Termination w.r.t. Q proof of /tmp/tmpgJunDb/mucrl1.trs

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

0 QTRS

↳1 DependencyPairsProof (⇔)

↳2 QDP

↳3 DependencyGraphProof (⇔)

↳4 AND

  ↳5 QDP

    ↳6 QDPOrderProof (⇔)

    ↳7 QDP

    ↳8 PisEmptyProof (⇔)

    ↳9 TRUE

  ↳10 QDP

    ↳11 QDPOrderProof (⇔)

    ↳12 QDP

    ↳13 PisEmptyProof (⇔)

    ↳14 TRUE

  ↳15 QDP

    ↳16 QDPOrderProof (⇔)

    ↳17 QDP

    ↳18 PisEmptyProof (⇔)

    ↳19 TRUE

  ↳20 QDP

    ↳21 QDPOrderProof (⇔)

    ↳22 QDP

    ↳23 PisEmptyProof (⇔)

    ↳24 TRUE

  ↳25 QDP

    ↳26 QDPOrderProof (⇔)

    ↳27 QDP

    ↳28 PisEmptyProof (⇔)

    ↳29 TRUE

  ↳30 QDP

    ↳31 QDPOrderProof (⇔)

    ↳32 QDP

    ↳33 PisEmptyProof (⇔)

    ↳34 TRUE

  ↳35 QDP

    ↳36 QDPOrderProof (⇔)

    ↳37 QDP

    ↳38 PisEmptyProof (⇔)

    ↳39 TRUE

  ↳40 QDP

    ↳41 QDPOrderProof (⇔)

    ↳42 QDP

    ↳43 QDPOrderProof (⇔)

    ↳44 QDP

    ↳45 PisEmptyProof (⇔)

    ↳46 TRUE

  ↳47 QDP

    ↳48 QDPOrderProof (⇔)

    ↳49 QDP

    ↳50 PisEmptyProof (⇔)

    ↳51 TRUE

  ↳52 QDP

    ↳53 QDPOrderProof (⇔)

    ↳54 QDP

    ↳55 PisEmptyProof (⇔)

    ↳56 TRUE

(0) Obligation:

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

or(T, T) → T
or(F, T) → T
or(T, F) → T
or(F, F) → F
and(T, B) → B
and(B, T) → B
and(F, B) → F
and(B, F) → F
imp(T, B) → B
imp(F, B) → T
not(T) → F
not(F) → T
if(T, B1, B2) → B1
if(F, B1, B2) → B2
eq(T, T) → T
eq(F, F) → T
eq(T, F) → F
eq(F, T) → F
eqt(nil, undefined) → F
eqt(nil, pid(N2)) → F
eqt(nil, int(N2)) → F
eqt(nil, cons(H2, T2)) → F
eqt(nil, tuple(H2, T2)) → F
eqt(nil, tuplenil(H2)) → F
eqt(a, nil) → F
eqt(a, a) → T
eqt(a, excl) → F
eqt(a, false) → F
eqt(a, lock) → F
eqt(a, locker) → F
eqt(a, mcrlrecord) → F
eqt(a, ok) → F
eqt(a, pending) → F
eqt(a, release) → F
eqt(a, request) → F
eqt(a, resource) → F
eqt(a, tag) → F
eqt(a, true) → F
eqt(a, undefined) → F
eqt(a, pid(N2)) → F
eqt(a, int(N2)) → F
eqt(a, cons(H2, T2)) → F
eqt(a, tuple(H2, T2)) → F
eqt(a, tuplenil(H2)) → F
eqt(excl, nil) → F
eqt(excl, a) → F
eqt(excl, excl) → T
eqt(excl, false) → F
eqt(excl, lock) → F
eqt(excl, locker) → F
eqt(excl, mcrlrecord) → F
eqt(excl, ok) → F
eqt(excl, pending) → F
eqt(excl, release) → F
eqt(excl, request) → F
eqt(excl, resource) → F
eqt(excl, tag) → F
eqt(excl, true) → F
eqt(excl, undefined) → F
eqt(excl, pid(N2)) → F
eqt(excl, eqt(false, int(N2))) → F
eqt(false, cons(H2, T2)) → F
eqt(false, tuple(H2, T2)) → F
eqt(false, tuplenil(H2)) → F
eqt(lock, nil) → F
eqt(lock, a) → F
eqt(lock, excl) → F
eqt(lock, false) → F
eqt(lock, lock) → T
eqt(lock, locker) → F
eqt(lock, mcrlrecord) → F
eqt(lock, ok) → F
eqt(lock, pending) → F
eqt(lock, release) → F
eqt(lock, request) → F
eqt(lock, resource) → F
eqt(lock, tag) → F
eqt(lock, true) → F
eqt(lock, undefined) → F
eqt(lock, pid(N2)) → F
eqt(lock, int(N2)) → F
eqt(lock, cons(H2, T2)) → F
eqt(lock, tuple(H2, T2)) → F
eqt(lock, tuplenil(H2)) → F
eqt(locker, nil) → F
eqt(locker, a) → F
eqt(locker, excl) → F
eqt(locker, false) → F
eqt(locker, lock) → F
eqt(locker, locker) → T
eqt(locker, mcrlrecord) → F
eqt(locker, ok) → F
eqt(locker, pending) → F
eqt(locker, release) → F
eqt(locker, request) → F
eqt(locker, resource) → F
eqt(locker, tag) → F
eqt(locker, true) → F
eqt(locker, undefined) → F
eqt(locker, pid(N2)) → F
eqt(locker, int(N2)) → F
eqt(locker, cons(H2, T2)) → F
eqt(locker, tuple(H2, T2)) → F
eqt(locker, tuplenil(H2)) → F
eqt(mcrlrecord, nil) → F
eqt(mcrlrecord, a) → F
eqt(mcrlrecord, excl) → F
eqt(mcrlrecord, false) → F
eqt(mcrlrecord, lock) → F
eqt(mcrlrecord, locker) → F
eqt(mcrlrecord, mcrlrecord) → T
eqt(mcrlrecord, ok) → F
eqt(mcrlrecord, pending) → F
eqt(mcrlrecord, release) → F
eqt(mcrlrecord, request) → F
eqt(mcrlrecord, resource) → F
eqt(ok, resource) → F
eqt(ok, tag) → F
eqt(ok, true) → F
eqt(ok, undefined) → F
eqt(ok, pid(N2)) → F
eqt(ok, int(N2)) → F
eqt(ok, cons(H2, T2)) → F
eqt(ok, tuple(H2, T2)) → F
eqt(ok, tuplenil(H2)) → F
eqt(pending, nil) → F
eqt(pending, a) → F
eqt(pending, excl) → F
eqt(pending, false) → F
eqt(pending, lock) → F
eqt(pending, locker) → F
eqt(pending, mcrlrecord) → F
eqt(pending, ok) → F
eqt(pending, pending) → T
eqt(pending, release) → F
eqt(pending, request) → F
eqt(pending, resource) → F
eqt(pending, tag) → F
eqt(pending, true) → F
eqt(pending, undefined) → F
eqt(pending, pid(N2)) → F
eqt(pending, int(N2)) → F
eqt(pending, cons(H2, T2)) → F
eqt(pending, tuple(H2, T2)) → F
eqt(pending, tuplenil(H2)) → F
eqt(release, nil) → F
eqt(release, a) → F
eqt(release, excl) → F
eqt(release, false) → F
eqt(release, lock) → F
eqt(release, locker) → F
eqt(release, mcrlrecord) → F
eqt(release, ok) → F
eqt(request, mcrlrecord) → F
eqt(request, ok) → F
eqt(request, pending) → F
eqt(request, release) → F
eqt(request, request) → T
eqt(request, resource) → F
eqt(request, tag) → F
eqt(request, true) → F
eqt(request, undefined) → F
eqt(request, pid(N2)) → F
eqt(request, int(N2)) → F
eqt(request, cons(H2, T2)) → F
eqt(request, tuple(H2, T2)) → F
eqt(request, tuplenil(H2)) → F
eqt(resource, nil) → F
eqt(resource, a) → F
eqt(resource, excl) → F
eqt(resource, false) → F
eqt(resource, lock) → F
eqt(resource, locker) → F
eqt(resource, mcrlrecord) → F
eqt(resource, ok) → F
eqt(resource, pending) → F
eqt(resource, release) → F
eqt(resource, request) → F
eqt(resource, resource) → T
eqt(resource, tag) → F
eqt(resource, true) → F
eqt(resource, undefined) → F
eqt(resource, pid(N2)) → F
eqt(resource, int(N2)) → F
eqt(resource, cons(H2, T2)) → F
eqt(resource, tuple(H2, T2)) → F
eqt(resource, tuplenil(H2)) → F
eqt(tag, nil) → F
eqt(tag, a) → F
eqt(tag, excl) → F
eqt(tag, false) → F
eqt(tag, lock) → F
eqt(tag, locker) → F
eqt(tag, mcrlrecord) → F
eqt(tag, ok) → F
eqt(tag, pending) → F
eqt(tag, release) → F
eqt(tag, request) → F
eqt(tag, resource) → F
eqt(tag, tag) → T
eqt(tag, true) → F
eqt(tag, undefined) → F
eqt(tag, pid(N2)) → F
eqt(tag, int(N2)) → F
eqt(tag, cons(H2, T2)) → F
eqt(tag, tuple(H2, T2)) → F
eqt(tag, tuplenil(H2)) → F
eqt(true, nil) → F
eqt(true, a) → F
eqt(true, excl) → F
eqt(true, false) → F
eqt(true, lock) → F
eqt(true, locker) → F
eqt(true, mcrlrecord) → F
eqt(true, ok) → F
eqt(true, pending) → F
eqt(true, release) → F
eqt(true, request) → F
eqt(true, resource) → F
eqt(true, tag) → F
eqt(true, true) → T
eqt(true, undefined) → F
eqt(true, pid(N2)) → F
eqt(true, int(N2)) → F
eqt(true, cons(H2, T2)) → F
eqt(true, tuple(H2, T2)) → F
eqt(true, tuplenil(H2)) → F
eqt(undefined, nil) → F
eqt(undefined, a) → F
eqt(undefined, tuplenil(H2)) → F
eqt(pid(N1), nil) → F
eqt(pid(N1), a) → F
eqt(pid(N1), excl) → F
eqt(pid(N1), false) → F
eqt(pid(N1), lock) → F
eqt(pid(N1), locker) → F
eqt(pid(N1), mcrlrecord) → F
eqt(pid(N1), ok) → F
eqt(pid(N1), pending) → F
eqt(pid(N1), release) → F
eqt(pid(N1), request) → F
eqt(pid(N1), resource) → F
eqt(pid(N1), tag) → F
eqt(pid(N1), true) → F
eqt(pid(N1), undefined) → F
eqt(pid(N1), pid(N2)) → eqt(N1, N2)
eqt(pid(N1), int(N2)) → F
eqt(pid(N1), cons(H2, T2)) → F
eqt(pid(N1), tuple(H2, T2)) → F
eqt(pid(N1), tuplenil(H2)) → F
eqt(int(N1), nil) → F
eqt(int(N1), a) → F
eqt(int(N1), excl) → F
eqt(int(N1), false) → F
eqt(int(N1), lock) → F
eqt(int(N1), locker) → F
eqt(int(N1), mcrlrecord) → F
eqt(int(N1), ok) → F
eqt(int(N1), pending) → F
eqt(int(N1), release) → F
eqt(int(N1), request) → F
eqt(int(N1), resource) → F
eqt(int(N1), tag) → F
eqt(int(N1), true) → F
eqt(int(N1), undefined) → F
eqt(cons(H1, T1), resource) → F
eqt(cons(H1, T1), tag) → F
eqt(cons(H1, T1), true) → F
eqt(cons(H1, T1), undefined) → F
eqt(cons(H1, T1), pid(N2)) → F
eqt(cons(H1, T1), int(N2)) → F
eqt(cons(H1, T1), cons(H2, T2)) → and(eqt(H1, H2), eqt(T1, T2))
eqt(cons(H1, T1), tuple(H2, T2)) → F
eqt(cons(H1, T1), tuplenil(H2)) → F
eqt(tuple(H1, T1), nil) → F
eqt(tuple(H1, T1), a) → F
eqt(tuple(H1, T1), excl) → F
eqt(tuple(H1, T1), false) → F
eqt(tuple(H1, T1), lock) → F
eqt(tuple(H1, T1), locker) → F
eqt(tuple(H1, T1), mcrlrecord) → F
eqt(tuple(H1, T1), ok) → F
eqt(tuple(H1, T1), pending) → F
eqt(tuple(H1, T1), release) → F
eqt(tuple(H1, T1), request) → F
eqt(tuple(H1, T1), resource) → F
eqt(tuple(H1, T1), tag) → F
eqt(tuple(H1, T1), true) → F
eqt(tuple(H1, T1), undefined) → F
eqt(tuple(H1, T1), pid(N2)) → F
eqt(tuple(H1, T1), int(N2)) → F
eqt(tuple(H1, T1), cons(H2, T2)) → F
eqt(tuple(H1, T1), tuple(H2, T2)) → and(eqt(H1, H2), eqt(T1, T2))
eqt(tuple(H1, T1), tuplenil(H2)) → F
eqt(tuplenil(H1), nil) → F
eqt(tuplenil(H1), a) → F
eqt(tuplenil(H1), excl) → F
eqt(tuplenil(H1), false) → F
eqt(tuplenil(H1), lock) → F
eqt(tuplenil(H1), locker) → F
eqt(tuplenil(H1), mcrlrecord) → F
eqt(tuplenil(H1), ok) → F
eqt(tuplenil(H1), pending) → F
eqt(tuplenil(H1), release) → F
eqt(tuplenil(H1), request) → F
eqt(tuplenil(H1), resource) → F
eqt(tuplenil(H1), tag) → F
eqt(tuplenil(H1), true) → F
eqt(tuplenil(H1), undefined) → F
eqt(tuplenil(H1), pid(N2)) → F
eqt(tuplenil(H1), int(N2)) → F
eqt(tuplenil(H1), cons(H2, T2)) → F
eqt(tuplenil(H1), tuple(H2, T2)) → F
eqt(tuplenil(H1), tuplenil(H2)) → eqt(H1, H2)
element(int(s(0)), tuplenil(T1)) → T1
element(int(s(0)), tuple(T1, T2)) → T1
element(int(s(s(N1))), tuple(T1, T2)) → element(int(s(N1)), T2)
record_new(lock) → tuple(mcrlrecord, tuple(lock, tuple(undefined, tuple(nil, tuplenil(nil)))))
record_extract(tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))), lock, resource) → tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2)))))
record_update(tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))), lock, pending, NewF) → tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(NewF)))))
record_updates(Record, Name, nil) → Record
record_updates(Record, Name, cons(tuple(Field, tuplenil(NewF)), Fields)) → record_updates(record_update(Record, Name, Field, NewF), Name, Fields)
locker2_map_promote_pending(nil, Pending) → nil
locker2_map_promote_pending(cons(Lock, Locks), Pending) → cons(locker2_promote_pending(Lock, Pending), locker2_map_promote_pending(Locks, Pending))
locker2_map_claim_lock(nil, Resources, Client) → nil
locker2_map_claim_lock(cons(Lock, Locks), Resources, Client) → cons(locker2_claim_lock(Lock, Resources, Client), locker2_map_claim_lock(Locks, Resources, Client))
locker2_map_add_pending(nil, Resources, Client) → nil
locker2_promote_pending(Lock, Client) → case0(Client, Lock, record_extract(Lock, lock, pending))
case0(Client, Lock, cons(Client, Pendings)) → record_updates(Lock, lock, cons(tuple(excl, tuplenil(Client)), cons(tuple(pending, tuplenil(Pendings)), nil)))
case0(Client, Lock, MCRLFree0) → Lock
locker2_remove_pending(Lock, Client) → record_updates(Lock, lock, cons(tuple(pending, tuplenil(subtract(record_extract(Lock, lock, pending), cons(Client, nil)))), nil))
locker2_add_pending(Lock, Resources, Client) → case1(Client, Resources, Lock, member(record_extract(Lock, lock, resource), Resources))
case1(Client, Resources, Lock, true) → record_updates(Lock, lock, cons(tuple(pending, tuplenil(append(record_extract(Lock, lock, pending), cons(Client, nil)))), nil))
case1(Client, Resources, Lock, false) → Lock
locker2_release_lock(Lock, Client) → case2(Client, Lock, gen_modtageq(Client, record_extract(Lock, lock, excl)))
case2(Client, Lock, true) → record_updates(Lock, lock, cons(tuple(excllock, excl), nil))
case4(Client, Lock, MCRLFree1) → false
locker2_obtainables(nil, Client) → true
locker2_obtainables(cons(Lock, Locks), Client) → case5(Client, Locks, Lock, member(Client, record_extract(Lock, lock, pending)))
case5(Client, Locks, Lock, true) → andt(locker2_obtainable(Lock, Client), locker2_obtainables(Locks, Client))
case5(Client, Locks, Lock, false) → locker2_obtainables(Locks, Client)
locker2_check_available(Resource, nil) → false
locker2_check_available(Resource, cons(Lock, Locks)) → case6(Locks, Lock, Resource, equal(Resource, record_extract(Lock, lock, resource)))
case6(Locks, Lock, Resource, true) → andt(equal(record_extract(Lock, lock, excl), nil), equal(record_extract(Lock, lock, pending), nil))
case6(Locks, Lock, Resource, false) → locker2_check_available(Resource, Locks)
locker2_check_availables(nil, Locks) → true
locker2_check_availables(cons(Resource, Resources), Locks) → andt(locker2_check_available(Resource, Locks), locker2_check_availables(Resources, Locks))
locker2_adduniq(nil, List) → List
append(cons(Head, Tail), List) → cons(Head, append(Tail, List))
subtract(List, nil) → List
subtract(List, cons(Head, Tail)) → subtract(delete(Head, List), Tail)
delete(E, nil) → nil
delete(E, cons(Head, Tail)) → case8(Tail, Head, E, equal(E, Head))
case8(Tail, Head, E, true) → Tail
case8(Tail, Head, E, false) → cons(Head, delete(E, Tail))
gen_tag(Pid) → tuple(Pid, tuplenil(tag))
gen_modtageq(Client1, Client2) → equal(Client1, Client2)
member(E, nil) → false
member(E, cons(Head, Tail)) → case9(Tail, Head, E, equal(E, Head))
case9(Tail, Head, E, true) → true
case9(Tail, Head, E, false) → member(E, Tail)
eqs(empty, empty) → T
eqs(empty, stack(E2, S2)) → F
eqs(stack(E1, S1), empty) → F
eqs(stack(E1, S1), stack(E2, S2)) → and(eqt(E1, E2), eqs(S1, S2))
pushs(E1, S1) → stack(E1, S1)
pops(stack(E1, S1)) → S1
tops(stack(E1, S1)) → E1
istops(E1, empty) → F
istops(E1, stack(E2, S1)) → eqt(E1, E2)
eqc(nocalls, nocalls) → T
eqc(nocalls, calls(E2, S2, CS2)) → F
eqc(calls(E1, S1, CS1), nocalls) → F
eqc(calls(E1, S1, CS1), calls(E2, S2, CS2)) → and(eqt(E1, E2), and(eqs(S1, S2), eqc(CS1, CS2)))
push(E1, E2, nocalls) → calls(E1, stack(E2, empty), nocalls)
push(E1, E2, calls(E3, S1, CS1)) → push1(E1, E2, E3, S1, CS1, eqt(E1, E3))
push1(E1, E2, E3, S1, CS1, T) → calls(E3, pushs(E2, S1), CS1)

Q is empty.

(1) DependencyPairsProof (EQUIVALENT transformation)

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

(2) Obligation:

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

EQT(pid(N1), pid(N2)) → EQT(N1, N2)
EQT(cons(H1, T1), cons(H2, T2)) → AND(eqt(H1, H2), eqt(T1, T2))
EQT(cons(H1, T1), cons(H2, T2)) → EQT(H1, H2)
EQT(cons(H1, T1), cons(H2, T2)) → EQT(T1, T2)
EQT(tuple(H1, T1), tuple(H2, T2)) → AND(eqt(H1, H2), eqt(T1, T2))
EQT(tuple(H1, T1), tuple(H2, T2)) → EQT(H1, H2)
EQT(tuple(H1, T1), tuple(H2, T2)) → EQT(T1, T2)
EQT(tuplenil(H1), tuplenil(H2)) → EQT(H1, H2)
ELEMENT(int(s(s(N1))), tuple(T1, T2)) → ELEMENT(int(s(N1)), T2)
RECORD_UPDATES(Record, Name, cons(tuple(Field, tuplenil(NewF)), Fields)) → RECORD_UPDATES(record_update(Record, Name, Field, NewF), Name, Fields)
RECORD_UPDATES(Record, Name, cons(tuple(Field, tuplenil(NewF)), Fields)) → RECORD_UPDATE(Record, Name, Field, NewF)
LOCKER2_MAP_PROMOTE_PENDING(cons(Lock, Locks), Pending) → LOCKER2_PROMOTE_PENDING(Lock, Pending)
LOCKER2_MAP_PROMOTE_PENDING(cons(Lock, Locks), Pending) → LOCKER2_MAP_PROMOTE_PENDING(Locks, Pending)
LOCKER2_MAP_CLAIM_LOCK(cons(Lock, Locks), Resources, Client) → LOCKER2_MAP_CLAIM_LOCK(Locks, Resources, Client)
LOCKER2_PROMOTE_PENDING(Lock, Client) → CASE0(Client, Lock, record_extract(Lock, lock, pending))
LOCKER2_PROMOTE_PENDING(Lock, Client) → RECORD_EXTRACT(Lock, lock, pending)
CASE0(Client, Lock, cons(Client, Pendings)) → RECORD_UPDATES(Lock, lock, cons(tuple(excl, tuplenil(Client)), cons(tuple(pending, tuplenil(Pendings)), nil)))
LOCKER2_REMOVE_PENDING(Lock, Client) → RECORD_UPDATES(Lock, lock, cons(tuple(pending, tuplenil(subtract(record_extract(Lock, lock, pending), cons(Client, nil)))), nil))
LOCKER2_REMOVE_PENDING(Lock, Client) → SUBTRACT(record_extract(Lock, lock, pending), cons(Client, nil))
LOCKER2_REMOVE_PENDING(Lock, Client) → RECORD_EXTRACT(Lock, lock, pending)
LOCKER2_ADD_PENDING(Lock, Resources, Client) → CASE1(Client, Resources, Lock, member(record_extract(Lock, lock, resource), Resources))
LOCKER2_ADD_PENDING(Lock, Resources, Client) → MEMBER(record_extract(Lock, lock, resource), Resources)
LOCKER2_ADD_PENDING(Lock, Resources, Client) → RECORD_EXTRACT(Lock, lock, resource)
CASE1(Client, Resources, Lock, true) → RECORD_UPDATES(Lock, lock, cons(tuple(pending, tuplenil(append(record_extract(Lock, lock, pending), cons(Client, nil)))), nil))
CASE1(Client, Resources, Lock, true) → APPEND(record_extract(Lock, lock, pending), cons(Client, nil))
CASE1(Client, Resources, Lock, true) → RECORD_EXTRACT(Lock, lock, pending)
LOCKER2_RELEASE_LOCK(Lock, Client) → CASE2(Client, Lock, gen_modtageq(Client, record_extract(Lock, lock, excl)))
LOCKER2_RELEASE_LOCK(Lock, Client) → GEN_MODTAGEQ(Client, record_extract(Lock, lock, excl))
LOCKER2_RELEASE_LOCK(Lock, Client) → RECORD_EXTRACT(Lock, lock, excl)
CASE2(Client, Lock, true) → RECORD_UPDATES(Lock, lock, cons(tuple(excllock, excl), nil))
LOCKER2_OBTAINABLES(cons(Lock, Locks), Client) → CASE5(Client, Locks, Lock, member(Client, record_extract(Lock, lock, pending)))
LOCKER2_OBTAINABLES(cons(Lock, Locks), Client) → MEMBER(Client, record_extract(Lock, lock, pending))
LOCKER2_OBTAINABLES(cons(Lock, Locks), Client) → RECORD_EXTRACT(Lock, lock, pending)
CASE5(Client, Locks, Lock, true) → LOCKER2_OBTAINABLES(Locks, Client)
CASE5(Client, Locks, Lock, false) → LOCKER2_OBTAINABLES(Locks, Client)
LOCKER2_CHECK_AVAILABLE(Resource, cons(Lock, Locks)) → CASE6(Locks, Lock, Resource, equal(Resource, record_extract(Lock, lock, resource)))
LOCKER2_CHECK_AVAILABLE(Resource, cons(Lock, Locks)) → RECORD_EXTRACT(Lock, lock, resource)
CASE6(Locks, Lock, Resource, true) → RECORD_EXTRACT(Lock, lock, excl)
CASE6(Locks, Lock, Resource, true) → RECORD_EXTRACT(Lock, lock, pending)
CASE6(Locks, Lock, Resource, false) → LOCKER2_CHECK_AVAILABLE(Resource, Locks)
LOCKER2_CHECK_AVAILABLES(cons(Resource, Resources), Locks) → LOCKER2_CHECK_AVAILABLE(Resource, Locks)
LOCKER2_CHECK_AVAILABLES(cons(Resource, Resources), Locks) → LOCKER2_CHECK_AVAILABLES(Resources, Locks)
APPEND(cons(Head, Tail), List) → APPEND(Tail, List)
SUBTRACT(List, cons(Head, Tail)) → SUBTRACT(delete(Head, List), Tail)
SUBTRACT(List, cons(Head, Tail)) → DELETE(Head, List)
DELETE(E, cons(Head, Tail)) → CASE8(Tail, Head, E, equal(E, Head))
CASE8(Tail, Head, E, false) → DELETE(E, Tail)
MEMBER(E, cons(Head, Tail)) → CASE9(Tail, Head, E, equal(E, Head))
CASE9(Tail, Head, E, false) → MEMBER(E, Tail)
EQS(stack(E1, S1), stack(E2, S2)) → AND(eqt(E1, E2), eqs(S1, S2))
EQS(stack(E1, S1), stack(E2, S2)) → EQT(E1, E2)
EQS(stack(E1, S1), stack(E2, S2)) → EQS(S1, S2)
ISTOPS(E1, stack(E2, S1)) → EQT(E1, E2)
EQC(calls(E1, S1, CS1), calls(E2, S2, CS2)) → AND(eqt(E1, E2), and(eqs(S1, S2), eqc(CS1, CS2)))
EQC(calls(E1, S1, CS1), calls(E2, S2, CS2)) → EQT(E1, E2)
EQC(calls(E1, S1, CS1), calls(E2, S2, CS2)) → AND(eqs(S1, S2), eqc(CS1, CS2))
EQC(calls(E1, S1, CS1), calls(E2, S2, CS2)) → EQS(S1, S2)
EQC(calls(E1, S1, CS1), calls(E2, S2, CS2)) → EQC(CS1, CS2)
PUSH(E1, E2, calls(E3, S1, CS1)) → PUSH1(E1, E2, E3, S1, CS1, eqt(E1, E3))
PUSH(E1, E2, calls(E3, S1, CS1)) → EQT(E1, E3)
PUSH1(E1, E2, E3, S1, CS1, T) → PUSHS(E2, S1)

The TRS R consists of the following rules:

or(T, T) → T
or(F, T) → T
or(T, F) → T
or(F, F) → F
and(T, B) → B
and(B, T) → B
and(F, B) → F
and(B, F) → F
imp(T, B) → B
imp(F, B) → T
not(T) → F
not(F) → T
if(T, B1, B2) → B1
if(F, B1, B2) → B2
eq(T, T) → T
eq(F, F) → T
eq(T, F) → F
eq(F, T) → F
eqt(nil, undefined) → F
eqt(nil, pid(N2)) → F
eqt(nil, int(N2)) → F
eqt(nil, cons(H2, T2)) → F
eqt(nil, tuple(H2, T2)) → F
eqt(nil, tuplenil(H2)) → F
eqt(a, nil) → F
eqt(a, a) → T
eqt(a, excl) → F
eqt(a, false) → F
eqt(a, lock) → F
eqt(a, locker) → F
eqt(a, mcrlrecord) → F
eqt(a, ok) → F
eqt(a, pending) → F
eqt(a, release) → F
eqt(a, request) → F
eqt(a, resource) → F
eqt(a, tag) → F
eqt(a, true) → F
eqt(a, undefined) → F
eqt(a, pid(N2)) → F
eqt(a, int(N2)) → F
eqt(a, cons(H2, T2)) → F
eqt(a, tuple(H2, T2)) → F
eqt(a, tuplenil(H2)) → F
eqt(excl, nil) → F
eqt(excl, a) → F
eqt(excl, excl) → T
eqt(excl, false) → F
eqt(excl, lock) → F
eqt(excl, locker) → F
eqt(excl, mcrlrecord) → F
eqt(excl, ok) → F
eqt(excl, pending) → F
eqt(excl, release) → F
eqt(excl, request) → F
eqt(excl, resource) → F
eqt(excl, tag) → F
eqt(excl, true) → F
eqt(excl, undefined) → F
eqt(excl, pid(N2)) → F
eqt(excl, eqt(false, int(N2))) → F
eqt(false, cons(H2, T2)) → F
eqt(false, tuple(H2, T2)) → F
eqt(false, tuplenil(H2)) → F
eqt(lock, nil) → F
eqt(lock, a) → F
eqt(lock, excl) → F
eqt(lock, false) → F
eqt(lock, lock) → T
eqt(lock, locker) → F
eqt(lock, mcrlrecord) → F
eqt(lock, ok) → F
eqt(lock, pending) → F
eqt(lock, release) → F
eqt(lock, request) → F
eqt(lock, resource) → F
eqt(lock, tag) → F
eqt(lock, true) → F
eqt(lock, undefined) → F
eqt(lock, pid(N2)) → F
eqt(lock, int(N2)) → F
eqt(lock, cons(H2, T2)) → F
eqt(lock, tuple(H2, T2)) → F
eqt(lock, tuplenil(H2)) → F
eqt(locker, nil) → F
eqt(locker, a) → F
eqt(locker, excl) → F
eqt(locker, false) → F
eqt(locker, lock) → F
eqt(locker, locker) → T
eqt(locker, mcrlrecord) → F
eqt(locker, ok) → F
eqt(locker, pending) → F
eqt(locker, release) → F
eqt(locker, request) → F
eqt(locker, resource) → F
eqt(locker, tag) → F
eqt(locker, true) → F
eqt(locker, undefined) → F
eqt(locker, pid(N2)) → F
eqt(locker, int(N2)) → F
eqt(locker, cons(H2, T2)) → F
eqt(locker, tuple(H2, T2)) → F
eqt(locker, tuplenil(H2)) → F
eqt(mcrlrecord, nil) → F
eqt(mcrlrecord, a) → F
eqt(mcrlrecord, excl) → F
eqt(mcrlrecord, false) → F
eqt(mcrlrecord, lock) → F
eqt(mcrlrecord, locker) → F
eqt(mcrlrecord, mcrlrecord) → T
eqt(mcrlrecord, ok) → F
eqt(mcrlrecord, pending) → F
eqt(mcrlrecord, release) → F
eqt(mcrlrecord, request) → F
eqt(mcrlrecord, resource) → F
eqt(ok, resource) → F
eqt(ok, tag) → F
eqt(ok, true) → F
eqt(ok, undefined) → F
eqt(ok, pid(N2)) → F
eqt(ok, int(N2)) → F
eqt(ok, cons(H2, T2)) → F
eqt(ok, tuple(H2, T2)) → F
eqt(ok, tuplenil(H2)) → F
eqt(pending, nil) → F
eqt(pending, a) → F
eqt(pending, excl) → F
eqt(pending, false) → F
eqt(pending, lock) → F
eqt(pending, locker) → F
eqt(pending, mcrlrecord) → F
eqt(pending, ok) → F
eqt(pending, pending) → T
eqt(pending, release) → F
eqt(pending, request) → F
eqt(pending, resource) → F
eqt(pending, tag) → F
eqt(pending, true) → F
eqt(pending, undefined) → F
eqt(pending, pid(N2)) → F
eqt(pending, int(N2)) → F
eqt(pending, cons(H2, T2)) → F
eqt(pending, tuple(H2, T2)) → F
eqt(pending, tuplenil(H2)) → F
eqt(release, nil) → F
eqt(release, a) → F
eqt(release, excl) → F
eqt(release, false) → F
eqt(release, lock) → F
eqt(release, locker) → F
eqt(release, mcrlrecord) → F
eqt(release, ok) → F
eqt(request, mcrlrecord) → F
eqt(request, ok) → F
eqt(request, pending) → F
eqt(request, release) → F
eqt(request, request) → T
eqt(request, resource) → F
eqt(request, tag) → F
eqt(request, true) → F
eqt(request, undefined) → F
eqt(request, pid(N2)) → F
eqt(request, int(N2)) → F
eqt(request, cons(H2, T2)) → F
eqt(request, tuple(H2, T2)) → F
eqt(request, tuplenil(H2)) → F
eqt(resource, nil) → F
eqt(resource, a) → F
eqt(resource, excl) → F
eqt(resource, false) → F
eqt(resource, lock) → F
eqt(resource, locker) → F
eqt(resource, mcrlrecord) → F
eqt(resource, ok) → F
eqt(resource, pending) → F
eqt(resource, release) → F
eqt(resource, request) → F
eqt(resource, resource) → T
eqt(resource, tag) → F
eqt(resource, true) → F
eqt(resource, undefined) → F
eqt(resource, pid(N2)) → F
eqt(resource, int(N2)) → F
eqt(resource, cons(H2, T2)) → F
eqt(resource, tuple(H2, T2)) → F
eqt(resource, tuplenil(H2)) → F
eqt(tag, nil) → F
eqt(tag, a) → F
eqt(tag, excl) → F
eqt(tag, false) → F
eqt(tag, lock) → F
eqt(tag, locker) → F
eqt(tag, mcrlrecord) → F
eqt(tag, ok) → F
eqt(tag, pending) → F
eqt(tag, release) → F
eqt(tag, request) → F
eqt(tag, resource) → F
eqt(tag, tag) → T
eqt(tag, true) → F
eqt(tag, undefined) → F
eqt(tag, pid(N2)) → F
eqt(tag, int(N2)) → F
eqt(tag, cons(H2, T2)) → F
eqt(tag, tuple(H2, T2)) → F
eqt(tag, tuplenil(H2)) → F
eqt(true, nil) → F
eqt(true, a) → F
eqt(true, excl) → F
eqt(true, false) → F
eqt(true, lock) → F
eqt(true, locker) → F
eqt(true, mcrlrecord) → F
eqt(true, ok) → F
eqt(true, pending) → F
eqt(true, release) → F
eqt(true, request) → F
eqt(true, resource) → F
eqt(true, tag) → F
eqt(true, true) → T
eqt(true, undefined) → F
eqt(true, pid(N2)) → F
eqt(true, int(N2)) → F
eqt(true, cons(H2, T2)) → F
eqt(true, tuple(H2, T2)) → F
eqt(true, tuplenil(H2)) → F
eqt(undefined, nil) → F
eqt(undefined, a) → F
eqt(undefined, tuplenil(H2)) → F
eqt(pid(N1), nil) → F
eqt(pid(N1), a) → F
eqt(pid(N1), excl) → F
eqt(pid(N1), false) → F
eqt(pid(N1), lock) → F
eqt(pid(N1), locker) → F
eqt(pid(N1), mcrlrecord) → F
eqt(pid(N1), ok) → F
eqt(pid(N1), pending) → F
eqt(pid(N1), release) → F
eqt(pid(N1), request) → F
eqt(pid(N1), resource) → F
eqt(pid(N1), tag) → F
eqt(pid(N1), true) → F
eqt(pid(N1), undefined) → F
eqt(pid(N1), pid(N2)) → eqt(N1, N2)
eqt(pid(N1), int(N2)) → F
eqt(pid(N1), cons(H2, T2)) → F
eqt(pid(N1), tuple(H2, T2)) → F
eqt(pid(N1), tuplenil(H2)) → F
eqt(int(N1), nil) → F
eqt(int(N1), a) → F
eqt(int(N1), excl) → F
eqt(int(N1), false) → F
eqt(int(N1), lock) → F
eqt(int(N1), locker) → F
eqt(int(N1), mcrlrecord) → F
eqt(int(N1), ok) → F
eqt(int(N1), pending) → F
eqt(int(N1), release) → F
eqt(int(N1), request) → F
eqt(int(N1), resource) → F
eqt(int(N1), tag) → F
eqt(int(N1), true) → F
eqt(int(N1), undefined) → F
eqt(cons(H1, T1), resource) → F
eqt(cons(H1, T1), tag) → F
eqt(cons(H1, T1), true) → F
eqt(cons(H1, T1), undefined) → F
eqt(cons(H1, T1), pid(N2)) → F
eqt(cons(H1, T1), int(N2)) → F
eqt(cons(H1, T1), cons(H2, T2)) → and(eqt(H1, H2), eqt(T1, T2))
eqt(cons(H1, T1), tuple(H2, T2)) → F
eqt(cons(H1, T1), tuplenil(H2)) → F
eqt(tuple(H1, T1), nil) → F
eqt(tuple(H1, T1), a) → F
eqt(tuple(H1, T1), excl) → F
eqt(tuple(H1, T1), false) → F
eqt(tuple(H1, T1), lock) → F
eqt(tuple(H1, T1), locker) → F
eqt(tuple(H1, T1), mcrlrecord) → F
eqt(tuple(H1, T1), ok) → F
eqt(tuple(H1, T1), pending) → F
eqt(tuple(H1, T1), release) → F
eqt(tuple(H1, T1), request) → F
eqt(tuple(H1, T1), resource) → F
eqt(tuple(H1, T1), tag) → F
eqt(tuple(H1, T1), true) → F
eqt(tuple(H1, T1), undefined) → F
eqt(tuple(H1, T1), pid(N2)) → F
eqt(tuple(H1, T1), int(N2)) → F
eqt(tuple(H1, T1), cons(H2, T2)) → F
eqt(tuple(H1, T1), tuple(H2, T2)) → and(eqt(H1, H2), eqt(T1, T2))
eqt(tuple(H1, T1), tuplenil(H2)) → F
eqt(tuplenil(H1), nil) → F
eqt(tuplenil(H1), a) → F
eqt(tuplenil(H1), excl) → F
eqt(tuplenil(H1), false) → F
eqt(tuplenil(H1), lock) → F
eqt(tuplenil(H1), locker) → F
eqt(tuplenil(H1), mcrlrecord) → F
eqt(tuplenil(H1), ok) → F
eqt(tuplenil(H1), pending) → F
eqt(tuplenil(H1), release) → F
eqt(tuplenil(H1), request) → F
eqt(tuplenil(H1), resource) → F
eqt(tuplenil(H1), tag) → F
eqt(tuplenil(H1), true) → F
eqt(tuplenil(H1), undefined) → F
eqt(tuplenil(H1), pid(N2)) → F
eqt(tuplenil(H1), int(N2)) → F
eqt(tuplenil(H1), cons(H2, T2)) → F
eqt(tuplenil(H1), tuple(H2, T2)) → F
eqt(tuplenil(H1), tuplenil(H2)) → eqt(H1, H2)
element(int(s(0)), tuplenil(T1)) → T1
element(int(s(0)), tuple(T1, T2)) → T1
element(int(s(s(N1))), tuple(T1, T2)) → element(int(s(N1)), T2)
record_new(lock) → tuple(mcrlrecord, tuple(lock, tuple(undefined, tuple(nil, tuplenil(nil)))))
record_extract(tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))), lock, resource) → tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2)))))
record_update(tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))), lock, pending, NewF) → tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(NewF)))))
record_updates(Record, Name, nil) → Record
record_updates(Record, Name, cons(tuple(Field, tuplenil(NewF)), Fields)) → record_updates(record_update(Record, Name, Field, NewF), Name, Fields)
locker2_map_promote_pending(nil, Pending) → nil
locker2_map_promote_pending(cons(Lock, Locks), Pending) → cons(locker2_promote_pending(Lock, Pending), locker2_map_promote_pending(Locks, Pending))
locker2_map_claim_lock(nil, Resources, Client) → nil
locker2_map_claim_lock(cons(Lock, Locks), Resources, Client) → cons(locker2_claim_lock(Lock, Resources, Client), locker2_map_claim_lock(Locks, Resources, Client))
locker2_map_add_pending(nil, Resources, Client) → nil
locker2_promote_pending(Lock, Client) → case0(Client, Lock, record_extract(Lock, lock, pending))
case0(Client, Lock, cons(Client, Pendings)) → record_updates(Lock, lock, cons(tuple(excl, tuplenil(Client)), cons(tuple(pending, tuplenil(Pendings)), nil)))
case0(Client, Lock, MCRLFree0) → Lock
locker2_remove_pending(Lock, Client) → record_updates(Lock, lock, cons(tuple(pending, tuplenil(subtract(record_extract(Lock, lock, pending), cons(Client, nil)))), nil))
locker2_add_pending(Lock, Resources, Client) → case1(Client, Resources, Lock, member(record_extract(Lock, lock, resource), Resources))
case1(Client, Resources, Lock, true) → record_updates(Lock, lock, cons(tuple(pending, tuplenil(append(record_extract(Lock, lock, pending), cons(Client, nil)))), nil))
case1(Client, Resources, Lock, false) → Lock
locker2_release_lock(Lock, Client) → case2(Client, Lock, gen_modtageq(Client, record_extract(Lock, lock, excl)))
case2(Client, Lock, true) → record_updates(Lock, lock, cons(tuple(excllock, excl), nil))
case4(Client, Lock, MCRLFree1) → false
locker2_obtainables(nil, Client) → true
locker2_obtainables(cons(Lock, Locks), Client) → case5(Client, Locks, Lock, member(Client, record_extract(Lock, lock, pending)))
case5(Client, Locks, Lock, true) → andt(locker2_obtainable(Lock, Client), locker2_obtainables(Locks, Client))
case5(Client, Locks, Lock, false) → locker2_obtainables(Locks, Client)
locker2_check_available(Resource, nil) → false
locker2_check_available(Resource, cons(Lock, Locks)) → case6(Locks, Lock, Resource, equal(Resource, record_extract(Lock, lock, resource)))
case6(Locks, Lock, Resource, true) → andt(equal(record_extract(Lock, lock, excl), nil), equal(record_extract(Lock, lock, pending), nil))
case6(Locks, Lock, Resource, false) → locker2_check_available(Resource, Locks)
locker2_check_availables(nil, Locks) → true
locker2_check_availables(cons(Resource, Resources), Locks) → andt(locker2_check_available(Resource, Locks), locker2_check_availables(Resources, Locks))
locker2_adduniq(nil, List) → List
append(cons(Head, Tail), List) → cons(Head, append(Tail, List))
subtract(List, nil) → List
subtract(List, cons(Head, Tail)) → subtract(delete(Head, List), Tail)
delete(E, nil) → nil
delete(E, cons(Head, Tail)) → case8(Tail, Head, E, equal(E, Head))
case8(Tail, Head, E, true) → Tail
case8(Tail, Head, E, false) → cons(Head, delete(E, Tail))
gen_tag(Pid) → tuple(Pid, tuplenil(tag))
gen_modtageq(Client1, Client2) → equal(Client1, Client2)
member(E, nil) → false
member(E, cons(Head, Tail)) → case9(Tail, Head, E, equal(E, Head))
case9(Tail, Head, E, true) → true
case9(Tail, Head, E, false) → member(E, Tail)
eqs(empty, empty) → T
eqs(empty, stack(E2, S2)) → F
eqs(stack(E1, S1), empty) → F
eqs(stack(E1, S1), stack(E2, S2)) → and(eqt(E1, E2), eqs(S1, S2))
pushs(E1, S1) → stack(E1, S1)
pops(stack(E1, S1)) → S1
tops(stack(E1, S1)) → E1
istops(E1, empty) → F
istops(E1, stack(E2, S1)) → eqt(E1, E2)
eqc(nocalls, nocalls) → T
eqc(nocalls, calls(E2, S2, CS2)) → F
eqc(calls(E1, S1, CS1), nocalls) → F
eqc(calls(E1, S1, CS1), calls(E2, S2, CS2)) → and(eqt(E1, E2), and(eqs(S1, S2), eqc(CS1, CS2)))
push(E1, E2, nocalls) → calls(E1, stack(E2, empty), nocalls)
push(E1, E2, calls(E3, S1, CS1)) → push1(E1, E2, E3, S1, CS1, eqt(E1, E3))
push1(E1, E2, E3, S1, CS1, T) → calls(E3, pushs(E2, S1), CS1)

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

(3) DependencyGraphProof (EQUIVALENT transformation)

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

(4) Complex Obligation (AND)

(5) Obligation:

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

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

The TRS R consists of the following rules:

or(T, T) → T
or(F, T) → T
or(T, F) → T
or(F, F) → F
and(T, B) → B
and(B, T) → B
and(F, B) → F
and(B, F) → F
imp(T, B) → B
imp(F, B) → T
not(T) → F
not(F) → T
if(T, B1, B2) → B1
if(F, B1, B2) → B2
eq(T, T) → T
eq(F, F) → T
eq(T, F) → F
eq(F, T) → F
eqt(nil, undefined) → F
eqt(nil, pid(N2)) → F
eqt(nil, int(N2)) → F
eqt(nil, cons(H2, T2)) → F
eqt(nil, tuple(H2, T2)) → F
eqt(nil, tuplenil(H2)) → F
eqt(a, nil) → F
eqt(a, a) → T
eqt(a, excl) → F
eqt(a, false) → F
eqt(a, lock) → F
eqt(a, locker) → F
eqt(a, mcrlrecord) → F
eqt(a, ok) → F
eqt(a, pending) → F
eqt(a, release) → F
eqt(a, request) → F
eqt(a, resource) → F
eqt(a, tag) → F
eqt(a, true) → F
eqt(a, undefined) → F
eqt(a, pid(N2)) → F
eqt(a, int(N2)) → F
eqt(a, cons(H2, T2)) → F
eqt(a, tuple(H2, T2)) → F
eqt(a, tuplenil(H2)) → F
eqt(excl, nil) → F
eqt(excl, a) → F
eqt(excl, excl) → T
eqt(excl, false) → F
eqt(excl, lock) → F
eqt(excl, locker) → F
eqt(excl, mcrlrecord) → F
eqt(excl, ok) → F
eqt(excl, pending) → F
eqt(excl, release) → F
eqt(excl, request) → F
eqt(excl, resource) → F
eqt(excl, tag) → F
eqt(excl, true) → F
eqt(excl, undefined) → F
eqt(excl, pid(N2)) → F
eqt(excl, eqt(false, int(N2))) → F
eqt(false, cons(H2, T2)) → F
eqt(false, tuple(H2, T2)) → F
eqt(false, tuplenil(H2)) → F
eqt(lock, nil) → F
eqt(lock, a) → F
eqt(lock, excl) → F
eqt(lock, false) → F
eqt(lock, lock) → T
eqt(lock, locker) → F
eqt(lock, mcrlrecord) → F
eqt(lock, ok) → F
eqt(lock, pending) → F
eqt(lock, release) → F
eqt(lock, request) → F
eqt(lock, resource) → F
eqt(lock, tag) → F
eqt(lock, true) → F
eqt(lock, undefined) → F
eqt(lock, pid(N2)) → F
eqt(lock, int(N2)) → F
eqt(lock, cons(H2, T2)) → F
eqt(lock, tuple(H2, T2)) → F
eqt(lock, tuplenil(H2)) → F
eqt(locker, nil) → F
eqt(locker, a) → F
eqt(locker, excl) → F
eqt(locker, false) → F
eqt(locker, lock) → F
eqt(locker, locker) → T
eqt(locker, mcrlrecord) → F
eqt(locker, ok) → F
eqt(locker, pending) → F
eqt(locker, release) → F
eqt(locker, request) → F
eqt(locker, resource) → F
eqt(locker, tag) → F
eqt(locker, true) → F
eqt(locker, undefined) → F
eqt(locker, pid(N2)) → F
eqt(locker, int(N2)) → F
eqt(locker, cons(H2, T2)) → F
eqt(locker, tuple(H2, T2)) → F
eqt(locker, tuplenil(H2)) → F
eqt(mcrlrecord, nil) → F
eqt(mcrlrecord, a) → F
eqt(mcrlrecord, excl) → F
eqt(mcrlrecord, false) → F
eqt(mcrlrecord, lock) → F
eqt(mcrlrecord, locker) → F
eqt(mcrlrecord, mcrlrecord) → T
eqt(mcrlrecord, ok) → F
eqt(mcrlrecord, pending) → F
eqt(mcrlrecord, release) → F
eqt(mcrlrecord, request) → F
eqt(mcrlrecord, resource) → F
eqt(ok, resource) → F
eqt(ok, tag) → F
eqt(ok, true) → F
eqt(ok, undefined) → F
eqt(ok, pid(N2)) → F
eqt(ok, int(N2)) → F
eqt(ok, cons(H2, T2)) → F
eqt(ok, tuple(H2, T2)) → F
eqt(ok, tuplenil(H2)) → F
eqt(pending, nil) → F
eqt(pending, a) → F
eqt(pending, excl) → F
eqt(pending, false) → F
eqt(pending, lock) → F
eqt(pending, locker) → F
eqt(pending, mcrlrecord) → F
eqt(pending, ok) → F
eqt(pending, pending) → T
eqt(pending, release) → F
eqt(pending, request) → F
eqt(pending, resource) → F
eqt(pending, tag) → F
eqt(pending, true) → F
eqt(pending, undefined) → F
eqt(pending, pid(N2)) → F
eqt(pending, int(N2)) → F
eqt(pending, cons(H2, T2)) → F
eqt(pending, tuple(H2, T2)) → F
eqt(pending, tuplenil(H2)) → F
eqt(release, nil) → F
eqt(release, a) → F
eqt(release, excl) → F
eqt(release, false) → F
eqt(release, lock) → F
eqt(release, locker) → F
eqt(release, mcrlrecord) → F
eqt(release, ok) → F
eqt(request, mcrlrecord) → F
eqt(request, ok) → F
eqt(request, pending) → F
eqt(request, release) → F
eqt(request, request) → T
eqt(request, resource) → F
eqt(request, tag) → F
eqt(request, true) → F
eqt(request, undefined) → F
eqt(request, pid(N2)) → F
eqt(request, int(N2)) → F
eqt(request, cons(H2, T2)) → F
eqt(request, tuple(H2, T2)) → F
eqt(request, tuplenil(H2)) → F
eqt(resource, nil) → F
eqt(resource, a) → F
eqt(resource, excl) → F
eqt(resource, false) → F
eqt(resource, lock) → F
eqt(resource, locker) → F
eqt(resource, mcrlrecord) → F
eqt(resource, ok) → F
eqt(resource, pending) → F
eqt(resource, release) → F
eqt(resource, request) → F
eqt(resource, resource) → T
eqt(resource, tag) → F
eqt(resource, true) → F
eqt(resource, undefined) → F
eqt(resource, pid(N2)) → F
eqt(resource, int(N2)) → F
eqt(resource, cons(H2, T2)) → F
eqt(resource, tuple(H2, T2)) → F
eqt(resource, tuplenil(H2)) → F
eqt(tag, nil) → F
eqt(tag, a) → F
eqt(tag, excl) → F
eqt(tag, false) → F
eqt(tag, lock) → F
eqt(tag, locker) → F
eqt(tag, mcrlrecord) → F
eqt(tag, ok) → F
eqt(tag, pending) → F
eqt(tag, release) → F
eqt(tag, request) → F
eqt(tag, resource) → F
eqt(tag, tag) → T
eqt(tag, true) → F
eqt(tag, undefined) → F
eqt(tag, pid(N2)) → F
eqt(tag, int(N2)) → F
eqt(tag, cons(H2, T2)) → F
eqt(tag, tuple(H2, T2)) → F
eqt(tag, tuplenil(H2)) → F
eqt(true, nil) → F
eqt(true, a) → F
eqt(true, excl) → F
eqt(true, false) → F
eqt(true, lock) → F
eqt(true, locker) → F
eqt(true, mcrlrecord) → F
eqt(true, ok) → F
eqt(true, pending) → F
eqt(true, release) → F
eqt(true, request) → F
eqt(true, resource) → F
eqt(true, tag) → F
eqt(true, true) → T
eqt(true, undefined) → F
eqt(true, pid(N2)) → F
eqt(true, int(N2)) → F
eqt(true, cons(H2, T2)) → F
eqt(true, tuple(H2, T2)) → F
eqt(true, tuplenil(H2)) → F
eqt(undefined, nil) → F
eqt(undefined, a) → F
eqt(undefined, tuplenil(H2)) → F
eqt(pid(N1), nil) → F
eqt(pid(N1), a) → F
eqt(pid(N1), excl) → F
eqt(pid(N1), false) → F
eqt(pid(N1), lock) → F
eqt(pid(N1), locker) → F
eqt(pid(N1), mcrlrecord) → F
eqt(pid(N1), ok) → F
eqt(pid(N1), pending) → F
eqt(pid(N1), release) → F
eqt(pid(N1), request) → F
eqt(pid(N1), resource) → F
eqt(pid(N1), tag) → F
eqt(pid(N1), true) → F
eqt(pid(N1), undefined) → F
eqt(pid(N1), pid(N2)) → eqt(N1, N2)
eqt(pid(N1), int(N2)) → F
eqt(pid(N1), cons(H2, T2)) → F
eqt(pid(N1), tuple(H2, T2)) → F
eqt(pid(N1), tuplenil(H2)) → F
eqt(int(N1), nil) → F
eqt(int(N1), a) → F
eqt(int(N1), excl) → F
eqt(int(N1), false) → F
eqt(int(N1), lock) → F
eqt(int(N1), locker) → F
eqt(int(N1), mcrlrecord) → F
eqt(int(N1), ok) → F
eqt(int(N1), pending) → F
eqt(int(N1), release) → F
eqt(int(N1), request) → F
eqt(int(N1), resource) → F
eqt(int(N1), tag) → F
eqt(int(N1), true) → F
eqt(int(N1), undefined) → F
eqt(cons(H1, T1), resource) → F
eqt(cons(H1, T1), tag) → F
eqt(cons(H1, T1), true) → F
eqt(cons(H1, T1), undefined) → F
eqt(cons(H1, T1), pid(N2)) → F
eqt(cons(H1, T1), int(N2)) → F
eqt(cons(H1, T1), cons(H2, T2)) → and(eqt(H1, H2), eqt(T1, T2))
eqt(cons(H1, T1), tuple(H2, T2)) → F
eqt(cons(H1, T1), tuplenil(H2)) → F
eqt(tuple(H1, T1), nil) → F
eqt(tuple(H1, T1), a) → F
eqt(tuple(H1, T1), excl) → F
eqt(tuple(H1, T1), false) → F
eqt(tuple(H1, T1), lock) → F
eqt(tuple(H1, T1), locker) → F
eqt(tuple(H1, T1), mcrlrecord) → F
eqt(tuple(H1, T1), ok) → F
eqt(tuple(H1, T1), pending) → F
eqt(tuple(H1, T1), release) → F
eqt(tuple(H1, T1), request) → F
eqt(tuple(H1, T1), resource) → F
eqt(tuple(H1, T1), tag) → F
eqt(tuple(H1, T1), true) → F
eqt(tuple(H1, T1), undefined) → F
eqt(tuple(H1, T1), pid(N2)) → F
eqt(tuple(H1, T1), int(N2)) → F
eqt(tuple(H1, T1), cons(H2, T2)) → F
eqt(tuple(H1, T1), tuple(H2, T2)) → and(eqt(H1, H2), eqt(T1, T2))
eqt(tuple(H1, T1), tuplenil(H2)) → F
eqt(tuplenil(H1), nil) → F
eqt(tuplenil(H1), a) → F
eqt(tuplenil(H1), excl) → F
eqt(tuplenil(H1), false) → F
eqt(tuplenil(H1), lock) → F
eqt(tuplenil(H1), locker) → F
eqt(tuplenil(H1), mcrlrecord) → F
eqt(tuplenil(H1), ok) → F
eqt(tuplenil(H1), pending) → F
eqt(tuplenil(H1), release) → F
eqt(tuplenil(H1), request) → F
eqt(tuplenil(H1), resource) → F
eqt(tuplenil(H1), tag) → F
eqt(tuplenil(H1), true) → F
eqt(tuplenil(H1), undefined) → F
eqt(tuplenil(H1), pid(N2)) → F
eqt(tuplenil(H1), int(N2)) → F
eqt(tuplenil(H1), cons(H2, T2)) → F
eqt(tuplenil(H1), tuple(H2, T2)) → F
eqt(tuplenil(H1), tuplenil(H2)) → eqt(H1, H2)
element(int(s(0)), tuplenil(T1)) → T1
element(int(s(0)), tuple(T1, T2)) → T1
element(int(s(s(N1))), tuple(T1, T2)) → element(int(s(N1)), T2)
record_new(lock) → tuple(mcrlrecord, tuple(lock, tuple(undefined, tuple(nil, tuplenil(nil)))))
record_extract(tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))), lock, resource) → tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2)))))
record_update(tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))), lock, pending, NewF) → tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(NewF)))))
record_updates(Record, Name, nil) → Record
record_updates(Record, Name, cons(tuple(Field, tuplenil(NewF)), Fields)) → record_updates(record_update(Record, Name, Field, NewF), Name, Fields)
locker2_map_promote_pending(nil, Pending) → nil
locker2_map_promote_pending(cons(Lock, Locks), Pending) → cons(locker2_promote_pending(Lock, Pending), locker2_map_promote_pending(Locks, Pending))
locker2_map_claim_lock(nil, Resources, Client) → nil
locker2_map_claim_lock(cons(Lock, Locks), Resources, Client) → cons(locker2_claim_lock(Lock, Resources, Client), locker2_map_claim_lock(Locks, Resources, Client))
locker2_map_add_pending(nil, Resources, Client) → nil
locker2_promote_pending(Lock, Client) → case0(Client, Lock, record_extract(Lock, lock, pending))
case0(Client, Lock, cons(Client, Pendings)) → record_updates(Lock, lock, cons(tuple(excl, tuplenil(Client)), cons(tuple(pending, tuplenil(Pendings)), nil)))
case0(Client, Lock, MCRLFree0) → Lock
locker2_remove_pending(Lock, Client) → record_updates(Lock, lock, cons(tuple(pending, tuplenil(subtract(record_extract(Lock, lock, pending), cons(Client, nil)))), nil))
locker2_add_pending(Lock, Resources, Client) → case1(Client, Resources, Lock, member(record_extract(Lock, lock, resource), Resources))
case1(Client, Resources, Lock, true) → record_updates(Lock, lock, cons(tuple(pending, tuplenil(append(record_extract(Lock, lock, pending), cons(Client, nil)))), nil))
case1(Client, Resources, Lock, false) → Lock
locker2_release_lock(Lock, Client) → case2(Client, Lock, gen_modtageq(Client, record_extract(Lock, lock, excl)))
case2(Client, Lock, true) → record_updates(Lock, lock, cons(tuple(excllock, excl), nil))
case4(Client, Lock, MCRLFree1) → false
locker2_obtainables(nil, Client) → true
locker2_obtainables(cons(Lock, Locks), Client) → case5(Client, Locks, Lock, member(Client, record_extract(Lock, lock, pending)))
case5(Client, Locks, Lock, true) → andt(locker2_obtainable(Lock, Client), locker2_obtainables(Locks, Client))
case5(Client, Locks, Lock, false) → locker2_obtainables(Locks, Client)
locker2_check_available(Resource, nil) → false
locker2_check_available(Resource, cons(Lock, Locks)) → case6(Locks, Lock, Resource, equal(Resource, record_extract(Lock, lock, resource)))
case6(Locks, Lock, Resource, true) → andt(equal(record_extract(Lock, lock, excl), nil), equal(record_extract(Lock, lock, pending), nil))
case6(Locks, Lock, Resource, false) → locker2_check_available(Resource, Locks)
locker2_check_availables(nil, Locks) → true
locker2_check_availables(cons(Resource, Resources), Locks) → andt(locker2_check_available(Resource, Locks), locker2_check_availables(Resources, Locks))
locker2_adduniq(nil, List) → List
append(cons(Head, Tail), List) → cons(Head, append(Tail, List))
subtract(List, nil) → List
subtract(List, cons(Head, Tail)) → subtract(delete(Head, List), Tail)
delete(E, nil) → nil
delete(E, cons(Head, Tail)) → case8(Tail, Head, E, equal(E, Head))
case8(Tail, Head, E, true) → Tail
case8(Tail, Head, E, false) → cons(Head, delete(E, Tail))
gen_tag(Pid) → tuple(Pid, tuplenil(tag))
gen_modtageq(Client1, Client2) → equal(Client1, Client2)
member(E, nil) → false
member(E, cons(Head, Tail)) → case9(Tail, Head, E, equal(E, Head))
case9(Tail, Head, E, true) → true
case9(Tail, Head, E, false) → member(E, Tail)
eqs(empty, empty) → T
eqs(empty, stack(E2, S2)) → F
eqs(stack(E1, S1), empty) → F
eqs(stack(E1, S1), stack(E2, S2)) → and(eqt(E1, E2), eqs(S1, S2))
pushs(E1, S1) → stack(E1, S1)
pops(stack(E1, S1)) → S1
tops(stack(E1, S1)) → E1
istops(E1, empty) → F
istops(E1, stack(E2, S1)) → eqt(E1, E2)
eqc(nocalls, nocalls) → T
eqc(nocalls, calls(E2, S2, CS2)) → F
eqc(calls(E1, S1, CS1), nocalls) → F
eqc(calls(E1, S1, CS1), calls(E2, S2, CS2)) → and(eqt(E1, E2), and(eqs(S1, S2), eqc(CS1, CS2)))
push(E1, E2, nocalls) → calls(E1, stack(E2, empty), nocalls)
push(E1, E2, calls(E3, S1, CS1)) → push1(E1, E2, E3, S1, CS1, eqt(E1, E3))
push1(E1, E2, E3, S1, CS1, T) → calls(E3, pushs(E2, S1), CS1)

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

(6) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

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

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
SUBTRACT(x1, x2) = SUBTRACT(x2)
cons(x1, x2) = cons(x1, x2)
delete(x1, x2) = delete(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) = eq
eqt(x1, x2) = eqt(x2)
nil = nil
undefined = undefined
pid(x1) = 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(x1, x2)
s(x1) = s(x1)
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)
locker2_promote_pending(x1, x2) = locker2_promote_pending(x1)
locker2_map_claim_lock(x1, x2, x3) = locker2_map_claim_lock(x1, x2)
locker2_claim_lock(x1, x2, x3) = locker2_claim_lock(x1, x2)
locker2_map_add_pending(x1, x2, x3) = locker2_map_add_pending(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, x4)
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) = x2
excllock = excllock
case4(x1, x2, x3) = case4(x3)
locker2_obtainables(x1, x2) = x1
case5(x1, x2, x3, x4) = x2
andt(x1, x2) = x2
locker2_obtainable(x1, x2) = locker2_obtainable
locker2_check_available(x1, x2) = locker2_check_available(x2)
case6(x1, x2, x3, x4) = case6(x1, x4)
equal(x1, x2) = equal
locker2_check_availables(x1, x2) = locker2_check_availables
locker2_adduniq(x1, x2) = x2
case8(x1, x2, x3, x4) = case8(x1, x2, x3, x4)
gen_tag(x1) = gen_tag(x1)
case9(x1, x2, x3, x4) = case9(x1, x3, x4)
eqs(x1, x2) = eqs(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(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, a, release] > [pending, locker2_obtainable, equal]
imp₁ > [T, F, a, release] > [pending, locker2_obtainable, equal]
not₁ > [pending, locker2_obtainable, equal]
if₂ > [pending, locker2_obtainable, equal]
eq > [T, F, a, release] > [pending, locker2_obtainable, equal]
[eqt₁, eqs₁, empty, stack₂, pushs₂, istops₂, eqc₁, nocalls, push₃, push1₄] > calls₃ > and₂ > [T, F, a, release] > [pending, locker2_obtainable, equal]
locker > [pending, locker2_obtainable, equal]
ok > [pending, locker2_obtainable, equal]
request > [T, F, a, release] > [pending, locker2_obtainable, equal]
s₁ > element₂ > [pending, locker2_obtainable, equal]
0 > [pending, locker2_obtainable, equal]
record_new > [cons₂, lock, record_updates₃] > SUBTRACT₁ > [pending, locker2_obtainable, equal]
record_new > [cons₂, lock, record_updates₃] > nil > true > [pending, locker2_obtainable, equal]
record_new > [cons₂, lock, record_updates₃] > [tuple₂, record_update₂] > mcrlrecord > [pending, locker2_obtainable, equal]
record_new > [cons₂, lock, record_updates₃] > record_extract₂ > [pending, locker2_obtainable, equal]
record_new > [cons₂, lock, record_updates₃] > locker2_{claim_lock₂} > [pending, locker2_obtainable, equal]
record_new > [cons₂, lock, record_updates₃] > locker2_{check_availables} > true > [pending, locker2_obtainable, equal]
record_new > undefined > [T, F, a, release] > [pending, locker2_obtainable, equal]
[locker2_{map_{promote_pending₁}}, locker2_{promote_pending₁}] > [excl, case0₂, case2₂] > [cons₂, lock, record_updates₃] > SUBTRACT₁ > [pending, locker2_obtainable, equal]
[locker2_{map_{promote_pending₁}}, locker2_{promote_pending₁}] > [excl, case0₂, case2₂] > [cons₂, lock, record_updates₃] > nil > true > [pending, locker2_obtainable, equal]
[locker2_{map_{promote_pending₁}}, locker2_{promote_pending₁}] > [excl, case0₂, case2₂] > [cons₂, lock, record_updates₃] > [tuple₂, record_update₂] > mcrlrecord > [pending, locker2_obtainable, equal]
[locker2_{map_{promote_pending₁}}, locker2_{promote_pending₁}] > [excl, case0₂, case2₂] > [cons₂, lock, record_updates₃] > record_extract₂ > [pending, locker2_obtainable, equal]
[locker2_{map_{promote_pending₁}}, locker2_{promote_pending₁}] > [excl, case0₂, case2₂] > [cons₂, lock, record_updates₃] > locker2_{claim_lock₂} > [pending, locker2_obtainable, equal]
[locker2_{map_{promote_pending₁}}, locker2_{promote_pending₁}] > [excl, case0₂, case2₂] > [cons₂, lock, record_updates₃] > locker2_{check_availables} > true > [pending, locker2_obtainable, equal]
[locker2_{map_{promote_pending₁}}, locker2_{promote_pending₁}] > [excl, case0₂, case2₂] > [T, F, a, release] > [pending, locker2_obtainable, equal]
[locker2_{map_{promote_pending₁}}, locker2_{promote_pending₁}] > [excl, case0₂, case2₂] > excllock > [pending, locker2_obtainable, equal]
locker2_{map_{claim_lock₂}} > [cons₂, lock, record_updates₃] > SUBTRACT₁ > [pending, locker2_obtainable, equal]
locker2_{map_{claim_lock₂}} > [cons₂, lock, record_updates₃] > nil > true > [pending, locker2_obtainable, equal]
locker2_{map_{claim_lock₂}} > [cons₂, lock, record_updates₃] > [tuple₂, record_update₂] > mcrlrecord > [pending, locker2_obtainable, equal]
locker2_{map_{claim_lock₂}} > [cons₂, lock, record_updates₃] > record_extract₂ > [pending, locker2_obtainable, equal]
locker2_{map_{claim_lock₂}} > [cons₂, lock, record_updates₃] > locker2_{claim_lock₂} > [pending, locker2_obtainable, equal]
locker2_{map_{claim_lock₂}} > [cons₂, lock, record_updates₃] > locker2_{check_availables} > true > [pending, locker2_obtainable, equal]
locker2_{map_{add_pending₁}} > nil > true > [pending, locker2_obtainable, equal]
locker2_{remove_pending₂} > subtract₂ > [delete₂, case8₄] > [cons₂, lock, record_updates₃] > SUBTRACT₁ > [pending, locker2_obtainable, equal]
locker2_{remove_pending₂} > subtract₂ > [delete₂, case8₄] > [cons₂, lock, record_updates₃] > nil > true > [pending, locker2_obtainable, equal]
locker2_{remove_pending₂} > subtract₂ > [delete₂, case8₄] > [cons₂, lock, record_updates₃] > [tuple₂, record_update₂] > mcrlrecord > [pending, locker2_obtainable, equal]
locker2_{remove_pending₂} > subtract₂ > [delete₂, case8₄] > [cons₂, lock, record_updates₃] > record_extract₂ > [pending, locker2_obtainable, equal]
locker2_{remove_pending₂} > subtract₂ > [delete₂, case8₄] > [cons₂, lock, record_updates₃] > locker2_{claim_lock₂} > [pending, locker2_obtainable, equal]
locker2_{remove_pending₂} > subtract₂ > [delete₂, case8₄] > [cons₂, lock, record_updates₃] > locker2_{check_availables} > true > [pending, locker2_obtainable, equal]
locker2_{add_pending₃} > resource > [cons₂, lock, record_updates₃] > SUBTRACT₁ > [pending, locker2_obtainable, equal]
locker2_{add_pending₃} > resource > [cons₂, lock, record_updates₃] > nil > true > [pending, locker2_obtainable, equal]
locker2_{add_pending₃} > resource > [cons₂, lock, record_updates₃] > [tuple₂, record_update₂] > mcrlrecord > [pending, locker2_obtainable, equal]
locker2_{add_pending₃} > resource > [cons₂, lock, record_updates₃] > record_extract₂ > [pending, locker2_obtainable, equal]
locker2_{add_pending₃} > resource > [cons₂, lock, record_updates₃] > locker2_{claim_lock₂} > [pending, locker2_obtainable, equal]
locker2_{add_pending₃} > resource > [cons₂, lock, record_updates₃] > locker2_{check_availables} > true > [pending, locker2_obtainable, equal]
locker2_{add_pending₃} > resource > [T, F, a, release] > [pending, locker2_obtainable, equal]
locker2_{add_pending₃} > case1₄ > append₁ > [cons₂, lock, record_updates₃] > SUBTRACT₁ > [pending, locker2_obtainable, equal]
locker2_{add_pending₃} > case1₄ > append₁ > [cons₂, lock, record_updates₃] > nil > true > [pending, locker2_obtainable, equal]
locker2_{add_pending₃} > case1₄ > append₁ > [cons₂, lock, record_updates₃] > [tuple₂, record_update₂] > mcrlrecord > [pending, locker2_obtainable, equal]
locker2_{add_pending₃} > case1₄ > append₁ > [cons₂, lock, record_updates₃] > record_extract₂ > [pending, locker2_obtainable, equal]
locker2_{add_pending₃} > case1₄ > append₁ > [cons₂, lock, record_updates₃] > locker2_{claim_lock₂} > [pending, locker2_obtainable, equal]
locker2_{add_pending₃} > case1₄ > append₁ > [cons₂, lock, record_updates₃] > locker2_{check_availables} > true > [pending, locker2_obtainable, equal]
locker2_{add_pending₃} > [member₂, case9₃] > false > [cons₂, lock, record_updates₃] > SUBTRACT₁ > [pending, locker2_obtainable, equal]
locker2_{add_pending₃} > [member₂, case9₃] > false > [cons₂, lock, record_updates₃] > nil > true > [pending, locker2_obtainable, equal]
locker2_{add_pending₃} > [member₂, case9₃] > false > [cons₂, lock, record_updates₃] > [tuple₂, record_update₂] > mcrlrecord > [pending, locker2_obtainable, equal]
locker2_{add_pending₃} > [member₂, case9₃] > false > [cons₂, lock, record_updates₃] > record_extract₂ > [pending, locker2_obtainable, equal]
locker2_{add_pending₃} > [member₂, case9₃] > false > [cons₂, lock, record_updates₃] > locker2_{claim_lock₂} > [pending, locker2_obtainable, equal]
locker2_{add_pending₃} > [member₂, case9₃] > false > [cons₂, lock, record_updates₃] > locker2_{check_availables} > true > [pending, locker2_obtainable, equal]
locker2_{add_pending₃} > [member₂, case9₃] > false > [T, F, a, release] > [pending, locker2_obtainable, equal]
locker2_{release_lock₂} > [excl, case0₂, case2₂] > [cons₂, lock, record_updates₃] > SUBTRACT₁ > [pending, locker2_obtainable, equal]
locker2_{release_lock₂} > [excl, case0₂, case2₂] > [cons₂, lock, record_updates₃] > nil > true > [pending, locker2_obtainable, equal]
locker2_{release_lock₂} > [excl, case0₂, case2₂] > [cons₂, lock, record_updates₃] > [tuple₂, record_update₂] > mcrlrecord > [pending, locker2_obtainable, equal]
locker2_{release_lock₂} > [excl, case0₂, case2₂] > [cons₂, lock, record_updates₃] > record_extract₂ > [pending, locker2_obtainable, equal]
locker2_{release_lock₂} > [excl, case0₂, case2₂] > [cons₂, lock, record_updates₃] > locker2_{claim_lock₂} > [pending, locker2_obtainable, equal]
locker2_{release_lock₂} > [excl, case0₂, case2₂] > [cons₂, lock, record_updates₃] > locker2_{check_availables} > true > [pending, locker2_obtainable, equal]
locker2_{release_lock₂} > [excl, case0₂, case2₂] > [T, F, a, release] > [pending, locker2_obtainable, equal]
locker2_{release_lock₂} > [excl, case0₂, case2₂] > excllock > [pending, locker2_obtainable, equal]
case4₁ > false > [cons₂, lock, record_updates₃] > SUBTRACT₁ > [pending, locker2_obtainable, equal]
case4₁ > false > [cons₂, lock, record_updates₃] > nil > true > [pending, locker2_obtainable, equal]
case4₁ > false > [cons₂, lock, record_updates₃] > [tuple₂, record_update₂] > mcrlrecord > [pending, locker2_obtainable, equal]
case4₁ > false > [cons₂, lock, record_updates₃] > record_extract₂ > [pending, locker2_obtainable, equal]
case4₁ > false > [cons₂, lock, record_updates₃] > locker2_{claim_lock₂} > [pending, locker2_obtainable, equal]
case4₁ > false > [cons₂, lock, record_updates₃] > locker2_{check_availables} > true > [pending, locker2_obtainable, equal]
case4₁ > false > [T, F, a, release] > [pending, locker2_obtainable, equal]
[locker2_{check_available₁}, case6₂] > false > [cons₂, lock, record_updates₃] > SUBTRACT₁ > [pending, locker2_obtainable, equal]
[locker2_{check_available₁}, case6₂] > false > [cons₂, lock, record_updates₃] > nil > true > [pending, locker2_obtainable, equal]
[locker2_{check_available₁}, case6₂] > false > [cons₂, lock, record_updates₃] > [tuple₂, record_update₂] > mcrlrecord > [pending, locker2_obtainable, equal]
[locker2_{check_available₁}, case6₂] > false > [cons₂, lock, record_updates₃] > record_extract₂ > [pending, locker2_obtainable, equal]
[locker2_{check_available₁}, case6₂] > false > [cons₂, lock, record_updates₃] > locker2_{claim_lock₂} > [pending, locker2_obtainable, equal]
[locker2_{check_available₁}, case6₂] > false > [cons₂, lock, record_updates₃] > locker2_{check_availables} > true > [pending, locker2_obtainable, equal]
[locker2_{check_available₁}, case6₂] > false > [T, F, a, release] > [pending, locker2_obtainable, equal]
gen_tag₁ > [tuple₂, record_update₂] > mcrlrecord > [pending, locker2_obtainable, equal]
gen_tag₁ > tag > [pending, locker2_obtainable, equal]
tops₁ > [pending, locker2_obtainable, equal]

