TRS Equational pair #487092776

details

property	value
status	complete
benchmark	sequent_modulo.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n142.star.cs.uiowa.edu
space	Mixed_AC

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	18.4996 seconds
cpu usage	24.7974
user time	23.8862
system time	0.911209
max virtual memory	1.8339932E7
max residence set size	2338112.0

stage attributes

key	value
starexec-result	YES

output

YES
proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


Termination of the given ETRS could be proven:

(0) ETRS
(1) EquationalDependencyPairsProof [EQUIVALENT, 198 ms]
(2) EDP
(3) EDependencyGraphProof [EQUIVALENT, 0 ms]
(4) AND
    (5) EDP
        (6) ESharpUsableEquationsProof [EQUIVALENT, 0 ms]
        (7) EDP
        (8) EUsableRulesReductionPairsProof [EQUIVALENT, 46 ms]
        (9) EDP
        (10) ERuleRemovalProof [EQUIVALENT, 6 ms]
        (11) EDP
        (12) PisEmptyProof [EQUIVALENT, 0 ms]
        (13) YES
    (14) EDP
        (15) ESharpUsableEquationsProof [EQUIVALENT, 61 ms]
        (16) EDP
        (17) EDPPoloProof [EQUIVALENT, 3151 ms]
        (18) EDP
        (19) PisEmptyProof [EQUIVALENT, 0 ms]
        (20) YES
    (21) EDP
        (22) ESharpUsableEquationsProof [EQUIVALENT, 0 ms]
        (23) EDP
        (24) EUsableRulesReductionPairsProof [EQUIVALENT, 14 ms]
        (25) EDP
        (26) PisEmptyProof [EQUIVALENT, 0 ms]
        (27) YES
    (28) EDP
        (29) ESharpUsableEquationsProof [EQUIVALENT, 0 ms]
        (30) EDP
        (31) EUsableRulesReductionPairsProof [EQUIVALENT, 28 ms]
        (32) EDP
        (33) PisEmptyProof [EQUIVALENT, 0 ms]
        (34) YES
    (35) EDP
        (36) ESharpUsableEquationsProof [EQUIVALENT, 0 ms]
        (37) EDP
        (38) EDPPoloProof [EQUIVALENT, 0 ms]
        (39) EDP
        (40) PisEmptyProof [EQUIVALENT, 0 ms]
        (41) YES
    (42) EDP
        (43) ESharpUsableEquationsProof [EQUIVALENT, 0 ms]
        (44) EDP
        (45) EDPPoloProof [EQUIVALENT, 0 ms]
        (46) EDP
        (47) EDPPoloProof [EQUIVALENT, 0 ms]
        (48) EDP
        (49) PisEmptyProof [EQUIVALENT, 0 ms]
        (50) YES


----------------------------------------

(0)
Obligation:
Equational rewrite system:
The TRS R consists of the following rules:

   substt(ef(x), y) -> ef(substt(x, y))
   substf(Pe(x), y) -> Pe(substt(x, y))
   substf(neg(f), s) -> neg(substf(f, s))
   substf(and(f, g), s) -> and(substf(f, s), substf(g, s))
   substf(or(f, g), s) -> or(substf(f, s), substf(g, s))
   substf(imp(f, g), s) -> imp(substf(f, s), substf(g, s))
   substf(forall(f), s) -> forall(substf(f, .(1, ron(s, shift))))
   substf(exists(f), s) -> exists(substf(f, .(1, ron(s, shift))))
   substt(x, id) -> x
   substf(f, id) -> f
   substt(substt(x, s), t) -> substt(x, ron(s, t))
   substf(substf(f, s), t) -> substf(f, ron(s, t))
   substt(1, .(x, s)) -> x
   ron(id, s) -> s
   ron(shift, .(x, s)) -> s
   ron(ron(s, t), u) -> ron(s, ron(t, u))
   ron(.(x, s), t) -> .(substt(x, t), ron(s, t))
   ron(s, id) -> s
   .(1, shift) -> id
   .(substt(1, s), ron(shift, s)) -> s
   virg(emptyfset, a) -> a
   virg(a, a) -> a
   *(emptysset, a) -> a
   *(a, a) -> a
   neg(neg(f)) -> f
   and(f, f) -> f
   or(f, f) -> f
   imp(f, g) -> or(neg(f), g)
   exists(f) -> neg(forall(neg(f)))
   sequent(virg(convf(neg(f)), a), b) -> sequent(a, virg(convf(f), b))
   sequent(convf(neg(f)), b) -> sequent(emptyfset, virg(convf(f), b))
   sequent(a, virg(convf(neg(f)), b)) -> sequent(virg(convf(f), a), b)
   sequent(a, convf(neg(f))) -> sequent(virg(convf(f), a), emptyfset)

popout

output may be truncated. 'popout' for the full output.

job log

popout

actions all output return to TRS Equational