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TRS Outer 67415 pair #381918014
details
property
value
status
complete
benchmark
#4.13.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n026.star.cs.uiowa.edu
space
Strategy_outermost_added_08
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
17.0446679592 seconds
cpu usage
43.770638025
max memory
4.664881152E9
stage attributes
key
value
output-size
58424
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Outermost Termination of the given OTRS could be proven: (0) OTRS (1) Thiemann-SpecialC-Transformation [EQUIVALENT, 0 ms] (2) QTRS (3)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) UsableRulesReductionPairsProof [EQUIVALENT, 0 ms] (13) QDP (14) DependencyGraphProof [EQUIVALENT, 0 ms] (15) TRUE (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) TransformationProof [EQUIVALENT, 0 ms] (26) QDP (27) TransformationProof [EQUIVALENT, 0 ms] (28) QDP (29) TransformationProof [EQUIVALENT, 0 ms] (30) QDP (31) DependencyGraphProof [EQUIVALENT, 0 ms] (32) QDP (33) SemLabProof [SOUND, 148 ms] (34) QDP (35) QDPOrderProof [EQUIVALENT, 62 ms] (36) QDP (37) PisEmptyProof [EQUIVALENT, 0 ms] (38) YES ---------------------------------------- (0) Obligation: Term rewrite system R: The TRS R consists of the following rules: f(0, 1, x) -> f(x, x, x) f(x, y, z) -> 2 0 -> 2 1 -> 2 g(x, x, y) -> y g(x, y, y) -> x 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(f(x_1, x_2, x_3)) -> check_f(redex_f(x_1, x_2, x_3)) reduce(g(x_1, x_2, x_3)) -> check_g(redex_g(x_1, x_2, x_3)) redex_f(0, 1, x) -> result_f(f(x, x, x)) redex_f(x, y, z) -> result_f(2) reduce(0) -> go_up(2) reduce(1) -> go_up(2) redex_g(x, x, y) -> result_g(y) redex_g(x, y, y) -> result_g(x) check_f(result_f(x)) -> go_up(x) check_g(result_g(x)) -> go_up(x) check_f(redex_f(x_1, x_2, x_3)) -> in_f_1(reduce(x_1), x_2, x_3) check_f(redex_f(x_1, x_2, x_3)) -> in_f_2(x_1, reduce(x_2), x_3) check_f(redex_f(x_1, x_2, x_3)) -> in_f_3(x_1, x_2, reduce(x_3)) check_g(redex_g(x_1, x_2, x_3)) -> in_g_1(reduce(x_1), x_2, x_3) check_g(redex_g(x_1, x_2, x_3)) -> in_g_2(x_1, reduce(x_2), x_3) check_g(redex_g(x_1, x_2, x_3)) -> in_g_3(x_1, x_2, reduce(x_3))
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