpending2 > case1₃ > [mcrlrecord, record_extract3] > [T, F, int] > pushs₂ > stack₂
locker2_addpending2 > case1₃ > [mcrlrecord, record_extract3] > [T, F, int] > calls₃
locker2_addpending2 > case1₃ > pending > [cons₂, lock, case8₂] > record_updates3 > [tuple₂, record_update2]
locker2_addpending2 > [member₂, case9₂] > [false, locker2_obtainables2, case5₂] > [mcrlrecord, record_extract3] > [cons₂, lock, case8₂] > record_updates3 > [tuple₂, record_update2]
locker2_addpending2 > [member₂, case9₂] > [false, locker2_obtainables2, case5₂] > [mcrlrecord, record_extract3] > [T, F, int] > element₁
locker2_addpending2 > [member₂, case9₂] > [false, locker2_obtainables2, case5₂] > [mcrlrecord, record_extract3] > [T, F, int] > pushs₂ > stack₂
locker2_addpending2 > [member₂, case9₂] > [false, locker2_obtainables2, case5₂] > [mcrlrecord, record_extract3] > [T, F, int] > calls₃
locker2_addpending2 > [member₂, case9₂] > [false, locker2_obtainables2, case5₂] > true > nil
locker2_addpending2 > [member₂, case9₂] > [false, locker2_obtainables2, case5₂] > true > excl
locker2_addpending2 > [member₂, case9₂] > [false, locker2_obtainables2, case5₂] > true > pending > [cons₂, lock, case8₂] > record_updates3 > [tuple₂, record_update2]
locker2_addpending2 > [member₂, case9₂] > [false, locker2_obtainables2, case5₂] > andt
locker2_addpending2 > [member₂, case9₂] > [false, locker2_obtainables2, case5₂] > locker2_obtainable1
[locker2_releaselock2, case2₂] > nil
[locker2_releaselock2, case2₂] > excl
[locker2_releaselock2, case2₂] > [mcrlrecord, record_extract3] > [cons₂, lock, case8₂] > record_updates3 > [tuple₂, record_update2]
[locker2_releaselock2, case2₂] > [mcrlrecord, record_extract3] > [T, F, int] > element₁
[locker2_releaselock2, case2₂] > [mcrlrecord, record_extract3] > [T, F, int] > pushs₂ > stack₂
[locker2_releaselock2, case2₂] > [mcrlrecord, record_extract3] > [T, F, int] > calls₃
[locker2_releaselock2, case2₂] > gen_modtageq1
[locker2_releaselock2, case2₂] > excllock
case4 > [false, locker2_obtainables2, case5₂] > [mcrlrecord, record_extract3] > [cons₂, lock, case8₂] > record_updates3 > [tuple₂, record_update2]
case4 > [false, locker2_obtainables2, case5₂] > [mcrlrecord, record_extract3] > [T, F, int] > element₁
case4 > [false, locker2_obtainables2, case5₂] > [mcrlrecord, record_extract3] > [T, F, int] > pushs₂ > stack₂
case4 > [false, locker2_obtainables2, case5₂] > [mcrlrecord, record_extract3] > [T, F, int] > calls₃
case4 > [false, locker2_obtainables2, case5₂] > true > nil
case4 > [false, locker2_obtainables2, case5₂] > true > excl
case4 > [false, locker2_obtainables2, case5₂] > true > pending > [cons₂, lock, case8₂] > record_updates3 > [tuple₂, record_update2]
case4 > [false, locker2_obtainables2, case5₂] > andt
case4 > [false, locker2_obtainables2, case5₂] > locker2_obtainable1
locker2_{checkavailables} > [locker2_{checkavailable2}, case6₃] > [false, locker2_obtainables2, case5₂] > [mcrlrecord, record_extract3] > [cons₂, lock, case8₂] > record_updates3 > [tuple₂, record_update2]
locker2_{checkavailables} > [locker2_{checkavailable2}, case6₃] > [false, locker2_obtainables2, case5₂] > [mcrlrecord, record_extract3] > [T, F, int] > element₁
locker2_{checkavailables} > [locker2_{checkavailable2}, case6₃] > [false, locker2_obtainables2, case5₂] > [mcrlrecord, record_extract3] > [T, F, int] > pushs₂ > stack₂
locker2_{checkavailables} > [locker2_{checkavailable2}, case6₃] > [false, locker2_obtainables2, case5₂] > [mcrlrecord, record_extract3] > [T, F, int] > calls₃
locker2_{checkavailables} > [locker2_{checkavailable2}, case6₃] > [false, locker2_obtainables2, case5₂] > true > nil
locker2_{checkavailables} > [locker2_{checkavailable2}, case6₃] > [false, locker2_obtainables2, case5₂] > true > excl
locker2_{checkavailables} > [locker2_{checkavailable2}, case6₃] > [false, locker2_obtainables2, case5₂] > true > pending > [cons₂, lock, case8₂] > record_updates3 > [tuple₂, record_update2]
locker2_{checkavailables} > [locker2_{checkavailable2}, case6₃] > [false, locker2_obtainables2, case5₂] > andt
locker2_{checkavailables} > [locker2_{checkavailable2}, case6₃] > [false, locker2_obtainables2, case5₂] > locker2_obtainable1
locker2_{checkavailables} > [locker2_{checkavailable2}, case6₃] > resource > [cons₂, lock, case8₂] > record_updates3 > [tuple₂, record_update2]
push₃ > empty
push₃ > nocalls > stack₂
push₃ > nocalls > calls₃
push₃ > push1₄ > pushs₂ > stack₂
push₃ > push1₄ > calls₃

Status:

push1₄: [1,4,2,3]
case2₂: [1,2]
push₃: [3,2,1]
locker2_{removepending2}: [1,2]
locker2_{mappromotepending2}: [1,2]
member₂: [2,1]
gen_tag1: [1]
pushs₂: [2,1]
locker2_{checkavailables}: []
locker2_{checkavailable2}: [2,1]
excllock: []
nil: []
locker2_releaselock2: [2,1]
locker2_obtainable1: [1]
locker2_obtainables2: [1,2]
gen_modtageq1: [1]
T: []
or: []
resource: []
locker: []
true: []
record_new: []
empty: []
eqc₂: [2,1]
element₁: [1]
pid₁: [1]
ok: []
F: []
lock: []
case8₂: [2,1]
case0₂: [2,1]
case6₃: [1,2,3]
calls₃: [2,3,1]
eqt₁: [1]
eqs₂: [2,1]
and₂: [2,1]
locker2_claimlock3: [2,3,1]
stack₂: [2,1]
if₃: [1,2,3]
pending: []
istops₂: [2,1]
locker2_{mapclaimlock3}: [2,3,1]
case5₂: [2,1]
case1₃: [1,3,2]
undefined: []
tag: []
case9₂: [1,2]
mcrlrecord: []
a: []
request: []
excl: []
int: []
record_update2: [1,2]
record_updates3: [2,3,1]
locker2_{promotepending2}: [2,1]
andt: []
nocalls: []
s: []
LOCKER2_{CHECKAVAILABLES2}: [2,1]
0: []
locker2_addpending2: [1,2]
cons₂: [1,2]
locker2_{mapaddpending3}: [1,3,2]
record_extract3: [2,1,3]
release: []
false: []
imp₂: [2,1]
tuple₂: [1,2]
case4: []

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)
cons(x1, x2)  =  cons(x1, x2)
or(x1, x2)  =  x1
T  =  T
F  =  F
and(x1, x2)  =  and(x1, x2)
imp(x1, x2)  =  x2
not(x1)  =  not(x1)
if(x1, x2, x3)  =  if(x1, x2, x3)
eq(x1, x2)  =  eq(x1, x2)
eqt(x1, x2)  =  eqt(x1)
nil  =  nil
undefined  =  undefined
pid(x1)  =  pid(x1)
int(x1)  =  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)  =  x2
s(x1)  =  s
0  =  0
record_new(x1)  =  record_new
record_extract(x1, x2, x3)  =  record_extract(x1, x3)
record_update(x1, x2, x3, x4)  =  record_update(x1, 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, x2, x3)
locker2_claim_lock(x1, x2, x3)  =  locker2_claim_lock(x2)
locker2_map_add_pending(x1, x2, x3)  =  locker2_map_add_pending(x3)
case0(x1, x2, x3)  =  case0(x1, x2, x3)
locker2_remove_pending(x1, x2)  =  locker2_remove_pending(x1)
subtract(x1, x2)  =  x1
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(x1, x2)
append(x1, x2)  =  append(x1, x2)
locker2_release_lock(x1, x2)  =  locker2_release_lock(x1)
case2(x1, x2, x3)  =  case2(x2)
gen_modtageq(x1, x2)  =  gen_modtageq(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)  =  andt
locker2_obtainable(x1, x2)  =  locker2_obtainable(x1, x2)
locker2_check_available(x1, x2)  =  locker2_check_available
case6(x1, x2, x3, x4)  =  case6
equal(x1, x2)  =  equal(x2)
locker2_check_availables(x1, x2)  =  locker2_check_availables(x1)
locker2_adduniq(x1, x2)  =  x2
delete(x1, x2)  =  x2
case8(x1, x2, x3, x4)  =  case8(x1, x2)
gen_tag(x1)  =  gen_tag(x1)
case9(x1, x2, x3, x4)  =  case9(x1, x3)
eqs(x1, x2)  =  eqs(x1, 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
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:

not₁ > [F, eqt₁, release] > [cons₂, and₂, case8₂] > LOCKER2_{MAPCLAIMLOCK2} > [T, lock]
not₁ > [F, eqt₁, release] > [cons₂, and₂, case8₂] > tuple₂ > [T, lock]
not₁ > [F, eqt₁, release] > [cons₂, and₂, case8₂] > [true, member₂, case9₂] > [T, lock]
if₃ > [T, lock]
eq₂ > [F, eqt₁, release] > [cons₂, and₂, case8₂] > LOCKER2_{MAPCLAIMLOCK2} > [T, lock]
eq₂ > [F, eqt₁, release] > [cons₂, and₂, case8₂] > tuple₂ > [T, lock]
eq₂ > [F, eqt₁, release] > [cons₂, and₂, case8₂] > [true, member₂, case9₂] > [T, lock]
pid₁ > [T, lock]
a > [T, lock]
locker > [T, lock]
ok > [T, lock]
request > [T, lock]
[tag, gen_tag1] > [F, eqt₁, release] > [cons₂, and₂, case8₂] > LOCKER2_{MAPCLAIMLOCK2} > [T, lock]
[tag, gen_tag1] > [F, eqt₁, release] > [cons₂, and₂, case8₂] > tuple₂ > [T, lock]
[tag, gen_tag1] > [F, eqt₁, release] > [cons₂, and₂, case8₂] > [true, member₂, case9₂] > [T, lock]
s > [T, lock]
0 > [T, lock]
record_new > nil > false > [true, member₂, case9₂] > [T, lock]
record_new > undefined > [T, lock]
record_new > mcrlrecord > tuple₂ > [T, lock]
[locker2_{mappromotepending2}, locker2_{promotepending2}] > record_extract2 > mcrlrecord > tuple₂ > [T, lock]
[locker2_{mappromotepending2}, locker2_{promotepending2}] > case0₃ > [cons₂, and₂, case8₂] > LOCKER2_{MAPCLAIMLOCK2} > [T, lock]
[locker2_{mappromotepending2}, locker2_{promotepending2}] > case0₃ > [cons₂, and₂, case8₂] > tuple₂ > [T, lock]
[locker2_{mappromotepending2}, locker2_{promotepending2}] > case0₃ > [cons₂, and₂, case8₂] > [true, member₂, case9₂] > [T, lock]
[locker2_{mappromotepending2}, locker2_{promotepending2}] > case0₃ > nil > false > [true, member₂, case9₂] > [T, lock]
[locker2_{mappromotepending2}, locker2_{promotepending2}] > case0₃ > excl > [T, lock]
[locker2_{mappromotepending2}, locker2_{promotepending2}] > case0₃ > pending > mcrlrecord > tuple₂ > [T, lock]
[locker2_{mappromotepending2}, locker2_{promotepending2}] > case0₃ > record_updates3 > record_update2 > tuple₂ > [T, lock]
locker2_{mapclaimlock3} > [cons₂, and₂, case8₂] > LOCKER2_{MAPCLAIMLOCK2} > [T, lock]
locker2_{mapclaimlock3} > [cons₂, and₂, case8₂] > tuple₂ > [T, lock]
locker2_{mapclaimlock3} > [cons₂, and₂, case8₂] > [true, member₂, case9₂] > [T, lock]
locker2_{mapclaimlock3} > nil > false > [true, member₂, case9₂] > [T, lock]
locker2_{mapclaimlock3} > locker2_claimlock1 > [T, lock]
locker2_{mapaddpending1} > nil > false > [true, member₂, case9₂] > [T, lock]
locker2_{removepending1} > [cons₂, and₂, case8₂] > LOCKER2_{MAPCLAIMLOCK2} > [T, lock]
locker2_{removepending1} > [cons₂, and₂, case8₂] > tuple₂ > [T, lock]
locker2_{removepending1} > [cons₂, and₂, case8₂] > [true, member₂, case9₂] > [T, lock]
locker2_{removepending1} > nil > false > [true, member₂, case9₂] > [T, lock]
locker2_{removepending1} > pending > mcrlrecord > tuple₂ > [T, lock]
locker2_{removepending1} > record_extract2 > mcrlrecord > tuple₂ > [T, lock]
locker2_{removepending1} > record_updates3 > record_update2 > tuple₂ > [T, lock]
locker2_addpending3 > resource > [F, eqt₁, release] > [cons₂, and₂, case8₂] > LOCKER2_{MAPCLAIMLOCK2} > [T, lock]
locker2_addpending3 > resource > [F, eqt₁, release] > [cons₂, and₂, case8₂] > tuple₂ > [T, lock]
locker2_addpending3 > resource > [F, eqt₁, release] > [cons₂, and₂, case8₂] > [true, member₂, case9₂] > [T, lock]
locker2_addpending3 > resource > mcrlrecord > tuple₂ > [T, lock]
locker2_addpending3 > case1₃ > nil > false > [true, member₂, case9₂] > [T, lock]
locker2_addpending3 > case1₃ > pending > mcrlrecord > tuple₂ > [T, lock]
locker2_addpending3 > case1₃ > record_extract2 > mcrlrecord > tuple₂ > [T, lock]
locker2_addpending3 > case1₃ > record_updates3 > record_update2 > tuple₂ > [T, lock]
locker2_addpending3 > case1₃ > append₂ > [cons₂, and₂, case8₂] > LOCKER2_{MAPCLAIMLOCK2} > [T, lock]
locker2_addpending3 > case1₃ > append₂ > [cons₂, and₂, case8₂] > tuple₂ > [T, lock]
locker2_addpending3 > case1₃ > append₂ > [cons₂, and₂, case8₂] > [true, member₂, case9₂] > [T, lock]
locker2_releaselock1 > record_extract2 > mcrlrecord > tuple₂ > [T, lock]
locker2_releaselock1 > case2₁ > [cons₂, and₂, case8₂] > LOCKER2_{MAPCLAIMLOCK2} > [T, lock]
locker2_releaselock1 > case2₁ > [cons₂, and₂, case8₂] > tuple₂ > [T, lock]
locker2_releaselock1 > case2₁ > [cons₂, and₂, case8₂] > [true, member₂, case9₂] > [T, lock]
locker2_releaselock1 > case2₁ > nil > false > [true, member₂, case9₂] > [T, lock]
locker2_releaselock1 > case2₁ > excl > [T, lock]
locker2_releaselock1 > case2₁ > record_updates3 > record_update2 > tuple₂ > [T, lock]
locker2_releaselock1 > case2₁ > excllock > [T, lock]
gen_modtageq1 > equal₁ > [T, lock]
case4 > false > [true, member₂, case9₂] > [T, lock]
[locker2_obtainables2, case5₃] > pending > mcrlrecord > tuple₂ > [T, lock]
[locker2_obtainables2, case5₃] > record_extract2 > mcrlrecord > tuple₂ > [T, lock]
[locker2_obtainables2, case5₃] > [andt, locker2_{checkavailable}, case6] > excl > [T, lock]
[locker2_obtainables2, case5₃] > [andt, locker2_{checkavailable}, case6] > false > [true, member₂, case9₂] > [T, lock]
locker2_obtainable2 > [T, lock]
locker2_{checkavailables1} > [andt, locker2_{checkavailable}, case6] > excl > [T, lock]
locker2_{checkavailables1} > [andt, locker2_{checkavailable}, case6] > false > [true, member₂, case9₂] > [T, lock]
pops₁ > [T, lock]
tops₁ > [T, lock]
istops₂ > [F, eqt₁, release] > [cons₂, and₂, case8₂] > LOCKER2_{MAPCLAIMLOCK2} > [T, lock]
istops₂ > [F, eqt₁, release] > [cons₂, and₂, case8₂] > tuple₂ > [T, lock]
istops₂ > [F, eqt₁, release] > [cons₂, and₂, case8₂] > [true, member₂, case9₂] > [T, lock]
eqc₂ > eqs₂ > [F, eqt₁, release] > [cons₂, and₂, case8₂] > LOCKER2_{MAPCLAIMLOCK2} > [T, lock]
eqc₂ > eqs₂ > [F, eqt₁, release] > [cons₂, and₂, case8₂] > tuple₂ > [T, lock]
eqc₂ > eqs₂ > [F, eqt₁, release] > [cons₂, and₂, case8₂] > [true, member₂, case9₂] > [T, lock]
nocalls > [F, eqt₁, release] > [cons₂, and₂, case8₂] > LOCKER2_{MAPCLAIMLOCK2} > [T, lock]
nocalls > [F, eqt₁, release] > [cons₂, and₂, case8₂] > tuple₂ > [T, lock]
nocalls > [F, eqt₁, release] > [cons₂, and₂, case8₂] > [true, member₂, case9₂] > [T, lock]
nocalls > empty > [T, lock]
nocalls > stack₂ > [cons₂, and₂, case8₂] > LOCKER2_{MAPCLAIMLOCK2} > [T, lock]
nocalls > stack₂ > [cons₂, and₂, case8₂] > tuple₂ > [T, lock]
nocalls > stack₂ > [cons₂, and₂, case8₂] > [true, member₂, case9₂] > [T, lock]
nocalls > calls₃ > [cons₂, and₂, case8₂] > LOCKER2_{MAPCLAIMLOCK2} > [T, lock]
nocalls > calls₃ > [cons₂, and₂, case8₂] > tuple₂ > [T, lock]
nocalls > calls₃ > [cons₂, and₂, case8₂] > [true, member₂, case9₂] > [T, lock]
push₃ > [F, eqt₁, release] > [cons₂, and₂, case8₂] > LOCKER2_{MAPCLAIMLOCK2} > [T, lock]
push₃ > [F, eqt₁, release] > [cons₂, and₂, case8₂] > tuple₂ > [T, lock]
push₃ > [F, eqt₁, release] > [cons₂, and₂, case8₂] > [true, member₂, case9₂] > [T, lock]
push₃ > empty > [T, lock]
push₃ > push1₄ > pushs₂ > stack₂ > [cons₂, and₂, case8₂] > LOCKER2_{MAPCLAIMLOCK2} > [T, lock]
push₃ > push1₄ > pushs₂ > stack₂ > [cons₂, and₂, case8₂] > tuple₂ > [T, lock]
push₃ > push1₄ > pushs₂ > stack₂ > [cons₂, and₂, case8₂] > [true, member₂, case9₂] > [T, lock]
push₃ > push1₄ > calls₃ > [cons₂, and₂, case8₂] > LOCKER2_{MAPCLAIMLOCK2} > [T, lock]
push₃ > push1₄ > calls₃ > [cons₂, and₂, case8₂] > tuple₂ > [T, lock]
push₃ > push1₄ > calls₃ > [cons₂, and₂, case8₂] > [true, member₂, case9₂] > [T, lock]

