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

(0) Obligation:

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

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

Q is empty.

(1) QTRSRRRProof (EQUIVALENT transformation)

Used ordering:
Recursive path order with status [RPO].
Quasi-Precedence:

or₂ > nil
imp₂ > T > [F, tuple₂, ok, nocalls] > and₂ > nil
not₁ > T > [F, tuple₂, ok, nocalls] > and₂ > nil
if₃ > nil
eq₂ > T > [F, tuple₂, ok, nocalls] > and₂ > nil
pid₁ > [F, tuple₂, ok, nocalls] > and₂ > nil
int₁ > [F, tuple₂, ok, nocalls] > and₂ > nil
int₁ > s₁ > element₂ > nil
a > T > [F, tuple₂, ok, nocalls] > and₂ > nil
locker > T > [F, tuple₂, ok, nocalls] > and₂ > nil
release > nil
request > T > [F, tuple₂, ok, nocalls] > and₂ > nil
[tag, gen_tag1] > T > [F, tuple₂, ok, nocalls] > and₂ > nil
[tag, gen_tag1] > [tuplenil₁, mcrlrecord, resource] > [F, tuple₂, ok, nocalls] > and₂ > nil
0 > nil
record_new1 > undefined > [F, tuple₂, ok, nocalls] > and₂ > nil
record_new1 > [lock, record_update4] > [tuplenil₁, mcrlrecord, resource] > [F, tuple₂, ok, nocalls] > and₂ > nil
locker2_{mappromotepending2} > locker2_{promotepending2} > case0₃ > cons₂ > excl > T > [F, tuple₂, ok, nocalls] > and₂ > nil
locker2_{mappromotepending2} > locker2_{promotepending2} > case0₃ > cons₂ > record_updates3 > [lock, record_update4] > [tuplenil₁, mcrlrecord, resource] > [F, tuple₂, ok, nocalls] > and₂ > nil
locker2_{mappromotepending2} > locker2_{promotepending2} > case0₃ > cons₂ > locker2_claimlock3 > nil
locker2_{mappromotepending2} > locker2_{promotepending2} > case0₃ > cons₂ > [locker2_{checkavailable2}, case6₄] > [false, member₂, equal₂, case9₄] > nil
locker2_{mappromotepending2} > locker2_{promotepending2} > case0₃ > cons₂ > [locker2_{checkavailable2}, case6₄] > pending > nil
locker2_{mappromotepending2} > locker2_{promotepending2} > case0₃ > cons₂ > [locker2_{checkavailable2}, case6₄] > record_extract3 > nil
locker2_{mappromotepending2} > locker2_{promotepending2} > case0₃ > cons₂ > [locker2_{checkavailable2}, case6₄] > andt₂ > nil
locker2_{mapclaimlock3} > cons₂ > excl > T > [F, tuple₂, ok, nocalls] > and₂ > nil
locker2_{mapclaimlock3} > cons₂ > record_updates3 > [lock, record_update4] > [tuplenil₁, mcrlrecord, resource] > [F, tuple₂, ok, nocalls] > and₂ > nil
locker2_{mapclaimlock3} > cons₂ > locker2_claimlock3 > nil
locker2_{mapclaimlock3} > cons₂ > [locker2_{checkavailable2}, case6₄] > [false, member₂, equal₂, case9₄] > nil
locker2_{mapclaimlock3} > cons₂ > [locker2_{checkavailable2}, case6₄] > pending > nil
locker2_{mapclaimlock3} > cons₂ > [locker2_{checkavailable2}, case6₄] > record_extract3 > nil
locker2_{mapclaimlock3} > cons₂ > [locker2_{checkavailable2}, case6₄] > andt₂ > nil
locker2_{mapaddpending3} > nil
locker2_{removepending2} > subtract₂ > [delete₂, case8₄] > cons₂ > excl > T > [F, tuple₂, ok, nocalls] > and₂ > nil
locker2_{removepending2} > subtract₂ > [delete₂, case8₄] > cons₂ > record_updates3 > [lock, record_update4] > [tuplenil₁, mcrlrecord, resource] > [F, tuple₂, ok, nocalls] > and₂ > nil
locker2_{removepending2} > subtract₂ > [delete₂, case8₄] > cons₂ > locker2_claimlock3 > nil
locker2_{removepending2} > subtract₂ > [delete₂, case8₄] > cons₂ > [locker2_{checkavailable2}, case6₄] > [false, member₂, equal₂, case9₄] > nil
locker2_{removepending2} > subtract₂ > [delete₂, case8₄] > cons₂ > [locker2_{checkavailable2}, case6₄] > pending > nil
locker2_{removepending2} > subtract₂ > [delete₂, case8₄] > cons₂ > [locker2_{checkavailable2}, case6₄] > record_extract3 > nil
locker2_{removepending2} > subtract₂ > [delete₂, case8₄] > cons₂ > [locker2_{checkavailable2}, case6₄] > andt₂ > nil
locker2_addpending3 > case1₄ > [true, append₂, excllock] > cons₂ > excl > T > [F, tuple₂, ok, nocalls] > and₂ > nil