Status:

SUBTRACT₁: [1]
cons₂: [1,2]
delete₂: [2,1]
or: []
T: []
F: []
and₂: [1,2]
imp₁: [1]
not₁: [1]
if₂: [1,2]
eq: []
eqt₁: [1]
nil: []
undefined: []
tuple₂: [1,2]
a: []
excl: []
false: []
lock: []
locker: []
mcrlrecord: []
ok: []
pending: []
release: []
request: []
resource: []
tag: []
true: []
element₂: [2,1]
s₁: [1]
0: []
record_new: []
record_extract₂: [2,1]
record_update₂: [1,2]
record_updates₃: [3,2,1]
locker2_{map_{promote_pending₁}}: [1]
locker2_{promote_pending₁}: [1]
locker2_{map_{claim_lock₂}}: [1,2]
locker2_{claim_lock₂}: [2,1]
locker2_{map_{add_pending₁}}: [1]
case0₂: [1,2]
locker2_{remove_pending₂}: [2,1]
subtract₂: [2,1]
locker2_{add_pending₃}: [3,2,1]
case1₄: [4,3,2,1]
member₂: [2,1]
append₁: [1]
locker2_{release_lock₂}: [2,1]
case2₂: [1,2]
excllock: []
case4₁: [1]
locker2_obtainable: []
locker2_{check_available₁}: [1]
case6₂: [1,2]
equal: []
locker2_{check_availables}: []
case8₄: [1,3,4,2]
gen_tag₁: [1]
case9₃: [1,2,3]
eqs₁: [1]
empty: []
stack₂: [1,2]
pushs₂: [1,2]
tops₁: [1]
istops₂: [2,1]
eqc₁: [1]
nocalls: []
calls₃: [2,1,3]
push₃: [2,3,1]
push1₄: [1,3,2,4]

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) = 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(x2)
eqt(x1, x2) = x2
nil = nil
undefined = undefined
pid(x1) = 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, 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(x3)
locker2_map_add_pending(x1, x2, x3) = locker2_map_add_pending
case0(x1, x2, x3) = case0(x2, x3)
locker2_remove_pending(x1, x2) = locker2_remove_pending(x1, x2)
subtract(x1, x2) = x1
locker2_add_pending(x1, x2, x3) = locker2_add_pending(x1, x2, x3)
case1(x1, x2, x3, x4) = case1(x1, 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(x1, x2)
excllock = excllock
case4(x1, x2, x3) = case4
locker2_obtainables(x1, x2) = locker2_obtainables
case5(x1, x2, x3, x4) = x4
andt(x1, x2) = x1
locker2_obtainable(x1, x2) = locker2_obtainable
locker2_check_available(x1, x2) = locker2_check_available(x2)
case6(x1, x2, x3, x4) = case6(x1, x2)
equal(x1, x2) = x2
locker2_check_availables(x1, x2) = locker2_check_availables(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) = eqs(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(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:

APPEND₂ > [T, F, not, undefined, lock, record_extract₂]
or₂ > [T, F, not, undefined, lock, record_extract₂]
if₃ > [T, F, not, undefined, lock, record_extract₂]
eq₁ > [T, F, not, undefined, lock, record_extract₂]
a > [T, F, not, undefined, lock, record_extract₂]
locker > [T, F, not, undefined, lock, record_extract₂]
ok > [T, F, not, undefined, lock, record_extract₂]
release > [T, F, not, undefined, lock, record_extract₂]
request > [T, F, not, undefined, lock, record_extract₂]
resource > [tuple₂, record_update₃] > [and₂, stack₂, pushs₂] > [T, F, not, undefined, lock, record_extract₂]
resource > [tuple₂, record_update₃] > mcrlrecord > [T, F, not, undefined, lock, record_extract₂]
resource > [tuple₂, record_update₃] > s > [T, F, not, undefined, lock, record_extract₂]
0 > [T, F, not, undefined, lock, record_extract₂]
record_new > [nil, locker2_{map_{add_pending}}] > [T, F, not, undefined, lock, record_extract₂]
record_new > [tuple₂, record_update₃] > [and₂, stack₂, pushs₂] > [T, F, not, undefined, lock, record_extract₂]
record_new > [tuple₂, record_update₃] > mcrlrecord > [T, F, not, undefined, lock, record_extract₂]
record_new > [tuple₂, record_update₃] > s > [T, F, not, undefined, lock, record_extract₂]
[locker2_{map_{promote_pending₁}}, locker2_{promote_pending₁}] > case0₂ > [excl, case2₁] > [cons₂, case8₂] > [and₂, stack₂, pushs₂] > [T, F, not, undefined, lock, record_extract₂]
[locker2_{map_{promote_pending₁}}, locker2_{promote_pending₁}] > case0₂ > [excl, case2₁] > [cons₂, case8₂] > [nil, locker2_{map_{add_pending}}] > [T, F, not, undefined, lock, record_extract₂]
[locker2_{map_{promote_pending₁}}, locker2_{promote_pending₁}] > case0₂ > [excl, case2₁] > record_updates₃ > [tuple₂, record_update₃] > [and₂, stack₂, pushs₂] > [T, F, not, undefined, lock, record_extract₂]
[locker2_{map_{promote_pending₁}}, locker2_{promote_pending₁}] > case0₂ > [excl, case2₁] > record_updates₃ > [tuple₂, record_update₃] > mcrlrecord > [T, F, not, undefined, lock, record_extract₂]
[locker2_{map_{promote_pending₁}}, locker2_{promote_pending₁}] > case0₂ > [excl, case2₁] > record_updates₃ > [tuple₂, record_update₃] > s > [T, F, not, undefined, lock, record_extract₂]
[locker2_{map_{promote_pending₁}}, locker2_{promote_pending₁}] > case0₂ > [excl, case2₁] > excllock > [T, F, not, undefined, lock, record_extract₂]
[locker2_{map_{promote_pending₁}}, locker2_{promote_pending₁}] > case0₂ > pending > [tuple₂, record_update₃] > [and₂, stack₂, pushs₂] > [T, F, not, undefined, lock, record_extract₂]
[locker2_{map_{promote_pending₁}}, locker2_{promote_pending₁}] > case0₂ > pending > [tuple₂, record_update₃] > mcrlrecord > [T, F, not, undefined, lock, record_extract₂]
[locker2_{map_{promote_pending₁}}, locker2_{promote_pending₁}] > case0₂ > pending > [tuple₂, record_update₃] > s > [T, F, not, undefined, lock, record_extract₂]
locker2_{map_{claim_lock₃}} > [cons₂, case8₂] > [and₂, stack₂, pushs₂] > [T, F, not, undefined, lock, record_extract₂]
locker2_{map_{claim_lock₃}} > [cons₂, case8₂] > [nil, locker2_{map_{add_pending}}] > [T, F, not, undefined, lock, record_extract₂]
locker2_{map_{claim_lock₃}} > locker2_{claim_lock₁} > [T, F, not, undefined, lock, record_extract₂]
locker2_{remove_pending₂} > [cons₂, case8₂] > [and₂, stack₂, pushs₂] > [T, F, not, undefined, lock, record_extract₂]
locker2_{remove_pending₂} > [cons₂, case8₂] > [nil, locker2_{map_{add_pending}}] > [T, F, not, undefined, lock, record_extract₂]
locker2_{remove_pending₂} > pending > [tuple₂, record_update₃] > [and₂, stack₂, pushs₂] > [T, F, not, undefined, lock, record_extract₂]
locker2_{remove_pending₂} > pending > [tuple₂, record_update₃] > mcrlrecord > [T, F, not, undefined, lock, record_extract₂]
locker2_{remove_pending₂} > pending > [tuple₂, record_update₃] > s > [T, F, not, undefined, lock, record_extract₂]
locker2_{remove_pending₂} > record_updates₃ > [tuple₂, record_update₃] > [and₂, stack₂, pushs₂] > [T, F, not, undefined, lock, record_extract₂]
locker2_{remove_pending₂} > record_updates₃ > [tuple₂, record_update₃] > mcrlrecord > [T, F, not, undefined, lock, record_extract₂]
locker2_{remove_pending₂} > record_updates₃ > [tuple₂, record_update₃] > s > [T, F, not, undefined, lock, record_extract₂]
locker2_{add_pending₃} > [false, member, locker2_obtainables, locker2_{check_available₁}, case6₂, locker2_{check_{availables₁}}, case9] > [excl, case2₁] > [cons₂, case8₂] > [and₂, stack₂, pushs₂] > [T, F, not, undefined, lock, record_extract₂]
locker2_{add_pending₃} > [false, member, locker2_obtainables, locker2_{check_available₁}, case6₂, locker2_{check_{availables₁}}, case9] > [excl, case2₁] > [cons₂, case8₂] > [nil, locker2_{map_{add_pending}}] > [T, F, not, undefined, lock, record_extract₂]
locker2_{add_pending₃} > [false, member, locker2_obtainables, locker2_{check_available₁}, case6₂, locker2_{check_{availables₁}}, case9] > [excl, case2₁] > record_updates₃ > [tuple₂, record_update₃] > [and₂, stack₂, pushs₂] > [T, F, not, undefined, lock, record_extract₂]
locker2_{add_pending₃} > [false, member, locker2_obtainables, locker2_{check_available₁}, case6₂, locker2_{check_{availables₁}}, case9] > [excl, case2₁] > record_updates₃ > [tuple₂, record_update₃] > mcrlrecord > [T, F, not, undefined, lock, record_extract₂]
locker2_{add_pending₃} > [false, member, locker2_obtainables, locker2_{check_available₁}, case6₂, locker2_{check_{availables₁}}, case9] > [excl, case2₁] > record_updates₃ > [tuple₂, record_update₃] > s > [T, F, not, undefined, lock, record_extract₂]
locker2_{add_pending₃} > [false, member, locker2_obtainables, locker2_{check_available₁}, case6₂, locker2_{check_{availables₁}}, case9] > [excl, case2₁] > excllock > [T, F, not, undefined, lock, record_extract₂]
locker2_{add_pending₃} > [false, member, locker2_obtainables, locker2_{check_available₁}, case6₂, locker2_{check_{availables₁}}, case9] > pending > [tuple₂, record_update₃] > [and₂, stack₂, pushs₂] > [T, F, not, undefined, lock, record_extract₂]
locker2_{add_pending₃} > [false, member, locker2_obtainables, locker2_{check_available₁}, case6₂, locker2_{check_{availables₁}}, case9] > pending > [tuple₂, record_update₃] > mcrlrecord > [T, F, not, undefined, lock, record_extract₂]
locker2_{add_pending₃} > [false, member, locker2_obtainables, locker2_{check_available₁}, case6₂, locker2_{check_{availables₁}}, case9] > pending > [tuple₂, record_update₃] > s > [T, F, not, undefined, lock, record_extract₂]
locker2_{add_pending₃} > [false, member, locker2_obtainables, locker2_{check_available₁}, case6₂, locker2_{check_{availables₁}}, case9] > [true, locker2_obtainable] > [cons₂, case8₂] > [and₂, stack₂, pushs₂] > [T, F, not, undefined, lock, record_extract₂]
locker2_{add_pending₃} > [false, member, locker2_obtainables, locker2_{check_available₁}, case6₂, locker2_{check_{availables₁}}, case9] > [true, locker2_obtainable] > [cons₂, case8₂] > [nil, locker2_{map_{add_pending}}] > [T, F, not, undefined, lock, record_extract₂]
locker2_{add_pending₃} > case1₂ > [cons₂, case8₂] > [and₂, stack₂, pushs₂] > [T, F, not, undefined, lock, record_extract₂]
locker2_{add_pending₃} > case1₂ > [cons₂, case8₂] > [nil, locker2_{map_{add_pending}}] > [T, F, not, undefined, lock, record_extract₂]
locker2_{add_pending₃} > case1₂ > pending > [tuple₂, record_update₃] > [and₂, stack₂, pushs₂] > [T, F, not, undefined, lock, record_extract₂]
locker2_{add_pending₃} > case1₂ > pending > [tuple₂, record_update₃] > mcrlrecord > [T, F, not, undefined, lock, record_extract₂]
locker2_{add_pending₃} > case1₂ > pending > [tuple₂, record_update₃] > s > [T, F, not, undefined, lock, record_extract₂]
locker2_{add_pending₃} > case1₂ > record_updates₃ > [tuple₂, record_update₃] > [and₂, stack₂, pushs₂] > [T, F, not, undefined, lock, record_extract₂]
locker2_{add_pending₃} > case1₂ > record_updates₃ > [tuple₂, record_update₃] > mcrlrecord > [T, F, not, undefined, lock, record_extract₂]
locker2_{add_pending₃} > case1₂ > record_updates₃ > [tuple₂, record_update₃] > s > [T, F, not, undefined, lock, record_extract₂]
locker2_{release_lock₂} > [excl, case2₁] > [cons₂, case8₂] > [and₂, stack₂, pushs₂] > [T, F, not, undefined, lock, record_extract₂]
locker2_{release_lock₂} > [excl, case2₁] > [cons₂, case8₂] > [nil, locker2_{map_{add_pending}}] > [T, F, not, undefined, lock, record_extract₂]
locker2_{release_lock₂} > [excl, case2₁] > record_updates₃ > [tuple₂, record_update₃] > [and₂, stack₂, pushs₂] > [T, F, not, undefined, lock, record_extract₂]
locker2_{release_lock₂} > [excl, case2₁] > record_updates₃ > [tuple₂, record_update₃] > mcrlrecord > [T, F, not, undefined, lock, record_extract₂]
locker2_{release_lock₂} > [excl, case2₁] > record_updates₃ > [tuple₂, record_update₃] > s > [T, F, not, undefined, lock, record_extract₂]
locker2_{release_lock₂} > [excl, case2₁] > excllock > [T, F, not, undefined, lock, record_extract₂]
locker2_{release_lock₂} > gen_modtageq₂ > [T, F, not, undefined, lock, record_extract₂]
case4 > [false, member, locker2_obtainables, locker2_{check_available₁}, case6₂, locker2_{check_{availables₁}}, case9] > [excl, case2₁] > [cons₂, case8₂] > [and₂, stack₂, pushs₂] > [T, F, not, undefined, lock, record_extract₂]
case4 > [false, member, locker2_obtainables, locker2_{check_available₁}, case6₂, locker2_{check_{availables₁}}, case9] > [excl, case2₁] > [cons₂, case8₂] > [nil, locker2_{map_{add_pending}}] > [T, F, not, undefined, lock, record_extract₂]
case4 > [false, member, locker2_obtainables, locker2_{check_available₁}, case6₂, locker2_{check_{availables₁}}, case9] > [excl, case2₁] > record_updates₃ > [tuple₂, record_update₃] > [and₂, stack₂, pushs₂] > [T, F, not, undefined, lock, record_extract₂]
case4 > [false, member, locker2_obtainables, locker2_{check_available₁}, case6₂, locker2_{check_{availables₁}}, case9] > [excl, case2₁] > record_updates₃ > [tuple₂, record_update₃] > mcrlrecord > [T, F, not, undefined, lock, record_extract₂]
case4 > [false, member, locker2_obtainables, locker2_{check_available₁}, case6₂, locker2_{check_{availables₁}}, case9] > [excl, case2₁] > record_updates₃ > [tuple₂, record_update₃] > s > [T, F, not, undefined, lock, record_extract₂]
case4 > [false, member, locker2_obtainables, locker2_{check_available₁}, case6₂, locker2_{check_{availables₁}}, case9] > [excl, case2₁] > excllock > [T, F, not, undefined, lock, record_extract₂]
case4 > [false, member, locker2_obtainables, locker2_{check_available₁}, case6₂, locker2_{check_{availables₁}}, case9] > pending > [tuple₂, record_update₃] > [and₂, stack₂, pushs₂] > [T, F, not, undefined, lock, record_extract₂]
case4 > [false, member, locker2_obtainables, locker2_{check_available₁}, case6₂, locker2_{check_{availables₁}}, case9] > pending > [tuple₂, record_update₃] > mcrlrecord > [T, F, not, undefined, lock, record_extract₂]
case4 > [false, member, locker2_obtainables, locker2_{check_available₁}, case6₂, locker2_{check_{availables₁}}, case9] > pending > [tuple₂, record_update₃] > s > [T, F, not, undefined, lock, record_extract₂]
case4 > [false, member, locker2_obtainables, locker2_{check_available₁}, case6₂, locker2_{check_{availables₁}}, case9] > [true, locker2_obtainable] > [cons₂, case8₂] > [and₂, stack₂, pushs₂] > [T, F, not, undefined, lock, record_extract₂]
case4 > [false, member, locker2_obtainables, locker2_{check_available₁}, case6₂, locker2_{check_{availables₁}}, case9] > [true, locker2_obtainable] > [cons₂, case8₂] > [nil, locker2_{map_{add_pending}}] > [T, F, not, undefined, lock, record_extract₂]
gen_tag₁ > [tuple₂, record_update₃] > [and₂, stack₂, pushs₂] > [T, F, not, undefined, lock, record_extract₂]
gen_tag₁ > [tuple₂, record_update₃] > mcrlrecord > [T, F, not, undefined, lock, record_extract₂]
gen_tag₁ > [tuple₂, record_update₃] > s > [T, F, not, undefined, lock, record_extract₂]
gen_tag₁ > tag > [T, F, not, undefined, lock, record_extract₂]
tops₁ > [T, F, not, undefined, lock, record_extract₂]
istops₁ > [T, F, not, undefined, lock, record_extract₂]
eqc₂ > eqs₁ > [and₂, stack₂, pushs₂] > [T, F, not, undefined, lock, record_extract₂]
push₃ > [empty, nocalls] > [and₂, stack₂, pushs₂] > [T, F, not, undefined, lock, record_extract₂]
push₃ > push1₄ > calls₃ > [and₂, stack₂, pushs₂] > [T, F, not, undefined, lock, record_extract₂]

Status:

APPEND₂: [2,1]
cons₂: [2,1]
or₂: [2,1]
T: []
F: []
and₂: [1,2]
not: []
if₃: [1,2,3]
eq₁: [1]
nil: []
undefined: []
tuple₂: [1,2]
a: []
excl: []
false: []
lock: []
locker: []
mcrlrecord: []
ok: []
pending: []
release: []
request: []
resource: []
tag: []
true: []
s: []
0: []
record_new: []
record_extract₂: [2,1]
record_update₃: [1,3,2]
record_updates₃: [2,3,1]
locker2_{map_{promote_pending₁}}: [1]
locker2_{promote_pending₁}: [1]
locker2_{map_{claim_lock₃}}: [3,2,1]
locker2_{claim_lock₁}: [1]
locker2_{map_{add_pending}}: []
case0₂: [2,1]
locker2_{remove_pending₂}: [2,1]
locker2_{add_pending₃}: [3,1,2]
case1₂: [1,2]
member: []
locker2_{release_lock₂}: [2,1]
case2₁: [1]
gen_modtageq₂: [1,2]
excllock: []
case4: []
locker2_obtainables: []
locker2_obtainable: []
locker2_{check_available₁}: [1]
case6₂: [1,2]
locker2_{check_{availables₁}}: [1]
case8₂: [1,2]
gen_tag₁: [1]
case9: []
eqs₁: [1]
empty: []
stack₂: [2,1]
pushs₂: [2,1]
tops₁: [1]
istops₁: [1]
eqc₂: [2,1]
nocalls: []
calls₃: [3,2,1]
push₃: [3,2,1]
push1₄: [3,4,2,1]

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)

(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(x2)
not(x1) = not
if(x1, x2, x3) = if(x2, x3)
eq(x1, x2) = eq
eqt(x1, x2) = eqt(x1)
nil = nil
undefined = undefined
pid(x1) = pid(x1)
int(x1) = int(x1)
tuple(x1, x2) = tuple(x1, x2)
tuplenil(x1) = x1
a = a
excl = excl
false = false
lock = lock
locker = locker
mcrlrecord = mcrlrecord
ok = ok
pending = pending
release = release
request = request
resource = resource
tag = tag
true = true
element(x1, x2) = element(x1, x2)
s(x1) = s
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, 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
locker2_map_add_pending(x1, x2, x3) = locker2_map_add_pending
case0(x1, x2, x3) = case0(x1, x2, x3)
locker2_remove_pending(x1, x2) = locker2_remove_pending(x1, x2)
subtract(x1, x2) = subtract(x1, x2)
locker2_add_pending(x1, x2, x3) = locker2_add_pending(x1, x2, x3)
case1(x1, x2, x3, x4) = case1(x1, x2, x3)
member(x1, x2) = member
append(x1, x2) = x1
locker2_release_lock(x1, x2) = locker2_release_lock(x1, x2)
case2(x1, x2, x3) = case2(x2, x3)
gen_modtageq(x1, x2) = gen_modtageq
excllock = excllock
case4(x1, x2, x3) = case4(x3)
locker2_obtainables(x1, x2) = locker2_obtainables(x1)
case5(x1, x2, x3, x4) = case5(x2)
andt(x1, x2) = x2
locker2_obtainable(x1, x2) = locker2_obtainable
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(x1, x2)
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) = x1
tops(x1) = tops(x1)
istops(x1, x2) = istops(x1, x2)
eqc(x1, x2) = eqc(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(x2, x3, x4, x5, x6)

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

LOCKER2_{CHECK_{AVAILABLES₂}} > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
or > [T, imp₁, eqt₁, pid₁, nocalls] > and₂ > [F, undefined, empty] > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
not > [T, imp₁, eqt₁, pid₁, nocalls] > and₂ > [F, undefined, empty] > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
if₂ > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
eq > [T, imp₁, eqt₁, pid₁, nocalls] > and₂ > [F, undefined, empty] > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
a > [T, imp₁, eqt₁, pid₁, nocalls] > and₂ > [F, undefined, empty] > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
locker > [T, imp₁, eqt₁, pid₁, nocalls] > and₂ > [F, undefined, empty] > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
ok > [F, undefined, empty] > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
release > [F, undefined, empty] > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
request > [T, imp₁, eqt₁, pid₁, nocalls] > and₂ > [F, undefined, empty] > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
s > int₁ > [F, undefined, empty] > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
s > int₁ > element₂ > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
0 > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
[locker2_{map_{promote_pending₂}}, locker2_{promote_pending₂}] > [nil, record_new₁, locker2_{map_{add_pending}}, case0₃] > [cons₂, locker2_{map_{claim_lock₃}}] > tuple₂ > mcrlrecord > [F, undefined, empty] > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
[locker2_{map_{promote_pending₂}}, locker2_{promote_pending₂}] > [nil, record_new₁, locker2_{map_{add_pending}}, case0₃] > [cons₂, locker2_{map_{claim_lock₃}}] > locker2_{claim_lock} > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
[locker2_{map_{promote_pending₂}}, locker2_{promote_pending₂}] > [nil, record_new₁, locker2_{map_{add_pending}}, case0₃] > excl > [F, undefined, empty] > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
[locker2_{map_{promote_pending₂}}, locker2_{promote_pending₂}] > [nil, record_new₁, locker2_{map_{add_pending}}, case0₃] > pending > tuple₂ > mcrlrecord > [F, undefined, empty] > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
[locker2_{map_{promote_pending₂}}, locker2_{promote_pending₂}] > [nil, record_new₁, locker2_{map_{add_pending}}, case0₃] > record_updates₃ > record_update₄ > tuple₂ > mcrlrecord > [F, undefined, empty] > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
[locker2_{map_{promote_pending₂}}, locker2_{promote_pending₂}] > record_extract₂ > tuple₂ > mcrlrecord > [F, undefined, empty] > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
locker2_{remove_pending₂} > [nil, record_new₁, locker2_{map_{add_pending}}, case0₃] > [cons₂, locker2_{map_{claim_lock₃}}] > tuple₂ > mcrlrecord > [F, undefined, empty] > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
locker2_{remove_pending₂} > [nil, record_new₁, locker2_{map_{add_pending}}, case0₃] > [cons₂, locker2_{map_{claim_lock₃}}] > locker2_{claim_lock} > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
locker2_{remove_pending₂} > [nil, record_new₁, locker2_{map_{add_pending}}, case0₃] > excl > [F, undefined, empty] > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
locker2_{remove_pending₂} > [nil, record_new₁, locker2_{map_{add_pending}}, case0₃] > pending > tuple₂ > mcrlrecord > [F, undefined, empty] > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
locker2_{remove_pending₂} > [nil, record_new₁, locker2_{map_{add_pending}}, case0₃] > record_updates₃ > record_update₄ > tuple₂ > mcrlrecord > [F, undefined, empty] > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
locker2_{remove_pending₂} > record_extract₂ > tuple₂ > mcrlrecord > [F, undefined, empty] > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
locker2_{remove_pending₂} > subtract₂ > [delete₂, case8₄] > [cons₂, locker2_{map_{claim_lock₃}}] > tuple₂ > mcrlrecord > [F, undefined, empty] > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
locker2_{remove_pending₂} > subtract₂ > [delete₂, case8₄] > [cons₂, locker2_{map_{claim_lock₃}}] > locker2_{claim_lock} > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
locker2_{add_pending₃} > case1₃ > [nil, record_new₁, locker2_{map_{add_pending}}, case0₃] > [cons₂, locker2_{map_{claim_lock₃}}] > tuple₂ > mcrlrecord > [F, undefined, empty] > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
locker2_{add_pending₃} > case1₃ > [nil, record_new₁, locker2_{map_{add_pending}}, case0₃] > [cons₂, locker2_{map_{claim_lock₃}}] > locker2_{claim_lock} > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
locker2_{add_pending₃} > case1₃ > [nil, record_new₁, locker2_{map_{add_pending}}, case0₃] > excl > [F, undefined, empty] > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
locker2_{add_pending₃} > case1₃ > [nil, record_new₁, locker2_{map_{add_pending}}, case0₃] > pending > tuple₂ > mcrlrecord > [F, undefined, empty] > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
locker2_{add_pending₃} > case1₃ > [nil, record_new₁, locker2_{map_{add_pending}}, case0₃] > record_updates₃ > record_update₄ > tuple₂ > mcrlrecord > [F, undefined, empty] > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
locker2_{add_pending₃} > case1₃ > record_extract₂ > tuple₂ > mcrlrecord > [F, undefined, empty] > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
locker2_{add_pending₃} > [member, case9] > [false, locker2_{check_available}] > record_extract₂ > tuple₂ > mcrlrecord > [F, undefined, empty] > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
locker2_{add_pending₃} > [member, case9] > [false, locker2_{check_available}] > [delete₂, case8₄] > [cons₂, locker2_{map_{claim_lock₃}}] > tuple₂ > mcrlrecord > [F, undefined, empty] > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
locker2_{add_pending₃} > [member, case9] > [false, locker2_{check_available}] > [delete₂, case8₄] > [cons₂, locker2_{map_{claim_lock₃}}] > locker2_{claim_lock} > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
locker2_{add_pending₃} > [member, case9] > true > [T, imp₁, eqt₁, pid₁, nocalls] > and₂ > [F, undefined, empty] > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
locker2_{add_pending₃} > [member, case9] > true > [nil, record_new₁, locker2_{map_{add_pending}}, case0₃] > [cons₂, locker2_{map_{claim_lock₃}}] > tuple₂ > mcrlrecord > [F, undefined, empty] > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
locker2_{add_pending₃} > [member, case9] > true > [nil, record_new₁, locker2_{map_{add_pending}}, case0₃] > [cons₂, locker2_{map_{claim_lock₃}}] > locker2_{claim_lock} > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
locker2_{add_pending₃} > [member, case9] > true > [nil, record_new₁, locker2_{map_{add_pending}}, case0₃] > excl > [F, undefined, empty] > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
locker2_{add_pending₃} > [member, case9] > true > [nil, record_new₁, locker2_{map_{add_pending}}, case0₃] > pending > tuple₂ > mcrlrecord > [F, undefined, empty] > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
locker2_{add_pending₃} > [member, case9] > true > [nil, record_new₁, locker2_{map_{add_pending}}, case0₃] > record_updates₃ > record_update₄ > tuple₂ > mcrlrecord > [F, undefined, empty] > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
locker2_{add_pending₃} > [member, case9] > true > record_extract₂ > tuple₂ > mcrlrecord > [F, undefined, empty] > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
[locker2_{release_lock₂}, case2₂] > [nil, record_new₁, locker2_{map_{add_pending}}, case0₃] > [cons₂, locker2_{map_{claim_lock₃}}] > tuple₂ > mcrlrecord > [F, undefined, empty] > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
[locker2_{release_lock₂}, case2₂] > [nil, record_new₁, locker2_{map_{add_pending}}, case0₃] > [cons₂, locker2_{map_{claim_lock₃}}] > locker2_{claim_lock} > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
[locker2_{release_lock₂}, case2₂] > [nil, record_new₁, locker2_{map_{add_pending}}, case0₃] > excl > [F, undefined, empty] > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
[locker2_{release_lock₂}, case2₂] > [nil, record_new₁, locker2_{map_{add_pending}}, case0₃] > pending > tuple₂ > mcrlrecord > [F, undefined, empty] > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
[locker2_{release_lock₂}, case2₂] > [nil, record_new₁, locker2_{map_{add_pending}}, case0₃] > record_updates₃ > record_update₄ > tuple₂ > mcrlrecord > [F, undefined, empty] > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
[locker2_{release_lock₂}, case2₂] > record_extract₂ > tuple₂ > mcrlrecord > [F, undefined, empty] > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
case4₁ > [false, locker2_{check_available}] > record_extract₂ > tuple₂ > mcrlrecord > [F, undefined, empty] > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
case4₁ > [false, locker2_{check_available}] > [delete₂, case8₄] > [cons₂, locker2_{map_{claim_lock₃}}] > tuple₂ > mcrlrecord > [F, undefined, empty] > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
case4₁ > [false, locker2_{check_available}] > [delete₂, case8₄] > [cons₂, locker2_{map_{claim_lock₃}}] > locker2_{claim_lock} > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
[locker2_{obtainables₁}, case5₁] > [member, case9] > [false, locker2_{check_available}] > record_extract₂ > tuple₂ > mcrlrecord > [F, undefined, empty] > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
[locker2_{obtainables₁}, case5₁] > [member, case9] > [false, locker2_{check_available}] > [delete₂, case8₄] > [cons₂, locker2_{map_{claim_lock₃}}] > tuple₂ > mcrlrecord > [F, undefined, empty] > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
[locker2_{obtainables₁}, case5₁] > [member, case9] > [false, locker2_{check_available}] > [delete₂, case8₄] > [cons₂, locker2_{map_{claim_lock₃}}] > locker2_{claim_lock} > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
[locker2_{obtainables₁}, case5₁] > [member, case9] > true > [T, imp₁, eqt₁, pid₁, nocalls] > and₂ > [F, undefined, empty] > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
[locker2_{obtainables₁}, case5₁] > [member, case9] > true > [nil, record_new₁, locker2_{map_{add_pending}}, case0₃] > [cons₂, locker2_{map_{claim_lock₃}}] > tuple₂ > mcrlrecord > [F, undefined, empty] > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
[locker2_{obtainables₁}, case5₁] > [member, case9] > true > [nil, record_new₁, locker2_{map_{add_pending}}, case0₃] > [cons₂, locker2_{map_{claim_lock₃}}] > locker2_{claim_lock} > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
[locker2_{obtainables₁}, case5₁] > [member, case9] > true > [nil, record_new₁, locker2_{map_{add_pending}}, case0₃] > excl > [F, undefined, empty] > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
[locker2_{obtainables₁}, case5₁] > [member, case9] > true > [nil, record_new₁, locker2_{map_{add_pending}}, case0₃] > pending > tuple₂ > mcrlrecord > [F, undefined, empty] > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
[locker2_{obtainables₁}, case5₁] > [member, case9] > true > [nil, record_new₁, locker2_{map_{add_pending}}, case0₃] > record_updates₃ > record_update₄ > tuple₂ > mcrlrecord > [F, undefined, empty] > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
[locker2_{obtainables₁}, case5₁] > [member, case9] > true > record_extract₂ > tuple₂ > mcrlrecord > [F, undefined, empty] > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
locker2_{check_{availables₂}} > true > [T, imp₁, eqt₁, pid₁, nocalls] > and₂ > [F, undefined, empty] > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
locker2_{check_{availables₂}} > true > [nil, record_new₁, locker2_{map_{add_pending}}, case0₃] > [cons₂, locker2_{map_{claim_lock₃}}] > tuple₂ > mcrlrecord > [F, undefined, empty] > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
locker2_{check_{availables₂}} > true > [nil, record_new₁, locker2_{map_{add_pending}}, case0₃] > [cons₂, locker2_{map_{claim_lock₃}}] > locker2_{claim_lock} > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
locker2_{check_{availables₂}} > true > [nil, record_new₁, locker2_{map_{add_pending}}, case0₃] > excl > [F, undefined, empty] > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
locker2_{check_{availables₂}} > true > [nil, record_new₁, locker2_{map_{add_pending}}, case0₃] > pending > tuple₂ > mcrlrecord > [F, undefined, empty] > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
locker2_{check_{availables₂}} > true > [nil, record_new₁, locker2_{map_{add_pending}}, case0₃] > record_updates₃ > record_update₄ > tuple₂ > mcrlrecord > [F, undefined, empty] > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
locker2_{check_{availables₂}} > true > record_extract₂ > tuple₂ > mcrlrecord > [F, undefined, empty] > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
gen_tag₁ > tuple₂ > mcrlrecord > [F, undefined, empty] > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
gen_tag₁ > tag > [T, imp₁, eqt₁, pid₁, nocalls] > and₂ > [F, undefined, empty] > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
tops₁ > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
istops₂ > [T, imp₁, eqt₁, pid₁, nocalls] > and₂ > [F, undefined, empty] > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
push₃ > push1₅ > pushs₂ > stack₂ > [T, imp₁, eqt₁, pid₁, nocalls] > and₂ > [F, undefined, empty] > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
push₃ > push1₅ > calls₃ > eqs₁ > [T, imp₁, eqt₁, pid₁, nocalls] > and₂ > [F, undefined, empty] > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]
push₃ > push1₅ > calls₃ > eqc₁ > [lock, resource, gen_modtageq, excllock, locker2_obtainable, equal]

Status:

LOCKER2_{CHECK_{AVAILABLES₂}}: [2,1]
cons₂: [1,2]
or: []
T: []
F: []
and₂: [2,1]
imp₁: [1]
not: []
if₂: [1,2]
eq: []
eqt₁: [1]
nil: []
undefined: []
pid₁: [1]
int₁: [1]
tuple₂: [1,2]
a: []
excl: []
false: []
lock: []
locker: []
mcrlrecord: []
ok: []
pending: []
release: []
request: []
resource: []
tag: []
true: []
element₂: [1,2]
s: []
0: []
record_new₁: [1]
record_extract₂: [1,2]
record_update₄: [2,3,1,4]
record_updates₃: [3,2,1]
locker2_{map_{promote_pending₂}}: [2,1]
locker2_{promote_pending₂}: [2,1]
locker2_{map_{claim_lock₃}}: [1,3,2]
locker2_{claim_lock}: []
locker2_{map_{add_pending}}: []
case0₃: [2,1,3]
locker2_{remove_pending₂}: [2,1]
subtract₂: [2,1]
locker2_{add_pending₃}: [1,2,3]
case1₃: [3,2,1]
member: []
locker2_{release_lock₂}: [1,2]
case2₂: [1,2]
gen_modtageq: []
excllock: []
case4₁: [1]
locker2_{obtainables₁}: [1]
case5₁: [1]
locker2_obtainable: []
locker2_{check_available}: []
equal: []
locker2_{check_{availables₂}}: [2,1]
delete₂: [2,1]
case8₄: [1,3,4,2]
gen_tag₁: [1]
case9: []
eqs₁: [1]
empty: []
stack₂: [1,2]
pushs₂: [1,2]
tops₁: [1]
istops₂: [2,1]
eqc₁: [1]
nocalls: []
calls₃: [3,1,2]
push₃: [3,1,2]
push1₅: [5,4,3,2,1]

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)

(17) Obligation:

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

or(T, T) → T
or(F, T) → T
or(T, F) → T
or(F, F) → F
and(T, B) → B
and(B, T) → B
and(F, B) → F
and(B, F) → F
imp(T, B) → B
imp(F, B) → T
not(T) → F
not(F) → T
if(T, B1, B2) → B1
if(F, B1, B2) → B2
eq(T, T) → T
eq(F, F) → T
eq(T, F) → F
eq(F, T) → F
eqt(nil, undefined) → F
eqt(nil, pid(N2)) → F
eqt(nil, int(N2)) → F
eqt(nil, cons(H2, T2)) → F
eqt(nil, tuple(H2, T2)) → F
eqt(nil, tuplenil(H2)) → F
eqt(a, nil) → F
eqt(a, a) → T
eqt(a, excl) → F
eqt(a, false) → F
eqt(a, lock) → F
eqt(a, locker) → F
eqt(a, mcrlrecord) → F
eqt(a, ok) → F
eqt(a, pending) → F
eqt(a, release) → F
eqt(a, request) → F
eqt(a, resource) → F
eqt(a, tag) → F
eqt(a, true) → F
eqt(a, undefined) → F
eqt(a, pid(N2)) → F
eqt(a, int(N2)) → F
eqt(a, cons(H2, T2)) → F
eqt(a, tuple(H2, T2)) → F
eqt(a, tuplenil(H2)) → F
eqt(excl, nil) → F
eqt(excl, a) → F
eqt(excl, excl) → T
eqt(excl, false) → F
eqt(excl, lock) → F
eqt(excl, locker) → F
eqt(excl, mcrlrecord) → F
eqt(excl, ok) → F
eqt(excl, pending) → F
eqt(excl, release) → F
eqt(excl, request) → F
eqt(excl, resource) → F
eqt(excl, tag) → F
eqt(excl, true) → F
eqt(excl, undefined) → F
eqt(excl, pid(N2)) → F
eqt(excl, eqt(false, int(N2))) → F
eqt(false, cons(H2, T2)) → F
eqt(false, tuple(H2, T2)) → F
eqt(false, tuplenil(H2)) → F
eqt(lock, nil) → F
eqt(lock, a) → F
eqt(lock, excl) → F
eqt(lock, false) → F
eqt(lock, lock) → T
eqt(lock, locker) → F
eqt(lock, mcrlrecord) → F
eqt(lock, ok) → F
eqt(lock, pending) → F
eqt(lock, release) → F
eqt(lock, request) → F
eqt(lock, resource) → F
eqt(lock, tag) → F
eqt(lock, true) → F
eqt(lock, undefined) → F
eqt(lock, pid(N2)) → F
eqt(lock, int(N2)) → F
eqt(lock, cons(H2, T2)) → F
eqt(lock, tuple(H2, T2)) → F
eqt(lock, tuplenil(H2)) → F
eqt(locker, nil) → F
eqt(locker, a) → F
eqt(locker, excl) → F
eqt(locker, false) → F
eqt(locker, lock) → F
eqt(locker, locker) → T
eqt(locker, mcrlrecord) → F
eqt(locker, ok) → F
eqt(locker, pending) → F
eqt(locker, release) → F
eqt(locker, request) → F
eqt(locker, resource) → F
eqt(locker, tag) → F
eqt(locker, true) → F
eqt(locker, undefined) → F
eqt(locker, pid(N2)) → F
eqt(locker, int(N2)) → F
eqt(locker, cons(H2, T2)) → F
eqt(locker, tuple(H2, T2)) → F
eqt(locker, tuplenil(H2)) → F
eqt(mcrlrecord, nil) → F
eqt(mcrlrecord, a) → F
eqt(mcrlrecord, excl) → F
eqt(mcrlrecord, false) → F
eqt(mcrlrecord, lock) → F
eqt(mcrlrecord, locker) → F
eqt(mcrlrecord, mcrlrecord) → T
eqt(mcrlrecord, ok) → F
eqt(mcrlrecord, pending) → F
eqt(mcrlrecord, release) → F
eqt(mcrlrecord, request) → F
eqt(mcrlrecord, resource) → F
eqt(ok, resource) → F
eqt(ok, tag) → F
eqt(ok, true) → F
eqt(ok, undefined) → F
eqt(ok, pid(N2)) → F
eqt(ok, int(N2)) → F
eqt(ok, cons(H2, T2)) → F
eqt(ok, tuple(H2, T2)) → F
eqt(ok, tuplenil(H2)) → F
eqt(pending, nil) → F
eqt(pending, a) → F
eqt(pending, excl) → F
eqt(pending, false) → F
eqt(pending, lock) → F
eqt(pending, locker) → F
eqt(pending, mcrlrecord) → F
eqt(pending, ok) → F
eqt(pending, pending) → T
eqt(pending, release) → F
eqt(pending, request) → F
eqt(pending, resource) → F
eqt(pending, tag) → F
eqt(pending, true) → F
eqt(pending, undefined) → F
eqt(pending, pid(N2)) → F
eqt(pending, int(N2)) → F
eqt(pending, cons(H2, T2)) → F
eqt(pending, tuple(H2, T2)) → F
eqt(pending, tuplenil(H2)) → F
eqt(release, nil) → F
eqt(release, a) → F
eqt(release, excl) → F
eqt(release, false) → F
eqt(release, lock) → F
eqt(release, locker) → F
eqt(release, mcrlrecord) → F
eqt(release, ok) → F
eqt(request, mcrlrecord) → F
eqt(request, ok) → F
eqt(request, pending) → F
eqt(request, release) → F
eqt(request, request) → T
eqt(request, resource) → F
eqt(request, tag) → F
eqt(request, true) → F
eqt(request, undefined) → F
eqt(request, pid(N2)) → F
eqt(request, int(N2)) → F
eqt(request, cons(H2, T2)) → F
eqt(request, tuple(H2, T2)) → F
eqt(request, tuplenil(H2)) → F
eqt(resource, nil) → F
eqt(resource, a) → F
eqt(resource, excl) → F
eqt(resource, false) → F
eqt(resource, lock) → F
eqt(resource, locker) → F
eqt(resource, mcrlrecord) → F
eqt(resource, ok) → F
eqt(resource, pending) → F
eqt(resource, release) → F
eqt(resource, request) → F
eqt(resource, resource) → T
eqt(resource, tag) → F
eqt(resource, true) → F
eqt(resource, undefined) → F
eqt(resource, pid(N2)) → F
eqt(resource, int(N2)) → F
eqt(resource, cons(H2, T2)) → F
eqt(resource, tuple(H2, T2)) → F
eqt(resource, tuplenil(H2)) → F
eqt(tag, nil) → F
eqt(tag, a) → F
eqt(tag, excl) → F
eqt(tag, false) → F
eqt(tag, lock) → F
eqt(tag, locker) → F
eqt(tag, mcrlrecord) → F
eqt(tag, ok) → F
eqt(tag, pending) → F
eqt(tag, release) → F
eqt(tag, request) → F
eqt(tag, resource) → F
eqt(tag, tag) → T
eqt(tag, true) → F
eqt(tag, undefined) → F
eqt(tag, pid(N2)) → F
eqt(tag, int(N2)) → F
eqt(tag, cons(H2, T2)) → F
eqt(tag, tuple(H2, T2)) → F
eqt(tag, tuplenil(H2)) → F
eqt(true, nil) → F
eqt(true, a) → F
eqt(true, excl) → F
eqt(true, false) → F
eqt(true, lock) → F
eqt(true, locker) → F
eqt(true, mcrlrecord) → F
eqt(true, ok) → F
eqt(true, pending) → F
eqt(true, release) → F
eqt(true, request) → F
eqt(true, resource) → F
eqt(true, tag) → F
eqt(true, true) → T
eqt(true, undefined) → F
eqt(true, pid(N2)) → F
eqt(true, int(N2)) → F
eqt(true, cons(H2, T2)) → F
eqt(true, tuple(H2, T2)) → F
eqt(true, tuplenil(H2)) → F
eqt(undefined, nil) → F
eqt(undefined, a) → F
eqt(undefined, tuplenil(H2)) → F
eqt(pid(N1), nil) → F
eqt(pid(N1), a) → F
eqt(pid(N1), excl) → F
eqt(pid(N1), false) → F
eqt(pid(N1), lock) → F
eqt(pid(N1), locker) → F
eqt(pid(N1), mcrlrecord) → F
eqt(pid(N1), ok) → F
eqt(pid(N1), pending) → F
eqt(pid(N1), release) → F
eqt(pid(N1), request) → F
eqt(pid(N1), resource) → F
eqt(pid(N1), tag) → F
eqt(pid(N1), true) → F
eqt(pid(N1), undefined) → F
eqt(pid(N1), pid(N2)) → eqt(N1, N2)
eqt(pid(N1), int(N2)) → F
eqt(pid(N1), cons(H2, T2)) → F
eqt(pid(N1), tuple(H2, T2)) → F
eqt(pid(N1), tuplenil(H2)) → F
eqt(int(N1), nil) → F
eqt(int(N1), a) → F
eqt(int(N1), excl) → F
eqt(int(N1), false) → F
eqt(int(N1), lock) → F
eqt(int(N1), locker) → F
eqt(int(N1), mcrlrecord) → F
eqt(int(N1), ok) → F
eqt(int(N1), pending) → F
eqt(int(N1), release) → F
eqt(int(N1), request) → F
eqt(int(N1), resource) → F
eqt(int(N1), tag) → F
eqt(int(N1), true) → F
eqt(int(N1), undefined) → F
eqt(cons(H1, T1), resource) → F
eqt(cons(H1, T1), tag) → F
eqt(cons(H1, T1), true) → F
eqt(cons(H1, T1), undefined) → F
eqt(cons(H1, T1), pid(N2)) → F
eqt(cons(H1, T1), int(N2)) → F
eqt(cons(H1, T1), cons(H2, T2)) → and(eqt(H1, H2), eqt(T1, T2))
eqt(cons(H1, T1), tuple(H2, T2)) → F
eqt(cons(H1, T1), tuplenil(H2)) → F
eqt(tuple(H1, T1), nil) → F
eqt(tuple(H1, T1), a) → F
eqt(tuple(H1, T1), excl) → F
eqt(tuple(H1, T1), false) → F
eqt(tuple(H1, T1), lock) → F
eqt(tuple(H1, T1), locker) → F
eqt(tuple(H1, T1), mcrlrecord) → F
eqt(tuple(H1, T1), ok) → F
eqt(tuple(H1, T1), pending) → F
eqt(tuple(H1, T1), release) → F
eqt(tuple(H1, T1), request) → F
eqt(tuple(H1, T1), resource) → F
eqt(tuple(H1, T1), tag) → F
eqt(tuple(H1, T1), true) → F
eqt(tuple(H1, T1), undefined) → F
eqt(tuple(H1, T1), pid(N2)) → F
eqt(tuple(H1, T1), int(N2)) → F
eqt(tuple(H1, T1), cons(H2, T2)) → F
eqt(tuple(H1, T1), tuple(H2, T2)) → and(eqt(H1, H2), eqt(T1, T2))
eqt(tuple(H1, T1), tuplenil(H2)) → F
eqt(tuplenil(H1), nil) → F
eqt(tuplenil(H1), a) → F
eqt(tuplenil(H1), excl) → F
eqt(tuplenil(H1), false) → F
eqt(tuplenil(H1), lock) → F
eqt(tuplenil(H1), locker) → F
eqt(tuplenil(H1), mcrlrecord) → F
eqt(tuplenil(H1), ok) → F
eqt(tuplenil(H1), pending) → F
eqt(tuplenil(H1), release) → F
eqt(tuplenil(H1), request) → F
eqt(tuplenil(H1), resource) → F
eqt(tuplenil(H1), tag) → F
eqt(tuplenil(H1), true) → F
eqt(tuplenil(H1), undefined) → F
eqt(tuplenil(H1), pid(N2)) → F
eqt(tuplenil(H1), int(N2)) → F
eqt(tuplenil(H1), cons(H2, T2)) → F
eqt(tuplenil(H1), tuple(H2, T2)) → F
eqt(tuplenil(H1), tuplenil(H2)) → eqt(H1, H2)
element(int(s(0)), tuplenil(T1)) → T1
element(int(s(0)), tuple(T1, T2)) → T1
element(int(s(s(N1))), tuple(T1, T2)) → element(int(s(N1)), T2)
record_new(lock) → tuple(mcrlrecord, tuple(lock, tuple(undefined, tuple(nil, tuplenil(nil)))))
record_extract(tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))), lock, resource) → tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2)))))
record_update(tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))), lock, pending, NewF) → tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(NewF)))))
record_updates(Record, Name, nil) → Record
record_updates(Record, Name, cons(tuple(Field, tuplenil(NewF)), Fields)) → record_updates(record_update(Record, Name, Field, NewF), Name, Fields)
locker2_map_promote_pending(nil, Pending) → nil
locker2_map_promote_pending(cons(Lock, Locks), Pending) → cons(locker2_promote_pending(Lock, Pending), locker2_map_promote_pending(Locks, Pending))
locker2_map_claim_lock(nil, Resources, Client) → nil
locker2_map_claim_lock(cons(Lock, Locks), Resources, Client) → cons(locker2_claim_lock(Lock, Resources, Client), locker2_map_claim_lock(Locks, Resources, Client))
locker2_map_add_pending(nil, Resources, Client) → nil
locker2_promote_pending(Lock, Client) → case0(Client, Lock, record_extract(Lock, lock, pending))
case0(Client, Lock, cons(Client, Pendings)) → record_updates(Lock, lock, cons(tuple(excl, tuplenil(Client)), cons(tuple(pending, tuplenil(Pendings)), nil)))
case0(Client, Lock, MCRLFree0) → Lock
locker2_remove_pending(Lock, Client) → record_updates(Lock, lock, cons(tuple(pending, tuplenil(subtract(record_extract(Lock, lock, pending), cons(Client, nil)))), nil))
locker2_add_pending(Lock, Resources, Client) → case1(Client, Resources, Lock, member(record_extract(Lock, lock, resource), Resources))
case1(Client, Resources, Lock, true) → record_updates(Lock, lock, cons(tuple(pending, tuplenil(append(record_extract(Lock, lock, pending), cons(Client, nil)))), nil))
case1(Client, Resources, Lock, false) → Lock
locker2_release_lock(Lock, Client) → case2(Client, Lock, gen_modtageq(Client, record_extract(Lock, lock, excl)))
case2(Client, Lock, true) → record_updates(Lock, lock, cons(tuple(excllock, excl), nil))
case4(Client, Lock, MCRLFree1) → false
locker2_obtainables(nil, Client) → true
locker2_obtainables(cons(Lock, Locks), Client) → case5(Client, Locks, Lock, member(Client, record_extract(Lock, lock, pending)))
case5(Client, Locks, Lock, true) → andt(locker2_obtainable(Lock, Client), locker2_obtainables(Locks, Client))
case5(Client, Locks, Lock, false) → locker2_obtainables(Locks, Client)
locker2_check_available(Resource, nil) → false
locker2_check_available(Resource, cons(Lock, Locks)) → case6(Locks, Lock, Resource, equal(Resource, record_extract(Lock, lock, resource)))
case6(Locks, Lock, Resource, true) → andt(equal(record_extract(Lock, lock, excl), nil), equal(record_extract(Lock, lock, pending), nil))
case6(Locks, Lock, Resource, false) → locker2_check_available(Resource, Locks)
locker2_check_availables(nil, Locks) → true
locker2_check_availables(cons(Resource, Resources), Locks) → andt(locker2_check_available(Resource, Locks), locker2_check_availables(Resources, Locks))
locker2_adduniq(nil, List) → List
append(cons(Head, Tail), List) → cons(Head, append(Tail, List))
subtract(List, nil) → List
subtract(List, cons(Head, Tail)) → subtract(delete(Head, List), Tail)
delete(E, nil) → nil
delete(E, cons(Head, Tail)) → case8(Tail, Head, E, equal(E, Head))
case8(Tail, Head, E, true) → Tail
case8(Tail, Head, E, false) → cons(Head, delete(E, Tail))
gen_tag(Pid) → tuple(Pid, tuplenil(tag))
gen_modtageq(Client1, Client2) → equal(Client1, Client2)
member(E, nil) → false
member(E, cons(Head, Tail)) → case9(Tail, Head, E, equal(E, Head))
case9(Tail, Head, E, true) → true
case9(Tail, Head, E, false) → member(E, Tail)
eqs(empty, empty) → T
eqs(empty, stack(E2, S2)) → F
eqs(stack(E1, S1), empty) → F
eqs(stack(E1, S1), stack(E2, S2)) → and(eqt(E1, E2), eqs(S1, S2))
pushs(E1, S1) → stack(E1, S1)
pops(stack(E1, S1)) → S1
tops(stack(E1, S1)) → E1
istops(E1, empty) → F
istops(E1, stack(E2, S1)) → eqt(E1, E2)
eqc(nocalls, nocalls) → T
eqc(nocalls, calls(E2, S2, CS2)) → F
eqc(calls(E1, S1, CS1), nocalls) → F
eqc(calls(E1, S1, CS1), calls(E2, S2, CS2)) → and(eqt(E1, E2), and(eqs(S1, S2), eqc(CS1, CS2)))
push(E1, E2, nocalls) → calls(E1, stack(E2, empty), nocalls)
push(E1, E2, calls(E3, S1, CS1)) → push1(E1, E2, E3, S1, CS1, eqt(E1, E3))
push1(E1, E2, E3, S1, CS1, T) → calls(E3, pushs(E2, S1), CS1)

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

(18) PisEmptyProof (EQUIVALENT transformation)

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

(19) TRUE

(20) Obligation:

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

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

The TRS R consists of the following rules:

or(T, T) → T
or(F, T) → T
or(T, F) → T
or(F, F) → F
and(T, B) → B
and(B, T) → B
and(F, B) → F
and(B, F) → F
imp(T, B) → B
imp(F, B) → T
not(T) → F
not(F) → T
if(T, B1, B2) → B1
if(F, B1, B2) → B2
eq(T, T) → T
eq(F, F) → T
eq(T, F) → F
eq(F, T) → F
eqt(nil, undefined) → F
eqt(nil, pid(N2)) → F
eqt(nil, int(N2)) → F
eqt(nil, cons(H2, T2)) → F
eqt(nil, tuple(H2, T2)) → F
eqt(nil, tuplenil(H2)) → F
eqt(a, nil) → F
eqt(a, a) → T
eqt(a, excl) → F
eqt(a, false) → F
eqt(a, lock) → F
eqt(a, locker) → F
eqt(a, mcrlrecord) → F
eqt(a, ok) → F
eqt(a, pending) → F
eqt(a, release) → F
eqt(a, request) → F
eqt(a, resource) → F
eqt(a, tag) → F
eqt(a, true) → F
eqt(a, undefined) → F
eqt(a, pid(N2)) → F
eqt(a, int(N2)) → F
eqt(a, cons(H2, T2)) → F
eqt(a, tuple(H2, T2)) → F
eqt(a, tuplenil(H2)) → F
eqt(excl, nil) → F
eqt(excl, a) → F
eqt(excl, excl) → T
eqt(excl, false) → F
eqt(excl, lock) → F
eqt(excl, locker) → F
eqt(excl, mcrlrecord) → F
eqt(excl, ok) → F
eqt(excl, pending) → F
eqt(excl, release) → F
eqt(excl, request) → F
eqt(excl, resource) → F
eqt(excl, tag) → F
eqt(excl, true) → F
eqt(excl, undefined) → F
eqt(excl, pid(N2)) → F
eqt(excl, eqt(false, int(N2))) → F
eqt(false, cons(H2, T2)) → F
eqt(false, tuple(H2, T2)) → F
eqt(false, tuplenil(H2)) → F
eqt(lock, nil) → F
eqt(lock, a) → F
eqt(lock, excl) → F
eqt(lock, false) → F
eqt(lock, lock) → T
eqt(lock, locker) → F
eqt(lock, mcrlrecord) → F
eqt(lock, ok) → F
eqt(lock, pending) → F
eqt(lock, release) → F
eqt(lock, request) → F
eqt(lock, resource) → F
eqt(lock, tag) → F
eqt(lock, true) → F
eqt(lock, undefined) → F
eqt(lock, pid(N2)) → F
eqt(lock, int(N2)) → F
eqt(lock, cons(H2, T2)) → F
eqt(lock, tuple(H2, T2)) → F
eqt(lock, tuplenil(H2)) → F
eqt(locker, nil) → F
eqt(locker, a) → F
eqt(locker, excl) → F
eqt(locker, false) → F
eqt(locker, lock) → F
eqt(locker, locker) → T
eqt(locker, mcrlrecord) → F
eqt(locker, ok) → F
eqt(locker, pending) → F
eqt(locker, release) → F
eqt(locker, request) → F
eqt(locker, resource) → F
eqt(locker, tag) → F
eqt(locker, true) → F
eqt(locker, undefined) → F
eqt(locker, pid(N2)) → F
eqt(locker, int(N2)) → F
eqt(locker, cons(H2, T2)) → F
eqt(locker, tuple(H2, T2)) → F
eqt(locker, tuplenil(H2)) → F
eqt(mcrlrecord, nil) → F
eqt(mcrlrecord, a) → F
eqt(mcrlrecord, excl) → F
eqt(mcrlrecord, false) → F
eqt(mcrlrecord, lock) → F
eqt(mcrlrecord, locker) → F
eqt(mcrlrecord, mcrlrecord) → T
eqt(mcrlrecord, ok) → F
eqt(mcrlrecord, pending) → F
eqt(mcrlrecord, release) → F
eqt(mcrlrecord, request) → F
eqt(mcrlrecord, resource) → F
eqt(ok, resource) → F
eqt(ok, tag) → F
eqt(ok, true) → F
eqt(ok, undefined) → F
eqt(ok, pid(N2)) → F
eqt(ok, int(N2)) → F
eqt(ok, cons(H2, T2)) → F
eqt(ok, tuple(H2, T2)) → F
eqt(ok, tuplenil(H2)) → F
eqt(pending, nil) → F
eqt(pending, a) → F
eqt(pending, excl) → F
eqt(pending, false) → F
eqt(pending, lock) → F
eqt(pending, locker) → F
eqt(pending, mcrlrecord) → F
eqt(pending, ok) → F
eqt(pending, pending) → T
eqt(pending, release) → F
eqt(pending, request) → F
eqt(pending, resource) → F
eqt(pending, tag) → F
eqt(pending, true) → F
eqt(pending, undefined) → F
eqt(pending, pid(N2)) → F
eqt(pending, int(N2)) → F
eqt(pending, cons(H2, T2)) → F
eqt(pending, tuple(H2, T2)) → F
eqt(pending, tuplenil(H2)) → F
eqt(release, nil) → F
eqt(release, a) → F
eqt(release, excl) → F
eqt(release, false) → F
eqt(release, lock) → F
eqt(release, locker) → F
eqt(release, mcrlrecord) → F
eqt(release, ok) → F
eqt(request, mcrlrecord) → F
eqt(request, ok) → F
eqt(request, pending) → F
eqt(request, release) → F
eqt(request, request) → T
eqt(request, resource) → F
eqt(request, tag) → F
eqt(request, true) → F
eqt(request, undefined) → F
eqt(request, pid(N2)) → F
eqt(request, int(N2)) → F
eqt(request, cons(H2, T2)) → F
eqt(request, tuple(H2, T2)) → F
eqt(request, tuplenil(H2)) → F
eqt(resource, nil) → F
eqt(resource, a) → F
eqt(resource, excl) → F
eqt(resource, false) → F
eqt(resource, lock) → F
eqt(resource, locker) → F
eqt(resource, mcrlrecord) → F
eqt(resource, ok) → F
eqt(resource, pending) → F
eqt(resource, release) → F
eqt(resource, request) → F
eqt(resource, resource) → T
eqt(resource, tag) → F
eqt(resource, true) → F
eqt(resource, undefined) → F
eqt(resource, pid(N2)) → F
eqt(resource, int(N2)) → F
eqt(resource, cons(H2, T2)) → F
eqt(resource, tuple(H2, T2)) → F
eqt(resource, tuplenil(H2)) → F
eqt(tag, nil) → F
eqt(tag, a) → F
eqt(tag, excl) → F
eqt(tag, false) → F
eqt(tag, lock) → F
eqt(tag, locker) → F
eqt(tag, mcrlrecord) → F
eqt(tag, ok) → F
eqt(tag, pending) → F
eqt(tag, release) → F
eqt(tag, request) → F
eqt(tag, resource) → F
eqt(tag, tag) → T
eqt(tag, true) → F
eqt(tag, undefined) → F
eqt(tag, pid(N2)) → F
eqt(tag, int(N2)) → F
eqt(tag, cons(H2, T2)) → F
eqt(tag, tuple(H2, T2)) → F
eqt(tag, tuplenil(H2)) → F
eqt(true, nil) → F
eqt(true, a) → F
eqt(true, excl) → F
eqt(true, false) → F
eqt(true, lock) → F
eqt(true, locker) → F
eqt(true, mcrlrecord) → F
eqt(true, ok) → F
eqt(true, pending) → F
eqt(true, release) → F
eqt(true, request) → F
eqt(true, resource) → F
eqt(true, tag) → F
eqt(true, true) → T
eqt(true, undefined) → F
eqt(true, pid(N2)) → F
eqt(true, int(N2)) → F
eqt(true, cons(H2, T2)) → F
eqt(true, tuple(H2, T2)) → F
eqt(true, tuplenil(H2)) → F
eqt(undefined, nil) → F
eqt(undefined, a) → F
eqt(undefined, tuplenil(H2)) → F
eqt(pid(N1), nil) → F
eqt(pid(N1), a) → F
eqt(pid(N1), excl) → F
eqt(pid(N1), false) → F
eqt(pid(N1), lock) → F
eqt(pid(N1), locker) → F
eqt(pid(N1), mcrlrecord) → F
eqt(pid(N1), ok) → F
eqt(pid(N1), pending) → F
eqt(pid(N1), release) → F
eqt(pid(N1), request) → F
eqt(pid(N1), resource) → F
eqt(pid(N1), tag) → F
eqt(pid(N1), true) → F
eqt(pid(N1), undefined) → F
eqt(pid(N1), pid(N2)) → eqt(N1, N2)
eqt(pid(N1), int(N2)) → F
eqt(pid(N1), cons(H2, T2)) → F
eqt(pid(N1), tuple(H2, T2)) → F
eqt(pid(N1), tuplenil(H2)) → F
eqt(int(N1), nil) → F
eqt(int(N1), a) → F
eqt(int(N1), excl) → F
eqt(int(N1), false) → F
eqt(int(N1), lock) → F
eqt(int(N1), locker) → F
eqt(int(N1), mcrlrecord) → F
eqt(int(N1), ok) → F
eqt(int(N1), pending) → F
eqt(int(N1), release) → F
eqt(int(N1), request) → F
eqt(int(N1), resource) → F
eqt(int(N1), tag) → F
eqt(int(N1), true) → F
eqt(int(N1), undefined) → F
eqt(cons(H1, T1), resource) → F
eqt(cons(H1, T1), tag) → F
eqt(cons(H1, T1), true) → F
eqt(cons(H1, T1), undefined) → F
eqt(cons(H1, T1), pid(N2)) → F
eqt(cons(H1, T1), int(N2)) → F
eqt(cons(H1, T1), cons(H2, T2)) → and(eqt(H1, H2), eqt(T1, T2))
eqt(cons(H1, T1), tuple(H2, T2)) → F
eqt(cons(H1, T1), tuplenil(H2)) → F
eqt(tuple(H1, T1), nil) → F
eqt(tuple(H1, T1), a) → F
eqt(tuple(H1, T1), excl) → F
eqt(tuple(H1, T1), false) → F
eqt(tuple(H1, T1), lock) → F
eqt(tuple(H1, T1), locker) → F
eqt(tuple(H1, T1), mcrlrecord) → F
eqt(tuple(H1, T1), ok) → F
eqt(tuple(H1, T1), pending) → F
eqt(tuple(H1, T1), release) → F
eqt(tuple(H1, T1), request) → F
eqt(tuple(H1, T1), resource) → F
eqt(tuple(H1, T1), tag) → F
eqt(tuple(H1, T1), true) → F
eqt(tuple(H1, T1), undefined) → F
eqt(tuple(H1, T1), pid(N2)) → F
eqt(tuple(H1, T1), int(N2)) → F
eqt(tuple(H1, T1), cons(H2, T2)) → F
eqt(tuple(H1, T1), tuple(H2, T2)) → and(eqt(H1, H2), eqt(T1, T2))
eqt(tuple(H1, T1), tuplenil(H2)) → F
eqt(tuplenil(H1), nil) → F
eqt(tuplenil(H1), a) → F
eqt(tuplenil(H1), excl) → F
eqt(tuplenil(H1), false) → F
eqt(tuplenil(H1), lock) → F
eqt(tuplenil(H1), locker) → F
eqt(tuplenil(H1), mcrlrecord) → F
eqt(tuplenil(H1), ok) → F
eqt(tuplenil(H1), pending) → F
eqt(tuplenil(H1), release) → F
eqt(tuplenil(H1), request) → F
eqt(tuplenil(H1), resource) → F
eqt(tuplenil(H1), tag) → F
eqt(tuplenil(H1), true) → F
eqt(tuplenil(H1), undefined) → F
eqt(tuplenil(H1), pid(N2)) → F
eqt(tuplenil(H1), int(N2)) → F
eqt(tuplenil(H1), cons(H2, T2)) → F
eqt(tuplenil(H1), tuple(H2, T2)) → F
eqt(tuplenil(H1), tuplenil(H2)) → eqt(H1, H2)
element(int(s(0)), tuplenil(T1)) → T1
element(int(s(0)), tuple(T1, T2)) → T1
element(int(s(s(N1))), tuple(T1, T2)) → element(int(s(N1)), T2)
record_new(lock) → tuple(mcrlrecord, tuple(lock, tuple(undefined, tuple(nil, tuplenil(nil)))))
record_extract(tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))), lock, resource) → tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2)))))
record_update(tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))), lock, pending, NewF) → tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(NewF)))))
record_updates(Record, Name, nil) → Record
record_updates(Record, Name, cons(tuple(Field, tuplenil(NewF)), Fields)) → record_updates(record_update(Record, Name, Field, NewF), Name, Fields)
locker2_map_promote_pending(nil, Pending) → nil
locker2_map_promote_pending(cons(Lock, Locks), Pending) → cons(locker2_promote_pending(Lock, Pending), locker2_map_promote_pending(Locks, Pending))
locker2_map_claim_lock(nil, Resources, Client) → nil
locker2_map_claim_lock(cons(Lock, Locks), Resources, Client) → cons(locker2_claim_lock(Lock, Resources, Client), locker2_map_claim_lock(Locks, Resources, Client))
locker2_map_add_pending(nil, Resources, Client) → nil
locker2_promote_pending(Lock, Client) → case0(Client, Lock, record_extract(Lock, lock, pending))
case0(Client, Lock, cons(Client, Pendings)) → record_updates(Lock, lock, cons(tuple(excl, tuplenil(Client)), cons(tuple(pending, tuplenil(Pendings)), nil)))
case0(Client, Lock, MCRLFree0) → Lock
locker2_remove_pending(Lock, Client) → record_updates(Lock, lock, cons(tuple(pending, tuplenil(subtract(record_extract(Lock, lock, pending), cons(Client, nil)))), nil))
locker2_add_pending(Lock, Resources, Client) → case1(Client, Resources, Lock, member(record_extract(Lock, lock, resource), Resources))
case1(Client, Resources, Lock, true) → record_updates(Lock, lock, cons(tuple(pending, tuplenil(append(record_extract(Lock, lock, pending), cons(Client, nil)))), nil))
case1(Client, Resources, Lock, false) → Lock
locker2_release_lock(Lock, Client) → case2(Client, Lock, gen_modtageq(Client, record_extract(Lock, lock, excl)))
case2(Client, Lock, true) → record_updates(Lock, lock, cons(tuple(excllock, excl), nil))
case4(Client, Lock, MCRLFree1) → false
locker2_obtainables(nil, Client) → true
locker2_obtainables(cons(Lock, Locks), Client) → case5(Client, Locks, Lock, member(Client, record_extract(Lock, lock, pending)))
case5(Client, Locks, Lock, true) → andt(locker2_obtainable(Lock, Client), locker2_obtainables(Locks, Client))
case5(Client, Locks, Lock, false) → locker2_obtainables(Locks, Client)
locker2_check_available(Resource, nil) → false
locker2_check_available(Resource, cons(Lock, Locks)) → case6(Locks, Lock, Resource, equal(Resource, record_extract(Lock, lock, resource)))
case6(Locks, Lock, Resource, true) → andt(equal(record_extract(Lock, lock, excl), nil), equal(record_extract(Lock, lock, pending), nil))
case6(Locks, Lock, Resource, false) → locker2_check_available(Resource, Locks)
locker2_check_availables(nil, Locks) → true
locker2_check_availables(cons(Resource, Resources), Locks) → andt(locker2_check_available(Resource, Locks), locker2_check_availables(Resources, Locks))
locker2_adduniq(nil, List) → List
append(cons(Head, Tail), List) → cons(Head, append(Tail, List))
subtract(List, nil) → List
subtract(List, cons(Head, Tail)) → subtract(delete(Head, List), Tail)
delete(E, nil) → nil
delete(E, cons(Head, Tail)) → case8(Tail, Head, E, equal(E, Head))
case8(Tail, Head, E, true) → Tail
case8(Tail, Head, E, false) → cons(Head, delete(E, Tail))
gen_tag(Pid) → tuple(Pid, tuplenil(tag))
gen_modtageq(Client1, Client2) → equal(Client1, Client2)
member(E, nil) → false
member(E, cons(Head, Tail)) → case9(Tail, Head, E, equal(E, Head))
case9(Tail, Head, E, true) → true
case9(Tail, Head, E, false) → member(E, Tail)
eqs(empty, empty) → T
eqs(empty, stack(E2, S2)) → F
eqs(stack(E1, S1), empty) → F
eqs(stack(E1, S1), stack(E2, S2)) → and(eqt(E1, E2), eqs(S1, S2))
pushs(E1, S1) → stack(E1, S1)
pops(stack(E1, S1)) → S1
tops(stack(E1, S1)) → E1
istops(E1, empty) → F
istops(E1, stack(E2, S1)) → eqt(E1, E2)
eqc(nocalls, nocalls) → T
eqc(nocalls, calls(E2, S2, CS2)) → F
eqc(calls(E1, S1, CS1), nocalls) → F
eqc(calls(E1, S1, CS1), calls(E2, S2, CS2)) → and(eqt(E1, E2), and(eqs(S1, S2), eqc(CS1, CS2)))
push(E1, E2, nocalls) → calls(E1, stack(E2, empty), nocalls)
push(E1, E2, calls(E3, S1, CS1)) → push1(E1, E2, E3, S1, CS1, eqt(E1, E3))
push1(E1, E2, E3, S1, CS1, T) → calls(E3, pushs(E2, S1), CS1)

