Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
SRS Stand 10685 pair #381717249
details
property
value
status
complete
benchmark
size-12-alpha-3-num-279.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n053.star.cs.uiowa.edu
space
Waldmann_07_size12
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
6.9336309433 seconds
cpu usage
24.436818051
max memory
3.872301056E9
stage attributes
key
value
output-size
4554
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 2 ms] (2) QDP (3) QDPOrderProof [EQUIVALENT, 89 ms] (4) QDP (5) DependencyGraphProof [EQUIVALENT, 0 ms] (6) QDP (7) UsableRulesProof [EQUIVALENT, 0 ms] (8) QDP (9) QDPSizeChangeProof [EQUIVALENT, 0 ms] (10) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a(x1) -> x1 a(b(x1)) -> c(b(x1)) b(x1) -> a(a(c(x1))) c(c(x1)) -> b(x1) 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: A(b(x1)) -> C(b(x1)) B(x1) -> A(a(c(x1))) B(x1) -> A(c(x1)) B(x1) -> C(x1) C(c(x1)) -> B(x1) The TRS R consists of the following rules: a(x1) -> x1 a(b(x1)) -> c(b(x1)) b(x1) -> a(a(c(x1))) c(c(x1)) -> b(x1) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (3) QDPOrderProof (EQUIVALENT) We use the reduction pair processor [LPAR04,JAR06]. The following pairs can be oriented strictly and are deleted. A(b(x1)) -> C(b(x1)) The remaining pairs can at least be oriented weakly. Used ordering: Matrix interpretation [MATRO] with arctic natural numbers [ARCTIC]: <<< POL(A(x_1)) = [[-I]] + [[0A, 0A, -I]] * x_1 >>> <<< POL(b(x_1)) = [[-I], [0A], [0A]] + [[0A, 0A, 0A], [1A, 1A, 1A], [1A, 1A, 1A]] * x_1 >>> <<< POL(C(x_1)) = [[-I]] + [[0A, -I, -I]] * x_1 >>> <<< POL(B(x_1)) = [[-I]] + [[0A, 0A, 0A]] * x_1 >>> <<< POL(a(x_1)) = [[-I], [-I], [0A]] + [[0A, 0A, -I], [0A, 0A, -I], [0A, 1A, 0A]] * x_1 >>> <<< POL(c(x_1)) = [[-I], [-I], [0A]] + [[0A, 0A, 0A], [0A, 0A, 0A], [1A, 1A, 1A]] * x_1
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to SRS Stand 10685