Status:

pops₁: [1]
locker2_{checkavailables1}: [1]
eq₂: [1,2]
push1₄: [1,3,2,4]
push₃: [1,2,3]
locker2_{mappromotepending2}: [2,1]
locker2_{mapaddpending1}: [1]
member₂: [1,2]
case6: []
gen_tag1: [1]
pushs₂: [1,2]
excllock: []
nil: []
locker2_obtainables2: [2,1]
gen_modtageq1: [1]
T: []
locker2_addpending3: [3,2,1]
equal₁: [1]
resource: []
locker: []
true: []
record_new: []
empty: []
LOCKER2_{MAPCLAIMLOCK2}: [1,2]
eqc₂: [2,1]
locker2_releaselock1: [1]
locker2_obtainable2: [2,1]
pid₁: [1]
ok: []
F: []
lock: []
locker2_{removepending1}: [1]
tops₁: [1]
case8₂: [2,1]
case5₃: [1,2,3]
record_extract2: [2,1]
calls₃: [1,2,3]
eqt₁: [1]
eqs₂: [2,1]
and₂: [2,1]
append₂: [2,1]
stack₂: [1,2]
if₃: [1,2,3]
pending: []
locker2_claimlock1: [1]
case2₁: [1]
not₁: [1]
istops₂: [1,2]
locker2_{mapclaimlock3}: [1,2,3]
case1₃: [1,2,3]
undefined: []
tag: []
case9₂: [2,1]
mcrlrecord: []
a: []
request: []
excl: []
record_update2: [1,2]
record_updates3: [3,2,1]
locker2_{promotepending2}: [2,1]
andt: []
nocalls: []
s: []
0: []
cons₂: [1,2]
locker2_{checkavailable}: []
release: []
case0₃: [2,1,3]
false: []
tuple₂: [1,2]
case4: []

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, x3, 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(x1, x2, x3)
eq(x1, x2)  =  eq(x1, x2)
eqt(x1, x2)  =  eqt(x1, x2)
nil  =  nil
undefined  =  undefined
pid(x1)  =  x1
int(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)  =  x1
0  =  0
record_new(x1)  =  record_new
record_extract(x1, x2, x3)  =  x1
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)  =  x1
locker2_claim_lock(x1, x2, x3)  =  locker2_claim_lock
locker2_map_add_pending(x1, x2, x3)  =  locker2_map_add_pending(x1, x2, x3)
case0(x1, x2, x3)  =  case0(x1, x2, x3)
locker2_remove_pending(x1, x2)  =  locker2_remove_pending(x1, x2)
subtract(x1, x2)  =  x1
locker2_add_pending(x1, x2, x3)  =  locker2_add_pending(x1, x3)
case1(x1, x2, x3, x4)  =  case1(x1, x3)
member(x1, x2)  =  member(x1, x2)
append(x1, x2)  =  append(x1)
locker2_release_lock(x1, x2)  =  locker2_release_lock(x1, x2)
case2(x1, x2, x3)  =  case2(x1, x2)
gen_modtageq(x1, x2)  =  gen_modtageq(x1, x2)
excllock  =  excllock
case4(x1, x2, x3)  =  case4
locker2_obtainables(x1, x2)  =  locker2_obtainables(x1, x2)
case5(x1, x2, x3, x4)  =  case5(x1, x2, x3)
andt(x1, x2)  =  andt
locker2_obtainable(x1, x2)  =  x1
locker2_check_available(x1, x2)  =  locker2_check_available(x2)
case6(x1, x2, x3, x4)  =  case6(x1, x2)
equal(x1, x2)  =  equal(x1, x2)
locker2_check_availables(x1, x2)  =  locker2_check_availables(x1, x2)
locker2_adduniq(x1, x2)  =  locker2_adduniq(x1, x2)
delete(x1, x2)  =  x2
case8(x1, x2, x3, x4)  =  case8(x1, x2)
gen_tag(x1)  =  gen_tag(x1)
case9(x1, x2, x3, x4)  =  case9(x1, x2, x3)
eqs(x1, x2)  =  eqs(x1, x2)
empty  =  empty
stack(x1, x2)  =  stack(x1, x2)
pushs(x1, x2)  =  pushs(x1, x2)
pops(x1)  =  x1
tops(x1)  =  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(x2, x3, x4, x5)

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

or₂ > [F, not₁, release] > T > [false, locker2_claimlock]
imp₁ > T > [false, locker2_claimlock]
if₃ > [false, locker2_claimlock]
eq₂ > [false, locker2_claimlock]
a > [F, not₁, release] > T > [false, locker2_claimlock]
locker > [false, locker2_claimlock]
ok > [false, locker2_claimlock]
request > [false, locker2_claimlock]
resource > [lock, case1₂] > [RECORD_UPDATES3, record_update3, record_updates2] > tuple₂ > mcrlrecord > [false, locker2_claimlock]
resource > [lock, case1₂] > [F, not₁, release] > T > [false, locker2_claimlock]
resource > [lock, case1₂] > nil > [false, locker2_claimlock]
resource > [lock, case1₂] > undefined > [false, locker2_claimlock]
resource > [lock, case1₂] > append₁ > [cons₂, case8₂] > excl > [false, locker2_claimlock]
resource > [lock, case1₂] > append₁ > [cons₂, case8₂] > pending > mcrlrecord > [false, locker2_claimlock]
resource > [lock, case1₂] > append₁ > [cons₂, case8₂] > case6₂ > andt > [false, locker2_claimlock]
resource > [lock, case1₂] > append₁ > [cons₂, case8₂] > case6₂ > locker2_{checkavailable1} > [false, locker2_claimlock]
element₂ > [false, locker2_claimlock]
0 > [false, locker2_claimlock]
record_new > [lock, case1₂] > [RECORD_UPDATES3, record_update3, record_updates2] > tuple₂ > mcrlrecord > [false, locker2_claimlock]
record_new > [lock, case1₂] > [F, not₁, release] > T > [false, locker2_claimlock]
record_new > [lock, case1₂] > nil > [false, locker2_claimlock]
record_new > [lock, case1₂] > undefined > [false, locker2_claimlock]
record_new > [lock, case1₂] > append₁ > [cons₂, case8₂] > excl > [false, locker2_claimlock]
record_new > [lock, case1₂] > append₁ > [cons₂, case8₂] > pending > mcrlrecord > [false, locker2_claimlock]
record_new > [lock, case1₂] > append₁ > [cons₂, case8₂] > case6₂ > andt > [false, locker2_claimlock]
record_new > [lock, case1₂] > append₁ > [cons₂, case8₂] > case6₂ > locker2_{checkavailable1} > [false, locker2_claimlock]
locker2_{mappromotepending2} > locker2_{promotepending2} > [lock, case1₂] > [RECORD_UPDATES3, record_update3, record_updates2] > tuple₂ > mcrlrecord > [false, locker2_claimlock]
locker2_{mappromotepending2} > locker2_{promotepending2} > [lock, case1₂] > [F, not₁, release] > T > [false, locker2_claimlock]
locker2_{mappromotepending2} > locker2_{promotepending2} > [lock, case1₂] > nil > [false, locker2_claimlock]
locker2_{mappromotepending2} > locker2_{promotepending2} > [lock, case1₂] > undefined > [false, locker2_claimlock]
locker2_{mappromotepending2} > locker2_{promotepending2} > [lock, case1₂] > append₁ > [cons₂, case8₂] > excl > [false, locker2_claimlock]
locker2_{mappromotepending2} > locker2_{promotepending2} > [lock, case1₂] > append₁ > [cons₂, case8₂] > pending > mcrlrecord > [false, locker2_claimlock]
locker2_{mappromotepending2} > locker2_{promotepending2} > [lock, case1₂] > append₁ > [cons₂, case8₂] > case6₂ > andt > [false, locker2_claimlock]
locker2_{mappromotepending2} > locker2_{promotepending2} > [lock, case1₂] > append₁ > [cons₂, case8₂] > case6₂ > locker2_{checkavailable1} > [false, locker2_claimlock]
locker2_{mappromotepending2} > locker2_{promotepending2} > case0₃ > [RECORD_UPDATES3, record_update3, record_updates2] > tuple₂ > mcrlrecord > [false, locker2_claimlock]
locker2_{mappromotepending2} > locker2_{promotepending2} > case0₃ > [cons₂, case8₂] > excl > [false, locker2_claimlock]
locker2_{mappromotepending2} > locker2_{promotepending2} > case0₃ > [cons₂, case8₂] > pending > mcrlrecord > [false, locker2_claimlock]
locker2_{mappromotepending2} > locker2_{promotepending2} > case0₃ > [cons₂, case8₂] > case6₂ > andt > [false, locker2_claimlock]
locker2_{mappromotepending2} > locker2_{promotepending2} > case0₃ > [cons₂, case8₂] > case6₂ > locker2_{checkavailable1} > [false, locker2_claimlock]
locker2_{mappromotepending2} > locker2_{promotepending2} > case0₃ > nil > [false, locker2_claimlock]
locker2_{mapaddpending3} > nil > [false, locker2_claimlock]
locker2_{removepending2} > [lock, case1₂] > [RECORD_UPDATES3, record_update3, record_updates2] > tuple₂ > mcrlrecord > [false, locker2_claimlock]
locker2_{removepending2} > [lock, case1₂] > [F, not₁, release] > T > [false, locker2_claimlock]
locker2_{removepending2} > [lock, case1₂] > nil > [false, locker2_claimlock]
locker2_{removepending2} > [lock, case1₂] > undefined > [false, locker2_claimlock]
locker2_{removepending2} > [lock, case1₂] > append₁ > [cons₂, case8₂] > excl > [false, locker2_claimlock]
locker2_{removepending2} > [lock, case1₂] > append₁ > [cons₂, case8₂] > pending > mcrlrecord > [false, locker2_claimlock]
locker2_{removepending2} > [lock, case1₂] > append₁ > [cons₂, case8₂] > case6₂ > andt > [false, locker2_claimlock]
locker2_{removepending2} > [lock, case1₂] > append₁ > [cons₂, case8₂] > case6₂ > locker2_{checkavailable1} > [false, locker2_claimlock]
locker2_addpending2 > [lock, case1₂] > [RECORD_UPDATES3, record_update3, record_updates2] > tuple₂ > mcrlrecord > [false, locker2_claimlock]
locker2_addpending2 > [lock, case1₂] > [F, not₁, release] > T > [false, locker2_claimlock]
locker2_addpending2 > [lock, case1₂] > nil > [false, locker2_claimlock]
locker2_addpending2 > [lock, case1₂] > undefined > [false, locker2_claimlock]
locker2_addpending2 > [lock, case1₂] > append₁ > [cons₂, case8₂] > excl > [false, locker2_claimlock]
locker2_addpending2 > [lock, case1₂] > append₁ > [cons₂, case8₂] > pending > mcrlrecord > [false, locker2_claimlock]
locker2_addpending2 > [lock, case1₂] > append₁ > [cons₂, case8₂] > case6₂ > andt > [false, locker2_claimlock]
locker2_addpending2 > [lock, case1₂] > append₁ > [cons₂, case8₂] > case6₂ > locker2_{checkavailable1} > [false, locker2_claimlock]
[member₂, locker2_obtainables2, case5₃, case9₃] > [lock, case1₂] > [RECORD_UPDATES3, record_update3, record_updates2] > tuple₂ > mcrlrecord > [false, locker2_claimlock]
[member₂, locker2_obtainables2, case5₃, case9₃] > [lock, case1₂] > [F, not₁, release] > T > [false, locker2_claimlock]
[member₂, locker2_obtainables2, case5₃, case9₃] > [lock, case1₂] > nil > [false, locker2_claimlock]
[member₂, locker2_obtainables2, case5₃, case9₃] > [lock, case1₂] > undefined > [false, locker2_claimlock]
[member₂, locker2_obtainables2, case5₃, case9₃] > [lock, case1₂] > append₁ > [cons₂, case8₂] > excl > [false, locker2_claimlock]
[member₂, locker2_obtainables2, case5₃, case9₃] > [lock, case1₂] > append₁ > [cons₂, case8₂] > pending > mcrlrecord > [false, locker2_claimlock]
[member₂, locker2_obtainables2, case5₃, case9₃] > [lock, case1₂] > append₁ > [cons₂, case8₂] > case6₂ > andt > [false, locker2_claimlock]
[member₂, locker2_obtainables2, case5₃, case9₃] > [lock, case1₂] > append₁ > [cons₂, case8₂] > case6₂ > locker2_{checkavailable1} > [false, locker2_claimlock]
[member₂, locker2_obtainables2, case5₃, case9₃] > [true, locker2_{checkavailables2}] > [RECORD_UPDATES3, record_update3, record_updates2] > tuple₂ > mcrlrecord > [false, locker2_claimlock]
[member₂, locker2_obtainables2, case5₃, case9₃] > [true, locker2_{checkavailables2}] > [F, not₁, release] > T > [false, locker2_claimlock]
[member₂, locker2_obtainables2, case5₃, case9₃] > [true, locker2_{checkavailables2}] > nil > [false, locker2_claimlock]
[member₂, locker2_obtainables2, case5₃, case9₃] > [true, locker2_{checkavailables2}] > append₁ > [cons₂, case8₂] > excl > [false, locker2_claimlock]
[member₂, locker2_obtainables2, case5₃, case9₃] > [true, locker2_{checkavailables2}] > append₁ > [cons₂, case8₂] > pending > mcrlrecord > [false, locker2_claimlock]
[member₂, locker2_obtainables2, case5₃, case9₃] > [true, locker2_{checkavailables2}] > append₁ > [cons₂, case8₂] > case6₂ > andt > [false, locker2_claimlock]
[member₂, locker2_obtainables2, case5₃, case9₃] > [true, locker2_{checkavailables2}] > append₁ > [cons₂, case8₂] > case6₂ > locker2_{checkavailable1} > [false, locker2_claimlock]
[member₂, locker2_obtainables2, case5₃, case9₃] > [gen_modtageq2, equal₂] > [false, locker2_claimlock]
locker2_releaselock2 > [lock, case1₂] > [RECORD_UPDATES3, record_update3, record_updates2] > tuple₂ > mcrlrecord > [false, locker2_claimlock]
locker2_releaselock2 > [lock, case1₂] > [F, not₁, release] > T > [false, locker2_claimlock]
locker2_releaselock2 > [lock, case1₂] > nil > [false, locker2_claimlock]
locker2_releaselock2 > [lock, case1₂] > undefined > [false, locker2_claimlock]
locker2_releaselock2 > [lock, case1₂] > append₁ > [cons₂, case8₂] > excl > [false, locker2_claimlock]
locker2_releaselock2 > [lock, case1₂] > append₁ > [cons₂, case8₂] > pending > mcrlrecord > [false, locker2_claimlock]
locker2_releaselock2 > [lock, case1₂] > append₁ > [cons₂, case8₂] > case6₂ > andt > [false, locker2_claimlock]
locker2_releaselock2 > [lock, case1₂] > append₁ > [cons₂, case8₂] > case6₂ > locker2_{checkavailable1} > [false, locker2_claimlock]
locker2_releaselock2 > case2₂ > [RECORD_UPDATES3, record_update3, record_updates2] > tuple₂ > mcrlrecord > [false, locker2_claimlock]
locker2_releaselock2 > case2₂ > [cons₂, case8₂] > excl > [false, locker2_claimlock]
locker2_releaselock2 > case2₂ > [cons₂, case8₂] > pending > mcrlrecord > [false, locker2_claimlock]
locker2_releaselock2 > case2₂ > [cons₂, case8₂] > case6₂ > andt > [false, locker2_claimlock]
locker2_releaselock2 > case2₂ > [cons₂, case8₂] > case6₂ > locker2_{checkavailable1} > [false, locker2_claimlock]
locker2_releaselock2 > case2₂ > nil > [false, locker2_claimlock]
locker2_releaselock2 > case2₂ > excllock > [false, locker2_claimlock]
case4 > [false, locker2_claimlock]
locker2_adduniq2 > [false, locker2_claimlock]
gen_tag1 > tuple₂ > mcrlrecord > [false, locker2_claimlock]
gen_tag1 > tag > [false, locker2_claimlock]
eqc₂ > eqs₂ > [eqt₂, istops₂] > [F, not₁, release] > T > [false, locker2_claimlock]
eqc₂ > eqs₂ > [eqt₂, istops₂] > and₂ > [false, locker2_claimlock]
[push₃, push1₄] > empty > [F, not₁, release] > T > [false, locker2_claimlock]
[push₃, push1₄] > pushs₂ > stack₂ > [eqt₂, istops₂] > [F, not₁, release] > T > [false, locker2_claimlock]
[push₃, push1₄] > pushs₂ > stack₂ > [eqt₂, istops₂] > and₂ > [false, locker2_claimlock]
[push₃, push1₄] > nocalls > [false, locker2_claimlock]
[push₃, push1₄] > calls₃ > [F, not₁, release] > T > [false, locker2_claimlock]
[push₃, push1₄] > calls₃ > and₂ > [false, locker2_claimlock]

Status:

eq₂: [1,2]
push1₄: [2,3,1,4]
locker2_claimlock: []
case2₂: [1,2]
push₃: [3,1,2]
locker2_{removepending2}: [2,1]
locker2_{mappromotepending2}: [1,2]
member₂: [1,2]
gen_modtageq2: [1,2]
gen_tag1: [1]
equal₂: [1,2]
pushs₂: [1,2]
excllock: []
eqt₂: [1,2]
nil: []
element₂: [1,2]
locker2_releaselock2: [1,2]
locker2_obtainables2: [1,2]
T: []
resource: []
locker2_{checkavailable1}: [1]
locker: []
true: []
record_new: []
empty: []
eqc₂: [2,1]
imp₁: [1]
locker2_{checkavailables2}: [2,1]
ok: []
F: []
lock: []
append₁: [1]
case8₂: [1,2]
case5₃: [2,1,3]
or₂: [2,1]
calls₃: [3,2,1]
eqs₂: [2,1]
case1₂: [2,1]
and₂: [2,1]
stack₂: [1,2]
if₃: [1,2,3]
pending: []
not₁: [1]
istops₂: [1,2]
record_updates2: [2,1]
undefined: []
tag: []
mcrlrecord: []
a: []
request: []
excl: []
RECORD_UPDATES3: [3,1,2]
locker2_{promotepending2}: [1,2]
andt: []
nocalls: []
record_update3: [2,3,1]
0: []
case9₃: [3,1,2]
locker2_addpending2: [1,2]
cons₂: [2,1]
locker2_{mapaddpending3}: [3,1,2]
case6₂: [2,1]
release: []
case0₃: [1,3,2]
false: []
tuple₂: [1,2]
case4: []
locker2_adduniq2: [1,2]

