details

property	value
status	complete
benchmark	12.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n186.star.cs.uiowa.edu
space	Various_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.73934 seconds
cpu usage	3.88868
user time	3.71915
system time	0.169527
max virtual memory	1.8475476E7
max residence set size	247424.0

stage attributes

key	value
starexec-result	YES

output

YES proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 8 ms] (2) QDP (3) DependencyGraphProof [EQUIVALENT, 0 ms] (4) AND (5) QDP (6) UsableRulesProof [EQUIVALENT, 0 ms] (7) QDP (8) MRRProof [EQUIVALENT, 0 ms] (9) QDP (10) PisEmptyProof [EQUIVALENT, 0 ms] (11) YES (12) QDP (13) UsableRulesProof [EQUIVALENT, 0 ms] (14) QDP (15) QDPSizeChangeProof [EQUIVALENT, 0 ms] (16) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: O(0) -> 0 +(0, x) -> x +(x, 0) -> x +(O(x), O(y)) -> O(+(x, y)) +(O(x), I(y)) -> I(+(x, y)) +(I(x), O(y)) -> I(+(x, y)) +(I(x), I(y)) -> O(+(+(x, y), I(0))) *(0, x) -> 0 *(x, 0) -> 0 *(O(x), y) -> O(*(x, y)) *(I(x), y) -> +(O(*(x, y)), y) Q is empty. ---------------------------------------- (1) DependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. ---------------------------------------- (2) Obligation: Q DP problem: The TRS P consists of the following rules: +^1(O(x), O(y)) -> O^1(+(x, y)) +^1(O(x), O(y)) -> +^1(x, y) +^1(O(x), I(y)) -> +^1(x, y) +^1(I(x), O(y)) -> +^1(x, y) +^1(I(x), I(y)) -> O^1(+(+(x, y), I(0))) +^1(I(x), I(y)) -> +^1(+(x, y), I(0)) +^1(I(x), I(y)) -> +^1(x, y) *^1(O(x), y) -> O^1(*(x, y)) *^1(O(x), y) -> *^1(x, y) *^1(I(x), y) -> +^1(O(*(x, y)), y) *^1(I(x), y) -> O^1(*(x, y)) *^1(I(x), y) -> *^1(x, y) The TRS R consists of the following rules: O(0) -> 0 +(0, x) -> x +(x, 0) -> x +(O(x), O(y)) -> O(+(x, y)) +(O(x), I(y)) -> I(+(x, y)) +(I(x), O(y)) -> I(+(x, y)) +(I(x), I(y)) -> O(+(+(x, y), I(0))) *(0, x) -> 0 *(x, 0) -> 0 *(O(x), y) -> O(*(x, y)) *(I(x), y) -> +(O(*(x, y)), y) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (3) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs with 5 less nodes. ---------------------------------------- (4) Complex Obligation (AND) ---------------------------------------- (5) Obligation: popout

output may be truncated. 'popout' for the full output.

job log

popout

actions

all output return to TRS Standard