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

(21) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

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

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
LOCKER2_MAP_CLAIM_LOCK(x1, x2, x3) = LOCKER2_MAP_CLAIM_LOCK(x1, x2, x3)
cons(x1, x2) = cons(x1, x2)
or(x1, x2) = or(x1, x2)
T = T
F = F
and(x1, x2) = and(x1, x2)
imp(x1, x2) = imp(x2)
not(x1) = not
if(x1, x2, x3) = if(x2, x3)
eq(x1, x2) = eq(x1, x2)
eqt(x1, x2) = eqt(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(x1, 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, 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)
locker2_map_claim_lock(x1, x2, x3) = x1
locker2_claim_lock(x1, x2, x3) = x1
locker2_map_add_pending(x1, x2, x3) = locker2_map_add_pending
case0(x1, x2, x3) = case0(x2, x3)
locker2_remove_pending(x1, x2) = locker2_remove_pending(x1, x2)
subtract(x1, x2) = subtract(x1, x2)
locker2_add_pending(x1, x2, x3) = locker2_add_pending(x1, x2, x3)
case1(x1, x2, x3, x4) = case1(x1, x2, x3, x4)
member(x1, x2) = member(x1, x2)
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)
excllock = excllock
case4(x1, x2, x3) = case4
locker2_obtainables(x1, x2) = locker2_obtainables
case5(x1, x2, x3, x4) = case5
andt(x1, x2) = x1
locker2_obtainable(x1, x2) = locker2_obtainable
locker2_check_available(x1, x2) = x1
case6(x1, x2, x3, x4) = x3
equal(x1, x2) = equal
locker2_check_availables(x1, x2) = locker2_check_availables(x1)
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(x1, 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
calls(x1, x2, x3) = calls(x1, x2, x3)
push(x1, x2, x3) = push(x1, x2, x3)
push1(x1, x2, x3, x4, x5, x6) = push1(x2, x3, x4, x5)

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

LOCKER2_{MAP_{CLAIM_LOCK₃}} > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
imp₁ > [T, eqt₁, nocalls] > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > undefined > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
imp₁ > [T, eqt₁, nocalls] > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > mcrlrecord > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
imp₁ > [T, eqt₁, nocalls] > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > append₂ > cons₂ > excl > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
imp₁ > [T, eqt₁, nocalls] > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > append₂ > cons₂ > record_extract₃ > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
imp₁ > [T, eqt₁, nocalls] > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > append₂ > cons₂ > record_updates₃ > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
imp₁ > [T, eqt₁, nocalls] > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > append₂ > cons₂ > [member₂, case9₃] > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
imp₁ > [T, eqt₁, nocalls] > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > excllock > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
imp₁ > [T, eqt₁, nocalls] > and₂ > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
imp₁ > [T, eqt₁, nocalls] > [pushs₂, push1₄] > stack₂ > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
imp₁ > [T, eqt₁, nocalls] > [pushs₂, push1₄] > calls₃ > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
not > [T, eqt₁, nocalls] > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > undefined > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
not > [T, eqt₁, nocalls] > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > mcrlrecord > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
not > [T, eqt₁, nocalls] > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > append₂ > cons₂ > excl > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
not > [T, eqt₁, nocalls] > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > append₂ > cons₂ > record_extract₃ > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
not > [T, eqt₁, nocalls] > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > append₂ > cons₂ > record_updates₃ > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
not > [T, eqt₁, nocalls] > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > append₂ > cons₂ > [member₂, case9₃] > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
not > [T, eqt₁, nocalls] > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > excllock > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
not > [T, eqt₁, nocalls] > and₂ > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
not > [T, eqt₁, nocalls] > [pushs₂, push1₄] > stack₂ > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
not > [T, eqt₁, nocalls] > [pushs₂, push1₄] > calls₃ > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
if₂ > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
eq₂ > [T, eqt₁, nocalls] > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > undefined > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
eq₂ > [T, eqt₁, nocalls] > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > mcrlrecord > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
eq₂ > [T, eqt₁, nocalls] > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > append₂ > cons₂ > excl > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
eq₂ > [T, eqt₁, nocalls] > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > append₂ > cons₂ > record_extract₃ > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
eq₂ > [T, eqt₁, nocalls] > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > append₂ > cons₂ > record_updates₃ > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
eq₂ > [T, eqt₁, nocalls] > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > append₂ > cons₂ > [member₂, case9₃] > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
eq₂ > [T, eqt₁, nocalls] > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > excllock > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
eq₂ > [T, eqt₁, nocalls] > and₂ > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
eq₂ > [T, eqt₁, nocalls] > [pushs₂, push1₄] > stack₂ > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
eq₂ > [T, eqt₁, nocalls] > [pushs₂, push1₄] > calls₃ > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
pid₁ > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
a > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
locker > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
ok > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
release > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
request > [T, eqt₁, nocalls] > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > undefined > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
request > [T, eqt₁, nocalls] > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > mcrlrecord > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
request > [T, eqt₁, nocalls] > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > append₂ > cons₂ > excl > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
request > [T, eqt₁, nocalls] > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > append₂ > cons₂ > record_extract₃ > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
request > [T, eqt₁, nocalls] > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > append₂ > cons₂ > record_updates₃ > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
request > [T, eqt₁, nocalls] > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > append₂ > cons₂ > [member₂, case9₃] > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
request > [T, eqt₁, nocalls] > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > excllock > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
request > [T, eqt₁, nocalls] > and₂ > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
request > [T, eqt₁, nocalls] > [pushs₂, push1₄] > stack₂ > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
request > [T, eqt₁, nocalls] > [pushs₂, push1₄] > calls₃ > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
0 > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
[locker2_{map_{promote_pending₂}}, locker2_{promote_pending₁}] > case0₂ > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > undefined > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
[locker2_{map_{promote_pending₂}}, locker2_{promote_pending₁}] > case0₂ > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > mcrlrecord > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
[locker2_{map_{promote_pending₂}}, locker2_{promote_pending₁}] > case0₂ > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > append₂ > cons₂ > excl > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
[locker2_{map_{promote_pending₂}}, locker2_{promote_pending₁}] > case0₂ > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > append₂ > cons₂ > record_extract₃ > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
[locker2_{map_{promote_pending₂}}, locker2_{promote_pending₁}] > case0₂ > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > append₂ > cons₂ > record_updates₃ > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
[locker2_{map_{promote_pending₂}}, locker2_{promote_pending₁}] > case0₂ > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > append₂ > cons₂ > [member₂, case9₃] > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
[locker2_{map_{promote_pending₂}}, locker2_{promote_pending₁}] > case0₂ > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > excllock > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
locker2_{remove_pending₂} > subtract₂ > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > undefined > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
locker2_{remove_pending₂} > subtract₂ > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > mcrlrecord > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
locker2_{remove_pending₂} > subtract₂ > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > append₂ > cons₂ > excl > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
locker2_{remove_pending₂} > subtract₂ > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > append₂ > cons₂ > record_extract₃ > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
locker2_{remove_pending₂} > subtract₂ > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > append₂ > cons₂ > record_updates₃ > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
locker2_{remove_pending₂} > subtract₂ > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > append₂ > cons₂ > [member₂, case9₃] > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
locker2_{remove_pending₂} > subtract₂ > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > excllock > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
locker2_{add_pending₃} > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > undefined > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
locker2_{add_pending₃} > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > mcrlrecord > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
locker2_{add_pending₃} > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > append₂ > cons₂ > excl > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
locker2_{add_pending₃} > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > append₂ > cons₂ > record_extract₃ > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
locker2_{add_pending₃} > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > append₂ > cons₂ > record_updates₃ > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
locker2_{add_pending₃} > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > append₂ > cons₂ > [member₂, case9₃] > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
locker2_{add_pending₃} > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > excllock > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
locker2_{release_lock₂} > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > undefined > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
locker2_{release_lock₂} > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > mcrlrecord > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
locker2_{release_lock₂} > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > append₂ > cons₂ > excl > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
locker2_{release_lock₂} > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > append₂ > cons₂ > record_extract₃ > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
locker2_{release_lock₂} > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > append₂ > cons₂ > record_updates₃ > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
locker2_{release_lock₂} > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > append₂ > cons₂ > [member₂, case9₃] > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
locker2_{release_lock₂} > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > excllock > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
locker2_{release_lock₂} > case2₃ > cons₂ > excl > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
locker2_{release_lock₂} > case2₃ > cons₂ > record_extract₃ > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
locker2_{release_lock₂} > case2₃ > cons₂ > record_updates₃ > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
locker2_{release_lock₂} > case2₃ > cons₂ > [member₂, case9₃] > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
locker2_{release_lock₂} > case2₃ > excllock > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
locker2_{release_lock₂} > gen_modtageq₁ > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
[locker2_obtainables, case5] > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > undefined > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
[locker2_obtainables, case5] > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > mcrlrecord > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
[locker2_obtainables, case5] > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > append₂ > cons₂ > excl > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
[locker2_obtainables, case5] > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > append₂ > cons₂ > record_extract₃ > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
[locker2_obtainables, case5] > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > append₂ > cons₂ > record_updates₃ > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
[locker2_obtainables, case5] > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > append₂ > cons₂ > [member₂, case9₃] > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
[locker2_obtainables, case5] > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > excllock > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
[locker2_obtainables, case5] > locker2_obtainable > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
gen_tag₁ > tag > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
tops₁ > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
istops₂ > [T, eqt₁, nocalls] > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > undefined > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
istops₂ > [T, eqt₁, nocalls] > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > mcrlrecord > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
istops₂ > [T, eqt₁, nocalls] > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > append₂ > cons₂ > excl > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
istops₂ > [T, eqt₁, nocalls] > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > append₂ > cons₂ > record_extract₃ > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
istops₂ > [T, eqt₁, nocalls] > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > append₂ > cons₂ > record_updates₃ > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
istops₂ > [T, eqt₁, nocalls] > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > append₂ > cons₂ > [member₂, case9₃] > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
istops₂ > [T, eqt₁, nocalls] > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > excllock > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
istops₂ > [T, eqt₁, nocalls] > and₂ > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
istops₂ > [T, eqt₁, nocalls] > [pushs₂, push1₄] > stack₂ > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
istops₂ > [T, eqt₁, nocalls] > [pushs₂, push1₄] > calls₃ > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
eqc₂ > eqs₂ > [T, eqt₁, nocalls] > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > undefined > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
eqc₂ > eqs₂ > [T, eqt₁, nocalls] > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > mcrlrecord > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
eqc₂ > eqs₂ > [T, eqt₁, nocalls] > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > append₂ > cons₂ > excl > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
eqc₂ > eqs₂ > [T, eqt₁, nocalls] > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > append₂ > cons₂ > record_extract₃ > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
eqc₂ > eqs₂ > [T, eqt₁, nocalls] > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > append₂ > cons₂ > record_updates₃ > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
eqc₂ > eqs₂ > [T, eqt₁, nocalls] > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > append₂ > cons₂ > [member₂, case9₃] > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
eqc₂ > eqs₂ > [T, eqt₁, nocalls] > [or₂, F, nil, lock, true, record_new₁, locker2_{map_{add_pending}}, case1₄, locker2_{check_{availables₁}}, delete₂, case8₄] > excllock > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
eqc₂ > eqs₂ > [T, eqt₁, nocalls] > and₂ > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
eqc₂ > eqs₂ > [T, eqt₁, nocalls] > [pushs₂, push1₄] > stack₂ > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
eqc₂ > eqs₂ > [T, eqt₁, nocalls] > [pushs₂, push1₄] > calls₃ > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
push₃ > [pushs₂, push1₄] > stack₂ > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]
push₃ > [pushs₂, push1₄] > calls₃ > [tuple₂, false, pending, resource, element₂, s, record_update₂, case4, equal, empty]

Status:

LOCKER2_{MAP_{CLAIM_LOCK₃}}: [3,2,1]
cons₂: [1,2]
or₂: [2,1]
T: []
F: []
and₂: [1,2]
imp₁: [1]
not: []
if₂: [1,2]
eq₂: [2,1]
eqt₁: [1]
nil: []
undefined: []
pid₁: [1]
tuple₂: [1,2]
a: []
excl: []
false: []
lock: []
locker: []
mcrlrecord: []
ok: []
pending: []
release: []
request: []
resource: []
tag: []
true: []
element₂: [1,2]
s: []
0: []
record_new₁: [1]
record_extract₃: [2,1,3]
record_update₂: [1,2]
record_updates₃: [2,3,1]
locker2_{map_{promote_pending₂}}: [1,2]
locker2_{promote_pending₁}: [1]
locker2_{map_{add_pending}}: []
case0₂: [2,1]
locker2_{remove_pending₂}: [2,1]
subtract₂: [2,1]
locker2_{add_pending₃}: [2,3,1]
case1₄: [1,2,3,4]
member₂: [2,1]
append₂: [2,1]
locker2_{release_lock₂}: [2,1]
case2₃: [3,2,1]
gen_modtageq₁: [1]
excllock: []
case4: []
locker2_obtainables: []
case5: []
locker2_obtainable: []
equal: []
locker2_{check_{availables₁}}: [1]
delete₂: [2,1]
case8₄: [1,3,4,2]
gen_tag₁: [1]
case9₃: [1,2,3]
eqs₂: [2,1]
empty: []
stack₂: [1,2]
pushs₂: [1,2]
tops₁: [1]
istops₂: [2,1]
eqc₂: [1,2]
nocalls: []
calls₃: [3,2,1]
push₃: [1,2,3]
push1₄: [1,3,4,2]

The following usable rules [FROCOS05] were oriented:

or(T, T) → T
or(F, T) → T
or(T, F) → T
or(F, F) → F
and(T, B) → B
and(B, T) → B
and(F, B) → F
and(B, F) → F
imp(T, B) → B
imp(F, B) → T
not(T) → F
not(F) → T
if(T, B1, B2) → B1
if(F, B1, B2) → B2
eq(T, T) → T
eq(F, F) → T
eq(T, F) → F
eq(F, T) → F
eqt(nil, undefined) → F
eqt(nil, pid(N2)) → F
eqt(nil, int(N2)) → F
eqt(nil, cons(H2, T2)) → F
eqt(nil, tuple(H2, T2)) → F
eqt(nil, tuplenil(H2)) → F
eqt(a, nil) → F
eqt(a, a) → T
eqt(a, excl) → F
eqt(a, false) → F
eqt(a, lock) → F
eqt(a, locker) → F
eqt(a, mcrlrecord) → F
eqt(a, ok) → F
eqt(a, pending) → F
eqt(a, release) → F
eqt(a, request) → F
eqt(a, resource) → F
eqt(a, tag) → F
eqt(a, true) → F
eqt(a, undefined) → F
eqt(a, pid(N2)) → F
eqt(a, int(N2)) → F
eqt(a, cons(H2, T2)) → F
eqt(a, tuple(H2, T2)) → F
eqt(a, tuplenil(H2)) → F
eqt(excl, nil) → F
eqt(excl, a) → F
eqt(excl, excl) → T
eqt(excl, false) → F
eqt(excl, lock) → F
eqt(excl, locker) → F
eqt(excl, mcrlrecord) → F
eqt(excl, ok) → F
eqt(excl, pending) → F
eqt(excl, release) → F
eqt(excl, request) → F
eqt(excl, resource) → F
eqt(excl, tag) → F
eqt(excl, true) → F
eqt(excl, undefined) → F
eqt(excl, pid(N2)) → F
eqt(excl, eqt(false, int(N2))) → F
eqt(false, cons(H2, T2)) → F
eqt(false, tuple(H2, T2)) → F
eqt(false, tuplenil(H2)) → F
eqt(lock, nil) → F
eqt(lock, a) → F
eqt(lock, excl) → F
eqt(lock, false) → F
eqt(lock, lock) → T
eqt(lock, locker) → F
eqt(lock, mcrlrecord) → F
eqt(lock, ok) → F
eqt(lock, pending) → F
eqt(lock, release) → F
eqt(lock, request) → F
eqt(lock, resource) → F
eqt(lock, tag) → F
eqt(lock, true) → F
eqt(lock, undefined) → F
eqt(lock, pid(N2)) → F
eqt(lock, int(N2)) → F
eqt(lock, cons(H2, T2)) → F
eqt(lock, tuple(H2, T2)) → F
eqt(lock, tuplenil(H2)) → F
eqt(locker, nil) → F
eqt(locker, a) → F
eqt(locker, excl) → F
eqt(locker, false) → F
eqt(locker, lock) → F
eqt(locker, locker) → T
eqt(locker, mcrlrecord) → F
eqt(locker, ok) → F
eqt(locker, pending) → F
eqt(locker, release) → F
eqt(locker, request) → F
eqt(locker, resource) → F
eqt(locker, tag) → F
eqt(locker, true) → F
eqt(locker, undefined) → F
eqt(locker, pid(N2)) → F
eqt(locker, int(N2)) → F
eqt(locker, cons(H2, T2)) → F
eqt(locker, tuple(H2, T2)) → F
eqt(locker, tuplenil(H2)) → F
eqt(mcrlrecord, nil) → F
eqt(mcrlrecord, a) → F
eqt(mcrlrecord, excl) → F
eqt(mcrlrecord, false) → F
eqt(mcrlrecord, lock) → F
eqt(mcrlrecord, locker) → F
eqt(mcrlrecord, mcrlrecord) → T
eqt(mcrlrecord, ok) → F
eqt(mcrlrecord, pending) → F
eqt(mcrlrecord, release) → F
eqt(mcrlrecord, request) → F
eqt(mcrlrecord, resource) → F
eqt(ok, resource) → F
eqt(ok, tag) → F
eqt(ok, true) → F
eqt(ok, undefined) → F
eqt(ok, pid(N2)) → F
eqt(ok, int(N2)) → F
eqt(ok, cons(H2, T2)) → F
eqt(ok, tuple(H2, T2)) → F
eqt(ok, tuplenil(H2)) → F
eqt(pending, nil) → F
eqt(pending, a) → F
eqt(pending, excl) → F
eqt(pending, false) → F
eqt(pending, lock) → F
eqt(pending, locker) → F
eqt(pending, mcrlrecord) → F
eqt(pending, ok) → F
eqt(pending, pending) → T
eqt(pending, release) → F
eqt(pending, request) → F
eqt(pending, resource) → F
eqt(pending, tag) → F
eqt(pending, true) → F
eqt(pending, undefined) → F
eqt(pending, pid(N2)) → F
eqt(pending, int(N2)) → F
eqt(pending, cons(H2, T2)) → F
eqt(pending, tuple(H2, T2)) → F
eqt(pending, tuplenil(H2)) → F
eqt(release, nil) → F
eqt(release, a) → F
eqt(release, excl) → F
eqt(release, false) → F
eqt(release, lock) → F
eqt(release, locker) → F
eqt(release, mcrlrecord) → F
eqt(release, ok) → F
eqt(request, mcrlrecord) → F
eqt(request, ok) → F
eqt(request, pending) → F
eqt(request, release) → F
eqt(request, request) → T
eqt(request, resource) → F
eqt(request, tag) → F
eqt(request, true) → F
eqt(request, undefined) → F
eqt(request, pid(N2)) → F
eqt(request, int(N2)) → F
eqt(request, cons(H2, T2)) → F
eqt(request, tuple(H2, T2)) → F
eqt(request, tuplenil(H2)) → F
eqt(resource, nil) → F
eqt(resource, a) → F
eqt(resource, excl) → F
eqt(resource, false) → F
eqt(resource, lock) → F
eqt(resource, locker) → F
eqt(resource, mcrlrecord) → F
eqt(resource, ok) → F
eqt(resource, pending) → F
eqt(resource, release) → F
eqt(resource, request) → F
eqt(resource, resource) → T
eqt(resource, tag) → F
eqt(resource, true) → F
eqt(resource, undefined) → F
eqt(resource, pid(N2)) → F
eqt(resource, int(N2)) → F
eqt(resource, cons(H2, T2)) → F
eqt(resource, tuple(H2, T2)) → F
eqt(resource, tuplenil(H2)) → F
eqt(tag, nil) → F
eqt(tag, a) → F
eqt(tag, excl) → F
eqt(tag, false) → F
eqt(tag, lock) → F
eqt(tag, locker) → F
eqt(tag, mcrlrecord) → F
eqt(tag, ok) → F
eqt(tag, pending) → F
eqt(tag, release) → F
eqt(tag, request) → F
eqt(tag, resource) → F
eqt(tag, tag) → T
eqt(tag, true) → F
eqt(tag, undefined) → F
eqt(tag, pid(N2)) → F
eqt(tag, int(N2)) → F
eqt(tag, cons(H2, T2)) → F
eqt(tag, tuple(H2, T2)) → F
eqt(tag, tuplenil(H2)) → F
eqt(true, nil) → F
eqt(true, a) → F
eqt(true, excl) → F
eqt(true, false) → F
eqt(true, lock) → F
eqt(true, locker) → F
eqt(true, mcrlrecord) → F
eqt(true, ok) → F
eqt(true, pending) → F
eqt(true, release) → F
eqt(true, request) → F
eqt(true, resource) → F
eqt(true, tag) → F
eqt(true, true) → T
eqt(true, undefined) → F
eqt(true, pid(N2)) → F
eqt(true, int(N2)) → F
eqt(true, cons(H2, T2)) → F
eqt(true, tuple(H2, T2)) → F
eqt(true, tuplenil(H2)) → F
eqt(undefined, nil) → F
eqt(undefined, a) → F
eqt(undefined, tuplenil(H2)) → F
eqt(pid(N1), nil) → F
eqt(pid(N1), a) → F
eqt(pid(N1), excl) → F
eqt(pid(N1), false) → F
eqt(pid(N1), lock) → F
eqt(pid(N1), locker) → F
eqt(pid(N1), mcrlrecord) → F
eqt(pid(N1), ok) → F
eqt(pid(N1), pending) → F
eqt(pid(N1), release) → F
eqt(pid(N1), request) → F
eqt(pid(N1), resource) → F
eqt(pid(N1), tag) → F
eqt(pid(N1), true) → F
eqt(pid(N1), undefined) → F
eqt(pid(N1), pid(N2)) → eqt(N1, N2)
eqt(pid(N1), int(N2)) → F
eqt(pid(N1), cons(H2, T2)) → F
eqt(pid(N1), tuple(H2, T2)) → F
eqt(pid(N1), tuplenil(H2)) → F
eqt(int(N1), nil) → F
eqt(int(N1), a) → F
eqt(int(N1), excl) → F
eqt(int(N1), false) → F
eqt(int(N1), lock) → F
eqt(int(N1), locker) → F
eqt(int(N1), mcrlrecord) → F
eqt(int(N1), ok) → F
eqt(int(N1), pending) → F
eqt(int(N1), release) → F
eqt(int(N1), request) → F
eqt(int(N1), resource) → F
eqt(int(N1), tag) → F
eqt(int(N1), true) → F
eqt(int(N1), undefined) → F
eqt(cons(H1, T1), resource) → F
eqt(cons(H1, T1), tag) → F
eqt(cons(H1, T1), true) → F
eqt(cons(H1, T1), undefined) → F
eqt(cons(H1, T1), pid(N2)) → F
eqt(cons(H1, T1), int(N2)) → F
eqt(cons(H1, T1), cons(H2, T2)) → and(eqt(H1, H2), eqt(T1, T2))
eqt(cons(H1, T1), tuple(H2, T2)) → F
eqt(cons(H1, T1), tuplenil(H2)) → F
eqt(tuple(H1, T1), nil) → F
eqt(tuple(H1, T1), a) → F
eqt(tuple(H1, T1), excl) → F
eqt(tuple(H1, T1), false) → F
eqt(tuple(H1, T1), lock) → F
eqt(tuple(H1, T1), locker) → F
eqt(tuple(H1, T1), mcrlrecord) → F
eqt(tuple(H1, T1), ok) → F
eqt(tuple(H1, T1), pending) → F
eqt(tuple(H1, T1), release) → F
eqt(tuple(H1, T1), request) → F
eqt(tuple(H1, T1), resource) → F
eqt(tuple(H1, T1), tag) → F
eqt(tuple(H1, T1), true) → F
eqt(tuple(H1, T1), undefined) → F
eqt(tuple(H1, T1), pid(N2)) → F
eqt(tuple(H1, T1), int(N2)) → F
eqt(tuple(H1, T1), cons(H2, T2)) → F
eqt(tuple(H1, T1), tuple(H2, T2)) → and(eqt(H1, H2), eqt(T1, T2))
eqt(tuple(H1, T1), tuplenil(H2)) → F
eqt(tuplenil(H1), nil) → F
eqt(tuplenil(H1), a) → F
eqt(tuplenil(H1), excl) → F
eqt(tuplenil(H1), false) → F
eqt(tuplenil(H1), lock) → F
eqt(tuplenil(H1), locker) → F
eqt(tuplenil(H1), mcrlrecord) → F
eqt(tuplenil(H1), ok) → F
eqt(tuplenil(H1), pending) → F
eqt(tuplenil(H1), release) → F
eqt(tuplenil(H1), request) → F
eqt(tuplenil(H1), resource) → F
eqt(tuplenil(H1), tag) → F
eqt(tuplenil(H1), true) → F
eqt(tuplenil(H1), undefined) → F
eqt(tuplenil(H1), pid(N2)) → F
eqt(tuplenil(H1), int(N2)) → F
eqt(tuplenil(H1), cons(H2, T2)) → F
eqt(tuplenil(H1), tuple(H2, T2)) → F
eqt(tuplenil(H1), tuplenil(H2)) → eqt(H1, H2)
element(int(s(0)), tuplenil(T1)) → T1
element(int(s(0)), tuple(T1, T2)) → T1
element(int(s(s(N1))), tuple(T1, T2)) → element(int(s(N1)), T2)
record_new(lock) → tuple(mcrlrecord, tuple(lock, tuple(undefined, tuple(nil, tuplenil(nil)))))
record_extract(tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))), lock, resource) → tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2)))))
record_update(tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))), lock, pending, NewF) → tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(NewF)))))
record_updates(Record, Name, nil) → Record
record_updates(Record, Name, cons(tuple(Field, tuplenil(NewF)), Fields)) → record_updates(record_update(Record, Name, Field, NewF), Name, Fields)
locker2_map_promote_pending(nil, Pending) → nil
locker2_map_promote_pending(cons(Lock, Locks), Pending) → cons(locker2_promote_pending(Lock, Pending), locker2_map_promote_pending(Locks, Pending))
locker2_map_claim_lock(nil, Resources, Client) → nil
locker2_map_claim_lock(cons(Lock, Locks), Resources, Client) → cons(locker2_claim_lock(Lock, Resources, Client), locker2_map_claim_lock(Locks, Resources, Client))
locker2_map_add_pending(nil, Resources, Client) → nil
locker2_promote_pending(Lock, Client) → case0(Client, Lock, record_extract(Lock, lock, pending))
case0(Client, Lock, cons(Client, Pendings)) → record_updates(Lock, lock, cons(tuple(excl, tuplenil(Client)), cons(tuple(pending, tuplenil(Pendings)), nil)))
case0(Client, Lock, MCRLFree0) → Lock
locker2_remove_pending(Lock, Client) → record_updates(Lock, lock, cons(tuple(pending, tuplenil(subtract(record_extract(Lock, lock, pending), cons(Client, nil)))), nil))
locker2_add_pending(Lock, Resources, Client) → case1(Client, Resources, Lock, member(record_extract(Lock, lock, resource), Resources))
case1(Client, Resources, Lock, true) → record_updates(Lock, lock, cons(tuple(pending, tuplenil(append(record_extract(Lock, lock, pending), cons(Client, nil)))), nil))
case1(Client, Resources, Lock, false) → Lock
locker2_release_lock(Lock, Client) → case2(Client, Lock, gen_modtageq(Client, record_extract(Lock, lock, excl)))
case2(Client, Lock, true) → record_updates(Lock, lock, cons(tuple(excllock, excl), nil))
case4(Client, Lock, MCRLFree1) → false
locker2_obtainables(nil, Client) → true
locker2_obtainables(cons(Lock, Locks), Client) → case5(Client, Locks, Lock, member(Client, record_extract(Lock, lock, pending)))
case5(Client, Locks, Lock, true) → andt(locker2_obtainable(Lock, Client), locker2_obtainables(Locks, Client))
case5(Client, Locks, Lock, false) → locker2_obtainables(Locks, Client)
locker2_check_available(Resource, nil) → false
locker2_check_available(Resource, cons(Lock, Locks)) → case6(Locks, Lock, Resource, equal(Resource, record_extract(Lock, lock, resource)))
case6(Locks, Lock, Resource, true) → andt(equal(record_extract(Lock, lock, excl), nil), equal(record_extract(Lock, lock, pending), nil))
case6(Locks, Lock, Resource, false) → locker2_check_available(Resource, Locks)
locker2_check_availables(nil, Locks) → true
locker2_check_availables(cons(Resource, Resources), Locks) → andt(locker2_check_available(Resource, Locks), locker2_check_availables(Resources, Locks))
locker2_adduniq(nil, List) → List
append(cons(Head, Tail), List) → cons(Head, append(Tail, List))
subtract(List, nil) → List
subtract(List, cons(Head, Tail)) → subtract(delete(Head, List), Tail)
delete(E, nil) → nil
delete(E, cons(Head, Tail)) → case8(Tail, Head, E, equal(E, Head))
case8(Tail, Head, E, true) → Tail
case8(Tail, Head, E, false) → cons(Head, delete(E, Tail))
gen_tag(Pid) → tuple(Pid, tuplenil(tag))
gen_modtageq(Client1, Client2) → equal(Client1, Client2)
member(E, nil) → false
member(E, cons(Head, Tail)) → case9(Tail, Head, E, equal(E, Head))
case9(Tail, Head, E, true) → true
case9(Tail, Head, E, false) → member(E, Tail)
eqs(empty, empty) → T
eqs(empty, stack(E2, S2)) → F
eqs(stack(E1, S1), empty) → F
eqs(stack(E1, S1), stack(E2, S2)) → and(eqt(E1, E2), eqs(S1, S2))
pushs(E1, S1) → stack(E1, S1)
pops(stack(E1, S1)) → S1
tops(stack(E1, S1)) → E1
istops(E1, empty) → F
istops(E1, stack(E2, S1)) → eqt(E1, E2)
eqc(nocalls, nocalls) → T
eqc(nocalls, calls(E2, S2, CS2)) → F
eqc(calls(E1, S1, CS1), nocalls) → F
eqc(calls(E1, S1, CS1), calls(E2, S2, CS2)) → and(eqt(E1, E2), and(eqs(S1, S2), eqc(CS1, CS2)))
push(E1, E2, nocalls) → calls(E1, stack(E2, empty), nocalls)
push(E1, E2, calls(E3, S1, CS1)) → push1(E1, E2, E3, S1, CS1, eqt(E1, E3))
push1(E1, E2, E3, S1, CS1, T) → calls(E3, pushs(E2, S1), CS1)

(22) Obligation:

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

or(T, T) → T
or(F, T) → T
or(T, F) → T
or(F, F) → F
and(T, B) → B
and(B, T) → B
and(F, B) → F
and(B, F) → F
imp(T, B) → B
imp(F, B) → T
not(T) → F
not(F) → T
if(T, B1, B2) → B1
if(F, B1, B2) → B2
eq(T, T) → T
eq(F, F) → T
eq(T, F) → F
eq(F, T) → F
eqt(nil, undefined) → F
eqt(nil, pid(N2)) → F
eqt(nil, int(N2)) → F
eqt(nil, cons(H2, T2)) → F
eqt(nil, tuple(H2, T2)) → F
eqt(nil, tuplenil(H2)) → F
eqt(a, nil) → F
eqt(a, a) → T
eqt(a, excl) → F
eqt(a, false) → F
eqt(a, lock) → F
eqt(a, locker) → F
eqt(a, mcrlrecord) → F
eqt(a, ok) → F
eqt(a, pending) → F
eqt(a, release) → F
eqt(a, request) → F
eqt(a, resource) → F
eqt(a, tag) → F
eqt(a, true) → F
eqt(a, undefined) → F
eqt(a, pid(N2)) → F
eqt(a, int(N2)) → F
eqt(a, cons(H2, T2)) → F
eqt(a, tuple(H2, T2)) → F
eqt(a, tuplenil(H2)) → F
eqt(excl, nil) → F
eqt(excl, a) → F
eqt(excl, excl) → T
eqt(excl, false) → F
eqt(excl, lock) → F
eqt(excl, locker) → F
eqt(excl, mcrlrecord) → F
eqt(excl, ok) → F
eqt(excl, pending) → F
eqt(excl, release) → F
eqt(excl, request) → F
eqt(excl, resource) → F
eqt(excl, tag) → F
eqt(excl, true) → F
eqt(excl, undefined) → F
eqt(excl, pid(N2)) → F
eqt(excl, eqt(false, int(N2))) → F
eqt(false, cons(H2, T2)) → F
eqt(false, tuple(H2, T2)) → F
eqt(false, tuplenil(H2)) → F
eqt(lock, nil) → F
eqt(lock, a) → F
eqt(lock, excl) → F
eqt(lock, false) → F
eqt(lock, lock) → T
eqt(lock, locker) → F
eqt(lock, mcrlrecord) → F
eqt(lock, ok) → F
eqt(lock, pending) → F
eqt(lock, release) → F
eqt(lock, request) → F
eqt(lock, resource) → F
eqt(lock, tag) → F
eqt(lock, true) → F
eqt(lock, undefined) → F
eqt(lock, pid(N2)) → F
eqt(lock, int(N2)) → F
eqt(lock, cons(H2, T2)) → F
eqt(lock, tuple(H2, T2)) → F
eqt(lock, tuplenil(H2)) → F
eqt(locker, nil) → F
eqt(locker, a) → F
eqt(locker, excl) → F
eqt(locker, false) → F
eqt(locker, lock) → F
eqt(locker, locker) → T
eqt(locker, mcrlrecord) → F
eqt(locker, ok) → F
eqt(locker, pending) → F
eqt(locker, release) → F
eqt(locker, request) → F
eqt(locker, resource) → F
eqt(locker, tag) → F
eqt(locker, true) → F
eqt(locker, undefined) → F
eqt(locker, pid(N2)) → F
eqt(locker, int(N2)) → F
eqt(locker, cons(H2, T2)) → F
eqt(locker, tuple(H2, T2)) → F
eqt(locker, tuplenil(H2)) → F
eqt(mcrlrecord, nil) → F
eqt(mcrlrecord, a) → F
eqt(mcrlrecord, excl) → F
eqt(mcrlrecord, false) → F
eqt(mcrlrecord, lock) → F
eqt(mcrlrecord, locker) → F
eqt(mcrlrecord, mcrlrecord) → T
eqt(mcrlrecord, ok) → F
eqt(mcrlrecord, pending) → F
eqt(mcrlrecord, release) → F
eqt(mcrlrecord, request) → F
eqt(mcrlrecord, resource) → F
eqt(ok, resource) → F
eqt(ok, tag) → F
eqt(ok, true) → F
eqt(ok, undefined) → F
eqt(ok, pid(N2)) → F
eqt(ok, int(N2)) → F
eqt(ok, cons(H2, T2)) → F
eqt(ok, tuple(H2, T2)) → F
eqt(ok, tuplenil(H2)) → F
eqt(pending, nil) → F
eqt(pending, a) → F
eqt(pending, excl) → F
eqt(pending, false) → F
eqt(pending, lock) → F
eqt(pending, locker) → F
eqt(pending, mcrlrecord) → F
eqt(pending, ok) → F
eqt(pending, pending) → T
eqt(pending, release) → F
eqt(pending, request) → F
eqt(pending, resource) → F
eqt(pending, tag) → F
eqt(pending, true) → F
eqt(pending, undefined) → F
eqt(pending, pid(N2)) → F
eqt(pending, int(N2)) → F
eqt(pending, cons(H2, T2)) → F
eqt(pending, tuple(H2, T2)) → F
eqt(pending, tuplenil(H2)) → F
eqt(release, nil) → F
eqt(release, a) → F
eqt(release, excl) → F
eqt(release, false) → F
eqt(release, lock) → F
eqt(release, locker) → F
eqt(release, mcrlrecord) → F
eqt(release, ok) → F
eqt(request, mcrlrecord) → F
eqt(request, ok) → F
eqt(request, pending) → F
eqt(request, release) → F
eqt(request, request) → T
eqt(request, resource) → F
eqt(request, tag) → F
eqt(request, true) → F
eqt(request, undefined) → F
eqt(request, pid(N2)) → F
eqt(request, int(N2)) → F
eqt(request, cons(H2, T2)) → F
eqt(request, tuple(H2, T2)) → F
eqt(request, tuplenil(H2)) → F
eqt(resource, nil) → F
eqt(resource, a) → F
eqt(resource, excl) → F
eqt(resource, false) → F
eqt(resource, lock) → F
eqt(resource, locker) → F
eqt(resource, mcrlrecord) → F
eqt(resource, ok) → F
eqt(resource, pending) → F
eqt(resource, release) → F
eqt(resource, request) → F
eqt(resource, resource) → T
eqt(resource, tag) → F
eqt(resource, true) → F
eqt(resource, undefined) → F
eqt(resource, pid(N2)) → F
eqt(resource, int(N2)) → F
eqt(resource, cons(H2, T2)) → F
eqt(resource, tuple(H2, T2)) → F
eqt(resource, tuplenil(H2)) → F
eqt(tag, nil) → F
eqt(tag, a) → F
eqt(tag, excl) → F
eqt(tag, false) → F
eqt(tag, lock) → F
eqt(tag, locker) → F
eqt(tag, mcrlrecord) → F
eqt(tag, ok) → F
eqt(tag, pending) → F
eqt(tag, release) → F
eqt(tag, request) → F
eqt(tag, resource) → F
eqt(tag, tag) → T
eqt(tag, true) → F
eqt(tag, undefined) → F
eqt(tag, pid(N2)) → F
eqt(tag, int(N2)) → F
eqt(tag, cons(H2, T2)) → F
eqt(tag, tuple(H2, T2)) → F
eqt(tag, tuplenil(H2)) → F
eqt(true, nil) → F
eqt(true, a) → F
eqt(true, excl) → F
eqt(true, false) → F
eqt(true, lock) → F
eqt(true, locker) → F
eqt(true, mcrlrecord) → F
eqt(true, ok) → F
eqt(true, pending) → F
eqt(true, release) → F
eqt(true, request) → F
eqt(true, resource) → F
eqt(true, tag) → F
eqt(true, true) → T
eqt(true, undefined) → F
eqt(true, pid(N2)) → F
eqt(true, int(N2)) → F
eqt(true, cons(H2, T2)) → F
eqt(true, tuple(H2, T2)) → F
eqt(true, tuplenil(H2)) → F
eqt(undefined, nil) → F
eqt(undefined, a) → F
eqt(undefined, tuplenil(H2)) → F
eqt(pid(N1), nil) → F
eqt(pid(N1), a) → F
eqt(pid(N1), excl) → F
eqt(pid(N1), false) → F
eqt(pid(N1), lock) → F
eqt(pid(N1), locker) → F
eqt(pid(N1), mcrlrecord) → F
eqt(pid(N1), ok) → F
eqt(pid(N1), pending) → F
eqt(pid(N1), release) → F
eqt(pid(N1), request) → F
eqt(pid(N1), resource) → F
eqt(pid(N1), tag) → F
eqt(pid(N1), true) → F
eqt(pid(N1), undefined) → F
eqt(pid(N1), pid(N2)) → eqt(N1, N2)
eqt(pid(N1), int(N2)) → F
eqt(pid(N1), cons(H2, T2)) → F
eqt(pid(N1), tuple(H2, T2)) → F
eqt(pid(N1), tuplenil(H2)) → F
eqt(int(N1), nil) → F
eqt(int(N1), a) → F
eqt(int(N1), excl) → F
eqt(int(N1), false) → F
eqt(int(N1), lock) → F
eqt(int(N1), locker) → F
eqt(int(N1), mcrlrecord) → F
eqt(int(N1), ok) → F
eqt(int(N1), pending) → F
eqt(int(N1), release) → F
eqt(int(N1), request) → F
eqt(int(N1), resource) → F
eqt(int(N1), tag) → F
eqt(int(N1), true) → F
eqt(int(N1), undefined) → F
eqt(cons(H1, T1), resource) → F
eqt(cons(H1, T1), tag) → F
eqt(cons(H1, T1), true) → F
eqt(cons(H1, T1), undefined) → F
eqt(cons(H1, T1), pid(N2)) → F
eqt(cons(H1, T1), int(N2)) → F
eqt(cons(H1, T1), cons(H2, T2)) → and(eqt(H1, H2), eqt(T1, T2))
eqt(cons(H1, T1), tuple(H2, T2)) → F
eqt(cons(H1, T1), tuplenil(H2)) → F
eqt(tuple(H1, T1), nil) → F
eqt(tuple(H1, T1), a) → F
eqt(tuple(H1, T1), excl) → F
eqt(tuple(H1, T1), false) → F
eqt(tuple(H1, T1), lock) → F
eqt(tuple(H1, T1), locker) → F
eqt(tuple(H1, T1), mcrlrecord) → F
eqt(tuple(H1, T1), ok) → F
eqt(tuple(H1, T1), pending) → F
eqt(tuple(H1, T1), release) → F
eqt(tuple(H1, T1), request) → F
eqt(tuple(H1, T1), resource) → F
eqt(tuple(H1, T1), tag) → F
eqt(tuple(H1, T1), true) → F
eqt(tuple(H1, T1), undefined) → F
eqt(tuple(H1, T1), pid(N2)) → F
eqt(tuple(H1, T1), int(N2)) → F
eqt(tuple(H1, T1), cons(H2, T2)) → F
eqt(tuple(H1, T1), tuple(H2, T2)) → and(eqt(H1, H2), eqt(T1, T2))
eqt(tuple(H1, T1), tuplenil(H2)) → F
eqt(tuplenil(H1), nil) → F
eqt(tuplenil(H1), a) → F
eqt(tuplenil(H1), excl) → F
eqt(tuplenil(H1), false) → F
eqt(tuplenil(H1), lock) → F
eqt(tuplenil(H1), locker) → F
eqt(tuplenil(H1), mcrlrecord) → F
eqt(tuplenil(H1), ok) → F
eqt(tuplenil(H1), pending) → F
eqt(tuplenil(H1), release) → F
eqt(tuplenil(H1), request) → F
eqt(tuplenil(H1), resource) → F
eqt(tuplenil(H1), tag) → F
eqt(tuplenil(H1), true) → F
eqt(tuplenil(H1), undefined) → F
eqt(tuplenil(H1), pid(N2)) → F
eqt(tuplenil(H1), int(N2)) → F
eqt(tuplenil(H1), cons(H2, T2)) → F
eqt(tuplenil(H1), tuple(H2, T2)) → F
eqt(tuplenil(H1), tuplenil(H2)) → eqt(H1, H2)
element(int(s(0)), tuplenil(T1)) → T1
element(int(s(0)), tuple(T1, T2)) → T1
element(int(s(s(N1))), tuple(T1, T2)) → element(int(s(N1)), T2)
record_new(lock) → tuple(mcrlrecord, tuple(lock, tuple(undefined, tuple(nil, tuplenil(nil)))))
record_extract(tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))), lock, resource) → tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2)))))
record_update(tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))), lock, pending, NewF) → tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(NewF)))))
record_updates(Record, Name, nil) → Record
record_updates(Record, Name, cons(tuple(Field, tuplenil(NewF)), Fields)) → record_updates(record_update(Record, Name, Field, NewF), Name, Fields)
locker2_map_promote_pending(nil, Pending) → nil
locker2_map_promote_pending(cons(Lock, Locks), Pending) → cons(locker2_promote_pending(Lock, Pending), locker2_map_promote_pending(Locks, Pending))
locker2_map_claim_lock(nil, Resources, Client) → nil
locker2_map_claim_lock(cons(Lock, Locks), Resources, Client) → cons(locker2_claim_lock(Lock, Resources, Client), locker2_map_claim_lock(Locks, Resources, Client))
locker2_map_add_pending(nil, Resources, Client) → nil
locker2_promote_pending(Lock, Client) → case0(Client, Lock, record_extract(Lock, lock, pending))
case0(Client, Lock, cons(Client, Pendings)) → record_updates(Lock, lock, cons(tuple(excl, tuplenil(Client)), cons(tuple(pending, tuplenil(Pendings)), nil)))
case0(Client, Lock, MCRLFree0) → Lock
locker2_remove_pending(Lock, Client) → record_updates(Lock, lock, cons(tuple(pending, tuplenil(subtract(record_extract(Lock, lock, pending), cons(Client, nil)))), nil))
locker2_add_pending(Lock, Resources, Client) → case1(Client, Resources, Lock, member(record_extract(Lock, lock, resource), Resources))
case1(Client, Resources, Lock, true) → record_updates(Lock, lock, cons(tuple(pending, tuplenil(append(record_extract(Lock, lock, pending), cons(Client, nil)))), nil))
case1(Client, Resources, Lock, false) → Lock
locker2_release_lock(Lock, Client) → case2(Client, Lock, gen_modtageq(Client, record_extract(Lock, lock, excl)))
case2(Client, Lock, true) → record_updates(Lock, lock, cons(tuple(excllock, excl), nil))
case4(Client, Lock, MCRLFree1) → false
locker2_obtainables(nil, Client) → true
locker2_obtainables(cons(Lock, Locks), Client) → case5(Client, Locks, Lock, member(Client, record_extract(Lock, lock, pending)))
case5(Client, Locks, Lock, true) → andt(locker2_obtainable(Lock, Client), locker2_obtainables(Locks, Client))
case5(Client, Locks, Lock, false) → locker2_obtainables(Locks, Client)
locker2_check_available(Resource, nil) → false
locker2_check_available(Resource, cons(Lock, Locks)) → case6(Locks, Lock, Resource, equal(Resource, record_extract(Lock, lock, resource)))
case6(Locks, Lock, Resource, true) → andt(equal(record_extract(Lock, lock, excl), nil), equal(record_extract(Lock, lock, pending), nil))
case6(Locks, Lock, Resource, false) → locker2_check_available(Resource, Locks)
locker2_check_availables(nil, Locks) → true
locker2_check_availables(cons(Resource, Resources), Locks) → andt(locker2_check_available(Resource, Locks), locker2_check_availables(Resources, Locks))
locker2_adduniq(nil, List) → List
append(cons(Head, Tail), List) → cons(Head, append(Tail, List))
subtract(List, nil) → List
subtract(List, cons(Head, Tail)) → subtract(delete(Head, List), Tail)
delete(E, nil) → nil
delete(E, cons(Head, Tail)) → case8(Tail, Head, E, equal(E, Head))
case8(Tail, Head, E, true) → Tail
case8(Tail, Head, E, false) → cons(Head, delete(E, Tail))
gen_tag(Pid) → tuple(Pid, tuplenil(tag))
gen_modtageq(Client1, Client2) → equal(Client1, Client2)
member(E, nil) → false
member(E, cons(Head, Tail)) → case9(Tail, Head, E, equal(E, Head))
case9(Tail, Head, E, true) → true
case9(Tail, Head, E, false) → member(E, Tail)
eqs(empty, empty) → T
eqs(empty, stack(E2, S2)) → F
eqs(stack(E1, S1), empty) → F
eqs(stack(E1, S1), stack(E2, S2)) → and(eqt(E1, E2), eqs(S1, S2))
pushs(E1, S1) → stack(E1, S1)
pops(stack(E1, S1)) → S1
tops(stack(E1, S1)) → E1
istops(E1, empty) → F
istops(E1, stack(E2, S1)) → eqt(E1, E2)
eqc(nocalls, nocalls) → T
eqc(nocalls, calls(E2, S2, CS2)) → F
eqc(calls(E1, S1, CS1), nocalls) → F
eqc(calls(E1, S1, CS1), calls(E2, S2, CS2)) → and(eqt(E1, E2), and(eqs(S1, S2), eqc(CS1, CS2)))
push(E1, E2, nocalls) → calls(E1, stack(E2, empty), nocalls)
push(E1, E2, calls(E3, S1, CS1)) → push1(E1, E2, E3, S1, CS1, eqt(E1, E3))
push1(E1, E2, E3, S1, CS1, T) → calls(E3, pushs(E2, S1), CS1)

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

(23) PisEmptyProof (EQUIVALENT transformation)

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

(24) TRUE

(25) Obligation:

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

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

The TRS R consists of the following rules:

or(T, T) → T
or(F, T) → T
or(T, F) → T
or(F, F) → F
and(T, B) → B
and(B, T) → B
and(F, B) → F
and(B, F) → F
imp(T, B) → B
imp(F, B) → T
not(T) → F
not(F) → T
if(T, B1, B2) → B1
if(F, B1, B2) → B2
eq(T, T) → T
eq(F, F) → T
eq(T, F) → F
eq(F, T) → F
eqt(nil, undefined) → F
eqt(nil, pid(N2)) → F
eqt(nil, int(N2)) → F
eqt(nil, cons(H2, T2)) → F
eqt(nil, tuple(H2, T2)) → F
eqt(nil, tuplenil(H2)) → F
eqt(a, nil) → F
eqt(a, a) → T
eqt(a, excl) → F
eqt(a, false) → F
eqt(a, lock) → F
eqt(a, locker) → F
eqt(a, mcrlrecord) → F
eqt(a, ok) → F
eqt(a, pending) → F
eqt(a, release) → F
eqt(a, request) → F
eqt(a, resource) → F
eqt(a, tag) → F
eqt(a, true) → F
eqt(a, undefined) → F
eqt(a, pid(N2)) → F
eqt(a, int(N2)) → F
eqt(a, cons(H2, T2)) → F
eqt(a, tuple(H2, T2)) → F
eqt(a, tuplenil(H2)) → F
eqt(excl, nil) → F
eqt(excl, a) → F
eqt(excl, excl) → T
eqt(excl, false) → F
eqt(excl, lock) → F
eqt(excl, locker) → F
eqt(excl, mcrlrecord) → F
eqt(excl, ok) → F
eqt(excl, pending) → F
eqt(excl, release) → F
eqt(excl, request) → F
eqt(excl, resource) → F
eqt(excl, tag) → F
eqt(excl, true) → F
eqt(excl, undefined) → F
eqt(excl, pid(N2)) → F
eqt(excl, eqt(false, int(N2))) → F
eqt(false, cons(H2, T2)) → F
eqt(false, tuple(H2, T2)) → F
eqt(false, tuplenil(H2)) → F
eqt(lock, nil) → F
eqt(lock, a) → F
eqt(lock, excl) → F
eqt(lock, false) → F
eqt(lock, lock) → T
eqt(lock, locker) → F
eqt(lock, mcrlrecord) → F
eqt(lock, ok) → F
eqt(lock, pending) → F
eqt(lock, release) → F
eqt(lock, request) → F
eqt(lock, resource) → F
eqt(lock, tag) → F
eqt(lock, true) → F
eqt(lock, undefined) → F
eqt(lock, pid(N2)) → F
eqt(lock, int(N2)) → F
eqt(lock, cons(H2, T2)) → F
eqt(lock, tuple(H2, T2)) → F
eqt(lock, tuplenil(H2)) → F
eqt(locker, nil) → F
eqt(locker, a) → F
eqt(locker, excl) → F
eqt(locker, false) → F
eqt(locker, lock) → F
eqt(locker, locker) → T
eqt(locker, mcrlrecord) → F
eqt(locker, ok) → F
eqt(locker, pending) → F
eqt(locker, release) → F
eqt(locker, request) → F
eqt(locker, resource) → F
eqt(locker, tag) → F
eqt(locker, true) → F
eqt(locker, undefined) → F
eqt(locker, pid(N2)) → F
eqt(locker, int(N2)) → F
eqt(locker, cons(H2, T2)) → F
eqt(locker, tuple(H2, T2)) → F
eqt(locker, tuplenil(H2)) → F
eqt(mcrlrecord, nil) → F
eqt(mcrlrecord, a) → F
eqt(mcrlrecord, excl) → F
eqt(mcrlrecord, false) → F
eqt(mcrlrecord, lock) → F
eqt(mcrlrecord, locker) → F
eqt(mcrlrecord, mcrlrecord) → T
eqt(mcrlrecord, ok) → F
eqt(mcrlrecord, pending) → F
eqt(mcrlrecord, release) → F
eqt(mcrlrecord, request) → F
eqt(mcrlrecord, resource) → F
eqt(ok, resource) → F
eqt(ok, tag) → F
eqt(ok, true) → F
eqt(ok, undefined) → F
eqt(ok, pid(N2)) → F
eqt(ok, int(N2)) → F
eqt(ok, cons(H2, T2)) → F
eqt(ok, tuple(H2, T2)) → F
eqt(ok, tuplenil(H2)) → F
eqt(pending, nil) → F
eqt(pending, a) → F
eqt(pending, excl) → F
eqt(pending, false) → F
eqt(pending, lock) → F
eqt(pending, locker) → F
eqt(pending, mcrlrecord) → F
eqt(pending, ok) → F
eqt(pending, pending) → T
eqt(pending, release) → F
eqt(pending, request) → F
eqt(pending, resource) → F
eqt(pending, tag) → F
eqt(pending, true) → F
eqt(pending, undefined) → F
eqt(pending, pid(N2)) → F
eqt(pending, int(N2)) → F
eqt(pending, cons(H2, T2)) → F
eqt(pending, tuple(H2, T2)) → F
eqt(pending, tuplenil(H2)) → F
eqt(release, nil) → F
eqt(release, a) → F
eqt(release, excl) → F
eqt(release, false) → F
eqt(release, lock) → F
eqt(release, locker) → F
eqt(release, mcrlrecord) → F
eqt(release, ok) → F
eqt(request, mcrlrecord) → F
eqt(request, ok) → F
eqt(request, pending) → F
eqt(request, release) → F
eqt(request, request) → T
eqt(request, resource) → F
eqt(request, tag) → F
eqt(request, true) → F
eqt(request, undefined) → F
eqt(request, pid(N2)) → F
eqt(request, int(N2)) → F
eqt(request, cons(H2, T2)) → F
eqt(request, tuple(H2, T2)) → F
eqt(request, tuplenil(H2)) → F
eqt(resource, nil) → F
eqt(resource, a) → F
eqt(resource, excl) → F
eqt(resource, false) → F
eqt(resource, lock) → F
eqt(resource, locker) → F
eqt(resource, mcrlrecord) → F
eqt(resource, ok) → F
eqt(resource, pending) → F
eqt(resource, release) → F
eqt(resource, request) → F
eqt(resource, resource) → T
eqt(resource, tag) → F
eqt(resource, true) → F
eqt(resource, undefined) → F
eqt(resource, pid(N2)) → F
eqt(resource, int(N2)) → F
eqt(resource, cons(H2, T2)) → F
eqt(resource, tuple(H2, T2)) → F
eqt(resource, tuplenil(H2)) → F
eqt(tag, nil) → F
eqt(tag, a) → F
eqt(tag, excl) → F
eqt(tag, false) → F
eqt(tag, lock) → F
eqt(tag, locker) → F
eqt(tag, mcrlrecord) → F
eqt(tag, ok) → F
eqt(tag, pending) → F
eqt(tag, release) → F
eqt(tag, request) → F
eqt(tag, resource) → F
eqt(tag, tag) → T
eqt(tag, true) → F
eqt(tag, undefined) → F
eqt(tag, pid(N2)) → F
eqt(tag, int(N2)) → F
eqt(tag, cons(H2, T2)) → F
eqt(tag, tuple(H2, T2)) → F
eqt(tag, tuplenil(H2)) → F
eqt(true, nil) → F
eqt(true, a) → F
eqt(true, excl) → F
eqt(true, false) → F
eqt(true, lock) → F
eqt(true, locker) → F
eqt(true, mcrlrecord) → F
eqt(true, ok) → F
eqt(true, pending) → F
eqt(true, release) → F
eqt(true, request) → F
eqt(true, resource) → F
eqt(true, tag) → F
eqt(true, true) → T
eqt(true, undefined) → F
eqt(true, pid(N2)) → F
eqt(true, int(N2)) → F
eqt(true, cons(H2, T2)) → F
eqt(true, tuple(H2, T2)) → F
eqt(true, tuplenil(H2)) → F
eqt(undefined, nil) → F
eqt(undefined, a) → F
eqt(undefined, tuplenil(H2)) → F
eqt(pid(N1), nil) → F
eqt(pid(N1), a) → F
eqt(pid(N1), excl) → F
eqt(pid(N1), false) → F
eqt(pid(N1), lock) → F
eqt(pid(N1), locker) → F
eqt(pid(N1), mcrlrecord) → F
eqt(pid(N1), ok) → F
eqt(pid(N1), pending) → F
eqt(pid(N1), release) → F
eqt(pid(N1), request) → F
eqt(pid(N1), resource) → F
eqt(pid(N1), tag) → F
eqt(pid(N1), true) → F
eqt(pid(N1), undefined) → F
eqt(pid(N1), pid(N2)) → eqt(N1, N2)
eqt(pid(N1), int(N2)) → F
eqt(pid(N1), cons(H2, T2)) → F
eqt(pid(N1), tuple(H2, T2)) → F
eqt(pid(N1), tuplenil(H2)) → F
eqt(int(N1), nil) → F
eqt(int(N1), a) → F
eqt(int(N1), excl) → F
eqt(int(N1), false) → F
eqt(int(N1), lock) → F
eqt(int(N1), locker) → F
eqt(int(N1), mcrlrecord) → F
eqt(int(N1), ok) → F
eqt(int(N1), pending) → F
eqt(int(N1), release) → F
eqt(int(N1), request) → F
eqt(int(N1), resource) → F
eqt(int(N1), tag) → F
eqt(int(N1), true) → F
eqt(int(N1), undefined) → F
eqt(cons(H1, T1), resource) → F
eqt(cons(H1, T1), tag) → F
eqt(cons(H1, T1), true) → F
eqt(cons(H1, T1), undefined) → F
eqt(cons(H1, T1), pid(N2)) → F
eqt(cons(H1, T1), int(N2)) → F
eqt(cons(H1, T1), cons(H2, T2)) → and(eqt(H1, H2), eqt(T1, T2))
eqt(cons(H1, T1), tuple(H2, T2)) → F
eqt(cons(H1, T1), tuplenil(H2)) → F
eqt(tuple(H1, T1), nil) → F
eqt(tuple(H1, T1), a) → F
eqt(tuple(H1, T1), excl) → F
eqt(tuple(H1, T1), false) → F
eqt(tuple(H1, T1), lock) → F
eqt(tuple(H1, T1), locker) → F
eqt(tuple(H1, T1), mcrlrecord) → F
eqt(tuple(H1, T1), ok) → F
eqt(tuple(H1, T1), pending) → F
eqt(tuple(H1, T1), release) → F
eqt(tuple(H1, T1), request) → F
eqt(tuple(H1, T1), resource) → F
eqt(tuple(H1, T1), tag) → F
eqt(tuple(H1, T1), true) → F
eqt(tuple(H1, T1), undefined) → F
eqt(tuple(H1, T1), pid(N2)) → F
eqt(tuple(H1, T1), int(N2)) → F
eqt(tuple(H1, T1), cons(H2, T2)) → F
eqt(tuple(H1, T1), tuple(H2, T2)) → and(eqt(H1, H2), eqt(T1, T2))
eqt(tuple(H1, T1), tuplenil(H2)) → F
eqt(tuplenil(H1), nil) → F
eqt(tuplenil(H1), a) → F
eqt(tuplenil(H1), excl) → F
eqt(tuplenil(H1), false) → F
eqt(tuplenil(H1), lock) → F
eqt(tuplenil(H1), locker) → F
eqt(tuplenil(H1), mcrlrecord) → F
eqt(tuplenil(H1), ok) → F
eqt(tuplenil(H1), pending) → F
eqt(tuplenil(H1), release) → F
eqt(tuplenil(H1), request) → F
eqt(tuplenil(H1), resource) → F
eqt(tuplenil(H1), tag) → F
eqt(tuplenil(H1), true) → F
eqt(tuplenil(H1), undefined) → F
eqt(tuplenil(H1), pid(N2)) → F
eqt(tuplenil(H1), int(N2)) → F
eqt(tuplenil(H1), cons(H2, T2)) → F
eqt(tuplenil(H1), tuple(H2, T2)) → F
eqt(tuplenil(H1), tuplenil(H2)) → eqt(H1, H2)
element(int(s(0)), tuplenil(T1)) → T1
element(int(s(0)), tuple(T1, T2)) → T1
element(int(s(s(N1))), tuple(T1, T2)) → element(int(s(N1)), T2)
record_new(lock) → tuple(mcrlrecord, tuple(lock, tuple(undefined, tuple(nil, tuplenil(nil)))))
record_extract(tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))), lock, resource) → tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2)))))
record_update(tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))), lock, pending, NewF) → tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(NewF)))))
record_updates(Record, Name, nil) → Record
record_updates(Record, Name, cons(tuple(Field, tuplenil(NewF)), Fields)) → record_updates(record_update(Record, Name, Field, NewF), Name, Fields)
locker2_map_promote_pending(nil, Pending) → nil
locker2_map_promote_pending(cons(Lock, Locks), Pending) → cons(locker2_promote_pending(Lock, Pending), locker2_map_promote_pending(Locks, Pending))
locker2_map_claim_lock(nil, Resources, Client) → nil
locker2_map_claim_lock(cons(Lock, Locks), Resources, Client) → cons(locker2_claim_lock(Lock, Resources, Client), locker2_map_claim_lock(Locks, Resources, Client))
locker2_map_add_pending(nil, Resources, Client) → nil
locker2_promote_pending(Lock, Client) → case0(Client, Lock, record_extract(Lock, lock, pending))
case0(Client, Lock, cons(Client, Pendings)) → record_updates(Lock, lock, cons(tuple(excl, tuplenil(Client)), cons(tuple(pending, tuplenil(Pendings)), nil)))
case0(Client, Lock, MCRLFree0) → Lock
locker2_remove_pending(Lock, Client) → record_updates(Lock, lock, cons(tuple(pending, tuplenil(subtract(record_extract(Lock, lock, pending), cons(Client, nil)))), nil))
locker2_add_pending(Lock, Resources, Client) → case1(Client, Resources, Lock, member(record_extract(Lock, lock, resource), Resources))
case1(Client, Resources, Lock, true) → record_updates(Lock, lock, cons(tuple(pending, tuplenil(append(record_extract(Lock, lock, pending), cons(Client, nil)))), nil))
case1(Client, Resources, Lock, false) → Lock
locker2_release_lock(Lock, Client) → case2(Client, Lock, gen_modtageq(Client, record_extract(Lock, lock, excl)))
case2(Client, Lock, true) → record_updates(Lock, lock, cons(tuple(excllock, excl), nil))
case4(Client, Lock, MCRLFree1) → false
locker2_obtainables(nil, Client) → true
locker2_obtainables(cons(Lock, Locks), Client) → case5(Client, Locks, Lock, member(Client, record_extract(Lock, lock, pending)))
case5(Client, Locks, Lock, true) → andt(locker2_obtainable(Lock, Client), locker2_obtainables(Locks, Client))
case5(Client, Locks, Lock, false) → locker2_obtainables(Locks, Client)
locker2_check_available(Resource, nil) → false
locker2_check_available(Resource, cons(Lock, Locks)) → case6(Locks, Lock, Resource, equal(Resource, record_extract(Lock, lock, resource)))
case6(Locks, Lock, Resource, true) → andt(equal(record_extract(Lock, lock, excl), nil), equal(record_extract(Lock, lock, pending), nil))
case6(Locks, Lock, Resource, false) → locker2_check_available(Resource, Locks)
locker2_check_availables(nil, Locks) → true
locker2_check_availables(cons(Resource, Resources), Locks) → andt(locker2_check_available(Resource, Locks), locker2_check_availables(Resources, Locks))
locker2_adduniq(nil, List) → List
append(cons(Head, Tail), List) → cons(Head, append(Tail, List))
subtract(List, nil) → List
subtract(List, cons(Head, Tail)) → subtract(delete(Head, List), Tail)
delete(E, nil) → nil
delete(E, cons(Head, Tail)) → case8(Tail, Head, E, equal(E, Head))
case8(Tail, Head, E, true) → Tail
case8(Tail, Head, E, false) → cons(Head, delete(E, Tail))
gen_tag(Pid) → tuple(Pid, tuplenil(tag))
gen_modtageq(Client1, Client2) → equal(Client1, Client2)
member(E, nil) → false
member(E, cons(Head, Tail)) → case9(Tail, Head, E, equal(E, Head))
case9(Tail, Head, E, true) → true
case9(Tail, Head, E, false) → member(E, Tail)
eqs(empty, empty) → T
eqs(empty, stack(E2, S2)) → F
eqs(stack(E1, S1), empty) → F
eqs(stack(E1, S1), stack(E2, S2)) → and(eqt(E1, E2), eqs(S1, S2))
pushs(E1, S1) → stack(E1, S1)
pops(stack(E1, S1)) → S1
tops(stack(E1, S1)) → E1
istops(E1, empty) → F
istops(E1, stack(E2, S1)) → eqt(E1, E2)
eqc(nocalls, nocalls) → T
eqc(nocalls, calls(E2, S2, CS2)) → F
eqc(calls(E1, S1, CS1), nocalls) → F
eqc(calls(E1, S1, CS1), calls(E2, S2, CS2)) → and(eqt(E1, E2), and(eqs(S1, S2), eqc(CS1, CS2)))
push(E1, E2, nocalls) → calls(E1, stack(E2, empty), nocalls)
push(E1, E2, calls(E3, S1, CS1)) → push1(E1, E2, E3, S1, CS1, eqt(E1, E3))
push1(E1, E2, E3, S1, CS1, T) → calls(E3, pushs(E2, S1), CS1)

