Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
TRS Equat 89423 pair #381732608
details
property
value
status
complete
benchmark
AC47.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n114.star.cs.uiowa.edu
space
Mixed_AC_and_C
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
3.03861713409 seconds
cpu usage
7.526936747
max memory
5.10394368E8
stage attributes
key
value
output-size
30501
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given ETRS could be proven: (0) ETRS (1) EquationalDependencyPairsProof [EQUIVALENT, 0 ms] (2) EDP (3) EDependencyGraphProof [EQUIVALENT, 0 ms] (4) AND (5) EDP (6) ESharpUsableEquationsProof [EQUIVALENT, 0 ms] (7) EDP (8) EUsableRulesReductionPairsProof [EQUIVALENT, 0 ms] (9) EDP (10) PisEmptyProof [EQUIVALENT, 0 ms] (11) YES (12) EDP (13) ESharpUsableEquationsProof [EQUIVALENT, 0 ms] (14) EDP (15) EUsableRulesReductionPairsProof [EQUIVALENT, 0 ms] (16) EDP (17) PisEmptyProof [EQUIVALENT, 0 ms] (18) YES (19) EDP (20) ESharpUsableEquationsProof [EQUIVALENT, 0 ms] (21) EDP (22) EUsableRulesReductionPairsProof [EQUIVALENT, 0 ms] (23) EDP (24) PisEmptyProof [EQUIVALENT, 0 ms] (25) YES (26) EDP (27) ESharpUsableEquationsProof [EQUIVALENT, 0 ms] (28) EDP (29) EDPPoloProof [EQUIVALENT, 19 ms] (30) EDP (31) EDependencyGraphProof [EQUIVALENT, 0 ms] (32) EDP (33) EDPPoloProof [EQUIVALENT, 10 ms] (34) EDP (35) EDependencyGraphProof [EQUIVALENT, 0 ms] (36) TRUE ---------------------------------------- (0) Obligation: Equational rewrite system: The TRS R consists of the following rules: eq(0, 0) -> true eq(0, s(x)) -> false eq(s(x), 0) -> false eq(s(x), s(y)) -> eq(x, y) or(true, y) -> true or(false, y) -> y union(empty, h) -> h union(edge(x, y, i), h) -> edge(x, y, union(i, h)) reach(x, y, empty, h) -> false reach(x, y, edge(u, v, i), h) -> if_reach_1(eq(x, u), x, y, edge(u, v, i), h) if_reach_1(true, x, y, edge(u, v, i), h) -> if_reach_2(eq(y, v), x, y, edge(u, v, i), h) if_reach_1(false, x, y, edge(u, v, i), h) -> reach(x, y, i, edge(u, v, h)) if_reach_2(true, x, y, edge(u, v, i), h) -> true if_reach_2(false, x, y, edge(u, v, i), h) -> or(reach(x, y, i, h), reach(v, y, union(i, h), empty)) The set E consists of the following equations: eq(x, y) == eq(y, x) or(x, y) == or(y, x) or(or(x, y), z) == or(x, or(y, z)) ---------------------------------------- (1) EquationalDependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,DA_STEIN] we result in the following initial EDP problem: The TRS P consists of the following rules: EQ(s(x), s(y)) -> EQ(x, y) UNION(edge(x, y, i), h) -> UNION(i, h) REACH(x, y, edge(u, v, i), h) -> IF_REACH_1(eq(x, u), x, y, edge(u, v, i), h) REACH(x, y, edge(u, v, i), h) -> EQ(x, u) IF_REACH_1(true, x, y, edge(u, v, i), h) -> IF_REACH_2(eq(y, v), x, y, edge(u, v, i), h) IF_REACH_1(true, x, y, edge(u, v, i), h) -> EQ(y, v) IF_REACH_1(false, x, y, edge(u, v, i), h) -> REACH(x, y, i, edge(u, v, h)) IF_REACH_2(false, x, y, edge(u, v, i), h) -> OR(reach(x, y, i, h), reach(v, y, union(i, h), empty)) IF_REACH_2(false, x, y, edge(u, v, i), h) -> REACH(x, y, i, h) IF_REACH_2(false, x, y, edge(u, v, i), h) -> REACH(v, y, union(i, h), empty) IF_REACH_2(false, x, y, edge(u, v, i), h) -> UNION(i, h) OR(or(true, y), ext) -> OR(true, ext)
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to TRS Equat 89423