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, x2)
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)  =  x2
not(x1)  =  not
if(x1, x2, x3)  =  if(x1, x2, x3)
eq(x1, x2)  =  eq
eqt(x1, x2)  =  eqt(x2)
nil  =  nil
undefined  =  undefined
pid(x1)  =  x1
int(x1)  =  int
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)  =  x2
s(x1)  =  x1
0  =  0
record_new(x1)  =  record_new
record_extract(x1, x2, x3)  =  x1
record_update(x1, x2, x3, x4)  =  record_update(x1, 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, x2, x3)
locker2_claim_lock(x1, x2, x3)  =  locker2_claim_lock(x1, x2, x3)
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)
member(x1, x2)  =  member
append(x1, x2)  =  append(x1, x2)
locker2_release_lock(x1, x2)  =  locker2_release_lock(x1, x2)
case2(x1, x2, x3)  =  case2(x1, x2, x3)
gen_modtageq(x1, x2)  =  gen_modtageq(x1, x2)
excllock  =  excllock
case4(x1, x2, x3)  =  case4(x2)
locker2_obtainables(x1, x2)  =  locker2_obtainables(x1, x2)
case5(x1, x2, x3, x4)  =  case5(x1, x2)
andt(x1, x2)  =  andt
locker2_obtainable(x1, x2)  =  locker2_obtainable
locker2_check_available(x1, x2)  =  locker2_check_available(x2)
case6(x1, x2, x3, x4)  =  case6(x1)
equal(x1, x2)  =  x1
locker2_check_availables(x1, x2)  =  x1
locker2_adduniq(x1, x2)  =  x2
delete(x1, x2)  =  x2
case8(x1, x2, x3, x4)  =  case8(x1, x2)
gen_tag(x1)  =  gen_tag(x1)
case9(x1, x2, x3, x4)  =  case9
eqs(x1, x2)  =  eqs(x2)
empty  =  empty
stack(x1, x2)  =  stack(x1, x2)
pushs(x1, x2)  =  pushs(x1, x2)
pops(x1)  =  x1
tops(x1)  =  x1
istops(x1, x2)  =  istops(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, lock, locker2_claimlock3, andt]
not > [F, eq] > [T, lock, locker2_claimlock3, andt]
if₃ > [T, lock, locker2_claimlock3, andt]
int > [T, lock, locker2_claimlock3, andt]
a > [T, lock, locker2_claimlock3, andt]
locker > [F, eq] > [T, lock, locker2_claimlock3, andt]
ok > [F, eq] > [T, lock, locker2_claimlock3, andt]
release > [F, eq] > [T, lock, locker2_claimlock3, andt]
request > [F, eq] > [T, lock, locker2_claimlock3, andt]
0 > [T, lock, locker2_claimlock3, andt]
record_new > [nil, excl, pending, record_updates3, case0₃] > [cons₂, record_update2, case8₂] > LOCKER2_{MAPPROMOTEPENDING2} > [T, lock, locker2_claimlock3, andt]
record_new > [nil, excl, pending, record_updates3, case0₃] > [cons₂, record_update2, case8₂] > and₂ > [T, lock, locker2_claimlock3, andt]
record_new > [nil, excl, pending, record_updates3, case0₃] > [cons₂, record_update2, case8₂] > tuple₂ > [T, lock, locker2_claimlock3, andt]
record_new > [nil, excl, pending, record_updates3, case0₃] > [cons₂, record_update2, case8₂] > [locker2_obtainables2, case5₂] > [T, lock, locker2_claimlock3, andt]
record_new > [nil, excl, pending, record_updates3, case0₃] > [false, case4₁] > [locker2_obtainables2, case5₂] > [T, lock, locker2_claimlock3, andt]
record_new > [nil, excl, pending, record_updates3, case0₃] > true > tuple₂ > [T, lock, locker2_claimlock3, andt]
record_new > [nil, excl, pending, record_updates3, case0₃] > true > [locker2_obtainables2, case5₂] > [T, lock, locker2_claimlock3, andt]
record_new > undefined > [F, eq] > [T, lock, locker2_claimlock3, andt]
record_new > mcrlrecord > [F, eq] > [T, lock, locker2_claimlock3, andt]
record_new > mcrlrecord > tuple₂ > [T, lock, locker2_claimlock3, andt]
[locker2_{mappromotepending2}, locker2_{promotepending2}] > [nil, excl, pending, record_updates3, case0₃] > [cons₂, record_update2, case8₂] > LOCKER2_{MAPPROMOTEPENDING2} > [T, lock, locker2_claimlock3, andt]
[locker2_{mappromotepending2}, locker2_{promotepending2}] > [nil, excl, pending, record_updates3, case0₃] > [cons₂, record_update2, case8₂] > and₂ > [T, lock, locker2_claimlock3, andt]
[locker2_{mappromotepending2}, locker2_{promotepending2}] > [nil, excl, pending, record_updates3, case0₃] > [cons₂, record_update2, case8₂] > tuple₂ > [T, lock, locker2_claimlock3, andt]
[locker2_{mappromotepending2}, locker2_{promotepending2}] > [nil, excl, pending, record_updates3, case0₃] > [cons₂, record_update2, case8₂] > [locker2_obtainables2, case5₂] > [T, lock, locker2_claimlock3, andt]
[locker2_{mappromotepending2}, locker2_{promotepending2}] > [nil, excl, pending, record_updates3, case0₃] > [false, case4₁] > [locker2_obtainables2, case5₂] > [T, lock, locker2_claimlock3, andt]
[locker2_{mappromotepending2}, locker2_{promotepending2}] > [nil, excl, pending, record_updates3, case0₃] > true > tuple₂ > [T, lock, locker2_claimlock3, andt]
[locker2_{mappromotepending2}, locker2_{promotepending2}] > [nil, excl, pending, record_updates3, case0₃] > true > [locker2_obtainables2, case5₂] > [T, lock, locker2_claimlock3, andt]
locker2_{mapclaimlock3} > [nil, excl, pending, record_updates3, case0₃] > [cons₂, record_update2, case8₂] > LOCKER2_{MAPPROMOTEPENDING2} > [T, lock, locker2_claimlock3, andt]
locker2_{mapclaimlock3} > [nil, excl, pending, record_updates3, case0₃] > [cons₂, record_update2, case8₂] > and₂ > [T, lock, locker2_claimlock3, andt]
locker2_{mapclaimlock3} > [nil, excl, pending, record_updates3, case0₃] > [cons₂, record_update2, case8₂] > tuple₂ > [T, lock, locker2_claimlock3, andt]
locker2_{mapclaimlock3} > [nil, excl, pending, record_updates3, case0₃] > [cons₂, record_update2, case8₂] > [locker2_obtainables2, case5₂] > [T, lock, locker2_claimlock3, andt]
locker2_{mapclaimlock3} > [nil, excl, pending, record_updates3, case0₃] > [false, case4₁] > [locker2_obtainables2, case5₂] > [T, lock, locker2_claimlock3, andt]
locker2_{mapclaimlock3} > [nil, excl, pending, record_updates3, case0₃] > true > tuple₂ > [T, lock, locker2_claimlock3, andt]
locker2_{mapclaimlock3} > [nil, excl, pending, record_updates3, case0₃] > true > [locker2_obtainables2, case5₂] > [T, lock, locker2_claimlock3, andt]
locker2_{mapaddpending} > [nil, excl, pending, record_updates3, case0₃] > [cons₂, record_update2, case8₂] > LOCKER2_{MAPPROMOTEPENDING2} > [T, lock, locker2_claimlock3, andt]
locker2_{mapaddpending} > [nil, excl, pending, record_updates3, case0₃] > [cons₂, record_update2, case8₂] > and₂ > [T, lock, locker2_claimlock3, andt]
locker2_{mapaddpending} > [nil, excl, pending, record_updates3, case0₃] > [cons₂, record_update2, case8₂] > tuple₂ > [T, lock, locker2_claimlock3, andt]
locker2_{mapaddpending} > [nil, excl, pending, record_updates3, case0₃] > [cons₂, record_update2, case8₂] > [locker2_obtainables2, case5₂] > [T, lock, locker2_claimlock3, andt]
locker2_{mapaddpending} > [nil, excl, pending, record_updates3, case0₃] > [false, case4₁] > [locker2_obtainables2, case5₂] > [T, lock, locker2_claimlock3, andt]
locker2_{mapaddpending} > [nil, excl, pending, record_updates3, case0₃] > true > tuple₂ > [T, lock, locker2_claimlock3, andt]
locker2_{mapaddpending} > [nil, excl, pending, record_updates3, case0₃] > true > [locker2_obtainables2, case5₂] > [T, lock, locker2_claimlock3, andt]
[locker2_{removepending2}, subtract₁] > [nil, excl, pending, record_updates3, case0₃] > [cons₂, record_update2, case8₂] > LOCKER2_{MAPPROMOTEPENDING2} > [T, lock, locker2_claimlock3, andt]
[locker2_{removepending2}, subtract₁] > [nil, excl, pending, record_updates3, case0₃] > [cons₂, record_update2, case8₂] > and₂ > [T, lock, locker2_claimlock3, andt]
[locker2_{removepending2}, subtract₁] > [nil, excl, pending, record_updates3, case0₃] > [cons₂, record_update2, case8₂] > tuple₂ > [T, lock, locker2_claimlock3, andt]
[locker2_{removepending2}, subtract₁] > [nil, excl, pending, record_updates3, case0₃] > [cons₂, record_update2, case8₂] > [locker2_obtainables2, case5₂] > [T, lock, locker2_claimlock3, andt]
[locker2_{removepending2}, subtract₁] > [nil, excl, pending, record_updates3, case0₃] > [false, case4₁] > [locker2_obtainables2, case5₂] > [T, lock, locker2_claimlock3, andt]
[locker2_{removepending2}, subtract₁] > [nil, excl, pending, record_updates3, case0₃] > true > tuple₂ > [T, lock, locker2_claimlock3, andt]
[locker2_{removepending2}, subtract₁] > [nil, excl, pending, record_updates3, case0₃] > true > [locker2_obtainables2, case5₂] > [T, lock, locker2_claimlock3, andt]
locker2_addpending3 > resource > [F, eq] > [T, lock, locker2_claimlock3, andt]
locker2_addpending3 > resource > tuple₂ > [T, lock, locker2_claimlock3, andt]
locker2_addpending3 > case1₃ > [nil, excl, pending, record_updates3, case0₃] > [cons₂, record_update2, case8₂] > LOCKER2_{MAPPROMOTEPENDING2} > [T, lock, locker2_claimlock3, andt]
locker2_addpending3 > case1₃ > [nil, excl, pending, record_updates3, case0₃] > [cons₂, record_update2, case8₂] > and₂ > [T, lock, locker2_claimlock3, andt]
locker2_addpending3 > case1₃ > [nil, excl, pending, record_updates3, case0₃] > [cons₂, record_update2, case8₂] > tuple₂ > [T, lock, locker2_claimlock3, andt]
locker2_addpending3 > case1₃ > [nil, excl, pending, record_updates3, case0₃] > [cons₂, record_update2, case8₂] > [locker2_obtainables2, case5₂] > [T, lock, locker2_claimlock3, andt]
locker2_addpending3 > case1₃ > [nil, excl, pending, record_updates3, case0₃] > [false, case4₁] > [locker2_obtainables2, case5₂] > [T, lock, locker2_claimlock3, andt]
locker2_addpending3 > case1₃ > [nil, excl, pending, record_updates3, case0₃] > true > tuple₂ > [T, lock, locker2_claimlock3, andt]
locker2_addpending3 > case1₃ > [nil, excl, pending, record_updates3, case0₃] > true > [locker2_obtainables2, case5₂] > [T, lock, locker2_claimlock3, andt]
locker2_addpending3 > case1₃ > append₂ > [cons₂, record_update2, case8₂] > LOCKER2_{MAPPROMOTEPENDING2} > [T, lock, locker2_claimlock3, andt]
locker2_addpending3 > case1₃ > append₂ > [cons₂, record_update2, case8₂] > and₂ > [T, lock, locker2_claimlock3, andt]
locker2_addpending3 > case1₃ > append₂ > [cons₂, record_update2, case8₂] > tuple₂ > [T, lock, locker2_claimlock3, andt]
locker2_addpending3 > case1₃ > append₂ > [cons₂, record_update2, case8₂] > [locker2_obtainables2, case5₂] > [T, lock, locker2_claimlock3, andt]
locker2_addpending3 > [member, case9] > [false, case4₁] > [locker2_obtainables2, case5₂] > [T, lock, locker2_claimlock3, andt]
locker2_addpending3 > [member, case9] > true > tuple₂ > [T, lock, locker2_claimlock3, andt]
locker2_addpending3 > [member, case9] > true > [locker2_obtainables2, case5₂] > [T, lock, locker2_claimlock3, andt]
locker2_releaselock2 > case2₃ > [nil, excl, pending, record_updates3, case0₃] > [cons₂, record_update2, case8₂] > LOCKER2_{MAPPROMOTEPENDING2} > [T, lock, locker2_claimlock3, andt]
locker2_releaselock2 > case2₃ > [nil, excl, pending, record_updates3, case0₃] > [cons₂, record_update2, case8₂] > and₂ > [T, lock, locker2_claimlock3, andt]
locker2_releaselock2 > case2₃ > [nil, excl, pending, record_updates3, case0₃] > [cons₂, record_update2, case8₂] > tuple₂ > [T, lock, locker2_claimlock3, andt]
locker2_releaselock2 > case2₃ > [nil, excl, pending, record_updates3, case0₃] > [cons₂, record_update2, case8₂] > [locker2_obtainables2, case5₂] > [T, lock, locker2_claimlock3, andt]
locker2_releaselock2 > case2₃ > [nil, excl, pending, record_updates3, case0₃] > [false, case4₁] > [locker2_obtainables2, case5₂] > [T, lock, locker2_claimlock3, andt]
locker2_releaselock2 > case2₃ > [nil, excl, pending, record_updates3, case0₃] > true > tuple₂ > [T, lock, locker2_claimlock3, andt]
locker2_releaselock2 > case2₃ > [nil, excl, pending, record_updates3, case0₃] > true > [locker2_obtainables2, case5₂] > [T, lock, locker2_claimlock3, andt]
locker2_releaselock2 > case2₃ > excllock > [T, lock, locker2_claimlock3, andt]
locker2_releaselock2 > gen_modtageq2 > [T, lock, locker2_claimlock3, andt]
locker2_obtainable > [T, lock, locker2_claimlock3, andt]
[locker2_{checkavailable1}, case6₁] > [nil, excl, pending, record_updates3, case0₃] > [cons₂, record_update2, case8₂] > LOCKER2_{MAPPROMOTEPENDING2} > [T, lock, locker2_claimlock3, andt]
[locker2_{checkavailable1}, case6₁] > [nil, excl, pending, record_updates3, case0₃] > [cons₂, record_update2, case8₂] > and₂ > [T, lock, locker2_claimlock3, andt]
[locker2_{checkavailable1}, case6₁] > [nil, excl, pending, record_updates3, case0₃] > [cons₂, record_update2, case8₂] > tuple₂ > [T, lock, locker2_claimlock3, andt]
[locker2_{checkavailable1}, case6₁] > [nil, excl, pending, record_updates3, case0₃] > [cons₂, record_update2, case8₂] > [locker2_obtainables2, case5₂] > [T, lock, locker2_claimlock3, andt]
[locker2_{checkavailable1}, case6₁] > [nil, excl, pending, record_updates3, case0₃] > [false, case4₁] > [locker2_obtainables2, case5₂] > [T, lock, locker2_claimlock3, andt]
[locker2_{checkavailable1}, case6₁] > [nil, excl, pending, record_updates3, case0₃] > true > tuple₂ > [T, lock, locker2_claimlock3, andt]
[locker2_{checkavailable1}, case6₁] > [nil, excl, pending, record_updates3, case0₃] > true > [locker2_obtainables2, case5₂] > [T, lock, locker2_claimlock3, andt]
gen_tag1 > tuple₂ > [T, lock, locker2_claimlock3, andt]
gen_tag1 > tag > [T, lock, locker2_claimlock3, andt]
istops₁ > eqt₁ > [F, eq] > [T, lock, locker2_claimlock3, andt]
istops₁ > eqt₁ > and₂ > [T, lock, locker2_claimlock3, andt]
eqc₁ > eqs₁ > eqt₁ > [F, eq] > [T, lock, locker2_claimlock3, andt]
eqc₁ > eqs₁ > eqt₁ > and₂ > [T, lock, locker2_claimlock3, andt]
nocalls > [F, eq] > [T, lock, locker2_claimlock3, andt]
nocalls > empty > [T, lock, locker2_claimlock3, andt]
nocalls > [stack₂, pushs₂] > [T, lock, locker2_claimlock3, andt]
nocalls > calls₃ > [T, lock, locker2_claimlock3, andt]
push₃ > empty > [T, lock, locker2_claimlock3, andt]
push₃ > push1₄ > [stack₂, pushs₂] > [T, lock, locker2_claimlock3, andt]
push₃ > push1₄ > calls₃ > [T, lock, locker2_claimlock3, andt]

Status:

locker2_obtainable: []
push1₄: [2,1,4,3]
push₃: [2,1,3]
locker2_{removepending2}: [1,2]
locker2_{mappromotepending2}: [2,1]
gen_modtageq2: [1,2]
gen_tag1: [1]
pushs₂: [2,1]
excllock: []
nil: []
locker2_releaselock2: [2,1]
locker2_obtainables2: [1,2]
locker2_{mapaddpending}: []
T: []
locker2_addpending3: [3,1,2]
case6₁: [1]
resource: []
locker2_{checkavailable1}: [1]
eqc₁: [1]
locker: []
true: []
record_new: []
empty: []
member: []
case2₃: [2,3,1]
ok: []
case9: []
F: []
lock: []
case8₂: [2,1]
or₂: [1,2]
calls₃: [2,1,3]
not: []
eqt₁: [1]
and₂: [2,1]
locker2_claimlock3: [3,2,1]
append₂: [1,2]
case4₁: [1]
stack₂: [2,1]
if₃: [1,2,3]
pending: []
subtract₁: [1]
istops₁: [1]
LOCKER2_{MAPPROMOTEPENDING2}: [2,1]
locker2_{mapclaimlock3}: [2,1,3]
case5₂: [2,1]
case1₃: [1,3,2]
undefined: []
tag: []
eq: []
mcrlrecord: []
a: []
request: []
excl: []
int: []
record_update2: [1,2]
record_updates3: [2,3,1]
locker2_{promotepending2}: [2,1]
andt: []
nocalls: []
0: []
cons₂: [1,2]
release: []
case0₃: [3,2,1]
eqs₁: [1]
false: []
tuple₂: [2,1]

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)

(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
s(x1)  =  s
tuple(x1, x2)  =  tuple(x1, x2)
or(x1, x2)  =  or
T  =  T
F  =  F
and(x1, x2)  =  and(x1, x2)
imp(x1, x2)  =  imp(x1, x2)
not(x1)  =  not(x1)
if(x1, x2, x3)  =  if(x2, x3)
eq(x1, x2)  =  eq(x1, x2)
eqt(x1, x2)  =  eqt(x1, x2)
nil  =  nil
undefined  =  undefined
pid(x1)  =  x1
cons(x1, x2)  =  cons(x1, x2)
tuplenil(x1)  =  tuplenil(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)  =  x2
0  =  0
record_new(x1)  =  record_new
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, x2, x3)
locker2_claim_lock(x1, x2, x3)  =  locker2_claim_lock(x1, x2, x3)
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)
case1(x1, x2, x3, x4)  =  case1(x3)
member(x1, x2)  =  member(x1, x2)
append(x1, x2)  =  x1
locker2_release_lock(x1, x2)  =  locker2_release_lock(x1, x2)
case2(x1, x2, x3)  =  case2(x1, x2, x3)
gen_modtageq(x1, x2)  =  gen_modtageq
excllock  =  excllock
case4(x1, x2, x3)  =  case4
locker2_obtainables(x1, x2)  =  locker2_obtainables(x1, x2)
case5(x1, x2, x3, x4)  =  case5(x1, x2, x3)
andt(x1, x2)  =  andt(x2)
locker2_obtainable(x1, x2)  =  x2
locker2_check_available(x1, x2)  =  x2
case6(x1, x2, x3, x4)  =  case6(x1, x4)
equal(x1, x2)  =  equal
locker2_check_availables(x1, x2)  =  locker2_check_availables(x1, x2)
locker2_adduniq(x1, x2)  =  locker2_adduniq(x1, 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)  =  case9(x1, x2, x3)
eqs(x1, x2)  =  eqs(x1, 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
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:

