/export/starexec/sandbox/solver/bin/starexec_run_rcdcRelativeAlsoLower /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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WORST_CASE(?, O(1))
proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(1, 1).

(0) DCpxTrs
(1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms]
(2) CpxRelTRS
(3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 57 ms]
(4) CpxRelTRS
(5) NarrowingOnBasicTermsTerminatesProof [FINISHED, 0 ms]
(6) BOUNDS(1, 1)


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(0)
Obligation:
The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(1, 1).


The TRS R consists of the following rules:

   c -> f
   f -> g

S is empty.
Rewrite Strategy: FULL
----------------------------------------

(1) DerivationalComplexityToRuntimeComplexityProof (BOTH BOUNDS(ID, ID))
The following rules have been added to S to convert the given derivational complexity problem to a runtime complexity problem:

   encArg(g) -> g
   encArg(cons_c) -> c
   encArg(cons_f) -> f
   encode_c -> c
   encode_f -> f
   encode_g -> g


----------------------------------------

(2)
Obligation:
The Runtime Complexity (full) of the given CpxRelTRS could be proven to be BOUNDS(1, 1).


The TRS R consists of the following rules:

   c -> f
   f -> g

The (relative) TRS S consists of the following rules:

   encArg(g) -> g
   encArg(cons_c) -> c
   encArg(cons_f) -> f
   encode_c -> c
   encode_f -> f
   encode_g -> g

Rewrite Strategy: FULL
----------------------------------------

(3) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID))
proved innermost termination of relative rules
----------------------------------------

(4)
Obligation:
The Runtime Complexity (full) of the given CpxRelTRS could be proven to be BOUNDS(1, 1).


The TRS R consists of the following rules:

   c -> f
   f -> g

The (relative) TRS S consists of the following rules:

   encArg(g) -> g
   encArg(cons_c) -> c
   encArg(cons_f) -> f
   encode_c -> c
   encode_f -> f
   encode_g -> g

Rewrite Strategy: FULL
----------------------------------------

(5) NarrowingOnBasicTermsTerminatesProof (FINISHED)
Constant runtime complexity proven by termination of constructor-based narrowing.

The maximal most general narrowing sequences give rise to the following rewrite sequences:

encode_g ->^* g

encode_f ->^* g

encode_c ->^* g

encArg(cons_f) ->^* g

encArg(cons_c) ->^* g

encArg(g) ->^* g

f ->^* g

c ->^* g




----------------------------------------

(6)
BOUNDS(1, 1)