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TRS Stand 20472 pair #381717055
details
property
value
status
complete
benchmark
PEANO_nokinds-noand_FR.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n012.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
Wanda
configuration
FirstOrder
runtime (wallclock)
0.699924945831 seconds
cpu usage
0.68788828
max memory
1.572864E7
stage attributes
key
value
output-size
35233
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_FirstOrder /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES We consider the system theBenchmark. We are asked to determine termination of the following first-order TRS. 0 : [] --> o U11 : [o * o] --> o U12 : [o] --> o U21 : [o] --> o U31 : [o * o] --> o U41 : [o * o * o] --> o U42 : [o * o * o] --> o activate : [o] --> o isNat : [o] --> o n!6220!62200 : [] --> o n!6220!6220plus : [o * o] --> o n!6220!6220s : [o] --> o plus : [o * o] --> o s : [o] --> o tt : [] --> o U11(tt, X) => U12(isNat(activate(X))) U12(tt) => tt U21(tt) => tt U31(tt, X) => activate(X) U41(tt, X, Y) => U42(isNat(activate(Y)), activate(X), activate(Y)) U42(tt, X, Y) => s(plus(activate(Y), activate(X))) isNat(n!6220!62200) => tt isNat(n!6220!6220plus(X, Y)) => U11(isNat(activate(X)), activate(Y)) isNat(n!6220!6220s(X)) => U21(isNat(activate(X))) plus(X, 0) => U31(isNat(X), X) plus(X, s(Y)) => U41(isNat(Y), Y, X) 0 => n!6220!62200 plus(X, Y) => n!6220!6220plus(X, Y) s(X) => n!6220!6220s(X) activate(n!6220!62200) => 0 activate(n!6220!6220plus(X, Y)) => plus(activate(X), activate(Y)) activate(n!6220!6220s(X)) => s(activate(X)) activate(X) => X We use the dependency pair framework as described in [Kop12, Ch. 6/7], with static dependency pairs (see [KusIsoSakBla09] and the adaptation for AFSMs in [Kop12, Ch. 7.8]). We thus obtain the following dependency pair problem (P_0, R_0, minimal, formative): Dependency Pairs P_0: 0] U11#(tt, X) =#> U12#(isNat(activate(X))) 1] U11#(tt, X) =#> isNat#(activate(X)) 2] U11#(tt, X) =#> activate#(X) 3] U31#(tt, X) =#> activate#(X) 4] U41#(tt, X, Y) =#> U42#(isNat(activate(Y)), activate(X), activate(Y)) 5] U41#(tt, X, Y) =#> isNat#(activate(Y)) 6] U41#(tt, X, Y) =#> activate#(Y) 7] U41#(tt, X, Y) =#> activate#(X) 8] U41#(tt, X, Y) =#> activate#(Y) 9] U42#(tt, X, Y) =#> s#(plus(activate(Y), activate(X))) 10] U42#(tt, X, Y) =#> plus#(activate(Y), activate(X)) 11] U42#(tt, X, Y) =#> activate#(Y) 12] U42#(tt, X, Y) =#> activate#(X) 13] isNat#(n!6220!6220plus(X, Y)) =#> U11#(isNat(activate(X)), activate(Y)) 14] isNat#(n!6220!6220plus(X, Y)) =#> isNat#(activate(X)) 15] isNat#(n!6220!6220plus(X, Y)) =#> activate#(X) 16] isNat#(n!6220!6220plus(X, Y)) =#> activate#(Y) 17] isNat#(n!6220!6220s(X)) =#> U21#(isNat(activate(X))) 18] isNat#(n!6220!6220s(X)) =#> isNat#(activate(X)) 19] isNat#(n!6220!6220s(X)) =#> activate#(X) 20] plus#(X, 0) =#> U31#(isNat(X), X) 21] plus#(X, 0) =#> isNat#(X) 22] plus#(X, s(Y)) =#> U41#(isNat(Y), Y, X) 23] plus#(X, s(Y)) =#> isNat#(Y) 24] activate#(n!6220!62200) =#> 0# 25] activate#(n!6220!6220plus(X, Y)) =#> plus#(activate(X), activate(Y)) 26] activate#(n!6220!6220plus(X, Y)) =#> activate#(X) 27] activate#(n!6220!6220plus(X, Y)) =#> activate#(Y) 28] activate#(n!6220!6220s(X)) =#> s#(activate(X)) 29] activate#(n!6220!6220s(X)) =#> activate#(X) Rules R_0: U11(tt, X) => U12(isNat(activate(X))) U12(tt) => tt U21(tt) => tt U31(tt, X) => activate(X) U41(tt, X, Y) => U42(isNat(activate(Y)), activate(X), activate(Y)) U42(tt, X, Y) => s(plus(activate(Y), activate(X))) isNat(n!6220!62200) => tt isNat(n!6220!6220plus(X, Y)) => U11(isNat(activate(X)), activate(Y)) isNat(n!6220!6220s(X)) => U21(isNat(activate(X))) plus(X, 0) => U31(isNat(X), X) plus(X, s(Y)) => U41(isNat(Y), Y, X) 0 => n!6220!62200 plus(X, Y) => n!6220!6220plus(X, Y) s(X) => n!6220!6220s(X) activate(n!6220!62200) => 0
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