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TRS Outer 67415 pair #381918010
details
property
value
status
complete
benchmark
f_2_1.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n057.star.cs.uiowa.edu
space
Zantema_08
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.74237513542 seconds
cpu usage
8.549193607
max memory
7.29264128E8
stage attributes
key
value
output-size
21750
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Outermost Termination of the given OTRS could be proven: (0) OTRS (1) Thiemann-SpecialC-Transformation [EQUIVALENT, 0 ms] (2) QTRS (3) DependencyPairsProof [EQUIVALENT, 0 ms] (4) QDP (5) DependencyGraphProof [EQUIVALENT, 0 ms] (6) AND (7) QDP (8) UsableRulesProof [EQUIVALENT, 0 ms] (9) QDP (10) QReductionProof [EQUIVALENT, 0 ms] (11) QDP (12) MRRProof [EQUIVALENT, 0 ms] (13) QDP (14) PisEmptyProof [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) UsableRulesProof [EQUIVALENT, 0 ms] (24) QDP (25) QDPOrderProof [EQUIVALENT, 11 ms] (26) QDP (27) QDPOrderProof [EQUIVALENT, 0 ms] (28) QDP (29) QDPOrderProof [EQUIVALENT, 41 ms] (30) QDP (31) PisEmptyProof [EQUIVALENT, 0 ms] (32) YES ---------------------------------------- (0) Obligation: Term rewrite system R: The TRS R consists of the following rules: a -> f(a) g(f(x)) -> f(g(x)) f(f(x)) -> b Outermost Strategy. ---------------------------------------- (1) Thiemann-SpecialC-Transformation (EQUIVALENT) We applied the Thiemann-SpecialC transformation to transform the outermost TRS to an innermost TRS. ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: top(go_up(x)) -> top(reduce(x)) reduce(g(x_1)) -> check_g(redex_g(x_1)) reduce(f(x_1)) -> check_f(redex_f(x_1)) reduce(a) -> go_up(f(a)) redex_g(f(x)) -> result_g(f(g(x))) redex_f(f(x)) -> result_f(b) check_g(result_g(x)) -> go_up(x) check_f(result_f(x)) -> go_up(x) check_g(redex_g(x_1)) -> in_g_1(reduce(x_1)) check_f(redex_f(x_1)) -> in_f_1(reduce(x_1)) in_f_1(go_up(x_1)) -> go_up(f(x_1)) in_g_1(go_up(x_1)) -> go_up(g(x_1)) The set Q consists of the following terms: top(go_up(x0)) reduce(g(x0)) reduce(f(x0)) reduce(a) redex_g(f(x0)) redex_f(f(x0)) check_g(result_g(x0)) check_f(result_f(x0)) check_g(redex_g(x0)) check_f(redex_f(x0)) in_f_1(go_up(x0))
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