locker2_addpending3 > case1₄ > [true, append₂, excllock] > cons₂ > record_updates3 > [lock, record_update4] > [tuplenil₁, mcrlrecord, resource] > [F, tuple₂, ok, nocalls] > and₂ > nil
locker2_addpending3 > case1₄ > [true, append₂, excllock] > cons₂ > locker2_claimlock3 > nil
locker2_addpending3 > case1₄ > [true, append₂, excllock] > cons₂ > [locker2_{checkavailable2}, case6₄] > [false, member₂, equal₂, case9₄] > nil
locker2_addpending3 > case1₄ > [true, append₂, excllock] > cons₂ > [locker2_{checkavailable2}, case6₄] > pending > nil
locker2_addpending3 > case1₄ > [true, append₂, excllock] > cons₂ > [locker2_{checkavailable2}, case6₄] > record_extract3 > nil
locker2_addpending3 > case1₄ > [true, append₂, excllock] > cons₂ > [locker2_{checkavailable2}, case6₄] > andt₂ > nil
locker2_releaselock2 > case2₃ > cons₂ > excl > T > [F, tuple₂, ok, nocalls] > and₂ > nil
locker2_releaselock2 > case2₃ > cons₂ > record_updates3 > [lock, record_update4] > [tuplenil₁, mcrlrecord, resource] > [F, tuple₂, ok, nocalls] > and₂ > nil
locker2_releaselock2 > case2₃ > cons₂ > locker2_claimlock3 > nil
locker2_releaselock2 > case2₃ > cons₂ > [locker2_{checkavailable2}, case6₄] > [false, member₂, equal₂, case9₄] > nil
locker2_releaselock2 > case2₃ > cons₂ > [locker2_{checkavailable2}, case6₄] > pending > nil
locker2_releaselock2 > case2₃ > cons₂ > [locker2_{checkavailable2}, case6₄] > record_extract3 > nil
locker2_releaselock2 > case2₃ > cons₂ > [locker2_{checkavailable2}, case6₄] > andt₂ > nil
locker2_releaselock2 > gen_modtageq2 > [false, member₂, equal₂, case9₄] > nil
case4₃ > [false, member₂, equal₂, case9₄] > nil
[locker2_obtainables2, case5₄] > [true, append₂, excllock] > cons₂ > excl > T > [F, tuple₂, ok, nocalls] > and₂ > nil
[locker2_obtainables2, case5₄] > [true, append₂, excllock] > cons₂ > record_updates3 > [lock, record_update4] > [tuplenil₁, mcrlrecord, resource] > [F, tuple₂, ok, nocalls] > and₂ > nil
[locker2_obtainables2, case5₄] > [true, append₂, excllock] > cons₂ > locker2_claimlock3 > nil
[locker2_obtainables2, case5₄] > [true, append₂, excllock] > cons₂ > [locker2_{checkavailable2}, case6₄] > [false, member₂, equal₂, case9₄] > nil
[locker2_obtainables2, case5₄] > [true, append₂, excllock] > cons₂ > [locker2_{checkavailable2}, case6₄] > pending > nil
[locker2_obtainables2, case5₄] > [true, append₂, excllock] > cons₂ > [locker2_{checkavailable2}, case6₄] > record_extract3 > nil
[locker2_obtainables2, case5₄] > [true, append₂, excllock] > cons₂ > [locker2_{checkavailable2}, case6₄] > andt₂ > nil
[locker2_obtainables2, case5₄] > locker2_obtainable2 > nil
locker2_{checkavailables2} > [true, append₂, excllock] > cons₂ > excl > T > [F, tuple₂, ok, nocalls] > and₂ > nil
locker2_{checkavailables2} > [true, append₂, excllock] > cons₂ > record_updates3 > [lock, record_update4] > [tuplenil₁, mcrlrecord, resource] > [F, tuple₂, ok, nocalls] > and₂ > nil
locker2_{checkavailables2} > [true, append₂, excllock] > cons₂ > locker2_claimlock3 > nil
locker2_{checkavailables2} > [true, append₂, excllock] > cons₂ > [locker2_{checkavailable2}, case6₄] > [false, member₂, equal₂, case9₄] > nil
locker2_{checkavailables2} > [true, append₂, excllock] > cons₂ > [locker2_{checkavailable2}, case6₄] > pending > nil
locker2_{checkavailables2} > [true, append₂, excllock] > cons₂ > [locker2_{checkavailable2}, case6₄] > record_extract3 > nil
locker2_{checkavailables2} > [true, append₂, excllock] > cons₂ > [locker2_{checkavailable2}, case6₄] > andt₂ > nil
locker2_adduniq2 > nil
pops₁ > nil
tops₁ > nil
istops₂ > [eqt₂, calls₃] > T > [F, tuple₂, ok, nocalls] > and₂ > nil
eqc₂ > eqs₂ > [eqt₂, calls₃] > T > [F, tuple₂, ok, nocalls] > and₂ > nil
push₃ > empty > [F, tuple₂, ok, nocalls] > and₂ > nil
push₃ > push1₆ > [eqt₂, calls₃] > T > [F, tuple₂, ok, nocalls] > and₂ > nil
push₃ > push1₆ > [stack₂, pushs₂] > [F, tuple₂, ok, nocalls] > and₂ > nil

