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TRS Outer 67415 pair #381918024
details
property
value
status
complete
benchmark
f_2_2.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n053.star.cs.uiowa.edu
space
Zantema_08
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
3.11301898956 seconds
cpu usage
9.558774332
max memory
7.78375168E8
stage attributes
key
value
output-size
31665
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Outermost Termination of the given OTRS could be proven: (0) OTRS (1) Raffelsieper-Zantema-Transformation [SOUND, 0 ms] (2) QTRS (3) AAECC Innermost [EQUIVALENT, 4 ms] (4) QTRS (5) DependencyPairsProof [EQUIVALENT, 0 ms] (6) QDP (7) DependencyGraphProof [EQUIVALENT, 0 ms] (8) AND (9) QDP (10) UsableRulesProof [EQUIVALENT, 0 ms] (11) QDP (12) QReductionProof [EQUIVALENT, 0 ms] (13) QDP (14) QDPSizeChangeProof [EQUIVALENT, 0 ms] (15) YES (16) QDP (17) UsableRulesProof [EQUIVALENT, 0 ms] (18) QDP (19) QReductionProof [EQUIVALENT, 0 ms] (20) QDP (21) TransformationProof [EQUIVALENT, 0 ms] (22) QDP (23) DependencyGraphProof [EQUIVALENT, 0 ms] (24) QDP (25) UsableRulesProof [EQUIVALENT, 0 ms] (26) QDP (27) TransformationProof [EQUIVALENT, 0 ms] (28) QDP (29) TransformationProof [EQUIVALENT, 0 ms] (30) QDP (31) TransformationProof [EQUIVALENT, 0 ms] (32) QDP (33) DependencyGraphProof [EQUIVALENT, 0 ms] (34) QDP (35) TransformationProof [EQUIVALENT, 0 ms] (36) QDP (37) QDPOrderProof [EQUIVALENT, 8 ms] (38) QDP (39) DependencyGraphProof [EQUIVALENT, 0 ms] (40) QDP (41) QDPOrderProof [EQUIVALENT, 7 ms] (42) QDP (43) QDPOrderProof [EQUIVALENT, 48 ms] (44) QDP (45) PisEmptyProof [EQUIVALENT, 0 ms] (46) YES ---------------------------------------- (0) Obligation: Term rewrite system R: The TRS R consists of the following rules: a -> f(a) g(f(x)) -> f(g(g(x))) f(f(x)) -> b 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(a) -> up(f(a)) down(g(f(x))) -> up(f(g(g(x)))) down(f(f(x))) -> up(b) top(up(x)) -> top(down(x)) down(f(a)) -> f_flat(down(a)) down(f(g(y4))) -> f_flat(down(g(y4))) down(f(b)) -> f_flat(down(b)) down(f(fresh_constant)) -> f_flat(down(fresh_constant)) down(g(a)) -> g_flat(down(a)) down(g(g(y7))) -> g_flat(down(g(y7))) down(g(b)) -> g_flat(down(b)) down(g(fresh_constant)) -> g_flat(down(fresh_constant))
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