ELEMENT₂ > int > s > [andt₁, equal]
ELEMENT₂ > int > F > [andt₁, equal]
imp₂ > [or, T, true, empty] > [tuple₂, tuplenil₁, lock] > [andt₁, equal]
imp₂ > [or, T, true, empty] > [and₂, calls₃] > F > [andt₁, equal]
imp₂ > [or, T, true, empty] > [nil, false] > F > [andt₁, equal]
imp₂ > [or, T, true, empty] > excl > F > [andt₁, equal]
not₁ > [or, T, true, empty] > [tuple₂, tuplenil₁, lock] > [andt₁, equal]
not₁ > [or, T, true, empty] > [and₂, calls₃] > F > [andt₁, equal]
not₁ > [or, T, true, empty] > [nil, false] > F > [andt₁, equal]
not₁ > [or, T, true, empty] > excl > F > [andt₁, equal]
if₂ > [andt₁, equal]
eq₂ > [or, T, true, empty] > [tuple₂, tuplenil₁, lock] > [andt₁, equal]
eq₂ > [or, T, true, empty] > [and₂, calls₃] > F > [andt₁, equal]
eq₂ > [or, T, true, empty] > [nil, false] > F > [andt₁, equal]
eq₂ > [or, T, true, empty] > excl > F > [andt₁, equal]
a > [or, T, true, empty] > [tuple₂, tuplenil₁, lock] > [andt₁, equal]
a > [or, T, true, empty] > [and₂, calls₃] > F > [andt₁, equal]
a > [or, T, true, empty] > [nil, false] > F > [andt₁, equal]
a > [or, T, true, empty] > excl > F > [andt₁, equal]
locker > [or, T, true, empty] > [tuple₂, tuplenil₁, lock] > [andt₁, equal]
locker > [or, T, true, empty] > [and₂, calls₃] > F > [andt₁, equal]
locker > [or, T, true, empty] > [nil, false] > F > [andt₁, equal]
locker > [or, T, true, empty] > excl > F > [andt₁, equal]
ok > F > [andt₁, equal]
release > F > [andt₁, equal]
request > [or, T, true, empty] > [tuple₂, tuplenil₁, lock] > [andt₁, equal]
request > [or, T, true, empty] > [and₂, calls₃] > F > [andt₁, equal]
request > [or, T, true, empty] > [nil, false] > F > [andt₁, equal]
request > [or, T, true, empty] > excl > F > [andt₁, equal]
0 > [andt₁, equal]
record_new > [nil, false] > F > [andt₁, equal]
record_new > undefined > F > [andt₁, equal]
record_new > mcrlrecord > [tuple₂, tuplenil₁, lock] > [andt₁, equal]
record_new > mcrlrecord > F > [andt₁, equal]
[locker2_{mappromotepending2}, locker2_{promotepending2}] > [cons₂, pending, record_extract3, record_updates3, case0₃, case6₂] > eqt₂ > [or, T, true, empty] > [tuple₂, tuplenil₁, lock] > [andt₁, equal]
[locker2_{mappromotepending2}, locker2_{promotepending2}] > [cons₂, pending, record_extract3, record_updates3, case0₃, case6₂] > eqt₂ > [or, T, true, empty] > [and₂, calls₃] > F > [andt₁, equal]
[locker2_{mappromotepending2}, locker2_{promotepending2}] > [cons₂, pending, record_extract3, record_updates3, case0₃, case6₂] > eqt₂ > [or, T, true, empty] > [nil, false] > F > [andt₁, equal]
[locker2_{mappromotepending2}, locker2_{promotepending2}] > [cons₂, pending, record_extract3, record_updates3, case0₃, case6₂] > eqt₂ > [or, T, true, empty] > excl > F > [andt₁, equal]
[locker2_{mappromotepending2}, locker2_{promotepending2}] > [cons₂, pending, record_extract3, record_updates3, case0₃, case6₂] > mcrlrecord > [tuple₂, tuplenil₁, lock] > [andt₁, equal]
[locker2_{mappromotepending2}, locker2_{promotepending2}] > [cons₂, pending, record_extract3, record_updates3, case0₃, case6₂] > mcrlrecord > F > [andt₁, equal]
[locker2_{mappromotepending2}, locker2_{promotepending2}] > [cons₂, pending, record_extract3, record_updates3, case0₃, case6₂] > record_update4 > [tuple₂, tuplenil₁, lock] > [andt₁, equal]
[locker2_{mappromotepending2}, locker2_{promotepending2}] > [cons₂, pending, record_extract3, record_updates3, case0₃, case6₂] > locker2_claimlock3 > [andt₁, equal]
[locker2_{mappromotepending2}, locker2_{promotepending2}] > [cons₂, pending, record_extract3, record_updates3, case0₃, case6₂] > [locker2_obtainables2, case5₃] > [or, T, true, empty] > [tuple₂, tuplenil₁, lock] > [andt₁, equal]
[locker2_{mappromotepending2}, locker2_{promotepending2}] > [cons₂, pending, record_extract3, record_updates3, case0₃, case6₂] > [locker2_obtainables2, case5₃] > [or, T, true, empty] > [and₂, calls₃] > F > [andt₁, equal]
[locker2_{mappromotepending2}, locker2_{promotepending2}] > [cons₂, pending, record_extract3, record_updates3, case0₃, case6₂] > [locker2_obtainables2, case5₃] > [or, T, true, empty] > [nil, false] > F > [andt₁, equal]
[locker2_{mappromotepending2}, locker2_{promotepending2}] > [cons₂, pending, record_extract3, record_updates3, case0₃, case6₂] > [locker2_obtainables2, case5₃] > [or, T, true, empty] > excl > F > [andt₁, equal]
locker2_{mapclaimlock3} > [cons₂, pending, record_extract3, record_updates3, case0₃, case6₂] > eqt₂ > [or, T, true, empty] > [tuple₂, tuplenil₁, lock] > [andt₁, equal]
locker2_{mapclaimlock3} > [cons₂, pending, record_extract3, record_updates3, case0₃, case6₂] > eqt₂ > [or, T, true, empty] > [and₂, calls₃] > F > [andt₁, equal]
locker2_{mapclaimlock3} > [cons₂, pending, record_extract3, record_updates3, case0₃, case6₂] > eqt₂ > [or, T, true, empty] > [nil, false] > F > [andt₁, equal]
locker2_{mapclaimlock3} > [cons₂, pending, record_extract3, record_updates3, case0₃, case6₂] > eqt₂ > [or, T, true, empty] > excl > F > [andt₁, equal]
locker2_{mapclaimlock3} > [cons₂, pending, record_extract3, record_updates3, case0₃, case6₂] > mcrlrecord > [tuple₂, tuplenil₁, lock] > [andt₁, equal]
locker2_{mapclaimlock3} > [cons₂, pending, record_extract3, record_updates3, case0₃, case6₂] > mcrlrecord > F > [andt₁, equal]
locker2_{mapclaimlock3} > [cons₂, pending, record_extract3, record_updates3, case0₃, case6₂] > record_update4 > [tuple₂, tuplenil₁, lock] > [andt₁, equal]
locker2_{mapclaimlock3} > [cons₂, pending, record_extract3, record_updates3, case0₃, case6₂] > locker2_claimlock3 > [andt₁, equal]
locker2_{mapclaimlock3} > [cons₂, pending, record_extract3, record_updates3, case0₃, case6₂] > [locker2_obtainables2, case5₃] > [or, T, true, empty] > [tuple₂, tuplenil₁, lock] > [andt₁, equal]
locker2_{mapclaimlock3} > [cons₂, pending, record_extract3, record_updates3, case0₃, case6₂] > [locker2_obtainables2, case5₃] > [or, T, true, empty] > [and₂, calls₃] > F > [andt₁, equal]
locker2_{mapclaimlock3} > [cons₂, pending, record_extract3, record_updates3, case0₃, case6₂] > [locker2_obtainables2, case5₃] > [or, T, true, empty] > [nil, false] > F > [andt₁, equal]
locker2_{mapclaimlock3} > [cons₂, pending, record_extract3, record_updates3, case0₃, case6₂] > [locker2_obtainables2, case5₃] > [or, T, true, empty] > excl > F > [andt₁, equal]
locker2_{mapaddpending} > [nil, false] > F > [andt₁, equal]
locker2_{removepending2} > [subtract₂, delete₂, case8₃] > [cons₂, pending, record_extract3, record_updates3, case0₃, case6₂] > eqt₂ > [or, T, true, empty] > [tuple₂, tuplenil₁, lock] > [andt₁, equal]
locker2_{removepending2} > [subtract₂, delete₂, case8₃] > [cons₂, pending, record_extract3, record_updates3, case0₃, case6₂] > eqt₂ > [or, T, true, empty] > [and₂, calls₃] > F > [andt₁, equal]
locker2_{removepending2} > [subtract₂, delete₂, case8₃] > [cons₂, pending, record_extract3, record_updates3, case0₃, case6₂] > eqt₂ > [or, T, true, empty] > [nil, false] > F > [andt₁, equal]
locker2_{removepending2} > [subtract₂, delete₂, case8₃] > [cons₂, pending, record_extract3, record_updates3, case0₃, case6₂] > eqt₂ > [or, T, true, empty] > excl > F > [andt₁, equal]
locker2_{removepending2} > [subtract₂, delete₂, case8₃] > [cons₂, pending, record_extract3, record_updates3, case0₃, case6₂] > mcrlrecord > [tuple₂, tuplenil₁, lock] > [andt₁, equal]
locker2_{removepending2} > [subtract₂, delete₂, case8₃] > [cons₂, pending, record_extract3, record_updates3, case0₃, case6₂] > mcrlrecord > F > [andt₁, equal]
locker2_{removepending2} > [subtract₂, delete₂, case8₃] > [cons₂, pending, record_extract3, record_updates3, case0₃, case6₂] > record_update4 > [tuple₂, tuplenil₁, lock] > [andt₁, equal]
locker2_{removepending2} > [subtract₂, delete₂, case8₃] > [cons₂, pending, record_extract3, record_updates3, case0₃, case6₂] > locker2_claimlock3 > [andt₁, equal]
locker2_{removepending2} > [subtract₂, delete₂, case8₃] > [cons₂, pending, record_extract3, record_updates3, case0₃, case6₂] > [locker2_obtainables2, case5₃] > [or, T, true, empty] > [tuple₂, tuplenil₁, lock] > [andt₁, equal]
locker2_{removepending2} > [subtract₂, delete₂, case8₃] > [cons₂, pending, record_extract3, record_updates3, case0₃, case6₂] > [locker2_obtainables2, case5₃] > [or, T, true, empty] > [and₂, calls₃] > F > [andt₁, equal]
locker2_{removepending2} > [subtract₂, delete₂, case8₃] > [cons₂, pending, record_extract3, record_updates3, case0₃, case6₂] > [locker2_obtainables2, case5₃] > [or, T, true, empty] > [nil, false] > F > [andt₁, equal]
locker2_{removepending2} > [subtract₂, delete₂, case8₃] > [cons₂, pending, record_extract3, record_updates3, case0₃, case6₂] > [locker2_obtainables2, case5₃] > [or, T, true, empty] > excl > F > [andt₁, equal]
[locker2_addpending1, member₂, case9₃] > resource > [or, T, true, empty] > [tuple₂, tuplenil₁, lock] > [andt₁, equal]
[locker2_addpending1, member₂, case9₃] > resource > [or, T, true, empty] > [and₂, calls₃] > F > [andt₁, equal]
[locker2_addpending1, member₂, case9₃] > resource > [or, T, true, empty] > [nil, false] > F > [andt₁, equal]
[locker2_addpending1, member₂, case9₃] > resource > [or, T, true, empty] > excl > F > [andt₁, equal]
[locker2_addpending1, member₂, case9₃] > resource > mcrlrecord > [tuple₂, tuplenil₁, lock] > [andt₁, equal]
[locker2_addpending1, member₂, case9₃] > resource > mcrlrecord > F > [andt₁, equal]
[locker2_addpending1, member₂, case9₃] > case1₁ > [cons₂, pending, record_extract3, record_updates3, case0₃, case6₂] > eqt₂ > [or, T, true, empty] > [tuple₂, tuplenil₁, lock] > [andt₁, equal]
[locker2_addpending1, member₂, case9₃] > case1₁ > [cons₂, pending, record_extract3, record_updates3, case0₃, case6₂] > eqt₂ > [or, T, true, empty] > [and₂, calls₃] > F > [andt₁, equal]
[locker2_addpending1, member₂, case9₃] > case1₁ > [cons₂, pending, record_extract3, record_updates3, case0₃, case6₂] > eqt₂ > [or, T, true, empty] > [nil, false] > F > [andt₁, equal]
[locker2_addpending1, member₂, case9₃] > case1₁ > [cons₂, pending, record_extract3, record_updates3, case0₃, case6₂] > eqt₂ > [or, T, true, empty] > excl > F > [andt₁, equal]
[locker2_addpending1, member₂, case9₃] > case1₁ > [cons₂, pending, record_extract3, record_updates3, case0₃, case6₂] > mcrlrecord > [tuple₂, tuplenil₁, lock] > [andt₁, equal]
[locker2_addpending1, member₂, case9₃] > case1₁ > [cons₂, pending, record_extract3, record_updates3, case0₃, case6₂] > mcrlrecord > F > [andt₁, equal]
[locker2_addpending1, member₂, case9₃] > case1₁ > [cons₂, pending, record_extract3, record_updates3, case0₃, case6₂] > record_update4 > [tuple₂, tuplenil₁, lock] > [andt₁, equal]
[locker2_addpending1, member₂, case9₃] > case1₁ > [cons₂, pending, record_extract3, record_updates3, case0₃, case6₂] > locker2_claimlock3 > [andt₁, equal]
[locker2_addpending1, member₂, case9₃] > case1₁ > [cons₂, pending, record_extract3, record_updates3, case0₃, case6₂] > [locker2_obtainables2, case5₃] > [or, T, true, empty] > [tuple₂, tuplenil₁, lock] > [andt₁, equal]
[locker2_addpending1, member₂, case9₃] > case1₁ > [cons₂, pending, record_extract3, record_updates3, case0₃, case6₂] > [locker2_obtainables2, case5₃] > [or, T, true, empty] > [and₂, calls₃] > F > [andt₁, equal]
[locker2_addpending1, member₂, case9₃] > case1₁ > [cons₂, pending, record_extract3, record_updates3, case0₃, case6₂] > [locker2_obtainables2, case5₃] > [or, T, true, empty] > [nil, false] > F > [andt₁, equal]
[locker2_addpending1, member₂, case9₃] > case1₁ > [cons₂, pending, record_extract3, record_updates3, case0₃, case6₂] > [locker2_obtainables2, case5₃] > [or, T, true, empty] > excl > F > [andt₁, equal]
locker2_releaselock2 > case2₃ > [cons₂, pending, record_extract3, record_updates3, case0₃, case6₂] > eqt₂ > [or, T, true, empty] > [tuple₂, tuplenil₁, lock] > [andt₁, equal]
locker2_releaselock2 > case2₃ > [cons₂, pending, record_extract3, record_updates3, case0₃, case6₂] > eqt₂ > [or, T, true, empty] > [and₂, calls₃] > F > [andt₁, equal]
locker2_releaselock2 > case2₃ > [cons₂, pending, record_extract3, record_updates3, case0₃, case6₂] > eqt₂ > [or, T, true, empty] > [nil, false] > F > [andt₁, equal]
locker2_releaselock2 > case2₃ > [cons₂, pending, record_extract3, record_updates3, case0₃, case6₂] > eqt₂ > [or, T, true, empty] > excl > F > [andt₁, equal]
locker2_releaselock2 > case2₃ > [cons₂, pending, record_extract3, record_updates3, case0₃, case6₂] > mcrlrecord > [tuple₂, tuplenil₁, lock] > [andt₁, equal]
locker2_releaselock2 > case2₃ > [cons₂, pending, record_extract3, record_updates3, case0₃, case6₂] > mcrlrecord > F > [andt₁, equal]
locker2_releaselock2 > case2₃ > [cons₂, pending, record_extract3, record_updates3, case0₃, case6₂] > record_update4 > [tuple₂, tuplenil₁, lock] > [andt₁, equal]
locker2_releaselock2 > case2₃ > [cons₂, pending, record_extract3, record_updates3, case0₃, case6₂] > locker2_claimlock3 > [andt₁, equal]
locker2_releaselock2 > case2₃ > [cons₂, pending, record_extract3, record_updates3, case0₃, case6₂] > [locker2_obtainables2, case5₃] > [or, T, true, empty] > [tuple₂, tuplenil₁, lock] > [andt₁, equal]
locker2_releaselock2 > case2₃ > [cons₂, pending, record_extract3, record_updates3, case0₃, case6₂] > [locker2_obtainables2, case5₃] > [or, T, true, empty] > [and₂, calls₃] > F > [andt₁, equal]
locker2_releaselock2 > case2₃ > [cons₂, pending, record_extract3, record_updates3, case0₃, case6₂] > [locker2_obtainables2, case5₃] > [or, T, true, empty] > [nil, false] > F > [andt₁, equal]
locker2_releaselock2 > case2₃ > [cons₂, pending, record_extract3, record_updates3, case0₃, case6₂] > [locker2_obtainables2, case5₃] > [or, T, true, empty] > excl > F > [andt₁, equal]
locker2_releaselock2 > case2₃ > excllock > [andt₁, equal]
locker2_releaselock2 > gen_modtageq > [andt₁, equal]
case4 > [nil, false] > F > [andt₁, equal]
locker2_{checkavailables2} > [or, T, true, empty] > [tuple₂, tuplenil₁, lock] > [andt₁, equal]
locker2_{checkavailables2} > [or, T, true, empty] > [and₂, calls₃] > F > [andt₁, equal]
locker2_{checkavailables2} > [or, T, true, empty] > [nil, false] > F > [andt₁, equal]
locker2_{checkavailables2} > [or, T, true, empty] > excl > F > [andt₁, equal]
locker2_adduniq2 > [andt₁, equal]
gen_tag1 > [tuple₂, tuplenil₁, lock] > [andt₁, equal]
gen_tag1 > tag > F > [andt₁, equal]
pops₁ > [andt₁, equal]
tops₁ > [andt₁, equal]
istops₂ > eqt₂ > [or, T, true, empty] > [tuple₂, tuplenil₁, lock] > [andt₁, equal]
istops₂ > eqt₂ > [or, T, true, empty] > [and₂, calls₃] > F > [andt₁, equal]
istops₂ > eqt₂ > [or, T, true, empty] > [nil, false] > F > [andt₁, equal]
istops₂ > eqt₂ > [or, T, true, empty] > excl > F > [andt₁, equal]
eqc₂ > [eqs₂, stack₂] > eqt₂ > [or, T, true, empty] > [tuple₂, tuplenil₁, lock] > [andt₁, equal]
eqc₂ > [eqs₂, stack₂] > eqt₂ > [or, T, true, empty] > [and₂, calls₃] > F > [andt₁, equal]
eqc₂ > [eqs₂, stack₂] > eqt₂ > [or, T, true, empty] > [nil, false] > F > [andt₁, equal]
eqc₂ > [eqs₂, stack₂] > eqt₂ > [or, T, true, empty] > excl > F > [andt₁, equal]
push₃ > nocalls > [andt₁, equal]
push₃ > push1₆ > pushs₂ > [eqs₂, stack₂] > eqt₂ > [or, T, true, empty] > [tuple₂, tuplenil₁, lock] > [andt₁, equal]
push₃ > push1₆ > pushs₂ > [eqs₂, stack₂] > eqt₂ > [or, T, true, empty] > [and₂, calls₃] > F > [andt₁, equal]
push₃ > push1₆ > pushs₂ > [eqs₂, stack₂] > eqt₂ > [or, T, true, empty] > [nil, false] > F > [andt₁, equal]
push₃ > push1₆ > pushs₂ > [eqs₂, stack₂] > eqt₂ > [or, T, true, empty] > excl > F > [andt₁, equal]

