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TRS Equat 89423 pair #381732709
details
property
value
status
complete
benchmark
AC46.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n086.star.cs.uiowa.edu
space
Mixed_C
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.68618702888 seconds
cpu usage
6.51273442
max memory
3.35491072E8
stage attributes
key
value
output-size
37834
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox2/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given ETRS could be proven: (0) ETRS (1) EquationalDependencyPairsProof [EQUIVALENT, 0 ms] (2) EDP (3) EDependencyGraphProof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, 3 ms] (16) EDP (17) PisEmptyProof [EQUIVALENT, 0 ms] (18) YES (19) EDP (20) ESharpUsableEquationsProof [EQUIVALENT, 0 ms] (21) EDP (22) EDPPoloProof [EQUIVALENT, 14 ms] (23) EDP (24) PisEmptyProof [EQUIVALENT, 0 ms] (25) YES (26) EDP (27) EUsableRulesReductionPairsProof [EQUIVALENT, 0 ms] (28) EDP (29) PisEmptyProof [EQUIVALENT, 0 ms] (30) YES (31) EDP (32) ESharpUsableEquationsProof [EQUIVALENT, 0 ms] (33) EDP (34) EDPPoloProof [EQUIVALENT, 0 ms] (35) EDP (36) PisEmptyProof [EQUIVALENT, 0 ms] (37) YES (38) EDP (39) ESharpUsableEquationsProof [EQUIVALENT, 0 ms] (40) EDP (41) EDPPoloProof [EQUIVALENT, 47 ms] (42) EDP (43) EDPPoloProof [EQUIVALENT, 0 ms] (44) EDP (45) EDependencyGraphProof [EQUIVALENT, 0 ms] (46) 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) le(0, y) -> true le(s(x), 0) -> false le(s(x), s(y)) -> le(x, y) app(nil, y) -> y app(add(n, x), y) -> add(n, app(x, y)) min(add(n, nil)) -> n min(add(n, add(m, x))) -> if_min(le(n, m), add(n, add(m, x))) if_min(true, add(n, add(m, x))) -> min(add(n, x)) if_min(false, add(n, add(m, x))) -> min(add(m, x)) rm(n, nil) -> nil rm(n, add(m, x)) -> if_rm(eq(n, m), n, add(m, x)) if_rm(true, n, add(m, x)) -> rm(n, x) if_rm(false, n, add(m, x)) -> add(m, rm(n, x)) minsort(nil, nil) -> nil minsort(add(n, x), y) -> if_minsort(eq(n, min(add(n, x))), add(n, x), y) if_minsort(true, add(n, x), y) -> add(n, minsort(app(rm(n, x), y), nil)) if_minsort(false, add(n, x), y) -> minsort(x, add(n, y)) The set E consists of the following equations: eq(x, y) == eq(y, x) ---------------------------------------- (1) EquationalDependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,DA_STEIN] we result in the following initial EDP problem:
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