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

(26) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

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

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
RECORD_UPDATES(x1, x2, x3) = RECORD_UPDATES(x2, x3)
cons(x1, x2) = cons(x1, x2)
tuple(x1, x2) = tuple(x1, x2)
tuplenil(x1) = x1
record_update(x1, x2, x3, x4) = record_update(x1, x4)
or(x1, x2) = or(x1, x2)
T = T
F = F
and(x1, x2) = and(x1, x2)
imp(x1, x2) = imp(x2)
not(x1) = not
if(x1, x2, x3) = if(x2, x3)
eq(x1, x2) = eq
eqt(x1, x2) = x1
nil = nil
undefined = undefined
pid(x1) = pid(x1)
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) = element(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, 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, x3)
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(x1, x2, x3)
locker2_remove_pending(x1, x2) = locker2_remove_pending(x1, x2)
subtract(x1, x2) = subtract(x1, x2)
locker2_add_pending(x1, x2, x3) = locker2_add_pending(x1, x2, x3)
case1(x1, x2, x3, x4) = case1(x1, 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) = 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
case6(x1, x2, x3, x4) = x4
equal(x1, x2) = equal
locker2_check_availables(x1, x2) = locker2_check_availables
locker2_adduniq(x1, x2) = x2
delete(x1, x2) = delete(x2)
case8(x1, x2, x3, x4) = case8(x1, x2, 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, 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, locker2_{obtainable₂}, equal, istops₂]
imp₁ > [T, not, eqs₁] > [F, locker2_{obtainable₂}, equal, istops₂]
if₂ > [F, locker2_{obtainable₂}, equal, istops₂]
eq > [T, not, eqs₁] > [F, locker2_{obtainable₂}, equal, istops₂]
pid₁ > [F, locker2_{obtainable₂}, equal, istops₂]
a > [T, not, eqs₁] > [F, locker2_{obtainable₂}, equal, istops₂]
locker > [T, not, eqs₁] > [F, locker2_{obtainable₂}, equal, istops₂]
ok > [F, locker2_{obtainable₂}, equal, istops₂]
release > [F, locker2_{obtainable₂}, equal, istops₂]
request > [T, not, eqs₁] > [F, locker2_{obtainable₂}, equal, istops₂]
element₁ > int > [F, locker2_{obtainable₂}, equal, istops₂]
0 > [F, locker2_{obtainable₂}, equal, istops₂]
record_new > [record_update₂, lock] > [tuple₂, and₂] > RECORD_UPDATES₂ > [F, locker2_{obtainable₂}, equal, istops₂]
record_new > [record_update₂, lock] > [tuple₂, and₂] > mcrlrecord > [T, not, eqs₁] > [F, locker2_{obtainable₂}, equal, istops₂]
record_new > [record_update₂, lock] > [nil, locker2_{map_{add_pending}}] > [false, locker2_{check_available}] > locker2_{obtainables₁} > [F, locker2_{obtainable₂}, equal, istops₂]
record_new > [record_update₂, lock] > [nil, locker2_{map_{add_pending}}] > true > excl > [T, not, eqs₁] > [F, locker2_{obtainable₂}, equal, istops₂]
record_new > [record_update₂, lock] > [nil, locker2_{map_{add_pending}}] > true > excllock > [F, locker2_{obtainable₂}, equal, istops₂]
record_new > [record_update₂, lock] > [nil, locker2_{map_{add_pending}}] > true > locker2_{obtainables₁} > [F, locker2_{obtainable₂}, equal, istops₂]
record_new > [record_update₂, lock] > undefined > [F, locker2_{obtainable₂}, equal, istops₂]
locker2_{map_{promote_pending₂}} > locker2_{promote_pending₂} > case0₃ > [cons₂, locker2_{check_availables}] > [tuple₂, and₂] > RECORD_UPDATES₂ > [F, locker2_{obtainable₂}, equal, istops₂]
locker2_{map_{promote_pending₂}} > locker2_{promote_pending₂} > case0₃ > [cons₂, locker2_{check_availables}] > [tuple₂, and₂] > mcrlrecord > [T, not, eqs₁] > [F, locker2_{obtainable₂}, equal, istops₂]
locker2_{map_{promote_pending₂}} > locker2_{promote_pending₂} > case0₃ > [cons₂, locker2_{check_availables}] > [nil, locker2_{map_{add_pending}}] > [false, locker2_{check_available}] > locker2_{obtainables₁} > [F, locker2_{obtainable₂}, equal, istops₂]
locker2_{map_{promote_pending₂}} > locker2_{promote_pending₂} > case0₃ > [cons₂, locker2_{check_availables}] > [nil, locker2_{map_{add_pending}}] > true > excl > [T, not, eqs₁] > [F, locker2_{obtainable₂}, equal, istops₂]
locker2_{map_{promote_pending₂}} > locker2_{promote_pending₂} > case0₃ > [cons₂, locker2_{check_availables}] > [nil, locker2_{map_{add_pending}}] > true > excllock > [F, locker2_{obtainable₂}, equal, istops₂]
locker2_{map_{promote_pending₂}} > locker2_{promote_pending₂} > case0₃ > [cons₂, locker2_{check_availables}] > [nil, locker2_{map_{add_pending}}] > true > locker2_{obtainables₁} > [F, locker2_{obtainable₂}, equal, istops₂]
locker2_{map_{promote_pending₂}} > locker2_{promote_pending₂} > case0₃ > [cons₂, locker2_{check_availables}] > case5₁ > locker2_{obtainables₁} > [F, locker2_{obtainable₂}, equal, istops₂]
locker2_{map_{promote_pending₂}} > locker2_{promote_pending₂} > case0₃ > pending > [record_update₂, lock] > [tuple₂, and₂] > RECORD_UPDATES₂ > [F, locker2_{obtainable₂}, equal, istops₂]
locker2_{map_{promote_pending₂}} > locker2_{promote_pending₂} > case0₃ > pending > [record_update₂, lock] > [tuple₂, and₂] > mcrlrecord > [T, not, eqs₁] > [F, locker2_{obtainable₂}, equal, istops₂]
locker2_{map_{promote_pending₂}} > locker2_{promote_pending₂} > case0₃ > pending > [record_update₂, lock] > [nil, locker2_{map_{add_pending}}] > [false, locker2_{check_available}] > locker2_{obtainables₁} > [F, locker2_{obtainable₂}, equal, istops₂]
locker2_{map_{promote_pending₂}} > locker2_{promote_pending₂} > case0₃ > pending > [record_update₂, lock] > [nil, locker2_{map_{add_pending}}] > true > excl > [T, not, eqs₁] > [F, locker2_{obtainable₂}, equal, istops₂]
locker2_{map_{promote_pending₂}} > locker2_{promote_pending₂} > case0₃ > pending > [record_update₂, lock] > [nil, locker2_{map_{add_pending}}] > true > excllock > [F, locker2_{obtainable₂}, equal, istops₂]
locker2_{map_{promote_pending₂}} > locker2_{promote_pending₂} > case0₃ > pending > [record_update₂, lock] > [nil, locker2_{map_{add_pending}}] > true > locker2_{obtainables₁} > [F, locker2_{obtainable₂}, equal, istops₂]
locker2_{map_{promote_pending₂}} > locker2_{promote_pending₂} > case0₃ > pending > [record_update₂, lock] > undefined > [F, locker2_{obtainable₂}, equal, istops₂]
locker2_{map_{promote_pending₂}} > locker2_{promote_pending₂} > case0₃ > record_updates₃ > [record_update₂, lock] > [tuple₂, and₂] > RECORD_UPDATES₂ > [F, locker2_{obtainable₂}, equal, istops₂]
locker2_{map_{promote_pending₂}} > locker2_{promote_pending₂} > case0₃ > record_updates₃ > [record_update₂, lock] > [tuple₂, and₂] > mcrlrecord > [T, not, eqs₁] > [F, locker2_{obtainable₂}, equal, istops₂]
locker2_{map_{promote_pending₂}} > locker2_{promote_pending₂} > case0₃ > record_updates₃ > [record_update₂, lock] > [nil, locker2_{map_{add_pending}}] > [false, locker2_{check_available}] > locker2_{obtainables₁} > [F, locker2_{obtainable₂}, equal, istops₂]
locker2_{map_{promote_pending₂}} > locker2_{promote_pending₂} > case0₃ > record_updates₃ > [record_update₂, lock] > [nil, locker2_{map_{add_pending}}] > true > excl > [T, not, eqs₁] > [F, locker2_{obtainable₂}, equal, istops₂]
locker2_{map_{promote_pending₂}} > locker2_{promote_pending₂} > case0₃ > record_updates₃ > [record_update₂, lock] > [nil, locker2_{map_{add_pending}}] > true > excllock > [F, locker2_{obtainable₂}, equal, istops₂]
locker2_{map_{promote_pending₂}} > locker2_{promote_pending₂} > case0₃ > record_updates₃ > [record_update₂, lock] > [nil, locker2_{map_{add_pending}}] > true > locker2_{obtainables₁} > [F, locker2_{obtainable₂}, equal, istops₂]
locker2_{map_{promote_pending₂}} > locker2_{promote_pending₂} > case0₃ > record_updates₃ > [record_update₂, lock] > undefined > [F, locker2_{obtainable₂}, equal, istops₂]
locker2_{map_{claim_lock₂}} > [cons₂, locker2_{check_availables}] > [tuple₂, and₂] > RECORD_UPDATES₂ > [F, locker2_{obtainable₂}, equal, istops₂]
locker2_{map_{claim_lock₂}} > [cons₂, locker2_{check_availables}] > [tuple₂, and₂] > mcrlrecord > [T, not, eqs₁] > [F, locker2_{obtainable₂}, equal, istops₂]
locker2_{map_{claim_lock₂}} > [cons₂, locker2_{check_availables}] > [nil, locker2_{map_{add_pending}}] > [false, locker2_{check_available}] > locker2_{obtainables₁} > [F, locker2_{obtainable₂}, equal, istops₂]
locker2_{map_{claim_lock₂}} > [cons₂, locker2_{check_availables}] > [nil, locker2_{map_{add_pending}}] > true > excl > [T, not, eqs₁] > [F, locker2_{obtainable₂}, equal, istops₂]
locker2_{map_{claim_lock₂}} > [cons₂, locker2_{check_availables}] > [nil, locker2_{map_{add_pending}}] > true > excllock > [F, locker2_{obtainable₂}, equal, istops₂]
locker2_{map_{claim_lock₂}} > [cons₂, locker2_{check_availables}] > [nil, locker2_{map_{add_pending}}] > true > locker2_{obtainables₁} > [F, locker2_{obtainable₂}, equal, istops₂]
locker2_{map_{claim_lock₂}} > [cons₂, locker2_{check_availables}] > case5₁ > locker2_{obtainables₁} > [F, locker2_{obtainable₂}, equal, istops₂]
locker2_{map_{claim_lock₂}} > locker2_{claim_lock} > [F, locker2_{obtainable₂}, equal, istops₂]
locker2_{remove_pending₂} > pending > [record_update₂, lock] > [tuple₂, and₂] > RECORD_UPDATES₂ > [F, locker2_{obtainable₂}, equal, istops₂]
locker2_{remove_pending₂} > pending > [record_update₂, lock] > [tuple₂, and₂] > mcrlrecord > [T, not, eqs₁] > [F, locker2_{obtainable₂}, equal, istops₂]
locker2_{remove_pending₂} > pending > [record_update₂, lock] > [nil, locker2_{map_{add_pending}}] > [false, locker2_{check_available}] > locker2_{obtainables₁} > [F, locker2_{obtainable₂}, equal, istops₂]
locker2_{remove_pending₂} > pending > [record_update₂, lock] > [nil, locker2_{map_{add_pending}}] > true > excl > [T, not, eqs₁] > [F, locker2_{obtainable₂}, equal, istops₂]
locker2_{remove_pending₂} > pending > [record_update₂, lock] > [nil, locker2_{map_{add_pending}}] > true > excllock > [F, locker2_{obtainable₂}, equal, istops₂]
locker2_{remove_pending₂} > pending > [record_update₂, lock] > [nil, locker2_{map_{add_pending}}] > true > locker2_{obtainables₁} > [F, locker2_{obtainable₂}, equal, istops₂]
locker2_{remove_pending₂} > pending > [record_update₂, lock] > undefined > [F, locker2_{obtainable₂}, equal, istops₂]
locker2_{remove_pending₂} > record_updates₃ > [record_update₂, lock] > [tuple₂, and₂] > RECORD_UPDATES₂ > [F, locker2_{obtainable₂}, equal, istops₂]
locker2_{remove_pending₂} > record_updates₃ > [record_update₂, lock] > [tuple₂, and₂] > mcrlrecord > [T, not, eqs₁] > [F, locker2_{obtainable₂}, equal, istops₂]
locker2_{remove_pending₂} > record_updates₃ > [record_update₂, lock] > [nil, locker2_{map_{add_pending}}] > [false, locker2_{check_available}] > locker2_{obtainables₁} > [F, locker2_{obtainable₂}, equal, istops₂]
locker2_{remove_pending₂} > record_updates₃ > [record_update₂, lock] > [nil, locker2_{map_{add_pending}}] > true > excl > [T, not, eqs₁] > [F, locker2_{obtainable₂}, equal, istops₂]
locker2_{remove_pending₂} > record_updates₃ > [record_update₂, lock] > [nil, locker2_{map_{add_pending}}] > true > excllock > [F, locker2_{obtainable₂}, equal, istops₂]
locker2_{remove_pending₂} > record_updates₃ > [record_update₂, lock] > [nil, locker2_{map_{add_pending}}] > true > locker2_{obtainables₁} > [F, locker2_{obtainable₂}, equal, istops₂]
locker2_{remove_pending₂} > record_updates₃ > [record_update₂, lock] > undefined > [F, locker2_{obtainable₂}, equal, istops₂]
locker2_{remove_pending₂} > subtract₂ > [delete₁, case8₃] > [cons₂, locker2_{check_availables}] > [tuple₂, and₂] > RECORD_UPDATES₂ > [F, locker2_{obtainable₂}, equal, istops₂]
locker2_{remove_pending₂} > subtract₂ > [delete₁, case8₃] > [cons₂, locker2_{check_availables}] > [tuple₂, and₂] > mcrlrecord > [T, not, eqs₁] > [F, locker2_{obtainable₂}, equal, istops₂]
locker2_{remove_pending₂} > subtract₂ > [delete₁, case8₃] > [cons₂, locker2_{check_availables}] > [nil, locker2_{map_{add_pending}}] > [false, locker2_{check_available}] > locker2_{obtainables₁} > [F, locker2_{obtainable₂}, equal, istops₂]
locker2_{remove_pending₂} > subtract₂ > [delete₁, case8₃] > [cons₂, locker2_{check_availables}] > [nil, locker2_{map_{add_pending}}] > true > excl > [T, not, eqs₁] > [F, locker2_{obtainable₂}, equal, istops₂]
locker2_{remove_pending₂} > subtract₂ > [delete₁, case8₃] > [cons₂, locker2_{check_availables}] > [nil, locker2_{map_{add_pending}}] > true > excllock > [F, locker2_{obtainable₂}, equal, istops₂]
locker2_{remove_pending₂} > subtract₂ > [delete₁, case8₃] > [cons₂, locker2_{check_availables}] > [nil, locker2_{map_{add_pending}}] > true > locker2_{obtainables₁} > [F, locker2_{obtainable₂}, equal, istops₂]
locker2_{remove_pending₂} > subtract₂ > [delete₁, case8₃] > [cons₂, locker2_{check_availables}] > case5₁ > locker2_{obtainables₁} > [F, locker2_{obtainable₂}, equal, istops₂]
[locker2_{add_pending₃}, case1₂] > [cons₂, locker2_{check_availables}] > [tuple₂, and₂] > RECORD_UPDATES₂ > [F, locker2_{obtainable₂}, equal, istops₂]
[locker2_{add_pending₃}, case1₂] > [cons₂, locker2_{check_availables}] > [tuple₂, and₂] > mcrlrecord > [T, not, eqs₁] > [F, locker2_{obtainable₂}, equal, istops₂]
[locker2_{add_pending₃}, case1₂] > [cons₂, locker2_{check_availables}] > [nil, locker2_{map_{add_pending}}] > [false, locker2_{check_available}] > locker2_{obtainables₁} > [F, locker2_{obtainable₂}, equal, istops₂]
[locker2_{add_pending₃}, case1₂] > [cons₂, locker2_{check_availables}] > [nil, locker2_{map_{add_pending}}] > true > excl > [T, not, eqs₁] > [F, locker2_{obtainable₂}, equal, istops₂]
[locker2_{add_pending₃}, case1₂] > [cons₂, locker2_{check_availables}] > [nil, locker2_{map_{add_pending}}] > true > excllock > [F, locker2_{obtainable₂}, equal, istops₂]
[locker2_{add_pending₃}, case1₂] > [cons₂, locker2_{check_availables}] > [nil, locker2_{map_{add_pending}}] > true > locker2_{obtainables₁} > [F, locker2_{obtainable₂}, equal, istops₂]
[locker2_{add_pending₃}, case1₂] > [cons₂, locker2_{check_availables}] > case5₁ > locker2_{obtainables₁} > [F, locker2_{obtainable₂}, equal, istops₂]
[locker2_{add_pending₃}, case1₂] > pending > [record_update₂, lock] > [tuple₂, and₂] > RECORD_UPDATES₂ > [F, locker2_{obtainable₂}, equal, istops₂]
[locker2_{add_pending₃}, case1₂] > pending > [record_update₂, lock] > [tuple₂, and₂] > mcrlrecord > [T, not, eqs₁] > [F, locker2_{obtainable₂}, equal, istops₂]
[locker2_{add_pending₃}, case1₂] > pending > [record_update₂, lock] > [nil, locker2_{map_{add_pending}}] > [false, locker2_{check_available}] > locker2_{obtainables₁} > [F, locker2_{obtainable₂}, equal, istops₂]
[locker2_{add_pending₃}, case1₂] > pending > [record_update₂, lock] > [nil, locker2_{map_{add_pending}}] > true > excl > [T, not, eqs₁] > [F, locker2_{obtainable₂}, equal, istops₂]
[locker2_{add_pending₃}, case1₂] > pending > [record_update₂, lock] > [nil, locker2_{map_{add_pending}}] > true > excllock > [F, locker2_{obtainable₂}, equal, istops₂]
[locker2_{add_pending₃}, case1₂] > pending > [record_update₂, lock] > [nil, locker2_{map_{add_pending}}] > true > locker2_{obtainables₁} > [F, locker2_{obtainable₂}, equal, istops₂]
[locker2_{add_pending₃}, case1₂] > pending > [record_update₂, lock] > undefined > [F, locker2_{obtainable₂}, equal, istops₂]
[locker2_{add_pending₃}, case1₂] > resource > [tuple₂, and₂] > RECORD_UPDATES₂ > [F, locker2_{obtainable₂}, equal, istops₂]
[locker2_{add_pending₃}, case1₂] > resource > [tuple₂, and₂] > mcrlrecord > [T, not, eqs₁] > [F, locker2_{obtainable₂}, equal, istops₂]
[locker2_{add_pending₃}, case1₂] > record_updates₃ > [record_update₂, lock] > [tuple₂, and₂] > RECORD_UPDATES₂ > [F, locker2_{obtainable₂}, equal, istops₂]
[locker2_{add_pending₃}, case1₂] > record_updates₃ > [record_update₂, lock] > [tuple₂, and₂] > mcrlrecord > [T, not, eqs₁] > [F, locker2_{obtainable₂}, equal, istops₂]
[locker2_{add_pending₃}, case1₂] > record_updates₃ > [record_update₂, lock] > [nil, locker2_{map_{add_pending}}] > [false, locker2_{check_available}] > locker2_{obtainables₁} > [F, locker2_{obtainable₂}, equal, istops₂]
[locker2_{add_pending₃}, case1₂] > record_updates₃ > [record_update₂, lock] > [nil, locker2_{map_{add_pending}}] > true > excl > [T, not, eqs₁] > [F, locker2_{obtainable₂}, equal, istops₂]
[locker2_{add_pending₃}, case1₂] > record_updates₃ > [record_update₂, lock] > [nil, locker2_{map_{add_pending}}] > true > excllock > [F, locker2_{obtainable₂}, equal, istops₂]
[locker2_{add_pending₃}, case1₂] > record_updates₃ > [record_update₂, lock] > [nil, locker2_{map_{add_pending}}] > true > locker2_{obtainables₁} > [F, locker2_{obtainable₂}, equal, istops₂]
[locker2_{add_pending₃}, case1₂] > record_updates₃ > [record_update₂, lock] > undefined > [F, locker2_{obtainable₂}, equal, istops₂]
[locker2_{add_pending₃}, case1₂] > [member, case9] > [false, locker2_{check_available}] > locker2_{obtainables₁} > [F, locker2_{obtainable₂}, equal, istops₂]
[locker2_{add_pending₃}, case1₂] > [member, case9] > true > excl > [T, not, eqs₁] > [F, locker2_{obtainable₂}, equal, istops₂]
[locker2_{add_pending₃}, case1₂] > [member, case9] > true > excllock > [F, locker2_{obtainable₂}, equal, istops₂]
[locker2_{add_pending₃}, case1₂] > [member, case9] > true > locker2_{obtainables₁} > [F, locker2_{obtainable₂}, equal, istops₂]
locker2_{release_lock₂} > case2₁ > [cons₂, locker2_{check_availables}] > [tuple₂, and₂] > RECORD_UPDATES₂ > [F, locker2_{obtainable₂}, equal, istops₂]
locker2_{release_lock₂} > case2₁ > [cons₂, locker2_{check_availables}] > [tuple₂, and₂] > mcrlrecord > [T, not, eqs₁] > [F, locker2_{obtainable₂}, equal, istops₂]
locker2_{release_lock₂} > case2₁ > [cons₂, locker2_{check_availables}] > [nil, locker2_{map_{add_pending}}] > [false, locker2_{check_available}] > locker2_{obtainables₁} > [F, locker2_{obtainable₂}, equal, istops₂]
locker2_{release_lock₂} > case2₁ > [cons₂, locker2_{check_availables}] > [nil, locker2_{map_{add_pending}}] > true > excl > [T, not, eqs₁] > [F, locker2_{obtainable₂}, equal, istops₂]
locker2_{release_lock₂} > case2₁ > [cons₂, locker2_{check_availables}] > [nil, locker2_{map_{add_pending}}] > true > excllock > [F, locker2_{obtainable₂}, equal, istops₂]
locker2_{release_lock₂} > case2₁ > [cons₂, locker2_{check_availables}] > [nil, locker2_{map_{add_pending}}] > true > locker2_{obtainables₁} > [F, locker2_{obtainable₂}, equal, istops₂]
locker2_{release_lock₂} > case2₁ > [cons₂, locker2_{check_availables}] > case5₁ > locker2_{obtainables₁} > [F, locker2_{obtainable₂}, equal, istops₂]
locker2_{release_lock₂} > case2₁ > record_updates₃ > [record_update₂, lock] > [tuple₂, and₂] > RECORD_UPDATES₂ > [F, locker2_{obtainable₂}, equal, istops₂]
locker2_{release_lock₂} > case2₁ > record_updates₃ > [record_update₂, lock] > [tuple₂, and₂] > mcrlrecord > [T, not, eqs₁] > [F, locker2_{obtainable₂}, equal, istops₂]
locker2_{release_lock₂} > case2₁ > record_updates₃ > [record_update₂, lock] > [nil, locker2_{map_{add_pending}}] > [false, locker2_{check_available}] > locker2_{obtainables₁} > [F, locker2_{obtainable₂}, equal, istops₂]
locker2_{release_lock₂} > case2₁ > record_updates₃ > [record_update₂, lock] > [nil, locker2_{map_{add_pending}}] > true > excl > [T, not, eqs₁] > [F, locker2_{obtainable₂}, equal, istops₂]
locker2_{release_lock₂} > case2₁ > record_updates₃ > [record_update₂, lock] > [nil, locker2_{map_{add_pending}}] > true > excllock > [F, locker2_{obtainable₂}, equal, istops₂]
locker2_{release_lock₂} > case2₁ > record_updates₃ > [record_update₂, lock] > [nil, locker2_{map_{add_pending}}] > true > locker2_{obtainables₁} > [F, locker2_{obtainable₂}, equal, istops₂]
locker2_{release_lock₂} > case2₁ > record_updates₃ > [record_update₂, lock] > undefined > [F, locker2_{obtainable₂}, equal, istops₂]
case4 > [false, locker2_{check_available}] > locker2_{obtainables₁} > [F, locker2_{obtainable₂}, equal, istops₂]
gen_tag₁ > [tuple₂, and₂] > RECORD_UPDATES₂ > [F, locker2_{obtainable₂}, equal, istops₂]
gen_tag₁ > [tuple₂, and₂] > mcrlrecord > [T, not, eqs₁] > [F, locker2_{obtainable₂}, equal, istops₂]
gen_tag₁ > tag > [T, not, eqs₁] > [F, locker2_{obtainable₂}, equal, istops₂]
pops₁ > [F, locker2_{obtainable₂}, equal, istops₂]
tops₁ > [F, locker2_{obtainable₂}, equal, istops₂]
eqc₂ > [tuple₂, and₂] > RECORD_UPDATES₂ > [F, locker2_{obtainable₂}, equal, istops₂]
eqc₂ > [tuple₂, and₂] > mcrlrecord > [T, not, eqs₁] > [F, locker2_{obtainable₂}, equal, istops₂]
push₃ > nocalls > [T, not, eqs₁] > [F, locker2_{obtainable₂}, equal, istops₂]
push₃ > nocalls > empty > [F, locker2_{obtainable₂}, equal, istops₂]
push₃ > push1₄ > [stack₂, pushs₂] > [tuple₂, and₂] > RECORD_UPDATES₂ > [F, locker2_{obtainable₂}, equal, istops₂]
push₃ > push1₄ > [stack₂, pushs₂] > [tuple₂, and₂] > mcrlrecord > [T, not, eqs₁] > [F, locker2_{obtainable₂}, equal, istops₂]
push₃ > push1₄ > calls₃ > [T, not, eqs₁] > [F, locker2_{obtainable₂}, equal, istops₂]

Status:

RECORD_UPDATES₂: [2,1]
cons₂: [2,1]
tuple₂: [1,2]
record_update₂: [2,1]
or₂: [2,1]
T: []
F: []
and₂: [1,2]
imp₁: [1]
not: []
if₂: [1,2]
eq: []
nil: []
undefined: []
pid₁: [1]
int: []
a: []
excl: []
false: []
lock: []
locker: []
mcrlrecord: []
ok: []
pending: []
release: []
request: []
resource: []
tag: []
true: []
element₁: [1]
0: []
record_new: []
record_updates₃: [2,3,1]
locker2_{map_{promote_pending₂}}: [1,2]
locker2_{promote_pending₂}: [2,1]
locker2_{map_{claim_lock₂}}: [2,1]
locker2_{claim_lock}: []
locker2_{map_{add_pending}}: []
case0₃: [1,3,2]
locker2_{remove_pending₂}: [2,1]
subtract₂: [2,1]
locker2_{add_pending₃}: [1,3,2]
case1₂: [2,1]
member: []
locker2_{release_lock₂}: [2,1]
case2₁: [1]
excllock: []
case4: []
locker2_{obtainables₁}: [1]
case5₁: [1]
locker2_{obtainable₂}: [2,1]
locker2_{check_available}: []
equal: []
locker2_{check_availables}: []
delete₁: [1]
case8₃: [1,2,3]
gen_tag₁: [1]
case9: []
eqs₁: [1]
empty: []
stack₂: [2,1]
pushs₂: [2,1]
pops₁: [1]
tops₁: [1]
istops₂: [2,1]
eqc₂: [1,2]
nocalls: []
calls₃: [3,2,1]
push₃: [2,3,1]
push1₄: [3,2,1,4]

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) = x1
cons(x1, x2) = cons(x1, x2)
or(x1, x2) = or
T = T
F = F
and(x1, x2) = and(x1, x2)
imp(x1, x2) = imp(x2)
not(x1) = not
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
tuple(x1, x2) = tuple(x1, x2)
tuplenil(x1) = x1
a = a
excl = excl
false = false
lock = lock
locker = locker
mcrlrecord = mcrlrecord
ok = ok
pending = pending
release = release
request = request
resource = resource
tag = tag
true = true
element(x1, x2) = element(x2)
s(x1) = s(x1)
0 = 0
record_new(x1) = record_new(x1)
record_extract(x1, x2, x3) = x1
record_update(x1, x2, x3, x4) = record_update(x1, x2, x3, x4)
record_updates(x1, x2, x3) = record_updates(x1, x2, x3)
locker2_map_promote_pending(x1, x2) = locker2_map_promote_pending(x1, x2)
locker2_promote_pending(x1, x2) = locker2_promote_pending(x1, x2)
locker2_map_claim_lock(x1, x2, x3) = locker2_map_claim_lock(x1, x2, x3)
locker2_claim_lock(x1, x2, x3) = x3
locker2_map_add_pending(x1, x2, x3) = locker2_map_add_pending
case0(x1, x2, x3) = case0(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, x2, x3)
case1(x1, x2, x3, x4) = case1(x1, x3, x4)
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(x2)
excllock = excllock
case4(x1, x2, x3) = case4(x3)
locker2_obtainables(x1, x2) = locker2_obtainables(x1)
case5(x1, x2, x3, x4) = case5(x2, x3)
andt(x1, x2) = andt(x1, x2)
locker2_obtainable(x1, x2) = locker2_obtainable
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(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) = 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
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, eq, empty, nocalls] > calls₃ > and₂ > [nil, false, lock, member, excllock, locker2_obtainable, locker2_{check_available}, equal]
imp₁ > [T, F, eq, empty, nocalls] > calls₃ > and₂ > [nil, false, lock, member, excllock, locker2_obtainable, locker2_{check_available}, equal]
not > [T, F, eq, empty, nocalls] > calls₃ > and₂ > [nil, false, lock, member, excllock, locker2_obtainable, locker2_{check_available}, equal]
if₃ > [nil, false, lock, member, excllock, locker2_obtainable, locker2_{check_available}, equal]
a > [T, F, eq, empty, nocalls] > calls₃ > and₂ > [nil, false, lock, member, excllock, locker2_obtainable, locker2_{check_available}, equal]
locker > [T, F, eq, empty, nocalls] > calls₃ > and₂ > [nil, false, lock, member, excllock, locker2_obtainable, locker2_{check_available}, equal]
[mcrlrecord, record_new₁] > [T, F, eq, empty, nocalls] > calls₃ > and₂ > [nil, false, lock, member, excllock, locker2_obtainable, locker2_{check_available}, equal]
[mcrlrecord, record_new₁] > undefined > [nil, false, lock, member, excllock, locker2_obtainable, locker2_{check_available}, equal]
[mcrlrecord, record_new₁] > [tuple₂, element₁] > [nil, false, lock, member, excllock, locker2_obtainable, locker2_{check_available}, equal]
ok > [T, F, eq, empty, nocalls] > calls₃ > and₂ > [nil, false, lock, member, excllock, locker2_obtainable, locker2_{check_available}, equal]
release > [T, F, eq, empty, nocalls] > calls₃ > and₂ > [nil, false, lock, member, excllock, locker2_obtainable, locker2_{check_available}, equal]
request > [T, F, eq, empty, nocalls] > calls₃ > and₂ > [nil, false, lock, member, excllock, locker2_obtainable, locker2_{check_available}, equal]
s₁ > int > [tuple₂, element₁] > [nil, false, lock, member, excllock, locker2_obtainable, locker2_{check_available}, equal]
0 > [nil, false, lock, member, excllock, locker2_obtainable, locker2_{check_available}, equal]
locker2_{map_{promote_pending₂}} > locker2_{promote_pending₂} > case0₃ > [cons₂, pending, case8₂] > [tuple₂, element₁] > [nil, false, lock, member, excllock, locker2_obtainable, locker2_{check_available}, equal]
locker2_{map_{promote_pending₂}} > locker2_{promote_pending₂} > case0₃ > excl > [nil, false, lock, member, excllock, locker2_obtainable, locker2_{check_available}, equal]
locker2_{map_{promote_pending₂}} > locker2_{promote_pending₂} > case0₃ > [record_update₄, record_updates₃] > [tuple₂, element₁] > [nil, false, lock, member, excllock, locker2_obtainable, locker2_{check_available}, equal]
locker2_{map_{claim_lock₃}} > [cons₂, pending, case8₂] > [tuple₂, element₁] > [nil, false, lock, member, excllock, locker2_obtainable, locker2_{check_available}, equal]
locker2_{map_{add_pending}} > [nil, false, lock, member, excllock, locker2_obtainable, locker2_{check_available}, equal]
locker2_{remove_pending₂} > [cons₂, pending, case8₂] > [tuple₂, element₁] > [nil, false, lock, member, excllock, locker2_obtainable, locker2_{check_available}, equal]
locker2_{remove_pending₂} > [record_update₄, record_updates₃] > [tuple₂, element₁] > [nil, false, lock, member, excllock, locker2_obtainable, locker2_{check_available}, equal]
[locker2_{add_pending₃}, case1₃] > resource > [tuple₂, element₁] > [nil, false, lock, member, excllock, locker2_obtainable, locker2_{check_available}, equal]
[locker2_{add_pending₃}, case1₃] > [record_update₄, record_updates₃] > [tuple₂, element₁] > [nil, false, lock, member, excllock, locker2_obtainable, locker2_{check_available}, equal]
[locker2_{add_pending₃}, case1₃] > append₂ > [cons₂, pending, case8₂] > [tuple₂, element₁] > [nil, false, lock, member, excllock, locker2_obtainable, locker2_{check_available}, equal]
locker2_{release_lock₂} > case2₃ > [cons₂, pending, case8₂] > [tuple₂, element₁] > [nil, false, lock, member, excllock, locker2_obtainable, locker2_{check_available}, equal]
locker2_{release_lock₂} > case2₃ > excl > [nil, false, lock, member, excllock, locker2_obtainable, locker2_{check_available}, equal]
locker2_{release_lock₂} > case2₃ > [record_update₄, record_updates₃] > [tuple₂, element₁] > [nil, false, lock, member, excllock, locker2_obtainable, locker2_{check_available}, equal]
locker2_{release_lock₂} > gen_modtageq₁ > [nil, false, lock, member, excllock, locker2_obtainable, locker2_{check_available}, equal]
case4₁ > [nil, false, lock, member, excllock, locker2_obtainable, locker2_{check_available}, equal]
locker2_{check_{availables₂}} > [true, locker2_{obtainables₁}, case5₂] > [cons₂, pending, case8₂] > [tuple₂, element₁] > [nil, false, lock, member, excllock, locker2_obtainable, locker2_{check_available}, equal]
locker2_{check_{availables₂}} > [true, locker2_{obtainables₁}, case5₂] > [T, F, eq, empty, nocalls] > calls₃ > and₂ > [nil, false, lock, member, excllock, locker2_obtainable, locker2_{check_available}, equal]
locker2_{check_{availables₂}} > [true, locker2_{obtainables₁}, case5₂] > excl > [nil, false, lock, member, excllock, locker2_obtainable, locker2_{check_available}, equal]
locker2_{check_{availables₂}} > [true, locker2_{obtainables₁}, case5₂] > [record_update₄, record_updates₃] > [tuple₂, element₁] > [nil, false, lock, member, excllock, locker2_obtainable, locker2_{check_available}, equal]
locker2_{check_{availables₂}} > [true, locker2_{obtainables₁}, case5₂] > andt₂ > [nil, false, lock, member, excllock, locker2_obtainable, locker2_{check_available}, equal]
gen_tag₁ > [tuple₂, element₁] > [nil, false, lock, member, excllock, locker2_obtainable, locker2_{check_available}, equal]
gen_tag₁ > tag > [T, F, eq, empty, nocalls] > calls₃ > and₂ > [nil, false, lock, member, excllock, locker2_obtainable, locker2_{check_available}, equal]
tops₁ > [nil, false, lock, member, excllock, locker2_obtainable, locker2_{check_available}, equal]
istops₂ > [eqt₂, eqs₂, eqc₂] > [T, F, eq, empty, nocalls] > calls₃ > and₂ > [nil, false, lock, member, excllock, locker2_obtainable, locker2_{check_available}, equal]
push₃ > push1₄ > [stack₂, pushs₂] > [eqt₂, eqs₂, eqc₂] > [T, F, eq, empty, nocalls] > calls₃ > and₂ > [nil, false, lock, member, excllock, locker2_obtainable, locker2_{check_available}, equal]

Status:

cons₂: [2,1]
or: []
T: []
F: []
and₂: [2,1]
imp₁: [1]
not: []
if₃: [1,2,3]
eq: []
eqt₂: [2,1]
nil: []
undefined: []
int: []
tuple₂: [2,1]
a: []
excl: []
false: []
lock: []
locker: []
mcrlrecord: []
ok: []
pending: []
release: []
request: []
resource: []
tag: []
true: []
element₁: [1]
s₁: [1]
0: []
record_new₁: [1]
record_update₄: [3,2,1,4]
record_updates₃: [3,2,1]
locker2_{map_{promote_pending₂}}: [1,2]
locker2_{promote_pending₂}: [2,1]
locker2_{map_{claim_lock₃}}: [3,2,1]
locker2_{map_{add_pending}}: []
case0₃: [1,3,2]
locker2_{remove_pending₂}: [2,1]
locker2_{add_pending₃}: [3,1,2]
case1₃: [1,2,3]
member: []
append₂: [1,2]
locker2_{release_lock₂}: [2,1]
case2₃: [3,1,2]
gen_modtageq₁: [1]
excllock: []
case4₁: [1]
locker2_{obtainables₁}: [1]
case5₂: [1,2]
andt₂: [1,2]
locker2_obtainable: []
locker2_{check_available}: []
equal: []
locker2_{check_{availables₂}}: [1,2]
case8₂: [1,2]
gen_tag₁: [1]
eqs₂: [2,1]
empty: []
stack₂: [1,2]
pushs₂: [1,2]
tops₁: [1]
istops₂: [2,1]
eqc₂: [2,1]
nocalls: []
calls₃: [3,2,1]
push₃: [3,2,1]
push1₄: [4,2,3,1]

The following usable rules [FROCOS05] were oriented:

or(T, T) → T
or(F, T) → T
or(T, F) → T
or(F, F) → F
and(T, B) → B
and(B, T) → B
and(F, B) → F
and(B, F) → F
imp(T, B) → B
imp(F, B) → T
not(T) → F
not(F) → T
if(T, B1, B2) → B1
if(F, B1, B2) → B2
eq(T, T) → T
eq(F, F) → T
eq(T, F) → F
eq(F, T) → F
eqt(nil, undefined) → F
eqt(nil, pid(N2)) → F
eqt(nil, int(N2)) → F
eqt(nil, cons(H2, T2)) → F
eqt(nil, tuple(H2, T2)) → F
eqt(nil, tuplenil(H2)) → F
eqt(a, nil) → F
eqt(a, a) → T
eqt(a, excl) → F
eqt(a, false) → F
eqt(a, lock) → F
eqt(a, locker) → F
eqt(a, mcrlrecord) → F
eqt(a, ok) → F
eqt(a, pending) → F
eqt(a, release) → F
eqt(a, request) → F
eqt(a, resource) → F
eqt(a, tag) → F
eqt(a, true) → F
eqt(a, undefined) → F
eqt(a, pid(N2)) → F
eqt(a, int(N2)) → F
eqt(a, cons(H2, T2)) → F
eqt(a, tuple(H2, T2)) → F
eqt(a, tuplenil(H2)) → F
eqt(excl, nil) → F
eqt(excl, a) → F
eqt(excl, excl) → T
eqt(excl, false) → F
eqt(excl, lock) → F
eqt(excl, locker) → F
eqt(excl, mcrlrecord) → F
eqt(excl, ok) → F
eqt(excl, pending) → F
eqt(excl, release) → F
eqt(excl, request) → F
eqt(excl, resource) → F
eqt(excl, tag) → F
eqt(excl, true) → F
eqt(excl, undefined) → F
eqt(excl, pid(N2)) → F
eqt(excl, eqt(false, int(N2))) → F
eqt(false, cons(H2, T2)) → F
eqt(false, tuple(H2, T2)) → F
eqt(false, tuplenil(H2)) → F
eqt(lock, nil) → F
eqt(lock, a) → F
eqt(lock, excl) → F
eqt(lock, false) → F
eqt(lock, lock) → T
eqt(lock, locker) → F
eqt(lock, mcrlrecord) → F
eqt(lock, ok) → F
eqt(lock, pending) → F
eqt(lock, release) → F
eqt(lock, request) → F
eqt(lock, resource) → F
eqt(lock, tag) → F
eqt(lock, true) → F
eqt(lock, undefined) → F
eqt(lock, pid(N2)) → F
eqt(lock, int(N2)) → F
eqt(lock, cons(H2, T2)) → F
eqt(lock, tuple(H2, T2)) → F
eqt(lock, tuplenil(H2)) → F
eqt(locker, nil) → F
eqt(locker, a) → F
eqt(locker, excl) → F
eqt(locker, false) → F
eqt(locker, lock) → F
eqt(locker, locker) → T
eqt(locker, mcrlrecord) → F
eqt(locker, ok) → F
eqt(locker, pending) → F
eqt(locker, release) → F
eqt(locker, request) → F
eqt(locker, resource) → F
eqt(locker, tag) → F
eqt(locker, true) → F
eqt(locker, undefined) → F
eqt(locker, pid(N2)) → F
eqt(locker, int(N2)) → F
eqt(locker, cons(H2, T2)) → F
eqt(locker, tuple(H2, T2)) → F
eqt(locker, tuplenil(H2)) → F
eqt(mcrlrecord, nil) → F
eqt(mcrlrecord, a) → F
eqt(mcrlrecord, excl) → F
eqt(mcrlrecord, false) → F
eqt(mcrlrecord, lock) → F
eqt(mcrlrecord, locker) → F
eqt(mcrlrecord, mcrlrecord) → T
eqt(mcrlrecord, ok) → F
eqt(mcrlrecord, pending) → F
eqt(mcrlrecord, release) → F
eqt(mcrlrecord, request) → F
eqt(mcrlrecord, resource) → F
eqt(ok, resource) → F
eqt(ok, tag) → F
eqt(ok, true) → F
eqt(ok, undefined) → F
eqt(ok, pid(N2)) → F
eqt(ok, int(N2)) → F
eqt(ok, cons(H2, T2)) → F
eqt(ok, tuple(H2, T2)) → F
eqt(ok, tuplenil(H2)) → F
eqt(pending, nil) → F
eqt(pending, a) → F
eqt(pending, excl) → F
eqt(pending, false) → F
eqt(pending, lock) → F
eqt(pending, locker) → F
eqt(pending, mcrlrecord) → F
eqt(pending, ok) → F
eqt(pending, pending) → T
eqt(pending, release) → F
eqt(pending, request) → F
eqt(pending, resource) → F
eqt(pending, tag) → F
eqt(pending, true) → F
eqt(pending, undefined) → F
eqt(pending, pid(N2)) → F
eqt(pending, int(N2)) → F
eqt(pending, cons(H2, T2)) → F
eqt(pending, tuple(H2, T2)) → F
eqt(pending, tuplenil(H2)) → F
eqt(release, nil) → F
eqt(release, a) → F
eqt(release, excl) → F
eqt(release, false) → F
eqt(release, lock) → F
eqt(release, locker) → F
eqt(release, mcrlrecord) → F
eqt(release, ok) → F
eqt(request, mcrlrecord) → F
eqt(request, ok) → F
eqt(request, pending) → F
eqt(request, release) → F
eqt(request, request) → T
eqt(request, resource) → F
eqt(request, tag) → F
eqt(request, true) → F
eqt(request, undefined) → F
eqt(request, pid(N2)) → F
eqt(request, int(N2)) → F
eqt(request, cons(H2, T2)) → F
eqt(request, tuple(H2, T2)) → F
eqt(request, tuplenil(H2)) → F
eqt(resource, nil) → F
eqt(resource, a) → F
eqt(resource, excl) → F
eqt(resource, false) → F
eqt(resource, lock) → F
eqt(resource, locker) → F
eqt(resource, mcrlrecord) → F
eqt(resource, ok) → F
eqt(resource, pending) → F
eqt(resource, release) → F
eqt(resource, request) → F
eqt(resource, resource) → T
eqt(resource, tag) → F
eqt(resource, true) → F
eqt(resource, undefined) → F
eqt(resource, pid(N2)) → F
eqt(resource, int(N2)) → F
eqt(resource, cons(H2, T2)) → F
eqt(resource, tuple(H2, T2)) → F
eqt(resource, tuplenil(H2)) → F
eqt(tag, nil) → F
eqt(tag, a) → F
eqt(tag, excl) → F
eqt(tag, false) → F
eqt(tag, lock) → F
eqt(tag, locker) → F
eqt(tag, mcrlrecord) → F
eqt(tag, ok) → F
eqt(tag, pending) → F
eqt(tag, release) → F
eqt(tag, request) → F
eqt(tag, resource) → F
eqt(tag, tag) → T
eqt(tag, true) → F
eqt(tag, undefined) → F
eqt(tag, pid(N2)) → F
eqt(tag, int(N2)) → F
eqt(tag, cons(H2, T2)) → F
eqt(tag, tuple(H2, T2)) → F
eqt(tag, tuplenil(H2)) → F
eqt(true, nil) → F
eqt(true, a) → F
eqt(true, excl) → F
eqt(true, false) → F
eqt(true, lock) → F
eqt(true, locker) → F
eqt(true, mcrlrecord) → F
eqt(true, ok) → F
eqt(true, pending) → F
eqt(true, release) → F
eqt(true, request) → F
eqt(true, resource) → F
eqt(true, tag) → F
eqt(true, true) → T
eqt(true, undefined) → F
eqt(true, pid(N2)) → F
eqt(true, int(N2)) → F
eqt(true, cons(H2, T2)) → F
eqt(true, tuple(H2, T2)) → F
eqt(true, tuplenil(H2)) → F
eqt(undefined, nil) → F
eqt(undefined, a) → F
eqt(undefined, tuplenil(H2)) → F
eqt(pid(N1), nil) → F
eqt(pid(N1), a) → F
eqt(pid(N1), excl) → F
eqt(pid(N1), false) → F
eqt(pid(N1), lock) → F
eqt(pid(N1), locker) → F
eqt(pid(N1), mcrlrecord) → F
eqt(pid(N1), ok) → F
eqt(pid(N1), pending) → F
eqt(pid(N1), release) → F
eqt(pid(N1), request) → F
eqt(pid(N1), resource) → F
eqt(pid(N1), tag) → F
eqt(pid(N1), true) → F
eqt(pid(N1), undefined) → F
eqt(pid(N1), pid(N2)) → eqt(N1, N2)
eqt(pid(N1), int(N2)) → F
eqt(pid(N1), cons(H2, T2)) → F
eqt(pid(N1), tuple(H2, T2)) → F
eqt(pid(N1), tuplenil(H2)) → F
eqt(int(N1), nil) → F
eqt(int(N1), a) → F
eqt(int(N1), excl) → F
eqt(int(N1), false) → F
eqt(int(N1), lock) → F
eqt(int(N1), locker) → F
eqt(int(N1), mcrlrecord) → F
eqt(int(N1), ok) → F
eqt(int(N1), pending) → F
eqt(int(N1), release) → F
eqt(int(N1), request) → F
eqt(int(N1), resource) → F
eqt(int(N1), tag) → F
eqt(int(N1), true) → F
eqt(int(N1), undefined) → F
eqt(cons(H1, T1), resource) → F
eqt(cons(H1, T1), tag) → F
eqt(cons(H1, T1), true) → F
eqt(cons(H1, T1), undefined) → F
eqt(cons(H1, T1), pid(N2)) → F
eqt(cons(H1, T1), int(N2)) → F
eqt(cons(H1, T1), cons(H2, T2)) → and(eqt(H1, H2), eqt(T1, T2))
eqt(cons(H1, T1), tuple(H2, T2)) → F
eqt(cons(H1, T1), tuplenil(H2)) → F
eqt(tuple(H1, T1), nil) → F
eqt(tuple(H1, T1), a) → F
eqt(tuple(H1, T1), excl) → F
eqt(tuple(H1, T1), false) → F
eqt(tuple(H1, T1), lock) → F
eqt(tuple(H1, T1), locker) → F
eqt(tuple(H1, T1), mcrlrecord) → F
eqt(tuple(H1, T1), ok) → F
eqt(tuple(H1, T1), pending) → F
eqt(tuple(H1, T1), release) → F
eqt(tuple(H1, T1), request) → F
eqt(tuple(H1, T1), resource) → F
eqt(tuple(H1, T1), tag) → F
eqt(tuple(H1, T1), true) → F
eqt(tuple(H1, T1), undefined) → F
eqt(tuple(H1, T1), pid(N2)) → F
eqt(tuple(H1, T1), int(N2)) → F
eqt(tuple(H1, T1), cons(H2, T2)) → F
eqt(tuple(H1, T1), tuple(H2, T2)) → and(eqt(H1, H2), eqt(T1, T2))
eqt(tuple(H1, T1), tuplenil(H2)) → F
eqt(tuplenil(H1), nil) → F
eqt(tuplenil(H1), a) → F
eqt(tuplenil(H1), excl) → F
eqt(tuplenil(H1), false) → F
eqt(tuplenil(H1), lock) → F
eqt(tuplenil(H1), locker) → F
eqt(tuplenil(H1), mcrlrecord) → F
eqt(tuplenil(H1), ok) → F
eqt(tuplenil(H1), pending) → F
eqt(tuplenil(H1), release) → F
eqt(tuplenil(H1), request) → F
eqt(tuplenil(H1), resource) → F
eqt(tuplenil(H1), tag) → F
eqt(tuplenil(H1), true) → F
eqt(tuplenil(H1), undefined) → F
eqt(tuplenil(H1), pid(N2)) → F
eqt(tuplenil(H1), int(N2)) → F
eqt(tuplenil(H1), cons(H2, T2)) → F
eqt(tuplenil(H1), tuple(H2, T2)) → F
eqt(tuplenil(H1), tuplenil(H2)) → eqt(H1, H2)
element(int(s(0)), tuplenil(T1)) → T1
element(int(s(0)), tuple(T1, T2)) → T1
element(int(s(s(N1))), tuple(T1, T2)) → element(int(s(N1)), T2)
record_new(lock) → tuple(mcrlrecord, tuple(lock, tuple(undefined, tuple(nil, tuplenil(nil)))))
record_extract(tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))), lock, resource) → tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2)))))
record_update(tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))), lock, pending, NewF) → tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(NewF)))))
record_updates(Record, Name, nil) → Record
record_updates(Record, Name, cons(tuple(Field, tuplenil(NewF)), Fields)) → record_updates(record_update(Record, Name, Field, NewF), Name, Fields)
locker2_map_promote_pending(nil, Pending) → nil
locker2_map_promote_pending(cons(Lock, Locks), Pending) → cons(locker2_promote_pending(Lock, Pending), locker2_map_promote_pending(Locks, Pending))
locker2_map_claim_lock(nil, Resources, Client) → nil
locker2_map_claim_lock(cons(Lock, Locks), Resources, Client) → cons(locker2_claim_lock(Lock, Resources, Client), locker2_map_claim_lock(Locks, Resources, Client))
locker2_map_add_pending(nil, Resources, Client) → nil
locker2_promote_pending(Lock, Client) → case0(Client, Lock, record_extract(Lock, lock, pending))
case0(Client, Lock, cons(Client, Pendings)) → record_updates(Lock, lock, cons(tuple(excl, tuplenil(Client)), cons(tuple(pending, tuplenil(Pendings)), nil)))
case0(Client, Lock, MCRLFree0) → Lock
locker2_remove_pending(Lock, Client) → record_updates(Lock, lock, cons(tuple(pending, tuplenil(subtract(record_extract(Lock, lock, pending), cons(Client, nil)))), nil))
locker2_add_pending(Lock, Resources, Client) → case1(Client, Resources, Lock, member(record_extract(Lock, lock, resource), Resources))
case1(Client, Resources, Lock, true) → record_updates(Lock, lock, cons(tuple(pending, tuplenil(append(record_extract(Lock, lock, pending), cons(Client, nil)))), nil))
case1(Client, Resources, Lock, false) → Lock
locker2_release_lock(Lock, Client) → case2(Client, Lock, gen_modtageq(Client, record_extract(Lock, lock, excl)))
case2(Client, Lock, true) → record_updates(Lock, lock, cons(tuple(excllock, excl), nil))
case4(Client, Lock, MCRLFree1) → false
locker2_obtainables(nil, Client) → true
locker2_obtainables(cons(Lock, Locks), Client) → case5(Client, Locks, Lock, member(Client, record_extract(Lock, lock, pending)))
case5(Client, Locks, Lock, true) → andt(locker2_obtainable(Lock, Client), locker2_obtainables(Locks, Client))
case5(Client, Locks, Lock, false) → locker2_obtainables(Locks, Client)
locker2_check_available(Resource, nil) → false
locker2_check_available(Resource, cons(Lock, Locks)) → case6(Locks, Lock, Resource, equal(Resource, record_extract(Lock, lock, resource)))
case6(Locks, Lock, Resource, true) → andt(equal(record_extract(Lock, lock, excl), nil), equal(record_extract(Lock, lock, pending), nil))
case6(Locks, Lock, Resource, false) → locker2_check_available(Resource, Locks)
locker2_check_availables(nil, Locks) → true
locker2_check_availables(cons(Resource, Resources), Locks) → andt(locker2_check_available(Resource, Locks), locker2_check_availables(Resources, Locks))
locker2_adduniq(nil, List) → List
append(cons(Head, Tail), List) → cons(Head, append(Tail, List))
subtract(List, nil) → List
subtract(List, cons(Head, Tail)) → subtract(delete(Head, List), Tail)
delete(E, nil) → nil
delete(E, cons(Head, Tail)) → case8(Tail, Head, E, equal(E, Head))
case8(Tail, Head, E, true) → Tail
case8(Tail, Head, E, false) → cons(Head, delete(E, Tail))
gen_tag(Pid) → tuple(Pid, tuplenil(tag))
gen_modtageq(Client1, Client2) → equal(Client1, Client2)
member(E, nil) → false
member(E, cons(Head, Tail)) → case9(Tail, Head, E, equal(E, Head))
case9(Tail, Head, E, true) → true
case9(Tail, Head, E, false) → member(E, Tail)
eqs(empty, empty) → T
eqs(empty, stack(E2, S2)) → F
eqs(stack(E1, S1), empty) → F
eqs(stack(E1, S1), stack(E2, S2)) → and(eqt(E1, E2), eqs(S1, S2))
pushs(E1, S1) → stack(E1, S1)
pops(stack(E1, S1)) → S1
tops(stack(E1, S1)) → E1
istops(E1, empty) → F
istops(E1, stack(E2, S1)) → eqt(E1, E2)
eqc(nocalls, nocalls) → T
eqc(nocalls, calls(E2, S2, CS2)) → F
eqc(calls(E1, S1, CS1), nocalls) → F
eqc(calls(E1, S1, CS1), calls(E2, S2, CS2)) → and(eqt(E1, E2), and(eqs(S1, S2), eqc(CS1, CS2)))
push(E1, E2, nocalls) → calls(E1, stack(E2, empty), nocalls)
push(E1, E2, calls(E3, S1, CS1)) → push1(E1, E2, E3, S1, CS1, eqt(E1, E3))
push1(E1, E2, E3, S1, CS1, T) → calls(E3, pushs(E2, S1), CS1)

(32) Obligation:

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

or(T, T) → T
or(F, T) → T
or(T, F) → T
or(F, F) → F
and(T, B) → B
and(B, T) → B
and(F, B) → F
and(B, F) → F
imp(T, B) → B
imp(F, B) → T
not(T) → F
not(F) → T
if(T, B1, B2) → B1
if(F, B1, B2) → B2
eq(T, T) → T
eq(F, F) → T
eq(T, F) → F
eq(F, T) → F
eqt(nil, undefined) → F
eqt(nil, pid(N2)) → F
eqt(nil, int(N2)) → F
eqt(nil, cons(H2, T2)) → F
eqt(nil, tuple(H2, T2)) → F
eqt(nil, tuplenil(H2)) → F
eqt(a, nil) → F
eqt(a, a) → T
eqt(a, excl) → F
eqt(a, false) → F
eqt(a, lock) → F
eqt(a, locker) → F
eqt(a, mcrlrecord) → F
eqt(a, ok) → F
eqt(a, pending) → F
eqt(a, release) → F
eqt(a, request) → F
eqt(a, resource) → F
eqt(a, tag) → F
eqt(a, true) → F
eqt(a, undefined) → F
eqt(a, pid(N2)) → F
eqt(a, int(N2)) → F
eqt(a, cons(H2, T2)) → F
eqt(a, tuple(H2, T2)) → F
eqt(a, tuplenil(H2)) → F
eqt(excl, nil) → F
eqt(excl, a) → F
eqt(excl, excl) → T
eqt(excl, false) → F
eqt(excl, lock) → F
eqt(excl, locker) → F
eqt(excl, mcrlrecord) → F
eqt(excl, ok) → F
eqt(excl, pending) → F
eqt(excl, release) → F
eqt(excl, request) → F
eqt(excl, resource) → F
eqt(excl, tag) → F
eqt(excl, true) → F
eqt(excl, undefined) → F
eqt(excl, pid(N2)) → F
eqt(excl, eqt(false, int(N2))) → F
eqt(false, cons(H2, T2)) → F
eqt(false, tuple(H2, T2)) → F
eqt(false, tuplenil(H2)) → F
eqt(lock, nil) → F
eqt(lock, a) → F
eqt(lock, excl) → F
eqt(lock, false) → F
eqt(lock, lock) → T
eqt(lock, locker) → F
eqt(lock, mcrlrecord) → F
eqt(lock, ok) → F
eqt(lock, pending) → F
eqt(lock, release) → F
eqt(lock, request) → F
eqt(lock, resource) → F
eqt(lock, tag) → F
eqt(lock, true) → F
eqt(lock, undefined) → F
eqt(lock, pid(N2)) → F
eqt(lock, int(N2)) → F
eqt(lock, cons(H2, T2)) → F
eqt(lock, tuple(H2, T2)) → F
eqt(lock, tuplenil(H2)) → F
eqt(locker, nil) → F
eqt(locker, a) → F
eqt(locker, excl) → F
eqt(locker, false) → F
eqt(locker, lock) → F
eqt(locker, locker) → T
eqt(locker, mcrlrecord) → F
eqt(locker, ok) → F
eqt(locker, pending) → F
eqt(locker, release) → F
eqt(locker, request) → F
eqt(locker, resource) → F
eqt(locker, tag) → F
eqt(locker, true) → F
eqt(locker, undefined) → F
eqt(locker, pid(N2)) → F
eqt(locker, int(N2)) → F
eqt(locker, cons(H2, T2)) → F
eqt(locker, tuple(H2, T2)) → F
eqt(locker, tuplenil(H2)) → F
eqt(mcrlrecord, nil) → F
eqt(mcrlrecord, a) → F
eqt(mcrlrecord, excl) → F
eqt(mcrlrecord, false) → F
eqt(mcrlrecord, lock) → F
eqt(mcrlrecord, locker) → F
eqt(mcrlrecord, mcrlrecord) → T
eqt(mcrlrecord, ok) → F
eqt(mcrlrecord, pending) → F
eqt(mcrlrecord, release) → F
eqt(mcrlrecord, request) → F
eqt(mcrlrecord, resource) → F
eqt(ok, resource) → F
eqt(ok, tag) → F
eqt(ok, true) → F
eqt(ok, undefined) → F
eqt(ok, pid(N2)) → F
eqt(ok, int(N2)) → F
eqt(ok, cons(H2, T2)) → F
eqt(ok, tuple(H2, T2)) → F
eqt(ok, tuplenil(H2)) → F
eqt(pending, nil) → F
eqt(pending, a) → F
eqt(pending, excl) → F
eqt(pending, false) → F
eqt(pending, lock) → F
eqt(pending, locker) → F
eqt(pending, mcrlrecord) → F
eqt(pending, ok) → F
eqt(pending, pending) → T
eqt(pending, release) → F
eqt(pending, request) → F
eqt(pending, resource) → F
eqt(pending, tag) → F
eqt(pending, true) → F
eqt(pending, undefined) → F
eqt(pending, pid(N2)) → F
eqt(pending, int(N2)) → F
eqt(pending, cons(H2, T2)) → F
eqt(pending, tuple(H2, T2)) → F
eqt(pending, tuplenil(H2)) → F
eqt(release, nil) → F
eqt(release, a) → F
eqt(release, excl) → F
eqt(release, false) → F
eqt(release, lock) → F
eqt(release, locker) → F
eqt(release, mcrlrecord) → F
eqt(release, ok) → F
eqt(request, mcrlrecord) → F
eqt(request, ok) → F
eqt(request, pending) → F
eqt(request, release) → F
eqt(request, request) → T
eqt(request, resource) → F
eqt(request, tag) → F
eqt(request, true) → F
eqt(request, undefined) → F
eqt(request, pid(N2)) → F
eqt(request, int(N2)) → F
eqt(request, cons(H2, T2)) → F
eqt(request, tuple(H2, T2)) → F
eqt(request, tuplenil(H2)) → F
eqt(resource, nil) → F
eqt(resource, a) → F
eqt(resource, excl) → F
eqt(resource, false) → F
eqt(resource, lock) → F
eqt(resource, locker) → F
eqt(resource, mcrlrecord) → F
eqt(resource, ok) → F
eqt(resource, pending) → F
eqt(resource, release) → F
eqt(resource, request) → F
eqt(resource, resource) → T
eqt(resource, tag) → F
eqt(resource, true) → F
eqt(resource, undefined) → F
eqt(resource, pid(N2)) → F
eqt(resource, int(N2)) → F
eqt(resource, cons(H2, T2)) → F
eqt(resource, tuple(H2, T2)) → F
eqt(resource, tuplenil(H2)) → F
eqt(tag, nil) → F
eqt(tag, a) → F
eqt(tag, excl) → F
eqt(tag, false) → F
eqt(tag, lock) → F
eqt(tag, locker) → F
eqt(tag, mcrlrecord) → F
eqt(tag, ok) → F
eqt(tag, pending) → F
eqt(tag, release) → F
eqt(tag, request) → F
eqt(tag, resource) → F
eqt(tag, tag) → T
eqt(tag, true) → F
eqt(tag, undefined) → F
eqt(tag, pid(N2)) → F
eqt(tag, int(N2)) → F
eqt(tag, cons(H2, T2)) → F
eqt(tag, tuple(H2, T2)) → F
eqt(tag, tuplenil(H2)) → F
eqt(true, nil) → F
eqt(true, a) → F
eqt(true, excl) → F
eqt(true, false) → F
eqt(true, lock) → F
eqt(true, locker) → F
eqt(true, mcrlrecord) → F
eqt(true, ok) → F
eqt(true, pending) → F
eqt(true, release) → F
eqt(true, request) → F
eqt(true, resource) → F
eqt(true, tag) → F
eqt(true, true) → T
eqt(true, undefined) → F
eqt(true, pid(N2)) → F
eqt(true, int(N2)) → F
eqt(true, cons(H2, T2)) → F
eqt(true, tuple(H2, T2)) → F
eqt(true, tuplenil(H2)) → F
eqt(undefined, nil) → F
eqt(undefined, a) → F
eqt(undefined, tuplenil(H2)) → F
eqt(pid(N1), nil) → F
eqt(pid(N1), a) → F
eqt(pid(N1), excl) → F
eqt(pid(N1), false) → F
eqt(pid(N1), lock) → F
eqt(pid(N1), locker) → F
eqt(pid(N1), mcrlrecord) → F
eqt(pid(N1), ok) → F
eqt(pid(N1), pending) → F
eqt(pid(N1), release) → F
eqt(pid(N1), request) → F
eqt(pid(N1), resource) → F
eqt(pid(N1), tag) → F
eqt(pid(N1), true) → F
eqt(pid(N1), undefined) → F
eqt(pid(N1), pid(N2)) → eqt(N1, N2)
eqt(pid(N1), int(N2)) → F
eqt(pid(N1), cons(H2, T2)) → F
eqt(pid(N1), tuple(H2, T2)) → F
eqt(pid(N1), tuplenil(H2)) → F
eqt(int(N1), nil) → F
eqt(int(N1), a) → F
eqt(int(N1), excl) → F
eqt(int(N1), false) → F
eqt(int(N1), lock) → F
eqt(int(N1), locker) → F
eqt(int(N1), mcrlrecord) → F
eqt(int(N1), ok) → F
eqt(int(N1), pending) → F
eqt(int(N1), release) → F
eqt(int(N1), request) → F
eqt(int(N1), resource) → F
eqt(int(N1), tag) → F
eqt(int(N1), true) → F
eqt(int(N1), undefined) → F
eqt(cons(H1, T1), resource) → F
eqt(cons(H1, T1), tag) → F
eqt(cons(H1, T1), true) → F
eqt(cons(H1, T1), undefined) → F
eqt(cons(H1, T1), pid(N2)) → F
eqt(cons(H1, T1), int(N2)) → F
eqt(cons(H1, T1), cons(H2, T2)) → and(eqt(H1, H2), eqt(T1, T2))
eqt(cons(H1, T1), tuple(H2, T2)) → F
eqt(cons(H1, T1), tuplenil(H2)) → F
eqt(tuple(H1, T1), nil) → F
eqt(tuple(H1, T1), a) → F
eqt(tuple(H1, T1), excl) → F
eqt(tuple(H1, T1), false) → F
eqt(tuple(H1, T1), lock) → F
eqt(tuple(H1, T1), locker) → F
eqt(tuple(H1, T1), mcrlrecord) → F
eqt(tuple(H1, T1), ok) → F
eqt(tuple(H1, T1), pending) → F
eqt(tuple(H1, T1), release) → F
eqt(tuple(H1, T1), request) → F
eqt(tuple(H1, T1), resource) → F
eqt(tuple(H1, T1), tag) → F
eqt(tuple(H1, T1), true) → F
eqt(tuple(H1, T1), undefined) → F
eqt(tuple(H1, T1), pid(N2)) → F
eqt(tuple(H1, T1), int(N2)) → F
eqt(tuple(H1, T1), cons(H2, T2)) → F
eqt(tuple(H1, T1), tuple(H2, T2)) → and(eqt(H1, H2), eqt(T1, T2))
eqt(tuple(H1, T1), tuplenil(H2)) → F
eqt(tuplenil(H1), nil) → F
eqt(tuplenil(H1), a) → F
eqt(tuplenil(H1), excl) → F
eqt(tuplenil(H1), false) → F
eqt(tuplenil(H1), lock) → F
eqt(tuplenil(H1), locker) → F
eqt(tuplenil(H1), mcrlrecord) → F
eqt(tuplenil(H1), ok) → F
eqt(tuplenil(H1), pending) → F
eqt(tuplenil(H1), release) → F
eqt(tuplenil(H1), request) → F
eqt(tuplenil(H1), resource) → F
eqt(tuplenil(H1), tag) → F
eqt(tuplenil(H1), true) → F
eqt(tuplenil(H1), undefined) → F
eqt(tuplenil(H1), pid(N2)) → F
eqt(tuplenil(H1), int(N2)) → F
eqt(tuplenil(H1), cons(H2, T2)) → F
eqt(tuplenil(H1), tuple(H2, T2)) → F
eqt(tuplenil(H1), tuplenil(H2)) → eqt(H1, H2)
element(int(s(0)), tuplenil(T1)) → T1
element(int(s(0)), tuple(T1, T2)) → T1
element(int(s(s(N1))), tuple(T1, T2)) → element(int(s(N1)), T2)
record_new(lock) → tuple(mcrlrecord, tuple(lock, tuple(undefined, tuple(nil, tuplenil(nil)))))
record_extract(tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))), lock, resource) → tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2)))))
record_update(tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))), lock, pending, NewF) → tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(NewF)))))
record_updates(Record, Name, nil) → Record
record_updates(Record, Name, cons(tuple(Field, tuplenil(NewF)), Fields)) → record_updates(record_update(Record, Name, Field, NewF), Name, Fields)
locker2_map_promote_pending(nil, Pending) → nil
locker2_map_promote_pending(cons(Lock, Locks), Pending) → cons(locker2_promote_pending(Lock, Pending), locker2_map_promote_pending(Locks, Pending))
locker2_map_claim_lock(nil, Resources, Client) → nil
locker2_map_claim_lock(cons(Lock, Locks), Resources, Client) → cons(locker2_claim_lock(Lock, Resources, Client), locker2_map_claim_lock(Locks, Resources, Client))
locker2_map_add_pending(nil, Resources, Client) → nil
locker2_promote_pending(Lock, Client) → case0(Client, Lock, record_extract(Lock, lock, pending))
case0(Client, Lock, cons(Client, Pendings)) → record_updates(Lock, lock, cons(tuple(excl, tuplenil(Client)), cons(tuple(pending, tuplenil(Pendings)), nil)))
case0(Client, Lock, MCRLFree0) → Lock
locker2_remove_pending(Lock, Client) → record_updates(Lock, lock, cons(tuple(pending, tuplenil(subtract(record_extract(Lock, lock, pending), cons(Client, nil)))), nil))
locker2_add_pending(Lock, Resources, Client) → case1(Client, Resources, Lock, member(record_extract(Lock, lock, resource), Resources))
case1(Client, Resources, Lock, true) → record_updates(Lock, lock, cons(tuple(pending, tuplenil(append(record_extract(Lock, lock, pending), cons(Client, nil)))), nil))
case1(Client, Resources, Lock, false) → Lock
locker2_release_lock(Lock, Client) → case2(Client, Lock, gen_modtageq(Client, record_extract(Lock, lock, excl)))
case2(Client, Lock, true) → record_updates(Lock, lock, cons(tuple(excllock, excl), nil))
case4(Client, Lock, MCRLFree1) → false
locker2_obtainables(nil, Client) → true
locker2_obtainables(cons(Lock, Locks), Client) → case5(Client, Locks, Lock, member(Client, record_extract(Lock, lock, pending)))
case5(Client, Locks, Lock, true) → andt(locker2_obtainable(Lock, Client), locker2_obtainables(Locks, Client))
case5(Client, Locks, Lock, false) → locker2_obtainables(Locks, Client)
locker2_check_available(Resource, nil) → false
locker2_check_available(Resource, cons(Lock, Locks)) → case6(Locks, Lock, Resource, equal(Resource, record_extract(Lock, lock, resource)))
case6(Locks, Lock, Resource, true) → andt(equal(record_extract(Lock, lock, excl), nil), equal(record_extract(Lock, lock, pending), nil))
case6(Locks, Lock, Resource, false) → locker2_check_available(Resource, Locks)
locker2_check_availables(nil, Locks) → true
locker2_check_availables(cons(Resource, Resources), Locks) → andt(locker2_check_available(Resource, Locks), locker2_check_availables(Resources, Locks))
locker2_adduniq(nil, List) → List
append(cons(Head, Tail), List) → cons(Head, append(Tail, List))
subtract(List, nil) → List
subtract(List, cons(Head, Tail)) → subtract(delete(Head, List), Tail)
delete(E, nil) → nil
delete(E, cons(Head, Tail)) → case8(Tail, Head, E, equal(E, Head))
case8(Tail, Head, E, true) → Tail
case8(Tail, Head, E, false) → cons(Head, delete(E, Tail))
gen_tag(Pid) → tuple(Pid, tuplenil(tag))
gen_modtageq(Client1, Client2) → equal(Client1, Client2)
member(E, nil) → false
member(E, cons(Head, Tail)) → case9(Tail, Head, E, equal(E, Head))
case9(Tail, Head, E, true) → true
case9(Tail, Head, E, false) → member(E, Tail)
eqs(empty, empty) → T
eqs(empty, stack(E2, S2)) → F
eqs(stack(E1, S1), empty) → F
eqs(stack(E1, S1), stack(E2, S2)) → and(eqt(E1, E2), eqs(S1, S2))
pushs(E1, S1) → stack(E1, S1)
pops(stack(E1, S1)) → S1
tops(stack(E1, S1)) → E1
istops(E1, empty) → F
istops(E1, stack(E2, S1)) → eqt(E1, E2)
eqc(nocalls, nocalls) → T
eqc(nocalls, calls(E2, S2, CS2)) → F
eqc(calls(E1, S1, CS1), nocalls) → F
eqc(calls(E1, S1, CS1), calls(E2, S2, CS2)) → and(eqt(E1, E2), and(eqs(S1, S2), eqc(CS1, CS2)))
push(E1, E2, nocalls) → calls(E1, stack(E2, empty), nocalls)
push(E1, E2, calls(E3, S1, CS1)) → push1(E1, E2, E3, S1, CS1, eqt(E1, E3))
push1(E1, E2, E3, S1, CS1, T) → calls(E3, pushs(E2, S1), CS1)

