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TRS Condi 20667 pair #381733000
details
property
value
status
complete
benchmark
fib.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n002.star.cs.uiowa.edu
space
Mixed_CTRS
run statistics
property
value
solver
muterm 5.18
configuration
default
runtime (wallclock)
0.0858500003815 seconds
cpu usage
0.069649135
max memory
2.3031808E7
stage attributes
key
value
output-size
4173
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Problem 1: (VAR x x' y y' z) (RULES fib(0) -> pair(0,s(0)) fib(s(x)) -> pair(z,plus(y,z)) | fib(x) -> pair(y,z) plus(x,y) -> s(plus(x',y')) | x -> s(x'), y -> y' plus(x,y) -> y' | x -> 0, y -> y' ) Problem 1: Valid CTRS Processor: -> Rules: fib(0) -> pair(0,s(0)) fib(s(x)) -> pair(z,plus(y,z)) | fib(x) -> pair(y,z) plus(x,y) -> s(plus(x',y')) | x -> s(x'), y -> y' plus(x,y) -> y' | x -> 0, y -> y' -> The system is a deterministic 3-CTRS. Problem 1: Dependency Pairs Processor: Conditional Termination Problem 1: -> Pairs: FIB(s(x)) -> PLUS(y,z) | fib(x) -> pair(y,z) PLUS(x,y) -> PLUS(x',y') | x -> s(x'), y -> y' -> QPairs: Empty -> Rules: fib(0) -> pair(0,s(0)) fib(s(x)) -> pair(z,plus(y,z)) | fib(x) -> pair(y,z) plus(x,y) -> s(plus(x',y')) | x -> s(x'), y -> y' plus(x,y) -> y' | x -> 0, y -> y' Conditional Termination Problem 2: -> Pairs: FIB(s(x)) -> FIB(x) -> QPairs: FIB(s(x)) -> PLUS(y,z) | fib(x) -> pair(y,z) PLUS(x,y) -> PLUS(x',y') | x -> s(x'), y -> y' -> Rules: fib(0) -> pair(0,s(0)) fib(s(x)) -> pair(z,plus(y,z)) | fib(x) -> pair(y,z) plus(x,y) -> s(plus(x',y')) | x -> s(x'), y -> y' plus(x,y) -> y' | x -> 0, y -> y' The problem is decomposed in 2 subproblems. Problem 1.1: SCC Processor: -> Pairs: FIB(s(x)) -> PLUS(y,z) | fib(x) -> pair(y,z) PLUS(x,y) -> PLUS(x',y') | x -> s(x'), y -> y' -> QPairs: Empty -> Rules: fib(0) -> pair(0,s(0)) fib(s(x)) -> pair(z,plus(y,z)) | fib(x) -> pair(y,z) plus(x,y) -> s(plus(x',y')) | x -> s(x'), y -> y' plus(x,y) -> y' | x -> 0, y -> y' ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: PLUS(x,y) -> PLUS(x',y') | x -> s(x'), y -> y' ->->-> Rules: fib(0) -> pair(0,s(0)) fib(s(x)) -> pair(z,plus(y,z)) | fib(x) -> pair(y,z) plus(x,y) -> s(plus(x',y')) | x -> s(x'), y -> y' plus(x,y) -> y' | x -> 0, y -> y' Problem 1.1: Reduction Triple Processor: -> Pairs: PLUS(x,y) -> PLUS(x',y') | x -> s(x'), y -> y' -> QPairs: Empty -> Rules: fib(0) -> pair(0,s(0)) fib(s(x)) -> pair(z,plus(y,z)) | fib(x) -> pair(y,z) plus(x,y) -> s(plus(x',y')) | x -> s(x'), y -> y' plus(x,y) -> y' | x -> 0, y -> y' -> Usable rules: Empty ->Interpretation type: Linear ->Coefficients: Integer Numbers ->Dimension:
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