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TRS Equational pair #516978125
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
n170.star.cs.uiowa.edu
space
Mixed_AC
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
12.7091560364 seconds
cpu usage
31.189416128
max memory
1.355677696E9
stage attributes
key
value
output-size
136391
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination of the given ETRS could be proven: (0) ETRS (1) EquationalDependencyPairsProof [EQUIVALENT, 282 ms] (2) EDP (3) EDependencyGraphProof [EQUIVALENT, 0 ms] (4) AND (5) EDP (6) ESharpUsableEquationsProof [EQUIVALENT, 0 ms] (7) EDP (8) EUsableRulesReductionPairsProof [EQUIVALENT, 51 ms] (9) EDP (10) ERuleRemovalProof [EQUIVALENT, 0 ms] (11) EDP (12) PisEmptyProof [EQUIVALENT, 0 ms] (13) YES (14) EDP (15) ESharpUsableEquationsProof [EQUIVALENT, 130 ms] (16) EDP (17) EDPPoloProof [EQUIVALENT, 3258 ms] (18) EDP (19) EDPPoloProof [EQUIVALENT, 1407 ms] (20) EDP (21) PisEmptyProof [EQUIVALENT, 0 ms] (22) YES (23) EDP (24) ESharpUsableEquationsProof [EQUIVALENT, 29 ms] (25) EDP (26) EUsableRulesReductionPairsProof [EQUIVALENT, 0 ms] (27) EDP (28) PisEmptyProof [EQUIVALENT, 0 ms] (29) YES (30) EDP (31) ESharpUsableEquationsProof [EQUIVALENT, 0 ms] (32) EDP (33) EUsableRulesReductionPairsProof [EQUIVALENT, 16 ms] (34) EDP (35) PisEmptyProof [EQUIVALENT, 0 ms] (36) YES (37) EDP (38) ESharpUsableEquationsProof [EQUIVALENT, 0 ms] (39) EDP (40) EDPPoloProof [EQUIVALENT, 0 ms] (41) EDP (42) PisEmptyProof [EQUIVALENT, 0 ms] (43) YES (44) EDP (45) ESharpUsableEquationsProof [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
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