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SRS Standard pair #487091274
details
property
value
status
complete
benchmark
z076.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n148.star.cs.uiowa.edu
space
Zantema_04
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.0765779 seconds
cpu usage
0.065003
user time
0.023942
system time
0.041061
max virtual memory
113188.0
max residence set size
4756.0
stage attributes
key
value
starexec-result
YES
output
YES Problem 1: (VAR v_NonEmpty:S x1:S) (RULES f(0(x1:S)) -> 0(x1:S) f(s(x1:S)) -> s(s(f(p(s(x1:S))))) p(s(x1:S)) -> x1:S ) Problem 1: Innermost Equivalent Processor: -> Rules: f(0(x1:S)) -> 0(x1:S) f(s(x1:S)) -> s(s(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: F(s(x1:S)) -> F(p(s(x1:S))) F(s(x1:S)) -> P(s(x1:S)) -> Rules: f(0(x1:S)) -> 0(x1:S) f(s(x1:S)) -> s(s(f(p(s(x1:S))))) p(s(x1:S)) -> x1:S Problem 1: SCC Processor: -> Pairs: F(s(x1:S)) -> F(p(s(x1:S))) F(s(x1:S)) -> P(s(x1:S)) -> Rules: f(0(x1:S)) -> 0(x1:S) f(s(x1:S)) -> s(s(f(p(s(x1:S))))) p(s(x1:S)) -> x1:S ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: F(s(x1:S)) -> F(p(s(x1:S))) ->->-> Rules: f(0(x1:S)) -> 0(x1:S) f(s(x1:S)) -> s(s(f(p(s(x1:S))))) p(s(x1:S)) -> x1:S Problem 1: Reduction Pairs Processor: -> Pairs: F(s(x1:S)) -> F(p(s(x1:S))) -> Rules: f(0(x1:S)) -> 0(x1:S) f(s(x1:S)) -> s(s(f(p(s(x1:S))))) p(s(x1:S)) -> x1:S -> Usable rules: p(s(x1:S)) -> x1:S ->Interpretation type: Linear ->Coefficients: All rationals ->Dimension: 1 ->Bound: 2 ->Interpretation: [f](X) = 0 [p](X) = 1/2.X [0](X) = 0 [fSNonEmpty] = 0 [s](X) = 2.X + 1/2 [F](X) = 2.X [P](X) = 0 Problem 1: SCC Processor: -> Pairs: Empty -> Rules: f(0(x1:S)) -> 0(x1:S) f(s(x1:S)) -> s(s(f(p(s(x1:S))))) p(s(x1:S)) -> x1:S ->Strongly Connected Components: There is no strongly connected component The problem is finite.
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