Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
TRS Stand 20472 pair #381711466
details
property
value
status
complete
benchmark
#4.33.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n036.star.cs.uiowa.edu
space
Strategy_removed_AG01
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.85586214066 seconds
cpu usage
4.164418054
max memory
2.09993728E8
stage attributes
key
value
output-size
10534
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) Overlay + Local Confluence [EQUIVALENT, 0 ms] (2) QTRS (3) DependencyPairsProof [EQUIVALENT, 19 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) PisEmptyProof [EQUIVALENT, 0 ms] (15) YES (16) QDP (17) UsableRulesProof [EQUIVALENT, 0 ms] (18) QDP (19) QReductionProof [EQUIVALENT, 0 ms] (20) QDP (21) QDPOrderProof [EQUIVALENT, 14 ms] (22) QDP (23) PisEmptyProof [EQUIVALENT, 0 ms] (24) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: sum(cons(s(n), x), cons(m, y)) -> sum(cons(n, x), cons(s(m), y)) sum(cons(0, x), y) -> sum(x, y) sum(nil, y) -> y weight(cons(n, cons(m, x))) -> weight(sum(cons(n, cons(m, x)), cons(0, x))) weight(cons(n, nil)) -> n Q is empty. ---------------------------------------- (1) Overlay + Local Confluence (EQUIVALENT) The TRS is overlay and locally confluent. By [NOC] we can switch to innermost. ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: sum(cons(s(n), x), cons(m, y)) -> sum(cons(n, x), cons(s(m), y)) sum(cons(0, x), y) -> sum(x, y) sum(nil, y) -> y weight(cons(n, cons(m, x))) -> weight(sum(cons(n, cons(m, x)), cons(0, x))) weight(cons(n, nil)) -> n The set Q consists of the following terms: sum(cons(s(x0), x1), cons(x2, x3)) sum(cons(0, x0), x1) sum(nil, x0) weight(cons(x0, cons(x1, x2))) weight(cons(x0, nil)) ---------------------------------------- (3) DependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. ---------------------------------------- (4) Obligation: Q DP problem: The TRS P consists of the following rules: SUM(cons(s(n), x), cons(m, y)) -> SUM(cons(n, x), cons(s(m), y)) SUM(cons(0, x), y) -> SUM(x, y) WEIGHT(cons(n, cons(m, x))) -> WEIGHT(sum(cons(n, cons(m, x)), cons(0, x))) WEIGHT(cons(n, cons(m, x))) -> SUM(cons(n, cons(m, x)), cons(0, x)) The TRS R consists of the following rules: sum(cons(s(n), x), cons(m, y)) -> sum(cons(n, x), cons(s(m), y))
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to TRS Stand 20472