Status:

pops₁: [1]
eq₂: [1,2]
push₃: [3,1,2]
delete₂: [1,2]
locker2_{removepending2}: [2,1]
locker2_{mappromotepending2}: [2,1]
member₂: [1,2]
gen_tag1: [1]
pushs₂: [1,2]
excllock: []
eqt₂: [2,1]
nil: []
locker2_releaselock2: [1,2]
locker2_obtainables2: [1,2]
locker2_{mapaddpending}: []
T: []
or: []
resource: []
locker: []
true: []
record_new: []
empty: []
eqc₂: [1,2]
push1₆: [5,4,6,2,1,3]
gen_modtageq: []
locker2_{checkavailables2}: [2,1]
case8₃: [3,1,2]
case2₃: [2,3,1]
ok: []
F: []
lock: []
tops₁: [1]
locker2_addpending1: [1]
case5₃: [2,1,3]
equal: []
calls₃: [3,1,2]
tuplenil₁: [1]
eqs₂: [1,2]
and₂: [2,1]
locker2_claimlock3: [1,2,3]
stack₂: [1,2]
pending: []
not₁: [1]
istops₂: [2,1]
locker2_{mapclaimlock3}: [2,1,3]
record_update4: [3,2,1,4]
andt₁: [1]
undefined: []
tag: []
mcrlrecord: []
a: []
request: []
if₂: [1,2]
excl: []
subtract₂: [2,1]
int: []
record_updates3: [2,3,1]
locker2_{promotepending2}: [2,1]
nocalls: []
s: []
0: []
case9₃: [3,1,2]
cons₂: [1,2]
ELEMENT₂: [1,2]
record_extract3: [2,3,1]
case6₂: [2,1]
release: []
case0₃: [3,1,2]
false: []
case1₁: [1]
tuple₂: [1,2]
imp₂: [1,2]
case4: []
locker2_adduniq2: [1,2]

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(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)  =  x1
cons(x1, x2)  =  cons(x1, x2)
pid(x1)  =  x1
tuple(x1, x2)  =  tuple(x1, x2)
tuplenil(x1)  =  x1
or(x1, x2)  =  or
T  =  T
F  =  F
and(x1, x2)  =  and(x1, x2)
imp(x1, x2)  =  imp(x1, x2)
not(x1)  =  x1
if(x1, x2, x3)  =  if(x2, x3)
eq(x1, x2)  =  x1
eqt(x1, x2)  =  eqt(x1)
nil  =  nil
undefined  =  undefined
int(x1)  =  int
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)  =  x2
s(x1)  =  s
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)
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)  =  locker2_claim_lock
locker2_map_add_pending(x1, x2, x3)  =  locker2_map_add_pending(x1, x2, x3)
case0(x1, x2, x3)  =  case0(x2, x3)
locker2_remove_pending(x1, x2)  =  locker2_remove_pending(x1)
subtract(x1, x2)  =  x1
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(x1)
append(x1, x2)  =  x1
locker2_release_lock(x1, x2)  =  locker2_release_lock(x1, x2)
case2(x1, x2, x3)  =  case2(x1, x2, x3)
gen_modtageq(x1, x2)  =  gen_modtageq(x1, x2)
excllock  =  excllock
case4(x1, x2, x3)  =  case4
locker2_obtainables(x1, x2)  =  locker2_obtainables
case5(x1, x2, x3, x4)  =  case5
andt(x1, x2)  =  x2
locker2_obtainable(x1, x2)  =  locker2_obtainable(x1, x2)
locker2_check_available(x1, x2)  =  locker2_check_available
case6(x1, x2, x3, x4)  =  case6
equal(x1, x2)  =  x2
locker2_check_availables(x1, x2)  =  locker2_check_availables(x1)
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)  =  case9(x3)
eqs(x1, x2)  =  eqs(x1, x2)
empty  =  empty
stack(x1, x2)  =  stack(x1, x2)
pushs(x1, x2)  =  pushs(x1, x2)
pops(x1)  =  pops(x1)
tops(x1)  =  x1
istops(x1, x2)  =  istops(x1)
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)

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

or > [T, F, eqt₁, istops₁] > and₂
or > [T, F, eqt₁, istops₁] > calls₃
[undefined, record_new1] > [nil, locker2_{checkavailable}, case6] > [false, case4]
[undefined, record_new1] > [nil, locker2_{checkavailable}, case6] > lock > tuple₂
[undefined, record_new1] > [nil, locker2_{checkavailable}, case6] > pending
[undefined, record_new1] > mcrlrecord > [T, F, eqt₁, istops₁] > and₂
[undefined, record_new1] > mcrlrecord > [T, F, eqt₁, istops₁] > calls₃
[undefined, record_new1] > mcrlrecord > lock > tuple₂
int > [T, F, eqt₁, istops₁] > and₂
int > [T, F, eqt₁, istops₁] > calls₃
int > s
a > [T, F, eqt₁, istops₁] > and₂
a > [T, F, eqt₁, istops₁] > calls₃
locker > [T, F, eqt₁, istops₁] > and₂
locker > [T, F, eqt₁, istops₁] > calls₃
ok > [T, F, eqt₁, istops₁] > and₂
ok > [T, F, eqt₁, istops₁] > calls₃
release > [T, F, eqt₁, istops₁] > and₂
release > [T, F, eqt₁, istops₁] > calls₃
locker2_{mappromotepending1} > locker2_{promotepending1} > record_extract3 > lock > tuple₂
locker2_{mappromotepending1} > locker2_{promotepending1} > case0₂ > [nil, locker2_{checkavailable}, case6] > [false, case4]
locker2_{mappromotepending1} > locker2_{promotepending1} > case0₂ > [nil, locker2_{checkavailable}, case6] > lock > tuple₂
locker2_{mappromotepending1} > locker2_{promotepending1} > case0₂ > [nil, locker2_{checkavailable}, case6] > pending
locker2_{mappromotepending1} > locker2_{promotepending1} > case0₂ > excl
locker2_{mappromotepending1} > locker2_{promotepending1} > case0₂ > record_updates3 > [cons₂, record_update4, case8₂] > tuple₂
locker2_{mappromotepending1} > locker2_{promotepending1} > case0₂ > record_updates3 > [cons₂, record_update4, case8₂] > pending
locker2_{mapclaimlock3} > [cons₂, record_update4, case8₂] > tuple₂
locker2_{mapclaimlock3} > [cons₂, record_update4, case8₂] > pending
locker2_{mapclaimlock3} > [nil, locker2_{checkavailable}, case6] > [false, case4]
locker2_{mapclaimlock3} > [nil, locker2_{checkavailable}, case6] > lock > tuple₂
locker2_{mapclaimlock3} > [nil, locker2_{checkavailable}, case6] > pending
locker2_{mapclaimlock3} > locker2_claimlock
locker2_{mapaddpending3} > [nil, locker2_{checkavailable}, case6] > [false, case4]
locker2_{mapaddpending3} > [nil, locker2_{checkavailable}, case6] > lock > tuple₂
locker2_{mapaddpending3} > [nil, locker2_{checkavailable}, case6] > pending
locker2_{removepending1} > [nil, locker2_{checkavailable}, case6] > [false, case4]
locker2_{removepending1} > [nil, locker2_{checkavailable}, case6] > lock > tuple₂
locker2_{removepending1} > [nil, locker2_{checkavailable}, case6] > pending
locker2_{removepending1} > record_extract3 > lock > tuple₂
locker2_{removepending1} > record_updates3 > [cons₂, record_update4, case8₂] > tuple₂
locker2_{removepending1} > record_updates3 > [cons₂, record_update4, case8₂] > pending
[locker2_addpending3, case1₃] > [nil, locker2_{checkavailable}, case6] > [false, case4]
[locker2_addpending3, case1₃] > [nil, locker2_{checkavailable}, case6] > lock > tuple₂
[locker2_addpending3, case1₃] > [nil, locker2_{checkavailable}, case6] > pending
[locker2_addpending3, case1₃] > resource > [T, F, eqt₁, istops₁] > and₂
[locker2_addpending3, case1₃] > resource > [T, F, eqt₁, istops₁] > calls₃
[locker2_addpending3, case1₃] > resource > lock > tuple₂
[locker2_addpending3, case1₃] > record_extract3 > lock > tuple₂
[locker2_addpending3, case1₃] > record_updates3 > [cons₂, record_update4, case8₂] > tuple₂
[locker2_addpending3, case1₃] > record_updates3 > [cons₂, record_update4, case8₂] > pending
locker2_releaselock2 > record_extract3 > lock > tuple₂
locker2_releaselock2 > case2₃ > [nil, locker2_{checkavailable}, case6] > [false, case4]
locker2_releaselock2 > case2₃ > [nil, locker2_{checkavailable}, case6] > lock > tuple₂
locker2_releaselock2 > case2₃ > [nil, locker2_{checkavailable}, case6] > pending
locker2_releaselock2 > case2₃ > excl
locker2_releaselock2 > case2₃ > record_updates3 > [cons₂, record_update4, case8₂] > tuple₂
locker2_releaselock2 > case2₃ > record_updates3 > [cons₂, record_update4, case8₂] > pending
locker2_releaselock2 > gen_modtageq2
[locker2_obtainables, case5] > [member₁, case9₁] > [true, locker2_{checkavailables1}] > [T, F, eqt₁, istops₁] > and₂
[locker2_obtainables, case5] > [member₁, case9₁] > [true, locker2_{checkavailables1}] > [T, F, eqt₁, istops₁] > calls₃
[locker2_obtainables, case5] > [member₁, case9₁] > [true, locker2_{checkavailables1}] > [nil, locker2_{checkavailable}, case6] > [false, case4]
[locker2_obtainables, case5] > [member₁, case9₁] > [true, locker2_{checkavailables1}] > [nil, locker2_{checkavailable}, case6] > lock > tuple₂
[locker2_obtainables, case5] > [member₁, case9₁] > [true, locker2_{checkavailables1}] > [nil, locker2_{checkavailable}, case6] > pending
[locker2_obtainables, case5] > [member₁, case9₁] > [true, locker2_{checkavailables1}] > excl
[locker2_obtainables, case5] > [member₁, case9₁] > [true, locker2_{checkavailables1}] > record_extract3 > lock > tuple₂
[locker2_obtainables, case5] > [member₁, case9₁] > [true, locker2_{checkavailables1}] > record_updates3 > [cons₂, record_update4, case8₂] > tuple₂
[locker2_obtainables, case5] > [member₁, case9₁] > [true, locker2_{checkavailables1}] > record_updates3 > [cons₂, record_update4, case8₂] > pending
[locker2_obtainables, case5] > [member₁, case9₁] > [true, locker2_{checkavailables1}] > excllock
[locker2_obtainables, case5] > [member₁, case9₁] > [true, locker2_{checkavailables1}] > locker2_obtainable2
gen_tag1 > tuple₂
gen_tag1 > tag
[eqs₂, eqc₂] > [T, F, eqt₁, istops₁] > and₂
[eqs₂, eqc₂] > [T, F, eqt₁, istops₁] > calls₃
push₃ > nocalls > empty > [T, F, eqt₁, istops₁] > and₂
push₃ > nocalls > empty > [T, F, eqt₁, istops₁] > calls₃
push₃ > nocalls > stack₂ > [T, F, eqt₁, istops₁] > and₂
push₃ > nocalls > stack₂ > [T, F, eqt₁, istops₁] > calls₃
push₃ > push1₅ > pushs₂ > stack₂ > [T, F, eqt₁, istops₁] > and₂
push₃ > push1₅ > pushs₂ > stack₂ > [T, F, eqt₁, istops₁] > calls₃

Status:

pops₁: [1]
locker2_{checkavailables1}: [1]
locker2_claimlock: []
push₃: [2,1,3]
case9₁: [1]
gen_modtageq2: [1,2]
case6: []
gen_tag1: [1]
pushs₂: [1,2]
record_new1: [1]
excllock: []
nil: []
locker2_releaselock2: [1,2]
locker2_adduniq1: [1]
member₁: [1]
T: []
locker2_addpending3: [3,1,2]
or: []
resource: []
locker: []
true: []
empty: []
eqc₂: [2,1]
locker2_obtainable2: [2,1]
push1₅: [2,4,3,5,1]
case2₃: [3,1,2]
case5: []
ok: []
F: []
lock: []
locker2_{mappromotepending1}: [1]
locker2_{removepending1}: [1]
case8₂: [1,2]
case0₂: [1,2]
calls₃: [3,2,1]
eqt₁: [1]
eqs₂: [2,1]
and₂: [2,1]
stack₂: [1,2]
pending: []
istops₁: [1]
locker2_{promotepending1}: [1]
locker2_{mapclaimlock3}: [3,1,2]
record_update4: [4,3,1,2]
case1₃: [1,3,2]
undefined: []
tag: []
mcrlrecord: []
a: []
request: []
if₂: [1,2]
excl: []
int: []
record_updates3: [2,3,1]
nocalls: []
s: []
0: []
cons₂: [2,1]
locker2_{mapaddpending3}: [3,1,2]
locker2_{checkavailable}: []
record_extract3: [2,3,1]
release: []
false: []
tuple₂: [2,1]
imp₂: [2,1]
case4: []
locker2_obtainables: []

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(pid(N1), pid(N2)) → EQT(N1, N2)
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(pid(N1), pid(N2)) → EQT(N1, N2)

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
EQT(x1, x2)  =  EQT(x1)
pid(x1)  =  pid(x1)
tuplenil(x1)  =  x1
or(x1, x2)  =  or
T  =  T
F  =  F
and(x1, x2)  =  and(x1, x2)
imp(x1, x2)  =  imp(x1, x2)
not(x1)  =  not
if(x1, x2, x3)  =  if(x2, x3)
eq(x1, x2)  =  eq(x1, x2)
eqt(x1, x2)  =  eqt(x1)
nil  =  nil
undefined  =  undefined
int(x1)  =  int
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)  =  x2
s(x1)  =  s
0  =  0
record_new(x1)  =  record_new
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, x2, x3)
locker2_claim_lock(x1, x2, x3)  =  locker2_claim_lock(x1, x2)
locker2_map_add_pending(x1, x2, x3)  =  locker2_map_add_pending(x1, x2, x3)
case0(x1, x2, x3)  =  case0(x1, x2, x3)
locker2_remove_pending(x1, x2)  =  locker2_remove_pending(x1, x2)
subtract(x1, x2)  =  x1
locker2_add_pending(x1, x2, x3)  =  locker2_add_pending(x1)
case1(x1, x2, x3, x4)  =  case1(x3)
member(x1, x2)  =  member
append(x1, x2)  =  x1
locker2_release_lock(x1, x2)  =  locker2_release_lock(x1, x2)
case2(x1, x2, x3)  =  case2(x2, x3)
gen_modtageq(x1, x2)  =  gen_modtageq(x1, x2)
excllock  =  excllock
case4(x1, x2, x3)  =  case4
locker2_obtainables(x1, x2)  =  locker2_obtainables(x1)
case5(x1, x2, x3, x4)  =  case5(x2)
andt(x1, x2)  =  x2
locker2_obtainable(x1, x2)  =  locker2_obtainable(x1, x2)
locker2_check_available(x1, x2)  =  locker2_check_available(x1, x2)
case6(x1, x2, x3, x4)  =  case6(x1, x3)
equal(x1, x2)  =  equal
locker2_check_availables(x1, x2)  =  locker2_check_availables
locker2_adduniq(x1, x2)  =  locker2_adduniq(x1, 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(x1, x2)
empty  =  empty
stack(x1, x2)  =  stack(x1, x2)
pushs(x1, x2)  =  pushs(x1, x2)
pops(x1)  =  pops(x1)
tops(x1)  =  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:

