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TRS Outer 67415 pair #381918002
details
property
value
status
complete
benchmark
Ex24_Luc06_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n048.star.cs.uiowa.edu
space
Strategy_outermost_added_08
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.53261089325 seconds
cpu usage
7.80748761
max memory
5.70540032E8
stage attributes
key
value
output-size
37120
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Outermost Termination of the given OTRS could be proven: (0) OTRS (1) Thiemann-SpecialC-Transformation [EQUIVALENT, 0 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 116 ms] (4) QTRS (5) QTRSRRRProof [EQUIVALENT, 36 ms] (6) QTRS (7) QTRSRRRProof [EQUIVALENT, 17 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) UsableRulesReductionPairsProof [EQUIVALENT, 0 ms] (19) QDP (20) DependencyGraphProof [EQUIVALENT, 0 ms] (21) TRUE (22) QDP (23) UsableRulesProof [EQUIVALENT, 0 ms] (24) QDP (25) QReductionProof [EQUIVALENT, 0 ms] (26) QDP (27) QDPSizeChangeProof [EQUIVALENT, 0 ms] (28) YES (29) QDP (30) UsableRulesProof [EQUIVALENT, 0 ms] (31) QDP (32) QReductionProof [EQUIVALENT, 0 ms] (33) QDP (34) QDPOrderProof [EQUIVALENT, 54 ms] (35) QDP (36) PisEmptyProof [EQUIVALENT, 0 ms] (37) YES ---------------------------------------- (0) Obligation: Term rewrite system R: The TRS R consists of the following rules: a__f(b, X, c) -> a__f(X, a__c, X) a__c -> b mark(f(X1, X2, X3)) -> a__f(X1, mark(X2), X3) mark(c) -> a__c mark(b) -> b a__f(X1, X2, X3) -> f(X1, X2, X3) a__c -> c 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(a__f(x_1, x_2, x_3)) -> check_a__f(redex_a__f(x_1, x_2, x_3)) reduce(mark(x_1)) -> check_mark(redex_mark(x_1)) redex_a__f(b, X, c) -> result_a__f(a__f(X, a__c, X)) reduce(a__c) -> go_up(b) redex_mark(f(X1, X2, X3)) -> result_mark(a__f(X1, mark(X2), X3)) redex_mark(c) -> result_mark(a__c) redex_mark(b) -> result_mark(b) redex_a__f(X1, X2, X3) -> result_a__f(f(X1, X2, X3)) reduce(a__c) -> go_up(c) check_a__f(result_a__f(x)) -> go_up(x) check_mark(result_mark(x)) -> go_up(x) check_a__f(redex_a__f(x_1, x_2, x_3)) -> in_a__f_1(reduce(x_1), x_2, x_3) check_a__f(redex_a__f(x_1, x_2, x_3)) -> in_a__f_2(x_1, reduce(x_2), x_3) check_a__f(redex_a__f(x_1, x_2, x_3)) -> in_a__f_3(x_1, x_2, reduce(x_3)) check_mark(redex_mark(x_1)) -> in_mark_1(reduce(x_1)) reduce(f(x_1, x_2, x_3)) -> in_f_1(reduce(x_1), x_2, x_3)
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