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SRS Stand 10685 pair #381719492
details
property
value
status
complete
benchmark
z077.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n042.star.cs.uiowa.edu
space
Zantema_04
run statistics
property
value
solver
muterm 5.18
configuration
default
runtime (wallclock)
0.016548871994 seconds
cpu usage
0.013195822
max memory
1478656.0
stage attributes
key
value
output-size
2285
starexec-result
YES
output
/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES Problem 1: (VAR x1) (RULES d(0(x1)) -> 0(x1) d(s(x1)) -> s(s(d(x1))) f(0(x1)) -> s(0(x1)) f(s(x1)) -> d(f(x1)) ) Problem 1: Innermost Equivalent Processor: -> Rules: d(0(x1)) -> 0(x1) d(s(x1)) -> s(s(d(x1))) f(0(x1)) -> s(0(x1)) f(s(x1)) -> d(f(x1)) -> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination. Problem 1: Dependency Pairs Processor: -> Pairs: D(s(x1)) -> D(x1) F(s(x1)) -> D(f(x1)) F(s(x1)) -> F(x1) -> Rules: d(0(x1)) -> 0(x1) d(s(x1)) -> s(s(d(x1))) f(0(x1)) -> s(0(x1)) f(s(x1)) -> d(f(x1)) Problem 1: SCC Processor: -> Pairs: D(s(x1)) -> D(x1) F(s(x1)) -> D(f(x1)) F(s(x1)) -> F(x1) -> Rules: d(0(x1)) -> 0(x1) d(s(x1)) -> s(s(d(x1))) f(0(x1)) -> s(0(x1)) f(s(x1)) -> d(f(x1)) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: D(s(x1)) -> D(x1) ->->-> Rules: d(0(x1)) -> 0(x1) d(s(x1)) -> s(s(d(x1))) f(0(x1)) -> s(0(x1)) f(s(x1)) -> d(f(x1)) ->->Cycle: ->->-> Pairs: F(s(x1)) -> F(x1) ->->-> Rules: d(0(x1)) -> 0(x1) d(s(x1)) -> s(s(d(x1))) f(0(x1)) -> s(0(x1)) f(s(x1)) -> d(f(x1)) The problem is decomposed in 2 subproblems. Problem 1.1: Subterm Processor: -> Pairs: D(s(x1)) -> D(x1) -> Rules: d(0(x1)) -> 0(x1) d(s(x1)) -> s(s(d(x1))) f(0(x1)) -> s(0(x1)) f(s(x1)) -> d(f(x1)) ->Projection: pi(D) = 1 Problem 1.1: SCC Processor: -> Pairs: Empty -> Rules: d(0(x1)) -> 0(x1) d(s(x1)) -> s(s(d(x1))) f(0(x1)) -> s(0(x1)) f(s(x1)) -> d(f(x1)) ->Strongly Connected Components: There is no strongly connected component
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