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

(33) PisEmptyProof (EQUIVALENT transformation)

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

(34) TRUE

(35) Obligation:

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

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

The TRS R consists of the following rules:

or(T, T) → T
or(F, T) → T
or(T, F) → T
or(F, F) → F
and(T, B) → B
and(B, T) → B
and(F, B) → F
and(B, F) → F
imp(T, B) → B
imp(F, B) → T
not(T) → F
not(F) → T
if(T, B1, B2) → B1
if(F, B1, B2) → B2
eq(T, T) → T
eq(F, F) → T
eq(T, F) → F
eq(F, T) → F
eqt(nil, undefined) → F
eqt(nil, pid(N2)) → F
eqt(nil, int(N2)) → F
eqt(nil, cons(H2, T2)) → F
eqt(nil, tuple(H2, T2)) → F
eqt(nil, tuplenil(H2)) → F
eqt(a, nil) → F
eqt(a, a) → T
eqt(a, excl) → F
eqt(a, false) → F
eqt(a, lock) → F
eqt(a, locker) → F
eqt(a, mcrlrecord) → F
eqt(a, ok) → F
eqt(a, pending) → F
eqt(a, release) → F
eqt(a, request) → F
eqt(a, resource) → F
eqt(a, tag) → F
eqt(a, true) → F
eqt(a, undefined) → F
eqt(a, pid(N2)) → F
eqt(a, int(N2)) → F
eqt(a, cons(H2, T2)) → F
eqt(a, tuple(H2, T2)) → F
eqt(a, tuplenil(H2)) → F
eqt(excl, nil) → F
eqt(excl, a) → F
eqt(excl, excl) → T
eqt(excl, false) → F
eqt(excl, lock) → F
eqt(excl, locker) → F
eqt(excl, mcrlrecord) → F
eqt(excl, ok) → F
eqt(excl, pending) → F
eqt(excl, release) → F
eqt(excl, request) → F
eqt(excl, resource) → F
eqt(excl, tag) → F
eqt(excl, true) → F
eqt(excl, undefined) → F
eqt(excl, pid(N2)) → F
eqt(excl, eqt(false, int(N2))) → F
eqt(false, cons(H2, T2)) → F
eqt(false, tuple(H2, T2)) → F
eqt(false, tuplenil(H2)) → F
eqt(lock, nil) → F
eqt(lock, a) → F
eqt(lock, excl) → F
eqt(lock, false) → F
eqt(lock, lock) → T
eqt(lock, locker) → F
eqt(lock, mcrlrecord) → F
eqt(lock, ok) → F
eqt(lock, pending) → F
eqt(lock, release) → F
eqt(lock, request) → F
eqt(lock, resource) → F
eqt(lock, tag) → F
eqt(lock, true) → F
eqt(lock, undefined) → F
eqt(lock, pid(N2)) → F
eqt(lock, int(N2)) → F
eqt(lock, cons(H2, T2)) → F
eqt(lock, tuple(H2, T2)) → F
eqt(lock, tuplenil(H2)) → F
eqt(locker, nil) → F
eqt(locker, a) → F
eqt(locker, excl) → F
eqt(locker, false) → F
eqt(locker, lock) → F
eqt(locker, locker) → T
eqt(locker, mcrlrecord) → F
eqt(locker, ok) → F
eqt(locker, pending) → F
eqt(locker, release) → F
eqt(locker, request) → F
eqt(locker, resource) → F
eqt(locker, tag) → F
eqt(locker, true) → F
eqt(locker, undefined) → F
eqt(locker, pid(N2)) → F
eqt(locker, int(N2)) → F
eqt(locker, cons(H2, T2)) → F
eqt(locker, tuple(H2, T2)) → F
eqt(locker, tuplenil(H2)) → F
eqt(mcrlrecord, nil) → F
eqt(mcrlrecord, a) → F
eqt(mcrlrecord, excl) → F
eqt(mcrlrecord, false) → F
eqt(mcrlrecord, lock) → F
eqt(mcrlrecord, locker) → F
eqt(mcrlrecord, mcrlrecord) → T
eqt(mcrlrecord, ok) → F
eqt(mcrlrecord, pending) → F
eqt(mcrlrecord, release) → F
eqt(mcrlrecord, request) → F
eqt(mcrlrecord, resource) → F
eqt(ok, resource) → F
eqt(ok, tag) → F
eqt(ok, true) → F
eqt(ok, undefined) → F
eqt(ok, pid(N2)) → F
eqt(ok, int(N2)) → F
eqt(ok, cons(H2, T2)) → F
eqt(ok, tuple(H2, T2)) → F
eqt(ok, tuplenil(H2)) → F
eqt(pending, nil) → F
eqt(pending, a) → F
eqt(pending, excl) → F
eqt(pending, false) → F
eqt(pending, lock) → F
eqt(pending, locker) → F
eqt(pending, mcrlrecord) → F
eqt(pending, ok) → F
eqt(pending, pending) → T
eqt(pending, release) → F
eqt(pending, request) → F
eqt(pending, resource) → F
eqt(pending, tag) → F
eqt(pending, true) → F
eqt(pending, undefined) → F
eqt(pending, pid(N2)) → F
eqt(pending, int(N2)) → F
eqt(pending, cons(H2, T2)) → F
eqt(pending, tuple(H2, T2)) → F
eqt(pending, tuplenil(H2)) → F
eqt(release, nil) → F
eqt(release, a) → F
eqt(release, excl) → F
eqt(release, false) → F
eqt(release, lock) → F
eqt(release, locker) → F
eqt(release, mcrlrecord) → F
eqt(release, ok) → F
eqt(request, mcrlrecord) → F
eqt(request, ok) → F
eqt(request, pending) → F
eqt(request, release) → F
eqt(request, request) → T
eqt(request, resource) → F
eqt(request, tag) → F
eqt(request, true) → F
eqt(request, undefined) → F
eqt(request, pid(N2)) → F
eqt(request, int(N2)) → F
eqt(request, cons(H2, T2)) → F
eqt(request, tuple(H2, T2)) → F
eqt(request, tuplenil(H2)) → F
eqt(resource, nil) → F
eqt(resource, a) → F
eqt(resource, excl) → F
eqt(resource, false) → F
eqt(resource, lock) → F
eqt(resource, locker) → F
eqt(resource, mcrlrecord) → F
eqt(resource, ok) → F
eqt(resource, pending) → F
eqt(resource, release) → F
eqt(resource, request) → F
eqt(resource, resource) → T
eqt(resource, tag) → F
eqt(resource, true) → F
eqt(resource, undefined) → F
eqt(resource, pid(N2)) → F
eqt(resource, int(N2)) → F
eqt(resource, cons(H2, T2)) → F
eqt(resource, tuple(H2, T2)) → F
eqt(resource, tuplenil(H2)) → F
eqt(tag, nil) → F
eqt(tag, a) → F
eqt(tag, excl) → F
eqt(tag, false) → F
eqt(tag, lock) → F
eqt(tag, locker) → F
eqt(tag, mcrlrecord) → F
eqt(tag, ok) → F
eqt(tag, pending) → F
eqt(tag, release) → F
eqt(tag, request) → F
eqt(tag, resource) → F
eqt(tag, tag) → T
eqt(tag, true) → F
eqt(tag, undefined) → F
eqt(tag, pid(N2)) → F
eqt(tag, int(N2)) → F
eqt(tag, cons(H2, T2)) → F
eqt(tag, tuple(H2, T2)) → F
eqt(tag, tuplenil(H2)) → F
eqt(true, nil) → F
eqt(true, a) → F
eqt(true, excl) → F
eqt(true, false) → F
eqt(true, lock) → F
eqt(true, locker) → F
eqt(true, mcrlrecord) → F
eqt(true, ok) → F
eqt(true, pending) → F
eqt(true, release) → F
eqt(true, request) → F
eqt(true, resource) → F
eqt(true, tag) → F
eqt(true, true) → T
eqt(true, undefined) → F
eqt(true, pid(N2)) → F
eqt(true, int(N2)) → F
eqt(true, cons(H2, T2)) → F
eqt(true, tuple(H2, T2)) → F
eqt(true, tuplenil(H2)) → F
eqt(undefined, nil) → F
eqt(undefined, a) → F
eqt(undefined, tuplenil(H2)) → F
eqt(pid(N1), nil) → F
eqt(pid(N1), a) → F
eqt(pid(N1), excl) → F
eqt(pid(N1), false) → F
eqt(pid(N1), lock) → F
eqt(pid(N1), locker) → F
eqt(pid(N1), mcrlrecord) → F
eqt(pid(N1), ok) → F
eqt(pid(N1), pending) → F
eqt(pid(N1), release) → F
eqt(pid(N1), request) → F
eqt(pid(N1), resource) → F
eqt(pid(N1), tag) → F
eqt(pid(N1), true) → F
eqt(pid(N1), undefined) → F
eqt(pid(N1), pid(N2)) → eqt(N1, N2)
eqt(pid(N1), int(N2)) → F
eqt(pid(N1), cons(H2, T2)) → F
eqt(pid(N1), tuple(H2, T2)) → F
eqt(pid(N1), tuplenil(H2)) → F
eqt(int(N1), nil) → F
eqt(int(N1), a) → F
eqt(int(N1), excl) → F
eqt(int(N1), false) → F
eqt(int(N1), lock) → F
eqt(int(N1), locker) → F
eqt(int(N1), mcrlrecord) → F
eqt(int(N1), ok) → F
eqt(int(N1), pending) → F
eqt(int(N1), release) → F
eqt(int(N1), request) → F
eqt(int(N1), resource) → F
eqt(int(N1), tag) → F
eqt(int(N1), true) → F
eqt(int(N1), undefined) → F
eqt(cons(H1, T1), resource) → F
eqt(cons(H1, T1), tag) → F
eqt(cons(H1, T1), true) → F
eqt(cons(H1, T1), undefined) → F
eqt(cons(H1, T1), pid(N2)) → F
eqt(cons(H1, T1), int(N2)) → F
eqt(cons(H1, T1), cons(H2, T2)) → and(eqt(H1, H2), eqt(T1, T2))
eqt(cons(H1, T1), tuple(H2, T2)) → F
eqt(cons(H1, T1), tuplenil(H2)) → F
eqt(tuple(H1, T1), nil) → F
eqt(tuple(H1, T1), a) → F
eqt(tuple(H1, T1), excl) → F
eqt(tuple(H1, T1), false) → F
eqt(tuple(H1, T1), lock) → F
eqt(tuple(H1, T1), locker) → F
eqt(tuple(H1, T1), mcrlrecord) → F
eqt(tuple(H1, T1), ok) → F
eqt(tuple(H1, T1), pending) → F
eqt(tuple(H1, T1), release) → F
eqt(tuple(H1, T1), request) → F
eqt(tuple(H1, T1), resource) → F
eqt(tuple(H1, T1), tag) → F
eqt(tuple(H1, T1), true) → F
eqt(tuple(H1, T1), undefined) → F
eqt(tuple(H1, T1), pid(N2)) → F
eqt(tuple(H1, T1), int(N2)) → F
eqt(tuple(H1, T1), cons(H2, T2)) → F
eqt(tuple(H1, T1), tuple(H2, T2)) → and(eqt(H1, H2), eqt(T1, T2))
eqt(tuple(H1, T1), tuplenil(H2)) → F
eqt(tuplenil(H1), nil) → F
eqt(tuplenil(H1), a) → F
eqt(tuplenil(H1), excl) → F
eqt(tuplenil(H1), false) → F
eqt(tuplenil(H1), lock) → F
eqt(tuplenil(H1), locker) → F
eqt(tuplenil(H1), mcrlrecord) → F
eqt(tuplenil(H1), ok) → F
eqt(tuplenil(H1), pending) → F
eqt(tuplenil(H1), release) → F
eqt(tuplenil(H1), request) → F
eqt(tuplenil(H1), resource) → F
eqt(tuplenil(H1), tag) → F
eqt(tuplenil(H1), true) → F
eqt(tuplenil(H1), undefined) → F
eqt(tuplenil(H1), pid(N2)) → F
eqt(tuplenil(H1), int(N2)) → F
eqt(tuplenil(H1), cons(H2, T2)) → F
eqt(tuplenil(H1), tuple(H2, T2)) → F
eqt(tuplenil(H1), tuplenil(H2)) → eqt(H1, H2)
element(int(s(0)), tuplenil(T1)) → T1
element(int(s(0)), tuple(T1, T2)) → T1
element(int(s(s(N1))), tuple(T1, T2)) → element(int(s(N1)), T2)
record_new(lock) → tuple(mcrlrecord, tuple(lock, tuple(undefined, tuple(nil, tuplenil(nil)))))
record_extract(tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))), lock, resource) → tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2)))))
record_update(tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))), lock, pending, NewF) → tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(NewF)))))
record_updates(Record, Name, nil) → Record
record_updates(Record, Name, cons(tuple(Field, tuplenil(NewF)), Fields)) → record_updates(record_update(Record, Name, Field, NewF), Name, Fields)
locker2_map_promote_pending(nil, Pending) → nil
locker2_map_promote_pending(cons(Lock, Locks), Pending) → cons(locker2_promote_pending(Lock, Pending), locker2_map_promote_pending(Locks, Pending))
locker2_map_claim_lock(nil, Resources, Client) → nil
locker2_map_claim_lock(cons(Lock, Locks), Resources, Client) → cons(locker2_claim_lock(Lock, Resources, Client), locker2_map_claim_lock(Locks, Resources, Client))
locker2_map_add_pending(nil, Resources, Client) → nil
locker2_promote_pending(Lock, Client) → case0(Client, Lock, record_extract(Lock, lock, pending))
case0(Client, Lock, cons(Client, Pendings)) → record_updates(Lock, lock, cons(tuple(excl, tuplenil(Client)), cons(tuple(pending, tuplenil(Pendings)), nil)))
case0(Client, Lock, MCRLFree0) → Lock
locker2_remove_pending(Lock, Client) → record_updates(Lock, lock, cons(tuple(pending, tuplenil(subtract(record_extract(Lock, lock, pending), cons(Client, nil)))), nil))
locker2_add_pending(Lock, Resources, Client) → case1(Client, Resources, Lock, member(record_extract(Lock, lock, resource), Resources))
case1(Client, Resources, Lock, true) → record_updates(Lock, lock, cons(tuple(pending, tuplenil(append(record_extract(Lock, lock, pending), cons(Client, nil)))), nil))
case1(Client, Resources, Lock, false) → Lock
locker2_release_lock(Lock, Client) → case2(Client, Lock, gen_modtageq(Client, record_extract(Lock, lock, excl)))
case2(Client, Lock, true) → record_updates(Lock, lock, cons(tuple(excllock, excl), nil))
case4(Client, Lock, MCRLFree1) → false
locker2_obtainables(nil, Client) → true
locker2_obtainables(cons(Lock, Locks), Client) → case5(Client, Locks, Lock, member(Client, record_extract(Lock, lock, pending)))
case5(Client, Locks, Lock, true) → andt(locker2_obtainable(Lock, Client), locker2_obtainables(Locks, Client))
case5(Client, Locks, Lock, false) → locker2_obtainables(Locks, Client)
locker2_check_available(Resource, nil) → false
locker2_check_available(Resource, cons(Lock, Locks)) → case6(Locks, Lock, Resource, equal(Resource, record_extract(Lock, lock, resource)))
case6(Locks, Lock, Resource, true) → andt(equal(record_extract(Lock, lock, excl), nil), equal(record_extract(Lock, lock, pending), nil))
case6(Locks, Lock, Resource, false) → locker2_check_available(Resource, Locks)
locker2_check_availables(nil, Locks) → true
locker2_check_availables(cons(Resource, Resources), Locks) → andt(locker2_check_available(Resource, Locks), locker2_check_availables(Resources, Locks))
locker2_adduniq(nil, List) → List
append(cons(Head, Tail), List) → cons(Head, append(Tail, List))
subtract(List, nil) → List
subtract(List, cons(Head, Tail)) → subtract(delete(Head, List), Tail)
delete(E, nil) → nil
delete(E, cons(Head, Tail)) → case8(Tail, Head, E, equal(E, Head))
case8(Tail, Head, E, true) → Tail
case8(Tail, Head, E, false) → cons(Head, delete(E, Tail))
gen_tag(Pid) → tuple(Pid, tuplenil(tag))
gen_modtageq(Client1, Client2) → equal(Client1, Client2)
member(E, nil) → false
member(E, cons(Head, Tail)) → case9(Tail, Head, E, equal(E, Head))
case9(Tail, Head, E, true) → true
case9(Tail, Head, E, false) → member(E, Tail)
eqs(empty, empty) → T
eqs(empty, stack(E2, S2)) → F
eqs(stack(E1, S1), empty) → F
eqs(stack(E1, S1), stack(E2, S2)) → and(eqt(E1, E2), eqs(S1, S2))
pushs(E1, S1) → stack(E1, S1)
pops(stack(E1, S1)) → S1
tops(stack(E1, S1)) → E1
istops(E1, empty) → F
istops(E1, stack(E2, S1)) → eqt(E1, E2)
eqc(nocalls, nocalls) → T
eqc(nocalls, calls(E2, S2, CS2)) → F
eqc(calls(E1, S1, CS1), nocalls) → F
eqc(calls(E1, S1, CS1), calls(E2, S2, CS2)) → and(eqt(E1, E2), and(eqs(S1, S2), eqc(CS1, CS2)))
push(E1, E2, nocalls) → calls(E1, stack(E2, empty), nocalls)
push(E1, E2, calls(E3, S1, CS1)) → push1(E1, E2, E3, S1, CS1, eqt(E1, E3))
push1(E1, E2, E3, S1, CS1, T) → calls(E3, pushs(E2, S1), CS1)

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

(36) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

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

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
ELEMENT(x1, x2) = ELEMENT(x1, x2)
int(x1) = int(x1)
s(x1) = x1
tuple(x1, x2) = tuple(x1, x2)
or(x1, x2) = or
T = T
F = F
and(x1, x2) = and(x1, x2)
imp(x1, x2) = 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)
cons(x1, x2) = cons(x1, x2)
tuplenil(x1) = x1
a = a
excl = excl
false = false
lock = lock
locker = locker
mcrlrecord = mcrlrecord
ok = ok
pending = pending
release = release
request = request
resource = resource
tag = tag
true = true
element(x1, x2) = x2
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, x3, x4)
record_updates(x1, x2, x3) = record_updates(x1, 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
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, x3)
case1(x1, x2, x3, x4) = case1(x2, x3)
member(x1, x2) = member
append(x1, x2) = x1
locker2_release_lock(x1, x2) = locker2_release_lock(x1)
case2(x1, x2, x3) = case2(x2)
gen_modtageq(x1, x2) = x1
excllock = excllock
case4(x1, x2, x3) = x3
locker2_obtainables(x1, x2) = x2
case5(x1, x2, x3, x4) = x1
andt(x1, x2) = andt
locker2_obtainable(x1, x2) = x2
locker2_check_available(x1, x2) = x1
case6(x1, x2, x3, x4) = x3
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
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
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:

int₁ > ELEMENT₂ > [T, F, a, excl, false, true, andt, nocalls]
or > [T, F, a, excl, false, true, andt, nocalls]
if₂ > [T, F, a, excl, false, true, andt, nocalls]
eq > [T, F, a, excl, false, true, andt, nocalls]
pid₁ > [T, F, a, excl, false, true, andt, nocalls]
locker > [T, F, a, excl, false, true, andt, nocalls]
ok > [T, F, a, excl, false, true, andt, nocalls]
release > [T, F, a, excl, false, true, andt, nocalls]
request > [T, F, a, excl, false, true, andt, nocalls]
0 > [T, F, a, excl, false, true, andt, nocalls]
record_new > mcrlrecord > lock > [tuple₂, and₂, stack₂] > [T, F, a, excl, false, true, andt, nocalls]
record_new > mcrlrecord > lock > nil > [T, F, a, excl, false, true, andt, nocalls]
record_new > mcrlrecord > lock > undefined > [T, F, a, excl, false, true, andt, nocalls]
[locker2_{map_{promote_pending₁}}, locker2_{promote_pending₁}] > case0₂ > nil > [T, F, a, excl, false, true, andt, nocalls]
[locker2_{map_{promote_pending₁}}, locker2_{promote_pending₁}] > case0₂ > [cons₂, record_extract₂, case8₂] > [tuple₂, and₂, stack₂] > [T, F, a, excl, false, true, andt, nocalls]
[locker2_{map_{promote_pending₁}}, locker2_{promote_pending₁}] > case0₂ > pending > [tuple₂, and₂, stack₂] > [T, F, a, excl, false, true, andt, nocalls]
[locker2_{map_{promote_pending₁}}, locker2_{promote_pending₁}] > case0₂ > [record_update₃, record_updates₂] > [tuple₂, and₂, stack₂] > [T, F, a, excl, false, true, andt, nocalls]
[locker2_{map_{claim_lock₃}}, locker2_{claim_lock}] > [cons₂, record_extract₂, case8₂] > [tuple₂, and₂, stack₂] > [T, F, a, excl, false, true, andt, nocalls]
locker2_{map_{add_pending}} > nil > [T, F, a, excl, false, true, andt, nocalls]
locker2_{remove_pending₂} > [cons₂, record_extract₂, case8₂] > [tuple₂, and₂, stack₂] > [T, F, a, excl, false, true, andt, nocalls]
locker2_{remove_pending₂} > lock > [tuple₂, and₂, stack₂] > [T, F, a, excl, false, true, andt, nocalls]
locker2_{remove_pending₂} > lock > nil > [T, F, a, excl, false, true, andt, nocalls]
locker2_{remove_pending₂} > lock > undefined > [T, F, a, excl, false, true, andt, nocalls]
locker2_{remove_pending₂} > pending > [tuple₂, and₂, stack₂] > [T, F, a, excl, false, true, andt, nocalls]
locker2_{remove_pending₂} > [record_update₃, record_updates₂] > [tuple₂, and₂, stack₂] > [T, F, a, excl, false, true, andt, nocalls]
locker2_{add_pending₃} > resource > [tuple₂, and₂, stack₂] > [T, F, a, excl, false, true, andt, nocalls]
locker2_{add_pending₃} > case1₂ > [cons₂, record_extract₂, case8₂] > [tuple₂, and₂, stack₂] > [T, F, a, excl, false, true, andt, nocalls]
locker2_{add_pending₃} > case1₂ > lock > [tuple₂, and₂, stack₂] > [T, F, a, excl, false, true, andt, nocalls]
locker2_{add_pending₃} > case1₂ > lock > nil > [T, F, a, excl, false, true, andt, nocalls]
locker2_{add_pending₃} > case1₂ > lock > undefined > [T, F, a, excl, false, true, andt, nocalls]
locker2_{add_pending₃} > case1₂ > pending > [tuple₂, and₂, stack₂] > [T, F, a, excl, false, true, andt, nocalls]
locker2_{add_pending₃} > case1₂ > [record_update₃, record_updates₂] > [tuple₂, and₂, stack₂] > [T, F, a, excl, false, true, andt, nocalls]
locker2_{add_pending₃} > [member, case9] > [T, F, a, excl, false, true, andt, nocalls]
[locker2_{release_lock₁}, case2₁] > [cons₂, record_extract₂, case8₂] > [tuple₂, and₂, stack₂] > [T, F, a, excl, false, true, andt, nocalls]
[locker2_{release_lock₁}, case2₁] > lock > [tuple₂, and₂, stack₂] > [T, F, a, excl, false, true, andt, nocalls]
[locker2_{release_lock₁}, case2₁] > lock > nil > [T, F, a, excl, false, true, andt, nocalls]
[locker2_{release_lock₁}, case2₁] > lock > undefined > [T, F, a, excl, false, true, andt, nocalls]
[locker2_{release_lock₁}, case2₁] > [record_update₃, record_updates₂] > [tuple₂, and₂, stack₂] > [T, F, a, excl, false, true, andt, nocalls]
[locker2_{release_lock₁}, case2₁] > excllock > [T, F, a, excl, false, true, andt, nocalls]
locker2_{check_availables} > [T, F, a, excl, false, true, andt, nocalls]
gen_tag₁ > [tuple₂, and₂, stack₂] > [T, F, a, excl, false, true, andt, nocalls]
gen_tag₁ > tag > [T, F, a, excl, false, true, andt, nocalls]
tops₁ > [T, F, a, excl, false, true, andt, nocalls]
istops₂ > [T, F, a, excl, false, true, andt, nocalls]
eqc₂ > eqs₂ > [tuple₂, and₂, stack₂] > [T, F, a, excl, false, true, andt, nocalls]
push₃ > empty > [T, F, a, excl, false, true, andt, nocalls]
push₃ > push1₆ > pushs₂ > [tuple₂, and₂, stack₂] > [T, F, a, excl, false, true, andt, nocalls]
push₃ > push1₆ > calls₃ > [tuple₂, and₂, stack₂] > [T, F, a, excl, false, true, andt, nocalls]

Status:

ELEMENT₂: [2,1]
int₁: [1]
tuple₂: [1,2]
or: []
T: []
F: []
and₂: [1,2]
if₂: [1,2]
eq: []
nil: []
undefined: []
pid₁: [1]
cons₂: [2,1]
a: []
excl: []
false: []
lock: []
locker: []
mcrlrecord: []
ok: []
pending: []
release: []
request: []
resource: []
tag: []
true: []
0: []
record_new: []
record_extract₂: [1,2]
record_update₃: [2,1,3]
record_updates₂: [2,1]
locker2_{map_{promote_pending₁}}: [1]
locker2_{promote_pending₁}: [1]
locker2_{map_{claim_lock₃}}: [1,2,3]
locker2_{claim_lock}: []
locker2_{map_{add_pending}}: []
case0₂: [2,1]
locker2_{remove_pending₂}: [2,1]
locker2_{add_pending₃}: [3,2,1]
case1₂: [1,2]
member: []
locker2_{release_lock₁}: [1]
case2₁: [1]
excllock: []
andt: []
locker2_{check_availables}: []
case8₂: [1,2]
gen_tag₁: [1]
case9: []
eqs₂: [1,2]
empty: []
stack₂: [2,1]
pushs₂: [1,2]
tops₁: [1]
istops₂: [2,1]
eqc₂: [2,1]
nocalls: []
calls₃: [2,1,3]
push₃: [1,2,3]
push1₆: [6,5,4,3,1,2]

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

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
EQT(x1, x2) = x2
cons(x1, x2) = cons(x1, x2)
pid(x1) = pid(x1)
tuple(x1, x2) = tuple(x1, x2)
tuplenil(x1) = x1
or(x1, x2) = or(x2)
T = T
F = F
and(x1, x2) = and(x1, x2)
imp(x1, x2) = x2
not(x1) = not
if(x1, x2, x3) = if(x2, x3)
eq(x1, x2) = eq(x1, x2)
eqt(x1, x2) = eqt(x1, x2)
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(x1)
0 = 0
record_new(x1) = record_new
record_extract(x1, x2, x3) = x1
record_update(x1, x2, x3, x4) = record_update(x1, 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(x1, x2, x3)
case0(x1, x2, x3) = case0(x1, x2, x3)
locker2_remove_pending(x1, x2) = locker2_remove_pending(x1, x2)
subtract(x1, x2) = subtract(x1, x2)
locker2_add_pending(x1, x2, x3) = locker2_add_pending(x1, x2, x3)
case1(x1, x2, x3, x4) = case1(x1, x2, x3)
member(x1, x2) = x2
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) = x2
excllock = excllock
case4(x1, x2, x3) = case4(x3)
locker2_obtainables(x1, x2) = locker2_obtainables(x1)
case5(x1, x2, x3, x4) = case5(x2, x4)
andt(x1, x2) = x1
locker2_obtainable(x1, x2) = locker2_obtainable
locker2_check_available(x1, x2) = locker2_check_available(x1)
case6(x1, x2, x3, x4) = case6(x3)
equal(x1, x2) = equal
locker2_check_availables(x1, x2) = locker2_check_availables(x1)
locker2_adduniq(x1, x2) = x2
delete(x1, x2) = delete(x2)
case8(x1, x2, x3, x4) = case8(x1, x2, x4)
gen_tag(x1) = gen_tag(x1)
case9(x1, x2, x3, x4) = case9(x1, x2, 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) = 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)

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

pid₁ > [F, not] > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
or₁ > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
if₂ > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
eq₂ > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
int > [F, not] > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
int > s₁ > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
a > [F, not] > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
locker > [F, not] > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
ok > [F, not] > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
release > [F, not] > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
request > [F, not] > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
0 > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
record_new > [cons₂, tuple₂, record_update₃] > and₂ > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
record_new > [cons₂, tuple₂, record_update₃] > [locker2_{check_available₁}, case6₁] > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
record_new > [cons₂, tuple₂, record_update₃] > case9₃ > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
record_new > [nil, locker2_{map_{add_pending₃}}] > [F, not] > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
record_new > undefined > [F, not] > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
locker2_{map_{promote_pending₂}} > locker2_{promote_pending₂} > case0₃ > pending > [cons₂, tuple₂, record_update₃] > and₂ > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
locker2_{map_{promote_pending₂}} > locker2_{promote_pending₂} > case0₃ > pending > [cons₂, tuple₂, record_update₃] > [locker2_{check_available₁}, case6₁] > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
locker2_{map_{promote_pending₂}} > locker2_{promote_pending₂} > case0₃ > pending > [cons₂, tuple₂, record_update₃] > case9₃ > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
locker2_{map_{promote_pending₂}} > locker2_{promote_pending₂} > case0₃ > pending > [F, not] > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
locker2_{map_{promote_pending₂}} > locker2_{promote_pending₂} > case0₃ > [record_updates₃, case2₂] > [cons₂, tuple₂, record_update₃] > and₂ > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
locker2_{map_{promote_pending₂}} > locker2_{promote_pending₂} > case0₃ > [record_updates₃, case2₂] > [cons₂, tuple₂, record_update₃] > [locker2_{check_available₁}, case6₁] > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
locker2_{map_{promote_pending₂}} > locker2_{promote_pending₂} > case0₃ > [record_updates₃, case2₂] > [cons₂, tuple₂, record_update₃] > case9₃ > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
locker2_{map_{promote_pending₂}} > locker2_{promote_pending₂} > case0₃ > [record_updates₃, case2₂] > [nil, locker2_{map_{add_pending₃}}] > [F, not] > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
locker2_{map_{promote_pending₂}} > locker2_{promote_pending₂} > case0₃ > [record_updates₃, case2₂] > excl > [F, not] > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
locker2_{map_{promote_pending₂}} > locker2_{promote_pending₂} > case0₃ > [record_updates₃, case2₂] > excllock > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
locker2_{map_{claim_lock₃}} > [cons₂, tuple₂, record_update₃] > and₂ > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
locker2_{map_{claim_lock₃}} > [cons₂, tuple₂, record_update₃] > [locker2_{check_available₁}, case6₁] > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
locker2_{map_{claim_lock₃}} > [cons₂, tuple₂, record_update₃] > case9₃ > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
locker2_{map_{claim_lock₃}} > [nil, locker2_{map_{add_pending₃}}] > [F, not] > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
locker2_{map_{claim_lock₃}} > locker2_{claim_lock₃} > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
locker2_{remove_pending₂} > pending > [cons₂, tuple₂, record_update₃] > and₂ > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
locker2_{remove_pending₂} > pending > [cons₂, tuple₂, record_update₃] > [locker2_{check_available₁}, case6₁] > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
locker2_{remove_pending₂} > pending > [cons₂, tuple₂, record_update₃] > case9₃ > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
locker2_{remove_pending₂} > pending > [F, not] > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
locker2_{remove_pending₂} > [record_updates₃, case2₂] > [cons₂, tuple₂, record_update₃] > and₂ > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
locker2_{remove_pending₂} > [record_updates₃, case2₂] > [cons₂, tuple₂, record_update₃] > [locker2_{check_available₁}, case6₁] > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
locker2_{remove_pending₂} > [record_updates₃, case2₂] > [cons₂, tuple₂, record_update₃] > case9₃ > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
locker2_{remove_pending₂} > [record_updates₃, case2₂] > [nil, locker2_{map_{add_pending₃}}] > [F, not] > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
locker2_{remove_pending₂} > [record_updates₃, case2₂] > excl > [F, not] > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
locker2_{remove_pending₂} > [record_updates₃, case2₂] > excllock > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
locker2_{remove_pending₂} > subtract₂ > [delete₁, case8₃] > [cons₂, tuple₂, record_update₃] > and₂ > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
locker2_{remove_pending₂} > subtract₂ > [delete₁, case8₃] > [cons₂, tuple₂, record_update₃] > [locker2_{check_available₁}, case6₁] > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
locker2_{remove_pending₂} > subtract₂ > [delete₁, case8₃] > [cons₂, tuple₂, record_update₃] > case9₃ > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
locker2_{remove_pending₂} > subtract₂ > [delete₁, case8₃] > [nil, locker2_{map_{add_pending₃}}] > [F, not] > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
locker2_{add_pending₃} > resource > [cons₂, tuple₂, record_update₃] > and₂ > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
locker2_{add_pending₃} > resource > [cons₂, tuple₂, record_update₃] > [locker2_{check_available₁}, case6₁] > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
locker2_{add_pending₃} > resource > [cons₂, tuple₂, record_update₃] > case9₃ > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
locker2_{add_pending₃} > resource > [F, not] > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
locker2_{add_pending₃} > case1₃ > pending > [cons₂, tuple₂, record_update₃] > and₂ > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
locker2_{add_pending₃} > case1₃ > pending > [cons₂, tuple₂, record_update₃] > [locker2_{check_available₁}, case6₁] > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
locker2_{add_pending₃} > case1₃ > pending > [cons₂, tuple₂, record_update₃] > case9₃ > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
locker2_{add_pending₃} > case1₃ > pending > [F, not] > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
locker2_{add_pending₃} > case1₃ > [record_updates₃, case2₂] > [cons₂, tuple₂, record_update₃] > and₂ > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
locker2_{add_pending₃} > case1₃ > [record_updates₃, case2₂] > [cons₂, tuple₂, record_update₃] > [locker2_{check_available₁}, case6₁] > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
locker2_{add_pending₃} > case1₃ > [record_updates₃, case2₂] > [cons₂, tuple₂, record_update₃] > case9₃ > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
locker2_{add_pending₃} > case1₃ > [record_updates₃, case2₂] > [nil, locker2_{map_{add_pending₃}}] > [F, not] > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
locker2_{add_pending₃} > case1₃ > [record_updates₃, case2₂] > excl > [F, not] > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
locker2_{add_pending₃} > case1₃ > [record_updates₃, case2₂] > excllock > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
locker2_{release_lock₂} > [record_updates₃, case2₂] > [cons₂, tuple₂, record_update₃] > and₂ > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
locker2_{release_lock₂} > [record_updates₃, case2₂] > [cons₂, tuple₂, record_update₃] > [locker2_{check_available₁}, case6₁] > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
locker2_{release_lock₂} > [record_updates₃, case2₂] > [cons₂, tuple₂, record_update₃] > case9₃ > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
locker2_{release_lock₂} > [record_updates₃, case2₂] > [nil, locker2_{map_{add_pending₃}}] > [F, not] > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
locker2_{release_lock₂} > [record_updates₃, case2₂] > excl > [F, not] > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
locker2_{release_lock₂} > [record_updates₃, case2₂] > excllock > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
case4₁ > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
locker2_{check_{availables₁}} > [true, locker2_{obtainables₁}, case5₂] > pending > [cons₂, tuple₂, record_update₃] > and₂ > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
locker2_{check_{availables₁}} > [true, locker2_{obtainables₁}, case5₂] > pending > [cons₂, tuple₂, record_update₃] > [locker2_{check_available₁}, case6₁] > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
locker2_{check_{availables₁}} > [true, locker2_{obtainables₁}, case5₂] > pending > [cons₂, tuple₂, record_update₃] > case9₃ > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
locker2_{check_{availables₁}} > [true, locker2_{obtainables₁}, case5₂] > pending > [F, not] > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
locker2_{check_{availables₁}} > [true, locker2_{obtainables₁}, case5₂] > [record_updates₃, case2₂] > [cons₂, tuple₂, record_update₃] > and₂ > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
locker2_{check_{availables₁}} > [true, locker2_{obtainables₁}, case5₂] > [record_updates₃, case2₂] > [cons₂, tuple₂, record_update₃] > [locker2_{check_available₁}, case6₁] > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
locker2_{check_{availables₁}} > [true, locker2_{obtainables₁}, case5₂] > [record_updates₃, case2₂] > [cons₂, tuple₂, record_update₃] > case9₃ > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
locker2_{check_{availables₁}} > [true, locker2_{obtainables₁}, case5₂] > [record_updates₃, case2₂] > [nil, locker2_{map_{add_pending₃}}] > [F, not] > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
locker2_{check_{availables₁}} > [true, locker2_{obtainables₁}, case5₂] > [record_updates₃, case2₂] > excl > [F, not] > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
locker2_{check_{availables₁}} > [true, locker2_{obtainables₁}, case5₂] > [record_updates₃, case2₂] > excllock > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
gen_tag₁ > [cons₂, tuple₂, record_update₃] > and₂ > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
gen_tag₁ > [cons₂, tuple₂, record_update₃] > [locker2_{check_available₁}, case6₁] > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
gen_tag₁ > [cons₂, tuple₂, record_update₃] > case9₃ > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
gen_tag₁ > tag > [F, not] > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
pops₁ > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
tops₁ > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
istops₂ > eqt₂ > [F, not] > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
istops₂ > eqt₂ > and₂ > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
eqc₂ > eqs₂ > eqt₂ > [F, not] > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
eqc₂ > eqs₂ > eqt₂ > and₂ > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
nocalls > empty > [F, not] > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
nocalls > [stack₂, pushs₂] > [F, not] > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
nocalls > [stack₂, pushs₂] > and₂ > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
nocalls > calls₃ > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
push₃ > push1₅ > [stack₂, pushs₂] > [F, not] > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
push₃ > push1₅ > [stack₂, pushs₂] > and₂ > [T, false, lock, mcrlrecord, locker2_obtainable, equal]
push₃ > push1₅ > calls₃ > [T, false, lock, mcrlrecord, locker2_obtainable, equal]

Status:

cons₂: [1,2]
pid₁: [1]
tuple₂: [1,2]
or₁: [1]
T: []
F: []
and₂: [1,2]
not: []
if₂: [1,2]
eq₂: [2,1]
eqt₂: [1,2]
nil: []
undefined: []
int: []
a: []
excl: []
false: []
lock: []
locker: []
mcrlrecord: []
ok: []
pending: []
release: []
request: []
resource: []
tag: []
true: []
s₁: [1]
0: []
record_new: []
record_update₃: [1,3,2]
record_updates₃: [2,3,1]
locker2_{map_{promote_pending₂}}: [1,2]
locker2_{promote_pending₂}: [1,2]
locker2_{map_{claim_lock₃}}: [3,2,1]
locker2_{claim_lock₃}: [3,2,1]
locker2_{map_{add_pending₃}}: [2,1,3]
case0₃: [2,1,3]
locker2_{remove_pending₂}: [2,1]
subtract₂: [2,1]
locker2_{add_pending₃}: [3,2,1]
case1₃: [1,2,3]
locker2_{release_lock₂}: [2,1]
case2₂: [1,2]
excllock: []
case4₁: [1]
locker2_{obtainables₁}: [1]
case5₂: [1,2]
locker2_obtainable: []
locker2_{check_available₁}: [1]
case6₁: [1]
equal: []
locker2_{check_{availables₁}}: [1]
delete₁: [1]
case8₃: [1,2,3]
gen_tag₁: [1]
case9₃: [1,2,3]
eqs₂: [1,2]
empty: []
stack₂: [1,2]
pushs₂: [1,2]
pops₁: [1]
tops₁: [1]
istops₂: [2,1]
eqc₂: [2,1]
nocalls: []
calls₃: [1,2,3]
push₃: [3,1,2]
push1₅: [3,5,1,4,2]

The following usable rules [FROCOS05] were oriented:

or(T, T) → T
or(F, T) → T
or(T, F) → T
or(F, F) → F
and(T, B) → B
and(B, T) → B
and(F, B) → F
and(B, F) → F
imp(T, B) → B
imp(F, B) → T
not(T) → F
not(F) → T
if(T, B1, B2) → B1
if(F, B1, B2) → B2
eq(T, T) → T
eq(F, F) → T
eq(T, F) → F
eq(F, T) → F
eqt(nil, undefined) → F
eqt(nil, pid(N2)) → F
eqt(nil, int(N2)) → F
eqt(nil, cons(H2, T2)) → F
eqt(nil, tuple(H2, T2)) → F
eqt(nil, tuplenil(H2)) → F
eqt(a, nil) → F
eqt(a, a) → T
eqt(a, excl) → F
eqt(a, false) → F
eqt(a, lock) → F
eqt(a, locker) → F
eqt(a, mcrlrecord) → F
eqt(a, ok) → F
eqt(a, pending) → F
eqt(a, release) → F
eqt(a, request) → F
eqt(a, resource) → F
eqt(a, tag) → F
eqt(a, true) → F
eqt(a, undefined) → F
eqt(a, pid(N2)) → F
eqt(a, int(N2)) → F
eqt(a, cons(H2, T2)) → F
eqt(a, tuple(H2, T2)) → F
eqt(a, tuplenil(H2)) → F
eqt(excl, nil) → F
eqt(excl, a) → F
eqt(excl, excl) → T
eqt(excl, false) → F
eqt(excl, lock) → F
eqt(excl, locker) → F
eqt(excl, mcrlrecord) → F
eqt(excl, ok) → F
eqt(excl, pending) → F
eqt(excl, release) → F
eqt(excl, request) → F
eqt(excl, resource) → F
eqt(excl, tag) → F
eqt(excl, true) → F
eqt(excl, undefined) → F
eqt(excl, pid(N2)) → F
eqt(excl, eqt(false, int(N2))) → F
eqt(false, cons(H2, T2)) → F
eqt(false, tuple(H2, T2)) → F
eqt(false, tuplenil(H2)) → F
eqt(lock, nil) → F
eqt(lock, a) → F
eqt(lock, excl) → F
eqt(lock, false) → F
eqt(lock, lock) → T
eqt(lock, locker) → F
eqt(lock, mcrlrecord) → F
eqt(lock, ok) → F
eqt(lock, pending) → F
eqt(lock, release) → F
eqt(lock, request) → F
eqt(lock, resource) → F
eqt(lock, tag) → F
eqt(lock, true) → F
eqt(lock, undefined) → F
eqt(lock, pid(N2)) → F
eqt(lock, int(N2)) → F
eqt(lock, cons(H2, T2)) → F
eqt(lock, tuple(H2, T2)) → F
eqt(lock, tuplenil(H2)) → F
eqt(locker, nil) → F
eqt(locker, a) → F
eqt(locker, excl) → F
eqt(locker, false) → F
eqt(locker, lock) → F
eqt(locker, locker) → T
eqt(locker, mcrlrecord) → F
eqt(locker, ok) → F
eqt(locker, pending) → F
eqt(locker, release) → F
eqt(locker, request) → F
eqt(locker, resource) → F
eqt(locker, tag) → F
eqt(locker, true) → F
eqt(locker, undefined) → F
eqt(locker, pid(N2)) → F
eqt(locker, int(N2)) → F
eqt(locker, cons(H2, T2)) → F
eqt(locker, tuple(H2, T2)) → F
eqt(locker, tuplenil(H2)) → F
eqt(mcrlrecord, nil) → F
eqt(mcrlrecord, a) → F
eqt(mcrlrecord, excl) → F
eqt(mcrlrecord, false) → F
eqt(mcrlrecord, lock) → F
eqt(mcrlrecord, locker) → F
eqt(mcrlrecord, mcrlrecord) → T
eqt(mcrlrecord, ok) → F
eqt(mcrlrecord, pending) → F
eqt(mcrlrecord, release) → F
eqt(mcrlrecord, request) → F
eqt(mcrlrecord, resource) → F
eqt(ok, resource) → F
eqt(ok, tag) → F
eqt(ok, true) → F
eqt(ok, undefined) → F
eqt(ok, pid(N2)) → F
eqt(ok, int(N2)) → F
eqt(ok, cons(H2, T2)) → F
eqt(ok, tuple(H2, T2)) → F
eqt(ok, tuplenil(H2)) → F
eqt(pending, nil) → F
eqt(pending, a) → F
eqt(pending, excl) → F
eqt(pending, false) → F
eqt(pending, lock) → F
eqt(pending, locker) → F
eqt(pending, mcrlrecord) → F
eqt(pending, ok) → F
eqt(pending, pending) → T
eqt(pending, release) → F
eqt(pending, request) → F
eqt(pending, resource) → F
eqt(pending, tag) → F
eqt(pending, true) → F
eqt(pending, undefined) → F
eqt(pending, pid(N2)) → F
eqt(pending, int(N2)) → F
eqt(pending, cons(H2, T2)) → F
eqt(pending, tuple(H2, T2)) → F
eqt(pending, tuplenil(H2)) → F
eqt(release, nil) → F
eqt(release, a) → F
eqt(release, excl) → F
eqt(release, false) → F
eqt(release, lock) → F
eqt(release, locker) → F
eqt(release, mcrlrecord) → F
eqt(release, ok) → F
eqt(request, mcrlrecord) → F
eqt(request, ok) → F
eqt(request, pending) → F
eqt(request, release) → F
eqt(request, request) → T
eqt(request, resource) → F
eqt(request, tag) → F
eqt(request, true) → F
eqt(request, undefined) → F
eqt(request, pid(N2)) → F
eqt(request, int(N2)) → F
eqt(request, cons(H2, T2)) → F
eqt(request, tuple(H2, T2)) → F
eqt(request, tuplenil(H2)) → F
eqt(resource, nil) → F
eqt(resource, a) → F
eqt(resource, excl) → F
eqt(resource, false) → F
eqt(resource, lock) → F
eqt(resource, locker) → F
eqt(resource, mcrlrecord) → F
eqt(resource, ok) → F
eqt(resource, pending) → F
eqt(resource, release) → F
eqt(resource, request) → F
eqt(resource, resource) → T
eqt(resource, tag) → F
eqt(resource, true) → F
eqt(resource, undefined) → F
eqt(resource, pid(N2)) → F
eqt(resource, int(N2)) → F
eqt(resource, cons(H2, T2)) → F
eqt(resource, tuple(H2, T2)) → F
eqt(resource, tuplenil(H2)) → F
eqt(tag, nil) → F
eqt(tag, a) → F
eqt(tag, excl) → F
eqt(tag, false) → F
eqt(tag, lock) → F
eqt(tag, locker) → F
eqt(tag, mcrlrecord) → F
eqt(tag, ok) → F
eqt(tag, pending) → F
eqt(tag, release) → F
eqt(tag, request) → F
eqt(tag, resource) → F
eqt(tag, tag) → T
eqt(tag, true) → F
eqt(tag, undefined) → F
eqt(tag, pid(N2)) → F
eqt(tag, int(N2)) → F
eqt(tag, cons(H2, T2)) → F
eqt(tag, tuple(H2, T2)) → F
eqt(tag, tuplenil(H2)) → F
eqt(true, nil) → F
eqt(true, a) → F
eqt(true, excl) → F
eqt(true, false) → F
eqt(true, lock) → F
eqt(true, locker) → F
eqt(true, mcrlrecord) → F
eqt(true, ok) → F
eqt(true, pending) → F
eqt(true, release) → F
eqt(true, request) → F
eqt(true, resource) → F
eqt(true, tag) → F
eqt(true, true) → T
eqt(true, undefined) → F
eqt(true, pid(N2)) → F
eqt(true, int(N2)) → F
eqt(true, cons(H2, T2)) → F
eqt(true, tuple(H2, T2)) → F
eqt(true, tuplenil(H2)) → F
eqt(undefined, nil) → F
eqt(undefined, a) → F
eqt(undefined, tuplenil(H2)) → F
eqt(pid(N1), nil) → F
eqt(pid(N1), a) → F
eqt(pid(N1), excl) → F
eqt(pid(N1), false) → F
eqt(pid(N1), lock) → F
eqt(pid(N1), locker) → F
eqt(pid(N1), mcrlrecord) → F
eqt(pid(N1), ok) → F
eqt(pid(N1), pending) → F
eqt(pid(N1), release) → F
eqt(pid(N1), request) → F
eqt(pid(N1), resource) → F
eqt(pid(N1), tag) → F
eqt(pid(N1), true) → F
eqt(pid(N1), undefined) → F
eqt(pid(N1), pid(N2)) → eqt(N1, N2)
eqt(pid(N1), int(N2)) → F
eqt(pid(N1), cons(H2, T2)) → F
eqt(pid(N1), tuple(H2, T2)) → F
eqt(pid(N1), tuplenil(H2)) → F
eqt(int(N1), nil) → F
eqt(int(N1), a) → F
eqt(int(N1), excl) → F
eqt(int(N1), false) → F
eqt(int(N1), lock) → F
eqt(int(N1), locker) → F
eqt(int(N1), mcrlrecord) → F
eqt(int(N1), ok) → F
eqt(int(N1), pending) → F
eqt(int(N1), release) → F
eqt(int(N1), request) → F
eqt(int(N1), resource) → F
eqt(int(N1), tag) → F
eqt(int(N1), true) → F
eqt(int(N1), undefined) → F
eqt(cons(H1, T1), resource) → F
eqt(cons(H1, T1), tag) → F
eqt(cons(H1, T1), true) → F
eqt(cons(H1, T1), undefined) → F
eqt(cons(H1, T1), pid(N2)) → F
eqt(cons(H1, T1), int(N2)) → F
eqt(cons(H1, T1), cons(H2, T2)) → and(eqt(H1, H2), eqt(T1, T2))
eqt(cons(H1, T1), tuple(H2, T2)) → F
eqt(cons(H1, T1), tuplenil(H2)) → F
eqt(tuple(H1, T1), nil) → F
eqt(tuple(H1, T1), a) → F
eqt(tuple(H1, T1), excl) → F
eqt(tuple(H1, T1), false) → F
eqt(tuple(H1, T1), lock) → F
eqt(tuple(H1, T1), locker) → F
eqt(tuple(H1, T1), mcrlrecord) → F
eqt(tuple(H1, T1), ok) → F
eqt(tuple(H1, T1), pending) → F
eqt(tuple(H1, T1), release) → F
eqt(tuple(H1, T1), request) → F
eqt(tuple(H1, T1), resource) → F
eqt(tuple(H1, T1), tag) → F
eqt(tuple(H1, T1), true) → F
eqt(tuple(H1, T1), undefined) → F
eqt(tuple(H1, T1), pid(N2)) → F
eqt(tuple(H1, T1), int(N2)) → F
eqt(tuple(H1, T1), cons(H2, T2)) → F
eqt(tuple(H1, T1), tuple(H2, T2)) → and(eqt(H1, H2), eqt(T1, T2))
eqt(tuple(H1, T1), tuplenil(H2)) → F
eqt(tuplenil(H1), nil) → F
eqt(tuplenil(H1), a) → F
eqt(tuplenil(H1), excl) → F
eqt(tuplenil(H1), false) → F
eqt(tuplenil(H1), lock) → F
eqt(tuplenil(H1), locker) → F
eqt(tuplenil(H1), mcrlrecord) → F
eqt(tuplenil(H1), ok) → F
eqt(tuplenil(H1), pending) → F
eqt(tuplenil(H1), release) → F
eqt(tuplenil(H1), request) → F
eqt(tuplenil(H1), resource) → F
eqt(tuplenil(H1), tag) → F
eqt(tuplenil(H1), true) → F
eqt(tuplenil(H1), undefined) → F
eqt(tuplenil(H1), pid(N2)) → F
eqt(tuplenil(H1), int(N2)) → F
eqt(tuplenil(H1), cons(H2, T2)) → F
eqt(tuplenil(H1), tuple(H2, T2)) → F
eqt(tuplenil(H1), tuplenil(H2)) → eqt(H1, H2)
element(int(s(0)), tuplenil(T1)) → T1
element(int(s(0)), tuple(T1, T2)) → T1
element(int(s(s(N1))), tuple(T1, T2)) → element(int(s(N1)), T2)
record_new(lock) → tuple(mcrlrecord, tuple(lock, tuple(undefined, tuple(nil, tuplenil(nil)))))
record_extract(tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))), lock, resource) → tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2)))))
record_update(tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))), lock, pending, NewF) → tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(NewF)))))
record_updates(Record, Name, nil) → Record
record_updates(Record, Name, cons(tuple(Field, tuplenil(NewF)), Fields)) → record_updates(record_update(Record, Name, Field, NewF), Name, Fields)
locker2_map_promote_pending(nil, Pending) → nil
locker2_map_promote_pending(cons(Lock, Locks), Pending) → cons(locker2_promote_pending(Lock, Pending), locker2_map_promote_pending(Locks, Pending))
locker2_map_claim_lock(nil, Resources, Client) → nil
locker2_map_claim_lock(cons(Lock, Locks), Resources, Client) → cons(locker2_claim_lock(Lock, Resources, Client), locker2_map_claim_lock(Locks, Resources, Client))
locker2_map_add_pending(nil, Resources, Client) → nil
locker2_promote_pending(Lock, Client) → case0(Client, Lock, record_extract(Lock, lock, pending))
case0(Client, Lock, cons(Client, Pendings)) → record_updates(Lock, lock, cons(tuple(excl, tuplenil(Client)), cons(tuple(pending, tuplenil(Pendings)), nil)))
case0(Client, Lock, MCRLFree0) → Lock
locker2_remove_pending(Lock, Client) → record_updates(Lock, lock, cons(tuple(pending, tuplenil(subtract(record_extract(Lock, lock, pending), cons(Client, nil)))), nil))
locker2_add_pending(Lock, Resources, Client) → case1(Client, Resources, Lock, member(record_extract(Lock, lock, resource), Resources))
case1(Client, Resources, Lock, true) → record_updates(Lock, lock, cons(tuple(pending, tuplenil(append(record_extract(Lock, lock, pending), cons(Client, nil)))), nil))
case1(Client, Resources, Lock, false) → Lock
locker2_release_lock(Lock, Client) → case2(Client, Lock, gen_modtageq(Client, record_extract(Lock, lock, excl)))
case2(Client, Lock, true) → record_updates(Lock, lock, cons(tuple(excllock, excl), nil))
case4(Client, Lock, MCRLFree1) → false
locker2_obtainables(nil, Client) → true
locker2_obtainables(cons(Lock, Locks), Client) → case5(Client, Locks, Lock, member(Client, record_extract(Lock, lock, pending)))
case5(Client, Locks, Lock, true) → andt(locker2_obtainable(Lock, Client), locker2_obtainables(Locks, Client))
case5(Client, Locks, Lock, false) → locker2_obtainables(Locks, Client)
locker2_check_available(Resource, nil) → false
locker2_check_available(Resource, cons(Lock, Locks)) → case6(Locks, Lock, Resource, equal(Resource, record_extract(Lock, lock, resource)))
case6(Locks, Lock, Resource, true) → andt(equal(record_extract(Lock, lock, excl), nil), equal(record_extract(Lock, lock, pending), nil))
case6(Locks, Lock, Resource, false) → locker2_check_available(Resource, Locks)
locker2_check_availables(nil, Locks) → true
locker2_check_availables(cons(Resource, Resources), Locks) → andt(locker2_check_available(Resource, Locks), locker2_check_availables(Resources, Locks))
locker2_adduniq(nil, List) → List
append(cons(Head, Tail), List) → cons(Head, append(Tail, List))
subtract(List, nil) → List
subtract(List, cons(Head, Tail)) → subtract(delete(Head, List), Tail)
delete(E, nil) → nil
delete(E, cons(Head, Tail)) → case8(Tail, Head, E, equal(E, Head))
case8(Tail, Head, E, true) → Tail
case8(Tail, Head, E, false) → cons(Head, delete(E, Tail))
gen_tag(Pid) → tuple(Pid, tuplenil(tag))
gen_modtageq(Client1, Client2) → equal(Client1, Client2)
member(E, nil) → false
member(E, cons(Head, Tail)) → case9(Tail, Head, E, equal(E, Head))
case9(Tail, Head, E, true) → true
case9(Tail, Head, E, false) → member(E, Tail)
eqs(empty, empty) → T
eqs(empty, stack(E2, S2)) → F
eqs(stack(E1, S1), empty) → F
eqs(stack(E1, S1), stack(E2, S2)) → and(eqt(E1, E2), eqs(S1, S2))
pushs(E1, S1) → stack(E1, S1)
pops(stack(E1, S1)) → S1
tops(stack(E1, S1)) → E1
istops(E1, empty) → F
istops(E1, stack(E2, S1)) → eqt(E1, E2)
eqc(nocalls, nocalls) → T
eqc(nocalls, calls(E2, S2, CS2)) → F
eqc(calls(E1, S1, CS1), nocalls) → F
eqc(calls(E1, S1, CS1), calls(E2, S2, CS2)) → and(eqt(E1, E2), and(eqs(S1, S2), eqc(CS1, CS2)))
push(E1, E2, nocalls) → calls(E1, stack(E2, empty), nocalls)
push(E1, E2, calls(E3, S1, CS1)) → push1(E1, E2, E3, S1, CS1, eqt(E1, E3))
push1(E1, E2, E3, S1, CS1, T) → calls(E3, pushs(E2, S1), CS1)

(42) Obligation:

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

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

The TRS R consists of the following rules:

or(T, T) → T
or(F, T) → T
or(T, F) → T
or(F, F) → F
and(T, B) → B
and(B, T) → B
and(F, B) → F
and(B, F) → F
imp(T, B) → B
imp(F, B) → T
not(T) → F
not(F) → T
if(T, B1, B2) → B1
if(F, B1, B2) → B2
eq(T, T) → T
eq(F, F) → T
eq(T, F) → F
eq(F, T) → F
eqt(nil, undefined) → F
eqt(nil, pid(N2)) → F
eqt(nil, int(N2)) → F
eqt(nil, cons(H2, T2)) → F
eqt(nil, tuple(H2, T2)) → F
eqt(nil, tuplenil(H2)) → F
eqt(a, nil) → F
eqt(a, a) → T
eqt(a, excl) → F
eqt(a, false) → F
eqt(a, lock) → F
eqt(a, locker) → F
eqt(a, mcrlrecord) → F
eqt(a, ok) → F
eqt(a, pending) → F
eqt(a, release) → F
eqt(a, request) → F
eqt(a, resource) → F
eqt(a, tag) → F
eqt(a, true) → F
eqt(a, undefined) → F
eqt(a, pid(N2)) → F
eqt(a, int(N2)) → F
eqt(a, cons(H2, T2)) → F
eqt(a, tuple(H2, T2)) → F
eqt(a, tuplenil(H2)) → F
eqt(excl, nil) → F
eqt(excl, a) → F
eqt(excl, excl) → T
eqt(excl, false) → F
eqt(excl, lock) → F
eqt(excl, locker) → F
eqt(excl, mcrlrecord) → F
eqt(excl, ok) → F
eqt(excl, pending) → F
eqt(excl, release) → F
eqt(excl, request) → F
eqt(excl, resource) → F
eqt(excl, tag) → F
eqt(excl, true) → F
eqt(excl, undefined) → F
eqt(excl, pid(N2)) → F
eqt(excl, eqt(false, int(N2))) → F
eqt(false, cons(H2, T2)) → F
eqt(false, tuple(H2, T2)) → F
eqt(false, tuplenil(H2)) → F
eqt(lock, nil) → F
eqt(lock, a) → F
eqt(lock, excl) → F
eqt(lock, false) → F
eqt(lock, lock) → T
eqt(lock, locker) → F
eqt(lock, mcrlrecord) → F
eqt(lock, ok) → F
eqt(lock, pending) → F
eqt(lock, release) → F
eqt(lock, request) → F
eqt(lock, resource) → F
eqt(lock, tag) → F
eqt(lock, true) → F
eqt(lock, undefined) → F
eqt(lock, pid(N2)) → F
eqt(lock, int(N2)) → F
eqt(lock, cons(H2, T2)) → F
eqt(lock, tuple(H2, T2)) → F
eqt(lock, tuplenil(H2)) → F
eqt(locker, nil) → F
eqt(locker, a) → F
eqt(locker, excl) → F
eqt(locker, false) → F
eqt(locker, lock) → F
eqt(locker, locker) → T
eqt(locker, mcrlrecord) → F
eqt(locker, ok) → F
eqt(locker, pending) → F
eqt(locker, release) → F
eqt(locker, request) → F
eqt(locker, resource) → F
eqt(locker, tag) → F
eqt(locker, true) → F
eqt(locker, undefined) → F
eqt(locker, pid(N2)) → F
eqt(locker, int(N2)) → F
eqt(locker, cons(H2, T2)) → F
eqt(locker, tuple(H2, T2)) → F
eqt(locker, tuplenil(H2)) → F
eqt(mcrlrecord, nil) → F
eqt(mcrlrecord, a) → F
eqt(mcrlrecord, excl) → F
eqt(mcrlrecord, false) → F
eqt(mcrlrecord, lock) → F
eqt(mcrlrecord, locker) → F
eqt(mcrlrecord, mcrlrecord) → T
eqt(mcrlrecord, ok) → F
eqt(mcrlrecord, pending) → F
eqt(mcrlrecord, release) → F
eqt(mcrlrecord, request) → F
eqt(mcrlrecord, resource) → F
eqt(ok, resource) → F
eqt(ok, tag) → F
eqt(ok, true) → F
eqt(ok, undefined) → F
eqt(ok, pid(N2)) → F
eqt(ok, int(N2)) → F
eqt(ok, cons(H2, T2)) → F
eqt(ok, tuple(H2, T2)) → F
eqt(ok, tuplenil(H2)) → F
eqt(pending, nil) → F
eqt(pending, a) → F
eqt(pending, excl) → F
eqt(pending, false) → F
eqt(pending, lock) → F
eqt(pending, locker) → F
eqt(pending, mcrlrecord) → F
eqt(pending, ok) → F
eqt(pending, pending) → T
eqt(pending, release) → F
eqt(pending, request) → F
eqt(pending, resource) → F
eqt(pending, tag) → F
eqt(pending, true) → F
eqt(pending, undefined) → F
eqt(pending, pid(N2)) → F
eqt(pending, int(N2)) → F
eqt(pending, cons(H2, T2)) → F
eqt(pending, tuple(H2, T2)) → F
eqt(pending, tuplenil(H2)) → F
eqt(release, nil) → F
eqt(release, a) → F
eqt(release, excl) → F
eqt(release, false) → F
eqt(release, lock) → F
eqt(release, locker) → F
eqt(release, mcrlrecord) → F
eqt(release, ok) → F
eqt(request, mcrlrecord) → F
eqt(request, ok) → F
eqt(request, pending) → F
eqt(request, release) → F
eqt(request, request) → T
eqt(request, resource) → F
eqt(request, tag) → F
eqt(request, true) → F
eqt(request, undefined) → F
eqt(request, pid(N2)) → F
eqt(request, int(N2)) → F
eqt(request, cons(H2, T2)) → F
eqt(request, tuple(H2, T2)) → F
eqt(request, tuplenil(H2)) → F
eqt(resource, nil) → F
eqt(resource, a) → F
eqt(resource, excl) → F
eqt(resource, false) → F
eqt(resource, lock) → F
eqt(resource, locker) → F
eqt(resource, mcrlrecord) → F
eqt(resource, ok) → F
eqt(resource, pending) → F
eqt(resource, release) → F
eqt(resource, request) → F
eqt(resource, resource) → T
eqt(resource, tag) → F
eqt(resource, true) → F
eqt(resource, undefined) → F
eqt(resource, pid(N2)) → F
eqt(resource, int(N2)) → F
eqt(resource, cons(H2, T2)) → F
eqt(resource, tuple(H2, T2)) → F
eqt(resource, tuplenil(H2)) → F
eqt(tag, nil) → F
eqt(tag, a) → F
eqt(tag, excl) → F
eqt(tag, false) → F
eqt(tag, lock) → F
eqt(tag, locker) → F
eqt(tag, mcrlrecord) → F
eqt(tag, ok) → F
eqt(tag, pending) → F
eqt(tag, release) → F
eqt(tag, request) → F
eqt(tag, resource) → F
eqt(tag, tag) → T
eqt(tag, true) → F
eqt(tag, undefined) → F
eqt(tag, pid(N2)) → F
eqt(tag, int(N2)) → F
eqt(tag, cons(H2, T2)) → F
eqt(tag, tuple(H2, T2)) → F
eqt(tag, tuplenil(H2)) → F
eqt(true, nil) → F
eqt(true, a) → F
eqt(true, excl) → F
eqt(true, false) → F
eqt(true, lock) → F
eqt(true, locker) → F
eqt(true, mcrlrecord) → F
eqt(true, ok) → F
eqt(true, pending) → F
eqt(true, release) → F
eqt(true, request) → F
eqt(true, resource) → F
eqt(true, tag) → F
eqt(true, true) → T
eqt(true, undefined) → F
eqt(true, pid(N2)) → F
eqt(true, int(N2)) → F
eqt(true, cons(H2, T2)) → F
eqt(true, tuple(H2, T2)) → F
eqt(true, tuplenil(H2)) → F
eqt(undefined, nil) → F
eqt(undefined, a) → F
eqt(undefined, tuplenil(H2)) → F
eqt(pid(N1), nil) → F
eqt(pid(N1), a) → F
eqt(pid(N1), excl) → F
eqt(pid(N1), false) → F
eqt(pid(N1), lock) → F
eqt(pid(N1), locker) → F
eqt(pid(N1), mcrlrecord) → F
eqt(pid(N1), ok) → F
eqt(pid(N1), pending) → F
eqt(pid(N1), release) → F
eqt(pid(N1), request) → F
eqt(pid(N1), resource) → F
eqt(pid(N1), tag) → F
eqt(pid(N1), true) → F
eqt(pid(N1), undefined) → F
eqt(pid(N1), pid(N2)) → eqt(N1, N2)
eqt(pid(N1), int(N2)) → F
eqt(pid(N1), cons(H2, T2)) → F
eqt(pid(N1), tuple(H2, T2)) → F
eqt(pid(N1), tuplenil(H2)) → F
eqt(int(N1), nil) → F
eqt(int(N1), a) → F
eqt(int(N1), excl) → F
eqt(int(N1), false) → F
eqt(int(N1), lock) → F
eqt(int(N1), locker) → F
eqt(int(N1), mcrlrecord) → F
eqt(int(N1), ok) → F
eqt(int(N1), pending) → F
eqt(int(N1), release) → F
eqt(int(N1), request) → F
eqt(int(N1), resource) → F
eqt(int(N1), tag) → F
eqt(int(N1), true) → F
eqt(int(N1), undefined) → F
eqt(cons(H1, T1), resource) → F
eqt(cons(H1, T1), tag) → F
eqt(cons(H1, T1), true) → F
eqt(cons(H1, T1), undefined) → F
eqt(cons(H1, T1), pid(N2)) → F
eqt(cons(H1, T1), int(N2)) → F
eqt(cons(H1, T1), cons(H2, T2)) → and(eqt(H1, H2), eqt(T1, T2))
eqt(cons(H1, T1), tuple(H2, T2)) → F
eqt(cons(H1, T1), tuplenil(H2)) → F
eqt(tuple(H1, T1), nil) → F
eqt(tuple(H1, T1), a) → F
eqt(tuple(H1, T1), excl) → F
eqt(tuple(H1, T1), false) → F
eqt(tuple(H1, T1), lock) → F
eqt(tuple(H1, T1), locker) → F
eqt(tuple(H1, T1), mcrlrecord) → F
eqt(tuple(H1, T1), ok) → F
eqt(tuple(H1, T1), pending) → F
eqt(tuple(H1, T1), release) → F
eqt(tuple(H1, T1), request) → F
eqt(tuple(H1, T1), resource) → F
eqt(tuple(H1, T1), tag) → F
eqt(tuple(H1, T1), true) → F
eqt(tuple(H1, T1), undefined) → F
eqt(tuple(H1, T1), pid(N2)) → F
eqt(tuple(H1, T1), int(N2)) → F
eqt(tuple(H1, T1), cons(H2, T2)) → F
eqt(tuple(H1, T1), tuple(H2, T2)) → and(eqt(H1, H2), eqt(T1, T2))
eqt(tuple(H1, T1), tuplenil(H2)) → F
eqt(tuplenil(H1), nil) → F
eqt(tuplenil(H1), a) → F
eqt(tuplenil(H1), excl) → F
eqt(tuplenil(H1), false) → F
eqt(tuplenil(H1), lock) → F
eqt(tuplenil(H1), locker) → F
eqt(tuplenil(H1), mcrlrecord) → F
eqt(tuplenil(H1), ok) → F
eqt(tuplenil(H1), pending) → F
eqt(tuplenil(H1), release) → F
eqt(tuplenil(H1), request) → F
eqt(tuplenil(H1), resource) → F
eqt(tuplenil(H1), tag) → F
eqt(tuplenil(H1), true) → F
eqt(tuplenil(H1), undefined) → F
eqt(tuplenil(H1), pid(N2)) → F
eqt(tuplenil(H1), int(N2)) → F
eqt(tuplenil(H1), cons(H2, T2)) → F
eqt(tuplenil(H1), tuple(H2, T2)) → F
eqt(tuplenil(H1), tuplenil(H2)) → eqt(H1, H2)
element(int(s(0)), tuplenil(T1)) → T1
element(int(s(0)), tuple(T1, T2)) → T1
element(int(s(s(N1))), tuple(T1, T2)) → element(int(s(N1)), T2)
record_new(lock) → tuple(mcrlrecord, tuple(lock, tuple(undefined, tuple(nil, tuplenil(nil)))))
record_extract(tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))), lock, resource) → tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2)))))
record_update(tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))), lock, pending, NewF) → tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(NewF)))))
record_updates(Record, Name, nil) → Record
record_updates(Record, Name, cons(tuple(Field, tuplenil(NewF)), Fields)) → record_updates(record_update(Record, Name, Field, NewF), Name, Fields)
locker2_map_promote_pending(nil, Pending) → nil
locker2_map_promote_pending(cons(Lock, Locks), Pending) → cons(locker2_promote_pending(Lock, Pending), locker2_map_promote_pending(Locks, Pending))
locker2_map_claim_lock(nil, Resources, Client) → nil
locker2_map_claim_lock(cons(Lock, Locks), Resources, Client) → cons(locker2_claim_lock(Lock, Resources, Client), locker2_map_claim_lock(Locks, Resources, Client))
locker2_map_add_pending(nil, Resources, Client) → nil
locker2_promote_pending(Lock, Client) → case0(Client, Lock, record_extract(Lock, lock, pending))
case0(Client, Lock, cons(Client, Pendings)) → record_updates(Lock, lock, cons(tuple(excl, tuplenil(Client)), cons(tuple(pending, tuplenil(Pendings)), nil)))
case0(Client, Lock, MCRLFree0) → Lock
locker2_remove_pending(Lock, Client) → record_updates(Lock, lock, cons(tuple(pending, tuplenil(subtract(record_extract(Lock, lock, pending), cons(Client, nil)))), nil))
locker2_add_pending(Lock, Resources, Client) → case1(Client, Resources, Lock, member(record_extract(Lock, lock, resource), Resources))
case1(Client, Resources, Lock, true) → record_updates(Lock, lock, cons(tuple(pending, tuplenil(append(record_extract(Lock, lock, pending), cons(Client, nil)))), nil))
case1(Client, Resources, Lock, false) → Lock
locker2_release_lock(Lock, Client) → case2(Client, Lock, gen_modtageq(Client, record_extract(Lock, lock, excl)))
case2(Client, Lock, true) → record_updates(Lock, lock, cons(tuple(excllock, excl), nil))
case4(Client, Lock, MCRLFree1) → false
locker2_obtainables(nil, Client) → true
locker2_obtainables(cons(Lock, Locks), Client) → case5(Client, Locks, Lock, member(Client, record_extract(Lock, lock, pending)))
case5(Client, Locks, Lock, true) → andt(locker2_obtainable(Lock, Client), locker2_obtainables(Locks, Client))
case5(Client, Locks, Lock, false) → locker2_obtainables(Locks, Client)
locker2_check_available(Resource, nil) → false
locker2_check_available(Resource, cons(Lock, Locks)) → case6(Locks, Lock, Resource, equal(Resource, record_extract(Lock, lock, resource)))
case6(Locks, Lock, Resource, true) → andt(equal(record_extract(Lock, lock, excl), nil), equal(record_extract(Lock, lock, pending), nil))
case6(Locks, Lock, Resource, false) → locker2_check_available(Resource, Locks)
locker2_check_availables(nil, Locks) → true
locker2_check_availables(cons(Resource, Resources), Locks) → andt(locker2_check_available(Resource, Locks), locker2_check_availables(Resources, Locks))
locker2_adduniq(nil, List) → List
append(cons(Head, Tail), List) → cons(Head, append(Tail, List))
subtract(List, nil) → List
subtract(List, cons(Head, Tail)) → subtract(delete(Head, List), Tail)
delete(E, nil) → nil
delete(E, cons(Head, Tail)) → case8(Tail, Head, E, equal(E, Head))
case8(Tail, Head, E, true) → Tail
case8(Tail, Head, E, false) → cons(Head, delete(E, Tail))
gen_tag(Pid) → tuple(Pid, tuplenil(tag))
gen_modtageq(Client1, Client2) → equal(Client1, Client2)
member(E, nil) → false
member(E, cons(Head, Tail)) → case9(Tail, Head, E, equal(E, Head))
case9(Tail, Head, E, true) → true
case9(Tail, Head, E, false) → member(E, Tail)
eqs(empty, empty) → T
eqs(empty, stack(E2, S2)) → F
eqs(stack(E1, S1), empty) → F
eqs(stack(E1, S1), stack(E2, S2)) → and(eqt(E1, E2), eqs(S1, S2))
pushs(E1, S1) → stack(E1, S1)
pops(stack(E1, S1)) → S1
tops(stack(E1, S1)) → E1
istops(E1, empty) → F
istops(E1, stack(E2, S1)) → eqt(E1, E2)
eqc(nocalls, nocalls) → T
eqc(nocalls, calls(E2, S2, CS2)) → F
eqc(calls(E1, S1, CS1), nocalls) → F
eqc(calls(E1, S1, CS1), calls(E2, S2, CS2)) → and(eqt(E1, E2), and(eqs(S1, S2), eqc(CS1, CS2)))
push(E1, E2, nocalls) → calls(E1, stack(E2, empty), nocalls)
push(E1, E2, calls(E3, S1, CS1)) → push1(E1, E2, E3, S1, CS1, eqt(E1, E3))
push1(E1, E2, E3, S1, CS1, T) → calls(E3, pushs(E2, S1), CS1)

