details

property	value
status	complete
benchmark	aprove2.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n149.star.cs.uiowa.edu
space	Secret_05_SRS

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	6.43553 seconds
cpu usage	22.0199
user time	20.9116
system time	1.10828
max virtual memory	6.2401276E7
max residence set size	2731424.0

stage attributes

key	value
starexec-result	YES

output

YES proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRS Reverse [EQUIVALENT, 0 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 4 ms] (4) QTRS (5) DependencyPairsProof [EQUIVALENT, 12 ms] (6) QDP (7) DependencyGraphProof [EQUIVALENT, 0 ms] (8) AND (9) QDP (10) UsableRulesProof [EQUIVALENT, 0 ms] (11) QDP (12) QDPSizeChangeProof [EQUIVALENT, 2 ms] (13) YES (14) QDP (15) UsableRulesProof [EQUIVALENT, 0 ms] (16) QDP (17) QDPSizeChangeProof [EQUIVALENT, 0 ms] (18) YES (19) QDP (20) UsableRulesProof [EQUIVALENT, 0 ms] (21) QDP (22) QDPOrderProof [EQUIVALENT, 136 ms] (23) QDP (24) UsableRulesProof [EQUIVALENT, 0 ms] (25) QDP (26) QDPSizeChangeProof [EQUIVALENT, 0 ms] (27) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: g(h(x1)) -> g(f(s(x1))) f(s(s(s(x1)))) -> h(f(s(h(x1)))) f(h(x1)) -> h(f(s(h(x1)))) h(x1) -> x1 f(f(s(s(x1)))) -> s(s(s(f(f(x1))))) b(a(x1)) -> a(b(x1)) a(a(a(x1))) -> b(a(a(b(x1)))) b(b(b(b(x1)))) -> a(x1) Q is empty. ---------------------------------------- (1) QTRS Reverse (EQUIVALENT) We applied the QTRS Reverse Processor [REVERSE]. ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: h(g(x1)) -> s(f(g(x1))) s(s(s(f(x1)))) -> h(s(f(h(x1)))) h(f(x1)) -> h(s(f(h(x1)))) h(x1) -> x1 s(s(f(f(x1)))) -> f(f(s(s(s(x1))))) a(b(x1)) -> b(a(x1)) a(a(a(x1))) -> b(a(a(b(x1)))) b(b(b(b(x1)))) -> a(x1) Q is empty. ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(a(x_1)) = 3 + x_1 POL(b(x_1)) = 1 + x_1 POL(f(x_1)) = x_1 POL(g(x_1)) = x_1 POL(h(x_1)) = x_1 POL(s(x_1)) = x_1 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: a(a(a(x1))) -> b(a(a(b(x1)))) b(b(b(b(x1)))) -> a(x1) ---------------------------------------- (4) popout

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