Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
TRS Equational pair #516978116
details
property
value
status
complete
benchmark
YWHM14_3.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n119.star.cs.uiowa.edu
space
Mixed_AC
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
2.47517895699 seconds
cpu usage
6.417071362
max memory
4.76827648E8
stage attributes
key
value
output-size
5772
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination of the given ETRS could be proven: (0) ETRS (1) RRRPoloETRSProof [EQUIVALENT, 194 ms] (2) ETRS (3) RRRPoloETRSProof [EQUIVALENT, 45 ms] (4) ETRS (5) RRRPoloETRSProof [EQUIVALENT, 25 ms] (6) ETRS (7) RRRPoloETRSProof [EQUIVALENT, 0 ms] (8) ETRS (9) RisEmptyProof [EQUIVALENT, 0 ms] (10) YES ---------------------------------------- (0) Obligation: Equational rewrite system: The TRS R consists of the following rules: f(plus(x, y)) -> plus(f(x), y) plus(g(x), y) -> g(plus(x, y)) plus(f(a), g(b)) -> plus(f(b), g(a)) h(a, b) -> h(b, a) h(a, g(g(a))) -> h(g(a), f(a)) h(g(a), a) -> h(a, g(b)) h(g(a), b) -> h(a, g(a)) The set E consists of the following equations: plus(x, y) == plus(y, x) plus(plus(x, y), z) == plus(x, plus(y, z)) ---------------------------------------- (1) RRRPoloETRSProof (EQUIVALENT) The following E TRS is given: Equational rewrite system: The TRS R consists of the following rules: f(plus(x, y)) -> plus(f(x), y) plus(g(x), y) -> g(plus(x, y)) plus(f(a), g(b)) -> plus(f(b), g(a)) h(a, b) -> h(b, a) h(a, g(g(a))) -> h(g(a), f(a)) h(g(a), a) -> h(a, g(b)) h(g(a), b) -> h(a, g(a)) The set E consists of the following equations: plus(x, y) == plus(y, x) plus(plus(x, y), z) == plus(x, plus(y, z)) The following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly by a polynomial ordering: f(plus(x, y)) -> plus(f(x), y) plus(g(x), y) -> g(plus(x, y)) h(a, g(g(a))) -> h(g(a), f(a)) Used ordering: Polynomial interpretation [POLO]: POL(a) = 0 POL(b) = 0 POL(f(x_1)) = 2 + 3*x_1 POL(g(x_1)) = 3 + x_1 POL(h(x_1, x_2)) = x_1 + x_2 POL(plus(x_1, x_2)) = 2 + 2*x_1 + x_1*x_2 + 2*x_2 ---------------------------------------- (2) Obligation: Equational rewrite system: The TRS R consists of the following rules: plus(f(a), g(b)) -> plus(f(b), g(a)) h(a, b) -> h(b, a) h(g(a), a) -> h(a, g(b)) h(g(a), b) -> h(a, g(a)) The set E consists of the following equations: plus(x, y) == plus(y, x) plus(plus(x, y), z) == plus(x, plus(y, z))
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to TRS Equational