or > [F, not] > [T, true, excllock] > [cons₂, case8₂] > nil
or > [F, not] > [T, true, excllock] > [cons₂, case8₂] > pending
or > [F, not] > [T, true, excllock] > [cons₂, case8₂] > resource > [lock, mcrlrecord]
or > [F, not] > [T, true, excllock] > [cons₂, case8₂] > record_extract3 > tuple₂ > [lock, mcrlrecord]
or > [F, not] > [T, true, excllock] > [cons₂, case8₂] > record_updates3 > record_update4 > tuple₂ > [lock, mcrlrecord]
or > [F, not] > [T, true, excllock] > excl
imp₂ > [T, true, excllock] > [cons₂, case8₂] > nil
imp₂ > [T, true, excllock] > [cons₂, case8₂] > pending
imp₂ > [T, true, excllock] > [cons₂, case8₂] > resource > [lock, mcrlrecord]
imp₂ > [T, true, excllock] > [cons₂, case8₂] > record_extract3 > tuple₂ > [lock, mcrlrecord]
imp₂ > [T, true, excllock] > [cons₂, case8₂] > record_updates3 > record_update4 > tuple₂ > [lock, mcrlrecord]
imp₂ > [T, true, excllock] > excl
eq₂ > [F, not] > [T, true, excllock] > [cons₂, case8₂] > nil
eq₂ > [F, not] > [T, true, excllock] > [cons₂, case8₂] > pending
eq₂ > [F, not] > [T, true, excllock] > [cons₂, case8₂] > resource > [lock, mcrlrecord]
eq₂ > [F, not] > [T, true, excllock] > [cons₂, case8₂] > record_extract3 > tuple₂ > [lock, mcrlrecord]
eq₂ > [F, not] > [T, true, excllock] > [cons₂, case8₂] > record_updates3 > record_update4 > tuple₂ > [lock, mcrlrecord]
eq₂ > [F, not] > [T, true, excllock] > excl
locker > [F, not] > [T, true, excllock] > [cons₂, case8₂] > nil
locker > [F, not] > [T, true, excllock] > [cons₂, case8₂] > pending
locker > [F, not] > [T, true, excllock] > [cons₂, case8₂] > resource > [lock, mcrlrecord]
locker > [F, not] > [T, true, excllock] > [cons₂, case8₂] > record_extract3 > tuple₂ > [lock, mcrlrecord]
locker > [F, not] > [T, true, excllock] > [cons₂, case8₂] > record_updates3 > record_update4 > tuple₂ > [lock, mcrlrecord]
locker > [F, not] > [T, true, excllock] > excl
request > [F, not] > [T, true, excllock] > [cons₂, case8₂] > nil
request > [F, not] > [T, true, excllock] > [cons₂, case8₂] > pending
request > [F, not] > [T, true, excllock] > [cons₂, case8₂] > resource > [lock, mcrlrecord]
request > [F, not] > [T, true, excllock] > [cons₂, case8₂] > record_extract3 > tuple₂ > [lock, mcrlrecord]
request > [F, not] > [T, true, excllock] > [cons₂, case8₂] > record_updates3 > record_update4 > tuple₂ > [lock, mcrlrecord]
request > [F, not] > [T, true, excllock] > excl
s > int
record_new > nil
record_new > undefined
record_new > tuple₂ > [lock, mcrlrecord]
[locker2_{mappromotepending2}, locker2_{promotepending2}] > case0₃ > [cons₂, case8₂] > nil
[locker2_{mappromotepending2}, locker2_{promotepending2}] > case0₃ > [cons₂, case8₂] > pending
[locker2_{mappromotepending2}, locker2_{promotepending2}] > case0₃ > [cons₂, case8₂] > resource > [lock, mcrlrecord]
[locker2_{mappromotepending2}, locker2_{promotepending2}] > case0₃ > [cons₂, case8₂] > record_extract3 > tuple₂ > [lock, mcrlrecord]
[locker2_{mappromotepending2}, locker2_{promotepending2}] > case0₃ > [cons₂, case8₂] > record_updates3 > record_update4 > tuple₂ > [lock, mcrlrecord]
[locker2_{mappromotepending2}, locker2_{promotepending2}] > case0₃ > excl
locker2_{mapclaimlock3} > [cons₂, case8₂] > nil
locker2_{mapclaimlock3} > [cons₂, case8₂] > pending
locker2_{mapclaimlock3} > [cons₂, case8₂] > resource > [lock, mcrlrecord]
locker2_{mapclaimlock3} > [cons₂, case8₂] > record_extract3 > tuple₂ > [lock, mcrlrecord]
locker2_{mapclaimlock3} > [cons₂, case8₂] > record_updates3 > record_update4 > tuple₂ > [lock, mcrlrecord]
locker2_{mapclaimlock3} > locker2_claimlock2
locker2_{mapaddpending3} > nil
locker2_{removepending2} > [cons₂, case8₂] > nil
locker2_{removepending2} > [cons₂, case8₂] > pending
locker2_{removepending2} > [cons₂, case8₂] > resource > [lock, mcrlrecord]
locker2_{removepending2} > [cons₂, case8₂] > record_extract3 > tuple₂ > [lock, mcrlrecord]
locker2_{removepending2} > [cons₂, case8₂] > record_updates3 > record_update4 > tuple₂ > [lock, mcrlrecord]
locker2_addpending1 > case1₁ > [cons₂, case8₂] > nil
locker2_addpending1 > case1₁ > [cons₂, case8₂] > pending
locker2_addpending1 > case1₁ > [cons₂, case8₂] > resource > [lock, mcrlrecord]
locker2_addpending1 > case1₁ > [cons₂, case8₂] > record_extract3 > tuple₂ > [lock, mcrlrecord]
locker2_addpending1 > case1₁ > [cons₂, case8₂] > record_updates3 > record_update4 > tuple₂ > [lock, mcrlrecord]
locker2_releaselock2 > case2₂ > [cons₂, case8₂] > nil
locker2_releaselock2 > case2₂ > [cons₂, case8₂] > pending
locker2_releaselock2 > case2₂ > [cons₂, case8₂] > resource > [lock, mcrlrecord]
locker2_releaselock2 > case2₂ > [cons₂, case8₂] > record_extract3 > tuple₂ > [lock, mcrlrecord]
locker2_releaselock2 > case2₂ > [cons₂, case8₂] > record_updates3 > record_update4 > tuple₂ > [lock, mcrlrecord]
locker2_releaselock2 > gen_modtageq2 > [false, member, equal] > [locker2_obtainables1, case5₁] > [T, true, excllock] > [cons₂, case8₂] > nil
locker2_releaselock2 > gen_modtageq2 > [false, member, equal] > [locker2_obtainables1, case5₁] > [T, true, excllock] > [cons₂, case8₂] > pending
locker2_releaselock2 > gen_modtageq2 > [false, member, equal] > [locker2_obtainables1, case5₁] > [T, true, excllock] > [cons₂, case8₂] > resource > [lock, mcrlrecord]
locker2_releaselock2 > gen_modtageq2 > [false, member, equal] > [locker2_obtainables1, case5₁] > [T, true, excllock] > [cons₂, case8₂] > record_extract3 > tuple₂ > [lock, mcrlrecord]
locker2_releaselock2 > gen_modtageq2 > [false, member, equal] > [locker2_obtainables1, case5₁] > [T, true, excllock] > [cons₂, case8₂] > record_updates3 > record_update4 > tuple₂ > [lock, mcrlrecord]
locker2_releaselock2 > gen_modtageq2 > [false, member, equal] > [locker2_obtainables1, case5₁] > [T, true, excllock] > excl
case4 > [false, member, equal] > [locker2_obtainables1, case5₁] > [T, true, excllock] > [cons₂, case8₂] > nil
case4 > [false, member, equal] > [locker2_obtainables1, case5₁] > [T, true, excllock] > [cons₂, case8₂] > pending
case4 > [false, member, equal] > [locker2_obtainables1, case5₁] > [T, true, excllock] > [cons₂, case8₂] > resource > [lock, mcrlrecord]
case4 > [false, member, equal] > [locker2_obtainables1, case5₁] > [T, true, excllock] > [cons₂, case8₂] > record_extract3 > tuple₂ > [lock, mcrlrecord]
case4 > [false, member, equal] > [locker2_obtainables1, case5₁] > [T, true, excllock] > [cons₂, case8₂] > record_updates3 > record_update4 > tuple₂ > [lock, mcrlrecord]
case4 > [false, member, equal] > [locker2_obtainables1, case5₁] > [T, true, excllock] > excl
[locker2_{checkavailable2}, case6₂] > [false, member, equal] > [locker2_obtainables1, case5₁] > [T, true, excllock] > [cons₂, case8₂] > nil
[locker2_{checkavailable2}, case6₂] > [false, member, equal] > [locker2_obtainables1, case5₁] > [T, true, excllock] > [cons₂, case8₂] > pending
[locker2_{checkavailable2}, case6₂] > [false, member, equal] > [locker2_obtainables1, case5₁] > [T, true, excllock] > [cons₂, case8₂] > resource > [lock, mcrlrecord]
[locker2_{checkavailable2}, case6₂] > [false, member, equal] > [locker2_obtainables1, case5₁] > [T, true, excllock] > [cons₂, case8₂] > record_extract3 > tuple₂ > [lock, mcrlrecord]
[locker2_{checkavailable2}, case6₂] > [false, member, equal] > [locker2_obtainables1, case5₁] > [T, true, excllock] > [cons₂, case8₂] > record_updates3 > record_update4 > tuple₂ > [lock, mcrlrecord]
[locker2_{checkavailable2}, case6₂] > [false, member, equal] > [locker2_obtainables1, case5₁] > [T, true, excllock] > excl
locker2_{checkavailables} > [T, true, excllock] > [cons₂, case8₂] > nil
locker2_{checkavailables} > [T, true, excllock] > [cons₂, case8₂] > pending
locker2_{checkavailables} > [T, true, excllock] > [cons₂, case8₂] > resource > [lock, mcrlrecord]
locker2_{checkavailables} > [T, true, excllock] > [cons₂, case8₂] > record_extract3 > tuple₂ > [lock, mcrlrecord]
locker2_{checkavailables} > [T, true, excllock] > [cons₂, case8₂] > record_updates3 > record_update4 > tuple₂ > [lock, mcrlrecord]
locker2_{checkavailables} > [T, true, excllock] > excl
gen_tag1 > tag > [T, true, excllock] > [cons₂, case8₂] > nil
gen_tag1 > tag > [T, true, excllock] > [cons₂, case8₂] > pending
gen_tag1 > tag > [T, true, excllock] > [cons₂, case8₂] > resource > [lock, mcrlrecord]
gen_tag1 > tag > [T, true, excllock] > [cons₂, case8₂] > record_extract3 > tuple₂ > [lock, mcrlrecord]
gen_tag1 > tag > [T, true, excllock] > [cons₂, case8₂] > record_updates3 > record_update4 > tuple₂ > [lock, mcrlrecord]
gen_tag1 > tag > [T, true, excllock] > excl
[eqs₂, eqc₂] > [eqt₁, empty, istops₂, nocalls, push₃] > and₂ > [F, not] > [T, true, excllock] > [cons₂, case8₂] > nil
[eqs₂, eqc₂] > [eqt₁, empty, istops₂, nocalls, push₃] > and₂ > [F, not] > [T, true, excllock] > [cons₂, case8₂] > pending
[eqs₂, eqc₂] > [eqt₁, empty, istops₂, nocalls, push₃] > and₂ > [F, not] > [T, true, excllock] > [cons₂, case8₂] > resource > [lock, mcrlrecord]
[eqs₂, eqc₂] > [eqt₁, empty, istops₂, nocalls, push₃] > and₂ > [F, not] > [T, true, excllock] > [cons₂, case8₂] > record_extract3 > tuple₂ > [lock, mcrlrecord]
[eqs₂, eqc₂] > [eqt₁, empty, istops₂, nocalls, push₃] > and₂ > [F, not] > [T, true, excllock] > [cons₂, case8₂] > record_updates3 > record_update4 > tuple₂ > [lock, mcrlrecord]
[eqs₂, eqc₂] > [eqt₁, empty, istops₂, nocalls, push₃] > and₂ > [F, not] > [T, true, excllock] > excl
[eqs₂, eqc₂] > [eqt₁, empty, istops₂, nocalls, push₃] > push1₆ > pushs₂ > stack₂
[eqs₂, eqc₂] > [eqt₁, empty, istops₂, nocalls, push₃] > push1₆ > calls₃ > [F, not] > [T, true, excllock] > [cons₂, case8₂] > nil
[eqs₂, eqc₂] > [eqt₁, empty, istops₂, nocalls, push₃] > push1₆ > calls₃ > [F, not] > [T, true, excllock] > [cons₂, case8₂] > pending
[eqs₂, eqc₂] > [eqt₁, empty, istops₂, nocalls, push₃] > push1₆ > calls₃ > [F, not] > [T, true, excllock] > [cons₂, case8₂] > resource > [lock, mcrlrecord]
[eqs₂, eqc₂] > [eqt₁, empty, istops₂, nocalls, push₃] > push1₆ > calls₃ > [F, not] > [T, true, excllock] > [cons₂, case8₂] > record_extract3 > tuple₂ > [lock, mcrlrecord]
[eqs₂, eqc₂] > [eqt₁, empty, istops₂, nocalls, push₃] > push1₆ > calls₃ > [F, not] > [T, true, excllock] > [cons₂, case8₂] > record_updates3 > record_update4 > tuple₂ > [lock, mcrlrecord]
[eqs₂, eqc₂] > [eqt₁, empty, istops₂, nocalls, push₃] > push1₆ > calls₃ > [F, not] > [T, true, excllock] > excl

Status:

pops₁: [1]
eq₂: [2,1]
case2₂: [2,1]
push₃: [1,3,2]
locker2_{removepending2}: [2,1]
locker2_{mappromotepending2}: [2,1]
gen_modtageq2: [2,1]
gen_tag1: [1]
pushs₂: [1,2]
locker2_{checkavailables}: []
locker2_{checkavailable2}: [1,2]
excllock: []
nil: []
locker2_releaselock2: [1,2]
T: []
EQT₁: [1]
or: []
resource: []
locker: []
true: []
record_new: []
empty: []
eqc₂: [1,2]
push1₆: [4,2,5,6,1,3]
member: []
locker2_obtainables1: [1]
locker2_obtainable2: [1,2]
pid₁: [1]
ok: []
F: []
lock: []
locker2_addpending1: [1]
case8₂: [1,2]
equal: []
calls₃: [2,1,3]
not: []
eqt₁: [1]
eqs₂: [1,2]
and₂: [2,1]
stack₂: [1,2]
pending: []
istops₂: [1,2]
locker2_{mapclaimlock3}: [1,2,3]
record_update4: [1,2,3,4]
undefined: []
tag: []
mcrlrecord: []
a: []
request: []
if₂: [1,2]
locker2_claimlock2: [1,2]
excl: []
int: []
record_updates3: [3,2,1]
locker2_{promotepending2}: [2,1]
nocalls: []
s: []
case5₁: [1]
0: []
cons₂: [2,1]
locker2_{mapaddpending3}: [3,2,1]
record_extract3: [1,2,3]
case6₂: [2,1]
release: []
case0₃: [3,1,2]
false: []
case1₁: [1]
imp₂: [1,2]
tuple₂: [2,1]
case4: []
locker2_adduniq2: [1,2]

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:
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.

(45) 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)  =  x2
T  =  T
F  =  F
and(x1, x2)  =  and(x1, x2)
imp(x1, x2)  =  x2
not(x1)  =  not
if(x1, x2, x3)  =  if(x1, x2, x3)
eq(x1, x2)  =  eq
eqt(x1, x2)  =  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)
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)  =  x2
s(x1)  =  x1
0  =  0
record_new(x1)  =  record_new
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)
locker2_promote_pending(x1, x2)  =  locker2_promote_pending(x1)
locker2_map_claim_lock(x1, x2, x3)  =  x1
locker2_claim_lock(x1, x2, x3)  =  locker2_claim_lock
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)
member(x1, x2)  =  member
append(x1, x2)  =  x1
locker2_release_lock(x1, x2)  =  locker2_release_lock(x1, x2)
case2(x1, x2, x3)  =  case2(x2)
gen_modtageq(x1, x2)  =  gen_modtageq(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)  =  x2
locker2_obtainable(x1, x2)  =  locker2_obtainable(x1, x2)
locker2_check_available(x1, x2)  =  locker2_check_available(x1, x2)
case6(x1, x2, x3, x4)  =  case6(x1, x2, x3)
equal(x1, x2)  =  x2
locker2_check_availables(x1, x2)  =  locker2_check_availables
locker2_adduniq(x1, x2)  =  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)  =  case9
eqs(x1, x2)  =  eqs(x1)
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)
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(x2, x3, x4, x5, x6)