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

(43) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

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

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
EQT(x1, x2) = x2
tuplenil(x1) = tuplenil(x1)
or(x1, x2) = x2
T = T
F = F
and(x1, x2) = and(x1, x2)
imp(x1, x2) = x2
not(x1) = not
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) = pid(x1)
int(x1) = 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) = s
0 = 0
record_new(x1) = record_new(x1)
record_extract(x1, x2, x3) = x1
record_update(x1, x2, x3, x4) = record_update(x1, x2, x3, x4)
record_updates(x1, x2, x3) = record_updates(x1, x2, x3)
locker2_map_promote_pending(x1, x2) = locker2_map_promote_pending(x1, x2)
locker2_promote_pending(x1, x2) = locker2_promote_pending(x1, x2)
locker2_map_claim_lock(x1, x2, x3) = 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(x1, x2, x3, x4)
member(x1, x2) = member(x1)
append(x1, x2) = append(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) = x1
case5(x1, x2, x3, x4) = case5(x2)
andt(x1, x2) = andt
locker2_obtainable(x1, x2) = locker2_obtainable(x1, x2)
locker2_check_available(x1, x2) = locker2_check_available(x2)
case6(x1, x2, x3, x4) = case6(x1)
equal(x1, x2) = equal(x1)
locker2_check_availables(x1, x2) = locker2_check_availables(x1, x2)
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(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:

not > [F, tuple₂, locker, release, request, s, nocalls] > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
if₂ > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
eq₂ > [F, tuple₂, locker, release, request, s, nocalls] > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
pid₁ > [eqt₂, push₃] > and₂ > [F, tuple₂, locker, release, request, s, nocalls] > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
pid₁ > [eqt₂, push₃] > push1₆ > pushs₂ > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
a > [F, tuple₂, locker, release, request, s, nocalls] > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
ok > [F, tuple₂, locker, release, request, s, nocalls] > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
[resource, locker2_{add_pending₃}] > case1₄ > record_updates₃ > [tuplenil₁, record_update₄] > [eqt₂, push₃] > and₂ > [F, tuple₂, locker, release, request, s, nocalls] > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
[resource, locker2_{add_pending₃}] > case1₄ > record_updates₃ > [tuplenil₁, record_update₄] > [eqt₂, push₃] > push1₆ > pushs₂ > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
[resource, locker2_{add_pending₃}] > case1₄ > record_updates₃ > [tuplenil₁, record_update₄] > mcrlrecord > [F, tuple₂, locker, release, request, s, nocalls] > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
[resource, locker2_{add_pending₃}] > case1₄ > append₁ > [cons₂, equal₁, locker2_{check_{availables₂}}] > [tuplenil₁, record_update₄] > [eqt₂, push₃] > and₂ > [F, tuple₂, locker, release, request, s, nocalls] > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
[resource, locker2_{add_pending₃}] > case1₄ > append₁ > [cons₂, equal₁, locker2_{check_{availables₂}}] > [tuplenil₁, record_update₄] > [eqt₂, push₃] > push1₆ > pushs₂ > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
[resource, locker2_{add_pending₃}] > case1₄ > append₁ > [cons₂, equal₁, locker2_{check_{availables₂}}] > [tuplenil₁, record_update₄] > mcrlrecord > [F, tuple₂, locker, release, request, s, nocalls] > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
[resource, locker2_{add_pending₃}] > case1₄ > append₁ > [cons₂, equal₁, locker2_{check_{availables₂}}] > [case5₁, andt, case6₁] > [nil, true, locker2_{map_{add_pending}}] > excl > [F, tuple₂, locker, release, request, s, nocalls] > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
[resource, locker2_{add_pending₃}] > case1₄ > append₁ > [cons₂, equal₁, locker2_{check_{availables₂}}] > [case5₁, andt, case6₁] > [nil, true, locker2_{map_{add_pending}}] > locker2_{obtainable₂} > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
[resource, locker2_{add_pending₃}] > case1₄ > append₁ > [cons₂, equal₁, locker2_{check_{availables₂}}] > [case5₁, andt, case6₁] > locker2_{check_available₁} > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
[resource, locker2_{add_pending₃}] > [member₁, case9₁] > [cons₂, equal₁, locker2_{check_{availables₂}}] > [tuplenil₁, record_update₄] > [eqt₂, push₃] > and₂ > [F, tuple₂, locker, release, request, s, nocalls] > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
[resource, locker2_{add_pending₃}] > [member₁, case9₁] > [cons₂, equal₁, locker2_{check_{availables₂}}] > [tuplenil₁, record_update₄] > [eqt₂, push₃] > push1₆ > pushs₂ > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
[resource, locker2_{add_pending₃}] > [member₁, case9₁] > [cons₂, equal₁, locker2_{check_{availables₂}}] > [tuplenil₁, record_update₄] > mcrlrecord > [F, tuple₂, locker, release, request, s, nocalls] > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
[resource, locker2_{add_pending₃}] > [member₁, case9₁] > [cons₂, equal₁, locker2_{check_{availables₂}}] > [case5₁, andt, case6₁] > [nil, true, locker2_{map_{add_pending}}] > excl > [F, tuple₂, locker, release, request, s, nocalls] > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
[resource, locker2_{add_pending₃}] > [member₁, case9₁] > [cons₂, equal₁, locker2_{check_{availables₂}}] > [case5₁, andt, case6₁] > [nil, true, locker2_{map_{add_pending}}] > locker2_{obtainable₂} > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
[resource, locker2_{add_pending₃}] > [member₁, case9₁] > [cons₂, equal₁, locker2_{check_{availables₂}}] > [case5₁, andt, case6₁] > locker2_{check_available₁} > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
0 > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
record_new₁ > [tuplenil₁, record_update₄] > [eqt₂, push₃] > and₂ > [F, tuple₂, locker, release, request, s, nocalls] > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
record_new₁ > [tuplenil₁, record_update₄] > [eqt₂, push₃] > push1₆ > pushs₂ > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
record_new₁ > [tuplenil₁, record_update₄] > mcrlrecord > [F, tuple₂, locker, release, request, s, nocalls] > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
record_new₁ > [nil, true, locker2_{map_{add_pending}}] > excl > [F, tuple₂, locker, release, request, s, nocalls] > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
record_new₁ > [nil, true, locker2_{map_{add_pending}}] > locker2_{obtainable₂} > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
record_new₁ > undefined > [F, tuple₂, locker, release, request, s, nocalls] > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
locker2_{map_{promote_pending₂}} > locker2_{promote_pending₂} > case0₂ > [cons₂, equal₁, locker2_{check_{availables₂}}] > [tuplenil₁, record_update₄] > [eqt₂, push₃] > and₂ > [F, tuple₂, locker, release, request, s, nocalls] > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
locker2_{map_{promote_pending₂}} > locker2_{promote_pending₂} > case0₂ > [cons₂, equal₁, locker2_{check_{availables₂}}] > [tuplenil₁, record_update₄] > [eqt₂, push₃] > push1₆ > pushs₂ > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
locker2_{map_{promote_pending₂}} > locker2_{promote_pending₂} > case0₂ > [cons₂, equal₁, locker2_{check_{availables₂}}] > [tuplenil₁, record_update₄] > mcrlrecord > [F, tuple₂, locker, release, request, s, nocalls] > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
locker2_{map_{promote_pending₂}} > locker2_{promote_pending₂} > case0₂ > [cons₂, equal₁, locker2_{check_{availables₂}}] > [case5₁, andt, case6₁] > [nil, true, locker2_{map_{add_pending}}] > excl > [F, tuple₂, locker, release, request, s, nocalls] > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
locker2_{map_{promote_pending₂}} > locker2_{promote_pending₂} > case0₂ > [cons₂, equal₁, locker2_{check_{availables₂}}] > [case5₁, andt, case6₁] > [nil, true, locker2_{map_{add_pending}}] > locker2_{obtainable₂} > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
locker2_{map_{promote_pending₂}} > locker2_{promote_pending₂} > case0₂ > [cons₂, equal₁, locker2_{check_{availables₂}}] > [case5₁, andt, case6₁] > locker2_{check_available₁} > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
locker2_{map_{promote_pending₂}} > locker2_{promote_pending₂} > case0₂ > record_updates₃ > [tuplenil₁, record_update₄] > [eqt₂, push₃] > and₂ > [F, tuple₂, locker, release, request, s, nocalls] > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
locker2_{map_{promote_pending₂}} > locker2_{promote_pending₂} > case0₂ > record_updates₃ > [tuplenil₁, record_update₄] > [eqt₂, push₃] > push1₆ > pushs₂ > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
locker2_{map_{promote_pending₂}} > locker2_{promote_pending₂} > case0₂ > record_updates₃ > [tuplenil₁, record_update₄] > mcrlrecord > [F, tuple₂, locker, release, request, s, nocalls] > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
locker2_{remove_pending₂} > record_updates₃ > [tuplenil₁, record_update₄] > [eqt₂, push₃] > and₂ > [F, tuple₂, locker, release, request, s, nocalls] > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
locker2_{remove_pending₂} > record_updates₃ > [tuplenil₁, record_update₄] > [eqt₂, push₃] > push1₆ > pushs₂ > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
locker2_{remove_pending₂} > record_updates₃ > [tuplenil₁, record_update₄] > mcrlrecord > [F, tuple₂, locker, release, request, s, nocalls] > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
locker2_{remove_pending₂} > subtract₂ > [delete₂, case8₃] > [cons₂, equal₁, locker2_{check_{availables₂}}] > [tuplenil₁, record_update₄] > [eqt₂, push₃] > and₂ > [F, tuple₂, locker, release, request, s, nocalls] > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
locker2_{remove_pending₂} > subtract₂ > [delete₂, case8₃] > [cons₂, equal₁, locker2_{check_{availables₂}}] > [tuplenil₁, record_update₄] > [eqt₂, push₃] > push1₆ > pushs₂ > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
locker2_{remove_pending₂} > subtract₂ > [delete₂, case8₃] > [cons₂, equal₁, locker2_{check_{availables₂}}] > [tuplenil₁, record_update₄] > mcrlrecord > [F, tuple₂, locker, release, request, s, nocalls] > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
locker2_{remove_pending₂} > subtract₂ > [delete₂, case8₃] > [cons₂, equal₁, locker2_{check_{availables₂}}] > [case5₁, andt, case6₁] > [nil, true, locker2_{map_{add_pending}}] > excl > [F, tuple₂, locker, release, request, s, nocalls] > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
locker2_{remove_pending₂} > subtract₂ > [delete₂, case8₃] > [cons₂, equal₁, locker2_{check_{availables₂}}] > [case5₁, andt, case6₁] > [nil, true, locker2_{map_{add_pending}}] > locker2_{obtainable₂} > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
locker2_{remove_pending₂} > subtract₂ > [delete₂, case8₃] > [cons₂, equal₁, locker2_{check_{availables₂}}] > [case5₁, andt, case6₁] > locker2_{check_available₁} > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
locker2_{release_lock₂} > case2₃ > [cons₂, equal₁, locker2_{check_{availables₂}}] > [tuplenil₁, record_update₄] > [eqt₂, push₃] > and₂ > [F, tuple₂, locker, release, request, s, nocalls] > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
locker2_{release_lock₂} > case2₃ > [cons₂, equal₁, locker2_{check_{availables₂}}] > [tuplenil₁, record_update₄] > [eqt₂, push₃] > push1₆ > pushs₂ > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
locker2_{release_lock₂} > case2₃ > [cons₂, equal₁, locker2_{check_{availables₂}}] > [tuplenil₁, record_update₄] > mcrlrecord > [F, tuple₂, locker, release, request, s, nocalls] > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
locker2_{release_lock₂} > case2₃ > [cons₂, equal₁, locker2_{check_{availables₂}}] > [case5₁, andt, case6₁] > [nil, true, locker2_{map_{add_pending}}] > excl > [F, tuple₂, locker, release, request, s, nocalls] > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
locker2_{release_lock₂} > case2₃ > [cons₂, equal₁, locker2_{check_{availables₂}}] > [case5₁, andt, case6₁] > [nil, true, locker2_{map_{add_pending}}] > locker2_{obtainable₂} > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
locker2_{release_lock₂} > case2₃ > [cons₂, equal₁, locker2_{check_{availables₂}}] > [case5₁, andt, case6₁] > locker2_{check_available₁} > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
locker2_{release_lock₂} > case2₃ > record_updates₃ > [tuplenil₁, record_update₄] > [eqt₂, push₃] > and₂ > [F, tuple₂, locker, release, request, s, nocalls] > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
locker2_{release_lock₂} > case2₃ > record_updates₃ > [tuplenil₁, record_update₄] > [eqt₂, push₃] > push1₆ > pushs₂ > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
locker2_{release_lock₂} > case2₃ > record_updates₃ > [tuplenil₁, record_update₄] > mcrlrecord > [F, tuple₂, locker, release, request, s, nocalls] > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
locker2_{release_lock₂} > case2₃ > excllock > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
locker2_{release_lock₂} > gen_modtageq₂ > [cons₂, equal₁, locker2_{check_{availables₂}}] > [tuplenil₁, record_update₄] > [eqt₂, push₃] > and₂ > [F, tuple₂, locker, release, request, s, nocalls] > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
locker2_{release_lock₂} > gen_modtageq₂ > [cons₂, equal₁, locker2_{check_{availables₂}}] > [tuplenil₁, record_update₄] > [eqt₂, push₃] > push1₆ > pushs₂ > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
locker2_{release_lock₂} > gen_modtageq₂ > [cons₂, equal₁, locker2_{check_{availables₂}}] > [tuplenil₁, record_update₄] > mcrlrecord > [F, tuple₂, locker, release, request, s, nocalls] > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
locker2_{release_lock₂} > gen_modtageq₂ > [cons₂, equal₁, locker2_{check_{availables₂}}] > [case5₁, andt, case6₁] > [nil, true, locker2_{map_{add_pending}}] > excl > [F, tuple₂, locker, release, request, s, nocalls] > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
locker2_{release_lock₂} > gen_modtageq₂ > [cons₂, equal₁, locker2_{check_{availables₂}}] > [case5₁, andt, case6₁] > [nil, true, locker2_{map_{add_pending}}] > locker2_{obtainable₂} > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
locker2_{release_lock₂} > gen_modtageq₂ > [cons₂, equal₁, locker2_{check_{availables₂}}] > [case5₁, andt, case6₁] > locker2_{check_available₁} > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
case4 > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
gen_tag₁ > [tuplenil₁, record_update₄] > [eqt₂, push₃] > and₂ > [F, tuple₂, locker, release, request, s, nocalls] > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
gen_tag₁ > [tuplenil₁, record_update₄] > [eqt₂, push₃] > push1₆ > pushs₂ > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
gen_tag₁ > [tuplenil₁, record_update₄] > mcrlrecord > [F, tuple₂, locker, release, request, s, nocalls] > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
gen_tag₁ > tag > [F, tuple₂, locker, release, request, s, nocalls] > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
pops₁ > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
tops₁ > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
istops₂ > [eqt₂, push₃] > and₂ > [F, tuple₂, locker, release, request, s, nocalls] > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
istops₂ > [eqt₂, push₃] > push1₆ > pushs₂ > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
eqc₂ > eqs₂ > [eqt₂, push₃] > and₂ > [F, tuple₂, locker, release, request, s, nocalls] > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]
eqc₂ > eqs₂ > [eqt₂, push₃] > push1₆ > pushs₂ > [T, false, lock, pending, locker2_{claim_lock}, empty, stack₂, calls₃]

Status:

tuplenil₁: [1]
T: []
F: []
and₂: [1,2]
not: []
if₂: [1,2]
eq₂: [2,1]
eqt₂: [1,2]
nil: []
undefined: []
pid₁: [1]
cons₂: [2,1]
tuple₂: [2,1]
a: []
excl: []
false: []
lock: []
locker: []
mcrlrecord: []
ok: []
pending: []
release: []
request: []
resource: []
tag: []
true: []
s: []
0: []
record_new₁: [1]
record_update₄: [4,3,2,1]
record_updates₃: [3,2,1]
locker2_{map_{promote_pending₂}}: [2,1]
locker2_{promote_pending₂}: [2,1]
locker2_{claim_lock}: []
locker2_{map_{add_pending}}: []
case0₂: [2,1]
locker2_{remove_pending₂}: [2,1]
subtract₂: [2,1]
locker2_{add_pending₃}: [3,2,1]
case1₄: [1,2,3,4]
member₁: [1]
append₁: [1]
locker2_{release_lock₂}: [2,1]
case2₃: [2,3,1]
gen_modtageq₂: [2,1]
excllock: []
case4: []
case5₁: [1]
andt: []
locker2_{obtainable₂}: [2,1]
locker2_{check_available₁}: [1]
case6₁: [1]
equal₁: [1]
locker2_{check_{availables₂}}: [2,1]
delete₂: [2,1]
case8₃: [1,3,2]
gen_tag₁: [1]
case9₁: [1]
eqs₂: [1,2]
empty: []
stack₂: [2,1]
pushs₂: [2,1]
pops₁: [1]
tops₁: [1]
istops₂: [2,1]
eqc₂: [1,2]
nocalls: []
calls₃: [2,3,1]
push₃: [1,3,2]
push1₆: [2,5,3,1,6,4]

The following usable rules [FROCOS05] were oriented:

or(T, T) → T
or(F, T) → T
or(T, F) → T
or(F, F) → F
and(T, B) → B
and(B, T) → B
and(F, B) → F
and(B, F) → F
imp(T, B) → B
imp(F, B) → T
not(T) → F
not(F) → T
if(T, B1, B2) → B1
if(F, B1, B2) → B2
eq(T, T) → T
eq(F, F) → T
eq(T, F) → F
eq(F, T) → F
eqt(nil, undefined) → F
eqt(nil, pid(N2)) → F
eqt(nil, int(N2)) → F
eqt(nil, cons(H2, T2)) → F
eqt(nil, tuple(H2, T2)) → F
eqt(nil, tuplenil(H2)) → F
eqt(a, nil) → F
eqt(a, a) → T
eqt(a, excl) → F
eqt(a, false) → F
eqt(a, lock) → F
eqt(a, locker) → F
eqt(a, mcrlrecord) → F
eqt(a, ok) → F
eqt(a, pending) → F
eqt(a, release) → F
eqt(a, request) → F
eqt(a, resource) → F
eqt(a, tag) → F
eqt(a, true) → F
eqt(a, undefined) → F
eqt(a, pid(N2)) → F
eqt(a, int(N2)) → F
eqt(a, cons(H2, T2)) → F
eqt(a, tuple(H2, T2)) → F
eqt(a, tuplenil(H2)) → F
eqt(excl, nil) → F
eqt(excl, a) → F
eqt(excl, excl) → T
eqt(excl, false) → F
eqt(excl, lock) → F
eqt(excl, locker) → F
eqt(excl, mcrlrecord) → F
eqt(excl, ok) → F
eqt(excl, pending) → F
eqt(excl, release) → F
eqt(excl, request) → F
eqt(excl, resource) → F
eqt(excl, tag) → F
eqt(excl, true) → F
eqt(excl, undefined) → F
eqt(excl, pid(N2)) → F
eqt(excl, eqt(false, int(N2))) → F
eqt(false, cons(H2, T2)) → F
eqt(false, tuple(H2, T2)) → F
eqt(false, tuplenil(H2)) → F
eqt(lock, nil) → F
eqt(lock, a) → F
eqt(lock, excl) → F
eqt(lock, false) → F
eqt(lock, lock) → T
eqt(lock, locker) → F
eqt(lock, mcrlrecord) → F
eqt(lock, ok) → F
eqt(lock, pending) → F
eqt(lock, release) → F
eqt(lock, request) → F
eqt(lock, resource) → F
eqt(lock, tag) → F
eqt(lock, true) → F
eqt(lock, undefined) → F
eqt(lock, pid(N2)) → F
eqt(lock, int(N2)) → F
eqt(lock, cons(H2, T2)) → F
eqt(lock, tuple(H2, T2)) → F
eqt(lock, tuplenil(H2)) → F
eqt(locker, nil) → F
eqt(locker, a) → F
eqt(locker, excl) → F
eqt(locker, false) → F
eqt(locker, lock) → F
eqt(locker, locker) → T
eqt(locker, mcrlrecord) → F
eqt(locker, ok) → F
eqt(locker, pending) → F
eqt(locker, release) → F
eqt(locker, request) → F
eqt(locker, resource) → F
eqt(locker, tag) → F
eqt(locker, true) → F
eqt(locker, undefined) → F
eqt(locker, pid(N2)) → F
eqt(locker, int(N2)) → F
eqt(locker, cons(H2, T2)) → F
eqt(locker, tuple(H2, T2)) → F
eqt(locker, tuplenil(H2)) → F
eqt(mcrlrecord, nil) → F
eqt(mcrlrecord, a) → F
eqt(mcrlrecord, excl) → F
eqt(mcrlrecord, false) → F
eqt(mcrlrecord, lock) → F
eqt(mcrlrecord, locker) → F
eqt(mcrlrecord, mcrlrecord) → T
eqt(mcrlrecord, ok) → F
eqt(mcrlrecord, pending) → F
eqt(mcrlrecord, release) → F
eqt(mcrlrecord, request) → F
eqt(mcrlrecord, resource) → F
eqt(ok, resource) → F
eqt(ok, tag) → F
eqt(ok, true) → F
eqt(ok, undefined) → F
eqt(ok, pid(N2)) → F
eqt(ok, int(N2)) → F
eqt(ok, cons(H2, T2)) → F
eqt(ok, tuple(H2, T2)) → F
eqt(ok, tuplenil(H2)) → F
eqt(pending, nil) → F
eqt(pending, a) → F
eqt(pending, excl) → F
eqt(pending, false) → F
eqt(pending, lock) → F
eqt(pending, locker) → F
eqt(pending, mcrlrecord) → F
eqt(pending, ok) → F
eqt(pending, pending) → T
eqt(pending, release) → F
eqt(pending, request) → F
eqt(pending, resource) → F
eqt(pending, tag) → F
eqt(pending, true) → F
eqt(pending, undefined) → F
eqt(pending, pid(N2)) → F
eqt(pending, int(N2)) → F
eqt(pending, cons(H2, T2)) → F
eqt(pending, tuple(H2, T2)) → F
eqt(pending, tuplenil(H2)) → F
eqt(release, nil) → F
eqt(release, a) → F
eqt(release, excl) → F
eqt(release, false) → F
eqt(release, lock) → F
eqt(release, locker) → F
eqt(release, mcrlrecord) → F
eqt(release, ok) → F
eqt(request, mcrlrecord) → F
eqt(request, ok) → F
eqt(request, pending) → F
eqt(request, release) → F
eqt(request, request) → T
eqt(request, resource) → F
eqt(request, tag) → F
eqt(request, true) → F
eqt(request, undefined) → F
eqt(request, pid(N2)) → F
eqt(request, int(N2)) → F
eqt(request, cons(H2, T2)) → F
eqt(request, tuple(H2, T2)) → F
eqt(request, tuplenil(H2)) → F
eqt(resource, nil) → F
eqt(resource, a) → F
eqt(resource, excl) → F
eqt(resource, false) → F
eqt(resource, lock) → F
eqt(resource, locker) → F
eqt(resource, mcrlrecord) → F
eqt(resource, ok) → F
eqt(resource, pending) → F
eqt(resource, release) → F
eqt(resource, request) → F
eqt(resource, resource) → T
eqt(resource, tag) → F
eqt(resource, true) → F
eqt(resource, undefined) → F
eqt(resource, pid(N2)) → F
eqt(resource, int(N2)) → F
eqt(resource, cons(H2, T2)) → F
eqt(resource, tuple(H2, T2)) → F
eqt(resource, tuplenil(H2)) → F
eqt(tag, nil) → F
eqt(tag, a) → F
eqt(tag, excl) → F
eqt(tag, false) → F
eqt(tag, lock) → F
eqt(tag, locker) → F
eqt(tag, mcrlrecord) → F
eqt(tag, ok) → F
eqt(tag, pending) → F
eqt(tag, release) → F
eqt(tag, request) → F
eqt(tag, resource) → F
eqt(tag, tag) → T
eqt(tag, true) → F
eqt(tag, undefined) → F
eqt(tag, pid(N2)) → F
eqt(tag, int(N2)) → F
eqt(tag, cons(H2, T2)) → F
eqt(tag, tuple(H2, T2)) → F
eqt(tag, tuplenil(H2)) → F
eqt(true, nil) → F
eqt(true, a) → F
eqt(true, excl) → F
eqt(true, false) → F
eqt(true, lock) → F
eqt(true, locker) → F
eqt(true, mcrlrecord) → F
eqt(true, ok) → F
eqt(true, pending) → F
eqt(true, release) → F
eqt(true, request) → F
eqt(true, resource) → F
eqt(true, tag) → F
eqt(true, true) → T
eqt(true, undefined) → F
eqt(true, pid(N2)) → F
eqt(true, int(N2)) → F
eqt(true, cons(H2, T2)) → F
eqt(true, tuple(H2, T2)) → F
eqt(true, tuplenil(H2)) → F
eqt(undefined, nil) → F
eqt(undefined, a) → F
eqt(undefined, tuplenil(H2)) → F
eqt(pid(N1), nil) → F
eqt(pid(N1), a) → F
eqt(pid(N1), excl) → F
eqt(pid(N1), false) → F
eqt(pid(N1), lock) → F
eqt(pid(N1), locker) → F
eqt(pid(N1), mcrlrecord) → F
eqt(pid(N1), ok) → F
eqt(pid(N1), pending) → F
eqt(pid(N1), release) → F
eqt(pid(N1), request) → F
eqt(pid(N1), resource) → F
eqt(pid(N1), tag) → F
eqt(pid(N1), true) → F
eqt(pid(N1), undefined) → F
eqt(pid(N1), pid(N2)) → eqt(N1, N2)
eqt(pid(N1), int(N2)) → F
eqt(pid(N1), cons(H2, T2)) → F
eqt(pid(N1), tuple(H2, T2)) → F
eqt(pid(N1), tuplenil(H2)) → F
eqt(int(N1), nil) → F
eqt(int(N1), a) → F
eqt(int(N1), excl) → F
eqt(int(N1), false) → F
eqt(int(N1), lock) → F
eqt(int(N1), locker) → F
eqt(int(N1), mcrlrecord) → F
eqt(int(N1), ok) → F
eqt(int(N1), pending) → F
eqt(int(N1), release) → F
eqt(int(N1), request) → F
eqt(int(N1), resource) → F
eqt(int(N1), tag) → F
eqt(int(N1), true) → F
eqt(int(N1), undefined) → F
eqt(cons(H1, T1), resource) → F
eqt(cons(H1, T1), tag) → F
eqt(cons(H1, T1), true) → F
eqt(cons(H1, T1), undefined) → F
eqt(cons(H1, T1), pid(N2)) → F
eqt(cons(H1, T1), int(N2)) → F
eqt(cons(H1, T1), cons(H2, T2)) → and(eqt(H1, H2), eqt(T1, T2))
eqt(cons(H1, T1), tuple(H2, T2)) → F
eqt(cons(H1, T1), tuplenil(H2)) → F
eqt(tuple(H1, T1), nil) → F
eqt(tuple(H1, T1), a) → F
eqt(tuple(H1, T1), excl) → F
eqt(tuple(H1, T1), false) → F
eqt(tuple(H1, T1), lock) → F
eqt(tuple(H1, T1), locker) → F
eqt(tuple(H1, T1), mcrlrecord) → F
eqt(tuple(H1, T1), ok) → F
eqt(tuple(H1, T1), pending) → F
eqt(tuple(H1, T1), release) → F
eqt(tuple(H1, T1), request) → F
eqt(tuple(H1, T1), resource) → F
eqt(tuple(H1, T1), tag) → F
eqt(tuple(H1, T1), true) → F
eqt(tuple(H1, T1), undefined) → F
eqt(tuple(H1, T1), pid(N2)) → F
eqt(tuple(H1, T1), int(N2)) → F
eqt(tuple(H1, T1), cons(H2, T2)) → F
eqt(tuple(H1, T1), tuple(H2, T2)) → and(eqt(H1, H2), eqt(T1, T2))
eqt(tuple(H1, T1), tuplenil(H2)) → F
eqt(tuplenil(H1), nil) → F
eqt(tuplenil(H1), a) → F
eqt(tuplenil(H1), excl) → F
eqt(tuplenil(H1), false) → F
eqt(tuplenil(H1), lock) → F
eqt(tuplenil(H1), locker) → F
eqt(tuplenil(H1), mcrlrecord) → F
eqt(tuplenil(H1), ok) → F
eqt(tuplenil(H1), pending) → F
eqt(tuplenil(H1), release) → F
eqt(tuplenil(H1), request) → F
eqt(tuplenil(H1), resource) → F
eqt(tuplenil(H1), tag) → F
eqt(tuplenil(H1), true) → F
eqt(tuplenil(H1), undefined) → F
eqt(tuplenil(H1), pid(N2)) → F
eqt(tuplenil(H1), int(N2)) → F
eqt(tuplenil(H1), cons(H2, T2)) → F
eqt(tuplenil(H1), tuple(H2, T2)) → F
eqt(tuplenil(H1), tuplenil(H2)) → eqt(H1, H2)
element(int(s(0)), tuplenil(T1)) → T1
element(int(s(0)), tuple(T1, T2)) → T1
element(int(s(s(N1))), tuple(T1, T2)) → element(int(s(N1)), T2)
record_new(lock) → tuple(mcrlrecord, tuple(lock, tuple(undefined, tuple(nil, tuplenil(nil)))))
record_extract(tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))), lock, resource) → tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2)))))
record_update(tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))), lock, pending, NewF) → tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(NewF)))))
record_updates(Record, Name, nil) → Record
record_updates(Record, Name, cons(tuple(Field, tuplenil(NewF)), Fields)) → record_updates(record_update(Record, Name, Field, NewF), Name, Fields)
locker2_map_promote_pending(nil, Pending) → nil
locker2_map_promote_pending(cons(Lock, Locks), Pending) → cons(locker2_promote_pending(Lock, Pending), locker2_map_promote_pending(Locks, Pending))
locker2_map_claim_lock(nil, Resources, Client) → nil
locker2_map_claim_lock(cons(Lock, Locks), Resources, Client) → cons(locker2_claim_lock(Lock, Resources, Client), locker2_map_claim_lock(Locks, Resources, Client))
locker2_map_add_pending(nil, Resources, Client) → nil
locker2_promote_pending(Lock, Client) → case0(Client, Lock, record_extract(Lock, lock, pending))
case0(Client, Lock, cons(Client, Pendings)) → record_updates(Lock, lock, cons(tuple(excl, tuplenil(Client)), cons(tuple(pending, tuplenil(Pendings)), nil)))
case0(Client, Lock, MCRLFree0) → Lock
locker2_remove_pending(Lock, Client) → record_updates(Lock, lock, cons(tuple(pending, tuplenil(subtract(record_extract(Lock, lock, pending), cons(Client, nil)))), nil))
locker2_add_pending(Lock, Resources, Client) → case1(Client, Resources, Lock, member(record_extract(Lock, lock, resource), Resources))
case1(Client, Resources, Lock, true) → record_updates(Lock, lock, cons(tuple(pending, tuplenil(append(record_extract(Lock, lock, pending), cons(Client, nil)))), nil))
case1(Client, Resources, Lock, false) → Lock
locker2_release_lock(Lock, Client) → case2(Client, Lock, gen_modtageq(Client, record_extract(Lock, lock, excl)))
case2(Client, Lock, true) → record_updates(Lock, lock, cons(tuple(excllock, excl), nil))
case4(Client, Lock, MCRLFree1) → false
locker2_obtainables(nil, Client) → true
locker2_obtainables(cons(Lock, Locks), Client) → case5(Client, Locks, Lock, member(Client, record_extract(Lock, lock, pending)))
case5(Client, Locks, Lock, true) → andt(locker2_obtainable(Lock, Client), locker2_obtainables(Locks, Client))
case5(Client, Locks, Lock, false) → locker2_obtainables(Locks, Client)
locker2_check_available(Resource, nil) → false
locker2_check_available(Resource, cons(Lock, Locks)) → case6(Locks, Lock, Resource, equal(Resource, record_extract(Lock, lock, resource)))
case6(Locks, Lock, Resource, true) → andt(equal(record_extract(Lock, lock, excl), nil), equal(record_extract(Lock, lock, pending), nil))
case6(Locks, Lock, Resource, false) → locker2_check_available(Resource, Locks)
locker2_check_availables(nil, Locks) → true
locker2_check_availables(cons(Resource, Resources), Locks) → andt(locker2_check_available(Resource, Locks), locker2_check_availables(Resources, Locks))
locker2_adduniq(nil, List) → List
append(cons(Head, Tail), List) → cons(Head, append(Tail, List))
subtract(List, nil) → List
subtract(List, cons(Head, Tail)) → subtract(delete(Head, List), Tail)
delete(E, nil) → nil
delete(E, cons(Head, Tail)) → case8(Tail, Head, E, equal(E, Head))
case8(Tail, Head, E, true) → Tail
case8(Tail, Head, E, false) → cons(Head, delete(E, Tail))
gen_tag(Pid) → tuple(Pid, tuplenil(tag))
gen_modtageq(Client1, Client2) → equal(Client1, Client2)
member(E, nil) → false
member(E, cons(Head, Tail)) → case9(Tail, Head, E, equal(E, Head))
case9(Tail, Head, E, true) → true
case9(Tail, Head, E, false) → member(E, Tail)
eqs(empty, empty) → T
eqs(empty, stack(E2, S2)) → F
eqs(stack(E1, S1), empty) → F
eqs(stack(E1, S1), stack(E2, S2)) → and(eqt(E1, E2), eqs(S1, S2))
pushs(E1, S1) → stack(E1, S1)
pops(stack(E1, S1)) → S1
tops(stack(E1, S1)) → E1
istops(E1, empty) → F
istops(E1, stack(E2, S1)) → eqt(E1, E2)
eqc(nocalls, nocalls) → T
eqc(nocalls, calls(E2, S2, CS2)) → F
eqc(calls(E1, S1, CS1), nocalls) → F
eqc(calls(E1, S1, CS1), calls(E2, S2, CS2)) → and(eqt(E1, E2), and(eqs(S1, S2), eqc(CS1, CS2)))
push(E1, E2, nocalls) → calls(E1, stack(E2, empty), nocalls)
push(E1, E2, calls(E3, S1, CS1)) → push1(E1, E2, E3, S1, CS1, eqt(E1, E3))
push1(E1, E2, E3, S1, CS1, T) → calls(E3, pushs(E2, S1), CS1)

(44) Obligation:

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

or(T, T) → T
or(F, T) → T
or(T, F) → T
or(F, F) → F
and(T, B) → B
and(B, T) → B
and(F, B) → F
and(B, F) → F
imp(T, B) → B
imp(F, B) → T
not(T) → F
not(F) → T
if(T, B1, B2) → B1
if(F, B1, B2) → B2
eq(T, T) → T
eq(F, F) → T
eq(T, F) → F
eq(F, T) → F
eqt(nil, undefined) → F
eqt(nil, pid(N2)) → F
eqt(nil, int(N2)) → F
eqt(nil, cons(H2, T2)) → F
eqt(nil, tuple(H2, T2)) → F
eqt(nil, tuplenil(H2)) → F
eqt(a, nil) → F
eqt(a, a) → T
eqt(a, excl) → F
eqt(a, false) → F
eqt(a, lock) → F
eqt(a, locker) → F
eqt(a, mcrlrecord) → F
eqt(a, ok) → F
eqt(a, pending) → F
eqt(a, release) → F
eqt(a, request) → F
eqt(a, resource) → F
eqt(a, tag) → F
eqt(a, true) → F
eqt(a, undefined) → F
eqt(a, pid(N2)) → F
eqt(a, int(N2)) → F
eqt(a, cons(H2, T2)) → F
eqt(a, tuple(H2, T2)) → F
eqt(a, tuplenil(H2)) → F
eqt(excl, nil) → F
eqt(excl, a) → F
eqt(excl, excl) → T
eqt(excl, false) → F
eqt(excl, lock) → F
eqt(excl, locker) → F
eqt(excl, mcrlrecord) → F
eqt(excl, ok) → F
eqt(excl, pending) → F
eqt(excl, release) → F
eqt(excl, request) → F
eqt(excl, resource) → F
eqt(excl, tag) → F
eqt(excl, true) → F
eqt(excl, undefined) → F
eqt(excl, pid(N2)) → F
eqt(excl, eqt(false, int(N2))) → F
eqt(false, cons(H2, T2)) → F
eqt(false, tuple(H2, T2)) → F
eqt(false, tuplenil(H2)) → F
eqt(lock, nil) → F
eqt(lock, a) → F
eqt(lock, excl) → F
eqt(lock, false) → F
eqt(lock, lock) → T
eqt(lock, locker) → F
eqt(lock, mcrlrecord) → F
eqt(lock, ok) → F
eqt(lock, pending) → F
eqt(lock, release) → F
eqt(lock, request) → F
eqt(lock, resource) → F
eqt(lock, tag) → F
eqt(lock, true) → F
eqt(lock, undefined) → F
eqt(lock, pid(N2)) → F
eqt(lock, int(N2)) → F
eqt(lock, cons(H2, T2)) → F
eqt(lock, tuple(H2, T2)) → F
eqt(lock, tuplenil(H2)) → F
eqt(locker, nil) → F
eqt(locker, a) → F
eqt(locker, excl) → F
eqt(locker, false) → F
eqt(locker, lock) → F
eqt(locker, locker) → T
eqt(locker, mcrlrecord) → F
eqt(locker, ok) → F
eqt(locker, pending) → F
eqt(locker, release) → F
eqt(locker, request) → F
eqt(locker, resource) → F
eqt(locker, tag) → F
eqt(locker, true) → F
eqt(locker, undefined) → F
eqt(locker, pid(N2)) → F
eqt(locker, int(N2)) → F
eqt(locker, cons(H2, T2)) → F
eqt(locker, tuple(H2, T2)) → F
eqt(locker, tuplenil(H2)) → F
eqt(mcrlrecord, nil) → F
eqt(mcrlrecord, a) → F
eqt(mcrlrecord, excl) → F
eqt(mcrlrecord, false) → F
eqt(mcrlrecord, lock) → F
eqt(mcrlrecord, locker) → F
eqt(mcrlrecord, mcrlrecord) → T
eqt(mcrlrecord, ok) → F
eqt(mcrlrecord, pending) → F
eqt(mcrlrecord, release) → F
eqt(mcrlrecord, request) → F
eqt(mcrlrecord, resource) → F
eqt(ok, resource) → F
eqt(ok, tag) → F
eqt(ok, true) → F
eqt(ok, undefined) → F
eqt(ok, pid(N2)) → F
eqt(ok, int(N2)) → F
eqt(ok, cons(H2, T2)) → F
eqt(ok, tuple(H2, T2)) → F
eqt(ok, tuplenil(H2)) → F
eqt(pending, nil) → F
eqt(pending, a) → F
eqt(pending, excl) → F
eqt(pending, false) → F
eqt(pending, lock) → F
eqt(pending, locker) → F
eqt(pending, mcrlrecord) → F
eqt(pending, ok) → F
eqt(pending, pending) → T
eqt(pending, release) → F
eqt(pending, request) → F
eqt(pending, resource) → F
eqt(pending, tag) → F
eqt(pending, true) → F
eqt(pending, undefined) → F
eqt(pending, pid(N2)) → F
eqt(pending, int(N2)) → F
eqt(pending, cons(H2, T2)) → F
eqt(pending, tuple(H2, T2)) → F
eqt(pending, tuplenil(H2)) → F
eqt(release, nil) → F
eqt(release, a) → F
eqt(release, excl) → F
eqt(release, false) → F
eqt(release, lock) → F
eqt(release, locker) → F
eqt(release, mcrlrecord) → F
eqt(release, ok) → F
eqt(request, mcrlrecord) → F
eqt(request, ok) → F
eqt(request, pending) → F
eqt(request, release) → F
eqt(request, request) → T
eqt(request, resource) → F
eqt(request, tag) → F
eqt(request, true) → F
eqt(request, undefined) → F
eqt(request, pid(N2)) → F
eqt(request, int(N2)) → F
eqt(request, cons(H2, T2)) → F
eqt(request, tuple(H2, T2)) → F
eqt(request, tuplenil(H2)) → F
eqt(resource, nil) → F
eqt(resource, a) → F
eqt(resource, excl) → F
eqt(resource, false) → F
eqt(resource, lock) → F
eqt(resource, locker) → F
eqt(resource, mcrlrecord) → F
eqt(resource, ok) → F
eqt(resource, pending) → F
eqt(resource, release) → F
eqt(resource, request) → F
eqt(resource, resource) → T
eqt(resource, tag) → F
eqt(resource, true) → F
eqt(resource, undefined) → F
eqt(resource, pid(N2)) → F
eqt(resource, int(N2)) → F
eqt(resource, cons(H2, T2)) → F
eqt(resource, tuple(H2, T2)) → F
eqt(resource, tuplenil(H2)) → F
eqt(tag, nil) → F
eqt(tag, a) → F
eqt(tag, excl) → F
eqt(tag, false) → F
eqt(tag, lock) → F
eqt(tag, locker) → F
eqt(tag, mcrlrecord) → F
eqt(tag, ok) → F
eqt(tag, pending) → F
eqt(tag, release) → F
eqt(tag, request) → F
eqt(tag, resource) → F
eqt(tag, tag) → T
eqt(tag, true) → F
eqt(tag, undefined) → F
eqt(tag, pid(N2)) → F
eqt(tag, int(N2)) → F
eqt(tag, cons(H2, T2)) → F
eqt(tag, tuple(H2, T2)) → F
eqt(tag, tuplenil(H2)) → F
eqt(true, nil) → F
eqt(true, a) → F
eqt(true, excl) → F
eqt(true, false) → F
eqt(true, lock) → F
eqt(true, locker) → F
eqt(true, mcrlrecord) → F
eqt(true, ok) → F
eqt(true, pending) → F
eqt(true, release) → F
eqt(true, request) → F
eqt(true, resource) → F
eqt(true, tag) → F
eqt(true, true) → T
eqt(true, undefined) → F
eqt(true, pid(N2)) → F
eqt(true, int(N2)) → F
eqt(true, cons(H2, T2)) → F
eqt(true, tuple(H2, T2)) → F
eqt(true, tuplenil(H2)) → F
eqt(undefined, nil) → F
eqt(undefined, a) → F
eqt(undefined, tuplenil(H2)) → F
eqt(pid(N1), nil) → F
eqt(pid(N1), a) → F
eqt(pid(N1), excl) → F
eqt(pid(N1), false) → F
eqt(pid(N1), lock) → F
eqt(pid(N1), locker) → F
eqt(pid(N1), mcrlrecord) → F
eqt(pid(N1), ok) → F
eqt(pid(N1), pending) → F
eqt(pid(N1), release) → F
eqt(pid(N1), request) → F
eqt(pid(N1), resource) → F
eqt(pid(N1), tag) → F
eqt(pid(N1), true) → F
eqt(pid(N1), undefined) → F
eqt(pid(N1), pid(N2)) → eqt(N1, N2)
eqt(pid(N1), int(N2)) → F
eqt(pid(N1), cons(H2, T2)) → F
eqt(pid(N1), tuple(H2, T2)) → F
eqt(pid(N1), tuplenil(H2)) → F
eqt(int(N1), nil) → F
eqt(int(N1), a) → F
eqt(int(N1), excl) → F
eqt(int(N1), false) → F
eqt(int(N1), lock) → F
eqt(int(N1), locker) → F
eqt(int(N1), mcrlrecord) → F
eqt(int(N1), ok) → F
eqt(int(N1), pending) → F
eqt(int(N1), release) → F
eqt(int(N1), request) → F
eqt(int(N1), resource) → F
eqt(int(N1), tag) → F
eqt(int(N1), true) → F
eqt(int(N1), undefined) → F
eqt(cons(H1, T1), resource) → F
eqt(cons(H1, T1), tag) → F
eqt(cons(H1, T1), true) → F
eqt(cons(H1, T1), undefined) → F
eqt(cons(H1, T1), pid(N2)) → F
eqt(cons(H1, T1), int(N2)) → F
eqt(cons(H1, T1), cons(H2, T2)) → and(eqt(H1, H2), eqt(T1, T2))
eqt(cons(H1, T1), tuple(H2, T2)) → F
eqt(cons(H1, T1), tuplenil(H2)) → F
eqt(tuple(H1, T1), nil) → F
eqt(tuple(H1, T1), a) → F
eqt(tuple(H1, T1), excl) → F
eqt(tuple(H1, T1), false) → F
eqt(tuple(H1, T1), lock) → F
eqt(tuple(H1, T1), locker) → F
eqt(tuple(H1, T1), mcrlrecord) → F
eqt(tuple(H1, T1), ok) → F
eqt(tuple(H1, T1), pending) → F
eqt(tuple(H1, T1), release) → F
eqt(tuple(H1, T1), request) → F
eqt(tuple(H1, T1), resource) → F
eqt(tuple(H1, T1), tag) → F
eqt(tuple(H1, T1), true) → F
eqt(tuple(H1, T1), undefined) → F
eqt(tuple(H1, T1), pid(N2)) → F
eqt(tuple(H1, T1), int(N2)) → F
eqt(tuple(H1, T1), cons(H2, T2)) → F
eqt(tuple(H1, T1), tuple(H2, T2)) → and(eqt(H1, H2), eqt(T1, T2))
eqt(tuple(H1, T1), tuplenil(H2)) → F
eqt(tuplenil(H1), nil) → F
eqt(tuplenil(H1), a) → F
eqt(tuplenil(H1), excl) → F
eqt(tuplenil(H1), false) → F
eqt(tuplenil(H1), lock) → F
eqt(tuplenil(H1), locker) → F
eqt(tuplenil(H1), mcrlrecord) → F
eqt(tuplenil(H1), ok) → F
eqt(tuplenil(H1), pending) → F
eqt(tuplenil(H1), release) → F
eqt(tuplenil(H1), request) → F
eqt(tuplenil(H1), resource) → F
eqt(tuplenil(H1), tag) → F
eqt(tuplenil(H1), true) → F
eqt(tuplenil(H1), undefined) → F
eqt(tuplenil(H1), pid(N2)) → F
eqt(tuplenil(H1), int(N2)) → F
eqt(tuplenil(H1), cons(H2, T2)) → F
eqt(tuplenil(H1), tuple(H2, T2)) → F
eqt(tuplenil(H1), tuplenil(H2)) → eqt(H1, H2)
element(int(s(0)), tuplenil(T1)) → T1
element(int(s(0)), tuple(T1, T2)) → T1
element(int(s(s(N1))), tuple(T1, T2)) → element(int(s(N1)), T2)
record_new(lock) → tuple(mcrlrecord, tuple(lock, tuple(undefined, tuple(nil, tuplenil(nil)))))
record_extract(tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))), lock, resource) → tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2)))))
record_update(tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))), lock, pending, NewF) → tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(NewF)))))
record_updates(Record, Name, nil) → Record
record_updates(Record, Name, cons(tuple(Field, tuplenil(NewF)), Fields)) → record_updates(record_update(Record, Name, Field, NewF), Name, Fields)
locker2_map_promote_pending(nil, Pending) → nil
locker2_map_promote_pending(cons(Lock, Locks), Pending) → cons(locker2_promote_pending(Lock, Pending), locker2_map_promote_pending(Locks, Pending))
locker2_map_claim_lock(nil, Resources, Client) → nil
locker2_map_claim_lock(cons(Lock, Locks), Resources, Client) → cons(locker2_claim_lock(Lock, Resources, Client), locker2_map_claim_lock(Locks, Resources, Client))
locker2_map_add_pending(nil, Resources, Client) → nil
locker2_promote_pending(Lock, Client) → case0(Client, Lock, record_extract(Lock, lock, pending))
case0(Client, Lock, cons(Client, Pendings)) → record_updates(Lock, lock, cons(tuple(excl, tuplenil(Client)), cons(tuple(pending, tuplenil(Pendings)), nil)))
case0(Client, Lock, MCRLFree0) → Lock
locker2_remove_pending(Lock, Client) → record_updates(Lock, lock, cons(tuple(pending, tuplenil(subtract(record_extract(Lock, lock, pending), cons(Client, nil)))), nil))
locker2_add_pending(Lock, Resources, Client) → case1(Client, Resources, Lock, member(record_extract(Lock, lock, resource), Resources))
case1(Client, Resources, Lock, true) → record_updates(Lock, lock, cons(tuple(pending, tuplenil(append(record_extract(Lock, lock, pending), cons(Client, nil)))), nil))
case1(Client, Resources, Lock, false) → Lock
locker2_release_lock(Lock, Client) → case2(Client, Lock, gen_modtageq(Client, record_extract(Lock, lock, excl)))
case2(Client, Lock, true) → record_updates(Lock, lock, cons(tuple(excllock, excl), nil))
case4(Client, Lock, MCRLFree1) → false
locker2_obtainables(nil, Client) → true
locker2_obtainables(cons(Lock, Locks), Client) → case5(Client, Locks, Lock, member(Client, record_extract(Lock, lock, pending)))
case5(Client, Locks, Lock, true) → andt(locker2_obtainable(Lock, Client), locker2_obtainables(Locks, Client))
case5(Client, Locks, Lock, false) → locker2_obtainables(Locks, Client)
locker2_check_available(Resource, nil) → false
locker2_check_available(Resource, cons(Lock, Locks)) → case6(Locks, Lock, Resource, equal(Resource, record_extract(Lock, lock, resource)))
case6(Locks, Lock, Resource, true) → andt(equal(record_extract(Lock, lock, excl), nil), equal(record_extract(Lock, lock, pending), nil))
case6(Locks, Lock, Resource, false) → locker2_check_available(Resource, Locks)
locker2_check_availables(nil, Locks) → true
locker2_check_availables(cons(Resource, Resources), Locks) → andt(locker2_check_available(Resource, Locks), locker2_check_availables(Resources, Locks))
locker2_adduniq(nil, List) → List
append(cons(Head, Tail), List) → cons(Head, append(Tail, List))
subtract(List, nil) → List
subtract(List, cons(Head, Tail)) → subtract(delete(Head, List), Tail)
delete(E, nil) → nil
delete(E, cons(Head, Tail)) → case8(Tail, Head, E, equal(E, Head))
case8(Tail, Head, E, true) → Tail
case8(Tail, Head, E, false) → cons(Head, delete(E, Tail))
gen_tag(Pid) → tuple(Pid, tuplenil(tag))
gen_modtageq(Client1, Client2) → equal(Client1, Client2)
member(E, nil) → false
member(E, cons(Head, Tail)) → case9(Tail, Head, E, equal(E, Head))
case9(Tail, Head, E, true) → true
case9(Tail, Head, E, false) → member(E, Tail)
eqs(empty, empty) → T
eqs(empty, stack(E2, S2)) → F
eqs(stack(E1, S1), empty) → F
eqs(stack(E1, S1), stack(E2, S2)) → and(eqt(E1, E2), eqs(S1, S2))
pushs(E1, S1) → stack(E1, S1)
pops(stack(E1, S1)) → S1
tops(stack(E1, S1)) → E1
istops(E1, empty) → F
istops(E1, stack(E2, S1)) → eqt(E1, E2)
eqc(nocalls, nocalls) → T
eqc(nocalls, calls(E2, S2, CS2)) → F
eqc(calls(E1, S1, CS1), nocalls) → F
eqc(calls(E1, S1, CS1), calls(E2, S2, CS2)) → and(eqt(E1, E2), and(eqs(S1, S2), eqc(CS1, CS2)))
push(E1, E2, nocalls) → calls(E1, stack(E2, empty), nocalls)
push(E1, E2, calls(E3, S1, CS1)) → push1(E1, E2, E3, S1, CS1, eqt(E1, E3))
push1(E1, E2, E3, S1, CS1, T) → calls(E3, pushs(E2, S1), CS1)

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

(45) PisEmptyProof (EQUIVALENT transformation)

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

(46) TRUE

(47) Obligation:

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

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

The TRS R consists of the following rules:

or(T, T) → T
or(F, T) → T
or(T, F) → T
or(F, F) → F
and(T, B) → B
and(B, T) → B
and(F, B) → F
and(B, F) → F
imp(T, B) → B
imp(F, B) → T
not(T) → F
not(F) → T
if(T, B1, B2) → B1
if(F, B1, B2) → B2
eq(T, T) → T
eq(F, F) → T
eq(T, F) → F
eq(F, T) → F
eqt(nil, undefined) → F
eqt(nil, pid(N2)) → F
eqt(nil, int(N2)) → F
eqt(nil, cons(H2, T2)) → F
eqt(nil, tuple(H2, T2)) → F
eqt(nil, tuplenil(H2)) → F
eqt(a, nil) → F
eqt(a, a) → T
eqt(a, excl) → F
eqt(a, false) → F
eqt(a, lock) → F
eqt(a, locker) → F
eqt(a, mcrlrecord) → F
eqt(a, ok) → F
eqt(a, pending) → F
eqt(a, release) → F
eqt(a, request) → F
eqt(a, resource) → F
eqt(a, tag) → F
eqt(a, true) → F
eqt(a, undefined) → F
eqt(a, pid(N2)) → F
eqt(a, int(N2)) → F
eqt(a, cons(H2, T2)) → F
eqt(a, tuple(H2, T2)) → F
eqt(a, tuplenil(H2)) → F
eqt(excl, nil) → F
eqt(excl, a) → F
eqt(excl, excl) → T
eqt(excl, false) → F
eqt(excl, lock) → F
eqt(excl, locker) → F
eqt(excl, mcrlrecord) → F
eqt(excl, ok) → F
eqt(excl, pending) → F
eqt(excl, release) → F
eqt(excl, request) → F
eqt(excl, resource) → F
eqt(excl, tag) → F
eqt(excl, true) → F
eqt(excl, undefined) → F
eqt(excl, pid(N2)) → F
eqt(excl, eqt(false, int(N2))) → F
eqt(false, cons(H2, T2)) → F
eqt(false, tuple(H2, T2)) → F
eqt(false, tuplenil(H2)) → F
eqt(lock, nil) → F
eqt(lock, a) → F
eqt(lock, excl) → F
eqt(lock, false) → F
eqt(lock, lock) → T
eqt(lock, locker) → F
eqt(lock, mcrlrecord) → F
eqt(lock, ok) → F
eqt(lock, pending) → F
eqt(lock, release) → F
eqt(lock, request) → F
eqt(lock, resource) → F
eqt(lock, tag) → F
eqt(lock, true) → F
eqt(lock, undefined) → F
eqt(lock, pid(N2)) → F
eqt(lock, int(N2)) → F
eqt(lock, cons(H2, T2)) → F
eqt(lock, tuple(H2, T2)) → F
eqt(lock, tuplenil(H2)) → F
eqt(locker, nil) → F
eqt(locker, a) → F
eqt(locker, excl) → F
eqt(locker, false) → F
eqt(locker, lock) → F
eqt(locker, locker) → T
eqt(locker, mcrlrecord) → F
eqt(locker, ok) → F
eqt(locker, pending) → F
eqt(locker, release) → F
eqt(locker, request) → F
eqt(locker, resource) → F
eqt(locker, tag) → F
eqt(locker, true) → F
eqt(locker, undefined) → F
eqt(locker, pid(N2)) → F
eqt(locker, int(N2)) → F
eqt(locker, cons(H2, T2)) → F
eqt(locker, tuple(H2, T2)) → F
eqt(locker, tuplenil(H2)) → F
eqt(mcrlrecord, nil) → F
eqt(mcrlrecord, a) → F
eqt(mcrlrecord, excl) → F
eqt(mcrlrecord, false) → F
eqt(mcrlrecord, lock) → F
eqt(mcrlrecord, locker) → F
eqt(mcrlrecord, mcrlrecord) → T
eqt(mcrlrecord, ok) → F
eqt(mcrlrecord, pending) → F
eqt(mcrlrecord, release) → F
eqt(mcrlrecord, request) → F
eqt(mcrlrecord, resource) → F
eqt(ok, resource) → F
eqt(ok, tag) → F
eqt(ok, true) → F
eqt(ok, undefined) → F
eqt(ok, pid(N2)) → F
eqt(ok, int(N2)) → F
eqt(ok, cons(H2, T2)) → F
eqt(ok, tuple(H2, T2)) → F
eqt(ok, tuplenil(H2)) → F
eqt(pending, nil) → F
eqt(pending, a) → F
eqt(pending, excl) → F
eqt(pending, false) → F
eqt(pending, lock) → F
eqt(pending, locker) → F
eqt(pending, mcrlrecord) → F
eqt(pending, ok) → F
eqt(pending, pending) → T
eqt(pending, release) → F
eqt(pending, request) → F
eqt(pending, resource) → F
eqt(pending, tag) → F
eqt(pending, true) → F
eqt(pending, undefined) → F
eqt(pending, pid(N2)) → F
eqt(pending, int(N2)) → F
eqt(pending, cons(H2, T2)) → F
eqt(pending, tuple(H2, T2)) → F
eqt(pending, tuplenil(H2)) → F
eqt(release, nil) → F
eqt(release, a) → F
eqt(release, excl) → F
eqt(release, false) → F
eqt(release, lock) → F
eqt(release, locker) → F
eqt(release, mcrlrecord) → F
eqt(release, ok) → F
eqt(request, mcrlrecord) → F
eqt(request, ok) → F
eqt(request, pending) → F
eqt(request, release) → F
eqt(request, request) → T
eqt(request, resource) → F
eqt(request, tag) → F
eqt(request, true) → F
eqt(request, undefined) → F
eqt(request, pid(N2)) → F
eqt(request, int(N2)) → F
eqt(request, cons(H2, T2)) → F
eqt(request, tuple(H2, T2)) → F
eqt(request, tuplenil(H2)) → F
eqt(resource, nil) → F
eqt(resource, a) → F
eqt(resource, excl) → F
eqt(resource, false) → F
eqt(resource, lock) → F
eqt(resource, locker) → F
eqt(resource, mcrlrecord) → F
eqt(resource, ok) → F
eqt(resource, pending) → F
eqt(resource, release) → F
eqt(resource, request) → F
eqt(resource, resource) → T
eqt(resource, tag) → F
eqt(resource, true) → F
eqt(resource, undefined) → F
eqt(resource, pid(N2)) → F
eqt(resource, int(N2)) → F
eqt(resource, cons(H2, T2)) → F
eqt(resource, tuple(H2, T2)) → F
eqt(resource, tuplenil(H2)) → F
eqt(tag, nil) → F
eqt(tag, a) → F
eqt(tag, excl) → F
eqt(tag, false) → F
eqt(tag, lock) → F
eqt(tag, locker) → F
eqt(tag, mcrlrecord) → F
eqt(tag, ok) → F
eqt(tag, pending) → F
eqt(tag, release) → F
eqt(tag, request) → F
eqt(tag, resource) → F
eqt(tag, tag) → T
eqt(tag, true) → F
eqt(tag, undefined) → F
eqt(tag, pid(N2)) → F
eqt(tag, int(N2)) → F
eqt(tag, cons(H2, T2)) → F
eqt(tag, tuple(H2, T2)) → F
eqt(tag, tuplenil(H2)) → F
eqt(true, nil) → F
eqt(true, a) → F
eqt(true, excl) → F
eqt(true, false) → F
eqt(true, lock) → F
eqt(true, locker) → F
eqt(true, mcrlrecord) → F
eqt(true, ok) → F
eqt(true, pending) → F
eqt(true, release) → F
eqt(true, request) → F
eqt(true, resource) → F
eqt(true, tag) → F
eqt(true, true) → T
eqt(true, undefined) → F
eqt(true, pid(N2)) → F
eqt(true, int(N2)) → F
eqt(true, cons(H2, T2)) → F
eqt(true, tuple(H2, T2)) → F
eqt(true, tuplenil(H2)) → F
eqt(undefined, nil) → F
eqt(undefined, a) → F
eqt(undefined, tuplenil(H2)) → F
eqt(pid(N1), nil) → F
eqt(pid(N1), a) → F
eqt(pid(N1), excl) → F
eqt(pid(N1), false) → F
eqt(pid(N1), lock) → F
eqt(pid(N1), locker) → F
eqt(pid(N1), mcrlrecord) → F
eqt(pid(N1), ok) → F
eqt(pid(N1), pending) → F
eqt(pid(N1), release) → F
eqt(pid(N1), request) → F
eqt(pid(N1), resource) → F
eqt(pid(N1), tag) → F
eqt(pid(N1), true) → F
eqt(pid(N1), undefined) → F
eqt(pid(N1), pid(N2)) → eqt(N1, N2)
eqt(pid(N1), int(N2)) → F
eqt(pid(N1), cons(H2, T2)) → F
eqt(pid(N1), tuple(H2, T2)) → F
eqt(pid(N1), tuplenil(H2)) → F
eqt(int(N1), nil) → F
eqt(int(N1), a) → F
eqt(int(N1), excl) → F
eqt(int(N1), false) → F
eqt(int(N1), lock) → F
eqt(int(N1), locker) → F
eqt(int(N1), mcrlrecord) → F
eqt(int(N1), ok) → F
eqt(int(N1), pending) → F
eqt(int(N1), release) → F
eqt(int(N1), request) → F
eqt(int(N1), resource) → F
eqt(int(N1), tag) → F
eqt(int(N1), true) → F
eqt(int(N1), undefined) → F
eqt(cons(H1, T1), resource) → F
eqt(cons(H1, T1), tag) → F
eqt(cons(H1, T1), true) → F
eqt(cons(H1, T1), undefined) → F
eqt(cons(H1, T1), pid(N2)) → F
eqt(cons(H1, T1), int(N2)) → F
eqt(cons(H1, T1), cons(H2, T2)) → and(eqt(H1, H2), eqt(T1, T2))
eqt(cons(H1, T1), tuple(H2, T2)) → F
eqt(cons(H1, T1), tuplenil(H2)) → F
eqt(tuple(H1, T1), nil) → F
eqt(tuple(H1, T1), a) → F
eqt(tuple(H1, T1), excl) → F
eqt(tuple(H1, T1), false) → F
eqt(tuple(H1, T1), lock) → F
eqt(tuple(H1, T1), locker) → F
eqt(tuple(H1, T1), mcrlrecord) → F
eqt(tuple(H1, T1), ok) → F
eqt(tuple(H1, T1), pending) → F
eqt(tuple(H1, T1), release) → F
eqt(tuple(H1, T1), request) → F
eqt(tuple(H1, T1), resource) → F
eqt(tuple(H1, T1), tag) → F
eqt(tuple(H1, T1), true) → F
eqt(tuple(H1, T1), undefined) → F
eqt(tuple(H1, T1), pid(N2)) → F
eqt(tuple(H1, T1), int(N2)) → F
eqt(tuple(H1, T1), cons(H2, T2)) → F
eqt(tuple(H1, T1), tuple(H2, T2)) → and(eqt(H1, H2), eqt(T1, T2))
eqt(tuple(H1, T1), tuplenil(H2)) → F
eqt(tuplenil(H1), nil) → F
eqt(tuplenil(H1), a) → F
eqt(tuplenil(H1), excl) → F
eqt(tuplenil(H1), false) → F
eqt(tuplenil(H1), lock) → F
eqt(tuplenil(H1), locker) → F
eqt(tuplenil(H1), mcrlrecord) → F
eqt(tuplenil(H1), ok) → F
eqt(tuplenil(H1), pending) → F
eqt(tuplenil(H1), release) → F
eqt(tuplenil(H1), request) → F
eqt(tuplenil(H1), resource) → F
eqt(tuplenil(H1), tag) → F
eqt(tuplenil(H1), true) → F
eqt(tuplenil(H1), undefined) → F
eqt(tuplenil(H1), pid(N2)) → F
eqt(tuplenil(H1), int(N2)) → F
eqt(tuplenil(H1), cons(H2, T2)) → F
eqt(tuplenil(H1), tuple(H2, T2)) → F
eqt(tuplenil(H1), tuplenil(H2)) → eqt(H1, H2)
element(int(s(0)), tuplenil(T1)) → T1
element(int(s(0)), tuple(T1, T2)) → T1
element(int(s(s(N1))), tuple(T1, T2)) → element(int(s(N1)), T2)
record_new(lock) → tuple(mcrlrecord, tuple(lock, tuple(undefined, tuple(nil, tuplenil(nil)))))
record_extract(tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))), lock, resource) → tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2)))))
record_update(tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))), lock, pending, NewF) → tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(NewF)))))
record_updates(Record, Name, nil) → Record
record_updates(Record, Name, cons(tuple(Field, tuplenil(NewF)), Fields)) → record_updates(record_update(Record, Name, Field, NewF), Name, Fields)
locker2_map_promote_pending(nil, Pending) → nil
locker2_map_promote_pending(cons(Lock, Locks), Pending) → cons(locker2_promote_pending(Lock, Pending), locker2_map_promote_pending(Locks, Pending))
locker2_map_claim_lock(nil, Resources, Client) → nil
locker2_map_claim_lock(cons(Lock, Locks), Resources, Client) → cons(locker2_claim_lock(Lock, Resources, Client), locker2_map_claim_lock(Locks, Resources, Client))
locker2_map_add_pending(nil, Resources, Client) → nil
locker2_promote_pending(Lock, Client) → case0(Client, Lock, record_extract(Lock, lock, pending))
case0(Client, Lock, cons(Client, Pendings)) → record_updates(Lock, lock, cons(tuple(excl, tuplenil(Client)), cons(tuple(pending, tuplenil(Pendings)), nil)))
case0(Client, Lock, MCRLFree0) → Lock
locker2_remove_pending(Lock, Client) → record_updates(Lock, lock, cons(tuple(pending, tuplenil(subtract(record_extract(Lock, lock, pending), cons(Client, nil)))), nil))
locker2_add_pending(Lock, Resources, Client) → case1(Client, Resources, Lock, member(record_extract(Lock, lock, resource), Resources))
case1(Client, Resources, Lock, true) → record_updates(Lock, lock, cons(tuple(pending, tuplenil(append(record_extract(Lock, lock, pending), cons(Client, nil)))), nil))
case1(Client, Resources, Lock, false) → Lock
locker2_release_lock(Lock, Client) → case2(Client, Lock, gen_modtageq(Client, record_extract(Lock, lock, excl)))
case2(Client, Lock, true) → record_updates(Lock, lock, cons(tuple(excllock, excl), nil))
case4(Client, Lock, MCRLFree1) → false
locker2_obtainables(nil, Client) → true
locker2_obtainables(cons(Lock, Locks), Client) → case5(Client, Locks, Lock, member(Client, record_extract(Lock, lock, pending)))
case5(Client, Locks, Lock, true) → andt(locker2_obtainable(Lock, Client), locker2_obtainables(Locks, Client))
case5(Client, Locks, Lock, false) → locker2_obtainables(Locks, Client)
locker2_check_available(Resource, nil) → false
locker2_check_available(Resource, cons(Lock, Locks)) → case6(Locks, Lock, Resource, equal(Resource, record_extract(Lock, lock, resource)))
case6(Locks, Lock, Resource, true) → andt(equal(record_extract(Lock, lock, excl), nil), equal(record_extract(Lock, lock, pending), nil))
case6(Locks, Lock, Resource, false) → locker2_check_available(Resource, Locks)
locker2_check_availables(nil, Locks) → true
locker2_check_availables(cons(Resource, Resources), Locks) → andt(locker2_check_available(Resource, Locks), locker2_check_availables(Resources, Locks))
locker2_adduniq(nil, List) → List
append(cons(Head, Tail), List) → cons(Head, append(Tail, List))
subtract(List, nil) → List
subtract(List, cons(Head, Tail)) → subtract(delete(Head, List), Tail)
delete(E, nil) → nil
delete(E, cons(Head, Tail)) → case8(Tail, Head, E, equal(E, Head))
case8(Tail, Head, E, true) → Tail
case8(Tail, Head, E, false) → cons(Head, delete(E, Tail))
gen_tag(Pid) → tuple(Pid, tuplenil(tag))
gen_modtageq(Client1, Client2) → equal(Client1, Client2)
member(E, nil) → false
member(E, cons(Head, Tail)) → case9(Tail, Head, E, equal(E, Head))
case9(Tail, Head, E, true) → true
case9(Tail, Head, E, false) → member(E, Tail)
eqs(empty, empty) → T
eqs(empty, stack(E2, S2)) → F
eqs(stack(E1, S1), empty) → F
eqs(stack(E1, S1), stack(E2, S2)) → and(eqt(E1, E2), eqs(S1, S2))
pushs(E1, S1) → stack(E1, S1)
pops(stack(E1, S1)) → S1
tops(stack(E1, S1)) → E1
istops(E1, empty) → F
istops(E1, stack(E2, S1)) → eqt(E1, E2)
eqc(nocalls, nocalls) → T
eqc(nocalls, calls(E2, S2, CS2)) → F
eqc(calls(E1, S1, CS1), nocalls) → F
eqc(calls(E1, S1, CS1), calls(E2, S2, CS2)) → and(eqt(E1, E2), and(eqs(S1, S2), eqc(CS1, CS2)))
push(E1, E2, nocalls) → calls(E1, stack(E2, empty), nocalls)
push(E1, E2, calls(E3, S1, CS1)) → push1(E1, E2, E3, S1, CS1, eqt(E1, E3))
push1(E1, E2, E3, S1, CS1, T) → calls(E3, pushs(E2, S1), CS1)

