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TRS Outer 67415 pair #381917994
details
property
value
status
complete
benchmark
ex6.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n077.star.cs.uiowa.edu
space
Mixed_outermost
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
14.0293269157 seconds
cpu usage
45.969074237
max memory
4.390363136E9
stage attributes
key
value
output-size
24217
starexec-result
YES
output
/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Outermost Termination of the given OTRS could be proven: (0) OTRS (1) Raffelsieper-Zantema-Transformation [SOUND, 0 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 55 ms] (4) QTRS (5) QTRSRRRProof [EQUIVALENT, 19 ms] (6) QTRS (7) AAECC Innermost [EQUIVALENT, 0 ms] (8) QTRS (9) DependencyPairsProof [EQUIVALENT, 0 ms] (10) QDP (11) DependencyGraphProof [EQUIVALENT, 0 ms] (12) AND (13) QDP (14) UsableRulesProof [EQUIVALENT, 0 ms] (15) QDP (16) QReductionProof [EQUIVALENT, 0 ms] (17) QDP (18) QDPSizeChangeProof [EQUIVALENT, 0 ms] (19) YES (20) QDP (21) UsableRulesProof [EQUIVALENT, 0 ms] (22) QDP (23) QReductionProof [EQUIVALENT, 0 ms] (24) QDP (25) TransformationProof [EQUIVALENT, 0 ms] (26) QDP (27) DependencyGraphProof [EQUIVALENT, 0 ms] (28) QDP (29) SemLabProof [SOUND, 76 ms] (30) QDP (31) UsableRulesReductionPairsProof [EQUIVALENT, 7 ms] (32) QDP (33) UsableRulesReductionPairsProof [EQUIVALENT, 0 ms] (34) QDP (35) MRRProof [EQUIVALENT, 0 ms] (36) QDP (37) UsableRulesReductionPairsProof [EQUIVALENT, 0 ms] (38) QDP (39) MRRProof [EQUIVALENT, 0 ms] (40) QDP (41) MRRProof [EQUIVALENT, 0 ms] (42) QDP (43) PisEmptyProof [EQUIVALENT, 0 ms] (44) YES ---------------------------------------- (0) Obligation: Term rewrite system R: The TRS R consists of the following rules: f(x, x) -> f(i(x), g(g(x))) f(x, y) -> x g(x) -> i(x) f(x, i(x)) -> f(x, x) f(i(x), i(g(x))) -> a Outermost Strategy. ---------------------------------------- (1) Raffelsieper-Zantema-Transformation (SOUND) We applied the Raffelsieper-Zantema transformation to transform the outermost TRS to a standard TRS. ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: down(f(x, x)) -> up(f(i(x), g(g(x)))) down(f(x, y)) -> up(x) down(g(x)) -> up(i(x)) down(f(x, i(x))) -> up(f(x, x)) down(f(i(x), i(g(x)))) -> up(a) top(up(x)) -> top(down(x)) down(i(y2)) -> i_flat(down(y2)) f_flat(up(x_1), block(x_2)) -> up(f(x_1, x_2)) f_flat(block(x_1), up(x_2)) -> up(f(x_1, x_2)) i_flat(up(x_1)) -> up(i(x_1)) g_flat(up(x_1)) -> up(g(x_1))
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