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

not > [F, nil] > [T, locker2_claimlock, empty]
if₃ > [T, locker2_claimlock, empty]
eq > [F, nil] > [T, locker2_claimlock, empty]
pid₁ > [F, nil] > [T, locker2_claimlock, empty]
a > [F, nil] > [T, locker2_claimlock, empty]
locker > [F, nil] > [T, locker2_claimlock, empty]
ok > [F, nil] > [T, locker2_claimlock, empty]
release > [F, nil] > [T, locker2_claimlock, empty]
request > [F, nil] > [T, locker2_claimlock, empty]
[tag, gen_tag1] > tuple₂ > [and₂, cons₂, locker2_obtainables2, case5₂] > [false, member, locker2_{checkavailable2}, case6₃, case9] > [true, locker2_{checkavailables}] > [F, nil] > [T, locker2_claimlock, empty]
[tag, gen_tag1] > tuple₂ > [and₂, cons₂, locker2_obtainables2, case5₂] > [false, member, locker2_{checkavailable2}, case6₃, case9] > [true, locker2_{checkavailables}] > locker2_obtainable2 > [T, locker2_claimlock, empty]
[tag, gen_tag1] > tuple₂ > int₁ > [F, nil] > [T, locker2_claimlock, empty]
[tag, gen_tag1] > tuple₂ > lock > tuplenil₁ > [F, nil] > [T, locker2_claimlock, empty]
0 > [T, locker2_claimlock, empty]
record_new > undefined > [F, nil] > [T, locker2_claimlock, empty]
record_new > mcrlrecord > tuple₂ > [and₂, cons₂, locker2_obtainables2, case5₂] > [false, member, locker2_{checkavailable2}, case6₃, case9] > [true, locker2_{checkavailables}] > [F, nil] > [T, locker2_claimlock, empty]
record_new > mcrlrecord > tuple₂ > [and₂, cons₂, locker2_obtainables2, case5₂] > [false, member, locker2_{checkavailable2}, case6₃, case9] > [true, locker2_{checkavailables}] > locker2_obtainable2 > [T, locker2_claimlock, empty]
record_new > mcrlrecord > tuple₂ > int₁ > [F, nil] > [T, locker2_claimlock, empty]
record_new > mcrlrecord > tuple₂ > lock > tuplenil₁ > [F, nil] > [T, locker2_claimlock, empty]
locker2_{mappromotepending1} > locker2_{promotepending1} > [excl, pending, case0₂] > mcrlrecord > tuple₂ > [and₂, cons₂, locker2_obtainables2, case5₂] > [false, member, locker2_{checkavailable2}, case6₃, case9] > [true, locker2_{checkavailables}] > [F, nil] > [T, locker2_claimlock, empty]
locker2_{mappromotepending1} > locker2_{promotepending1} > [excl, pending, case0₂] > mcrlrecord > tuple₂ > [and₂, cons₂, locker2_obtainables2, case5₂] > [false, member, locker2_{checkavailable2}, case6₃, case9] > [true, locker2_{checkavailables}] > locker2_obtainable2 > [T, locker2_claimlock, empty]
locker2_{mappromotepending1} > locker2_{promotepending1} > [excl, pending, case0₂] > mcrlrecord > tuple₂ > int₁ > [F, nil] > [T, locker2_claimlock, empty]
locker2_{mappromotepending1} > locker2_{promotepending1} > [excl, pending, case0₂] > mcrlrecord > tuple₂ > lock > tuplenil₁ > [F, nil] > [T, locker2_claimlock, empty]
locker2_{mappromotepending1} > locker2_{promotepending1} > [excl, pending, case0₂] > record_updates3 > record_update4 > tuple₂ > [and₂, cons₂, locker2_obtainables2, case5₂] > [false, member, locker2_{checkavailable2}, case6₃, case9] > [true, locker2_{checkavailables}] > [F, nil] > [T, locker2_claimlock, empty]
locker2_{mappromotepending1} > locker2_{promotepending1} > [excl, pending, case0₂] > record_updates3 > record_update4 > tuple₂ > [and₂, cons₂, locker2_obtainables2, case5₂] > [false, member, locker2_{checkavailable2}, case6₃, case9] > [true, locker2_{checkavailables}] > locker2_obtainable2 > [T, locker2_claimlock, empty]
locker2_{mappromotepending1} > locker2_{promotepending1} > [excl, pending, case0₂] > record_updates3 > record_update4 > tuple₂ > int₁ > [F, nil] > [T, locker2_claimlock, empty]
locker2_{mappromotepending1} > locker2_{promotepending1} > [excl, pending, case0₂] > record_updates3 > record_update4 > tuple₂ > lock > tuplenil₁ > [F, nil] > [T, locker2_claimlock, empty]
locker2_{mappromotepending1} > locker2_{promotepending1} > record_extract3 > tuplenil₁ > [F, nil] > [T, locker2_claimlock, empty]
locker2_{mapaddpending} > [F, nil] > [T, locker2_claimlock, empty]
locker2_{removepending2} > [excl, pending, case0₂] > mcrlrecord > tuple₂ > [and₂, cons₂, locker2_obtainables2, case5₂] > [false, member, locker2_{checkavailable2}, case6₃, case9] > [true, locker2_{checkavailables}] > [F, nil] > [T, locker2_claimlock, empty]
locker2_{removepending2} > [excl, pending, case0₂] > mcrlrecord > tuple₂ > [and₂, cons₂, locker2_obtainables2, case5₂] > [false, member, locker2_{checkavailable2}, case6₃, case9] > [true, locker2_{checkavailables}] > locker2_obtainable2 > [T, locker2_claimlock, empty]
locker2_{removepending2} > [excl, pending, case0₂] > mcrlrecord > tuple₂ > int₁ > [F, nil] > [T, locker2_claimlock, empty]
locker2_{removepending2} > [excl, pending, case0₂] > mcrlrecord > tuple₂ > lock > tuplenil₁ > [F, nil] > [T, locker2_claimlock, empty]
locker2_{removepending2} > [excl, pending, case0₂] > record_updates3 > record_update4 > tuple₂ > [and₂, cons₂, locker2_obtainables2, case5₂] > [false, member, locker2_{checkavailable2}, case6₃, case9] > [true, locker2_{checkavailables}] > [F, nil] > [T, locker2_claimlock, empty]
locker2_{removepending2} > [excl, pending, case0₂] > record_updates3 > record_update4 > tuple₂ > [and₂, cons₂, locker2_obtainables2, case5₂] > [false, member, locker2_{checkavailable2}, case6₃, case9] > [true, locker2_{checkavailables}] > locker2_obtainable2 > [T, locker2_claimlock, empty]
locker2_{removepending2} > [excl, pending, case0₂] > record_updates3 > record_update4 > tuple₂ > int₁ > [F, nil] > [T, locker2_claimlock, empty]
locker2_{removepending2} > [excl, pending, case0₂] > record_updates3 > record_update4 > tuple₂ > lock > tuplenil₁ > [F, nil] > [T, locker2_claimlock, empty]
locker2_{removepending2} > record_extract3 > tuplenil₁ > [F, nil] > [T, locker2_claimlock, empty]
locker2_{removepending2} > subtract₂ > [delete₂, case8₄] > [and₂, cons₂, locker2_obtainables2, case5₂] > [false, member, locker2_{checkavailable2}, case6₃, case9] > [true, locker2_{checkavailables}] > [F, nil] > [T, locker2_claimlock, empty]
locker2_{removepending2} > subtract₂ > [delete₂, case8₄] > [and₂, cons₂, locker2_obtainables2, case5₂] > [false, member, locker2_{checkavailable2}, case6₃, case9] > [true, locker2_{checkavailables}] > locker2_obtainable2 > [T, locker2_claimlock, empty]
[locker2_addpending1, case1₁] > [excl, pending, case0₂] > mcrlrecord > tuple₂ > [and₂, cons₂, locker2_obtainables2, case5₂] > [false, member, locker2_{checkavailable2}, case6₃, case9] > [true, locker2_{checkavailables}] > [F, nil] > [T, locker2_claimlock, empty]
[locker2_addpending1, case1₁] > [excl, pending, case0₂] > mcrlrecord > tuple₂ > [and₂, cons₂, locker2_obtainables2, case5₂] > [false, member, locker2_{checkavailable2}, case6₃, case9] > [true, locker2_{checkavailables}] > locker2_obtainable2 > [T, locker2_claimlock, empty]
[locker2_addpending1, case1₁] > [excl, pending, case0₂] > mcrlrecord > tuple₂ > int₁ > [F, nil] > [T, locker2_claimlock, empty]
[locker2_addpending1, case1₁] > [excl, pending, case0₂] > mcrlrecord > tuple₂ > lock > tuplenil₁ > [F, nil] > [T, locker2_claimlock, empty]
[locker2_addpending1, case1₁] > [excl, pending, case0₂] > record_updates3 > record_update4 > tuple₂ > [and₂, cons₂, locker2_obtainables2, case5₂] > [false, member, locker2_{checkavailable2}, case6₃, case9] > [true, locker2_{checkavailables}] > [F, nil] > [T, locker2_claimlock, empty]
[locker2_addpending1, case1₁] > [excl, pending, case0₂] > record_updates3 > record_update4 > tuple₂ > [and₂, cons₂, locker2_obtainables2, case5₂] > [false, member, locker2_{checkavailable2}, case6₃, case9] > [true, locker2_{checkavailables}] > locker2_obtainable2 > [T, locker2_claimlock, empty]
[locker2_addpending1, case1₁] > [excl, pending, case0₂] > record_updates3 > record_update4 > tuple₂ > int₁ > [F, nil] > [T, locker2_claimlock, empty]
[locker2_addpending1, case1₁] > [excl, pending, case0₂] > record_updates3 > record_update4 > tuple₂ > lock > tuplenil₁ > [F, nil] > [T, locker2_claimlock, empty]
[locker2_addpending1, case1₁] > resource > lock > tuplenil₁ > [F, nil] > [T, locker2_claimlock, empty]
[locker2_addpending1, case1₁] > record_extract3 > tuplenil₁ > [F, nil] > [T, locker2_claimlock, empty]
[locker2_releaselock2, case2₁] > [excl, pending, case0₂] > mcrlrecord > tuple₂ > [and₂, cons₂, locker2_obtainables2, case5₂] > [false, member, locker2_{checkavailable2}, case6₃, case9] > [true, locker2_{checkavailables}] > [F, nil] > [T, locker2_claimlock, empty]
[locker2_releaselock2, case2₁] > [excl, pending, case0₂] > mcrlrecord > tuple₂ > [and₂, cons₂, locker2_obtainables2, case5₂] > [false, member, locker2_{checkavailable2}, case6₃, case9] > [true, locker2_{checkavailables}] > locker2_obtainable2 > [T, locker2_claimlock, empty]
[locker2_releaselock2, case2₁] > [excl, pending, case0₂] > mcrlrecord > tuple₂ > int₁ > [F, nil] > [T, locker2_claimlock, empty]
[locker2_releaselock2, case2₁] > [excl, pending, case0₂] > mcrlrecord > tuple₂ > lock > tuplenil₁ > [F, nil] > [T, locker2_claimlock, empty]
[locker2_releaselock2, case2₁] > [excl, pending, case0₂] > record_updates3 > record_update4 > tuple₂ > [and₂, cons₂, locker2_obtainables2, case5₂] > [false, member, locker2_{checkavailable2}, case6₃, case9] > [true, locker2_{checkavailables}] > [F, nil] > [T, locker2_claimlock, empty]
[locker2_releaselock2, case2₁] > [excl, pending, case0₂] > record_updates3 > record_update4 > tuple₂ > [and₂, cons₂, locker2_obtainables2, case5₂] > [false, member, locker2_{checkavailable2}, case6₃, case9] > [true, locker2_{checkavailables}] > locker2_obtainable2 > [T, locker2_claimlock, empty]
[locker2_releaselock2, case2₁] > [excl, pending, case0₂] > record_updates3 > record_update4 > tuple₂ > int₁ > [F, nil] > [T, locker2_claimlock, empty]
[locker2_releaselock2, case2₁] > [excl, pending, case0₂] > record_updates3 > record_update4 > tuple₂ > lock > tuplenil₁ > [F, nil] > [T, locker2_claimlock, empty]
[locker2_releaselock2, case2₁] > record_extract3 > tuplenil₁ > [F, nil] > [T, locker2_claimlock, empty]
[locker2_releaselock2, case2₁] > gen_modtageq1 > [T, locker2_claimlock, empty]
[locker2_releaselock2, case2₁] > excllock > [T, locker2_claimlock, empty]
case4 > [false, member, locker2_{checkavailable2}, case6₃, case9] > [true, locker2_{checkavailables}] > [F, nil] > [T, locker2_claimlock, empty]
case4 > [false, member, locker2_{checkavailable2}, case6₃, case9] > [true, locker2_{checkavailables}] > locker2_obtainable2 > [T, locker2_claimlock, empty]
pops₁ > [T, locker2_claimlock, empty]
tops₁ > [T, locker2_claimlock, empty]
istops₁ > [F, nil] > [T, locker2_claimlock, empty]
eqc₂ > eqs₁ > [and₂, cons₂, locker2_obtainables2, case5₂] > [false, member, locker2_{checkavailable2}, case6₃, case9] > [true, locker2_{checkavailables}] > [F, nil] > [T, locker2_claimlock, empty]
eqc₂ > eqs₁ > [and₂, cons₂, locker2_obtainables2, case5₂] > [false, member, locker2_{checkavailable2}, case6₃, case9] > [true, locker2_{checkavailables}] > locker2_obtainable2 > [T, locker2_claimlock, empty]
nocalls > stack₂ > [F, nil] > [T, locker2_claimlock, empty]
nocalls > calls₃ > [F, nil] > [T, locker2_claimlock, empty]
push₃ > push1₅ > pushs₂ > stack₂ > [F, nil] > [T, locker2_claimlock, empty]
push₃ > push1₅ > calls₃ > [F, nil] > [T, locker2_claimlock, empty]

Status:

pops₁: [1]
case8₄: [3,1,4,2]
locker2_claimlock: []
push₃: [1,2,3]
delete₂: [1,2]
locker2_{removepending2}: [2,1]
gen_tag1: [1]
pushs₂: [1,2]
locker2_{checkavailables}: []
locker2_{checkavailable2}: [1,2]
excllock: []
nil: []
locker2_releaselock2: [1,2]
locker2_obtainables2: [2,1]
locker2_{mapaddpending}: []
gen_modtageq1: [1]
T: []
resource: []
locker: []
true: []
record_new: []
empty: []
eqc₂: [2,1]
member: []
locker2_obtainable2: [2,1]
push1₅: [3,5,2,4,1]
pid₁: [1]
ok: []
case9: []
F: []
lock: []
locker2_{mappromotepending1}: [1]
tops₁: [1]
locker2_addpending1: [1]
case0₂: [1,2]
case6₃: [3,1,2]
calls₃: [2,3,1]
tuplenil₁: [1]
not: []
and₂: [2,1]
stack₂: [2,1]
if₃: [1,2,3]
pending: []
istops₁: [1]
case2₁: [1]
int₁: [1]
locker2_{promotepending1}: [1]
record_update4: [3,2,1,4]
case5₂: [1,2]
undefined: []
tag: []
eq: []
mcrlrecord: []
a: []
request: []
excl: []
subtract₂: [2,1]
record_updates3: [3,1,2]
nocalls: []
0: []
cons₂: [2,1]
record_extract3: [2,3,1]
release: []
eqs₁: [1]
false: []
case1₁: [1]
tuple₂: [2,1]
case4: []

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)

(46) 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.

(47) PisEmptyProof (EQUIVALENT transformation)

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

(48) TRUE

(49) 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.

(50) 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)  =  x2
stack(x1, x2)  =  stack(x1, x2)
or(x1, x2)  =  or
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)  =  x2
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)  =  x1
0  =  0
record_new(x1)  =  record_new
record_extract(x1, x2, x3)  =  record_extract(x1)
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, x2, x3)
locker2_claim_lock(x1, x2, x3)  =  locker2_claim_lock(x1, x3)
locker2_map_add_pending(x1, x2, x3)  =  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(x1, x3)
member(x1, x2)  =  member(x1, x2)
append(x1, x2)  =  x1
locker2_release_lock(x1, x2)  =  locker2_release_lock(x1, x2)
case2(x1, x2, x3)  =  case2(x1, x2, x3)
gen_modtageq(x1, x2)  =  gen_modtageq(x1, x2)
excllock  =  excllock
case4(x1, x2, x3)  =  case4(x1, x2, x3)
locker2_obtainables(x1, x2)  =  locker2_obtainables(x1, x2)
case5(x1, x2, x3, x4)  =  case5(x1, x2, x3, x4)
andt(x1, x2)  =  andt(x2)
locker2_obtainable(x1, x2)  =  x2
locker2_check_available(x1, x2)  =  locker2_check_available(x1, x2)
case6(x1, x2, x3, x4)  =  case6(x1, x3)
equal(x1, x2)  =  x2
locker2_check_availables(x1, x2)  =  x1
locker2_adduniq(x1, x2)  =  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)  =  case9(x1, x2, x3, 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:

imp₁ > [or, T, F, locker, empty, nocalls] > [excl, andt₁]
not₁ > [excl, andt₁]
if₂ > [excl, andt₁]
pid₁ > [excl, andt₁]
a > [or, T, F, locker, empty, nocalls] > [excl, andt₁]
ok > [excl, andt₁]
release > [excl, andt₁]
request > [excl, andt₁]
element₂ > int₁ > [excl, andt₁]
0 > [excl, andt₁]
record_new > undefined > [excl, andt₁]
record_new > lock > [nil, cons₂, true] > [excl, andt₁]
record_new > lock > mcrlrecord > tuple₂ > [excl, andt₁]
[locker2_{mappromotepending2}, locker2_{promotepending2}] > lock > [nil, cons₂, true] > [excl, andt₁]
[locker2_{mappromotepending2}, locker2_{promotepending2}] > lock > mcrlrecord > tuple₂ > [excl, andt₁]
[locker2_{mappromotepending2}, locker2_{promotepending2}] > record_extract1 > [excl, andt₁]
[locker2_{mappromotepending2}, locker2_{promotepending2}] > case0₂ > [nil, cons₂, true] > [excl, andt₁]
[locker2_{mappromotepending2}, locker2_{promotepending2}] > case0₂ > pending > tuple₂ > [excl, andt₁]
[locker2_{mappromotepending2}, locker2_{promotepending2}] > case0₂ > [record_update3, record_updates2] > tuple₂ > [excl, andt₁]
locker2_{mapclaimlock3} > [nil, cons₂, true] > [excl, andt₁]
locker2_{mapclaimlock3} > locker2_claimlock2 > [excl, andt₁]
locker2_{removepending2} > lock > [nil, cons₂, true] > [excl, andt₁]
locker2_{removepending2} > lock > mcrlrecord > tuple₂ > [excl, andt₁]
locker2_{removepending2} > pending > tuple₂ > [excl, andt₁]
locker2_{removepending2} > record_extract1 > [excl, andt₁]
locker2_{removepending2} > [record_update3, record_updates2] > tuple₂ > [excl, andt₁]
locker2_{removepending2} > subtract₂ > [delete₂, case8₃] > [nil, cons₂, true] > [excl, andt₁]
[locker2_addpending3, case1₂] > [false, member₂, case9₄] > [nil, cons₂, true] > [excl, andt₁]
[locker2_addpending3, case1₂] > pending > tuple₂ > [excl, andt₁]
[locker2_addpending3, case1₂] > resource > [or, T, F, locker, empty, nocalls] > [excl, andt₁]
[locker2_addpending3, case1₂] > resource > lock > [nil, cons₂, true] > [excl, andt₁]
[locker2_addpending3, case1₂] > resource > lock > mcrlrecord > tuple₂ > [excl, andt₁]
[locker2_addpending3, case1₂] > record_extract1 > [excl, andt₁]
[locker2_addpending3, case1₂] > [record_update3, record_updates2] > tuple₂ > [excl, andt₁]
locker2_releaselock2 > lock > [nil, cons₂, true] > [excl, andt₁]
locker2_releaselock2 > lock > mcrlrecord > tuple₂ > [excl, andt₁]
locker2_releaselock2 > record_extract1 > [excl, andt₁]
locker2_releaselock2 > case2₃ > [nil, cons₂, true] > [excl, andt₁]
locker2_releaselock2 > case2₃ > [record_update3, record_updates2] > tuple₂ > [excl, andt₁]
locker2_releaselock2 > case2₃ > excllock > [excl, andt₁]
locker2_releaselock2 > gen_modtageq2 > [excl, andt₁]
case4₃ > [false, member₂, case9₄] > [nil, cons₂, true] > [excl, andt₁]
[locker2_obtainables2, case5₄] > [false, member₂, case9₄] > [nil, cons₂, true] > [excl, andt₁]
[locker2_obtainables2, case5₄] > record_extract1 > [excl, andt₁]
[locker2_{checkavailable2}, case6₂] > [false, member₂, case9₄] > [nil, cons₂, true] > [excl, andt₁]
[locker2_{checkavailable2}, case6₂] > pending > tuple₂ > [excl, andt₁]
[locker2_{checkavailable2}, case6₂] > record_extract1 > [excl, andt₁]
gen_tag1 > tuple₂ > [excl, andt₁]
gen_tag1 > tag > [excl, andt₁]
pops₁ > [excl, andt₁]
tops₁ > [excl, andt₁]
istops₂ > eqt₁ > and₂ > [or, T, F, locker, empty, nocalls] > [excl, andt₁]
eqc₂ > eqt₁ > and₂ > [or, T, F, locker, empty, nocalls] > [excl, andt₁]
push₃ > [stack₂, pushs₂, push1₆] > eqt₁ > and₂ > [or, T, F, locker, empty, nocalls] > [excl, andt₁]
push₃ > [stack₂, pushs₂, push1₆] > calls₃ > [or, T, F, locker, empty, nocalls] > [excl, andt₁]

Status:

pops₁: [1]
push₃: [1,2,3]
delete₂: [1,2]
locker2_{removepending2}: [1,2]
locker2_{mappromotepending2}: [2,1]
member₂: [1,2]
gen_modtageq2: [2,1]
gen_tag1: [1]
pushs₂: [1,2]
locker2_{checkavailable2}: [1,2]
excllock: []
nil: []
element₂: [1,2]
locker2_releaselock2: [2,1]
locker2_obtainables2: [2,1]
T: []
locker2_addpending3: [1,3,2]
or: []
resource: []
locker: []
true: []
record_new: []
empty: []
eqc₂: [2,1]
push1₆: [2,4,5,6,3,1]
imp₁: [1]
case8₃: [3,1,2]
case2₃: [3,1,2]
pid₁: [1]
ok: []
F: []
lock: []
tops₁: [1]
case0₂: [2,1]
calls₃: [3,2,1]
eqt₁: [1]
case1₂: [2,1]
and₂: [1,2]
stack₂: [1,2]
pending: []
not₁: [1]
int₁: [1]
istops₂: [1,2]
record_extract1: [1]
record_updates2: [2,1]
locker2_{mapclaimlock3}: [2,1,3]
andt₁: [1]
undefined: []
tag: []
mcrlrecord: []
a: []
request: []
if₂: [1,2]
locker2_claimlock2: [2,1]
excl: []
subtract₂: [2,1]
locker2_{promotepending2}: [2,1]
case4₃: [2,1,3]
nocalls: []
record_update3: [2,1,3]
0: []
cons₂: [1,2]
case5₄: [1,2,4,3]
case6₂: [2,1]
release: []
case9₄: [3,1,4,2]
false: []
tuple₂: [1,2]

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)

(51) 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.

(52) PisEmptyProof (EQUIVALENT transformation)

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

(53) TRUE

(54) 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.