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

(48) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

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

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
EQS(x1, x2) = EQS(x1)
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(x1, x2, x3)
eq(x1, x2) = eq
eqt(x1, x2) = eqt(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) = element(x1, x2)
s(x1) = x1
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, 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)
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, x4)
member(x1, x2) = member(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
locker2_obtainables(x1, x2) = x1
case5(x1, x2, x3, x4) = case5(x2, x3, x4)
andt(x1, x2) = andt(x1, x2)
locker2_obtainable(x1, x2) = locker2_obtainable
locker2_check_available(x1, x2) = locker2_check_available
case6(x1, x2, x3, x4) = case6
equal(x1, x2) = equal
locker2_check_availables(x1, x2) = locker2_check_availables(x1)
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)
eqs(x1, x2) = eqs(x1, x2)
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(x2, x3, x4, x5)

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

EQS₁ > [excl, record_extract₂, locker2_{claim_lock}, excllock, locker2_obtainable, empty]
imp₁ > [or, T, eq, eqt₁] > and₂ > [F, undefined, mcrlrecord] > tuple₂ > [excl, record_extract₂, locker2_{claim_lock}, excllock, locker2_obtainable, empty]
imp₁ > [or, T, eq, eqt₁] > pushs₂ > stack₂ > [excl, record_extract₂, locker2_{claim_lock}, excllock, locker2_obtainable, empty]
not₁ > [or, T, eq, eqt₁] > and₂ > [F, undefined, mcrlrecord] > tuple₂ > [excl, record_extract₂, locker2_{claim_lock}, excllock, locker2_obtainable, empty]
not₁ > [or, T, eq, eqt₁] > pushs₂ > stack₂ > [excl, record_extract₂, locker2_{claim_lock}, excllock, locker2_obtainable, empty]
if₃ > [excl, record_extract₂, locker2_{claim_lock}, excllock, locker2_obtainable, empty]
int > element₂ > [excl, record_extract₂, locker2_{claim_lock}, excllock, locker2_obtainable, empty]
a > [or, T, eq, eqt₁] > and₂ > [F, undefined, mcrlrecord] > tuple₂ > [excl, record_extract₂, locker2_{claim_lock}, excllock, locker2_obtainable, empty]
a > [or, T, eq, eqt₁] > pushs₂ > stack₂ > [excl, record_extract₂, locker2_{claim_lock}, excllock, locker2_obtainable, empty]
[lock, locker2_{add_pending₃}] > [or, T, eq, eqt₁] > and₂ > [F, undefined, mcrlrecord] > tuple₂ > [excl, record_extract₂, locker2_{claim_lock}, excllock, locker2_obtainable, empty]
[lock, locker2_{add_pending₃}] > [or, T, eq, eqt₁] > pushs₂ > stack₂ > [excl, record_extract₂, locker2_{claim_lock}, excllock, locker2_obtainable, empty]
[lock, locker2_{add_pending₃}] > resource > [F, undefined, mcrlrecord] > tuple₂ > [excl, record_extract₂, locker2_{claim_lock}, excllock, locker2_obtainable, empty]
[lock, locker2_{add_pending₃}] > case1₄ > [cons₂, case8₂] > pending > tuple₂ > [excl, record_extract₂, locker2_{claim_lock}, excllock, locker2_obtainable, empty]
[lock, locker2_{add_pending₃}] > case1₄ > [cons₂, case8₂] > case5₃ > andt₂ > [excl, record_extract₂, locker2_{claim_lock}, excllock, locker2_obtainable, empty]
[lock, locker2_{add_pending₃}] > case1₄ > [cons₂, case8₂] > case9₁ > [nil, true, locker2_{map_{add_pending}}] > [record_update₃, record_updates₂] > tuple₂ > [excl, record_extract₂, locker2_{claim_lock}, excllock, locker2_obtainable, empty]
[lock, locker2_{add_pending₃}] > case1₄ > [cons₂, case8₂] > case9₁ > [false, member₁] > [excl, record_extract₂, locker2_{claim_lock}, excllock, locker2_obtainable, empty]
locker > [excl, record_extract₂, locker2_{claim_lock}, excllock, locker2_obtainable, empty]
ok > [F, undefined, mcrlrecord] > tuple₂ > [excl, record_extract₂, locker2_{claim_lock}, excllock, locker2_obtainable, empty]
release > [F, undefined, mcrlrecord] > tuple₂ > [excl, record_extract₂, locker2_{claim_lock}, excllock, locker2_obtainable, empty]
request > [F, undefined, mcrlrecord] > tuple₂ > [excl, record_extract₂, locker2_{claim_lock}, excllock, locker2_obtainable, empty]
0 > [excl, record_extract₂, locker2_{claim_lock}, excllock, locker2_obtainable, empty]
record_new₁ > tuple₂ > [excl, record_extract₂, locker2_{claim_lock}, excllock, locker2_obtainable, empty]
locker2_{map_{promote_pending₂}} > locker2_{promote_pending₂} > case0₂ > [cons₂, case8₂] > pending > tuple₂ > [excl, record_extract₂, locker2_{claim_lock}, excllock, locker2_obtainable, empty]
locker2_{map_{promote_pending₂}} > locker2_{promote_pending₂} > case0₂ > [cons₂, case8₂] > case5₃ > andt₂ > [excl, record_extract₂, locker2_{claim_lock}, excllock, locker2_obtainable, empty]
locker2_{map_{promote_pending₂}} > locker2_{promote_pending₂} > case0₂ > [cons₂, case8₂] > case9₁ > [nil, true, locker2_{map_{add_pending}}] > [record_update₃, record_updates₂] > tuple₂ > [excl, record_extract₂, locker2_{claim_lock}, excllock, locker2_obtainable, empty]
locker2_{map_{promote_pending₂}} > locker2_{promote_pending₂} > case0₂ > [cons₂, case8₂] > case9₁ > [false, member₁] > [excl, record_extract₂, locker2_{claim_lock}, excllock, locker2_obtainable, empty]
locker2_{remove_pending₁} > [cons₂, case8₂] > pending > tuple₂ > [excl, record_extract₂, locker2_{claim_lock}, excllock, locker2_obtainable, empty]
locker2_{remove_pending₁} > [cons₂, case8₂] > case5₃ > andt₂ > [excl, record_extract₂, locker2_{claim_lock}, excllock, locker2_obtainable, empty]
locker2_{remove_pending₁} > [cons₂, case8₂] > case9₁ > [nil, true, locker2_{map_{add_pending}}] > [record_update₃, record_updates₂] > tuple₂ > [excl, record_extract₂, locker2_{claim_lock}, excllock, locker2_obtainable, empty]
locker2_{remove_pending₁} > [cons₂, case8₂] > case9₁ > [false, member₁] > [excl, record_extract₂, locker2_{claim_lock}, excllock, locker2_obtainable, empty]
locker2_{release_lock₂} > case2₃ > [cons₂, case8₂] > pending > tuple₂ > [excl, record_extract₂, locker2_{claim_lock}, excllock, locker2_obtainable, empty]
locker2_{release_lock₂} > case2₃ > [cons₂, case8₂] > case5₃ > andt₂ > [excl, record_extract₂, locker2_{claim_lock}, excllock, locker2_obtainable, empty]
locker2_{release_lock₂} > case2₃ > [cons₂, case8₂] > case9₁ > [nil, true, locker2_{map_{add_pending}}] > [record_update₃, record_updates₂] > tuple₂ > [excl, record_extract₂, locker2_{claim_lock}, excllock, locker2_obtainable, empty]
locker2_{release_lock₂} > case2₃ > [cons₂, case8₂] > case9₁ > [false, member₁] > [excl, record_extract₂, locker2_{claim_lock}, excllock, locker2_obtainable, empty]
locker2_{release_lock₂} > gen_modtageq₂ > equal > [excl, record_extract₂, locker2_{claim_lock}, excllock, locker2_obtainable, empty]
case4 > [false, member₁] > [excl, record_extract₂, locker2_{claim_lock}, excllock, locker2_obtainable, empty]
locker2_{check_{availables₁}} > [locker2_{check_available}, case6] > [nil, true, locker2_{map_{add_pending}}] > [record_update₃, record_updates₂] > tuple₂ > [excl, record_extract₂, locker2_{claim_lock}, excllock, locker2_obtainable, empty]
locker2_{check_{availables₁}} > [locker2_{check_available}, case6] > [false, member₁] > [excl, record_extract₂, locker2_{claim_lock}, excllock, locker2_obtainable, empty]
locker2_{check_{availables₁}} > [locker2_{check_available}, case6] > pending > tuple₂ > [excl, record_extract₂, locker2_{claim_lock}, excllock, locker2_obtainable, empty]
locker2_{check_{availables₁}} > [locker2_{check_available}, case6] > resource > [F, undefined, mcrlrecord] > tuple₂ > [excl, record_extract₂, locker2_{claim_lock}, excllock, locker2_obtainable, empty]
locker2_{check_{availables₁}} > [locker2_{check_available}, case6] > andt₂ > [excl, record_extract₂, locker2_{claim_lock}, excllock, locker2_obtainable, empty]
locker2_{check_{availables₁}} > [locker2_{check_available}, case6] > equal > [excl, record_extract₂, locker2_{claim_lock}, excllock, locker2_obtainable, empty]
locker2_adduniq₂ > [excl, record_extract₂, locker2_{claim_lock}, excllock, locker2_obtainable, empty]
gen_tag₁ > tag > [or, T, eq, eqt₁] > and₂ > [F, undefined, mcrlrecord] > tuple₂ > [excl, record_extract₂, locker2_{claim_lock}, excllock, locker2_obtainable, empty]
gen_tag₁ > tag > [or, T, eq, eqt₁] > pushs₂ > stack₂ > [excl, record_extract₂, locker2_{claim_lock}, excllock, locker2_obtainable, empty]
[eqs₂, eqc₂] > [or, T, eq, eqt₁] > and₂ > [F, undefined, mcrlrecord] > tuple₂ > [excl, record_extract₂, locker2_{claim_lock}, excllock, locker2_obtainable, empty]
[eqs₂, eqc₂] > [or, T, eq, eqt₁] > pushs₂ > stack₂ > [excl, record_extract₂, locker2_{claim_lock}, excllock, locker2_obtainable, empty]
pops₁ > [excl, record_extract₂, locker2_{claim_lock}, excllock, locker2_obtainable, empty]
tops₁ > [excl, record_extract₂, locker2_{claim_lock}, excllock, locker2_obtainable, empty]
istops₂ > [or, T, eq, eqt₁] > and₂ > [F, undefined, mcrlrecord] > tuple₂ > [excl, record_extract₂, locker2_{claim_lock}, excllock, locker2_obtainable, empty]
istops₂ > [or, T, eq, eqt₁] > pushs₂ > stack₂ > [excl, record_extract₂, locker2_{claim_lock}, excllock, locker2_obtainable, empty]
push₃ > nocalls > [or, T, eq, eqt₁] > and₂ > [F, undefined, mcrlrecord] > tuple₂ > [excl, record_extract₂, locker2_{claim_lock}, excllock, locker2_obtainable, empty]
push₃ > nocalls > [or, T, eq, eqt₁] > pushs₂ > stack₂ > [excl, record_extract₂, locker2_{claim_lock}, excllock, locker2_obtainable, empty]
push₃ > push1₄ > calls₃ > [or, T, eq, eqt₁] > and₂ > [F, undefined, mcrlrecord] > tuple₂ > [excl, record_extract₂, locker2_{claim_lock}, excllock, locker2_obtainable, empty]
push₃ > push1₄ > calls₃ > [or, T, eq, eqt₁] > pushs₂ > stack₂ > [excl, record_extract₂, locker2_{claim_lock}, excllock, locker2_obtainable, empty]

Status:

EQS₁: [1]
stack₂: [1,2]
or: []
T: []
F: []
and₂: [2,1]
imp₁: [1]
not₁: [1]
if₃: [1,2,3]
eq: []
eqt₁: [1]
nil: []
undefined: []
int: []
cons₂: [2,1]
tuple₂: [2,1]
a: []
excl: []
false: []
lock: []
locker: []
mcrlrecord: []
ok: []
pending: []
release: []
request: []
resource: []
tag: []
true: []
element₂: [1,2]
0: []
record_new₁: [1]
record_extract₂: [2,1]
record_update₃: [2,1,3]
record_updates₂: [2,1]
locker2_{map_{promote_pending₂}}: [1,2]
locker2_{promote_pending₂}: [2,1]
locker2_{claim_lock}: []
locker2_{map_{add_pending}}: []
case0₂: [2,1]
locker2_{remove_pending₁}: [1]
locker2_{add_pending₃}: [3,2,1]
case1₄: [4,3,2,1]
member₁: [1]
locker2_{release_lock₂}: [2,1]
case2₃: [3,2,1]
gen_modtageq₂: [1,2]
excllock: []
case4: []
case5₃: [2,1,3]
andt₂: [1,2]
locker2_obtainable: []
locker2_{check_available}: []
case6: []
equal: []
locker2_{check_{availables₁}}: [1]
locker2_adduniq₂: [1,2]
case8₂: [1,2]
gen_tag₁: [1]
case9₁: [1]
eqs₂: [1,2]
empty: []
pushs₂: [2,1]
pops₁: [1]
tops₁: [1]
istops₂: [2,1]
eqc₂: [1,2]
nocalls: []
calls₃: [3,2,1]
push₃: [3,1,2]
push1₄: [4,2,1,3]

The following usable rules [FROCOS05] were oriented:

or(T, T) → T
or(F, T) → T
or(T, F) → T
or(F, F) → F
and(T, B) → B
and(B, T) → B
and(F, B) → F
and(B, F) → F
imp(T, B) → B
imp(F, B) → T
not(T) → F
not(F) → T
if(T, B1, B2) → B1
if(F, B1, B2) → B2
eq(T, T) → T
eq(F, F) → T
eq(T, F) → F
eq(F, T) → F
eqt(nil, undefined) → F
eqt(nil, pid(N2)) → F
eqt(nil, int(N2)) → F
eqt(nil, cons(H2, T2)) → F
eqt(nil, tuple(H2, T2)) → F
eqt(nil, tuplenil(H2)) → F
eqt(a, nil) → F
eqt(a, a) → T
eqt(a, excl) → F
eqt(a, false) → F
eqt(a, lock) → F
eqt(a, locker) → F
eqt(a, mcrlrecord) → F
eqt(a, ok) → F
eqt(a, pending) → F
eqt(a, release) → F
eqt(a, request) → F
eqt(a, resource) → F
eqt(a, tag) → F
eqt(a, true) → F
eqt(a, undefined) → F
eqt(a, pid(N2)) → F
eqt(a, int(N2)) → F
eqt(a, cons(H2, T2)) → F
eqt(a, tuple(H2, T2)) → F
eqt(a, tuplenil(H2)) → F
eqt(excl, nil) → F
eqt(excl, a) → F
eqt(excl, excl) → T
eqt(excl, false) → F
eqt(excl, lock) → F
eqt(excl, locker) → F
eqt(excl, mcrlrecord) → F
eqt(excl, ok) → F
eqt(excl, pending) → F
eqt(excl, release) → F
eqt(excl, request) → F
eqt(excl, resource) → F
eqt(excl, tag) → F
eqt(excl, true) → F
eqt(excl, undefined) → F
eqt(excl, pid(N2)) → F
eqt(excl, eqt(false, int(N2))) → F
eqt(false, cons(H2, T2)) → F
eqt(false, tuple(H2, T2)) → F
eqt(false, tuplenil(H2)) → F
eqt(lock, nil) → F
eqt(lock, a) → F
eqt(lock, excl) → F
eqt(lock, false) → F
eqt(lock, lock) → T
eqt(lock, locker) → F
eqt(lock, mcrlrecord) → F
eqt(lock, ok) → F
eqt(lock, pending) → F
eqt(lock, release) → F
eqt(lock, request) → F
eqt(lock, resource) → F
eqt(lock, tag) → F
eqt(lock, true) → F
eqt(lock, undefined) → F
eqt(lock, pid(N2)) → F
eqt(lock, int(N2)) → F
eqt(lock, cons(H2, T2)) → F
eqt(lock, tuple(H2, T2)) → F
eqt(lock, tuplenil(H2)) → F
eqt(locker, nil) → F
eqt(locker, a) → F
eqt(locker, excl) → F
eqt(locker, false) → F
eqt(locker, lock) → F
eqt(locker, locker) → T
eqt(locker, mcrlrecord) → F
eqt(locker, ok) → F
eqt(locker, pending) → F
eqt(locker, release) → F
eqt(locker, request) → F
eqt(locker, resource) → F
eqt(locker, tag) → F
eqt(locker, true) → F
eqt(locker, undefined) → F
eqt(locker, pid(N2)) → F
eqt(locker, int(N2)) → F
eqt(locker, cons(H2, T2)) → F
eqt(locker, tuple(H2, T2)) → F
eqt(locker, tuplenil(H2)) → F
eqt(mcrlrecord, nil) → F
eqt(mcrlrecord, a) → F
eqt(mcrlrecord, excl) → F
eqt(mcrlrecord, false) → F
eqt(mcrlrecord, lock) → F
eqt(mcrlrecord, locker) → F
eqt(mcrlrecord, mcrlrecord) → T
eqt(mcrlrecord, ok) → F
eqt(mcrlrecord, pending) → F
eqt(mcrlrecord, release) → F
eqt(mcrlrecord, request) → F
eqt(mcrlrecord, resource) → F
eqt(ok, resource) → F
eqt(ok, tag) → F
eqt(ok, true) → F
eqt(ok, undefined) → F
eqt(ok, pid(N2)) → F
eqt(ok, int(N2)) → F
eqt(ok, cons(H2, T2)) → F
eqt(ok, tuple(H2, T2)) → F
eqt(ok, tuplenil(H2)) → F
eqt(pending, nil) → F
eqt(pending, a) → F
eqt(pending, excl) → F
eqt(pending, false) → F
eqt(pending, lock) → F
eqt(pending, locker) → F
eqt(pending, mcrlrecord) → F
eqt(pending, ok) → F
eqt(pending, pending) → T
eqt(pending, release) → F
eqt(pending, request) → F
eqt(pending, resource) → F
eqt(pending, tag) → F
eqt(pending, true) → F
eqt(pending, undefined) → F
eqt(pending, pid(N2)) → F
eqt(pending, int(N2)) → F
eqt(pending, cons(H2, T2)) → F
eqt(pending, tuple(H2, T2)) → F
eqt(pending, tuplenil(H2)) → F
eqt(release, nil) → F
eqt(release, a) → F
eqt(release, excl) → F
eqt(release, false) → F
eqt(release, lock) → F
eqt(release, locker) → F
eqt(release, mcrlrecord) → F
eqt(release, ok) → F
eqt(request, mcrlrecord) → F
eqt(request, ok) → F
eqt(request, pending) → F
eqt(request, release) → F
eqt(request, request) → T
eqt(request, resource) → F
eqt(request, tag) → F
eqt(request, true) → F
eqt(request, undefined) → F
eqt(request, pid(N2)) → F
eqt(request, int(N2)) → F
eqt(request, cons(H2, T2)) → F
eqt(request, tuple(H2, T2)) → F
eqt(request, tuplenil(H2)) → F
eqt(resource, nil) → F
eqt(resource, a) → F
eqt(resource, excl) → F
eqt(resource, false) → F
eqt(resource, lock) → F
eqt(resource, locker) → F
eqt(resource, mcrlrecord) → F
eqt(resource, ok) → F
eqt(resource, pending) → F
eqt(resource, release) → F
eqt(resource, request) → F
eqt(resource, resource) → T
eqt(resource, tag) → F
eqt(resource, true) → F
eqt(resource, undefined) → F
eqt(resource, pid(N2)) → F
eqt(resource, int(N2)) → F
eqt(resource, cons(H2, T2)) → F
eqt(resource, tuple(H2, T2)) → F
eqt(resource, tuplenil(H2)) → F
eqt(tag, nil) → F
eqt(tag, a) → F
eqt(tag, excl) → F
eqt(tag, false) → F
eqt(tag, lock) → F
eqt(tag, locker) → F
eqt(tag, mcrlrecord) → F
eqt(tag, ok) → F
eqt(tag, pending) → F
eqt(tag, release) → F
eqt(tag, request) → F
eqt(tag, resource) → F
eqt(tag, tag) → T
eqt(tag, true) → F
eqt(tag, undefined) → F
eqt(tag, pid(N2)) → F
eqt(tag, int(N2)) → F
eqt(tag, cons(H2, T2)) → F
eqt(tag, tuple(H2, T2)) → F
eqt(tag, tuplenil(H2)) → F
eqt(true, nil) → F
eqt(true, a) → F
eqt(true, excl) → F
eqt(true, false) → F
eqt(true, lock) → F
eqt(true, locker) → F
eqt(true, mcrlrecord) → F
eqt(true, ok) → F
eqt(true, pending) → F
eqt(true, release) → F
eqt(true, request) → F
eqt(true, resource) → F
eqt(true, tag) → F
eqt(true, true) → T
eqt(true, undefined) → F
eqt(true, pid(N2)) → F
eqt(true, int(N2)) → F
eqt(true, cons(H2, T2)) → F
eqt(true, tuple(H2, T2)) → F
eqt(true, tuplenil(H2)) → F
eqt(undefined, nil) → F
eqt(undefined, a) → F
eqt(undefined, tuplenil(H2)) → F
eqt(pid(N1), nil) → F
eqt(pid(N1), a) → F
eqt(pid(N1), excl) → F
eqt(pid(N1), false) → F
eqt(pid(N1), lock) → F
eqt(pid(N1), locker) → F
eqt(pid(N1), mcrlrecord) → F
eqt(pid(N1), ok) → F
eqt(pid(N1), pending) → F
eqt(pid(N1), release) → F
eqt(pid(N1), request) → F
eqt(pid(N1), resource) → F
eqt(pid(N1), tag) → F
eqt(pid(N1), true) → F
eqt(pid(N1), undefined) → F
eqt(pid(N1), pid(N2)) → eqt(N1, N2)
eqt(pid(N1), int(N2)) → F
eqt(pid(N1), cons(H2, T2)) → F
eqt(pid(N1), tuple(H2, T2)) → F
eqt(pid(N1), tuplenil(H2)) → F
eqt(int(N1), nil) → F
eqt(int(N1), a) → F
eqt(int(N1), excl) → F
eqt(int(N1), false) → F
eqt(int(N1), lock) → F
eqt(int(N1), locker) → F
eqt(int(N1), mcrlrecord) → F
eqt(int(N1), ok) → F
eqt(int(N1), pending) → F
eqt(int(N1), release) → F
eqt(int(N1), request) → F
eqt(int(N1), resource) → F
eqt(int(N1), tag) → F
eqt(int(N1), true) → F
eqt(int(N1), undefined) → F
eqt(cons(H1, T1), resource) → F
eqt(cons(H1, T1), tag) → F
eqt(cons(H1, T1), true) → F
eqt(cons(H1, T1), undefined) → F
eqt(cons(H1, T1), pid(N2)) → F
eqt(cons(H1, T1), int(N2)) → F
eqt(cons(H1, T1), cons(H2, T2)) → and(eqt(H1, H2), eqt(T1, T2))
eqt(cons(H1, T1), tuple(H2, T2)) → F
eqt(cons(H1, T1), tuplenil(H2)) → F
eqt(tuple(H1, T1), nil) → F
eqt(tuple(H1, T1), a) → F
eqt(tuple(H1, T1), excl) → F
eqt(tuple(H1, T1), false) → F
eqt(tuple(H1, T1), lock) → F
eqt(tuple(H1, T1), locker) → F
eqt(tuple(H1, T1), mcrlrecord) → F
eqt(tuple(H1, T1), ok) → F
eqt(tuple(H1, T1), pending) → F
eqt(tuple(H1, T1), release) → F
eqt(tuple(H1, T1), request) → F
eqt(tuple(H1, T1), resource) → F
eqt(tuple(H1, T1), tag) → F
eqt(tuple(H1, T1), true) → F
eqt(tuple(H1, T1), undefined) → F
eqt(tuple(H1, T1), pid(N2)) → F
eqt(tuple(H1, T1), int(N2)) → F
eqt(tuple(H1, T1), cons(H2, T2)) → F
eqt(tuple(H1, T1), tuple(H2, T2)) → and(eqt(H1, H2), eqt(T1, T2))
eqt(tuple(H1, T1), tuplenil(H2)) → F
eqt(tuplenil(H1), nil) → F
eqt(tuplenil(H1), a) → F
eqt(tuplenil(H1), excl) → F
eqt(tuplenil(H1), false) → F
eqt(tuplenil(H1), lock) → F
eqt(tuplenil(H1), locker) → F
eqt(tuplenil(H1), mcrlrecord) → F
eqt(tuplenil(H1), ok) → F
eqt(tuplenil(H1), pending) → F
eqt(tuplenil(H1), release) → F
eqt(tuplenil(H1), request) → F
eqt(tuplenil(H1), resource) → F
eqt(tuplenil(H1), tag) → F
eqt(tuplenil(H1), true) → F
eqt(tuplenil(H1), undefined) → F
eqt(tuplenil(H1), pid(N2)) → F
eqt(tuplenil(H1), int(N2)) → F
eqt(tuplenil(H1), cons(H2, T2)) → F
eqt(tuplenil(H1), tuple(H2, T2)) → F
eqt(tuplenil(H1), tuplenil(H2)) → eqt(H1, H2)
element(int(s(0)), tuplenil(T1)) → T1
element(int(s(0)), tuple(T1, T2)) → T1
element(int(s(s(N1))), tuple(T1, T2)) → element(int(s(N1)), T2)
record_new(lock) → tuple(mcrlrecord, tuple(lock, tuple(undefined, tuple(nil, tuplenil(nil)))))
record_extract(tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))), lock, resource) → tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2)))))
record_update(tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))), lock, pending, NewF) → tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(NewF)))))
record_updates(Record, Name, nil) → Record
record_updates(Record, Name, cons(tuple(Field, tuplenil(NewF)), Fields)) → record_updates(record_update(Record, Name, Field, NewF), Name, Fields)
locker2_map_promote_pending(nil, Pending) → nil
locker2_map_promote_pending(cons(Lock, Locks), Pending) → cons(locker2_promote_pending(Lock, Pending), locker2_map_promote_pending(Locks, Pending))
locker2_map_claim_lock(nil, Resources, Client) → nil
locker2_map_claim_lock(cons(Lock, Locks), Resources, Client) → cons(locker2_claim_lock(Lock, Resources, Client), locker2_map_claim_lock(Locks, Resources, Client))
locker2_map_add_pending(nil, Resources, Client) → nil
locker2_promote_pending(Lock, Client) → case0(Client, Lock, record_extract(Lock, lock, pending))
case0(Client, Lock, cons(Client, Pendings)) → record_updates(Lock, lock, cons(tuple(excl, tuplenil(Client)), cons(tuple(pending, tuplenil(Pendings)), nil)))
case0(Client, Lock, MCRLFree0) → Lock
locker2_remove_pending(Lock, Client) → record_updates(Lock, lock, cons(tuple(pending, tuplenil(subtract(record_extract(Lock, lock, pending), cons(Client, nil)))), nil))
locker2_add_pending(Lock, Resources, Client) → case1(Client, Resources, Lock, member(record_extract(Lock, lock, resource), Resources))
case1(Client, Resources, Lock, true) → record_updates(Lock, lock, cons(tuple(pending, tuplenil(append(record_extract(Lock, lock, pending), cons(Client, nil)))), nil))
case1(Client, Resources, Lock, false) → Lock
locker2_release_lock(Lock, Client) → case2(Client, Lock, gen_modtageq(Client, record_extract(Lock, lock, excl)))
case2(Client, Lock, true) → record_updates(Lock, lock, cons(tuple(excllock, excl), nil))
case4(Client, Lock, MCRLFree1) → false
locker2_obtainables(nil, Client) → true
locker2_obtainables(cons(Lock, Locks), Client) → case5(Client, Locks, Lock, member(Client, record_extract(Lock, lock, pending)))
case5(Client, Locks, Lock, true) → andt(locker2_obtainable(Lock, Client), locker2_obtainables(Locks, Client))
case5(Client, Locks, Lock, false) → locker2_obtainables(Locks, Client)
locker2_check_available(Resource, nil) → false
locker2_check_available(Resource, cons(Lock, Locks)) → case6(Locks, Lock, Resource, equal(Resource, record_extract(Lock, lock, resource)))
case6(Locks, Lock, Resource, true) → andt(equal(record_extract(Lock, lock, excl), nil), equal(record_extract(Lock, lock, pending), nil))
case6(Locks, Lock, Resource, false) → locker2_check_available(Resource, Locks)
locker2_check_availables(nil, Locks) → true
locker2_check_availables(cons(Resource, Resources), Locks) → andt(locker2_check_available(Resource, Locks), locker2_check_availables(Resources, Locks))
locker2_adduniq(nil, List) → List
append(cons(Head, Tail), List) → cons(Head, append(Tail, List))
subtract(List, nil) → List
subtract(List, cons(Head, Tail)) → subtract(delete(Head, List), Tail)
delete(E, nil) → nil
delete(E, cons(Head, Tail)) → case8(Tail, Head, E, equal(E, Head))
case8(Tail, Head, E, true) → Tail
case8(Tail, Head, E, false) → cons(Head, delete(E, Tail))
gen_tag(Pid) → tuple(Pid, tuplenil(tag))
gen_modtageq(Client1, Client2) → equal(Client1, Client2)
member(E, nil) → false
member(E, cons(Head, Tail)) → case9(Tail, Head, E, equal(E, Head))
case9(Tail, Head, E, true) → true
case9(Tail, Head, E, false) → member(E, Tail)
eqs(empty, empty) → T
eqs(empty, stack(E2, S2)) → F
eqs(stack(E1, S1), empty) → F
eqs(stack(E1, S1), stack(E2, S2)) → and(eqt(E1, E2), eqs(S1, S2))
pushs(E1, S1) → stack(E1, S1)
pops(stack(E1, S1)) → S1
tops(stack(E1, S1)) → E1
istops(E1, empty) → F
istops(E1, stack(E2, S1)) → eqt(E1, E2)
eqc(nocalls, nocalls) → T
eqc(nocalls, calls(E2, S2, CS2)) → F
eqc(calls(E1, S1, CS1), nocalls) → F
eqc(calls(E1, S1, CS1), calls(E2, S2, CS2)) → and(eqt(E1, E2), and(eqs(S1, S2), eqc(CS1, CS2)))
push(E1, E2, nocalls) → calls(E1, stack(E2, empty), nocalls)
push(E1, E2, calls(E3, S1, CS1)) → push1(E1, E2, E3, S1, CS1, eqt(E1, E3))
push1(E1, E2, E3, S1, CS1, T) → calls(E3, pushs(E2, S1), CS1)

(49) Obligation:

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

or(T, T) → T
or(F, T) → T
or(T, F) → T
or(F, F) → F
and(T, B) → B
and(B, T) → B
and(F, B) → F
and(B, F) → F
imp(T, B) → B
imp(F, B) → T
not(T) → F
not(F) → T
if(T, B1, B2) → B1
if(F, B1, B2) → B2
eq(T, T) → T
eq(F, F) → T
eq(T, F) → F
eq(F, T) → F
eqt(nil, undefined) → F
eqt(nil, pid(N2)) → F
eqt(nil, int(N2)) → F
eqt(nil, cons(H2, T2)) → F
eqt(nil, tuple(H2, T2)) → F
eqt(nil, tuplenil(H2)) → F
eqt(a, nil) → F
eqt(a, a) → T
eqt(a, excl) → F
eqt(a, false) → F
eqt(a, lock) → F
eqt(a, locker) → F
eqt(a, mcrlrecord) → F
eqt(a, ok) → F
eqt(a, pending) → F
eqt(a, release) → F
eqt(a, request) → F
eqt(a, resource) → F
eqt(a, tag) → F
eqt(a, true) → F
eqt(a, undefined) → F
eqt(a, pid(N2)) → F
eqt(a, int(N2)) → F
eqt(a, cons(H2, T2)) → F
eqt(a, tuple(H2, T2)) → F
eqt(a, tuplenil(H2)) → F
eqt(excl, nil) → F
eqt(excl, a) → F
eqt(excl, excl) → T
eqt(excl, false) → F
eqt(excl, lock) → F
eqt(excl, locker) → F
eqt(excl, mcrlrecord) → F
eqt(excl, ok) → F
eqt(excl, pending) → F
eqt(excl, release) → F
eqt(excl, request) → F
eqt(excl, resource) → F
eqt(excl, tag) → F
eqt(excl, true) → F
eqt(excl, undefined) → F
eqt(excl, pid(N2)) → F
eqt(excl, eqt(false, int(N2))) → F
eqt(false, cons(H2, T2)) → F
eqt(false, tuple(H2, T2)) → F
eqt(false, tuplenil(H2)) → F
eqt(lock, nil) → F
eqt(lock, a) → F
eqt(lock, excl) → F
eqt(lock, false) → F
eqt(lock, lock) → T
eqt(lock, locker) → F
eqt(lock, mcrlrecord) → F
eqt(lock, ok) → F
eqt(lock, pending) → F
eqt(lock, release) → F
eqt(lock, request) → F
eqt(lock, resource) → F
eqt(lock, tag) → F
eqt(lock, true) → F
eqt(lock, undefined) → F
eqt(lock, pid(N2)) → F
eqt(lock, int(N2)) → F
eqt(lock, cons(H2, T2)) → F
eqt(lock, tuple(H2, T2)) → F
eqt(lock, tuplenil(H2)) → F
eqt(locker, nil) → F
eqt(locker, a) → F
eqt(locker, excl) → F
eqt(locker, false) → F
eqt(locker, lock) → F
eqt(locker, locker) → T
eqt(locker, mcrlrecord) → F
eqt(locker, ok) → F
eqt(locker, pending) → F
eqt(locker, release) → F
eqt(locker, request) → F
eqt(locker, resource) → F
eqt(locker, tag) → F
eqt(locker, true) → F
eqt(locker, undefined) → F
eqt(locker, pid(N2)) → F
eqt(locker, int(N2)) → F
eqt(locker, cons(H2, T2)) → F
eqt(locker, tuple(H2, T2)) → F
eqt(locker, tuplenil(H2)) → F
eqt(mcrlrecord, nil) → F
eqt(mcrlrecord, a) → F
eqt(mcrlrecord, excl) → F
eqt(mcrlrecord, false) → F
eqt(mcrlrecord, lock) → F
eqt(mcrlrecord, locker) → F
eqt(mcrlrecord, mcrlrecord) → T
eqt(mcrlrecord, ok) → F
eqt(mcrlrecord, pending) → F
eqt(mcrlrecord, release) → F
eqt(mcrlrecord, request) → F
eqt(mcrlrecord, resource) → F
eqt(ok, resource) → F
eqt(ok, tag) → F
eqt(ok, true) → F
eqt(ok, undefined) → F
eqt(ok, pid(N2)) → F
eqt(ok, int(N2)) → F
eqt(ok, cons(H2, T2)) → F
eqt(ok, tuple(H2, T2)) → F
eqt(ok, tuplenil(H2)) → F
eqt(pending, nil) → F
eqt(pending, a) → F
eqt(pending, excl) → F
eqt(pending, false) → F
eqt(pending, lock) → F
eqt(pending, locker) → F
eqt(pending, mcrlrecord) → F
eqt(pending, ok) → F
eqt(pending, pending) → T
eqt(pending, release) → F
eqt(pending, request) → F
eqt(pending, resource) → F
eqt(pending, tag) → F
eqt(pending, true) → F
eqt(pending, undefined) → F
eqt(pending, pid(N2)) → F
eqt(pending, int(N2)) → F
eqt(pending, cons(H2, T2)) → F
eqt(pending, tuple(H2, T2)) → F
eqt(pending, tuplenil(H2)) → F
eqt(release, nil) → F
eqt(release, a) → F
eqt(release, excl) → F
eqt(release, false) → F
eqt(release, lock) → F
eqt(release, locker) → F
eqt(release, mcrlrecord) → F
eqt(release, ok) → F
eqt(request, mcrlrecord) → F
eqt(request, ok) → F
eqt(request, pending) → F
eqt(request, release) → F
eqt(request, request) → T
eqt(request, resource) → F
eqt(request, tag) → F
eqt(request, true) → F
eqt(request, undefined) → F
eqt(request, pid(N2)) → F
eqt(request, int(N2)) → F
eqt(request, cons(H2, T2)) → F
eqt(request, tuple(H2, T2)) → F
eqt(request, tuplenil(H2)) → F
eqt(resource, nil) → F
eqt(resource, a) → F
eqt(resource, excl) → F
eqt(resource, false) → F
eqt(resource, lock) → F
eqt(resource, locker) → F
eqt(resource, mcrlrecord) → F
eqt(resource, ok) → F
eqt(resource, pending) → F
eqt(resource, release) → F
eqt(resource, request) → F
eqt(resource, resource) → T
eqt(resource, tag) → F
eqt(resource, true) → F
eqt(resource, undefined) → F
eqt(resource, pid(N2)) → F
eqt(resource, int(N2)) → F
eqt(resource, cons(H2, T2)) → F
eqt(resource, tuple(H2, T2)) → F
eqt(resource, tuplenil(H2)) → F
eqt(tag, nil) → F
eqt(tag, a) → F
eqt(tag, excl) → F
eqt(tag, false) → F
eqt(tag, lock) → F
eqt(tag, locker) → F
eqt(tag, mcrlrecord) → F
eqt(tag, ok) → F
eqt(tag, pending) → F
eqt(tag, release) → F
eqt(tag, request) → F
eqt(tag, resource) → F
eqt(tag, tag) → T
eqt(tag, true) → F
eqt(tag, undefined) → F
eqt(tag, pid(N2)) → F
eqt(tag, int(N2)) → F
eqt(tag, cons(H2, T2)) → F
eqt(tag, tuple(H2, T2)) → F
eqt(tag, tuplenil(H2)) → F
eqt(true, nil) → F
eqt(true, a) → F
eqt(true, excl) → F
eqt(true, false) → F
eqt(true, lock) → F
eqt(true, locker) → F
eqt(true, mcrlrecord) → F
eqt(true, ok) → F
eqt(true, pending) → F
eqt(true, release) → F
eqt(true, request) → F
eqt(true, resource) → F
eqt(true, tag) → F
eqt(true, true) → T
eqt(true, undefined) → F
eqt(true, pid(N2)) → F
eqt(true, int(N2)) → F
eqt(true, cons(H2, T2)) → F
eqt(true, tuple(H2, T2)) → F
eqt(true, tuplenil(H2)) → F
eqt(undefined, nil) → F
eqt(undefined, a) → F
eqt(undefined, tuplenil(H2)) → F
eqt(pid(N1), nil) → F
eqt(pid(N1), a) → F
eqt(pid(N1), excl) → F
eqt(pid(N1), false) → F
eqt(pid(N1), lock) → F
eqt(pid(N1), locker) → F
eqt(pid(N1), mcrlrecord) → F
eqt(pid(N1), ok) → F
eqt(pid(N1), pending) → F
eqt(pid(N1), release) → F
eqt(pid(N1), request) → F
eqt(pid(N1), resource) → F
eqt(pid(N1), tag) → F
eqt(pid(N1), true) → F
eqt(pid(N1), undefined) → F
eqt(pid(N1), pid(N2)) → eqt(N1, N2)
eqt(pid(N1), int(N2)) → F
eqt(pid(N1), cons(H2, T2)) → F
eqt(pid(N1), tuple(H2, T2)) → F
eqt(pid(N1), tuplenil(H2)) → F
eqt(int(N1), nil) → F
eqt(int(N1), a) → F
eqt(int(N1), excl) → F
eqt(int(N1), false) → F
eqt(int(N1), lock) → F
eqt(int(N1), locker) → F
eqt(int(N1), mcrlrecord) → F
eqt(int(N1), ok) → F
eqt(int(N1), pending) → F
eqt(int(N1), release) → F
eqt(int(N1), request) → F
eqt(int(N1), resource) → F
eqt(int(N1), tag) → F
eqt(int(N1), true) → F
eqt(int(N1), undefined) → F
eqt(cons(H1, T1), resource) → F
eqt(cons(H1, T1), tag) → F
eqt(cons(H1, T1), true) → F
eqt(cons(H1, T1), undefined) → F
eqt(cons(H1, T1), pid(N2)) → F
eqt(cons(H1, T1), int(N2)) → F
eqt(cons(H1, T1), cons(H2, T2)) → and(eqt(H1, H2), eqt(T1, T2))
eqt(cons(H1, T1), tuple(H2, T2)) → F
eqt(cons(H1, T1), tuplenil(H2)) → F
eqt(tuple(H1, T1), nil) → F
eqt(tuple(H1, T1), a) → F
eqt(tuple(H1, T1), excl) → F
eqt(tuple(H1, T1), false) → F
eqt(tuple(H1, T1), lock) → F
eqt(tuple(H1, T1), locker) → F
eqt(tuple(H1, T1), mcrlrecord) → F
eqt(tuple(H1, T1), ok) → F
eqt(tuple(H1, T1), pending) → F
eqt(tuple(H1, T1), release) → F
eqt(tuple(H1, T1), request) → F
eqt(tuple(H1, T1), resource) → F
eqt(tuple(H1, T1), tag) → F
eqt(tuple(H1, T1), true) → F
eqt(tuple(H1, T1), undefined) → F
eqt(tuple(H1, T1), pid(N2)) → F
eqt(tuple(H1, T1), int(N2)) → F
eqt(tuple(H1, T1), cons(H2, T2)) → F
eqt(tuple(H1, T1), tuple(H2, T2)) → and(eqt(H1, H2), eqt(T1, T2))
eqt(tuple(H1, T1), tuplenil(H2)) → F
eqt(tuplenil(H1), nil) → F
eqt(tuplenil(H1), a) → F
eqt(tuplenil(H1), excl) → F
eqt(tuplenil(H1), false) → F
eqt(tuplenil(H1), lock) → F
eqt(tuplenil(H1), locker) → F
eqt(tuplenil(H1), mcrlrecord) → F
eqt(tuplenil(H1), ok) → F
eqt(tuplenil(H1), pending) → F
eqt(tuplenil(H1), release) → F
eqt(tuplenil(H1), request) → F
eqt(tuplenil(H1), resource) → F
eqt(tuplenil(H1), tag) → F
eqt(tuplenil(H1), true) → F
eqt(tuplenil(H1), undefined) → F
eqt(tuplenil(H1), pid(N2)) → F
eqt(tuplenil(H1), int(N2)) → F
eqt(tuplenil(H1), cons(H2, T2)) → F
eqt(tuplenil(H1), tuple(H2, T2)) → F
eqt(tuplenil(H1), tuplenil(H2)) → eqt(H1, H2)
element(int(s(0)), tuplenil(T1)) → T1
element(int(s(0)), tuple(T1, T2)) → T1
element(int(s(s(N1))), tuple(T1, T2)) → element(int(s(N1)), T2)
record_new(lock) → tuple(mcrlrecord, tuple(lock, tuple(undefined, tuple(nil, tuplenil(nil)))))
record_extract(tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))), lock, resource) → tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2)))))
record_update(tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))), lock, pending, NewF) → tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(NewF)))))
record_updates(Record, Name, nil) → Record
record_updates(Record, Name, cons(tuple(Field, tuplenil(NewF)), Fields)) → record_updates(record_update(Record, Name, Field, NewF), Name, Fields)
locker2_map_promote_pending(nil, Pending) → nil
locker2_map_promote_pending(cons(Lock, Locks), Pending) → cons(locker2_promote_pending(Lock, Pending), locker2_map_promote_pending(Locks, Pending))
locker2_map_claim_lock(nil, Resources, Client) → nil
locker2_map_claim_lock(cons(Lock, Locks), Resources, Client) → cons(locker2_claim_lock(Lock, Resources, Client), locker2_map_claim_lock(Locks, Resources, Client))
locker2_map_add_pending(nil, Resources, Client) → nil
locker2_promote_pending(Lock, Client) → case0(Client, Lock, record_extract(Lock, lock, pending))
case0(Client, Lock, cons(Client, Pendings)) → record_updates(Lock, lock, cons(tuple(excl, tuplenil(Client)), cons(tuple(pending, tuplenil(Pendings)), nil)))
case0(Client, Lock, MCRLFree0) → Lock
locker2_remove_pending(Lock, Client) → record_updates(Lock, lock, cons(tuple(pending, tuplenil(subtract(record_extract(Lock, lock, pending), cons(Client, nil)))), nil))
locker2_add_pending(Lock, Resources, Client) → case1(Client, Resources, Lock, member(record_extract(Lock, lock, resource), Resources))
case1(Client, Resources, Lock, true) → record_updates(Lock, lock, cons(tuple(pending, tuplenil(append(record_extract(Lock, lock, pending), cons(Client, nil)))), nil))
case1(Client, Resources, Lock, false) → Lock
locker2_release_lock(Lock, Client) → case2(Client, Lock, gen_modtageq(Client, record_extract(Lock, lock, excl)))
case2(Client, Lock, true) → record_updates(Lock, lock, cons(tuple(excllock, excl), nil))
case4(Client, Lock, MCRLFree1) → false
locker2_obtainables(nil, Client) → true
locker2_obtainables(cons(Lock, Locks), Client) → case5(Client, Locks, Lock, member(Client, record_extract(Lock, lock, pending)))
case5(Client, Locks, Lock, true) → andt(locker2_obtainable(Lock, Client), locker2_obtainables(Locks, Client))
case5(Client, Locks, Lock, false) → locker2_obtainables(Locks, Client)
locker2_check_available(Resource, nil) → false
locker2_check_available(Resource, cons(Lock, Locks)) → case6(Locks, Lock, Resource, equal(Resource, record_extract(Lock, lock, resource)))
case6(Locks, Lock, Resource, true) → andt(equal(record_extract(Lock, lock, excl), nil), equal(record_extract(Lock, lock, pending), nil))
case6(Locks, Lock, Resource, false) → locker2_check_available(Resource, Locks)
locker2_check_availables(nil, Locks) → true
locker2_check_availables(cons(Resource, Resources), Locks) → andt(locker2_check_available(Resource, Locks), locker2_check_availables(Resources, Locks))
locker2_adduniq(nil, List) → List
append(cons(Head, Tail), List) → cons(Head, append(Tail, List))
subtract(List, nil) → List
subtract(List, cons(Head, Tail)) → subtract(delete(Head, List), Tail)
delete(E, nil) → nil
delete(E, cons(Head, Tail)) → case8(Tail, Head, E, equal(E, Head))
case8(Tail, Head, E, true) → Tail
case8(Tail, Head, E, false) → cons(Head, delete(E, Tail))
gen_tag(Pid) → tuple(Pid, tuplenil(tag))
gen_modtageq(Client1, Client2) → equal(Client1, Client2)
member(E, nil) → false
member(E, cons(Head, Tail)) → case9(Tail, Head, E, equal(E, Head))
case9(Tail, Head, E, true) → true
case9(Tail, Head, E, false) → member(E, Tail)
eqs(empty, empty) → T
eqs(empty, stack(E2, S2)) → F
eqs(stack(E1, S1), empty) → F
eqs(stack(E1, S1), stack(E2, S2)) → and(eqt(E1, E2), eqs(S1, S2))
pushs(E1, S1) → stack(E1, S1)
pops(stack(E1, S1)) → S1
tops(stack(E1, S1)) → E1
istops(E1, empty) → F
istops(E1, stack(E2, S1)) → eqt(E1, E2)
eqc(nocalls, nocalls) → T
eqc(nocalls, calls(E2, S2, CS2)) → F
eqc(calls(E1, S1, CS1), nocalls) → F
eqc(calls(E1, S1, CS1), calls(E2, S2, CS2)) → and(eqt(E1, E2), and(eqs(S1, S2), eqc(CS1, CS2)))
push(E1, E2, nocalls) → calls(E1, stack(E2, empty), nocalls)
push(E1, E2, calls(E3, S1, CS1)) → push1(E1, E2, E3, S1, CS1, eqt(E1, E3))
push1(E1, E2, E3, S1, CS1, T) → calls(E3, pushs(E2, S1), CS1)

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

(50) PisEmptyProof (EQUIVALENT transformation)

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

(51) TRUE

(52) Obligation:

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

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

The TRS R consists of the following rules:

or(T, T) → T
or(F, T) → T
or(T, F) → T
or(F, F) → F
and(T, B) → B
and(B, T) → B
and(F, B) → F
and(B, F) → F
imp(T, B) → B
imp(F, B) → T
not(T) → F
not(F) → T
if(T, B1, B2) → B1
if(F, B1, B2) → B2
eq(T, T) → T
eq(F, F) → T
eq(T, F) → F
eq(F, T) → F
eqt(nil, undefined) → F
eqt(nil, pid(N2)) → F
eqt(nil, int(N2)) → F
eqt(nil, cons(H2, T2)) → F
eqt(nil, tuple(H2, T2)) → F
eqt(nil, tuplenil(H2)) → F
eqt(a, nil) → F
eqt(a, a) → T
eqt(a, excl) → F
eqt(a, false) → F
eqt(a, lock) → F
eqt(a, locker) → F
eqt(a, mcrlrecord) → F
eqt(a, ok) → F
eqt(a, pending) → F
eqt(a, release) → F
eqt(a, request) → F
eqt(a, resource) → F
eqt(a, tag) → F
eqt(a, true) → F
eqt(a, undefined) → F
eqt(a, pid(N2)) → F
eqt(a, int(N2)) → F
eqt(a, cons(H2, T2)) → F
eqt(a, tuple(H2, T2)) → F
eqt(a, tuplenil(H2)) → F
eqt(excl, nil) → F
eqt(excl, a) → F
eqt(excl, excl) → T
eqt(excl, false) → F
eqt(excl, lock) → F
eqt(excl, locker) → F
eqt(excl, mcrlrecord) → F
eqt(excl, ok) → F
eqt(excl, pending) → F
eqt(excl, release) → F
eqt(excl, request) → F
eqt(excl, resource) → F
eqt(excl, tag) → F
eqt(excl, true) → F
eqt(excl, undefined) → F
eqt(excl, pid(N2)) → F
eqt(excl, eqt(false, int(N2))) → F
eqt(false, cons(H2, T2)) → F
eqt(false, tuple(H2, T2)) → F
eqt(false, tuplenil(H2)) → F
eqt(lock, nil) → F
eqt(lock, a) → F
eqt(lock, excl) → F
eqt(lock, false) → F
eqt(lock, lock) → T
eqt(lock, locker) → F
eqt(lock, mcrlrecord) → F
eqt(lock, ok) → F
eqt(lock, pending) → F
eqt(lock, release) → F
eqt(lock, request) → F
eqt(lock, resource) → F
eqt(lock, tag) → F
eqt(lock, true) → F
eqt(lock, undefined) → F
eqt(lock, pid(N2)) → F
eqt(lock, int(N2)) → F
eqt(lock, cons(H2, T2)) → F
eqt(lock, tuple(H2, T2)) → F
eqt(lock, tuplenil(H2)) → F
eqt(locker, nil) → F
eqt(locker, a) → F
eqt(locker, excl) → F
eqt(locker, false) → F
eqt(locker, lock) → F
eqt(locker, locker) → T
eqt(locker, mcrlrecord) → F
eqt(locker, ok) → F
eqt(locker, pending) → F
eqt(locker, release) → F
eqt(locker, request) → F
eqt(locker, resource) → F
eqt(locker, tag) → F
eqt(locker, true) → F
eqt(locker, undefined) → F
eqt(locker, pid(N2)) → F
eqt(locker, int(N2)) → F
eqt(locker, cons(H2, T2)) → F
eqt(locker, tuple(H2, T2)) → F
eqt(locker, tuplenil(H2)) → F
eqt(mcrlrecord, nil) → F
eqt(mcrlrecord, a) → F
eqt(mcrlrecord, excl) → F
eqt(mcrlrecord, false) → F
eqt(mcrlrecord, lock) → F
eqt(mcrlrecord, locker) → F
eqt(mcrlrecord, mcrlrecord) → T
eqt(mcrlrecord, ok) → F
eqt(mcrlrecord, pending) → F
eqt(mcrlrecord, release) → F
eqt(mcrlrecord, request) → F
eqt(mcrlrecord, resource) → F
eqt(ok, resource) → F
eqt(ok, tag) → F
eqt(ok, true) → F
eqt(ok, undefined) → F
eqt(ok, pid(N2)) → F
eqt(ok, int(N2)) → F
eqt(ok, cons(H2, T2)) → F
eqt(ok, tuple(H2, T2)) → F
eqt(ok, tuplenil(H2)) → F
eqt(pending, nil) → F
eqt(pending, a) → F
eqt(pending, excl) → F
eqt(pending, false) → F
eqt(pending, lock) → F
eqt(pending, locker) → F
eqt(pending, mcrlrecord) → F
eqt(pending, ok) → F
eqt(pending, pending) → T
eqt(pending, release) → F
eqt(pending, request) → F
eqt(pending, resource) → F
eqt(pending, tag) → F
eqt(pending, true) → F
eqt(pending, undefined) → F
eqt(pending, pid(N2)) → F
eqt(pending, int(N2)) → F
eqt(pending, cons(H2, T2)) → F
eqt(pending, tuple(H2, T2)) → F
eqt(pending, tuplenil(H2)) → F
eqt(release, nil) → F
eqt(release, a) → F
eqt(release, excl) → F
eqt(release, false) → F
eqt(release, lock) → F
eqt(release, locker) → F
eqt(release, mcrlrecord) → F
eqt(release, ok) → F
eqt(request, mcrlrecord) → F
eqt(request, ok) → F
eqt(request, pending) → F
eqt(request, release) → F
eqt(request, request) → T
eqt(request, resource) → F
eqt(request, tag) → F
eqt(request, true) → F
eqt(request, undefined) → F
eqt(request, pid(N2)) → F
eqt(request, int(N2)) → F
eqt(request, cons(H2, T2)) → F
eqt(request, tuple(H2, T2)) → F
eqt(request, tuplenil(H2)) → F
eqt(resource, nil) → F
eqt(resource, a) → F
eqt(resource, excl) → F
eqt(resource, false) → F
eqt(resource, lock) → F
eqt(resource, locker) → F
eqt(resource, mcrlrecord) → F
eqt(resource, ok) → F
eqt(resource, pending) → F
eqt(resource, release) → F
eqt(resource, request) → F
eqt(resource, resource) → T
eqt(resource, tag) → F
eqt(resource, true) → F
eqt(resource, undefined) → F
eqt(resource, pid(N2)) → F
eqt(resource, int(N2)) → F
eqt(resource, cons(H2, T2)) → F
eqt(resource, tuple(H2, T2)) → F
eqt(resource, tuplenil(H2)) → F
eqt(tag, nil) → F
eqt(tag, a) → F
eqt(tag, excl) → F
eqt(tag, false) → F
eqt(tag, lock) → F
eqt(tag, locker) → F
eqt(tag, mcrlrecord) → F
eqt(tag, ok) → F
eqt(tag, pending) → F
eqt(tag, release) → F
eqt(tag, request) → F
eqt(tag, resource) → F
eqt(tag, tag) → T
eqt(tag, true) → F
eqt(tag, undefined) → F
eqt(tag, pid(N2)) → F
eqt(tag, int(N2)) → F
eqt(tag, cons(H2, T2)) → F
eqt(tag, tuple(H2, T2)) → F
eqt(tag, tuplenil(H2)) → F
eqt(true, nil) → F
eqt(true, a) → F
eqt(true, excl) → F
eqt(true, false) → F
eqt(true, lock) → F
eqt(true, locker) → F
eqt(true, mcrlrecord) → F
eqt(true, ok) → F
eqt(true, pending) → F
eqt(true, release) → F
eqt(true, request) → F
eqt(true, resource) → F
eqt(true, tag) → F
eqt(true, true) → T
eqt(true, undefined) → F
eqt(true, pid(N2)) → F
eqt(true, int(N2)) → F
eqt(true, cons(H2, T2)) → F
eqt(true, tuple(H2, T2)) → F
eqt(true, tuplenil(H2)) → F
eqt(undefined, nil) → F
eqt(undefined, a) → F
eqt(undefined, tuplenil(H2)) → F
eqt(pid(N1), nil) → F
eqt(pid(N1), a) → F
eqt(pid(N1), excl) → F
eqt(pid(N1), false) → F
eqt(pid(N1), lock) → F
eqt(pid(N1), locker) → F
eqt(pid(N1), mcrlrecord) → F
eqt(pid(N1), ok) → F
eqt(pid(N1), pending) → F
eqt(pid(N1), release) → F
eqt(pid(N1), request) → F
eqt(pid(N1), resource) → F
eqt(pid(N1), tag) → F
eqt(pid(N1), true) → F
eqt(pid(N1), undefined) → F
eqt(pid(N1), pid(N2)) → eqt(N1, N2)
eqt(pid(N1), int(N2)) → F
eqt(pid(N1), cons(H2, T2)) → F
eqt(pid(N1), tuple(H2, T2)) → F
eqt(pid(N1), tuplenil(H2)) → F
eqt(int(N1), nil) → F
eqt(int(N1), a) → F
eqt(int(N1), excl) → F
eqt(int(N1), false) → F
eqt(int(N1), lock) → F
eqt(int(N1), locker) → F
eqt(int(N1), mcrlrecord) → F
eqt(int(N1), ok) → F
eqt(int(N1), pending) → F
eqt(int(N1), release) → F
eqt(int(N1), request) → F
eqt(int(N1), resource) → F
eqt(int(N1), tag) → F
eqt(int(N1), true) → F
eqt(int(N1), undefined) → F
eqt(cons(H1, T1), resource) → F
eqt(cons(H1, T1), tag) → F
eqt(cons(H1, T1), true) → F
eqt(cons(H1, T1), undefined) → F
eqt(cons(H1, T1), pid(N2)) → F
eqt(cons(H1, T1), int(N2)) → F
eqt(cons(H1, T1), cons(H2, T2)) → and(eqt(H1, H2), eqt(T1, T2))
eqt(cons(H1, T1), tuple(H2, T2)) → F
eqt(cons(H1, T1), tuplenil(H2)) → F
eqt(tuple(H1, T1), nil) → F
eqt(tuple(H1, T1), a) → F
eqt(tuple(H1, T1), excl) → F
eqt(tuple(H1, T1), false) → F
eqt(tuple(H1, T1), lock) → F
eqt(tuple(H1, T1), locker) → F
eqt(tuple(H1, T1), mcrlrecord) → F
eqt(tuple(H1, T1), ok) → F
eqt(tuple(H1, T1), pending) → F
eqt(tuple(H1, T1), release) → F
eqt(tuple(H1, T1), request) → F
eqt(tuple(H1, T1), resource) → F
eqt(tuple(H1, T1), tag) → F
eqt(tuple(H1, T1), true) → F
eqt(tuple(H1, T1), undefined) → F
eqt(tuple(H1, T1), pid(N2)) → F
eqt(tuple(H1, T1), int(N2)) → F
eqt(tuple(H1, T1), cons(H2, T2)) → F
eqt(tuple(H1, T1), tuple(H2, T2)) → and(eqt(H1, H2), eqt(T1, T2))
eqt(tuple(H1, T1), tuplenil(H2)) → F
eqt(tuplenil(H1), nil) → F
eqt(tuplenil(H1), a) → F
eqt(tuplenil(H1), excl) → F
eqt(tuplenil(H1), false) → F
eqt(tuplenil(H1), lock) → F
eqt(tuplenil(H1), locker) → F
eqt(tuplenil(H1), mcrlrecord) → F
eqt(tuplenil(H1), ok) → F
eqt(tuplenil(H1), pending) → F
eqt(tuplenil(H1), release) → F
eqt(tuplenil(H1), request) → F
eqt(tuplenil(H1), resource) → F
eqt(tuplenil(H1), tag) → F
eqt(tuplenil(H1), true) → F
eqt(tuplenil(H1), undefined) → F
eqt(tuplenil(H1), pid(N2)) → F
eqt(tuplenil(H1), int(N2)) → F
eqt(tuplenil(H1), cons(H2, T2)) → F
eqt(tuplenil(H1), tuple(H2, T2)) → F
eqt(tuplenil(H1), tuplenil(H2)) → eqt(H1, H2)
element(int(s(0)), tuplenil(T1)) → T1
element(int(s(0)), tuple(T1, T2)) → T1
element(int(s(s(N1))), tuple(T1, T2)) → element(int(s(N1)), T2)
record_new(lock) → tuple(mcrlrecord, tuple(lock, tuple(undefined, tuple(nil, tuplenil(nil)))))
record_extract(tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))), lock, resource) → tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2)))))
record_update(tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))), lock, pending, NewF) → tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(NewF)))))
record_updates(Record, Name, nil) → Record
record_updates(Record, Name, cons(tuple(Field, tuplenil(NewF)), Fields)) → record_updates(record_update(Record, Name, Field, NewF), Name, Fields)
locker2_map_promote_pending(nil, Pending) → nil
locker2_map_promote_pending(cons(Lock, Locks), Pending) → cons(locker2_promote_pending(Lock, Pending), locker2_map_promote_pending(Locks, Pending))
locker2_map_claim_lock(nil, Resources, Client) → nil
locker2_map_claim_lock(cons(Lock, Locks), Resources, Client) → cons(locker2_claim_lock(Lock, Resources, Client), locker2_map_claim_lock(Locks, Resources, Client))
locker2_map_add_pending(nil, Resources, Client) → nil
locker2_promote_pending(Lock, Client) → case0(Client, Lock, record_extract(Lock, lock, pending))
case0(Client, Lock, cons(Client, Pendings)) → record_updates(Lock, lock, cons(tuple(excl, tuplenil(Client)), cons(tuple(pending, tuplenil(Pendings)), nil)))
case0(Client, Lock, MCRLFree0) → Lock
locker2_remove_pending(Lock, Client) → record_updates(Lock, lock, cons(tuple(pending, tuplenil(subtract(record_extract(Lock, lock, pending), cons(Client, nil)))), nil))
locker2_add_pending(Lock, Resources, Client) → case1(Client, Resources, Lock, member(record_extract(Lock, lock, resource), Resources))
case1(Client, Resources, Lock, true) → record_updates(Lock, lock, cons(tuple(pending, tuplenil(append(record_extract(Lock, lock, pending), cons(Client, nil)))), nil))
case1(Client, Resources, Lock, false) → Lock
locker2_release_lock(Lock, Client) → case2(Client, Lock, gen_modtageq(Client, record_extract(Lock, lock, excl)))
case2(Client, Lock, true) → record_updates(Lock, lock, cons(tuple(excllock, excl), nil))
case4(Client, Lock, MCRLFree1) → false
locker2_obtainables(nil, Client) → true
locker2_obtainables(cons(Lock, Locks), Client) → case5(Client, Locks, Lock, member(Client, record_extract(Lock, lock, pending)))
case5(Client, Locks, Lock, true) → andt(locker2_obtainable(Lock, Client), locker2_obtainables(Locks, Client))
case5(Client, Locks, Lock, false) → locker2_obtainables(Locks, Client)
locker2_check_available(Resource, nil) → false
locker2_check_available(Resource, cons(Lock, Locks)) → case6(Locks, Lock, Resource, equal(Resource, record_extract(Lock, lock, resource)))
case6(Locks, Lock, Resource, true) → andt(equal(record_extract(Lock, lock, excl), nil), equal(record_extract(Lock, lock, pending), nil))
case6(Locks, Lock, Resource, false) → locker2_check_available(Resource, Locks)
locker2_check_availables(nil, Locks) → true
locker2_check_availables(cons(Resource, Resources), Locks) → andt(locker2_check_available(Resource, Locks), locker2_check_availables(Resources, Locks))
locker2_adduniq(nil, List) → List
append(cons(Head, Tail), List) → cons(Head, append(Tail, List))
subtract(List, nil) → List
subtract(List, cons(Head, Tail)) → subtract(delete(Head, List), Tail)
delete(E, nil) → nil
delete(E, cons(Head, Tail)) → case8(Tail, Head, E, equal(E, Head))
case8(Tail, Head, E, true) → Tail
case8(Tail, Head, E, false) → cons(Head, delete(E, Tail))
gen_tag(Pid) → tuple(Pid, tuplenil(tag))
gen_modtageq(Client1, Client2) → equal(Client1, Client2)
member(E, nil) → false
member(E, cons(Head, Tail)) → case9(Tail, Head, E, equal(E, Head))
case9(Tail, Head, E, true) → true
case9(Tail, Head, E, false) → member(E, Tail)
eqs(empty, empty) → T
eqs(empty, stack(E2, S2)) → F
eqs(stack(E1, S1), empty) → F
eqs(stack(E1, S1), stack(E2, S2)) → and(eqt(E1, E2), eqs(S1, S2))
pushs(E1, S1) → stack(E1, S1)
pops(stack(E1, S1)) → S1
tops(stack(E1, S1)) → E1
istops(E1, empty) → F
istops(E1, stack(E2, S1)) → eqt(E1, E2)
eqc(nocalls, nocalls) → T
eqc(nocalls, calls(E2, S2, CS2)) → F
eqc(calls(E1, S1, CS1), nocalls) → F
eqc(calls(E1, S1, CS1), calls(E2, S2, CS2)) → and(eqt(E1, E2), and(eqs(S1, S2), eqc(CS1, CS2)))
push(E1, E2, nocalls) → calls(E1, stack(E2, empty), nocalls)
push(E1, E2, calls(E3, S1, CS1)) → push1(E1, E2, E3, S1, CS1, eqt(E1, E3))
push1(E1, E2, E3, S1, CS1, T) → calls(E3, pushs(E2, S1), CS1)

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

(53) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

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

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
EQC(x1, x2) = x2
calls(x1, x2, x3) = calls(x1, x2, x3)
or(x1, x2) = x1
T = T
F = F
and(x1, x2) = and(x1, x2)
imp(x1, x2) = imp(x2)
not(x1) = not
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) = pid(x1)
int(x1) = int
cons(x1, x2) = cons(x1, x2)
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) = 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, 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) = x2
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)
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, x4)
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(x1)
excllock = excllock
case4(x1, x2, x3) = case4
locker2_obtainables(x1, x2) = locker2_obtainables
case5(x1, x2, x3, x4) = case5
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) = x4
equal(x1, x2) = equal
locker2_check_availables(x1, x2) = locker2_check_availables(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) = 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) = tops(x1)
istops(x1, x2) = istops(x1, x2)
eqc(x1, x2) = eqc(x1, x2)
nocalls = nocalls
push(x1, x2, x3) = push(x1, x2, x3)
push1(x1, x2, x3, x4, x5, x6) = push1(x1, x2, x3, x4, x5, x6)