Status:

pops₁: multiset
eq₂: [1,2]
case8₄: [3,1,4,2]
push₃: multiset
delete₂: [1,2]
locker2_{removepending2}: [1,2]
locker2_{mappromotepending2}: [2,1]
member₂: [1,2]
gen_modtageq2: multiset
gen_tag1: [1]
equal₂: [1,2]
pushs₂: [2,1]
locker2_{checkavailable2}: [2,1]
record_new1: multiset
excllock: multiset
eqt₂: [1,2]
nil: multiset
element₂: [2,1]
locker2_releaselock2: [2,1]
locker2_obtainables2: [1,2]
T: multiset
locker2_addpending3: [3,2,1]
resource: multiset
locker: multiset
true: multiset
empty: multiset
eqc₂: multiset
push1₆: [4,5,1,3,6,2]
locker2_obtainable2: multiset
locker2_{checkavailables2}: multiset
case2₃: multiset
pid₁: multiset
ok: multiset
F: multiset
lock: multiset
tops₁: multiset
or₂: multiset
calls₃: [1,2,3]
tuplenil₁: [1]
eqs₂: multiset
and₂: multiset
locker2_claimlock3: multiset
append₂: multiset
andt₂: multiset
stack₂: [2,1]
case6₄: [1,3,4,2]
if₃: multiset
pending: multiset
not₁: [1]
int₁: [1]
istops₂: multiset
locker2_{mapclaimlock3}: [1,3,2]
s₁: multiset
record_update4: [1,3,4,2]
undefined: multiset
tag: multiset
mcrlrecord: multiset
a: multiset
request: multiset
excl: multiset
subtract₂: [2,1]
record_updates3: [2,3,1]
locker2_{promotepending2}: multiset
case4₃: multiset
nocalls: multiset
case1₄: [2,3,4,1]
0: multiset
cons₂: [2,1]
locker2_{mapaddpending3}: multiset
case5₄: [2,1,4,3]
record_extract3: multiset
release: multiset
case0₃: multiset
case9₄: [3,1,2,4]
false: multiset
imp₂: [2,1]
tuple₂: [1,2]
locker2_adduniq2: multiset

With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

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))
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)

(2) Obligation:

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

pushs(E1, S1) → stack(E1, S1)

Q is empty.

(3) QTRSRRRProof (EQUIVALENT transformation)

Used ordering:
Recursive path order with status [RPO].
Quasi-Precedence:

pushs₂ > stack₂

Status:

pushs₂: [2,1]
stack₂: multiset

With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

pushs(E1, S1) → stack(E1, S1)

(4) Obligation:

Q restricted rewrite system:
R is empty.
Q is empty.

(5) RisEmptyProof (EQUIVALENT transformation)

The TRS R is empty. Hence, termination is trivially proven.

(6) TRUE