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TRS Stand 20472 pair #381709785
details
property
value
status
complete
benchmark
otto06.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n055.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
3.26873397827 seconds
cpu usage
9.281787564
max memory
5.10050304E8
stage attributes
key
value
output-size
40851
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) Overlay + Local Confluence [EQUIVALENT, 0 ms] (2) QTRS (3) DependencyPairsProof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, 23 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) QDPSizeChangeProof [EQUIVALENT, 0 ms] (13) YES (14) QDP (15) UsableRulesProof [EQUIVALENT, 0 ms] (16) QDP (17) QReductionProof [EQUIVALENT, 0 ms] (18) QDP (19) QDPSizeChangeProof [EQUIVALENT, 0 ms] (20) YES (21) QDP (22) UsableRulesProof [EQUIVALENT, 0 ms] (23) QDP (24) QReductionProof [EQUIVALENT, 0 ms] (25) QDP (26) TransformationProof [EQUIVALENT, 0 ms] (27) QDP (28) UsableRulesProof [EQUIVALENT, 0 ms] (29) QDP (30) QReductionProof [EQUIVALENT, 0 ms] (31) QDP (32) TransformationProof [EQUIVALENT, 0 ms] (33) QDP (34) UsableRulesProof [EQUIVALENT, 0 ms] (35) QDP (36) QReductionProof [EQUIVALENT, 0 ms] (37) QDP (38) NonInfProof [EQUIVALENT, 57 ms] (39) AND (40) QDP (41) DependencyGraphProof [EQUIVALENT, 0 ms] (42) TRUE (43) QDP (44) DependencyGraphProof [EQUIVALENT, 0 ms] (45) TRUE (46) QDP (47) UsableRulesProof [EQUIVALENT, 0 ms] (48) QDP (49) QReductionProof [EQUIVALENT, 0 ms] (50) QDP (51) QDPSizeChangeProof [EQUIVALENT, 0 ms] (52) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: app(x, y) -> helpa(0, plus(length(x), length(y)), x, y) plus(x, 0) -> x plus(x, s(y)) -> s(plus(x, y)) length(nil) -> 0 length(cons(x, y)) -> s(length(y)) helpa(c, l, ys, zs) -> if(ge(c, l), c, l, ys, zs) ge(x, 0) -> true ge(0, s(x)) -> false ge(s(x), s(y)) -> ge(x, y) if(true, c, l, ys, zs) -> nil if(false, c, l, ys, zs) -> helpb(c, l, greater(ys, zs), smaller(ys, zs)) greater(ys, zs) -> helpc(ge(length(ys), length(zs)), ys, zs) smaller(ys, zs) -> helpc(ge(length(ys), length(zs)), zs, ys) helpc(true, ys, zs) -> ys helpc(false, ys, zs) -> zs helpb(c, l, cons(y, ys), zs) -> cons(y, helpa(s(c), l, ys, zs)) Q is empty. ---------------------------------------- (1) Overlay + Local Confluence (EQUIVALENT) The TRS is overlay and locally confluent. By [NOC] we can switch to innermost. ----------------------------------------
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