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

imp₁ > T > [excl, empty, nocalls]
not > [F, a, release] > T > [excl, empty, nocalls]
if₃ > [excl, empty, nocalls]
eq₂ > T > [excl, empty, nocalls]
pid₁ > [F, a, release] > T > [excl, empty, nocalls]
locker > T > [excl, empty, nocalls]
ok > [excl, empty, nocalls]
request > [F, a, release] > T > [excl, empty, nocalls]
[tag, gen_tag₁] > [F, a, release] > T > [excl, empty, nocalls]
[tag, gen_tag₁] > [cons₂, tuplenil₁, case8₂] > [nil, locker2_{map_{add_pending}}] > [excl, empty, nocalls]
[tag, gen_tag₁] > [cons₂, tuplenil₁, case8₂] > tuple₂ > and₂ > [excl, empty, nocalls]
[tag, gen_tag₁] > [cons₂, tuplenil₁, case8₂] > tuple₂ > int > [excl, empty, nocalls]
[tag, gen_tag₁] > [cons₂, tuplenil₁, case8₂] > tuple₂ > mcrlrecord > T > [excl, empty, nocalls]
[tag, gen_tag₁] > [cons₂, tuplenil₁, case8₂] > resource > T > [excl, empty, nocalls]
[tag, gen_tag₁] > [cons₂, tuplenil₁, case8₂] > record_extract₁ > [excl, empty, nocalls]
[tag, gen_tag₁] > [cons₂, tuplenil₁, case8₂] > andt > [excl, empty, nocalls]
0 > [excl, empty, nocalls]
record_new > [undefined, lock] > [cons₂, tuplenil₁, case8₂] > [nil, locker2_{map_{add_pending}}] > [excl, empty, nocalls]
record_new > [undefined, lock] > [cons₂, tuplenil₁, case8₂] > tuple₂ > and₂ > [excl, empty, nocalls]
record_new > [undefined, lock] > [cons₂, tuplenil₁, case8₂] > tuple₂ > int > [excl, empty, nocalls]
record_new > [undefined, lock] > [cons₂, tuplenil₁, case8₂] > tuple₂ > mcrlrecord > T > [excl, empty, nocalls]
record_new > [undefined, lock] > [cons₂, tuplenil₁, case8₂] > resource > T > [excl, empty, nocalls]
record_new > [undefined, lock] > [cons₂, tuplenil₁, case8₂] > record_extract₁ > [excl, empty, nocalls]
record_new > [undefined, lock] > [cons₂, tuplenil₁, case8₂] > andt > [excl, empty, nocalls]
[locker2_{map_{promote_pending₂}}, locker2_{promote_pending₂}] > case0₃ > [undefined, lock] > [cons₂, tuplenil₁, case8₂] > [nil, locker2_{map_{add_pending}}] > [excl, empty, nocalls]
[locker2_{map_{promote_pending₂}}, locker2_{promote_pending₂}] > case0₃ > [undefined, lock] > [cons₂, tuplenil₁, case8₂] > tuple₂ > and₂ > [excl, empty, nocalls]
[locker2_{map_{promote_pending₂}}, locker2_{promote_pending₂}] > case0₃ > [undefined, lock] > [cons₂, tuplenil₁, case8₂] > tuple₂ > int > [excl, empty, nocalls]
[locker2_{map_{promote_pending₂}}, locker2_{promote_pending₂}] > case0₃ > [undefined, lock] > [cons₂, tuplenil₁, case8₂] > tuple₂ > mcrlrecord > T > [excl, empty, nocalls]
[locker2_{map_{promote_pending₂}}, locker2_{promote_pending₂}] > case0₃ > [undefined, lock] > [cons₂, tuplenil₁, case8₂] > resource > T > [excl, empty, nocalls]
[locker2_{map_{promote_pending₂}}, locker2_{promote_pending₂}] > case0₃ > [undefined, lock] > [cons₂, tuplenil₁, case8₂] > record_extract₁ > [excl, empty, nocalls]
[locker2_{map_{promote_pending₂}}, locker2_{promote_pending₂}] > case0₃ > [undefined, lock] > [cons₂, tuplenil₁, case8₂] > andt > [excl, empty, nocalls]
[locker2_{map_{promote_pending₂}}, locker2_{promote_pending₂}] > case0₃ > pending > [cons₂, tuplenil₁, case8₂] > [nil, locker2_{map_{add_pending}}] > [excl, empty, nocalls]
[locker2_{map_{promote_pending₂}}, locker2_{promote_pending₂}] > case0₃ > pending > [cons₂, tuplenil₁, case8₂] > tuple₂ > and₂ > [excl, empty, nocalls]
[locker2_{map_{promote_pending₂}}, locker2_{promote_pending₂}] > case0₃ > pending > [cons₂, tuplenil₁, case8₂] > tuple₂ > int > [excl, empty, nocalls]
[locker2_{map_{promote_pending₂}}, locker2_{promote_pending₂}] > case0₃ > pending > [cons₂, tuplenil₁, case8₂] > tuple₂ > mcrlrecord > T > [excl, empty, nocalls]
[locker2_{map_{promote_pending₂}}, locker2_{promote_pending₂}] > case0₃ > pending > [cons₂, tuplenil₁, case8₂] > resource > T > [excl, empty, nocalls]
[locker2_{map_{promote_pending₂}}, locker2_{promote_pending₂}] > case0₃ > pending > [cons₂, tuplenil₁, case8₂] > record_extract₁ > [excl, empty, nocalls]
[locker2_{map_{promote_pending₂}}, locker2_{promote_pending₂}] > case0₃ > pending > [cons₂, tuplenil₁, case8₂] > andt > [excl, empty, nocalls]
[locker2_{map_{promote_pending₂}}, locker2_{promote_pending₂}] > case0₃ > [record_update₂, record_updates₃] > [cons₂, tuplenil₁, case8₂] > [nil, locker2_{map_{add_pending}}] > [excl, empty, nocalls]
[locker2_{map_{promote_pending₂}}, locker2_{promote_pending₂}] > case0₃ > [record_update₂, record_updates₃] > [cons₂, tuplenil₁, case8₂] > tuple₂ > and₂ > [excl, empty, nocalls]
[locker2_{map_{promote_pending₂}}, locker2_{promote_pending₂}] > case0₃ > [record_update₂, record_updates₃] > [cons₂, tuplenil₁, case8₂] > tuple₂ > int > [excl, empty, nocalls]
[locker2_{map_{promote_pending₂}}, locker2_{promote_pending₂}] > case0₃ > [record_update₂, record_updates₃] > [cons₂, tuplenil₁, case8₂] > tuple₂ > mcrlrecord > T > [excl, empty, nocalls]
[locker2_{map_{promote_pending₂}}, locker2_{promote_pending₂}] > case0₃ > [record_update₂, record_updates₃] > [cons₂, tuplenil₁, case8₂] > resource > T > [excl, empty, nocalls]
[locker2_{map_{promote_pending₂}}, locker2_{promote_pending₂}] > case0₃ > [record_update₂, record_updates₃] > [cons₂, tuplenil₁, case8₂] > record_extract₁ > [excl, empty, nocalls]
[locker2_{map_{promote_pending₂}}, locker2_{promote_pending₂}] > case0₃ > [record_update₂, record_updates₃] > [cons₂, tuplenil₁, case8₂] > andt > [excl, empty, nocalls]
locker2_{map_{claim_lock₃}} > [cons₂, tuplenil₁, case8₂] > [nil, locker2_{map_{add_pending}}] > [excl, empty, nocalls]
locker2_{map_{claim_lock₃}} > [cons₂, tuplenil₁, case8₂] > tuple₂ > and₂ > [excl, empty, nocalls]
locker2_{map_{claim_lock₃}} > [cons₂, tuplenil₁, case8₂] > tuple₂ > int > [excl, empty, nocalls]
locker2_{map_{claim_lock₃}} > [cons₂, tuplenil₁, case8₂] > tuple₂ > mcrlrecord > T > [excl, empty, nocalls]
locker2_{map_{claim_lock₃}} > [cons₂, tuplenil₁, case8₂] > resource > T > [excl, empty, nocalls]
locker2_{map_{claim_lock₃}} > [cons₂, tuplenil₁, case8₂] > record_extract₁ > [excl, empty, nocalls]
locker2_{map_{claim_lock₃}} > [cons₂, tuplenil₁, case8₂] > andt > [excl, empty, nocalls]
locker2_{remove_pending₁} > [undefined, lock] > [cons₂, tuplenil₁, case8₂] > [nil, locker2_{map_{add_pending}}] > [excl, empty, nocalls]
locker2_{remove_pending₁} > [undefined, lock] > [cons₂, tuplenil₁, case8₂] > tuple₂ > and₂ > [excl, empty, nocalls]
locker2_{remove_pending₁} > [undefined, lock] > [cons₂, tuplenil₁, case8₂] > tuple₂ > int > [excl, empty, nocalls]
locker2_{remove_pending₁} > [undefined, lock] > [cons₂, tuplenil₁, case8₂] > tuple₂ > mcrlrecord > T > [excl, empty, nocalls]
locker2_{remove_pending₁} > [undefined, lock] > [cons₂, tuplenil₁, case8₂] > resource > T > [excl, empty, nocalls]
locker2_{remove_pending₁} > [undefined, lock] > [cons₂, tuplenil₁, case8₂] > record_extract₁ > [excl, empty, nocalls]
locker2_{remove_pending₁} > [undefined, lock] > [cons₂, tuplenil₁, case8₂] > andt > [excl, empty, nocalls]
locker2_{remove_pending₁} > pending > [cons₂, tuplenil₁, case8₂] > [nil, locker2_{map_{add_pending}}] > [excl, empty, nocalls]
locker2_{remove_pending₁} > pending > [cons₂, tuplenil₁, case8₂] > tuple₂ > and₂ > [excl, empty, nocalls]
locker2_{remove_pending₁} > pending > [cons₂, tuplenil₁, case8₂] > tuple₂ > int > [excl, empty, nocalls]
locker2_{remove_pending₁} > pending > [cons₂, tuplenil₁, case8₂] > tuple₂ > mcrlrecord > T > [excl, empty, nocalls]
locker2_{remove_pending₁} > pending > [cons₂, tuplenil₁, case8₂] > resource > T > [excl, empty, nocalls]
locker2_{remove_pending₁} > pending > [cons₂, tuplenil₁, case8₂] > record_extract₁ > [excl, empty, nocalls]
locker2_{remove_pending₁} > pending > [cons₂, tuplenil₁, case8₂] > andt > [excl, empty, nocalls]
locker2_{remove_pending₁} > [record_update₂, record_updates₃] > [cons₂, tuplenil₁, case8₂] > [nil, locker2_{map_{add_pending}}] > [excl, empty, nocalls]
locker2_{remove_pending₁} > [record_update₂, record_updates₃] > [cons₂, tuplenil₁, case8₂] > tuple₂ > and₂ > [excl, empty, nocalls]
locker2_{remove_pending₁} > [record_update₂, record_updates₃] > [cons₂, tuplenil₁, case8₂] > tuple₂ > int > [excl, empty, nocalls]
locker2_{remove_pending₁} > [record_update₂, record_updates₃] > [cons₂, tuplenil₁, case8₂] > tuple₂ > mcrlrecord > T > [excl, empty, nocalls]
locker2_{remove_pending₁} > [record_update₂, record_updates₃] > [cons₂, tuplenil₁, case8₂] > resource > T > [excl, empty, nocalls]
locker2_{remove_pending₁} > [record_update₂, record_updates₃] > [cons₂, tuplenil₁, case8₂] > record_extract₁ > [excl, empty, nocalls]
locker2_{remove_pending₁} > [record_update₂, record_updates₃] > [cons₂, tuplenil₁, case8₂] > andt > [excl, empty, nocalls]
locker2_{add_pending₃} > [false, member, locker2_{check_available}] > [locker2_obtainables, case5] > true > [F, a, release] > T > [excl, empty, nocalls]
locker2_{add_pending₃} > [false, member, locker2_{check_available}] > [locker2_obtainables, case5] > true > [undefined, lock] > [cons₂, tuplenil₁, case8₂] > [nil, locker2_{map_{add_pending}}] > [excl, empty, nocalls]
locker2_{add_pending₃} > [false, member, locker2_{check_available}] > [locker2_obtainables, case5] > true > [undefined, lock] > [cons₂, tuplenil₁, case8₂] > tuple₂ > and₂ > [excl, empty, nocalls]
locker2_{add_pending₃} > [false, member, locker2_{check_available}] > [locker2_obtainables, case5] > true > [undefined, lock] > [cons₂, tuplenil₁, case8₂] > tuple₂ > int > [excl, empty, nocalls]
locker2_{add_pending₃} > [false, member, locker2_{check_available}] > [locker2_obtainables, case5] > true > [undefined, lock] > [cons₂, tuplenil₁, case8₂] > tuple₂ > mcrlrecord > T > [excl, empty, nocalls]
locker2_{add_pending₃} > [false, member, locker2_{check_available}] > [locker2_obtainables, case5] > true > [undefined, lock] > [cons₂, tuplenil₁, case8₂] > resource > T > [excl, empty, nocalls]
locker2_{add_pending₃} > [false, member, locker2_{check_available}] > [locker2_obtainables, case5] > true > [undefined, lock] > [cons₂, tuplenil₁, case8₂] > record_extract₁ > [excl, empty, nocalls]
locker2_{add_pending₃} > [false, member, locker2_{check_available}] > [locker2_obtainables, case5] > true > [undefined, lock] > [cons₂, tuplenil₁, case8₂] > andt > [excl, empty, nocalls]
locker2_{add_pending₃} > [false, member, locker2_{check_available}] > [locker2_obtainables, case5] > true > pending > [cons₂, tuplenil₁, case8₂] > [nil, locker2_{map_{add_pending}}] > [excl, empty, nocalls]
locker2_{add_pending₃} > [false, member, locker2_{check_available}] > [locker2_obtainables, case5] > true > pending > [cons₂, tuplenil₁, case8₂] > tuple₂ > and₂ > [excl, empty, nocalls]
locker2_{add_pending₃} > [false, member, locker2_{check_available}] > [locker2_obtainables, case5] > true > pending > [cons₂, tuplenil₁, case8₂] > tuple₂ > int > [excl, empty, nocalls]
locker2_{add_pending₃} > [false, member, locker2_{check_available}] > [locker2_obtainables, case5] > true > pending > [cons₂, tuplenil₁, case8₂] > tuple₂ > mcrlrecord > T > [excl, empty, nocalls]
locker2_{add_pending₃} > [false, member, locker2_{check_available}] > [locker2_obtainables, case5] > true > pending > [cons₂, tuplenil₁, case8₂] > resource > T > [excl, empty, nocalls]
locker2_{add_pending₃} > [false, member, locker2_{check_available}] > [locker2_obtainables, case5] > true > pending > [cons₂, tuplenil₁, case8₂] > record_extract₁ > [excl, empty, nocalls]
locker2_{add_pending₃} > [false, member, locker2_{check_available}] > [locker2_obtainables, case5] > true > pending > [cons₂, tuplenil₁, case8₂] > andt > [excl, empty, nocalls]
locker2_{add_pending₃} > [false, member, locker2_{check_available}] > [locker2_obtainables, case5] > true > [record_update₂, record_updates₃] > [cons₂, tuplenil₁, case8₂] > [nil, locker2_{map_{add_pending}}] > [excl, empty, nocalls]
locker2_{add_pending₃} > [false, member, locker2_{check_available}] > [locker2_obtainables, case5] > true > [record_update₂, record_updates₃] > [cons₂, tuplenil₁, case8₂] > tuple₂ > and₂ > [excl, empty, nocalls]
locker2_{add_pending₃} > [false, member, locker2_{check_available}] > [locker2_obtainables, case5] > true > [record_update₂, record_updates₃] > [cons₂, tuplenil₁, case8₂] > tuple₂ > int > [excl, empty, nocalls]
locker2_{add_pending₃} > [false, member, locker2_{check_available}] > [locker2_obtainables, case5] > true > [record_update₂, record_updates₃] > [cons₂, tuplenil₁, case8₂] > tuple₂ > mcrlrecord > T > [excl, empty, nocalls]
locker2_{add_pending₃} > [false, member, locker2_{check_available}] > [locker2_obtainables, case5] > true > [record_update₂, record_updates₃] > [cons₂, tuplenil₁, case8₂] > resource > T > [excl, empty, nocalls]
locker2_{add_pending₃} > [false, member, locker2_{check_available}] > [locker2_obtainables, case5] > true > [record_update₂, record_updates₃] > [cons₂, tuplenil₁, case8₂] > record_extract₁ > [excl, empty, nocalls]
locker2_{add_pending₃} > [false, member, locker2_{check_available}] > [locker2_obtainables, case5] > true > [record_update₂, record_updates₃] > [cons₂, tuplenil₁, case8₂] > andt > [excl, empty, nocalls]
locker2_{add_pending₃} > [false, member, locker2_{check_available}] > [locker2_obtainables, case5] > true > excllock > [excl, empty, nocalls]
locker2_{add_pending₃} > [false, member, locker2_{check_available}] > [locker2_obtainables, case5] > locker2_{obtainable₂} > [excl, empty, nocalls]
locker2_{add_pending₃} > [false, member, locker2_{check_available}] > equal > [excl, empty, nocalls]
locker2_{add_pending₃} > case1₄ > [undefined, lock] > [cons₂, tuplenil₁, case8₂] > [nil, locker2_{map_{add_pending}}] > [excl, empty, nocalls]
locker2_{add_pending₃} > case1₄ > [undefined, lock] > [cons₂, tuplenil₁, case8₂] > tuple₂ > and₂ > [excl, empty, nocalls]
locker2_{add_pending₃} > case1₄ > [undefined, lock] > [cons₂, tuplenil₁, case8₂] > tuple₂ > int > [excl, empty, nocalls]
locker2_{add_pending₃} > case1₄ > [undefined, lock] > [cons₂, tuplenil₁, case8₂] > tuple₂ > mcrlrecord > T > [excl, empty, nocalls]
locker2_{add_pending₃} > case1₄ > [undefined, lock] > [cons₂, tuplenil₁, case8₂] > resource > T > [excl, empty, nocalls]
locker2_{add_pending₃} > case1₄ > [undefined, lock] > [cons₂, tuplenil₁, case8₂] > record_extract₁ > [excl, empty, nocalls]
locker2_{add_pending₃} > case1₄ > [undefined, lock] > [cons₂, tuplenil₁, case8₂] > andt > [excl, empty, nocalls]
locker2_{add_pending₃} > case1₄ > pending > [cons₂, tuplenil₁, case8₂] > [nil, locker2_{map_{add_pending}}] > [excl, empty, nocalls]
locker2_{add_pending₃} > case1₄ > pending > [cons₂, tuplenil₁, case8₂] > tuple₂ > and₂ > [excl, empty, nocalls]
locker2_{add_pending₃} > case1₄ > pending > [cons₂, tuplenil₁, case8₂] > tuple₂ > int > [excl, empty, nocalls]
locker2_{add_pending₃} > case1₄ > pending > [cons₂, tuplenil₁, case8₂] > tuple₂ > mcrlrecord > T > [excl, empty, nocalls]
locker2_{add_pending₃} > case1₄ > pending > [cons₂, tuplenil₁, case8₂] > resource > T > [excl, empty, nocalls]
locker2_{add_pending₃} > case1₄ > pending > [cons₂, tuplenil₁, case8₂] > record_extract₁ > [excl, empty, nocalls]
locker2_{add_pending₃} > case1₄ > pending > [cons₂, tuplenil₁, case8₂] > andt > [excl, empty, nocalls]
locker2_{add_pending₃} > case1₄ > [record_update₂, record_updates₃] > [cons₂, tuplenil₁, case8₂] > [nil, locker2_{map_{add_pending}}] > [excl, empty, nocalls]
locker2_{add_pending₃} > case1₄ > [record_update₂, record_updates₃] > [cons₂, tuplenil₁, case8₂] > tuple₂ > and₂ > [excl, empty, nocalls]
locker2_{add_pending₃} > case1₄ > [record_update₂, record_updates₃] > [cons₂, tuplenil₁, case8₂] > tuple₂ > int > [excl, empty, nocalls]
locker2_{add_pending₃} > case1₄ > [record_update₂, record_updates₃] > [cons₂, tuplenil₁, case8₂] > tuple₂ > mcrlrecord > T > [excl, empty, nocalls]
locker2_{add_pending₃} > case1₄ > [record_update₂, record_updates₃] > [cons₂, tuplenil₁, case8₂] > resource > T > [excl, empty, nocalls]
locker2_{add_pending₃} > case1₄ > [record_update₂, record_updates₃] > [cons₂, tuplenil₁, case8₂] > record_extract₁ > [excl, empty, nocalls]
locker2_{add_pending₃} > case1₄ > [record_update₂, record_updates₃] > [cons₂, tuplenil₁, case8₂] > andt > [excl, empty, nocalls]
[locker2_{release_lock₂}, case2₁] > [undefined, lock] > [cons₂, tuplenil₁, case8₂] > [nil, locker2_{map_{add_pending}}] > [excl, empty, nocalls]
[locker2_{release_lock₂}, case2₁] > [undefined, lock] > [cons₂, tuplenil₁, case8₂] > tuple₂ > and₂ > [excl, empty, nocalls]
[locker2_{release_lock₂}, case2₁] > [undefined, lock] > [cons₂, tuplenil₁, case8₂] > tuple₂ > int > [excl, empty, nocalls]
[locker2_{release_lock₂}, case2₁] > [undefined, lock] > [cons₂, tuplenil₁, case8₂] > tuple₂ > mcrlrecord > T > [excl, empty, nocalls]
[locker2_{release_lock₂}, case2₁] > [undefined, lock] > [cons₂, tuplenil₁, case8₂] > resource > T > [excl, empty, nocalls]
[locker2_{release_lock₂}, case2₁] > [undefined, lock] > [cons₂, tuplenil₁, case8₂] > record_extract₁ > [excl, empty, nocalls]
[locker2_{release_lock₂}, case2₁] > [undefined, lock] > [cons₂, tuplenil₁, case8₂] > andt > [excl, empty, nocalls]
[locker2_{release_lock₂}, case2₁] > [record_update₂, record_updates₃] > [cons₂, tuplenil₁, case8₂] > [nil, locker2_{map_{add_pending}}] > [excl, empty, nocalls]
[locker2_{release_lock₂}, case2₁] > [record_update₂, record_updates₃] > [cons₂, tuplenil₁, case8₂] > tuple₂ > and₂ > [excl, empty, nocalls]
[locker2_{release_lock₂}, case2₁] > [record_update₂, record_updates₃] > [cons₂, tuplenil₁, case8₂] > tuple₂ > int > [excl, empty, nocalls]
[locker2_{release_lock₂}, case2₁] > [record_update₂, record_updates₃] > [cons₂, tuplenil₁, case8₂] > tuple₂ > mcrlrecord > T > [excl, empty, nocalls]
[locker2_{release_lock₂}, case2₁] > [record_update₂, record_updates₃] > [cons₂, tuplenil₁, case8₂] > resource > T > [excl, empty, nocalls]
[locker2_{release_lock₂}, case2₁] > [record_update₂, record_updates₃] > [cons₂, tuplenil₁, case8₂] > record_extract₁ > [excl, empty, nocalls]
[locker2_{release_lock₂}, case2₁] > [record_update₂, record_updates₃] > [cons₂, tuplenil₁, case8₂] > andt > [excl, empty, nocalls]
[locker2_{release_lock₂}, case2₁] > excllock > [excl, empty, nocalls]
gen_modtageq₁ > equal > [excl, empty, nocalls]
case4 > [false, member, locker2_{check_available}] > [locker2_obtainables, case5] > true > [F, a, release] > T > [excl, empty, nocalls]
case4 > [false, member, locker2_{check_available}] > [locker2_obtainables, case5] > true > [undefined, lock] > [cons₂, tuplenil₁, case8₂] > [nil, locker2_{map_{add_pending}}] > [excl, empty, nocalls]
case4 > [false, member, locker2_{check_available}] > [locker2_obtainables, case5] > true > [undefined, lock] > [cons₂, tuplenil₁, case8₂] > tuple₂ > and₂ > [excl, empty, nocalls]
case4 > [false, member, locker2_{check_available}] > [locker2_obtainables, case5] > true > [undefined, lock] > [cons₂, tuplenil₁, case8₂] > tuple₂ > int > [excl, empty, nocalls]
case4 > [false, member, locker2_{check_available}] > [locker2_obtainables, case5] > true > [undefined, lock] > [cons₂, tuplenil₁, case8₂] > tuple₂ > mcrlrecord > T > [excl, empty, nocalls]
case4 > [false, member, locker2_{check_available}] > [locker2_obtainables, case5] > true > [undefined, lock] > [cons₂, tuplenil₁, case8₂] > resource > T > [excl, empty, nocalls]
case4 > [false, member, locker2_{check_available}] > [locker2_obtainables, case5] > true > [undefined, lock] > [cons₂, tuplenil₁, case8₂] > record_extract₁ > [excl, empty, nocalls]
case4 > [false, member, locker2_{check_available}] > [locker2_obtainables, case5] > true > [undefined, lock] > [cons₂, tuplenil₁, case8₂] > andt > [excl, empty, nocalls]
case4 > [false, member, locker2_{check_available}] > [locker2_obtainables, case5] > true > pending > [cons₂, tuplenil₁, case8₂] > [nil, locker2_{map_{add_pending}}] > [excl, empty, nocalls]
case4 > [false, member, locker2_{check_available}] > [locker2_obtainables, case5] > true > pending > [cons₂, tuplenil₁, case8₂] > tuple₂ > and₂ > [excl, empty, nocalls]
case4 > [false, member, locker2_{check_available}] > [locker2_obtainables, case5] > true > pending > [cons₂, tuplenil₁, case8₂] > tuple₂ > int > [excl, empty, nocalls]
case4 > [false, member, locker2_{check_available}] > [locker2_obtainables, case5] > true > pending > [cons₂, tuplenil₁, case8₂] > tuple₂ > mcrlrecord > T > [excl, empty, nocalls]
case4 > [false, member, locker2_{check_available}] > [locker2_obtainables, case5] > true > pending > [cons₂, tuplenil₁, case8₂] > resource > T > [excl, empty, nocalls]
case4 > [false, member, locker2_{check_available}] > [locker2_obtainables, case5] > true > pending > [cons₂, tuplenil₁, case8₂] > record_extract₁ > [excl, empty, nocalls]
case4 > [false, member, locker2_{check_available}] > [locker2_obtainables, case5] > true > pending > [cons₂, tuplenil₁, case8₂] > andt > [excl, empty, nocalls]
case4 > [false, member, locker2_{check_available}] > [locker2_obtainables, case5] > true > [record_update₂, record_updates₃] > [cons₂, tuplenil₁, case8₂] > [nil, locker2_{map_{add_pending}}] > [excl, empty, nocalls]
case4 > [false, member, locker2_{check_available}] > [locker2_obtainables, case5] > true > [record_update₂, record_updates₃] > [cons₂, tuplenil₁, case8₂] > tuple₂ > and₂ > [excl, empty, nocalls]
case4 > [false, member, locker2_{check_available}] > [locker2_obtainables, case5] > true > [record_update₂, record_updates₃] > [cons₂, tuplenil₁, case8₂] > tuple₂ > int > [excl, empty, nocalls]
case4 > [false, member, locker2_{check_available}] > [locker2_obtainables, case5] > true > [record_update₂, record_updates₃] > [cons₂, tuplenil₁, case8₂] > tuple₂ > mcrlrecord > T > [excl, empty, nocalls]
case4 > [false, member, locker2_{check_available}] > [locker2_obtainables, case5] > true > [record_update₂, record_updates₃] > [cons₂, tuplenil₁, case8₂] > resource > T > [excl, empty, nocalls]
case4 > [false, member, locker2_{check_available}] > [locker2_obtainables, case5] > true > [record_update₂, record_updates₃] > [cons₂, tuplenil₁, case8₂] > record_extract₁ > [excl, empty, nocalls]
case4 > [false, member, locker2_{check_available}] > [locker2_obtainables, case5] > true > [record_update₂, record_updates₃] > [cons₂, tuplenil₁, case8₂] > andt > [excl, empty, nocalls]
case4 > [false, member, locker2_{check_available}] > [locker2_obtainables, case5] > true > excllock > [excl, empty, nocalls]
case4 > [false, member, locker2_{check_available}] > [locker2_obtainables, case5] > locker2_{obtainable₂} > [excl, empty, nocalls]
case4 > [false, member, locker2_{check_available}] > equal > [excl, empty, nocalls]
locker2_{check_{availables₁}} > true > [F, a, release] > T > [excl, empty, nocalls]
locker2_{check_{availables₁}} > true > [undefined, lock] > [cons₂, tuplenil₁, case8₂] > [nil, locker2_{map_{add_pending}}] > [excl, empty, nocalls]
locker2_{check_{availables₁}} > true > [undefined, lock] > [cons₂, tuplenil₁, case8₂] > tuple₂ > and₂ > [excl, empty, nocalls]
locker2_{check_{availables₁}} > true > [undefined, lock] > [cons₂, tuplenil₁, case8₂] > tuple₂ > int > [excl, empty, nocalls]
locker2_{check_{availables₁}} > true > [undefined, lock] > [cons₂, tuplenil₁, case8₂] > tuple₂ > mcrlrecord > T > [excl, empty, nocalls]
locker2_{check_{availables₁}} > true > [undefined, lock] > [cons₂, tuplenil₁, case8₂] > resource > T > [excl, empty, nocalls]
locker2_{check_{availables₁}} > true > [undefined, lock] > [cons₂, tuplenil₁, case8₂] > record_extract₁ > [excl, empty, nocalls]
locker2_{check_{availables₁}} > true > [undefined, lock] > [cons₂, tuplenil₁, case8₂] > andt > [excl, empty, nocalls]
locker2_{check_{availables₁}} > true > pending > [cons₂, tuplenil₁, case8₂] > [nil, locker2_{map_{add_pending}}] > [excl, empty, nocalls]
locker2_{check_{availables₁}} > true > pending > [cons₂, tuplenil₁, case8₂] > tuple₂ > and₂ > [excl, empty, nocalls]
locker2_{check_{availables₁}} > true > pending > [cons₂, tuplenil₁, case8₂] > tuple₂ > int > [excl, empty, nocalls]
locker2_{check_{availables₁}} > true > pending > [cons₂, tuplenil₁, case8₂] > tuple₂ > mcrlrecord > T > [excl, empty, nocalls]
locker2_{check_{availables₁}} > true > pending > [cons₂, tuplenil₁, case8₂] > resource > T > [excl, empty, nocalls]
locker2_{check_{availables₁}} > true > pending > [cons₂, tuplenil₁, case8₂] > record_extract₁ > [excl, empty, nocalls]
locker2_{check_{availables₁}} > true > pending > [cons₂, tuplenil₁, case8₂] > andt > [excl, empty, nocalls]
locker2_{check_{availables₁}} > true > [record_update₂, record_updates₃] > [cons₂, tuplenil₁, case8₂] > [nil, locker2_{map_{add_pending}}] > [excl, empty, nocalls]
locker2_{check_{availables₁}} > true > [record_update₂, record_updates₃] > [cons₂, tuplenil₁, case8₂] > tuple₂ > and₂ > [excl, empty, nocalls]
locker2_{check_{availables₁}} > true > [record_update₂, record_updates₃] > [cons₂, tuplenil₁, case8₂] > tuple₂ > int > [excl, empty, nocalls]
locker2_{check_{availables₁}} > true > [record_update₂, record_updates₃] > [cons₂, tuplenil₁, case8₂] > tuple₂ > mcrlrecord > T > [excl, empty, nocalls]
locker2_{check_{availables₁}} > true > [record_update₂, record_updates₃] > [cons₂, tuplenil₁, case8₂] > resource > T > [excl, empty, nocalls]
locker2_{check_{availables₁}} > true > [record_update₂, record_updates₃] > [cons₂, tuplenil₁, case8₂] > record_extract₁ > [excl, empty, nocalls]
locker2_{check_{availables₁}} > true > [record_update₂, record_updates₃] > [cons₂, tuplenil₁, case8₂] > andt > [excl, empty, nocalls]
locker2_{check_{availables₁}} > true > excllock > [excl, empty, nocalls]
[eqs₂, eqc₂] > [eqt₂, istops₂] > [F, a, release] > T > [excl, empty, nocalls]
[eqs₂, eqc₂] > [eqt₂, istops₂] > and₂ > [excl, empty, nocalls]
pops₁ > [excl, empty, nocalls]
tops₁ > [excl, empty, nocalls]
push₃ > [eqt₂, istops₂] > [F, a, release] > T > [excl, empty, nocalls]
push₃ > [eqt₂, istops₂] > and₂ > [excl, empty, nocalls]
push₃ > push1₆ > calls₃ > and₂ > [excl, empty, nocalls]
push₃ > push1₆ > [stack₂, pushs₂] > [excl, empty, nocalls]

Status:

calls₃: [3,2,1]
T: []
F: []
and₂: [1,2]
imp₁: [1]
not: []
if₃: [1,2,3]
eq₂: [2,1]
eqt₂: [1,2]
nil: []
undefined: []
pid₁: [1]
int: []
cons₂: [1,2]
tuple₂: [2,1]
tuplenil₁: [1]
a: []
excl: []
false: []
lock: []
locker: []
mcrlrecord: []
ok: []
pending: []
release: []
request: []
resource: []
tag: []
true: []
0: []
record_new: []
record_extract₁: [1]
record_update₂: [2,1]
record_updates₃: [3,2,1]
locker2_{map_{promote_pending₂}}: [2,1]
locker2_{promote_pending₂}: [2,1]
locker2_{map_{claim_lock₃}}: [3,1,2]
locker2_{map_{add_pending}}: []
case0₃: [1,3,2]
locker2_{remove_pending₁}: [1]
locker2_{add_pending₃}: [2,3,1]
case1₄: [4,2,3,1]
member: []
locker2_{release_lock₂}: [1,2]
case2₁: [1]
gen_modtageq₁: [1]
excllock: []
case4: []
locker2_obtainables: []
case5: []
andt: []
locker2_{obtainable₂}: [2,1]
locker2_{check_available}: []
equal: []
locker2_{check_{availables₁}}: [1]
case8₂: [2,1]
gen_tag₁: [1]
eqs₂: [1,2]
empty: []
stack₂: [1,2]
pushs₂: [1,2]
pops₁: [1]
tops₁: [1]
istops₂: [1,2]
eqc₂: [1,2]
nocalls: []
push₃: [3,2,1]
push1₆: [6,5,3,2,1,4]

The following usable rules [FROCOS05] were oriented:

or(T, T) → T
or(F, T) → T
or(T, F) → T
or(F, F) → F
and(T, B) → B
and(B, T) → B
and(F, B) → F
and(B, F) → F
imp(T, B) → B
imp(F, B) → T
not(T) → F
not(F) → T
if(T, B1, B2) → B1
if(F, B1, B2) → B2
eq(T, T) → T
eq(F, F) → T
eq(T, F) → F
eq(F, T) → F
eqt(nil, undefined) → F
eqt(nil, pid(N2)) → F
eqt(nil, int(N2)) → F
eqt(nil, cons(H2, T2)) → F
eqt(nil, tuple(H2, T2)) → F
eqt(nil, tuplenil(H2)) → F
eqt(a, nil) → F
eqt(a, a) → T
eqt(a, excl) → F
eqt(a, false) → F
eqt(a, lock) → F
eqt(a, locker) → F
eqt(a, mcrlrecord) → F
eqt(a, ok) → F
eqt(a, pending) → F
eqt(a, release) → F
eqt(a, request) → F
eqt(a, resource) → F
eqt(a, tag) → F
eqt(a, true) → F
eqt(a, undefined) → F
eqt(a, pid(N2)) → F
eqt(a, int(N2)) → F
eqt(a, cons(H2, T2)) → F
eqt(a, tuple(H2, T2)) → F
eqt(a, tuplenil(H2)) → F
eqt(excl, nil) → F
eqt(excl, a) → F
eqt(excl, excl) → T
eqt(excl, false) → F
eqt(excl, lock) → F
eqt(excl, locker) → F
eqt(excl, mcrlrecord) → F
eqt(excl, ok) → F
eqt(excl, pending) → F
eqt(excl, release) → F
eqt(excl, request) → F
eqt(excl, resource) → F
eqt(excl, tag) → F
eqt(excl, true) → F
eqt(excl, undefined) → F
eqt(excl, pid(N2)) → F
eqt(excl, eqt(false, int(N2))) → F
eqt(false, cons(H2, T2)) → F
eqt(false, tuple(H2, T2)) → F
eqt(false, tuplenil(H2)) → F
eqt(lock, nil) → F
eqt(lock, a) → F
eqt(lock, excl) → F
eqt(lock, false) → F
eqt(lock, lock) → T
eqt(lock, locker) → F
eqt(lock, mcrlrecord) → F
eqt(lock, ok) → F
eqt(lock, pending) → F
eqt(lock, release) → F
eqt(lock, request) → F
eqt(lock, resource) → F
eqt(lock, tag) → F
eqt(lock, true) → F
eqt(lock, undefined) → F
eqt(lock, pid(N2)) → F
eqt(lock, int(N2)) → F
eqt(lock, cons(H2, T2)) → F
eqt(lock, tuple(H2, T2)) → F
eqt(lock, tuplenil(H2)) → F
eqt(locker, nil) → F
eqt(locker, a) → F
eqt(locker, excl) → F
eqt(locker, false) → F
eqt(locker, lock) → F
eqt(locker, locker) → T
eqt(locker, mcrlrecord) → F
eqt(locker, ok) → F
eqt(locker, pending) → F
eqt(locker, release) → F
eqt(locker, request) → F
eqt(locker, resource) → F
eqt(locker, tag) → F
eqt(locker, true) → F
eqt(locker, undefined) → F
eqt(locker, pid(N2)) → F
eqt(locker, int(N2)) → F
eqt(locker, cons(H2, T2)) → F
eqt(locker, tuple(H2, T2)) → F
eqt(locker, tuplenil(H2)) → F
eqt(mcrlrecord, nil) → F
eqt(mcrlrecord, a) → F
eqt(mcrlrecord, excl) → F
eqt(mcrlrecord, false) → F
eqt(mcrlrecord, lock) → F
eqt(mcrlrecord, locker) → F
eqt(mcrlrecord, mcrlrecord) → T
eqt(mcrlrecord, ok) → F
eqt(mcrlrecord, pending) → F
eqt(mcrlrecord, release) → F
eqt(mcrlrecord, request) → F
eqt(mcrlrecord, resource) → F
eqt(ok, resource) → F
eqt(ok, tag) → F
eqt(ok, true) → F
eqt(ok, undefined) → F
eqt(ok, pid(N2)) → F
eqt(ok, int(N2)) → F
eqt(ok, cons(H2, T2)) → F
eqt(ok, tuple(H2, T2)) → F
eqt(ok, tuplenil(H2)) → F
eqt(pending, nil) → F
eqt(pending, a) → F
eqt(pending, excl) → F
eqt(pending, false) → F
eqt(pending, lock) → F
eqt(pending, locker) → F
eqt(pending, mcrlrecord) → F
eqt(pending, ok) → F
eqt(pending, pending) → T
eqt(pending, release) → F
eqt(pending, request) → F
eqt(pending, resource) → F
eqt(pending, tag) → F
eqt(pending, true) → F
eqt(pending, undefined) → F
eqt(pending, pid(N2)) → F
eqt(pending, int(N2)) → F
eqt(pending, cons(H2, T2)) → F
eqt(pending, tuple(H2, T2)) → F
eqt(pending, tuplenil(H2)) → F
eqt(release, nil) → F
eqt(release, a) → F
eqt(release, excl) → F
eqt(release, false) → F
eqt(release, lock) → F
eqt(release, locker) → F
eqt(release, mcrlrecord) → F
eqt(release, ok) → F
eqt(request, mcrlrecord) → F
eqt(request, ok) → F
eqt(request, pending) → F
eqt(request, release) → F
eqt(request, request) → T
eqt(request, resource) → F
eqt(request, tag) → F
eqt(request, true) → F
eqt(request, undefined) → F
eqt(request, pid(N2)) → F
eqt(request, int(N2)) → F
eqt(request, cons(H2, T2)) → F
eqt(request, tuple(H2, T2)) → F
eqt(request, tuplenil(H2)) → F
eqt(resource, nil) → F
eqt(resource, a) → F
eqt(resource, excl) → F
eqt(resource, false) → F
eqt(resource, lock) → F
eqt(resource, locker) → F
eqt(resource, mcrlrecord) → F
eqt(resource, ok) → F
eqt(resource, pending) → F
eqt(resource, release) → F
eqt(resource, request) → F
eqt(resource, resource) → T
eqt(resource, tag) → F
eqt(resource, true) → F
eqt(resource, undefined) → F
eqt(resource, pid(N2)) → F
eqt(resource, int(N2)) → F
eqt(resource, cons(H2, T2)) → F
eqt(resource, tuple(H2, T2)) → F
eqt(resource, tuplenil(H2)) → F
eqt(tag, nil) → F
eqt(tag, a) → F
eqt(tag, excl) → F
eqt(tag, false) → F
eqt(tag, lock) → F
eqt(tag, locker) → F
eqt(tag, mcrlrecord) → F
eqt(tag, ok) → F
eqt(tag, pending) → F
eqt(tag, release) → F
eqt(tag, request) → F
eqt(tag, resource) → F
eqt(tag, tag) → T
eqt(tag, true) → F
eqt(tag, undefined) → F
eqt(tag, pid(N2)) → F
eqt(tag, int(N2)) → F
eqt(tag, cons(H2, T2)) → F
eqt(tag, tuple(H2, T2)) → F
eqt(tag, tuplenil(H2)) → F
eqt(true, nil) → F
eqt(true, a) → F
eqt(true, excl) → F
eqt(true, false) → F
eqt(true, lock) → F
eqt(true, locker) → F
eqt(true, mcrlrecord) → F
eqt(true, ok) → F
eqt(true, pending) → F
eqt(true, release) → F
eqt(true, request) → F
eqt(true, resource) → F
eqt(true, tag) → F
eqt(true, true) → T
eqt(true, undefined) → F
eqt(true, pid(N2)) → F
eqt(true, int(N2)) → F
eqt(true, cons(H2, T2)) → F
eqt(true, tuple(H2, T2)) → F
eqt(true, tuplenil(H2)) → F
eqt(undefined, nil) → F
eqt(undefined, a) → F
eqt(undefined, tuplenil(H2)) → F
eqt(pid(N1), nil) → F
eqt(pid(N1), a) → F
eqt(pid(N1), excl) → F
eqt(pid(N1), false) → F
eqt(pid(N1), lock) → F
eqt(pid(N1), locker) → F
eqt(pid(N1), mcrlrecord) → F
eqt(pid(N1), ok) → F
eqt(pid(N1), pending) → F
eqt(pid(N1), release) → F
eqt(pid(N1), request) → F
eqt(pid(N1), resource) → F
eqt(pid(N1), tag) → F
eqt(pid(N1), true) → F
eqt(pid(N1), undefined) → F
eqt(pid(N1), pid(N2)) → eqt(N1, N2)
eqt(pid(N1), int(N2)) → F
eqt(pid(N1), cons(H2, T2)) → F
eqt(pid(N1), tuple(H2, T2)) → F
eqt(pid(N1), tuplenil(H2)) → F
eqt(int(N1), nil) → F
eqt(int(N1), a) → F
eqt(int(N1), excl) → F
eqt(int(N1), false) → F
eqt(int(N1), lock) → F
eqt(int(N1), locker) → F
eqt(int(N1), mcrlrecord) → F
eqt(int(N1), ok) → F
eqt(int(N1), pending) → F
eqt(int(N1), release) → F
eqt(int(N1), request) → F
eqt(int(N1), resource) → F
eqt(int(N1), tag) → F
eqt(int(N1), true) → F
eqt(int(N1), undefined) → F
eqt(cons(H1, T1), resource) → F
eqt(cons(H1, T1), tag) → F
eqt(cons(H1, T1), true) → F
eqt(cons(H1, T1), undefined) → F
eqt(cons(H1, T1), pid(N2)) → F
eqt(cons(H1, T1), int(N2)) → F
eqt(cons(H1, T1), cons(H2, T2)) → and(eqt(H1, H2), eqt(T1, T2))
eqt(cons(H1, T1), tuple(H2, T2)) → F
eqt(cons(H1, T1), tuplenil(H2)) → F
eqt(tuple(H1, T1), nil) → F
eqt(tuple(H1, T1), a) → F
eqt(tuple(H1, T1), excl) → F
eqt(tuple(H1, T1), false) → F
eqt(tuple(H1, T1), lock) → F
eqt(tuple(H1, T1), locker) → F
eqt(tuple(H1, T1), mcrlrecord) → F
eqt(tuple(H1, T1), ok) → F
eqt(tuple(H1, T1), pending) → F
eqt(tuple(H1, T1), release) → F
eqt(tuple(H1, T1), request) → F
eqt(tuple(H1, T1), resource) → F
eqt(tuple(H1, T1), tag) → F
eqt(tuple(H1, T1), true) → F
eqt(tuple(H1, T1), undefined) → F
eqt(tuple(H1, T1), pid(N2)) → F
eqt(tuple(H1, T1), int(N2)) → F
eqt(tuple(H1, T1), cons(H2, T2)) → F
eqt(tuple(H1, T1), tuple(H2, T2)) → and(eqt(H1, H2), eqt(T1, T2))
eqt(tuple(H1, T1), tuplenil(H2)) → F
eqt(tuplenil(H1), nil) → F
eqt(tuplenil(H1), a) → F
eqt(tuplenil(H1), excl) → F
eqt(tuplenil(H1), false) → F
eqt(tuplenil(H1), lock) → F
eqt(tuplenil(H1), locker) → F
eqt(tuplenil(H1), mcrlrecord) → F
eqt(tuplenil(H1), ok) → F
eqt(tuplenil(H1), pending) → F
eqt(tuplenil(H1), release) → F
eqt(tuplenil(H1), request) → F
eqt(tuplenil(H1), resource) → F
eqt(tuplenil(H1), tag) → F
eqt(tuplenil(H1), true) → F
eqt(tuplenil(H1), undefined) → F
eqt(tuplenil(H1), pid(N2)) → F
eqt(tuplenil(H1), int(N2)) → F
eqt(tuplenil(H1), cons(H2, T2)) → F
eqt(tuplenil(H1), tuple(H2, T2)) → F
eqt(tuplenil(H1), tuplenil(H2)) → eqt(H1, H2)
element(int(s(0)), tuplenil(T1)) → T1
element(int(s(0)), tuple(T1, T2)) → T1
element(int(s(s(N1))), tuple(T1, T2)) → element(int(s(N1)), T2)
record_new(lock) → tuple(mcrlrecord, tuple(lock, tuple(undefined, tuple(nil, tuplenil(nil)))))
record_extract(tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))), lock, resource) → tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2)))))
record_update(tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))), lock, pending, NewF) → tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(NewF)))))
record_updates(Record, Name, nil) → Record
record_updates(Record, Name, cons(tuple(Field, tuplenil(NewF)), Fields)) → record_updates(record_update(Record, Name, Field, NewF), Name, Fields)
locker2_map_promote_pending(nil, Pending) → nil
locker2_map_promote_pending(cons(Lock, Locks), Pending) → cons(locker2_promote_pending(Lock, Pending), locker2_map_promote_pending(Locks, Pending))
locker2_map_claim_lock(nil, Resources, Client) → nil
locker2_map_claim_lock(cons(Lock, Locks), Resources, Client) → cons(locker2_claim_lock(Lock, Resources, Client), locker2_map_claim_lock(Locks, Resources, Client))
locker2_map_add_pending(nil, Resources, Client) → nil
locker2_promote_pending(Lock, Client) → case0(Client, Lock, record_extract(Lock, lock, pending))
case0(Client, Lock, cons(Client, Pendings)) → record_updates(Lock, lock, cons(tuple(excl, tuplenil(Client)), cons(tuple(pending, tuplenil(Pendings)), nil)))
case0(Client, Lock, MCRLFree0) → Lock
locker2_remove_pending(Lock, Client) → record_updates(Lock, lock, cons(tuple(pending, tuplenil(subtract(record_extract(Lock, lock, pending), cons(Client, nil)))), nil))
locker2_add_pending(Lock, Resources, Client) → case1(Client, Resources, Lock, member(record_extract(Lock, lock, resource), Resources))
case1(Client, Resources, Lock, true) → record_updates(Lock, lock, cons(tuple(pending, tuplenil(append(record_extract(Lock, lock, pending), cons(Client, nil)))), nil))
case1(Client, Resources, Lock, false) → Lock
locker2_release_lock(Lock, Client) → case2(Client, Lock, gen_modtageq(Client, record_extract(Lock, lock, excl)))
case2(Client, Lock, true) → record_updates(Lock, lock, cons(tuple(excllock, excl), nil))
case4(Client, Lock, MCRLFree1) → false
locker2_obtainables(nil, Client) → true
locker2_obtainables(cons(Lock, Locks), Client) → case5(Client, Locks, Lock, member(Client, record_extract(Lock, lock, pending)))
case5(Client, Locks, Lock, true) → andt(locker2_obtainable(Lock, Client), locker2_obtainables(Locks, Client))
case5(Client, Locks, Lock, false) → locker2_obtainables(Locks, Client)
locker2_check_available(Resource, nil) → false
locker2_check_available(Resource, cons(Lock, Locks)) → case6(Locks, Lock, Resource, equal(Resource, record_extract(Lock, lock, resource)))
case6(Locks, Lock, Resource, true) → andt(equal(record_extract(Lock, lock, excl), nil), equal(record_extract(Lock, lock, pending), nil))
case6(Locks, Lock, Resource, false) → locker2_check_available(Resource, Locks)
locker2_check_availables(nil, Locks) → true
locker2_check_availables(cons(Resource, Resources), Locks) → andt(locker2_check_available(Resource, Locks), locker2_check_availables(Resources, Locks))
locker2_adduniq(nil, List) → List
append(cons(Head, Tail), List) → cons(Head, append(Tail, List))
subtract(List, nil) → List
subtract(List, cons(Head, Tail)) → subtract(delete(Head, List), Tail)
delete(E, nil) → nil
delete(E, cons(Head, Tail)) → case8(Tail, Head, E, equal(E, Head))
case8(Tail, Head, E, true) → Tail
case8(Tail, Head, E, false) → cons(Head, delete(E, Tail))
gen_tag(Pid) → tuple(Pid, tuplenil(tag))
gen_modtageq(Client1, Client2) → equal(Client1, Client2)
member(E, nil) → false
member(E, cons(Head, Tail)) → case9(Tail, Head, E, equal(E, Head))
case9(Tail, Head, E, true) → true
case9(Tail, Head, E, false) → member(E, Tail)
eqs(empty, empty) → T
eqs(empty, stack(E2, S2)) → F
eqs(stack(E1, S1), empty) → F
eqs(stack(E1, S1), stack(E2, S2)) → and(eqt(E1, E2), eqs(S1, S2))
pushs(E1, S1) → stack(E1, S1)
pops(stack(E1, S1)) → S1
tops(stack(E1, S1)) → E1
istops(E1, empty) → F
istops(E1, stack(E2, S1)) → eqt(E1, E2)
eqc(nocalls, nocalls) → T
eqc(nocalls, calls(E2, S2, CS2)) → F
eqc(calls(E1, S1, CS1), nocalls) → F
eqc(calls(E1, S1, CS1), calls(E2, S2, CS2)) → and(eqt(E1, E2), and(eqs(S1, S2), eqc(CS1, CS2)))
push(E1, E2, nocalls) → calls(E1, stack(E2, empty), nocalls)
push(E1, E2, calls(E3, S1, CS1)) → push1(E1, E2, E3, S1, CS1, eqt(E1, E3))
push1(E1, E2, E3, S1, CS1, T) → calls(E3, pushs(E2, S1), CS1)

(54) Obligation:

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

or(T, T) → T
or(F, T) → T
or(T, F) → T
or(F, F) → F
and(T, B) → B
and(B, T) → B
and(F, B) → F
and(B, F) → F
imp(T, B) → B
imp(F, B) → T
not(T) → F
not(F) → T
if(T, B1, B2) → B1
if(F, B1, B2) → B2
eq(T, T) → T
eq(F, F) → T
eq(T, F) → F
eq(F, T) → F
eqt(nil, undefined) → F
eqt(nil, pid(N2)) → F
eqt(nil, int(N2)) → F
eqt(nil, cons(H2, T2)) → F
eqt(nil, tuple(H2, T2)) → F
eqt(nil, tuplenil(H2)) → F
eqt(a, nil) → F
eqt(a, a) → T
eqt(a, excl) → F
eqt(a, false) → F
eqt(a, lock) → F
eqt(a, locker) → F
eqt(a, mcrlrecord) → F
eqt(a, ok) → F
eqt(a, pending) → F
eqt(a, release) → F
eqt(a, request) → F
eqt(a, resource) → F
eqt(a, tag) → F
eqt(a, true) → F
eqt(a, undefined) → F
eqt(a, pid(N2)) → F
eqt(a, int(N2)) → F
eqt(a, cons(H2, T2)) → F
eqt(a, tuple(H2, T2)) → F
eqt(a, tuplenil(H2)) → F
eqt(excl, nil) → F
eqt(excl, a) → F
eqt(excl, excl) → T
eqt(excl, false) → F
eqt(excl, lock) → F
eqt(excl, locker) → F
eqt(excl, mcrlrecord) → F
eqt(excl, ok) → F
eqt(excl, pending) → F
eqt(excl, release) → F
eqt(excl, request) → F
eqt(excl, resource) → F
eqt(excl, tag) → F
eqt(excl, true) → F
eqt(excl, undefined) → F
eqt(excl, pid(N2)) → F
eqt(excl, eqt(false, int(N2))) → F
eqt(false, cons(H2, T2)) → F
eqt(false, tuple(H2, T2)) → F
eqt(false, tuplenil(H2)) → F
eqt(lock, nil) → F
eqt(lock, a) → F
eqt(lock, excl) → F
eqt(lock, false) → F
eqt(lock, lock) → T
eqt(lock, locker) → F
eqt(lock, mcrlrecord) → F
eqt(lock, ok) → F
eqt(lock, pending) → F
eqt(lock, release) → F
eqt(lock, request) → F
eqt(lock, resource) → F
eqt(lock, tag) → F
eqt(lock, true) → F
eqt(lock, undefined) → F
eqt(lock, pid(N2)) → F
eqt(lock, int(N2)) → F
eqt(lock, cons(H2, T2)) → F
eqt(lock, tuple(H2, T2)) → F
eqt(lock, tuplenil(H2)) → F
eqt(locker, nil) → F
eqt(locker, a) → F
eqt(locker, excl) → F
eqt(locker, false) → F
eqt(locker, lock) → F
eqt(locker, locker) → T
eqt(locker, mcrlrecord) → F
eqt(locker, ok) → F
eqt(locker, pending) → F
eqt(locker, release) → F
eqt(locker, request) → F
eqt(locker, resource) → F
eqt(locker, tag) → F
eqt(locker, true) → F
eqt(locker, undefined) → F
eqt(locker, pid(N2)) → F
eqt(locker, int(N2)) → F
eqt(locker, cons(H2, T2)) → F
eqt(locker, tuple(H2, T2)) → F
eqt(locker, tuplenil(H2)) → F
eqt(mcrlrecord, nil) → F
eqt(mcrlrecord, a) → F
eqt(mcrlrecord, excl) → F
eqt(mcrlrecord, false) → F
eqt(mcrlrecord, lock) → F
eqt(mcrlrecord, locker) → F
eqt(mcrlrecord, mcrlrecord) → T
eqt(mcrlrecord, ok) → F
eqt(mcrlrecord, pending) → F
eqt(mcrlrecord, release) → F
eqt(mcrlrecord, request) → F
eqt(mcrlrecord, resource) → F
eqt(ok, resource) → F
eqt(ok, tag) → F
eqt(ok, true) → F
eqt(ok, undefined) → F
eqt(ok, pid(N2)) → F
eqt(ok, int(N2)) → F
eqt(ok, cons(H2, T2)) → F
eqt(ok, tuple(H2, T2)) → F
eqt(ok, tuplenil(H2)) → F
eqt(pending, nil) → F
eqt(pending, a) → F
eqt(pending, excl) → F
eqt(pending, false) → F
eqt(pending, lock) → F
eqt(pending, locker) → F
eqt(pending, mcrlrecord) → F
eqt(pending, ok) → F
eqt(pending, pending) → T
eqt(pending, release) → F
eqt(pending, request) → F
eqt(pending, resource) → F
eqt(pending, tag) → F
eqt(pending, true) → F
eqt(pending, undefined) → F
eqt(pending, pid(N2)) → F
eqt(pending, int(N2)) → F
eqt(pending, cons(H2, T2)) → F
eqt(pending, tuple(H2, T2)) → F
eqt(pending, tuplenil(H2)) → F
eqt(release, nil) → F
eqt(release, a) → F
eqt(release, excl) → F
eqt(release, false) → F
eqt(release, lock) → F
eqt(release, locker) → F
eqt(release, mcrlrecord) → F
eqt(release, ok) → F
eqt(request, mcrlrecord) → F
eqt(request, ok) → F
eqt(request, pending) → F
eqt(request, release) → F
eqt(request, request) → T
eqt(request, resource) → F
eqt(request, tag) → F
eqt(request, true) → F
eqt(request, undefined) → F
eqt(request, pid(N2)) → F
eqt(request, int(N2)) → F
eqt(request, cons(H2, T2)) → F
eqt(request, tuple(H2, T2)) → F
eqt(request, tuplenil(H2)) → F
eqt(resource, nil) → F
eqt(resource, a) → F
eqt(resource, excl) → F
eqt(resource, false) → F
eqt(resource, lock) → F
eqt(resource, locker) → F
eqt(resource, mcrlrecord) → F
eqt(resource, ok) → F
eqt(resource, pending) → F
eqt(resource, release) → F
eqt(resource, request) → F
eqt(resource, resource) → T
eqt(resource, tag) → F
eqt(resource, true) → F
eqt(resource, undefined) → F
eqt(resource, pid(N2)) → F
eqt(resource, int(N2)) → F
eqt(resource, cons(H2, T2)) → F
eqt(resource, tuple(H2, T2)) → F
eqt(resource, tuplenil(H2)) → F
eqt(tag, nil) → F
eqt(tag, a) → F
eqt(tag, excl) → F
eqt(tag, false) → F
eqt(tag, lock) → F
eqt(tag, locker) → F
eqt(tag, mcrlrecord) → F
eqt(tag, ok) → F
eqt(tag, pending) → F
eqt(tag, release) → F
eqt(tag, request) → F
eqt(tag, resource) → F
eqt(tag, tag) → T
eqt(tag, true) → F
eqt(tag, undefined) → F
eqt(tag, pid(N2)) → F
eqt(tag, int(N2)) → F
eqt(tag, cons(H2, T2)) → F
eqt(tag, tuple(H2, T2)) → F
eqt(tag, tuplenil(H2)) → F
eqt(true, nil) → F
eqt(true, a) → F
eqt(true, excl) → F
eqt(true, false) → F
eqt(true, lock) → F
eqt(true, locker) → F
eqt(true, mcrlrecord) → F
eqt(true, ok) → F
eqt(true, pending) → F
eqt(true, release) → F
eqt(true, request) → F
eqt(true, resource) → F
eqt(true, tag) → F
eqt(true, true) → T
eqt(true, undefined) → F
eqt(true, pid(N2)) → F
eqt(true, int(N2)) → F
eqt(true, cons(H2, T2)) → F
eqt(true, tuple(H2, T2)) → F
eqt(true, tuplenil(H2)) → F
eqt(undefined, nil) → F
eqt(undefined, a) → F
eqt(undefined, tuplenil(H2)) → F
eqt(pid(N1), nil) → F
eqt(pid(N1), a) → F
eqt(pid(N1), excl) → F
eqt(pid(N1), false) → F
eqt(pid(N1), lock) → F
eqt(pid(N1), locker) → F
eqt(pid(N1), mcrlrecord) → F
eqt(pid(N1), ok) → F
eqt(pid(N1), pending) → F
eqt(pid(N1), release) → F
eqt(pid(N1), request) → F
eqt(pid(N1), resource) → F
eqt(pid(N1), tag) → F
eqt(pid(N1), true) → F
eqt(pid(N1), undefined) → F
eqt(pid(N1), pid(N2)) → eqt(N1, N2)
eqt(pid(N1), int(N2)) → F
eqt(pid(N1), cons(H2, T2)) → F
eqt(pid(N1), tuple(H2, T2)) → F
eqt(pid(N1), tuplenil(H2)) → F
eqt(int(N1), nil) → F
eqt(int(N1), a) → F
eqt(int(N1), excl) → F
eqt(int(N1), false) → F
eqt(int(N1), lock) → F
eqt(int(N1), locker) → F
eqt(int(N1), mcrlrecord) → F
eqt(int(N1), ok) → F
eqt(int(N1), pending) → F
eqt(int(N1), release) → F
eqt(int(N1), request) → F
eqt(int(N1), resource) → F
eqt(int(N1), tag) → F
eqt(int(N1), true) → F
eqt(int(N1), undefined) → F
eqt(cons(H1, T1), resource) → F
eqt(cons(H1, T1), tag) → F
eqt(cons(H1, T1), true) → F
eqt(cons(H1, T1), undefined) → F
eqt(cons(H1, T1), pid(N2)) → F
eqt(cons(H1, T1), int(N2)) → F
eqt(cons(H1, T1), cons(H2, T2)) → and(eqt(H1, H2), eqt(T1, T2))
eqt(cons(H1, T1), tuple(H2, T2)) → F
eqt(cons(H1, T1), tuplenil(H2)) → F
eqt(tuple(H1, T1), nil) → F
eqt(tuple(H1, T1), a) → F
eqt(tuple(H1, T1), excl) → F
eqt(tuple(H1, T1), false) → F
eqt(tuple(H1, T1), lock) → F
eqt(tuple(H1, T1), locker) → F
eqt(tuple(H1, T1), mcrlrecord) → F
eqt(tuple(H1, T1), ok) → F
eqt(tuple(H1, T1), pending) → F
eqt(tuple(H1, T1), release) → F
eqt(tuple(H1, T1), request) → F
eqt(tuple(H1, T1), resource) → F
eqt(tuple(H1, T1), tag) → F
eqt(tuple(H1, T1), true) → F
eqt(tuple(H1, T1), undefined) → F
eqt(tuple(H1, T1), pid(N2)) → F
eqt(tuple(H1, T1), int(N2)) → F
eqt(tuple(H1, T1), cons(H2, T2)) → F
eqt(tuple(H1, T1), tuple(H2, T2)) → and(eqt(H1, H2), eqt(T1, T2))
eqt(tuple(H1, T1), tuplenil(H2)) → F
eqt(tuplenil(H1), nil) → F
eqt(tuplenil(H1), a) → F
eqt(tuplenil(H1), excl) → F
eqt(tuplenil(H1), false) → F
eqt(tuplenil(H1), lock) → F
eqt(tuplenil(H1), locker) → F
eqt(tuplenil(H1), mcrlrecord) → F
eqt(tuplenil(H1), ok) → F
eqt(tuplenil(H1), pending) → F
eqt(tuplenil(H1), release) → F
eqt(tuplenil(H1), request) → F
eqt(tuplenil(H1), resource) → F
eqt(tuplenil(H1), tag) → F
eqt(tuplenil(H1), true) → F
eqt(tuplenil(H1), undefined) → F
eqt(tuplenil(H1), pid(N2)) → F
eqt(tuplenil(H1), int(N2)) → F
eqt(tuplenil(H1), cons(H2, T2)) → F
eqt(tuplenil(H1), tuple(H2, T2)) → F
eqt(tuplenil(H1), tuplenil(H2)) → eqt(H1, H2)
element(int(s(0)), tuplenil(T1)) → T1
element(int(s(0)), tuple(T1, T2)) → T1
element(int(s(s(N1))), tuple(T1, T2)) → element(int(s(N1)), T2)
record_new(lock) → tuple(mcrlrecord, tuple(lock, tuple(undefined, tuple(nil, tuplenil(nil)))))
record_extract(tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))), lock, resource) → tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2)))))
record_update(tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))), lock, pending, NewF) → tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(NewF)))))
record_updates(Record, Name, nil) → Record
record_updates(Record, Name, cons(tuple(Field, tuplenil(NewF)), Fields)) → record_updates(record_update(Record, Name, Field, NewF), Name, Fields)
locker2_map_promote_pending(nil, Pending) → nil
locker2_map_promote_pending(cons(Lock, Locks), Pending) → cons(locker2_promote_pending(Lock, Pending), locker2_map_promote_pending(Locks, Pending))
locker2_map_claim_lock(nil, Resources, Client) → nil
locker2_map_claim_lock(cons(Lock, Locks), Resources, Client) → cons(locker2_claim_lock(Lock, Resources, Client), locker2_map_claim_lock(Locks, Resources, Client))
locker2_map_add_pending(nil, Resources, Client) → nil
locker2_promote_pending(Lock, Client) → case0(Client, Lock, record_extract(Lock, lock, pending))
case0(Client, Lock, cons(Client, Pendings)) → record_updates(Lock, lock, cons(tuple(excl, tuplenil(Client)), cons(tuple(pending, tuplenil(Pendings)), nil)))
case0(Client, Lock, MCRLFree0) → Lock
locker2_remove_pending(Lock, Client) → record_updates(Lock, lock, cons(tuple(pending, tuplenil(subtract(record_extract(Lock, lock, pending), cons(Client, nil)))), nil))
locker2_add_pending(Lock, Resources, Client) → case1(Client, Resources, Lock, member(record_extract(Lock, lock, resource), Resources))
case1(Client, Resources, Lock, true) → record_updates(Lock, lock, cons(tuple(pending, tuplenil(append(record_extract(Lock, lock, pending), cons(Client, nil)))), nil))
case1(Client, Resources, Lock, false) → Lock
locker2_release_lock(Lock, Client) → case2(Client, Lock, gen_modtageq(Client, record_extract(Lock, lock, excl)))
case2(Client, Lock, true) → record_updates(Lock, lock, cons(tuple(excllock, excl), nil))
case4(Client, Lock, MCRLFree1) → false
locker2_obtainables(nil, Client) → true
locker2_obtainables(cons(Lock, Locks), Client) → case5(Client, Locks, Lock, member(Client, record_extract(Lock, lock, pending)))
case5(Client, Locks, Lock, true) → andt(locker2_obtainable(Lock, Client), locker2_obtainables(Locks, Client))
case5(Client, Locks, Lock, false) → locker2_obtainables(Locks, Client)
locker2_check_available(Resource, nil) → false
locker2_check_available(Resource, cons(Lock, Locks)) → case6(Locks, Lock, Resource, equal(Resource, record_extract(Lock, lock, resource)))
case6(Locks, Lock, Resource, true) → andt(equal(record_extract(Lock, lock, excl), nil), equal(record_extract(Lock, lock, pending), nil))
case6(Locks, Lock, Resource, false) → locker2_check_available(Resource, Locks)
locker2_check_availables(nil, Locks) → true
locker2_check_availables(cons(Resource, Resources), Locks) → andt(locker2_check_available(Resource, Locks), locker2_check_availables(Resources, Locks))
locker2_adduniq(nil, List) → List
append(cons(Head, Tail), List) → cons(Head, append(Tail, List))
subtract(List, nil) → List
subtract(List, cons(Head, Tail)) → subtract(delete(Head, List), Tail)
delete(E, nil) → nil
delete(E, cons(Head, Tail)) → case8(Tail, Head, E, equal(E, Head))
case8(Tail, Head, E, true) → Tail
case8(Tail, Head, E, false) → cons(Head, delete(E, Tail))
gen_tag(Pid) → tuple(Pid, tuplenil(tag))
gen_modtageq(Client1, Client2) → equal(Client1, Client2)
member(E, nil) → false
member(E, cons(Head, Tail)) → case9(Tail, Head, E, equal(E, Head))
case9(Tail, Head, E, true) → true
case9(Tail, Head, E, false) → member(E, Tail)
eqs(empty, empty) → T
eqs(empty, stack(E2, S2)) → F
eqs(stack(E1, S1), empty) → F
eqs(stack(E1, S1), stack(E2, S2)) → and(eqt(E1, E2), eqs(S1, S2))
pushs(E1, S1) → stack(E1, S1)
pops(stack(E1, S1)) → S1
tops(stack(E1, S1)) → E1
istops(E1, empty) → F
istops(E1, stack(E2, S1)) → eqt(E1, E2)
eqc(nocalls, nocalls) → T
eqc(nocalls, calls(E2, S2, CS2)) → F
eqc(calls(E1, S1, CS1), nocalls) → F
eqc(calls(E1, S1, CS1), calls(E2, S2, CS2)) → and(eqt(E1, E2), and(eqs(S1, S2), eqc(CS1, CS2)))
push(E1, E2, nocalls) → calls(E1, stack(E2, empty), nocalls)
push(E1, E2, calls(E3, S1, CS1)) → push1(E1, E2, E3, S1, CS1, eqt(E1, E3))
push1(E1, E2, E3, S1, CS1, T) → calls(E3, pushs(E2, S1), CS1)

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

(55) PisEmptyProof (EQUIVALENT transformation)

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

(0) Obligation:

(1) DependencyPairsProof (EQUIVALENT transformation)

(2) Obligation:

(3) DependencyGraphProof (EQUIVALENT transformation)

(4) Complex Obligation (AND)

(5) Obligation:

(6) QDPOrderProof (EQUIVALENT transformation)

(7) Obligation:

(8) PisEmptyProof (EQUIVALENT transformation)

(9) TRUE

(10) Obligation:

(11) QDPOrderProof (EQUIVALENT transformation)

(12) Obligation:

(13) PisEmptyProof (EQUIVALENT transformation)

(14) TRUE

(15) Obligation:

(16) QDPOrderProof (EQUIVALENT transformation)

(17) Obligation:

(18) PisEmptyProof (EQUIVALENT transformation)

(19) TRUE

(20) Obligation:

(21) QDPOrderProof (EQUIVALENT transformation)

(22) Obligation:

(23) PisEmptyProof (EQUIVALENT transformation)

(24) TRUE

(25) Obligation:

(26) QDPOrderProof (EQUIVALENT transformation)

(27) Obligation:

(28) PisEmptyProof (EQUIVALENT transformation)

(29) TRUE

(30) Obligation:

(31) QDPOrderProof (EQUIVALENT transformation)

(32) Obligation:

(33) PisEmptyProof (EQUIVALENT transformation)

(34) TRUE

(35) Obligation:

(36) QDPOrderProof (EQUIVALENT transformation)

(37) Obligation:

(38) PisEmptyProof (EQUIVALENT transformation)

(39) TRUE

(40) Obligation:

(41) QDPOrderProof (EQUIVALENT transformation)

(42) Obligation:

(43) QDPOrderProof (EQUIVALENT transformation)

(44) Obligation:

(45) PisEmptyProof (EQUIVALENT transformation)

(46) TRUE

(47) Obligation:

(48) QDPOrderProof (EQUIVALENT transformation)

(49) Obligation:

(50) PisEmptyProof (EQUIVALENT transformation)

(51) TRUE

(52) Obligation:

(53) QDPOrderProof (EQUIVALENT transformation)

(54) Obligation:

(55) PisEmptyProof (EQUIVALENT transformation)

(56) TRUE