(55) 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(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(x1, x2, x3)
eq(x1, x2)  =  eq
eqt(x1, x2)  =  eqt(x1, x2)
nil  =  nil
undefined  =  undefined
pid(x1)  =  x1
int(x1)  =  int
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)  =  x2
s(x1)  =  s(x1)
0  =  0
record_new(x1)  =  record_new
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)  =  x1
locker2_claim_lock(x1, x2, x3)  =  locker2_claim_lock
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(x3)
member(x1, x2)  =  member(x1, x2)
append(x1, x2)  =  x1
locker2_release_lock(x1, x2)  =  locker2_release_lock(x1)
case2(x1, x2, x3)  =  case2(x2)
gen_modtageq(x1, x2)  =  gen_modtageq(x2)
excllock  =  excllock
case4(x1, x2, x3)  =  case4(x1, x2, x3)
locker2_obtainables(x1, x2)  =  locker2_obtainables
case5(x1, x2, x3, x4)  =  case5
andt(x1, x2)  =  x2
locker2_obtainable(x1, x2)  =  locker2_obtainable(x1, x2)
locker2_check_available(x1, x2)  =  locker2_check_available(x1, x2)
case6(x1, x2, x3, x4)  =  case6(x1, x3)
equal(x1, x2)  =  equal(x2)
locker2_check_availables(x1, x2)  =  locker2_check_availables
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)  =  case9(x1, x2, x3, x4)
eqs(x1, x2)  =  eqs(x1, x2)
empty  =  empty
stack(x1, x2)  =  stack(x1, x2)
pushs(x1, x2)  =  pushs(x1, x2)
pops(x1)  =  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)

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

EQC₂ > locker2_claimlock
or₁ > [T, not₁] > calls₃ > locker2_claimlock
or₁ > [T, not₁] > [stack₂, pushs₂] > F > locker2_claimlock
imp₁ > [T, not₁] > calls₃ > locker2_claimlock
imp₁ > [T, not₁] > [stack₂, pushs₂] > F > locker2_claimlock
if₃ > locker2_claimlock
eq > [T, not₁] > calls₃ > locker2_claimlock
eq > [T, not₁] > [stack₂, pushs₂] > F > locker2_claimlock
int > F > locker2_claimlock
int > s₁ > locker2_claimlock
a > F > locker2_claimlock
locker > [T, not₁] > calls₃ > locker2_claimlock
locker > [T, not₁] > [stack₂, pushs₂] > F > locker2_claimlock
ok > locker2_claimlock
release > locker2_claimlock
request > locker2_claimlock
resource > mcrlrecord > [lock, locker2_{promotepending2}] > [nil, case0₂] > cons₂ > F > locker2_claimlock
resource > mcrlrecord > [lock, locker2_{promotepending2}] > [nil, case0₂] > cons₂ > record_extract3 > tuple₂ > locker2_claimlock
resource > mcrlrecord > [lock, locker2_{promotepending2}] > [nil, case0₂] > cons₂ > [record_update3, record_updates2] > tuple₂ > locker2_claimlock
resource > mcrlrecord > [lock, locker2_{promotepending2}] > [nil, case0₂] > cons₂ > [member₂, case9₄] > locker2_claimlock
resource > mcrlrecord > [lock, locker2_{promotepending2}] > [nil, case0₂] > cons₂ > equal₁ > locker2_claimlock
resource > mcrlrecord > [lock, locker2_{promotepending2}] > [nil, case0₂] > excl > [T, not₁] > calls₃ > locker2_claimlock
resource > mcrlrecord > [lock, locker2_{promotepending2}] > [nil, case0₂] > excl > [T, not₁] > [stack₂, pushs₂] > F > locker2_claimlock
resource > mcrlrecord > [lock, locker2_{promotepending2}] > [nil, case0₂] > [false, case4₃] > [member₂, case9₄] > locker2_claimlock
resource > mcrlrecord > [lock, locker2_{promotepending2}] > [nil, case0₂] > pending > [T, not₁] > calls₃ > locker2_claimlock
resource > mcrlrecord > [lock, locker2_{promotepending2}] > [nil, case0₂] > pending > [T, not₁] > [stack₂, pushs₂] > F > locker2_claimlock
resource > mcrlrecord > [lock, locker2_{promotepending2}] > [nil, case0₂] > pending > tuple₂ > locker2_claimlock
[true, locker2_obtainables, case5, locker2_{checkavailables}] > [locker2_{checkavailable2}, case6₂] > [lock, locker2_{promotepending2}] > [nil, case0₂] > cons₂ > F > locker2_claimlock
[true, locker2_obtainables, case5, locker2_{checkavailables}] > [locker2_{checkavailable2}, case6₂] > [lock, locker2_{promotepending2}] > [nil, case0₂] > cons₂ > record_extract3 > tuple₂ > locker2_claimlock
[true, locker2_obtainables, case5, locker2_{checkavailables}] > [locker2_{checkavailable2}, case6₂] > [lock, locker2_{promotepending2}] > [nil, case0₂] > cons₂ > [record_update3, record_updates2] > tuple₂ > locker2_claimlock
[true, locker2_obtainables, case5, locker2_{checkavailables}] > [locker2_{checkavailable2}, case6₂] > [lock, locker2_{promotepending2}] > [nil, case0₂] > cons₂ > [member₂, case9₄] > locker2_claimlock
[true, locker2_obtainables, case5, locker2_{checkavailables}] > [locker2_{checkavailable2}, case6₂] > [lock, locker2_{promotepending2}] > [nil, case0₂] > cons₂ > equal₁ > locker2_claimlock
[true, locker2_obtainables, case5, locker2_{checkavailables}] > [locker2_{checkavailable2}, case6₂] > [lock, locker2_{promotepending2}] > [nil, case0₂] > excl > [T, not₁] > calls₃ > locker2_claimlock
[true, locker2_obtainables, case5, locker2_{checkavailables}] > [locker2_{checkavailable2}, case6₂] > [lock, locker2_{promotepending2}] > [nil, case0₂] > excl > [T, not₁] > [stack₂, pushs₂] > F > locker2_claimlock
[true, locker2_obtainables, case5, locker2_{checkavailables}] > [locker2_{checkavailable2}, case6₂] > [lock, locker2_{promotepending2}] > [nil, case0₂] > [false, case4₃] > [member₂, case9₄] > locker2_claimlock
[true, locker2_obtainables, case5, locker2_{checkavailables}] > [locker2_{checkavailable2}, case6₂] > [lock, locker2_{promotepending2}] > [nil, case0₂] > pending > [T, not₁] > calls₃ > locker2_claimlock
[true, locker2_obtainables, case5, locker2_{checkavailables}] > [locker2_{checkavailable2}, case6₂] > [lock, locker2_{promotepending2}] > [nil, case0₂] > pending > [T, not₁] > [stack₂, pushs₂] > F > locker2_claimlock
[true, locker2_obtainables, case5, locker2_{checkavailables}] > [locker2_{checkavailable2}, case6₂] > [lock, locker2_{promotepending2}] > [nil, case0₂] > pending > tuple₂ > locker2_claimlock
0 > locker2_claimlock
record_new > undefined > F > locker2_claimlock
record_new > mcrlrecord > [lock, locker2_{promotepending2}] > [nil, case0₂] > cons₂ > F > locker2_claimlock
record_new > mcrlrecord > [lock, locker2_{promotepending2}] > [nil, case0₂] > cons₂ > record_extract3 > tuple₂ > locker2_claimlock
record_new > mcrlrecord > [lock, locker2_{promotepending2}] > [nil, case0₂] > cons₂ > [record_update3, record_updates2] > tuple₂ > locker2_claimlock
record_new > mcrlrecord > [lock, locker2_{promotepending2}] > [nil, case0₂] > cons₂ > [member₂, case9₄] > locker2_claimlock
record_new > mcrlrecord > [lock, locker2_{promotepending2}] > [nil, case0₂] > cons₂ > equal₁ > locker2_claimlock
record_new > mcrlrecord > [lock, locker2_{promotepending2}] > [nil, case0₂] > excl > [T, not₁] > calls₃ > locker2_claimlock
record_new > mcrlrecord > [lock, locker2_{promotepending2}] > [nil, case0₂] > excl > [T, not₁] > [stack₂, pushs₂] > F > locker2_claimlock
record_new > mcrlrecord > [lock, locker2_{promotepending2}] > [nil, case0₂] > [false, case4₃] > [member₂, case9₄] > locker2_claimlock
record_new > mcrlrecord > [lock, locker2_{promotepending2}] > [nil, case0₂] > pending > [T, not₁] > calls₃ > locker2_claimlock
record_new > mcrlrecord > [lock, locker2_{promotepending2}] > [nil, case0₂] > pending > [T, not₁] > [stack₂, pushs₂] > F > locker2_claimlock
record_new > mcrlrecord > [lock, locker2_{promotepending2}] > [nil, case0₂] > pending > tuple₂ > locker2_claimlock
locker2_{mappromotepending2} > [lock, locker2_{promotepending2}] > [nil, case0₂] > cons₂ > F > locker2_claimlock
locker2_{mappromotepending2} > [lock, locker2_{promotepending2}] > [nil, case0₂] > cons₂ > record_extract3 > tuple₂ > locker2_claimlock
locker2_{mappromotepending2} > [lock, locker2_{promotepending2}] > [nil, case0₂] > cons₂ > [record_update3, record_updates2] > tuple₂ > locker2_claimlock
locker2_{mappromotepending2} > [lock, locker2_{promotepending2}] > [nil, case0₂] > cons₂ > [member₂, case9₄] > locker2_claimlock
locker2_{mappromotepending2} > [lock, locker2_{promotepending2}] > [nil, case0₂] > cons₂ > equal₁ > locker2_claimlock
locker2_{mappromotepending2} > [lock, locker2_{promotepending2}] > [nil, case0₂] > excl > [T, not₁] > calls₃ > locker2_claimlock
locker2_{mappromotepending2} > [lock, locker2_{promotepending2}] > [nil, case0₂] > excl > [T, not₁] > [stack₂, pushs₂] > F > locker2_claimlock
locker2_{mappromotepending2} > [lock, locker2_{promotepending2}] > [nil, case0₂] > [false, case4₃] > [member₂, case9₄] > locker2_claimlock
locker2_{mappromotepending2} > [lock, locker2_{promotepending2}] > [nil, case0₂] > pending > [T, not₁] > calls₃ > locker2_claimlock
locker2_{mappromotepending2} > [lock, locker2_{promotepending2}] > [nil, case0₂] > pending > [T, not₁] > [stack₂, pushs₂] > F > locker2_claimlock
locker2_{mappromotepending2} > [lock, locker2_{promotepending2}] > [nil, case0₂] > pending > tuple₂ > locker2_claimlock
locker2_{mapaddpending} > [nil, case0₂] > cons₂ > F > locker2_claimlock
locker2_{mapaddpending} > [nil, case0₂] > cons₂ > record_extract3 > tuple₂ > locker2_claimlock
locker2_{mapaddpending} > [nil, case0₂] > cons₂ > [record_update3, record_updates2] > tuple₂ > locker2_claimlock
locker2_{mapaddpending} > [nil, case0₂] > cons₂ > [member₂, case9₄] > locker2_claimlock
locker2_{mapaddpending} > [nil, case0₂] > cons₂ > equal₁ > locker2_claimlock
locker2_{mapaddpending} > [nil, case0₂] > excl > [T, not₁] > calls₃ > locker2_claimlock
locker2_{mapaddpending} > [nil, case0₂] > excl > [T, not₁] > [stack₂, pushs₂] > F > locker2_claimlock
locker2_{mapaddpending} > [nil, case0₂] > [false, case4₃] > [member₂, case9₄] > locker2_claimlock
locker2_{mapaddpending} > [nil, case0₂] > pending > [T, not₁] > calls₃ > locker2_claimlock
locker2_{mapaddpending} > [nil, case0₂] > pending > [T, not₁] > [stack₂, pushs₂] > F > locker2_claimlock
locker2_{mapaddpending} > [nil, case0₂] > pending > tuple₂ > locker2_claimlock
locker2_{removepending2} > [lock, locker2_{promotepending2}] > [nil, case0₂] > cons₂ > F > locker2_claimlock
locker2_{removepending2} > [lock, locker2_{promotepending2}] > [nil, case0₂] > cons₂ > record_extract3 > tuple₂ > locker2_claimlock
locker2_{removepending2} > [lock, locker2_{promotepending2}] > [nil, case0₂] > cons₂ > [record_update3, record_updates2] > tuple₂ > locker2_claimlock
locker2_{removepending2} > [lock, locker2_{promotepending2}] > [nil, case0₂] > cons₂ > [member₂, case9₄] > locker2_claimlock
locker2_{removepending2} > [lock, locker2_{promotepending2}] > [nil, case0₂] > cons₂ > equal₁ > locker2_claimlock
locker2_{removepending2} > [lock, locker2_{promotepending2}] > [nil, case0₂] > excl > [T, not₁] > calls₃ > locker2_claimlock
locker2_{removepending2} > [lock, locker2_{promotepending2}] > [nil, case0₂] > excl > [T, not₁] > [stack₂, pushs₂] > F > locker2_claimlock
locker2_{removepending2} > [lock, locker2_{promotepending2}] > [nil, case0₂] > [false, case4₃] > [member₂, case9₄] > locker2_claimlock
locker2_{removepending2} > [lock, locker2_{promotepending2}] > [nil, case0₂] > pending > [T, not₁] > calls₃ > locker2_claimlock
locker2_{removepending2} > [lock, locker2_{promotepending2}] > [nil, case0₂] > pending > [T, not₁] > [stack₂, pushs₂] > F > locker2_claimlock
locker2_{removepending2} > [lock, locker2_{promotepending2}] > [nil, case0₂] > pending > tuple₂ > locker2_claimlock
locker2_{removepending2} > subtract₂ > [delete₂, case8₄] > cons₂ > F > locker2_claimlock
locker2_{removepending2} > subtract₂ > [delete₂, case8₄] > cons₂ > record_extract3 > tuple₂ > locker2_claimlock
locker2_{removepending2} > subtract₂ > [delete₂, case8₄] > cons₂ > [record_update3, record_updates2] > tuple₂ > locker2_claimlock
locker2_{removepending2} > subtract₂ > [delete₂, case8₄] > cons₂ > [member₂, case9₄] > locker2_claimlock
locker2_{removepending2} > subtract₂ > [delete₂, case8₄] > cons₂ > equal₁ > locker2_claimlock
locker2_addpending3 > case1₁ > [lock, locker2_{promotepending2}] > [nil, case0₂] > cons₂ > F > locker2_claimlock
locker2_addpending3 > case1₁ > [lock, locker2_{promotepending2}] > [nil, case0₂] > cons₂ > record_extract3 > tuple₂ > locker2_claimlock
locker2_addpending3 > case1₁ > [lock, locker2_{promotepending2}] > [nil, case0₂] > cons₂ > [record_update3, record_updates2] > tuple₂ > locker2_claimlock
locker2_addpending3 > case1₁ > [lock, locker2_{promotepending2}] > [nil, case0₂] > cons₂ > [member₂, case9₄] > locker2_claimlock
locker2_addpending3 > case1₁ > [lock, locker2_{promotepending2}] > [nil, case0₂] > cons₂ > equal₁ > locker2_claimlock
locker2_addpending3 > case1₁ > [lock, locker2_{promotepending2}] > [nil, case0₂] > excl > [T, not₁] > calls₃ > locker2_claimlock
locker2_addpending3 > case1₁ > [lock, locker2_{promotepending2}] > [nil, case0₂] > excl > [T, not₁] > [stack₂, pushs₂] > F > locker2_claimlock
locker2_addpending3 > case1₁ > [lock, locker2_{promotepending2}] > [nil, case0₂] > [false, case4₃] > [member₂, case9₄] > locker2_claimlock
locker2_addpending3 > case1₁ > [lock, locker2_{promotepending2}] > [nil, case0₂] > pending > [T, not₁] > calls₃ > locker2_claimlock
locker2_addpending3 > case1₁ > [lock, locker2_{promotepending2}] > [nil, case0₂] > pending > [T, not₁] > [stack₂, pushs₂] > F > locker2_claimlock
locker2_addpending3 > case1₁ > [lock, locker2_{promotepending2}] > [nil, case0₂] > pending > tuple₂ > locker2_claimlock
[locker2_releaselock1, case2₁, excllock] > [lock, locker2_{promotepending2}] > [nil, case0₂] > cons₂ > F > locker2_claimlock
[locker2_releaselock1, case2₁, excllock] > [lock, locker2_{promotepending2}] > [nil, case0₂] > cons₂ > record_extract3 > tuple₂ > locker2_claimlock
[locker2_releaselock1, case2₁, excllock] > [lock, locker2_{promotepending2}] > [nil, case0₂] > cons₂ > [record_update3, record_updates2] > tuple₂ > locker2_claimlock
[locker2_releaselock1, case2₁, excllock] > [lock, locker2_{promotepending2}] > [nil, case0₂] > cons₂ > [member₂, case9₄] > locker2_claimlock
[locker2_releaselock1, case2₁, excllock] > [lock, locker2_{promotepending2}] > [nil, case0₂] > cons₂ > equal₁ > locker2_claimlock
[locker2_releaselock1, case2₁, excllock] > [lock, locker2_{promotepending2}] > [nil, case0₂] > excl > [T, not₁] > calls₃ > locker2_claimlock
[locker2_releaselock1, case2₁, excllock] > [lock, locker2_{promotepending2}] > [nil, case0₂] > excl > [T, not₁] > [stack₂, pushs₂] > F > locker2_claimlock
[locker2_releaselock1, case2₁, excllock] > [lock, locker2_{promotepending2}] > [nil, case0₂] > [false, case4₃] > [member₂, case9₄] > locker2_claimlock
[locker2_releaselock1, case2₁, excllock] > [lock, locker2_{promotepending2}] > [nil, case0₂] > pending > [T, not₁] > calls₃ > locker2_claimlock
[locker2_releaselock1, case2₁, excllock] > [lock, locker2_{promotepending2}] > [nil, case0₂] > pending > [T, not₁] > [stack₂, pushs₂] > F > locker2_claimlock
[locker2_releaselock1, case2₁, excllock] > [lock, locker2_{promotepending2}] > [nil, case0₂] > pending > tuple₂ > locker2_claimlock
[locker2_releaselock1, case2₁, excllock] > gen_modtageq1 > equal₁ > locker2_claimlock
locker2_obtainable2 > locker2_claimlock
locker2_adduniq1 > locker2_claimlock
gen_tag1 > tuple₂ > locker2_claimlock
gen_tag1 > tag > locker2_claimlock
[eqs₂, eqc₂] > eqt₂ > [T, not₁] > calls₃ > locker2_claimlock
[eqs₂, eqc₂] > eqt₂ > [T, not₁] > [stack₂, pushs₂] > F > locker2_claimlock
[eqs₂, eqc₂] > eqt₂ > and₂ > F > locker2_claimlock
[empty, push₃, push1₅] > nocalls > [T, not₁] > calls₃ > locker2_claimlock
[empty, push₃, push1₅] > nocalls > [T, not₁] > [stack₂, pushs₂] > F > locker2_claimlock
tops₁ > locker2_claimlock
istops₂ > eqt₂ > [T, not₁] > calls₃ > locker2_claimlock
istops₂ > eqt₂ > [T, not₁] > [stack₂, pushs₂] > F > locker2_claimlock
istops₂ > eqt₂ > and₂ > F > locker2_claimlock

Status:

case8₄: [3,1,2,4]
locker2_claimlock: []
push₃: [2,1,3]
delete₂: [1,2]
locker2_{removepending2}: [1,2]
locker2_{mappromotepending2}: [2,1]
member₂: [1,2]
gen_tag1: [1]
pushs₂: [1,2]
locker2_{checkavailables}: []
locker2_{checkavailable2}: [1,2]
excllock: []
eqt₂: [2,1]
nil: []
locker2_adduniq1: [1]
locker2_{mapaddpending}: []
gen_modtageq1: [1]
T: []
locker2_addpending3: [2,1,3]
equal₁: [1]
resource: []
locker: []
true: []
record_new: []
empty: []
eqc₂: [1,2]
imp₁: [1]
locker2_releaselock1: [1]
locker2_obtainable2: [1,2]
push1₅: [2,1,5,3,4]
case5: []
ok: []
F: []
lock: []
tops₁: [1]
case0₂: [2,1]
calls₃: [3,2,1]
eqs₂: [1,2]
and₂: [2,1]
stack₂: [1,2]
if₃: [1,2,3]
pending: []
case2₁: [1]
not₁: [1]
istops₂: [1,2]
record_updates2: [2,1]
s₁: [1]
undefined: []
tag: []
eq: []
mcrlrecord: []
a: []
request: []
excl: []
subtract₂: [2,1]
int: []
locker2_{promotepending2}: [2,1]
case4₃: [2,3,1]
nocalls: []
record_update3: [2,1,3]
0: []
cons₂: [2,1]
or₁: [1]
record_extract3: [1,3,2]
case6₂: [2,1]
release: []
case9₄: [3,1,4,2]
false: []
case1₁: [1]
tuple₂: [1,2]
locker2_obtainables: []
EQC₂: [2,1]

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)

(56) 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.

(57) PisEmptyProof (EQUIVALENT transformation)

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

(58) TRUE