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SRS Standard pair #516968580
details
property
value
status
complete
benchmark
z078.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n001.star.cs.uiowa.edu
space
Zantema_04
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.156409978867 seconds
cpu usage
0.086745569
max memory
3522560.0
stage attributes
key
value
output-size
3481
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 v_NonEmpty:S x1:S) (RULES d(0(x1:S)) -> 0(x1:S) d(s(x1:S)) -> s(s(d(p(s(x1:S))))) f(0(x1:S)) -> s(0(x1:S)) f(s(x1:S)) -> d(f(p(s(x1:S)))) p(s(x1:S)) -> x1:S ) Problem 1: Innermost Equivalent Processor: -> Rules: d(0(x1:S)) -> 0(x1:S) d(s(x1:S)) -> s(s(d(p(s(x1:S))))) f(0(x1:S)) -> s(0(x1:S)) f(s(x1:S)) -> d(f(p(s(x1:S)))) p(s(x1:S)) -> x1:S -> 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:S)) -> D(p(s(x1:S))) D(s(x1:S)) -> P(s(x1:S)) F(s(x1:S)) -> D(f(p(s(x1:S)))) F(s(x1:S)) -> F(p(s(x1:S))) F(s(x1:S)) -> P(s(x1:S)) -> Rules: d(0(x1:S)) -> 0(x1:S) d(s(x1:S)) -> s(s(d(p(s(x1:S))))) f(0(x1:S)) -> s(0(x1:S)) f(s(x1:S)) -> d(f(p(s(x1:S)))) p(s(x1:S)) -> x1:S Problem 1: SCC Processor: -> Pairs: D(s(x1:S)) -> D(p(s(x1:S))) D(s(x1:S)) -> P(s(x1:S)) F(s(x1:S)) -> D(f(p(s(x1:S)))) F(s(x1:S)) -> F(p(s(x1:S))) F(s(x1:S)) -> P(s(x1:S)) -> Rules: d(0(x1:S)) -> 0(x1:S) d(s(x1:S)) -> s(s(d(p(s(x1:S))))) f(0(x1:S)) -> s(0(x1:S)) f(s(x1:S)) -> d(f(p(s(x1:S)))) p(s(x1:S)) -> x1:S ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: D(s(x1:S)) -> D(p(s(x1:S))) ->->-> Rules: d(0(x1:S)) -> 0(x1:S) d(s(x1:S)) -> s(s(d(p(s(x1:S))))) f(0(x1:S)) -> s(0(x1:S)) f(s(x1:S)) -> d(f(p(s(x1:S)))) p(s(x1:S)) -> x1:S ->->Cycle: ->->-> Pairs: F(s(x1:S)) -> F(p(s(x1:S))) ->->-> Rules: d(0(x1:S)) -> 0(x1:S) d(s(x1:S)) -> s(s(d(p(s(x1:S))))) f(0(x1:S)) -> s(0(x1:S)) f(s(x1:S)) -> d(f(p(s(x1:S)))) p(s(x1:S)) -> x1:S The problem is decomposed in 2 subproblems. Problem 1.1: Reduction Pairs Processor: -> Pairs: D(s(x1:S)) -> D(p(s(x1:S))) -> Rules: d(0(x1:S)) -> 0(x1:S) d(s(x1:S)) -> s(s(d(p(s(x1:S))))) f(0(x1:S)) -> s(0(x1:S)) f(s(x1:S)) -> d(f(p(s(x1:S)))) p(s(x1:S)) -> x1:S -> Usable rules: p(s(x1:S)) -> x1:S ->Interpretation type: Linear
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