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TRS Outer 67415 pair #381918003
details
property
value
status
complete
benchmark
non-lin1.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n072.star.cs.uiowa.edu
space
Mixed_outermost
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.5809841156 seconds
cpu usage
3.679666643
max memory
2.38637056E8
stage attributes
key
value
output-size
14753
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Outermost Termination of the given OTRS could be proven: (0) OTRS (1) Thiemann-SpecialC-Transformation [EQUIVALENT, 0 ms] (2) QTRS (3)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) QDP (7) UsableRulesProof [EQUIVALENT, 0 ms] (8) QDP (9) QReductionProof [EQUIVALENT, 0 ms] (10) QDP (11) TransformationProof [EQUIVALENT, 0 ms] (12) QDP (13) UsableRulesProof [EQUIVALENT, 0 ms] (14) QDP (15) QReductionProof [EQUIVALENT, 0 ms] (16) QDP (17) TransformationProof [EQUIVALENT, 0 ms] (18) QDP (19) UsableRulesProof [EQUIVALENT, 0 ms] (20) QDP (21) QReductionProof [EQUIVALENT, 0 ms] (22) QDP (23) TransformationProof [EQUIVALENT, 0 ms] (24) QDP (25) TransformationProof [EQUIVALENT, 0 ms] (26) QDP (27) UsableRulesProof [EQUIVALENT, 0 ms] (28) QDP (29) QReductionProof [EQUIVALENT, 0 ms] (30) QDP (31) QDPOrderProof [EQUIVALENT, 3 ms] (32) QDP (33) DependencyGraphProof [EQUIVALENT, 0 ms] (34) TRUE ---------------------------------------- (0) Obligation: Term rewrite system R: The TRS R consists of the following rules: g(x, x) -> g(g(x, x), x) g(x, y) -> y 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, x_2)) -> check_g(redex_g(x_1, x_2)) redex_g(x, x) -> result_g(g(g(x, x), x)) redex_g(x, y) -> result_g(y) check_g(result_g(x)) -> go_up(x) check_g(redex_g(x_1, x_2)) -> in_g_1(reduce(x_1), x_2) check_g(redex_g(x_1, x_2)) -> in_g_2(x_1, reduce(x_2)) in_g_1(go_up(x_1), x_2) -> go_up(g(x_1, x_2)) in_g_2(x_1, go_up(x_2)) -> go_up(g(x_1, x_2)) The set Q consists of the following terms: top(go_up(x0)) reduce(g(x0, x1)) redex_g(x0, x1) check_g(result_g(x0)) in_g_1(go_up(x0), x1) in_g_2(x0, go_up(x1)) ---------------------------------------- (3) DependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. ----------------------------------------
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